%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SCT170^3 : TPTP v9.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.JrxzQYT8NE true
% Computer : n001.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 04:50:55 PM UTC 2025
% Result : Theorem 92.09s 12.21s
% Output : Refutation 92.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 154 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 755 ( 177 equ; 114 cnn)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 2472 ( 90 ~; 37 |; 55 &;2001 @)
% ( 47 <=>; 118 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 8 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 183 ( 183 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 32 usr; 14 con; 0-6 aty)
% ( 124 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 268 ( 48 ^; 220 !; 0 ?; 268 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_A1402527603le_alt_type,type,
list_A1402527603le_alt: $tType ).
thf(arrow_1389031998le_alt_type,type,
arrow_1389031998le_alt: $tType ).
thf(produc1572197287le_alt_type,type,
produc1572197287le_alt: $tType ).
thf(arrow_1196572341e_indi_type,type,
arrow_1196572341e_indi: $tType ).
thf(member1241905979_alt_o_type,type,
member1241905979_alt_o: ( produc1572197287le_alt > $o ) > ( ( produc1572197287le_alt > $o ) > $o ) > $o ).
thf(produc897867031le_alt_type,type,
produc897867031le_alt: arrow_1389031998le_alt > arrow_1389031998le_alt > produc1572197287le_alt ).
thf(b_type,type,
b: arrow_1389031998le_alt ).
thf('#sk7_type',type,
'#sk7': arrow_1196572341e_indi ).
thf(top_to54564308indi_o_type,type,
top_to54564308indi_o: arrow_1196572341e_indi > $o ).
thf(last_A2130988295le_alt_type,type,
last_A2130988295le_alt: list_A1402527603le_alt > arrow_1389031998le_alt ).
thf(hd_Arr731872705le_alt_type,type,
hd_Arr731872705le_alt: list_A1402527603le_alt > arrow_1389031998le_alt ).
thf(c_type,type,
c: arrow_1389031998le_alt ).
thf(cons_A1142416030le_alt_type,type,
cons_A1142416030le_alt: arrow_1389031998le_alt > list_A1402527603le_alt > list_A1402527603le_alt ).
thf(member822980838_alt_o_type,type,
member822980838_alt_o: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(ord_le602483040lt_o_o_type,type,
ord_le602483040lt_o_o: ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > ( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ) > $o ).
thf(append1092755459le_alt_type,type,
append1092755459le_alt: list_A1402527603le_alt > list_A1402527603le_alt > list_A1402527603le_alt ).
thf(butlas1188620858le_alt_type,type,
butlas1188620858le_alt: list_A1402527603le_alt > list_A1402527603le_alt ).
thf(arrow_1647925946e_Prof_type,type,
arrow_1647925946e_Prof: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(member285112084le_alt_type,type,
member285112084le_alt: produc1572197287le_alt > ( produc1572197287le_alt > $o ) > $o ).
thf(member998036369le_alt_type,type,
member998036369le_alt: arrow_1389031998le_alt > ( arrow_1389031998le_alt > $o ) > $o ).
thf(p_type,type,
p: arrow_1196572341e_indi > produc1572197287le_alt > $o ).
thf(nil_Ar52383470le_alt_type,type,
nil_Ar52383470le_alt: list_A1402527603le_alt ).
thf(distin1149997281le_alt_type,type,
distin1149997281le_alt: list_A1402527603le_alt > $o ).
thf(pi_Arr1309696186_alt_o_type,type,
pi_Arr1309696186_alt_o: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o ) > ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ).
thf(arrow_1865170000_below_type,type,
arrow_1865170000_below: ( produc1572197287le_alt > $o ) > arrow_1389031998le_alt > arrow_1389031998le_alt > produc1572197287le_alt > $o ).
thf(set_Ar1491127311le_alt_type,type,
set_Ar1491127311le_alt: list_A1402527603le_alt > arrow_1389031998le_alt > $o ).
thf('#ty_enc66_type',type,
'#ty_enc66': ( ( produc1572197287le_alt > $o ) > $o ) > arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o ).
thf(arrow_1982173296le_Lin_type,type,
arrow_1982173296le_Lin: ( produc1572197287le_alt > $o ) > $o ).
thf(ord_le865407012indi_o_type,type,
ord_le865407012indi_o: ( arrow_1196572341e_indi > $o ) > ( arrow_1196572341e_indi > $o ) > $o ).
thf(a_type,type,
a: arrow_1389031998le_alt ).
thf(member1818997282e_indi_type,type,
member1818997282e_indi: arrow_1196572341e_indi > ( arrow_1196572341e_indi > $o ) > $o ).
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,
distin1149997281le_alt @ ( cons_A1142416030le_alt @ a @ ( cons_A1142416030le_alt @ b @ ( cons_A1142416030le_alt @ c @ nil_Ar52383470le_alt ) ) ) ).
thf(zip_derived_cl2,plain,
distin1149997281le_alt @ ( cons_A1142416030le_alt @ a @ ( cons_A1142416030le_alt @ b @ ( cons_A1142416030le_alt @ c @ nil_Ar52383470le_alt ) ) ),
inference(cnf,[status(esa)],[fact_4_dist]) ).
thf(fact_37_list_Osimps_I2_J,axiom,
! [A_48: arrow_1389031998le_alt,List_5: list_A1402527603le_alt] :
( nil_Ar52383470le_alt
!= ( cons_A1142416030le_alt @ A_48 @ List_5 ) ) ).
thf(zip_derived_cl30,plain,
( !!
@ ^ [Y0: arrow_1389031998le_alt] :
( !!
@ ^ [Y1: list_A1402527603le_alt] :
( nil_Ar52383470le_alt
!= ( cons_A1142416030le_alt @ Y0 @ Y1 ) ) ) ),
inference(cnf,[status(esa)],[fact_37_list_Osimps_I2_J]) ).
thf(zip_derived_cl31,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ ( list_A1402527603le_alt != nil_Ar52383470le_alt ) ) @ cons_A1142416030le_alt ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl457,plain,
! [X2: arrow_1389031998le_alt] : ( !! @ ( '#B' @ ( list_A1402527603le_alt != nil_Ar52383470le_alt ) @ ( cons_A1142416030le_alt @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl458,plain,
! [X2: arrow_1389031998le_alt,X4: list_A1402527603le_alt] :
( nil_Ar52383470le_alt
!= ( cons_A1142416030le_alt @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl457]) ).
thf(zip_derived_cl459,plain,
! [X2: arrow_1389031998le_alt,X4: list_A1402527603le_alt] :
( nil_Ar52383470le_alt
!= ( cons_A1142416030le_alt @ X2 @ X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl458]) ).
thf(fact_583_hd_Osimps,axiom,
! [X_54: arrow_1389031998le_alt,Xs_77: list_A1402527603le_alt] :
( ( hd_Arr731872705le_alt @ ( cons_A1142416030le_alt @ X_54 @ Xs_77 ) )
= X_54 ) ).
thf(zip_derived_cl238,plain,
( !!
@ ^ [Y0: arrow_1389031998le_alt] :
( !!
@ ^ [Y1: list_A1402527603le_alt] :
( ( hd_Arr731872705le_alt @ ( cons_A1142416030le_alt @ Y0 @ Y1 ) )
= Y0 ) ) ),
inference(cnf,[status(esa)],[fact_583_hd_Osimps]) ).
thf(zip_derived_cl239,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ hd_Arr731872705le_alt ) @ cons_A1142416030le_alt ) ) ) @ '#I' ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl238]) ).
thf(zip_derived_cl559,plain,
! [X2: arrow_1389031998le_alt] : ( !! @ ( '#C' @ ( '#B' @ (=) @ ( '#B' @ hd_Arr731872705le_alt @ ( cons_A1142416030le_alt @ X2 ) ) ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl239]) ).
thf(zip_derived_cl560,plain,
! [X2: arrow_1389031998le_alt,X4: list_A1402527603le_alt] :
( ( hd_Arr731872705le_alt @ ( cons_A1142416030le_alt @ X2 @ X4 ) )
= X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl559]) ).
thf(zip_derived_cl561,plain,
! [X2: arrow_1389031998le_alt,X4: list_A1402527603le_alt] :
( ( hd_Arr731872705le_alt @ ( cons_A1142416030le_alt @ X2 @ X4 ) )
= X2 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl560]) ).
thf(fact_401_append__Nil,axiom,
! [Ys_57: list_A1402527603le_alt] :
( ( append1092755459le_alt @ nil_Ar52383470le_alt @ Ys_57 )
= Ys_57 ) ).
thf(zip_derived_cl147,plain,
( !!
@ ^ [Y0: list_A1402527603le_alt] :
( ( append1092755459le_alt @ nil_Ar52383470le_alt @ Y0 )
= Y0 ) ),
inference(cnf,[status(esa)],[fact_401_append__Nil]) ).
thf(zip_derived_cl148,plain,
!! @ ( '#S' @ ( '#B' @ (=) @ ( append1092755459le_alt @ nil_Ar52383470le_alt ) ) @ '#I' ),
inference(lams2combs,[status(thm)],[zip_derived_cl147]) ).
thf(zip_derived_cl427,plain,
! [X2: list_A1402527603le_alt] :
( ( append1092755459le_alt @ nil_Ar52383470le_alt @ X2 )
= X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl148]) ).
thf(zip_derived_cl428,plain,
! [X2: list_A1402527603le_alt] :
( ( append1092755459le_alt @ nil_Ar52383470le_alt @ X2 )
= X2 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl427]) ).
thf(fact_744_hd__in__set,axiom,
! [Xs_25: list_A1402527603le_alt] :
( ( Xs_25 != nil_Ar52383470le_alt )
=> ( member998036369le_alt @ ( hd_Arr731872705le_alt @ Xs_25 ) @ ( set_Ar1491127311le_alt @ Xs_25 ) ) ) ).
thf(zip_derived_cl321,plain,
( !!
@ ^ [Y0: list_A1402527603le_alt] :
( ( Y0 != nil_Ar52383470le_alt )
=> ( member998036369le_alt @ ( hd_Arr731872705le_alt @ Y0 ) @ ( set_Ar1491127311le_alt @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[fact_744_hd__in__set]) ).
thf(zip_derived_cl322,plain,
!! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ != @ nil_Ar52383470le_alt ) ) @ ( '#S' @ ( '#B' @ member998036369le_alt @ hd_Arr731872705le_alt ) @ set_Ar1491127311le_alt ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl321]) ).
thf(zip_derived_cl496,plain,
! [X2: list_A1402527603le_alt] :
( ( X2 != nil_Ar52383470le_alt )
=> ( member998036369le_alt @ ( hd_Arr731872705le_alt @ X2 ) @ ( set_Ar1491127311le_alt @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl322]) ).
thf(zip_derived_cl497,plain,
! [X2: list_A1402527603le_alt] :
( ~ ( ( X2 != nil_Ar52383470le_alt ) )
| ( member998036369le_alt @ ( hd_Arr731872705le_alt @ X2 ) @ ( set_Ar1491127311le_alt @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl496]) ).
thf(zip_derived_cl498,plain,
! [X2: list_A1402527603le_alt] :
( ( X2 = nil_Ar52383470le_alt )
| ( member998036369le_alt @ ( hd_Arr731872705le_alt @ X2 ) @ ( set_Ar1491127311le_alt @ X2 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl497]) ).
thf(fact_399_append__Cons,axiom,
! [X_86: arrow_1389031998le_alt,Xs_140: list_A1402527603le_alt,Ys_59: list_A1402527603le_alt] :
( ( append1092755459le_alt @ ( cons_A1142416030le_alt @ X_86 @ Xs_140 ) @ Ys_59 )
= ( cons_A1142416030le_alt @ X_86 @ ( append1092755459le_alt @ Xs_140 @ Ys_59 ) ) ) ).
thf(zip_derived_cl143,plain,
( !!
@ ^ [Y0: arrow_1389031998le_alt] :
( !!
@ ^ [Y1: list_A1402527603le_alt] :
( !!
@ ^ [Y2: list_A1402527603le_alt] :
( ( append1092755459le_alt @ ( cons_A1142416030le_alt @ Y0 @ Y1 ) @ Y2 )
= ( cons_A1142416030le_alt @ Y0 @ ( append1092755459le_alt @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf,[status(esa)],[fact_399_append__Cons]) ).
thf(zip_derived_cl144,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ append1092755459le_alt ) @ cons_A1142416030le_alt ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ cons_A1142416030le_alt ) ) @ append1092755459le_alt ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl143]) ).
thf(zip_derived_cl783,plain,
! [X2: arrow_1389031998le_alt] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ append1092755459le_alt @ ( cons_A1142416030le_alt @ X2 ) ) ) ) @ ( '#B' @ ( '#B' @ ( cons_A1142416030le_alt @ X2 ) ) @ append1092755459le_alt ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl144]) ).
thf(zip_derived_cl784,plain,
! [X2: arrow_1389031998le_alt,X4: list_A1402527603le_alt] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( append1092755459le_alt @ ( cons_A1142416030le_alt @ X2 @ X4 ) ) ) @ ( '#B' @ ( cons_A1142416030le_alt @ X2 ) @ ( append1092755459le_alt @ X4 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl783]) ).
thf(zip_derived_cl785,plain,
! [X2: arrow_1389031998le_alt,X4: list_A1402527603le_alt,X6: list_A1402527603le_alt] :
( ( append1092755459le_alt @ ( cons_A1142416030le_alt @ X2 @ X4 ) @ X6 )
= ( cons_A1142416030le_alt @ X2 @ ( append1092755459le_alt @ X4 @ X6 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl784]) ).
thf(zip_derived_cl786,plain,
! [X2: arrow_1389031998le_alt,X4: list_A1402527603le_alt,X6: list_A1402527603le_alt] :
( ( append1092755459le_alt @ ( cons_A1142416030le_alt @ X2 @ X4 ) @ X6 )
= ( cons_A1142416030le_alt @ X2 @ ( append1092755459le_alt @ X4 @ X6 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl785]) ).
thf(fact_423_last__snoc,axiom,
! [Xs_119: list_A1402527603le_alt,X_77: arrow_1389031998le_alt] :
( ( last_A2130988295le_alt @ ( append1092755459le_alt @ Xs_119 @ ( cons_A1142416030le_alt @ X_77 @ nil_Ar52383470le_alt ) ) )
= X_77 ) ).
thf(zip_derived_cl187,plain,
( !!
@ ^ [Y0: list_A1402527603le_alt] :
( !!
@ ^ [Y1: arrow_1389031998le_alt] :
( ( last_A2130988295le_alt @ ( append1092755459le_alt @ Y0 @ ( cons_A1142416030le_alt @ Y1 @ nil_Ar52383470le_alt ) ) )
= Y1 ) ) ),
inference(cnf,[status(esa)],[fact_423_last__snoc]) ).
thf(zip_derived_cl188,plain,
!! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ last_A2130988295le_alt ) @ ( '#C' @ ( '#B' @ '#B' @ append1092755459le_alt ) @ ( '#C' @ cons_A1142416030le_alt @ nil_Ar52383470le_alt ) ) ) ) ) @ '#I' ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl187]) ).
thf(zip_derived_cl603,plain,
! [X2: list_A1402527603le_alt] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ last_A2130988295le_alt @ ( '#B' @ ( append1092755459le_alt @ X2 ) @ ( '#C' @ cons_A1142416030le_alt @ nil_Ar52383470le_alt ) ) ) ) @ '#I' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl188]) ).
thf(zip_derived_cl604,plain,
! [X2: list_A1402527603le_alt,X4: arrow_1389031998le_alt] :
( ( last_A2130988295le_alt @ ( append1092755459le_alt @ X2 @ ( cons_A1142416030le_alt @ X4 @ nil_Ar52383470le_alt ) ) )
= X4 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl603]) ).
thf(zip_derived_cl605,plain,
! [X2: list_A1402527603le_alt,X4: arrow_1389031998le_alt] :
( ( last_A2130988295le_alt @ ( append1092755459le_alt @ X2 @ ( cons_A1142416030le_alt @ X4 @ nil_Ar52383470le_alt ) ) )
= X4 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl604]) ).
thf(fact_433_snoc__eq__iff__butlast,axiom,
! [Xs_118: list_A1402527603le_alt,X_75: arrow_1389031998le_alt,Ys_41: list_A1402527603le_alt] :
( ( ( append1092755459le_alt @ Xs_118 @ ( cons_A1142416030le_alt @ X_75 @ nil_Ar52383470le_alt ) )
= Ys_41 )
<=> ( ( ( last_A2130988295le_alt @ Ys_41 )
= X_75 )
& ( ( butlas1188620858le_alt @ Ys_41 )
= Xs_118 )
& ( Ys_41 != nil_Ar52383470le_alt ) ) ) ).
thf(zip_derived_cl189,plain,
( !!
@ ^ [Y0: list_A1402527603le_alt] :
( !!
@ ^ [Y1: arrow_1389031998le_alt] :
( !!
@ ^ [Y2: list_A1402527603le_alt] :
( ( ( append1092755459le_alt @ Y0 @ ( cons_A1142416030le_alt @ Y1 @ nil_Ar52383470le_alt ) )
= Y2 )
<=> ( ( ( last_A2130988295le_alt @ Y2 )
= Y1 )
& ( ( butlas1188620858le_alt @ Y2 )
= Y0 )
& ( Y2 != nil_Ar52383470le_alt ) ) ) ) ) ),
inference(cnf,[status(esa)],[fact_433_snoc__eq__iff__butlast]) ).
thf(zip_derived_cl190,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) @ ( '#B' @ ( '#B' @ (=) ) @ ( '#C' @ ( '#B' @ '#B' @ append1092755459le_alt ) @ ( '#C' @ cons_A1142416030le_alt @ nil_Ar52383470le_alt ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#C' @ ( '#B' @ (=) @ last_A2130988295le_alt ) ) ) ) ) @ ( '#C' @ ( '#B' @ (=) @ butlas1188620858le_alt ) ) ) ) ) @ ( '#C' @ != @ nil_Ar52383470le_alt ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl189]) ).
thf(zip_derived_cl960,plain,
! [X2: list_A1402527603le_alt] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ (=) @ ( '#B' @ ( append1092755459le_alt @ X2 ) @ ( '#C' @ cons_A1142416030le_alt @ nil_Ar52383470le_alt ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#C' @ ( '#B' @ (=) @ last_A2130988295le_alt ) ) ) ) @ ( '#C' @ ( '#B' @ (=) @ butlas1188620858le_alt ) @ X2 ) ) ) @ ( '#C' @ != @ nil_Ar52383470le_alt ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl190]) ).
thf(zip_derived_cl961,plain,
! [X2: list_A1402527603le_alt,X4: arrow_1389031998le_alt] :
( !!
@ ( '#S'
@ ( '#B' @ (<=>)
@ ( list_A1402527603le_alt
= ( append1092755459le_alt @ X2 @ ( cons_A1142416030le_alt @ X4 @ nil_Ar52383470le_alt ) ) ) )
@ ( '#S' @ ( '#S' @ ( '#B' @ (&) @ ( '#C' @ ( '#B' @ (=) @ last_A2130988295le_alt ) @ X4 ) ) @ ( '#C' @ ( '#B' @ (=) @ butlas1188620858le_alt ) @ X2 ) ) @ ( '#C' @ != @ nil_Ar52383470le_alt ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl960]) ).
thf(zip_derived_cl962,plain,
! [X2: list_A1402527603le_alt,X4: arrow_1389031998le_alt,X6: list_A1402527603le_alt] :
( ( ( append1092755459le_alt @ X2 @ ( cons_A1142416030le_alt @ X4 @ nil_Ar52383470le_alt ) )
= X6 )
<=> ( ( ( last_A2130988295le_alt @ X6 )
= X4 )
& ( ( butlas1188620858le_alt @ X6 )
= X2 )
& ( X6 != nil_Ar52383470le_alt ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl961]) ).
thf(zip_derived_cl963,plain,
! [X2: list_A1402527603le_alt,X4: arrow_1389031998le_alt,X6: list_A1402527603le_alt] :
( ( ( append1092755459le_alt @ X2 @ ( cons_A1142416030le_alt @ X4 @ nil_Ar52383470le_alt ) )
= X6 )
= ( ( ( last_A2130988295le_alt @ X6 )
= X4 )
& ( ( butlas1188620858le_alt @ X6 )
= X2 )
& ( X6 != nil_Ar52383470le_alt ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl962]) ).
thf(fact_321_mem__def,axiom,
! [X_102: produc1572197287le_alt > $o,A_36: ( produc1572197287le_alt > $o ) > $o] :
( ( member1241905979_alt_o @ X_102 @ A_36 )
<=> ( A_36 @ X_102 ) ) ).
thf(zip_derived_cl78,plain,
( !!
@ ^ [Y0: produc1572197287le_alt > $o] :
( !!
@ ^ [Y1: ( produc1572197287le_alt > $o ) > $o] :
( ( member1241905979_alt_o @ Y0 @ Y1 )
<=> ( Y1 @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[fact_321_mem__def]) ).
thf(zip_derived_cl79,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ member1241905979_alt_o ) ) @ ( '#C' @ '#I' ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl628,plain,
! [X2: produc1572197287le_alt > $o] : ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( member1241905979_alt_o @ X2 ) ) @ ( '#C' @ '#I' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl629,plain,
! [X2: produc1572197287le_alt > $o,X4: ( produc1572197287le_alt > $o ) > $o] :
( ( member1241905979_alt_o @ X2 @ X4 )
<=> ( X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl628]) ).
thf(zip_derived_cl630,plain,
! [X2: produc1572197287le_alt > $o,X4: ( produc1572197287le_alt > $o ) > $o] :
( ( member1241905979_alt_o @ X2 @ X4 )
= ( X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl629]) ).
thf(fact_319_mem__def,axiom,
! [X_102: produc1572197287le_alt,A_36: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ X_102 @ A_36 )
<=> ( A_36 @ X_102 ) ) ).
thf(zip_derived_cl74,plain,
( !!
@ ^ [Y0: produc1572197287le_alt] :
( !!
@ ^ [Y1: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ Y0 @ Y1 )
<=> ( Y1 @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[fact_319_mem__def]) ).
thf(zip_derived_cl75,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ member285112084le_alt ) ) @ ( '#C' @ '#I' ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl593,plain,
! [X2: produc1572197287le_alt] : ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( member285112084le_alt @ X2 ) ) @ ( '#C' @ '#I' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl594,plain,
! [X2: produc1572197287le_alt,X4: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ X2 @ X4 )
<=> ( X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl593]) ).
thf(zip_derived_cl595,plain,
! [X2: produc1572197287le_alt,X4: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ X2 @ X4 )
= ( X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl594]) ).
thf(fact_725_last__in__set,axiom,
! [As: list_A1402527603le_alt] :
( ( As != nil_Ar52383470le_alt )
=> ( member998036369le_alt @ ( last_A2130988295le_alt @ As ) @ ( set_Ar1491127311le_alt @ As ) ) ) ).
thf(zip_derived_cl315,plain,
( !!
@ ^ [Y0: list_A1402527603le_alt] :
( ( Y0 != nil_Ar52383470le_alt )
=> ( member998036369le_alt @ ( last_A2130988295le_alt @ Y0 ) @ ( set_Ar1491127311le_alt @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[fact_725_last__in__set]) ).
thf(zip_derived_cl316,plain,
!! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ != @ nil_Ar52383470le_alt ) ) @ ( '#S' @ ( '#B' @ member998036369le_alt @ last_A2130988295le_alt ) @ set_Ar1491127311le_alt ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl315]) ).
thf(zip_derived_cl493,plain,
! [X2: list_A1402527603le_alt] :
( ( X2 != nil_Ar52383470le_alt )
=> ( member998036369le_alt @ ( last_A2130988295le_alt @ X2 ) @ ( set_Ar1491127311le_alt @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl316]) ).
thf(zip_derived_cl494,plain,
! [X2: list_A1402527603le_alt] :
( ~ ( ( X2 != nil_Ar52383470le_alt ) )
| ( member998036369le_alt @ ( last_A2130988295le_alt @ X2 ) @ ( set_Ar1491127311le_alt @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl493]) ).
thf(zip_derived_cl495,plain,
! [X2: list_A1402527603le_alt] :
( ( X2 = nil_Ar52383470le_alt )
| ( member998036369le_alt @ ( last_A2130988295le_alt @ X2 ) @ ( set_Ar1491127311le_alt @ X2 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl494]) ).
thf(fact_316_mem__def,axiom,
! [X_102: arrow_1389031998le_alt,A_36: arrow_1389031998le_alt > $o] :
( ( member998036369le_alt @ X_102 @ A_36 )
<=> ( A_36 @ X_102 ) ) ).
thf(zip_derived_cl70,plain,
( !!
@ ^ [Y0: arrow_1389031998le_alt] :
( !!
@ ^ [Y1: arrow_1389031998le_alt > $o] :
( ( member998036369le_alt @ Y0 @ Y1 )
<=> ( Y1 @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[fact_316_mem__def]) ).
thf(zip_derived_cl71,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ member998036369le_alt ) ) @ ( '#C' @ '#I' ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl587,plain,
! [X2: arrow_1389031998le_alt] : ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( member998036369le_alt @ X2 ) ) @ ( '#C' @ '#I' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl588,plain,
! [X2: arrow_1389031998le_alt,X4: arrow_1389031998le_alt > $o] :
( ( member998036369le_alt @ X2 @ X4 )
<=> ( X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl587]) ).
thf(zip_derived_cl589,plain,
! [X2: arrow_1389031998le_alt,X4: arrow_1389031998le_alt > $o] :
( ( member998036369le_alt @ X2 @ X4 )
= ( X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl588]) ).
thf(fact_708_distinct_Osimps_I2_J,axiom,
! [X_31: arrow_1389031998le_alt,Xs_29: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ ( cons_A1142416030le_alt @ X_31 @ Xs_29 ) )
<=> ( ( distin1149997281le_alt @ Xs_29 )
& ~ ( member998036369le_alt @ X_31 @ ( set_Ar1491127311le_alt @ Xs_29 ) ) ) ) ).
thf(zip_derived_cl311,plain,
( !!
@ ^ [Y0: arrow_1389031998le_alt] :
( !!
@ ^ [Y1: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ ( cons_A1142416030le_alt @ Y0 @ Y1 ) )
<=> ( ( distin1149997281le_alt @ Y1 )
& ( (~) @ ( member998036369le_alt @ Y0 @ ( set_Ar1491127311le_alt @ Y1 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[fact_708_distinct_Osimps_I2_J]) ).
thf(zip_derived_cl312,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ distin1149997281le_alt ) @ cons_A1142416030le_alt ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ (&) @ distin1149997281le_alt ) ) @ ( '#B' @ ( '#B' @ (~) ) @ ( '#C' @ ( '#B' @ '#B' @ member998036369le_alt ) @ set_Ar1491127311le_alt ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl311]) ).
thf(zip_derived_cl765,plain,
! [X2: arrow_1389031998le_alt] : ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( '#B' @ distin1149997281le_alt @ ( cons_A1142416030le_alt @ X2 ) ) ) @ ( '#S' @ ( '#B' @ (&) @ distin1149997281le_alt ) @ ( '#B' @ (~) @ ( '#B' @ ( member998036369le_alt @ X2 ) @ set_Ar1491127311le_alt ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl312]) ).
thf(zip_derived_cl766,plain,
! [X2: arrow_1389031998le_alt,X4: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ ( cons_A1142416030le_alt @ X2 @ X4 ) )
<=> ( ( distin1149997281le_alt @ X4 )
& ( (~) @ ( member998036369le_alt @ X2 @ ( set_Ar1491127311le_alt @ X4 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl765]) ).
thf(zip_derived_cl767,plain,
! [X2: arrow_1389031998le_alt,X4: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ ( cons_A1142416030le_alt @ X2 @ X4 ) )
= ( ( distin1149997281le_alt @ X4 )
& ( (~) @ ( member998036369le_alt @ X2 @ ( set_Ar1491127311le_alt @ X4 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl766]) ).
thf(zip_derived_cl589_001,plain,
! [X2: arrow_1389031998le_alt,X4: arrow_1389031998le_alt > $o] :
( ( member998036369le_alt @ X2 @ X4 )
= ( X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl588]) ).
thf(zip_derived_cl768,plain,
! [X2: arrow_1389031998le_alt,X4: list_A1402527603le_alt] :
( ( distin1149997281le_alt @ ( cons_A1142416030le_alt @ X2 @ X4 ) )
= ( ( distin1149997281le_alt @ X4 )
& ( (~) @ ( set_Ar1491127311le_alt @ X4 @ X2 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl767,zip_derived_cl589]) ).
thf(conj_0,conjecture,
! [I: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ a @ b ) @ ( p @ I ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ a @ c ) @ ( arrow_1865170000_below @ ( p @ I ) @ c @ b ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [I: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ a @ b ) @ ( p @ I ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ a @ c ) @ ( arrow_1865170000_below @ ( p @ I ) @ c @ b ) ) ),
inference('cnf.neg',[status(esa)],[conj_0]) ).
thf(zip_derived_cl401,plain,
~ ( !!
@ ^ [Y0: arrow_1196572341e_indi] :
( ( member285112084le_alt @ ( produc897867031le_alt @ a @ b ) @ ( p @ Y0 ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ a @ c ) @ ( arrow_1865170000_below @ ( p @ Y0 ) @ c @ b ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl402,plain,
~ ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( '#B' @ ( member285112084le_alt @ ( produc897867031le_alt @ a @ b ) ) @ p ) ) @ ( '#B' @ ( member285112084le_alt @ ( produc897867031le_alt @ a @ c ) ) @ ( '#C' @ ( '#C' @ ( '#B' @ arrow_1865170000_below @ p ) @ c ) @ b ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl401]) ).
thf(zip_derived_cl449,plain,
~ ( ( member285112084le_alt @ ( produc897867031le_alt @ a @ b ) @ ( p @ '#sk7' ) )
<=> ( member285112084le_alt @ ( produc897867031le_alt @ a @ c ) @ ( arrow_1865170000_below @ ( p @ '#sk7' ) @ c @ b ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl402]) ).
thf(zip_derived_cl450,plain,
( ( member285112084le_alt @ ( produc897867031le_alt @ a @ b ) @ ( p @ '#sk7' ) )
!= ( member285112084le_alt @ ( produc897867031le_alt @ a @ c ) @ ( arrow_1865170000_below @ ( p @ '#sk7' ) @ c @ b ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl449]) ).
thf(zip_derived_cl595_002,plain,
! [X2: produc1572197287le_alt,X4: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ X2 @ X4 )
= ( X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl594]) ).
thf(zip_derived_cl595_003,plain,
! [X2: produc1572197287le_alt,X4: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ X2 @ X4 )
= ( X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl594]) ).
thf(zip_derived_cl596,plain,
( ( p @ '#sk7' @ ( produc897867031le_alt @ a @ b ) )
!= ( arrow_1865170000_below @ ( p @ '#sk7' ) @ c @ b @ ( produc897867031le_alt @ a @ c ) ) ),
inference(demod,[status(thm)],[zip_derived_cl450,zip_derived_cl595,zip_derived_cl595]) ).
thf(fact_367_iso__tuple__UNIV__I,axiom,
! [X_91: arrow_1196572341e_indi] : ( member1818997282e_indi @ X_91 @ top_to54564308indi_o ) ).
thf(zip_derived_cl103,plain,
( !!
@ ^ [Y0: arrow_1196572341e_indi] : ( member1818997282e_indi @ Y0 @ top_to54564308indi_o ) ),
inference(cnf,[status(esa)],[fact_367_iso__tuple__UNIV__I]) ).
thf(zip_derived_cl104,plain,
!! @ ( '#C' @ member1818997282e_indi @ top_to54564308indi_o ),
inference(lams2combs,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl406,plain,
! [X2: arrow_1196572341e_indi] : ( member1818997282e_indi @ X2 @ top_to54564308indi_o ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl104]) ).
thf(fact_12_in__below,axiom,
! [X: arrow_1389031998le_alt,Y: arrow_1389031998le_alt,L_4: produc1572197287le_alt > $o,A: arrow_1389031998le_alt,B: arrow_1389031998le_alt] :
( ( A != B )
=> ( ( member1241905979_alt_o @ L_4 @ arrow_1982173296le_Lin )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ ( arrow_1865170000_below @ L_4 @ A @ B ) )
<=> ( ( ( Y != A )
=> ( ( ( X != A )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X @ Y ) @ L_4 ) )
& ( ( X = A )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ B @ Y ) @ L_4 )
| ( Y = B ) ) ) ) )
& ( ( Y = A )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X @ B ) @ L_4 ) )
& ( X != Y ) ) ) ) ) ).
thf(zip_derived_cl11,plain,
( !!
@ ^ [Y0: arrow_1389031998le_alt] :
( !!
@ ^ [Y1: arrow_1389031998le_alt] :
( !!
@ ^ [Y2: produc1572197287le_alt > $o] :
( !!
@ ^ [Y3: arrow_1389031998le_alt] :
( !!
@ ^ [Y4: arrow_1389031998le_alt] :
( ( Y3 != Y4 )
=> ( ( member1241905979_alt_o @ Y2 @ arrow_1982173296le_Lin )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ Y0 @ Y1 ) @ ( arrow_1865170000_below @ Y2 @ Y3 @ Y4 ) )
<=> ( ( ( Y1 != Y3 )
=> ( ( ( Y0 != Y3 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ Y0 @ Y1 ) @ Y2 ) )
& ( ( Y0 = Y3 )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ Y4 @ Y1 ) @ Y2 )
| ( Y1 = Y4 ) ) ) ) )
& ( ( Y1 = Y3 )
=> ( member285112084le_alt @ ( produc897867031le_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' @ member1241905979_alt_o @ arrow_1982173296le_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' @ member285112084le_alt ) @ produc897867031le_alt ) ) ) ) ) @ arrow_1865170000_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' @ member285112084le_alt ) @ produc897867031le_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' @ member285112084le_alt ) @ ( '#C' @ produc897867031le_alt ) ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ (=) ) ) ) ) ) @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ member285112084le_alt ) @ produc897867031le_alt ) ) ) ) ) ) ) ) @ != ) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl464,plain,
! [X2: arrow_1389031998le_alt] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ != ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( '#C' @ member1241905979_alt_o @ arrow_1982173296le_Lin ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ member285112084le_alt @ ( produc897867031le_alt @ X2 ) ) ) ) ) @ arrow_1865170000_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_1389031998le_alt != X2 ) ) ) ) @ ( '#B' @ member285112084le_alt @ ( produc897867031le_alt @ X2 ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_1389031998le_alt = X2 ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ member285112084le_alt ) @ ( '#C' @ produc897867031le_alt ) ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ (=) ) ) ) ) @ ( '#C' @ ( '#B' @ member285112084le_alt @ ( produc897867031le_alt @ X2 ) ) ) ) ) ) ) ) @ ( arrow_1389031998le_alt != X2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl465,plain,
! [X2: arrow_1389031998le_alt,X4: arrow_1389031998le_alt] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ != ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( '#C' @ member1241905979_alt_o @ arrow_1982173296le_Lin ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) ) ) ) @ arrow_1865170000_below ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_1389031998le_alt != X4 ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#C' @ ( '#B' @ (=>) @ ( arrow_1389031998le_alt != X2 ) ) ) @ ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_1389031998le_alt = X2 ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#C' @ ( '#B' @ member285112084le_alt @ ( '#C' @ produc897867031le_alt @ X4 ) ) ) ) ) @ ( arrow_1389031998le_alt = X4 ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_1389031998le_alt = X4 ) ) ) ) @ ( '#C' @ ( '#B' @ member285112084le_alt @ ( produc897867031le_alt @ X2 ) ) ) ) ) ) ) @ ( X2 != X4 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl464]) ).
thf(zip_derived_cl466,plain,
! [X2: arrow_1389031998le_alt,X4: arrow_1389031998le_alt,X6: produc1572197287le_alt > $o] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ != ) ) @ ( '#B' @ ( '#B' @ ( (=>) @ ( member1241905979_alt_o @ X6 @ arrow_1982173296le_Lin ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) ) ) @ ( arrow_1865170000_below @ X6 ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_1389031998le_alt != X4 ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ (&) @ ( '#C' @ ( '#B' @ (=>) @ ( arrow_1389031998le_alt != X2 ) ) @ ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ X6 ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_1389031998le_alt = X2 ) ) ) @ ( '#S' @ ( '#B' @ (|) @ ( '#C' @ ( '#B' @ member285112084le_alt @ ( '#C' @ produc897867031le_alt @ X4 ) ) @ X6 ) ) @ ( arrow_1389031998le_alt = X4 ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_1389031998le_alt = X4 ) ) ) @ ( '#C' @ ( '#B' @ member285112084le_alt @ ( produc897867031le_alt @ X2 ) ) @ X6 ) ) ) ) @ ( X2 != X4 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl465]) ).
thf(zip_derived_cl467,plain,
! [X2: arrow_1389031998le_alt,X4: arrow_1389031998le_alt,X6: produc1572197287le_alt > $o,X8: arrow_1389031998le_alt] :
( !!
@ ( '#S' @ ( '#B' @ (=>) @ ( arrow_1389031998le_alt != X8 ) )
@ ( '#B' @ ( (=>) @ ( member1241905979_alt_o @ X6 @ arrow_1982173296le_Lin ) )
@ ( '#S' @ ( '#B' @ (<=>) @ ( '#B' @ ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) ) @ ( arrow_1865170000_below @ X6 @ X8 ) ) )
@ ( '#C'
@ ( '#S'
@ ( '#B' @ (&)
@ ( '#B' @ ( (=>) @ ( X4 != X8 ) )
@ ( '#B'
@ ( (&)
@ ( ( X2 != X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ X6 ) ) )
@ ( '#B' @ ( (=>) @ ( X2 = X8 ) ) @ ( '#S' @ ( '#B' @ (|) @ ( '#C' @ ( '#B' @ member285112084le_alt @ ( '#C' @ produc897867031le_alt @ X4 ) ) @ X6 ) ) @ ( arrow_1389031998le_alt = X4 ) ) ) ) ) )
@ ( '#B' @ ( (=>) @ ( X4 = X8 ) ) @ ( '#C' @ ( '#B' @ member285112084le_alt @ ( produc897867031le_alt @ X2 ) ) @ X6 ) ) )
@ ( X2 != X4 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl466]) ).
thf(zip_derived_cl468,plain,
! [X2: arrow_1389031998le_alt,X4: arrow_1389031998le_alt,X6: produc1572197287le_alt > $o,X8: arrow_1389031998le_alt,X10: arrow_1389031998le_alt] :
( ( X8 != X10 )
=> ( ( member1241905979_alt_o @ X6 @ arrow_1982173296le_Lin )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ ( arrow_1865170000_below @ X6 @ X8 @ X10 ) )
<=> ( ( ( X4 != X8 )
=> ( ( ( X2 != X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ X6 ) )
& ( ( X2 = X8 )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X10 @ X4 ) @ X6 )
| ( X4 = X10 ) ) ) ) )
& ( ( X4 = X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X10 ) @ X6 ) )
& ( X2 != X4 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl467]) ).
thf(zip_derived_cl469,plain,
! [X2: arrow_1389031998le_alt,X4: arrow_1389031998le_alt,X6: produc1572197287le_alt > $o,X8: arrow_1389031998le_alt,X10: arrow_1389031998le_alt] :
( ~ ( ( X8 != X10 ) )
| ( ( member1241905979_alt_o @ X6 @ arrow_1982173296le_Lin )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ ( arrow_1865170000_below @ X6 @ X8 @ X10 ) )
<=> ( ( ( X4 != X8 )
=> ( ( ( X2 != X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ X6 ) )
& ( ( X2 = X8 )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X10 @ X4 ) @ X6 )
| ( X4 = X10 ) ) ) ) )
& ( ( X4 = X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X10 ) @ X6 ) )
& ( X2 != X4 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl468]) ).
thf(zip_derived_cl470,plain,
! [X2: arrow_1389031998le_alt,X4: arrow_1389031998le_alt,X6: produc1572197287le_alt > $o,X8: arrow_1389031998le_alt,X10: arrow_1389031998le_alt] :
( ( X8 = X10 )
| ( ( member1241905979_alt_o @ X6 @ arrow_1982173296le_Lin )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ ( arrow_1865170000_below @ X6 @ X8 @ X10 ) )
<=> ( ( ( X4 != X8 )
=> ( ( ( X2 != X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ X6 ) )
& ( ( X2 = X8 )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X10 @ X4 ) @ X6 )
| ( X4 = X10 ) ) ) ) )
& ( ( X4 = X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X10 ) @ X6 ) )
& ( X2 != X4 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl469]) ).
thf(zip_derived_cl471,plain,
! [X2: arrow_1389031998le_alt,X4: arrow_1389031998le_alt,X6: produc1572197287le_alt > $o,X8: arrow_1389031998le_alt,X10: arrow_1389031998le_alt] :
( ~ ( member1241905979_alt_o @ X6 @ arrow_1982173296le_Lin )
| ( ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ ( arrow_1865170000_below @ X6 @ X8 @ X10 ) )
<=> ( ( ( X4 != X8 )
=> ( ( ( X2 != X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ X6 ) )
& ( ( X2 = X8 )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X10 @ X4 ) @ X6 )
| ( X4 = X10 ) ) ) ) )
& ( ( X4 = X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X10 ) @ X6 ) )
& ( X2 != X4 ) ) )
| ( X8 = X10 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl470]) ).
thf(zip_derived_cl472,plain,
! [X2: arrow_1389031998le_alt,X4: arrow_1389031998le_alt,X6: produc1572197287le_alt > $o,X8: arrow_1389031998le_alt,X10: arrow_1389031998le_alt] :
( ~ ( member1241905979_alt_o @ X6 @ arrow_1982173296le_Lin )
| ( ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ ( arrow_1865170000_below @ X6 @ X8 @ X10 ) )
= ( ( ( X4 != X8 )
=> ( ( ( X2 != X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ X6 ) )
& ( ( X2 = X8 )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X10 @ X4 ) @ X6 )
| ( X4 = X10 ) ) ) ) )
& ( ( X4 = X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X10 ) @ X6 ) )
& ( X2 != X4 ) ) )
| ( X8 = X10 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl471]) ).
thf(zip_derived_cl595_004,plain,
! [X2: produc1572197287le_alt,X4: produc1572197287le_alt > $o] :
( ( member285112084le_alt @ X2 @ X4 )
= ( X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl594]) ).
thf(zip_derived_cl597,plain,
! [X2: arrow_1389031998le_alt,X4: arrow_1389031998le_alt,X6: produc1572197287le_alt > $o,X8: arrow_1389031998le_alt,X10: arrow_1389031998le_alt] :
( ~ ( member1241905979_alt_o @ X6 @ arrow_1982173296le_Lin )
| ( ( arrow_1865170000_below @ X6 @ X8 @ X10 @ ( produc897867031le_alt @ X2 @ X4 ) )
= ( ( ( X4 != X8 )
=> ( ( ( X2 != X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ X6 ) )
& ( ( X2 = X8 )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X10 @ X4 ) @ X6 )
| ( X4 = X10 ) ) ) ) )
& ( ( X4 = X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X10 ) @ X6 ) )
& ( X2 != X4 ) ) )
| ( X8 = X10 ) ),
inference(demod,[status(thm)],[zip_derived_cl472,zip_derived_cl595]) ).
thf(zip_derived_cl630_005,plain,
! [X2: produc1572197287le_alt > $o,X4: ( produc1572197287le_alt > $o ) > $o] :
( ( member1241905979_alt_o @ X2 @ X4 )
= ( X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl629]) ).
thf(zip_derived_cl632,plain,
! [X2: arrow_1389031998le_alt,X4: arrow_1389031998le_alt,X6: produc1572197287le_alt > $o,X8: arrow_1389031998le_alt,X10: arrow_1389031998le_alt] :
( ~ ( arrow_1982173296le_Lin @ X6 )
| ( ( arrow_1865170000_below @ X6 @ X8 @ X10 @ ( produc897867031le_alt @ X2 @ X4 ) )
= ( ( ( X4 != X8 )
=> ( ( ( X2 != X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X4 ) @ X6 ) )
& ( ( X2 = X8 )
=> ( ( member285112084le_alt @ ( produc897867031le_alt @ X10 @ X4 ) @ X6 )
| ( X4 = X10 ) ) ) ) )
& ( ( X4 = X8 )
=> ( member285112084le_alt @ ( produc897867031le_alt @ X2 @ X10 ) @ X6 ) )
& ( X2 != X4 ) ) )
| ( X8 = X10 ) ),
inference(demod,[status(thm)],[zip_derived_cl597,zip_derived_cl630]) ).
thf(fact_320_mem__def,axiom,
! [X_102: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_36: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ X_102 @ A_36 )
<=> ( A_36 @ X_102 ) ) ).
thf(zip_derived_cl76,plain,
( !!
@ ^ [Y0: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( !!
@ ^ [Y1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ Y0 @ Y1 )
<=> ( Y1 @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[fact_320_mem__def]) ).
thf(zip_derived_cl77,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ member822980838_alt_o ) ) @ ( '#C' @ '#I' ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl625,plain,
! [X2: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( member822980838_alt_o @ X2 ) ) @ ( '#C' @ '#I' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl626,plain,
! [X2: arrow_1196572341e_indi > produc1572197287le_alt > $o,X4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ X2 @ X4 )
<=> ( X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl625]) ).
thf(zip_derived_cl627,plain,
! [X2: arrow_1196572341e_indi > produc1572197287le_alt > $o,X4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ X2 @ X4 )
= ( X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl626]) ).
thf(fact_130_funcset__mem,axiom,
! [X_106: arrow_1196572341e_indi,F_20: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_43: arrow_1196572341e_indi > $o,B_34: ( produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ F_20
@ ( pi_Arr1309696186_alt_o @ A_43
@ ^ [Uu: arrow_1196572341e_indi] : B_34 ) )
=> ( ( member1818997282e_indi @ X_106 @ A_43 )
=> ( member1241905979_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ) ).
thf(zip_derived_cl50,plain,
( !!
@ ^ [Y0: arrow_1196572341e_indi] :
( !!
@ ^ [Y1: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( !!
@ ^ [Y2: arrow_1196572341e_indi > $o] :
( !!
@ ^ [Y3: ( produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ Y1
@ ( pi_Arr1309696186_alt_o @ Y2
@ ^ [Y4: arrow_1196572341e_indi] : Y3 ) )
=> ( ( member1818997282e_indi @ Y0 @ Y2 )
=> ( member1241905979_alt_o @ ( Y1 @ Y0 ) @ Y3 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[fact_130_funcset__mem]) ).
thf(zip_derived_cl51,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ member822980838_alt_o ) ) @ ( '#C' @ ( '#B' @ '#B' @ pi_Arr1309696186_alt_o ) @ '#K' ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ member1818997282e_indi ) ) ) ) @ ( '#B' @ ( '#B' @ member1241905979_alt_o ) @ ( '#C' @ '#I' ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl917,plain,
! [X2: arrow_1196572341e_indi] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ member822980838_alt_o ) ) @ ( '#C' @ ( '#B' @ '#B' @ pi_Arr1309696186_alt_o ) @ '#K' ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( member1818997282e_indi @ X2 ) ) ) ) @ ( '#B' @ member1241905979_alt_o @ ( '#C' @ '#I' @ X2 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl918,plain,
! [X2: arrow_1196572341e_indi,X4: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ ( member822980838_alt_o @ X4 ) ) @ ( '#C' @ ( '#B' @ '#B' @ pi_Arr1309696186_alt_o ) @ '#K' ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( member1818997282e_indi @ X2 ) ) ) @ ( member1241905979_alt_o @ ( X4 @ X2 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl917]) ).
thf(zip_derived_cl919,plain,
! [X2: arrow_1196572341e_indi,X4: arrow_1196572341e_indi > produc1572197287le_alt > $o,X6: arrow_1196572341e_indi > $o] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ ( member822980838_alt_o @ X4 ) @ ( '#B' @ ( pi_Arr1309696186_alt_o @ X6 ) @ '#K' ) ) ) @ ( '#B' @ ( (=>) @ ( member1818997282e_indi @ X2 @ X6 ) ) @ ( member1241905979_alt_o @ ( X4 @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl918]) ).
thf(zip_derived_cl920,plain,
! [X2: arrow_1196572341e_indi,X4: arrow_1196572341e_indi > produc1572197287le_alt > $o,X6: arrow_1196572341e_indi > $o,X8: ( produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ X4 @ ( pi_Arr1309696186_alt_o @ X6 @ ( '#K' @ X8 ) ) )
=> ( ( member1818997282e_indi @ X2 @ X6 )
=> ( member1241905979_alt_o @ ( X4 @ X2 ) @ X8 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl919]) ).
thf(zip_derived_cl627_006,plain,
! [X2: arrow_1196572341e_indi > produc1572197287le_alt > $o,X4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( member822980838_alt_o @ X2 @ X4 )
= ( X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl626]) ).
thf(zip_derived_cl921,plain,
! [X2: arrow_1196572341e_indi,X4: arrow_1196572341e_indi > produc1572197287le_alt > $o,X6: arrow_1196572341e_indi > $o,X8: ( produc1572197287le_alt > $o ) > $o] :
( ( pi_Arr1309696186_alt_o @ X6 @ ( '#K' @ X8 ) @ X4 )
=> ( ( member1818997282e_indi @ X2 @ X6 )
=> ( member1241905979_alt_o @ ( X4 @ X2 ) @ X8 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl920,zip_derived_cl627]) ).
thf(zip_derived_cl922,plain,
! [X2: arrow_1196572341e_indi,X4: arrow_1196572341e_indi > produc1572197287le_alt > $o,X6: arrow_1196572341e_indi > $o,X8: ( produc1572197287le_alt > $o ) > $o] :
( ~ ( pi_Arr1309696186_alt_o @ X6 @ ( '#K' @ X8 ) @ X4 )
| ( ( member1818997282e_indi @ X2 @ X6 )
=> ( member1241905979_alt_o @ ( X4 @ X2 ) @ X8 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl921]) ).
thf(zip_derived_cl923,plain,
! [X2: arrow_1196572341e_indi,X4: arrow_1196572341e_indi > produc1572197287le_alt > $o,X6: arrow_1196572341e_indi > $o,X8: ( produc1572197287le_alt > $o ) > $o] :
( ~ ( member1818997282e_indi @ X2 @ X6 )
| ( member1241905979_alt_o @ ( X4 @ X2 ) @ X8 )
| ~ ( pi_Arr1309696186_alt_o @ X6 @ ( '#K' @ X8 ) @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl922]) ).
thf(zip_derived_cl10559,plain,
! [X2: arrow_1196572341e_indi,X4: arrow_1196572341e_indi > produc1572197287le_alt > $o,X6: arrow_1196572341e_indi > $o,X8: ( produc1572197287le_alt > $o ) > $o] :
( ~ ( member1818997282e_indi @ X2 @ X6 )
| ( member1241905979_alt_o @ ( X4 @ X2 ) @ X8 )
| ~ ( pi_Arr1309696186_alt_o @ X6 @ ( '#ty_enc66' @ X8 ) @ X4 ) ),
inference(remove_ty_args,[status(thm)],[zip_derived_cl923]) ).
thf(fact_0__096P_A_058_AProf_096,axiom,
member822980838_alt_o @ p @ arrow_1647925946e_Prof ).
thf(zip_derived_cl0,plain,
member822980838_alt_o @ p @ arrow_1647925946e_Prof,
inference(cnf,[status(esa)],[fact_0__096P_A_058_AProf_096]) ).
thf(fact_340_Prof__def,axiom,
( arrow_1647925946e_Prof
= ( pi_Arr1309696186_alt_o @ top_to54564308indi_o
@ ^ [Uu: arrow_1196572341e_indi] : arrow_1982173296le_Lin ) ) ).
thf(zip_derived_cl80,plain,
( arrow_1647925946e_Prof
= ( pi_Arr1309696186_alt_o @ top_to54564308indi_o
@ ^ [Y0: arrow_1196572341e_indi] : arrow_1982173296le_Lin ) ),
inference(cnf,[status(esa)],[fact_340_Prof__def]) ).
thf(zip_derived_cl81,plain,
( arrow_1647925946e_Prof
= ( pi_Arr1309696186_alt_o @ top_to54564308indi_o @ ( '#K' @ arrow_1982173296le_Lin ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl10549,plain,
( arrow_1647925946e_Prof
= ( pi_Arr1309696186_alt_o @ top_to54564308indi_o @ ( '#ty_enc66' @ arrow_1982173296le_Lin ) ) ),
inference(remove_ty_args,[status(thm)],[zip_derived_cl81]) ).
thf(fact_916_subsetD,axiom,
! [C_5: arrow_1196572341e_indi > produc1572197287le_alt > $o,A_13: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,B_9: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ A_13 @ B_9 )
=> ( ( member822980838_alt_o @ C_5 @ A_13 )
=> ( member822980838_alt_o @ C_5 @ B_9 ) ) ) ).
thf(zip_derived_cl361,plain,
( !!
@ ^ [Y0: arrow_1196572341e_indi > produc1572197287le_alt > $o] :
( !!
@ ^ [Y1: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( !!
@ ^ [Y2: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ Y1 @ Y2 )
=> ( ( member822980838_alt_o @ Y0 @ Y1 )
=> ( member822980838_alt_o @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf,[status(esa)],[fact_916_subsetD]) ).
thf(zip_derived_cl362,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ord_le602483040lt_o_o ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ member822980838_alt_o ) ) ) @ member822980838_alt_o ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl361]) ).
thf(zip_derived_cl792,plain,
! [X2: arrow_1196572341e_indi > produc1572197287le_alt > $o] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ord_le602483040lt_o_o ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( member822980838_alt_o @ X2 ) ) ) @ ( member822980838_alt_o @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl362]) ).
thf(zip_derived_cl793,plain,
! [X2: arrow_1196572341e_indi > produc1572197287le_alt > $o,X4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( ord_le602483040lt_o_o @ X4 ) ) @ ( '#B' @ ( (=>) @ ( member822980838_alt_o @ X2 @ X4 ) ) @ ( member822980838_alt_o @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl792]) ).
thf(zip_derived_cl794,plain,
! [X2: arrow_1196572341e_indi > produc1572197287le_alt > $o,X4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X6: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ( ord_le602483040lt_o_o @ X4 @ X6 )
=> ( ( member822980838_alt_o @ X2 @ X4 )
=> ( member822980838_alt_o @ X2 @ X6 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl793]) ).
thf(zip_derived_cl795,plain,
! [X2: arrow_1196572341e_indi > produc1572197287le_alt > $o,X4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X6: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ~ ( ord_le602483040lt_o_o @ X4 @ X6 )
| ( ( member822980838_alt_o @ X2 @ X4 )
=> ( member822980838_alt_o @ X2 @ X6 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl794]) ).
thf(zip_derived_cl796,plain,
! [X2: arrow_1196572341e_indi > produc1572197287le_alt > $o,X4: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o,X6: ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o] :
( ~ ( member822980838_alt_o @ X2 @ X4 )
| ( member822980838_alt_o @ X2 @ X6 )
| ~ ( ord_le602483040lt_o_o @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl795]) ).
thf(fact_349_top1I,axiom,
! [X_97: arrow_1196572341e_indi] : ( top_to54564308indi_o @ X_97 ) ).
thf(zip_derived_cl90,plain,
( !!
@ ^ [Y0: arrow_1196572341e_indi] : ( top_to54564308indi_o @ Y0 ) ),
inference(cnf,[status(esa)],[fact_349_top1I]) ).
thf(zip_derived_cl91,plain,
!! @ top_to54564308indi_o,
inference(lams2combs,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl405,plain,
! [X2: arrow_1196572341e_indi] : ( top_to54564308indi_o @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl91]) ).
thf(fact_989_top__greatest,axiom,
! [A_3: arrow_1196572341e_indi > $o] : ( ord_le865407012indi_o @ A_3 @ top_to54564308indi_o ) ).
thf(zip_derived_cl387,plain,
( !!
@ ^ [Y0: arrow_1196572341e_indi > $o] : ( ord_le865407012indi_o @ Y0 @ top_to54564308indi_o ) ),
inference(cnf,[status(esa)],[fact_989_top__greatest]) ).
thf(zip_derived_cl388,plain,
!! @ ( '#C' @ ord_le865407012indi_o @ top_to54564308indi_o ),
inference(lams2combs,[status(thm)],[zip_derived_cl387]) ).
thf(zip_derived_cl413,plain,
! [X2: arrow_1196572341e_indi > $o] : ( ord_le865407012indi_o @ X2 @ top_to54564308indi_o ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl388]) ).
thf(fact_921_Pi__anti__mono,axiom,
! [B_8: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o,A_12: arrow_1196572341e_indi > $o,A_11: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ A_12 @ A_11 )
=> ( ord_le602483040lt_o_o @ ( pi_Arr1309696186_alt_o @ A_11 @ B_8 ) @ ( pi_Arr1309696186_alt_o @ A_12 @ B_8 ) ) ) ).
thf(zip_derived_cl363,plain,
( !!
@ ^ [Y0: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o] :
( !!
@ ^ [Y1: arrow_1196572341e_indi > $o] :
( !!
@ ^ [Y2: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ Y1 @ Y2 )
=> ( ord_le602483040lt_o_o @ ( pi_Arr1309696186_alt_o @ Y2 @ Y0 ) @ ( pi_Arr1309696186_alt_o @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf,[status(esa)],[fact_921_Pi__anti__mono]) ).
thf(zip_derived_cl364,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ord_le865407012indi_o ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ ord_le602483040lt_o_o ) @ ( '#C' @ pi_Arr1309696186_alt_o ) ) ) ) @ ( '#C' @ pi_Arr1309696186_alt_o ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl363]) ).
thf(zip_derived_cl867,plain,
! [X2: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ord_le865407012indi_o ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ ord_le602483040lt_o_o @ ( '#C' @ pi_Arr1309696186_alt_o @ X2 ) ) ) @ ( '#C' @ pi_Arr1309696186_alt_o @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl364]) ).
thf(zip_derived_cl868,plain,
! [X2: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o,X4: arrow_1196572341e_indi > $o] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( ord_le865407012indi_o @ X4 ) ) @ ( '#C' @ ( '#B' @ ord_le602483040lt_o_o @ ( '#C' @ pi_Arr1309696186_alt_o @ X2 ) ) @ ( pi_Arr1309696186_alt_o @ X4 @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl867]) ).
thf(zip_derived_cl869,plain,
! [X2: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o,X4: arrow_1196572341e_indi > $o,X6: arrow_1196572341e_indi > $o] :
( ( ord_le865407012indi_o @ X4 @ X6 )
=> ( ord_le602483040lt_o_o @ ( pi_Arr1309696186_alt_o @ X6 @ X2 ) @ ( pi_Arr1309696186_alt_o @ X4 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl868]) ).
thf(zip_derived_cl870,plain,
! [X2: arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o,X4: arrow_1196572341e_indi > $o,X6: arrow_1196572341e_indi > $o] :
( ~ ( ord_le865407012indi_o @ X4 @ X6 )
| ( ord_le602483040lt_o_o @ ( pi_Arr1309696186_alt_o @ X6 @ X2 ) @ ( pi_Arr1309696186_alt_o @ X4 @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl869]) ).
thf(zip_derived_cl10570,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl2,zip_derived_cl459,zip_derived_cl561,zip_derived_cl428,zip_derived_cl498,zip_derived_cl786,zip_derived_cl605,zip_derived_cl963,zip_derived_cl630,zip_derived_cl595,zip_derived_cl495,zip_derived_cl589,zip_derived_cl768,zip_derived_cl596,zip_derived_cl406,zip_derived_cl632,zip_derived_cl627,zip_derived_cl10559,zip_derived_cl0,zip_derived_cl10549,zip_derived_cl796,zip_derived_cl405,zip_derived_cl413,zip_derived_cl870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SCT170^3 : TPTP v9.2.0. Released v5.3.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.JrxzQYT8NE true
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Oct 1 15:15:38 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Running portfolio for 300 s
% 0.13/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in HO mode
% 0.58/0.69 % Total configuration time : 828
% 0.58/0.69 % Estimated wc time : 1656
% 0.58/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.58/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.58/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.78 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.59/0.89 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 92.09/12.21 % Solved by lams/40_b.comb.sh.
% 92.09/12.21 % done 474 iterations in 11.408s
% 92.09/12.21 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 92.09/12.21 % SZS output start Refutation
% See solution above
% 92.09/12.22
% 92.09/12.22
% 92.09/12.22 % Terminating...
% 92.41/12.32 % Runner terminated.
% 92.41/12.33 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------