%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ITP009^1 : TPTP v9.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.U7RttnYuIi true
% Computer : n012.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 04:38:14 PM UTC 2025
% Result : Theorem 119.09s 15.73s
% Output : Refutation 119.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 131 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 790 ( 115 equ; 142 cnn)
% Maximal formula atoms : 22 ( 6 avg)
% Number of connectives : 19835 ( 32 ~; 13 |; 44 &;19307 @)
% ( 29 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 70 ( 23 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 33 usr; 23 con; 0-6 aty)
% ( 352 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 468 ( 66 ^; 402 !; 0 ?; 468 :)
% Comments :
%------------------------------------------------------------------------------
thf(du_type,type,
du: $tType ).
thf(d_type,type,
d: $tType ).
thf(u_type,type,
u: $tType ).
thf(c_2Equotient_2E_2D_2D_3E_2E2_type,type,
c_2Equotient_2E_2D_2D_3E_2E2: du > du > u ).
thf('#sk11_type',type,
'#sk11': u ).
thf(tyop_2Emin_2Efun_type,type,
tyop_2Emin_2Efun: d > d > d ).
thf('#sk9_type',type,
'#sk9': u ).
thf('#sk13_type',type,
'#sk13': u ).
thf('#sk3_type',type,
'#sk3': d ).
thf('#sk2_type',type,
'#sk2': d ).
thf(app_2E2_type,type,
app_2E2: du > du > u ).
thf(c_2Equotient_2E_3D_3D_3D_3E_2E4_type,type,
c_2Equotient_2E_3D_3D_3D_3E_2E4: du > du > du > du > u ).
thf(c_2Equotient_2E_3D_3D_3D_3E_2E0_type,type,
c_2Equotient_2E_3D_3D_3D_3E_2E0: u ).
thf('#sk4_type',type,
'#sk4': d ).
thf(c_2Ecombin_2EW_2E0_type,type,
c_2Ecombin_2EW_2E0: u ).
thf('#sk7_type',type,
'#sk7': u ).
thf('#sk8_type',type,
'#sk8': u ).
thf(c_2Equotient_2EQUOTIENT_2E3_type,type,
c_2Equotient_2EQUOTIENT_2E3: du > du > du > u ).
thf(s_type,type,
s: d > u > du ).
thf('#sk6_type',type,
'#sk6': u ).
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: d ).
thf(j_mono_2Etyop_2Emin_2Ebool_type,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf('#sk5_type',type,
'#sk5': d ).
thf('#sk10_type',type,
'#sk10': u ).
thf(c_2Equotient_2Erespects_2E0_type,type,
c_2Equotient_2Erespects_2E0: u ).
thf(c_2Equotient_2E_3D_3D_3D_3E_2E2_type,type,
c_2Equotient_2E_3D_3D_3D_3E_2E2: du > du > u ).
thf('#sk12_type',type,
'#sk12': u ).
thf(c_2Equotient_2E_2D_2D_3E_2E0_type,type,
c_2Equotient_2E_2D_2D_3E_2E0: u ).
thf(c_2Equotient_2Erespects_2E2_type,type,
c_2Equotient_2Erespects_2E2: du > du > u ).
thf(c_2Equotient_2E_2D_2D_3E_2E3_type,type,
c_2Equotient_2E_2D_2D_3E_2E3: du > du > du > u ).
thf(c_2Ecombin_2EW_2E2_type,type,
c_2Ecombin_2EW_2E2: du > du > u ).
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(thm_2Equotient_2EFUN__REL__EQ__REL,conjecture,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1abs1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2rep1_2E0 ) ) ) )
=> ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V4abs2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V5rep2_2E0 ) ) ) )
=> ! [V6f_2E0: u,V7g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V6f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V7g_2E0 ) ) ) )
<=> ( ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2rep1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V4abs2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V6f_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2rep1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V4abs2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V7g_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V7g_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V6f_2E0 ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1abs1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2rep1_2E0 ) ) ) )
=> ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V4abs2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V5rep2_2E0 ) ) ) )
=> ! [V6f_2E0: u,V7g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V6f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V7g_2E0 ) ) ) )
<=> ( ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2rep1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V4abs2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V6f_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2rep1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V4abs2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V7g_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V7g_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V6f_2E0 ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[thm_2Equotient_2EFUN__REL__EQ__REL]) ).
thf(zip_derived_cl32,plain,
~ ( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( !!
@ ^ [Y2: d] :
( !!
@ ^ [Y3: d] :
( !!
@ ^ [Y4: u] :
( !!
@ ^ [Y5: u] :
( !!
@ ^ [Y6: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y2 ) @ Y5 ) @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ Y0 ) @ Y6 ) ) ) )
=> ( !!
@ ^ [Y7: u] :
( !!
@ ^ [Y8: u] :
( !!
@ ^ [Y9: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ Y7 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ Y3 ) @ Y8 ) @ ( s @ ( tyop_2Emin_2Efun @ Y3 @ Y1 ) @ Y9 ) ) ) )
=> ( !!
@ ^ [Y10: u] :
( !!
@ ^ [Y11: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ Y7 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y10 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y11 ) ) ) )
<=> ( ( ( s @ ( tyop_2Emin_2Efun @ Y2 @ Y3 ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ Y0 ) @ Y6 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ Y3 ) @ Y8 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y10 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ Y2 @ Y3 ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ Y0 ) @ Y6 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ Y3 ) @ Y8 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y11 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ Y7 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y11 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ Y7 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl33,plain,
~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j_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E4 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl125,plain,
~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl126,plain,
~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk3' ) ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk3' ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ '#sk2' ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk3' ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl125]) ).
thf(zip_derived_cl127,plain,
~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk4' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk3' ) ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk4' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk3' ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk4' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ '#sk3' ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl126]) ).
thf(zip_derived_cl128,plain,
~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk4' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk5' @ '#sk3' ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl127]) ).
thf(zip_derived_cl129,plain,
~ ( !! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk4' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk5' @ '#sk3' ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl128]) ).
thf(zip_derived_cl130,plain,
~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk4' ) @ '#sk7' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk5' @ '#sk3' ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl129]) ).
thf(zip_derived_cl131,plain,
~ ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk4' ) @ '#sk7' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) ) ) )
=> ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk5' @ '#sk3' ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl130]) ).
thf(zip_derived_cl133,plain,
~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk5' @ '#sk3' ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl131]) ).
thf(zip_derived_cl134,plain,
~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk5' @ '#sk3' ) ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl133]) ).
thf(zip_derived_cl135,plain,
~ ( !! @ ( '#C' @ ( '#B' @ (=>) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk5' @ '#sk3' ) ) ) ) ) ) @ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl134]) ).
thf(zip_derived_cl136,plain,
~ ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk5' @ '#sk3' ) @ '#sk11' ) ) ) )
=> ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl135]) ).
thf(zip_derived_cl137,plain,
j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk5' @ '#sk3' ) @ '#sk11' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl136]) ).
thf(zip_derived_cl132,plain,
j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk4' ) @ '#sk7' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl131]) ).
thf(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(zip_derived_cl6,plain,
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( !!
@ ^ [Y2: d] :
( !!
@ ^ [Y3: d] :
( !!
@ ^ [Y4: u] :
( !!
@ ^ [Y5: u] :
( !!
@ ^ [Y6: u] :
( ( s @ ( tyop_2Emin_2Efun @ Y2 @ Y3 ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ Y0 ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ Y3 ) @ Y5 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y6 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ Y2 @ Y3 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ Y2 @ Y3 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y1 @ Y3 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ Y2 @ Y3 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y2 @ Y0 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y1 @ Y3 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ Y2 @ Y3 ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ Y0 ) @ Y4 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ Y3 ) @ Y5 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y6 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d]) ).
thf(zip_derived_cl7,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl116,plain,
! [X2: d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s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ X2 ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl117,plain,
! [X2: d,X4: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#B' @ ( '#B' @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#B' @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 ) ) ) @ ( '#B' @ ( '#B' @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ X2 ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 ) ) ) @ ( '#B' @ ( '#B' @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl118,plain,
! [X2: d,X4: d,X6: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X6 ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X6 ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#B' @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( tyop_2Emin_2Efun @ X6 ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 ) ) @ ( '#B' @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( tyop_2Emin_2Efun @ X6 ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#C' @ ( '#B' @ s @ ( '#B' @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X2 ) ) @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 ) ) @ ( '#B' @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( tyop_2Emin_2Efun @ X6 ) ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl117]) ).
thf(zip_derived_cl119,plain,
! [X2: d,X4: d,X6: d,X8: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl118]) ).
thf(zip_derived_cl120,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X10 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X10 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl119]) ).
thf(zip_derived_cl121,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u,X12: u] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X12 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X10 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X12 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl120]) ).
thf(zip_derived_cl122,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u,X12: u,X14: u] :
( ( s @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X12 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X14 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X10 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X12 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X14 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl123,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u,X12: u,X14: u] :
( ( s @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X12 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X14 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X10 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X12 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X14 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl122]) ).
thf(arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( !!
@ ^ [Y2: d] :
( !!
@ ^ [Y3: d] :
( !!
@ ^ [Y4: u] :
( !!
@ ^ [Y5: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y2 @ Y3 ) @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y2 ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y3 @ Y1 ) @ Y5 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y2 @ Y3 ) @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y3 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y2 @ Y3 ) @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y2 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y3 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y2 @ Y3 ) @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y2 ) @ Y4 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y3 @ Y1 ) @ Y5 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b]) ).
thf(zip_derived_cl3,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl84,plain,
! [X2: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl85,plain,
! [X2: d,X4: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#B' @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ X4 ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ X4 ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl86,plain,
! [X2: d,X4: d,X6: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ X4 ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#C' @ ( '#B' @ s @ ( '#B' @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X6 ) ) @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ X4 ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) ) ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl87,plain,
! [X2: d,X4: d,X6: d,X8: d] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl88,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X10 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X10 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl89,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u,X12: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ X12 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X10 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ X12 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl90,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u,X12: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ X12 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X10 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ X12 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl124,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u,X12: u,X14: u] :
( ( s @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X12 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X14 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X12 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X14 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl123,zip_derived_cl90]) ).
thf(thm_2Ecombin_2EW__THM,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u] :
( ( s @ A_27b @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ).
thf(zip_derived_cl24,plain,
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( ( s @ Y1 @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) @ Y2 ) @ ( s @ Y0 @ Y3 ) ) )
= ( s @ Y1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) @ Y2 ) @ ( s @ Y0 @ Y3 ) ) ) @ ( s @ Y0 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[thm_2Ecombin_2EW__THM]) ).
thf(zip_derived_cl25,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Ecombin_2EW_2E2 ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ s ) ) ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ s ) ) ) ) ) ) @ s ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl37,plain,
! [X2: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Ecombin_2EW_2E2 ) @ ( '#B' @ s @ ( '#B' @ ( tyop_2Emin_2Efun @ X2 ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ s @ ( '#B' @ ( tyop_2Emin_2Efun @ X2 ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl38,plain,
! [X2: d,X4: d] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ X4 ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ X4 ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl39,plain,
! [X2: d,X4: d,X6: u] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ ( s @ X4 ) @ ( '#B' @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) @ ( '#B' @ ( s @ X4 ) @ ( '#S' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) @ ( s @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl40,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( s @ X4 @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) @ ( s @ X2 @ X8 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) @ ( s @ X2 @ X8 ) ) ) @ ( s @ X2 @ X8 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl41,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( s @ X4 @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) @ ( s @ X2 @ X8 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) @ ( s @ X2 @ X8 ) ) ) @ ( s @ X2 @ X8 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X3_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X3_2E0 ) ) ) ) ) ).
thf(zip_derived_cl10,plain,
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( !!
@ ^ [Y4: u] :
( !!
@ ^ [Y5: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y5 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y2 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ Y3 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y4 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y5 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27b]) ).
thf(zip_derived_cl11,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E4 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#B' @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl91,plain,
! [X2: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#C' @ ( '#B' @ s @ ( '#B' @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl92,plain,
! [X2: d,X4: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl93,plain,
! [X2: d,X4: d,X6: u] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl94,plain,
! [X2: d,X4: d,X6: u,X8: u] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl95,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X10 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X10 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl96,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u,X12: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X12 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X10 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X12 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl97,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u,X12: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X12 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X10 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X12 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl96]) ).
thf(arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ).
thf(zip_derived_cl8,plain,
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ Y3 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y2 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ Y3 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b]) ).
thf(zip_derived_cl9,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#B' @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl61,plain,
! [X2: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#C' @ ( '#B' @ s @ ( '#B' @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl62,plain,
! [X2: d,X4: d] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl63,plain,
! [X2: d,X4: d,X6: u] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl64,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl65,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl98,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u,X12: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X12 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X10 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X12 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl97,zip_derived_cl65]) ).
thf(zip_derived_cl596,plain,
! [X0: u,X1: d,X2: d,X3: u,X4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X3 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl98]) ).
thf(zip_derived_cl702,plain,
! [X0: u,X1: d,X2: d,X3: u,X4: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X3 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X0 ) ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl596]) ).
thf(zip_derived_cl138,plain,
~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl136]) ).
thf(zip_derived_cl139,plain,
~ ( !!
@ ( '#S' @ ( '#B' @ (<=>) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk12' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) )
@ ( '#C'
@ ( '#S'
@ ( '#B' @ (&)
@ ( '#B'
@ ( du
= ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk12' ) ) ) )
@ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) )
@ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) ) ) ) ) )
@ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk12' ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl138]) ).
thf(zip_derived_cl140,plain,
~ ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk12' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk13' ) ) ) )
<=> ( ( ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk12' ) ) )
= ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk13' ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk13' ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk12' ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl139]) ).
thf(zip_derived_cl141,plain,
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk12' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk13' ) ) ) )
!= ( ( ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk12' ) ) )
= ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk13' ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk13' ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk12' ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl140]) ).
thf(arityeq2_2Ec_2Equotient_2Erespects_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Equotient_2Erespects_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(zip_derived_cl22,plain,
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y3 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) @ c_2Equotient_2Erespects_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) @ Y2 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[arityeq2_2Ec_2Equotient_2Erespects_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool]) ).
thf(zip_derived_cl23,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2Erespects_2E0 ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl55,plain,
! [X2: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 ) @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#C' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Equotient_2Erespects_2E0 ) ) ) @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl56,plain,
! [X2: d,X4: d] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ c_2Equotient_2Erespects_2E0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl57,plain,
! [X2: d,X4: d,X6: u] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ c_2Equotient_2Erespects_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ X6 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl58,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ c_2Equotient_2Erespects_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ X6 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl59,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ c_2Equotient_2Erespects_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ X6 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl58]) ).
thf(thm_2Equotient_2Erespects__def,axiom,
! [A_27a: d,A_27b: d] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ c_2Equotient_2Erespects_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ c_2Ecombin_2EW_2E0 ) ) ).
thf(zip_derived_cl30,plain,
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) @ c_2Equotient_2Erespects_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) @ c_2Ecombin_2EW_2E0 ) ) ) ),
inference(cnf,[status(esa)],[thm_2Equotient_2Erespects__def]) ).
thf(zip_derived_cl31,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ ( '#S' @ ( '#B' @ '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) @ tyop_2Emin_2Efun ) ) ) @ c_2Equotient_2Erespects_2E0 ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ ( '#S' @ ( '#B' @ '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) @ tyop_2Emin_2Efun ) ) ) @ c_2Ecombin_2EW_2E0 ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl34,plain,
! [X2: d] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#C' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#B' @ ( tyop_2Emin_2Efun @ X2 ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) @ c_2Equotient_2Erespects_2E0 ) ) @ ( '#C' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#B' @ ( tyop_2Emin_2Efun @ X2 ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) @ c_2Ecombin_2EW_2E0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl35,plain,
! [X2: d,X4: d] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ c_2Equotient_2Erespects_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ c_2Ecombin_2EW_2E0 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl36,plain,
! [X2: d,X4: d] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ c_2Equotient_2Erespects_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ c_2Ecombin_2EW_2E0 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl35]) ).
thf(arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ A_27b @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ c_2Ecombin_2EW_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(zip_derived_cl20,plain,
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( ( s @ Y1 @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) @ Y2 ) @ ( s @ Y0 @ Y3 ) ) )
= ( s @ Y1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) @ c_2Ecombin_2EW_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) @ Y2 ) ) ) @ ( s @ Y0 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b]) ).
thf(zip_derived_cl21,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Ecombin_2EW_2E2 ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ s ) ) ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ ( '#S' @ ( '#B' @ '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) @ tyop_2Emin_2Efun ) ) ) @ c_2Ecombin_2EW_2E0 ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) @ s ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl50,plain,
! [X2: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Ecombin_2EW_2E2 ) @ ( '#B' @ s @ ( '#B' @ ( tyop_2Emin_2Efun @ X2 ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#C' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( '#B' @ ( tyop_2Emin_2Efun @ X2 ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) @ c_2Ecombin_2EW_2E0 ) ) ) @ ( '#B' @ s @ ( '#B' @ ( tyop_2Emin_2Efun @ X2 ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl51,plain,
! [X2: d,X4: d] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ X4 ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ X4 ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ c_2Ecombin_2EW_2E0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl52,plain,
! [X2: d,X4: d,X6: u] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ ( s @ X4 ) @ ( '#B' @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) @ ( '#B' @ ( s @ X4 ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ c_2Ecombin_2EW_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) ) ) ) @ ( s @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl53,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( s @ X4 @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) @ ( s @ X2 @ X8 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ c_2Ecombin_2EW_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) ) ) @ ( s @ X2 @ X8 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl54,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( s @ X4 @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) @ ( s @ X2 @ X8 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ c_2Ecombin_2EW_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) ) ) @ ( s @ X2 @ X8 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl60,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl36,zip_derived_cl54]) ).
thf(zip_derived_cl60_001,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2Erespects_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl36,zip_derived_cl54]) ).
thf(zip_derived_cl142,plain,
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk12' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk13' ) ) ) )
!= ( ( ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk12' ) ) )
= ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk5' ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ '#sk4' @ '#sk2' ) @ '#sk8' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ '#sk5' ) @ '#sk10' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk13' ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk13' ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ ( tyop_2Emin_2Efun @ '#sk2' @ tyop_2Emin_2Ebool ) ) @ '#sk6' ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk3' @ ( tyop_2Emin_2Efun @ '#sk3' @ tyop_2Emin_2Ebool ) ) @ '#sk9' ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ '#sk2' @ '#sk3' ) @ '#sk12' ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl141,zip_derived_cl60,zip_derived_cl60]) ).
thf(zip_derived_cl596_002,plain,
! [X0: u,X1: d,X2: d,X3: u,X4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X3 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl98]) ).
thf(zip_derived_cl701,plain,
! [X0: u,X1: d,X2: d,X3: u,X4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X3 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X0 ) ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl596]) ).
thf(thm_2Equotient_2EFUN__QUOTIENT,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1abs1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2rep1_2E0 ) ) ) )
=> ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V4abs2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V5rep2_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2rep1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V4abs2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1abs1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V5rep2_2E0 ) ) ) ) ) ) ) ) ).
thf(zip_derived_cl28,plain,
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( !!
@ ^ [Y2: d] :
( !!
@ ^ [Y3: d] :
( !!
@ ^ [Y4: u] :
( !!
@ ^ [Y5: u] :
( !!
@ ^ [Y6: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y2 ) @ Y5 ) @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ Y0 ) @ Y6 ) ) ) )
=> ( !!
@ ^ [Y7: u] :
( !!
@ ^ [Y8: u] :
( !!
@ ^ [Y9: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ Y7 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ Y3 ) @ Y8 ) @ ( s @ ( tyop_2Emin_2Efun @ Y3 @ Y1 ) @ Y9 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y4 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) ) @ Y7 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ ( tyop_2Emin_2Efun @ Y2 @ Y3 ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ Y0 ) @ Y6 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ Y3 ) @ Y8 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ Y2 @ Y3 ) @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y2 ) @ Y5 ) @ ( s @ ( tyop_2Emin_2Efun @ Y3 @ Y1 ) @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[thm_2Equotient_2EFUN__QUOTIENT]) ).
thf(zip_derived_cl29,plain,
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j_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl151,plain,
! [X2: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#S' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ s ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) ) @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl152,plain,
! [X2: d,X4: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#B' @ ( '#B' @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ tyop_2Emin_2Efun ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl151]) ).
thf(zip_derived_cl153,plain,
! [X2: d,X4: d,X6: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#B' @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( tyop_2Emin_2Efun @ X6 ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#C' @ ( '#B' @ tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 ) ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl152]) ).
thf(zip_derived_cl154,plain,
! [X2: d,X4: d,X6: d,X8: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl155,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl154]) ).
thf(zip_derived_cl156,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u,X12: u] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl155]) ).
thf(zip_derived_cl157,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u,X12: u,X14: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X14 ) ) ) )
=> ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X14 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl156]) ).
thf(zip_derived_cl158,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u,X12: u,X14: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X14 ) ) ) )
| ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X14 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl157]) ).
thf(zip_derived_cl159,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u,X12: u,X14: u,X16: u] :
( ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X16 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X16 ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X14 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) ) ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X14 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl158]) ).
thf(zip_derived_cl160,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u,X12: u,X14: u,X16: u,X18: u] :
( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X16 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X18 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X16 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X14 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X18 ) ) ) ) @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) @ ( '#B' @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) ) ) ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X14 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl159]) ).
thf(zip_derived_cl161,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u,X12: u,X14: u,X16: u,X18: u,X20: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X16 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X18 ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ X20 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X16 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X14 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X18 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ X20 ) ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X14 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl160]) ).
thf(zip_derived_cl162,plain,
! [X2: d,X4: d,X6: d,X8: d,X10: u,X12: u,X14: u,X16: u,X18: u,X20: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X16 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X18 ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ X20 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X16 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ X6 @ X8 ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X14 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X8 ) @ X18 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X6 @ X8 ) @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) @ ( s @ ( tyop_2Emin_2Efun @ X8 @ X4 ) @ X20 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X6 ) @ X12 ) @ ( s @ ( tyop_2Emin_2Efun @ X6 @ X2 ) @ X14 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl161]) ).
thf(zip_derived_cl98_003,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u,X12: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X10 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X12 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient_2E_3D_3D_3D_3E_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ ( tyop_2Emin_2Efun @ X4 @ tyop_2Emin_2Ebool ) ) @ X8 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X10 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X12 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl97,zip_derived_cl65]) ).
thf(thm_2Equotient_2EQUOTIENT__REL,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1abs_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V2rep_2E0 ) ) ) )
=> ! [V3r_2E0: u,V4s_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V3r_2E0 ) ) ) @ ( s @ A_27a @ V4s_2E0 ) ) ) )
<=> ( ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1abs_2E0 ) @ ( s @ A_27a @ V3r_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1abs_2E0 ) @ ( s @ A_27a @ V4s_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V4s_2E0 ) ) ) @ ( s @ A_27a @ V4s_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V3r_2E0 ) ) ) @ ( s @ A_27a @ V3r_2E0 ) ) ) ) ) ) ) ).
thf(zip_derived_cl26,plain,
( !!
@ ^ [Y0: d] :
( !!
@ ^ [Y1: d] :
( !!
@ ^ [Y2: u] :
( !!
@ ^ [Y3: u] :
( !!
@ ^ [Y4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ Y0 ) @ Y4 ) ) ) )
=> ( !!
@ ^ [Y5: u] :
( !!
@ ^ [Y6: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y2 ) @ ( s @ Y0 @ Y5 ) ) ) @ ( s @ Y0 @ Y6 ) ) ) )
<=> ( ( ( s @ Y1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y3 ) @ ( s @ Y0 @ Y5 ) ) )
= ( s @ Y1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ Y1 ) @ Y3 ) @ ( s @ Y0 @ Y6 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y2 ) @ ( s @ Y0 @ Y6 ) ) ) @ ( s @ Y0 @ Y6 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) ) @ Y2 ) @ ( s @ Y0 @ Y5 ) ) ) @ ( s @ Y0 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[thm_2Equotient_2EQUOTIENT__REL]) ).
thf(zip_derived_cl27,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ s ) @ ( '#C' @ tyop_2Emin_2Efun ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ s ) ) ) ) ) ) @ s ) ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) @ s ) ) ) ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#B' @ ( '#B' @ s ) @ tyop_2Emin_2Efun ) ) ) ) ) @ s ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ s ) ) ) ) ) @ s ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ app_2E2 ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ s @ ( '#S' @ tyop_2Emin_2Efun @ ( '#C' @ tyop_2Emin_2Efun @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ s ) ) ) ) ) @ s ) ) ) ) ) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl106,plain,
! [X2: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) @ ( '#B' @ s @ ( '#C' @ tyop_2Emin_2Efun @ X2 ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ s ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ s @ ( tyop_2Emin_2Efun @ X2 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl107,plain,
! [X2: d,X4: d] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ X4 ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ X4 ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ app_2E2 ) @ ( '#B' @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl108,plain,
! [X2: d,X4: d,X6: u] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( s @ X4 ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( s @ X4 ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#S' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#S' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl109,plain,
! [X2: d,X4: d,X6: u,X8: u] : ( !! @ ( '#C' @ ( '#B' @ (=>) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) ) ) ) ) ) @ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=) @ ( '#B' @ ( s @ X4 ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) @ ( s @ X2 ) ) ) ) ) @ ( '#B' @ ( s @ X4 ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#S' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#S' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl110,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ X10 ) ) ) )
=> ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=) @ ( '#B' @ ( s @ X4 ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) @ ( s @ X2 ) ) ) ) ) @ ( '#B' @ ( s @ X4 ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#S' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#S' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl111,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ X10 ) ) ) )
| ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool ) @ ( '#B' @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=) @ ( '#B' @ ( s @ X4 ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) @ ( s @ X2 ) ) ) ) ) @ ( '#B' @ ( s @ X4 ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#S' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#S' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) @ ( s @ X2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl112,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u,X12: u] :
( ( !!
@ ( '#S' @ ( '#B' @ (<=>) @ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ X2 @ X12 ) ) ) ) @ ( s @ X2 ) ) ) ) )
@ ( '#C'
@ ( '#S'
@ ( '#B' @ (&)
@ ( '#B'
@ ( du
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) @ ( s @ X2 @ X12 ) ) ) )
@ ( '#B' @ ( s @ X4 ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) ) @ ( s @ X2 ) ) ) ) )
@ ( '#B' @ j_mono_2Etyop_2Emin_2Ebool @ ( '#B' @ ( s @ tyop_2Emin_2Ebool ) @ ( '#S' @ ( '#B' @ app_2E2 @ ( '#B' @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ ( '#B' @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) ) @ ( s @ X2 ) ) ) ) @ ( s @ X2 ) ) ) ) )
@ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ X2 @ X12 ) ) ) @ ( s @ X2 @ X12 ) ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ X10 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl113,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u,X12: u,X14: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ X2 @ X12 ) ) ) @ ( s @ X2 @ X14 ) ) ) )
<=> ( ( ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) @ ( s @ X2 @ X12 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) @ ( s @ X2 @ X14 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ X2 @ X14 ) ) ) @ ( s @ X2 @ X14 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ X2 @ X12 ) ) ) @ ( s @ X2 @ X12 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ X10 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl114,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u,X12: u,X14: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ X2 @ X12 ) ) ) @ ( s @ X2 @ X14 ) ) ) )
= ( ( ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) @ ( s @ X2 @ X12 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) @ ( s @ X2 @ X14 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ X2 @ X14 ) ) ) @ ( s @ X2 @ X14 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ X2 @ X12 ) ) ) @ ( s @ X2 @ X12 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ X10 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl41_004,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( s @ X4 @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) @ ( s @ X2 @ X8 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) @ ( s @ X2 @ X8 ) ) ) @ ( s @ X2 @ X8 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl41_005,plain,
! [X2: d,X4: d,X6: u,X8: u] :
( ( s @ X4 @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) @ ( s @ X2 @ X8 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ X4 ) ) @ X6 ) @ ( s @ X2 @ X8 ) ) ) @ ( s @ X2 @ X8 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl115,plain,
! [X2: d,X4: d,X6: u,X8: u,X10: u,X12: u,X14: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ X2 @ X12 ) ) ) @ ( s @ X2 @ X14 ) ) ) )
= ( ( ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) @ ( s @ X2 @ X12 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) @ ( s @ X2 @ X14 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ X2 @ X14 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EW_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ X2 @ X12 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X6 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X8 ) @ ( s @ ( tyop_2Emin_2Efun @ X4 @ X2 ) @ X10 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl114,zip_derived_cl41,zip_derived_cl41]) ).
thf(zip_derived_cl4088,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl137,zip_derived_cl132,zip_derived_cl124,zip_derived_cl702,zip_derived_cl142,zip_derived_cl701,zip_derived_cl162,zip_derived_cl98,zip_derived_cl115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP009^1 : TPTP v9.2.0. Bugfixed v7.5.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.U7RttnYuIi true
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 15:26:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.56/0.66 % Total configuration time : 828
% 0.56/0.66 % Estimated wc time : 1656
% 0.56/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.58/0.73 % /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
% 0.58/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.58/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.58/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.58/0.80 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.82 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.82 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.60/1.01 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 119.09/15.73 % Solved by lams/40_b.comb.sh.
% 119.09/15.73 % done 90 iterations in 14.681s
% 119.09/15.73 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 119.09/15.73 % SZS output start Refutation
% See solution above
% 119.09/15.77
% 119.09/15.77
% 119.09/15.77 % Terminating...
% 119.42/15.86 % Runner terminated.
% 119.42/15.86 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------