%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV146^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.OXDUHgpoUp true
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:57:15 PM UTC 2025
% Result : Theorem 14.94s 2.86s
% Output : Refutation 14.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 18
% Syntax : Number of formulae : 291 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 1901 ( 0 equ; 3 cnn)
% Maximal formula atoms : 30 ( 6 avg)
% Number of connectives : 5092 ( 376 ~; 504 |; 337 &;2793 @)
% ( 0 <=>; 487 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 159 ( 159 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-2 aty)
% ( 595 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 779 ( 595 ^; 184 !; 0 ?; 779 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf('#form79_type',type,
'#form79': ( a > $o ) > $o ).
thf('#sk6_type',type,
'#sk6': a ).
thf('#sk38_type',type,
'#sk38': ( a > $o ) > a ).
thf('#form648_type',type,
'#form648': $o ).
thf('#sk1_type',type,
'#sk1': a > a > $o ).
thf('#sk24_type',type,
'#sk24': ( a > $o ) > a ).
thf('#sk80_type',type,
'#sk80': ( a > $o ) > a ).
thf('#sk7_type',type,
'#sk7': a ).
thf('#form71_type',type,
'#form71': ( a > $o ) > $o ).
thf('#sk5_type',type,
'#sk5': a > $o ).
thf('#sk3_type',type,
'#sk3': a ).
thf('#sk72_type',type,
'#sk72': ( a > $o ) > a ).
thf('#sk4_type',type,
'#sk4': a ).
thf('#sk2_type',type,
'#sk2': a ).
thf('#sk8_type',type,
'#sk8': a > $o ).
thf(cTHM525_pme,conjecture,
! [Xr: a > a > $o] :
( ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ! [Xq: a > $o] :
( ( ! [Xv: a,Xw: a] :
( ( ( Xr @ Xv @ Xw )
& ( Xq @ Xv ) )
=> ( Xq @ Xw ) )
& ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xv: a,Xw: a] :
( ( ( Xr @ Xv @ Xw )
& ( Xq @ Xv ) )
=> ( Xq @ Xw ) )
& ! [Xw: a] :
( ( Xr @ Xy @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) )
& ! [Xq: a > $o] :
( ( ! [Xv: a,Xw: a] :
( ( ( Xr @ Xv @ Xw )
& ( Xq @ Xv ) )
=> ( Xq @ Xw ) )
& ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xv: a,Xw: a] :
( ( ( Xr @ Xv @ Xw )
& ( Xq @ Xv ) )
=> ( Xq @ Xw ) )
& ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [Xr: a > a > $o] :
( ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ! [Xq: a > $o] :
( ( ! [Xv: a,Xw: a] :
( ( ( Xr @ Xv @ Xw )
& ( Xq @ Xv ) )
=> ( Xq @ Xw ) )
& ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xv: a,Xw: a] :
( ( ( Xr @ Xv @ Xw )
& ( Xq @ Xv ) )
=> ( Xq @ Xw ) )
& ! [Xw: a] :
( ( Xr @ Xy @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) )
& ! [Xq: a > $o] :
( ( ! [Xv: a,Xw: a] :
( ( ( Xr @ Xv @ Xw )
& ( Xq @ Xv ) )
=> ( Xq @ Xw ) )
& ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xv: a,Xw: a] :
( ( ( Xr @ Xv @ Xw )
& ( Xq @ Xv ) )
=> ( Xq @ Xw ) )
& ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) ) ),
inference('cnf.neg',[status(esa)],[cTHM525_pme]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( Y0 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk2' @ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk2' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
( ~ ( ( '#sk1' @ '#sk2' @ '#sk3' )
=> ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk2' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk3' ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl6,plain,
( ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk2' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk3' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl8,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk2' @ Y0 )
=> ( '#sk5' @ Y0 ) ) ) )
=> ( '#sk5' @ '#sk3' ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl10,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk2' @ Y0 )
=> ( '#sk5' @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl14,plain,
( ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk2' @ Y0 )
=> ( '#sk5' @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl19,plain,
! [X2: a] :
( ( ( '#sk1' @ '#sk2' @ X2 )
=> ( '#sk5' @ X2 ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl25,plain,
! [X2: a] :
( ~ ( '#sk1' @ '#sk2' @ X2 )
| ( '#sk5' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl36,plain,
! [X2: a] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ '#sk4' @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ '#sk4' @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ( '#sk5' @ X2 )
| ~ ( '#sk1' @ '#sk2' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl44,plain,
! [X2: a] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk6' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk4' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ '#sk6' ) ) ) )
=> ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk4' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| ~ ( '#sk1' @ '#sk2' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl53,plain,
! [X2: a] :
( ~ ( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk6' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
& ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk6' ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) ) )
| ( '#sk5' @ X2 )
| ~ ( '#sk1' @ '#sk2' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl67,plain,
! [X2: a] :
( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk6' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
& ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk6' ) ) ) )
| ~ ( '#sk1' @ '#sk2' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl77,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk6' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
| ( '#sk5' @ X2 )
| ~ ( '#sk1' @ '#sk2' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl91,plain,
! [X2: a,X4: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( X4 @ Y0 ) ) ) )
=> ( X4 @ '#sk7' ) )
| ~ ( '#sk1' @ '#sk2' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl92,plain,
! [X0: a] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
=> ( '#sk8' @ '#sk7' ) )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk5' @ X0 ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl5,plain,
( ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl7,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ '#sk4' @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ '#sk4' @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl9,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk6' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk4' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ '#sk6' ) ) ) )
=> ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk4' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl12,plain,
( ~ ( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk6' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
& ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk6' ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl17,plain,
( ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl23,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
=> ( '#sk8' @ '#sk7' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl34,plain,
( ~ ( '#sk8' @ '#sk7' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl68,plain,
! [X2: a] :
( ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
| ~ ( '#sk1' @ '#sk2' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl79,plain,
! [X2: a] :
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
=> ( '#sk8' @ '#sk7' ) )
| ( '#sk5' @ X2 )
| ~ ( '#sk1' @ '#sk2' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl98,plain,
! [X2: a] :
( ~ ( '#sk8' @ '#sk7' )
| ~ ( '#sk1' @ '#sk2' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl210,plain,
( ~ ( '#sk8' @ '#sk7' )
| ( '#sk5' @ '#sk3' )
| ~ ( '#sk8' @ '#sk7' ) ),
inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl98]) ).
thf(zip_derived_cl213,plain,
( ( '#sk5' @ '#sk3' )
| ~ ( '#sk8' @ '#sk7' ) ),
inference(simplify,[status(thm)],[zip_derived_cl210]) ).
thf(zip_derived_cl11,plain,
( ~ ( '#sk5' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl15,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ '#sk4' @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ '#sk4' @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl20,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk6' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk4' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ '#sk6' ) ) ) )
=> ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk4' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl26,plain,
( ~ ( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk6' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
& ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk6' ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl38,plain,
( ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl47,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
=> ( '#sk8' @ '#sk7' ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl61,plain,
( ~ ( '#sk8' @ '#sk7' )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl217,plain,
~ ( '#sk8' @ '#sk7' ),
inference(clc,[status(thm)],[zip_derived_cl213,zip_derived_cl61]) ).
thf(zip_derived_cl643,plain,
! [X0: a] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
=> $false )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk5' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl92,zip_derived_cl217]) ).
thf(zip_derived_cl644,plain,
! [X0: a] :
( ( (~)
@ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) ) )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk5' @ X0 ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl643]) ).
thf(zip_derived_cl645,plain,
! [X0: a] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk5' @ X0 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl644]) ).
thf(zip_derived_cl646,plain,
! [X0: a] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) )
| ( '#sk5' @ X0 )
| ~ ( '#sk1' @ '#sk2' @ X0 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl645]) ).
thf(zip_derived_cl37,plain,
( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk6' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
& ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk6' ) ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl46,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk6' ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl57,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk6' ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl58,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
=> ( '#sk8' @ '#sk6' ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl513,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
| ( '#sk8' @ '#sk6' )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl514,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) )
| ~ ( '#sk5' @ '#sk3' )
| ( '#sk8' @ '#sk6' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl513]) ).
thf(zip_derived_cl515,plain,
( '#form648'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl647,plain,
! [X0: a] :
( ~ '#form648'
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk5' @ X0 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl646,zip_derived_cl515]) ).
thf(zip_derived_cl16,plain,
( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk6' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
& ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk6' ) ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl21,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk6' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl27,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk7' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl39,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
| ( X2 @ '#sk7' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl48,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( X2 @ Y0 ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( X2 @ '#sk7' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl62,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ ( '#sk24' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk24' @ X2 ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk7' )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl73,plain,
! [X2: a > $o] :
( ~ ( ( ( '#sk1' @ ( '#sk24' @ X2 ) @ ( '#sk38' @ X2 ) )
& ( X2 @ ( '#sk24' @ X2 ) ) )
=> ( X2 @ ( '#sk38' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( X2 @ Y0 ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( X2 @ '#sk7' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl85,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk38' @ X2 ) )
| ( X2 @ '#sk7' )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl105,plain,
! [X2: a > $o] :
( ( '#form71' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl648,plain,
! [X0: a] :
( ~ ( '#form71' @ '#sk8' )
| ( '#sk5' @ X0 )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ~ '#form648' ),
inference(renaming,[status(thm)],[zip_derived_cl647,zip_derived_cl105]) ).
thf(zip_derived_cl27_001,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk7' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl28,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
=> ( '#sk8' @ '#sk7' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl217_002,plain,
~ ( '#sk8' @ '#sk7' ),
inference(clc,[status(thm)],[zip_derived_cl213,zip_derived_cl61]) ).
thf(zip_derived_cl251,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
=> $false )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(demod,[status(thm)],[zip_derived_cl28,zip_derived_cl217]) ).
thf(zip_derived_cl252,plain,
( ( (~)
@ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl251]) ).
thf(zip_derived_cl253,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl252]) ).
thf(zip_derived_cl254,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl253]) ).
thf(zip_derived_cl105_003,plain,
! [X2: a > $o] :
( ( '#form71' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl255,plain,
( ~ ( '#form71' @ '#sk8' )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl254,zip_derived_cl105]) ).
thf(zip_derived_cl256,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ Y0 )
& ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) )
=> ( '#sk8' @ Y0 ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( '#form71' @ '#sk8' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl255]) ).
thf(zip_derived_cl257,plain,
( ~ ( ( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
& ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) )
=> ( '#sk8' @ ( '#sk38' @ '#sk8' ) ) )
| ~ ( '#form71' @ '#sk8' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl256]) ).
thf(zip_derived_cl258,plain,
( ( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
& ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( '#form71' @ '#sk8' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl257]) ).
thf(zip_derived_cl260,plain,
( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
| ~ ( '#form71' @ '#sk8' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl258]) ).
thf(zip_derived_cl33,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl41,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl50,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ X2 @ Y0 )
& ( '#sk8' @ X2 ) )
=> ( '#sk8' @ Y0 ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl64,plain,
! [X2: a,X4: a] :
( ( ( ( '#sk1' @ X2 @ X4 )
& ( '#sk8' @ X2 ) )
=> ( '#sk8' @ X4 ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl75,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk1' @ X2 @ X4 )
& ( '#sk8' @ X2 ) )
| ( '#sk8' @ X4 )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl88,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ~ ( '#sk8' @ X2 )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( '#sk8' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl594,plain,
( ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( '#form71' @ '#sk8' )
| ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl260,zip_derived_cl88]) ).
thf(zip_derived_cl619,plain,
( ~ ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ~ ( '#form71' @ '#sk8' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(simplify,[status(thm)],[zip_derived_cl594]) ).
thf(zip_derived_cl261,plain,
( ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ~ ( '#form71' @ '#sk8' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl258]) ).
thf(zip_derived_cl648_004,plain,
! [X0: a] :
( ~ ( '#form71' @ '#sk8' )
| ( '#sk5' @ X0 )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ~ '#form648' ),
inference(renaming,[status(thm)],[zip_derived_cl647,zip_derived_cl105]) ).
thf(zip_derived_cl667,plain,
( ~ ( '#form71' @ '#sk8' )
| ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ~ '#form648'
| ( '#sk5' @ '#sk3' )
| ~ ( '#form71' @ '#sk8' ) ),
inference('sup-',[status(thm)],[zip_derived_cl261,zip_derived_cl648]) ).
thf(zip_derived_cl679,plain,
( ( '#sk5' @ '#sk3' )
| ~ '#form648'
| ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ~ ( '#form71' @ '#sk8' ) ),
inference(simplify,[status(thm)],[zip_derived_cl667]) ).
thf(zip_derived_cl45,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk6' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl54,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk7' ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl55,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
=> ( '#sk8' @ '#sk7' ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl217_005,plain,
~ ( '#sk8' @ '#sk7' ),
inference(clc,[status(thm)],[zip_derived_cl213,zip_derived_cl61]) ).
thf(zip_derived_cl221,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
=> $false )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(demod,[status(thm)],[zip_derived_cl55,zip_derived_cl217]) ).
thf(zip_derived_cl222,plain,
( ( (~)
@ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl221]) ).
thf(zip_derived_cl223,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl222]) ).
thf(zip_derived_cl224,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( '#sk8' @ Y0 ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl223]) ).
thf(zip_derived_cl105_006,plain,
! [X2: a > $o] :
( ( '#form71' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl225,plain,
( ~ ( '#form71' @ '#sk8' )
| ~ ( '#sk5' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl224,zip_derived_cl105]) ).
thf(zip_derived_cl226,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ Y0 )
& ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) )
=> ( '#sk8' @ Y0 ) ) )
| ~ ( '#sk5' @ '#sk3' )
| ~ ( '#form71' @ '#sk8' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl225]) ).
thf(zip_derived_cl227,plain,
( ~ ( ( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
& ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) )
=> ( '#sk8' @ ( '#sk38' @ '#sk8' ) ) )
| ~ ( '#form71' @ '#sk8' )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl226]) ).
thf(zip_derived_cl228,plain,
( ( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
& ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) )
| ~ ( '#sk5' @ '#sk3' )
| ~ ( '#form71' @ '#sk8' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl227]) ).
thf(zip_derived_cl230,plain,
( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
| ~ ( '#form71' @ '#sk8' )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl228]) ).
thf(zip_derived_cl60,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl71,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl82,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ X2 @ Y0 )
& ( '#sk8' @ X2 ) )
=> ( '#sk8' @ Y0 ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl101,plain,
! [X2: a,X4: a] :
( ( ( ( '#sk1' @ X2 @ X4 )
& ( '#sk8' @ X2 ) )
=> ( '#sk8' @ X4 ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl122,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk1' @ X2 @ X4 )
& ( '#sk8' @ X2 ) )
| ( '#sk8' @ X4 )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl149,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ~ ( '#sk8' @ X2 )
| ~ ( '#sk5' @ '#sk3' )
| ( '#sk8' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl122]) ).
thf(zip_derived_cl393,plain,
( ~ ( '#sk5' @ '#sk3' )
| ~ ( '#form71' @ '#sk8' )
| ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ~ ( '#sk5' @ '#sk3' )
| ~ ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl230,zip_derived_cl149]) ).
thf(zip_derived_cl416,plain,
( ~ ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ~ ( '#form71' @ '#sk8' )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(simplify,[status(thm)],[zip_derived_cl393]) ).
thf(zip_derived_cl231,plain,
( ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ~ ( '#form71' @ '#sk8' )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl228]) ).
thf(zip_derived_cl546,plain,
( ~ ( '#sk5' @ '#sk3' )
| ~ ( '#form71' @ '#sk8' )
| ( '#sk8' @ ( '#sk38' @ '#sk8' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl416,zip_derived_cl231]) ).
thf(zip_derived_cl229,plain,
( ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ~ ( '#sk5' @ '#sk3' )
| ~ ( '#form71' @ '#sk8' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl227]) ).
thf(zip_derived_cl547,plain,
( ~ ( '#form71' @ '#sk8' )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl546,zip_derived_cl229]) ).
thf(zip_derived_cl687,plain,
( ~ ( '#form71' @ '#sk8' )
| ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ~ '#form648' ),
inference(clc,[status(thm)],[zip_derived_cl679,zip_derived_cl547]) ).
thf(zip_derived_cl515_007,plain,
( '#form648'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl516,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ Y0 )
& ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) )
=> ( '#sk8' @ Y0 ) ) )
| '#form648' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl515]) ).
thf(zip_derived_cl519,plain,
( ~ ( ( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
& ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) )
=> ( '#sk8' @ ( '#sk38' @ '#sk8' ) ) )
| '#form648' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl516]) ).
thf(zip_derived_cl521,plain,
( ( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
& ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) )
| '#form648' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl519]) ).
thf(zip_derived_cl524,plain,
( ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| '#form648' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl521]) ).
thf(zip_derived_cl688,plain,
( ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ~ ( '#form71' @ '#sk8' ) ),
inference(clc,[status(thm)],[zip_derived_cl687,zip_derived_cl524]) ).
thf(zip_derived_cl850,plain,
( ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( '#form71' @ '#sk8' )
| ( '#sk8' @ ( '#sk38' @ '#sk8' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl619,zip_derived_cl688]) ).
thf(zip_derived_cl259,plain,
( ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( '#form71' @ '#sk8' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl257]) ).
thf(zip_derived_cl648_008,plain,
! [X0: a] :
( ~ ( '#form71' @ '#sk8' )
| ( '#sk5' @ X0 )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ~ '#form648' ),
inference(renaming,[status(thm)],[zip_derived_cl647,zip_derived_cl105]) ).
thf(zip_derived_cl668,plain,
( ~ ( '#form71' @ '#sk8' )
| ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ~ '#form648'
| ( '#sk5' @ '#sk3' )
| ~ ( '#form71' @ '#sk8' ) ),
inference('sup-',[status(thm)],[zip_derived_cl259,zip_derived_cl648]) ).
thf(zip_derived_cl680,plain,
( ( '#sk5' @ '#sk3' )
| ~ '#form648'
| ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ~ ( '#form71' @ '#sk8' ) ),
inference(simplify,[status(thm)],[zip_derived_cl668]) ).
thf(zip_derived_cl547_009,plain,
( ~ ( '#form71' @ '#sk8' )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl546,zip_derived_cl229]) ).
thf(zip_derived_cl683,plain,
( ~ ( '#form71' @ '#sk8' )
| ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ~ '#form648' ),
inference(clc,[status(thm)],[zip_derived_cl680,zip_derived_cl547]) ).
thf(zip_derived_cl522,plain,
( ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| '#form648' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl519]) ).
thf(zip_derived_cl684,plain,
( ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ~ ( '#form71' @ '#sk8' ) ),
inference(clc,[status(thm)],[zip_derived_cl683,zip_derived_cl522]) ).
thf(zip_derived_cl851,plain,
( ~ ( '#form71' @ '#sk8' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl850,zip_derived_cl684]) ).
thf(zip_derived_cl859,plain,
( ~ '#form648'
| ( '#sk5' @ '#sk3' )
| ~ ( '#form71' @ '#sk8' )
| ~ ( '#form71' @ '#sk8' ) ),
inference('sup+',[status(thm)],[zip_derived_cl648,zip_derived_cl851]) ).
thf(zip_derived_cl870,plain,
( ~ ( '#form71' @ '#sk8' )
| ( '#sk5' @ '#sk3' )
| ~ '#form648' ),
inference(simplify,[status(thm)],[zip_derived_cl859]) ).
thf(zip_derived_cl547_010,plain,
( ~ ( '#form71' @ '#sk8' )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl546,zip_derived_cl229]) ).
thf(zip_derived_cl874,plain,
( ~ '#form648'
| ~ ( '#form71' @ '#sk8' ) ),
inference(clc,[status(thm)],[zip_derived_cl870,zip_derived_cl547]) ).
thf(zip_derived_cl523,plain,
( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
| '#form648' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl521]) ).
thf(zip_derived_cl88_011,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ~ ( '#sk8' @ X2 )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( '#sk8' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl593,plain,
( '#form648'
| ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl523,zip_derived_cl88]) ).
thf(zip_derived_cl522_012,plain,
( ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| '#form648' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl519]) ).
thf(zip_derived_cl627,plain,
( ~ ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| '#form648' ),
inference(clc,[status(thm)],[zip_derived_cl593,zip_derived_cl522]) ).
thf(zip_derived_cl524_013,plain,
( ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| '#form648' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl521]) ).
thf(zip_derived_cl628,plain,
( '#form648'
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl627,zip_derived_cl524]) ).
thf(zip_derived_cl523_014,plain,
( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
| '#form648' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl521]) ).
thf(zip_derived_cl97,plain,
! [X2: a] :
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
| ~ ( '#sk1' @ '#sk2' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl118,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
| ( '#sk5' @ X2 )
| ~ ( '#sk1' @ '#sk2' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl141,plain,
! [X2: a,X4: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ X4 @ Y0 )
& ( '#sk8' @ X4 ) )
=> ( '#sk8' @ Y0 ) ) )
| ~ ( '#sk1' @ '#sk2' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl118]) ).
thf(zip_derived_cl160,plain,
! [X2: a,X4: a,X6: a] :
( ( ( ( '#sk1' @ X4 @ X6 )
& ( '#sk8' @ X4 ) )
=> ( '#sk8' @ X6 ) )
| ( '#sk5' @ X2 )
| ~ ( '#sk1' @ '#sk2' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl141]) ).
thf(zip_derived_cl174,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( '#sk1' @ X4 @ X6 )
& ( '#sk8' @ X4 ) )
| ( '#sk8' @ X6 )
| ~ ( '#sk1' @ '#sk2' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl160]) ).
thf(zip_derived_cl184,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk1' @ X4 @ X6 )
| ~ ( '#sk8' @ X4 )
| ( '#sk5' @ X2 )
| ~ ( '#sk1' @ '#sk2' @ X2 )
| ( '#sk8' @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl174]) ).
thf(zip_derived_cl1365,plain,
! [X0: a] :
( '#form648'
| ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk5' @ X0 )
| ~ ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl523,zip_derived_cl184]) ).
thf(zip_derived_cl522_015,plain,
( ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| '#form648' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl519]) ).
thf(zip_derived_cl1884,plain,
! [X0: a] :
( ~ ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ( '#sk5' @ X0 )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| '#form648' ),
inference(clc,[status(thm)],[zip_derived_cl1365,zip_derived_cl522]) ).
thf(zip_derived_cl524_016,plain,
( ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| '#form648' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl521]) ).
thf(zip_derived_cl1885,plain,
! [X0: a] :
( '#form648'
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk5' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl1884,zip_derived_cl524]) ).
thf(zip_derived_cl1908,plain,
( '#form648'
| ( '#sk5' @ '#sk3' )
| '#form648' ),
inference('sup-',[status(thm)],[zip_derived_cl628,zip_derived_cl1885]) ).
thf(zip_derived_cl1923,plain,
( ( '#sk5' @ '#sk3' )
| '#form648' ),
inference(simplify,[status(thm)],[zip_derived_cl1908]) ).
thf(zip_derived_cl78,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk6' ) ) )
| ( '#sk5' @ X2 )
| ~ ( '#sk1' @ '#sk2' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl94,plain,
! [X2: a,X4: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X4 @ Y0 ) ) ) )
=> ( X4 @ '#sk6' ) )
| ~ ( '#sk1' @ '#sk2' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl95,plain,
! [X0: a] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
=> ( '#sk8' @ '#sk6' ) )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk5' @ X0 ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl793,plain,
! [X0: a] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
| ( '#sk8' @ '#sk6' )
| ( '#sk5' @ X0 )
| ~ ( '#sk1' @ '#sk2' @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl794,plain,
! [X0: a] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk5' @ X0 )
| ( '#sk8' @ '#sk6' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl793]) ).
thf(zip_derived_cl515_017,plain,
( '#form648'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl795,plain,
! [X0: a] :
( ~ '#form648'
| ( '#sk8' @ '#sk6' )
| ( '#sk5' @ X0 )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl794,zip_derived_cl515]) ).
thf(zip_derived_cl119,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) )
| ( '#sk5' @ X2 )
| ~ ( '#sk1' @ '#sk2' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl142,plain,
! [X2: a > $o] :
( ~ ( '#form79' @ X2 )
| ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl22,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk4' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk6' ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl30,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk6' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl40,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
| ( X2 @ '#sk6' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl49,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( X2 @ '#sk6' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl63,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ ( '#sk24' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk24' @ X2 ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk6' )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl74,plain,
! [X2: a > $o] :
( ~ ( ( ( '#sk1' @ ( '#sk24' @ X2 ) @ ( '#sk38' @ X2 ) )
& ( X2 @ ( '#sk24' @ X2 ) ) )
=> ( X2 @ ( '#sk38' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( X2 @ '#sk6' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl87,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk38' @ X2 ) )
| ( X2 @ '#sk6' )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl110,plain,
! [X2: a > $o] :
( ( '#form79' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl796,plain,
! [X0: a] :
( ~ ( '#form79' @ '#sk8' )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk5' @ X0 )
| ( '#sk8' @ '#sk6' )
| ~ '#form648' ),
inference(renaming,[status(thm)],[zip_derived_cl795,zip_derived_cl142,zip_derived_cl110]) ).
thf(zip_derived_cl110_018,plain,
! [X2: a > $o] :
( ( '#form79' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl111,plain,
! [X2: a > $o] :
( ~ ( ( '#sk1' @ '#sk4' @ ( '#sk80' @ X2 ) )
=> ( X2 @ ( '#sk80' @ X2 ) ) )
| ( '#form79' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl130,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk80' @ X2 ) )
| ( '#form79' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl129,plain,
! [X2: a > $o] :
( ( '#sk1' @ '#sk4' @ ( '#sk80' @ X2 ) )
| ( '#form79' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl42,plain,
( ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl51,plain,
! [X2: a] :
( ( ( '#sk1' @ '#sk4' @ X2 )
=> ( '#sk8' @ X2 ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl65,plain,
! [X2: a] :
( ~ ( '#sk1' @ '#sk4' @ X2 )
| ( '#sk8' @ X2 )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl453,plain,
! [X0: a > $o] :
( ( '#form79' @ X0 )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( '#sk8' @ ( '#sk80' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl129,zip_derived_cl65]) ).
thf(zip_derived_cl119_019,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) )
| ( '#sk5' @ X2 )
| ~ ( '#sk1' @ '#sk2' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl142_020,plain,
! [X2: a > $o] :
( ~ ( '#form79' @ X2 )
| ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl110_021,plain,
! [X2: a > $o] :
( ( '#form79' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl144,plain,
! [X2: a] :
( ( '#form79' @ '#sk8' )
| ~ ( '#sk1' @ '#sk2' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl119,zip_derived_cl142,zip_derived_cl110]) ).
thf(zip_derived_cl459,plain,
! [X0: a > $o] :
( ( '#sk8' @ ( '#sk80' @ X0 ) )
| ( '#form79' @ X0 )
| ( '#sk5' @ '#sk3' )
| ( '#form79' @ '#sk8' ) ),
inference('sup-',[status(thm)],[zip_derived_cl453,zip_derived_cl144]) ).
thf(zip_derived_cl130_022,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk80' @ X2 ) )
| ( '#form79' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl72,plain,
( ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl83,plain,
! [X2: a] :
( ( ( '#sk1' @ '#sk4' @ X2 )
=> ( '#sk8' @ X2 ) )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl102,plain,
! [X2: a] :
( ~ ( '#sk1' @ '#sk4' @ X2 )
| ( '#sk8' @ X2 )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl129_023,plain,
! [X2: a > $o] :
( ( '#sk1' @ '#sk4' @ ( '#sk80' @ X2 ) )
| ( '#form79' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl314,plain,
! [X0: a > $o] :
( ~ ( '#sk5' @ '#sk3' )
| ( '#sk8' @ ( '#sk80' @ X0 ) )
| ( '#form79' @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl102,zip_derived_cl129]) ).
thf(zip_derived_cl337,plain,
( ( '#form79' @ '#sk8' )
| ( '#form79' @ '#sk8' )
| ~ ( '#sk5' @ '#sk3' ) ),
inference('sup+',[status(thm)],[zip_derived_cl130,zip_derived_cl314]) ).
thf(zip_derived_cl345,plain,
( ~ ( '#sk5' @ '#sk3' )
| ( '#form79' @ '#sk8' ) ),
inference(simplify,[status(thm)],[zip_derived_cl337]) ).
thf(zip_derived_cl473,plain,
! [X0: a > $o] :
( ( '#form79' @ '#sk8' )
| ( '#form79' @ X0 )
| ( '#sk8' @ ( '#sk80' @ X0 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl459,zip_derived_cl345]) ).
thf(zip_derived_cl476,plain,
( ( '#form79' @ '#sk8' )
| ( '#form79' @ '#sk8' )
| ( '#form79' @ '#sk8' ) ),
inference('sup+',[status(thm)],[zip_derived_cl130,zip_derived_cl473]) ).
thf(zip_derived_cl482,plain,
'#form79' @ '#sk8',
inference(simplify,[status(thm)],[zip_derived_cl476]) ).
thf(zip_derived_cl797,plain,
! [X0: a] :
( ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk5' @ X0 )
| ( '#sk8' @ '#sk6' )
| ~ '#form648' ),
inference(demod,[status(thm)],[zip_derived_cl796,zip_derived_cl482]) ).
thf(zip_derived_cl30_024,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk6' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl31,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
=> ( '#sk8' @ '#sk6' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl370,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) )
| ( '#sk8' @ '#sk6' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl371,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( '#sk8' @ '#sk6' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl370]) ).
thf(zip_derived_cl142_025,plain,
! [X2: a > $o] :
( ~ ( '#form79' @ X2 )
| ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl110_026,plain,
! [X2: a > $o] :
( ( '#form79' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl372,plain,
( ~ ( '#form79' @ '#sk8' )
| ( '#sk8' @ '#sk6' )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl371,zip_derived_cl142,zip_derived_cl110]) ).
thf(zip_derived_cl373,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ Y0 )
& ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) )
=> ( '#sk8' @ Y0 ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( '#sk8' @ '#sk6' )
| ~ ( '#form79' @ '#sk8' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl372]) ).
thf(zip_derived_cl374,plain,
( ~ ( ( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
& ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) )
=> ( '#sk8' @ ( '#sk38' @ '#sk8' ) ) )
| ~ ( '#form79' @ '#sk8' )
| ( '#sk8' @ '#sk6' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl373]) ).
thf(zip_derived_cl375,plain,
( ( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
& ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( '#sk8' @ '#sk6' )
| ~ ( '#form79' @ '#sk8' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl374]) ).
thf(zip_derived_cl377,plain,
( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
| ~ ( '#form79' @ '#sk8' )
| ( '#sk8' @ '#sk6' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl375]) ).
thf(zip_derived_cl482_027,plain,
'#form79' @ '#sk8',
inference(simplify,[status(thm)],[zip_derived_cl476]) ).
thf(zip_derived_cl1311,plain,
( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
| ( '#sk8' @ '#sk6' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(demod,[status(thm)],[zip_derived_cl377,zip_derived_cl482]) ).
thf(zip_derived_cl88_028,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ~ ( '#sk8' @ X2 )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( '#sk8' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl1314,plain,
( ( '#sk1' @ '#sk2' @ '#sk3' )
| ( '#sk8' @ '#sk6' )
| ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1311,zip_derived_cl88]) ).
thf(zip_derived_cl1327,plain,
( ~ ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ( '#sk8' @ '#sk6' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1314]) ).
thf(zip_derived_cl378,plain,
( ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ~ ( '#form79' @ '#sk8' )
| ( '#sk8' @ '#sk6' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl375]) ).
thf(zip_derived_cl482_029,plain,
'#form79' @ '#sk8',
inference(simplify,[status(thm)],[zip_derived_cl476]) ).
thf(zip_derived_cl533,plain,
( ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ( '#sk8' @ '#sk6' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(demod,[status(thm)],[zip_derived_cl378,zip_derived_cl482]) ).
thf(zip_derived_cl797_030,plain,
! [X0: a] :
( ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk5' @ X0 )
| ( '#sk8' @ '#sk6' )
| ~ '#form648' ),
inference(demod,[status(thm)],[zip_derived_cl796,zip_derived_cl482]) ).
thf(zip_derived_cl809,plain,
( ( '#sk8' @ '#sk6' )
| ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ~ '#form648'
| ( '#sk8' @ '#sk6' )
| ( '#sk5' @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl533,zip_derived_cl797]) ).
thf(zip_derived_cl826,plain,
( ( '#sk5' @ '#sk3' )
| ~ '#form648'
| ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ( '#sk8' @ '#sk6' ) ),
inference(simplify,[status(thm)],[zip_derived_cl809]) ).
thf(zip_derived_cl514_031,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) )
| ~ ( '#sk5' @ '#sk3' )
| ( '#sk8' @ '#sk6' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl513]) ).
thf(zip_derived_cl515_032,plain,
( '#form648'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk8' @ Y0 ) )
=> ( '#sk8' @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl517,plain,
( ~ '#form648'
| ( '#sk8' @ '#sk6' )
| ~ ( '#sk5' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( '#sk8' @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl514,zip_derived_cl515]) ).
thf(zip_derived_cl142_033,plain,
! [X2: a > $o] :
( ~ ( '#form79' @ X2 )
| ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl110_034,plain,
! [X2: a > $o] :
( ( '#form79' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk4' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl518,plain,
( ~ ( '#form79' @ '#sk8' )
| ~ ( '#sk5' @ '#sk3' )
| ( '#sk8' @ '#sk6' )
| ~ '#form648' ),
inference(renaming,[status(thm)],[zip_derived_cl517,zip_derived_cl142,zip_derived_cl110]) ).
thf(zip_derived_cl482_035,plain,
'#form79' @ '#sk8',
inference(simplify,[status(thm)],[zip_derived_cl476]) ).
thf(zip_derived_cl520,plain,
( ~ ( '#sk5' @ '#sk3' )
| ( '#sk8' @ '#sk6' )
| ~ '#form648' ),
inference(demod,[status(thm)],[zip_derived_cl518,zip_derived_cl482]) ).
thf(zip_derived_cl840,plain,
( ( '#sk8' @ '#sk6' )
| ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ~ '#form648' ),
inference(clc,[status(thm)],[zip_derived_cl826,zip_derived_cl520]) ).
thf(zip_derived_cl524_036,plain,
( ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| '#form648' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl521]) ).
thf(zip_derived_cl841,plain,
( ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ( '#sk8' @ '#sk6' ) ),
inference(clc,[status(thm)],[zip_derived_cl840,zip_derived_cl524]) ).
thf(zip_derived_cl1332,plain,
( ( '#sk1' @ '#sk2' @ '#sk3' )
| ( '#sk8' @ '#sk6' )
| ( '#sk8' @ ( '#sk38' @ '#sk8' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1327,zip_derived_cl841]) ).
thf(zip_derived_cl376,plain,
( ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( '#sk8' @ '#sk6' )
| ~ ( '#form79' @ '#sk8' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl374]) ).
thf(zip_derived_cl482_037,plain,
'#form79' @ '#sk8',
inference(simplify,[status(thm)],[zip_derived_cl476]) ).
thf(zip_derived_cl492,plain,
( ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( '#sk8' @ '#sk6' ) ),
inference(demod,[status(thm)],[zip_derived_cl376,zip_derived_cl482]) ).
thf(zip_derived_cl797_038,plain,
! [X0: a] :
( ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk5' @ X0 )
| ( '#sk8' @ '#sk6' )
| ~ '#form648' ),
inference(demod,[status(thm)],[zip_derived_cl796,zip_derived_cl482]) ).
thf(zip_derived_cl810,plain,
( ( '#sk8' @ '#sk6' )
| ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ~ '#form648'
| ( '#sk8' @ '#sk6' )
| ( '#sk5' @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl492,zip_derived_cl797]) ).
thf(zip_derived_cl827,plain,
( ( '#sk5' @ '#sk3' )
| ~ '#form648'
| ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ( '#sk8' @ '#sk6' ) ),
inference(simplify,[status(thm)],[zip_derived_cl810]) ).
thf(zip_derived_cl520_039,plain,
( ~ ( '#sk5' @ '#sk3' )
| ( '#sk8' @ '#sk6' )
| ~ '#form648' ),
inference(demod,[status(thm)],[zip_derived_cl518,zip_derived_cl482]) ).
thf(zip_derived_cl834,plain,
( ( '#sk8' @ '#sk6' )
| ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ~ '#form648' ),
inference(clc,[status(thm)],[zip_derived_cl827,zip_derived_cl520]) ).
thf(zip_derived_cl522_040,plain,
( ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| '#form648' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl519]) ).
thf(zip_derived_cl835,plain,
( ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ( '#sk8' @ '#sk6' ) ),
inference(clc,[status(thm)],[zip_derived_cl834,zip_derived_cl522]) ).
thf(zip_derived_cl1333,plain,
( ( '#sk8' @ '#sk6' )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl1332,zip_derived_cl835]) ).
thf(zip_derived_cl1341,plain,
( ~ '#form648'
| ( '#sk8' @ '#sk6' )
| ( '#sk5' @ '#sk3' )
| ( '#sk8' @ '#sk6' ) ),
inference('sup+',[status(thm)],[zip_derived_cl797,zip_derived_cl1333]) ).
thf(zip_derived_cl1345,plain,
( ( '#sk5' @ '#sk3' )
| ( '#sk8' @ '#sk6' )
| ~ '#form648' ),
inference(simplify,[status(thm)],[zip_derived_cl1341]) ).
thf(zip_derived_cl520_041,plain,
( ~ ( '#sk5' @ '#sk3' )
| ( '#sk8' @ '#sk6' )
| ~ '#form648' ),
inference(demod,[status(thm)],[zip_derived_cl518,zip_derived_cl482]) ).
thf(zip_derived_cl1347,plain,
( ~ '#form648'
| ( '#sk8' @ '#sk6' ) ),
inference(clc,[status(thm)],[zip_derived_cl1345,zip_derived_cl520]) ).
thf(zip_derived_cl105_042,plain,
! [X2: a > $o] :
( ( '#form71' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk6' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl106,plain,
! [X2: a > $o] :
( ~ ( ( '#sk1' @ '#sk6' @ ( '#sk72' @ X2 ) )
=> ( X2 @ ( '#sk72' @ X2 ) ) )
| ( '#form71' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl126,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk72' @ X2 ) )
| ( '#form71' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl149_043,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ~ ( '#sk8' @ X2 )
| ~ ( '#sk5' @ '#sk3' )
| ( '#sk8' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl122]) ).
thf(zip_derived_cl125,plain,
! [X2: a > $o] :
( ( '#sk1' @ '#sk6' @ ( '#sk72' @ X2 ) )
| ( '#form71' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl386,plain,
! [X0: a > $o] :
( ( '#sk8' @ ( '#sk72' @ X0 ) )
| ~ ( '#sk5' @ '#sk3' )
| ~ ( '#sk8' @ '#sk6' )
| ( '#form71' @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl149,zip_derived_cl125]) ).
thf(zip_derived_cl570,plain,
( ( '#form71' @ '#sk8' )
| ( '#form71' @ '#sk8' )
| ~ ( '#sk8' @ '#sk6' )
| ~ ( '#sk5' @ '#sk3' ) ),
inference('sup+',[status(thm)],[zip_derived_cl126,zip_derived_cl386]) ).
thf(zip_derived_cl576,plain,
( ~ ( '#sk5' @ '#sk3' )
| ~ ( '#sk8' @ '#sk6' )
| ( '#form71' @ '#sk8' ) ),
inference(simplify,[status(thm)],[zip_derived_cl570]) ).
thf(zip_derived_cl547_044,plain,
( ~ ( '#form71' @ '#sk8' )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl546,zip_derived_cl229]) ).
thf(zip_derived_cl585,plain,
( ~ ( '#sk8' @ '#sk6' )
| ~ ( '#sk5' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl576,zip_derived_cl547]) ).
thf(zip_derived_cl1349,plain,
( ~ '#form648'
| ~ ( '#sk5' @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1347,zip_derived_cl585]) ).
thf(zip_derived_cl523_045,plain,
( ( '#sk1' @ ( '#sk24' @ '#sk8' ) @ ( '#sk38' @ '#sk8' ) )
| '#form648' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl521]) ).
thf(zip_derived_cl149_046,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ~ ( '#sk8' @ X2 )
| ~ ( '#sk5' @ '#sk3' )
| ( '#sk8' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl122]) ).
thf(zip_derived_cl525,plain,
( '#form648'
| ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| ~ ( '#sk5' @ '#sk3' )
| ~ ( '#sk8' @ ( '#sk24' @ '#sk8' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl523,zip_derived_cl149]) ).
thf(zip_derived_cl522_047,plain,
( ~ ( '#sk8' @ ( '#sk38' @ '#sk8' ) )
| '#form648' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl519]) ).
thf(zip_derived_cl538,plain,
( ~ ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| ~ ( '#sk5' @ '#sk3' )
| '#form648' ),
inference(clc,[status(thm)],[zip_derived_cl525,zip_derived_cl522]) ).
thf(zip_derived_cl524_048,plain,
( ( '#sk8' @ ( '#sk24' @ '#sk8' ) )
| '#form648' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl521]) ).
thf(zip_derived_cl539,plain,
( '#form648'
| ~ ( '#sk5' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl538,zip_derived_cl524]) ).
thf(zip_derived_cl1350,plain,
~ ( '#sk5' @ '#sk3' ),
inference(clc,[status(thm)],[zip_derived_cl1349,zip_derived_cl539]) ).
thf(zip_derived_cl1940,plain,
'#form648',
inference(clc,[status(thm)],[zip_derived_cl1923,zip_derived_cl1350]) ).
thf(zip_derived_cl1941,plain,
~ ( '#form71' @ '#sk8' ),
inference(demod,[status(thm)],[zip_derived_cl874,zip_derived_cl1940]) ).
thf(zip_derived_cl1347_049,plain,
( ~ '#form648'
| ( '#sk8' @ '#sk6' ) ),
inference(clc,[status(thm)],[zip_derived_cl1345,zip_derived_cl520]) ).
thf(zip_derived_cl125_050,plain,
! [X2: a > $o] :
( ( '#sk1' @ '#sk6' @ ( '#sk72' @ X2 ) )
| ( '#form71' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl88_051,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ~ ( '#sk8' @ X2 )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( '#sk8' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl596,plain,
! [X0: a > $o] :
( ( '#form71' @ X0 )
| ( '#sk8' @ ( '#sk72' @ X0 ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( '#sk8' @ '#sk6' ) ),
inference('sup-',[status(thm)],[zip_derived_cl125,zip_derived_cl88]) ).
thf(zip_derived_cl1348,plain,
! [X0: a > $o] :
( ~ '#form648'
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ( '#sk8' @ ( '#sk72' @ X0 ) )
| ( '#form71' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1347,zip_derived_cl596]) ).
thf(zip_derived_cl628_052,plain,
( '#form648'
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl627,zip_derived_cl524]) ).
thf(zip_derived_cl1382,plain,
! [X0: a > $o] :
( ( '#form71' @ X0 )
| ( '#sk8' @ ( '#sk72' @ X0 ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl1348,zip_derived_cl628]) ).
thf(zip_derived_cl125_053,plain,
! [X2: a > $o] :
( ( '#sk1' @ '#sk6' @ ( '#sk72' @ X2 ) )
| ( '#form71' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl184_054,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk1' @ X4 @ X6 )
| ~ ( '#sk8' @ X4 )
| ( '#sk5' @ X2 )
| ~ ( '#sk1' @ '#sk2' @ X2 )
| ( '#sk8' @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl174]) ).
thf(zip_derived_cl2321,plain,
! [X0: a > $o,X1: a] :
( ( '#form71' @ X0 )
| ( '#sk8' @ ( '#sk72' @ X0 ) )
| ~ ( '#sk1' @ '#sk2' @ X1 )
| ( '#sk5' @ X1 )
| ~ ( '#sk8' @ '#sk6' ) ),
inference('sup-',[status(thm)],[zip_derived_cl125,zip_derived_cl184]) ).
thf(zip_derived_cl1347_055,plain,
( ~ '#form648'
| ( '#sk8' @ '#sk6' ) ),
inference(clc,[status(thm)],[zip_derived_cl1345,zip_derived_cl520]) ).
thf(zip_derived_cl1940_056,plain,
'#form648',
inference(clc,[status(thm)],[zip_derived_cl1923,zip_derived_cl1350]) ).
thf(zip_derived_cl1942,plain,
'#sk8' @ '#sk6',
inference(demod,[status(thm)],[zip_derived_cl1347,zip_derived_cl1940]) ).
thf(zip_derived_cl2329,plain,
! [X0: a > $o,X1: a] :
( ( '#form71' @ X0 )
| ( '#sk8' @ ( '#sk72' @ X0 ) )
| ~ ( '#sk1' @ '#sk2' @ X1 )
| ( '#sk5' @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl2321,zip_derived_cl1942]) ).
thf(zip_derived_cl2337,plain,
! [X0: a > $o,X1: a > $o] :
( ( '#sk8' @ ( '#sk72' @ X1 ) )
| ( '#form71' @ X1 )
| ( '#sk5' @ '#sk3' )
| ( '#sk8' @ ( '#sk72' @ X0 ) )
| ( '#form71' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1382,zip_derived_cl2329]) ).
thf(zip_derived_cl1350_057,plain,
~ ( '#sk5' @ '#sk3' ),
inference(clc,[status(thm)],[zip_derived_cl1349,zip_derived_cl539]) ).
thf(zip_derived_cl2352,plain,
! [X0: a > $o,X1: a > $o] :
( ( '#sk8' @ ( '#sk72' @ X1 ) )
| ( '#form71' @ X1 )
| ( '#sk8' @ ( '#sk72' @ X0 ) )
| ( '#form71' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2337,zip_derived_cl1350]) ).
thf(zip_derived_cl2383,plain,
! [X0: a > $o] :
( ( '#form71' @ X0 )
| ( '#form71' @ X0 )
| ( '#sk8' @ ( '#sk72' @ X0 ) ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl2352]) ).
thf(zip_derived_cl2385,plain,
! [X0: a > $o] :
( ( '#sk8' @ ( '#sk72' @ X0 ) )
| ( '#form71' @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl2383]) ).
thf(zip_derived_cl126_058,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk72' @ X2 ) )
| ( '#form71' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl2404,plain,
( ( '#form71' @ '#sk8' )
| ( '#form71' @ '#sk8' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2385,zip_derived_cl126]) ).
thf(zip_derived_cl2416,plain,
'#form71' @ '#sk8',
inference(simplify,[status(thm)],[zip_derived_cl2404]) ).
thf(zip_derived_cl2419,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl1941,zip_derived_cl2416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SEV146^5 : TPTP v9.2.0. Released v4.0.0.
% 0.06/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.OXDUHgpoUp true
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 15:39:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Running portfolio for 300 s
% 0.13/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in HO mode
% 0.22/0.69 % Total configuration time : 828
% 0.22/0.69 % Estimated wc time : 1656
% 0.22/0.69 % Estimated cpu time (8 cpus) : 207.0
% 1.16/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.16/0.77 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.16/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.16/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.16/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.16/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.16/0.78 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.16/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 14.94/2.86 % Solved by lams/35_full_unif4.sh.
% 14.94/2.86 % done 291 iterations in 2.030s
% 14.94/2.86 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 14.94/2.86 % SZS output start Refutation
% See solution above
% 14.94/2.87
% 14.94/2.87
% 14.94/2.87 % Terminating...
% 15.59/3.08 % Runner terminated.
% 15.59/3.08 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------