%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV157^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.2D7k9p1gTt true
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:59:49 EDT 2023
% Result : Theorem 105.41s 14.10s
% Output : Refutation 105.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 50
% Syntax : Number of formulae : 271 ( 20 unt; 27 typ; 0 def)
% Number of atoms : 2717 ( 0 equ; 6 cnn)
% Maximal formula atoms : 70 ( 11 avg)
% Number of connectives : 9353 ( 325 ~; 617 |; 536 &;5573 @)
% ( 0 <=>; 818 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 12 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 539 ( 539 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 13 con; 0-2 aty)
% (1484 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1730 (1484 ^; 246 !; 0 ?;1730 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf('#sk250_type',type,
'#sk250': ( a > a > $o ) > a ).
thf('#sk4_type',type,
'#sk4': a ).
thf('#sk79_type',type,
'#sk79': a > a > $o ).
thf('#sk127_type',type,
'#sk127': ( a > a > $o ) > a ).
thf('#sk98_type',type,
'#sk98': ( a > a > $o ) > a ).
thf('#sk3_type',type,
'#sk3': a ).
thf('#sk551_type',type,
'#sk551': ( a > a > $o ) > a ).
thf('#form146_type',type,
'#form146': $o ).
thf('#sk543_type',type,
'#sk543': ( a > a > $o ) > a ).
thf('#sk6_type',type,
'#sk6': a ).
thf('#sk20_type',type,
'#sk20': a ).
thf('#sk2_type',type,
'#sk2': a > a > $o ).
thf('#sk8_type',type,
'#sk8': a ).
thf('#form10_type',type,
'#form10': $o ).
thf('#sk7_type',type,
'#sk7': a ).
thf('#form495_type',type,
'#form495': ( a > a > $o ) > $o ).
thf('#sk70_type',type,
'#sk70': ( a > a > $o ) > a ).
thf('#form19_type',type,
'#form19': $o ).
thf('#sk9_type',type,
'#sk9': a > a > $o ).
thf('#sk575_type',type,
'#sk575': ( a > a > $o ) > a ).
thf('#sk5_type',type,
'#sk5': a > a > $o ).
thf('#sk1_type',type,
'#sk1': a > a > $o ).
thf('#sk37_type',type,
'#sk37': a ).
thf('#sk184_type',type,
'#sk184': ( a > a > $o ) > a ).
thf('#sk524_type',type,
'#sk524': ( a > a > $o ) > a ).
thf('#form183_type',type,
'#form183': ( a > a > $o ) > $o ).
thf(cTHM250G_pme,conjecture,
! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xy0 @ Xz )
& ( Xp1 @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xz ) )
& ! [Xx0: a,Xy0: a] :
( ( ( S @ Xx0 @ Xy0 )
| ( R @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ( Xp1 @ Xx @ Xy ) )
| ~ ( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xy0 @ Xz ) )
& ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xz ) ) )
& ! [Xx0: a,Xy0: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( S @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) )
| ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( R @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xy0 @ Xz )
& ( Xp1 @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xz ) )
& ! [Xx0: a,Xy0: a] :
( ( ( S @ Xx0 @ Xy0 )
| ( R @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ( Xp1 @ Xx @ Xy ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xy0 @ Xz )
& ( Xp1 @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xz ) )
& ! [Xx0: a,Xy0: a] :
( ( ( S @ Xx0 @ Xy0 )
| ( R @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ( Xp1 @ Xx @ Xy ) )
| ~ ( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xy0 @ Xz ) )
& ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xz ) ) )
& ! [Xx0: a,Xy0: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( S @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) )
| ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( R @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xy0 @ Xz )
& ( Xp1 @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xz ) )
& ! [Xx0: a,Xy0: a] :
( ( ( S @ Xx0 @ Xy0 )
| ( R @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ( Xp1 @ Xx @ Xy ) ) ) ),
inference('cnf.neg',[status(esa)],[cTHM250G_pme]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( !!
@ ^ [Y1: a > a > $o] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( (~)
@ ( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( !!
@ ^ [Y7: a > a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( !!
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
& ( !!
@ ^ [Y7: a > a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( !!
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) ) )
=> ( !!
@ ^ [Y7: a > a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( !!
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( (~)
@ ( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
& ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y4 ) ) ) )
=> ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( '#sk1' @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( (~)
@ ( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
& ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y3 ) ) ) )
=> ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( '#sk2' @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( '#sk1' @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: a] :
( ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk3' @ Y0 ) ) )
| ( (~)
@ ( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
& ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( '#sk2' @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk3' @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
~ ( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( (~)
@ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl6,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl8,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl11,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl14,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
& ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ '#sk6' @ Y0 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ '#sk6' @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl17,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk7' @ Y0 ) ) )
& ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk6' @ '#sk7' ) ) ) )
=> ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk6' @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl20,plain,
( ~ ( ( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk7' @ '#sk8' ) ) )
& ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk7' ) ) ) )
=> ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk8' ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl23,plain,
( ( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk7' @ '#sk8' ) ) )
& ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk7' ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl29,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk7' ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl29_001,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk7' ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl37,plain,
( ~ '#form10'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl43,plain,
( '#form10'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk7' ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl29,zip_derived_cl37]) ).
thf(zip_derived_cl28,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk7' @ '#sk8' ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl32,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk7' @ '#sk8' ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl45,plain,
( '#form19'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl48,plain,
( ~ '#form19'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk7' ) ) )
| '#form10' ),
inference(renaming,[status(thm)],[zip_derived_cl43,zip_derived_cl45]) ).
thf(zip_derived_cl53,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk6' @ '#sk7' ) )
| '#form10'
| ~ '#form19' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl54,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk9' @ '#sk6' @ '#sk7' ) )
| '#form10'
| ~ '#form19' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl37_002,plain,
( ~ '#form10'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl38,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk3' @ '#sk4' ) )
| ~ '#form10' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl40,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk5' @ '#sk3' @ '#sk4' ) )
| ~ '#form10' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl5,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl7,plain,
~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk5' @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl10,plain,
~ ( '#sk5' @ '#sk3' @ '#sk4' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl470,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
=> $false )
| ~ '#form10' ),
inference(demod,[status(thm)],[zip_derived_cl40,zip_derived_cl10]) ).
thf(zip_derived_cl471,plain,
( ( (~)
@ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) ) )
| ~ '#form10' ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl470]) ).
thf(zip_derived_cl472,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
| ~ '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl471]) ).
thf(zip_derived_cl473,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
| ~ '#form10' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl472]) ).
thf(zip_derived_cl32_003,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk7' @ '#sk8' ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl45_004,plain,
( '#form19'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl47,plain,
! [X2: a > a > $o] :
( ~ '#form19'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk7' @ '#sk8' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl32,zip_derived_cl45]) ).
thf(zip_derived_cl37_005,plain,
( ~ '#form10'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl51,plain,
! [X2: a > a > $o] :
( '#form10'
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk7' @ '#sk8' ) )
| ~ '#form19' ),
inference(renaming,[status(thm)],[zip_derived_cl47,zip_derived_cl37]) ).
thf(zip_derived_cl61,plain,
! [X2: a > a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
| ( X2 @ '#sk7' @ '#sk8' )
| ~ '#form19'
| '#form10' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl68,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) )
| '#form10'
| ~ '#form19'
| ( X2 @ '#sk7' @ '#sk8' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl78,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( X2 @ Y0 @ Y1 )
& ( X2 @ ( '#sk70' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk70' @ X2 ) @ Y1 ) ) ) )
| ( X2 @ '#sk7' @ '#sk8' )
| ~ '#form19'
| '#form10'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl91,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk98' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk98' @ X2 ) ) )
=> ( X2 @ ( '#sk70' @ X2 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) )
| '#form10'
| ~ '#form19'
| ( X2 @ '#sk7' @ '#sk8' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl107,plain,
! [X2: a > a > $o] :
( ( '#form183' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl474,plain,
( ~ ( '#form183' @ '#sk5' )
| ~ '#form10'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl473,zip_derived_cl107]) ).
thf(zip_derived_cl107_006,plain,
! [X2: a > a > $o] :
( ( '#form183' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl108,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ ( '#sk184' @ X2 ) @ Y0 )
| ( '#sk1' @ ( '#sk184' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk184' @ X2 ) @ Y0 ) ) )
| ( '#form183' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl121,plain,
! [X2: a > a > $o] :
( ~ ( ( ( '#sk2' @ ( '#sk184' @ X2 ) @ ( '#sk250' @ X2 ) )
| ( '#sk1' @ ( '#sk184' @ X2 ) @ ( '#sk250' @ X2 ) ) )
=> ( X2 @ ( '#sk184' @ X2 ) @ ( '#sk250' @ X2 ) ) )
| ( '#form183' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl136,plain,
! [X2: a > a > $o] :
( ~ ( X2 @ ( '#sk184' @ X2 ) @ ( '#sk250' @ X2 ) )
| ( '#form183' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl135,plain,
! [X2: a > a > $o] :
( ( '#sk2' @ ( '#sk184' @ X2 ) @ ( '#sk250' @ X2 ) )
| ( '#sk1' @ ( '#sk184' @ X2 ) @ ( '#sk250' @ X2 ) )
| ( '#form183' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl145,plain,
! [X2: a > a > $o] :
( ( '#sk2' @ ( '#sk184' @ X2 ) @ ( '#sk250' @ X2 ) )
| ( '#sk1' @ ( '#sk184' @ X2 ) @ ( '#sk250' @ X2 ) )
| ( '#form183' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl135]) ).
thf(zip_derived_cl9,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl13,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl16,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
=> ( '#sk5' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl19,plain,
! [X2: a,X4: a] :
( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl22,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl26,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl204,plain,
! [X0: a > a > $o] :
( ( '#form183' @ X0 )
| ( '#sk1' @ ( '#sk184' @ X0 ) @ ( '#sk250' @ X0 ) )
| ( '#sk5' @ ( '#sk184' @ X0 ) @ ( '#sk250' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl145,zip_derived_cl26]) ).
thf(zip_derived_cl27,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl451,plain,
! [X0: a > a > $o] :
( ( '#sk5' @ ( '#sk184' @ X0 ) @ ( '#sk250' @ X0 ) )
| ( '#form183' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl204,zip_derived_cl27]) ).
thf(zip_derived_cl454,plain,
( ( '#form183' @ '#sk5' )
| ( '#form183' @ '#sk5' ) ),
inference('sup+',[status(thm)],[zip_derived_cl136,zip_derived_cl451]) ).
thf(zip_derived_cl456,plain,
'#form183' @ '#sk5',
inference(simplify,[status(thm)],[zip_derived_cl454]) ).
thf(zip_derived_cl475,plain,
( ~ '#form10'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl474,zip_derived_cl456]) ).
thf(zip_derived_cl476,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk5' @ Y0 @ Y1 )
& ( '#sk5' @ ( '#sk70' @ '#sk5' ) @ Y0 ) )
=> ( '#sk5' @ ( '#sk70' @ '#sk5' ) @ Y1 ) ) ) )
| ~ '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl475]) ).
thf(zip_derived_cl477,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk5' @ ( '#sk98' @ '#sk5' ) @ Y0 )
& ( '#sk5' @ ( '#sk70' @ '#sk5' ) @ ( '#sk98' @ '#sk5' ) ) )
=> ( '#sk5' @ ( '#sk70' @ '#sk5' ) @ Y0 ) ) )
| ~ '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl476]) ).
thf(zip_derived_cl478,plain,
( ~ ( ( ( '#sk5' @ ( '#sk98' @ '#sk5' ) @ ( '#sk127' @ '#sk5' ) )
& ( '#sk5' @ ( '#sk70' @ '#sk5' ) @ ( '#sk98' @ '#sk5' ) ) )
=> ( '#sk5' @ ( '#sk70' @ '#sk5' ) @ ( '#sk127' @ '#sk5' ) ) )
| ~ '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl477]) ).
thf(zip_derived_cl479,plain,
( ( ( '#sk5' @ ( '#sk98' @ '#sk5' ) @ ( '#sk127' @ '#sk5' ) )
& ( '#sk5' @ ( '#sk70' @ '#sk5' ) @ ( '#sk98' @ '#sk5' ) ) )
| ~ '#form10' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl478]) ).
thf(zip_derived_cl482,plain,
( ( '#sk5' @ ( '#sk70' @ '#sk5' ) @ ( '#sk98' @ '#sk5' ) )
| ~ '#form10' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl479]) ).
thf(zip_derived_cl481,plain,
( ( '#sk5' @ ( '#sk98' @ '#sk5' ) @ ( '#sk127' @ '#sk5' ) )
| ~ '#form10' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl479]) ).
thf(zip_derived_cl12,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl15,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk5' @ Y0 @ Y1 )
& ( '#sk5' @ X2 @ Y0 ) )
=> ( '#sk5' @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl18,plain,
! [X2: a,X4: a] :
( !!
@ ^ [Y0: a] :
( ( ( '#sk5' @ X4 @ Y0 )
& ( '#sk5' @ X2 @ X4 ) )
=> ( '#sk5' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21,plain,
! [X2: a,X4: a,X6: a] :
( ( ( '#sk5' @ X4 @ X6 )
& ( '#sk5' @ X2 @ X4 ) )
=> ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl25,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( '#sk5' @ X4 @ X6 )
& ( '#sk5' @ X2 @ X4 ) )
| ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl31,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk5' @ X4 @ X6 )
| ~ ( '#sk5' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl483,plain,
! [X0: a] :
( ~ '#form10'
| ( '#sk5' @ X0 @ ( '#sk127' @ '#sk5' ) )
| ~ ( '#sk5' @ X0 @ ( '#sk98' @ '#sk5' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl481,zip_derived_cl31]) ).
thf(zip_derived_cl507,plain,
( ~ '#form10'
| ( '#sk5' @ ( '#sk70' @ '#sk5' ) @ ( '#sk127' @ '#sk5' ) )
| ~ '#form10' ),
inference('sup-',[status(thm)],[zip_derived_cl482,zip_derived_cl483]) ).
thf(zip_derived_cl512,plain,
( ( '#sk5' @ ( '#sk70' @ '#sk5' ) @ ( '#sk127' @ '#sk5' ) )
| ~ '#form10' ),
inference(simplify,[status(thm)],[zip_derived_cl507]) ).
thf(zip_derived_cl480,plain,
( ~ ( '#sk5' @ ( '#sk70' @ '#sk5' ) @ ( '#sk127' @ '#sk5' ) )
| ~ '#form10' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl478]) ).
thf(zip_derived_cl517,plain,
~ '#form10',
inference(clc,[status(thm)],[zip_derived_cl512,zip_derived_cl480]) ).
thf(zip_derived_cl580,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk9' @ '#sk6' @ '#sk7' ) )
| ~ '#form19' ),
inference(demod,[status(thm)],[zip_derived_cl54,zip_derived_cl517]) ).
thf(zip_derived_cl581,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) ) )
| ( '#sk9' @ '#sk6' @ '#sk7' )
| ~ '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl580]) ).
thf(zip_derived_cl582,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) )
| ~ '#form19'
| ( '#sk9' @ '#sk6' @ '#sk7' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl581]) ).
thf(zip_derived_cl107_007,plain,
! [X2: a > a > $o] :
( ( '#form183' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl583,plain,
( ~ ( '#form183' @ '#sk9' )
| ( '#sk9' @ '#sk6' @ '#sk7' )
| ~ '#form19'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl582,zip_derived_cl107]) ).
thf(zip_derived_cl584,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk9' @ Y0 @ Y1 )
& ( '#sk9' @ ( '#sk70' @ '#sk9' ) @ Y0 ) )
=> ( '#sk9' @ ( '#sk70' @ '#sk9' ) @ Y1 ) ) ) )
| ~ '#form19'
| ( '#sk9' @ '#sk6' @ '#sk7' )
| ~ ( '#form183' @ '#sk9' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl583]) ).
thf(zip_derived_cl585,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk9' @ ( '#sk98' @ '#sk9' ) @ Y0 )
& ( '#sk9' @ ( '#sk70' @ '#sk9' ) @ ( '#sk98' @ '#sk9' ) ) )
=> ( '#sk9' @ ( '#sk70' @ '#sk9' ) @ Y0 ) ) )
| ~ ( '#form183' @ '#sk9' )
| ( '#sk9' @ '#sk6' @ '#sk7' )
| ~ '#form19' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl584]) ).
thf(zip_derived_cl45_008,plain,
( '#form19'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl46,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk20' @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk20' @ Y0 ) ) ) )
=> ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk20' @ Y0 ) ) ) ) )
| '#form19' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl52,plain,
( ~ ( ( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk2' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) ) )
=> ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) ) )
| '#form19' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl62,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk2' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) )
| '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl69,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk2' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) )
| '#form19' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl79,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk20' @ '#sk37' ) )
| '#form19'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl79_009,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk20' @ '#sk37' ) )
| '#form19'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl92,plain,
( ~ '#form146'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl99,plain,
! [X2: a > a > $o] :
( '#form146'
| '#form19'
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk20' @ '#sk37' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl79,zip_derived_cl92]) ).
thf(zip_derived_cl110,plain,
! [X2: a > a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
| ( X2 @ '#sk20' @ '#sk37' )
| '#form19'
| '#form146' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl122,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) )
| '#form146'
| '#form19'
| ( X2 @ '#sk20' @ '#sk37' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl137,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( X2 @ Y0 @ Y1 )
& ( X2 @ ( '#sk70' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk70' @ X2 ) @ Y1 ) ) ) )
| ( X2 @ '#sk20' @ '#sk37' )
| '#form19'
| '#form146'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl122]) ).
thf(zip_derived_cl146,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk98' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk98' @ X2 ) ) )
=> ( X2 @ ( '#sk70' @ X2 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) )
| '#form146'
| '#form19'
| ( X2 @ '#sk20' @ '#sk37' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl137]) ).
thf(zip_derived_cl153,plain,
! [X2: a > a > $o] :
( ( '#form495' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk98' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk98' @ X2 ) ) )
=> ( X2 @ ( '#sk70' @ X2 ) @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl586,plain,
( ~ ( '#form495' @ '#sk9' )
| ~ '#form19'
| ( '#sk9' @ '#sk6' @ '#sk7' )
| ~ ( '#form183' @ '#sk9' ) ),
inference(renaming,[status(thm)],[zip_derived_cl585,zip_derived_cl153]) ).
thf(zip_derived_cl32_010,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk7' @ '#sk8' ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl33,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk9' @ '#sk7' @ '#sk8' ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl45_011,plain,
( '#form19'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl277,plain,
( ~ '#form19'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk9' @ '#sk7' @ '#sk8' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl33,zip_derived_cl45]) ).
thf(zip_derived_cl37_012,plain,
( ~ '#form10'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl278,plain,
( '#form10'
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk9' @ '#sk7' @ '#sk8' ) )
| ~ '#form19' ),
inference(renaming,[status(thm)],[zip_derived_cl277,zip_derived_cl37]) ).
thf(zip_derived_cl279,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) ) )
| ( '#sk9' @ '#sk7' @ '#sk8' )
| ~ '#form19'
| '#form10' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl278]) ).
thf(zip_derived_cl280,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) )
| '#form10'
| ~ '#form19'
| ( '#sk9' @ '#sk7' @ '#sk8' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl279]) ).
thf(zip_derived_cl107_013,plain,
! [X2: a > a > $o] :
( ( '#form183' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl281,plain,
( ~ ( '#form183' @ '#sk9' )
| ( '#sk9' @ '#sk7' @ '#sk8' )
| ~ '#form19'
| '#form10'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl280,zip_derived_cl107]) ).
thf(zip_derived_cl282,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk9' @ Y0 @ Y1 )
& ( '#sk9' @ ( '#sk70' @ '#sk9' ) @ Y0 ) )
=> ( '#sk9' @ ( '#sk70' @ '#sk9' ) @ Y1 ) ) ) )
| '#form10'
| ~ '#form19'
| ( '#sk9' @ '#sk7' @ '#sk8' )
| ~ ( '#form183' @ '#sk9' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl281]) ).
thf(zip_derived_cl283,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk9' @ ( '#sk98' @ '#sk9' ) @ Y0 )
& ( '#sk9' @ ( '#sk70' @ '#sk9' ) @ ( '#sk98' @ '#sk9' ) ) )
=> ( '#sk9' @ ( '#sk70' @ '#sk9' ) @ Y0 ) ) )
| ~ ( '#form183' @ '#sk9' )
| ( '#sk9' @ '#sk7' @ '#sk8' )
| ~ '#form19'
| '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl282]) ).
thf(zip_derived_cl153_014,plain,
! [X2: a > a > $o] :
( ( '#form495' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk98' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk98' @ X2 ) ) )
=> ( X2 @ ( '#sk70' @ X2 ) @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl284,plain,
( ~ ( '#form495' @ '#sk9' )
| '#form10'
| ~ '#form19'
| ( '#sk9' @ '#sk7' @ '#sk8' )
| ~ ( '#form183' @ '#sk9' ) ),
inference(renaming,[status(thm)],[zip_derived_cl283,zip_derived_cl153]) ).
thf(zip_derived_cl517_015,plain,
~ '#form10',
inference(clc,[status(thm)],[zip_derived_cl512,zip_derived_cl480]) ).
thf(zip_derived_cl523,plain,
( ~ ( '#form495' @ '#sk9' )
| ~ '#form19'
| ( '#sk9' @ '#sk7' @ '#sk8' )
| ~ ( '#form183' @ '#sk9' ) ),
inference(demod,[status(thm)],[zip_derived_cl284,zip_derived_cl517]) ).
thf(zip_derived_cl24,plain,
( ~ ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk8' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl30,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk9' @ '#sk6' @ '#sk8' ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl37_016,plain,
( ~ '#form10'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl44,plain,
( '#form10'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk9' @ '#sk6' @ '#sk8' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl30,zip_derived_cl37]) ).
thf(zip_derived_cl45_017,plain,
( '#form19'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl50,plain,
( ~ '#form19'
| ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk9' @ '#sk6' @ '#sk8' ) )
| '#form10' ),
inference(renaming,[status(thm)],[zip_derived_cl44,zip_derived_cl45]) ).
thf(zip_derived_cl59,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) ) )
| '#form10'
| ~ '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl66,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk9' @ Y1 @ Y2 )
& ( '#sk9' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y2 ) ) ) ) )
| ~ '#form19'
| '#form10' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl76,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk9' @ Y0 @ Y1 )
& ( '#sk9' @ X2 @ Y0 ) )
=> ( '#sk9' @ X2 @ Y1 ) ) ) )
| '#form10'
| ~ '#form19' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl89,plain,
! [X2: a,X4: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk9' @ X4 @ Y0 )
& ( '#sk9' @ X2 @ X4 ) )
=> ( '#sk9' @ X2 @ Y0 ) ) )
| ~ '#form19'
| '#form10' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl105,plain,
! [X2: a,X4: a,X6: a] :
( ( ( ( '#sk9' @ X4 @ X6 )
& ( '#sk9' @ X2 @ X4 ) )
=> ( '#sk9' @ X2 @ X6 ) )
| '#form10'
| ~ '#form19' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl117,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( '#sk9' @ X4 @ X6 )
& ( '#sk9' @ X2 @ X4 ) )
| ( '#sk9' @ X2 @ X6 )
| ~ '#form19'
| '#form10' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl132,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk9' @ X4 @ X6 )
| ~ ( '#sk9' @ X2 @ X4 )
| '#form10'
| ~ '#form19'
| ( '#sk9' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl117]) ).
thf(zip_derived_cl517_018,plain,
~ '#form10',
inference(clc,[status(thm)],[zip_derived_cl512,zip_derived_cl480]) ).
thf(zip_derived_cl771,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk9' @ X4 @ X6 )
| ~ ( '#sk9' @ X2 @ X4 )
| ~ '#form19'
| ( '#sk9' @ X2 @ X6 ) ),
inference(demod,[status(thm)],[zip_derived_cl132,zip_derived_cl517]) ).
thf(zip_derived_cl781,plain,
! [X0: a] :
( ~ ( '#form183' @ '#sk9' )
| ~ '#form19'
| ~ ( '#form495' @ '#sk9' )
| ( '#sk9' @ X0 @ '#sk8' )
| ~ '#form19'
| ~ ( '#sk9' @ X0 @ '#sk7' ) ),
inference('sup-',[status(thm)],[zip_derived_cl523,zip_derived_cl771]) ).
thf(zip_derived_cl812,plain,
! [X0: a] :
( ~ ( '#sk9' @ X0 @ '#sk7' )
| ( '#sk9' @ X0 @ '#sk8' )
| ~ ( '#form495' @ '#sk9' )
| ~ '#form19'
| ~ ( '#form183' @ '#sk9' ) ),
inference(simplify,[status(thm)],[zip_derived_cl781]) ).
thf(zip_derived_cl145_019,plain,
! [X2: a > a > $o] :
( ( '#sk2' @ ( '#sk184' @ X2 ) @ ( '#sk250' @ X2 ) )
| ( '#sk1' @ ( '#sk184' @ X2 ) @ ( '#sk250' @ X2 ) )
| ( '#form183' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl135]) ).
thf(zip_derived_cl67,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk9' @ Y0 @ Y1 ) ) ) )
| ~ '#form19'
| '#form10' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl77,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
=> ( '#sk9' @ X2 @ Y0 ) ) )
| '#form10'
| ~ '#form19' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl90,plain,
! [X2: a,X4: a] :
( ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk9' @ X2 @ X4 ) )
| ~ '#form19'
| '#form10' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl106,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ( '#sk9' @ X2 @ X4 )
| '#form10'
| ~ '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl118,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ~ '#form19'
| '#form10'
| ( '#sk9' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl517_020,plain,
~ '#form10',
inference(clc,[status(thm)],[zip_derived_cl512,zip_derived_cl480]) ).
thf(zip_derived_cl519,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ~ '#form19'
| ( '#sk9' @ X2 @ X4 ) ),
inference(demod,[status(thm)],[zip_derived_cl118,zip_derived_cl517]) ).
thf(zip_derived_cl545,plain,
! [X0: a > a > $o] :
( ( '#form183' @ X0 )
| ( '#sk1' @ ( '#sk184' @ X0 ) @ ( '#sk250' @ X0 ) )
| ( '#sk9' @ ( '#sk184' @ X0 ) @ ( '#sk250' @ X0 ) )
| ~ '#form19' ),
inference('sup-',[status(thm)],[zip_derived_cl145,zip_derived_cl519]) ).
thf(zip_derived_cl119,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ~ '#form19'
| '#form10'
| ( '#sk9' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl517_021,plain,
~ '#form10',
inference(clc,[status(thm)],[zip_derived_cl512,zip_derived_cl480]) ).
thf(zip_derived_cl520,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ~ '#form19'
| ( '#sk9' @ X2 @ X4 ) ),
inference(demod,[status(thm)],[zip_derived_cl119,zip_derived_cl517]) ).
thf(zip_derived_cl651,plain,
! [X0: a > a > $o] :
( ~ '#form19'
| ( '#sk9' @ ( '#sk184' @ X0 ) @ ( '#sk250' @ X0 ) )
| ( '#form183' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl545,zip_derived_cl520]) ).
thf(zip_derived_cl136_022,plain,
! [X2: a > a > $o] :
( ~ ( X2 @ ( '#sk184' @ X2 ) @ ( '#sk250' @ X2 ) )
| ( '#form183' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl652,plain,
( ( '#form183' @ '#sk9' )
| ~ '#form19'
| ( '#form183' @ '#sk9' ) ),
inference('sup-',[status(thm)],[zip_derived_cl651,zip_derived_cl136]) ).
thf(zip_derived_cl655,plain,
( ~ '#form19'
| ( '#form183' @ '#sk9' ) ),
inference(simplify,[status(thm)],[zip_derived_cl652]) ).
thf(zip_derived_cl1054,plain,
! [X0: a] :
( ~ '#form19'
| ~ ( '#form495' @ '#sk9' )
| ( '#sk9' @ X0 @ '#sk8' )
| ~ ( '#sk9' @ X0 @ '#sk7' ) ),
inference(clc,[status(thm)],[zip_derived_cl812,zip_derived_cl655]) ).
thf(zip_derived_cl1055,plain,
( ~ ( '#form183' @ '#sk9' )
| ~ '#form19'
| ~ ( '#form495' @ '#sk9' )
| ( '#sk9' @ '#sk6' @ '#sk8' )
| ~ ( '#form495' @ '#sk9' )
| ~ '#form19' ),
inference('sup-',[status(thm)],[zip_derived_cl586,zip_derived_cl1054]) ).
thf(zip_derived_cl1061,plain,
( ( '#sk9' @ '#sk6' @ '#sk8' )
| ~ ( '#form495' @ '#sk9' )
| ~ '#form19'
| ~ ( '#form183' @ '#sk9' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1055]) ).
thf(zip_derived_cl60,plain,
( ~ ( '#sk9' @ '#sk6' @ '#sk8' )
| '#form10'
| ~ '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl517_023,plain,
~ '#form10',
inference(clc,[status(thm)],[zip_derived_cl512,zip_derived_cl480]) ).
thf(zip_derived_cl518,plain,
( ~ ( '#sk9' @ '#sk6' @ '#sk8' )
| ~ '#form19' ),
inference(demod,[status(thm)],[zip_derived_cl60,zip_derived_cl517]) ).
thf(zip_derived_cl1067,plain,
( ~ ( '#form183' @ '#sk9' )
| ~ '#form19'
| ~ ( '#form495' @ '#sk9' ) ),
inference(clc,[status(thm)],[zip_derived_cl1061,zip_derived_cl518]) ).
thf(zip_derived_cl655_024,plain,
( ~ '#form19'
| ( '#form183' @ '#sk9' ) ),
inference(simplify,[status(thm)],[zip_derived_cl652]) ).
thf(zip_derived_cl1068,plain,
( ~ ( '#form495' @ '#sk9' )
| ~ '#form19' ),
inference(clc,[status(thm)],[zip_derived_cl1067,zip_derived_cl655]) ).
thf(zip_derived_cl153_025,plain,
! [X2: a > a > $o] :
( ( '#form495' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk98' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk98' @ X2 ) ) )
=> ( X2 @ ( '#sk70' @ X2 ) @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl154,plain,
! [X2: a > a > $o] :
( ~ ( ( ( X2 @ ( '#sk98' @ X2 ) @ ( '#sk127' @ X2 ) )
& ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk98' @ X2 ) ) )
=> ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk127' @ X2 ) ) )
| ( '#form495' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl159,plain,
! [X2: a > a > $o] :
( ( ( X2 @ ( '#sk98' @ X2 ) @ ( '#sk127' @ X2 ) )
& ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk98' @ X2 ) ) )
| ( '#form495' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl154]) ).
thf(zip_derived_cl164,plain,
! [X2: a > a > $o] :
( ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk98' @ X2 ) )
| ( '#form495' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl159]) ).
thf(zip_derived_cl163,plain,
! [X2: a > a > $o] :
( ( X2 @ ( '#sk98' @ X2 ) @ ( '#sk127' @ X2 ) )
| ( '#form495' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl159]) ).
thf(zip_derived_cl63,plain,
( ~ ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) )
| '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl73,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk79' @ Y1 @ Y2 )
& ( '#sk79' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk79' @ '#sk20' @ '#sk37' ) )
| '#form19' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl85,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk79' @ Y1 @ Y2 )
& ( '#sk79' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) ) )
| '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl100,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk79' @ Y1 @ Y2 )
& ( '#sk79' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y2 ) ) ) ) )
| '#form19' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl112,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk79' @ Y0 @ Y1 )
& ( '#sk79' @ X2 @ Y0 ) )
=> ( '#sk79' @ X2 @ Y1 ) ) ) )
| '#form19' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl124,plain,
! [X2: a,X4: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk79' @ X4 @ Y0 )
& ( '#sk79' @ X2 @ X4 ) )
=> ( '#sk79' @ X2 @ Y0 ) ) )
| '#form19' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl139,plain,
! [X2: a,X4: a,X6: a] :
( ( ( ( '#sk79' @ X4 @ X6 )
& ( '#sk79' @ X2 @ X4 ) )
=> ( '#sk79' @ X2 @ X6 ) )
| '#form19' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl124]) ).
thf(zip_derived_cl148,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( '#sk79' @ X4 @ X6 )
& ( '#sk79' @ X2 @ X4 ) )
| ( '#sk79' @ X2 @ X6 )
| '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl139]) ).
thf(zip_derived_cl157,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk79' @ X4 @ X6 )
| ~ ( '#sk79' @ X2 @ X4 )
| '#form19'
| ( '#sk79' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl148]) ).
thf(zip_derived_cl340,plain,
! [X0: a] :
( ( '#form495' @ '#sk79' )
| ( '#sk79' @ X0 @ ( '#sk127' @ '#sk79' ) )
| '#form19'
| ~ ( '#sk79' @ X0 @ ( '#sk98' @ '#sk79' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl163,zip_derived_cl157]) ).
thf(zip_derived_cl79_026,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk20' @ '#sk37' ) )
| '#form19'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl80,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk79' @ Y1 @ Y2 )
& ( '#sk79' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk79' @ '#sk20' @ '#sk37' ) )
| '#form19'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl92_027,plain,
( ~ '#form146'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl1035,plain,
( '#form146'
| '#form19'
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk79' @ Y1 @ Y2 )
& ( '#sk79' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk79' @ '#sk20' @ '#sk37' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl80,zip_derived_cl92]) ).
thf(zip_derived_cl1036,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk79' @ Y1 @ Y2 )
& ( '#sk79' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) ) )
| ( '#sk79' @ '#sk20' @ '#sk37' )
| '#form19'
| '#form146' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1035]) ).
thf(zip_derived_cl86,plain,
( ~ ( '#sk79' @ '#sk20' @ '#sk37' )
| '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl1037,plain,
( '#form146'
| '#form19'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk79' @ Y1 @ Y2 )
& ( '#sk79' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1036,zip_derived_cl86]) ).
thf(zip_derived_cl1038,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk79' @ Y1 @ Y2 )
& ( '#sk79' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) )
| '#form19'
| '#form146' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1037]) ).
thf(zip_derived_cl1039,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk79' @ Y0 @ Y1 )
& ( '#sk79' @ ( '#sk70' @ '#sk79' ) @ Y0 ) )
=> ( '#sk79' @ ( '#sk70' @ '#sk79' ) @ Y1 ) ) ) )
| '#form146'
| '#form19'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1038]) ).
thf(zip_derived_cl1040,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk79' @ ( '#sk98' @ '#sk79' ) @ Y0 )
& ( '#sk79' @ ( '#sk70' @ '#sk79' ) @ ( '#sk98' @ '#sk79' ) ) )
=> ( '#sk79' @ ( '#sk70' @ '#sk79' ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) )
| '#form19'
| '#form146' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1039]) ).
thf(zip_derived_cl153_028,plain,
! [X2: a > a > $o] :
( ( '#form495' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk98' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk98' @ X2 ) ) )
=> ( X2 @ ( '#sk70' @ X2 ) @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl1041,plain,
( ~ ( '#form495' @ '#sk79' )
| '#form146'
| '#form19'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl1040,zip_derived_cl153]) ).
thf(zip_derived_cl92_029,plain,
( ~ '#form146'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk20' @ '#sk37' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl93,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk20' @ '#sk37' ) )
| ~ '#form146' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl94,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk79' @ Y1 @ Y2 )
& ( '#sk79' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk79' @ '#sk20' @ '#sk37' ) )
| ~ '#form146' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl195,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk79' @ Y1 @ Y2 )
& ( '#sk79' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) ) )
| ( '#sk79' @ '#sk20' @ '#sk37' )
| ~ '#form146' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl196,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk79' @ Y1 @ Y2 )
& ( '#sk79' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) )
| ~ '#form146'
| ( '#sk79' @ '#sk20' @ '#sk37' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl195]) ).
thf(zip_derived_cl197,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk79' @ Y0 @ Y1 )
& ( '#sk79' @ ( '#sk70' @ '#sk79' ) @ Y0 ) )
=> ( '#sk79' @ ( '#sk70' @ '#sk79' ) @ Y1 ) ) ) )
| ( '#sk79' @ '#sk20' @ '#sk37' )
| ~ '#form146'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl196]) ).
thf(zip_derived_cl198,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk79' @ ( '#sk98' @ '#sk79' ) @ Y0 )
& ( '#sk79' @ ( '#sk70' @ '#sk79' ) @ ( '#sk98' @ '#sk79' ) ) )
=> ( '#sk79' @ ( '#sk70' @ '#sk79' ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) )
| ~ '#form146'
| ( '#sk79' @ '#sk20' @ '#sk37' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl197]) ).
thf(zip_derived_cl153_030,plain,
! [X2: a > a > $o] :
( ( '#form495' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk98' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk98' @ X2 ) ) )
=> ( X2 @ ( '#sk70' @ X2 ) @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl199,plain,
( ~ ( '#form495' @ '#sk79' )
| ( '#sk79' @ '#sk20' @ '#sk37' )
| ~ '#form146'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl198,zip_derived_cl153]) ).
thf(zip_derived_cl200,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk543' @ '#sk79' ) @ Y0 )
=> ( '#sk79' @ ( '#sk543' @ '#sk79' ) @ Y0 ) ) )
| ~ '#form146'
| ( '#sk79' @ '#sk20' @ '#sk37' )
| ~ ( '#form495' @ '#sk79' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl199]) ).
thf(zip_derived_cl201,plain,
( ~ ( ( '#sk1' @ ( '#sk543' @ '#sk79' ) @ ( '#sk575' @ '#sk79' ) )
=> ( '#sk79' @ ( '#sk543' @ '#sk79' ) @ ( '#sk575' @ '#sk79' ) ) )
| ~ ( '#form495' @ '#sk79' )
| ( '#sk79' @ '#sk20' @ '#sk37' )
| ~ '#form146' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl200]) ).
thf(zip_derived_cl203,plain,
( ~ ( '#sk79' @ ( '#sk543' @ '#sk79' ) @ ( '#sk575' @ '#sk79' ) )
| ~ '#form146'
| ( '#sk79' @ '#sk20' @ '#sk37' )
| ~ ( '#form495' @ '#sk79' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl201]) ).
thf(zip_derived_cl202,plain,
( ( '#sk1' @ ( '#sk543' @ '#sk79' ) @ ( '#sk575' @ '#sk79' ) )
| ~ '#form146'
| ( '#sk79' @ '#sk20' @ '#sk37' )
| ~ ( '#form495' @ '#sk79' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl201]) ).
thf(zip_derived_cl101,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) )
| '#form19' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl113,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
=> ( '#sk79' @ X2 @ Y0 ) ) )
| '#form19' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl125,plain,
! [X2: a,X4: a] :
( ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk79' @ X2 @ X4 ) )
| '#form19' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl140,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ( '#sk79' @ X2 @ X4 )
| '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl125]) ).
thf(zip_derived_cl150,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| '#form19'
| ( '#sk79' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl140]) ).
thf(zip_derived_cl232,plain,
( ~ ( '#form495' @ '#sk79' )
| ( '#sk79' @ '#sk20' @ '#sk37' )
| ~ '#form146'
| ( '#sk79' @ ( '#sk543' @ '#sk79' ) @ ( '#sk575' @ '#sk79' ) )
| '#form19' ),
inference('sup-',[status(thm)],[zip_derived_cl202,zip_derived_cl150]) ).
thf(zip_derived_cl86_031,plain,
( ~ ( '#sk79' @ '#sk20' @ '#sk37' )
| '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl420,plain,
( '#form19'
| ( '#sk79' @ ( '#sk543' @ '#sk79' ) @ ( '#sk575' @ '#sk79' ) )
| ~ '#form146'
| ~ ( '#form495' @ '#sk79' ) ),
inference(clc,[status(thm)],[zip_derived_cl232,zip_derived_cl86]) ).
thf(zip_derived_cl423,plain,
( ~ ( '#form495' @ '#sk79' )
| ( '#sk79' @ '#sk20' @ '#sk37' )
| ~ '#form146'
| ~ ( '#form495' @ '#sk79' )
| ~ '#form146'
| '#form19' ),
inference('sup+',[status(thm)],[zip_derived_cl203,zip_derived_cl420]) ).
thf(zip_derived_cl427,plain,
( '#form19'
| ~ '#form146'
| ( '#sk79' @ '#sk20' @ '#sk37' )
| ~ ( '#form495' @ '#sk79' ) ),
inference(simplify,[status(thm)],[zip_derived_cl423]) ).
thf(zip_derived_cl86_032,plain,
( ~ ( '#sk79' @ '#sk20' @ '#sk37' )
| '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl433,plain,
( ~ ( '#form495' @ '#sk79' )
| ~ '#form146'
| '#form19' ),
inference(clc,[status(thm)],[zip_derived_cl427,zip_derived_cl86]) ).
thf(zip_derived_cl1042,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk79' @ Y0 @ Y1 ) ) ) )
| '#form19'
| ~ ( '#form495' @ '#sk79' ) ),
inference(clc,[status(thm)],[zip_derived_cl1041,zip_derived_cl433]) ).
thf(zip_derived_cl1043,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk524' @ '#sk79' ) @ Y0 )
=> ( '#sk79' @ ( '#sk524' @ '#sk79' ) @ Y0 ) ) )
| ~ ( '#form495' @ '#sk79' )
| '#form19' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1042]) ).
thf(zip_derived_cl1044,plain,
( ~ ( ( '#sk2' @ ( '#sk524' @ '#sk79' ) @ ( '#sk551' @ '#sk79' ) )
=> ( '#sk79' @ ( '#sk524' @ '#sk79' ) @ ( '#sk551' @ '#sk79' ) ) )
| '#form19'
| ~ ( '#form495' @ '#sk79' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1043]) ).
thf(zip_derived_cl1045,plain,
( ( '#sk2' @ ( '#sk524' @ '#sk79' ) @ ( '#sk551' @ '#sk79' ) )
| ~ ( '#form495' @ '#sk79' )
| '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1044]) ).
thf(zip_derived_cl149,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| '#form19'
| ( '#sk79' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl140]) ).
thf(zip_derived_cl1048,plain,
( '#form19'
| ~ ( '#form495' @ '#sk79' )
| ( '#sk79' @ ( '#sk524' @ '#sk79' ) @ ( '#sk551' @ '#sk79' ) )
| '#form19' ),
inference('sup-',[status(thm)],[zip_derived_cl1045,zip_derived_cl149]) ).
thf(zip_derived_cl1052,plain,
( ( '#sk79' @ ( '#sk524' @ '#sk79' ) @ ( '#sk551' @ '#sk79' ) )
| ~ ( '#form495' @ '#sk79' )
| '#form19' ),
inference(simplify,[status(thm)],[zip_derived_cl1048]) ).
thf(zip_derived_cl1046,plain,
( ~ ( '#sk79' @ ( '#sk524' @ '#sk79' ) @ ( '#sk551' @ '#sk79' ) )
| ~ ( '#form495' @ '#sk79' )
| '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1044]) ).
thf(zip_derived_cl1109,plain,
( '#form19'
| ~ ( '#form495' @ '#sk79' ) ),
inference(clc,[status(thm)],[zip_derived_cl1052,zip_derived_cl1046]) ).
thf(zip_derived_cl1347,plain,
! [X0: a] :
( ~ ( '#sk79' @ X0 @ ( '#sk98' @ '#sk79' ) )
| '#form19'
| ( '#sk79' @ X0 @ ( '#sk127' @ '#sk79' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl340,zip_derived_cl1109]) ).
thf(zip_derived_cl1348,plain,
( ( '#form495' @ '#sk79' )
| ( '#sk79' @ ( '#sk70' @ '#sk79' ) @ ( '#sk127' @ '#sk79' ) )
| '#form19' ),
inference('sup-',[status(thm)],[zip_derived_cl164,zip_derived_cl1347]) ).
thf(zip_derived_cl1109_033,plain,
( '#form19'
| ~ ( '#form495' @ '#sk79' ) ),
inference(clc,[status(thm)],[zip_derived_cl1052,zip_derived_cl1046]) ).
thf(zip_derived_cl1411,plain,
( '#form19'
| ( '#sk79' @ ( '#sk70' @ '#sk79' ) @ ( '#sk127' @ '#sk79' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1348,zip_derived_cl1109]) ).
thf(zip_derived_cl160,plain,
! [X2: a > a > $o] :
( ~ ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk127' @ X2 ) )
| ( '#form495' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl154]) ).
thf(zip_derived_cl1413,plain,
( '#form19'
| ( '#form495' @ '#sk79' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1411,zip_derived_cl160]) ).
thf(zip_derived_cl1109_034,plain,
( '#form19'
| ~ ( '#form495' @ '#sk79' ) ),
inference(clc,[status(thm)],[zip_derived_cl1052,zip_derived_cl1046]) ).
thf(zip_derived_cl1417,plain,
'#form19',
inference(clc,[status(thm)],[zip_derived_cl1413,zip_derived_cl1109]) ).
thf(zip_derived_cl1445,plain,
~ ( '#form495' @ '#sk9' ),
inference(demod,[status(thm)],[zip_derived_cl1068,zip_derived_cl1417]) ).
thf(zip_derived_cl164_035,plain,
! [X2: a > a > $o] :
( ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk98' @ X2 ) )
| ( '#form495' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl159]) ).
thf(zip_derived_cl163_036,plain,
! [X2: a > a > $o] :
( ( X2 @ ( '#sk98' @ X2 ) @ ( '#sk127' @ X2 ) )
| ( '#form495' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl159]) ).
thf(zip_derived_cl771_037,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk9' @ X4 @ X6 )
| ~ ( '#sk9' @ X2 @ X4 )
| ~ '#form19'
| ( '#sk9' @ X2 @ X6 ) ),
inference(demod,[status(thm)],[zip_derived_cl132,zip_derived_cl517]) ).
thf(zip_derived_cl1417_038,plain,
'#form19',
inference(clc,[status(thm)],[zip_derived_cl1413,zip_derived_cl1109]) ).
thf(zip_derived_cl1434,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk9' @ X4 @ X6 )
| ~ ( '#sk9' @ X2 @ X4 )
| ( '#sk9' @ X2 @ X6 ) ),
inference(demod,[status(thm)],[zip_derived_cl771,zip_derived_cl1417]) ).
thf(zip_derived_cl2012,plain,
! [X0: a] :
( ( '#form495' @ '#sk9' )
| ( '#sk9' @ X0 @ ( '#sk127' @ '#sk9' ) )
| ~ ( '#sk9' @ X0 @ ( '#sk98' @ '#sk9' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl163,zip_derived_cl1434]) ).
thf(zip_derived_cl1445_039,plain,
~ ( '#form495' @ '#sk9' ),
inference(demod,[status(thm)],[zip_derived_cl1068,zip_derived_cl1417]) ).
thf(zip_derived_cl2023,plain,
! [X0: a] :
( ( '#sk9' @ X0 @ ( '#sk127' @ '#sk9' ) )
| ~ ( '#sk9' @ X0 @ ( '#sk98' @ '#sk9' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2012,zip_derived_cl1445]) ).
thf(zip_derived_cl5442,plain,
( ( '#form495' @ '#sk9' )
| ( '#sk9' @ ( '#sk70' @ '#sk9' ) @ ( '#sk127' @ '#sk9' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl164,zip_derived_cl2023]) ).
thf(zip_derived_cl1445_040,plain,
~ ( '#form495' @ '#sk9' ),
inference(demod,[status(thm)],[zip_derived_cl1068,zip_derived_cl1417]) ).
thf(zip_derived_cl5449,plain,
'#sk9' @ ( '#sk70' @ '#sk9' ) @ ( '#sk127' @ '#sk9' ),
inference(demod,[status(thm)],[zip_derived_cl5442,zip_derived_cl1445]) ).
thf(zip_derived_cl160_041,plain,
! [X2: a > a > $o] :
( ~ ( X2 @ ( '#sk70' @ X2 ) @ ( '#sk127' @ X2 ) )
| ( '#form495' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl154]) ).
thf(zip_derived_cl6673,plain,
'#form495' @ '#sk9',
inference('sup-',[status(thm)],[zip_derived_cl5449,zip_derived_cl160]) ).
thf(zip_derived_cl6814,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl1445,zip_derived_cl6673]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEV157^5 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.2D7k9p1gTt true
% 0.14/0.35 % Computer : n003.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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 03:13:37 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.22/0.67 % Total configuration time : 828
% 0.22/0.67 % Estimated wc time : 1656
% 0.22/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.76 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.45/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.45/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 105.41/14.10 % Solved by lams/35_full_unif4.sh.
% 105.41/14.10 % done 663 iterations in 13.219s
% 105.41/14.10 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 105.41/14.10 % SZS output start Refutation
% See solution above
% 105.41/14.12
% 105.41/14.12
% 105.41/14.12 % Terminating...
% 105.82/14.21 % Runner terminated.
% 105.82/14.23 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------