%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV153^5 : 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.BJuZM2gUQu 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 19:59:47 EDT 2023
% Result : Theorem 51.00s 7.18s
% Output : Refutation 51.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 54
% Syntax : Number of formulae : 236 ( 7 unt; 31 typ; 0 def)
% Number of atoms : 2557 ( 0 equ; 7 cnn)
% Maximal formula atoms : 68 ( 12 avg)
% Number of connectives : 8429 ( 281 ~; 845 |; 588 &;4734 @)
% ( 0 <=>; 873 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 12 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 346 ( 346 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 13 con; 0-2 aty)
% (1108 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1321 (1110 ^; 211 !; 0 ?;1321 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf('#sk60_type',type,
'#sk60': ( a > $o ) > a ).
thf('#sk224_type',type,
'#sk224': ( a > $o ) > a ).
thf('#sk46_type',type,
'#sk46': a ).
thf('#form212_type',type,
'#form212': ( a > $o ) > $o ).
thf('#sk100_type',type,
'#sk100': a > $o ).
thf('#sk5_type',type,
'#sk5': a > $o ).
thf('#sk4_type',type,
'#sk4': a ).
thf('#sk139_type',type,
'#sk139': ( a > $o ) > a ).
thf('#sk56_type',type,
'#sk56': a ).
thf('#sk155_type',type,
'#sk155': ( a > $o ) > a ).
thf('#sk69_type',type,
'#sk69': a > $o ).
thf('#sk15_type',type,
'#sk15': ( a > $o ) > a ).
thf('#sk150_type',type,
'#sk150': ( a > $o ) > a ).
thf('#sk36_type',type,
'#sk36': a ).
thf('#form104_type',type,
'#form104': $o ).
thf('#sk68_type',type,
'#sk68': a ).
thf('#sk47_type',type,
'#sk47': a ).
thf('#form59_type',type,
'#form59': ( a > $o ) > $o ).
thf('#form35_type',type,
'#form35': $o ).
thf('#form45_type',type,
'#form45': $o ).
thf('#sk205_type',type,
'#sk205': ( a > $o ) > a ).
thf('#sk3_type',type,
'#sk3': a ).
thf('#sk1_type',type,
'#sk1': a > a > $o ).
thf('#sk21_type',type,
'#sk21': ( a > $o ) > a ).
thf('#form196_type',type,
'#form196': ( a > $o ) > $o ).
thf('#sk2_type',type,
'#sk2': a > a > $o ).
thf('#sk135_type',type,
'#sk135': ( a > $o ) > a ).
thf('#sk197_type',type,
'#sk197': ( a > $o ) > a ).
thf('#sk215_type',type,
'#sk215': ( a > $o ) > a ).
thf('#form204_type',type,
'#form204': ( a > $o ) > $o ).
thf(cTHM251H_pme,conjecture,
! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx @ Xw )
| ( R @ Xx @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) )
| ( ~ ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx @ Xw )
| ( R @ Xx @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) )
& ! [Xx0: a,Xy0: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( S @ Xu @ Xv )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( S @ Xx0 @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) )
| ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( R @ Xu @ Xv )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( R @ Xx0 @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx0 @ Xw )
| ( R @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xy0 @ Xw )
| ( R @ Xy0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) )
& ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx0 @ Xw )
| ( R @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx0 @ Xw )
| ( R @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx @ Xw )
| ( R @ Xx @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) )
| ( ~ ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx @ Xw )
| ( R @ Xx @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) )
& ! [Xx0: a,Xy0: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( S @ Xu @ Xv )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( S @ Xx0 @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) )
| ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( R @ Xu @ Xv )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( R @ Xx0 @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx0 @ Xw )
| ( R @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xy0 @ Xw )
| ( R @ Xy0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) )
& ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx0 @ Xw )
| ( R @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx0 @ Xw )
| ( R @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) ) ) ),
inference('cnf.neg',[status(esa)],[cTHM251H_pme]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( !!
@ ^ [Y1: a > a > $o] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( ( (~)
@ ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( ( Y1 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( ( Y1 @ Y4 @ Y7 )
| ( Y0 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( !!
@ ^ [Y7: a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !!
@ ^ [Y8: a] :
( ( ( Y1 @ Y5 @ Y8 )
| ( Y0 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !!
@ ^ [Y7: a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !!
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y0 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) )
=> ( !!
@ ^ [Y7: a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !!
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y0 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( Y0 @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( ( (~)
@ ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( Y0 @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( Y0 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( '#sk1' @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( '#sk1' @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( ( Y0 @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( ( Y0 @ Y3 @ Y6 )
| ( '#sk1' @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( '#sk1' @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
& ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( '#sk1' @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( '#sk1' @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( ( (~)
@ ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( '#sk2' @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk1' @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( '#sk1' @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y2 @ Y5 )
| ( '#sk1' @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y3 @ Y6 )
| ( '#sk1' @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
& ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y2 @ Y6 )
| ( '#sk1' @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) ) )
=> ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y2 @ Y6 )
| ( '#sk1' @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: a] :
( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ '#sk3' @ Y2 )
| ( '#sk1' @ '#sk3' @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( ( (~)
@ ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ '#sk3' @ Y2 )
| ( '#sk1' @ '#sk3' @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y2 @ Y5 )
| ( '#sk1' @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y1 @ Y5 )
| ( '#sk1' @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y1 @ Y5 )
| ( '#sk1' @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
~ ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) )
| ( ( (~)
@ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl5,plain,
~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl7,plain,
~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) )
=> ( '#sk5' @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl9,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) ),
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 ) )
=> ( '#sk5' @ 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 ) )
=> ( '#sk5' @ 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 ) )
=> ( '#sk5' @ 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 ) )
| ( '#sk5' @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl26,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ~ ( '#sk5' @ X2 )
| ( '#sk5' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl29,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ( '#sk5' @ X4 )
| ~ ( '#sk5' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl30,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk5' @ X4 )
| ~ ( '#sk5' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl6,plain,
~ ( ( (~)
@ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl8,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl11,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl12,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) )
=> ( '#sk5' @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl10,plain,
~ ( '#sk5' @ '#sk4' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl198,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) )
=> $false )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl12,zip_derived_cl10]) ).
thf(zip_derived_cl199,plain,
( ( (~)
@ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl198]) ).
thf(zip_derived_cl200,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl199]) ).
thf(zip_derived_cl11_001,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl15,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
| ( X2 @ '#sk4' )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl18,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ( X2 @ '#sk4' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk15' @ X2 ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk4' )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl25,plain,
! [X2: a > $o] :
( ~ ( ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) )
=> ( X2 @ ( '#sk21' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ( X2 @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl27,plain,
! [X2: a > $o] :
( ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) )
| ( X2 @ '#sk4' )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl27_002,plain,
! [X2: a > $o] :
( ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) )
| ( X2 @ '#sk4' )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl31,plain,
( '#form35'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl33,plain,
! [X2: a > $o] :
( ~ '#form35'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ( X2 @ '#sk4' )
| ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl27,zip_derived_cl31]) ).
thf(zip_derived_cl35,plain,
( '#form45'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl201,plain,
( ~ '#form45'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl200,zip_derived_cl35]) ).
thf(zip_derived_cl31_003,plain,
( '#form35'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl202,plain,
( ~ '#form35'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) )
| ~ '#form45' ),
inference(renaming,[status(thm)],[zip_derived_cl201,zip_derived_cl31]) ).
thf(zip_derived_cl203,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) )
| ~ '#form45'
| ~ '#form35' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl202]) ).
thf(zip_derived_cl28,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk21' @ X2 ) )
| ( X2 @ '#sk4' )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl31_004,plain,
( '#form35'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl34,plain,
! [X2: a > $o] :
( ~ '#form35'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ( X2 @ '#sk4' )
| ~ ( X2 @ ( '#sk21' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl28,zip_derived_cl31]) ).
thf(zip_derived_cl35_005,plain,
( '#form45'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl39,plain,
! [X2: a > $o] :
( ~ '#form45'
| ~ ( X2 @ ( '#sk21' @ X2 ) )
| ( X2 @ '#sk4' )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| ~ '#form35' ),
inference(renaming,[status(thm)],[zip_derived_cl34,zip_derived_cl35]) ).
thf(zip_derived_cl45,plain,
! [X2: a > $o] :
( ( '#form59' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl204,plain,
( ~ ( '#form59' @ '#sk5' )
| ~ '#form35'
| ~ '#form45'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl203,zip_derived_cl45]) ).
thf(zip_derived_cl205,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ ( '#sk15' @ '#sk5' ) @ Y0 )
| ( '#sk1' @ ( '#sk15' @ '#sk5' ) @ Y0 ) )
& ( '#sk5' @ ( '#sk15' @ '#sk5' ) ) )
=> ( '#sk5' @ Y0 ) ) )
| ~ '#form45'
| ~ '#form35'
| ~ ( '#form59' @ '#sk5' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl204]) ).
thf(zip_derived_cl206,plain,
( ~ ( ( ( ( '#sk2' @ ( '#sk15' @ '#sk5' ) @ ( '#sk21' @ '#sk5' ) )
| ( '#sk1' @ ( '#sk15' @ '#sk5' ) @ ( '#sk21' @ '#sk5' ) ) )
& ( '#sk5' @ ( '#sk15' @ '#sk5' ) ) )
=> ( '#sk5' @ ( '#sk21' @ '#sk5' ) ) )
| ~ ( '#form59' @ '#sk5' )
| ~ '#form35'
| ~ '#form45' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl205]) ).
thf(zip_derived_cl208,plain,
( ~ ( '#sk5' @ ( '#sk21' @ '#sk5' ) )
| ~ '#form45'
| ~ '#form35'
| ~ ( '#form59' @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl206]) ).
thf(zip_derived_cl35_006,plain,
( '#form45'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl36,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ '#sk46' @ Y3 )
| ( '#sk1' @ '#sk46' @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ '#sk46' @ Y3 )
| ( '#sk1' @ '#sk46' @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| '#form45' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl42,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ '#sk56' @ Y2 )
| ( '#sk1' @ '#sk56' @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ '#sk46' @ Y2 )
| ( '#sk1' @ '#sk46' @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ '#sk56' ) ) ) )
=> ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ '#sk46' @ Y2 )
| ( '#sk1' @ '#sk46' @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| '#form45' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl50,plain,
( ~ ( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk56' @ Y1 )
| ( '#sk1' @ '#sk56' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk68' ) ) )
& ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk46' @ Y1 )
| ( '#sk1' @ '#sk46' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk56' ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk46' @ Y1 )
| ( '#sk1' @ '#sk46' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk68' ) ) ) )
| '#form45' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl59,plain,
( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk56' @ Y1 )
| ( '#sk1' @ '#sk56' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk68' ) ) )
& ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk46' @ Y1 )
| ( '#sk1' @ '#sk46' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk56' ) ) ) )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl67,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk56' @ Y1 )
| ( '#sk1' @ '#sk56' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk68' ) ) )
| '#form45' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl80,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk68' ) )
| '#form45' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl81,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk100' @ Y0 ) )
=> ( '#sk100' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( '#sk100' @ Y0 ) ) ) )
=> ( '#sk100' @ '#sk68' ) )
| '#form45' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl219,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk100' @ Y0 ) )
=> ( '#sk100' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( '#sk100' @ Y0 ) ) ) )
| ( '#sk100' @ '#sk68' )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl60,plain,
( ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk46' @ Y1 )
| ( '#sk1' @ '#sk46' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk68' ) ) )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl71,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk100' @ Y0 ) )
=> ( '#sk100' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk46' @ Y0 )
| ( '#sk1' @ '#sk46' @ Y0 ) )
=> ( '#sk100' @ Y0 ) ) ) )
=> ( '#sk100' @ '#sk68' ) )
| '#form45' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl89,plain,
( ~ ( '#sk100' @ '#sk68' )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl220,plain,
( '#form45'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk100' @ Y0 ) )
=> ( '#sk100' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( '#sk100' @ Y0 ) ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl219,zip_derived_cl89]) ).
thf(zip_derived_cl221,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk100' @ Y0 ) )
=> ( '#sk100' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( '#sk100' @ Y0 ) ) )
| '#form45' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl220]) ).
thf(zip_derived_cl222,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ ( '#sk15' @ '#sk100' ) @ Y0 )
| ( '#sk1' @ ( '#sk15' @ '#sk100' ) @ Y0 ) )
& ( '#sk100' @ ( '#sk15' @ '#sk100' ) ) )
=> ( '#sk100' @ Y0 ) ) )
| '#form45'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( '#sk100' @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl221]) ).
thf(zip_derived_cl223,plain,
( ~ ( ( ( ( '#sk2' @ ( '#sk15' @ '#sk100' ) @ ( '#sk21' @ '#sk100' ) )
| ( '#sk1' @ ( '#sk15' @ '#sk100' ) @ ( '#sk21' @ '#sk100' ) ) )
& ( '#sk100' @ ( '#sk15' @ '#sk100' ) ) )
=> ( '#sk100' @ ( '#sk21' @ '#sk100' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( '#sk100' @ Y0 ) ) )
| '#form45' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl222]) ).
thf(zip_derived_cl225,plain,
( ~ ( '#sk100' @ ( '#sk21' @ '#sk100' ) )
| '#form45'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( '#sk100' @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl223]) ).
thf(zip_derived_cl227,plain,
( ~ ( ( ( '#sk2' @ '#sk56' @ ( '#sk215' @ '#sk100' ) )
| ( '#sk1' @ '#sk56' @ ( '#sk215' @ '#sk100' ) ) )
=> ( '#sk100' @ ( '#sk215' @ '#sk100' ) ) )
| '#form45'
| ~ ( '#sk100' @ ( '#sk21' @ '#sk100' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl225]) ).
thf(zip_derived_cl230,plain,
( ~ ( '#sk100' @ ( '#sk215' @ '#sk100' ) )
| ~ ( '#sk100' @ ( '#sk21' @ '#sk100' ) )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl227]) ).
thf(zip_derived_cl229,plain,
( ( '#sk2' @ '#sk56' @ ( '#sk215' @ '#sk100' ) )
| ( '#sk1' @ '#sk56' @ ( '#sk215' @ '#sk100' ) )
| ~ ( '#sk100' @ ( '#sk21' @ '#sk100' ) )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl227]) ).
thf(zip_derived_cl233,plain,
( ( '#sk2' @ '#sk56' @ ( '#sk215' @ '#sk100' ) )
| ( '#sk1' @ '#sk56' @ ( '#sk215' @ '#sk100' ) )
| '#form45'
| ~ ( '#sk100' @ ( '#sk21' @ '#sk100' ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl229]) ).
thf(zip_derived_cl207,plain,
( ( ( ( '#sk2' @ ( '#sk15' @ '#sk5' ) @ ( '#sk21' @ '#sk5' ) )
| ( '#sk1' @ ( '#sk15' @ '#sk5' ) @ ( '#sk21' @ '#sk5' ) ) )
& ( '#sk5' @ ( '#sk15' @ '#sk5' ) ) )
| ~ '#form45'
| ~ '#form35'
| ~ ( '#form59' @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl206]) ).
thf(zip_derived_cl80_007,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk68' ) )
| '#form45' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl94,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
| ( X2 @ '#sk68' )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl102,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| '#form45'
| ( X2 @ '#sk68' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl111,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk15' @ X2 ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk68' )
| '#form45'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl118,plain,
! [X2: a > $o] :
( ~ ( ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) )
=> ( X2 @ ( '#sk21' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| '#form45'
| ( X2 @ '#sk68' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl129,plain,
! [X2: a > $o] :
( ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) )
| ( X2 @ '#sk68' )
| '#form45'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl118]) ).
thf(zip_derived_cl144,plain,
! [X2: a > $o] :
( ~ ( '#form212' @ X2 )
| ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl209,plain,
( ( '#form212' @ '#sk5' )
| ~ ( '#form59' @ '#sk5' )
| ~ '#form35'
| ~ '#form45' ),
inference(renaming,[status(thm)],[zip_derived_cl207,zip_derived_cl144]) ).
thf(zip_derived_cl31_008,plain,
( '#form35'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl32,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk36' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk36' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ '#sk36' @ Y2 )
| ( '#sk1' @ '#sk36' @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| '#form35' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl38,plain,
( ~ ( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ '#sk36' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk36' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk36' @ Y1 )
| ( '#sk1' @ '#sk36' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) ) )
| '#form35' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl44,plain,
( ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk36' @ Y1 )
| ( '#sk1' @ '#sk36' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) )
| '#form35' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl53,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk69' @ Y0 ) )
=> ( '#sk69' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk36' @ Y0 )
| ( '#sk1' @ '#sk36' @ Y0 ) )
=> ( '#sk69' @ Y0 ) ) ) )
=> ( '#sk69' @ '#sk47' ) )
| '#form35' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl65,plain,
( ~ ( '#sk69' @ '#sk47' )
| '#form35' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl64,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk69' @ Y0 ) )
=> ( '#sk69' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk36' @ Y0 )
| ( '#sk1' @ '#sk36' @ Y0 ) )
=> ( '#sk69' @ Y0 ) ) ) )
| '#form35' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl78,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk69' @ Y0 ) )
=> ( '#sk69' @ Y1 ) ) ) )
| '#form35' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl92,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
& ( '#sk69' @ X2 ) )
=> ( '#sk69' @ Y0 ) ) )
| '#form35' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl100,plain,
! [X2: a,X4: a] :
( ( ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
& ( '#sk69' @ X2 ) )
=> ( '#sk69' @ X4 ) )
| '#form35' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl108,plain,
! [X2: a,X4: a] :
( ~ ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
& ( '#sk69' @ X2 ) )
| ( '#sk69' @ X4 )
| '#form35' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl117,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ~ ( '#sk69' @ X2 )
| '#form35'
| ( '#sk69' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl128,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk69' @ X4 )
| '#form35'
| ~ ( '#sk69' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl117]) ).
thf(zip_derived_cl43,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ '#sk36' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk36' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) )
| '#form35' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl51,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ '#sk36' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk36' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) )
| '#form35' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl61,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk47' ) )
| '#form35'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk36' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl72,plain,
( ~ '#form104'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk36' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl73,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk47' ) )
| ~ '#form104' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl91,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
| ( X2 @ '#sk47' )
| ~ '#form104' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl99,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) )
| ~ '#form104'
| ( X2 @ '#sk47' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl107,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ ( '#sk139' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk139' @ X2 ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk47' )
| ~ '#form104'
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl116,plain,
! [X2: a > $o] :
( ~ ( ( ( '#sk1' @ ( '#sk139' @ X2 ) @ ( '#sk155' @ X2 ) )
& ( X2 @ ( '#sk139' @ X2 ) ) )
=> ( X2 @ ( '#sk155' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) )
| ~ '#form104'
| ( X2 @ '#sk47' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl126,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk155' @ X2 ) )
| ( X2 @ '#sk47' )
| ~ '#form104'
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl126_009,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk155' @ X2 ) )
| ( X2 @ '#sk47' )
| ~ '#form104'
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl141,plain,
! [X2: a > $o] :
( ( '#form204' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl143,plain,
! [X2: a > $o] :
( ~ ( '#form204' @ X2 )
| ~ '#form104'
| ( X2 @ '#sk47' )
| ~ ( X2 @ ( '#sk155' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl126,zip_derived_cl141]) ).
thf(zip_derived_cl45_010,plain,
! [X2: a > $o] :
( ( '#form59' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl46,plain,
! [X2: a > $o] :
( ~ ( ( ( '#sk2' @ '#sk3' @ ( '#sk60' @ X2 ) )
| ( '#sk1' @ '#sk3' @ ( '#sk60' @ X2 ) ) )
=> ( X2 @ ( '#sk60' @ X2 ) ) )
| ( '#form59' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl54,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk3' @ ( '#sk60' @ X2 ) )
| ( '#sk1' @ '#sk3' @ ( '#sk60' @ X2 ) )
| ( '#form59' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl66,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk3' @ ( '#sk60' @ X2 ) )
| ( '#sk1' @ '#sk3' @ ( '#sk60' @ X2 ) )
| ( '#form59' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl125,plain,
! [X2: a > $o] :
( ( ( '#sk1' @ ( '#sk139' @ X2 ) @ ( '#sk155' @ X2 ) )
& ( X2 @ ( '#sk139' @ X2 ) ) )
| ( X2 @ '#sk47' )
| ~ '#form104'
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl140,plain,
! [X2: a > $o] :
( ( X2 @ ( '#sk139' @ X2 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) )
| ~ '#form104'
| ( X2 @ '#sk47' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl125]) ).
thf(zip_derived_cl141_011,plain,
! [X2: a > $o] :
( ( '#form204' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl158,plain,
! [X2: a > $o] :
( ~ ( '#form204'
@ ^ [Y0: a] : ( X2 @ Y0 ) )
| ( X2 @ '#sk47' )
| ~ '#form104'
| ( X2 @ ( '#sk139' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl140,zip_derived_cl141]) ).
thf(zip_derived_cl171,plain,
! [X2: a > $o] :
( ~ ( '#form204' @ X2 )
| ( X2 @ '#sk47' )
| ~ '#form104'
| ( X2 @ ( '#sk139' @ X2 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl158]) ).
thf(zip_derived_cl141_012,plain,
! [X2: a > $o] :
( ( '#form204' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl142,plain,
! [X2: a > $o] :
( ~ ( ( '#sk1' @ '#sk36' @ ( '#sk205' @ X2 ) )
=> ( X2 @ ( '#sk205' @ X2 ) ) )
| ( '#form204' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl141]) ).
thf(zip_derived_cl159,plain,
! [X2: a > $o] :
( ( '#sk1' @ '#sk36' @ ( '#sk205' @ X2 ) )
| ( '#form204' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl142]) ).
thf(zip_derived_cl160,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk205' @ X2 ) )
| ( '#form204' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl142]) ).
thf(zip_derived_cl139,plain,
! [X2: a > $o] :
( ( '#sk1' @ ( '#sk139' @ X2 ) @ ( '#sk155' @ X2 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) )
| ~ '#form104'
| ( X2 @ '#sk47' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl125]) ).
thf(zip_derived_cl141_013,plain,
! [X2: a > $o] :
( ( '#form204' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl157,plain,
! [X2: a > $o] :
( ~ ( '#form204'
@ ^ [Y0: a] : ( X2 @ Y0 ) )
| ( X2 @ '#sk47' )
| ~ '#form104'
| ( '#sk1' @ ( '#sk139' @ X2 ) @ ( '#sk155' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl139,zip_derived_cl141]) ).
thf(zip_derived_cl170,plain,
! [X2: a > $o] :
( ~ ( '#form204' @ X2 )
| ( X2 @ '#sk47' )
| ~ '#form104'
| ( '#sk1' @ ( '#sk139' @ X2 ) @ ( '#sk155' @ X2 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl157]) ).
thf(zip_derived_cl14,plain,
( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl17,plain,
! [X2: a] :
( ( ( '#sk2' @ '#sk3' @ X2 )
| ( '#sk1' @ '#sk3' @ X2 ) )
=> ( '#sk5' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl20,plain,
! [X2: a] :
( ~ ( ( '#sk2' @ '#sk3' @ X2 )
| ( '#sk1' @ '#sk3' @ X2 ) )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl23,plain,
! [X2: a] :
( ~ ( '#sk2' @ '#sk3' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl24,plain,
! [X2: a] :
( ~ ( '#sk1' @ '#sk3' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl55,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk60' @ X2 ) )
| ( '#form59' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl79,plain,
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk36' @ Y0 )
| ( '#sk1' @ '#sk36' @ Y0 ) )
=> ( '#sk69' @ Y0 ) ) )
| '#form35' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl93,plain,
! [X2: a] :
( ( ( ( '#sk2' @ '#sk36' @ X2 )
| ( '#sk1' @ '#sk36' @ X2 ) )
=> ( '#sk69' @ X2 ) )
| '#form35' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl101,plain,
! [X2: a] :
( ~ ( ( '#sk2' @ '#sk36' @ X2 )
| ( '#sk1' @ '#sk36' @ X2 ) )
| ( '#sk69' @ X2 )
| '#form35' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl110,plain,
! [X2: a] :
( ~ ( '#sk1' @ '#sk36' @ X2 )
| '#form35'
| ( '#sk69' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl61_014,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk47' ) )
| '#form35'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk36' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl62,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( '#sk69' @ Y0 ) )
=> ( '#sk69' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( '#sk69' @ Y0 ) ) ) )
=> ( '#sk69' @ '#sk47' ) )
| '#form35'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk36' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl72_015,plain,
( ~ '#form104'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk36' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl330,plain,
( '#form104'
| '#form35'
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( '#sk69' @ Y0 ) )
=> ( '#sk69' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( '#sk69' @ Y0 ) ) ) )
=> ( '#sk69' @ '#sk47' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl62,zip_derived_cl72]) ).
thf(zip_derived_cl331,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( '#sk69' @ Y0 ) )
=> ( '#sk69' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( '#sk69' @ Y0 ) ) ) )
| ( '#sk69' @ '#sk47' )
| '#form35'
| '#form104' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl330]) ).
thf(zip_derived_cl65_016,plain,
( ~ ( '#sk69' @ '#sk47' )
| '#form35' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl332,plain,
( '#form104'
| '#form35'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( '#sk69' @ Y0 ) )
=> ( '#sk69' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( '#sk69' @ Y0 ) ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl331,zip_derived_cl65]) ).
thf(zip_derived_cl333,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( '#sk69' @ Y0 ) )
=> ( '#sk69' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( '#sk69' @ Y0 ) ) )
| '#form35'
| '#form104' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl332]) ).
thf(zip_derived_cl61_017,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk47' ) )
| '#form35'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk36' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl72_018,plain,
( ~ '#form104'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk36' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk47' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl77,plain,
! [X2: a > $o] :
( '#form104'
| '#form35'
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk47' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl61,zip_derived_cl72]) ).
thf(zip_derived_cl90,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
| ( X2 @ '#sk47' )
| '#form35'
| '#form104' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl98,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) )
| '#form104'
| '#form35'
| ( X2 @ '#sk47' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl106,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ ( '#sk135' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk135' @ X2 ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk47' )
| '#form35'
| '#form104'
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl98]) ).
thf(zip_derived_cl115,plain,
! [X2: a > $o] :
( ~ ( ( ( '#sk2' @ ( '#sk135' @ X2 ) @ ( '#sk150' @ X2 ) )
& ( X2 @ ( '#sk135' @ X2 ) ) )
=> ( X2 @ ( '#sk150' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) )
| '#form104'
| '#form35'
| ( X2 @ '#sk47' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl124,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk150' @ X2 ) )
| ( X2 @ '#sk47' )
| '#form35'
| '#form104'
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl115]) ).
thf(zip_derived_cl136,plain,
! [X2: a > $o] :
( ( '#form196' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl334,plain,
( ~ ( '#form196' @ '#sk69' )
| '#form104'
| '#form35'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( '#sk69' @ Y0 ) )
=> ( '#sk69' @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl333,zip_derived_cl136]) ).
thf(zip_derived_cl335,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ ( '#sk135' @ '#sk69' ) @ Y0 )
& ( '#sk69' @ ( '#sk135' @ '#sk69' ) ) )
=> ( '#sk69' @ Y0 ) ) )
| '#form35'
| '#form104'
| ~ ( '#form196' @ '#sk69' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl334]) ).
thf(zip_derived_cl336,plain,
( ~ ( ( ( '#sk2' @ ( '#sk135' @ '#sk69' ) @ ( '#sk150' @ '#sk69' ) )
& ( '#sk69' @ ( '#sk135' @ '#sk69' ) ) )
=> ( '#sk69' @ ( '#sk150' @ '#sk69' ) ) )
| ~ ( '#form196' @ '#sk69' )
| '#form104'
| '#form35' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl335]) ).
thf(zip_derived_cl338,plain,
( ~ ( '#sk69' @ ( '#sk150' @ '#sk69' ) )
| '#form35'
| '#form104'
| ~ ( '#form196' @ '#sk69' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl336]) ).
thf(zip_derived_cl337,plain,
( ( ( '#sk2' @ ( '#sk135' @ '#sk69' ) @ ( '#sk150' @ '#sk69' ) )
& ( '#sk69' @ ( '#sk135' @ '#sk69' ) ) )
| '#form35'
| '#form104'
| ~ ( '#form196' @ '#sk69' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl336]) ).
thf(zip_derived_cl340,plain,
( ( '#sk69' @ ( '#sk135' @ '#sk69' ) )
| ~ ( '#form196' @ '#sk69' )
| '#form104'
| '#form35' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl337]) ).
thf(zip_derived_cl339,plain,
( ( '#sk2' @ ( '#sk135' @ '#sk69' ) @ ( '#sk150' @ '#sk69' ) )
| ~ ( '#form196' @ '#sk69' )
| '#form104'
| '#form35' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl337]) ).
thf(zip_derived_cl127,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ( '#sk69' @ X4 )
| '#form35'
| ~ ( '#sk69' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl117]) ).
thf(zip_derived_cl224,plain,
( ( ( ( '#sk2' @ ( '#sk15' @ '#sk100' ) @ ( '#sk21' @ '#sk100' ) )
| ( '#sk1' @ ( '#sk15' @ '#sk100' ) @ ( '#sk21' @ '#sk100' ) ) )
& ( '#sk100' @ ( '#sk15' @ '#sk100' ) ) )
| '#form45'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( '#sk100' @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl223]) ).
thf(zip_derived_cl144_019,plain,
! [X2: a > $o] :
( ~ ( '#form212' @ X2 )
| ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl226,plain,
( ( '#form212' @ '#sk100' )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk56' @ Y0 )
| ( '#sk1' @ '#sk56' @ Y0 ) )
=> ( '#sk100' @ Y0 ) ) )
| '#form45' ),
inference(renaming,[status(thm)],[zip_derived_cl224,zip_derived_cl144]) ).
thf(zip_derived_cl228,plain,
( ~ ( ( ( '#sk2' @ '#sk56' @ ( '#sk215' @ '#sk100' ) )
| ( '#sk1' @ '#sk56' @ ( '#sk215' @ '#sk100' ) ) )
=> ( '#sk100' @ ( '#sk215' @ '#sk100' ) ) )
| '#form45'
| ( '#form212' @ '#sk100' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl226]) ).
thf(zip_derived_cl231,plain,
( ( '#sk2' @ '#sk56' @ ( '#sk215' @ '#sk100' ) )
| ( '#sk1' @ '#sk56' @ ( '#sk215' @ '#sk100' ) )
| ( '#form212' @ '#sk100' )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl228]) ).
thf(zip_derived_cl234,plain,
( ( '#sk2' @ '#sk56' @ ( '#sk215' @ '#sk100' ) )
| ( '#sk1' @ '#sk56' @ ( '#sk215' @ '#sk100' ) )
| '#form45'
| ( '#form212' @ '#sk100' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl231]) ).
thf(zip_derived_cl232,plain,
( ~ ( '#sk100' @ ( '#sk215' @ '#sk100' ) )
| ( '#form212' @ '#sk100' )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl228]) ).
thf(zip_derived_cl136_020,plain,
! [X2: a > $o] :
( ( '#form196' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk36' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl137,plain,
! [X2: a > $o] :
( ~ ( ( '#sk2' @ '#sk36' @ ( '#sk197' @ X2 ) )
=> ( X2 @ ( '#sk197' @ X2 ) ) )
| ( '#form196' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl136]) ).
thf(zip_derived_cl155,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk36' @ ( '#sk197' @ X2 ) )
| ( '#form196' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl137]) ).
thf(zip_derived_cl156,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk197' @ X2 ) )
| ( '#form196' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl137]) ).
thf(zip_derived_cl109,plain,
! [X2: a] :
( ~ ( '#sk2' @ '#sk36' @ X2 )
| '#form35'
| ( '#sk69' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl68,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk46' @ Y1 )
| ( '#sk1' @ '#sk46' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk56' ) ) )
| '#form45' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl84,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk46' @ Y0 )
| ( '#sk1' @ '#sk46' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk56' ) )
| '#form45' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl95,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk46' @ Y0 )
| ( '#sk1' @ '#sk46' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
| ( X2 @ '#sk56' )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl103,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk46' @ Y0 )
| ( '#sk1' @ '#sk46' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| '#form45'
| ( X2 @ '#sk56' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl112,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk15' @ X2 ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk56' )
| '#form45'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk46' @ Y0 )
| ( '#sk1' @ '#sk46' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl119,plain,
! [X2: a > $o] :
( ~ ( ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) )
=> ( X2 @ ( '#sk21' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk46' @ Y0 )
| ( '#sk1' @ '#sk46' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| '#form45'
| ( X2 @ '#sk56' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl132,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk21' @ X2 ) )
| ( X2 @ '#sk56' )
| '#form45'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk46' @ Y0 )
| ( '#sk1' @ '#sk46' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl119]) ).
thf(zip_derived_cl150,plain,
! [X2: a > $o] :
( ~ ( ( ( '#sk2' @ '#sk46' @ ( '#sk224' @ X2 ) )
| ( '#sk1' @ '#sk46' @ ( '#sk224' @ X2 ) ) )
=> ( X2 @ ( '#sk224' @ X2 ) ) )
| '#form45'
| ( X2 @ '#sk56' )
| ~ ( X2 @ ( '#sk21' @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl132]) ).
thf(zip_derived_cl167,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk224' @ X2 ) )
| ~ ( X2 @ ( '#sk21' @ X2 ) )
| ( X2 @ '#sk56' )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl150]) ).
thf(zip_derived_cl166,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk46' @ ( '#sk224' @ X2 ) )
| ( '#sk1' @ '#sk46' @ ( '#sk224' @ X2 ) )
| ~ ( X2 @ ( '#sk21' @ X2 ) )
| ( X2 @ '#sk56' )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl150]) ).
thf(zip_derived_cl177,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk46' @ ( '#sk224' @ X2 ) )
| ( '#sk1' @ '#sk46' @ ( '#sk224' @ X2 ) )
| '#form45'
| ( X2 @ '#sk56' )
| ~ ( X2 @ ( '#sk21' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl166]) ).
thf(zip_derived_cl88,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk100' @ Y0 ) )
=> ( '#sk100' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk46' @ Y0 )
| ( '#sk1' @ '#sk46' @ Y0 ) )
=> ( '#sk100' @ Y0 ) ) ) )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl96,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk100' @ Y0 ) )
=> ( '#sk100' @ Y1 ) ) ) )
| '#form45' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl104,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
& ( '#sk100' @ X2 ) )
=> ( '#sk100' @ Y0 ) ) )
| '#form45' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl113,plain,
! [X2: a,X4: a] :
( ( ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
& ( '#sk100' @ X2 ) )
=> ( '#sk100' @ X4 ) )
| '#form45' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl120,plain,
! [X2: a,X4: a] :
( ~ ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
& ( '#sk100' @ X2 ) )
| ( '#sk100' @ X4 )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl133,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ~ ( '#sk100' @ X2 )
| '#form45'
| ( '#sk100' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl120]) ).
thf(zip_derived_cl151,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ( '#sk100' @ X4 )
| '#form45'
| ~ ( '#sk100' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl133]) ).
thf(zip_derived_cl152,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk100' @ X4 )
| '#form45'
| ~ ( '#sk100' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl133]) ).
thf(zip_derived_cl144_021,plain,
! [X2: a > $o] :
( ~ ( '#form212' @ X2 )
| ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl146,plain,
! [X2: a > $o] :
( ( X2 @ ( '#sk15' @ X2 ) )
| ~ ( '#form212' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl144]) ).
thf(zip_derived_cl145,plain,
! [X2: a > $o] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ~ ( '#form212' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl144]) ).
thf(zip_derived_cl162,plain,
! [X2: a > $o] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ~ ( '#form212' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl145]) ).
thf(zip_derived_cl131,plain,
! [X2: a > $o] :
( ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) )
| ( X2 @ '#sk56' )
| '#form45'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk46' @ Y0 )
| ( '#sk1' @ '#sk46' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl119]) ).
thf(zip_derived_cl144_022,plain,
! [X2: a > $o] :
( ~ ( '#form212' @ X2 )
| ( ( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) )
| ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk21' @ X2 ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl149,plain,
! [X2: a > $o] :
( ( '#form212' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk46' @ Y0 )
| ( '#sk1' @ '#sk46' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| '#form45'
| ( X2 @ '#sk56' ) ),
inference(renaming,[status(thm)],[zip_derived_cl131,zip_derived_cl144]) ).
thf(zip_derived_cl165,plain,
! [X2: a > $o] :
( ~ ( ( ( '#sk2' @ '#sk46' @ ( '#sk224' @ X2 ) )
| ( '#sk1' @ '#sk46' @ ( '#sk224' @ X2 ) ) )
=> ( X2 @ ( '#sk224' @ X2 ) ) )
| ( X2 @ '#sk56' )
| '#form45'
| ( '#form212' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl149]) ).
thf(zip_derived_cl175,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk46' @ ( '#sk224' @ X2 ) )
| ( '#sk1' @ '#sk46' @ ( '#sk224' @ X2 ) )
| ( '#form212' @ X2 )
| '#form45'
| ( X2 @ '#sk56' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl165]) ).
thf(zip_derived_cl179,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk46' @ ( '#sk224' @ X2 ) )
| ( '#sk1' @ '#sk46' @ ( '#sk224' @ X2 ) )
| ( X2 @ '#sk56' )
| '#form45'
| ( '#form212' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl175]) ).
thf(zip_derived_cl176,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk224' @ X2 ) )
| ( '#form212' @ X2 )
| '#form45'
| ( X2 @ '#sk56' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl165]) ).
thf(zip_derived_cl97,plain,
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk46' @ Y0 )
| ( '#sk1' @ '#sk46' @ Y0 ) )
=> ( '#sk100' @ Y0 ) ) )
| '#form45' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl105,plain,
! [X2: a] :
( ( ( ( '#sk2' @ '#sk46' @ X2 )
| ( '#sk1' @ '#sk46' @ X2 ) )
=> ( '#sk100' @ X2 ) )
| '#form45' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl114,plain,
! [X2: a] :
( ~ ( ( '#sk2' @ '#sk46' @ X2 )
| ( '#sk1' @ '#sk46' @ X2 ) )
| ( '#sk100' @ X2 )
| '#form45' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl121,plain,
! [X2: a] :
( ~ ( '#sk2' @ '#sk46' @ X2 )
| '#form45'
| ( '#sk100' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl122,plain,
! [X2: a] :
( ~ ( '#sk1' @ '#sk46' @ X2 )
| '#form45'
| ( '#sk100' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl9359,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl29,zip_derived_cl30,zip_derived_cl208,zip_derived_cl230,zip_derived_cl233,zip_derived_cl209,zip_derived_cl65,zip_derived_cl128,zip_derived_cl143,zip_derived_cl66,zip_derived_cl171,zip_derived_cl159,zip_derived_cl160,zip_derived_cl170,zip_derived_cl23,zip_derived_cl24,zip_derived_cl55,zip_derived_cl110,zip_derived_cl338,zip_derived_cl340,zip_derived_cl339,zip_derived_cl127,zip_derived_cl234,zip_derived_cl232,zip_derived_cl155,zip_derived_cl156,zip_derived_cl109,zip_derived_cl167,zip_derived_cl177,zip_derived_cl151,zip_derived_cl152,zip_derived_cl146,zip_derived_cl162,zip_derived_cl179,zip_derived_cl176,zip_derived_cl121,zip_derived_cl122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEV153^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.BJuZM2gUQu true
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 03:19:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.21/0.36 % Running in HO mode
% 0.21/0.69 % Total configuration time : 828
% 0.21/0.69 % Estimated wc time : 1656
% 0.21/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.83/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.83/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.83/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.46/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.46/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 51.00/7.18 % Solved by lams/20_acsne_simpl.sh.
% 51.00/7.18 % done 806 iterations in 6.243s
% 51.00/7.18 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 51.00/7.18 % SZS output start Refutation
% See solution above
% 51.00/7.19
% 51.00/7.19
% 51.00/7.19 % Terminating...
% 51.58/7.32 % Runner terminated.
% 51.58/7.32 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------