%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV156^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.XRKNuixuxX true
% Computer : n013.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 19:59:48 EDT 2023
% Result : Theorem 49.57s 7.12s
% Output : Refutation 49.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 46
% Syntax : Number of formulae : 182 ( 8 unt; 27 typ; 0 def)
% Number of atoms : 2028 ( 0 equ; 7 cnn)
% Maximal formula atoms : 70 ( 13 avg)
% Number of connectives : 7781 ( 195 ~; 442 |; 477 &;4660 @)
% ( 0 <=>; 704 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 14 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 515 ( 515 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 13 con; 0-2 aty)
% (1303 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1547 (1311 ^; 236 !; 0 ?;1547 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf('#sk4_type',type,
'#sk4': a ).
thf('#sk367_type',type,
'#sk367': ( a > a > $o ) > a ).
thf('#form14_type',type,
'#form14': $o ).
thf('#sk79_type',type,
'#sk79': ( a > a > $o ) > a ).
thf('#sk3_type',type,
'#sk3': a ).
thf('#sk66_type',type,
'#sk66': ( a > a > $o ) > a ).
thf('#sk162_type',type,
'#sk162': ( a > a > $o ) > a ).
thf('#sk35_type',type,
'#sk35': a ).
thf('#sk315_type',type,
'#sk315': ( a > a > $o ) > a ).
thf('#sk221_type',type,
'#sk221': ( a > a > $o ) > a ).
thf('#sk306_type',type,
'#sk306': ( a > a > $o ) > a ).
thf('#sk53_type',type,
'#sk53': ( a > a > $o ) > a ).
thf('#sk2_type',type,
'#sk2': a > a > $o ).
thf('#sk375_type',type,
'#sk375': ( a > a > $o ) > a ).
thf('#form88_type',type,
'#form88': $o ).
thf('#sk25_type',type,
'#sk25': a ).
thf('#sk36_type',type,
'#sk36': a ).
thf('#form193_type',type,
'#form193': ( a > a > $o ) > $o ).
thf('#sk5_type',type,
'#sk5': a > a > $o ).
thf('#sk15_type',type,
'#sk15': a ).
thf('#sk26_type',type,
'#sk26': a ).
thf('#sk54_type',type,
'#sk54': a > a > $o ).
thf('#sk1_type',type,
'#sk1': a > a > $o ).
thf('#sk55_type',type,
'#sk55': a > a > $o ).
thf('#form24_type',type,
'#form24': $o ).
thf('#form161_type',type,
'#form161': ( a > a > $o ) > $o ).
thf(cTHM250H_pme,conjecture,
! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xy0 @ Xz )
& ( Xp1 @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xz ) )
& ! [Xx0: a,Xy0: a] :
( ( ( S @ Xx0 @ Xy0 )
| ( R @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ( Xp1 @ Xx @ Xy ) )
| ( ~ ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xy0 @ Xz )
& ( Xp1 @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xz ) )
& ! [Xx0: a,Xy0: a] :
( ( ( S @ Xx0 @ Xy0 )
| ( R @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ( Xp1 @ Xx @ Xy ) )
& ! [Xx0: a,Xy0: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( S @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) )
| ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( R @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xy0 @ Xz ) )
& ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xz ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xy0 @ Xz )
& ( Xp1 @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xz ) )
& ! [Xx0: a,Xy0: a] :
( ( ( S @ Xx0 @ Xy0 )
| ( R @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ( Xp1 @ Xx @ Xy ) )
| ( ~ ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xy0 @ Xz )
& ( Xp1 @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xz ) )
& ! [Xx0: a,Xy0: a] :
( ( ( S @ Xx0 @ Xy0 )
| ( R @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ( Xp1 @ Xx @ Xy ) )
& ! [Xx0: a,Xy0: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( S @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) )
| ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( R @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xy0 @ Xz ) )
& ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xz ) ) ) ) ),
inference('cnf.neg',[status(esa)],[cTHM250H_pme]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( !!
@ ^ [Y1: a > a > $o] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( ( (~)
@ ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( !!
@ ^ [Y7: a > a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( !!
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
& ( !!
@ ^ [Y7: a > a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( !!
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) ) )
=> ( !!
@ ^ [Y7: a > a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( !!
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( ( (~)
@ ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( '#sk1' @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
& ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y4 ) ) ) )
=> ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( ( (~)
@ ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( '#sk2' @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( '#sk1' @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
& ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y3 ) ) ) )
=> ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: a] :
( ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk3' @ Y0 ) ) )
| ( ( (~)
@ ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk3' @ Y0 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( '#sk2' @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
& ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
~ ( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( ( (~)
@ ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl6,plain,
~ ( ( (~)
@ ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl8,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl11,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk3' @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl11_001,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk3' @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl17,plain,
( '#form14'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl19,plain,
! [X2: a > a > $o] :
( ~ '#form14'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk3' @ '#sk4' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl11,zip_derived_cl17]) ).
thf(zip_derived_cl22,plain,
( '#form24'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl23,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk25' @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk25' @ Y0 ) ) ) )
=> ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk25' @ Y0 ) ) ) ) )
| '#form24' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl29,plain,
( ~ ( ( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk2' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk25' @ '#sk35' ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk25' @ '#sk35' ) ) ) )
=> ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk25' @ '#sk35' ) ) ) )
| '#form24' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl35,plain,
( ~ ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk25' @ '#sk35' ) ) )
| '#form24' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl44,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk54' @ Y1 @ Y2 )
& ( '#sk54' @ Y0 @ Y1 ) )
=> ( '#sk54' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk54' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk54' @ '#sk25' @ '#sk35' ) )
| '#form24' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl58,plain,
( ~ ( '#sk54' @ '#sk25' @ '#sk35' )
| '#form24' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl34,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk2' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk25' @ '#sk35' ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk25' @ '#sk35' ) ) )
| '#form24' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl42,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk2' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk25' @ '#sk35' ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk25' @ '#sk35' ) ) )
| '#form24' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl51,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk25' @ '#sk35' ) )
| '#form24'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk25' @ '#sk35' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl74,plain,
( ~ '#form88'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk25' @ '#sk35' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl75,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk25' @ '#sk35' ) )
| ~ '#form88' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl91,plain,
! [X2: a > a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
| ( X2 @ '#sk25' @ '#sk35' )
| ~ '#form88' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl103,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) )
| ~ '#form88'
| ( X2 @ '#sk25' @ '#sk35' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl17_002,plain,
( '#form14'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl18,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
& ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ '#sk15' @ Y0 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ '#sk15' @ Y1 ) ) ) ) ) )
| '#form14' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl25,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk26' @ Y0 ) ) )
& ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk15' @ '#sk26' ) ) ) )
=> ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk15' @ Y0 ) ) ) ) )
| '#form14' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl30,plain,
( ~ ( ( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk26' @ '#sk36' ) ) )
& ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk15' @ '#sk26' ) ) ) )
=> ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk15' @ '#sk36' ) ) ) )
| '#form14' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl36,plain,
( ( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk26' @ '#sk36' ) ) )
& ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk15' @ '#sk26' ) ) ) )
| '#form14' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl45,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk26' @ '#sk36' ) ) )
| '#form14' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl59,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk26' @ '#sk36' ) )
| '#form14' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl84,plain,
! [X2: a > a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
| ( X2 @ '#sk26' @ '#sk36' )
| '#form14' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl94,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) )
| '#form14'
| ( X2 @ '#sk26' @ '#sk36' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl106,plain,
! [X2: a > a > $o] :
( ( '#form193' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl117,plain,
! [X2: a > a > $o] :
( ~ ( '#form193'
@ ^ [Y0: a,Y1: a] : ( X2 @ Y0 @ Y1 ) )
| ( X2 @ '#sk25' @ '#sk35' )
| ~ '#form88'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl103,zip_derived_cl106]) ).
thf(zip_derived_cl130,plain,
! [X2: a > a > $o] :
( ~ ( '#form193' @ X2 )
| ( X2 @ '#sk25' @ '#sk35' )
| ~ '#form88'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl117]) ).
thf(zip_derived_cl131,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk315' @ X2 ) @ Y0 )
=> ( X2 @ ( '#sk315' @ X2 ) @ Y0 ) ) )
| ~ '#form88'
| ( X2 @ '#sk25' @ '#sk35' )
| ~ ( '#form193' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl130]) ).
thf(zip_derived_cl143,plain,
! [X2: a > a > $o] :
( ~ ( ( '#sk1' @ ( '#sk315' @ X2 ) @ ( '#sk375' @ X2 ) )
=> ( X2 @ ( '#sk315' @ X2 ) @ ( '#sk375' @ X2 ) ) )
| ~ ( '#form193' @ X2 )
| ( X2 @ '#sk25' @ '#sk35' )
| ~ '#form88' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl131]) ).
thf(zip_derived_cl150,plain,
! [X2: a > a > $o] :
( ( '#sk1' @ ( '#sk315' @ X2 ) @ ( '#sk375' @ X2 ) )
| ~ '#form88'
| ( X2 @ '#sk25' @ '#sk35' )
| ~ ( '#form193' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl143]) ).
thf(zip_derived_cl57,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk54' @ Y1 @ Y2 )
& ( '#sk54' @ Y0 @ Y1 ) )
=> ( '#sk54' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk54' @ Y0 @ Y1 ) ) ) ) )
| '#form24' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl83,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk54' @ Y0 @ Y1 ) ) ) )
| '#form24' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl93,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
=> ( '#sk54' @ X2 @ Y0 ) ) )
| '#form24' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl105,plain,
! [X2: a,X4: a] :
( ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk54' @ X2 @ X4 ) )
| '#form24' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl119,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ( '#sk54' @ X2 @ X4 )
| '#form24' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl134,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| '#form24'
| ( '#sk54' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl119]) ).
thf(zip_derived_cl151,plain,
! [X2: a > a > $o] :
( ~ ( X2 @ ( '#sk315' @ X2 ) @ ( '#sk375' @ X2 ) )
| ~ '#form88'
| ( X2 @ '#sk25' @ '#sk35' )
| ~ ( '#form193' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl143]) ).
thf(zip_derived_cl37,plain,
( ~ ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk15' @ '#sk36' ) ) )
| '#form14' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl48,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk55' @ Y1 @ Y2 )
& ( '#sk55' @ Y0 @ Y1 ) )
=> ( '#sk55' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk55' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk55' @ '#sk15' @ '#sk36' ) )
| '#form14' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl72,plain,
( ~ ( '#sk55' @ '#sk15' @ '#sk36' )
| '#form14' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl51_003,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk25' @ '#sk35' ) )
| '#form24'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk25' @ '#sk35' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl53,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk54' @ Y1 @ Y2 )
& ( '#sk54' @ Y0 @ Y1 ) )
=> ( '#sk54' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk54' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk54' @ '#sk25' @ '#sk35' ) )
| '#form24'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk25' @ '#sk35' ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl74_004,plain,
( ~ '#form88'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk25' @ '#sk35' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl265,plain,
( '#form88'
| '#form24'
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk54' @ Y1 @ Y2 )
& ( '#sk54' @ Y0 @ Y1 ) )
=> ( '#sk54' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk54' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk54' @ '#sk25' @ '#sk35' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl53,zip_derived_cl74]) ).
thf(zip_derived_cl266,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk54' @ Y1 @ Y2 )
& ( '#sk54' @ Y0 @ Y1 ) )
=> ( '#sk54' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk54' @ Y0 @ Y1 ) ) ) ) )
| ( '#sk54' @ '#sk25' @ '#sk35' )
| '#form24'
| '#form88' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl265]) ).
thf(zip_derived_cl58_005,plain,
( ~ ( '#sk54' @ '#sk25' @ '#sk35' )
| '#form24' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl267,plain,
( '#form88'
| '#form24'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk54' @ Y1 @ Y2 )
& ( '#sk54' @ Y0 @ Y1 ) )
=> ( '#sk54' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk54' @ Y0 @ Y1 ) ) ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl266,zip_derived_cl58]) ).
thf(zip_derived_cl268,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk54' @ Y1 @ Y2 )
& ( '#sk54' @ Y0 @ Y1 ) )
=> ( '#sk54' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk54' @ Y0 @ Y1 ) ) ) )
| '#form24'
| '#form88' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl267]) ).
thf(zip_derived_cl106_006,plain,
! [X2: a > a > $o] :
( ( '#form193' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl269,plain,
( ~ ( '#form193' @ '#sk54' )
| '#form88'
| '#form24'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk54' @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl268,zip_derived_cl106]) ).
thf(zip_derived_cl270,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk306' @ '#sk54' ) @ Y0 )
=> ( '#sk54' @ ( '#sk306' @ '#sk54' ) @ Y0 ) ) )
| '#form24'
| '#form88'
| ~ ( '#form193' @ '#sk54' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl269]) ).
thf(zip_derived_cl271,plain,
( ~ ( ( '#sk2' @ ( '#sk306' @ '#sk54' ) @ ( '#sk367' @ '#sk54' ) )
=> ( '#sk54' @ ( '#sk306' @ '#sk54' ) @ ( '#sk367' @ '#sk54' ) ) )
| ~ ( '#form193' @ '#sk54' )
| '#form88'
| '#form24' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl270]) ).
thf(zip_derived_cl273,plain,
( ~ ( '#sk54' @ ( '#sk306' @ '#sk54' ) @ ( '#sk367' @ '#sk54' ) )
| '#form24'
| '#form88'
| ~ ( '#form193' @ '#sk54' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl271]) ).
thf(zip_derived_cl272,plain,
( ( '#sk2' @ ( '#sk306' @ '#sk54' ) @ ( '#sk367' @ '#sk54' ) )
| '#form24'
| '#form88'
| ~ ( '#form193' @ '#sk54' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl271]) ).
thf(zip_derived_cl11_007,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk3' @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl12,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk5' @ '#sk3' @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl5,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl7,plain,
~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk5' @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl10,plain,
~ ( '#sk5' @ '#sk3' @ '#sk4' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl175,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
=> $false )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl12,zip_derived_cl10]) ).
thf(zip_derived_cl176,plain,
( ( (~)
@ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl175]) ).
thf(zip_derived_cl177,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl176]) ).
thf(zip_derived_cl17_008,plain,
( '#form14'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl178,plain,
( ~ '#form14'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl177,zip_derived_cl17]) ).
thf(zip_derived_cl22_009,plain,
( '#form24'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl179,plain,
( ~ '#form24'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
| ~ '#form14' ),
inference(renaming,[status(thm)],[zip_derived_cl178,zip_derived_cl22]) ).
thf(zip_derived_cl180,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
| ~ '#form14'
| ~ '#form24' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl179]) ).
thf(zip_derived_cl106_010,plain,
! [X2: a > a > $o] :
( ( '#form193' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl181,plain,
( ~ ( '#form193' @ '#sk5' )
| ~ '#form24'
| ~ '#form14'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl180,zip_derived_cl106]) ).
thf(zip_derived_cl19_011,plain,
! [X2: a > a > $o] :
( ~ '#form14'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk3' @ '#sk4' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl11,zip_derived_cl17]) ).
thf(zip_derived_cl22_012,plain,
( '#form24'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl24,plain,
! [X2: a > a > $o] :
( ~ '#form24'
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk3' @ '#sk4' ) )
| ~ '#form14' ),
inference(renaming,[status(thm)],[zip_derived_cl19,zip_derived_cl22]) ).
thf(zip_derived_cl28,plain,
! [X2: a > a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
| ( X2 @ '#sk3' @ '#sk4' )
| ~ '#form14'
| ~ '#form24' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl33,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) )
| ~ '#form24'
| ~ '#form14'
| ( X2 @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl41,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( X2 @ Y0 @ Y1 )
& ( X2 @ ( '#sk53' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk53' @ X2 ) @ Y1 ) ) ) )
| ( X2 @ '#sk3' @ '#sk4' )
| ~ '#form14'
| ~ '#form24'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl50,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk66' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk53' @ X2 ) @ ( '#sk66' @ X2 ) ) )
=> ( X2 @ ( '#sk53' @ X2 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) )
| ~ '#form24'
| ~ '#form14'
| ( X2 @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl73,plain,
! [X2: a > a > $o] :
( ~ ( ( ( X2 @ ( '#sk66' @ X2 ) @ ( '#sk79' @ X2 ) )
& ( X2 @ ( '#sk53' @ X2 ) @ ( '#sk66' @ X2 ) ) )
=> ( X2 @ ( '#sk53' @ X2 ) @ ( '#sk79' @ X2 ) ) )
| ( X2 @ '#sk3' @ '#sk4' )
| ~ '#form14'
| ~ '#form24'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl88,plain,
! [X2: a > a > $o] :
( ( ( X2 @ ( '#sk66' @ X2 ) @ ( '#sk79' @ X2 ) )
& ( X2 @ ( '#sk53' @ X2 ) @ ( '#sk66' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) )
| ~ '#form24'
| ~ '#form14'
| ( X2 @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl98,plain,
! [X2: a > a > $o] :
( ( '#form161' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl182,plain,
( ~ ( '#form161' @ '#sk5' )
| ~ '#form14'
| ~ '#form24'
| ~ ( '#form193' @ '#sk5' ) ),
inference(renaming,[status(thm)],[zip_derived_cl181,zip_derived_cl98]) ).
thf(zip_derived_cl133,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| '#form24'
| ( '#sk54' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl119]) ).
thf(zip_derived_cl94_013,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) )
| '#form14'
| ( X2 @ '#sk26' @ '#sk36' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl106_014,plain,
! [X2: a > a > $o] :
( ( '#form193' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl108,plain,
! [X2: a > a > $o] :
( ~ ( '#form193' @ X2 )
| ( X2 @ '#sk26' @ '#sk36' )
| '#form14'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl94,zip_derived_cl106]) ).
thf(zip_derived_cl98_015,plain,
! [X2: a > a > $o] :
( ( '#form161' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl120,plain,
! [X2: a > a > $o] :
( ~ ( '#form161'
@ ^ [Y0: a,Y1: a] : ( X2 @ Y0 @ Y1 ) )
| '#form14'
| ( X2 @ '#sk26' @ '#sk36' )
| ~ ( '#form193' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl108,zip_derived_cl98]) ).
thf(zip_derived_cl135,plain,
! [X2: a > a > $o] :
( ~ ( '#form161' @ X2 )
| '#form14'
| ( X2 @ '#sk26' @ '#sk36' )
| ~ ( '#form193' @ X2 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl120]) ).
thf(zip_derived_cl82,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk54' @ Y1 @ Y2 )
& ( '#sk54' @ Y0 @ Y1 ) )
=> ( '#sk54' @ Y0 @ Y2 ) ) ) ) )
| '#form24' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl92,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk54' @ Y0 @ Y1 )
& ( '#sk54' @ X2 @ Y0 ) )
=> ( '#sk54' @ X2 @ Y1 ) ) ) )
| '#form24' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl104,plain,
! [X2: a,X4: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk54' @ X4 @ Y0 )
& ( '#sk54' @ X2 @ X4 ) )
=> ( '#sk54' @ X2 @ Y0 ) ) )
| '#form24' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl118,plain,
! [X2: a,X4: a,X6: a] :
( ( ( ( '#sk54' @ X4 @ X6 )
& ( '#sk54' @ X2 @ X4 ) )
=> ( '#sk54' @ X2 @ X6 ) )
| '#form24' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl132,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( '#sk54' @ X4 @ X6 )
& ( '#sk54' @ X2 @ X4 ) )
| ( '#sk54' @ X2 @ X6 )
| '#form24' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl118]) ).
thf(zip_derived_cl144,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk54' @ X4 @ X6 )
| ~ ( '#sk54' @ X2 @ X4 )
| '#form24'
| ( '#sk54' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl132]) ).
thf(zip_derived_cl106_016,plain,
! [X2: a > a > $o] :
( ( '#form193' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl107,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( X2 @ Y0 @ Y1 )
& ( X2 @ ( '#sk53' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk53' @ X2 ) @ Y1 ) ) ) )
| ( '#form193' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl121,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk66' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk53' @ X2 ) @ ( '#sk66' @ X2 ) ) )
=> ( X2 @ ( '#sk53' @ X2 ) @ Y0 ) ) )
| ( '#form193' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl136,plain,
! [X2: a > a > $o] :
( ~ ( ( ( X2 @ ( '#sk66' @ X2 ) @ ( '#sk79' @ X2 ) )
& ( X2 @ ( '#sk53' @ X2 ) @ ( '#sk66' @ X2 ) ) )
=> ( X2 @ ( '#sk53' @ X2 ) @ ( '#sk79' @ X2 ) ) )
| ( '#form193' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl145,plain,
! [X2: a > a > $o] :
( ( ( X2 @ ( '#sk66' @ X2 ) @ ( '#sk79' @ X2 ) )
& ( X2 @ ( '#sk53' @ X2 ) @ ( '#sk66' @ X2 ) ) )
| ( '#form193' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl136]) ).
thf(zip_derived_cl152,plain,
! [X2: a > a > $o] :
( ( X2 @ ( '#sk66' @ X2 ) @ ( '#sk79' @ X2 ) )
| ( '#form193' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl145]) ).
thf(zip_derived_cl98_017,plain,
! [X2: a > a > $o] :
( ( '#form161' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl99,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ ( '#sk162' @ X2 ) @ Y0 )
| ( '#sk1' @ ( '#sk162' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk162' @ X2 ) @ Y0 ) ) )
| ( '#form161' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl98]) ).
thf(zip_derived_cl114,plain,
! [X2: a > a > $o] :
( ~ ( ( ( '#sk2' @ ( '#sk162' @ X2 ) @ ( '#sk221' @ X2 ) )
| ( '#sk1' @ ( '#sk162' @ X2 ) @ ( '#sk221' @ X2 ) ) )
=> ( X2 @ ( '#sk162' @ X2 ) @ ( '#sk221' @ X2 ) ) )
| ( '#form161' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl126,plain,
! [X2: a > a > $o] :
( ( '#sk2' @ ( '#sk162' @ X2 ) @ ( '#sk221' @ X2 ) )
| ( '#sk1' @ ( '#sk162' @ X2 ) @ ( '#sk221' @ X2 ) )
| ( '#form161' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl141,plain,
! [X2: a > a > $o] :
( ( '#sk2' @ ( '#sk162' @ X2 ) @ ( '#sk221' @ X2 ) )
| ( '#sk1' @ ( '#sk162' @ X2 ) @ ( '#sk221' @ X2 ) )
| ( '#form161' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl126]) ).
thf(zip_derived_cl46,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk15' @ '#sk26' ) ) )
| '#form14' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl65,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk15' @ '#sk26' ) )
| '#form14' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl85,plain,
! [X2: a > a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
| ( X2 @ '#sk15' @ '#sk26' )
| '#form14' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl95,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) )
| '#form14'
| ( X2 @ '#sk15' @ '#sk26' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl106_018,plain,
! [X2: a > a > $o] :
( ( '#form193' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl109,plain,
! [X2: a > a > $o] :
( ~ ( '#form193'
@ ^ [Y0: a,Y1: a] : ( X2 @ Y0 @ Y1 ) )
| ( X2 @ '#sk15' @ '#sk26' )
| '#form14'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl95,zip_derived_cl106]) ).
thf(zip_derived_cl122,plain,
! [X2: a > a > $o] :
( ~ ( '#form193' @ X2 )
| ( X2 @ '#sk15' @ '#sk26' )
| '#form14'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl98_019,plain,
! [X2: a > a > $o] :
( ( '#form161' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123,plain,
! [X2: a > a > $o] :
( ~ ( '#form161'
@ ^ [Y0: a,Y1: a] : ( X2 @ Y0 @ Y1 ) )
| '#form14'
| ( X2 @ '#sk15' @ '#sk26' )
| ~ ( '#form193' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl122,zip_derived_cl98]) ).
thf(zip_derived_cl137,plain,
! [X2: a > a > $o] :
( ~ ( '#form161' @ X2 )
| '#form14'
| ( X2 @ '#sk15' @ '#sk26' )
| ~ ( '#form193' @ X2 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl123]) ).
thf(zip_derived_cl9,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl16,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl21,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
=> ( '#sk5' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl27,plain,
! [X2: a,X4: a] :
( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl32,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl40,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl39,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl153,plain,
! [X2: a > a > $o] :
( ( X2 @ ( '#sk53' @ X2 ) @ ( '#sk66' @ X2 ) )
| ( '#form193' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl145]) ).
thf(zip_derived_cl146,plain,
! [X2: a > a > $o] :
( ~ ( X2 @ ( '#sk53' @ X2 ) @ ( '#sk79' @ X2 ) )
| ( '#form193' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl136]) ).
thf(zip_derived_cl15,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl20,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk5' @ Y0 @ Y1 )
& ( '#sk5' @ X2 @ Y0 ) )
=> ( '#sk5' @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl26,plain,
! [X2: a,X4: a] :
( !!
@ ^ [Y0: a] :
( ( ( '#sk5' @ X4 @ Y0 )
& ( '#sk5' @ X2 @ X4 ) )
=> ( '#sk5' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl31,plain,
! [X2: a,X4: a,X6: a] :
( ( ( '#sk5' @ X4 @ X6 )
& ( '#sk5' @ X2 @ X4 ) )
=> ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl38,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( '#sk5' @ X4 @ X6 )
& ( '#sk5' @ X2 @ X4 ) )
| ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl49,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk5' @ X4 @ X6 )
| ~ ( '#sk5' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl71,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk55' @ Y1 @ Y2 )
& ( '#sk55' @ Y0 @ Y1 ) )
=> ( '#sk55' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk55' @ Y0 @ Y1 ) ) ) ) )
| '#form14' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl86,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk55' @ Y1 @ Y2 )
& ( '#sk55' @ Y0 @ Y1 ) )
=> ( '#sk55' @ Y0 @ Y2 ) ) ) ) )
| '#form14' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl96,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk55' @ Y0 @ Y1 )
& ( '#sk55' @ X2 @ Y0 ) )
=> ( '#sk55' @ X2 @ Y1 ) ) ) )
| '#form14' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl110,plain,
! [X2: a,X4: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk55' @ X4 @ Y0 )
& ( '#sk55' @ X2 @ X4 ) )
=> ( '#sk55' @ X2 @ Y0 ) ) )
| '#form14' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl124,plain,
! [X2: a,X4: a,X6: a] :
( ( ( ( '#sk55' @ X4 @ X6 )
& ( '#sk55' @ X2 @ X4 ) )
=> ( '#sk55' @ X2 @ X6 ) )
| '#form14' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl138,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( '#sk55' @ X4 @ X6 )
& ( '#sk55' @ X2 @ X4 ) )
| ( '#sk55' @ X2 @ X6 )
| '#form14' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl124]) ).
thf(zip_derived_cl147,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk55' @ X4 @ X6 )
| ~ ( '#sk55' @ X2 @ X4 )
| '#form14'
| ( '#sk55' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl138]) ).
thf(zip_derived_cl87,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk55' @ Y0 @ Y1 ) ) ) )
| '#form14' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl97,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
=> ( '#sk55' @ X2 @ Y0 ) ) )
| '#form14' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl111,plain,
! [X2: a,X4: a] :
( ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk55' @ X2 @ X4 ) )
| '#form14' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl125,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ( '#sk55' @ X2 @ X4 )
| '#form14' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl140,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| '#form14'
| ( '#sk55' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl125]) ).
thf(zip_derived_cl139,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| '#form14'
| ( '#sk55' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl125]) ).
thf(zip_derived_cl127,plain,
! [X2: a > a > $o] :
( ~ ( X2 @ ( '#sk162' @ X2 ) @ ( '#sk221' @ X2 ) )
| ( '#form161' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl7591,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl58,zip_derived_cl150,zip_derived_cl134,zip_derived_cl151,zip_derived_cl72,zip_derived_cl273,zip_derived_cl272,zip_derived_cl182,zip_derived_cl133,zip_derived_cl135,zip_derived_cl144,zip_derived_cl152,zip_derived_cl141,zip_derived_cl137,zip_derived_cl40,zip_derived_cl39,zip_derived_cl153,zip_derived_cl146,zip_derived_cl49,zip_derived_cl147,zip_derived_cl140,zip_derived_cl139,zip_derived_cl127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEV156^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.XRKNuixuxX true
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 03:36:17 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.22/0.36 % Python version: Python 3.6.8
% 0.22/0.37 % Running in HO mode
% 0.23/0.67 % Total configuration time : 828
% 0.23/0.67 % Estimated wc time : 1656
% 0.23/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.23/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.23/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.23/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.23/0.79 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.98/0.81 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.98/0.81 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.98/0.81 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.98/0.81 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 49.57/7.12 % Solved by lams/20_acsne_simpl.sh.
% 49.57/7.12 % done 834 iterations in 6.148s
% 49.57/7.12 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 49.57/7.12 % SZS output start Refutation
% See solution above
% 49.57/7.13
% 49.57/7.13
% 49.57/7.13 % Terminating...
% 49.57/7.18 % Runner terminated.
% 49.57/7.19 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------