%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV155^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.OiYWMnQwbv true
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:57:16 PM UTC 2025
% Result : Theorem 63.33s 8.61s
% Output : Refutation 63.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 27
% Syntax : Number of formulae : 181 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 2173 ( 0 equ; 1 cnn)
% Maximal formula atoms : 69 ( 12 avg)
% Number of connectives : 8231 ( 235 ~; 513 |; 488 &;4899 @)
% ( 0 <=>; 747 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 14 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 498 ( 498 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 13 con; 0-2 aty)
% (1349 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1595 (1353 ^; 242 !; 0 ?;1595 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf('#sk4_type',type,
'#sk4': a ).
thf('#sk430_type',type,
'#sk430': ( a > a > $o ) > a ).
thf('#sk30_type',type,
'#sk30': a > a > $o ).
thf('#sk3_type',type,
'#sk3': a ).
thf('#sk12_type',type,
'#sk12': a ).
thf('#form290_type',type,
'#form290': ( a > a > $o ) > $o ).
thf('#sk21_type',type,
'#sk21': a > a > $o ).
thf('#form100_type',type,
'#form100': ( a > a > $o ) > $o ).
thf('#sk101_type',type,
'#sk101': ( a > a > $o ) > a ).
thf('#sk47_type',type,
'#sk47': ( a > a > $o ) > a ).
thf('#sk6_type',type,
'#sk6': a ).
thf('#sk2_type',type,
'#sk2': a > a > $o ).
thf('#form269_type',type,
'#form269': ( a > a > $o ) > $o ).
thf('#sk8_type',type,
'#sk8': a ).
thf('#sk10_type',type,
'#sk10': a ).
thf('#sk7_type',type,
'#sk7': a ).
thf('#form91_type',type,
'#form91': $o ).
thf('#sk74_type',type,
'#sk74': ( a > a > $o ) > a ).
thf('#form9_type',type,
'#form9': $o ).
thf('#sk155_type',type,
'#sk155': ( a > a > $o ) > a ).
thf('#sk410_type',type,
'#sk410': ( a > a > $o ) > a ).
thf('#form11_type',type,
'#form11': $o ).
thf('#sk339_type',type,
'#sk339': ( a > a > $o ) > a ).
thf('#sk5_type',type,
'#sk5': a > a > $o ).
thf('#sk1_type',type,
'#sk1': a > a > $o ).
thf('#sk180_type',type,
'#sk180': ( a > a > $o ) > a ).
thf('#sk358_type',type,
'#sk358': ( a > a > $o ) > a ).
thf(cTHM250D_pme,conjecture,
! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xy0 @ Xz ) )
& ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xz ) ) )
& ! [Xx0: a,Xy0: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( S @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) )
| ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( R @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xy0 @ Xz )
& ( Xp1 @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xz ) )
& ! [Xx0: a,Xy0: a] :
( ( ( S @ Xx0 @ Xy0 )
| ( R @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ( Xp1 @ Xx @ Xy ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xy0 @ Xz )
& ( Xp1 @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xz ) )
& ! [Xx0: a,Xy0: a] :
( ( ( S @ Xx0 @ Xy0 )
| ( R @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ( Xp1 @ Xx @ Xy ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xy0 @ Xz ) )
& ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz0: a] :
( ( ( Xp1 @ Xy1 @ Xz0 )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz0 ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xz ) ) )
& ! [Xx0: a,Xy0: a] :
( ( ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( S @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) )
| ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( R @ Xx1 @ Xy1 )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx1: a,Xy1: a,Xz: a] :
( ( ( Xp1 @ Xy1 @ Xz )
& ( Xp1 @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xz ) )
& ! [Xx1: a,Xy1: a] :
( ( ( S @ Xx1 @ Xy1 )
| ( R @ Xx1 @ Xy1 ) )
=> ( Xp1 @ Xx1 @ Xy1 ) ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xy0 @ Xz )
& ( Xp1 @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xz ) )
& ! [Xx0: a,Xy0: a] :
( ( ( S @ Xx0 @ Xy0 )
| ( R @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ( Xp1 @ Xx @ Xy ) ) )
=> ! [Xp1: a > a > $o] :
( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xy0 @ Xz )
& ( Xp1 @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xz ) )
& ! [Xx0: a,Xy0: a] :
( ( ( S @ Xx0 @ Xy0 )
| ( R @ Xx0 @ Xy0 ) )
=> ( Xp1 @ Xx0 @ Xy0 ) ) )
=> ( Xp1 @ Xx @ Xy ) ) ),
inference('cnf.neg',[status(esa)],[cTHM250D_pme]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( !!
@ ^ [Y1: a > a > $o] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( !!
@ ^ [Y7: a > a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( !!
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
& ( !!
@ ^ [Y7: a > a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( !!
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y5 ) ) ) )
=> ( !!
@ ^ [Y7: a > a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( !!
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y10 )
& ( Y7 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
& ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y4 ) ) ) )
=> ( !!
@ ^ [Y6: a > a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y9 )
& ( Y6 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( '#sk1' @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y0 @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
& ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y3 ) ) ) )
=> ( !!
@ ^ [Y5: a > a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( '#sk2' @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( '#sk1' @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: a] :
( ( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
& ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y4: a > a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( '#sk2' @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk3' @ Y0 ) ) ) )
=> ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk3' @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
~ ( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) )
=> ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl5,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl7,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl9,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl12,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
& ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ '#sk6' @ Y0 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ '#sk6' @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl15,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk7' @ Y0 ) ) )
& ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk6' @ '#sk7' ) ) ) )
=> ( !!
@ ^ [Y1: a > a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ '#sk6' @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl18,plain,
( ~ ( ( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk7' @ '#sk8' ) ) )
& ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk7' ) ) ) )
=> ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk8' ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21,plain,
( ( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk7' @ '#sk8' ) ) )
& ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk7' ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl25,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk7' @ '#sk8' ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl25_001,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk7' @ '#sk8' ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl33,plain,
( ~ '#form11'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl38,plain,
( '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk7' @ '#sk8' ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl25,zip_derived_cl33]) ).
thf(zip_derived_cl22,plain,
( ~ ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk8' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl27,plain,
( '#form9'
| ~ ( !!
@ ^ [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_cl43,plain,
( ~ '#form9'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk7' @ '#sk8' ) ) )
| '#form11' ),
inference(renaming,[status(thm)],[zip_derived_cl38,zip_derived_cl27]) ).
thf(zip_derived_cl50,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk7' @ '#sk8' ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl68,plain,
! [X2: a > a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
| ( X2 @ '#sk7' @ '#sk8' )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl81,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 ) ) ) )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk7' @ '#sk8' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl81_002,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 ) ) ) )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk7' @ '#sk8' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl96,plain,
! [X2: a > a > $o] :
( ( '#form100' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl98,plain,
! [X2: a > a > $o] :
( ~ ( '#form100' @ X2 )
| ( X2 @ '#sk7' @ '#sk8' )
| ~ '#form9'
| '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl81,zip_derived_cl96]) ).
thf(zip_derived_cl107,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( X2 @ Y0 @ Y1 )
& ( X2 @ ( '#sk47' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk47' @ X2 ) @ Y1 ) ) ) )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk7' @ '#sk8' )
| ~ ( '#form100' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl98]) ).
thf(zip_derived_cl119,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk74' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk74' @ X2 ) ) )
=> ( X2 @ ( '#sk47' @ X2 ) @ Y0 ) ) )
| ~ ( '#form100' @ X2 )
| ( X2 @ '#sk7' @ '#sk8' )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl134,plain,
! [X2: a > a > $o] :
( ( '#form290' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk74' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk74' @ X2 ) ) )
=> ( X2 @ ( '#sk47' @ X2 ) @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl135,plain,
! [X2: a > a > $o] :
( ~ ( ( ( X2 @ ( '#sk74' @ X2 ) @ ( '#sk180' @ X2 ) )
& ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk74' @ X2 ) ) )
=> ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk180' @ X2 ) ) )
| ( '#form290' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl134]) ).
thf(zip_derived_cl149,plain,
! [X2: a > a > $o] :
( ( ( X2 @ ( '#sk74' @ X2 ) @ ( '#sk180' @ X2 ) )
& ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk74' @ X2 ) ) )
| ( '#form290' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl135]) ).
thf(zip_derived_cl156,plain,
! [X2: a > a > $o] :
( ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk74' @ X2 ) )
| ( '#form290' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl149]) ).
thf(zip_derived_cl50_003,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk7' @ '#sk8' ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl51,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk21' @ Y1 @ Y2 )
& ( '#sk21' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk21' @ '#sk7' @ '#sk8' ) )
| '#form11'
| ~ '#form9' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl218,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk21' @ Y1 @ Y2 )
& ( '#sk21' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y1 ) ) ) ) )
| ( '#sk21' @ '#sk7' @ '#sk8' )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl219,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk21' @ Y1 @ Y2 )
& ( '#sk21' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y1 ) ) ) )
| '#form11'
| ~ '#form9'
| ( '#sk21' @ '#sk7' @ '#sk8' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl218]) ).
thf(zip_derived_cl27_004,plain,
( '#form9'
| ~ ( !!
@ ^ [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_cl28,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 @ '#sk10' @ 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 @ '#sk10' @ 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 @ '#sk10' @ Y0 ) ) ) ) )
| '#form9' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl41,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 @ '#sk10' @ '#sk12' ) ) )
| ( !!
@ ^ [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 @ '#sk10' @ '#sk12' ) ) ) )
=> ( !!
@ ^ [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 @ '#sk10' @ '#sk12' ) ) ) )
| '#form9' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl48,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 @ '#sk10' @ '#sk12' ) ) )
| ( !!
@ ^ [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 @ '#sk10' @ '#sk12' ) ) )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl63,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk2' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk10' @ '#sk12' ) ) )
| ( !!
@ ^ [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 @ '#sk10' @ '#sk12' ) ) )
| '#form9' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl73,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 @ '#sk10' @ '#sk12' ) )
| '#form9'
| ( !!
@ ^ [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 @ '#sk10' @ '#sk12' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl73_005,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 @ '#sk10' @ '#sk12' ) )
| '#form9'
| ( !!
@ ^ [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 @ '#sk10' @ '#sk12' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl86,plain,
( ~ '#form91'
| ( !!
@ ^ [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 @ '#sk10' @ '#sk12' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl93,plain,
! [X2: a > a > $o] :
( '#form91'
| '#form9'
| ( ( ( !!
@ ^ [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 @ '#sk10' @ '#sk12' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl73,zip_derived_cl86]) ).
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] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
| ( X2 @ '#sk10' @ '#sk12' )
| '#form9'
| '#form91' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl115,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 ) ) ) )
| '#form91'
| '#form9'
| ( X2 @ '#sk10' @ '#sk12' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl128,plain,
! [X2: a > a > $o] :
( ( '#form269' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl220,plain,
( ~ ( '#form269' @ '#sk21' )
| ( '#sk21' @ '#sk7' @ '#sk8' )
| ~ '#form9'
| '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl219,zip_derived_cl128]) ).
thf(zip_derived_cl96_006,plain,
! [X2: a > a > $o] :
( ( '#form100' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl221,plain,
( ~ ( '#form100' @ '#sk21' )
| '#form11'
| ~ '#form9'
| ( '#sk21' @ '#sk7' @ '#sk8' )
| ~ ( '#form269' @ '#sk21' ) ),
inference(renaming,[status(thm)],[zip_derived_cl220,zip_derived_cl96]) ).
thf(zip_derived_cl26,plain,
( ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk7' ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl33_007,plain,
( ~ '#form11'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl39,plain,
( '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk7' ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl26,zip_derived_cl33]) ).
thf(zip_derived_cl27_008,plain,
( '#form9'
| ~ ( !!
@ ^ [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_cl45,plain,
( ~ '#form9'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk7' ) ) )
| '#form11' ),
inference(renaming,[status(thm)],[zip_derived_cl39,zip_derived_cl27]) ).
thf(zip_derived_cl56,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk6' @ '#sk7' ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl57,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk21' @ Y1 @ Y2 )
& ( '#sk21' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk21' @ '#sk6' @ '#sk7' ) )
| '#form11'
| ~ '#form9' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl273,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk21' @ Y1 @ Y2 )
& ( '#sk21' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y1 ) ) ) ) )
| ( '#sk21' @ '#sk6' @ '#sk7' )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl274,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk21' @ Y1 @ Y2 )
& ( '#sk21' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y1 ) ) ) )
| '#form11'
| ~ '#form9'
| ( '#sk21' @ '#sk6' @ '#sk7' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl273]) ).
thf(zip_derived_cl128_009,plain,
! [X2: a > a > $o] :
( ( '#form269' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl275,plain,
( ~ ( '#form269' @ '#sk21' )
| ( '#sk21' @ '#sk6' @ '#sk7' )
| ~ '#form9'
| '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl274,zip_derived_cl128]) ).
thf(zip_derived_cl96_010,plain,
! [X2: a > a > $o] :
( ( '#form100' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl276,plain,
( ~ ( '#form100' @ '#sk21' )
| '#form11'
| ~ '#form9'
| ( '#sk21' @ '#sk6' @ '#sk7' )
| ~ ( '#form269' @ '#sk21' ) ),
inference(renaming,[status(thm)],[zip_derived_cl275,zip_derived_cl96]) ).
thf(zip_derived_cl22_011,plain,
( ~ ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk8' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl27_012,plain,
( '#form9'
| ~ ( !!
@ ^ [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_cl29,plain,
( ~ '#form9'
| ( !!
@ ^ [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 @ '#sk6' @ '#sk8' ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl22,zip_derived_cl27]) ).
thf(zip_derived_cl33_013,plain,
( ~ '#form11'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl40,plain,
( '#form11'
| ~ ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk6' @ '#sk8' ) ) )
| ~ '#form9' ),
inference(renaming,[status(thm)],[zip_derived_cl29,zip_derived_cl33]) ).
thf(zip_derived_cl47,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk21' @ Y1 @ Y2 )
& ( '#sk21' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk21' @ '#sk6' @ '#sk8' ) )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl62,plain,
( ~ ( '#sk21' @ '#sk6' @ '#sk8' )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl119_014,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk74' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk74' @ X2 ) ) )
=> ( X2 @ ( '#sk47' @ X2 ) @ Y0 ) ) )
| ~ ( '#form100' @ X2 )
| ( X2 @ '#sk7' @ '#sk8' )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl134_015,plain,
! [X2: a > a > $o] :
( ( '#form290' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk74' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk74' @ X2 ) ) )
=> ( X2 @ ( '#sk47' @ X2 ) @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl136,plain,
! [X2: a > a > $o] :
( ~ ( '#form290' @ X2 )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk7' @ '#sk8' )
| ~ ( '#form100' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl119,zip_derived_cl134]) ).
thf(zip_derived_cl61,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk21' @ Y1 @ Y2 )
& ( '#sk21' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y1 ) ) ) ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl71,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk21' @ Y1 @ Y2 )
& ( '#sk21' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y2 ) ) ) ) )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl84,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk21' @ Y0 @ Y1 )
& ( '#sk21' @ X2 @ Y0 ) )
=> ( '#sk21' @ X2 @ Y1 ) ) ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl101,plain,
! [X2: a,X4: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk21' @ X4 @ Y0 )
& ( '#sk21' @ X2 @ X4 ) )
=> ( '#sk21' @ X2 @ Y0 ) ) )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl113,plain,
! [X2: a,X4: a,X6: a] :
( ( ( ( '#sk21' @ X4 @ X6 )
& ( '#sk21' @ X2 @ X4 ) )
=> ( '#sk21' @ X2 @ X6 ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl125,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( '#sk21' @ X4 @ X6 )
& ( '#sk21' @ X2 @ X4 ) )
| ( '#sk21' @ X2 @ X6 )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl141,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk21' @ X4 @ X6 )
| ~ ( '#sk21' @ X2 @ X4 )
| '#form11'
| ~ '#form9'
| ( '#sk21' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl125]) ).
thf(zip_derived_cl56_016,plain,
! [X2: a > a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ '#sk6' @ '#sk7' ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl70,plain,
! [X2: a > a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
| ( X2 @ '#sk6' @ '#sk7' )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl83,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 ) ) ) )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk6' @ '#sk7' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl96_017,plain,
! [X2: a > a > $o] :
( ( '#form100' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl100,plain,
! [X2: a > a > $o] :
( ~ ( '#form100'
@ ^ [Y0: a,Y1: a] : ( X2 @ Y0 @ Y1 ) )
| ( X2 @ '#sk6' @ '#sk7' )
| ~ '#form9'
| '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl83,zip_derived_cl96]) ).
thf(zip_derived_cl111,plain,
! [X2: a > a > $o] :
( ~ ( '#form100' @ X2 )
| ( X2 @ '#sk6' @ '#sk7' )
| ~ '#form9'
| '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl112,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( X2 @ Y0 @ Y1 )
& ( X2 @ ( '#sk47' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk47' @ X2 ) @ Y1 ) ) ) )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk6' @ '#sk7' )
| ~ ( '#form100' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl124,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk74' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk74' @ X2 ) ) )
=> ( X2 @ ( '#sk47' @ X2 ) @ Y0 ) ) )
| ~ ( '#form100' @ X2 )
| ( X2 @ '#sk6' @ '#sk7' )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl134_018,plain,
! [X2: a > a > $o] :
( ( '#form290' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk74' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk74' @ X2 ) ) )
=> ( X2 @ ( '#sk47' @ X2 ) @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl140,plain,
! [X2: a > a > $o] :
( ~ ( '#form290' @ X2 )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk6' @ '#sk7' )
| ~ ( '#form100' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl124,zip_derived_cl134]) ).
thf(zip_derived_cl72,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk21' @ Y0 @ Y1 ) ) ) )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl85,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
=> ( '#sk21' @ X2 @ Y0 ) ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl102,plain,
! [X2: a,X4: a] :
( ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk21' @ X2 @ X4 ) )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl114,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ( '#sk21' @ X2 @ X4 )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl127,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ~ '#form9'
| '#form11'
| ( '#sk21' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl126,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ~ '#form9'
| '#form11'
| ( '#sk21' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl33_019,plain,
( ~ '#form11'
| ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl34,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' ) )
| ~ '#form11' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl35,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' ) )
| ~ '#form11' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl34]) ).
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' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl8,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_cl6]) ).
thf(zip_derived_cl11,plain,
~ ( '#sk5' @ '#sk3' @ '#sk4' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl186,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 )
| ~ '#form11' ),
inference(demod,[status(thm)],[zip_derived_cl35,zip_derived_cl11]) ).
thf(zip_derived_cl187,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 ) ) ) ) ) )
| ~ '#form11' ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl186]) ).
thf(zip_derived_cl188,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 ) ) ) ) )
| ~ '#form11' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl187]) ).
thf(zip_derived_cl189,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 ) ) ) )
| ~ '#form11' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl188]) ).
thf(zip_derived_cl128_020,plain,
! [X2: a > a > $o] :
( ( '#form269' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl190,plain,
( ~ ( '#form269' @ '#sk5' )
| ~ '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl189,zip_derived_cl128]) ).
thf(zip_derived_cl96_021,plain,
! [X2: a > a > $o] :
( ( '#form100' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl191,plain,
( ~ ( '#form100' @ '#sk5' )
| ~ '#form11'
| ~ ( '#form269' @ '#sk5' ) ),
inference(renaming,[status(thm)],[zip_derived_cl190,zip_derived_cl96]) ).
thf(zip_derived_cl96_022,plain,
! [X2: a > a > $o] :
( ( '#form100' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl97,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ ( '#sk101' @ X2 ) @ Y0 )
| ( '#sk1' @ ( '#sk101' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk101' @ X2 ) @ Y0 ) ) )
| ( '#form100' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl108,plain,
! [X2: a > a > $o] :
( ~ ( ( ( '#sk2' @ ( '#sk101' @ X2 ) @ ( '#sk155' @ X2 ) )
| ( '#sk1' @ ( '#sk101' @ X2 ) @ ( '#sk155' @ X2 ) ) )
=> ( X2 @ ( '#sk101' @ X2 ) @ ( '#sk155' @ X2 ) ) )
| ( '#form100' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl120,plain,
! [X2: a > a > $o] :
( ( '#sk2' @ ( '#sk101' @ X2 ) @ ( '#sk155' @ X2 ) )
| ( '#sk1' @ ( '#sk101' @ X2 ) @ ( '#sk155' @ X2 ) )
| ( '#form100' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl137,plain,
! [X2: a > a > $o] :
( ( '#sk2' @ ( '#sk101' @ X2 ) @ ( '#sk155' @ X2 ) )
| ( '#sk1' @ ( '#sk101' @ X2 ) @ ( '#sk155' @ X2 ) )
| ( '#form100' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl120]) ).
thf(zip_derived_cl49,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 @ '#sk10' @ '#sk12' ) ) )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl67,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk30' @ Y1 @ Y2 )
& ( '#sk30' @ Y0 @ Y1 ) )
=> ( '#sk30' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk30' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk30' @ '#sk10' @ '#sk12' ) )
| '#form9' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl80,plain,
( ~ ( '#sk30' @ '#sk10' @ '#sk12' )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl79,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk30' @ Y1 @ Y2 )
& ( '#sk30' @ Y0 @ Y1 ) )
=> ( '#sk30' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk30' @ Y0 @ Y1 ) ) ) ) )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl95,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk30' @ Y0 @ Y1 ) ) ) )
| '#form9' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl106,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
=> ( '#sk30' @ X2 @ Y0 ) ) )
| '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl118,plain,
! [X2: a,X4: a] :
( ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk30' @ X2 @ X4 ) )
| '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl133,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ( '#sk30' @ X2 @ X4 )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl118]) ).
thf(zip_derived_cl148,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| '#form9'
| ( '#sk30' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl133]) ).
thf(zip_derived_cl86_023,plain,
( ~ '#form91'
| ( !!
@ ^ [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 @ '#sk10' @ '#sk12' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl87,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 @ '#sk10' @ '#sk12' ) )
| ~ '#form91' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl104,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 @ '#sk10' @ '#sk12' )
| ~ '#form91' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl116,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 ) ) ) )
| ~ '#form91'
| ( X2 @ '#sk10' @ '#sk12' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl128_024,plain,
! [X2: a > a > $o] :
( ( '#form269' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl131,plain,
! [X2: a > a > $o] :
( ~ ( '#form269'
@ ^ [Y0: a,Y1: a] : ( X2 @ Y0 @ Y1 ) )
| ( X2 @ '#sk10' @ '#sk12' )
| ~ '#form91'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl116,zip_derived_cl128]) ).
thf(zip_derived_cl144,plain,
! [X2: a > a > $o] :
( ~ ( '#form269' @ X2 )
| ( X2 @ '#sk10' @ '#sk12' )
| ~ '#form91'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl131]) ).
thf(zip_derived_cl145,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk358' @ X2 ) @ Y0 )
=> ( X2 @ ( '#sk358' @ X2 ) @ Y0 ) ) )
| ~ '#form91'
| ( X2 @ '#sk10' @ '#sk12' )
| ~ ( '#form269' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl144]) ).
thf(zip_derived_cl153,plain,
! [X2: a > a > $o] :
( ~ ( ( '#sk1' @ ( '#sk358' @ X2 ) @ ( '#sk430' @ X2 ) )
=> ( X2 @ ( '#sk358' @ X2 ) @ ( '#sk430' @ X2 ) ) )
| ~ ( '#form269' @ X2 )
| ( X2 @ '#sk10' @ '#sk12' )
| ~ '#form91' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl145]) ).
thf(zip_derived_cl162,plain,
! [X2: a > a > $o] :
( ~ ( X2 @ ( '#sk358' @ X2 ) @ ( '#sk430' @ X2 ) )
| ~ '#form91'
| ( X2 @ '#sk10' @ '#sk12' )
| ~ ( '#form269' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl10,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_cl8]) ).
thf(zip_derived_cl13,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl16,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk5' @ Y0 @ Y1 )
& ( '#sk5' @ X2 @ Y0 ) )
=> ( '#sk5' @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl19,plain,
! [X2: a,X4: a] :
( !!
@ ^ [Y0: a] :
( ( ( '#sk5' @ X4 @ Y0 )
& ( '#sk5' @ X2 @ X4 ) )
=> ( '#sk5' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl23,plain,
! [X2: a,X4: a,X6: a] :
( ( ( '#sk5' @ X4 @ X6 )
& ( '#sk5' @ X2 @ X4 ) )
=> ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl30,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( '#sk5' @ X4 @ X6 )
& ( '#sk5' @ X2 @ X4 ) )
| ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl42,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk5' @ X4 @ X6 )
| ~ ( '#sk5' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl14,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl17,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
=> ( '#sk5' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl20,plain,
! [X2: a,X4: a] :
( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl24,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl32,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl31,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl121,plain,
! [X2: a > a > $o] :
( ~ ( X2 @ ( '#sk101' @ X2 ) @ ( '#sk155' @ X2 ) )
| ( '#form100' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl161,plain,
! [X2: a > a > $o] :
( ( '#sk1' @ ( '#sk358' @ X2 ) @ ( '#sk430' @ X2 ) )
| ~ '#form91'
| ( X2 @ '#sk10' @ '#sk12' )
| ~ ( '#form269' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl73_025,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 @ '#sk10' @ '#sk12' ) )
| '#form9'
| ( !!
@ ^ [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 @ '#sk10' @ '#sk12' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl74,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk30' @ Y1 @ Y2 )
& ( '#sk30' @ Y0 @ Y1 ) )
=> ( '#sk30' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk30' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk30' @ '#sk10' @ '#sk12' ) )
| '#form9'
| ( !!
@ ^ [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 @ '#sk10' @ '#sk12' ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl86_026,plain,
( ~ '#form91'
| ( !!
@ ^ [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 @ '#sk10' @ '#sk12' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl227,plain,
( '#form91'
| '#form9'
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk30' @ Y1 @ Y2 )
& ( '#sk30' @ Y0 @ Y1 ) )
=> ( '#sk30' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk30' @ Y0 @ Y1 ) ) ) ) )
=> ( '#sk30' @ '#sk10' @ '#sk12' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl74,zip_derived_cl86]) ).
thf(zip_derived_cl228,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk30' @ Y1 @ Y2 )
& ( '#sk30' @ Y0 @ Y1 ) )
=> ( '#sk30' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk30' @ Y0 @ Y1 ) ) ) ) )
| ( '#sk30' @ '#sk10' @ '#sk12' )
| '#form9'
| '#form91' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl227]) ).
thf(zip_derived_cl80_027,plain,
( ~ ( '#sk30' @ '#sk10' @ '#sk12' )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl229,plain,
( '#form91'
| '#form9'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk30' @ Y1 @ Y2 )
& ( '#sk30' @ Y0 @ Y1 ) )
=> ( '#sk30' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk30' @ Y0 @ Y1 ) ) ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl228,zip_derived_cl80]) ).
thf(zip_derived_cl230,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk30' @ Y1 @ Y2 )
& ( '#sk30' @ Y0 @ Y1 ) )
=> ( '#sk30' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk30' @ Y0 @ Y1 ) ) ) )
| '#form9'
| '#form91' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl229]) ).
thf(zip_derived_cl128_028,plain,
! [X2: a > a > $o] :
( ( '#form269' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl231,plain,
( ~ ( '#form269' @ '#sk30' )
| '#form91'
| '#form9'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk30' @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl230,zip_derived_cl128]) ).
thf(zip_derived_cl232,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk339' @ '#sk30' ) @ Y0 )
=> ( '#sk30' @ ( '#sk339' @ '#sk30' ) @ Y0 ) ) )
| '#form9'
| '#form91'
| ~ ( '#form269' @ '#sk30' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl231]) ).
thf(zip_derived_cl233,plain,
( ~ ( ( '#sk2' @ ( '#sk339' @ '#sk30' ) @ ( '#sk410' @ '#sk30' ) )
=> ( '#sk30' @ ( '#sk339' @ '#sk30' ) @ ( '#sk410' @ '#sk30' ) ) )
| ~ ( '#form269' @ '#sk30' )
| '#form91'
| '#form9' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl232]) ).
thf(zip_derived_cl235,plain,
( ~ ( '#sk30' @ ( '#sk339' @ '#sk30' ) @ ( '#sk410' @ '#sk30' ) )
| '#form9'
| '#form91'
| ~ ( '#form269' @ '#sk30' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl233]) ).
thf(zip_derived_cl234,plain,
( ( '#sk2' @ ( '#sk339' @ '#sk30' ) @ ( '#sk410' @ '#sk30' ) )
| '#form9'
| '#form91'
| ~ ( '#form269' @ '#sk30' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl233]) ).
thf(zip_derived_cl147,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| '#form9'
| ( '#sk30' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl133]) ).
thf(zip_derived_cl128_029,plain,
! [X2: a > a > $o] :
( ( '#form269' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl129,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( X2 @ Y0 @ Y1 )
& ( X2 @ ( '#sk47' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk47' @ X2 ) @ Y1 ) ) ) )
| ( '#form269' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl128]) ).
thf(zip_derived_cl143,plain,
! [X2: a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( X2 @ ( '#sk74' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk74' @ X2 ) ) )
=> ( X2 @ ( '#sk47' @ X2 ) @ Y0 ) ) )
| ( '#form269' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl129]) ).
thf(zip_derived_cl152,plain,
! [X2: a > a > $o] :
( ~ ( ( ( X2 @ ( '#sk74' @ X2 ) @ ( '#sk180' @ X2 ) )
& ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk74' @ X2 ) ) )
=> ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk180' @ X2 ) ) )
| ( '#form269' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl143]) ).
thf(zip_derived_cl159,plain,
! [X2: a > a > $o] :
( ( ( X2 @ ( '#sk74' @ X2 ) @ ( '#sk180' @ X2 ) )
& ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk74' @ X2 ) ) )
| ( '#form269' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl152]) ).
thf(zip_derived_cl163,plain,
! [X2: a > a > $o] :
( ( X2 @ ( '#sk74' @ X2 ) @ ( '#sk180' @ X2 ) )
| ( '#form269' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl159]) ).
thf(zip_derived_cl160,plain,
! [X2: a > a > $o] :
( ~ ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk180' @ X2 ) )
| ( '#form269' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl152]) ).
thf(zip_derived_cl164,plain,
! [X2: a > a > $o] :
( ( X2 @ ( '#sk47' @ X2 ) @ ( '#sk74' @ X2 ) )
| ( '#form269' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl159]) ).
thf(zip_derived_cl94,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk30' @ Y1 @ Y2 )
& ( '#sk30' @ Y0 @ Y1 ) )
=> ( '#sk30' @ Y0 @ Y2 ) ) ) ) )
| '#form9' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl105,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk30' @ Y0 @ Y1 )
& ( '#sk30' @ X2 @ Y0 ) )
=> ( '#sk30' @ X2 @ Y1 ) ) ) )
| '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl117,plain,
! [X2: a,X4: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk30' @ X4 @ Y0 )
& ( '#sk30' @ X2 @ X4 ) )
=> ( '#sk30' @ X2 @ Y0 ) ) )
| '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl132,plain,
! [X2: a,X4: a,X6: a] :
( ( ( ( '#sk30' @ X4 @ X6 )
& ( '#sk30' @ X2 @ X4 ) )
=> ( '#sk30' @ X2 @ X6 ) )
| '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl117]) ).
thf(zip_derived_cl146,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( '#sk30' @ X4 @ X6 )
& ( '#sk30' @ X2 @ X4 ) )
| ( '#sk30' @ X2 @ X6 )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl132]) ).
thf(zip_derived_cl154,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk30' @ X4 @ X6 )
| ~ ( '#sk30' @ X2 @ X4 )
| '#form9'
| ( '#sk30' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl146]) ).
thf(zip_derived_cl4364,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl156,zip_derived_cl221,zip_derived_cl276,zip_derived_cl62,zip_derived_cl136,zip_derived_cl141,zip_derived_cl140,zip_derived_cl127,zip_derived_cl126,zip_derived_cl191,zip_derived_cl137,zip_derived_cl80,zip_derived_cl148,zip_derived_cl162,zip_derived_cl42,zip_derived_cl32,zip_derived_cl31,zip_derived_cl121,zip_derived_cl161,zip_derived_cl235,zip_derived_cl234,zip_derived_cl147,zip_derived_cl163,zip_derived_cl160,zip_derived_cl164,zip_derived_cl154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV155^5 : TPTP v9.2.0. Released v4.0.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.OiYWMnQwbv true
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 1 15:37:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.57/0.64 % Total configuration time : 828
% 0.57/0.64 % Estimated wc time : 1656
% 0.57/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.57/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.57/0.80 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.57/0.81 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.83 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 63.33/8.61 % Solved by lams/20_acsne_simpl.sh.
% 63.33/8.61 % done 496 iterations in 7.552s
% 63.33/8.61 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 63.33/8.61 % SZS output start Refutation
% See solution above
% 63.33/8.63
% 63.33/8.63
% 63.33/8.63 % Terminating...
% 63.35/8.70 % Runner terminated.
% 63.35/8.72 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------