TSTP Solution File: SEV154^5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV154^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.OgdwqMPACI true
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:59:47 EDT 2023
% Result : Theorem 49.88s 7.09s
% Output : Refutation 50.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 58
% Syntax : Number of formulae : 244 ( 7 unt; 32 typ; 0 def)
% Number of atoms : 2251 ( 0 equ; 6 cnn)
% Maximal formula atoms : 68 ( 10 avg)
% Number of connectives : 7312 ( 314 ~; 804 |; 485 &;4045 @)
% ( 0 <=>; 753 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 12 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 316 ( 316 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 13 con; 0-2 aty)
% ( 911 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1128 ( 915 ^; 213 !; 0 ?;1128 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf('#sk12_type',type,
'#sk12': a ).
thf('#sk20_type',type,
'#sk20': a > $o ).
thf('#form46_type',type,
'#form46': $o ).
thf('#sk16_type',type,
'#sk16': a > $o ).
thf('#sk6_type',type,
'#sk6': a ).
thf('#sk165_type',type,
'#sk165': ( a > $o ) > a ).
thf('#sk39_type',type,
'#sk39': ( a > $o ) > a ).
thf('#sk5_type',type,
'#sk5': a > $o ).
thf('#form164_type',type,
'#form164': ( a > $o ) > $o ).
thf('#sk4_type',type,
'#sk4': a ).
thf('#form272_type',type,
'#form272': ( a > $o ) > $o ).
thf('#sk273_type',type,
'#sk273': ( a > $o ) > a ).
thf('#sk80_type',type,
'#sk80': ( a > $o ) > a ).
thf('#form9_type',type,
'#form9': $o ).
thf('#form11_type',type,
'#form11': $o ).
thf('#sk8_type',type,
'#sk8': a ).
thf('#form264_type',type,
'#form264': ( a > $o ) > $o ).
thf('#sk136_type',type,
'#sk136': ( a > $o ) > a ).
thf('#form79_type',type,
'#form79': ( a > $o ) > $o ).
thf('#sk265_type',type,
'#sk265': ( a > $o ) > a ).
thf('#sk3_type',type,
'#sk3': a ).
thf('#sk7_type',type,
'#sk7': a ).
thf('#sk27_type',type,
'#sk27': ( a > $o ) > a ).
thf('#sk1_type',type,
'#sk1': a > a > $o ).
thf('#sk170_type',type,
'#sk170': ( a > $o ) > a ).
thf('#sk122_type',type,
'#sk122': ( a > $o ) > a ).
thf('#sk175_type',type,
'#sk175': ( a > $o ) > a ).
thf('#sk2_type',type,
'#sk2': a > a > $o ).
thf('#sk126_type',type,
'#sk126': ( a > $o ) > a ).
thf('#form135_type',type,
'#form135': ( a > $o ) > $o ).
thf('#sk10_type',type,
'#sk10': a ).
thf(cTHM251G_pme,conjecture,
! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx @ Xw )
| ( R @ Xx @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) )
| ~ ( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xy0 @ Xw )
| ( R @ Xy0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) )
& ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx0 @ Xw )
| ( R @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx0 @ Xw )
| ( R @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) )
& ! [Xx0: a,Xy0: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( S @ Xu @ Xv )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( S @ Xx0 @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) )
| ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( R @ Xu @ Xv )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( R @ Xx0 @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx0 @ Xw )
| ( R @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx @ Xw )
| ( R @ Xx @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx @ Xw )
| ( R @ Xx @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) )
| ~ ( ( ! [Xx0: a,Xy0: a,Xz: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xy0 @ Xw )
| ( R @ Xy0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) )
& ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx0 @ Xw )
| ( R @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx0 @ Xw )
| ( R @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xz ) ) )
& ! [Xx0: a,Xy0: a] :
( ( ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( S @ Xu @ Xv )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( S @ Xx0 @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) )
| ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( R @ Xu @ Xv )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( R @ Xx0 @ Xw )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx0 @ Xw )
| ( R @ Xx0 @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy0 ) ) ) )
=> ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx @ Xw )
| ( R @ Xx @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) ) ) ),
inference('cnf.neg',[status(esa)],[cTHM251G_pme]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( !!
@ ^ [Y1: a > a > $o] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( (~)
@ ( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( !!
@ ^ [Y7: a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !!
@ ^ [Y8: a] :
( ( ( Y1 @ Y5 @ Y8 )
| ( Y0 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !!
@ ^ [Y7: a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !!
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y0 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) )
=> ( !!
@ ^ [Y7: a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !!
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y0 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( ( Y1 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( ( Y1 @ Y4 @ Y7 )
| ( Y0 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( Y0 @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( (~)
@ ( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( '#sk1' @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
& ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( '#sk1' @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y7 @ Y8 )
| ( '#sk1' @ Y7 @ Y8 ) )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( '#sk1' @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( Y0 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( '#sk1' @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( '#sk1' @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( ( Y0 @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( ( Y0 @ Y3 @ Y6 )
| ( '#sk1' @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( Y0 @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( (~)
@ ( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y3 @ Y6 )
| ( '#sk1' @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
& ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y2 @ Y6 )
| ( '#sk1' @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) ) )
=> ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( ( '#sk2' @ Y6 @ Y7 )
| ( '#sk1' @ Y6 @ Y7 ) )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y2 @ Y6 )
| ( '#sk1' @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( '#sk2' @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk1' @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( '#sk1' @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y2 @ Y5 )
| ( '#sk1' @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: a] :
( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ '#sk3' @ Y2 )
| ( '#sk1' @ '#sk3' @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( (~)
@ ( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y2 @ Y5 )
| ( '#sk1' @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y1 @ Y5 )
| ( '#sk1' @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( ( '#sk2' @ Y5 @ Y6 )
| ( '#sk1' @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y1 @ Y5 )
| ( '#sk1' @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ '#sk3' @ Y2 )
| ( '#sk1' @ '#sk3' @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
~ ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) )
| ( (~)
@ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl6,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl8,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl11,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( '#sk2' @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y0 @ Y4 )
| ( '#sk1' @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl14,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ '#sk6' @ Y3 )
| ( '#sk1' @ '#sk6' @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ '#sk6' @ Y3 )
| ( '#sk1' @ '#sk6' @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl17,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ '#sk7' @ Y2 )
| ( '#sk1' @ '#sk7' @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ '#sk6' @ Y2 )
| ( '#sk1' @ '#sk6' @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ '#sk7' ) ) ) )
=> ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ '#sk6' @ Y2 )
| ( '#sk1' @ '#sk6' @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl20,plain,
( ~ ( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk7' @ Y1 )
| ( '#sk1' @ '#sk7' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk8' ) ) )
& ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk6' @ Y1 )
| ( '#sk1' @ '#sk6' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk6' @ Y1 )
| ( '#sk1' @ '#sk6' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk8' ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl24,plain,
( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk7' @ Y1 )
| ( '#sk1' @ '#sk7' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk8' ) ) )
& ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk6' @ Y1 )
| ( '#sk1' @ '#sk6' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl27,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk7' @ Y1 )
| ( '#sk1' @ '#sk7' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk8' ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl27_001,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk7' @ Y1 )
| ( '#sk1' @ '#sk7' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk8' ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl34,plain,
( ~ '#form11'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl37,plain,
( '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk7' @ Y1 )
| ( '#sk1' @ '#sk7' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk8' ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl27,zip_derived_cl34]) ).
thf(zip_derived_cl25,plain,
( ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk6' @ Y1 )
| ( '#sk1' @ '#sk6' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk8' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl29,plain,
( '#form9'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl41,plain,
( ~ '#form9'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk7' @ Y1 )
| ( '#sk1' @ '#sk7' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk8' ) ) )
| '#form11' ),
inference(renaming,[status(thm)],[zip_derived_cl37,zip_derived_cl29]) ).
thf(zip_derived_cl48,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk7' @ Y0 )
| ( '#sk1' @ '#sk7' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk8' ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl62,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk7' @ Y0 )
| ( '#sk1' @ '#sk7' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
| ( X2 @ '#sk8' )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl73,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk7' @ Y0 )
| ( '#sk1' @ '#sk7' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk8' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl86,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ ( '#sk27' @ X2 ) @ Y0 )
| ( '#sk1' @ ( '#sk27' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk27' @ X2 ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk8' )
| ~ '#form9'
| '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk7' @ Y0 )
| ( '#sk1' @ '#sk7' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl96,plain,
! [X2: a > $o] :
( ~ ( ( ( ( '#sk2' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) )
| ( '#sk1' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) ) )
& ( X2 @ ( '#sk27' @ X2 ) ) )
=> ( X2 @ ( '#sk39' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk7' @ Y0 )
| ( '#sk1' @ '#sk7' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk8' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl111,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk39' @ X2 ) )
| ( X2 @ '#sk8' )
| ~ '#form9'
| '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk7' @ Y0 )
| ( '#sk1' @ '#sk7' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl126,plain,
! [X2: a > $o] :
( ( '#form135' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk7' @ Y0 )
| ( '#sk1' @ '#sk7' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl127,plain,
! [X2: a > $o] :
( ~ ( ( ( '#sk2' @ '#sk7' @ ( '#sk136' @ X2 ) )
| ( '#sk1' @ '#sk7' @ ( '#sk136' @ X2 ) ) )
=> ( X2 @ ( '#sk136' @ X2 ) ) )
| ( '#form135' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl126]) ).
thf(zip_derived_cl146,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk136' @ X2 ) )
| ( '#form135' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl127]) ).
thf(zip_derived_cl145,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk7' @ ( '#sk136' @ X2 ) )
| ( '#sk1' @ '#sk7' @ ( '#sk136' @ X2 ) )
| ( '#form135' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl127]) ).
thf(zip_derived_cl160,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk7' @ ( '#sk136' @ X2 ) )
| ( '#sk1' @ '#sk7' @ ( '#sk136' @ X2 ) )
| ( '#form135' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl145]) ).
thf(zip_derived_cl48_002,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk7' @ Y0 )
| ( '#sk1' @ '#sk7' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk8' ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl49,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk16' @ Y0 ) )
=> ( '#sk16' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk7' @ Y0 )
| ( '#sk1' @ '#sk7' @ Y0 ) )
=> ( '#sk16' @ Y0 ) ) ) )
=> ( '#sk16' @ '#sk8' ) )
| '#form11'
| ~ '#form9' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl236,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk16' @ Y0 ) )
=> ( '#sk16' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk7' @ Y0 )
| ( '#sk1' @ '#sk7' @ Y0 ) )
=> ( '#sk16' @ Y0 ) ) ) )
| ( '#sk16' @ '#sk8' )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl25_003,plain,
( ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk6' @ Y1 )
| ( '#sk1' @ '#sk6' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk8' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl29_004,plain,
( '#form9'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl31,plain,
( ~ '#form9'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk6' @ Y1 )
| ( '#sk1' @ '#sk6' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk8' ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl25,zip_derived_cl29]) ).
thf(zip_derived_cl34_005,plain,
( ~ '#form11'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl39,plain,
( '#form11'
| ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk6' @ Y1 )
| ( '#sk1' @ '#sk6' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk8' ) ) )
| ~ '#form9' ),
inference(renaming,[status(thm)],[zip_derived_cl31,zip_derived_cl34]) ).
thf(zip_derived_cl45,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk16' @ Y0 ) )
=> ( '#sk16' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( '#sk16' @ Y0 ) ) ) )
=> ( '#sk16' @ '#sk8' ) )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl56,plain,
( ~ ( '#sk16' @ '#sk8' )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl237,plain,
( '#form11'
| ~ '#form9'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk16' @ Y0 ) )
=> ( '#sk16' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk7' @ Y0 )
| ( '#sk1' @ '#sk7' @ Y0 ) )
=> ( '#sk16' @ Y0 ) ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl236,zip_derived_cl56]) ).
thf(zip_derived_cl238,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk16' @ Y0 ) )
=> ( '#sk16' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk7' @ Y0 )
| ( '#sk1' @ '#sk7' @ Y0 ) )
=> ( '#sk16' @ Y0 ) ) )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl237]) ).
thf(zip_derived_cl126_006,plain,
! [X2: a > $o] :
( ( '#form135' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk7' @ Y0 )
| ( '#sk1' @ '#sk7' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl239,plain,
( ~ ( '#form135' @ '#sk16' )
| '#form11'
| ~ '#form9'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk16' @ Y0 ) )
=> ( '#sk16' @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl238,zip_derived_cl126]) ).
thf(zip_derived_cl240,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ ( '#sk27' @ '#sk16' ) @ Y0 )
| ( '#sk1' @ ( '#sk27' @ '#sk16' ) @ Y0 ) )
& ( '#sk16' @ ( '#sk27' @ '#sk16' ) ) )
=> ( '#sk16' @ Y0 ) ) )
| ~ '#form9'
| '#form11'
| ~ ( '#form135' @ '#sk16' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl239]) ).
thf(zip_derived_cl241,plain,
( ~ ( ( ( ( '#sk2' @ ( '#sk27' @ '#sk16' ) @ ( '#sk39' @ '#sk16' ) )
| ( '#sk1' @ ( '#sk27' @ '#sk16' ) @ ( '#sk39' @ '#sk16' ) ) )
& ( '#sk16' @ ( '#sk27' @ '#sk16' ) ) )
=> ( '#sk16' @ ( '#sk39' @ '#sk16' ) ) )
| ~ ( '#form135' @ '#sk16' )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl240]) ).
thf(zip_derived_cl243,plain,
( ~ ( '#sk16' @ ( '#sk39' @ '#sk16' ) )
| ~ '#form9'
| '#form11'
| ~ ( '#form135' @ '#sk16' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl241]) ).
thf(zip_derived_cl242,plain,
( ( ( ( '#sk2' @ ( '#sk27' @ '#sk16' ) @ ( '#sk39' @ '#sk16' ) )
| ( '#sk1' @ ( '#sk27' @ '#sk16' ) @ ( '#sk39' @ '#sk16' ) ) )
& ( '#sk16' @ ( '#sk27' @ '#sk16' ) ) )
| ~ '#form9'
| '#form11'
| ~ ( '#form135' @ '#sk16' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl241]) ).
thf(zip_derived_cl245,plain,
( ( '#sk16' @ ( '#sk27' @ '#sk16' ) )
| ~ ( '#form135' @ '#sk16' )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl242]) ).
thf(zip_derived_cl244,plain,
( ( '#sk2' @ ( '#sk27' @ '#sk16' ) @ ( '#sk39' @ '#sk16' ) )
| ( '#sk1' @ ( '#sk27' @ '#sk16' ) @ ( '#sk39' @ '#sk16' ) )
| ~ ( '#form135' @ '#sk16' )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl242]) ).
thf(zip_derived_cl246,plain,
( ( '#sk2' @ ( '#sk27' @ '#sk16' ) @ ( '#sk39' @ '#sk16' ) )
| ( '#sk1' @ ( '#sk27' @ '#sk16' ) @ ( '#sk39' @ '#sk16' ) )
| ~ '#form9'
| '#form11'
| ~ ( '#form135' @ '#sk16' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl244]) ).
thf(zip_derived_cl29_007,plain,
( '#form9'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl30,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk10' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk10' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ '#sk10' @ Y2 )
| ( '#sk1' @ '#sk10' @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| '#form9' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl40,plain,
( ~ ( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ '#sk10' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk10' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk10' @ Y1 )
| ( '#sk1' @ '#sk10' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) ) )
| '#form9' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl46,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ '#sk10' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk10' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl57,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ '#sk10' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk10' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) )
| '#form9' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl67,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk12' ) )
| '#form9'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk10' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl78,plain,
( ~ '#form46'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk10' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl79,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk12' ) )
| ~ '#form46' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl93,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
| ( X2 @ '#sk12' )
| ~ '#form46' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl107,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) )
| ~ '#form46'
| ( X2 @ '#sk12' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl120,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ ( '#sk126' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk126' @ X2 ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk12' )
| ~ '#form46'
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl141,plain,
! [X2: a > $o] :
( ~ ( ( ( '#sk1' @ ( '#sk126' @ X2 ) @ ( '#sk175' @ X2 ) )
& ( X2 @ ( '#sk126' @ X2 ) ) )
=> ( X2 @ ( '#sk175' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) )
| ~ '#form46'
| ( X2 @ '#sk12' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl120]) ).
thf(zip_derived_cl153,plain,
! [X2: a > $o] :
( ( ( '#sk1' @ ( '#sk126' @ X2 ) @ ( '#sk175' @ X2 ) )
& ( X2 @ ( '#sk126' @ X2 ) ) )
| ( X2 @ '#sk12' )
| ~ '#form46'
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl141]) ).
thf(zip_derived_cl171,plain,
! [X2: a > $o] :
( ( X2 @ ( '#sk126' @ X2 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) )
| ~ '#form46'
| ( X2 @ '#sk12' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl154,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk175' @ X2 ) )
| ( X2 @ '#sk12' )
| ~ '#form46'
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl141]) ).
thf(zip_derived_cl172,plain,
! [X2: a > $o] :
( ( '#form272' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl180,plain,
! [X2: a > $o] :
( ~ ( '#form272'
@ ^ [Y0: a] : ( X2 @ Y0 ) )
| ( X2 @ '#sk12' )
| ~ '#form46'
| ( X2 @ ( '#sk126' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl171,zip_derived_cl172]) ).
thf(zip_derived_cl186,plain,
! [X2: a > $o] :
( ~ ( '#form272' @ X2 )
| ( X2 @ '#sk12' )
| ~ '#form46'
| ( X2 @ ( '#sk126' @ X2 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl180]) ).
thf(zip_derived_cl47,plain,
( ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk10' @ Y1 )
| ( '#sk1' @ '#sk10' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl61,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk20' @ Y0 ) )
=> ( '#sk20' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk10' @ Y0 )
| ( '#sk1' @ '#sk10' @ Y0 ) )
=> ( '#sk20' @ Y0 ) ) ) )
=> ( '#sk20' @ '#sk12' ) )
| '#form9' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl72,plain,
( ~ ( '#sk20' @ '#sk12' )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl28,plain,
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk6' @ Y1 )
| ( '#sk1' @ '#sk6' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl34_008,plain,
( ~ '#form11'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl38,plain,
( '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk6' @ Y1 )
| ( '#sk1' @ '#sk6' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl28,zip_derived_cl34]) ).
thf(zip_derived_cl29_009,plain,
( '#form9'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( ( '#sk2' @ Y3 @ Y4 )
| ( '#sk1' @ Y3 @ Y4 ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y0 @ Y3 )
| ( '#sk1' @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl43,plain,
( ~ '#form9'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk6' @ Y1 )
| ( '#sk1' @ '#sk6' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk7' ) ) )
| '#form11' ),
inference(renaming,[status(thm)],[zip_derived_cl38,zip_derived_cl29]) ).
thf(zip_derived_cl52,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk7' ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl64,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
| ( X2 @ '#sk7' )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl75,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk7' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl89,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ ( '#sk27' @ X2 ) @ Y0 )
| ( '#sk1' @ ( '#sk27' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk27' @ X2 ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk7' )
| ~ '#form9'
| '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl102,plain,
! [X2: a > $o] :
( ~ ( ( ( ( '#sk2' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) )
| ( '#sk1' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) ) )
& ( X2 @ ( '#sk27' @ X2 ) ) )
=> ( X2 @ ( '#sk39' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk7' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl117,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk39' @ X2 ) )
| ( X2 @ '#sk7' )
| ~ '#form9'
| '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl117_010,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk39' @ X2 ) )
| ( X2 @ '#sk7' )
| ~ '#form9'
| '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl135,plain,
! [X2: a > $o] :
( ( '#form164' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl137,plain,
! [X2: a > $o] :
( ~ ( '#form164' @ X2 )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk7' )
| ~ ( X2 @ ( '#sk39' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl117,zip_derived_cl135]) ).
thf(zip_derived_cl116,plain,
! [X2: a > $o] :
( ( ( ( '#sk2' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) )
| ( '#sk1' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) ) )
& ( X2 @ ( '#sk27' @ X2 ) ) )
| ( X2 @ '#sk7' )
| ~ '#form9'
| '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl134,plain,
! [X2: a > $o] :
( ( X2 @ ( '#sk27' @ X2 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk7' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl135_011,plain,
! [X2: a > $o] :
( ( '#form164' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl148,plain,
! [X2: a > $o] :
( ~ ( '#form164'
@ ^ [Y0: a] : ( X2 @ Y0 ) )
| ( X2 @ '#sk7' )
| ~ '#form9'
| '#form11'
| ( X2 @ ( '#sk27' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl134,zip_derived_cl135]) ).
thf(zip_derived_cl163,plain,
! [X2: a > $o] :
( ~ ( '#form164' @ X2 )
| ( X2 @ '#sk7' )
| ~ '#form9'
| '#form11'
| ( X2 @ ( '#sk27' @ X2 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl148]) ).
thf(zip_derived_cl55,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk16' @ Y0 ) )
=> ( '#sk16' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( '#sk16' @ Y0 ) ) ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl65,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk16' @ Y0 ) )
=> ( '#sk16' @ Y1 ) ) ) )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl76,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
& ( '#sk16' @ X2 ) )
=> ( '#sk16' @ Y0 ) ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl90,plain,
! [X2: a,X4: a] :
( ( ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
& ( '#sk16' @ X2 ) )
=> ( '#sk16' @ X4 ) )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl103,plain,
! [X2: a,X4: a] :
( ~ ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
& ( '#sk16' @ X2 ) )
| ( '#sk16' @ X4 )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl118,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ~ ( '#sk16' @ X2 )
| ~ '#form9'
| '#form11'
| ( '#sk16' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl138,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ( '#sk16' @ X4 )
| '#form11'
| ~ '#form9'
| ~ ( '#sk16' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl118]) ).
thf(zip_derived_cl154_012,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk175' @ X2 ) )
| ( X2 @ '#sk12' )
| ~ '#form46'
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl141]) ).
thf(zip_derived_cl172_013,plain,
! [X2: a > $o] :
( ( '#form272' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl174,plain,
! [X2: a > $o] :
( ~ ( '#form272' @ X2 )
| ~ '#form46'
| ( X2 @ '#sk12' )
| ~ ( X2 @ ( '#sk175' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl154,zip_derived_cl172]) ).
thf(zip_derived_cl135_014,plain,
! [X2: a > $o] :
( ( '#form164' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl136,plain,
! [X2: a > $o] :
( ~ ( ( ( '#sk2' @ '#sk6' @ ( '#sk165' @ X2 ) )
| ( '#sk1' @ '#sk6' @ ( '#sk165' @ X2 ) ) )
=> ( X2 @ ( '#sk165' @ X2 ) ) )
| ( '#form164' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl135]) ).
thf(zip_derived_cl149,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk6' @ ( '#sk165' @ X2 ) )
| ( '#sk1' @ '#sk6' @ ( '#sk165' @ X2 ) )
| ( '#form164' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl136]) ).
thf(zip_derived_cl164,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk6' @ ( '#sk165' @ X2 ) )
| ( '#sk1' @ '#sk6' @ ( '#sk165' @ X2 ) )
| ( '#form164' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl149]) ).
thf(zip_derived_cl150,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk165' @ X2 ) )
| ( '#form164' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl136]) ).
thf(zip_derived_cl133,plain,
! [X2: a > $o] :
( ( '#sk2' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) )
| ( '#sk1' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk7' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl135_015,plain,
! [X2: a > $o] :
( ( '#form164' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl147,plain,
! [X2: a > $o] :
( ~ ( '#form164'
@ ^ [Y0: a] : ( X2 @ Y0 ) )
| ( X2 @ '#sk7' )
| ~ '#form9'
| '#form11'
| ( '#sk2' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) )
| ( '#sk1' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl133,zip_derived_cl135]) ).
thf(zip_derived_cl161,plain,
! [X2: a > $o] :
( ~ ( '#form164' @ X2 )
| ( X2 @ '#sk7' )
| ~ '#form9'
| '#form11'
| ( '#sk2' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) )
| ( '#sk1' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl147]) ).
thf(zip_derived_cl162,plain,
! [X2: a > $o] :
( ( '#sk2' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) )
| ( '#sk1' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) )
| '#form11'
| ~ '#form9'
| ( X2 @ '#sk7' )
| ~ ( '#form164' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl161]) ).
thf(zip_derived_cl139,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk16' @ X4 )
| '#form11'
| ~ '#form9'
| ~ ( '#sk16' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl118]) ).
thf(zip_derived_cl172_016,plain,
! [X2: a > $o] :
( ( '#form272' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl173,plain,
! [X2: a > $o] :
( ~ ( ( '#sk1' @ '#sk10' @ ( '#sk273' @ X2 ) )
=> ( X2 @ ( '#sk273' @ X2 ) ) )
| ( '#form272' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl172]) ).
thf(zip_derived_cl181,plain,
! [X2: a > $o] :
( ( '#sk1' @ '#sk10' @ ( '#sk273' @ X2 ) )
| ( '#form272' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl173]) ).
thf(zip_derived_cl182,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk273' @ X2 ) )
| ( '#form272' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl173]) ).
thf(zip_derived_cl67_017,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk12' ) )
| '#form9'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk10' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl68,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( '#sk20' @ Y0 ) )
=> ( '#sk20' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( '#sk20' @ Y0 ) ) ) )
=> ( '#sk20' @ '#sk12' ) )
| '#form9'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk10' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl78_018,plain,
( ~ '#form46'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk10' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl257,plain,
( '#form46'
| '#form9'
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( '#sk20' @ Y0 ) )
=> ( '#sk20' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( '#sk20' @ Y0 ) ) ) )
=> ( '#sk20' @ '#sk12' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl68,zip_derived_cl78]) ).
thf(zip_derived_cl258,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( '#sk20' @ Y0 ) )
=> ( '#sk20' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( '#sk20' @ Y0 ) ) ) )
| ( '#sk20' @ '#sk12' )
| '#form9'
| '#form46' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl257]) ).
thf(zip_derived_cl72_019,plain,
( ~ ( '#sk20' @ '#sk12' )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl259,plain,
( '#form46'
| '#form9'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( '#sk20' @ Y0 ) )
=> ( '#sk20' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( '#sk20' @ Y0 ) ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl258,zip_derived_cl72]) ).
thf(zip_derived_cl260,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( '#sk20' @ Y0 ) )
=> ( '#sk20' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( '#sk20' @ Y0 ) ) )
| '#form9'
| '#form46' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl259]) ).
thf(zip_derived_cl67_020,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk12' ) )
| '#form9'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk10' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl78_021,plain,
( ~ '#form46'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk10' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk12' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl83,plain,
! [X2: a > $o] :
( '#form46'
| '#form9'
| ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk12' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl67,zip_derived_cl78]) ).
thf(zip_derived_cl92,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) )
| ( X2 @ '#sk12' )
| '#form9'
| '#form46' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl106,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) )
| '#form46'
| '#form9'
| ( X2 @ '#sk12' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl119,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ ( '#sk122' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk122' @ X2 ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk12' )
| '#form9'
| '#form46'
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl140,plain,
! [X2: a > $o] :
( ~ ( ( ( '#sk2' @ ( '#sk122' @ X2 ) @ ( '#sk170' @ X2 ) )
& ( X2 @ ( '#sk122' @ X2 ) ) )
=> ( X2 @ ( '#sk170' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) )
| '#form46'
| '#form9'
| ( X2 @ '#sk12' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl119]) ).
thf(zip_derived_cl152,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk170' @ X2 ) )
| ( X2 @ '#sk12' )
| '#form9'
| '#form46'
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl140]) ).
thf(zip_derived_cl167,plain,
! [X2: a > $o] :
( ( '#form264' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl261,plain,
( ~ ( '#form264' @ '#sk20' )
| '#form46'
| '#form9'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( '#sk20' @ Y0 ) )
=> ( '#sk20' @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl260,zip_derived_cl167]) ).
thf(zip_derived_cl262,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ ( '#sk122' @ '#sk20' ) @ Y0 )
& ( '#sk20' @ ( '#sk122' @ '#sk20' ) ) )
=> ( '#sk20' @ Y0 ) ) )
| '#form9'
| '#form46'
| ~ ( '#form264' @ '#sk20' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl261]) ).
thf(zip_derived_cl263,plain,
( ~ ( ( ( '#sk2' @ ( '#sk122' @ '#sk20' ) @ ( '#sk170' @ '#sk20' ) )
& ( '#sk20' @ ( '#sk122' @ '#sk20' ) ) )
=> ( '#sk20' @ ( '#sk170' @ '#sk20' ) ) )
| ~ ( '#form264' @ '#sk20' )
| '#form46'
| '#form9' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl262]) ).
thf(zip_derived_cl264,plain,
( ( ( '#sk2' @ ( '#sk122' @ '#sk20' ) @ ( '#sk170' @ '#sk20' ) )
& ( '#sk20' @ ( '#sk122' @ '#sk20' ) ) )
| '#form9'
| '#form46'
| ~ ( '#form264' @ '#sk20' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl263]) ).
thf(zip_derived_cl267,plain,
( ( '#sk20' @ ( '#sk122' @ '#sk20' ) )
| ~ ( '#form264' @ '#sk20' )
| '#form46'
| '#form9' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl264]) ).
thf(zip_derived_cl170,plain,
! [X2: a > $o] :
( ( '#sk1' @ ( '#sk126' @ X2 ) @ ( '#sk175' @ X2 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) )
| ~ '#form46'
| ( X2 @ '#sk12' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl172_022,plain,
! [X2: a > $o] :
( ( '#form272' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl179,plain,
! [X2: a > $o] :
( ~ ( '#form272'
@ ^ [Y0: a] : ( X2 @ Y0 ) )
| ( X2 @ '#sk12' )
| ~ '#form46'
| ( '#sk1' @ ( '#sk126' @ X2 ) @ ( '#sk175' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl170,zip_derived_cl172]) ).
thf(zip_derived_cl185,plain,
! [X2: a > $o] :
( ~ ( '#form272' @ X2 )
| ( X2 @ '#sk12' )
| ~ '#form46'
| ( '#sk1' @ ( '#sk126' @ X2 ) @ ( '#sk175' @ X2 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl179]) ).
thf(zip_derived_cl71,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk20' @ Y0 ) )
=> ( '#sk20' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk10' @ Y0 )
| ( '#sk1' @ '#sk10' @ Y0 ) )
=> ( '#sk20' @ Y0 ) ) ) )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl84,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk20' @ Y0 ) )
=> ( '#sk20' @ Y1 ) ) ) )
| '#form9' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl94,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
& ( '#sk20' @ X2 ) )
=> ( '#sk20' @ Y0 ) ) )
| '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl108,plain,
! [X2: a,X4: a] :
( ( ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
& ( '#sk20' @ X2 ) )
=> ( '#sk20' @ X4 ) )
| '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl121,plain,
! [X2: a,X4: a] :
( ~ ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
& ( '#sk20' @ X2 ) )
| ( '#sk20' @ X4 )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl142,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ~ ( '#sk20' @ X2 )
| '#form9'
| ( '#sk20' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl156,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk20' @ X4 )
| '#form9'
| ~ ( '#sk20' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl142]) ).
thf(zip_derived_cl66,plain,
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk6' @ Y0 )
| ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( '#sk16' @ Y0 ) ) )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl77,plain,
! [X2: a] :
( ( ( ( '#sk2' @ '#sk6' @ X2 )
| ( '#sk1' @ '#sk6' @ X2 ) )
=> ( '#sk16' @ X2 ) )
| '#form11'
| ~ '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl91,plain,
! [X2: a] :
( ~ ( ( '#sk2' @ '#sk6' @ X2 )
| ( '#sk1' @ '#sk6' @ X2 ) )
| ( '#sk16' @ X2 )
| ~ '#form9'
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl104,plain,
! [X2: a] :
( ~ ( '#sk2' @ '#sk6' @ X2 )
| '#form11'
| ~ '#form9'
| ( '#sk16' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl105,plain,
! [X2: a] :
( ~ ( '#sk1' @ '#sk6' @ X2 )
| '#form11'
| ~ '#form9'
| ( '#sk16' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl85,plain,
( ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk10' @ Y0 )
| ( '#sk1' @ '#sk10' @ Y0 ) )
=> ( '#sk20' @ Y0 ) ) )
| '#form9' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl95,plain,
! [X2: a] :
( ( ( ( '#sk2' @ '#sk10' @ X2 )
| ( '#sk1' @ '#sk10' @ X2 ) )
=> ( '#sk20' @ X2 ) )
| '#form9' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl109,plain,
! [X2: a] :
( ~ ( ( '#sk2' @ '#sk10' @ X2 )
| ( '#sk1' @ '#sk10' @ X2 ) )
| ( '#sk20' @ X2 )
| '#form9' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl123,plain,
! [X2: a] :
( ~ ( '#sk1' @ '#sk10' @ X2 )
| '#form9'
| ( '#sk20' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl265,plain,
( ~ ( '#sk20' @ ( '#sk170' @ '#sk20' ) )
| '#form9'
| '#form46'
| ~ ( '#form264' @ '#sk20' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl263]) ).
thf(zip_derived_cl34_023,plain,
( ~ '#form11'
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl35,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk4' ) )
| ~ '#form11' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl42,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
| ( X2 @ '#sk4' )
| ~ '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl51,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| ~ '#form11'
| ( X2 @ '#sk4' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl63,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ ( '#sk27' @ X2 ) @ Y0 )
| ( '#sk1' @ ( '#sk27' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk27' @ X2 ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk4' )
| ~ '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl74,plain,
! [X2: a > $o] :
( ~ ( ( ( ( '#sk2' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) )
| ( '#sk1' @ ( '#sk27' @ X2 ) @ ( '#sk39' @ X2 ) ) )
& ( X2 @ ( '#sk27' @ X2 ) ) )
=> ( X2 @ ( '#sk39' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) )
| ~ '#form11'
| ( X2 @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl88,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk39' @ X2 ) )
| ( X2 @ '#sk4' )
| ~ '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl99,plain,
! [X2: a > $o] :
( ( '#form79' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl100,plain,
! [X2: a > $o] :
( ~ ( ( ( '#sk2' @ '#sk3' @ ( '#sk80' @ X2 ) )
| ( '#sk1' @ '#sk3' @ ( '#sk80' @ X2 ) ) )
=> ( X2 @ ( '#sk80' @ X2 ) ) )
| ( '#form79' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl114,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk3' @ ( '#sk80' @ X2 ) )
| ( '#sk1' @ '#sk3' @ ( '#sk80' @ X2 ) )
| ( '#form79' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl132,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk3' @ ( '#sk80' @ X2 ) )
| ( '#sk1' @ '#sk3' @ ( '#sk80' @ X2 ) )
| ( '#form79' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl115,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk80' @ X2 ) )
| ( '#form79' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl35_024,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk4' ) )
| ~ '#form11' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl36,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) )
=> ( '#sk5' @ '#sk4' ) )
| ~ '#form11' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl5,plain,
~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl7,plain,
~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) )
=> ( '#sk5' @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl10,plain,
~ ( '#sk5' @ '#sk4' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl214,plain,
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) )
=> $false )
| ~ '#form11' ),
inference(demod,[status(thm)],[zip_derived_cl36,zip_derived_cl10]) ).
thf(zip_derived_cl215,plain,
( ( (~)
@ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) ) )
| ~ '#form11' ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl214]) ).
thf(zip_derived_cl216,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) )
| ~ '#form11' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl215]) ).
thf(zip_derived_cl217,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) )
| ~ '#form11' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl216]) ).
thf(zip_derived_cl99_025,plain,
! [X2: a > $o] :
( ( '#form79' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl218,plain,
( ~ ( '#form79' @ '#sk5' )
| ~ '#form11'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl217,zip_derived_cl99]) ).
thf(zip_derived_cl219,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ ( '#sk27' @ '#sk5' ) @ Y0 )
| ( '#sk1' @ ( '#sk27' @ '#sk5' ) @ Y0 ) )
& ( '#sk5' @ ( '#sk27' @ '#sk5' ) ) )
=> ( '#sk5' @ Y0 ) ) )
| ~ '#form11'
| ~ ( '#form79' @ '#sk5' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl218]) ).
thf(zip_derived_cl220,plain,
( ~ ( ( ( ( '#sk2' @ ( '#sk27' @ '#sk5' ) @ ( '#sk39' @ '#sk5' ) )
| ( '#sk1' @ ( '#sk27' @ '#sk5' ) @ ( '#sk39' @ '#sk5' ) ) )
& ( '#sk5' @ ( '#sk27' @ '#sk5' ) ) )
=> ( '#sk5' @ ( '#sk39' @ '#sk5' ) ) )
| ~ ( '#form79' @ '#sk5' )
| ~ '#form11' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl219]) ).
thf(zip_derived_cl222,plain,
( ~ ( '#sk5' @ ( '#sk39' @ '#sk5' ) )
| ~ '#form11'
| ~ ( '#form79' @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl220]) ).
thf(zip_derived_cl221,plain,
( ( ( ( '#sk2' @ ( '#sk27' @ '#sk5' ) @ ( '#sk39' @ '#sk5' ) )
| ( '#sk1' @ ( '#sk27' @ '#sk5' ) @ ( '#sk39' @ '#sk5' ) ) )
& ( '#sk5' @ ( '#sk27' @ '#sk5' ) ) )
| ~ '#form11'
| ~ ( '#form79' @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl220]) ).
thf(zip_derived_cl224,plain,
( ( '#sk5' @ ( '#sk27' @ '#sk5' ) )
| ~ ( '#form79' @ '#sk5' )
| ~ '#form11' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl221]) ).
thf(zip_derived_cl223,plain,
( ( '#sk2' @ ( '#sk27' @ '#sk5' ) @ ( '#sk39' @ '#sk5' ) )
| ( '#sk1' @ ( '#sk27' @ '#sk5' ) @ ( '#sk39' @ '#sk5' ) )
| ~ ( '#form79' @ '#sk5' )
| ~ '#form11' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl221]) ).
thf(zip_derived_cl225,plain,
( ( '#sk2' @ ( '#sk27' @ '#sk5' ) @ ( '#sk39' @ '#sk5' ) )
| ( '#sk1' @ ( '#sk27' @ '#sk5' ) @ ( '#sk39' @ '#sk5' ) )
| ~ '#form11'
| ~ ( '#form79' @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl223]) ).
thf(zip_derived_cl9,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl12,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl15,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
& ( '#sk5' @ X2 ) )
=> ( '#sk5' @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl18,plain,
! [X2: a,X4: a] :
( ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
& ( '#sk5' @ X2 ) )
=> ( '#sk5' @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21,plain,
! [X2: a,X4: a] :
( ~ ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
& ( '#sk5' @ X2 ) )
| ( '#sk5' @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl26,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ~ ( '#sk5' @ X2 )
| ( '#sk5' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl32,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ( '#sk5' @ X4 )
| ~ ( '#sk5' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl266,plain,
( ( '#sk2' @ ( '#sk122' @ '#sk20' ) @ ( '#sk170' @ '#sk20' ) )
| ~ ( '#form264' @ '#sk20' )
| '#form46'
| '#form9' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl264]) ).
thf(zip_derived_cl13,plain,
( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl16,plain,
! [X2: a] :
( ( ( '#sk2' @ '#sk3' @ X2 )
| ( '#sk1' @ '#sk3' @ X2 ) )
=> ( '#sk5' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl19,plain,
! [X2: a] :
( ~ ( ( '#sk2' @ '#sk3' @ X2 )
| ( '#sk1' @ '#sk3' @ X2 ) )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl22,plain,
! [X2: a] :
( ~ ( '#sk2' @ '#sk3' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl23,plain,
! [X2: a] :
( ~ ( '#sk1' @ '#sk3' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl33,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk5' @ X4 )
| ~ ( '#sk5' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl155,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ( '#sk20' @ X4 )
| '#form9'
| ~ ( '#sk20' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl142]) ).
thf(zip_derived_cl167_026,plain,
! [X2: a > $o] :
( ( '#form264' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk10' @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl168,plain,
! [X2: a > $o] :
( ~ ( ( '#sk2' @ '#sk10' @ ( '#sk265' @ X2 ) )
=> ( X2 @ ( '#sk265' @ X2 ) ) )
| ( '#form264' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl167]) ).
thf(zip_derived_cl177,plain,
! [X2: a > $o] :
( ( '#sk2' @ '#sk10' @ ( '#sk265' @ X2 ) )
| ( '#form264' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl168]) ).
thf(zip_derived_cl178,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk265' @ X2 ) )
| ( '#form264' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl168]) ).
thf(zip_derived_cl122,plain,
! [X2: a] :
( ~ ( '#sk2' @ '#sk10' @ X2 )
| '#form9'
| ( '#sk20' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl8308,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl146,zip_derived_cl160,zip_derived_cl243,zip_derived_cl245,zip_derived_cl246,zip_derived_cl186,zip_derived_cl72,zip_derived_cl137,zip_derived_cl163,zip_derived_cl138,zip_derived_cl174,zip_derived_cl164,zip_derived_cl150,zip_derived_cl162,zip_derived_cl139,zip_derived_cl181,zip_derived_cl182,zip_derived_cl267,zip_derived_cl185,zip_derived_cl156,zip_derived_cl104,zip_derived_cl105,zip_derived_cl123,zip_derived_cl265,zip_derived_cl132,zip_derived_cl115,zip_derived_cl222,zip_derived_cl224,zip_derived_cl225,zip_derived_cl32,zip_derived_cl266,zip_derived_cl22,zip_derived_cl23,zip_derived_cl33,zip_derived_cl155,zip_derived_cl177,zip_derived_cl178,zip_derived_cl122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV154^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.OgdwqMPACI true
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 04:06:54 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.21/0.67 % Total configuration time : 828
% 0.21/0.67 % Estimated wc time : 1656
% 0.21/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.79 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.82 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 49.88/7.09 % Solved by lams/20_acsne_simpl.sh.
% 49.88/7.09 % done 929 iterations in 6.103s
% 49.88/7.09 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 49.88/7.09 % SZS output start Refutation
% See solution above
% 50.09/7.10
% 50.09/7.10
% 50.09/7.10 % Terminating...
% 50.31/7.19 % Runner terminated.
% 50.31/7.21 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------