TSTP Solution File: SEV148^5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV148^5 : 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.WYq2ykaSyQ true
% Computer : n024.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 19:59:46 EDT 2023
% Result : Theorem 37.75s 7.14s
% Output : Refutation 37.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 52
% Syntax : Number of formulae : 184 ( 8 unt; 24 typ; 0 def)
% Number of atoms : 1407 ( 0 equ; 1 cnn)
% Maximal formula atoms : 38 ( 8 avg)
% Number of connectives : 5593 ( 226 ~; 412 |; 391 &;3176 @)
% ( 0 <=>; 633 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 14 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 432 ( 432 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 5 con; 0-2 aty)
% ( 755 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1040 ( 764 ^; 276 !; 0 ?;1040 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf('#sk348_type',type,
'#sk348': ( a > $o ) > a ).
thf('#form410_type',type,
'#form410': ( a > $o ) > ( a > $o ) > $o ).
thf('#sk3_type',type,
'#sk3': a ).
thf('#sk115_type',type,
'#sk115': ( a > $o ) > a ).
thf('#sk376_type',type,
'#sk376': ( a > $o ) > a ).
thf('#sk411_type',type,
'#sk411': ( a > $o ) > ( a > $o ) > a ).
thf('#sk4_type',type,
'#sk4': a ).
thf('#form195_type',type,
'#form195': ( a > $o ) > ( a > $o ) > $o ).
thf('#sk1_type',type,
'#sk1': a > a > $o ).
thf('#form37_type',type,
'#form37': ( a > $o ) > $o ).
thf('#sk21_type',type,
'#sk21': ( a > $o ) > a ).
thf('#form186_type',type,
'#form186': ( a > $o ) > $o ).
thf('#form173_type',type,
'#form173': ( a > $o ) > $o ).
thf('#sk131_type',type,
'#sk131': ( a > $o ) > a ).
thf('#form222_type',type,
'#form222': ( a > $o ) > $o ).
thf('#sk38_type',type,
'#sk38': ( a > $o ) > a ).
thf('#sk223_type',type,
'#sk223': ( a > $o ) > a ).
thf('#sk15_type',type,
'#sk15': ( a > $o ) > a ).
thf('#sk5_type',type,
'#sk5': a > $o ).
thf('#sk423_type',type,
'#sk423': ( a > $o ) > a ).
thf('#form422_type',type,
'#form422': ( a > $o ) > $o ).
thf('#sk196_type',type,
'#sk196': ( a > $o ) > ( a > $o ) > a ).
thf('#sk2_type',type,
'#sk2': a > a > $o ).
thf(cTHM251C_pme,conjecture,
! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
( ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ! [Xq0: a > $o] :
( ( ! [Xu0: a,Xv0: a] :
( ( ( S @ Xu0 @ Xv0 )
& ( Xq0 @ Xu0 ) )
=> ( Xq0 @ Xv0 ) )
& ! [Xw: a] :
( ( S @ Xu @ Xw )
=> ( Xq0 @ Xw ) ) )
=> ( Xq0 @ Xv ) )
| ! [Xq0: a > $o] :
( ( ! [Xu0: a,Xv0: a] :
( ( ( R @ Xu0 @ Xv0 )
& ( Xq0 @ Xu0 ) )
=> ( Xq0 @ Xv0 ) )
& ! [Xw: a] :
( ( R @ Xu @ Xw )
=> ( Xq0 @ Xw ) ) )
=> ( Xq0 @ Xv ) ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ! [Xq0: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( S @ Xu @ Xv )
& ( Xq0 @ Xu ) )
=> ( Xq0 @ Xv ) )
& ! [Xw0: a] :
( ( S @ Xx @ Xw0 )
=> ( Xq0 @ Xw0 ) ) )
=> ( Xq0 @ Xw ) )
| ! [Xq0: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( R @ Xu @ Xv )
& ( Xq0 @ Xu ) )
=> ( Xq0 @ Xv ) )
& ! [Xw0: a] :
( ( R @ Xx @ Xw0 )
=> ( Xq0 @ Xw0 ) ) )
=> ( Xq0 @ Xw ) ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) )
=> ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx @ Xw )
| ( R @ Xx @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) ) ) ).
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] :
( ( ( ! [Xq0: a > $o] :
( ( ! [Xu0: a,Xv0: a] :
( ( ( S @ Xu0 @ Xv0 )
& ( Xq0 @ Xu0 ) )
=> ( Xq0 @ Xv0 ) )
& ! [Xw: a] :
( ( S @ Xu @ Xw )
=> ( Xq0 @ Xw ) ) )
=> ( Xq0 @ Xv ) )
| ! [Xq0: a > $o] :
( ( ! [Xu0: a,Xv0: a] :
( ( ( R @ Xu0 @ Xv0 )
& ( Xq0 @ Xu0 ) )
=> ( Xq0 @ Xv0 ) )
& ! [Xw: a] :
( ( R @ Xu @ Xw )
=> ( Xq0 @ Xw ) ) )
=> ( Xq0 @ Xv ) ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ! [Xq0: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( S @ Xu @ Xv )
& ( Xq0 @ Xu ) )
=> ( Xq0 @ Xv ) )
& ! [Xw0: a] :
( ( S @ Xx @ Xw0 )
=> ( Xq0 @ Xw0 ) ) )
=> ( Xq0 @ Xw ) )
| ! [Xq0: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( R @ Xu @ Xv )
& ( Xq0 @ Xu ) )
=> ( Xq0 @ Xv ) )
& ! [Xw0: a] :
( ( R @ Xx @ Xw0 )
=> ( Xq0 @ Xw0 ) ) )
=> ( Xq0 @ Xw ) ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) )
=> ! [Xq: a > $o] :
( ( ! [Xu: a,Xv: a] :
( ( ( ( S @ Xu @ Xv )
| ( R @ Xu @ Xv ) )
& ( Xq @ Xu ) )
=> ( Xq @ Xv ) )
& ! [Xw: a] :
( ( ( S @ Xx @ Xw )
| ( R @ Xx @ Xw ) )
=> ( Xq @ Xw ) ) )
=> ( Xq @ Xy ) ) ),
inference('cnf.neg',[status(esa)],[cTHM251C_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] :
( ( ( ( !!
@ ^ [Y7: a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !!
@ ^ [Y8: a] :
( ( Y1 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
| ( !!
@ ^ [Y7: a > $o] :
( ( ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y0 @ Y8 @ Y9 )
& ( Y7 @ Y8 ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !!
@ ^ [Y8: a] :
( ( Y0 @ Y5 @ Y8 )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( Y1 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !!
@ ^ [Y6: a > $o] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( Y0 @ Y2 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
=> ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( ( Y1 @ Y5 @ Y6 )
| ( Y0 @ Y5 @ Y6 ) )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( ( Y1 @ Y2 @ Y5 )
| ( Y0 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) ),
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] :
( ( ( ( !!
@ ^ [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] :
( ( ( '#sk1' @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !!
@ ^ [Y7: a] :
( ( '#sk1' @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( Y0 @ Y1 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( '#sk1' @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( '#sk1' @ Y1 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
=> ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( ( Y0 @ Y4 @ Y5 )
| ( '#sk1' @ Y4 @ Y5 ) )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( ( Y0 @ Y1 @ Y4 )
| ( '#sk1' @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ),
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] :
( ( ( ( !!
@ ^ [Y5: a > $o] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( '#sk2' @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: a] :
( ( '#sk2' @ 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 ) ) ) )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk2' @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( '#sk2' @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !!
@ ^ [Y4: a > $o] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( '#sk1' @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: a] :
( ( '#sk1' @ Y0 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ 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_cl1]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: a] :
( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [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 ) ) ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk2' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk2' @ '#sk3' @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !!
@ ^ [Y3: a > $o] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: a] :
( ( '#sk1' @ '#sk3' @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ( '#sk2' @ Y2 @ Y3 )
| ( '#sk1' @ Y2 @ Y3 ) )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ '#sk3' @ Y2 )
| ( '#sk1' @ '#sk3' @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
~ ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [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 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ '#sk3' @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ '#sk3' @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [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 ) ) ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk2' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk2' @ '#sk3' @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !!
@ ^ [Y2: a > $o] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ '#sk3' @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl7,plain,
! [X2: a > $o] :
( ( ( !!
@ ^ [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 ) ) ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk4' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl10,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [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 ) ) ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X2 @ Y0 ) ) ) )
| ( X2 @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl13,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [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 ) ) ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk4' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl16,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk4' )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl19,plain,
! [X2: a > $o] :
( ~ ( ( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) )
=> ( X2 @ ( '#sk21' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl22,plain,
! [X2: a > $o] :
( ( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) ) )
& ( X2 @ ( '#sk15' @ X2 ) ) )
| ( X2 @ '#sk4' )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl27,plain,
! [X2: a > $o] :
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk4' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl23,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk21' @ X2 ) )
| ( X2 @ '#sk4' )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl29,plain,
! [X2: a > $o] :
( ( '#form37' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl33,plain,
! [X2: a > $o] :
( ~ ( '#form37'
@ ^ [Y0: a] : ( X2 @ Y0 ) )
| ( X2 @ '#sk4' )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl27,zip_derived_cl29]) ).
thf(zip_derived_cl39,plain,
! [X2: a > $o] :
( ~ ( '#form37' @ X2 )
| ( X2 @ '#sk4' )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl40,plain,
! [X2: a > $o] :
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X2 @ '#sk4' )
| ~ ( '#form37' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl43,plain,
! [X2: a > $o,X4: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) )
=> ( X4 @ ( '#sk21' @ X2 ) ) )
| ~ ( '#form37' @ X2 )
| ( X2 @ '#sk4' )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl47,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X2 @ '#sk4' )
| ~ ( '#form37' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl49,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form37' @ X2 )
| ( X2 @ '#sk4' )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X4 @ ( '#sk21' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl51,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ ( '#sk115' @ X4 ) @ Y0 )
& ( X4 @ ( '#sk115' @ X4 ) ) )
=> ( X4 @ Y0 ) ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X2 @ '#sk4' )
| ~ ( '#form37' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl53,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( ( ( '#sk2' @ ( '#sk115' @ X4 ) @ ( '#sk131' @ X4 ) )
& ( X4 @ ( '#sk115' @ X4 ) ) )
=> ( X4 @ ( '#sk131' @ X4 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form37' @ X2 )
| ( X2 @ '#sk4' )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X4 @ ( '#sk21' @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl56,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( X4 @ ( '#sk131' @ X4 ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X2 @ '#sk4' )
| ~ ( '#form37' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl61,plain,
! [X2: a > $o] :
( ~ ( '#form173' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl62,plain,
! [X2: a > $o,X4: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) )
=> ( X4 @ ( '#sk21' @ X2 ) ) )
| ~ ( '#form173' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl76,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ~ ( '#form173' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl89,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form173' @ X2 )
| ( X4 @ ( '#sk21' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl97,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ ( '#sk348' @ X4 ) @ Y0 )
& ( X4 @ ( '#sk348' @ X4 ) ) )
=> ( X4 @ Y0 ) ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ~ ( '#form173' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl99,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( ( ( '#sk1' @ ( '#sk348' @ X4 ) @ ( '#sk376' @ X4 ) )
& ( X4 @ ( '#sk348' @ X4 ) ) )
=> ( X4 @ ( '#sk376' @ X4 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form173' @ X2 )
| ( X4 @ ( '#sk21' @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl102,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( X4 @ ( '#sk376' @ X4 ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ~ ( '#form173' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl102_001,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( X4 @ ( '#sk376' @ X4 ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ~ ( '#form173' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl107,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form410' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl109,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form410' @ X2 @ X4 )
| ~ ( '#form173' @ X2 )
| ( X4 @ ( '#sk21' @ X2 ) )
| ~ ( X4 @ ( '#sk376' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl102,zip_derived_cl107]) ).
thf(zip_derived_cl101,plain,
! [X2: a > $o,X4: a > $o] :
( ( ( '#sk1' @ ( '#sk348' @ X4 ) @ ( '#sk376' @ X4 ) )
& ( X4 @ ( '#sk348' @ X4 ) ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ~ ( '#form173' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl106,plain,
! [X2: a > $o,X4: a > $o] :
( ( X4 @ ( '#sk348' @ X4 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form173' @ X2 )
| ( X4 @ ( '#sk21' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl107_002,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form410' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl116,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form410' @ X2
@ ^ [Y0: a] : ( X4 @ Y0 ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ~ ( '#form173' @ X2 )
| ( X4 @ ( '#sk348' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl106,zip_derived_cl107]) ).
thf(zip_derived_cl124,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form410' @ X2 @ X4 )
| ( X4 @ ( '#sk21' @ X2 ) )
| ~ ( '#form173' @ X2 )
| ( X4 @ ( '#sk348' @ X4 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl105,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#sk1' @ ( '#sk348' @ X4 ) @ ( '#sk376' @ X4 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form173' @ X2 )
| ( X4 @ ( '#sk21' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl107_003,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form410' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl115,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form410' @ X2
@ ^ [Y0: a] : ( X4 @ Y0 ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ~ ( '#form173' @ X2 )
| ( '#sk1' @ ( '#sk348' @ X4 ) @ ( '#sk376' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl105,zip_derived_cl107]) ).
thf(zip_derived_cl123,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form410' @ X2 @ X4 )
| ( X4 @ ( '#sk21' @ X2 ) )
| ~ ( '#form173' @ X2 )
| ( '#sk1' @ ( '#sk348' @ X4 ) @ ( '#sk376' @ X4 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl115]) ).
thf(zip_derived_cl6,plain,
~ ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ( '#sk2' @ Y1 @ Y2 )
| ( '#sk1' @ Y1 @ Y2 ) )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ '#sk3' @ Y1 )
| ( '#sk1' @ '#sk3' @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ '#sk4' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
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 ) ) ) )
=> ( '#sk5' @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl12,plain,
~ ( '#sk5' @ '#sk4' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl107_004,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form410' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl108,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk411' @ X2 @ X4 ) )
=> ( X4 @ ( '#sk411' @ X2 @ X4 ) ) )
| ( '#form410' @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl118,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( X4 @ ( '#sk411' @ X2 @ X4 ) )
| ( '#form410' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl56_005,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( X4 @ ( '#sk131' @ X4 ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X2 @ '#sk4' )
| ~ ( '#form37' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl61_006,plain,
! [X2: a > $o] :
( ~ ( '#form173' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl64,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form173' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form37' @ X2 )
| ( X2 @ '#sk4' )
| ( X4 @ ( '#sk21' @ X2 ) )
| ~ ( X4 @ ( '#sk131' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl56,zip_derived_cl61]) ).
thf(zip_derived_cl55,plain,
! [X2: a > $o,X4: a > $o] :
( ( ( '#sk2' @ ( '#sk115' @ X4 ) @ ( '#sk131' @ X4 ) )
& ( X4 @ ( '#sk115' @ X4 ) ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X2 @ '#sk4' )
| ~ ( '#form37' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl59,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#sk2' @ ( '#sk115' @ X4 ) @ ( '#sk131' @ X4 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form37' @ X2 )
| ( X2 @ '#sk4' )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X4 @ ( '#sk21' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl71,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form195' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl75,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form195' @ X2
@ ^ [Y0: a] : ( X4 @ Y0 ) )
| ~ ( X4 @ ( '#sk131' @ X4 ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ( X2 @ '#sk4' )
| ~ ( '#form37' @ X2 )
| ( '#form173' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl64,zip_derived_cl71]) ).
thf(zip_derived_cl88,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form195' @ X2 @ X4 )
| ~ ( X4 @ ( '#sk131' @ X4 ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ( X2 @ '#sk4' )
| ~ ( '#form37' @ X2 )
| ( '#form173' @ X2 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl60,plain,
! [X2: a > $o,X4: a > $o] :
( ( X4 @ ( '#sk115' @ X4 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form37' @ X2 )
| ( X2 @ '#sk4' )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X4 @ ( '#sk21' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl71_007,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form195' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl74,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form195' @ X2
@ ^ [Y0: a] : ( X4 @ Y0 ) )
| ( X4 @ ( '#sk21' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X2 @ '#sk4' )
| ~ ( '#form37' @ X2 )
| ( X4 @ ( '#sk115' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl60,zip_derived_cl71]) ).
thf(zip_derived_cl86,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form195' @ X2 @ X4 )
| ( X4 @ ( '#sk21' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X2 @ '#sk4' )
| ~ ( '#form37' @ X2 )
| ( X4 @ ( '#sk115' @ X4 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl61_008,plain,
! [X2: a > $o] :
( ~ ( '#form173' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl87,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form173' @ X2 )
| ( X4 @ ( '#sk115' @ X4 ) )
| ~ ( '#form37' @ X2 )
| ( X2 @ '#sk4' )
| ( X4 @ ( '#sk21' @ X2 ) )
| ~ ( '#form195' @ X2 @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl86,zip_derived_cl61]) ).
thf(zip_derived_cl7_009,plain,
! [X2: a > $o] :
( ( ( !!
@ ^ [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 ) ) ) )
& ( X2 @ Y0 ) )
=> ( X2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X2 @ Y0 ) ) ) )
=> ( X2 @ '#sk4' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl8,plain,
( ( ( !!
@ ^ [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 ) ) ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( '#sk5' @ Y0 ) ) ) )
=> ( '#sk5' @ '#sk4' ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl12_010,plain,
~ ( '#sk5' @ '#sk4' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl145,plain,
( ( ( !!
@ ^ [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 ) ) ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( '#sk5' @ Y0 ) ) ) )
=> $false ),
inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl12]) ).
thf(zip_derived_cl146,plain,
( (~)
@ ( ( !!
@ ^ [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 ) ) ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( '#sk5' @ Y0 ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl145]) ).
thf(zip_derived_cl147,plain,
~ ( ( !!
@ ^ [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 ) ) ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( '#sk5' @ Y0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl146]) ).
thf(zip_derived_cl148,plain,
( ~ ( !!
@ ^ [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 ) ) ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( '#sk5' @ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl147]) ).
thf(zip_derived_cl29_011,plain,
! [X2: a > $o] :
( ( '#form37' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl149,plain,
( ~ ( '#form37' @ '#sk5' )
| ~ ( !!
@ ^ [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 ) ) ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl148,zip_derived_cl29]) ).
thf(zip_derived_cl150,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ ( '#sk15' @ '#sk5' ) @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ ( '#sk15' @ '#sk5' ) @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
& ( '#sk5' @ ( '#sk15' @ '#sk5' ) ) )
=> ( '#sk5' @ Y0 ) ) )
| ~ ( '#form37' @ '#sk5' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl149]) ).
thf(zip_derived_cl151,plain,
( ~ ( ( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ ( '#sk15' @ '#sk5' ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ '#sk5' ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ '#sk5' ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ '#sk5' ) ) ) ) )
& ( '#sk5' @ ( '#sk15' @ '#sk5' ) ) )
=> ( '#sk5' @ ( '#sk21' @ '#sk5' ) ) )
| ~ ( '#form37' @ '#sk5' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl150]) ).
thf(zip_derived_cl153,plain,
( ~ ( '#sk5' @ ( '#sk21' @ '#sk5' ) )
| ~ ( '#form37' @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl151]) ).
thf(zip_derived_cl59_012,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#sk2' @ ( '#sk115' @ X4 ) @ ( '#sk131' @ X4 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form37' @ X2 )
| ( X2 @ '#sk4' )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X4 @ ( '#sk21' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl71_013,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form195' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl73,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form195' @ X2 @ X4 )
| ( X4 @ ( '#sk21' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) )
| ( X2 @ '#sk4' )
| ~ ( '#form37' @ X2 )
| ( '#sk2' @ ( '#sk115' @ X4 ) @ ( '#sk131' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl59,zip_derived_cl71]) ).
thf(zip_derived_cl61_014,plain,
! [X2: a > $o] :
( ~ ( '#form173' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ X2 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl83,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form173' @ X2 )
| ( '#sk2' @ ( '#sk115' @ X4 ) @ ( '#sk131' @ X4 ) )
| ~ ( '#form37' @ X2 )
| ( X2 @ '#sk4' )
| ( X4 @ ( '#sk21' @ X2 ) )
| ~ ( '#form195' @ X2 @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl73,zip_derived_cl61]) ).
thf(zip_derived_cl71_015,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form195' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl72,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk196' @ X2 @ X4 ) )
=> ( X4 @ ( '#sk196' @ X2 @ X4 ) ) )
| ( '#form195' @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl85,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( X4 @ ( '#sk196' @ X2 @ X4 ) )
| ( '#form195' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl117,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#sk1' @ ( '#sk15' @ X2 ) @ ( '#sk411' @ X2 @ X4 ) )
| ( '#form410' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl152,plain,
( ( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ ( '#sk15' @ '#sk5' ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ '#sk5' ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ ( '#sk15' @ '#sk5' ) @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk21' @ '#sk5' ) ) ) ) )
& ( '#sk5' @ ( '#sk15' @ '#sk5' ) ) )
| ~ ( '#form37' @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl151]) ).
thf(zip_derived_cl155,plain,
( ( '#sk5' @ ( '#sk15' @ '#sk5' ) )
| ~ ( '#form37' @ '#sk5' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl152]) ).
thf(zip_derived_cl29_016,plain,
! [X2: a > $o] :
( ( '#form37' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk2' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk2' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ '#sk3' @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl30,plain,
! [X2: a > $o] :
( ~ ( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) ) )
=> ( X2 @ ( '#sk38' @ X2 ) ) )
| ( '#form37' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl36,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk38' @ X2 ) )
| ( '#form37' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl84,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#sk2' @ ( '#sk15' @ X2 ) @ ( '#sk196' @ X2 @ X4 ) )
| ( '#form195' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl35,plain,
! [X2: a > $o] :
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( '#form37' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl42,plain,
! [X2: a > $o] :
( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk2' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk2' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( '#form37' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl45,plain,
! [X2: a > $o,X4: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) )
=> ( X4 @ ( '#sk38' @ X2 ) ) )
| ( '#form37' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl48,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( '#form37' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl50,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk2' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) )
| ( '#form37' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( X4 @ ( '#sk38' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl52,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ ( '#sk115' @ X4 ) @ Y0 )
& ( X4 @ ( '#sk115' @ X4 ) ) )
=> ( X4 @ Y0 ) ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( '#form37' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl54,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( ( ( '#sk2' @ ( '#sk115' @ X4 ) @ ( '#sk131' @ X4 ) )
& ( X4 @ ( '#sk115' @ X4 ) ) )
=> ( X4 @ ( '#sk131' @ X4 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) )
| ( '#form37' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( X4 @ ( '#sk38' @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl58,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( X4 @ ( '#sk131' @ X4 ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( '#form37' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl58_017,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( X4 @ ( '#sk131' @ X4 ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( '#form37' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl67,plain,
! [X2: a > $o] :
( ~ ( '#form186' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl70,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form186' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) )
| ( '#form37' @ X2 )
| ( X4 @ ( '#sk38' @ X2 ) )
| ~ ( X4 @ ( '#sk131' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl58,zip_derived_cl67]) ).
thf(zip_derived_cl57,plain,
! [X2: a > $o,X4: a > $o] :
( ( ( '#sk2' @ ( '#sk115' @ X4 ) @ ( '#sk131' @ X4 ) )
& ( X4 @ ( '#sk115' @ X4 ) ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( '#form37' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl65,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#sk2' @ ( '#sk115' @ X4 ) @ ( '#sk131' @ X4 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) )
| ( '#form37' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( X4 @ ( '#sk38' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl77,plain,
! [X4: a > $o] :
( ( '#form222' @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl81,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form222'
@ ^ [Y0: a] : ( X4 @ Y0 ) )
| ~ ( X4 @ ( '#sk131' @ X4 ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ( '#form37' @ X2 )
| ( '#form186' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl70,zip_derived_cl77]) ).
thf(zip_derived_cl95,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form222' @ X4 )
| ~ ( X4 @ ( '#sk131' @ X4 ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ( '#form37' @ X2 )
| ( '#form186' @ X2 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl11,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_cl9]) ).
thf(zip_derived_cl14,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ( '#sk2' @ Y0 @ Y1 )
| ( '#sk1' @ Y0 @ Y1 ) )
& ( '#sk5' @ Y0 ) )
=> ( '#sk5' @ Y1 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl17,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( ( ( ( '#sk2' @ X2 @ Y0 )
| ( '#sk1' @ X2 @ Y0 ) )
& ( '#sk5' @ X2 ) )
=> ( '#sk5' @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl20,plain,
! [X2: a,X4: a] :
( ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
& ( '#sk5' @ X2 ) )
=> ( '#sk5' @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl24,plain,
! [X2: a,X4: a] :
( ~ ( ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
& ( '#sk5' @ X2 ) )
| ( '#sk5' @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl32,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk2' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 ) )
| ~ ( '#sk5' @ X2 )
| ( '#sk5' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl37,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ( '#sk5' @ X4 )
| ~ ( '#sk5' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl67_018,plain,
! [X2: a > $o] :
( ~ ( '#form186' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl68,plain,
! [X2: a > $o,X4: a > $o] :
( ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) )
=> ( X4 @ ( '#sk38' @ X2 ) ) )
| ~ ( '#form186' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl82,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ~ ( '#form186' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl96,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( X4 @ Y0 ) )
=> ( X4 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form186' @ X2 )
| ( X4 @ ( '#sk38' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl98,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ ( '#sk348' @ X4 ) @ Y0 )
& ( X4 @ ( '#sk348' @ X4 ) ) )
=> ( X4 @ Y0 ) ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ~ ( '#form186' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl100,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( ( ( '#sk1' @ ( '#sk348' @ X4 ) @ ( '#sk376' @ X4 ) )
& ( X4 @ ( '#sk348' @ X4 ) ) )
=> ( X4 @ ( '#sk376' @ X4 ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form186' @ X2 )
| ( X4 @ ( '#sk38' @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl98]) ).
thf(zip_derived_cl104,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( X4 @ ( '#sk376' @ X4 ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ~ ( '#form186' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl104_019,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( X4 @ ( '#sk376' @ X4 ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ~ ( '#form186' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl112,plain,
! [X4: a > $o] :
( ( '#form422' @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl114,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form422' @ X4 )
| ~ ( '#form186' @ X2 )
| ( X4 @ ( '#sk38' @ X2 ) )
| ~ ( X4 @ ( '#sk376' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl104,zip_derived_cl112]) ).
thf(zip_derived_cl38,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk5' @ X4 )
| ~ ( '#sk5' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl103,plain,
! [X2: a > $o,X4: a > $o] :
( ( ( '#sk1' @ ( '#sk348' @ X4 ) @ ( '#sk376' @ X4 ) )
& ( X4 @ ( '#sk348' @ X4 ) ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ~ ( '#form186' @ X2 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl111,plain,
! [X2: a > $o,X4: a > $o] :
( ( X4 @ ( '#sk348' @ X4 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form186' @ X2 )
| ( X4 @ ( '#sk38' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl112_020,plain,
! [X4: a > $o] :
( ( '#form422' @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl120,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form422'
@ ^ [Y0: a] : ( X4 @ Y0 ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ~ ( '#form186' @ X2 )
| ( X4 @ ( '#sk348' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl111,zip_derived_cl112]) ).
thf(zip_derived_cl126,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form422' @ X4 )
| ( X4 @ ( '#sk38' @ X2 ) )
| ~ ( '#form186' @ X2 )
| ( X4 @ ( '#sk348' @ X4 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl120]) ).
thf(zip_derived_cl112_021,plain,
! [X4: a > $o] :
( ( '#form422' @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl113,plain,
! [X4: a > $o] :
( ~ ( ( '#sk1' @ '#sk3' @ ( '#sk423' @ X4 ) )
=> ( X4 @ ( '#sk423' @ X4 ) ) )
| ( '#form422' @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl121,plain,
! [X4: a > $o] :
( ( '#sk1' @ '#sk3' @ ( '#sk423' @ X4 ) )
| ( '#form422' @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl122,plain,
! [X4: a > $o] :
( ~ ( X4 @ ( '#sk423' @ X4 ) )
| ( '#form422' @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl110,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#sk1' @ ( '#sk348' @ X4 ) @ ( '#sk376' @ X4 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) )
| ~ ( '#form186' @ X2 )
| ( X4 @ ( '#sk38' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl112_022,plain,
! [X4: a > $o] :
( ( '#form422' @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl119,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form422'
@ ^ [Y0: a] : ( X4 @ Y0 ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ~ ( '#form186' @ X2 )
| ( '#sk1' @ ( '#sk348' @ X4 ) @ ( '#sk376' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl110,zip_derived_cl112]) ).
thf(zip_derived_cl125,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form422' @ X4 )
| ( X4 @ ( '#sk38' @ X2 ) )
| ~ ( '#form186' @ X2 )
| ( '#sk1' @ ( '#sk348' @ X4 ) @ ( '#sk376' @ X4 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl119]) ).
thf(zip_derived_cl66,plain,
! [X2: a > $o,X4: a > $o] :
( ( X4 @ ( '#sk115' @ X4 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) )
| ( '#form37' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( X4 @ ( '#sk38' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl77_023,plain,
! [X4: a > $o] :
( ( '#form222' @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl80,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form222'
@ ^ [Y0: a] : ( X4 @ Y0 ) )
| ( X4 @ ( '#sk38' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( '#form37' @ X2 )
| ( X4 @ ( '#sk115' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl66,zip_derived_cl77]) ).
thf(zip_derived_cl93,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form222' @ X4 )
| ( X4 @ ( '#sk38' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( '#form37' @ X2 )
| ( X4 @ ( '#sk115' @ X4 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl67_024,plain,
! [X2: a > $o] :
( ~ ( '#form186' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl94,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form186' @ X2 )
| ( X4 @ ( '#sk115' @ X4 ) )
| ( '#form37' @ X2 )
| ( X4 @ ( '#sk38' @ X2 ) )
| ~ ( '#form222' @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl93,zip_derived_cl67]) ).
thf(zip_derived_cl15,plain,
( !!
@ ^ [Y0: a] :
( ( ( '#sk2' @ '#sk3' @ Y0 )
| ( '#sk1' @ '#sk3' @ Y0 ) )
=> ( '#sk5' @ Y0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl18,plain,
! [X2: a] :
( ( ( '#sk2' @ '#sk3' @ X2 )
| ( '#sk1' @ '#sk3' @ X2 ) )
=> ( '#sk5' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21,plain,
! [X2: a] :
( ~ ( ( '#sk2' @ '#sk3' @ X2 )
| ( '#sk1' @ '#sk3' @ X2 ) )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl26,plain,
! [X2: a] :
( ~ ( '#sk1' @ '#sk3' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl65_025,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#sk2' @ ( '#sk115' @ X4 ) @ ( '#sk131' @ X4 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) )
| ( '#form37' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( X4 @ ( '#sk38' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl77_026,plain,
! [X4: a > $o] :
( ( '#form222' @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl79,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( '#form222' @ X4 )
| ( X4 @ ( '#sk38' @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) )
| ( '#form37' @ X2 )
| ( '#sk2' @ ( '#sk115' @ X4 ) @ ( '#sk131' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl65,zip_derived_cl77]) ).
thf(zip_derived_cl67_027,plain,
! [X2: a > $o] :
( ~ ( '#form186' @ X2 )
| ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ '#sk3' @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ ( '#sk38' @ X2 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl90,plain,
! [X2: a > $o,X4: a > $o] :
( ( '#form186' @ X2 )
| ( '#sk2' @ ( '#sk115' @ X4 ) @ ( '#sk131' @ X4 ) )
| ( '#form37' @ X2 )
| ( X4 @ ( '#sk38' @ X2 ) )
| ~ ( '#form222' @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl79,zip_derived_cl67]) ).
thf(zip_derived_cl77_028,plain,
! [X4: a > $o] :
( ( '#form222' @ X4 )
| ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk3' @ Y0 )
=> ( X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl78,plain,
! [X4: a > $o] :
( ~ ( ( '#sk2' @ '#sk3' @ ( '#sk223' @ X4 ) )
=> ( X4 @ ( '#sk223' @ X4 ) ) )
| ( '#form222' @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl91,plain,
! [X4: a > $o] :
( ( '#sk2' @ '#sk3' @ ( '#sk223' @ X4 ) )
| ( '#form222' @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl92,plain,
! [X4: a > $o] :
( ~ ( X4 @ ( '#sk223' @ X4 ) )
| ( '#form222' @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl25,plain,
! [X2: a] :
( ~ ( '#sk2' @ '#sk3' @ X2 )
| ( '#sk5' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl6613,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl109,zip_derived_cl124,zip_derived_cl123,zip_derived_cl12,zip_derived_cl118,zip_derived_cl88,zip_derived_cl87,zip_derived_cl153,zip_derived_cl83,zip_derived_cl85,zip_derived_cl117,zip_derived_cl155,zip_derived_cl36,zip_derived_cl84,zip_derived_cl95,zip_derived_cl37,zip_derived_cl114,zip_derived_cl38,zip_derived_cl126,zip_derived_cl121,zip_derived_cl122,zip_derived_cl125,zip_derived_cl94,zip_derived_cl26,zip_derived_cl90,zip_derived_cl91,zip_derived_cl92,zip_derived_cl25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEV148^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.WYq2ykaSyQ true
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 24 03:39:24 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % Running portfolio for 300 s
% 0.13/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in HO mode
% 0.20/0.64 % Total configuration time : 828
% 0.20/0.64 % Estimated wc time : 1656
% 0.20/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.52/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.52/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.55/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.55/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.55/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.55/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 37.75/7.14 % Solved by lams/20_acsne_simpl.sh.
% 37.75/7.14 % done 345 iterations in 6.133s
% 37.75/7.14 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 37.75/7.14 % SZS output start Refutation
% See solution above
% 37.75/7.15
% 37.75/7.15
% 37.75/7.15 % Terminating...
% 38.81/7.39 % Runner terminated.
% 38.81/7.40 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------