TSTP Solution File: SEV010^5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV010^5 : 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.3KiOpWdBTt true
% Computer : n029.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 19:59:16 EDT 2023
% Result : Theorem 26.23s 3.95s
% Output : Refutation 26.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 9
% Syntax : Number of formulae : 201 ( 16 unt; 8 typ; 0 def)
% Number of atoms : 1088 ( 89 equ; 0 cnn)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 3037 ( 192 ~; 250 |; 93 &;2220 @)
% ( 45 <=>; 84 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 4 con; 0-2 aty)
% ( 121 !!; 32 ??; 0 @@+; 0 @@-)
% Number of variables : 507 ( 301 ^; 196 !; 10 ?; 507 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf('#sk1_type',type,
'#sk1': a > a > $o ).
thf('#sk2_type',type,
'#sk2': a ).
thf('#sk24_type',type,
'#sk24': ( a > $o ) > a > $o ).
thf('#sk28_type',type,
'#sk28': ( a > $o ) > a ).
thf('#_fresh_sk90_type',type,
'#_fresh_sk90': ( a > $o ) > a ).
thf('#_fresh_sk52_type',type,
'#_fresh_sk52': ( a > $o ) > a ).
thf('#sk17_type',type,
'#sk17': ( a > $o ) > a ).
thf(cTHM260_pme,conjecture,
! [R: a > a > $o] :
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( ( R @ Xy @ Xz )
& ( R @ Xx @ Xy ) )
=> ( R @ Xx @ Xz ) )
& ! [Xx: a,Xy: a] :
( ( R @ Xx @ Xy )
=> ( R @ Xy @ Xx ) )
& ! [Xx: a] : ( R @ Xx @ Xx ) )
=> ( ! [Xx: a] :
? [Xp: a > $o] :
( ? [Xz: a] : ( Xp @ Xz )
& ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ! [Xy: a] :
( ( Xp @ Xy )
<=> ( R @ Xx0 @ Xy ) ) )
& ( Xp @ Xx )
& ! [Xq: a > $o] :
( ( ( Xq @ Xx )
& ! [Xx0: a] :
( ( Xq @ Xx0 )
=> ! [Xy: a] :
( ( Xq @ Xy )
<=> ( R @ Xx0 @ Xy ) ) )
& ? [Xz: a] : ( Xq @ Xz ) )
=> ( Xq = Xp ) ) )
& ! [Xp: a > $o] :
( ( ! [Xx: a] :
( ( Xp @ Xx )
=> ! [Xy: a] :
( ( Xp @ Xy )
<=> ( R @ Xx @ Xy ) ) )
& ? [Xz: a] : ( Xp @ Xz ) )
=> ? [Xz: a] : ( Xp @ Xz ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [R: a > a > $o] :
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( ( R @ Xy @ Xz )
& ( R @ Xx @ Xy ) )
=> ( R @ Xx @ Xz ) )
& ! [Xx: a,Xy: a] :
( ( R @ Xx @ Xy )
=> ( R @ Xy @ Xx ) )
& ! [Xx: a] : ( R @ Xx @ Xx ) )
=> ( ! [Xx: a] :
? [Xp: a > $o] :
( ? [Xz: a] : ( Xp @ Xz )
& ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ! [Xy: a] :
( ( Xp @ Xy )
<=> ( R @ Xx0 @ Xy ) ) )
& ( Xp @ Xx )
& ! [Xq: a > $o] :
( ( ( Xq @ Xx )
& ! [Xx0: a] :
( ( Xq @ Xx0 )
=> ! [Xy: a] :
( ( Xq @ Xy )
<=> ( R @ Xx0 @ Xy ) ) )
& ? [Xz: a] : ( Xq @ Xz ) )
=> ( Xq = Xp ) ) )
& ! [Xp: a > $o] :
( ( ! [Xx: a] :
( ( Xp @ Xx )
=> ! [Xy: a] :
( ( Xp @ Xy )
<=> ( R @ Xx @ Xy ) ) )
& ? [Xz: a] : ( Xp @ Xz ) )
=> ? [Xz: a] : ( Xp @ Xz ) ) ) ),
inference('cnf.neg',[status(esa)],[cTHM260_pme]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a > $o] :
( ( ??
@ ^ [Y3: a] : ( Y2 @ Y3 ) )
& ( !!
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !!
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
<=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( Y2 @ Y1 )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !!
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !!
@ ^ [Y5: a] :
( ( Y3 @ Y5 )
<=> ( Y0 @ Y4 @ Y5 ) ) ) ) )
& ( ??
@ ^ [Y4: a] : ( Y3 @ Y4 ) ) )
=> ( Y3 = Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: a > $o] :
( ( ( !!
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !!
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
<=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( ??
@ ^ [Y2: a] : ( Y1 @ Y2 ) ) )
=> ( ??
@ ^ [Y2: a] : ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !!
@ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) ) )
=> ( !!
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a > $o] :
( ( ??
@ ^ [Y3: a] : ( Y2 @ Y3 ) )
& ( !!
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !!
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
<=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
& ( Y2 @ Y1 )
& ( !!
@ ^ [Y3: a > $o] :
( ( ( Y3 @ Y1 )
& ( !!
@ ^ [Y4: a] :
( ( Y3 @ Y4 )
=> ( !!
@ ^ [Y5: a] :
( ( Y3 @ Y5 )
<=> ( Y0 @ Y4 @ Y5 ) ) ) ) )
& ( ??
@ ^ [Y4: a] : ( Y3 @ Y4 ) ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1' @ Y1 @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: a] : ( '#sk1' @ Y0 @ Y0 ) ) )
=> ( !!
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a > $o] :
( ( ??
@ ^ [Y2: a] : ( Y1 @ Y2 ) )
& ( !!
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !!
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
<=> ( '#sk1' @ Y2 @ Y3 ) ) ) ) )
& ( Y1 @ Y0 )
& ( !!
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !!
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !!
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
<=> ( '#sk1' @ Y3 @ Y4 ) ) ) ) )
& ( ??
@ ^ [Y3: a] : ( Y2 @ Y3 ) ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1' @ Y1 @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: a] : ( '#sk1' @ Y0 @ Y0 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl7,plain,
( !!
@ ^ [Y0: a] : ( '#sk1' @ Y0 @ Y0 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl11,plain,
! [X2: a] : ( '#sk1' @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl4,plain,
~ ( !!
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a > $o] :
( ( ??
@ ^ [Y2: a] : ( Y1 @ Y2 ) )
& ( !!
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !!
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
<=> ( '#sk1' @ Y2 @ Y3 ) ) ) ) )
& ( Y1 @ Y0 )
& ( !!
@ ^ [Y2: a > $o] :
( ( ( Y2 @ Y0 )
& ( !!
@ ^ [Y3: a] :
( ( Y2 @ Y3 )
=> ( !!
@ ^ [Y4: a] :
( ( Y2 @ Y4 )
<=> ( '#sk1' @ Y3 @ Y4 ) ) ) ) )
& ( ??
@ ^ [Y3: a] : ( Y2 @ Y3 ) ) )
=> ( Y2 = Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl8,plain,
~ ( ??
@ ^ [Y0: a > $o] :
( ( ??
@ ^ [Y1: a] : ( Y0 @ Y1 ) )
& ( !!
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
<=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ '#sk2' )
& ( !!
@ ^ [Y1: a > $o] :
( ( ( Y1 @ '#sk2' )
& ( !!
@ ^ [Y2: a] :
( ( Y1 @ Y2 )
=> ( !!
@ ^ [Y3: a] :
( ( Y1 @ Y3 )
<=> ( '#sk1' @ Y2 @ Y3 ) ) ) ) )
& ( ??
@ ^ [Y2: a] : ( Y1 @ Y2 ) ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl12,plain,
! [X2: a > $o] :
~ ( ( ??
@ ^ [Y0: a] : ( X2 @ Y0 ) )
& ( !!
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( !!
@ ^ [Y1: a] :
( ( X2 @ Y1 )
<=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
& ( X2 @ '#sk2' )
& ( !!
@ ^ [Y0: a > $o] :
( ( ( Y0 @ '#sk2' )
& ( !!
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
<=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( ??
@ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
=> ( Y0 = X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl15,plain,
! [X2: a > $o] :
( ~ ( ??
@ ^ [Y0: a] : ( X2 @ Y0 ) )
| ~ ( !!
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( !!
@ ^ [Y1: a] :
( ( X2 @ Y1 )
<=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
| ~ ( X2 @ '#sk2' )
| ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( Y0 @ '#sk2' )
& ( !!
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
<=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( ??
@ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
=> ( Y0 = X2 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl18,plain,
! [X2: a > $o,X4: a] :
( ~ ( X2 @ X4 )
| ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( Y0 @ '#sk2' )
& ( !!
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
<=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( ??
@ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
=> ( Y0 = X2 ) ) )
| ~ ( X2 @ '#sk2' )
| ~ ( !!
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( !!
@ ^ [Y1: a] :
( ( X2 @ Y1 )
<=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl20,plain,
! [X0: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( X0 @ Y0 )
=> ( !!
@ ^ [Y1: a] :
( ( X0 @ Y1 )
<=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( Y0 @ '#sk2' )
& ( !!
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
<=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( ??
@ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
=> ( Y0 = X0 ) ) )
| ~ ( X0 @ '#sk2' ) ),
inference(condensation,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl21,plain,
! [X0: a > $o] :
( ~ ( ( X0 @ ( '#sk17' @ X0 ) )
=> ( !!
@ ^ [Y0: a] :
( ( X0 @ Y0 )
<=> ( '#sk1' @ ( '#sk17' @ X0 ) @ Y0 ) ) ) )
| ~ ( X0 @ '#sk2' )
| ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( Y0 @ '#sk2' )
& ( !!
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
<=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( ??
@ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
=> ( Y0 = X0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl24,plain,
! [X0: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( X0 @ Y0 )
<=> ( '#sk1' @ ( '#sk17' @ X0 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( Y0 @ '#sk2' )
& ( !!
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
<=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( ??
@ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
=> ( Y0 = X0 ) ) )
| ~ ( X0 @ '#sk2' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl27,plain,
! [X0: a > $o] :
( ~ ( ( X0 @ ( '#sk28' @ X0 ) )
<=> ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
| ~ ( X0 @ '#sk2' )
| ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( Y0 @ '#sk2' )
& ( !!
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
<=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( ??
@ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
=> ( Y0 = X0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl30,plain,
! [X0: a > $o] :
( ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
| ~ ( X0 @ '#sk2' )
| ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( Y0 @ '#sk2' )
& ( !!
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
<=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( ??
@ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
=> ( Y0 = X0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl31,plain,
! [X0: a > $o] :
( ~ ( ( ( '#sk24' @ X0 @ '#sk2' )
& ( !!
@ ^ [Y0: a] :
( ( '#sk24' @ X0 @ Y0 )
=> ( !!
@ ^ [Y1: a] :
( ( '#sk24' @ X0 @ Y1 )
<=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
& ( ??
@ ^ [Y0: a] : ( '#sk24' @ X0 @ Y0 ) ) )
=> ( ( '#sk24' @ X0 )
= X0 ) )
| ~ ( X0 @ '#sk2' )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl38,plain,
! [X0: a > $o] :
( ( ( '#sk24' @ X0 )
!= X0 )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
| ~ ( X0 @ '#sk2' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl44,plain,
! [X0: a > $o] :
( ( ( '#sk24' @ X0 )
!= X0 )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
| ~ ( X0 @ '#sk2' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl45,plain,
! [X0: a > $o] :
( ( ( '#sk24' @ X0 @ ( '#_fresh_sk90' @ X0 ) )
!= ( X0 @ ( '#_fresh_sk90' @ X0 ) ) )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
| ~ ( X0 @ '#sk2' ) ),
inference(neg_ext_simpl,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl148,plain,
( ( ( ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( '#sk28'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) )
!= ( '#sk1'
@ ( '#sk17'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) )
@ ( '#sk28'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) ) )
| ( ( '#sk24'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( '#_fresh_sk90'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( '#_fresh_sk90'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl45]) ).
thf(zip_derived_cl153,plain,
( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl148]) ).
thf(zip_derived_cl11_001,plain,
! [X2: a] : ( '#sk1' @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl23,plain,
! [X0: a > $o] :
( ( X0 @ ( '#sk17' @ X0 ) )
| ~ ( !!
@ ^ [Y0: a > $o] :
( ( ( Y0 @ '#sk2' )
& ( !!
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
<=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( ??
@ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
=> ( Y0 = X0 ) ) )
| ~ ( X0 @ '#sk2' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl26,plain,
! [X0: a > $o] :
( ~ ( ( ( '#sk24' @ X0 @ '#sk2' )
& ( !!
@ ^ [Y0: a] :
( ( '#sk24' @ X0 @ Y0 )
=> ( !!
@ ^ [Y1: a] :
( ( '#sk24' @ X0 @ Y1 )
<=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
& ( ??
@ ^ [Y0: a] : ( '#sk24' @ X0 @ Y0 ) ) )
=> ( ( '#sk24' @ X0 )
= X0 ) )
| ~ ( X0 @ '#sk2' )
| ( X0 @ ( '#sk17' @ X0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl28,plain,
! [X0: a > $o] :
( ( ( '#sk24' @ X0 @ '#sk2' )
& ( !!
@ ^ [Y0: a] :
( ( '#sk24' @ X0 @ Y0 )
=> ( !!
@ ^ [Y1: a] :
( ( '#sk24' @ X0 @ Y1 )
<=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
& ( ??
@ ^ [Y0: a] : ( '#sk24' @ X0 @ Y0 ) ) )
| ( X0 @ ( '#sk17' @ X0 ) )
| ~ ( X0 @ '#sk2' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl32,plain,
! [X0: a > $o] :
( ( '#sk24' @ X0 @ '#sk2' )
| ~ ( X0 @ '#sk2' )
| ( X0 @ ( '#sk17' @ X0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl85,plain,
( ( ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( '#sk17'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) )
| ( '#sk24'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl32]) ).
thf(zip_derived_cl89,plain,
( ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl11_002,plain,
! [X2: a] : ( '#sk1' @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl33,plain,
! [X0: a > $o] :
( ( !!
@ ^ [Y0: a] :
( ( '#sk24' @ X0 @ Y0 )
=> ( !!
@ ^ [Y1: a] :
( ( '#sk24' @ X0 @ Y1 )
<=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
| ~ ( X0 @ '#sk2' )
| ( X0 @ ( '#sk17' @ X0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl39,plain,
! [X0: a > $o,X2: a] :
( ( ( '#sk24' @ X0 @ X2 )
=> ( !!
@ ^ [Y0: a] :
( ( '#sk24' @ X0 @ Y0 )
<=> ( '#sk1' @ X2 @ Y0 ) ) ) )
| ( X0 @ ( '#sk17' @ X0 ) )
| ~ ( X0 @ '#sk2' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl46,plain,
! [X0: a > $o,X2: a] :
( ~ ( '#sk24' @ X0 @ X2 )
| ( !!
@ ^ [Y0: a] :
( ( '#sk24' @ X0 @ Y0 )
<=> ( '#sk1' @ X2 @ Y0 ) ) )
| ~ ( X0 @ '#sk2' )
| ( X0 @ ( '#sk17' @ X0 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl49,plain,
! [X0: a > $o,X2: a,X4: a] :
( ( ( '#sk24' @ X0 @ X4 )
<=> ( '#sk1' @ X2 @ X4 ) )
| ( X0 @ ( '#sk17' @ X0 ) )
| ~ ( X0 @ '#sk2' )
| ~ ( '#sk24' @ X0 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl51,plain,
! [X0: a > $o,X2: a,X4: a] :
( ( ( '#sk24' @ X0 @ X4 )
= ( '#sk1' @ X2 @ X4 ) )
| ( X0 @ ( '#sk17' @ X0 ) )
| ~ ( X0 @ '#sk2' )
| ~ ( '#sk24' @ X0 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl244,plain,
! [X0: a,X1: a] :
( ~ ( '#sk24'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ X0 )
| ( ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( '#sk17'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) )
| ( ( '#sk24'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ X1 )
= ( '#sk1' @ X0 @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl51]) ).
thf(zip_derived_cl248,plain,
! [X0: a,X1: a] :
( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
| ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
= ( '#sk1' @ X0 @ X1 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl244]) ).
thf(zip_derived_cl1309,plain,
! [X0: a] :
( ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
= ( '#sk1' @ '#sk2' @ X0 ) )
| ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl248]) ).
thf(zip_derived_cl1326,plain,
! [X0: a] :
( ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
= ( '#sk1' @ '#sk2' @ X0 ) )
| ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1309]) ).
thf(zip_derived_cl11_003,plain,
! [X2: a] : ( '#sk1' @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl29,plain,
! [X0: a > $o] :
( ( ( '#sk24' @ X0 )
!= X0 )
| ( X0 @ ( '#sk17' @ X0 ) )
| ~ ( X0 @ '#sk2' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl35,plain,
! [X0: a > $o] :
( ( ( '#sk24' @ X0 )
!= X0 )
| ( X0 @ ( '#sk17' @ X0 ) )
| ~ ( X0 @ '#sk2' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl36,plain,
! [X0: a > $o] :
( ( ( '#sk24' @ X0 @ ( '#_fresh_sk52' @ X0 ) )
!= ( X0 @ ( '#_fresh_sk52' @ X0 ) ) )
| ( X0 @ ( '#sk17' @ X0 ) )
| ~ ( X0 @ '#sk2' ) ),
inference(neg_ext_simpl,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl136,plain,
( ( ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( '#sk17'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) )
| ( ( '#sk24'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( '#_fresh_sk52'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( '#_fresh_sk52'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl36]) ).
thf(zip_derived_cl141,plain,
( ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk52' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ '#sk2' @ ( '#_fresh_sk52' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl136]) ).
thf(zip_derived_cl1338,plain,
( ( ( '#sk1' @ '#sk2' @ ( '#_fresh_sk52' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ '#sk2' @ ( '#_fresh_sk52' @ ( '#sk1' @ '#sk2' ) ) ) )
| ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1326,zip_derived_cl141]) ).
thf(zip_derived_cl1371,plain,
'#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1338]) ).
thf(zip_derived_cl6,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1' @ Y1 @ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl10,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1' @ Y0 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl14,plain,
! [X2: a,X4: a] :
( ( '#sk1' @ X2 @ X4 )
=> ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl17,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl1401,plain,
'#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2',
inference('sup-',[status(thm)],[zip_derived_cl1371,zip_derived_cl17]) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl9,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk1' @ X2 @ Y0 ) )
=> ( '#sk1' @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl13,plain,
! [X2: a,X4: a] :
( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ X4 @ Y0 )
& ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk1' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl16,plain,
! [X2: a,X4: a,X6: a] :
( ( ( '#sk1' @ X4 @ X6 )
& ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl19,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( '#sk1' @ X4 @ X6 )
& ( '#sk1' @ X2 @ X4 ) )
| ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl22,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk1' @ X4 @ X6 )
| ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl1420,plain,
! [X0: a] :
( ( '#sk1' @ X0 @ '#sk2' )
| ~ ( '#sk1' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1401,zip_derived_cl22]) ).
thf(zip_derived_cl11_004,plain,
! [X2: a] : ( '#sk1' @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl37,plain,
! [X0: a > $o] :
( ( ( '#sk24' @ X0 @ '#sk2' )
& ( !!
@ ^ [Y0: a] :
( ( '#sk24' @ X0 @ Y0 )
=> ( !!
@ ^ [Y1: a] :
( ( '#sk24' @ X0 @ Y1 )
<=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
& ( ??
@ ^ [Y0: a] : ( '#sk24' @ X0 @ Y0 ) ) )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
| ~ ( X0 @ '#sk2' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl41,plain,
! [X0: a > $o] :
( ( '#sk24' @ X0 @ '#sk2' )
| ~ ( X0 @ '#sk2' )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl147,plain,
( ( ( ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( '#sk28'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) )
!= ( '#sk1'
@ ( '#sk17'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) )
@ ( '#sk28'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) ) )
| ( '#sk24'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl41]) ).
thf(zip_derived_cl152,plain,
( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl147]) ).
thf(zip_derived_cl223,plain,
( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl152]) ).
thf(zip_derived_cl17_005,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl251,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl223,zip_derived_cl17]) ).
thf(zip_derived_cl1564,plain,
( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
inference('sup+',[status(thm)],[zip_derived_cl1420,zip_derived_cl251]) ).
thf(zip_derived_cl17_006,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl2562,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1564,zip_derived_cl17]) ).
thf(zip_derived_cl11_007,plain,
! [X2: a] : ( '#sk1' @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl42,plain,
! [X0: a > $o] :
( ( !!
@ ^ [Y0: a] :
( ( '#sk24' @ X0 @ Y0 )
=> ( !!
@ ^ [Y1: a] :
( ( '#sk24' @ X0 @ Y1 )
<=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
| ~ ( X0 @ '#sk2' )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl47,plain,
! [X0: a > $o,X2: a] :
( ( ( '#sk24' @ X0 @ X2 )
=> ( !!
@ ^ [Y0: a] :
( ( '#sk24' @ X0 @ Y0 )
<=> ( '#sk1' @ X2 @ Y0 ) ) ) )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
| ~ ( X0 @ '#sk2' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl50,plain,
! [X0: a > $o,X2: a] :
( ~ ( '#sk24' @ X0 @ X2 )
| ( !!
@ ^ [Y0: a] :
( ( '#sk24' @ X0 @ Y0 )
<=> ( '#sk1' @ X2 @ Y0 ) ) )
| ~ ( X0 @ '#sk2' )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl52,plain,
! [X0: a > $o,X2: a,X4: a] :
( ( ( '#sk24' @ X0 @ X4 )
<=> ( '#sk1' @ X2 @ X4 ) )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
| ~ ( X0 @ '#sk2' )
| ~ ( '#sk24' @ X0 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl53,plain,
! [X0: a > $o,X2: a,X4: a] :
( ( ( '#sk24' @ X0 @ X4 )
= ( '#sk1' @ X2 @ X4 ) )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
| ~ ( X0 @ '#sk2' )
| ~ ( '#sk24' @ X0 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl322,plain,
! [X0: a,X1: a] :
( ~ ( '#sk24'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ X0 )
| ( ( ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( '#sk28'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) )
!= ( '#sk1'
@ ( '#sk17'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) )
@ ( '#sk28'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) ) )
| ( ( '#sk24'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ X1 )
= ( '#sk1' @ X0 @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl53]) ).
thf(zip_derived_cl327,plain,
! [X0: a,X1: a] :
( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
| ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
= ( '#sk1' @ X0 @ X1 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl322]) ).
thf(zip_derived_cl2522,plain,
! [X0: a,X1: a] :
( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
= ( '#sk1' @ X0 @ X1 ) )
| ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl327]) ).
thf(zip_derived_cl3524,plain,
! [X0: a] :
( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
= ( '#sk1' @ '#sk2' @ X0 ) )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2562,zip_derived_cl2522]) ).
thf(zip_derived_cl3539,plain,
! [X0: a] :
( ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
= ( '#sk1' @ '#sk2' @ X0 ) )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl3524]) ).
thf(zip_derived_cl17_008,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl3564,plain,
! [X0: a] :
( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
= ( '#sk1' @ '#sk2' @ X0 ) )
| ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3539,zip_derived_cl17]) ).
thf(zip_derived_cl1420_009,plain,
! [X0: a] :
( ( '#sk1' @ X0 @ '#sk2' )
| ~ ( '#sk1' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1401,zip_derived_cl22]) ).
thf(zip_derived_cl3591,plain,
! [X0: a] :
( ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
= ( '#sk1' @ '#sk2' @ X0 ) )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl3564,zip_derived_cl1420]) ).
thf(zip_derived_cl17_010,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl3613,plain,
! [X0: a] :
( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
= ( '#sk1' @ '#sk2' @ X0 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl3591,zip_derived_cl17]) ).
thf(zip_derived_cl17_011,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl3621,plain,
! [X0: a] :
( ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
= ( '#sk1' @ '#sk2' @ X0 ) )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3613,zip_derived_cl17]) ).
thf(zip_derived_cl153_012,plain,
( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl148]) ).
thf(zip_derived_cl378,plain,
( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl3675,plain,
( ( ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3621,zip_derived_cl378]) ).
thf(zip_derived_cl3699,plain,
( ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl3675]) ).
thf(zip_derived_cl17_013,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl3751,plain,
( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3699,zip_derived_cl17]) ).
thf(zip_derived_cl1420_014,plain,
! [X0: a] :
( ( '#sk1' @ X0 @ '#sk2' )
| ~ ( '#sk1' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1401,zip_derived_cl22]) ).
thf(zip_derived_cl3921,plain,
( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl3751,zip_derived_cl1420]) ).
thf(zip_derived_cl17_015,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl3935,plain,
'#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2',
inference(clc,[status(thm)],[zip_derived_cl3921,zip_derived_cl17]) ).
thf(zip_derived_cl17_016,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl3942,plain,
'#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl3935,zip_derived_cl17]) ).
thf(zip_derived_cl3950,plain,
( ~ ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl153,zip_derived_cl3942]) ).
thf(zip_derived_cl3935_017,plain,
'#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2',
inference(clc,[status(thm)],[zip_derived_cl3921,zip_derived_cl17]) ).
thf(zip_derived_cl1371_018,plain,
'#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1338]) ).
thf(zip_derived_cl22_019,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk1' @ X4 @ X6 )
| ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl1400,plain,
! [X0: a] :
( ( '#sk1' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
| ~ ( '#sk1' @ X0 @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1371,zip_derived_cl22]) ).
thf(zip_derived_cl17_020,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl1629,plain,
! [X0: a] :
( ~ ( '#sk1' @ X0 @ '#sk2' )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1400,zip_derived_cl17]) ).
thf(zip_derived_cl3936,plain,
'#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl3935,zip_derived_cl1629]) ).
thf(zip_derived_cl4005,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3950,zip_derived_cl3936]) ).
thf(zip_derived_cl153_021,plain,
( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl148]) ).
thf(zip_derived_cl380,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl3179,plain,
( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl380]) ).
thf(zip_derived_cl17_022,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl3251,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3179,zip_derived_cl17]) ).
thf(zip_derived_cl1420_023,plain,
! [X0: a] :
( ( '#sk1' @ X0 @ '#sk2' )
| ~ ( '#sk1' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1401,zip_derived_cl22]) ).
thf(zip_derived_cl3285,plain,
( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl3251,zip_derived_cl1420]) ).
thf(zip_derived_cl17_024,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl3299,plain,
( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl3285,zip_derived_cl17]) ).
thf(zip_derived_cl1629_025,plain,
! [X0: a] :
( ~ ( '#sk1' @ X0 @ '#sk2' )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1400,zip_derived_cl17]) ).
thf(zip_derived_cl3300,plain,
( ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3299,zip_derived_cl1629]) ).
thf(zip_derived_cl380_026,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl3340,plain,
( ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3300,zip_derived_cl380]) ).
thf(zip_derived_cl3370,plain,
( ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl3340]) ).
thf(zip_derived_cl3299_027,plain,
( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl3285,zip_derived_cl17]) ).
thf(zip_derived_cl17_028,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl3306,plain,
( ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3299,zip_derived_cl17]) ).
thf(zip_derived_cl3398,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl3370,zip_derived_cl3306]) ).
thf(zip_derived_cl152_029,plain,
( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl147]) ).
thf(zip_derived_cl224,plain,
( ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ~ ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl152]) ).
thf(zip_derived_cl11_030,plain,
! [X2: a] : ( '#sk1' @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl3613_031,plain,
! [X0: a] :
( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
= ( '#sk1' @ '#sk2' @ X0 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl3591,zip_derived_cl17]) ).
thf(zip_derived_cl3622,plain,
! [X0: a] :
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
| ~ ( '#sk1' @ '#sk2' @ X0 )
| ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl3613]) ).
thf(zip_derived_cl3838,plain,
( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl3622]) ).
thf(zip_derived_cl1629_032,plain,
! [X0: a] :
( ~ ( '#sk1' @ X0 @ '#sk2' )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1400,zip_derived_cl17]) ).
thf(zip_derived_cl3846,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3838,zip_derived_cl1629]) ).
thf(zip_derived_cl3878,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' )
| ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
inference('sup+',[status(thm)],[zip_derived_cl224,zip_derived_cl3846]) ).
thf(zip_derived_cl3898,plain,
( ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
inference(simplify,[status(thm)],[zip_derived_cl3878]) ).
thf(zip_derived_cl2562_033,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1564,zip_derived_cl17]) ).
thf(zip_derived_cl3904,plain,
'#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2',
inference(clc,[status(thm)],[zip_derived_cl3898,zip_derived_cl2562]) ).
thf(zip_derived_cl327_034,plain,
! [X0: a,X1: a] :
( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
| ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
= ( '#sk1' @ X0 @ X1 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl322]) ).
thf(zip_derived_cl2525,plain,
! [X0: a,X1: a] :
( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
| ( '#sk1' @ X0 @ X1 )
| ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
| ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl327]) ).
thf(zip_derived_cl3942_035,plain,
'#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl3935,zip_derived_cl17]) ).
thf(zip_derived_cl3959,plain,
! [X0: a,X1: a] :
( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
| ( '#sk1' @ X0 @ X1 )
| ~ ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2525,zip_derived_cl3942]) ).
thf(zip_derived_cl3936_036,plain,
'#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl3935,zip_derived_cl1629]) ).
thf(zip_derived_cl4066,plain,
! [X0: a,X1: a] :
( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
| ( '#sk1' @ X0 @ X1 )
| ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl3959,zip_derived_cl3936]) ).
thf(zip_derived_cl4069,plain,
! [X0: a] :
( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
| ( '#sk1' @ X0 @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl3904,zip_derived_cl4066]) ).
thf(zip_derived_cl4081,plain,
( ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl3398,zip_derived_cl4069]) ).
thf(zip_derived_cl17_037,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl4127,plain,
'#sk1' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2',
inference(clc,[status(thm)],[zip_derived_cl4081,zip_derived_cl17]) ).
thf(zip_derived_cl17_038,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl4134,plain,
'#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl4127,zip_derived_cl17]) ).
thf(zip_derived_cl4142,plain,
~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4005,zip_derived_cl4134]) ).
thf(zip_derived_cl11_039,plain,
! [X2: a] : ( '#sk1' @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl1371_040,plain,
'#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1338]) ).
thf(zip_derived_cl53_041,plain,
! [X0: a > $o,X2: a,X4: a] :
( ( ( '#sk24' @ X0 @ X4 )
= ( '#sk1' @ X2 @ X4 ) )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
| ~ ( X0 @ '#sk2' )
| ~ ( '#sk24' @ X0 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl312,plain,
! [X0: a > $o,X2: a,X4: a] :
( ( '#sk24' @ X0 @ X4 )
| ~ ( '#sk1' @ X2 @ X4 )
| ~ ( '#sk24' @ X0 @ X2 )
| ~ ( X0 @ '#sk2' )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl2641,plain,
! [X0: a > $o] :
( ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
| ~ ( X0 @ '#sk2' )
| ~ ( '#sk24' @ X0 @ '#sk2' )
| ( '#sk24' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1371,zip_derived_cl312]) ).
thf(zip_derived_cl41_042,plain,
! [X0: a > $o] :
( ( '#sk24' @ X0 @ '#sk2' )
| ~ ( X0 @ '#sk2' )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl2664,plain,
! [X0: a > $o] :
( ( '#sk24' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
| ~ ( X0 @ '#sk2' )
| ( ( X0 @ ( '#sk28' @ X0 ) )
!= ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl2641,zip_derived_cl41]) ).
thf(zip_derived_cl2670,plain,
( ( ( ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( '#sk28'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) )
!= ( '#sk1'
@ ( '#sk17'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) )
@ ( '#sk28'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) ) ) ) )
| ( '#sk24'
@ ^ [Y0: a] :
( '#sk1'
@ ( ^ [Y1: a] :
( ^ [Y2: a] : '#sk2'
@ Y1 )
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl2664]) ).
thf(zip_derived_cl2674,plain,
( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl2670]) ).
thf(zip_derived_cl2677,plain,
( ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ~ ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl2674]) ).
thf(zip_derived_cl2674_043,plain,
( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl2670]) ).
thf(zip_derived_cl2676,plain,
( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl2674]) ).
thf(zip_derived_cl17_044,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl3037,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2676,zip_derived_cl17]) ).
thf(zip_derived_cl1420_045,plain,
! [X0: a] :
( ( '#sk1' @ X0 @ '#sk2' )
| ~ ( '#sk1' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1401,zip_derived_cl22]) ).
thf(zip_derived_cl3064,plain,
( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl3037,zip_derived_cl1420]) ).
thf(zip_derived_cl17_046,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl3078,plain,
( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl3064,zip_derived_cl17]) ).
thf(zip_derived_cl1629_047,plain,
! [X0: a] :
( ~ ( '#sk1' @ X0 @ '#sk2' )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1400,zip_derived_cl17]) ).
thf(zip_derived_cl3079,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3078,zip_derived_cl1629]) ).
thf(zip_derived_cl3107,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
| ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2677,zip_derived_cl3079]) ).
thf(zip_derived_cl3127,plain,
( ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl3107]) ).
thf(zip_derived_cl3078_048,plain,
( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl3064,zip_derived_cl17]) ).
thf(zip_derived_cl17_049,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl3085,plain,
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
| ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3078,zip_derived_cl17]) ).
thf(zip_derived_cl3148,plain,
'#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ),
inference(clc,[status(thm)],[zip_derived_cl3127,zip_derived_cl3085]) ).
thf(zip_derived_cl327_050,plain,
! [X0: a,X1: a] :
( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
| ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
| ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
= ( '#sk1' @ X0 @ X1 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl322]) ).
thf(zip_derived_cl2524,plain,
! [X0: a,X1: a] :
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
| ~ ( '#sk1' @ X0 @ X1 )
| ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
!= ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
| ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl327]) ).
thf(zip_derived_cl3942_051,plain,
'#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl3935,zip_derived_cl17]) ).
thf(zip_derived_cl3958,plain,
! [X0: a,X1: a] :
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
| ~ ( '#sk1' @ X0 @ X1 )
| ~ ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
| ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2524,zip_derived_cl3942]) ).
thf(zip_derived_cl3936_052,plain,
'#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl3935,zip_derived_cl1629]) ).
thf(zip_derived_cl4359,plain,
! [X0: a,X1: a] :
( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
| ~ ( '#sk1' @ X0 @ X1 )
| ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl3958,zip_derived_cl3936]) ).
thf(zip_derived_cl4360,plain,
! [X0: a] :
( ~ ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ X0 )
| ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl3148,zip_derived_cl4359]) ).
thf(zip_derived_cl4127_053,plain,
'#sk1' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2',
inference(clc,[status(thm)],[zip_derived_cl4081,zip_derived_cl17]) ).
thf(zip_derived_cl1629_054,plain,
! [X0: a] :
( ~ ( '#sk1' @ X0 @ '#sk2' )
| ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1400,zip_derived_cl17]) ).
thf(zip_derived_cl4128,plain,
'#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl4127,zip_derived_cl1629]) ).
thf(zip_derived_cl4371,plain,
'#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ),
inference('sup+',[status(thm)],[zip_derived_cl4360,zip_derived_cl4128]) ).
thf(zip_derived_cl4399,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl4142,zip_derived_cl4371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEV010^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.3KiOpWdBTt true
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 02:46:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % 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
% 0.20/0.64 % Total configuration time : 828
% 0.20/0.64 % Estimated wc time : 1656
% 0.20/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 26.23/3.95 % Solved by lams/20_acsne_simpl.sh.
% 26.23/3.95 % done 1215 iterations in 3.166s
% 26.23/3.95 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 26.23/3.95 % SZS output start Refutation
% See solution above
% 26.23/3.95
% 26.23/3.95
% 26.23/3.95 % Terminating...
% 26.77/4.06 % Runner terminated.
% 26.77/4.09 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------