TSTP Solution File: SEV238^5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV238^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.7sF37GvJAe true
% Computer : n002.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 20:00:08 EDT 2023
% Result : Theorem 8.23s 1.71s
% Output : Refutation 8.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of formulae : 96 ( 7 unt; 6 typ; 0 def)
% Number of atoms : 876 ( 2 equ; 0 cnn)
% Maximal formula atoms : 48 ( 9 avg)
% Number of connectives : 2769 ( 79 ~; 82 |; 201 &;1713 @)
% ( 6 <=>; 290 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 229 ( 229 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 6 usr; 6 con; 0-2 aty)
% ( 236 !!; 162 ??; 0 @@+; 0 @@-)
% Number of variables : 664 ( 556 ^; 88 !; 20 ?; 664 :)
% Comments :
%------------------------------------------------------------------------------
thf('#sk29_type',type,
'#sk29': ( $i > $o ) > $i ).
thf('#sk9_type',type,
'#sk9': $i > $o ).
thf('#sk1_type',type,
'#sk1': ( $i > $o ) > $i > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf('#sk8_type',type,
'#sk8': ( $i > $o ) > $i ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(cTHM2D_pme,conjecture,
! [K: ( $i > $o ) > $i > $o] :
( ( ( ! [Xx: $i] :
( ? [S: $i > $o] :
( ! [Xx0: $i] :
( ( S @ Xx0 )
=> ( K @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) )
=> ! [Xx: $i] :
( ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
=> ( K
@ ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
@ Xx ) ) )
& ! [Xx: $i > $o] :
( ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
=> ! [Xx0: $i] :
( ( K @ Xx @ Xx0 )
=> ( K
@ ^ [Xx1: $i] :
? [S: $i > $o] :
( ! [Xx2: $i] :
( ( S @ Xx2 )
=> ( K @ S @ Xx2 ) )
& ( S @ Xx1 ) )
@ Xx0 ) ) ) )
=> ! [Xx: $i] :
( ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
<=> ( ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
& ! [Xx0: $i] :
( ( K
@ ^ [Xx1: $i] :
? [S: $i > $o] :
( ! [Xx2: $i] :
( ( S @ Xx2 )
=> ( K @ S @ Xx2 ) )
& ( S @ Xx1 ) )
@ Xx0 )
=> ( K
@ ( K
@ ^ [Xx1: $i] :
? [S: $i > $o] :
( ! [Xx2: $i] :
( ( S @ Xx2 )
=> ( K @ S @ Xx2 ) )
& ( S @ Xx1 ) ) )
@ Xx0 ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [K: ( $i > $o ) > $i > $o] :
( ( ( ! [Xx: $i] :
( ? [S: $i > $o] :
( ! [Xx0: $i] :
( ( S @ Xx0 )
=> ( K @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) )
=> ! [Xx: $i] :
( ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
=> ( K
@ ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
@ Xx ) ) )
& ! [Xx: $i > $o] :
( ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
=> ! [Xx0: $i] :
( ( K @ Xx @ Xx0 )
=> ( K
@ ^ [Xx1: $i] :
? [S: $i > $o] :
( ! [Xx2: $i] :
( ( S @ Xx2 )
=> ( K @ S @ Xx2 ) )
& ( S @ Xx1 ) )
@ Xx0 ) ) ) )
=> ! [Xx: $i] :
( ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
<=> ( ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
& ! [Xx0: $i] :
( ( K
@ ^ [Xx1: $i] :
? [S: $i > $o] :
( ! [Xx2: $i] :
( ( S @ Xx2 )
=> ( K @ S @ Xx2 ) )
& ( S @ Xx1 ) )
@ Xx0 )
=> ( K
@ ( K
@ ^ [Xx1: $i] :
? [S: $i > $o] :
( ! [Xx2: $i] :
( ( S @ Xx2 )
=> ( K @ S @ Xx2 ) )
& ( S @ Xx1 ) ) )
@ Xx0 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[cTHM2D_pme]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: ( $i > $o ) > $i > $o] :
( ( ( ( !!
@ ^ [Y1: $i] :
( ( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
=> ( Y0
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( Y0
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 )
=> ( Y0
@ ( Y0
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) ) )
@ Y1 ) ) ) )
& ( !!
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) ) ) )
=> ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i > $o] :
( ( !!
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
=> ( Y0 @ Y4 @ Y5 ) ) )
& ( Y4 @ Y3 ) ) )
@ Y2 ) ) ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( Y0
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 )
<=> ( ( Y0
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 )
& ( !!
@ ^ [Y2: $i] :
( ( Y0
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i > $o] :
( ( !!
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
=> ( Y0 @ Y4 @ Y5 ) ) )
& ( Y4 @ Y3 ) ) )
@ Y2 )
=> ( Y0
@ ( Y0
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i > $o] :
( ( !!
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
=> ( Y0 @ Y4 @ Y5 ) ) )
& ( Y4 @ Y3 ) ) ) )
@ Y2 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( ( ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) )
& ( !!
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1'
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( '#sk1' @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
<=> ( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
& ( !!
@ ^ [Y1: $i] :
( ( '#sk1'
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( '#sk1' @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( '#sk1' @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) ) )
@ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
<=> ( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
& ( !!
@ ^ [Y1: $i] :
( ( '#sk1'
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( '#sk1' @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( '#sk1' @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) ) )
@ Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
~ ( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
<=> ( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
& ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl9,plain,
( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
!= ( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
& ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl9_001,plain,
( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
!= ( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
& ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl45,plain,
( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
| ( $false
& ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ) ),
inference(bool_hoist,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl46,plain,
( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl46_002,plain,
( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl115,plain,
~ ( $true
& ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9,zip_derived_cl46,zip_derived_cl46]) ).
thf(zip_derived_cl116,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl115]) ).
thf(zip_derived_cl121,plain,
~ ( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl123,plain,
~ ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl2,plain,
( ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) )
& ( !!
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1'
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( '#sk1' @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl7,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl10,plain,
( ~ ( ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk3' ) ) )
=> ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl13,plain,
( ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl17,plain,
! [X2: $i] :
( ( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X2 ) )
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl22,plain,
! [X2: $i] :
( ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X2 )
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl192,plain,
( ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' )
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl123,zip_derived_cl22]) ).
thf(zip_derived_cl122,plain,
( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl193,plain,
~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' ),
inference(demod,[status(thm)],[zip_derived_cl192,zip_derived_cl122]) ).
thf(zip_derived_cl122_003,plain,
( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl12,plain,
( ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk3' ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl16,plain,
( ( ( !!
@ ^ [Y0: $i] :
( ( '#sk9' @ Y0 )
=> ( '#sk1' @ '#sk9' @ Y0 ) ) )
& ( '#sk9' @ '#sk3' ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl20,plain,
( ( !!
@ ^ [Y0: $i] :
( ( '#sk9' @ Y0 )
=> ( '#sk1' @ '#sk9' @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl26,plain,
! [X2: $i] :
( ( ( '#sk9' @ X2 )
=> ( '#sk1' @ '#sk9' @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl30,plain,
! [X2: $i] :
( ~ ( '#sk9' @ X2 )
| ( '#sk1' @ '#sk9' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl33,plain,
! [X2: $i,X4: $i] :
( ( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X4 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X4 ) )
| ( '#sk1' @ '#sk9' @ X2 )
| ~ ( '#sk9' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl36,plain,
! [X2: $i,X4: $i] :
( ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X4 )
| ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X4 )
| ~ ( '#sk9' @ X2 )
| ( '#sk1' @ '#sk9' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl124,plain,
! [X0: $i] :
( ( '#sk1' @ '#sk9' @ X0 )
| ~ ( '#sk9' @ X0 )
| ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl122,zip_derived_cl36]) ).
thf(zip_derived_cl123_004,plain,
~ ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl277,plain,
! [X0: $i] :
( ~ ( '#sk9' @ X0 )
| ( '#sk1' @ '#sk9' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl124,zip_derived_cl123]) ).
thf(zip_derived_cl277_005,plain,
! [X0: $i] :
( ~ ( '#sk9' @ X0 )
| ( '#sk1' @ '#sk9' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl124,zip_derived_cl123]) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1'
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( '#sk1' @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl8,plain,
! [X2: $i > $o] :
( ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl11,plain,
! [X2: $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl14,plain,
! [X2: $i > $o] :
( ~ ( ( X2 @ ( '#sk8' @ X2 ) )
=> ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ ( '#sk8' @ X2 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl19,plain,
! [X2: $i > $o] :
( ~ ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ ( '#sk8' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl24,plain,
! [X2: $i > $o,X4: $i > $o] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
=> ( '#sk1' @ X4 @ Y0 ) ) )
& ( X4 @ ( '#sk8' @ X2 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl29,plain,
! [X2: $i > $o,X4: $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
=> ( '#sk1' @ X4 @ Y0 ) ) )
| ~ ( X4 @ ( '#sk8' @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl32,plain,
! [X2: $i > $o,X4: $i > $o] :
( ~ ( ( X4 @ ( '#sk29' @ X4 ) )
=> ( '#sk1' @ X4 @ ( '#sk29' @ X4 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
| ~ ( X4 @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl35,plain,
! [X2: $i > $o,X4: $i > $o] :
( ~ ( '#sk1' @ X4 @ ( '#sk29' @ X4 ) )
| ~ ( X4 @ ( '#sk8' @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl38,plain,
! [X2: $i > $o,X4: $i > $o,X6: $i] :
( ( ( '#sk1' @ X2 @ X6 )
=> ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X6 ) )
| ~ ( X4 @ ( '#sk8' @ X2 ) )
| ~ ( '#sk1' @ X4 @ ( '#sk29' @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl40,plain,
! [X2: $i > $o,X4: $i > $o,X6: $i] :
( ~ ( '#sk1' @ X2 @ X6 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X6 )
| ~ ( '#sk1' @ X4 @ ( '#sk29' @ X4 ) )
| ~ ( X4 @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl279,plain,
! [X0: $i > $o,X1: $i] :
( ~ ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ~ ( '#sk9' @ ( '#sk8' @ X0 ) )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X1 )
| ~ ( '#sk1' @ X0 @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl277,zip_derived_cl40]) ).
thf(zip_derived_cl8_006,plain,
! [X2: $i > $o] :
( ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl15,plain,
( ( !!
@ ^ [Y0: $i] :
( ( '#sk9' @ Y0 )
=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl125,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk9' @ Y0 )
=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl126,plain,
( ~ ( ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
=> ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ ( '#sk8' @ '#sk9' ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl125]) ).
thf(zip_derived_cl128,plain,
( ~ ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ ( '#sk8' @ '#sk9' ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl126]) ).
thf(zip_derived_cl130,plain,
! [X2: $i > $o] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( '#sk1' @ X2 @ Y0 ) ) )
& ( X2 @ ( '#sk8' @ '#sk9' ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl128]) ).
thf(zip_derived_cl133,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( '#sk9' @ Y0 )
=> ( '#sk1' @ '#sk9' @ Y0 ) ) )
& ( '#sk9' @ ( '#sk8' @ '#sk9' ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl130]) ).
thf(zip_derived_cl350,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk9' @ Y0 )
=> ( '#sk1' @ '#sk9' @ Y0 ) ) )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl133]) ).
thf(zip_derived_cl351,plain,
( ~ ( ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
=> ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl350]) ).
thf(zip_derived_cl352,plain,
( ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl351]) ).
thf(zip_derived_cl354,plain,
! [X2: $i] :
( ( ( '#sk1' @ '#sk9' @ X2 )
=> ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 ) )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
| ( '#sk9' @ ( '#sk29' @ '#sk9' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl352]) ).
thf(zip_derived_cl356,plain,
! [X2: $i] :
( ~ ( '#sk1' @ '#sk9' @ X2 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl354]) ).
thf(zip_derived_cl18,plain,
! [X2: $i > $o] :
( ( X2 @ ( '#sk8' @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl23,plain,
! [X2: $i > $o,X4: $i] :
( ( ( '#sk1' @ X2 @ X4 )
=> ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X4 ) )
| ( X2 @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl28,plain,
! [X2: $i > $o,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X4 )
| ( X2 @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl358,plain,
! [X2: $i] :
( ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ~ ( '#sk1' @ '#sk9' @ X2 ) ),
inference(clc,[status(thm)],[zip_derived_cl356,zip_derived_cl28]) ).
thf(zip_derived_cl193_007,plain,
~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' ),
inference(demod,[status(thm)],[zip_derived_cl192,zip_derived_cl122]) ).
thf(zip_derived_cl360,plain,
( ~ ( '#sk1' @ '#sk9' @ '#sk3' )
| ( '#sk9' @ ( '#sk29' @ '#sk9' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl358,zip_derived_cl193]) ).
thf(zip_derived_cl277_008,plain,
! [X0: $i] :
( ~ ( '#sk9' @ X0 )
| ( '#sk1' @ '#sk9' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl124,zip_derived_cl123]) ).
thf(zip_derived_cl369,plain,
( ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ~ ( '#sk9' @ '#sk3' ) ),
inference('sup+',[status(thm)],[zip_derived_cl360,zip_derived_cl277]) ).
thf(zip_derived_cl123_009,plain,
~ ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl21,plain,
( ( '#sk9' @ '#sk3' )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl27,plain,
! [X2: $i] :
( ( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X2 ) )
| ( '#sk9' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl31,plain,
! [X2: $i] :
( ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X2 )
| ( '#sk9' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl385,plain,
( ( '#sk9' @ '#sk3' )
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl123,zip_derived_cl31]) ).
thf(zip_derived_cl122_010,plain,
( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl386,plain,
'#sk9' @ '#sk3',
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl122]) ).
thf(zip_derived_cl401,plain,
'#sk9' @ ( '#sk29' @ '#sk9' ),
inference(demod,[status(thm)],[zip_derived_cl369,zip_derived_cl386]) ).
thf(zip_derived_cl496,plain,
! [X0: $i > $o,X1: $i] :
( ~ ( '#sk9' @ ( '#sk8' @ X0 ) )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X1 )
| ~ ( '#sk1' @ X0 @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl279,zip_derived_cl401]) ).
thf(zip_derived_cl501,plain,
! [X0: $i] :
( ~ ( '#sk9' @ X0 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X0 )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl277,zip_derived_cl496]) ).
thf(zip_derived_cl277_011,plain,
! [X0: $i] :
( ~ ( '#sk9' @ X0 )
| ( '#sk1' @ '#sk9' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl124,zip_derived_cl123]) ).
thf(zip_derived_cl28_012,plain,
! [X2: $i > $o,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X4 )
| ( X2 @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl280,plain,
! [X0: $i] :
( ~ ( '#sk9' @ X0 )
| ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl277,zip_derived_cl28]) ).
thf(zip_derived_cl193_013,plain,
~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' ),
inference(demod,[status(thm)],[zip_derived_cl192,zip_derived_cl122]) ).
thf(zip_derived_cl317,plain,
( ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
| ~ ( '#sk9' @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl280,zip_derived_cl193]) ).
thf(zip_derived_cl386_014,plain,
'#sk9' @ '#sk3',
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl122]) ).
thf(zip_derived_cl400,plain,
'#sk9' @ ( '#sk8' @ '#sk9' ),
inference(demod,[status(thm)],[zip_derived_cl317,zip_derived_cl386]) ).
thf(zip_derived_cl505,plain,
! [X0: $i] :
( ~ ( '#sk9' @ X0 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl501,zip_derived_cl400]) ).
thf(zip_derived_cl688,plain,
~ ( '#sk9' @ '#sk3' ),
inference('sup+',[status(thm)],[zip_derived_cl193,zip_derived_cl505]) ).
thf(zip_derived_cl386_015,plain,
'#sk9' @ '#sk3',
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl122]) ).
thf(zip_derived_cl689,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl688,zip_derived_cl386]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : SEV238^5 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.16 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.7sF37GvJAe true
% 0.16/0.38 % Computer : n002.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Thu Aug 24 03:49:16 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.16/0.38 % Running portfolio for 300 s
% 0.16/0.38 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.38 % Number of cores: 8
% 0.16/0.38 % Python version: Python 3.6.8
% 0.16/0.39 % Running in HO mode
% 0.23/0.68 % Total configuration time : 828
% 0.23/0.68 % Estimated wc time : 1656
% 0.23/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.70/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.70/0.79 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.70/0.79 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.19/0.80 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.19/0.80 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.19/0.82 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.19/0.83 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.19/0.84 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 8.23/1.71 % Solved by lams/35_full_unif4.sh.
% 8.23/1.71 % done 94 iterations in 0.871s
% 8.23/1.71 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 8.23/1.71 % SZS output start Refutation
% See solution above
% 8.23/1.71
% 8.23/1.71
% 8.23/1.72 % Terminating...
% 8.39/1.81 % Runner terminated.
% 8.39/1.82 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------