TSTP Solution File: SEV206^5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV206^5 : 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.zp56TdENwd true
% Computer : n004.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 20:00:00 EDT 2023
% Result : Theorem 203.06s 26.66s
% Output : Refutation 203.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 33
% Syntax : Number of formulae : 134 ( 9 unt; 24 typ; 0 def)
% Number of atoms : 862 ( 398 equ; 198 cnn)
% Maximal formula atoms : 66 ( 7 avg)
% Number of connectives : 6897 ( 75 ~; 226 |; 198 &;6065 @)
% ( 0 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 77 ( 18 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 283 ( 283 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 23 usr; 12 con; 0-6 aty)
% ( 103 !!; 162 ??; 0 @@+; 0 @@-)
% Number of variables : 271 ( 30 ^; 205 !; 24 ?; 271 :)
% ( 12 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(iS_type,type,
iS: $tType ).
thf(x_type,type,
x: iS ).
thf('#sk12_type',type,
'#sk12': ( iS > iS > iS > $o ) > iS ).
thf('#sk5_type',type,
'#sk5': ( iS > $o ) > iS ).
thf('#sk11_type',type,
'#sk11': ( iS > iS > iS > $o ) > iS ).
thf('#sk10_type',type,
'#sk10': ( iS > iS > iS > $o ) > iS ).
thf(z_type,type,
z: iS ).
thf(c0_type,type,
c0: iS ).
thf('#sk9_type',type,
'#sk9': ( iS > iS > iS > $o ) > iS ).
thf(cP_type,type,
cP: iS > iS > iS ).
thf('#sk4_type',type,
'#sk4': ( iS > iS > iS > $o ) > iS ).
thf('#form13_type',type,
'#form13': ( iS > iS > iS > $o ) > $o ).
thf('#sk7_type',type,
'#sk7': ( iS > iS > iS > $o ) > iS ).
thf(y_type,type,
y: iS ).
thf('#sk1_type',type,
'#sk1': iS > iS > iS > $o ).
thf('#sk2_type',type,
'#sk2': ( iS > iS > iS > $o ) > iS ).
thf('#sk8_type',type,
'#sk8': ( iS > iS > iS > $o ) > iS ).
thf('#sk6_type',type,
'#sk6': ( iS > iS > iS > $o ) > iS ).
thf('#sk3_type',type,
'#sk3': ( iS > $o ) > iS ).
thf(s_comb_type,type,
'#S':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( A > B ) > A > C ) ).
thf(c_comb_type,type,
'#C':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > B > A > C ) ).
thf(b_comb_type,type,
'#B':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B ) > ( C > A ) > C > B ) ).
thf(k_comb_type,type,
'#K':
!>[A: $tType,B: $tType] : ( B > A > B ) ).
thf(i_comb_type,type,
'#I':
!>[A: $tType] : ( A > A ) ).
thf(cS_INCL_LEM8_pme,conjecture,
( ( ! [X: iS > $o] :
( ( ! [Xx0: iS,Xy0: iS] :
( ( ( X @ Xy0 )
& ( X @ Xx0 ) )
=> ( X @ ( cP @ Xx0 @ Xy0 ) ) )
& ( X @ c0 ) )
=> ! [Xx0: iS] : ( X @ Xx0 ) )
& ! [Xx0: iS,Xy0: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx0 @ Xu )
= ( cP @ Xy0 @ Xv ) )
=> ( ( Xu = Xv )
& ( Xx0 = Xy0 ) ) )
& ! [Xx0: iS,Xy0: iS] :
( ( cP @ Xx0 @ Xy0 )
!= c0 ) )
=> ( ! [R: iS > iS > iS > $o] :
( ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ x @ y @ y ) )
=> ! [R: iS > iS > iS > $o] :
( ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ ( cP @ z @ x ) @ ( cP @ z @ y ) @ ( cP @ z @ y ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( ( ! [X: iS > $o] :
( ( ! [Xx0: iS,Xy0: iS] :
( ( ( X @ Xy0 )
& ( X @ Xx0 ) )
=> ( X @ ( cP @ Xx0 @ Xy0 ) ) )
& ( X @ c0 ) )
=> ! [Xx0: iS] : ( X @ Xx0 ) )
& ! [Xx0: iS,Xy0: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx0 @ Xu )
= ( cP @ Xy0 @ Xv ) )
=> ( ( Xu = Xv )
& ( Xx0 = Xy0 ) ) )
& ! [Xx0: iS,Xy0: iS] :
( ( cP @ Xx0 @ Xy0 )
!= c0 ) )
=> ( ! [R: iS > iS > iS > $o] :
( ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ x @ y @ y ) )
=> ! [R: iS > iS > iS > $o] :
( ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ ( cP @ z @ x ) @ ( cP @ z @ y ) @ ( cP @ z @ y ) ) ) ) ),
inference('cnf.neg',[status(esa)],[cS_INCL_LEM8_pme]) ).
thf(zip_derived_cl0,plain,
~ ( ( ( !!
@ ^ [Y0: iS > $o] :
( ( ( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !!
@ ^ [Y1: iS] : ( Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( cP @ Y0 @ Y2 )
= ( cP @ Y1 @ Y3 ) )
=> ( ( Y2 = Y3 )
& ( Y0 = Y1 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( ( cP @ Y0 @ Y1 )
!= c0 ) ) ) )
=> ( ( !!
@ ^ [Y0: iS > iS > iS > $o] :
( ( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ x @ y @ y ) ) )
=> ( !!
@ ^ [Y0: iS > iS > iS > $o] :
( ( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ ( cP @ z @ x ) @ ( cP @ z @ y ) @ ( cP @ z @ y ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#S' @ ( '#B' @ (&) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ (&) ) ) ) @ '#I' ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ '#B' ) @ cP ) ) ) ) ) @ ( '#C' @ '#I' @ c0 ) ) ) @ !! ) )
& ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=) ) @ cP ) ) ) ) @ cP ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) ) @ (=) ) ) ) ) ) )
& ( !! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ != ) @ cP ) ) @ c0 ) ) ) )
=> ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ '#I' ) ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) ) @ '#I' ) ) ) ) ) @ ( '#C' @ ( '#C' @ ( '#C' @ '#I' @ x ) @ y ) @ y ) ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ '#I' ) ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) ) @ '#I' ) ) ) ) ) @ ( '#C' @ ( '#C' @ ( '#C' @ '#I' @ ( cP @ z @ x ) ) @ ( cP @ z @ y ) ) @ ( cP @ z @ y ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
~ ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ '#I' ) ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) ) @ '#I' ) ) ) ) ) @ ( '#C' @ ( '#C' @ ( '#C' @ '#I' @ x ) @ y ) @ y ) ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ '#I' ) ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) ) @ '#I' ) ) ) ) ) @ ( '#C' @ ( '#C' @ ( '#C' @ '#I' @ ( cP @ z @ x ) ) @ ( cP @ z @ y ) ) @ ( cP @ z @ y ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl7,plain,
!! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ '#I' ) ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) ) @ '#I' ) ) ) ) ) @ ( '#C' @ ( '#C' @ ( '#C' @ '#I' @ x ) @ y ) @ y ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl12,plain,
! [X2: iS > iS > iS > $o] :
( ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ X2 ) ) ) ) ) ) ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) @ X2 ) ) ) )
=> ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl17,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ X2 ) ) ) ) ) ) ) ) ) @ X2 ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) @ X2 ) ) ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl23,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( !!
@ ( '#B' @ !!
@ ( '#S'
@ ( '#B' @ '#S'
@ ( '#B' @ ( '#B' @ (=>) )
@ ( '#S'
@ ( '#B' @ '#S'
@ ( '#S'
@ ( '#B' @ '#S'
@ ( '#B' @ ( '#B' @ (|) )
@ ( '#B' @ ( '#B' @ ?? )
@ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) )
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) )
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#S' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) )
@ ( '#C'
@ ( '#B' @ '#B'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) )
@ ( '#B'
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B' @ ( '#B' @ (&) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk2' @ X2 ) ) )
@ cP ) ) ) ) ) )
@ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) )
@ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) )
@ X2 ) ) ) ) ) ) ) )
@ X2 ) ) ) ) ) ) ) ) )
@ ( '#B'
@ ( '#C'
@ ( '#B' @ (&)
@ ( iS
= ( '#sk2' @ X2 ) ) ) )
@ ( '#C' @ (=) @ c0 ) ) ) )
@ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) )
@ ( ( '#sk2' @ X2 )
= c0 ) ) ) ) )
@ ( X2 @ ( '#sk2' @ X2 ) ) ) ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl27,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( !!
@ ( '#S'
@ ( '#B' @ (=>)
@ ( '#S'
@ ( '#S'
@ ( '#B' @ (|)
@ ( '#B' @ ??
@ ( '#B' @ ( '#B' @ ?? )
@ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) )
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#S' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) )
@ ( '#C'
@ ( '#B' @ '#S'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) )
@ ( '#B'
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) )
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B' @ ( '#B' @ (&) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk2' @ X2 ) ) )
@ cP ) ) ) ) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk4' @ X2 ) ) )
@ cP ) ) ) ) ) ) ) )
@ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) )
@ X2 ) ) ) ) ) ) )
@ X2 ) ) ) ) ) ) ) )
@ ( '#C'
@ ( '#B' @ (&)
@ ( iS
= ( '#sk2' @ X2 ) ) )
@ ( ( '#sk4' @ X2 )
= c0 ) ) )
@ ( '#C'
@ ( '#B' @ (&)
@ ( iS
= ( '#sk4' @ X2 ) ) )
@ ( ( '#sk2' @ X2 )
= c0 ) ) ) )
@ ( X2 @ ( '#sk2' @ X2 ) @ ( '#sk4' @ X2 ) ) ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl31,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( ( ( ??
@ ( '#B' @ ??
@ ( '#B' @ ( '#B' @ ?? )
@ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) )
@ ( '#C'
@ ( '#B' @ '#S'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) )
@ ( '#S'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#S' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) )
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) )
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B' @ ( '#B' @ (&) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk2' @ X2 ) ) )
@ cP ) ) ) ) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk4' @ X2 ) ) )
@ cP ) ) ) ) ) ) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk6' @ X2 ) ) )
@ cP ) ) ) ) ) ) )
@ X2 ) ) ) ) ) )
@ X2 ) ) ) ) ) ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) ) )
=> ( X2 @ ( '#sk2' @ X2 ) @ ( '#sk4' @ X2 ) @ ( '#sk6' @ X2 ) ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl38,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ( '#B' @ ??
@ ( '#B' @ ( '#B' @ ?? )
@ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) )
@ ( '#C'
@ ( '#B' @ '#S'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) )
@ ( '#S'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#S' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) )
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) )
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B' @ ( '#B' @ (&) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk2' @ X2 ) ) )
@ cP ) ) ) ) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk4' @ X2 ) ) )
@ cP ) ) ) ) ) ) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk6' @ X2 ) ) )
@ cP ) ) ) ) ) ) )
@ X2 ) ) ) ) ) )
@ X2 ) ) ) ) ) ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl46,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ( '#B' @ ??
@ ( '#B' @ ( '#B' @ ?? )
@ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) )
@ ( '#C'
@ ( '#B' @ '#S'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) )
@ ( '#S'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#S' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) )
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) )
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B' @ ( '#B' @ (&) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk2' @ X2 ) ) )
@ cP ) ) ) ) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk4' @ X2 ) ) )
@ cP ) ) ) ) ) ) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk6' @ X2 ) ) )
@ cP ) ) ) ) ) ) )
@ X2 ) ) ) ) ) )
@ X2 ) ) ) ) ) ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl52,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ( '#B' @ ??
@ ( '#B' @ ( '#B' @ ?? )
@ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) )
@ ( '#S'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#S' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) )
@ ( '#C'
@ ( '#B' @ '#S'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) )
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) )
@ ( '#C'
@ ( '#B' @ '#B'
@ ( '#B' @ '#B'
@ ( '#B' @ (&)
@ ( '#B'
@ ( iS
= ( '#sk2' @ X2 ) )
@ ( cP @ ( '#sk7' @ X2 ) ) ) ) ) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk4' @ X2 ) ) )
@ cP ) ) ) ) ) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk6' @ X2 ) ) )
@ cP ) ) ) ) ) )
@ ( X2 @ ( '#sk7' @ X2 ) ) ) ) ) ) )
@ X2 ) ) ) ) ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl58,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ( '#B' @ ??
@ ( '#B' @ ( '#B' @ ?? )
@ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) )
@ ( '#C'
@ ( '#B' @ '#S'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) )
@ ( '#S'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#S' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) )
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B'
@ ( '#B'
@ ( (&)
@ ( ( '#sk2' @ X2 )
= ( cP @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X2 ) ) ) ) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk4' @ X2 ) ) )
@ cP ) ) ) ) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk6' @ X2 ) ) )
@ cP ) ) ) ) )
@ ( X2 @ ( '#sk7' @ X2 ) ) ) ) ) )
@ ( X2 @ ( '#sk8' @ X2 ) ) ) ) ) ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl62,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ( '#B' @ ??
@ ( '#B' @ ( '#B' @ ?? )
@ ( '#S'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#S' )
@ ( '#C'
@ ( '#B' @ '#S'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#C'
@ ( '#B' @ '#B'
@ ( '#B' @ '#B'
@ ( '#B'
@ ( (&)
@ ( ( '#sk2' @ X2 )
= ( cP @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X2 ) ) ) )
@ ( '#B'
@ ( iS
= ( '#sk4' @ X2 ) )
@ ( cP @ ( '#sk9' @ X2 ) ) ) ) ) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk6' @ X2 ) ) )
@ cP ) ) ) )
@ ( X2 @ ( '#sk7' @ X2 ) @ ( '#sk9' @ X2 ) ) ) ) )
@ ( X2 @ ( '#sk8' @ X2 ) ) ) ) ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl64,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ( '#B' @ ??
@ ( '#C'
@ ( '#B' @ '#S'
@ ( '#S'
@ ( '#B' @ '#C'
@ ( '#B'
@ ( '#B'
@ ( ( ( '#sk2' @ X2 )
= ( cP @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X2 ) ) )
& ( ( '#sk4' @ X2 )
= ( cP @ ( '#sk9' @ X2 ) @ ( '#sk10' @ X2 ) ) ) ) )
@ ( '#B'
@ ( '#B'
@ ( iS
= ( '#sk6' @ X2 ) ) )
@ cP ) ) )
@ ( X2 @ ( '#sk7' @ X2 ) @ ( '#sk9' @ X2 ) ) ) )
@ ( X2 @ ( '#sk8' @ X2 ) @ ( '#sk10' @ X2 ) ) ) ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl66,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ( '#S'
@ ( '#C'
@ ( '#B'
@ ( ( ( '#sk2' @ X2 )
= ( cP @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X2 ) ) )
& ( ( '#sk4' @ X2 )
= ( cP @ ( '#sk9' @ X2 ) @ ( '#sk10' @ X2 ) ) ) )
@ ( '#B'
@ ( iS
= ( '#sk6' @ X2 ) )
@ ( cP @ ( '#sk11' @ X2 ) ) ) )
@ ( X2 @ ( '#sk7' @ X2 ) @ ( '#sk9' @ X2 ) @ ( '#sk11' @ X2 ) ) )
@ ( X2 @ ( '#sk8' @ X2 ) @ ( '#sk10' @ X2 ) ) ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl68,plain,
! [X2: iS > iS > iS > $o] :
( ( ( ( '#sk2' @ X2 )
= ( cP @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X2 ) ) )
& ( ( '#sk4' @ X2 )
= ( cP @ ( '#sk9' @ X2 ) @ ( '#sk10' @ X2 ) ) )
& ( ( '#sk6' @ X2 )
= ( cP @ ( '#sk11' @ X2 ) @ ( '#sk12' @ X2 ) ) )
& ( X2 @ ( '#sk7' @ X2 ) @ ( '#sk9' @ X2 ) @ ( '#sk11' @ X2 ) )
& ( X2 @ ( '#sk8' @ X2 ) @ ( '#sk10' @ X2 ) @ ( '#sk12' @ X2 ) ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl71,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk4' @ X2 )
= ( cP @ ( '#sk9' @ X2 ) @ ( '#sk10' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl79,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk4' @ X2 )
= ( cP @ ( '#sk9' @ X2 ) @ ( '#sk10' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl80,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y )
| ( ( '#sk4' @ X2 )
= ( cP @ ( '#sk9' @ X2 ) @ ( '#sk10' @ X2 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl94,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y )
| ( ( '#sk4' @ X2 )
= ( cP @ ( '#sk9' @ X2 ) @ ( '#sk10' @ X2 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl72,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk6' @ X2 )
= ( cP @ ( '#sk11' @ X2 ) @ ( '#sk12' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl82,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk6' @ X2 )
= ( cP @ ( '#sk11' @ X2 ) @ ( '#sk12' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl83,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form13' @ X2 )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl95,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form13' @ X2 )
| ( ( '#sk4' @ X2 )
= ( cP @ ( '#sk9' @ X2 ) @ ( '#sk10' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl94,zip_derived_cl83]) ).
thf(zip_derived_cl83_001,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form13' @ X2 )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl84,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
| ~ ( '#form13' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl100,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
| ~ ( '#form13' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl70,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= ( cP @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl76,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= ( cP @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl77,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y )
| ( ( '#sk2' @ X2 )
= ( cP @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X2 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl90,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y )
| ( ( '#sk2' @ X2 )
= ( cP @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X2 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl83_002,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form13' @ X2 )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl91,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form13' @ X2 )
| ( ( '#sk2' @ X2 )
= ( cP @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl90,zip_derived_cl83]) ).
thf(zip_derived_cl2,plain,
( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#S' @ ( '#B' @ (&) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ (&) ) ) ) @ '#I' ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ '#B' ) @ cP ) ) ) ) ) @ ( '#C' @ '#I' @ c0 ) ) ) @ !! ) )
& ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=) ) @ cP ) ) ) ) @ cP ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) ) @ (=) ) ) ) ) ) )
& ( !! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ != ) @ cP ) ) @ c0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
!! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ != ) @ cP ) ) @ c0 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl11,plain,
! [X2: iS] : ( !! @ ( '#C' @ ( '#B' @ != @ ( cP @ X2 ) ) @ c0 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl16,plain,
! [X2: iS,X4: iS] :
( ( cP @ X2 @ X4 )
!= c0 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl22,plain,
! [X2: iS,X4: iS] :
( ( cP @ X2 @ X4 )
!= c0 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl78,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= c0 )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y )
| ( ( '#sk2' @ X2 )
= ( cP @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X2 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl92,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= c0 )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y )
| ( ( '#sk2' @ X2 )
= ( cP @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X2 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl83_003,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form13' @ X2 )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl93,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form13' @ X2 )
| ( ( '#sk2' @ X2 )
= ( cP @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( ( '#sk2' @ X2 )
= c0 ) ),
inference(renaming,[status(thm)],[zip_derived_cl92,zip_derived_cl83]) ).
thf(zip_derived_cl82_004,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk6' @ X2 )
= ( cP @ ( '#sk11' @ X2 ) @ ( '#sk12' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl83_005,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form13' @ X2 )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl86,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form13' @ X2 )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y )
| ( ( '#sk6' @ X2 )
= ( cP @ ( '#sk11' @ X2 ) @ ( '#sk12' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl82,zip_derived_cl83]) ).
thf(zip_derived_cl99,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= c0 )
| ( ( '#sk6' @ X2 )
= ( cP @ ( '#sk11' @ X2 ) @ ( '#sk12' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( '#form13' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl107,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= c0 )
| ( ( '#sk6' @ X2 )
= ( cP @ ( '#sk11' @ X2 ) @ ( '#sk12' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( '#form13' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl81,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= c0 )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y )
| ( ( '#sk4' @ X2 )
= ( cP @ ( '#sk9' @ X2 ) @ ( '#sk10' @ X2 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl96,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= c0 )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y )
| ( ( '#sk4' @ X2 )
= ( cP @ ( '#sk9' @ X2 ) @ ( '#sk10' @ X2 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl83_006,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form13' @ X2 )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl97,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form13' @ X2 )
| ( ( '#sk4' @ X2 )
= ( cP @ ( '#sk9' @ X2 ) @ ( '#sk10' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( ( '#sk2' @ X2 )
= c0 ) ),
inference(renaming,[status(thm)],[zip_derived_cl96,zip_derived_cl83]) ).
thf(zip_derived_cl73,plain,
! [X2: iS > iS > iS > $o] :
( ( X2 @ ( '#sk7' @ X2 ) @ ( '#sk9' @ X2 ) @ ( '#sk11' @ X2 ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl83_007,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form13' @ X2 )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl87,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form13' @ X2 )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y )
| ( X2 @ ( '#sk7' @ X2 ) @ ( '#sk9' @ X2 ) @ ( '#sk11' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl73,zip_derived_cl83]) ).
thf(zip_derived_cl102,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
| ( X2 @ ( '#sk7' @ X2 ) @ ( '#sk9' @ X2 ) @ ( '#sk11' @ X2 ) )
| ( X2 @ x @ y @ y )
| ( '#form13' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl108,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
| ( X2 @ ( '#sk7' @ X2 ) @ ( '#sk9' @ X2 ) @ ( '#sk11' @ X2 ) )
| ( X2 @ x @ y @ y )
| ( '#form13' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl103,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= c0 )
| ( X2 @ ( '#sk7' @ X2 ) @ ( '#sk9' @ X2 ) @ ( '#sk11' @ X2 ) )
| ( X2 @ x @ y @ y )
| ( '#form13' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl109,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= c0 )
| ( X2 @ ( '#sk7' @ X2 ) @ ( '#sk9' @ X2 ) @ ( '#sk11' @ X2 ) )
| ( X2 @ x @ y @ y )
| ( '#form13' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl8,plain,
~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ '#I' ) ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) ) @ '#I' ) ) ) ) ) @ ( '#C' @ ( '#C' @ ( '#C' @ '#I' @ ( cP @ z @ x ) ) @ ( cP @ z @ y ) ) @ ( cP @ z @ y ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl13,plain,
~ ( ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) @ '#sk1' ) ) ) )
=> ( '#sk1' @ ( cP @ z @ x ) @ ( cP @ z @ y ) @ ( cP @ z @ y ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl19,plain,
~ ( '#sk1' @ ( cP @ z @ x ) @ ( cP @ z @ y ) @ ( cP @ z @ y ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl18,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) ) ) @ '#sk1' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl24,plain,
! [X2: iS] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#B' @ ( '#B' @ ?? ) @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ ( iS = X2 ) ) @ cP ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ (&) @ ( iS = X2 ) ) ) @ ( '#C' @ (=) @ c0 ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ (=) ) ) @ ( X2 = c0 ) ) ) ) ) @ ( '#sk1' @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl28,plain,
! [X2: iS,X4: iS] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#S' @ ( '#S' @ ( '#B' @ (|) @ ( '#B' @ ?? @ ( '#B' @ ( '#B' @ ?? ) @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ ( iS = X2 ) ) @ cP ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( iS = X4 ) ) @ cP ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ cP ) ) ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ (&) @ ( iS = X2 ) ) @ ( X4 = c0 ) ) ) @ ( '#C' @ ( '#B' @ (&) @ ( iS = X4 ) ) @ ( X2 = c0 ) ) ) ) @ ( '#sk1' @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl32,plain,
! [X2: iS,X4: iS,X6: iS] :
( ( ( ?? @ ( '#B' @ ?? @ ( '#B' @ ( '#B' @ ?? ) @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ ( iS = X2 ) ) @ cP ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( iS = X4 ) ) @ cP ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( iS = X6 ) ) @ cP ) ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) )
| ( ( X2 = X6 )
& ( X4 = c0 ) )
| ( ( X4 = X6 )
& ( X2 = c0 ) ) )
=> ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl40,plain,
! [X2: iS,X4: iS,X6: iS] :
( ~ ( ( ?? @ ( '#B' @ ?? @ ( '#B' @ ( '#B' @ ?? ) @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ ( iS = X2 ) ) @ cP ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( iS = X4 ) ) @ cP ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( iS = X6 ) ) @ cP ) ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) )
| ( ( X2 = X6 )
& ( X4 = c0 ) )
| ( ( X4 = X6 )
& ( X2 = c0 ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl48,plain,
! [X2: iS,X4: iS,X6: iS] :
( ~ ( ( X2 = X6 )
& ( X4 = c0 ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl54,plain,
! [X2: iS,X4: iS,X6: iS] :
( ( X2 != X6 )
| ( X4 != c0 )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl60,plain,
! [X2: iS,X4: iS,X6: iS] :
( ( X2 != X6 )
| ( X4 != c0 )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl4,plain,
!! @ ( '#S' @ ( '#B' @ (=>) @ ( '#S' @ ( '#B' @ (&) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ (&) ) ) ) @ '#I' ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ '#B' ) @ cP ) ) ) ) ) @ ( '#C' @ '#I' @ c0 ) ) ) @ !! ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl9,plain,
! [X2: iS > $o] :
( ( ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ ( '#B' @ (&) @ X2 ) ) @ X2 ) ) ) @ ( '#B' @ ( '#B' @ X2 ) @ cP ) ) ) )
& ( X2 @ c0 ) )
=> ( !! @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl14,plain,
! [X2: iS > $o] :
( ~ ( ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ ( '#B' @ (&) @ X2 ) ) @ X2 ) ) ) @ ( '#B' @ ( '#B' @ X2 ) @ cP ) ) ) )
& ( X2 @ c0 ) )
| ( !! @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl20,plain,
! [X2: iS > $o] :
( ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ ( '#B' @ (&) @ X2 ) ) @ X2 ) ) ) @ ( '#B' @ ( '#B' @ X2 ) @ cP ) ) ) )
| ~ ( X2 @ c0 )
| ( !! @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl25,plain,
! [X2: iS > $o] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ ( '#B' @ (&) @ X2 ) @ ( X2 @ ( '#sk3' @ X2 ) ) ) ) @ ( '#B' @ X2 @ ( cP @ ( '#sk3' @ X2 ) ) ) ) )
| ( !! @ X2 )
| ~ ( X2 @ c0 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl29,plain,
! [X2: iS > $o] :
( ~ ( ( ( X2 @ ( '#sk5' @ X2 ) )
& ( X2 @ ( '#sk3' @ X2 ) ) )
=> ( X2 @ ( cP @ ( '#sk3' @ X2 ) @ ( '#sk5' @ X2 ) ) ) )
| ~ ( X2 @ c0 )
| ( !! @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl34,plain,
! [X2: iS > $o] :
( ~ ( X2 @ ( cP @ ( '#sk3' @ X2 ) @ ( '#sk5' @ X2 ) ) )
| ( !! @ X2 )
| ~ ( X2 @ c0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl43,plain,
! [X2: iS > $o,X4: iS] :
( ( X2 @ X4 )
| ~ ( X2 @ c0 )
| ~ ( X2 @ ( cP @ ( '#sk3' @ X2 ) @ ( '#sk5' @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl74,plain,
! [X2: iS > iS > iS > $o] :
( ( X2 @ ( '#sk8' @ X2 ) @ ( '#sk10' @ X2 ) @ ( '#sk12' @ X2 ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl83_008,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form13' @ X2 )
| ( ( ( '#sk2' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk4' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl88,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form13' @ X2 )
| ( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
& ( ( '#sk2' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y )
| ( X2 @ ( '#sk8' @ X2 ) @ ( '#sk10' @ X2 ) @ ( '#sk12' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl74,zip_derived_cl83]) ).
thf(zip_derived_cl104,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
| ( X2 @ ( '#sk8' @ X2 ) @ ( '#sk10' @ X2 ) @ ( '#sk12' @ X2 ) )
| ( X2 @ x @ y @ y )
| ( '#form13' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl110,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk4' @ X2 )
= ( '#sk6' @ X2 ) )
| ( X2 @ ( '#sk8' @ X2 ) @ ( '#sk10' @ X2 ) @ ( '#sk12' @ X2 ) )
| ( X2 @ x @ y @ y )
| ( '#form13' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl33,plain,
! [X2: iS > $o] :
( ( ( X2 @ ( '#sk5' @ X2 ) )
& ( X2 @ ( '#sk3' @ X2 ) ) )
| ( !! @ X2 )
| ~ ( X2 @ c0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl42,plain,
! [X2: iS > $o] :
( ( X2 @ ( '#sk3' @ X2 ) )
| ~ ( X2 @ c0 )
| ( !! @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl51,plain,
! [X2: iS > $o,X4: iS] :
( ( X2 @ X4 )
| ~ ( X2 @ c0 )
| ( X2 @ ( '#sk3' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl57,plain,
! [X0: iS > $o] :
( ( X0 @ ( '#sk3' @ X0 ) )
| ~ ( X0 @ c0 ) ),
inference(condensation,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl49,plain,
! [X2: iS,X4: iS,X6: iS] :
( ~ ( ( X4 = X6 )
& ( X2 = c0 ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl55,plain,
! [X2: iS,X4: iS,X6: iS] :
( ( X4 != X6 )
| ( X2 != c0 )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl61,plain,
! [X2: iS,X4: iS,X6: iS] :
( ( X4 != X6 )
| ( X2 != c0 )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl41,plain,
! [X2: iS > $o] :
( ( X2 @ ( '#sk5' @ X2 ) )
| ~ ( X2 @ c0 )
| ( !! @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl50,plain,
! [X2: iS > $o,X4: iS] :
( ( X2 @ X4 )
| ~ ( X2 @ c0 )
| ( X2 @ ( '#sk5' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl56,plain,
! [X0: iS > $o] :
( ( X0 @ ( '#sk5' @ X0 ) )
| ~ ( X0 @ c0 ) ),
inference(condensation,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl47,plain,
! [X2: iS,X4: iS,X6: iS] :
( ~ ( ?? @ ( '#B' @ ?? @ ( '#B' @ ( '#B' @ ?? ) @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ ( iS = X2 ) ) @ cP ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( iS = X4 ) ) @ cP ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( iS = X6 ) ) @ cP ) ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl53,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS] :
( ~ ( ?? @ ( '#B' @ ?? @ ( '#B' @ ( '#B' @ ?? ) @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ (&) @ ( '#B' @ ( iS = X2 ) @ ( cP @ X8 ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( iS = X4 ) ) @ cP ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( iS = X6 ) ) @ cP ) ) ) ) ) ) @ ( '#sk1' @ X8 ) ) ) ) ) ) @ '#sk1' ) ) ) ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl59,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS] :
( ~ ( ??
@ ( '#B' @ ??
@ ( '#B' @ ( '#B' @ ?? )
@ ( '#B' @ ( '#B' @ ( '#B' @ ?? ) )
@ ( '#C'
@ ( '#B' @ '#S'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) )
@ ( '#S'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#S' )
@ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) )
@ ( '#C'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B' @ ( '#B' @ '#B' )
@ ( '#B'
@ ( '#B'
@ ( (&)
@ ( X2
= ( cP @ X8 @ X10 ) ) ) )
@ ( '#B' @ ( '#B' @ ( iS = X4 ) ) @ cP ) ) ) ) )
@ ( '#B' @ ( '#B' @ ( iS = X6 ) ) @ cP ) ) ) ) )
@ ( '#sk1' @ X8 ) ) ) ) )
@ ( '#sk1' @ X10 ) ) ) ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl63,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS] :
( ~ ( ??
@ ( '#B' @ ??
@ ( '#B' @ ( '#B' @ ?? )
@ ( '#S'
@ ( '#B' @ '#C'
@ ( '#B' @ ( '#B' @ '#S' )
@ ( '#C'
@ ( '#B' @ '#S'
@ ( '#B' @ ( '#B' @ '#C' )
@ ( '#C'
@ ( '#B' @ '#B'
@ ( '#B' @ '#B'
@ ( '#B'
@ ( (&)
@ ( X2
= ( cP @ X8 @ X10 ) ) )
@ ( '#B' @ ( iS = X4 ) @ ( cP @ X12 ) ) ) ) )
@ ( '#B' @ ( '#B' @ ( iS = X6 ) ) @ cP ) ) ) )
@ ( '#sk1' @ X8 @ X12 ) ) ) )
@ ( '#sk1' @ X10 ) ) ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl65,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS] :
( ~ ( ??
@ ( '#B' @ ??
@ ( '#C'
@ ( '#B' @ '#S'
@ ( '#S'
@ ( '#B' @ '#C'
@ ( '#B'
@ ( '#B'
@ ( ( X2
= ( cP @ X8 @ X10 ) )
& ( X4
= ( cP @ X12 @ X14 ) ) ) )
@ ( '#B' @ ( '#B' @ ( iS = X6 ) ) @ cP ) ) )
@ ( '#sk1' @ X8 @ X12 ) ) )
@ ( '#sk1' @ X10 @ X14 ) ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl67,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS,X16: iS] :
( ~ ( ??
@ ( '#S'
@ ( '#C'
@ ( '#B'
@ ( ( X2
= ( cP @ X8 @ X10 ) )
& ( X4
= ( cP @ X12 @ X14 ) ) )
@ ( '#B' @ ( iS = X6 ) @ ( cP @ X16 ) ) )
@ ( '#sk1' @ X8 @ X12 @ X16 ) )
@ ( '#sk1' @ X10 @ X14 ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl69,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS,X16: iS,X18: iS] :
( ~ ( ( X2
= ( cP @ X8 @ X10 ) )
& ( X4
= ( cP @ X12 @ X14 ) )
& ( X6
= ( cP @ X16 @ X18 ) )
& ( '#sk1' @ X8 @ X12 @ X16 )
& ( '#sk1' @ X10 @ X14 @ X18 ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl75,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS,X16: iS,X18: iS] :
( ( X2
!= ( cP @ X8 @ X10 ) )
| ( X4
!= ( cP @ X12 @ X14 ) )
| ( X6
!= ( cP @ X16 @ X18 ) )
| ~ ( '#sk1' @ X8 @ X12 @ X16 )
| ~ ( '#sk1' @ X10 @ X14 @ X18 )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl89,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS,X16: iS,X18: iS] :
( ( X2
!= ( cP @ X8 @ X10 ) )
| ( X4
!= ( cP @ X12 @ X14 ) )
| ( X6
!= ( cP @ X16 @ X18 ) )
| ~ ( '#sk1' @ X8 @ X12 @ X16 )
| ~ ( '#sk1' @ X10 @ X14 @ X18 )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl105,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= c0 )
| ( X2 @ ( '#sk8' @ X2 ) @ ( '#sk10' @ X2 ) @ ( '#sk12' @ X2 ) )
| ( X2 @ x @ y @ y )
| ( '#form13' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl111,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk2' @ X2 )
= c0 )
| ( X2 @ ( '#sk8' @ X2 ) @ ( '#sk10' @ X2 ) @ ( '#sk12' @ X2 ) )
| ( X2 @ x @ y @ y )
| ( '#form13' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl39,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( X2 @ ( '#sk2' @ X2 ) @ ( '#sk4' @ X2 ) @ ( '#sk6' @ X2 ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl85,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk4' @ X2 )
= c0 )
| ~ ( '#form13' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl101,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk4' @ X2 )
= c0 )
| ~ ( '#form13' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl21750,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl95,zip_derived_cl100,zip_derived_cl91,zip_derived_cl22,zip_derived_cl93,zip_derived_cl107,zip_derived_cl97,zip_derived_cl108,zip_derived_cl109,zip_derived_cl19,zip_derived_cl60,zip_derived_cl43,zip_derived_cl110,zip_derived_cl57,zip_derived_cl61,zip_derived_cl56,zip_derived_cl89,zip_derived_cl111,zip_derived_cl39,zip_derived_cl101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV206^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.zp56TdENwd true
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 02:31:53 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.21/0.65 % Total configuration time : 828
% 0.21/0.65 % Estimated wc time : 1656
% 0.21/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.79 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 203.06/26.66 % Solved by lams/40_b.comb.sh.
% 203.06/26.66 % done 672 iterations in 25.714s
% 203.06/26.66 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 203.06/26.66 % SZS output start Refutation
% See solution above
% 203.06/26.67
% 203.06/26.67
% 203.06/26.67 % Terminating...
% 203.06/26.72 % Runner terminated.
% 203.06/26.73 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------