TSTP Solution File: SEV041^5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV041^5 : 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.IeQzcZIP3m true
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:59:23 EDT 2023
% Result : Theorem 15.72s 2.81s
% Output : Refutation 15.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 39
% Syntax : Number of formulae : 262 ( 20 unt; 24 typ; 0 def)
% Number of atoms : 1737 ( 80 equ; 0 cnn)
% Maximal formula atoms : 65 ( 7 avg)
% Number of connectives : 5210 ( 285 ~; 329 |; 146 &;3429 @)
% ( 5 <=>; 380 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 208 ( 208 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 13 con; 0-3 aty)
% ( 636 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 966 ( 688 ^; 278 !; 0 ?; 966 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(b_type,type,
b: $tType ).
thf('#sk7_type',type,
'#sk7': a > b ).
thf('#sk15_type',type,
'#sk15': a ).
thf('#sk8_type',type,
'#sk8': a > b ).
thf('#sk11_type',type,
'#sk11': a > b ).
thf('#sk1_type',type,
'#sk1': a > a > $o ).
thf('#sk14_type',type,
'#sk14': a ).
thf('#sk9_type',type,
'#sk9': a > b ).
thf('#form10_type',type,
'#form10': $o ).
thf('#sk17_type',type,
'#sk17': a ).
thf('#sk4_type',type,
'#sk4': a > b > b > $o ).
thf('#form13_type',type,
'#form13': $o ).
thf('#sk19_type',type,
'#sk19': a ).
thf('#sk21_type',type,
'#sk21': a ).
thf('#_fresh_sk6_type',type,
'#_fresh_sk6': a > b ).
thf('#sk18_type',type,
'#sk18': a ).
thf('#sk3_type',type,
'#sk3': a > b > b > $o ).
thf('#form20_type',type,
'#form20': $o ).
thf('#sk2_type',type,
'#sk2': a > a > $o ).
thf('#sk22_type',type,
'#sk22': a ).
thf('#sk16_type',type,
'#sk16': a ).
thf('#sk12_type',type,
'#sk12': a > b ).
thf('#_fresh_sk5_type',type,
'#_fresh_sk5': a > b ).
thf(cTHM517_pme,conjecture,
! [Xp: a > a > $o,Xq: a > a > $o,Xr: a > b > b > $o,Xs: a > b > b > $o] :
( ( ( Xp = Xq )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xp @ Xy @ Xz )
& ( Xp @ Xx @ Xy ) )
=> ( Xp @ Xx @ Xz ) )
& ! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( Xp @ Xy @ Xx ) ) )
=> ( ! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( ( ( Xr @ Xx )
= ( Xr @ Xy ) )
& ! [Xx0: b,Xy0: b,Xz: b] :
( ( ( Xr @ Xx @ Xy0 @ Xz )
& ( Xr @ Xx @ Xx0 @ Xy0 ) )
=> ( Xr @ Xx @ Xx0 @ Xz ) )
& ! [Xx0: b,Xy0: b] :
( ( Xr @ Xx @ Xx0 @ Xy0 )
=> ( Xr @ Xx @ Xy0 @ Xx0 ) ) ) )
=> ( ! [Xx: a] :
( ( Xp @ Xx @ Xx )
=> ( ( ( Xr @ Xx )
= ( Xs @ Xx ) )
& ! [Xx0: b,Xy: b,Xz: b] :
( ( ( Xr @ Xx @ Xy @ Xz )
& ( Xr @ Xx @ Xx0 @ Xy ) )
=> ( Xr @ Xx @ Xx0 @ Xz ) )
& ! [Xx0: b,Xy: b] :
( ( Xr @ Xx @ Xx0 @ Xy )
=> ( Xr @ Xx @ Xy @ Xx0 ) ) ) )
=> ( ( ( ^ [Xf: a > b,Xg: a > b] :
! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) )
= ( ^ [Xf: a > b,Xg: a > b] :
! [Xx: a,Xy: a] :
( ( Xq @ Xx @ Xy )
=> ( Xs @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) )
& ! [Xx: a > b,Xy: a > b,Xz: a > b] :
( ( ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) )
& ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) ) )
=> ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
& ! [Xx: a > b,Xy: a > b] :
( ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
=> ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [Xp: a > a > $o,Xq: a > a > $o,Xr: a > b > b > $o,Xs: a > b > b > $o] :
( ( ( Xp = Xq )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xp @ Xy @ Xz )
& ( Xp @ Xx @ Xy ) )
=> ( Xp @ Xx @ Xz ) )
& ! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( Xp @ Xy @ Xx ) ) )
=> ( ! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( ( ( Xr @ Xx )
= ( Xr @ Xy ) )
& ! [Xx0: b,Xy0: b,Xz: b] :
( ( ( Xr @ Xx @ Xy0 @ Xz )
& ( Xr @ Xx @ Xx0 @ Xy0 ) )
=> ( Xr @ Xx @ Xx0 @ Xz ) )
& ! [Xx0: b,Xy0: b] :
( ( Xr @ Xx @ Xx0 @ Xy0 )
=> ( Xr @ Xx @ Xy0 @ Xx0 ) ) ) )
=> ( ! [Xx: a] :
( ( Xp @ Xx @ Xx )
=> ( ( ( Xr @ Xx )
= ( Xs @ Xx ) )
& ! [Xx0: b,Xy: b,Xz: b] :
( ( ( Xr @ Xx @ Xy @ Xz )
& ( Xr @ Xx @ Xx0 @ Xy ) )
=> ( Xr @ Xx @ Xx0 @ Xz ) )
& ! [Xx0: b,Xy: b] :
( ( Xr @ Xx @ Xx0 @ Xy )
=> ( Xr @ Xx @ Xy @ Xx0 ) ) ) )
=> ( ( ( ^ [Xf: a > b,Xg: a > b] :
! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) )
= ( ^ [Xf: a > b,Xg: a > b] :
! [Xx: a,Xy: a] :
( ( Xq @ Xx @ Xy )
=> ( Xs @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) )
& ! [Xx: a > b,Xy: a > b,Xz: a > b] :
( ( ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) )
& ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) ) )
=> ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
& ! [Xx: a > b,Xy: a > b] :
( ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
=> ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[cTHM517_pme]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( !!
@ ^ [Y1: a > a > $o] :
( !!
@ ^ [Y2: a > b > b > $o] :
( !!
@ ^ [Y3: a > b > b > $o] :
( ( ( Y0 = Y1 )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y0 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y0 @ Y5 @ Y4 ) ) ) ) )
=> ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( ( ( Y2 @ Y4 )
= ( Y2 @ Y5 ) )
& ( !!
@ ^ [Y6: b] :
( !!
@ ^ [Y7: b] :
( !!
@ ^ [Y8: b] :
( ( ( Y2 @ Y4 @ Y7 @ Y8 )
& ( Y2 @ Y4 @ Y6 @ Y7 ) )
=> ( Y2 @ Y4 @ Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y6: b] :
( !!
@ ^ [Y7: b] :
( ( Y2 @ Y4 @ Y6 @ Y7 )
=> ( Y2 @ Y4 @ Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y4 )
=> ( ( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
& ( !!
@ ^ [Y5: b] :
( !!
@ ^ [Y6: b] :
( !!
@ ^ [Y7: b] :
( ( ( Y2 @ Y4 @ Y6 @ Y7 )
& ( Y2 @ Y4 @ Y5 @ Y6 ) )
=> ( Y2 @ Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: b] :
( !!
@ ^ [Y6: b] :
( ( Y2 @ Y4 @ Y5 @ Y6 )
=> ( Y2 @ Y4 @ Y6 @ Y5 ) ) ) ) ) ) )
=> ( ( ( ^ [Y4: a > b,Y5: a > b] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y2 @ Y6 @ ( Y4 @ Y6 ) @ ( Y5 @ Y7 ) ) ) ) ) )
= ( ^ [Y4: a > b,Y5: a > b] :
( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( Y1 @ Y6 @ Y7 )
=> ( Y3 @ Y6 @ ( Y4 @ Y6 ) @ ( Y5 @ Y7 ) ) ) ) ) ) )
& ( !!
@ ^ [Y4: a > b] :
( !!
@ ^ [Y5: a > b] :
( !!
@ ^ [Y6: a > b] :
( ( ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y2 @ Y7 @ ( Y5 @ Y7 ) @ ( Y6 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y2 @ Y7 @ ( Y4 @ Y7 ) @ ( Y5 @ Y8 ) ) ) ) ) )
=> ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( Y0 @ Y7 @ Y8 )
=> ( Y2 @ Y7 @ ( Y4 @ Y7 ) @ ( Y6 @ Y8 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y4: a > b] :
( !!
@ ^ [Y5: a > b] :
( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y2 @ Y6 @ ( Y4 @ Y6 ) @ ( Y5 @ Y7 ) ) ) ) )
=> ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y2 @ Y6 @ ( Y5 @ Y6 ) @ ( Y4 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( !!
@ ^ [Y0: a > a > $o] :
( !!
@ ^ [Y1: a > b > b > $o] :
( !!
@ ^ [Y2: a > b > b > $o] :
( ( ( '#sk1' = Y0 )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( '#sk1' @ Y4 @ Y5 )
& ( '#sk1' @ Y3 @ Y4 ) )
=> ( '#sk1' @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk1' @ Y4 @ Y3 ) ) ) ) )
=> ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( ( ( Y1 @ Y3 )
= ( Y1 @ Y4 ) )
& ( !!
@ ^ [Y5: b] :
( !!
@ ^ [Y6: b] :
( !!
@ ^ [Y7: b] :
( ( ( Y1 @ Y3 @ Y6 @ Y7 )
& ( Y1 @ Y3 @ Y5 @ Y6 ) )
=> ( Y1 @ Y3 @ Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y5: b] :
( !!
@ ^ [Y6: b] :
( ( Y1 @ Y3 @ Y5 @ Y6 )
=> ( Y1 @ Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y3 @ Y3 )
=> ( ( ( Y1 @ Y3 )
= ( Y2 @ Y3 ) )
& ( !!
@ ^ [Y4: b] :
( !!
@ ^ [Y5: b] :
( !!
@ ^ [Y6: b] :
( ( ( Y1 @ Y3 @ Y5 @ Y6 )
& ( Y1 @ Y3 @ Y4 @ Y5 ) )
=> ( Y1 @ Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: b] :
( !!
@ ^ [Y5: b] :
( ( Y1 @ Y3 @ Y4 @ Y5 )
=> ( Y1 @ Y3 @ Y5 @ Y4 ) ) ) ) ) ) )
=> ( ( ( ^ [Y3: a > b,Y4: a > b] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( '#sk1' @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) ) )
= ( ^ [Y3: a > b,Y4: a > b] :
( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y2 @ Y5 @ ( Y3 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) ) ) )
& ( !!
@ ^ [Y3: a > b] :
( !!
@ ^ [Y4: a > b] :
( !!
@ ^ [Y5: a > b] :
( ( ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( '#sk1' @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y4 @ Y6 ) @ ( Y5 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( '#sk1' @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y4 @ Y7 ) ) ) ) ) )
=> ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( '#sk1' @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y5 @ Y7 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y3: a > b] :
( !!
@ ^ [Y4: a > b] :
( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( '#sk1' @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
=> ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( '#sk1' @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y4 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: a > b > b > $o] :
( !!
@ ^ [Y1: a > b > b > $o] :
( ( ( '#sk1' = '#sk2' )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( '#sk1' @ Y3 @ Y4 )
& ( '#sk1' @ Y2 @ Y3 ) )
=> ( '#sk1' @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk1' @ Y3 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( ( ( Y0 @ Y2 )
= ( Y0 @ Y3 ) )
& ( !!
@ ^ [Y4: b] :
( !!
@ ^ [Y5: b] :
( !!
@ ^ [Y6: b] :
( ( ( Y0 @ Y2 @ Y5 @ Y6 )
& ( Y0 @ Y2 @ Y4 @ Y5 ) )
=> ( Y0 @ Y2 @ Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y4: b] :
( !!
@ ^ [Y5: b] :
( ( Y0 @ Y2 @ Y4 @ Y5 )
=> ( Y0 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y2 @ Y2 )
=> ( ( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) )
& ( !!
@ ^ [Y3: b] :
( !!
@ ^ [Y4: b] :
( !!
@ ^ [Y5: b] :
( ( ( Y0 @ Y2 @ Y4 @ Y5 )
& ( Y0 @ Y2 @ Y3 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: b] :
( !!
@ ^ [Y4: b] :
( ( Y0 @ Y2 @ Y3 @ Y4 )
=> ( Y0 @ Y2 @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( ( ^ [Y2: a > b,Y3: a > b] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y2 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) ) )
= ( ^ [Y2: a > b,Y3: a > b] :
( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( '#sk2' @ Y4 @ Y5 )
=> ( Y1 @ Y4 @ ( Y2 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: a > b] :
( !!
@ ^ [Y3: a > b] :
( !!
@ ^ [Y4: a > b] :
( ( ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( '#sk1' @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y3 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( '#sk1' @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) )
=> ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( '#sk1' @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: a > b] :
( !!
@ ^ [Y3: a > b] :
( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y2 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
=> ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: a > b > b > $o] :
( ( ( '#sk1' = '#sk2' )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( '#sk1' @ Y2 @ Y3 )
& ( '#sk1' @ Y1 @ Y2 ) )
=> ( '#sk1' @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( '#sk1' @ Y2 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( ( ( '#sk3' @ Y1 )
= ( '#sk3' @ Y2 ) )
& ( !!
@ ^ [Y3: b] :
( !!
@ ^ [Y4: b] :
( !!
@ ^ [Y5: b] :
( ( ( '#sk3' @ Y1 @ Y4 @ Y5 )
& ( '#sk3' @ Y1 @ Y3 @ Y4 ) )
=> ( '#sk3' @ Y1 @ Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y3: b] :
( !!
@ ^ [Y4: b] :
( ( '#sk3' @ Y1 @ Y3 @ Y4 )
=> ( '#sk3' @ Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y1 @ Y1 )
=> ( ( ( '#sk3' @ Y1 )
= ( Y0 @ Y1 ) )
& ( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( !!
@ ^ [Y4: b] :
( ( ( '#sk3' @ Y1 @ Y3 @ Y4 )
& ( '#sk3' @ Y1 @ Y2 @ Y3 ) )
=> ( '#sk3' @ Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( ( '#sk3' @ Y1 @ Y2 @ Y3 )
=> ( '#sk3' @ Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( ( ^ [Y1: a > b,Y2: a > b] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) )
= ( ^ [Y1: a > b,Y2: a > b] :
( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk2' @ Y3 @ Y4 )
=> ( Y0 @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: a > b] :
( !!
@ ^ [Y2: a > b] :
( !!
@ ^ [Y3: a > b] :
( ( ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( '#sk3' @ Y4 @ ( Y2 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( '#sk3' @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) )
=> ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( '#sk3' @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: a > b] :
( !!
@ ^ [Y2: a > b] :
( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
=> ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
~ ( ( ( '#sk1' = '#sk2' )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1' @ Y1 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( ( ( '#sk3' @ Y0 )
= ( '#sk3' @ Y1 ) )
& ( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( !!
@ ^ [Y4: b] :
( ( ( '#sk3' @ Y0 @ Y3 @ Y4 )
& ( '#sk3' @ Y0 @ Y2 @ Y3 ) )
=> ( '#sk3' @ Y0 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( ( '#sk3' @ Y0 @ Y2 @ Y3 )
=> ( '#sk3' @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ Y0 @ Y0 )
=> ( ( ( '#sk3' @ Y0 )
= ( '#sk4' @ Y0 ) )
& ( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( ( ( '#sk3' @ Y0 @ Y2 @ Y3 )
& ( '#sk3' @ Y0 @ Y1 @ Y2 ) )
=> ( '#sk3' @ Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( ( '#sk3' @ Y0 @ Y1 @ Y2 )
=> ( '#sk3' @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) )
= ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y2 @ Y3 )
=> ( '#sk4' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( !!
@ ^ [Y2: a > b] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl6,plain,
~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( ( ( '#sk3' @ Y0 )
= ( '#sk3' @ Y1 ) )
& ( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( !!
@ ^ [Y4: b] :
( ( ( '#sk3' @ Y0 @ Y3 @ Y4 )
& ( '#sk3' @ Y0 @ Y2 @ Y3 ) )
=> ( '#sk3' @ Y0 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( ( '#sk3' @ Y0 @ Y2 @ Y3 )
=> ( '#sk3' @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ Y0 @ Y0 )
=> ( ( ( '#sk3' @ Y0 )
= ( '#sk4' @ Y0 ) )
& ( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( ( ( '#sk3' @ Y0 @ Y2 @ Y3 )
& ( '#sk3' @ Y0 @ Y1 @ Y2 ) )
=> ( '#sk3' @ Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( ( '#sk3' @ Y0 @ Y1 @ Y2 )
=> ( '#sk3' @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) )
= ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y2 @ Y3 )
=> ( '#sk4' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( !!
@ ^ [Y2: a > b] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl11,plain,
~ ( ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ Y0 @ Y0 )
=> ( ( ( '#sk3' @ Y0 )
= ( '#sk4' @ Y0 ) )
& ( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( ( ( '#sk3' @ Y0 @ Y2 @ Y3 )
& ( '#sk3' @ Y0 @ Y1 @ Y2 ) )
=> ( '#sk3' @ Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( ( '#sk3' @ Y0 @ Y1 @ Y2 )
=> ( '#sk3' @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) )
= ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y2 @ Y3 )
=> ( '#sk4' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( !!
@ ^ [Y2: a > b] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl18,plain,
~ ( ( ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) )
= ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y2 @ Y3 )
=> ( '#sk4' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( !!
@ ^ [Y2: a > b] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl23,plain,
( ( ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) )
!= ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y2 @ Y3 )
=> ( '#sk4' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( !!
@ ^ [Y2: a > b] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl28,plain,
( ( ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) )
!= ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y2 @ Y3 )
=> ( '#sk4' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( !!
@ ^ [Y2: a > b] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl29,plain,
( ( ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
@ '#_fresh_sk5'
@ '#_fresh_sk6' )
!= ( ^ [Y0: a > b,Y1: a > b] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk2' @ Y2 @ Y3 )
=> ( '#sk4' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
@ '#_fresh_sk5'
@ '#_fresh_sk6' ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( !!
@ ^ [Y2: a > b] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(neg_ext_simpl,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl30,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
!= ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( !!
@ ^ [Y2: a > b] :
( ( ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( '#sk3' @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl31,plain,
( ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( '#sk7' @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( '#sk7' @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
!= ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl39,plain,
( ~ ( !!
@ ^ [Y0: a > b] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( '#sk3' @ Y1 @ ( '#sk8' @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( '#sk3' @ Y1 @ ( '#sk7' @ Y1 ) @ ( '#sk8' @ Y2 ) ) ) ) ) )
=> ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( '#sk3' @ Y1 @ ( '#sk7' @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
!= ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl49,plain,
( ~ ( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk8' @ Y0 ) @ ( '#sk9' @ Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk9' @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
!= ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl55,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk9' @ Y1 ) ) ) ) )
| ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
!= ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl54,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk8' @ Y0 ) @ ( '#sk9' @ Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
!= ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl60,plain,
( '#form10'
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl63,plain,
( ~ '#form10'
| ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
!= ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk9' @ Y1 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl55,zip_derived_cl60]) ).
thf(zip_derived_cl63_001,plain,
( ~ '#form10'
| ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
!= ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk9' @ Y1 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl55,zip_derived_cl60]) ).
thf(zip_derived_cl69,plain,
( '#form13'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
<=> ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl72,plain,
( ~ '#form13'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk9' @ Y1 ) ) ) ) )
| ~ '#form10' ),
inference(renaming,[status(thm)],[zip_derived_cl63,zip_derived_cl69]) ).
thf(zip_derived_cl79,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk14' @ Y0 )
=> ( '#sk3' @ '#sk14' @ ( '#sk7' @ '#sk14' ) @ ( '#sk9' @ Y0 ) ) ) )
| ~ '#form10'
| ~ '#form13' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl86,plain,
( ~ ( ( '#sk1' @ '#sk14' @ '#sk17' )
=> ( '#sk3' @ '#sk14' @ ( '#sk7' @ '#sk14' ) @ ( '#sk9' @ '#sk17' ) ) )
| ~ '#form13'
| ~ '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl93,plain,
( ( '#sk1' @ '#sk14' @ '#sk17' )
| ~ '#form10'
| ~ '#form13' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl5,plain,
( ( '#sk1' = '#sk2' )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1' @ Y1 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl9,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1' @ Y1 @ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl15,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1' @ Y0 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl20,plain,
! [X2: a,X4: a] :
( ( '#sk1' @ X2 @ X4 )
=> ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl25,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl131,plain,
( ~ '#form13'
| ~ '#form10'
| ( '#sk1' @ '#sk17' @ '#sk14' ) ),
inference('sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl25]) ).
thf(zip_derived_cl10,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( ( ( '#sk3' @ Y0 )
= ( '#sk3' @ Y1 ) )
& ( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( !!
@ ^ [Y4: b] :
( ( ( '#sk3' @ Y0 @ Y3 @ Y4 )
& ( '#sk3' @ Y0 @ Y2 @ Y3 ) )
=> ( '#sk3' @ Y0 @ Y2 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( ( '#sk3' @ Y0 @ Y2 @ Y3 )
=> ( '#sk3' @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl16,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( ( '#sk1' @ X2 @ Y0 )
=> ( ( ( '#sk3' @ X2 )
= ( '#sk3' @ Y0 ) )
& ( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( ( ( '#sk3' @ X2 @ Y2 @ Y3 )
& ( '#sk3' @ X2 @ Y1 @ Y2 ) )
=> ( '#sk3' @ X2 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( ( '#sk3' @ X2 @ Y1 @ Y2 )
=> ( '#sk3' @ X2 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl21,plain,
! [X2: a,X4: a] :
( ( '#sk1' @ X2 @ X4 )
=> ( ( ( '#sk3' @ X2 )
= ( '#sk3' @ X4 ) )
& ( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( ( ( '#sk3' @ X2 @ Y1 @ Y2 )
& ( '#sk3' @ X2 @ Y0 @ Y1 ) )
=> ( '#sk3' @ X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( ( '#sk3' @ X2 @ Y0 @ Y1 )
=> ( '#sk3' @ X2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl26,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( ( ( '#sk3' @ X2 )
= ( '#sk3' @ X4 ) )
& ( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( ( ( '#sk3' @ X2 @ Y1 @ Y2 )
& ( '#sk3' @ X2 @ Y0 @ Y1 ) )
=> ( '#sk3' @ X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( ( '#sk3' @ X2 @ Y0 @ Y1 )
=> ( '#sk3' @ X2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl33,plain,
! [X2: a,X4: a] :
( ( ( '#sk3' @ X2 )
= ( '#sk3' @ X4 ) )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl41,plain,
! [X2: a,X4: a] :
( ( ( '#sk3' @ X2 )
= ( '#sk3' @ X4 ) )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl42,plain,
! [X2: a,X4: a,X6: b,X7: b] :
( ( ( '#sk3' @ X2 @ X6 @ X7 )
= ( '#sk3' @ X4 @ X6 @ X7 ) )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl214,plain,
! [X0: b,X1: b] :
( ~ '#form10'
| ~ '#form13'
| ( ( '#sk3' @ '#sk17' @ X1 @ X0 )
= ( '#sk3' @ '#sk14' @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl131,zip_derived_cl42]) ).
thf(zip_derived_cl54_002,plain,
( ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk8' @ Y0 ) @ ( '#sk9' @ Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
!= ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl60_003,plain,
( '#form10'
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl62,plain,
( ~ '#form10'
| ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
!= ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk8' @ Y0 ) @ ( '#sk9' @ Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl54,zip_derived_cl60]) ).
thf(zip_derived_cl67,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) )
| ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
!= ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) )
| ~ '#form10' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl69_004,plain,
( '#form13'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
<=> ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl76,plain,
( ~ '#form13'
| ~ '#form10'
| ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk7' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl67,zip_derived_cl69]) ).
thf(zip_derived_cl83,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk3' @ X2 @ ( '#sk7' @ X2 ) @ ( '#sk8' @ Y0 ) ) ) )
| ~ '#form10'
| ~ '#form13' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl90,plain,
! [X2: a,X4: a] :
( ( ( '#sk1' @ X2 @ X4 )
=> ( '#sk3' @ X2 @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X4 ) ) )
| ~ '#form13'
| ~ '#form10' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl99,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk3' @ X2 @ ( '#sk7' @ X2 ) @ ( '#sk8' @ X4 ) )
| ~ '#form10'
| ~ '#form13' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl780,plain,
! [X0: a] :
( ( '#sk3' @ '#sk17' @ ( '#sk7' @ '#sk14' ) @ ( '#sk8' @ X0 ) )
| ~ '#form13'
| ~ '#form10'
| ~ '#form13'
| ~ '#form10'
| ~ ( '#sk1' @ '#sk14' @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl214,zip_derived_cl99]) ).
thf(zip_derived_cl805,plain,
! [X0: a] :
( ~ ( '#sk1' @ '#sk14' @ X0 )
| ~ '#form10'
| ~ '#form13'
| ( '#sk3' @ '#sk17' @ ( '#sk7' @ '#sk14' ) @ ( '#sk8' @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl780]) ).
thf(zip_derived_cl60_005,plain,
( '#form10'
| ~ ( !!
@ ^ [Y0: a > b] :
( !!
@ ^ [Y1: a > b] :
( ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( '#sk3' @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl61,plain,
( ~ ( !!
@ ^ [Y0: a > b] :
( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( '#sk3' @ Y1 @ ( '#sk11' @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( '#sk3' @ Y1 @ ( Y0 @ Y1 ) @ ( '#sk11' @ Y2 ) ) ) ) ) ) )
| '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl68,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk11' @ Y0 ) @ ( '#sk12' @ Y1 ) ) ) ) )
=> ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk12' @ Y0 ) @ ( '#sk11' @ Y1 ) ) ) ) ) )
| '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl78,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk12' @ Y0 ) @ ( '#sk11' @ Y1 ) ) ) ) )
| '#form10' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl85,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk16' @ Y0 )
=> ( '#sk3' @ '#sk16' @ ( '#sk12' @ '#sk16' ) @ ( '#sk11' @ Y0 ) ) ) )
| '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl92,plain,
( ~ ( ( '#sk1' @ '#sk16' @ '#sk19' )
=> ( '#sk3' @ '#sk16' @ ( '#sk12' @ '#sk16' ) @ ( '#sk11' @ '#sk19' ) ) )
| '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl101,plain,
( ( '#sk1' @ '#sk16' @ '#sk19' )
| '#form10' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl25_006,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl137,plain,
( '#form10'
| ( '#sk1' @ '#sk19' @ '#sk16' ) ),
inference('sup-',[status(thm)],[zip_derived_cl101,zip_derived_cl25]) ).
thf(zip_derived_cl77,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk11' @ Y0 ) @ ( '#sk12' @ Y1 ) ) ) ) )
| '#form10' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl84,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk3' @ X2 @ ( '#sk11' @ X2 ) @ ( '#sk12' @ Y0 ) ) ) )
| '#form10' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl91,plain,
! [X2: a,X4: a] :
( ( ( '#sk1' @ X2 @ X4 )
=> ( '#sk3' @ X2 @ ( '#sk11' @ X2 ) @ ( '#sk12' @ X4 ) ) )
| '#form10' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl100,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk3' @ X2 @ ( '#sk11' @ X2 ) @ ( '#sk12' @ X4 ) )
| '#form10' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl465,plain,
( '#form10'
| '#form10'
| ( '#sk3' @ '#sk19' @ ( '#sk11' @ '#sk19' ) @ ( '#sk12' @ '#sk16' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl137,zip_derived_cl100]) ).
thf(zip_derived_cl483,plain,
( ( '#sk3' @ '#sk19' @ ( '#sk11' @ '#sk19' ) @ ( '#sk12' @ '#sk16' ) )
| '#form10' ),
inference(simplify,[status(thm)],[zip_derived_cl465]) ).
thf(zip_derived_cl17,plain,
( !!
@ ^ [Y0: a] :
( ( '#sk1' @ Y0 @ Y0 )
=> ( ( ( '#sk3' @ Y0 )
= ( '#sk4' @ Y0 ) )
& ( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( ( ( '#sk3' @ Y0 @ Y2 @ Y3 )
& ( '#sk3' @ Y0 @ Y1 @ Y2 ) )
=> ( '#sk3' @ Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( ( '#sk3' @ Y0 @ Y1 @ Y2 )
=> ( '#sk3' @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl22,plain,
! [X2: a] :
( ( '#sk1' @ X2 @ X2 )
=> ( ( ( '#sk3' @ X2 )
= ( '#sk4' @ X2 ) )
& ( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( ( ( '#sk3' @ X2 @ Y1 @ Y2 )
& ( '#sk3' @ X2 @ Y0 @ Y1 ) )
=> ( '#sk3' @ X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( ( '#sk3' @ X2 @ Y0 @ Y1 )
=> ( '#sk3' @ X2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl27,plain,
! [X2: a] :
( ~ ( '#sk1' @ X2 @ X2 )
| ( ( ( '#sk3' @ X2 )
= ( '#sk4' @ X2 ) )
& ( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( ( ( '#sk3' @ X2 @ Y1 @ Y2 )
& ( '#sk3' @ X2 @ Y0 @ Y1 ) )
=> ( '#sk3' @ X2 @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( ( '#sk3' @ X2 @ Y0 @ Y1 )
=> ( '#sk3' @ X2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl36,plain,
! [X2: a] :
( ( ( '#sk3' @ X2 )
= ( '#sk4' @ X2 ) )
| ~ ( '#sk1' @ X2 @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl45,plain,
! [X2: a] :
( ( ( '#sk3' @ X2 )
= ( '#sk4' @ X2 ) )
| ~ ( '#sk1' @ X2 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl46,plain,
! [X2: a,X4: b,X5: b] :
( ( ( '#sk3' @ X2 @ X4 @ X5 )
= ( '#sk4' @ X2 @ X4 @ X5 ) )
| ~ ( '#sk1' @ X2 @ X2 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl1046,plain,
( ( '#sk4' @ '#sk19' @ ( '#sk11' @ '#sk19' ) @ ( '#sk12' @ '#sk16' ) )
| '#form10'
| ~ ( '#sk1' @ '#sk19' @ '#sk19' ) ),
inference('sup+',[status(thm)],[zip_derived_cl483,zip_derived_cl46]) ).
thf(zip_derived_cl137_007,plain,
( '#form10'
| ( '#sk1' @ '#sk19' @ '#sk16' ) ),
inference('sup-',[status(thm)],[zip_derived_cl101,zip_derived_cl25]) ).
thf(zip_derived_cl101_008,plain,
( ( '#sk1' @ '#sk16' @ '#sk19' )
| '#form10' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl8,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl14,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk1' @ X2 @ Y0 ) )
=> ( '#sk1' @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl19,plain,
! [X2: a,X4: a] :
( !!
@ ^ [Y0: a] :
( ( ( '#sk1' @ X4 @ Y0 )
& ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk1' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl24,plain,
! [X2: a,X4: a,X6: a] :
( ( ( '#sk1' @ X4 @ X6 )
& ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl32,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( '#sk1' @ X4 @ X6 )
& ( '#sk1' @ X2 @ X4 ) )
| ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl40,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk1' @ X4 @ X6 )
| ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl162,plain,
! [X0: a] :
( '#form10'
| ( '#sk1' @ X0 @ '#sk19' )
| ~ ( '#sk1' @ X0 @ '#sk16' ) ),
inference('sup-',[status(thm)],[zip_derived_cl101,zip_derived_cl40]) ).
thf(zip_derived_cl659,plain,
( '#form10'
| ( '#sk1' @ '#sk19' @ '#sk19' )
| '#form10' ),
inference('sup-',[status(thm)],[zip_derived_cl137,zip_derived_cl162]) ).
thf(zip_derived_cl665,plain,
( ( '#sk1' @ '#sk19' @ '#sk19' )
| '#form10' ),
inference(simplify,[status(thm)],[zip_derived_cl659]) ).
thf(zip_derived_cl1532,plain,
( '#form10'
| ( '#sk4' @ '#sk19' @ ( '#sk11' @ '#sk19' ) @ ( '#sk12' @ '#sk16' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1046,zip_derived_cl665]) ).
thf(zip_derived_cl46_009,plain,
! [X2: a,X4: b,X5: b] :
( ( ( '#sk3' @ X2 @ X4 @ X5 )
= ( '#sk4' @ X2 @ X4 @ X5 ) )
| ~ ( '#sk1' @ X2 @ X2 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl35,plain,
! [X2: a,X4: a] :
( ( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( ( '#sk3' @ X2 @ Y0 @ Y1 )
=> ( '#sk3' @ X2 @ Y1 @ Y0 ) ) ) )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl44,plain,
! [X2: a,X4: a,X6: b] :
( ( !!
@ ^ [Y0: b] :
( ( '#sk3' @ X2 @ X6 @ Y0 )
=> ( '#sk3' @ X2 @ Y0 @ X6 ) ) )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl51,plain,
! [X2: a,X4: a,X6: b,X8: b] :
( ( ( '#sk3' @ X2 @ X6 @ X8 )
=> ( '#sk3' @ X2 @ X8 @ X6 ) )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl57,plain,
! [X2: a,X4: a,X6: b,X8: b] :
( ~ ( '#sk3' @ X2 @ X6 @ X8 )
| ( '#sk3' @ X2 @ X8 @ X6 )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl283,plain,
! [X0: b,X1: b,X2: a,X3: a] :
( ~ ( '#sk4' @ X2 @ X1 @ X0 )
| ~ ( '#sk1' @ X2 @ X2 )
| ~ ( '#sk1' @ X2 @ X3 )
| ( '#sk3' @ X2 @ X0 @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl46,zip_derived_cl57]) ).
thf(zip_derived_cl1379,plain,
! [X0: b,X1: b,X2: a] :
( ~ ( '#sk4' @ X2 @ X1 @ X0 )
| ~ ( '#sk1' @ X2 @ X2 )
| ( '#sk3' @ X2 @ X0 @ X1 ) ),
inference(condensation,[status(thm)],[zip_derived_cl283]) ).
thf(zip_derived_cl1533,plain,
( '#form10'
| ( '#sk3' @ '#sk19' @ ( '#sk12' @ '#sk16' ) @ ( '#sk11' @ '#sk19' ) )
| ~ ( '#sk1' @ '#sk19' @ '#sk19' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1532,zip_derived_cl1379]) ).
thf(zip_derived_cl102,plain,
( ~ ( '#sk3' @ '#sk16' @ ( '#sk12' @ '#sk16' ) @ ( '#sk11' @ '#sk19' ) )
| '#form10' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl137_010,plain,
( '#form10'
| ( '#sk1' @ '#sk19' @ '#sk16' ) ),
inference('sup-',[status(thm)],[zip_derived_cl101,zip_derived_cl25]) ).
thf(zip_derived_cl42_011,plain,
! [X2: a,X4: a,X6: b,X7: b] :
( ( ( '#sk3' @ X2 @ X6 @ X7 )
= ( '#sk3' @ X4 @ X6 @ X7 ) )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl213,plain,
! [X0: b,X1: b] :
( '#form10'
| ( ( '#sk3' @ '#sk19' @ X1 @ X0 )
= ( '#sk3' @ '#sk16' @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl137,zip_derived_cl42]) ).
thf(zip_derived_cl350,plain,
( ~ ( '#sk3' @ '#sk19' @ ( '#sk12' @ '#sk16' ) @ ( '#sk11' @ '#sk19' ) )
| '#form10'
| '#form10' ),
inference('sup+',[status(thm)],[zip_derived_cl102,zip_derived_cl213]) ).
thf(zip_derived_cl367,plain,
( '#form10'
| ~ ( '#sk3' @ '#sk19' @ ( '#sk12' @ '#sk16' ) @ ( '#sk11' @ '#sk19' ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl350]) ).
thf(zip_derived_cl4073,plain,
( ~ ( '#sk1' @ '#sk19' @ '#sk19' )
| '#form10' ),
inference(clc,[status(thm)],[zip_derived_cl1533,zip_derived_cl367]) ).
thf(zip_derived_cl665_012,plain,
( ( '#sk1' @ '#sk19' @ '#sk19' )
| '#form10' ),
inference(simplify,[status(thm)],[zip_derived_cl659]) ).
thf(zip_derived_cl4074,plain,
'#form10',
inference(clc,[status(thm)],[zip_derived_cl4073,zip_derived_cl665]) ).
thf(zip_derived_cl69_013,plain,
( '#form13'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
<=> ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl71,plain,
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
| '#form13' ),
inference(lazy_cnf_xor,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl80,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ '#sk15' @ Y0 )
=> ( '#sk3' @ '#sk15' @ ( '#_fresh_sk5' @ '#sk15' ) @ ( '#_fresh_sk6' @ Y0 ) ) ) )
| '#form13'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl87,plain,
( ~ ( ( '#sk1' @ '#sk15' @ '#sk18' )
=> ( '#sk3' @ '#sk15' @ ( '#_fresh_sk5' @ '#sk15' ) @ ( '#_fresh_sk6' @ '#sk18' ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
| '#form13' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl95,plain,
( ( '#sk1' @ '#sk15' @ '#sk18' )
| '#form13'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl103,plain,
( '#form20'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl104,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ '#sk21' @ Y0 )
=> ( '#sk4' @ '#sk21' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ Y0 ) ) ) )
| '#form20' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl110,plain,
( ~ ( ( '#sk2' @ '#sk21' @ '#sk22' )
=> ( '#sk4' @ '#sk21' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) ) )
| '#form20' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl112,plain,
( ( '#sk2' @ '#sk21' @ '#sk22' )
| '#form20' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl7,plain,
'#sk1' = '#sk2',
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl12,plain,
'#sk1' = '#sk2',
inference('simplify nested equalities',[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl13,plain,
! [X2: a,X3: a] :
( ( '#sk1' @ X2 @ X3 )
= ( '#sk2' @ X2 @ X3 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl115,plain,
! [X2: a,X3: a] :
( ( '#sk1' @ X2 @ X3 )
| ~ ( '#sk2' @ X2 @ X3 ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl144,plain,
( '#form20'
| ( '#sk1' @ '#sk21' @ '#sk22' ) ),
inference('sup-',[status(thm)],[zip_derived_cl112,zip_derived_cl115]) ).
thf(zip_derived_cl69_014,plain,
( '#form13'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
<=> ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl70,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
| ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
| '#form13' ),
inference(lazy_cnf_xor,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl81,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk3' @ X2 @ ( '#_fresh_sk5' @ X2 ) @ ( '#_fresh_sk6' @ Y0 ) ) ) )
| '#form13'
| ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl88,plain,
! [X2: a,X4: a] :
( ( ( '#sk1' @ X2 @ X4 )
=> ( '#sk3' @ X2 @ ( '#_fresh_sk5' @ X2 ) @ ( '#_fresh_sk6' @ X4 ) ) )
| ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
| '#form13' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl97,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk3' @ X2 @ ( '#_fresh_sk5' @ X2 ) @ ( '#_fresh_sk6' @ X4 ) )
| '#form13'
| ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl97_015,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk3' @ X2 @ ( '#_fresh_sk5' @ X2 ) @ ( '#_fresh_sk6' @ X4 ) )
| '#form13'
| ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl107,plain,
( ~ '#form20'
| ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl103_016,plain,
( '#form20'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl109,plain,
! [X2: a,X4: a] :
( '#form20'
| '#form13'
| ( '#sk3' @ X2 @ ( '#_fresh_sk5' @ X2 ) @ ( '#_fresh_sk6' @ X4 ) )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl97,zip_derived_cl107,zip_derived_cl103]) ).
thf(zip_derived_cl526,plain,
( '#form20'
| ( '#sk3' @ '#sk21' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) )
| '#form13'
| '#form20' ),
inference('sup-',[status(thm)],[zip_derived_cl144,zip_derived_cl109]) ).
thf(zip_derived_cl548,plain,
( '#form13'
| ( '#sk3' @ '#sk21' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) )
| '#form20' ),
inference(simplify,[status(thm)],[zip_derived_cl526]) ).
thf(zip_derived_cl112_017,plain,
( ( '#sk2' @ '#sk21' @ '#sk22' )
| '#form20' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl13_018,plain,
! [X2: a,X3: a] :
( ( '#sk1' @ X2 @ X3 )
= ( '#sk2' @ X2 @ X3 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl25_019,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl121,plain,
! [X0: a,X1: a] :
( ~ ( '#sk2' @ X1 @ X0 )
| ( '#sk1' @ X0 @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl25]) ).
thf(zip_derived_cl143,plain,
( '#form20'
| ( '#sk1' @ '#sk22' @ '#sk21' ) ),
inference('sup-',[status(thm)],[zip_derived_cl112,zip_derived_cl121]) ).
thf(zip_derived_cl42_020,plain,
! [X2: a,X4: a,X6: b,X7: b] :
( ( ( '#sk3' @ X2 @ X6 @ X7 )
= ( '#sk3' @ X4 @ X6 @ X7 ) )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl211,plain,
! [X0: b,X1: b] :
( '#form20'
| ( ( '#sk3' @ '#sk22' @ X1 @ X0 )
= ( '#sk3' @ '#sk21' @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl143,zip_derived_cl42]) ).
thf(zip_derived_cl211_021,plain,
! [X0: b,X1: b] :
( '#form20'
| ( ( '#sk3' @ '#sk22' @ X1 @ X0 )
= ( '#sk3' @ '#sk21' @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl143,zip_derived_cl42]) ).
thf(zip_derived_cl46_022,plain,
! [X2: a,X4: b,X5: b] :
( ( ( '#sk3' @ X2 @ X4 @ X5 )
= ( '#sk4' @ X2 @ X4 @ X5 ) )
| ~ ( '#sk1' @ X2 @ X2 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl113,plain,
( ~ ( '#sk4' @ '#sk21' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) )
| '#form20' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl254,plain,
( ~ ( '#sk3' @ '#sk21' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) )
| ~ ( '#sk1' @ '#sk21' @ '#sk21' )
| '#form20' ),
inference('sup-',[status(thm)],[zip_derived_cl46,zip_derived_cl113]) ).
thf(zip_derived_cl431,plain,
( ~ ( '#sk3' @ '#sk22' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) )
| '#form20'
| '#form20'
| ~ ( '#sk1' @ '#sk21' @ '#sk21' ) ),
inference('sup-',[status(thm)],[zip_derived_cl211,zip_derived_cl254]) ).
thf(zip_derived_cl437,plain,
( ~ ( '#sk1' @ '#sk21' @ '#sk21' )
| '#form20'
| ~ ( '#sk3' @ '#sk22' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl431]) ).
thf(zip_derived_cl46_023,plain,
! [X2: a,X4: b,X5: b] :
( ( ( '#sk3' @ X2 @ X4 @ X5 )
= ( '#sk4' @ X2 @ X4 @ X5 ) )
| ~ ( '#sk1' @ X2 @ X2 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl648,plain,
( ~ ( '#sk4' @ '#sk22' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) )
| '#form20'
| ~ ( '#sk1' @ '#sk21' @ '#sk21' )
| ~ ( '#sk1' @ '#sk22' @ '#sk22' ) ),
inference('sup+',[status(thm)],[zip_derived_cl437,zip_derived_cl46]) ).
thf(zip_derived_cl144_024,plain,
( '#form20'
| ( '#sk1' @ '#sk21' @ '#sk22' ) ),
inference('sup-',[status(thm)],[zip_derived_cl112,zip_derived_cl115]) ).
thf(zip_derived_cl143_025,plain,
( '#form20'
| ( '#sk1' @ '#sk22' @ '#sk21' ) ),
inference('sup-',[status(thm)],[zip_derived_cl112,zip_derived_cl121]) ).
thf(zip_derived_cl40_026,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk1' @ X4 @ X6 )
| ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl173,plain,
! [X0: a] :
( '#form20'
| ( '#sk1' @ X0 @ '#sk21' )
| ~ ( '#sk1' @ X0 @ '#sk22' ) ),
inference('sup-',[status(thm)],[zip_derived_cl143,zip_derived_cl40]) ).
thf(zip_derived_cl705,plain,
( '#form20'
| ( '#sk1' @ '#sk21' @ '#sk21' )
| '#form20' ),
inference('sup-',[status(thm)],[zip_derived_cl144,zip_derived_cl173]) ).
thf(zip_derived_cl709,plain,
( ( '#sk1' @ '#sk21' @ '#sk21' )
| '#form20' ),
inference(simplify,[status(thm)],[zip_derived_cl705]) ).
thf(zip_derived_cl1212,plain,
( ~ ( '#sk1' @ '#sk22' @ '#sk22' )
| '#form20'
| ~ ( '#sk4' @ '#sk22' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl648,zip_derived_cl709]) ).
thf(zip_derived_cl143_027,plain,
( '#form20'
| ( '#sk1' @ '#sk22' @ '#sk21' ) ),
inference('sup-',[status(thm)],[zip_derived_cl112,zip_derived_cl121]) ).
thf(zip_derived_cl144_028,plain,
( '#form20'
| ( '#sk1' @ '#sk21' @ '#sk22' ) ),
inference('sup-',[status(thm)],[zip_derived_cl112,zip_derived_cl115]) ).
thf(zip_derived_cl40_029,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk1' @ X4 @ X6 )
| ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl181,plain,
! [X0: a] :
( '#form20'
| ( '#sk1' @ X0 @ '#sk22' )
| ~ ( '#sk1' @ X0 @ '#sk21' ) ),
inference('sup-',[status(thm)],[zip_derived_cl144,zip_derived_cl40]) ).
thf(zip_derived_cl711,plain,
( '#form20'
| ( '#sk1' @ '#sk22' @ '#sk22' )
| '#form20' ),
inference('sup-',[status(thm)],[zip_derived_cl143,zip_derived_cl181]) ).
thf(zip_derived_cl715,plain,
( ( '#sk1' @ '#sk22' @ '#sk22' )
| '#form20' ),
inference(simplify,[status(thm)],[zip_derived_cl711]) ).
thf(zip_derived_cl1213,plain,
( ~ ( '#sk4' @ '#sk22' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) )
| '#form20' ),
inference(clc,[status(thm)],[zip_derived_cl1212,zip_derived_cl715]) ).
thf(zip_derived_cl46_030,plain,
! [X2: a,X4: b,X5: b] :
( ( ( '#sk3' @ X2 @ X4 @ X5 )
= ( '#sk4' @ X2 @ X4 @ X5 ) )
| ~ ( '#sk1' @ X2 @ X2 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl1214,plain,
( ~ ( '#sk3' @ '#sk22' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) )
| '#form20'
| ~ ( '#sk1' @ '#sk22' @ '#sk22' ) ),
inference('sup+',[status(thm)],[zip_derived_cl1213,zip_derived_cl46]) ).
thf(zip_derived_cl715_031,plain,
( ( '#sk1' @ '#sk22' @ '#sk22' )
| '#form20' ),
inference(simplify,[status(thm)],[zip_derived_cl711]) ).
thf(zip_derived_cl1218,plain,
( '#form20'
| ~ ( '#sk3' @ '#sk22' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1214,zip_derived_cl715]) ).
thf(zip_derived_cl1221,plain,
( ~ ( '#sk3' @ '#sk21' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) )
| '#form20'
| '#form20' ),
inference('sup-',[status(thm)],[zip_derived_cl211,zip_derived_cl1218]) ).
thf(zip_derived_cl1227,plain,
( '#form20'
| ~ ( '#sk3' @ '#sk21' @ ( '#_fresh_sk5' @ '#sk21' ) @ ( '#_fresh_sk6' @ '#sk22' ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1221]) ).
thf(zip_derived_cl2877,plain,
( '#form20'
| '#form13' ),
inference(clc,[status(thm)],[zip_derived_cl548,zip_derived_cl1227]) ).
thf(zip_derived_cl95_032,plain,
( ( '#sk1' @ '#sk15' @ '#sk18' )
| '#form13'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl103_033,plain,
( '#form20'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl105,plain,
( ~ '#form20'
| '#form13'
| ( '#sk1' @ '#sk15' @ '#sk18' ) ),
inference(renaming,[status(thm)],[zip_derived_cl95,zip_derived_cl103]) ).
thf(zip_derived_cl105_034,plain,
( ~ '#form20'
| '#form13'
| ( '#sk1' @ '#sk15' @ '#sk18' ) ),
inference(renaming,[status(thm)],[zip_derived_cl95,zip_derived_cl103]) ).
thf(zip_derived_cl25_035,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl413,plain,
( '#form13'
| ~ '#form20'
| ( '#sk1' @ '#sk18' @ '#sk15' ) ),
inference('sup-',[status(thm)],[zip_derived_cl105,zip_derived_cl25]) ).
thf(zip_derived_cl40_036,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk1' @ X4 @ X6 )
| ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl487,plain,
! [X0: a] :
( ~ '#form20'
| '#form13'
| ( '#sk1' @ X0 @ '#sk15' )
| ~ ( '#sk1' @ X0 @ '#sk18' ) ),
inference('sup-',[status(thm)],[zip_derived_cl413,zip_derived_cl40]) ).
thf(zip_derived_cl1367,plain,
( '#form13'
| ~ '#form20'
| ( '#sk1' @ '#sk15' @ '#sk15' )
| '#form13'
| ~ '#form20' ),
inference('sup-',[status(thm)],[zip_derived_cl105,zip_derived_cl487]) ).
thf(zip_derived_cl1373,plain,
( ( '#sk1' @ '#sk15' @ '#sk15' )
| ~ '#form20'
| '#form13' ),
inference(simplify,[status(thm)],[zip_derived_cl1367]) ).
thf(zip_derived_cl107_037,plain,
( ~ '#form20'
| ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl108,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( '#sk2' @ X2 @ Y0 )
=> ( '#sk4' @ X2 @ ( '#_fresh_sk5' @ X2 ) @ ( '#_fresh_sk6' @ Y0 ) ) ) )
| ~ '#form20' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl111,plain,
! [X2: a,X4: a] :
( ( ( '#sk2' @ X2 @ X4 )
=> ( '#sk4' @ X2 @ ( '#_fresh_sk5' @ X2 ) @ ( '#_fresh_sk6' @ X4 ) ) )
| ~ '#form20' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl114,plain,
! [X2: a,X4: a] :
( ~ ( '#sk2' @ X2 @ X4 )
| ( '#sk4' @ X2 @ ( '#_fresh_sk5' @ X2 ) @ ( '#_fresh_sk6' @ X4 ) )
| ~ '#form20' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl46_038,plain,
! [X2: a,X4: b,X5: b] :
( ( ( '#sk3' @ X2 @ X4 @ X5 )
= ( '#sk4' @ X2 @ X4 @ X5 ) )
| ~ ( '#sk1' @ X2 @ X2 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl96,plain,
( ~ ( '#sk3' @ '#sk15' @ ( '#_fresh_sk5' @ '#sk15' ) @ ( '#_fresh_sk6' @ '#sk18' ) )
| '#form13'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl103_039,plain,
( '#form20'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl106,plain,
( ~ '#form20'
| '#form13'
| ~ ( '#sk3' @ '#sk15' @ ( '#_fresh_sk5' @ '#sk15' ) @ ( '#_fresh_sk6' @ '#sk18' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl96,zip_derived_cl103]) ).
thf(zip_derived_cl252,plain,
( ~ ( '#sk4' @ '#sk15' @ ( '#_fresh_sk5' @ '#sk15' ) @ ( '#_fresh_sk6' @ '#sk18' ) )
| ~ ( '#sk1' @ '#sk15' @ '#sk15' )
| '#form13'
| ~ '#form20' ),
inference('sup-',[status(thm)],[zip_derived_cl46,zip_derived_cl106]) ).
thf(zip_derived_cl825,plain,
( ~ '#form20'
| ~ ( '#sk2' @ '#sk15' @ '#sk18' )
| ~ '#form20'
| '#form13'
| ~ ( '#sk1' @ '#sk15' @ '#sk15' ) ),
inference('sup-',[status(thm)],[zip_derived_cl114,zip_derived_cl252]) ).
thf(zip_derived_cl831,plain,
( ~ ( '#sk1' @ '#sk15' @ '#sk15' )
| '#form13'
| ~ ( '#sk2' @ '#sk15' @ '#sk18' )
| ~ '#form20' ),
inference(simplify,[status(thm)],[zip_derived_cl825]) ).
thf(zip_derived_cl105_040,plain,
( ~ '#form20'
| '#form13'
| ( '#sk1' @ '#sk15' @ '#sk18' ) ),
inference(renaming,[status(thm)],[zip_derived_cl95,zip_derived_cl103]) ).
thf(zip_derived_cl13_041,plain,
! [X2: a,X3: a] :
( ( '#sk1' @ X2 @ X3 )
= ( '#sk2' @ X2 @ X3 ) ),
inference(arg_cong_simpl,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl116,plain,
! [X2: a,X3: a] :
( ~ ( '#sk1' @ X2 @ X3 )
| ( '#sk2' @ X2 @ X3 ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl414,plain,
( '#form13'
| ~ '#form20'
| ( '#sk2' @ '#sk15' @ '#sk18' ) ),
inference('sup-',[status(thm)],[zip_derived_cl105,zip_derived_cl116]) ).
thf(zip_derived_cl839,plain,
( ~ '#form20'
| '#form13'
| ~ ( '#sk1' @ '#sk15' @ '#sk15' ) ),
inference(clc,[status(thm)],[zip_derived_cl831,zip_derived_cl414]) ).
thf(zip_derived_cl1376,plain,
( '#form13'
| ~ '#form20' ),
inference(clc,[status(thm)],[zip_derived_cl1373,zip_derived_cl839]) ).
thf(zip_derived_cl2878,plain,
'#form13',
inference(clc,[status(thm)],[zip_derived_cl2877,zip_derived_cl1376]) ).
thf(zip_derived_cl4550,plain,
! [X0: a] :
( ~ ( '#sk1' @ '#sk14' @ X0 )
| ( '#sk3' @ '#sk17' @ ( '#sk7' @ '#sk14' ) @ ( '#sk8' @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl805,zip_derived_cl4074,zip_derived_cl2878]) ).
thf(zip_derived_cl66,plain,
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk8' @ Y0 ) @ ( '#sk9' @ Y1 ) ) ) ) )
| ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
!= ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) )
| ~ '#form10' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl69_042,plain,
( '#form13'
| ~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) )
<=> ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk4' @ Y0 @ ( '#_fresh_sk5' @ Y0 ) @ ( '#_fresh_sk6' @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl75,plain,
( ~ '#form13'
| ~ '#form10'
| ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk3' @ Y0 @ ( '#sk8' @ Y0 ) @ ( '#sk9' @ Y1 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl66,zip_derived_cl69]) ).
thf(zip_derived_cl82,plain,
! [X2: a] :
( ( !!
@ ^ [Y0: a] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk3' @ X2 @ ( '#sk8' @ X2 ) @ ( '#sk9' @ Y0 ) ) ) )
| ~ '#form10'
| ~ '#form13' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl89,plain,
! [X2: a,X4: a] :
( ( ( '#sk1' @ X2 @ X4 )
=> ( '#sk3' @ X2 @ ( '#sk8' @ X2 ) @ ( '#sk9' @ X4 ) ) )
| ~ '#form13'
| ~ '#form10' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl98,plain,
! [X2: a,X4: a] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk3' @ X2 @ ( '#sk8' @ X2 ) @ ( '#sk9' @ X4 ) )
| ~ '#form10'
| ~ '#form13' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl34,plain,
! [X2: a,X4: a] :
( ( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( ( ( '#sk3' @ X2 @ Y1 @ Y2 )
& ( '#sk3' @ X2 @ Y0 @ Y1 ) )
=> ( '#sk3' @ X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl43,plain,
! [X2: a,X4: a,X6: b] :
( ( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( ( ( '#sk3' @ X2 @ Y0 @ Y1 )
& ( '#sk3' @ X2 @ X6 @ Y0 ) )
=> ( '#sk3' @ X2 @ X6 @ Y1 ) ) ) )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl50,plain,
! [X2: a,X4: a,X6: b,X8: b] :
( ( !!
@ ^ [Y0: b] :
( ( ( '#sk3' @ X2 @ X8 @ Y0 )
& ( '#sk3' @ X2 @ X6 @ X8 ) )
=> ( '#sk3' @ X2 @ X6 @ Y0 ) ) )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl56,plain,
! [X2: a,X4: a,X6: b,X8: b,X10: b] :
( ( ( ( '#sk3' @ X2 @ X8 @ X10 )
& ( '#sk3' @ X2 @ X6 @ X8 ) )
=> ( '#sk3' @ X2 @ X6 @ X10 ) )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl64,plain,
! [X2: a,X4: a,X6: b,X8: b,X10: b] :
( ~ ( ( '#sk3' @ X2 @ X8 @ X10 )
& ( '#sk3' @ X2 @ X6 @ X8 ) )
| ( '#sk3' @ X2 @ X6 @ X10 )
| ~ ( '#sk1' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl73,plain,
! [X2: a,X4: a,X6: b,X8: b,X10: b] :
( ~ ( '#sk3' @ X2 @ X8 @ X10 )
| ~ ( '#sk3' @ X2 @ X6 @ X8 )
| ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk3' @ X2 @ X6 @ X10 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl331,plain,
! [X0: a,X1: a,X2: b,X3: a] :
( ~ '#form13'
| ~ '#form10'
| ~ ( '#sk1' @ X1 @ X0 )
| ( '#sk3' @ X1 @ X2 @ ( '#sk9' @ X0 ) )
| ~ ( '#sk1' @ X1 @ X3 )
| ~ ( '#sk3' @ X1 @ X2 @ ( '#sk8' @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl98,zip_derived_cl73]) ).
thf(zip_derived_cl2463,plain,
! [X0: a,X1: b,X2: a] :
( ~ '#form13'
| ~ '#form10'
| ~ ( '#sk3' @ X0 @ X1 @ ( '#sk8' @ X0 ) )
| ( '#sk3' @ X0 @ X1 @ ( '#sk9' @ X2 ) )
| ~ ( '#sk1' @ X0 @ X2 ) ),
inference(condensation,[status(thm)],[zip_derived_cl331]) ).
thf(zip_derived_cl2878_043,plain,
'#form13',
inference(clc,[status(thm)],[zip_derived_cl2877,zip_derived_cl1376]) ).
thf(zip_derived_cl2911,plain,
! [X0: a,X1: b,X2: a] :
( ~ '#form10'
| ~ ( '#sk3' @ X0 @ X1 @ ( '#sk8' @ X0 ) )
| ( '#sk3' @ X0 @ X1 @ ( '#sk9' @ X2 ) )
| ~ ( '#sk1' @ X0 @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl2463,zip_derived_cl2878]) ).
thf(zip_derived_cl4074_044,plain,
'#form10',
inference(clc,[status(thm)],[zip_derived_cl4073,zip_derived_cl665]) ).
thf(zip_derived_cl12480,plain,
! [X0: a,X1: b,X2: a] :
( ~ ( '#sk3' @ X0 @ X1 @ ( '#sk8' @ X0 ) )
| ( '#sk3' @ X0 @ X1 @ ( '#sk9' @ X2 ) )
| ~ ( '#sk1' @ X0 @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl2911,zip_derived_cl4074]) ).
thf(zip_derived_cl12493,plain,
! [X0: a] :
( ~ ( '#sk1' @ '#sk14' @ '#sk17' )
| ~ ( '#sk1' @ '#sk17' @ X0 )
| ( '#sk3' @ '#sk17' @ ( '#sk7' @ '#sk14' ) @ ( '#sk9' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl4550,zip_derived_cl12480]) ).
thf(zip_derived_cl93_045,plain,
( ( '#sk1' @ '#sk14' @ '#sk17' )
| ~ '#form10'
| ~ '#form13' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl2878_046,plain,
'#form13',
inference(clc,[status(thm)],[zip_derived_cl2877,zip_derived_cl1376]) ).
thf(zip_derived_cl2879,plain,
( ( '#sk1' @ '#sk14' @ '#sk17' )
| ~ '#form10' ),
inference(demod,[status(thm)],[zip_derived_cl93,zip_derived_cl2878]) ).
thf(zip_derived_cl4074_047,plain,
'#form10',
inference(clc,[status(thm)],[zip_derived_cl4073,zip_derived_cl665]) ).
thf(zip_derived_cl4075,plain,
'#sk1' @ '#sk14' @ '#sk17',
inference(demod,[status(thm)],[zip_derived_cl2879,zip_derived_cl4074]) ).
thf(zip_derived_cl12528,plain,
! [X0: a] :
( ~ ( '#sk1' @ '#sk17' @ X0 )
| ( '#sk3' @ '#sk17' @ ( '#sk7' @ '#sk14' ) @ ( '#sk9' @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl12493,zip_derived_cl4075]) ).
thf(zip_derived_cl214_048,plain,
! [X0: b,X1: b] :
( ~ '#form10'
| ~ '#form13'
| ( ( '#sk3' @ '#sk17' @ X1 @ X0 )
= ( '#sk3' @ '#sk14' @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl131,zip_derived_cl42]) ).
thf(zip_derived_cl94,plain,
( ~ ( '#sk3' @ '#sk14' @ ( '#sk7' @ '#sk14' ) @ ( '#sk9' @ '#sk17' ) )
| ~ '#form10'
| ~ '#form13' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl778,plain,
( ~ ( '#sk3' @ '#sk17' @ ( '#sk7' @ '#sk14' ) @ ( '#sk9' @ '#sk17' ) )
| ~ '#form13'
| ~ '#form10'
| ~ '#form13'
| ~ '#form10' ),
inference('sup-',[status(thm)],[zip_derived_cl214,zip_derived_cl94]) ).
thf(zip_derived_cl803,plain,
( ~ '#form10'
| ~ '#form13'
| ~ ( '#sk3' @ '#sk17' @ ( '#sk7' @ '#sk14' ) @ ( '#sk9' @ '#sk17' ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl778]) ).
thf(zip_derived_cl2878_049,plain,
'#form13',
inference(clc,[status(thm)],[zip_derived_cl2877,zip_derived_cl1376]) ).
thf(zip_derived_cl2901,plain,
( ~ '#form10'
| ~ ( '#sk3' @ '#sk17' @ ( '#sk7' @ '#sk14' ) @ ( '#sk9' @ '#sk17' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl803,zip_derived_cl2878]) ).
thf(zip_derived_cl4074_050,plain,
'#form10',
inference(clc,[status(thm)],[zip_derived_cl4073,zip_derived_cl665]) ).
thf(zip_derived_cl4092,plain,
~ ( '#sk3' @ '#sk17' @ ( '#sk7' @ '#sk14' ) @ ( '#sk9' @ '#sk17' ) ),
inference(demod,[status(thm)],[zip_derived_cl2901,zip_derived_cl4074]) ).
thf(zip_derived_cl12577,plain,
~ ( '#sk1' @ '#sk17' @ '#sk17' ),
inference('sup-',[status(thm)],[zip_derived_cl12528,zip_derived_cl4092]) ).
thf(zip_derived_cl131_051,plain,
( ~ '#form13'
| ~ '#form10'
| ( '#sk1' @ '#sk17' @ '#sk14' ) ),
inference('sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl25]) ).
thf(zip_derived_cl93_052,plain,
( ( '#sk1' @ '#sk14' @ '#sk17' )
| ~ '#form10'
| ~ '#form13' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl40_053,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( '#sk1' @ X4 @ X6 )
| ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl163,plain,
! [X0: a] :
( ~ '#form13'
| ~ '#form10'
| ( '#sk1' @ X0 @ '#sk17' )
| ~ ( '#sk1' @ X0 @ '#sk14' ) ),
inference('sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl40]) ).
thf(zip_derived_cl239,plain,
( ~ '#form10'
| ~ '#form13'
| ( '#sk1' @ '#sk17' @ '#sk17' )
| ~ '#form10'
| ~ '#form13' ),
inference('sup-',[status(thm)],[zip_derived_cl131,zip_derived_cl163]) ).
thf(zip_derived_cl243,plain,
( ( '#sk1' @ '#sk17' @ '#sk17' )
| ~ '#form13'
| ~ '#form10' ),
inference(simplify,[status(thm)],[zip_derived_cl239]) ).
thf(zip_derived_cl2878_054,plain,
'#form13',
inference(clc,[status(thm)],[zip_derived_cl2877,zip_derived_cl1376]) ).
thf(zip_derived_cl2890,plain,
( ( '#sk1' @ '#sk17' @ '#sk17' )
| ~ '#form10' ),
inference(demod,[status(thm)],[zip_derived_cl243,zip_derived_cl2878]) ).
thf(zip_derived_cl4074_055,plain,
'#form10',
inference(clc,[status(thm)],[zip_derived_cl4073,zip_derived_cl665]) ).
thf(zip_derived_cl4084,plain,
'#sk1' @ '#sk17' @ '#sk17',
inference(demod,[status(thm)],[zip_derived_cl2890,zip_derived_cl4074]) ).
thf(zip_derived_cl12614,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl12577,zip_derived_cl4084]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV041^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.IeQzcZIP3m true
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 02:55:02 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.37 % Running in HO mode
% 0.23/0.65 % Total configuration time : 828
% 0.23/0.65 % Estimated wc time : 1656
% 0.23/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.23/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.23/0.77 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.23/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.23/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.23/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.23/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.23/0.80 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.23/0.80 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 15.72/2.81 % Solved by lams/20_acsne_simpl.sh.
% 15.72/2.81 % done 4247 iterations in 1.906s
% 15.72/2.81 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 15.72/2.81 % SZS output start Refutation
% See solution above
% 15.72/2.82
% 15.72/2.82
% 15.72/2.82 % Terminating...
% 15.72/2.89 % Runner terminated.
% 15.72/2.90 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------