TSTP Solution File: SEV210^5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV210^5 : 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.fLxQLT8mkM true
% Computer : n028.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 20:00:01 EDT 2023
% Result : Theorem 54.74s 7.69s
% Output : Refutation 54.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 34
% Syntax : Number of formulae : 133 ( 4 unt; 19 typ; 0 def)
% Number of atoms : 946 ( 506 equ; 0 cnn)
% Maximal formula atoms : 65 ( 8 avg)
% Number of connectives : 3334 ( 72 ~; 266 |; 392 &;2209 @)
% ( 0 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 14 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 343 ( 343 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 18 usr; 8 con; 0-3 aty)
% ( 81 !!; 241 ??; 0 @@+; 0 @@-)
% Number of variables : 577 ( 322 ^; 219 !; 36 ?; 577 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf('#sk687_type',type,
'#sk687': ( a > a > a > $o ) > a ).
thf('#sk15_type',type,
'#sk15': a > a > a > $o ).
thf(y_type,type,
y: a ).
thf('#sk794_type',type,
'#sk794': ( a > a > a > $o ) > a ).
thf('#sk341_type',type,
'#sk341': ( a > a > a > $o ) > a ).
thf(u_type,type,
u: a ).
thf(cZ_type,type,
cZ: a ).
thf('#sk590_type',type,
'#sk590': ( a > a > a > $o ) > a ).
thf('#sk113_type',type,
'#sk113': ( a > a > a > $o ) > a ).
thf('#sk30_type',type,
'#sk30': ( a > a > a > $o ) > a ).
thf(x_type,type,
x: a ).
thf('#sk426_type',type,
'#sk426': ( a > a > a > $o ) > a ).
thf(cP_type,type,
cP: a > a > a ).
thf('#form1238_type',type,
'#form1238': ( a > a > a > $o ) > $o ).
thf(v_type,type,
v: a ).
thf('#sk66_type',type,
'#sk66': ( a > a > a > $o ) > a ).
thf('#form969_type',type,
'#form969': ( a > a > a > $o ) > $o ).
thf('#sk503_type',type,
'#sk503': ( a > a > a > $o ) > a ).
thf(cS_LEM1E_pme,conjecture,
( ( ! [X: a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ( ( X @ Xy0 )
& ( X @ Xx0 ) )
=> ( X @ ( cP @ Xx0 @ Xy0 ) ) )
& ( X @ cZ ) )
=> ! [Xx0: a] : ( X @ Xx0 ) )
& ! [Xx0: a,Xy0: a,Xu0: a,Xv0: a] :
( ( ( cP @ Xx0 @ Xu0 )
= ( cP @ Xy0 @ Xv0 ) )
=> ( ( Xu0 = Xv0 )
& ( Xx0 = Xy0 ) ) )
& ! [Xx0: a,Xy0: a] :
( ( cP @ Xx0 @ Xy0 )
!= cZ ) )
=> ( ! [R: a > a > a > $o] :
( ! [Xa: a,Xb: a,Xc: a] :
( ( ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = cZ ) )
| ( ( Xb = Xc )
& ( Xa = cZ ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ x @ u @ u ) )
=> ( ! [R: a > a > a > $o] :
( ! [Xa: a,Xb: a,Xc: a] :
( ( ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = cZ ) )
| ( ( Xb = Xc )
& ( Xa = cZ ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ y @ v @ v ) )
=> ! [R: a > a > a > $o] :
( ! [Xa: a,Xb: a,Xc: a] :
( ( ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = cZ ) )
| ( ( Xb = Xc )
& ( Xa = cZ ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( ( ! [X: a > $o] :
( ( ! [Xx0: a,Xy0: a] :
( ( ( X @ Xy0 )
& ( X @ Xx0 ) )
=> ( X @ ( cP @ Xx0 @ Xy0 ) ) )
& ( X @ cZ ) )
=> ! [Xx0: a] : ( X @ Xx0 ) )
& ! [Xx0: a,Xy0: a,Xu0: a,Xv0: a] :
( ( ( cP @ Xx0 @ Xu0 )
= ( cP @ Xy0 @ Xv0 ) )
=> ( ( Xu0 = Xv0 )
& ( Xx0 = Xy0 ) ) )
& ! [Xx0: a,Xy0: a] :
( ( cP @ Xx0 @ Xy0 )
!= cZ ) )
=> ( ! [R: a > a > a > $o] :
( ! [Xa: a,Xb: a,Xc: a] :
( ( ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = cZ ) )
| ( ( Xb = Xc )
& ( Xa = cZ ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ x @ u @ u ) )
=> ( ! [R: a > a > a > $o] :
( ! [Xa: a,Xb: a,Xc: a] :
( ( ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = cZ ) )
| ( ( Xb = Xc )
& ( Xa = cZ ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ y @ v @ v ) )
=> ! [R: a > a > a > $o] :
( ! [Xa: a,Xb: a,Xc: a] :
( ( ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = cZ ) )
| ( ( Xb = Xc )
& ( Xa = cZ ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[cS_LEM1E_pme]) ).
thf(zip_derived_cl0,plain,
~ ( ( ( !!
@ ^ [Y0: a > $o] :
( ( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ cZ ) )
=> ( !!
@ ^ [Y1: a] : ( Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( cP @ Y0 @ Y2 )
= ( cP @ Y1 @ Y3 ) )
=> ( ( Y2 = Y3 )
& ( Y0 = Y1 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( cP @ Y0 @ Y1 )
!= cZ ) ) ) )
=> ( ( !!
@ ^ [Y0: a > a > a > $o] :
( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ??
@ ^ [Y9: a] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = cZ ) )
| ( ( Y2 = Y3 )
& ( Y1 = cZ ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ x @ u @ u ) ) )
=> ( ( !!
@ ^ [Y0: a > a > a > $o] :
( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ??
@ ^ [Y9: a] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = cZ ) )
| ( ( Y2 = Y3 )
& ( Y1 = cZ ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ y @ v @ v ) ) )
=> ( !!
@ ^ [Y0: a > a > a > $o] :
( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ??
@ ^ [Y9: a] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = cZ ) )
| ( ( Y2 = Y3 )
& ( Y1 = cZ ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2,plain,
~ ( ( !!
@ ^ [Y0: a > a > a > $o] :
( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ??
@ ^ [Y9: a] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = cZ ) )
| ( ( Y2 = Y3 )
& ( Y1 = cZ ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ x @ u @ u ) ) )
=> ( ( !!
@ ^ [Y0: a > a > a > $o] :
( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ??
@ ^ [Y9: a] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = cZ ) )
| ( ( Y2 = Y3 )
& ( Y1 = cZ ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ y @ v @ v ) ) )
=> ( !!
@ ^ [Y0: a > a > a > $o] :
( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ??
@ ^ [Y9: a] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = cZ ) )
| ( ( Y2 = Y3 )
& ( Y1 = cZ ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl7,plain,
~ ( ( !!
@ ^ [Y0: a > a > a > $o] :
( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ??
@ ^ [Y9: a] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = cZ ) )
| ( ( Y2 = Y3 )
& ( Y1 = cZ ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ y @ v @ v ) ) )
=> ( !!
@ ^ [Y0: a > a > a > $o] :
( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ??
@ ^ [Y9: a] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = cZ ) )
| ( ( Y2 = Y3 )
& ( Y1 = cZ ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl13,plain,
~ ( !!
@ ^ [Y0: a > a > a > $o] :
( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ??
@ ^ [Y9: a] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = cZ ) )
| ( ( Y2 = Y3 )
& ( Y1 = cZ ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl21,plain,
~ ( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ( Y0
= ( cP @ Y3 @ Y4 ) )
& ( Y1
= ( cP @ Y5 @ Y6 ) )
& ( Y2
= ( cP @ Y7 @ Y8 ) )
& ( '#sk15' @ Y3 @ Y5 @ Y7 )
& ( '#sk15' @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = cZ ) )
| ( ( Y1 = Y2 )
& ( Y0 = cZ ) ) )
=> ( '#sk15' @ Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( '#sk15' @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl28,plain,
~ ( '#sk15' @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl27,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ( Y0
= ( cP @ Y3 @ Y4 ) )
& ( Y1
= ( cP @ Y5 @ Y6 ) )
& ( Y2
= ( cP @ Y7 @ Y8 ) )
& ( '#sk15' @ Y3 @ Y5 @ Y7 )
& ( '#sk15' @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = cZ ) )
| ( ( Y1 = Y2 )
& ( Y0 = cZ ) ) )
=> ( '#sk15' @ Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl33,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ( X2
= ( cP @ Y2 @ Y3 ) )
& ( Y0
= ( cP @ Y4 @ Y5 ) )
& ( Y1
= ( cP @ Y6 @ Y7 ) )
& ( '#sk15' @ Y2 @ Y4 @ Y6 )
& ( '#sk15' @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
| ( ( X2 = Y1 )
& ( Y0 = cZ ) )
| ( ( Y0 = Y1 )
& ( X2 = cZ ) ) )
=> ( '#sk15' @ X2 @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl38,plain,
! [X2: a,X4: a] :
( !!
@ ^ [Y0: a] :
( ( ( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ( X2
= ( cP @ Y1 @ Y2 ) )
& ( X4
= ( cP @ Y3 @ Y4 ) )
& ( Y0
= ( cP @ Y5 @ Y6 ) )
& ( '#sk15' @ Y1 @ Y3 @ Y5 )
& ( '#sk15' @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
| ( ( X2 = Y0 )
& ( X4 = cZ ) )
| ( ( X4 = Y0 )
& ( X2 = cZ ) ) )
=> ( '#sk15' @ X2 @ X4 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl47,plain,
! [X2: a,X4: a,X6: a] :
( ( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( X2
= ( cP @ Y0 @ Y1 ) )
& ( X4
= ( cP @ Y2 @ Y3 ) )
& ( X6
= ( cP @ Y4 @ Y5 ) )
& ( '#sk15' @ Y0 @ Y2 @ Y4 )
& ( '#sk15' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( X2 = X6 )
& ( X4 = cZ ) )
| ( ( X4 = X6 )
& ( X2 = cZ ) ) )
=> ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl56,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( X2
= ( cP @ Y0 @ Y1 ) )
& ( X4
= ( cP @ Y2 @ Y3 ) )
& ( X6
= ( cP @ Y4 @ Y5 ) )
& ( '#sk15' @ Y0 @ Y2 @ Y4 )
& ( '#sk15' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( X2 = X6 )
& ( X4 = cZ ) )
| ( ( X4 = X6 )
& ( X2 = cZ ) ) )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl63,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( X4 = X6 )
& ( X2 = cZ ) )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl70,plain,
! [X2: a,X4: a,X6: a] :
( ( X4 != X6 )
| ( X2 != cZ )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl76,plain,
! [X2: a,X4: a,X6: a] :
( ( X4 != X6 )
| ( X2 != cZ )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl77,plain,
! [X6: a] : ( '#sk15' @ cZ @ X6 @ X6 ),
inference(simplify,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl12,plain,
( !!
@ ^ [Y0: a > a > a > $o] :
( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ??
@ ^ [Y9: a] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = cZ ) )
| ( ( Y2 = Y3 )
& ( Y1 = cZ ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ y @ v @ v ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl18,plain,
! [X2: a > a > a > $o] :
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ( Y0
= ( cP @ Y3 @ Y4 ) )
& ( Y1
= ( cP @ Y5 @ Y6 ) )
& ( Y2
= ( cP @ Y7 @ Y8 ) )
& ( X2 @ Y3 @ Y5 @ Y7 )
& ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = cZ ) )
| ( ( Y1 = Y2 )
& ( Y0 = cZ ) ) )
=> ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( X2 @ y @ v @ v ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl26,plain,
! [X2: a > a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ( Y0
= ( cP @ Y3 @ Y4 ) )
& ( Y1
= ( cP @ Y5 @ Y6 ) )
& ( Y2
= ( cP @ Y7 @ Y8 ) )
& ( X2 @ Y3 @ Y5 @ Y7 )
& ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = cZ ) )
| ( ( Y1 = Y2 )
& ( Y0 = cZ ) ) )
=> ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
| ( X2 @ y @ v @ v ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl32,plain,
! [X2: a > a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( Y0
= ( cP @ Y4 @ Y5 ) )
& ( Y1
= ( cP @ Y6 @ Y7 ) )
& ( X2 @ Y2 @ Y4 @ Y6 )
& ( X2 @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
| ( ( ( '#sk30' @ X2 )
= Y1 )
& ( Y0 = cZ ) )
| ( ( Y0 = Y1 )
& ( ( '#sk30' @ X2 )
= cZ ) ) )
=> ( X2 @ ( '#sk30' @ X2 ) @ Y0 @ Y1 ) ) ) )
| ( X2 @ y @ v @ v ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl37,plain,
! [X2: a > a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( ( '#sk66' @ X2 )
= ( cP @ Y3 @ Y4 ) )
& ( Y0
= ( cP @ Y5 @ Y6 ) )
& ( X2 @ Y1 @ Y3 @ Y5 )
& ( X2 @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
| ( ( ( '#sk30' @ X2 )
= Y0 )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( ( ( '#sk66' @ X2 )
= Y0 )
& ( ( '#sk30' @ X2 )
= cZ ) ) )
=> ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk66' @ X2 ) @ Y0 ) ) )
| ( X2 @ y @ v @ v ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl46,plain,
! [X2: a > a > a > $o] :
( ~ ( ( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk66' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) ) )
=> ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk66' @ X2 ) @ ( '#sk113' @ X2 ) ) )
| ( X2 @ y @ v @ v ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl54,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk66' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( X2 @ y @ v @ v ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl60,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk66' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( X2 @ y @ v @ v ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl67,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ Y0 ) )
& ( ( '#sk66' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y3 @ Y4 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ Y1 @ Y3 )
& ( X2 @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
| ( X2 @ y @ v @ v )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl72,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ Y0 @ Y2 )
& ( X2 @ ( '#sk426' @ X2 ) @ Y1 @ Y3 ) ) ) ) ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( X2 @ y @ v @ v ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl79,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ Y0 ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ Y1 )
& ( X2 @ ( '#sk426' @ X2 ) @ Y0 @ Y2 ) ) ) ) )
| ( X2 @ y @ v @ v )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl82,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ Y1 ) ) ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( X2 @ y @ v @ v ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl85,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ ( '#sk687' @ X2 ) )
& ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ Y0 ) ) )
| ( X2 @ y @ v @ v )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl92,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form969' @ X2 )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl93,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
| ~ ( '#form969' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl109,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
| ~ ( '#form969' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl62,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( X2 = X6 )
& ( X4 = cZ ) )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl69,plain,
! [X2: a,X4: a,X6: a] :
( ( X2 != X6 )
| ( X4 != cZ )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl74,plain,
! [X2: a,X4: a,X6: a] :
( ( X2 != X6 )
| ( X4 != cZ )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl75,plain,
! [X6: a] : ( '#sk15' @ X6 @ cZ @ X6 ),
inference(simplify,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl6,plain,
( !!
@ ^ [Y0: a > a > a > $o] :
( ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ??
@ ^ [Y9: a] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = cZ ) )
| ( ( Y2 = Y3 )
& ( Y1 = cZ ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ x @ u @ u ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl11,plain,
! [X2: a > a > a > $o] :
( ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ( Y0
= ( cP @ Y3 @ Y4 ) )
& ( Y1
= ( cP @ Y5 @ Y6 ) )
& ( Y2
= ( cP @ Y7 @ Y8 ) )
& ( X2 @ Y3 @ Y5 @ Y7 )
& ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = cZ ) )
| ( ( Y1 = Y2 )
& ( Y0 = cZ ) ) )
=> ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( X2 @ x @ u @ u ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl17,plain,
! [X2: a > a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ??
@ ^ [Y8: a] :
( ( Y0
= ( cP @ Y3 @ Y4 ) )
& ( Y1
= ( cP @ Y5 @ Y6 ) )
& ( Y2
= ( cP @ Y7 @ Y8 ) )
& ( X2 @ Y3 @ Y5 @ Y7 )
& ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = cZ ) )
| ( ( Y1 = Y2 )
& ( Y0 = cZ ) ) )
=> ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
| ( X2 @ x @ u @ u ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl25,plain,
! [X2: a > a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( Y0
= ( cP @ Y4 @ Y5 ) )
& ( Y1
= ( cP @ Y6 @ Y7 ) )
& ( X2 @ Y2 @ Y4 @ Y6 )
& ( X2 @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
| ( ( ( '#sk30' @ X2 )
= Y1 )
& ( Y0 = cZ ) )
| ( ( Y0 = Y1 )
& ( ( '#sk30' @ X2 )
= cZ ) ) )
=> ( X2 @ ( '#sk30' @ X2 ) @ Y0 @ Y1 ) ) ) )
| ( X2 @ x @ u @ u ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl31,plain,
! [X2: a > a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( ( '#sk66' @ X2 )
= ( cP @ Y3 @ Y4 ) )
& ( Y0
= ( cP @ Y5 @ Y6 ) )
& ( X2 @ Y1 @ Y3 @ Y5 )
& ( X2 @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
| ( ( ( '#sk30' @ X2 )
= Y0 )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( ( ( '#sk66' @ X2 )
= Y0 )
& ( ( '#sk30' @ X2 )
= cZ ) ) )
=> ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk66' @ X2 ) @ Y0 ) ) )
| ( X2 @ x @ u @ u ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl36,plain,
! [X2: a > a > a > $o] :
( ~ ( ( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk66' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) ) )
=> ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk66' @ X2 ) @ ( '#sk113' @ X2 ) ) )
| ( X2 @ x @ u @ u ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl44,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk66' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( X2 @ x @ u @ u ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl53,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk66' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( X2 @ x @ u @ u ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl59,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ Y0 ) )
& ( ( '#sk66' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y3 @ Y4 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ Y1 @ Y3 )
& ( X2 @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
| ( X2 @ x @ u @ u )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl66,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ Y0 @ Y2 )
& ( X2 @ ( '#sk426' @ X2 ) @ Y1 @ Y3 ) ) ) ) ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( X2 @ x @ u @ u ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl71,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ Y0 ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ Y1 )
& ( X2 @ ( '#sk426' @ X2 ) @ Y0 @ Y2 ) ) ) ) )
| ( X2 @ x @ u @ u )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl78,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk113' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ Y1 ) ) ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( X2 @ x @ u @ u ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl81,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ ( '#sk687' @ X2 ) )
& ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ Y0 ) ) )
| ( X2 @ x @ u @ u )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl84,plain,
! [X2: a > a > a > $o] :
( ( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ ( '#sk794' @ X2 ) ) )
& ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ ( '#sk687' @ X2 ) )
& ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk794' @ X2 ) ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( X2 @ x @ u @ u ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl87,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
| ( X2 @ x @ u @ u )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl97,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
| ( X2 @ x @ u @ u )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl92_001,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form969' @ X2 )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl98,plain,
! [X2: a > a > a > $o] :
( ( '#form969' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( X2 @ x @ u @ u )
| ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl97,zip_derived_cl92]) ).
thf(zip_derived_cl85_002,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ ( '#sk687' @ X2 ) )
& ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ Y0 ) ) )
| ( X2 @ y @ v @ v )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl92_003,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form969' @ X2 )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl95,plain,
! [X2: a > a > a > $o] :
( ( '#form969' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( X2 @ y @ v @ v )
| ( ??
@ ^ [Y0: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ ( '#sk687' @ X2 ) )
& ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl85,zip_derived_cl92]) ).
thf(zip_derived_cl105,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1238' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl112,plain,
! [X2: a > a > a > $o] :
( ( '#form1238' @ X2 )
| ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
| ( X2 @ x @ u @ u )
| ( '#form969' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl98,zip_derived_cl105]) ).
thf(zip_derived_cl105_004,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1238' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl106,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
| ~ ( '#form1238' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl118,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
| ~ ( '#form1238' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl94,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk30' @ X2 )
= cZ )
| ~ ( '#form969' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl110,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk30' @ X2 )
= cZ )
| ~ ( '#form969' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl45,plain,
! [X2: a > a > a > $o] :
( ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk66' @ X2 ) @ ( '#sk113' @ X2 ) )
| ( X2 @ x @ u @ u ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl88,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
| ( X2 @ x @ u @ u )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl99,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
| ( X2 @ x @ u @ u )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl92_005,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form969' @ X2 )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl100,plain,
! [X2: a > a > a > $o] :
( ( '#form969' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( X2 @ x @ u @ u )
| ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl99,zip_derived_cl92]) ).
thf(zip_derived_cl105_006,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1238' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl113,plain,
! [X2: a > a > a > $o] :
( ( '#form1238' @ X2 )
| ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
| ( X2 @ x @ u @ u )
| ( '#form969' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl100,zip_derived_cl105]) ).
thf(zip_derived_cl95_007,plain,
! [X2: a > a > a > $o] :
( ( '#form969' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( X2 @ y @ v @ v )
| ( ??
@ ^ [Y0: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ ( '#sk687' @ X2 ) )
& ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl85,zip_derived_cl92]) ).
thf(zip_derived_cl105_008,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1238' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl108,plain,
! [X2: a > a > a > $o] :
( ( '#form1238' @ X2 )
| ( ??
@ ^ [Y0: a] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ ( '#sk687' @ X2 ) )
& ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ Y0 ) ) )
| ( X2 @ y @ v @ v )
| ( '#form969' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl95,zip_derived_cl105]) ).
thf(zip_derived_cl117,plain,
! [X2: a > a > a > $o] :
( ( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
& ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ ( '#sk794' @ X2 ) ) )
& ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ ( '#sk687' @ X2 ) )
& ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk794' @ X2 ) ) )
| ( '#form969' @ X2 )
| ( X2 @ y @ v @ v )
| ( '#form1238' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl122,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
| ( '#form1238' @ X2 )
| ( X2 @ y @ v @ v )
| ( '#form969' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl117]) ).
thf(zip_derived_cl127,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk30' @ X2 )
= ( cP @ ( '#sk341' @ X2 ) @ ( '#sk426' @ X2 ) ) )
| ( '#form1238' @ X2 )
| ( X2 @ y @ v @ v )
| ( '#form969' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl122]) ).
thf(zip_derived_cl107,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk66' @ X2 )
= cZ )
| ~ ( '#form1238' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl119,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk66' @ X2 )
= cZ )
| ~ ( '#form1238' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl89,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ ( '#sk794' @ X2 ) ) )
| ( X2 @ x @ u @ u )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl101,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ ( '#sk794' @ X2 ) ) )
| ( X2 @ x @ u @ u )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl92_009,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form969' @ X2 )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl102,plain,
! [X2: a > a > a > $o] :
( ( '#form969' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( X2 @ x @ u @ u )
| ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ ( '#sk794' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl101,zip_derived_cl92]) ).
thf(zip_derived_cl105_010,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1238' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl114,plain,
! [X2: a > a > a > $o] :
( ( '#form1238' @ X2 )
| ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ ( '#sk794' @ X2 ) ) )
| ( X2 @ x @ u @ u )
| ( '#form969' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl102,zip_derived_cl105]) ).
thf(zip_derived_cl55,plain,
! [X2: a > a > a > $o] :
( ~ ( X2 @ ( '#sk30' @ X2 ) @ ( '#sk66' @ X2 ) @ ( '#sk113' @ X2 ) )
| ( X2 @ y @ v @ v ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl123,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
| ( '#form1238' @ X2 )
| ( X2 @ y @ v @ v )
| ( '#form969' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl117]) ).
thf(zip_derived_cl128,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk66' @ X2 )
= ( cP @ ( '#sk503' @ X2 ) @ ( '#sk590' @ X2 ) ) )
| ( '#form1238' @ X2 )
| ( X2 @ y @ v @ v )
| ( '#form969' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl123]) ).
thf(zip_derived_cl90,plain,
! [X2: a > a > a > $o] :
( ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ ( '#sk687' @ X2 ) )
| ( X2 @ x @ u @ u )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl92_011,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form969' @ X2 )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl103,plain,
! [X2: a > a > a > $o] :
( ( '#form969' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( X2 @ x @ u @ u )
| ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ ( '#sk687' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl90,zip_derived_cl92]) ).
thf(zip_derived_cl105_012,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1238' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl115,plain,
! [X2: a > a > a > $o] :
( ( '#form1238' @ X2 )
| ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ ( '#sk687' @ X2 ) )
| ( X2 @ x @ u @ u )
| ( '#form969' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl103,zip_derived_cl105]) ).
thf(zip_derived_cl124,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ ( '#sk794' @ X2 ) ) )
| ( '#form1238' @ X2 )
| ( X2 @ y @ v @ v )
| ( '#form969' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl117]) ).
thf(zip_derived_cl129,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk113' @ X2 )
= ( cP @ ( '#sk687' @ X2 ) @ ( '#sk794' @ X2 ) ) )
| ( '#form1238' @ X2 )
| ( X2 @ y @ v @ v )
| ( '#form969' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl124]) ).
thf(zip_derived_cl91,plain,
! [X2: a > a > a > $o] :
( ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk794' @ X2 ) )
| ( X2 @ x @ u @ u )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl92_013,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form969' @ X2 )
| ( ( ( '#sk66' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk30' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl104,plain,
! [X2: a > a > a > $o] :
( ( '#form969' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) )
| ( X2 @ x @ u @ u )
| ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk794' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl91,zip_derived_cl92]) ).
thf(zip_derived_cl105_014,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1238' @ X2 )
| ( ( ( '#sk30' @ X2 )
= ( '#sk113' @ X2 ) )
& ( ( '#sk66' @ X2 )
= cZ ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl116,plain,
! [X2: a > a > a > $o] :
( ( '#form1238' @ X2 )
| ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk794' @ X2 ) )
| ( X2 @ x @ u @ u )
| ( '#form969' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl104,zip_derived_cl105]) ).
thf(zip_derived_cl125,plain,
! [X2: a > a > a > $o] :
( ( X2 @ ( '#sk341' @ X2 ) @ ( '#sk503' @ X2 ) @ ( '#sk687' @ X2 ) )
| ( '#form1238' @ X2 )
| ( X2 @ y @ v @ v )
| ( '#form969' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl117]) ).
thf(zip_derived_cl126,plain,
! [X2: a > a > a > $o] :
( ( X2 @ ( '#sk426' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk794' @ X2 ) )
| ( '#form1238' @ X2 )
| ( X2 @ y @ v @ v )
| ( '#form969' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl117]) ).
thf(zip_derived_cl61,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( X2
= ( cP @ Y0 @ Y1 ) )
& ( X4
= ( cP @ Y2 @ Y3 ) )
& ( X6
= ( cP @ Y4 @ Y5 ) )
& ( '#sk15' @ Y0 @ Y2 @ Y4 )
& ( '#sk15' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl68,plain,
! [X2: a,X4: a,X6: a,X8: a] :
( ~ ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ( X2
= ( cP @ X8 @ Y0 ) )
& ( X4
= ( cP @ Y1 @ Y2 ) )
& ( X6
= ( cP @ Y3 @ Y4 ) )
& ( '#sk15' @ X8 @ Y1 @ Y3 )
& ( '#sk15' @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl73,plain,
! [X2: a,X4: a,X6: a,X8: a,X10: a] :
( ~ ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ( X2
= ( cP @ X8 @ X10 ) )
& ( X4
= ( cP @ Y0 @ Y1 ) )
& ( X6
= ( cP @ Y2 @ Y3 ) )
& ( '#sk15' @ X8 @ Y0 @ Y2 )
& ( '#sk15' @ X10 @ Y1 @ Y3 ) ) ) ) ) )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl80,plain,
! [X2: a,X4: a,X6: a,X8: a,X10: a,X12: a] :
( ~ ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ( X2
= ( cP @ X8 @ X10 ) )
& ( X4
= ( cP @ X12 @ Y0 ) )
& ( X6
= ( cP @ Y1 @ Y2 ) )
& ( '#sk15' @ X8 @ X12 @ Y1 )
& ( '#sk15' @ X10 @ Y0 @ Y2 ) ) ) ) )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl83,plain,
! [X2: a,X4: a,X6: a,X8: a,X10: a,X12: a,X14: a] :
( ~ ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ( X2
= ( cP @ X8 @ X10 ) )
& ( X4
= ( cP @ X12 @ X14 ) )
& ( X6
= ( cP @ Y0 @ Y1 ) )
& ( '#sk15' @ X8 @ X12 @ Y0 )
& ( '#sk15' @ X10 @ X14 @ Y1 ) ) ) )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl86,plain,
! [X2: a,X4: a,X6: a,X8: a,X10: a,X12: a,X14: a,X16: a] :
( ~ ( ??
@ ^ [Y0: a] :
( ( X2
= ( cP @ X8 @ X10 ) )
& ( X4
= ( cP @ X12 @ X14 ) )
& ( X6
= ( cP @ X16 @ Y0 ) )
& ( '#sk15' @ X8 @ X12 @ X16 )
& ( '#sk15' @ X10 @ X14 @ Y0 ) ) )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl96,plain,
! [X2: a,X4: a,X6: a,X8: a,X10: a,X12: a,X14: a,X16: a,X18: a] :
( ~ ( ( X2
= ( cP @ X8 @ X10 ) )
& ( X4
= ( cP @ X12 @ X14 ) )
& ( X6
= ( cP @ X16 @ X18 ) )
& ( '#sk15' @ X8 @ X12 @ X16 )
& ( '#sk15' @ X10 @ X14 @ X18 ) )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl111,plain,
! [X2: a,X4: a,X6: a,X8: a,X10: a,X12: a,X14: a,X16: a,X18: a] :
( ( X2
!= ( cP @ X8 @ X10 ) )
| ( X4
!= ( cP @ X12 @ X14 ) )
| ( X6
!= ( cP @ X16 @ X18 ) )
| ~ ( '#sk15' @ X8 @ X12 @ X16 )
| ~ ( '#sk15' @ X10 @ X14 @ X18 )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl120,plain,
! [X2: a,X4: a,X6: a,X8: a,X10: a,X12: a,X14: a,X16: a,X18: a] :
( ( X2
!= ( cP @ X8 @ X10 ) )
| ( X4
!= ( cP @ X12 @ X14 ) )
| ( X6
!= ( cP @ X16 @ X18 ) )
| ~ ( '#sk15' @ X8 @ X12 @ X16 )
| ~ ( '#sk15' @ X10 @ X14 @ X18 )
| ( '#sk15' @ X2 @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl121,plain,
! [X8: a,X10: a,X12: a,X14: a,X16: a,X18: a] :
( ( '#sk15' @ ( cP @ X8 @ X10 ) @ ( cP @ X12 @ X14 ) @ ( cP @ X16 @ X18 ) )
| ~ ( '#sk15' @ X10 @ X14 @ X18 )
| ~ ( '#sk15' @ X8 @ X12 @ X16 ) ),
inference(simplify,[status(thm)],[zip_derived_cl120]) ).
thf(zip_derived_cl9590,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl28,zip_derived_cl77,zip_derived_cl109,zip_derived_cl75,zip_derived_cl112,zip_derived_cl118,zip_derived_cl110,zip_derived_cl45,zip_derived_cl113,zip_derived_cl127,zip_derived_cl119,zip_derived_cl114,zip_derived_cl55,zip_derived_cl128,zip_derived_cl115,zip_derived_cl129,zip_derived_cl116,zip_derived_cl125,zip_derived_cl126,zip_derived_cl121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV210^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.fLxQLT8mkM true
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 03:27:19 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.20/0.67 % Total configuration time : 828
% 0.20/0.67 % Estimated wc time : 1656
% 0.20/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.77 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.05/0.80 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.05/0.81 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.05/0.82 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 54.74/7.69 % Solved by lams/20_acsne_simpl.sh.
% 54.74/7.69 % done 614 iterations in 6.769s
% 54.74/7.69 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 54.74/7.69 % SZS output start Refutation
% See solution above
% 54.74/7.69
% 54.74/7.69
% 54.74/7.69 % Terminating...
% 55.32/7.79 % Runner terminated.
% 55.32/7.80 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------