TSTP Solution File: SEV208^5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV208^5 : 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.Vt4lk2cEvx true
% Computer : n006.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 49.35s 7.23s
% Output : Refutation 49.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 34
% Syntax : Number of formulae : 132 ( 4 unt; 19 typ; 0 def)
% Number of atoms : 870 ( 477 equ; 0 cnn)
% Maximal formula atoms : 51 ( 7 avg)
% Number of connectives : 3068 ( 67 ~; 260 |; 362 &;2052 @)
% ( 0 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 14 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 331 ( 331 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 18 usr; 8 con; 0-3 aty)
% ( 59 !!; 219 ??; 0 @@+; 0 @@-)
% Number of variables : 513 ( 278 ^; 199 !; 36 ?; 513 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf('#form1044_type',type,
'#form1044': ( a > a > a > $o ) > $o ).
thf(w_type,type,
w: a ).
thf('#sk804_type',type,
'#sk804': ( a > a > a > $o ) > a ).
thf('#sk344_type',type,
'#sk344': ( a > a > a > $o ) > a ).
thf('#sk692_type',type,
'#sk692': ( a > a > a > $o ) > a ).
thf('#sk416_type',type,
'#sk416': ( a > a > a > $o ) > a ).
thf(y_type,type,
y: a ).
thf(c0_type,type,
c0: a ).
thf('#sk29_type',type,
'#sk29': ( a > a > a > $o ) > a ).
thf('#sk59_type',type,
'#sk59': ( a > a > a > $o ) > a ).
thf(x_type,type,
x: a ).
thf(cP_type,type,
cP: a > a > a ).
thf(z_type,type,
z: a ).
thf('#sk590_type',type,
'#sk590': ( a > a > a > $o ) > a ).
thf('#sk498_type',type,
'#sk498': ( a > a > a > $o ) > a ).
thf('#sk1_type',type,
'#sk1': a > a > a > $o ).
thf('#sk111_type',type,
'#sk111': ( a > a > a > $o ) > a ).
thf('#form989_type',type,
'#form989': ( a > a > a > $o ) > $o ).
thf(cS_INCL_LEM1_pme,conjecture,
( ( ! [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 = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ w @ z @ z ) )
& ! [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 = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ x @ y @ y ) ) )
=> ! [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 = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( ( ! [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 = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ w @ z @ z ) )
& ! [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 = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ x @ y @ y ) ) )
=> ! [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 = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ),
inference('cnf.neg',[status(esa)],[cS_INCL_LEM1_pme]) ).
thf(zip_derived_cl0,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 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ w @ z @ z ) ) )
& ( !!
@ ^ [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 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ x @ y @ y ) ) ) )
=> ( !!
@ ^ [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 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ) ),
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 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl5,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 ) )
& ( '#sk1' @ Y3 @ Y5 @ Y7 )
& ( '#sk1' @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = c0 ) )
| ( ( Y1 = Y2 )
& ( Y0 = c0 ) ) )
=> ( '#sk1' @ Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( '#sk1' @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl10,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 ) )
& ( '#sk1' @ Y3 @ Y5 @ Y7 )
& ( '#sk1' @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = c0 ) )
| ( ( Y1 = Y2 )
& ( Y0 = c0 ) ) )
=> ( '#sk1' @ Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl14,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 ) )
& ( '#sk1' @ Y2 @ Y4 @ Y6 )
& ( '#sk1' @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
| ( ( X2 = Y1 )
& ( Y0 = c0 ) )
| ( ( Y0 = Y1 )
& ( X2 = c0 ) ) )
=> ( '#sk1' @ X2 @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl17,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 ) )
& ( '#sk1' @ Y1 @ Y3 @ Y5 )
& ( '#sk1' @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
| ( ( X2 = Y0 )
& ( X4 = c0 ) )
| ( ( X4 = Y0 )
& ( X2 = c0 ) ) )
=> ( '#sk1' @ X2 @ X4 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl20,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 ) )
& ( '#sk1' @ Y0 @ Y2 @ Y4 )
& ( '#sk1' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( X2 = X6 )
& ( X4 = c0 ) )
| ( ( X4 = X6 )
& ( X2 = c0 ) ) )
=> ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl23,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 ) )
& ( '#sk1' @ Y0 @ Y2 @ Y4 )
& ( '#sk1' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( X2 = X6 )
& ( X4 = c0 ) )
| ( ( X4 = X6 )
& ( X2 = c0 ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl30,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( X4 = X6 )
& ( X2 = c0 ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl35,plain,
! [X2: a,X4: a,X6: a] :
( ( X4 != X6 )
| ( X2 != c0 )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl41,plain,
! [X2: a,X4: a,X6: a] :
( ( X4 != X6 )
| ( X2 != c0 )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl42,plain,
! [X6: a] : ( '#sk1' @ c0 @ X6 @ X6 ),
inference(simplify,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl29,plain,
! [X2: a,X4: a,X6: a] :
( ~ ( ( X2 = X6 )
& ( X4 = c0 ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl34,plain,
! [X2: a,X4: a,X6: a] :
( ( X2 != X6 )
| ( X4 != c0 )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl39,plain,
! [X2: a,X4: a,X6: a] :
( ( X2 != X6 )
| ( X4 != c0 )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl40,plain,
! [X6: a] : ( '#sk1' @ X6 @ c0 @ X6 ),
inference(simplify,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl1,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 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ w @ z @ z ) ) )
& ( !!
@ ^ [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 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ x @ y @ y ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,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 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ w @ z @ z ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,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 = c0 ) )
| ( ( Y1 = Y2 )
& ( Y0 = c0 ) ) )
=> ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( X2 @ w @ z @ z ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl12,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 = c0 ) )
| ( ( Y1 = Y2 )
& ( Y0 = c0 ) ) )
=> ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
| ( X2 @ w @ z @ z ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl15,plain,
! [X2: a > a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( Y0
= ( cP @ Y4 @ Y5 ) )
& ( Y1
= ( cP @ Y6 @ Y7 ) )
& ( X2 @ Y2 @ Y4 @ Y6 )
& ( X2 @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
| ( ( ( '#sk29' @ X2 )
= Y1 )
& ( Y0 = c0 ) )
| ( ( Y0 = Y1 )
& ( ( '#sk29' @ X2 )
= c0 ) ) )
=> ( X2 @ ( '#sk29' @ X2 ) @ Y0 @ Y1 ) ) ) )
| ( X2 @ w @ z @ z ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl18,plain,
! [X2: a > a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( ( '#sk59' @ X2 )
= ( cP @ Y3 @ Y4 ) )
& ( Y0
= ( cP @ Y5 @ Y6 ) )
& ( X2 @ Y1 @ Y3 @ Y5 )
& ( X2 @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
| ( ( ( '#sk29' @ X2 )
= Y0 )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= Y0 )
& ( ( '#sk29' @ X2 )
= c0 ) ) )
=> ( X2 @ ( '#sk29' @ X2 ) @ ( '#sk59' @ X2 ) @ Y0 ) ) )
| ( X2 @ w @ z @ z ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21,plain,
! [X2: a > a > a > $o] :
( ~ ( ( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk59' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) ) )
=> ( X2 @ ( '#sk29' @ X2 ) @ ( '#sk59' @ X2 ) @ ( '#sk111' @ X2 ) ) )
| ( X2 @ w @ z @ z ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl24,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk59' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( X2 @ w @ z @ z ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl31,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk59' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( X2 @ w @ z @ z ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl36,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ Y0 ) )
& ( ( '#sk59' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y3 @ Y4 ) )
& ( X2 @ ( '#sk344' @ X2 ) @ Y1 @ Y3 )
& ( X2 @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
| ( X2 @ w @ z @ z )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl43,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
& ( ( '#sk59' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( X2 @ ( '#sk344' @ X2 ) @ Y0 @ Y2 )
& ( X2 @ ( '#sk416' @ X2 ) @ Y1 @ Y3 ) ) ) ) ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( X2 @ w @ z @ z ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl46,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
& ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ Y0 ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ Y1 )
& ( X2 @ ( '#sk416' @ X2 ) @ Y0 @ Y2 ) ) ) ) )
| ( X2 @ w @ z @ z )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl49,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
& ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ Y1 ) ) ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( X2 @ w @ z @ z ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl52,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
& ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk111' @ X2 )
= ( cP @ ( '#sk692' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
& ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ Y0 ) ) )
| ( X2 @ w @ z @ z )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl55,plain,
! [X2: a > a > a > $o] :
( ( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
& ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk111' @ X2 )
= ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
& ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
& ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( X2 @ w @ z @ z ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl58,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
| ( X2 @ w @ z @ z )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl69,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
| ( X2 @ w @ z @ z )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl70,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1044' @ X2 )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl71,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
| ~ ( '#form1044' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl84,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
| ~ ( '#form1044' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl11,plain,
~ ( '#sk1' @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl4,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 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ x @ y @ y ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl8,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 = c0 ) )
| ( ( Y1 = Y2 )
& ( Y0 = c0 ) ) )
=> ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl13,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 = c0 ) )
| ( ( Y1 = Y2 )
& ( Y0 = c0 ) ) )
=> ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl16,plain,
! [X2: a > a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ??
@ ^ [Y7: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( Y0
= ( cP @ Y4 @ Y5 ) )
& ( Y1
= ( cP @ Y6 @ Y7 ) )
& ( X2 @ Y2 @ Y4 @ Y6 )
& ( X2 @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
| ( ( ( '#sk29' @ X2 )
= Y1 )
& ( Y0 = c0 ) )
| ( ( Y0 = Y1 )
& ( ( '#sk29' @ X2 )
= c0 ) ) )
=> ( X2 @ ( '#sk29' @ X2 ) @ Y0 @ Y1 ) ) ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl19,plain,
! [X2: a > a > a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( ( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ??
@ ^ [Y6: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( ( '#sk59' @ X2 )
= ( cP @ Y3 @ Y4 ) )
& ( Y0
= ( cP @ Y5 @ Y6 ) )
& ( X2 @ Y1 @ Y3 @ Y5 )
& ( X2 @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
| ( ( ( '#sk29' @ X2 )
= Y0 )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= Y0 )
& ( ( '#sk29' @ X2 )
= c0 ) ) )
=> ( X2 @ ( '#sk29' @ X2 ) @ ( '#sk59' @ X2 ) @ Y0 ) ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl22,plain,
! [X2: a > a > a > $o] :
( ~ ( ( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk59' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) ) )
=> ( X2 @ ( '#sk29' @ X2 ) @ ( '#sk59' @ X2 ) @ ( '#sk111' @ X2 ) ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl26,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk59' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl32,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ??
@ ^ [Y4: a] :
( ??
@ ^ [Y5: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk59' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_or,[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] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ Y0 ) )
& ( ( '#sk59' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y3 @ Y4 ) )
& ( X2 @ ( '#sk344' @ X2 ) @ Y1 @ Y3 )
& ( X2 @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl44,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ??
@ ^ [Y3: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
& ( ( '#sk59' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( X2 @ ( '#sk344' @ X2 ) @ Y0 @ Y2 )
& ( X2 @ ( '#sk416' @ X2 ) @ Y1 @ Y3 ) ) ) ) ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl47,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ??
@ ^ [Y2: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
& ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ Y0 ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ Y1 )
& ( X2 @ ( '#sk416' @ X2 ) @ Y0 @ Y2 ) ) ) ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl50,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ??
@ ^ [Y1: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
& ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk111' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ Y1 ) ) ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl53,plain,
! [X2: a > a > a > $o] :
( ( ??
@ ^ [Y0: a] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
& ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk111' @ X2 )
= ( cP @ ( '#sk692' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
& ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ Y0 ) ) )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl56,plain,
! [X2: a > a > a > $o] :
( ( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
& ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk111' @ X2 )
= ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
& ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
& ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl63,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form989' @ X2 )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl64,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
| ~ ( '#form989' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl81,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
| ~ ( '#form989' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl56_001,plain,
! [X2: a > a > a > $o] :
( ( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
& ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk111' @ X2 )
= ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
& ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
& ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl63_002,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form989' @ X2 )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl66,plain,
! [X2: a > a > a > $o] :
( ( '#form989' @ X2 )
| ( X2 @ x @ y @ y )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
& ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk111' @ X2 )
= ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
& ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
& ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl56,zip_derived_cl63]) ).
thf(zip_derived_cl70_003,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1044' @ X2 )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl80,plain,
! [X2: a > a > a > $o] :
( ( '#form1044' @ X2 )
| ( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
& ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
& ( ( '#sk111' @ X2 )
= ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
& ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
& ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) ) )
| ( X2 @ x @ y @ y )
| ( '#form989' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl66,zip_derived_cl70]) ).
thf(zip_derived_cl90,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
| ( '#form989' @ X2 )
| ( X2 @ x @ y @ y )
| ( '#form1044' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl95,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
| ( '#form989' @ X2 )
| ( X2 @ x @ y @ y )
| ( '#form1044' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl65,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk59' @ X2 )
= c0 )
| ~ ( '#form989' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl82,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk59' @ X2 )
= c0 )
| ~ ( '#form989' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl27,plain,
! [X2: a > a > a > $o] :
( ~ ( X2 @ ( '#sk29' @ X2 ) @ ( '#sk59' @ X2 ) @ ( '#sk111' @ X2 ) )
| ( X2 @ x @ y @ y ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl91,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
| ( '#form989' @ X2 )
| ( X2 @ x @ y @ y )
| ( '#form1044' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl96,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
| ( '#form989' @ X2 )
| ( X2 @ x @ y @ y )
| ( '#form1044' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl69_004,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
| ( X2 @ w @ z @ z )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl70_005,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1044' @ X2 )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl73,plain,
! [X2: a > a > a > $o] :
( ( '#form1044' @ X2 )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( X2 @ w @ z @ z )
| ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl69,zip_derived_cl70]) ).
thf(zip_derived_cl63_006,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form989' @ X2 )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl83,plain,
! [X2: a > a > a > $o] :
( ( '#form989' @ X2 )
| ( ( '#sk29' @ X2 )
= ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
| ( X2 @ w @ z @ z )
| ( '#form1044' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl73,zip_derived_cl63]) ).
thf(zip_derived_cl72,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk29' @ X2 )
= c0 )
| ~ ( '#form1044' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl85,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk29' @ X2 )
= c0 )
| ~ ( '#form1044' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl92,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk111' @ X2 )
= ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
| ( '#form989' @ X2 )
| ( X2 @ x @ y @ y )
| ( '#form1044' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl97,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk111' @ X2 )
= ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
| ( '#form989' @ X2 )
| ( X2 @ x @ y @ y )
| ( '#form1044' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl25,plain,
! [X2: a > a > a > $o] :
( ~ ( X2 @ ( '#sk29' @ X2 ) @ ( '#sk59' @ X2 ) @ ( '#sk111' @ X2 ) )
| ( X2 @ w @ z @ z ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl59,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
| ( X2 @ w @ z @ z )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl74,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
| ( X2 @ w @ z @ z )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl70_007,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1044' @ X2 )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl75,plain,
! [X2: a > a > a > $o] :
( ( '#form1044' @ X2 )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( X2 @ w @ z @ z )
| ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl74,zip_derived_cl70]) ).
thf(zip_derived_cl63_008,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form989' @ X2 )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl86,plain,
! [X2: a > a > a > $o] :
( ( '#form989' @ X2 )
| ( ( '#sk59' @ X2 )
= ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
| ( X2 @ w @ z @ z )
| ( '#form1044' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl75,zip_derived_cl63]) ).
thf(zip_derived_cl93,plain,
! [X2: a > a > a > $o] :
( ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
| ( '#form989' @ X2 )
| ( X2 @ x @ y @ y )
| ( '#form1044' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl60,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk111' @ X2 )
= ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
| ( X2 @ w @ z @ z )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl76,plain,
! [X2: a > a > a > $o] :
( ( ( '#sk111' @ X2 )
= ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
| ( X2 @ w @ z @ z )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl70_009,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1044' @ X2 )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl77,plain,
! [X2: a > a > a > $o] :
( ( '#form1044' @ X2 )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( X2 @ w @ z @ z )
| ( ( '#sk111' @ X2 )
= ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl76,zip_derived_cl70]) ).
thf(zip_derived_cl63_010,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form989' @ X2 )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl87,plain,
! [X2: a > a > a > $o] :
( ( '#form989' @ X2 )
| ( ( '#sk111' @ X2 )
= ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
| ( X2 @ w @ z @ z )
| ( '#form1044' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl77,zip_derived_cl63]) ).
thf(zip_derived_cl94,plain,
! [X2: a > a > a > $o] :
( ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) )
| ( '#form989' @ X2 )
| ( X2 @ x @ y @ y )
| ( '#form1044' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl61,plain,
! [X2: a > a > a > $o] :
( ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
| ( X2 @ w @ z @ z )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl70_011,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1044' @ X2 )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl78,plain,
! [X2: a > a > a > $o] :
( ( '#form1044' @ X2 )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( X2 @ w @ z @ z )
| ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl61,zip_derived_cl70]) ).
thf(zip_derived_cl63_012,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form989' @ X2 )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl88,plain,
! [X2: a > a > a > $o] :
( ( '#form989' @ X2 )
| ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
| ( X2 @ w @ z @ z )
| ( '#form1044' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl78,zip_derived_cl63]) ).
thf(zip_derived_cl62,plain,
! [X2: a > a > a > $o] :
( ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) )
| ( X2 @ w @ z @ z )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl70_013,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form1044' @ X2 )
| ( ( ( '#sk59' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk29' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl79,plain,
! [X2: a > a > a > $o] :
( ( '#form1044' @ X2 )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) )
| ( X2 @ w @ z @ z )
| ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl62,zip_derived_cl70]) ).
thf(zip_derived_cl63_014,plain,
! [X2: a > a > a > $o] :
( ~ ( '#form989' @ X2 )
| ( ( ( '#sk29' @ X2 )
= ( '#sk111' @ X2 ) )
& ( ( '#sk59' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl89,plain,
! [X2: a > a > a > $o] :
( ( '#form989' @ X2 )
| ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) )
| ( X2 @ w @ z @ z )
| ( '#form1044' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl79,zip_derived_cl63]) ).
thf(zip_derived_cl28,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 ) )
& ( '#sk1' @ Y0 @ Y2 @ Y4 )
& ( '#sk1' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl33,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 ) )
& ( '#sk1' @ X8 @ Y1 @ Y3 )
& ( '#sk1' @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl38,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 ) )
& ( '#sk1' @ X8 @ Y0 @ Y2 )
& ( '#sk1' @ X10 @ Y1 @ Y3 ) ) ) ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl45,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 ) )
& ( '#sk1' @ X8 @ X12 @ Y1 )
& ( '#sk1' @ X10 @ Y0 @ Y2 ) ) ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl48,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 ) )
& ( '#sk1' @ X8 @ X12 @ Y0 )
& ( '#sk1' @ X10 @ X14 @ Y1 ) ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl51,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 ) )
& ( '#sk1' @ X8 @ X12 @ X16 )
& ( '#sk1' @ X10 @ X14 @ Y0 ) ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl54,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 ) )
& ( '#sk1' @ X8 @ X12 @ X16 )
& ( '#sk1' @ X10 @ X14 @ X18 ) )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl57,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 ) )
| ~ ( '#sk1' @ X8 @ X12 @ X16 )
| ~ ( '#sk1' @ X10 @ X14 @ X18 )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl67,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 ) )
| ~ ( '#sk1' @ X8 @ X12 @ X16 )
| ~ ( '#sk1' @ X10 @ X14 @ X18 )
| ( '#sk1' @ X2 @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl68,plain,
! [X8: a,X10: a,X12: a,X14: a,X16: a,X18: a] :
( ( '#sk1' @ ( cP @ X8 @ X10 ) @ ( cP @ X12 @ X14 ) @ ( cP @ X16 @ X18 ) )
| ~ ( '#sk1' @ X10 @ X14 @ X18 )
| ~ ( '#sk1' @ X8 @ X12 @ X16 ) ),
inference(simplify,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl5349,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl42,zip_derived_cl40,zip_derived_cl84,zip_derived_cl11,zip_derived_cl81,zip_derived_cl95,zip_derived_cl82,zip_derived_cl27,zip_derived_cl96,zip_derived_cl83,zip_derived_cl85,zip_derived_cl97,zip_derived_cl25,zip_derived_cl86,zip_derived_cl93,zip_derived_cl87,zip_derived_cl94,zip_derived_cl88,zip_derived_cl89,zip_derived_cl68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV208^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Vt4lk2cEvx true
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 02:09:37 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
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.56/0.78 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 49.35/7.23 % Solved by lams/20_acsne_simpl.sh.
% 49.35/7.23 % done 491 iterations in 6.341s
% 49.35/7.23 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 49.35/7.23 % SZS output start Refutation
% See solution above
% 49.35/7.23
% 49.35/7.23
% 49.35/7.23 % Terminating...
% 51.47/7.34 % Runner terminated.
% 51.49/7.35 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------