TSTP Solution File: SEV310^5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV310^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.qWfSiDq9kE true
% Computer : n026.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 20:00:23 EDT 2023
% Result : Theorem 51.58s 7.28s
% Output : Refutation 51.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 26
% Syntax : Number of formulae : 115 ( 11 unt; 10 typ; 0 def)
% Number of atoms : 851 ( 9 equ; 0 cnn)
% Maximal formula atoms : 26 ( 8 avg)
% Number of connectives : 2702 ( 89 ~; 125 |; 0 &;1630 @)
% ( 0 <=>; 455 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 13 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 274 ( 274 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-2 aty)
% ( 403 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 633 ( 501 ^; 132 !; 0 ?; 633 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf('#sk1_type',type,
'#sk1': a ).
thf('#form1076_type',type,
'#form1076': ( a > $o ) > $o ).
thf('#l_lift30859_type',type,
'#l_lift30859': a > $o ).
thf('#sk336_type',type,
'#sk336': ( a > $o ) > a ).
thf('#sk12_type',type,
'#sk12': ( a > $o ) > ( a > $o ) > a ).
thf(cK_type,type,
cK: ( a > $o ) > a > $o ).
thf('#sk244_type',type,
'#sk244': ( a > $o ) > a > $o ).
thf('#form811_type',type,
'#form811': $o ).
thf('#sk236_type',type,
'#sk236': ( a > $o ) > a ).
thf(cTHM90A_pme,conjecture,
( ! [X: a > $o,Y: a > $o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: a] :
( ( cK @ X @ Xx )
=> ( cK @ Y @ Xx ) ) )
=> ! [Xx: a] :
( ! [S: a > $o] :
( ! [Xx0: a] :
( ( cK @ S @ Xx0 )
=> ( S @ Xx0 ) )
=> ( S @ Xx ) )
=> ( cK
@ ^ [Xx0: a] :
! [S: a > $o] :
( ! [Xx1: a] :
( ( cK @ S @ Xx1 )
=> ( S @ Xx1 ) )
=> ( S @ Xx0 ) )
@ Xx ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( ! [X: a > $o,Y: a > $o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: a] :
( ( cK @ X @ Xx )
=> ( cK @ Y @ Xx ) ) )
=> ! [Xx: a] :
( ! [S: a > $o] :
( ! [Xx0: a] :
( ( cK @ S @ Xx0 )
=> ( S @ Xx0 ) )
=> ( S @ Xx ) )
=> ( cK
@ ^ [Xx0: a] :
! [S: a > $o] :
( ! [Xx1: a] :
( ( cK @ S @ Xx1 )
=> ( S @ Xx1 ) )
=> ( S @ Xx0 ) )
@ Xx ) ) ),
inference('cnf.neg',[status(esa)],[cTHM90A_pme]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: a > $o] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !!
@ ^ [Y2: a] :
( ( cK @ Y0 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: a] :
( ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: a > $o] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !!
@ ^ [Y2: a] :
( ( cK @ Y0 @ Y2 )
=> ( cK @ Y1 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
! [X2: a > $o] :
( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( X2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y1: a] :
( ( cK @ X2 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl23,plain,
( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y1: a] :
( ( cK
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a > $o] :
( ( !!
@ ^ [Y4: a] :
( ( cK @ Y3 @ Y4 )
=> ( Y3 @ Y4 ) ) )
=> ( Y3 @ Y2 ) ) )
@ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl88,plain,
! [X2: a > $o] :
( ( !!
@ ^ [Y0: a] :
( ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( X2 @ Y0 ) ) )
=> ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK @ X2 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl91,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( X2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK @ X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl92,plain,
! [X2: a > $o] :
( ~ ( ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X2 ) ) ) )
=> ( X2 @ ( '#sk336' @ X2 ) ) )
| ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK @ X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl93,plain,
! [X2: a > $o] :
( ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK @ X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl95,plain,
! [X2: a > $o,X4: a > $o] :
( ( ( !!
@ ^ [Y0: a] :
( ( cK @ X4 @ Y0 )
=> ( X4 @ Y0 ) ) )
=> ( X4 @ ( '#sk336' @ X2 ) ) )
| ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK @ X2 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl97,plain,
! [X0: a > $o] :
( ( ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) ) )
| ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK @ X0 @ Y0 ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl276,plain,
! [X0: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) )
| ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK @ X0 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: a] :
( ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
=> ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl4,plain,
~ ( ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ '#sk1' ) ) )
=> ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ '#sk1' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl6,plain,
( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ '#sk1' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl9,plain,
! [X2: a > $o] :
( ( !!
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( X2 @ Y0 ) ) )
=> ( X2 @ '#sk1' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl21,plain,
( ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ '#sk1' ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl108,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ '#sk1' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl109,plain,
( ~ ( ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0
@ ( '#sk236'
@ ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ '#sk1' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl110,plain,
( ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ '#sk1' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl112,plain,
! [X2: a > $o] :
( ( ( !!
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( X2 @ Y0 ) ) )
=> ( X2 @ '#sk1' ) )
| ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl114,plain,
( ( ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ '#sk1' ) ) ) )
| ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl185,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ '#sk1' ) ) )
| ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl186,plain,
( ~ ( ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0
@ ( '#sk236'
@ ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ '#sk1' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl185]) ).
thf(zip_derived_cl187,plain,
( ~ ( $false
=> ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0
@ ( '#sk236'
@ ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ '#sk1' ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl186]) ).
thf(zip_derived_cl188,plain,
( ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ '#sk1' ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl187]) ).
thf(zip_derived_cl189,plain,
! [X2: a > $o] :
( ( ( !!
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( X2 @ Y0 ) ) )
=> ( X2 @ '#sk1' ) )
| ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl188]) ).
thf(zip_derived_cl191,plain,
( ( ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ '#sk1' ) ) ) )
| ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl189]) ).
thf(zip_derived_cl264,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ '#sk1' ) ) )
| ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl191]) ).
thf(zip_derived_cl265,plain,
( '#form811'
| ~ ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl277,plain,
! [X0: a > $o] :
( ~ '#form811'
| ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK @ X0 @ Y0 ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl276,zip_derived_cl265]) ).
thf(zip_derived_cl278,plain,
! [X0: a > $o,X2: a] :
( ( ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X2 )
=> ( cK @ X0 @ X2 ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) )
| ~ '#form811' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl277]) ).
thf(zip_derived_cl279,plain,
! [X0: a > $o,X2: a] :
( ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X2 )
| ( cK @ X0 @ X2 )
| ~ '#form811'
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl278]) ).
thf(zip_derived_cl280,plain,
! [X0: a > $o,X2: a,X4: a > $o] :
( ( ( !!
@ ^ [Y0: a] :
( ( cK @ X4 @ Y0 )
=> ( X4 @ Y0 ) ) )
=> ( X4 @ ( '#sk336' @ X0 ) ) )
| ~ '#form811'
| ( cK @ X0 @ X2 )
| ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl279]) ).
thf(zip_derived_cl282,plain,
! [X0: a > $o,X1: a] :
( ( ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) ) )
| ~ '#form811'
| ( cK @ X0 @ X1 )
| ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X1 ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl280]) ).
thf(zip_derived_cl314,plain,
! [X0: a > $o,X1: a] :
( ~ ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) )
| ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X1 )
| ( cK @ X0 @ X1 )
| ~ '#form811' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl282]) ).
thf(zip_derived_cl265_001,plain,
( '#form811'
| ~ ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl315,plain,
! [X0: a > $o,X1: a] :
( ~ '#form811'
| ~ '#form811'
| ( cK @ X0 @ X1 )
| ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X1 )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl314,zip_derived_cl265]) ).
thf(zip_derived_cl316,plain,
! [X0: a > $o,X1: a] :
( ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) )
| ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X1 )
| ( cK @ X0 @ X1 )
| ~ '#form811' ),
inference(simplify,[status(thm)],[zip_derived_cl315]) ).
thf(zip_derived_cl317,plain,
! [X0: a > $o,X1: a,X3: a > $o] :
( ( ( !!
@ ^ [Y0: a] :
( ( cK @ X3 @ Y0 )
=> ( X3 @ Y0 ) ) )
=> ( X3 @ ( '#sk336' @ X0 ) ) )
| ~ '#form811'
| ( cK @ X0 @ X1 )
| ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X1 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl316]) ).
thf(zip_derived_cl319,plain,
! [X0: a > $o,X1: a] :
( ( ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) ) )
| ~ '#form811'
| ( cK @ X0 @ X1 )
| ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X1 ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl317]) ).
thf(zip_derived_cl332,plain,
! [X0: a > $o,X1: a] :
( ~ ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) )
| ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X1 )
| ( cK @ X0 @ X1 )
| ~ '#form811' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl319]) ).
thf(zip_derived_cl265_002,plain,
( '#form811'
| ~ ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl333,plain,
! [X0: a > $o,X1: a] :
( ~ '#form811'
| ~ '#form811'
| ( cK @ X0 @ X1 )
| ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X1 )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl332,zip_derived_cl265]) ).
thf(zip_derived_cl334,plain,
! [X0: a > $o,X1: a] :
( ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) )
| ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X1 )
| ( cK @ X0 @ X1 )
| ~ '#form811' ),
inference(simplify,[status(thm)],[zip_derived_cl333]) ).
thf(zip_derived_cl335,plain,
! [X0: a > $o] :
( ~ ( '#form1076' @ X0 )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl336,plain,
! [X0: a > $o,X2: a > $o] :
( ( ( !!
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( X2 @ Y0 ) ) )
=> ( X2 @ ( '#sk336' @ X0 ) ) )
| ~ ( '#form1076' @ X0 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl335]) ).
thf(zip_derived_cl340,plain,
! [X0: a > $o,X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( X2 @ Y0 ) ) )
| ( X2 @ ( '#sk336' @ X0 ) )
| ~ ( '#form1076' @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl336]) ).
thf(zip_derived_cl341,plain,
! [X0: a > $o,X2: a > $o] :
( ~ ( ( cK @ X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) )
=> ( X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) ) )
| ~ ( '#form1076' @ X0 )
| ( X2 @ ( '#sk336' @ X0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl340]) ).
thf(zip_derived_cl342,plain,
! [X0: a > $o,X2: a > $o] :
( ( cK @ X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) )
| ( X2 @ ( '#sk336' @ X0 ) )
| ~ ( '#form1076' @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl341]) ).
thf(zip_derived_cl265_003,plain,
( '#form811'
| ~ ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl266,plain,
( ~ ( ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0
@ ( '#sk236'
@ ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ) )
| '#form811' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl265]) ).
thf(zip_derived_cl270,plain,
( ~ ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0
@ ( '#sk236'
@ ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) )
| '#form811' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl266]) ).
thf(zip_derived_cl271,plain,
( ~ ( ( !!
@ ^ [Y0: a] :
( ( cK
@ ( '#sk244'
@ ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ Y0 )
=> ( '#sk244'
@ ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) )
=> ( '#sk244'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) ) )
| '#form811' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl270]) ).
thf(zip_derived_cl273,plain,
( ~ ( '#sk244'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ ( '#sk236'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| '#form811' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl271]) ).
thf(zip_derived_cl7,plain,
~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl8258,plain,
! [X1: a] :
( ( '#l_lift30859' @ X1 )
= ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl8258_004,plain,
! [X1: a] :
( ( '#l_lift30859' @ X1 )
= ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl8271,plain,
( ~ ( '#sk244' @ ( cK @ '#l_lift30859' ) @ ( '#sk236' @ ( cK @ '#l_lift30859' ) ) )
| '#form811' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl273,zip_derived_cl8258,zip_derived_cl8258]) ).
thf(zip_derived_cl334_005,plain,
! [X0: a > $o,X1: a] :
( ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) )
| ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X1 )
| ( cK @ X0 @ X1 )
| ~ '#form811' ),
inference(simplify,[status(thm)],[zip_derived_cl333]) ).
thf(zip_derived_cl335_006,plain,
! [X0: a > $o] :
( ~ ( '#form1076' @ X0 )
| ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk336' @ X0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl339,plain,
! [X0: a > $o,X1: a] :
( ( '#form1076' @ X0 )
| ~ '#form811'
| ( cK @ X0 @ X1 )
| ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X1 ) ),
inference(renaming,[status(thm)],[zip_derived_cl334,zip_derived_cl335]) ).
thf(zip_derived_cl8258_007,plain,
! [X1: a] :
( ( '#l_lift30859' @ X1 )
= ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl8273,plain,
! [X0: a > $o,X1: a] :
( ( '#form1076' @ X0 )
| ~ '#form811'
| ( cK @ X0 @ X1 )
| ~ ( cK @ '#l_lift30859' @ X1 ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl339,zip_derived_cl8258]) ).
thf(zip_derived_cl94,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk336' @ X2 ) )
| ( !!
@ ^ [Y0: a] :
( ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( cK @ X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl98,plain,
! [X2: a > $o,X4: a] :
( ( ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X4 )
=> ( cK @ X2 @ X4 ) )
| ~ ( X2 @ ( '#sk336' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl100,plain,
! [X2: a > $o,X4: a] :
( ~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X4 )
| ( cK @ X2 @ X4 )
| ~ ( X2 @ ( '#sk336' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl98]) ).
thf(zip_derived_cl8258_008,plain,
! [X1: a] :
( ( '#l_lift30859' @ X1 )
= ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl8263,plain,
! [X2: a > $o,X4: a] :
( ~ ( cK @ '#l_lift30859' @ X4 )
| ( cK @ X2 @ X4 )
| ~ ( X2 @ ( '#sk336' @ X2 ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl100,zip_derived_cl8258]) ).
thf(zip_derived_cl272,plain,
( ( !!
@ ^ [Y0: a] :
( ( cK
@ ( '#sk244'
@ ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ Y0 )
=> ( '#sk244'
@ ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) )
| '#form811' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl271]) ).
thf(zip_derived_cl274,plain,
! [X2: a] :
( ( ( cK
@ ( '#sk244'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
@ X2 )
=> ( '#sk244'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ X2 ) )
| '#form811' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl272]) ).
thf(zip_derived_cl275,plain,
! [X2: a] :
( ~ ( cK
@ ( '#sk244'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
@ X2 )
| ( '#sk244'
@ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ X2 )
| '#form811' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl274]) ).
thf(zip_derived_cl8258_009,plain,
! [X1: a] :
( ( '#l_lift30859' @ X1 )
= ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl8258_010,plain,
! [X1: a] :
( ( '#l_lift30859' @ X1 )
= ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl8272,plain,
! [X2: a] :
( ~ ( cK @ ( '#sk244' @ ( cK @ '#l_lift30859' ) ) @ X2 )
| ( '#sk244' @ ( cK @ '#l_lift30859' ) @ X2 )
| '#form811' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl275,zip_derived_cl8258,zip_derived_cl8258]) ).
thf(zip_derived_cl8258_011,plain,
! [X1: a] :
( ( '#l_lift30859' @ X1 )
= ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3_012,plain,
! [X2: a > $o] :
( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( X2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y1: a] :
( ( cK @ X2 @ Y1 )
=> ( cK @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl5,plain,
! [X2: a > $o,X4: a > $o] :
( ( !!
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X4 @ Y0 ) ) )
=> ( !!
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( cK @ X4 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl8,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X4 @ Y0 ) ) )
| ( !!
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( cK @ X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl10,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( ( X2 @ ( '#sk12' @ X2 @ X4 ) )
=> ( X4 @ ( '#sk12' @ X2 @ X4 ) ) )
| ( !!
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( cK @ X4 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl12,plain,
! [X2: a > $o,X4: a > $o] :
( ( X2 @ ( '#sk12' @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( cK @ X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl15,plain,
! [X2: a > $o,X4: a > $o,X6: a] :
( ( ( cK @ X2 @ X6 )
=> ( cK @ X4 @ X6 ) )
| ( X2 @ ( '#sk12' @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl19,plain,
! [X2: a > $o,X4: a > $o,X6: a] :
( ~ ( cK @ X2 @ X6 )
| ( cK @ X4 @ X6 )
| ( X2 @ ( '#sk12' @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl7_013,plain,
~ ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl8258_014,plain,
! [X1: a] :
( ( '#l_lift30859' @ X1 )
= ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl8259,plain,
~ ( cK @ '#l_lift30859' @ '#sk1' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl7,zip_derived_cl8258]) ).
thf(zip_derived_cl13,plain,
! [X2: a > $o,X4: a > $o] :
( ~ ( X4 @ ( '#sk12' @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( cK @ X4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl16,plain,
! [X2: a > $o,X4: a > $o,X6: a] :
( ( ( cK @ X2 @ X6 )
=> ( cK @ X4 @ X6 ) )
| ~ ( X4 @ ( '#sk12' @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl20,plain,
! [X2: a > $o,X4: a > $o,X6: a] :
( ~ ( cK @ X2 @ X6 )
| ( cK @ X4 @ X6 )
| ~ ( X4 @ ( '#sk12' @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl9_015,plain,
! [X2: a > $o] :
( ( !!
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( X2 @ Y0 ) ) )
=> ( X2 @ '#sk1' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl11,plain,
! [X2: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( X2 @ Y0 ) ) )
| ( X2 @ '#sk1' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl14,plain,
! [X2: a > $o] :
( ~ ( ( cK @ X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) )
=> ( X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) ) )
| ( X2 @ '#sk1' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl17,plain,
! [X2: a > $o] :
( ( cK @ X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) )
| ( X2 @ '#sk1' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl18,plain,
! [X2: a > $o] :
( ~ ( X2 @ ( '#sk12' @ ( cK @ X2 ) @ X2 ) )
| ( X2 @ '#sk1' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl5_016,plain,
! [X2: a > $o,X4: a > $o] :
( ( !!
@ ^ [Y0: a] :
( ( X2 @ Y0 )
=> ( X4 @ Y0 ) ) )
=> ( !!
@ ^ [Y0: a] :
( ( cK @ X2 @ Y0 )
=> ( cK @ X4 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl22,plain,
! [X0: a > $o] :
( ( !!
@ ^ [Y0: a] :
( ( X0 @ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: a] :
( ( cK @ X0 @ Y0 )
=> ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl58,plain,
! [X0: a > $o] :
( ~ ( !!
@ ^ [Y0: a] :
( ( X0 @ Y0 )
=> ( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: a] :
( ( cK @ X0 @ Y0 )
=> ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl59,plain,
! [X0: a > $o] :
( ~ ( ( X0 @ ( '#sk236' @ X0 ) )
=> ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ ( '#sk236' @ X0 ) ) ) ) )
| ( !!
@ ^ [Y0: a] :
( ( cK @ X0 @ Y0 )
=> ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl60,plain,
! [X0: a > $o] :
( ( X0 @ ( '#sk236' @ X0 ) )
| ( !!
@ ^ [Y0: a] :
( ( cK @ X0 @ Y0 )
=> ( cK
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a > $o] :
( ( !!
@ ^ [Y3: a] :
( ( cK @ Y2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl62,plain,
! [X0: a > $o,X2: a] :
( ( ( cK @ X0 @ X2 )
=> ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X2 ) )
| ( X0 @ ( '#sk236' @ X0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl64,plain,
! [X0: a > $o,X2: a] :
( ~ ( cK @ X0 @ X2 )
| ( cK
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a > $o] :
( ( !!
@ ^ [Y2: a] :
( ( cK @ Y1 @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( Y1 @ Y0 ) ) )
@ X2 )
| ( X0 @ ( '#sk236' @ X0 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl8258_017,plain,
! [X1: a] :
( ( '#l_lift30859' @ X1 )
= ( !!
@ ^ [Y0: a > $o] :
( ( !!
@ ^ [Y1: a] :
( ( cK @ Y0 @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl8260,plain,
! [X0: a > $o,X2: a] :
( ~ ( cK @ X0 @ X2 )
| ( cK @ '#l_lift30859' @ X2 )
| ( X0 @ ( '#sk236' @ X0 ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl64,zip_derived_cl8258]) ).
thf(zip_derived_cl8282,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl342,zip_derived_cl8271,zip_derived_cl8273,zip_derived_cl8263,zip_derived_cl8272,zip_derived_cl8258,zip_derived_cl19,zip_derived_cl8259,zip_derived_cl20,zip_derived_cl17,zip_derived_cl18,zip_derived_cl8260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV310^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.qWfSiDq9kE true
% 0.13/0.35 % Computer : n026.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 04:23:32 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/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
% 0.21/0.65 % Total configuration time : 828
% 0.21/0.65 % Estimated wc time : 1656
% 0.21/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 51.58/7.28 % Solved by lams/20_acsne_simpl.sh.
% 51.58/7.28 % done 288 iterations in 6.414s
% 51.58/7.28 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 51.58/7.28 % SZS output start Refutation
% See solution above
% 51.58/7.28
% 51.58/7.28
% 51.58/7.28 % Terminating...
% 52.20/7.40 % Runner terminated.
% 52.20/7.40 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------