TSTP Solution File: SEV254^5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV254^5 : 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.B6gKofhvN5 true
% Computer : n031.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 20:00:12 EDT 2023
% Result : Theorem 65.44s 9.08s
% Output : Refutation 65.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 13
% Syntax : Number of formulae : 151 ( 13 unt; 8 typ; 0 def)
% Number of atoms : 1161 ( 3 equ; 0 cnn)
% Maximal formula atoms : 37 ( 8 avg)
% Number of connectives : 3323 ( 162 ~; 161 |; 217 &;1993 @)
% ( 6 <=>; 326 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 247 ( 247 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 6 con; 0-2 aty)
% ( 271 !!; 187 ??; 0 @@+; 0 @@-)
% Number of variables : 716 ( 615 ^; 85 !; 16 ?; 716 :)
% Comments :
%------------------------------------------------------------------------------
thf('#sk1_type',type,
'#sk1': ( $i > $o ) > $i > $o ).
thf('#sk29_type',type,
'#sk29': ( $i > $o ) > $i ).
thf('#sk8_type',type,
'#sk8': ( $i > $o ) > $i ).
thf('#sk2_type',type,
'#sk2': $i ).
thf('#form143_type',type,
'#form143': $o ).
thf('#sk9_type',type,
'#sk9': $i > $o ).
thf('#sk144_type',type,
'#sk144': $i > $o ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(cTHM2C_pme,conjecture,
! [K: ( $i > $o ) > $i > $o] :
( ( ( ! [Xx: $i] :
( ? [S: $i > $o] :
( ! [Xx0: $i] :
( ( S @ Xx0 )
=> ( K @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) )
=> ! [Xx: $i] :
( ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
=> ( K
@ ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
@ Xx ) ) )
& ! [Xx: $i > $o] :
( ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
=> ! [Xx0: $i] :
( ( K @ Xx @ Xx0 )
=> ( K
@ ^ [Xx1: $i] :
? [S: $i > $o] :
( ! [Xx2: $i] :
( ( S @ Xx2 )
=> ( K @ S @ Xx2 ) )
& ( S @ Xx1 ) )
@ Xx0 ) ) ) )
=> ! [Xx: $i] :
( ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
<=> ? [S: $i > $o] :
( ! [Xx0: $i] :
( ( S @ Xx0 )
=> ( K @ S @ Xx0 ) )
& ( S @ Xx ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [K: ( $i > $o ) > $i > $o] :
( ( ( ! [Xx: $i] :
( ? [S: $i > $o] :
( ! [Xx0: $i] :
( ( S @ Xx0 )
=> ( K @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) )
=> ! [Xx: $i] :
( ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
=> ( K
@ ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
@ Xx ) ) )
& ! [Xx: $i > $o] :
( ! [Xx0: $i] :
( ( Xx @ Xx0 )
=> ? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) ) )
=> ! [Xx0: $i] :
( ( K @ Xx @ Xx0 )
=> ( K
@ ^ [Xx1: $i] :
? [S: $i > $o] :
( ! [Xx2: $i] :
( ( S @ Xx2 )
=> ( K @ S @ Xx2 ) )
& ( S @ Xx1 ) )
@ Xx0 ) ) ) )
=> ! [Xx: $i] :
( ( K
@ ^ [Xx0: $i] :
? [S: $i > $o] :
( ! [Xx1: $i] :
( ( S @ Xx1 )
=> ( K @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx )
<=> ? [S: $i > $o] :
( ! [Xx0: $i] :
( ( S @ Xx0 )
=> ( K @ S @ Xx0 ) )
& ( S @ Xx ) ) ) ),
inference('cnf.neg',[status(esa)],[cTHM2C_pme]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: ( $i > $o ) > $i > $o] :
( ( ( ( !!
@ ^ [Y1: $i] :
( ( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
=> ( Y0
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( Y0
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 )
=> ( Y0
@ ( Y0
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) ) )
@ Y1 ) ) ) )
& ( !!
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) ) ) )
=> ( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0
@ ^ [Y3: $i] :
( ??
@ ^ [Y4: $i > $o] :
( ( !!
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
=> ( Y0 @ Y4 @ Y5 ) ) )
& ( Y4 @ Y3 ) ) )
@ Y2 ) ) ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( Y0
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( Y0 @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 )
<=> ( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y0 @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( ( ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) )
& ( !!
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1'
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( '#sk1' @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
<=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
<=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
~ ( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
<=> ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl9,plain,
( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
!= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl43,plain,
( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
| ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl43_001,plain,
( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
| ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl119,plain,
( ~ '#form143'
| ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123,plain,
( '#form143'
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl43,zip_derived_cl119]) ).
thf(zip_derived_cl9_002,plain,
( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
!= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl133,plain,
( ~ ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) )
| '#form143' ),
inference('sup-',[status(thm)],[zip_derived_cl123,zip_derived_cl9]) ).
thf(zip_derived_cl144,plain,
! [X2: $i > $o] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( '#sk1' @ X2 @ Y0 ) ) )
& ( X2 @ '#sk2' ) )
| '#form143' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl133]) ).
thf(zip_derived_cl146,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) )
& ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ) )
| '#form143' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl144]) ).
thf(zip_derived_cl2368,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) )
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
| '#form143' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl146]) ).
thf(zip_derived_cl123_003,plain,
( '#form143'
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl43,zip_derived_cl119]) ).
thf(zip_derived_cl2369,plain,
( '#form143'
| ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl2368,zip_derived_cl123]) ).
thf(zip_derived_cl2370,plain,
( ~ ( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) )
| '#form143' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2369]) ).
thf(zip_derived_cl2371,plain,
( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| '#form143' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2370]) ).
thf(zip_derived_cl119_004,plain,
( ~ '#form143'
| ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl122,plain,
( ( ( !!
@ ^ [Y0: $i] :
( ( '#sk144' @ Y0 )
=> ( '#sk1' @ '#sk144' @ Y0 ) ) )
& ( '#sk144' @ '#sk2' ) )
| ~ '#form143' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl119]) ).
thf(zip_derived_cl124,plain,
( ( !!
@ ^ [Y0: $i] :
( ( '#sk144' @ Y0 )
=> ( '#sk1' @ '#sk144' @ Y0 ) ) )
| ~ '#form143' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl122]) ).
thf(zip_derived_cl126,plain,
! [X2: $i] :
( ( ( '#sk144' @ X2 )
=> ( '#sk1' @ '#sk144' @ X2 ) )
| ~ '#form143' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl124]) ).
thf(zip_derived_cl127,plain,
! [X2: $i] :
( ~ ( '#sk144' @ X2 )
| ( '#sk1' @ '#sk144' @ X2 )
| ~ '#form143' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl126]) ).
thf(zip_derived_cl127_005,plain,
! [X2: $i] :
( ~ ( '#sk144' @ X2 )
| ( '#sk1' @ '#sk144' @ X2 )
| ~ '#form143' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl126]) ).
thf(zip_derived_cl2,plain,
( ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) )
& ( !!
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1'
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( '#sk1' @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1'
@ ^ [Y2: $i] :
( ??
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y3 @ Y4 )
=> ( '#sk1' @ Y3 @ Y4 ) ) )
& ( Y3 @ Y2 ) ) )
@ Y1 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl8,plain,
! [X2: $i > $o] :
( ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl121,plain,
( ( !!
@ ^ [Y0: $i] :
( ( '#sk144' @ Y0 )
=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk144' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl447,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk144' @ Y0 )
=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk144' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl448,plain,
( ~ ( ( '#sk144' @ ( '#sk8' @ '#sk144' ) )
=> ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ ( '#sk8' @ '#sk144' ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk144' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl447]) ).
thf(zip_derived_cl450,plain,
( ~ ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ ( '#sk8' @ '#sk144' ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk144' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl448]) ).
thf(zip_derived_cl452,plain,
! [X2: $i > $o] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( '#sk1' @ X2 @ Y0 ) ) )
& ( X2 @ ( '#sk8' @ '#sk144' ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk144' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl450]) ).
thf(zip_derived_cl453,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( '#sk144' @ Y0 )
=> ( '#sk1' @ '#sk144' @ Y0 ) ) )
& ( '#sk144' @ ( '#sk8' @ '#sk144' ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk144' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl452]) ).
thf(zip_derived_cl1757,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk144' @ Y0 )
=> ( '#sk1' @ '#sk144' @ Y0 ) ) )
| ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk144' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl453]) ).
thf(zip_derived_cl1758,plain,
( ~ ( ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
=> ( '#sk1' @ '#sk144' @ ( '#sk29' @ '#sk144' ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk144' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
| ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1757]) ).
thf(zip_derived_cl1760,plain,
( ~ ( '#sk1' @ '#sk144' @ ( '#sk29' @ '#sk144' ) )
| ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk144' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1758]) ).
thf(zip_derived_cl1762,plain,
! [X2: $i] :
( ( ( '#sk1' @ '#sk144' @ X2 )
=> ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 ) )
| ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) )
| ~ ( '#sk1' @ '#sk144' @ ( '#sk29' @ '#sk144' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1760]) ).
thf(zip_derived_cl1764,plain,
! [X2: $i] :
( ~ ( '#sk1' @ '#sk144' @ X2 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ~ ( '#sk1' @ '#sk144' @ ( '#sk29' @ '#sk144' ) )
| ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1762]) ).
thf(zip_derived_cl8_006,plain,
! [X2: $i > $o] :
( ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl11,plain,
! [X2: $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl14,plain,
! [X2: $i > $o] :
( ~ ( ( X2 @ ( '#sk8' @ X2 ) )
=> ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ ( '#sk8' @ X2 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl18,plain,
! [X2: $i > $o] :
( ( X2 @ ( '#sk8' @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl23,plain,
! [X2: $i > $o,X4: $i] :
( ( ( '#sk1' @ X2 @ X4 )
=> ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X4 ) )
| ( X2 @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl28,plain,
! [X2: $i > $o,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X4 )
| ( X2 @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl1766,plain,
! [X2: $i] :
( ~ ( '#sk1' @ '#sk144' @ ( '#sk29' @ '#sk144' ) )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ~ ( '#sk1' @ '#sk144' @ X2 ) ),
inference(clc,[status(thm)],[zip_derived_cl1764,zip_derived_cl28]) ).
thf(zip_derived_cl9_007,plain,
( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
!= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl44,plain,
( ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
| ~ ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl44_008,plain,
( ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' )
| ~ ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl476,plain,
( '#form143'
| ~ ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl119_009,plain,
( ~ '#form143'
| ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl482,plain,
( ~ '#form143'
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl44,zip_derived_cl476,zip_derived_cl119]) ).
thf(zip_derived_cl2411,plain,
( ~ ( '#sk1' @ '#sk144' @ '#sk2' )
| ~ ( '#sk1' @ '#sk144' @ ( '#sk29' @ '#sk144' ) )
| ~ '#form143' ),
inference('sup-',[status(thm)],[zip_derived_cl1766,zip_derived_cl482]) ).
thf(zip_derived_cl2429,plain,
( ~ '#form143'
| ~ ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
| ~ '#form143'
| ~ ( '#sk1' @ '#sk144' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl127,zip_derived_cl2411]) ).
thf(zip_derived_cl2430,plain,
( ~ ( '#sk1' @ '#sk144' @ '#sk2' )
| ~ ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
| ~ '#form143' ),
inference(simplify,[status(thm)],[zip_derived_cl2429]) ).
thf(zip_derived_cl127_010,plain,
! [X2: $i] :
( ~ ( '#sk144' @ X2 )
| ( '#sk1' @ '#sk144' @ X2 )
| ~ '#form143' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl126]) ).
thf(zip_derived_cl1759,plain,
( ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
| ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk144' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1758]) ).
thf(zip_derived_cl1761,plain,
! [X2: $i] :
( ( ( '#sk1' @ '#sk144' @ X2 )
=> ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 ) )
| ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) )
| ( '#sk144' @ ( '#sk29' @ '#sk144' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1759]) ).
thf(zip_derived_cl1763,plain,
! [X2: $i] :
( ~ ( '#sk1' @ '#sk144' @ X2 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
| ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1761]) ).
thf(zip_derived_cl28_011,plain,
! [X2: $i > $o,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X4 )
| ( X2 @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl1765,plain,
! [X2: $i] :
( ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ~ ( '#sk1' @ '#sk144' @ X2 ) ),
inference(clc,[status(thm)],[zip_derived_cl1763,zip_derived_cl28]) ).
thf(zip_derived_cl482_012,plain,
( ~ '#form143'
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl44,zip_derived_cl476,zip_derived_cl119]) ).
thf(zip_derived_cl1767,plain,
( ~ ( '#sk1' @ '#sk144' @ '#sk2' )
| ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
| ~ '#form143' ),
inference('sup-',[status(thm)],[zip_derived_cl1765,zip_derived_cl482]) ).
thf(zip_derived_cl1786,plain,
( ~ '#form143'
| ~ ( '#sk144' @ '#sk2' )
| ~ '#form143'
| ( '#sk144' @ ( '#sk29' @ '#sk144' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl127,zip_derived_cl1767]) ).
thf(zip_derived_cl1790,plain,
( ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
| ~ ( '#sk144' @ '#sk2' )
| ~ '#form143' ),
inference(simplify,[status(thm)],[zip_derived_cl1786]) ).
thf(zip_derived_cl125,plain,
( ( '#sk144' @ '#sk2' )
| ~ '#form143' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl122]) ).
thf(zip_derived_cl1814,plain,
( ~ '#form143'
| ( '#sk144' @ ( '#sk29' @ '#sk144' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1790,zip_derived_cl125]) ).
thf(zip_derived_cl2432,plain,
( ~ '#form143'
| ~ ( '#sk1' @ '#sk144' @ '#sk2' ) ),
inference(clc,[status(thm)],[zip_derived_cl2430,zip_derived_cl1814]) ).
thf(zip_derived_cl2437,plain,
( ~ '#form143'
| ~ ( '#sk144' @ '#sk2' )
| ~ '#form143' ),
inference('sup-',[status(thm)],[zip_derived_cl127,zip_derived_cl2432]) ).
thf(zip_derived_cl2442,plain,
( ~ ( '#sk144' @ '#sk2' )
| ~ '#form143' ),
inference(simplify,[status(thm)],[zip_derived_cl2437]) ).
thf(zip_derived_cl125_013,plain,
( ( '#sk144' @ '#sk2' )
| ~ '#form143' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl122]) ).
thf(zip_derived_cl2452,plain,
~ '#form143',
inference(clc,[status(thm)],[zip_derived_cl2442,zip_derived_cl125]) ).
thf(zip_derived_cl2480,plain,
( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2371,zip_derived_cl2452]) ).
thf(zip_derived_cl4,plain,
( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl7,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl10,plain,
( ~ ( ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk3' ) ) )
=> ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl12,plain,
( ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk3' ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl16,plain,
( ( ( !!
@ ^ [Y0: $i] :
( ( '#sk9' @ Y0 )
=> ( '#sk1' @ '#sk9' @ Y0 ) ) )
& ( '#sk9' @ '#sk3' ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl20,plain,
( ( !!
@ ^ [Y0: $i] :
( ( '#sk9' @ Y0 )
=> ( '#sk1' @ '#sk9' @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl26,plain,
! [X2: $i] :
( ( ( '#sk9' @ X2 )
=> ( '#sk1' @ '#sk9' @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl30,plain,
! [X2: $i] :
( ~ ( '#sk9' @ X2 )
| ( '#sk1' @ '#sk9' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl33,plain,
! [X2: $i,X4: $i] :
( ( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X4 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X4 ) )
| ( '#sk1' @ '#sk9' @ X2 )
| ~ ( '#sk9' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl36,plain,
! [X2: $i,X4: $i] :
( ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X4 )
| ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X4 )
| ~ ( '#sk9' @ X2 )
| ( '#sk1' @ '#sk9' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl2663,plain,
! [X0: $i] :
( ( '#sk1' @ '#sk9' @ X0 )
| ~ ( '#sk9' @ X0 )
| ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2480,zip_derived_cl36]) ).
thf(zip_derived_cl2372,plain,
( ~ ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| '#form143' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2370]) ).
thf(zip_derived_cl2452_014,plain,
~ '#form143',
inference(clc,[status(thm)],[zip_derived_cl2442,zip_derived_cl125]) ).
thf(zip_derived_cl3116,plain,
~ ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2372,zip_derived_cl2452]) ).
thf(zip_derived_cl6411,plain,
! [X0: $i] :
( ~ ( '#sk9' @ X0 )
| ( '#sk1' @ '#sk9' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl2663,zip_derived_cl3116]) ).
thf(zip_derived_cl6411_015,plain,
! [X0: $i] :
( ~ ( '#sk9' @ X0 )
| ( '#sk1' @ '#sk9' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl2663,zip_derived_cl3116]) ).
thf(zip_derived_cl13,plain,
( ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl17,plain,
! [X2: $i] :
( ( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X2 ) )
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl22,plain,
! [X2: $i] :
( ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X2 )
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl144_016,plain,
! [X2: $i > $o] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( '#sk1' @ X2 @ Y0 ) ) )
& ( X2 @ '#sk2' ) )
| '#form143' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl133]) ).
thf(zip_derived_cl149,plain,
! [X2: $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( '#sk1' @ X2 @ Y0 ) ) )
| ~ ( X2 @ '#sk2' )
| '#form143' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl144]) ).
thf(zip_derived_cl150,plain,
! [X2: $i > $o] :
( ~ ( ( X2 @ ( '#sk29' @ X2 ) )
=> ( '#sk1' @ X2 @ ( '#sk29' @ X2 ) ) )
| '#form143'
| ~ ( X2 @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl149]) ).
thf(zip_derived_cl152,plain,
! [X2: $i > $o] :
( ~ ( '#sk1' @ X2 @ ( '#sk29' @ X2 ) )
| ~ ( X2 @ '#sk2' )
| '#form143' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl150]) ).
thf(zip_derived_cl2452_017,plain,
~ '#form143',
inference(clc,[status(thm)],[zip_derived_cl2442,zip_derived_cl125]) ).
thf(zip_derived_cl2455,plain,
! [X2: $i > $o] :
( ~ ( '#sk1' @ X2 @ ( '#sk29' @ X2 ) )
| ~ ( X2 @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl152,zip_derived_cl2452]) ).
thf(zip_derived_cl2682,plain,
( ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' )
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl2455]) ).
thf(zip_derived_cl2480_018,plain,
( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2371,zip_derived_cl2452]) ).
thf(zip_derived_cl123_019,plain,
( '#form143'
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl43,zip_derived_cl119]) ).
thf(zip_derived_cl2452_020,plain,
~ '#form143',
inference(clc,[status(thm)],[zip_derived_cl2442,zip_derived_cl125]) ).
thf(zip_derived_cl2453,plain,
( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ),
inference(demod,[status(thm)],[zip_derived_cl123,zip_derived_cl2452]) ).
thf(zip_derived_cl2689,plain,
~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' ),
inference(demod,[status(thm)],[zip_derived_cl2682,zip_derived_cl2480,zip_derived_cl2453]) ).
thf(zip_derived_cl8_021,plain,
! [X2: $i > $o] :
( ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl15,plain,
( ( !!
@ ^ [Y0: $i] :
( ( '#sk9' @ Y0 )
=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl264,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk9' @ Y0 )
=> ( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl265,plain,
( ~ ( ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
=> ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ ( '#sk8' @ '#sk9' ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl264]) ).
thf(zip_derived_cl267,plain,
( ~ ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ ( '#sk8' @ '#sk9' ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl265]) ).
thf(zip_derived_cl269,plain,
! [X2: $i > $o] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( '#sk1' @ X2 @ Y0 ) ) )
& ( X2 @ ( '#sk8' @ '#sk9' ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl267]) ).
thf(zip_derived_cl273,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( '#sk9' @ Y0 )
=> ( '#sk1' @ '#sk9' @ Y0 ) ) )
& ( '#sk9' @ ( '#sk8' @ '#sk9' ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl269]) ).
thf(zip_derived_cl1669,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk9' @ Y0 )
=> ( '#sk1' @ '#sk9' @ Y0 ) ) )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl273]) ).
thf(zip_derived_cl1670,plain,
( ~ ( ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
=> ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1669]) ).
thf(zip_derived_cl1672,plain,
( ~ ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1670]) ).
thf(zip_derived_cl1674,plain,
! [X2: $i] :
( ( ( '#sk1' @ '#sk9' @ X2 )
=> ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 ) )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
| ~ ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1672]) ).
thf(zip_derived_cl1676,plain,
! [X2: $i] :
( ~ ( '#sk1' @ '#sk9' @ X2 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ~ ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1674]) ).
thf(zip_derived_cl28_022,plain,
! [X2: $i > $o,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X4 )
| ( X2 @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl1678,plain,
! [X2: $i] :
( ~ ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ~ ( '#sk1' @ '#sk9' @ X2 ) ),
inference(clc,[status(thm)],[zip_derived_cl1676,zip_derived_cl28]) ).
thf(zip_derived_cl2722,plain,
( ~ ( '#sk1' @ '#sk9' @ '#sk3' )
| ~ ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2689,zip_derived_cl1678]) ).
thf(zip_derived_cl6412,plain,
( ~ ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ~ ( '#sk1' @ '#sk9' @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl6411,zip_derived_cl2722]) ).
thf(zip_derived_cl2689_023,plain,
~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk3' ),
inference(demod,[status(thm)],[zip_derived_cl2682,zip_derived_cl2480,zip_derived_cl2453]) ).
thf(zip_derived_cl1671,plain,
( ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ '#sk9' @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1670]) ).
thf(zip_derived_cl1673,plain,
! [X2: $i] :
( ( ( '#sk1' @ '#sk9' @ X2 )
=> ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 ) )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
| ( '#sk9' @ ( '#sk29' @ '#sk9' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1671]) ).
thf(zip_derived_cl1675,plain,
! [X2: $i] :
( ~ ( '#sk1' @ '#sk9' @ X2 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1673]) ).
thf(zip_derived_cl28_024,plain,
! [X2: $i > $o,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X4 )
| ( X2 @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl1677,plain,
! [X2: $i] :
( ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ~ ( '#sk1' @ '#sk9' @ X2 ) ),
inference(clc,[status(thm)],[zip_derived_cl1675,zip_derived_cl28]) ).
thf(zip_derived_cl2723,plain,
( ~ ( '#sk1' @ '#sk9' @ '#sk3' )
| ( '#sk9' @ ( '#sk29' @ '#sk9' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2689,zip_derived_cl1677]) ).
thf(zip_derived_cl6411_025,plain,
! [X0: $i] :
( ~ ( '#sk9' @ X0 )
| ( '#sk1' @ '#sk9' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl2663,zip_derived_cl3116]) ).
thf(zip_derived_cl6436,plain,
( ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ~ ( '#sk9' @ '#sk3' ) ),
inference('sup+',[status(thm)],[zip_derived_cl2723,zip_derived_cl6411]) ).
thf(zip_derived_cl21,plain,
( ( '#sk9' @ '#sk3' )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) ) )
@ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl27,plain,
! [X2: $i] :
( ( ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
=> ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X2 ) )
| ( '#sk9' @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl31,plain,
! [X2: $i] :
( ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X2 )
| ( '#sk1'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) )
@ X2 )
| ( '#sk9' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl2455_026,plain,
! [X2: $i > $o] :
( ~ ( '#sk1' @ X2 @ ( '#sk29' @ X2 ) )
| ~ ( X2 @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl152,zip_derived_cl2452]) ).
thf(zip_derived_cl2681,plain,
( ( '#sk9' @ '#sk3' )
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) )
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl2455]) ).
thf(zip_derived_cl2480_027,plain,
( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ ( '#sk29'
@ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2371,zip_derived_cl2452]) ).
thf(zip_derived_cl2453_028,plain,
( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ),
inference(demod,[status(thm)],[zip_derived_cl123,zip_derived_cl2452]) ).
thf(zip_derived_cl2688,plain,
'#sk9' @ '#sk3',
inference(demod,[status(thm)],[zip_derived_cl2681,zip_derived_cl2480,zip_derived_cl2453]) ).
thf(zip_derived_cl6442,plain,
'#sk9' @ ( '#sk29' @ '#sk9' ),
inference(demod,[status(thm)],[zip_derived_cl6436,zip_derived_cl2688]) ).
thf(zip_derived_cl6548,plain,
~ ( '#sk1' @ '#sk9' @ '#sk3' ),
inference(demod,[status(thm)],[zip_derived_cl6412,zip_derived_cl6442]) ).
thf(zip_derived_cl6558,plain,
~ ( '#sk9' @ '#sk3' ),
inference('sup-',[status(thm)],[zip_derived_cl6411,zip_derived_cl6548]) ).
thf(zip_derived_cl2688_029,plain,
'#sk9' @ '#sk3',
inference(demod,[status(thm)],[zip_derived_cl2681,zip_derived_cl2480,zip_derived_cl2453]) ).
thf(zip_derived_cl6565,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl6558,zip_derived_cl2688]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEV254^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.B6gKofhvN5 true
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 02:23:51 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.22/0.66 % Total configuration time : 828
% 0.22/0.66 % Estimated wc time : 1656
% 0.22/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.76 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.23/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.23/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.23/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.23/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.23/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 65.44/9.08 % Solved by lams/35_full_unif4.sh.
% 65.44/9.08 % done 847 iterations in 8.274s
% 65.44/9.08 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 65.44/9.08 % SZS output start Refutation
% See solution above
% 65.44/9.09
% 65.44/9.09
% 65.44/9.09 % Terminating...
% 66.47/9.21 % Runner terminated.
% 66.47/9.22 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------