%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV254^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.3YdpPn4oYg true
% Computer : n016.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 Oct 2 04:57:28 PM UTC 2025
% Result : Theorem 57.01s 7.76s
% Output : Refutation 57.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 102 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 867 ( 20 equ; 0 cnn)
% Maximal formula atoms : 37 ( 8 avg)
% Number of connectives : 2655 ( 100 ~; 115 |; 178 &;1613 @)
% ( 6 <=>; 271 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 221 ( 221 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 6 con; 0-2 aty)
% ( 221 !!; 151 ??; 0 @@+; 0 @@-)
% Number of variables : 613 ( 483 ^; 114 !; 16 ?; 613 :)
% Comments :
%------------------------------------------------------------------------------
thf('#sk1_type',type,
'#sk1': ( $i > $o ) > $i > $o ).
thf('#sk962_type',type,
'#sk962': $i > $o ).
thf('#form2740_type',type,
'#form2740': $o ).
thf('#sk29_type',type,
'#sk29': ( $i > $o ) > $i ).
thf('#sk8_type',type,
'#sk8': ( $i > $o ) > $i ).
thf('#l_lift4380_type',type,
'#l_lift4380': $i > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf('#sk9_type',type,
'#sk9': $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_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_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_cl51,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_cl52,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_cl51]) ).
thf(zip_derived_cl54,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_cl52]) ).
thf(zip_derived_cl56,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_cl54]) ).
thf(zip_derived_cl58,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_cl56]) ).
thf(zip_derived_cl71,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_cl58]) ).
thf(zip_derived_cl72,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_cl71]) ).
thf(zip_derived_cl73,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_cl72]) ).
thf(zip_derived_cl75,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_cl73]) ).
thf(zip_derived_cl77,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_cl75]) ).
thf(zip_derived_cl8_001,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_cl79,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_cl77,zip_derived_cl28]) ).
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_cl3031,plain,
! [X1: $i] :
( ( '#l_lift4380' @ X1 )
= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3039,plain,
! [X2: $i] :
( ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ( '#sk1' @ '#l_lift4380' @ X2 )
| ~ ( '#sk1' @ '#sk9' @ X2 ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl79,zip_derived_cl3031]) ).
thf(zip_derived_cl74,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_cl72]) ).
thf(zip_derived_cl76,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_cl74]) ).
thf(zip_derived_cl78,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_cl76]) ).
thf(zip_derived_cl28_002,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_cl80,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_cl78,zip_derived_cl28]) ).
thf(zip_derived_cl3031_003,plain,
! [X1: $i] :
( ( '#l_lift4380' @ X1 )
= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3040,plain,
! [X2: $i] :
( ~ ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) )
| ( '#sk1' @ '#l_lift4380' @ X2 )
| ~ ( '#sk1' @ '#sk9' @ X2 ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl80,zip_derived_cl3031]) ).
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_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_cl3031_004,plain,
! [X1: $i] :
( ( '#l_lift4380' @ X1 )
= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3031_005,plain,
! [X1: $i] :
( ( '#l_lift4380' @ X1 )
= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3031_006,plain,
! [X1: $i] :
( ( '#l_lift4380' @ X1 )
= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3033,plain,
! [X2: $i] :
( ~ ( '#sk1' @ '#l_lift4380' @ X2 )
| ( '#sk1' @ ( '#sk1' @ '#l_lift4380' ) @ X2 )
| ~ ( '#sk1' @ '#l_lift4380' @ '#sk3' ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl22,zip_derived_cl3031,zip_derived_cl3031,zip_derived_cl3031]) ).
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_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_cl3031_007,plain,
! [X1: $i] :
( ( '#l_lift4380' @ X1 )
= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3031_008,plain,
! [X1: $i] :
( ( '#l_lift4380' @ X1 )
= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3035,plain,
! [X2: $i] :
( ~ ( '#sk1' @ '#l_lift4380' @ X2 )
| ( '#sk1' @ ( '#sk1' @ '#l_lift4380' ) @ X2 )
| ( '#sk9' @ '#sk3' ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl31,zip_derived_cl3031,zip_derived_cl3031]) ).
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_cl3031_009,plain,
! [X1: $i] :
( ( '#l_lift4380' @ X1 )
= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3031_010,plain,
! [X1: $i] :
( ( '#l_lift4380' @ X1 )
= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3036,plain,
! [X2: $i,X4: $i] :
( ~ ( '#sk1' @ '#l_lift4380' @ X4 )
| ( '#sk1' @ ( '#sk1' @ '#l_lift4380' ) @ X4 )
| ~ ( '#sk9' @ X2 )
| ( '#sk1' @ '#sk9' @ X2 ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl36,zip_derived_cl3031,zip_derived_cl3031]) ).
thf(zip_derived_cl9_011,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_cl732,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_cl758,plain,
( ( ( !!
@ ^ [Y0: $i] :
( ( '#sk962' @ Y0 )
=> ( '#sk1' @ '#sk962' @ Y0 ) ) )
& ( '#sk962' @ '#sk2' ) )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl732]) ).
thf(zip_derived_cl760,plain,
( ( '#sk962' @ '#sk2' )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl758]) ).
thf(zip_derived_cl9_012,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_cl763,plain,
( ~ ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) )
| ( '#sk962' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl760,zip_derived_cl9]) ).
thf(zip_derived_cl1788,plain,
( '#form2740'
| ~ ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl1789,plain,
! [X2: $i > $o] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( '#sk1' @ X2 @ Y0 ) ) )
& ( X2 @ '#sk2' ) )
| '#form2740' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1788]) ).
thf(zip_derived_cl1795,plain,
! [X2: $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( '#sk1' @ X2 @ Y0 ) ) )
| ~ ( X2 @ '#sk2' )
| '#form2740' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1789]) ).
thf(zip_derived_cl1796,plain,
! [X2: $i > $o] :
( ~ ( ( X2 @ ( '#sk29' @ X2 ) )
=> ( '#sk1' @ X2 @ ( '#sk29' @ X2 ) ) )
| '#form2740'
| ~ ( X2 @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1795]) ).
thf(zip_derived_cl1798,plain,
! [X2: $i > $o] :
( ~ ( '#sk1' @ X2 @ ( '#sk29' @ X2 ) )
| ~ ( X2 @ '#sk2' )
| '#form2740' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1796]) ).
thf(zip_derived_cl19,plain,
! [X2: $i > $o] :
( ~ ( ??
@ ^ [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_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl24,plain,
! [X2: $i > $o,X4: $i > $o] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
=> ( '#sk1' @ X4 @ Y0 ) ) )
& ( X4 @ ( '#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_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl29,plain,
! [X2: $i > $o,X4: $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( X4 @ Y0 )
=> ( '#sk1' @ X4 @ Y0 ) ) )
| ~ ( X4 @ ( '#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_and,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl32,plain,
! [X2: $i > $o,X4: $i > $o] :
( ~ ( ( X4 @ ( '#sk29' @ X4 ) )
=> ( '#sk1' @ X4 @ ( '#sk29' @ X4 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk1'
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) )
& ( Y2 @ Y1 ) ) )
@ Y0 ) ) )
| ~ ( X4 @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl35,plain,
! [X2: $i > $o,X4: $i > $o] :
( ~ ( '#sk1' @ X4 @ ( '#sk29' @ X4 ) )
| ~ ( X4 @ ( '#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_cl32]) ).
thf(zip_derived_cl38,plain,
! [X2: $i > $o,X4: $i > $o,X6: $i] :
( ( ( '#sk1' @ X2 @ X6 )
=> ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X6 ) )
| ~ ( X4 @ ( '#sk8' @ X2 ) )
| ~ ( '#sk1' @ X4 @ ( '#sk29' @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl40,plain,
! [X2: $i > $o,X4: $i > $o,X6: $i] :
( ~ ( '#sk1' @ X2 @ X6 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X6 )
| ~ ( '#sk1' @ X4 @ ( '#sk29' @ X4 ) )
| ~ ( X4 @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl3031_013,plain,
! [X1: $i] :
( ( '#l_lift4380' @ X1 )
= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3038,plain,
! [X2: $i > $o,X4: $i > $o,X6: $i] :
( ~ ( '#sk1' @ X2 @ X6 )
| ( '#sk1' @ '#l_lift4380' @ X6 )
| ~ ( '#sk1' @ X4 @ ( '#sk29' @ X4 ) )
| ~ ( X4 @ ( '#sk8' @ X2 ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl40,zip_derived_cl3031]) ).
thf(zip_derived_cl1797,plain,
! [X2: $i > $o] :
( ( X2 @ ( '#sk29' @ X2 ) )
| ~ ( X2 @ '#sk2' )
| '#form2740' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1796]) ).
thf(zip_derived_cl34,plain,
! [X2: $i > $o,X4: $i > $o] :
( ( X4 @ ( '#sk29' @ X4 ) )
| ~ ( X4 @ ( '#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_cl32]) ).
thf(zip_derived_cl37,plain,
! [X2: $i > $o,X4: $i > $o,X6: $i] :
( ( ( '#sk1' @ X2 @ X6 )
=> ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X6 ) )
| ~ ( X4 @ ( '#sk8' @ X2 ) )
| ( X4 @ ( '#sk29' @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl39,plain,
! [X2: $i > $o,X4: $i > $o,X6: $i] :
( ~ ( '#sk1' @ X2 @ X6 )
| ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ X6 )
| ( X4 @ ( '#sk29' @ X4 ) )
| ~ ( X4 @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl3031_014,plain,
! [X1: $i] :
( ( '#l_lift4380' @ X1 )
= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3037,plain,
! [X2: $i > $o,X4: $i > $o,X6: $i] :
( ~ ( '#sk1' @ X2 @ X6 )
| ( '#sk1' @ '#l_lift4380' @ X6 )
| ( X4 @ ( '#sk29' @ X4 ) )
| ~ ( X4 @ ( '#sk8' @ X2 ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl39,zip_derived_cl3031]) ).
thf(zip_derived_cl9_015,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_cl733,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_cl1788_016,plain,
( '#form2740'
| ~ ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl2238,plain,
( ~ '#form2740'
| ~ ( '#sk1'
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) )
& ( Y1 @ Y0 ) ) )
@ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl733,zip_derived_cl1788]) ).
thf(zip_derived_cl3031_017,plain,
! [X1: $i] :
( ( '#l_lift4380' @ X1 )
= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3056,plain,
( ~ '#form2740'
| ~ ( '#sk1' @ '#l_lift4380' @ '#sk2' ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl2238,zip_derived_cl3031]) ).
thf(zip_derived_cl28_018,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_cl9_019,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_cl901,plain,
! [X0: $i > $o] :
( ~ ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) )
| ( X0 @ ( '#sk8' @ X0 ) )
| ~ ( '#sk1' @ X0 @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl9]) ).
thf(zip_derived_cl9_020,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_cl3031_021,plain,
! [X1: $i] :
( ( '#l_lift4380' @ X1 )
= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ X1 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl3032,plain,
( ( '#sk1' @ '#l_lift4380' @ '#sk2' )
!= ( ??
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) )
& ( Y0 @ '#sk2' ) ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl9,zip_derived_cl3031]) ).
thf(zip_derived_cl3068,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl3039,zip_derived_cl3040,zip_derived_cl3033,zip_derived_cl3035,zip_derived_cl3036,zip_derived_cl1798,zip_derived_cl3038,zip_derived_cl1797,zip_derived_cl3037,zip_derived_cl3056,zip_derived_cl901,zip_derived_cl3032]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SEV254^5 : TPTP v9.2.0. Released v4.0.0.
% 0.05/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.3YdpPn4oYg true
% 0.10/0.31 % Computer : n016.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Oct 1 15:40:53 EDT 2025
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % Running portfolio for 300 s
% 0.10/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.32 % Number of cores: 8
% 0.10/0.32 % Python version: Python 3.6.8
% 0.10/0.32 % Running in HO mode
% 0.46/0.61 % Total configuration time : 828
% 0.46/0.61 % Estimated wc time : 1656
% 0.46/0.61 % Estimated cpu time (8 cpus) : 207.0
% 0.49/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 57.01/7.76 % Solved by lams/20_acsne_simpl.sh.
% 57.01/7.76 % done 387 iterations in 6.990s
% 57.01/7.76 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 57.01/7.76 % SZS output start Refutation
% See solution above
% 57.01/7.77
% 57.01/7.77
% 57.01/7.77 % Terminating...
% 57.01/7.85 % Runner terminated.
% 57.01/7.86 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------