%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL872^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Prk4Dku1wE true
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:37:30 PM UTC 2026
% Result : Theorem 9.80s 1.95s
% Output : Refutation 9.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 23
% Syntax : Number of formulae : 140 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 799 ( 26 equ; 144 cnn)
% Maximal formula atoms : 25 ( 5 avg)
% Number of connectives : 2069 ( 316 ~; 291 |; 55 &;1223 @)
% ( 3 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 117 ( 117 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 23 usr; 11 con; 0-4 aty)
% ( 135 !!; 22 ??; 0 @@+; 0 @@-)
% Number of variables : 382 ( 215 ^; 162 !; 5 ?; 382 :)
% Comments :
%------------------------------------------------------------------------------
thf('#sk114_type',type,
'#sk114': $i ).
thf(mbox_type,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk116_type',type,
'#sk116': $i ).
thf('#sk117_type',type,
'#sk117': $i ).
thf('#sk16_type',type,
'#sk16': $i > $i > $i ).
thf(i_type,type,
i: $i > $i > $o ).
thf(confluence_type,type,
confluence: ( $i > $i > $o ) > ( $i > $i > $o ) > ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf('#sk12_type',type,
'#sk12': ( $i > $o ) > $i > $i ).
thf('#sk118_type',type,
'#sk118': $i ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf('#sk27_type',type,
'#sk27': ( $i > $o ) > $i > $i ).
thf('#form3_type',type,
'#form3': $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mdia_type,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk112_type',type,
'#sk112': $i ).
thf('#sk113_type',type,
'#sk113': $i ).
thf('#sk115_type',type,
'#sk115': $i > $o ).
thf(j_type,type,
j: $i > $i > $o ).
thf(k_type,type,
k: $i > $i > $o ).
thf(l_type,type,
l: $i > $i > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mforall_prop_type,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(confluence,axiom,
( confluence
= ( ^ [I: $i > $i > $o,J: $i > $i > $o,K: $i > $i > $o,L: $i > $i > $o] :
! [A: $i,B: $i,C: $i] :
( ( ( I @ A @ B )
& ( K @ A @ C ) )
=> ? [D: $i] :
( ( L @ C @ D )
& ( J @ B @ D ) ) ) ) ) ).
thf('0',plain,
( confluence
= ( ^ [I: $i > $i > $o,J: $i > $i > $o,K: $i > $i > $o,L: $i > $i > $o] :
! [A: $i,B: $i,C: $i] :
( ( ( I @ A @ B )
& ( K @ A @ C ) )
=> ? [D: $i] :
( ( L @ C @ D )
& ( J @ B @ D ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[confluence]) ).
thf('1',plain,
( confluence
= ( ^ [V_1: $i > $i > $o,V_2: $i > $i > $o,V_3: $i > $i > $o,V_4: $i > $i > $o] :
! [X4: $i,X6: $i,X8: $i] :
( ( ( V_1 @ X4 @ X6 )
& ( V_3 @ X4 @ X8 ) )
=> ? [X10: $i] :
( ( V_4 @ X8 @ X10 )
& ( V_2 @ X6 @ X10 ) ) ) ) ),
define([status(thm)]) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('2',plain,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('3',plain,
( mvalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
define([status(thm)]) ).
thf(mdia,axiom,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ) ).
thf(mbox,axiom,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( R @ W @ V ) ) ) ) ).
thf('4',plain,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( R @ W @ V ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox]) ).
thf('5',plain,
( mbox
= ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i] :
! [X4: $i] :
( ( V_2 @ X4 )
| ~ ( V_1 @ V_3 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(mnot,axiom,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ) ).
thf('6',plain,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('7',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('8',plain,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mdia,'5','7']) ).
thf('9',plain,
( mdia
= ( ^ [V_1: $i > $i > $o,V_2: $i > $o] : ( mnot @ ( mbox @ V_1 @ ( mnot @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf(mforall_prop,axiom,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
thf('10',plain,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mforall_prop]) ).
thf('11',plain,
( mforall_prop
= ( ^ [V_1: ( $i > $o ) > $i > $o,V_2: $i] :
! [X4: $i > $o] : ( V_1 @ X4 @ V_2 ) ) ),
define([status(thm)]) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
thf(mor,axiom,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ) ).
thf('12',plain,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('13',plain,
( mor
= ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
( ( V_1 @ V_3 )
| ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('14',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'13','7']) ).
thf('15',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
define([status(thm)]) ).
thf(conj,conjecture,
( ( mvalid
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mimplies @ ( mdia @ i @ ( mbox @ j @ P ) ) @ ( mbox @ k @ ( mdia @ l @ P ) ) ) ) )
<=> ( confluence @ i @ j @ k @ l ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i > $o] :
( ! [X12: $i] :
( ~ ( k @ X4 @ X12 )
| ~ ! [X14: $i] :
( ~ ( l @ X12 @ X14 )
| ~ ( X6 @ X14 ) ) )
| ! [X8: $i] :
( ~ ( i @ X4 @ X8 )
| ~ ! [X10: $i] :
( ~ ( j @ X8 @ X10 )
| ( X6 @ X10 ) ) ) )
<=> ! [X16: $i,X18: $i,X20: $i] :
( ( ( k @ X16 @ X20 )
& ( i @ X16 @ X18 ) )
=> ? [X22: $i] :
( ( j @ X18 @ X22 )
& ( l @ X20 @ X22 ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i > $o] :
( ! [X12: $i] :
( ~ ( k @ X4 @ X12 )
| ~ ! [X14: $i] :
( ~ ( l @ X12 @ X14 )
| ~ ( X6 @ X14 ) ) )
| ! [X8: $i] :
( ~ ( i @ X4 @ X8 )
| ~ ! [X10: $i] :
( ~ ( j @ X8 @ X10 )
| ( X6 @ X10 ) ) ) )
<=> ! [X16: $i,X18: $i,X20: $i] :
( ( ( k @ X16 @ X20 )
& ( i @ X16 @ X18 ) )
=> ? [X22: $i] :
( ( j @ X18 @ X22 )
& ( l @ X20 @ X22 ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( k @ Y0 @ Y2 ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( l @ Y2 @ Y3 ) )
| ( (~) @ ( Y1 @ Y3 ) ) ) ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( i @ Y0 @ Y2 ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( j @ Y2 @ Y3 ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
!= ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( k @ Y0 @ Y2 )
& ( i @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( j @ Y1 @ Y3 )
& ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl2,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( k @ Y0 @ Y2 ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( l @ Y2 @ Y3 ) )
| ( (~) @ ( Y1 @ Y3 ) ) ) ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( i @ Y0 @ Y2 ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( j @ Y2 @ Y3 ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( k @ Y0 @ Y2 )
& ( i @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( j @ Y1 @ Y3 )
& ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl45,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( k @ Y0 @ Y2 )
& ( i @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( j @ Y1 @ Y3 )
& ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl46,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( k @ '#sk112' @ Y1 )
& ( i @ '#sk112' @ Y0 ) )
=> ( ??
@ ^ [Y2: $i] :
( ( j @ Y0 @ Y2 )
& ( l @ Y1 @ Y2 ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl49,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( ( k @ '#sk112' @ Y0 )
& ( i @ '#sk112' @ '#sk114' ) )
=> ( ??
@ ^ [Y1: $i] :
( ( j @ '#sk114' @ Y1 )
& ( l @ Y0 @ Y1 ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl52,plain,
( ~ ( ( ( k @ '#sk112' @ '#sk116' )
& ( i @ '#sk112' @ '#sk114' ) )
=> ( ??
@ ^ [Y0: $i] :
( ( j @ '#sk114' @ Y0 )
& ( l @ '#sk116' @ Y0 ) ) ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl55,plain,
( ( ( k @ '#sk112' @ '#sk116' )
& ( i @ '#sk112' @ '#sk114' ) )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl59,plain,
( ( k @ '#sk112' @ '#sk116' )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl2_001,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( k @ Y0 @ Y2 ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( l @ Y2 @ Y3 ) )
| ( (~) @ ( Y1 @ Y3 ) ) ) ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( i @ Y0 @ Y2 ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( j @ Y2 @ Y3 ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( k @ Y0 @ Y2 )
& ( i @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( j @ Y1 @ Y3 )
& ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl45_002,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( k @ Y0 @ Y2 )
& ( i @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( j @ Y1 @ Y3 )
& ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl0_003,plain,
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( k @ Y0 @ Y2 ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( l @ Y2 @ Y3 ) )
| ( (~) @ ( Y1 @ Y3 ) ) ) ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( i @ Y0 @ Y2 ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( j @ Y2 @ Y3 ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
!= ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( k @ Y0 @ Y2 )
& ( i @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( j @ Y1 @ Y3 )
& ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( k @ Y0 @ Y2 ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( l @ Y2 @ Y3 ) )
| ( (~) @ ( Y1 @ Y3 ) ) ) ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( i @ Y0 @ Y2 ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( j @ Y2 @ Y3 ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( k @ Y0 @ Y2 )
& ( i @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( j @ Y1 @ Y3 )
& ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( k @ X2 @ Y1 ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( l @ Y1 @ Y2 ) )
| ( (~) @ ( Y0 @ Y2 ) ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( i @ X2 @ Y1 ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( j @ Y1 @ Y2 ) )
| ( Y0 @ Y2 ) ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( k @ Y0 @ Y2 )
& ( i @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( j @ Y1 @ Y3 )
& ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
! [X2: $i,X4: $i > $o] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( k @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( l @ Y0 @ Y1 ) )
| ( (~) @ ( X4 @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( i @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( j @ Y0 @ Y1 ) )
| ( X4 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( k @ Y0 @ Y2 )
& ( i @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( j @ Y1 @ Y3 )
& ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl7,plain,
( ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( k @ Y0 @ Y2 )
& ( i @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( j @ Y1 @ Y3 )
& ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl47,plain,
( ~ '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( k @ Y0 @ Y2 ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( l @ Y2 @ Y3 ) )
| ( (~) @ ( Y1 @ Y3 ) ) ) ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( i @ Y0 @ Y2 ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( j @ Y2 @ Y3 ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl2,zip_derived_cl45,zip_derived_cl7]) ).
thf(zip_derived_cl48,plain,
( ~ ( !!
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( k @ '#sk113' @ Y1 ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( l @ Y1 @ Y2 ) )
| ( (~) @ ( Y0 @ Y2 ) ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( i @ '#sk113' @ Y1 ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( j @ Y1 @ Y2 ) )
| ( Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl51,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( k @ '#sk113' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( l @ Y0 @ Y1 ) )
| ( (~) @ ( '#sk115' @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( i @ '#sk113' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( j @ Y0 @ Y1 ) )
| ( '#sk115' @ Y1 ) ) ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl54,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( i @ '#sk113' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( j @ Y0 @ Y1 ) )
| ( '#sk115' @ Y1 ) ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl58,plain,
( ~ ( ( (~) @ ( i @ '#sk113' @ '#sk118' ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( j @ '#sk118' @ Y0 ) )
| ( '#sk115' @ Y0 ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl65,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( j @ '#sk118' @ Y0 ) )
| ( '#sk115' @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl68,plain,
! [X2: $i] :
( ( (~) @ ( j @ '#sk118' @ X2 ) )
| ( '#sk115' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl70,plain,
! [X2: $i] :
( ~ ( j @ '#sk118' @ X2 )
| ( '#sk115' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl53,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( k @ '#sk113' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( l @ Y0 @ Y1 ) )
| ( (~) @ ( '#sk115' @ Y1 ) ) ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl57,plain,
( ~ ( ( (~) @ ( k @ '#sk113' @ '#sk117' ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( l @ '#sk117' @ Y0 ) )
| ( (~) @ ( '#sk115' @ Y0 ) ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl62,plain,
( ( k @ '#sk113' @ '#sk117' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl7_004,plain,
( ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( k @ Y0 @ Y2 )
& ( i @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( j @ Y1 @ Y3 )
& ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl8,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( k @ X2 @ Y1 )
& ( i @ X2 @ Y0 ) )
=> ( ??
@ ^ [Y2: $i] :
( ( j @ Y0 @ Y2 )
& ( l @ Y1 @ Y2 ) ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl11,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( ( k @ X2 @ Y0 )
& ( i @ X2 @ X4 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( j @ X4 @ Y1 )
& ( l @ Y0 @ Y1 ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl13,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( ( k @ X2 @ X6 )
& ( i @ X2 @ X4 ) )
=> ( ??
@ ^ [Y0: $i] :
( ( j @ X4 @ Y0 )
& ( l @ X6 @ Y0 ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl15,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( k @ X2 @ X6 )
& ( i @ X2 @ X4 ) )
| ( ??
@ ^ [Y0: $i] :
( ( j @ X4 @ Y0 )
& ( l @ X6 @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl17,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( k @ X2 @ X6 )
| ~ ( i @ X2 @ X4 )
| ~ '#form3'
| ( ??
@ ^ [Y0: $i] :
( ( j @ X4 @ Y0 )
& ( l @ X6 @ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl20,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( j @ X4 @ ( '#sk16' @ X4 @ X6 ) )
& ( l @ X6 @ ( '#sk16' @ X4 @ X6 ) ) )
| ~ '#form3'
| ~ ( i @ X2 @ X4 )
| ~ ( k @ X2 @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl23,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( j @ X4 @ ( '#sk16' @ X4 @ X6 ) )
| ~ ( k @ X2 @ X6 )
| ~ ( i @ X2 @ X4 )
| ~ '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl76,plain,
! [X0: $i] :
( ~ '#form3'
| ~ '#form3'
| ~ ( i @ '#sk113' @ X0 )
| ( j @ X0 @ ( '#sk16' @ X0 @ '#sk117' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl23]) ).
thf(zip_derived_cl80,plain,
! [X0: $i] :
( ( j @ X0 @ ( '#sk16' @ X0 @ '#sk117' ) )
| ~ ( i @ '#sk113' @ X0 )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl169,plain,
( ~ '#form3'
| ( '#sk115' @ ( '#sk16' @ '#sk118' @ '#sk117' ) )
| ~ '#form3'
| ~ ( i @ '#sk113' @ '#sk118' ) ),
inference('sup+',[status(thm)],[zip_derived_cl70,zip_derived_cl80]) ).
thf(zip_derived_cl172,plain,
( ~ ( i @ '#sk113' @ '#sk118' )
| ( '#sk115' @ ( '#sk16' @ '#sk118' @ '#sk117' ) )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl169]) ).
thf(zip_derived_cl64,plain,
( ( i @ '#sk113' @ '#sk118' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl176,plain,
( ~ '#form3'
| ( '#sk115' @ ( '#sk16' @ '#sk118' @ '#sk117' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl172,zip_derived_cl64]) ).
thf(zip_derived_cl62_005,plain,
( ( k @ '#sk113' @ '#sk117' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( l @ X6 @ ( '#sk16' @ X4 @ X6 ) )
| ~ ( k @ X2 @ X6 )
| ~ ( i @ X2 @ X4 )
| ~ '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl75,plain,
! [X0: $i] :
( ~ '#form3'
| ~ '#form3'
| ~ ( i @ '#sk113' @ X0 )
| ( l @ '#sk117' @ ( '#sk16' @ X0 @ '#sk117' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl24]) ).
thf(zip_derived_cl79,plain,
! [X0: $i] :
( ( l @ '#sk117' @ ( '#sk16' @ X0 @ '#sk117' ) )
| ~ ( i @ '#sk113' @ X0 )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl63,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( l @ '#sk117' @ Y0 ) )
| ( (~) @ ( '#sk115' @ Y0 ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl67,plain,
! [X2: $i] :
( ( (~) @ ( l @ '#sk117' @ X2 ) )
| ( (~) @ ( '#sk115' @ X2 ) )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl69,plain,
! [X2: $i] :
( ~ ( l @ '#sk117' @ X2 )
| ~ ( '#sk115' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl107,plain,
! [X0: $i] :
( ~ '#form3'
| ~ ( i @ '#sk113' @ X0 )
| ~ '#form3'
| ~ ( '#sk115' @ ( '#sk16' @ X0 @ '#sk117' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl79,zip_derived_cl69]) ).
thf(zip_derived_cl109,plain,
! [X0: $i] :
( ~ ( '#sk115' @ ( '#sk16' @ X0 @ '#sk117' ) )
| ~ ( i @ '#sk113' @ X0 )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl177,plain,
( ~ '#form3'
| ~ '#form3'
| ~ ( i @ '#sk113' @ '#sk118' ) ),
inference('sup-',[status(thm)],[zip_derived_cl176,zip_derived_cl109]) ).
thf(zip_derived_cl179,plain,
( ~ ( i @ '#sk113' @ '#sk118' )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl177]) ).
thf(zip_derived_cl64_006,plain,
( ( i @ '#sk113' @ '#sk118' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl181,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).
thf(zip_derived_cl186,plain,
k @ '#sk112' @ '#sk116',
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl181]) ).
thf(zip_derived_cl60,plain,
( ( i @ '#sk112' @ '#sk114' )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl4_007,plain,
! [X2: $i,X4: $i > $o] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( k @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( l @ Y0 @ Y1 ) )
| ( (~) @ ( X4 @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( i @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( j @ Y0 @ Y1 ) )
| ( X4 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( k @ Y0 @ Y2 )
& ( i @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( j @ Y1 @ Y3 )
& ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl7_008,plain,
( ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( k @ Y0 @ Y2 )
& ( i @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( j @ Y1 @ Y3 )
& ( l @ Y2 @ Y3 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl9,plain,
! [X2: $i,X4: $i > $o] :
( '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( k @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( l @ Y0 @ Y1 ) )
| ( (~) @ ( X4 @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( i @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( j @ Y0 @ Y1 ) )
| ( X4 @ Y1 ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl4,zip_derived_cl7]) ).
thf(zip_derived_cl10,plain,
! [X2: $i,X4: $i > $o] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( k @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( l @ Y0 @ Y1 ) )
| ( (~) @ ( X4 @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( i @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( j @ Y0 @ Y1 ) )
| ( X4 @ Y1 ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl12,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( (~) @ ( k @ X2 @ X6 ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( l @ X6 @ Y0 ) )
| ( (~) @ ( X4 @ Y0 ) ) ) ) )
| '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( i @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( j @ Y0 @ Y1 ) )
| ( X4 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl14,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ~ ( k @ X2 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( l @ X6 @ Y0 ) )
| ( (~) @ ( X4 @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( i @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( j @ Y0 @ Y1 ) )
| ( X4 @ Y1 ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl16,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ~ ( ( (~) @ ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) ) )
| ( (~) @ ( X4 @ ( '#sk12' @ X4 @ X6 ) ) ) )
| '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( i @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( j @ Y0 @ Y1 ) )
| ( X4 @ Y1 ) ) ) ) ) )
| ~ ( k @ X2 @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl18,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) )
| ~ ( k @ X2 @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( i @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( j @ Y0 @ Y1 ) )
| ( X4 @ Y1 ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl21,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
( ( (~) @ ( i @ X2 @ X8 ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( j @ X8 @ Y0 ) )
| ( X4 @ Y0 ) ) ) )
| '#form3'
| ~ ( k @ X2 @ X6 )
| ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl25,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
( ~ ( i @ X2 @ X8 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( j @ X8 @ Y0 ) )
| ( X4 @ Y0 ) ) )
| ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) )
| ~ ( k @ X2 @ X6 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl27,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
( ~ ( ( (~) @ ( j @ X8 @ ( '#sk27' @ X4 @ X8 ) ) )
| ( X4 @ ( '#sk27' @ X4 @ X8 ) ) )
| '#form3'
| ~ ( k @ X2 @ X6 )
| ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) )
| ~ ( i @ X2 @ X8 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
( ~ ( X4 @ ( '#sk27' @ X4 @ X8 ) )
| ~ ( i @ X2 @ X8 )
| ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) )
| ~ ( k @ X2 @ X6 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl93,plain,
! [X0: $i,X1: $i > $o] :
( '#form3'
| '#form3'
| ~ ( k @ '#sk112' @ X0 )
| ( l @ X0 @ ( '#sk12' @ X1 @ X0 ) )
| ~ ( X1 @ ( '#sk27' @ X1 @ '#sk114' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl60,zip_derived_cl30]) ).
thf(zip_derived_cl101,plain,
! [X0: $i,X1: $i > $o] :
( ~ ( X1 @ ( '#sk27' @ X1 @ '#sk114' ) )
| ( l @ X0 @ ( '#sk12' @ X1 @ X0 ) )
| ~ ( k @ '#sk112' @ X0 )
| '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl181_009,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).
thf(zip_derived_cl739,plain,
! [X0: $i,X1: $i > $o] :
( ~ ( X1 @ ( '#sk27' @ X1 @ '#sk114' ) )
| ( l @ X0 @ ( '#sk12' @ X1 @ X0 ) )
| ~ ( k @ '#sk112' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl101,zip_derived_cl181]) ).
thf(zip_derived_cl740,plain,
! [X0: $i > $o] :
( ( l @ '#sk116' @ ( '#sk12' @ X0 @ '#sk116' ) )
| ~ ( X0 @ ( '#sk27' @ X0 @ '#sk114' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl186,zip_derived_cl739]) ).
thf(zip_derived_cl186_010,plain,
k @ '#sk112' @ '#sk116',
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl181]) ).
thf(zip_derived_cl60_011,plain,
( ( i @ '#sk112' @ '#sk114' )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl19,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( X4 @ ( '#sk12' @ X4 @ X6 ) )
| ~ ( k @ X2 @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( i @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( j @ Y0 @ Y1 ) )
| ( X4 @ Y1 ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl22,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
( ( (~) @ ( i @ X2 @ X8 ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( j @ X8 @ Y0 ) )
| ( X4 @ Y0 ) ) ) )
| '#form3'
| ~ ( k @ X2 @ X6 )
| ( X4 @ ( '#sk12' @ X4 @ X6 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl26,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
( ~ ( i @ X2 @ X8 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( j @ X8 @ Y0 ) )
| ( X4 @ Y0 ) ) )
| ( X4 @ ( '#sk12' @ X4 @ X6 ) )
| ~ ( k @ X2 @ X6 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl28,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
( ~ ( ( (~) @ ( j @ X8 @ ( '#sk27' @ X4 @ X8 ) ) )
| ( X4 @ ( '#sk27' @ X4 @ X8 ) ) )
| '#form3'
| ~ ( k @ X2 @ X6 )
| ( X4 @ ( '#sk12' @ X4 @ X6 ) )
| ~ ( i @ X2 @ X8 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl31,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
( ( j @ X8 @ ( '#sk27' @ X4 @ X8 ) )
| ~ ( i @ X2 @ X8 )
| ( X4 @ ( '#sk12' @ X4 @ X6 ) )
| ~ ( k @ X2 @ X6 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl92,plain,
! [X0: $i,X1: $i > $o] :
( '#form3'
| '#form3'
| ~ ( k @ '#sk112' @ X0 )
| ( X1 @ ( '#sk12' @ X1 @ X0 ) )
| ( j @ '#sk114' @ ( '#sk27' @ X1 @ '#sk114' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl60,zip_derived_cl31]) ).
thf(zip_derived_cl100,plain,
! [X0: $i,X1: $i > $o] :
( ( j @ '#sk114' @ ( '#sk27' @ X1 @ '#sk114' ) )
| ( X1 @ ( '#sk12' @ X1 @ X0 ) )
| ~ ( k @ '#sk112' @ X0 )
| '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl181_012,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).
thf(zip_derived_cl522,plain,
! [X0: $i,X1: $i > $o] :
( ( j @ '#sk114' @ ( '#sk27' @ X1 @ '#sk114' ) )
| ( X1 @ ( '#sk12' @ X1 @ X0 ) )
| ~ ( k @ '#sk112' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl100,zip_derived_cl181]) ).
thf(zip_derived_cl523,plain,
! [X0: $i > $o] :
( ( X0 @ ( '#sk12' @ X0 @ '#sk116' ) )
| ( j @ '#sk114' @ ( '#sk27' @ X0 @ '#sk114' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl186,zip_derived_cl522]) ).
thf(zip_derived_cl186_013,plain,
k @ '#sk112' @ '#sk116',
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl181]) ).
thf(zip_derived_cl60_014,plain,
( ( i @ '#sk112' @ '#sk114' )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl181_015,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).
thf(zip_derived_cl187,plain,
i @ '#sk112' @ '#sk114',
inference(demod,[status(thm)],[zip_derived_cl60,zip_derived_cl181]) ).
thf(zip_derived_cl32,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
( ~ ( X4 @ ( '#sk27' @ X4 @ X8 ) )
| ~ ( i @ X2 @ X8 )
| ( X4 @ ( '#sk12' @ X4 @ X6 ) )
| ~ ( k @ X2 @ X6 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl181_016,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).
thf(zip_derived_cl185,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
( ~ ( X4 @ ( '#sk27' @ X4 @ X8 ) )
| ~ ( i @ X2 @ X8 )
| ( X4 @ ( '#sk12' @ X4 @ X6 ) )
| ~ ( k @ X2 @ X6 ) ),
inference(demod,[status(thm)],[zip_derived_cl32,zip_derived_cl181]) ).
thf(zip_derived_cl326,plain,
! [X0: $i,X1: $i > $o] :
( ~ ( k @ '#sk112' @ X0 )
| ( X1 @ ( '#sk12' @ X1 @ X0 ) )
| ~ ( X1 @ ( '#sk27' @ X1 @ '#sk114' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl187,zip_derived_cl185]) ).
thf(zip_derived_cl348,plain,
! [X0: $i > $o] :
( ~ ( X0 @ ( '#sk27' @ X0 @ '#sk114' ) )
| ( X0 @ ( '#sk12' @ X0 @ '#sk116' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl186,zip_derived_cl326]) ).
thf(zip_derived_cl532,plain,
( ( j @ '#sk114' @ ( '#sk12' @ ( j @ '#sk114' ) @ '#sk116' ) )
| ( j @ '#sk114' @ ( '#sk12' @ ( j @ '#sk114' ) @ '#sk116' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl523,zip_derived_cl348]) ).
thf(zip_derived_cl602,plain,
j @ '#sk114' @ ( '#sk12' @ ( j @ '#sk114' ) @ '#sk116' ),
inference(simplify,[status(thm)],[zip_derived_cl532]) ).
thf(zip_derived_cl56,plain,
( ~ ( ??
@ ^ [Y0: $i] :
( ( j @ '#sk114' @ Y0 )
& ( l @ '#sk116' @ Y0 ) ) )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl61,plain,
! [X2: $i] :
( ~ ( ( j @ '#sk114' @ X2 )
& ( l @ '#sk116' @ X2 ) )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl66,plain,
! [X2: $i] :
( ~ ( j @ '#sk114' @ X2 )
| ~ ( l @ '#sk116' @ X2 )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl181_017,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).
thf(zip_derived_cl188,plain,
! [X2: $i] :
( ~ ( j @ '#sk114' @ X2 )
| ~ ( l @ '#sk116' @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl66,zip_derived_cl181]) ).
thf(zip_derived_cl640,plain,
~ ( l @ '#sk116' @ ( '#sk12' @ ( j @ '#sk114' ) @ '#sk116' ) ),
inference('sup-',[status(thm)],[zip_derived_cl602,zip_derived_cl188]) ).
thf(zip_derived_cl763,plain,
~ ( j @ '#sk114' @ ( '#sk27' @ ( j @ '#sk114' ) @ '#sk114' ) ),
inference('sup-',[status(thm)],[zip_derived_cl740,zip_derived_cl640]) ).
thf(zip_derived_cl186_018,plain,
k @ '#sk112' @ '#sk116',
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl181]) ).
thf(zip_derived_cl60_019,plain,
( ( i @ '#sk112' @ '#sk114' )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl29,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
( ( j @ X8 @ ( '#sk27' @ X4 @ X8 ) )
| ~ ( i @ X2 @ X8 )
| ( l @ X6 @ ( '#sk12' @ X4 @ X6 ) )
| ~ ( k @ X2 @ X6 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl94,plain,
! [X0: $i,X1: $i > $o] :
( '#form3'
| '#form3'
| ~ ( k @ '#sk112' @ X0 )
| ( l @ X0 @ ( '#sk12' @ X1 @ X0 ) )
| ( j @ '#sk114' @ ( '#sk27' @ X1 @ '#sk114' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl60,zip_derived_cl29]) ).
thf(zip_derived_cl102,plain,
! [X0: $i,X1: $i > $o] :
( ( j @ '#sk114' @ ( '#sk27' @ X1 @ '#sk114' ) )
| ( l @ X0 @ ( '#sk12' @ X1 @ X0 ) )
| ~ ( k @ '#sk112' @ X0 )
| '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl181_020,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl179,zip_derived_cl64]) ).
thf(zip_derived_cl803,plain,
! [X0: $i,X1: $i > $o] :
( ( j @ '#sk114' @ ( '#sk27' @ X1 @ '#sk114' ) )
| ( l @ X0 @ ( '#sk12' @ X1 @ X0 ) )
| ~ ( k @ '#sk112' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl102,zip_derived_cl181]) ).
thf(zip_derived_cl804,plain,
! [X0: $i > $o] :
( ( l @ '#sk116' @ ( '#sk12' @ X0 @ '#sk116' ) )
| ( j @ '#sk114' @ ( '#sk27' @ X0 @ '#sk114' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl186,zip_derived_cl803]) ).
thf(zip_derived_cl640_021,plain,
~ ( l @ '#sk116' @ ( '#sk12' @ ( j @ '#sk114' ) @ '#sk116' ) ),
inference('sup-',[status(thm)],[zip_derived_cl602,zip_derived_cl188]) ).
thf(zip_derived_cl818,plain,
j @ '#sk114' @ ( '#sk27' @ ( j @ '#sk114' ) @ '#sk114' ),
inference('sup-',[status(thm)],[zip_derived_cl804,zip_derived_cl640]) ).
thf(zip_derived_cl828,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl763,zip_derived_cl818]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL872^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Prk4Dku1wE true
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 4 15:15:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Running portfolio for 300 s
% 0.10/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Number of cores: 8
% 0.10/0.37 % Python version: Python 3.12.3
% 0.10/0.38 % Running in HO mode
% 0.44/0.67 % Total configuration time : 828
% 0.44/0.67 % Estimated wc time : 1656
% 0.44/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.49/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.49/0.81 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.49/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.49/0.81 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.49/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.49/0.82 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.49/0.87 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.49/0.88 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.52/0.93 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 9.80/1.95 % Solved by lams/20_acsne_simpl.sh.
% 9.80/1.95 % done 136 iterations in 1.020s
% 9.80/1.95 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 9.80/1.95 % SZS output start Refutation
% See solution above
% 9.80/1.96
% 9.80/1.96
% 9.80/1.96 % Terminating...
% 9.80/2.01 % Runner terminated.
% 9.80/2.04 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------