%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL861^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.yBQuSEt89d true
% Computer : n019.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 01:37:29 PM UTC 2026
% Result : Theorem 0.50s 1.01s
% Output : Refutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 80 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 484 ( 11 equ; 0 cnn)
% Maximal formula atoms : 22 ( 6 avg)
% Number of connectives : 1298 ( 81 ~; 69 |; 110 &; 781 @)
% ( 5 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 11 con; 0-2 aty)
% ( 184 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 265 ( 193 ^; 72 !; 0 ?; 265 :)
% Comments :
%------------------------------------------------------------------------------
thf('#sk4_type',type,
'#sk4': $i ).
thf(meuclidean_type,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf('#form5_type',type,
'#form5': $o ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf('#sk1_type',type,
'#sk1': $i > $i > $o ).
thf('#sk7_type',type,
'#sk7': $i ).
thf('#sk6_type',type,
'#sk6': $i ).
thf(mtransitive_type,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf('#sk8_type',type,
'#sk8': $i ).
thf('#sk9_type',type,
'#sk9': $i ).
thf(meuclidean,axiom,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ) ).
thf('0',plain,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[meuclidean]) ).
thf('1',plain,
( meuclidean
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i,X6: $i,X8: $i] :
( ( ( V_1 @ X4 @ X6 )
& ( V_1 @ X4 @ X8 ) )
=> ( V_1 @ X6 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(mtransitive,axiom,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ) ).
thf('2',plain,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mtransitive]) ).
thf('3',plain,
( mtransitive
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i,X6: $i,X8: $i] :
( ( ( V_1 @ X4 @ X6 )
& ( V_1 @ X6 @ X8 ) )
=> ( V_1 @ X4 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ) ).
thf('4',plain,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
inference(simplify_rw_rule,[status(thm)],[mreflexive]) ).
thf('5',plain,
( mreflexive
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i] : ( V_1 @ X4 @ X4 ) ) ),
define([status(thm)]) ).
thf(conj,conjecture,
! [R: $i > $i > $o] :
( ( ( mreflexive @ R )
& ( meuclidean @ R ) )
<=> ( ( mreflexive @ R )
& ( mtransitive @ R )
& ( meuclidean @ R ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i > $i > $o] :
( ( ! [X8: $i,X10: $i,X12: $i] :
( ( ( X4 @ X8 @ X12 )
& ( X4 @ X8 @ X10 ) )
=> ( X4 @ X10 @ X12 ) )
& ! [X6: $i] : ( X4 @ X6 @ X6 ) )
<=> ( ! [X22: $i,X24: $i,X26: $i] :
( ( ( X4 @ X22 @ X26 )
& ( X4 @ X22 @ X24 ) )
=> ( X4 @ X24 @ X26 ) )
& ! [X16: $i,X18: $i,X20: $i] :
( ( ( X4 @ X18 @ X20 )
& ( X4 @ X16 @ X18 ) )
=> ( X4 @ X16 @ X20 ) )
& ! [X14: $i] : ( X4 @ X14 @ X14 ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i > $i > $o] :
( ( ! [X8: $i,X10: $i,X12: $i] :
( ( ( X4 @ X8 @ X12 )
& ( X4 @ X8 @ X10 ) )
=> ( X4 @ X10 @ X12 ) )
& ! [X6: $i] : ( X4 @ X6 @ X6 ) )
<=> ( ! [X22: $i,X24: $i,X26: $i] :
( ( ( X4 @ X22 @ X26 )
& ( X4 @ X22 @ X24 ) )
=> ( X4 @ X24 @ X26 ) )
& ! [X16: $i,X18: $i,X20: $i] :
( ( ( X4 @ X18 @ X20 )
& ( X4 @ X16 @ X18 ) )
=> ( X4 @ X16 @ X20 ) )
& ! [X14: $i] : ( X4 @ X14 @ X14 ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
<=> ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) )
<=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) )
!= ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl30,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl31,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
| ~ ( $true
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& $true ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl32,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl33,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( '#sk1' @ '#sk2' @ Y1 )
& ( '#sk1' @ '#sk2' @ Y0 ) )
=> ( '#sk1' @ Y0 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl34,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( ( '#sk1' @ '#sk2' @ Y0 )
& ( '#sk1' @ '#sk2' @ '#sk3' ) )
=> ( '#sk1' @ '#sk3' @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl35,plain,
( ~ ( ( ( '#sk1' @ '#sk2' @ '#sk4' )
& ( '#sk1' @ '#sk2' @ '#sk3' ) )
=> ( '#sk1' @ '#sk3' @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl37,plain,
( ~ ( '#sk1' @ '#sk3' @ '#sk4' )
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl40,plain,
( '#form5'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl41,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk1' @ '#sk6' @ Y0 ) )
=> ( '#sk1' @ '#sk6' @ Y1 ) ) ) )
| '#form5' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl46,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( ( '#sk1' @ '#sk8' @ Y0 )
& ( '#sk1' @ '#sk6' @ '#sk8' ) )
=> ( '#sk1' @ '#sk6' @ Y0 ) ) )
| '#form5' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl50,plain,
( ~ ( ( ( '#sk1' @ '#sk8' @ '#sk9' )
& ( '#sk1' @ '#sk6' @ '#sk8' ) )
=> ( '#sk1' @ '#sk6' @ '#sk9' ) )
| '#form5' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl54,plain,
( ~ ( '#sk1' @ '#sk6' @ '#sk9' )
| '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl36,plain,
( ( ( '#sk1' @ '#sk2' @ '#sk4' )
& ( '#sk1' @ '#sk2' @ '#sk3' ) )
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl39,plain,
( ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl40_001,plain,
( '#form5'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl44,plain,
( ~ '#form5'
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(renaming,[status(thm)],[zip_derived_cl39,zip_derived_cl40]) ).
thf(zip_derived_cl48,plain,
( ~ ( '#sk1' @ '#sk7' @ '#sk7' )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ '#form5' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl2_002,plain,
( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) )
!= ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) )
| ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl6,plain,
( ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
| ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl10,plain,
( ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
| ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& $false ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl11,plain,
( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl12,plain,
! [X2: $i] : ( '#sk1' @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl52,plain,
( ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ '#form5' ),
inference(demod,[status(thm)],[zip_derived_cl48,zip_derived_cl12]) ).
thf(zip_derived_cl38,plain,
( ( '#sk1' @ '#sk2' @ '#sk4' )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl40_003,plain,
( '#form5'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl43,plain,
( ~ '#form5'
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
| ( '#sk1' @ '#sk2' @ '#sk4' ) ),
inference(renaming,[status(thm)],[zip_derived_cl38,zip_derived_cl40]) ).
thf(zip_derived_cl47,plain,
( ~ ( '#sk1' @ '#sk7' @ '#sk7' )
| ( '#sk1' @ '#sk2' @ '#sk4' )
| ~ '#form5' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl12_004,plain,
! [X2: $i] : ( '#sk1' @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl51,plain,
( ( '#sk1' @ '#sk2' @ '#sk4' )
| ~ '#form5' ),
inference(demod,[status(thm)],[zip_derived_cl47,zip_derived_cl12]) ).
thf(zip_derived_cl5,plain,
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
| ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl7,plain,
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
| ( $false
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl8,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y0 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl9,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( '#sk1' @ X2 @ Y1 )
& ( '#sk1' @ X2 @ Y0 ) )
=> ( '#sk1' @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl13,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( '#sk1' @ X2 @ Y0 )
& ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk1' @ X4 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl14,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( '#sk1' @ X2 @ X6 )
& ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk1' @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl15,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( '#sk1' @ X2 @ X6 )
& ( '#sk1' @ X2 @ X4 ) )
| ( '#sk1' @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl16,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#sk1' @ X2 @ X6 )
| ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl58,plain,
! [X0: $i] :
( ~ '#form5'
| ( '#sk1' @ X0 @ '#sk4' )
| ~ ( '#sk1' @ '#sk2' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl16]) ).
thf(zip_derived_cl90,plain,
( ~ '#form5'
| ( '#sk1' @ '#sk3' @ '#sk4' )
| ~ '#form5' ),
inference('sup-',[status(thm)],[zip_derived_cl52,zip_derived_cl58]) ).
thf(zip_derived_cl96,plain,
( ( '#sk1' @ '#sk3' @ '#sk4' )
| ~ '#form5' ),
inference(simplify,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl37_005,plain,
( ~ ( '#sk1' @ '#sk3' @ '#sk4' )
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl40_006,plain,
( '#form5'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl42,plain,
( ~ '#form5'
| ~ ( !!
@ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
| ~ ( '#sk1' @ '#sk3' @ '#sk4' ) ),
inference(renaming,[status(thm)],[zip_derived_cl37,zip_derived_cl40]) ).
thf(zip_derived_cl45,plain,
( ~ ( '#sk1' @ '#sk7' @ '#sk7' )
| ~ ( '#sk1' @ '#sk3' @ '#sk4' )
| ~ '#form5' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl12_007,plain,
! [X2: $i] : ( '#sk1' @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl49,plain,
( ~ ( '#sk1' @ '#sk3' @ '#sk4' )
| ~ '#form5' ),
inference(demod,[status(thm)],[zip_derived_cl45,zip_derived_cl12]) ).
thf(zip_derived_cl122,plain,
~ '#form5',
inference(clc,[status(thm)],[zip_derived_cl96,zip_derived_cl49]) ).
thf(zip_derived_cl123,plain,
~ ( '#sk1' @ '#sk6' @ '#sk9' ),
inference(demod,[status(thm)],[zip_derived_cl54,zip_derived_cl122]) ).
thf(zip_derived_cl53,plain,
( ( ( '#sk1' @ '#sk8' @ '#sk9' )
& ( '#sk1' @ '#sk6' @ '#sk8' ) )
| '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl56,plain,
( ( '#sk1' @ '#sk6' @ '#sk8' )
| '#form5' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl12_008,plain,
! [X2: $i] : ( '#sk1' @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl16_009,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#sk1' @ X2 @ X6 )
| ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl17,plain,
! [X0: $i,X1: $i] :
( ( '#sk1' @ X1 @ X0 )
| ~ ( '#sk1' @ X0 @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl16]) ).
thf(zip_derived_cl77,plain,
( '#form5'
| ( '#sk1' @ '#sk8' @ '#sk6' ) ),
inference('sup-',[status(thm)],[zip_derived_cl56,zip_derived_cl17]) ).
thf(zip_derived_cl122_010,plain,
~ '#form5',
inference(clc,[status(thm)],[zip_derived_cl96,zip_derived_cl49]) ).
thf(zip_derived_cl127,plain,
'#sk1' @ '#sk8' @ '#sk6',
inference(demod,[status(thm)],[zip_derived_cl77,zip_derived_cl122]) ).
thf(zip_derived_cl55,plain,
( ( '#sk1' @ '#sk8' @ '#sk9' )
| '#form5' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl122_011,plain,
~ '#form5',
inference(clc,[status(thm)],[zip_derived_cl96,zip_derived_cl49]) ).
thf(zip_derived_cl124,plain,
'#sk1' @ '#sk8' @ '#sk9',
inference(demod,[status(thm)],[zip_derived_cl55,zip_derived_cl122]) ).
thf(zip_derived_cl16_012,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#sk1' @ X2 @ X6 )
| ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl129,plain,
! [X0: $i] :
( ( '#sk1' @ X0 @ '#sk9' )
| ~ ( '#sk1' @ '#sk8' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl124,zip_derived_cl16]) ).
thf(zip_derived_cl148,plain,
'#sk1' @ '#sk6' @ '#sk9',
inference('sup-',[status(thm)],[zip_derived_cl127,zip_derived_cl129]) ).
thf(zip_derived_cl166,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl123,zip_derived_cl148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL861^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.yBQuSEt89d true
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 4 19:39:53 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Running portfolio for 300 s
% 0.10/0.38 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Number of cores: 8
% 0.10/0.38 % Python version: Python 3.12.3
% 0.10/0.39 % 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
% 0.48/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.48/0.82 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.48/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.48/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.48/0.84 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.48/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.48/0.86 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.48/0.90 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.50/1.01 % Solved by lams/20_acsne_simpl.sh.
% 0.50/1.01 % done 70 iterations in 0.078s
% 0.50/1.01 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.50/1.01 % SZS output start Refutation
% See solution above
% 0.50/1.01
% 0.50/1.01
% 0.50/1.01 % Terminating...
% 0.50/1.06 % Runner terminated.
% 3.25/1.07 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------