%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL725^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.y7zZaftcHb true
% Computer : n008.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 01:37:07 PM UTC 2026
% Result : Theorem 2.81s 1.13s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 31
% Syntax : Number of formulae : 172 ( 56 unt; 0 typ; 0 def)
% Number of atoms : 922 ( 27 equ; 178 cnn)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 1994 ( 357 ~; 351 |; 17 &;1113 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 18 usr; 10 con; 0-3 aty)
% ( 141 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 289 ( 183 ^; 106 !; 0 ?; 289 :)
% Comments :
%------------------------------------------------------------------------------
thf(rel_s5_type,type,
rel_s5: $i > $i > $o ).
thf('#sk6_type',type,
'#sk6': $i ).
thf(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(phi_type,type,
phi: $i > $o ).
thf(mdia_s5_type,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf('#sk7_type',type,
'#sk7': $i ).
thf(mtransitive_type,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(mbox_s5_type,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(msymmetric_type,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf('#sk2_type',type,
'#sk2': $i ).
thf('#sk5_type',type,
'#sk5': $i ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf('#form4_type',type,
'#form4': $o ).
thf(mdia_s5,axiom,
( mdia_s5
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) ) ) ) ).
thf(mbox_s5,axiom,
( mbox_s5
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_s5 @ W @ V ) ) ) ) ).
thf('0',plain,
( mbox_s5
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_s5 @ W @ V ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox_s5]) ).
thf('1',plain,
( mbox_s5
= ( ^ [V_1: $i > $o,V_2: $i] :
! [X4: $i] :
( ( V_1 @ X4 )
| ~ ( rel_s5 @ V_2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(mnot,axiom,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ) ).
thf('2',plain,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('3',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('4',plain,
( mdia_s5
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Phi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mdia_s5,'1','3']) ).
thf('5',plain,
( mdia_s5
= ( ^ [V_1: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ V_1 ) ) ) ) ),
define([status(thm)]) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('6',plain,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('7',plain,
( mvalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
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('8',plain,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('9',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('10',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'9','3']) ).
thf('11',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
define([status(thm)]) ).
thf(conj,conjecture,
( ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i] :
( ! [X6: $i] :
( ~ ( rel_s5 @ X4 @ X6 )
| ~ ! [X8: $i] :
( ~ ( rel_s5 @ X6 @ X8 )
| ~ ( phi @ X8 ) ) )
| ~ ( phi @ X4 ) )
& ! [X10: $i] :
( ! [X14: $i] :
( ~ ( rel_s5 @ X10 @ X14 )
| ! [X16: $i] :
( ~ ( rel_s5 @ X14 @ X16 )
| ( phi @ X16 ) ) )
| ~ ! [X12: $i] :
( ~ ( rel_s5 @ X10 @ X12 )
| ( phi @ X12 ) ) )
& ! [X18: $i] :
( ( phi @ X18 )
| ~ ! [X20: $i] :
( ~ ( rel_s5 @ X18 @ X20 )
| ( phi @ X20 ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i] :
( ! [X6: $i] :
( ~ ( rel_s5 @ X4 @ X6 )
| ~ ! [X8: $i] :
( ~ ( rel_s5 @ X6 @ X8 )
| ~ ( phi @ X8 ) ) )
| ~ ( phi @ X4 ) )
& ! [X10: $i] :
( ! [X14: $i] :
( ~ ( rel_s5 @ X10 @ X14 )
| ! [X16: $i] :
( ~ ( rel_s5 @ X14 @ X16 )
| ( phi @ X16 ) ) )
| ~ ! [X12: $i] :
( ~ ( rel_s5 @ X10 @ X12 )
| ( phi @ X12 ) ) )
& ! [X18: $i] :
( ( phi @ X18 )
| ~ ! [X20: $i] :
( ~ ( rel_s5 @ X18 @ X20 )
| ( phi @ X20 ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( (~) @ ( phi @ Y2 ) ) ) ) ) ) )
| ( (~) @ ( phi @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( phi @ Y2 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl25,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( (~) @ ( phi @ Y2 ) ) ) ) ) ) )
| ( (~) @ ( phi @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( phi @ Y2 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl26,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( phi @ Y1 ) ) ) ) ) ) )
| ( (~) @ ( phi @ '#sk1' ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( phi @ Y2 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl28,plain,
( ( phi @ '#sk1' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( phi @ Y2 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl30,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( phi @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) )
| ( phi @ '#sk1' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl33,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) )
| ( phi @ '#sk1' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl27,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( phi @ Y1 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( phi @ Y2 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl29,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk2' ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( phi @ Y2 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl31,plain,
( ( rel_s5 @ '#sk1' @ '#sk2' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( phi @ Y2 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl35,plain,
( '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl39,plain,
( ~ '#form4'
| ( phi @ '#sk1' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl33,zip_derived_cl35]) ).
thf(zip_derived_cl45,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk3' @ '#sk6' ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk6' @ Y0 ) )
| ( phi @ Y0 ) ) ) )
| ( phi @ '#sk1' )
| ~ '#form4' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl53,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk6' @ Y0 ) )
| ( phi @ Y0 ) ) )
| ~ '#form4'
| ( phi @ '#sk1' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl60,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk6' @ '#sk7' ) )
| ( phi @ '#sk7' ) )
| ( phi @ '#sk1' )
| ~ '#form4' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl67,plain,
( ( rel_s5 @ '#sk6' @ '#sk7' )
| ~ '#form4'
| ( phi @ '#sk1' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl35_001,plain,
( '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl36,plain,
( ~ ( ( phi @ '#sk5' )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk5' @ Y0 ) )
| ( phi @ Y0 ) ) ) ) )
| '#form4' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl42,plain,
( ~ ( phi @ '#sk5' )
| '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl43,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk5' @ Y0 ) )
| ( phi @ Y0 ) ) )
| '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl49,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk5' @ X2 ) )
| ( phi @ X2 )
| '#form4' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl57,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk5' @ X2 )
| ( phi @ X2 )
| '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl100,plain,
( '#form4'
| '#form4'
| ~ ( rel_s5 @ '#sk5' @ '#sk5' ) ),
inference('sup+',[status(thm)],[zip_derived_cl42,zip_derived_cl57]) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ) ).
thf('12',plain,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
inference(simplify_rw_rule,[status(thm)],[mreflexive]) ).
thf('13',plain,
( mreflexive
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i] : ( V_1 @ X4 @ X4 ) ) ),
define([status(thm)]) ).
thf(a1,axiom,
mreflexive @ rel_s5 ).
thf(zf_stmt_2,axiom,
! [X4: $i] : ( rel_s5 @ X4 @ X4 ) ).
thf(zip_derived_cl0,plain,
( !!
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl4,plain,
! [X2: $i] : ( rel_s5 @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl109,plain,
( '#form4'
| '#form4' ),
inference(demod,[status(thm)],[zip_derived_cl100,zip_derived_cl4]) ).
thf(zip_derived_cl110,plain,
'#form4',
inference(simplify,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl119,plain,
( ( rel_s5 @ '#sk6' @ '#sk7' )
| ( phi @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl67,zip_derived_cl110]) ).
thf(zip_derived_cl32,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( phi @ Y2 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl35_002,plain,
( '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl38,plain,
( ~ '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( phi @ Y2 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl32,zip_derived_cl35]) ).
thf(zip_derived_cl44,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( phi @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) )
| ~ '#form4' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl50,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) )
| ~ '#form4'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl58,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk3' @ '#sk6' ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk6' @ Y0 ) )
| ( phi @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) )
| ~ '#form4' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl65,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk6' @ Y0 ) )
| ( phi @ Y0 ) ) )
| ~ '#form4'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl71,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk6' @ '#sk7' ) )
| ( phi @ '#sk7' ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) )
| ~ '#form4' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl76,plain,
( ( rel_s5 @ '#sk6' @ '#sk7' )
| ~ '#form4'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl79,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ X2 ) )
| ( (~) @ ( phi @ X2 ) )
| ~ '#form4'
| ( rel_s5 @ '#sk6' @ '#sk7' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl81,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk2' @ X2 )
| ~ ( phi @ X2 )
| ( rel_s5 @ '#sk6' @ '#sk7' )
| ~ '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl110_003,plain,
'#form4',
inference(simplify,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl299,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk2' @ X2 )
| ~ ( phi @ X2 )
| ( rel_s5 @ '#sk6' @ '#sk7' ) ),
inference(demod,[status(thm)],[zip_derived_cl81,zip_derived_cl110]) ).
thf(zip_derived_cl310,plain,
( ( rel_s5 @ '#sk6' @ '#sk7' )
| ( rel_s5 @ '#sk6' @ '#sk7' )
| ~ ( rel_s5 @ '#sk2' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl119,zip_derived_cl299]) ).
thf(zip_derived_cl324,plain,
( ~ ( rel_s5 @ '#sk2' @ '#sk1' )
| ( rel_s5 @ '#sk6' @ '#sk7' ) ),
inference(simplify,[status(thm)],[zip_derived_cl310]) ).
thf(zip_derived_cl31_004,plain,
( ( rel_s5 @ '#sk1' @ '#sk2' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( phi @ Y2 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl35_005,plain,
( '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl37,plain,
( ~ '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( phi @ Y2 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) )
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl31,zip_derived_cl35]) ).
thf(zip_derived_cl41,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( phi @ Y0 ) ) ) ) )
| ( rel_s5 @ '#sk1' @ '#sk2' )
| ~ '#form4' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl47,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) )
| ~ '#form4'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl55,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk3' @ '#sk6' ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk6' @ Y0 ) )
| ( phi @ Y0 ) ) ) )
| ( rel_s5 @ '#sk1' @ '#sk2' )
| ~ '#form4' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl62,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk6' @ Y0 ) )
| ( phi @ Y0 ) ) )
| ~ '#form4'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl69,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk6' @ '#sk7' ) )
| ( phi @ '#sk7' ) )
| ( rel_s5 @ '#sk1' @ '#sk2' )
| ~ '#form4' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl73,plain,
( ( rel_s5 @ '#sk6' @ '#sk7' )
| ~ '#form4'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl110_006,plain,
'#form4',
inference(simplify,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl184,plain,
( ( rel_s5 @ '#sk6' @ '#sk7' )
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl73,zip_derived_cl110]) ).
thf(msymmetric,axiom,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ) ).
thf('14',plain,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[msymmetric]) ).
thf('15',plain,
( msymmetric
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i,X6: $i] :
( ( V_1 @ X4 @ X6 )
=> ( V_1 @ X6 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(a3,axiom,
msymmetric @ rel_s5 ).
thf(zf_stmt_3,axiom,
! [X4: $i,X6: $i] :
( ( rel_s5 @ X4 @ X6 )
=> ( rel_s5 @ X6 @ X4 ) ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl5,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( rel_s5 @ X2 @ Y0 )
=> ( rel_s5 @ Y0 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl6,plain,
! [X2: $i,X4: $i] :
( ( rel_s5 @ X2 @ X4 )
=> ( rel_s5 @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl7,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ X2 @ X4 )
| ( rel_s5 @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl186,plain,
( ( rel_s5 @ '#sk6' @ '#sk7' )
| ( rel_s5 @ '#sk2' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl184,zip_derived_cl7]) ).
thf(zip_derived_cl328,plain,
rel_s5 @ '#sk6' @ '#sk7',
inference(clc,[status(thm)],[zip_derived_cl324,zip_derived_cl186]) ).
thf(zip_derived_cl7_007,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ X2 @ X4 )
| ( rel_s5 @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl330,plain,
rel_s5 @ '#sk7' @ '#sk6',
inference('sup-',[status(thm)],[zip_derived_cl328,zip_derived_cl7]) ).
thf(zip_derived_cl52,plain,
( ( rel_s5 @ '#sk3' @ '#sk6' )
| ~ '#form4'
| ( phi @ '#sk1' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl110_008,plain,
'#form4',
inference(simplify,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl117,plain,
( ( rel_s5 @ '#sk3' @ '#sk6' )
| ( phi @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl52,zip_derived_cl110]) ).
thf(zip_derived_cl64,plain,
( ( rel_s5 @ '#sk3' @ '#sk6' )
| ~ '#form4'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl70,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ X2 ) )
| ( (~) @ ( phi @ X2 ) )
| ~ '#form4'
| ( rel_s5 @ '#sk3' @ '#sk6' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl75,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk2' @ X2 )
| ~ ( phi @ X2 )
| ( rel_s5 @ '#sk3' @ '#sk6' )
| ~ '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl110_009,plain,
'#form4',
inference(simplify,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl193,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk2' @ X2 )
| ~ ( phi @ X2 )
| ( rel_s5 @ '#sk3' @ '#sk6' ) ),
inference(demod,[status(thm)],[zip_derived_cl75,zip_derived_cl110]) ).
thf(zip_derived_cl210,plain,
( ( rel_s5 @ '#sk3' @ '#sk6' )
| ( rel_s5 @ '#sk3' @ '#sk6' )
| ~ ( rel_s5 @ '#sk2' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl117,zip_derived_cl193]) ).
thf(zip_derived_cl230,plain,
( ~ ( rel_s5 @ '#sk2' @ '#sk1' )
| ( rel_s5 @ '#sk3' @ '#sk6' ) ),
inference(simplify,[status(thm)],[zip_derived_cl210]) ).
thf(zip_derived_cl61,plain,
( ( rel_s5 @ '#sk3' @ '#sk6' )
| ~ '#form4'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl110_010,plain,
'#form4',
inference(simplify,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl118,plain,
( ( rel_s5 @ '#sk3' @ '#sk6' )
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl61,zip_derived_cl110]) ).
thf(zip_derived_cl7_011,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ X2 @ X4 )
| ( rel_s5 @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl130,plain,
( ( rel_s5 @ '#sk3' @ '#sk6' )
| ( rel_s5 @ '#sk2' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl118,zip_derived_cl7]) ).
thf(zip_derived_cl234,plain,
rel_s5 @ '#sk3' @ '#sk6',
inference(clc,[status(thm)],[zip_derived_cl230,zip_derived_cl130]) ).
thf(zip_derived_cl7_012,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ X2 @ X4 )
| ( rel_s5 @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl237,plain,
rel_s5 @ '#sk6' @ '#sk3',
inference('sup-',[status(thm)],[zip_derived_cl234,zip_derived_cl7]) ).
thf(mtransitive,axiom,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ) ).
thf('16',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('17',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(a2,axiom,
mtransitive @ rel_s5 ).
thf(zf_stmt_4,axiom,
! [X4: $i,X6: $i,X8: $i] :
( ( ( rel_s5 @ X6 @ X8 )
& ( rel_s5 @ X4 @ X6 ) )
=> ( rel_s5 @ X4 @ X8 ) ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y1 @ Y2 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y0 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl12,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y0 @ Y1 )
& ( rel_s5 @ X2 @ Y0 ) )
=> ( rel_s5 @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl13,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( rel_s5 @ X4 @ Y0 )
& ( rel_s5 @ X2 @ X4 ) )
=> ( rel_s5 @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl14,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( rel_s5 @ X4 @ X6 )
& ( rel_s5 @ X2 @ X4 ) )
=> ( rel_s5 @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl15,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( rel_s5 @ X4 @ X6 )
& ( rel_s5 @ X2 @ X4 ) )
| ( rel_s5 @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl16,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( rel_s5 @ X4 @ X6 )
| ~ ( rel_s5 @ X2 @ X4 )
| ( rel_s5 @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl241,plain,
! [X0: $i] :
( ( rel_s5 @ X0 @ '#sk3' )
| ~ ( rel_s5 @ X0 @ '#sk6' ) ),
inference('sup-',[status(thm)],[zip_derived_cl237,zip_derived_cl16]) ).
thf(zip_derived_cl333,plain,
rel_s5 @ '#sk7' @ '#sk3',
inference('sup-',[status(thm)],[zip_derived_cl330,zip_derived_cl241]) ).
thf(zip_derived_cl7_013,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ X2 @ X4 )
| ( rel_s5 @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl341,plain,
rel_s5 @ '#sk3' @ '#sk7',
inference('sup-',[status(thm)],[zip_derived_cl333,zip_derived_cl7]) ).
thf(zip_derived_cl34,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( phi @ Y0 ) ) )
| ( phi @ '#sk1' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl35_014,plain,
( '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( phi @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl40,plain,
( ~ '#form4'
| ( phi @ '#sk1' )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( phi @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl34,zip_derived_cl35]) ).
thf(zip_derived_cl46,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ X2 ) )
| ( phi @ X2 )
| ( phi @ '#sk1' )
| ~ '#form4' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl54,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk3' @ X2 )
| ( phi @ X2 )
| ~ '#form4'
| ( phi @ '#sk1' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl110_015,plain,
'#form4',
inference(simplify,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl126,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk3' @ X2 )
| ( phi @ X2 )
| ( phi @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl54,zip_derived_cl110]) ).
thf(zip_derived_cl347,plain,
( ( phi @ '#sk1' )
| ( phi @ '#sk7' ) ),
inference('sup-',[status(thm)],[zip_derived_cl341,zip_derived_cl126]) ).
thf(zip_derived_cl68,plain,
( ~ ( phi @ '#sk7' )
| ~ '#form4'
| ( phi @ '#sk1' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl110_016,plain,
'#form4',
inference(simplify,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl120,plain,
( ~ ( phi @ '#sk7' )
| ( phi @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl68,zip_derived_cl110]) ).
thf(zip_derived_cl361,plain,
phi @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl347,zip_derived_cl120]) ).
thf(zip_derived_cl361_017,plain,
phi @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl347,zip_derived_cl120]) ).
thf(zip_derived_cl51,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( phi @ Y0 ) ) )
| ~ '#form4'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl59,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ X2 ) )
| ( phi @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) )
| ~ '#form4' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl66,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk3' @ X2 )
| ( phi @ X2 )
| ~ '#form4'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl72,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ X4 ) )
| ( (~) @ ( phi @ X4 ) )
| ~ '#form4'
| ( phi @ X2 )
| ~ ( rel_s5 @ '#sk3' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl78,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ '#sk2' @ X4 )
| ~ ( phi @ X4 )
| ~ ( rel_s5 @ '#sk3' @ X2 )
| ( phi @ X2 )
| ~ '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl110_018,plain,
'#form4',
inference(simplify,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl263,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ '#sk2' @ X4 )
| ~ ( phi @ X4 )
| ~ ( rel_s5 @ '#sk3' @ X2 )
| ( phi @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl78,zip_derived_cl110]) ).
thf(zip_derived_cl362,plain,
! [X0: $i] :
( ( phi @ X0 )
| ~ ( rel_s5 @ '#sk3' @ X0 )
| ~ ( rel_s5 @ '#sk2' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl361,zip_derived_cl263]) ).
thf(zip_derived_cl74,plain,
( ~ ( phi @ '#sk7' )
| ~ '#form4'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl110_019,plain,
'#form4',
inference(simplify,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl121,plain,
( ~ ( phi @ '#sk7' )
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl74,zip_derived_cl110]) ).
thf(zip_derived_cl48,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ Y0 ) )
| ( phi @ Y0 ) ) )
| ~ '#form4'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl56,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk3' @ X2 ) )
| ( phi @ X2 )
| ( rel_s5 @ '#sk1' @ '#sk2' )
| ~ '#form4' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl63,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk3' @ X2 )
| ( phi @ X2 )
| ~ '#form4'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl110_020,plain,
'#form4',
inference(simplify,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl157,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk3' @ X2 )
| ( phi @ X2 )
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl63,zip_derived_cl110]) ).
thf(zip_derived_cl163,plain,
( ( rel_s5 @ '#sk1' @ '#sk2' )
| ( rel_s5 @ '#sk1' @ '#sk2' )
| ~ ( rel_s5 @ '#sk3' @ '#sk7' ) ),
inference('sup+',[status(thm)],[zip_derived_cl121,zip_derived_cl157]) ).
thf(zip_derived_cl170,plain,
( ~ ( rel_s5 @ '#sk3' @ '#sk7' )
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(simplify,[status(thm)],[zip_derived_cl163]) ).
thf(zip_derived_cl341_021,plain,
rel_s5 @ '#sk3' @ '#sk7',
inference('sup-',[status(thm)],[zip_derived_cl333,zip_derived_cl7]) ).
thf(zip_derived_cl346,plain,
rel_s5 @ '#sk1' @ '#sk2',
inference(demod,[status(thm)],[zip_derived_cl170,zip_derived_cl341]) ).
thf(zip_derived_cl7_022,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ X2 @ X4 )
| ( rel_s5 @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl354,plain,
rel_s5 @ '#sk2' @ '#sk1',
inference('sup-',[status(thm)],[zip_derived_cl346,zip_derived_cl7]) ).
thf(zip_derived_cl364,plain,
! [X0: $i] :
( ( phi @ X0 )
| ~ ( rel_s5 @ '#sk3' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl362,zip_derived_cl354]) ).
thf(zip_derived_cl77,plain,
( ~ ( phi @ '#sk7' )
| ~ '#form4'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( (~) @ ( phi @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl80,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ X2 ) )
| ( (~) @ ( phi @ X2 ) )
| ~ '#form4'
| ~ ( phi @ '#sk7' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl82,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk2' @ X2 )
| ~ ( phi @ X2 )
| ~ ( phi @ '#sk7' )
| ~ '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl110_023,plain,
'#form4',
inference(simplify,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl122,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk2' @ X2 )
| ~ ( phi @ X2 )
| ~ ( phi @ '#sk7' ) ),
inference(demod,[status(thm)],[zip_derived_cl82,zip_derived_cl110]) ).
thf(zip_derived_cl367,plain,
! [X0: $i] :
( ~ ( rel_s5 @ '#sk3' @ '#sk7' )
| ~ ( phi @ X0 )
| ~ ( rel_s5 @ '#sk2' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl364,zip_derived_cl122]) ).
thf(zip_derived_cl341_024,plain,
rel_s5 @ '#sk3' @ '#sk7',
inference('sup-',[status(thm)],[zip_derived_cl333,zip_derived_cl7]) ).
thf(zip_derived_cl374,plain,
! [X0: $i] :
( ~ ( phi @ X0 )
| ~ ( rel_s5 @ '#sk2' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl367,zip_derived_cl341]) ).
thf(zip_derived_cl383,plain,
~ ( rel_s5 @ '#sk2' @ '#sk1' ),
inference('sup-',[status(thm)],[zip_derived_cl361,zip_derived_cl374]) ).
thf(zip_derived_cl354_025,plain,
rel_s5 @ '#sk2' @ '#sk1',
inference('sup-',[status(thm)],[zip_derived_cl346,zip_derived_cl7]) ).
thf(zip_derived_cl386,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl383,zip_derived_cl354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL725^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.04 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.y7zZaftcHb true
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 5 14:58:08 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Running portfolio for 300 s
% 0.12/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Number of cores: 8
% 0.12/0.38 % Python version: Python 3.12.3
% 0.12/0.38 % Running in HO mode
% 0.41/0.69 % Total configuration time : 828
% 0.41/0.69 % Estimated wc time : 1656
% 0.41/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.47/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.47/0.82 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.47/0.82 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.47/0.82 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.47/0.82 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.47/0.87 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.47/0.87 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.47/0.88 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.47/0.90 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 0.50/0.96 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 2.81/1.13 % Solved by lams/35_full_unif4.sh.
% 2.81/1.13 % done 114 iterations in 0.228s
% 2.81/1.13 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 2.81/1.13 % SZS output start Refutation
% See solution above
% 2.81/1.13
% 2.81/1.13
% 2.81/1.13 % Terminating...
% 2.27/1.21 % Runner terminated.
% 2.27/1.24 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------