TSTP Solution File: SYO445^1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO445^1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Vve0aSyzXB true
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 05:51:12 EDT 2023
% Result : Theorem 1.71s 1.20s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 48
% Syntax : Number of formulae : 240 ( 48 unt; 18 typ; 0 def)
% Number of atoms : 1234 ( 30 equ; 247 cnn)
% Maximal formula atoms : 46 ( 5 avg)
% Number of connectives : 2809 ( 477 ~; 554 |; 9 &;1634 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 18 usr; 8 con; 0-3 aty)
% ( 120 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 320 ( 171 ^; 149 !; 0 ?; 320 :)
% Comments :
%------------------------------------------------------------------------------
thf(q_type,type,
q: $i > $o ).
thf(rel_s5_type,type,
rel_s5: $i > $i > $o ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk5_type',type,
'#sk5': $i > $i ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(p_type,type,
p: $i > $o ).
thf(mdia_s5_type,type,
mdia_s5: ( $i > $o ) > $i > $o ).
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(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf('#form3_type',type,
'#form3': $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(mequiv,axiom,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
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(mand,axiom,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
thf('12',plain,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand,'9','3']) ).
thf('13',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf('14',plain,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mequiv,'11','13','9','3']) ).
thf('15',plain,
( mequiv
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ ( mimplies @ V_1 @ V_2 ) @ ( mimplies @ V_2 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(prove,conjecture,
mvalid @ ( mequiv @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
~ ( ~ ( ~ ! [X20: $i] :
( ~ ( rel_s5 @ X4 @ X20 )
| ~ ( q @ X20 ) )
| ! [X18: $i] :
( ~ ( rel_s5 @ X4 @ X18 )
| ( p @ X18 ) )
| ~ ! [X14: $i] :
( ~ ( rel_s5 @ X4 @ X14 )
| ~ ! [X16: $i] :
( ~ ( rel_s5 @ X14 @ X16 )
| ~ ( q @ X16 ) )
| ( p @ X14 ) ) )
| ~ ( ! [X10: $i] :
( ~ ( rel_s5 @ X4 @ X10 )
| ~ ! [X12: $i] :
( ~ ( rel_s5 @ X10 @ X12 )
| ~ ( q @ X12 ) )
| ( p @ X10 ) )
| ~ ( ~ ! [X8: $i] :
( ~ ( rel_s5 @ X4 @ X8 )
| ~ ( q @ X8 ) )
| ! [X6: $i] :
( ~ ( rel_s5 @ X4 @ X6 )
| ( p @ X6 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
~ ( ~ ( ~ ! [X20: $i] :
( ~ ( rel_s5 @ X4 @ X20 )
| ~ ( q @ X20 ) )
| ! [X18: $i] :
( ~ ( rel_s5 @ X4 @ X18 )
| ( p @ X18 ) )
| ~ ! [X14: $i] :
( ~ ( rel_s5 @ X4 @ X14 )
| ~ ! [X16: $i] :
( ~ ( rel_s5 @ X14 @ X16 )
| ~ ( q @ X16 ) )
| ( p @ X14 ) ) )
| ~ ( ! [X10: $i] :
( ~ ( rel_s5 @ X4 @ X10 )
| ~ ! [X12: $i] :
( ~ ( rel_s5 @ X10 @ X12 )
| ~ ( q @ X12 ) )
| ( p @ X10 ) )
| ~ ( ~ ! [X8: $i] :
( ~ ( rel_s5 @ X4 @ X8 )
| ~ ( q @ X8 ) )
| ! [X6: $i] :
( ~ ( rel_s5 @ X4 @ X6 )
| ( p @ X6 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: $i] :
( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( (~) @ ( q @ Y2 ) ) ) ) )
| ( p @ Y1 ) ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( (~) @ ( q @ Y2 ) ) ) ) )
| ( p @ Y1 ) ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl13,plain,
( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl14,plain,
( ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl15,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl18,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) )
| ( (~)
@ ( ( (~) @ $false )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl19,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl20,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ X2 ) )
| ( (~) @ ( q @ X2 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl28,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk1' @ X2 )
| ~ ( q @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl28_001,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk1' @ X2 )
| ~ ( q @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl32,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl34,plain,
! [X2: $i] :
( ~ '#form3'
| ~ ( q @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl28,zip_derived_cl32]) ).
thf(zip_derived_cl32_002,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl33,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk4' ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk4' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( p @ '#sk4' ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl39,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk4' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl43,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk4' @ X2 ) )
| ( (~) @ ( q @ X2 ) )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl46,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk4' @ X2 )
| ~ ( q @ X2 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl46_003,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk4' @ X2 )
| ~ ( q @ X2 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl38,plain,
( ( rel_s5 @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl38_004,plain,
( ( rel_s5 @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl17,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl24,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) )
| ~ ( $false
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl25,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) )
| ~ ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl26,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl27,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ X2 ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ X2 @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( p @ X2 )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl31,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ X2 @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| ( p @ X2 )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl37,plain,
! [X2: $i] :
( ~ ( ( (~) @ ( rel_s5 @ X2 @ ( '#sk5' @ X2 ) ) )
| ( (~) @ ( q @ ( '#sk5' @ X2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl41,plain,
! [X2: $i] :
( ( rel_s5 @ X2 @ ( '#sk5' @ X2 ) )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( p @ X2 )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl44,plain,
! [X2: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( rel_s5 @ X2 @ ( '#sk5' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl47,plain,
! [X2: $i] :
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) ) )
| ( (~) @ ( q @ ( '#sk5' @ '#sk1' ) ) ) )
| ( rel_s5 @ X2 @ ( '#sk5' @ X2 ) )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( p @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl49,plain,
! [X2: $i] :
( ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( rel_s5 @ X2 @ ( '#sk5' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl53,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ X4 ) )
| ( p @ X4 )
| ( rel_s5 @ X2 @ ( '#sk5' @ X2 ) )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( p @ X2 )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl57,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ '#sk1' @ X4 )
| ( p @ X4 )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( rel_s5 @ X2 @ ( '#sk5' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl121,plain,
! [X0: $i] :
( '#form3'
| ( rel_s5 @ X0 @ ( '#sk5' @ X0 ) )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( p @ X0 )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl57]) ).
thf(zip_derived_cl40,plain,
( ~ ( p @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl360,plain,
! [X0: $i] :
( ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( rel_s5 @ X0 @ ( '#sk5' @ X0 ) )
| '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl121,zip_derived_cl40]) ).
thf(zip_derived_cl362,plain,
( '#form3'
| '#form3'
| ( rel_s5 @ '#sk4' @ ( '#sk5' @ '#sk4' ) )
| ( p @ '#sk4' )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl360]) ).
thf(zip_derived_cl369,plain,
( ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ '#sk4' )
| ( rel_s5 @ '#sk4' @ ( '#sk5' @ '#sk4' ) )
| '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl362]) ).
thf(zip_derived_cl40_005,plain,
( ~ ( p @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl755,plain,
( '#form3'
| ( rel_s5 @ '#sk4' @ ( '#sk5' @ '#sk4' ) )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl369,zip_derived_cl40]) ).
thf(zip_derived_cl770,plain,
( '#form3'
| ~ ( q @ ( '#sk5' @ '#sk4' ) )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl46,zip_derived_cl755]) ).
thf(zip_derived_cl786,plain,
( ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ~ ( q @ ( '#sk5' @ '#sk4' ) )
| '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl770]) ).
thf(zip_derived_cl46_006,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk4' @ X2 )
| ~ ( q @ X2 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl38_007,plain,
( ( rel_s5 @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl42,plain,
! [X2: $i] :
( ( q @ ( '#sk5' @ X2 ) )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( p @ X2 )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl45,plain,
! [X2: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( q @ ( '#sk5' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl48,plain,
! [X2: $i] :
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) ) )
| ( (~) @ ( q @ ( '#sk5' @ '#sk1' ) ) ) )
| ( q @ ( '#sk5' @ X2 ) )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( p @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl51,plain,
! [X2: $i] :
( ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( q @ ( '#sk5' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl55,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ X4 ) )
| ( p @ X4 )
| ( q @ ( '#sk5' @ X2 ) )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( p @ X2 )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl59,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ '#sk1' @ X4 )
| ( p @ X4 )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( q @ ( '#sk5' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl215,plain,
! [X0: $i] :
( ( q @ ( '#sk5' @ X0 ) )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( p @ X0 )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ X0 ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl217,plain,
! [X0: $i] :
( ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( q @ ( '#sk5' @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl215]) ).
thf(zip_derived_cl229,plain,
( '#form3'
| ( q @ ( '#sk5' @ '#sk4' ) )
| ( p @ '#sk4' )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl217]) ).
thf(zip_derived_cl40_008,plain,
( ~ ( p @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl570,plain,
( ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( q @ ( '#sk5' @ '#sk4' ) )
| '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl229,zip_derived_cl40]) ).
thf(msymmetric,axiom,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ) ).
thf('16',plain,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[msymmetric]) ).
thf('17',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_2,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_2]) ).
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_cl579,plain,
( '#form3'
| ( q @ ( '#sk5' @ '#sk4' ) )
| ( rel_s5 @ ( '#sk5' @ '#sk1' ) @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl570,zip_derived_cl7]) ).
thf(zip_derived_cl38_009,plain,
( ( rel_s5 @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(mtransitive,axiom,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ) ).
thf('18',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('19',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_3,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_3]) ).
thf(zip_derived_cl8,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_cl9,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_cl8]) ).
thf(zip_derived_cl10,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_cl9]) ).
thf(zip_derived_cl11,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_cl10]) ).
thf(zip_derived_cl12,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_cl11]) ).
thf(zip_derived_cl98,plain,
! [X0: $i] :
( '#form3'
| ( rel_s5 @ X0 @ '#sk4' )
| ~ ( rel_s5 @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl12]) ).
thf(zip_derived_cl595,plain,
( ( q @ ( '#sk5' @ '#sk4' ) )
| '#form3'
| ( rel_s5 @ ( '#sk5' @ '#sk1' ) @ '#sk4' )
| '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl579,zip_derived_cl98]) ).
thf(zip_derived_cl603,plain,
( ( rel_s5 @ ( '#sk5' @ '#sk1' ) @ '#sk4' )
| '#form3'
| ( q @ ( '#sk5' @ '#sk4' ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl595]) ).
thf(zip_derived_cl7_010,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_cl607,plain,
( ( q @ ( '#sk5' @ '#sk4' ) )
| '#form3'
| ( rel_s5 @ '#sk4' @ ( '#sk5' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl603,zip_derived_cl7]) ).
thf(zip_derived_cl673,plain,
( '#form3'
| ~ ( q @ ( '#sk5' @ '#sk1' ) )
| '#form3'
| ( q @ ( '#sk5' @ '#sk4' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl46,zip_derived_cl607]) ).
thf(zip_derived_cl678,plain,
( ( q @ ( '#sk5' @ '#sk4' ) )
| ~ ( q @ ( '#sk5' @ '#sk1' ) )
| '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl673]) ).
thf(zip_derived_cl52,plain,
! [X2: $i] :
( ( q @ ( '#sk5' @ '#sk1' ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( q @ ( '#sk5' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl56,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ X4 ) )
| ( p @ X4 )
| ( q @ ( '#sk5' @ X2 ) )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( p @ X2 )
| ( q @ ( '#sk5' @ '#sk1' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl60,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ '#sk1' @ X4 )
| ( p @ X4 )
| ( q @ ( '#sk5' @ '#sk1' ) )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( q @ ( '#sk5' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl292,plain,
! [X0: $i] :
( ( q @ ( '#sk5' @ X0 ) )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( p @ X0 )
| ( q @ ( '#sk5' @ '#sk1' ) )
| ( p @ X0 ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl293,plain,
! [X0: $i] :
( ( q @ ( '#sk5' @ '#sk1' ) )
| ( p @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( q @ ( '#sk5' @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl292]) ).
thf(zip_derived_cl38_011,plain,
( ( rel_s5 @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl310,plain,
( ( q @ ( '#sk5' @ '#sk4' ) )
| ( p @ '#sk4' )
| ( q @ ( '#sk5' @ '#sk1' ) )
| '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl293,zip_derived_cl38]) ).
thf(zip_derived_cl40_012,plain,
( ~ ( p @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl564,plain,
( '#form3'
| ( q @ ( '#sk5' @ '#sk1' ) )
| ( q @ ( '#sk5' @ '#sk4' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl310,zip_derived_cl40]) ).
thf(zip_derived_cl682,plain,
( '#form3'
| ( q @ ( '#sk5' @ '#sk4' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl678,zip_derived_cl564]) ).
thf(zip_derived_cl792,plain,
( '#form3'
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl786,zip_derived_cl682]) ).
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_cl800,plain,
( '#form3'
| ( rel_s5 @ ( '#sk5' @ '#sk1' ) @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl792,zip_derived_cl7]) ).
thf(zip_derived_cl98_014,plain,
! [X0: $i] :
( '#form3'
| ( rel_s5 @ X0 @ '#sk4' )
| ~ ( rel_s5 @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl12]) ).
thf(zip_derived_cl813,plain,
( '#form3'
| ( rel_s5 @ ( '#sk5' @ '#sk1' ) @ '#sk4' )
| '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl800,zip_derived_cl98]) ).
thf(zip_derived_cl821,plain,
( ( rel_s5 @ ( '#sk5' @ '#sk1' ) @ '#sk4' )
| '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl813]) ).
thf(zip_derived_cl7_015,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_cl825,plain,
( '#form3'
| ( rel_s5 @ '#sk4' @ ( '#sk5' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl821,zip_derived_cl7]) ).
thf(zip_derived_cl834,plain,
( '#form3'
| ~ ( q @ ( '#sk5' @ '#sk1' ) )
| '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl46,zip_derived_cl825]) ).
thf(zip_derived_cl839,plain,
( ~ ( q @ ( '#sk5' @ '#sk1' ) )
| '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl834]) ).
thf(zip_derived_cl46_016,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk4' @ X2 )
| ~ ( q @ X2 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl38_017,plain,
( ( rel_s5 @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl50,plain,
! [X2: $i] :
( ( q @ ( '#sk5' @ '#sk1' ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( rel_s5 @ X2 @ ( '#sk5' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl54,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ X4 ) )
| ( p @ X4 )
| ( rel_s5 @ X2 @ ( '#sk5' @ X2 ) )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( p @ X2 )
| ( q @ ( '#sk5' @ '#sk1' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl58,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ '#sk1' @ X4 )
| ( p @ X4 )
| ( q @ ( '#sk5' @ '#sk1' ) )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( rel_s5 @ X2 @ ( '#sk5' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl152,plain,
! [X0: $i] :
( '#form3'
| ( rel_s5 @ X0 @ ( '#sk5' @ X0 ) )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( p @ X0 )
| ( q @ ( '#sk5' @ '#sk1' ) )
| ( p @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl58]) ).
thf(zip_derived_cl40_018,plain,
( ~ ( p @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl613,plain,
! [X0: $i] :
( ( q @ ( '#sk5' @ '#sk1' ) )
| ( p @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( rel_s5 @ X0 @ ( '#sk5' @ X0 ) )
| '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl152,zip_derived_cl40]) ).
thf(zip_derived_cl624,plain,
( '#form3'
| ~ ( q @ ( '#sk5' @ '#sk4' ) )
| '#form3'
| ~ ( rel_s5 @ '#sk1' @ '#sk4' )
| ( p @ '#sk4' )
| ( q @ ( '#sk5' @ '#sk1' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl46,zip_derived_cl613]) ).
thf(zip_derived_cl640,plain,
( ( q @ ( '#sk5' @ '#sk1' ) )
| ( p @ '#sk4' )
| ~ ( rel_s5 @ '#sk1' @ '#sk4' )
| ~ ( q @ ( '#sk5' @ '#sk4' ) )
| '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl624]) ).
thf(zip_derived_cl40_019,plain,
( ~ ( p @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl688,plain,
( '#form3'
| ~ ( q @ ( '#sk5' @ '#sk4' ) )
| ~ ( rel_s5 @ '#sk1' @ '#sk4' )
| ( q @ ( '#sk5' @ '#sk1' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl640,zip_derived_cl40]) ).
thf(zip_derived_cl682_020,plain,
( '#form3'
| ( q @ ( '#sk5' @ '#sk4' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl678,zip_derived_cl564]) ).
thf(zip_derived_cl689,plain,
( ( q @ ( '#sk5' @ '#sk1' ) )
| ~ ( rel_s5 @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl688,zip_derived_cl682]) ).
thf(zip_derived_cl38_021,plain,
( ( rel_s5 @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl690,plain,
( '#form3'
| ( q @ ( '#sk5' @ '#sk1' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl689,zip_derived_cl38]) ).
thf(zip_derived_cl843,plain,
'#form3',
inference(clc,[status(thm)],[zip_derived_cl839,zip_derived_cl690]) ).
thf(zip_derived_cl844,plain,
! [X2: $i] :
( ~ ( q @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl34,zip_derived_cl843]) ).
thf(zip_derived_cl16,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl21,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| $true ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl22,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( p @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl23,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk2' ) )
| ( p @ '#sk2' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl29,plain,
( ( rel_s5 @ '#sk1' @ '#sk2' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl32_022,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl35,plain,
( ~ '#form3'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl29,zip_derived_cl32]) ).
thf(zip_derived_cl843_023,plain,
'#form3',
inference(clc,[status(thm)],[zip_derived_cl839,zip_derived_cl690]) ).
thf(zip_derived_cl845,plain,
rel_s5 @ '#sk1' @ '#sk2',
inference(demod,[status(thm)],[zip_derived_cl35,zip_derived_cl843]) ).
thf(zip_derived_cl58_024,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ '#sk1' @ X4 )
| ( p @ X4 )
| ( q @ ( '#sk5' @ '#sk1' ) )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( rel_s5 @ X2 @ ( '#sk5' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl844_025,plain,
! [X2: $i] :
( ~ ( q @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl34,zip_derived_cl843]) ).
thf(zip_derived_cl35_026,plain,
( ~ '#form3'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl29,zip_derived_cl32]) ).
thf(zip_derived_cl35_027,plain,
( ~ '#form3'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl29,zip_derived_cl32]) ).
thf(zip_derived_cl57_028,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ '#sk1' @ X4 )
| ( p @ X4 )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( rel_s5 @ X2 @ ( '#sk5' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl122,plain,
! [X0: $i] :
( ~ '#form3'
| ( rel_s5 @ X0 @ ( '#sk5' @ X0 ) )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( p @ X0 )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl57]) ).
thf(zip_derived_cl360_029,plain,
! [X0: $i] :
( ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( rel_s5 @ X0 @ ( '#sk5' @ X0 ) )
| '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl121,zip_derived_cl40]) ).
thf(zip_derived_cl427,plain,
! [X0: $i] :
( ( p @ '#sk2' )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( rel_s5 @ X0 @ ( '#sk5' @ X0 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl122,zip_derived_cl360]) ).
thf(zip_derived_cl430,plain,
( ~ '#form3'
| ( rel_s5 @ '#sk2' @ ( '#sk5' @ '#sk2' ) )
| ( p @ '#sk2' )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl427]) ).
thf(zip_derived_cl436,plain,
( ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ '#sk2' )
| ( rel_s5 @ '#sk2' @ ( '#sk5' @ '#sk2' ) )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl430]) ).
thf(zip_derived_cl30,plain,
( ~ ( p @ '#sk2' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl32_030,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) )
| ( p @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl36,plain,
( ~ '#form3'
| ~ ( p @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl30,zip_derived_cl32]) ).
thf(zip_derived_cl843_031,plain,
'#form3',
inference(clc,[status(thm)],[zip_derived_cl839,zip_derived_cl690]) ).
thf(zip_derived_cl846,plain,
~ ( p @ '#sk2' ),
inference(demod,[status(thm)],[zip_derived_cl36,zip_derived_cl843]) ).
thf(zip_derived_cl843_032,plain,
'#form3',
inference(clc,[status(thm)],[zip_derived_cl839,zip_derived_cl690]) ).
thf(zip_derived_cl924,plain,
( ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( rel_s5 @ '#sk2' @ ( '#sk5' @ '#sk2' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl436,zip_derived_cl846,zip_derived_cl843]) ).
thf(zip_derived_cl844_033,plain,
! [X2: $i] :
( ~ ( q @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl34,zip_derived_cl843]) ).
thf(zip_derived_cl931,plain,
( ( rel_s5 @ '#sk2' @ ( '#sk5' @ '#sk2' ) )
| ~ ( q @ ( '#sk5' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl924,zip_derived_cl844]) ).
thf(zip_derived_cl7_034,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_cl948,plain,
( ~ ( q @ ( '#sk5' @ '#sk1' ) )
| ( rel_s5 @ ( '#sk5' @ '#sk2' ) @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl931,zip_derived_cl7]) ).
thf(zip_derived_cl35_035,plain,
( ~ '#form3'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl29,zip_derived_cl32]) ).
thf(zip_derived_cl7_036,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_cl74,plain,
( ~ '#form3'
| ( rel_s5 @ '#sk2' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl7]) ).
thf(zip_derived_cl12_037,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_cl11]) ).
thf(zip_derived_cl85,plain,
! [X0: $i] :
( ~ '#form3'
| ( rel_s5 @ X0 @ '#sk1' )
| ~ ( rel_s5 @ X0 @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl74,zip_derived_cl12]) ).
thf(zip_derived_cl843_038,plain,
'#form3',
inference(clc,[status(thm)],[zip_derived_cl839,zip_derived_cl690]) ).
thf(zip_derived_cl849,plain,
! [X0: $i] :
( ( rel_s5 @ X0 @ '#sk1' )
| ~ ( rel_s5 @ X0 @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl85,zip_derived_cl843]) ).
thf(zip_derived_cl951,plain,
( ~ ( q @ ( '#sk5' @ '#sk1' ) )
| ( rel_s5 @ ( '#sk5' @ '#sk2' ) @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl948,zip_derived_cl849]) ).
thf(zip_derived_cl7_039,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_cl959,plain,
( ~ ( q @ ( '#sk5' @ '#sk1' ) )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl951,zip_derived_cl7]) ).
thf(zip_derived_cl975,plain,
( ~ ( q @ ( '#sk5' @ '#sk2' ) )
| ~ ( q @ ( '#sk5' @ '#sk1' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl844,zip_derived_cl959]) ).
thf(zip_derived_cl293_040,plain,
! [X0: $i] :
( ( q @ ( '#sk5' @ '#sk1' ) )
| ( p @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( q @ ( '#sk5' @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl292]) ).
thf(zip_derived_cl35_041,plain,
( ~ '#form3'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl29,zip_derived_cl32]) ).
thf(zip_derived_cl311,plain,
( ( q @ ( '#sk5' @ '#sk2' ) )
| ( p @ '#sk2' )
| ( q @ ( '#sk5' @ '#sk1' ) )
| ~ '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl293,zip_derived_cl35]) ).
thf(zip_derived_cl36_042,plain,
( ~ '#form3'
| ~ ( p @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl30,zip_derived_cl32]) ).
thf(zip_derived_cl555,plain,
( ~ '#form3'
| ( q @ ( '#sk5' @ '#sk1' ) )
| ( q @ ( '#sk5' @ '#sk2' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl311,zip_derived_cl36]) ).
thf(zip_derived_cl34_043,plain,
! [X2: $i] :
( ~ '#form3'
| ~ ( q @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl28,zip_derived_cl32]) ).
thf(zip_derived_cl35_044,plain,
( ~ '#form3'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl29,zip_derived_cl32]) ).
thf(zip_derived_cl217_045,plain,
! [X0: $i] :
( ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( p @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( q @ ( '#sk5' @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl215]) ).
thf(zip_derived_cl230,plain,
( ~ '#form3'
| ( q @ ( '#sk5' @ '#sk2' ) )
| ( p @ '#sk2' )
| ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl217]) ).
thf(zip_derived_cl36_046,plain,
( ~ '#form3'
| ~ ( p @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl30,zip_derived_cl32]) ).
thf(zip_derived_cl267,plain,
( ( rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk1' ) )
| ( q @ ( '#sk5' @ '#sk2' ) )
| ~ '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl230,zip_derived_cl36]) ).
thf(zip_derived_cl274,plain,
( ~ ( q @ ( '#sk5' @ '#sk1' ) )
| ~ '#form3'
| ~ '#form3'
| ( q @ ( '#sk5' @ '#sk2' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl34,zip_derived_cl267]) ).
thf(zip_derived_cl282,plain,
( ( q @ ( '#sk5' @ '#sk2' ) )
| ~ '#form3'
| ~ ( q @ ( '#sk5' @ '#sk1' ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl274]) ).
thf(zip_derived_cl556,plain,
( ( q @ ( '#sk5' @ '#sk2' ) )
| ~ '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl555,zip_derived_cl282]) ).
thf(zip_derived_cl843_047,plain,
'#form3',
inference(clc,[status(thm)],[zip_derived_cl839,zip_derived_cl690]) ).
thf(zip_derived_cl851,plain,
q @ ( '#sk5' @ '#sk2' ),
inference(demod,[status(thm)],[zip_derived_cl556,zip_derived_cl843]) ).
thf(zip_derived_cl985,plain,
~ ( q @ ( '#sk5' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl975,zip_derived_cl851]) ).
thf(zip_derived_cl989,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ '#sk1' @ X4 )
| ( p @ X4 )
| ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ( rel_s5 @ X2 @ ( '#sk5' @ X2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl58,zip_derived_cl985]) ).
thf(zip_derived_cl1028,plain,
! [X0: $i] :
( ( rel_s5 @ X0 @ ( '#sk5' @ X0 ) )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( p @ X0 )
| ( p @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl845,zip_derived_cl989]) ).
thf(zip_derived_cl846_048,plain,
~ ( p @ '#sk2' ),
inference(demod,[status(thm)],[zip_derived_cl36,zip_derived_cl843]) ).
thf(zip_derived_cl1035,plain,
! [X0: $i] :
( ( rel_s5 @ X0 @ ( '#sk5' @ X0 ) )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( p @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1028,zip_derived_cl846]) ).
thf(zip_derived_cl7_049,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_cl1044,plain,
! [X0: $i] :
( ( p @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ( rel_s5 @ ( '#sk5' @ X0 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1035,zip_derived_cl7]) ).
thf(zip_derived_cl849_050,plain,
! [X0: $i] :
( ( rel_s5 @ X0 @ '#sk1' )
| ~ ( rel_s5 @ X0 @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl85,zip_derived_cl843]) ).
thf(zip_derived_cl1065,plain,
( ~ ( rel_s5 @ '#sk1' @ '#sk2' )
| ( p @ '#sk2' )
| ( rel_s5 @ ( '#sk5' @ '#sk2' ) @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1044,zip_derived_cl849]) ).
thf(zip_derived_cl845_051,plain,
rel_s5 @ '#sk1' @ '#sk2',
inference(demod,[status(thm)],[zip_derived_cl35,zip_derived_cl843]) ).
thf(zip_derived_cl846_052,plain,
~ ( p @ '#sk2' ),
inference(demod,[status(thm)],[zip_derived_cl36,zip_derived_cl843]) ).
thf(zip_derived_cl1073,plain,
rel_s5 @ ( '#sk5' @ '#sk2' ) @ '#sk1',
inference(demod,[status(thm)],[zip_derived_cl1065,zip_derived_cl845,zip_derived_cl846]) ).
thf(zip_derived_cl7_053,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_cl1079,plain,
rel_s5 @ '#sk1' @ ( '#sk5' @ '#sk2' ),
inference('sup-',[status(thm)],[zip_derived_cl1073,zip_derived_cl7]) ).
thf(zip_derived_cl1094,plain,
~ ( q @ ( '#sk5' @ '#sk2' ) ),
inference('sup+',[status(thm)],[zip_derived_cl844,zip_derived_cl1079]) ).
thf(zip_derived_cl851_054,plain,
q @ ( '#sk5' @ '#sk2' ),
inference(demod,[status(thm)],[zip_derived_cl556,zip_derived_cl843]) ).
thf(zip_derived_cl1101,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl1094,zip_derived_cl851]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15 % Problem : SYO445^1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.16 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Vve0aSyzXB true
% 0.16/0.37 % Computer : n022.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sat Aug 26 02:31:10 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.16/0.37 % Running portfolio for 300 s
% 0.16/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.37 % Number of cores: 8
% 0.16/0.38 % Python version: Python 3.6.8
% 0.16/0.38 % Running in HO mode
% 0.24/0.71 % Total configuration time : 828
% 0.24/0.71 % Estimated wc time : 1656
% 0.24/0.71 % Estimated cpu time (8 cpus) : 207.0
% 1.16/0.79 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.51/0.82 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.51/0.82 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.51/0.83 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.51/0.83 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.51/0.83 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.51/0.83 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.51/0.85 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.65/0.91 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.65/0.93 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 1.71/1.20 % Solved by lams/30_sp5.sh.
% 1.71/1.20 % done 280 iterations in 0.251s
% 1.71/1.20 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.71/1.20 % SZS output start Refutation
% See solution above
% 1.99/1.20
% 1.99/1.20
% 1.99/1.20 % Terminating...
% 2.20/1.38 % Runner terminated.
% 2.20/1.42 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------