TSTP Solution File: SYO447^1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO447^1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.3dCOgm95m1 true
% Computer : n011.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 05:51:13 EDT 2023
% Result : Theorem 5.17s 1.27s
% Output : Refutation 5.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 50
% Syntax : Number of formulae : 148 ( 39 unt; 19 typ; 0 def)
% Number of atoms : 846 ( 30 equ; 225 cnn)
% Maximal formula atoms : 46 ( 6 avg)
% Number of connectives : 1765 ( 375 ~; 293 |; 12 &; 965 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 19 usr; 9 con; 0-3 aty)
% ( 100 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 228 ( 151 ^; 77 !; 0 ?; 228 :)
% 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 ).
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('#sk6_type',type,
'#sk6': $i > $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(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 @ ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mdia_s5 @ ( mand @ p @ ( mbox_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 )
| ~ ( p @ X14 )
| ~ ! [X16: $i] :
( ~ ( rel_s5 @ X14 @ X16 )
| ( q @ X16 ) ) ) )
| ~ ( ~ ! [X10: $i] :
( ~ ( rel_s5 @ X4 @ X10 )
| ~ ( p @ X10 )
| ~ ! [X12: $i] :
( ~ ( rel_s5 @ X10 @ X12 )
| ( q @ X12 ) ) )
| ! [X6: $i] :
( ~ ( rel_s5 @ X4 @ X6 )
| ~ ( p @ X6 ) )
| ~ ! [X8: $i] :
( ~ ( rel_s5 @ X4 @ X8 )
| ( q @ X8 ) ) ) ) ).
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 )
| ~ ( p @ X14 )
| ~ ! [X16: $i] :
( ~ ( rel_s5 @ X14 @ X16 )
| ( q @ X16 ) ) ) )
| ~ ( ~ ! [X10: $i] :
( ~ ( rel_s5 @ X4 @ X10 )
| ~ ( p @ X10 )
| ~ ! [X12: $i] :
( ~ ( rel_s5 @ X10 @ X12 )
| ( q @ X12 ) ) )
| ! [X6: $i] :
( ~ ( rel_s5 @ X4 @ X6 )
| ~ ( p @ X6 ) )
| ~ ! [X8: $i] :
( ~ ( rel_s5 @ X4 @ X8 )
| ( q @ X8 ) ) ) ),
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 ) )
| ( (~) @ ( p @ Y1 ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( q @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( p @ Y1 ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s5 @ Y1 @ Y2 ) )
| ( q @ Y2 ) ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( p @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl4,plain,
( ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl11,plain,
( ~ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) ) )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl13,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl14,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ~ ( ( (~) @ $true )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl15,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl16,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk2' ) )
| ( (~) @ ( p @ '#sk2' ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( q @ 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_cl15]) ).
thf(zip_derived_cl17,plain,
( '#form3'
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl19,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl58,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk4' ) )
| ( (~) @ ( p @ '#sk4' ) ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl339,plain,
( ( rel_s5 @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl12,plain,
( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl12_001,plain,
( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl82,plain,
( ~ '#form3'
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl17_002,plain,
( '#form3'
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl84,plain,
( '#form3'
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl12,zip_derived_cl82,zip_derived_cl17]) ).
thf(zip_derived_cl210,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl287,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ X2 ) )
| ( (~) @ ( p @ X2 ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ X2 @ Y0 ) )
| ( q @ Y0 ) ) ) )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl210]) ).
thf(zip_derived_cl444,plain,
( ( (~) @ $true )
| ( (~) @ ( p @ '#sk4' ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) ) )
| '#form3'
| '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl339,zip_derived_cl287]) ).
thf(zip_derived_cl456,plain,
( '#form3'
| ( (~) @ $true )
| ( (~) @ ( p @ '#sk4' ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl444]) ).
thf(zip_derived_cl457,plain,
( '#form3'
| ( (~) @ ( p @ '#sk4' ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl456]) ).
thf(zip_derived_cl478,plain,
( ~ ( p @ '#sk4' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl457]) ).
thf(zip_derived_cl340,plain,
( ( p @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl486,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl478,zip_derived_cl340]) ).
thf(zip_derived_cl16_003,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk2' ) )
| ( (~) @ ( p @ '#sk2' ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( q @ 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_cl15]) ).
thf(zip_derived_cl17_004,plain,
( '#form3'
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl20,plain,
( ~ '#form3'
| ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk2' ) )
| ( (~) @ ( p @ '#sk2' ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl59,plain,
( ( rel_s5 @ '#sk1' @ '#sk2' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl82_005,plain,
( ~ '#form3'
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl83,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl85,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk5' ) )
| ( q @ '#sk5' ) )
| ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl166,plain,
( ( rel_s5 @ '#sk1' @ '#sk5' )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl200,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ X2 ) )
| ( (~) @ ( p @ X2 ) )
| ~ '#form3'
| ( rel_s5 @ '#sk1' @ '#sk5' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl166]) ).
thf(zip_derived_cl61,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl20_006,plain,
( ~ '#form3'
| ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk2' ) )
| ( (~) @ ( p @ '#sk2' ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl16,zip_derived_cl17]) ).
thf(zip_derived_cl62,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk2' ) )
| ( (~) @ ( p @ '#sk2' ) )
| ( (~) @ $true ) )
| ~ '#form3'
| ~ '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl20]) ).
thf(zip_derived_cl64,plain,
( ~ '#form3'
| ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk2' ) )
| ( (~) @ ( p @ '#sk2' ) )
| ( (~) @ $true ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl65,plain,
( ~ '#form3'
| ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk2' ) )
| ( (~) @ ( p @ '#sk2' ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl808,plain,
( ( rel_s5 @ '#sk1' @ '#sk5' )
| ~ '#form3'
| ~ '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl200,zip_derived_cl65]) ).
thf(zip_derived_cl843,plain,
( ~ '#form3'
| ( rel_s5 @ '#sk1' @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl808]) ).
thf(zip_derived_cl59_007,plain,
( ( rel_s5 @ '#sk1' @ '#sk2' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).
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_cl6,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_cl8,plain,
! [X2: $i,X4: $i] :
( ( rel_s5 @ X2 @ X4 )
=> ( rel_s5 @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ X2 @ X4 )
| ( rel_s5 @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl94,plain,
( ~ '#form3'
| ( rel_s5 @ '#sk2' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl59,zip_derived_cl30]) ).
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_cl7,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_cl7]) ).
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_cl172,plain,
! [X0: $i] :
( ( ( ( rel_s5 @ '#sk1' @ X0 )
& $true )
=> ( rel_s5 @ '#sk2' @ X0 ) )
| ~ '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl94,zip_derived_cl10]) ).
thf(zip_derived_cl183,plain,
! [X0: $i] :
( ( ( rel_s5 @ '#sk1' @ X0 )
=> ( rel_s5 @ '#sk2' @ X0 ) )
| ~ '#form3' ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl172]) ).
thf(zip_derived_cl1033,plain,
( ( $true
=> ( rel_s5 @ '#sk2' @ '#sk5' ) )
| ~ '#form3'
| ~ '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl843,zip_derived_cl183]) ).
thf(zip_derived_cl1062,plain,
( ~ '#form3'
| ( $true
=> ( rel_s5 @ '#sk2' @ '#sk5' ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1033]) ).
thf(zip_derived_cl1063,plain,
( ~ '#form3'
| ( rel_s5 @ '#sk2' @ '#sk5' ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl1062]) ).
thf(zip_derived_cl61_008,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl63,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk2' @ X2 ) )
| ( q @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl216,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk2' @ X2 )
| ( q @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl1212,plain,
( ~ '#form3'
| ~ '#form3'
| ( q @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1063,zip_derived_cl216]) ).
thf(zip_derived_cl1240,plain,
( ( q @ '#sk5' )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl1212]) ).
thf(zip_derived_cl167,plain,
( ~ ( q @ '#sk5' )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl191,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ X2 ) )
| ( (~) @ ( p @ X2 ) )
| ~ '#form3'
| ~ ( q @ '#sk5' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl167]) ).
thf(zip_derived_cl778,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk1' @ X2 )
| ~ ( p @ X2 )
| ~ ( q @ '#sk5' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl191]) ).
thf(zip_derived_cl1270,plain,
! [X0: $i] :
( ~ '#form3'
| ~ '#form3'
| ~ ( p @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1240,zip_derived_cl778]) ).
thf(zip_derived_cl1286,plain,
! [X0: $i] :
( ~ ( rel_s5 @ '#sk1' @ X0 )
| ~ ( p @ X0 )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl1270]) ).
thf(zip_derived_cl1308,plain,
( ~ '#form3'
| ~ '#form3'
| ~ ( p @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl59,zip_derived_cl1286]) ).
thf(zip_derived_cl1316,plain,
( ~ ( p @ '#sk2' )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl1308]) ).
thf(zip_derived_cl60,plain,
( ( p @ '#sk2' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl1326,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl1316,zip_derived_cl60]) ).
thf(zip_derived_cl1347,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl486,zip_derived_cl1326]) ).
thf(zip_derived_cl1352,plain,
~ ( ( (~) @ ( rel_s5 @ '#sk4' @ ( '#sk6' @ '#sk4' ) ) )
| ( q @ ( '#sk6' @ '#sk4' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1347]) ).
thf(zip_derived_cl1411,plain,
~ ( q @ ( '#sk6' @ '#sk4' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl1352]) ).
thf(zip_derived_cl1352_009,plain,
~ ( ( (~) @ ( rel_s5 @ '#sk4' @ ( '#sk6' @ '#sk4' ) ) )
| ( q @ ( '#sk6' @ '#sk4' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1347]) ).
thf(zip_derived_cl1411_010,plain,
~ ( q @ ( '#sk6' @ '#sk4' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl1352]) ).
thf(zip_derived_cl1412,plain,
~ ( ( (~) @ ( rel_s5 @ '#sk4' @ ( '#sk6' @ '#sk4' ) ) )
| $false ),
inference(demod,[status(thm)],[zip_derived_cl1352,zip_derived_cl1411]) ).
thf(zip_derived_cl1413,plain,
~ ( (~) @ ( rel_s5 @ '#sk4' @ ( '#sk6' @ '#sk4' ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl1412]) ).
thf(zip_derived_cl1414,plain,
rel_s5 @ '#sk4' @ ( '#sk6' @ '#sk4' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl1413]) ).
thf(zip_derived_cl339_011,plain,
( ( rel_s5 @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl10_012,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_cl44,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_cl361,plain,
! [X0: $i] :
( ~ ( ( rel_s5 @ '#sk4' @ X0 )
& $true )
| '#form3'
| ( rel_s5 @ '#sk1' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl339,zip_derived_cl44]) ).
thf(zip_derived_cl386,plain,
! [X0: $i] :
( ~ ( rel_s5 @ '#sk4' @ X0 )
| '#form3'
| ( rel_s5 @ '#sk1' @ X0 ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl361]) ).
thf(zip_derived_cl1326_013,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl1316,zip_derived_cl60]) ).
thf(zip_derived_cl1529,plain,
! [X0: $i] :
( ~ ( rel_s5 @ '#sk4' @ X0 )
| ( rel_s5 @ '#sk1' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl386,zip_derived_cl1326]) ).
thf(zip_derived_cl1575,plain,
rel_s5 @ '#sk1' @ ( '#sk6' @ '#sk4' ),
inference('sup-',[status(thm)],[zip_derived_cl1414,zip_derived_cl1529]) ).
thf(zip_derived_cl18,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( q @ Y0 ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl24,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ X2 ) )
| ( q @ X2 )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl144,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk1' @ X2 )
| ( q @ X2 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl1326_014,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl1316,zip_derived_cl60]) ).
thf(zip_derived_cl1334,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk1' @ X2 )
| ( q @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl144,zip_derived_cl1326]) ).
thf(zip_derived_cl1620,plain,
q @ ( '#sk6' @ '#sk4' ),
inference('sup-',[status(thm)],[zip_derived_cl1575,zip_derived_cl1334]) ).
thf(zip_derived_cl1662,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl1411,zip_derived_cl1620]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO447^1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.3dCOgm95m1 true
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 04:48:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.20/0.68 % Total configuration time : 828
% 0.20/0.68 % Estimated wc time : 1656
% 0.20/0.68 % Estimated cpu time (8 cpus) : 207.0
% 1.01/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 1.01/0.76 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.01/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.01/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.01/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.01/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.01/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.01/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.46/0.85 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.46/0.87 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 5.17/1.27 % Solved by lams/35_full_unif.sh.
% 5.17/1.27 % done 326 iterations in 0.329s
% 5.17/1.27 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 5.17/1.27 % SZS output start Refutation
% See solution above
% 5.17/1.28
% 5.17/1.28
% 5.17/1.28 % Terminating...
% 5.31/1.39 % Runner terminated.
% 5.33/1.40 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------