TSTP Solution File: SYO446^1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO446^1 : 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.oxUQgrfJq0 true
% Computer : n031.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 2.48s 0.88s
% Output : Refutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 49
% Syntax : Number of formulae : 155 ( 45 unt; 19 typ; 0 def)
% Number of atoms : 932 ( 30 equ; 238 cnn)
% Maximal formula atoms : 46 ( 6 avg)
% Number of connectives : 2041 ( 436 ~; 357 |; 9 &;1114 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 89 ( 89 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 19 usr; 10 con; 0-3 aty)
% ( 110 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 272 ( 161 ^; 111 !; 0 ?; 272 :)
% 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 ).
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('#form4_type',type,
'#form4': $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf('#sk3_type',type,
'#sk3': $i ).
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 @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
~ ( ~ ( ~ ! [X18: $i] :
( ~ ( rel_s5 @ X4 @ X18 )
| ~ ( p @ X18 )
| ! [X20: $i] :
( ~ ( rel_s5 @ X18 @ X20 )
| ~ ( q @ X20 ) ) )
| ! [X14: $i] :
( ~ ( rel_s5 @ X4 @ X14 )
| ~ ( p @ X14 ) )
| ! [X16: $i] :
( ~ ( rel_s5 @ X4 @ X16 )
| ~ ( q @ X16 ) ) )
| ~ ( ~ ( ! [X12: $i] :
( ~ ( rel_s5 @ X4 @ X12 )
| ~ ( q @ X12 ) )
| ! [X10: $i] :
( ~ ( rel_s5 @ X4 @ X10 )
| ~ ( p @ X10 ) ) )
| ! [X6: $i] :
( ~ ( rel_s5 @ X4 @ X6 )
| ~ ( p @ X6 )
| ! [X8: $i] :
( ~ ( rel_s5 @ X6 @ X8 )
| ~ ( q @ X8 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
~ ( ~ ( ~ ! [X18: $i] :
( ~ ( rel_s5 @ X4 @ X18 )
| ~ ( p @ X18 )
| ! [X20: $i] :
( ~ ( rel_s5 @ X18 @ X20 )
| ~ ( q @ X20 ) ) )
| ! [X14: $i] :
( ~ ( rel_s5 @ X4 @ X14 )
| ~ ( p @ X14 ) )
| ! [X16: $i] :
( ~ ( rel_s5 @ X4 @ X16 )
| ~ ( q @ X16 ) ) )
| ~ ( ~ ( ! [X12: $i] :
( ~ ( rel_s5 @ X4 @ X12 )
| ~ ( q @ X12 ) )
| ! [X10: $i] :
( ~ ( rel_s5 @ X4 @ X10 )
| ~ ( p @ X10 ) ) )
| ! [X6: $i] :
( ~ ( rel_s5 @ X4 @ X6 )
| ~ ( p @ X6 )
| ! [X8: $i] :
( ~ ( rel_s5 @ X6 @ X8 )
| ~ ( q @ X8 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: $i] :
( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [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 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl25,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 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [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 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl26,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 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| ~ ( ( (~)
@ ( ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl28,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ~ ( ( (~)
@ ( ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl34,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ~ ( ( (~)
@ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| $true ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl35,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl36,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk2' ) )
| ( (~) @ ( p @ '#sk2' ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl42,plain,
( ( p @ '#sk2' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl29,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| ~ ( ( (~)
@ ( ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl37,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| ~ ( ( (~)
@ ( $true
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl38,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl39,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk3' ) )
| ( (~) @ ( q @ '#sk3' ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl43,plain,
( '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl48,plain,
( ~ '#form4'
| ( p @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl42,zip_derived_cl43]) ).
thf(zip_derived_cl43_001,plain,
( '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl44,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk5' ) )
| ( (~) @ ( p @ '#sk5' ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk5' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) ) )
| '#form4' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl53,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk5' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl55,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk5' @ '#sk6' ) )
| ( (~) @ ( q @ '#sk6' ) ) )
| '#form4' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl58,plain,
( ( q @ '#sk6' )
| '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl52,plain,
( ( p @ '#sk5' )
| '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl57,plain,
( ( rel_s5 @ '#sk5' @ '#sk6' )
| '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl27,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 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl30,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 ) ) ) ) ) )
| $false ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl31,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_cl30]) ).
thf(zip_derived_cl32,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 nested equalities',[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl33,plain,
! [X2: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ X2 ) )
| ( (~) @ ( p @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ X2 @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl40,plain,
! [X2: $i] :
( ~ ( rel_s5 @ '#sk1' @ X2 )
| ~ ( p @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ X2 @ Y0 ) )
| ( (~) @ ( q @ 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_cl33]) ).
thf(zip_derived_cl46,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s5 @ X2 @ X4 ) )
| ( (~) @ ( q @ X4 ) )
| ( !!
@ ^ [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_forall,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl54,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s5 @ X2 @ X4 )
| ~ ( q @ X4 )
| ~ ( 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_cl46]) ).
thf(zip_derived_cl56,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ~ ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ~ ( q @ X4 )
| ~ ( rel_s5 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl59,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ X6 ) )
| ( (~) @ ( q @ X6 ) )
| ~ ( rel_s5 @ X2 @ X4 )
| ~ ( q @ X4 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ~ ( p @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl60,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( rel_s5 @ '#sk1' @ X6 )
| ~ ( q @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) ) ) )
| ~ ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ~ ( q @ X4 )
| ~ ( rel_s5 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl61,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ X8 ) )
| ( (~) @ ( p @ X8 ) )
| ~ ( rel_s5 @ X2 @ X4 )
| ~ ( q @ X4 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ~ ( p @ X2 )
| ~ ( q @ X6 )
| ~ ( rel_s5 @ '#sk1' @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl62,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( rel_s5 @ '#sk1' @ X8 )
| ~ ( p @ X8 )
| ~ ( rel_s5 @ '#sk1' @ X6 )
| ~ ( q @ X6 )
| ~ ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ~ ( q @ X4 )
| ~ ( rel_s5 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl96,plain,
! [X0: $i,X1: $i] :
( '#form4'
| ~ ( q @ '#sk6' )
| ~ ( rel_s5 @ '#sk1' @ '#sk5' )
| ~ ( p @ '#sk5' )
| ~ ( q @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ~ ( p @ X1 )
| ~ ( rel_s5 @ '#sk1' @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl62]) ).
thf(zip_derived_cl58_002,plain,
( ( q @ '#sk6' )
| '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl374,plain,
! [X0: $i,X1: $i] :
( ~ ( rel_s5 @ '#sk1' @ X1 )
| ~ ( p @ X1 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ~ ( q @ X0 )
| ~ ( p @ '#sk5' )
| ~ ( rel_s5 @ '#sk1' @ '#sk5' )
| '#form4' ),
inference(clc,[status(thm)],[zip_derived_cl96,zip_derived_cl58]) ).
thf(zip_derived_cl52_003,plain,
( ( p @ '#sk5' )
| '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl375,plain,
! [X0: $i,X1: $i] :
( '#form4'
| ~ ( rel_s5 @ '#sk1' @ '#sk5' )
| ~ ( q @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ~ ( p @ X1 )
| ~ ( rel_s5 @ '#sk1' @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl374,zip_derived_cl52]) ).
thf(zip_derived_cl51,plain,
( ( rel_s5 @ '#sk1' @ '#sk5' )
| '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl376,plain,
! [X0: $i,X1: $i] :
( ~ ( rel_s5 @ '#sk1' @ X1 )
| ~ ( p @ X1 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ~ ( q @ X0 )
| '#form4' ),
inference(clc,[status(thm)],[zip_derived_cl375,zip_derived_cl51]) ).
thf(zip_derived_cl377,plain,
! [X0: $i] :
( '#form4'
| '#form4'
| ~ ( q @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ~ ( rel_s5 @ '#sk1' @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl52,zip_derived_cl376]) ).
thf(zip_derived_cl381,plain,
! [X0: $i] :
( ~ ( rel_s5 @ '#sk1' @ '#sk5' )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ~ ( q @ X0 )
| '#form4' ),
inference(simplify,[status(thm)],[zip_derived_cl377]) ).
thf(zip_derived_cl51_004,plain,
( ( rel_s5 @ '#sk1' @ '#sk5' )
| '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl389,plain,
! [X0: $i] :
( '#form4'
| ~ ( q @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl381,zip_derived_cl51]) ).
thf(zip_derived_cl392,plain,
( '#form4'
| ~ ( rel_s5 @ '#sk1' @ '#sk6' )
| '#form4' ),
inference('sup-',[status(thm)],[zip_derived_cl58,zip_derived_cl389]) ).
thf(zip_derived_cl398,plain,
( ~ ( rel_s5 @ '#sk1' @ '#sk6' )
| '#form4' ),
inference(simplify,[status(thm)],[zip_derived_cl392]) ).
thf(zip_derived_cl51_005,plain,
( ( rel_s5 @ '#sk1' @ '#sk5' )
| '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl57_006,plain,
( ( rel_s5 @ '#sk5' @ '#sk6' )
| '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl55]) ).
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_2,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_2]) ).
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_cl83,plain,
! [X0: $i] :
( '#form4'
| ( rel_s5 @ X0 @ '#sk6' )
| ~ ( rel_s5 @ X0 @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl16]) ).
thf(zip_derived_cl222,plain,
( '#form4'
| ( rel_s5 @ '#sk1' @ '#sk6' )
| '#form4' ),
inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl83]) ).
thf(zip_derived_cl228,plain,
( ( rel_s5 @ '#sk1' @ '#sk6' )
| '#form4' ),
inference(simplify,[status(thm)],[zip_derived_cl222]) ).
thf(zip_derived_cl402,plain,
'#form4',
inference(clc,[status(thm)],[zip_derived_cl398,zip_derived_cl228]) ).
thf(zip_derived_cl404,plain,
p @ '#sk2',
inference(demod,[status(thm)],[zip_derived_cl48,zip_derived_cl402]) ).
thf(zip_derived_cl39_007,plain,
( ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk3' ) )
| ( (~) @ ( q @ '#sk3' ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl43_008,plain,
( '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl45,plain,
( ~ '#form4'
| ~ ( ( (~) @ ( rel_s5 @ '#sk1' @ '#sk3' ) )
| ( (~) @ ( q @ '#sk3' ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl39,zip_derived_cl43]) ).
thf(zip_derived_cl50,plain,
( ( q @ '#sk3' )
| ~ '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl402_009,plain,
'#form4',
inference(clc,[status(thm)],[zip_derived_cl398,zip_derived_cl228]) ).
thf(zip_derived_cl406,plain,
q @ '#sk3',
inference(demod,[status(thm)],[zip_derived_cl50,zip_derived_cl402]) ).
thf(zip_derived_cl49,plain,
( ( rel_s5 @ '#sk1' @ '#sk3' )
| ~ '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).
thf(msymmetric,axiom,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ) ).
thf('18',plain,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[msymmetric]) ).
thf('19',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_cl68,plain,
( ~ '#form4'
| ( rel_s5 @ '#sk3' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl49,zip_derived_cl7]) ).
thf(zip_derived_cl41,plain,
( ( rel_s5 @ '#sk1' @ '#sk2' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl43_010,plain,
( '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s5 @ '#sk1' @ Y0 ) )
| ( (~) @ ( p @ Y0 ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s5 @ Y0 @ Y1 ) )
| ( (~) @ ( q @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl47,plain,
( ~ '#form4'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl41,zip_derived_cl43]) ).
thf(zip_derived_cl16_011,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_cl63,plain,
! [X0: $i] :
( ~ '#form4'
| ( rel_s5 @ X0 @ '#sk2' )
| ~ ( rel_s5 @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl47,zip_derived_cl16]) ).
thf(zip_derived_cl120,plain,
( ~ '#form4'
| ( rel_s5 @ '#sk3' @ '#sk2' )
| ~ '#form4' ),
inference('sup-',[status(thm)],[zip_derived_cl68,zip_derived_cl63]) ).
thf(zip_derived_cl127,plain,
( ( rel_s5 @ '#sk3' @ '#sk2' )
| ~ '#form4' ),
inference(simplify,[status(thm)],[zip_derived_cl120]) ).
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_cl133,plain,
( ~ '#form4'
| ( rel_s5 @ '#sk2' @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl127,zip_derived_cl7]) ).
thf(zip_derived_cl402_013,plain,
'#form4',
inference(clc,[status(thm)],[zip_derived_cl398,zip_derived_cl228]) ).
thf(zip_derived_cl415,plain,
rel_s5 @ '#sk2' @ '#sk3',
inference(demod,[status(thm)],[zip_derived_cl133,zip_derived_cl402]) ).
thf(zip_derived_cl62_014,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( rel_s5 @ '#sk1' @ X8 )
| ~ ( p @ X8 )
| ~ ( rel_s5 @ '#sk1' @ X6 )
| ~ ( q @ X6 )
| ~ ( p @ X2 )
| ~ ( rel_s5 @ '#sk1' @ X2 )
| ~ ( q @ X4 )
| ~ ( rel_s5 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl472,plain,
! [X0: $i,X1: $i] :
( ~ ( q @ '#sk3' )
| ~ ( rel_s5 @ '#sk1' @ '#sk2' )
| ~ ( p @ '#sk2' )
| ~ ( q @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ~ ( p @ X1 )
| ~ ( rel_s5 @ '#sk1' @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl415,zip_derived_cl62]) ).
thf(zip_derived_cl406_015,plain,
q @ '#sk3',
inference(demod,[status(thm)],[zip_derived_cl50,zip_derived_cl402]) ).
thf(zip_derived_cl47_016,plain,
( ~ '#form4'
| ( rel_s5 @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl41,zip_derived_cl43]) ).
thf(zip_derived_cl402_017,plain,
'#form4',
inference(clc,[status(thm)],[zip_derived_cl398,zip_derived_cl228]) ).
thf(zip_derived_cl403,plain,
rel_s5 @ '#sk1' @ '#sk2',
inference(demod,[status(thm)],[zip_derived_cl47,zip_derived_cl402]) ).
thf(zip_derived_cl404_018,plain,
p @ '#sk2',
inference(demod,[status(thm)],[zip_derived_cl48,zip_derived_cl402]) ).
thf(zip_derived_cl477,plain,
! [X0: $i,X1: $i] :
( ~ ( q @ X0 )
| ~ ( rel_s5 @ '#sk1' @ X0 )
| ~ ( p @ X1 )
| ~ ( rel_s5 @ '#sk1' @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl472,zip_derived_cl406,zip_derived_cl403,zip_derived_cl404]) ).
thf(zip_derived_cl531,plain,
! [X0: $i] :
( ~ ( rel_s5 @ '#sk1' @ X0 )
| ~ ( p @ X0 )
| ~ ( rel_s5 @ '#sk1' @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl406,zip_derived_cl477]) ).
thf(zip_derived_cl49_019,plain,
( ( rel_s5 @ '#sk1' @ '#sk3' )
| ~ '#form4' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl402_020,plain,
'#form4',
inference(clc,[status(thm)],[zip_derived_cl398,zip_derived_cl228]) ).
thf(zip_derived_cl405,plain,
rel_s5 @ '#sk1' @ '#sk3',
inference(demod,[status(thm)],[zip_derived_cl49,zip_derived_cl402]) ).
thf(zip_derived_cl533,plain,
! [X0: $i] :
( ~ ( rel_s5 @ '#sk1' @ X0 )
| ~ ( p @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl531,zip_derived_cl405]) ).
thf(zip_derived_cl536,plain,
~ ( rel_s5 @ '#sk1' @ '#sk2' ),
inference('sup-',[status(thm)],[zip_derived_cl404,zip_derived_cl533]) ).
thf(zip_derived_cl403_021,plain,
rel_s5 @ '#sk1' @ '#sk2',
inference(demod,[status(thm)],[zip_derived_cl47,zip_derived_cl402]) ).
thf(zip_derived_cl539,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl536,zip_derived_cl403]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SYO446^1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.oxUQgrfJq0 true
% 0.10/0.31 % Computer : n031.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Aug 26 07:32:37 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % Running portfolio for 300 s
% 0.10/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.31 % Number of cores: 8
% 0.10/0.31 % Python version: Python 3.6.8
% 0.10/0.31 % Running in HO mode
% 0.15/0.48 % Total configuration time : 828
% 0.15/0.48 % Estimated wc time : 1656
% 0.15/0.48 % Estimated cpu time (8 cpus) : 207.0
% 0.15/0.56 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.15/0.60 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.15/0.60 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.15/0.60 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.15/0.60 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.15/0.60 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.15/0.60 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.15/0.60 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.15/0.74 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 2.06/0.81 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 2.37/0.81 % /export/starexec/sandbox/solver/bin/lams/15_old_s4.sh running for 30s
% 2.48/0.88 % Solved by lams/35_full_unif4.sh.
% 2.48/0.88 % done 252 iterations in 0.207s
% 2.48/0.88 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 2.48/0.88 % SZS output start Refutation
% See solution above
% 2.48/0.88
% 2.48/0.88
% 2.48/0.88 % Terminating...
% 3.88/1.28 % Runner terminated.
% 3.88/1.28 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------