TSTP Solution File: SYN045^7 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYN045^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ZobRGlaF2A true
% Computer : n029.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 04:01:18 EDT 2023
% Result : Theorem 1.46s 0.94s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 43
% Syntax : Number of formulae : 160 ( 34 unt; 21 typ; 0 def)
% Number of atoms : 1447 ( 18 equ; 381 cnn)
% Maximal formula atoms : 78 ( 10 avg)
% Number of connectives : 3131 ( 618 ~; 627 |; 0 &;1662 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 21 usr; 15 con; 0-3 aty)
% ( 224 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 339 ( 260 ^; 79 !; 0 ?; 339 :)
% Comments :
%------------------------------------------------------------------------------
thf('#sk4_type',type,
'#sk4': $i ).
thf(r_type,type,
r: $i > $o ).
thf('#sk7_type',type,
'#sk7': $i ).
thf(rel_s4_type,type,
rel_s4: $i > $i > $o ).
thf('#form10_type',type,
'#form10': $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#form3_type',type,
'#form3': $o ).
thf('#sk5_type',type,
'#sk5': $i ).
thf('#sk8_type',type,
'#sk8': $i ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(p_type,type,
p: $i > $o ).
thf('#sk9_type',type,
'#sk9': $i ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf('#sk11_type',type,
'#sk11': $i ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk6_type',type,
'#sk6': $i ).
thf(q_type,type,
q: $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_s4 @ W @ V ) ) ) ) ).
thf('0',plain,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_s4 @ W @ V ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox_s4]) ).
thf('1',plain,
( mbox_s4
= ( ^ [V_1: $i > $o,V_2: $i] :
! [X4: $i] :
( ( V_1 @ X4 )
| ~ ( rel_s4 @ V_2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('2',plain,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('3',plain,
( mvalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
define([status(thm)]) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
thf(mor,axiom,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ) ).
thf('4',plain,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('5',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(mnot,axiom,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ) ).
thf('6',plain,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('7',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('8',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'5','7']) ).
thf('9',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('10',plain,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand,'5','7']) ).
thf('11',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf(pel13,conjecture,
mvalid @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
~ ( ~ ! [X22: $i] :
( ~ ( rel_s4 @ X4 @ X22 )
| ~ ( ~ ! [X36: $i] :
( ~ ( rel_s4 @ X22 @ X36 )
| ( r @ X36 ) )
| ~ ! [X34: $i] :
( ~ ( rel_s4 @ X22 @ X34 )
| ( q @ X34 ) ) )
| ! [X32: $i] :
( ~ ( rel_s4 @ X22 @ X32 )
| ( p @ X32 ) )
| ~ ( ! [X26: $i] :
( ~ ( rel_s4 @ X22 @ X26 )
| ( q @ X26 ) )
| ! [X24: $i] :
( ~ ( rel_s4 @ X22 @ X24 )
| ( p @ X24 ) ) )
| ~ ( ! [X30: $i] :
( ~ ( rel_s4 @ X22 @ X30 )
| ( r @ X30 ) )
| ! [X28: $i] :
( ~ ( rel_s4 @ X22 @ X28 )
| ( p @ X28 ) ) ) )
| ~ ! [X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ( ~ ( ! [X20: $i] :
( ~ ( rel_s4 @ X6 @ X20 )
| ( r @ X20 ) )
| ! [X18: $i] :
( ~ ( rel_s4 @ X6 @ X18 )
| ( p @ X18 ) ) )
| ~ ( ! [X16: $i] :
( ~ ( rel_s4 @ X6 @ X16 )
| ( q @ X16 ) )
| ! [X14: $i] :
( ~ ( rel_s4 @ X6 @ X14 )
| ( p @ X14 ) ) ) )
| ~ ( ~ ( ~ ! [X12: $i] :
( ~ ( rel_s4 @ X6 @ X12 )
| ( r @ X12 ) )
| ~ ! [X10: $i] :
( ~ ( rel_s4 @ X6 @ X10 )
| ( q @ X10 ) ) )
| ! [X8: $i] :
( ~ ( rel_s4 @ X6 @ X8 )
| ( p @ X8 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
~ ( ~ ! [X22: $i] :
( ~ ( rel_s4 @ X4 @ X22 )
| ~ ( ~ ! [X36: $i] :
( ~ ( rel_s4 @ X22 @ X36 )
| ( r @ X36 ) )
| ~ ! [X34: $i] :
( ~ ( rel_s4 @ X22 @ X34 )
| ( q @ X34 ) ) )
| ! [X32: $i] :
( ~ ( rel_s4 @ X22 @ X32 )
| ( p @ X32 ) )
| ~ ( ! [X26: $i] :
( ~ ( rel_s4 @ X22 @ X26 )
| ( q @ X26 ) )
| ! [X24: $i] :
( ~ ( rel_s4 @ X22 @ X24 )
| ( p @ X24 ) ) )
| ~ ( ! [X30: $i] :
( ~ ( rel_s4 @ X22 @ X30 )
| ( r @ X30 ) )
| ! [X28: $i] :
( ~ ( rel_s4 @ X22 @ X28 )
| ( p @ X28 ) ) ) )
| ~ ! [X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ( ~ ( ! [X20: $i] :
( ~ ( rel_s4 @ X6 @ X20 )
| ( r @ X20 ) )
| ! [X18: $i] :
( ~ ( rel_s4 @ X6 @ X18 )
| ( p @ X18 ) ) )
| ~ ( ! [X16: $i] :
( ~ ( rel_s4 @ X6 @ X16 )
| ( q @ X16 ) )
| ! [X14: $i] :
( ~ ( rel_s4 @ X6 @ X14 )
| ( p @ X14 ) ) ) )
| ~ ( ~ ( ~ ! [X12: $i] :
( ~ ( rel_s4 @ X6 @ X12 )
| ( r @ X12 ) )
| ~ ! [X10: $i] :
( ~ ( rel_s4 @ X6 @ X10 )
| ( q @ X10 ) ) )
| ! [X8: $i] :
( ~ ( rel_s4 @ X6 @ X8 )
| ( p @ X8 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: $i] :
( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( r @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( q @ Y2 ) ) ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( p @ Y2 ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( q @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( p @ Y2 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( r @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( p @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( r @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( p @ Y2 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( q @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( p @ Y2 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( r @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( q @ Y2 ) ) ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk1' @ '#sk2' ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( r @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
( ( rel_s4 @ '#sk1' @ '#sk2' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl9,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl10,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk1' @ '#sk4' ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( r @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl17,plain,
( ( (~)
@ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl23,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl31,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl39,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| $true ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl40,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) )
| '#form3' ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl41,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk4' @ '#sk8' ) )
| ( p @ '#sk8' ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl50,plain,
( ( rel_s4 @ '#sk4' @ '#sk8' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl6,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl9_001,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl13,plain,
( ~ '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl6,zip_derived_cl9]) ).
thf(zip_derived_cl20,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk5' ) )
| ( p @ '#sk5' ) )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl26,plain,
( ( rel_s4 @ '#sk2' @ '#sk5' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl8,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl9_002,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl15,plain,
( ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl8,zip_derived_cl9]) ).
thf(zip_derived_cl22,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl29,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( r @ X2 )
| ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl37,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( r @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl47,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X4 ) )
| ( p @ X4 )
| ~ '#form3'
| ( r @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl59,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s4 @ '#sk2' @ X4 )
| ( p @ X4 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ( r @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl89,plain,
! [X0: $i] :
( ~ '#form3'
| ~ '#form3'
| ( r @ X0 )
| ~ ( rel_s4 @ '#sk2' @ X0 )
| ( p @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl59]) ).
thf(zip_derived_cl95,plain,
! [X0: $i] :
( ( p @ '#sk5' )
| ~ ( rel_s4 @ '#sk2' @ X0 )
| ( r @ X0 )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl27,plain,
( ~ ( p @ '#sk5' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl127,plain,
! [X0: $i] :
( ~ '#form3'
| ( r @ X0 )
| ~ ( rel_s4 @ '#sk2' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl95,zip_derived_cl27]) ).
thf(zip_derived_cl26_003,plain,
( ( rel_s4 @ '#sk2' @ '#sk5' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl7,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl9_004,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl14,plain,
( ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl7,zip_derived_cl9]) ).
thf(zip_derived_cl21,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl28,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( q @ X2 )
| ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl36,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( q @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( p @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl46,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X4 ) )
| ( p @ X4 )
| ~ '#form3'
| ( q @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl58,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s4 @ '#sk2' @ X4 )
| ( p @ X4 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ( q @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl77,plain,
! [X0: $i] :
( ~ '#form3'
| ~ '#form3'
| ( q @ X0 )
| ~ ( rel_s4 @ '#sk2' @ X0 )
| ( p @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl58]) ).
thf(zip_derived_cl83,plain,
! [X0: $i] :
( ( p @ '#sk5' )
| ~ ( rel_s4 @ '#sk2' @ X0 )
| ( q @ X0 )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl27_005,plain,
( ~ ( p @ '#sk5' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl99,plain,
! [X0: $i] :
( ~ '#form3'
| ( q @ X0 )
| ~ ( rel_s4 @ '#sk2' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl83,zip_derived_cl27]) ).
thf(zip_derived_cl5,plain,
( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( r @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl9_006,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( r @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( q @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( p @ Y1 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl12,plain,
( ~ '#form3'
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( r @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl5,zip_derived_cl9]) ).
thf(zip_derived_cl19,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( r @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl25,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk6' ) )
| ( r @ '#sk6' ) )
| ~ '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl35,plain,
( ~ ( r @ '#sk6' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl45,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk9' ) )
| ( q @ '#sk9' ) )
| ~ '#form3'
| ~ ( r @ '#sk6' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl57,plain,
( ~ ( q @ '#sk9' )
| ~ ( r @ '#sk6' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl101,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk9' )
| ~ '#form3'
| ~ '#form3'
| ~ ( r @ '#sk6' ) ),
inference('sup-',[status(thm)],[zip_derived_cl99,zip_derived_cl57]) ).
thf(zip_derived_cl111,plain,
( ~ ( r @ '#sk6' )
| ~ '#form3'
| ~ ( rel_s4 @ '#sk2' @ '#sk9' ) ),
inference(simplify,[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl56,plain,
( ( rel_s4 @ '#sk2' @ '#sk9' )
| ~ ( r @ '#sk6' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl121,plain,
( ~ '#form3'
| ~ ( r @ '#sk6' ) ),
inference(clc,[status(thm)],[zip_derived_cl111,zip_derived_cl56]) ).
thf(zip_derived_cl129,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk6' )
| ~ '#form3'
| ~ '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl127,zip_derived_cl121]) ).
thf(zip_derived_cl134,plain,
( ~ '#form3'
| ~ ( rel_s4 @ '#sk2' @ '#sk6' ) ),
inference(simplify,[status(thm)],[zip_derived_cl129]) ).
thf(zip_derived_cl34,plain,
( ( rel_s4 @ '#sk2' @ '#sk6' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( q @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl44,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk9' ) )
| ( q @ '#sk9' ) )
| ~ '#form3'
| ( rel_s4 @ '#sk2' @ '#sk6' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl55,plain,
( ~ ( q @ '#sk9' )
| ( rel_s4 @ '#sk2' @ '#sk6' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl99_007,plain,
! [X0: $i] :
( ~ '#form3'
| ( q @ X0 )
| ~ ( rel_s4 @ '#sk2' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl83,zip_derived_cl27]) ).
thf(zip_derived_cl104,plain,
( ~ '#form3'
| ( rel_s4 @ '#sk2' @ '#sk6' )
| ~ ( rel_s4 @ '#sk2' @ '#sk9' )
| ~ '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl55,zip_derived_cl99]) ).
thf(zip_derived_cl110,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk9' )
| ( rel_s4 @ '#sk2' @ '#sk6' )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl54,plain,
( ( rel_s4 @ '#sk2' @ '#sk9' )
| ( rel_s4 @ '#sk2' @ '#sk6' )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl116,plain,
( ~ '#form3'
| ( rel_s4 @ '#sk2' @ '#sk6' ) ),
inference(clc,[status(thm)],[zip_derived_cl110,zip_derived_cl54]) ).
thf(zip_derived_cl136,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl134,zip_derived_cl116]) ).
thf(zip_derived_cl138,plain,
rel_s4 @ '#sk4' @ '#sk8',
inference(demod,[status(thm)],[zip_derived_cl50,zip_derived_cl136]) ).
thf(zip_derived_cl18,plain,
( ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( r @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl24,plain,
( ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( r @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl33,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl43,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ X2 ) )
| ( q @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl53,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk4' @ X2 )
| ( q @ X2 )
| '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl66,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ X4 ) )
| ( p @ X4 )
| '#form3'
| ( q @ X2 )
| ~ ( rel_s4 @ '#sk4' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl70,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s4 @ '#sk4' @ X4 )
| ( p @ X4 )
| ~ ( rel_s4 @ '#sk4' @ X2 )
| ( q @ X2 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl136_008,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl134,zip_derived_cl116]) ).
thf(zip_derived_cl161,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s4 @ '#sk4' @ X4 )
| ( p @ X4 )
| ~ ( rel_s4 @ '#sk4' @ X2 )
| ( q @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl70,zip_derived_cl136]) ).
thf(zip_derived_cl163,plain,
! [X0: $i] :
( ( q @ X0 )
| ~ ( rel_s4 @ '#sk4' @ X0 )
| ( p @ '#sk8' ) ),
inference('sup-',[status(thm)],[zip_derived_cl138,zip_derived_cl161]) ).
thf(zip_derived_cl51,plain,
( ~ ( p @ '#sk8' )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl136_009,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl134,zip_derived_cl116]) ).
thf(zip_derived_cl139,plain,
~ ( p @ '#sk8' ),
inference(demod,[status(thm)],[zip_derived_cl51,zip_derived_cl136]) ).
thf(zip_derived_cl172,plain,
! [X0: $i] :
( ~ ( rel_s4 @ '#sk4' @ X0 )
| ( q @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl163,zip_derived_cl139]) ).
thf(zip_derived_cl30,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( r @ Y0 ) ) )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl38,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk4' @ '#sk7' ) )
| ( r @ '#sk7' ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl48,plain,
( ( rel_s4 @ '#sk4' @ '#sk7' )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl60,plain,
( '#form10'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl61,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| '#form10' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl67,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk4' @ '#sk11' ) )
| ( q @ '#sk11' ) )
| '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl72,plain,
( ~ ( q @ '#sk11' )
| '#form10' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl138_010,plain,
rel_s4 @ '#sk4' @ '#sk8',
inference(demod,[status(thm)],[zip_derived_cl50,zip_derived_cl136]) ).
thf(zip_derived_cl32,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( r @ Y0 ) ) )
| '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl42,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ X2 ) )
| ( r @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl52,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk4' @ X2 )
| ( r @ X2 )
| '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl65,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ X4 ) )
| ( p @ X4 )
| '#form3'
| ( r @ X2 )
| ~ ( rel_s4 @ '#sk4' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl69,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s4 @ '#sk4' @ X4 )
| ( p @ X4 )
| ~ ( rel_s4 @ '#sk4' @ X2 )
| ( r @ X2 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl136_011,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl134,zip_derived_cl116]) ).
thf(zip_derived_cl143,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s4 @ '#sk4' @ X4 )
| ( p @ X4 )
| ~ ( rel_s4 @ '#sk4' @ X2 )
| ( r @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl69,zip_derived_cl136]) ).
thf(zip_derived_cl148,plain,
! [X0: $i] :
( ( r @ X0 )
| ~ ( rel_s4 @ '#sk4' @ X0 )
| ( p @ '#sk8' ) ),
inference('sup-',[status(thm)],[zip_derived_cl138,zip_derived_cl143]) ).
thf(zip_derived_cl139_012,plain,
~ ( p @ '#sk8' ),
inference(demod,[status(thm)],[zip_derived_cl51,zip_derived_cl136]) ).
thf(zip_derived_cl152,plain,
! [X0: $i] :
( ~ ( rel_s4 @ '#sk4' @ X0 )
| ( r @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl148,zip_derived_cl139]) ).
thf(zip_derived_cl49,plain,
( ~ ( r @ '#sk7' )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl60_013,plain,
( '#form10'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl64,plain,
( ~ '#form10'
| '#form3'
| ~ ( r @ '#sk7' ) ),
inference(renaming,[status(thm)],[zip_derived_cl49,zip_derived_cl60]) ).
thf(zip_derived_cl136_014,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl134,zip_derived_cl116]) ).
thf(zip_derived_cl141,plain,
( ~ '#form10'
| ~ ( r @ '#sk7' ) ),
inference(demod,[status(thm)],[zip_derived_cl64,zip_derived_cl136]) ).
thf(zip_derived_cl153,plain,
( ~ ( rel_s4 @ '#sk4' @ '#sk7' )
| ~ '#form10' ),
inference('sup-',[status(thm)],[zip_derived_cl152,zip_derived_cl141]) ).
thf(zip_derived_cl48_015,plain,
( ( rel_s4 @ '#sk4' @ '#sk7' )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl60_016,plain,
( '#form10'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( p @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl63,plain,
( ~ '#form10'
| '#form3'
| ( rel_s4 @ '#sk4' @ '#sk7' ) ),
inference(renaming,[status(thm)],[zip_derived_cl48,zip_derived_cl60]) ).
thf(zip_derived_cl136_017,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl134,zip_derived_cl116]) ).
thf(zip_derived_cl140,plain,
( ~ '#form10'
| ( rel_s4 @ '#sk4' @ '#sk7' ) ),
inference(demod,[status(thm)],[zip_derived_cl63,zip_derived_cl136]) ).
thf(zip_derived_cl155,plain,
~ '#form10',
inference(clc,[status(thm)],[zip_derived_cl153,zip_derived_cl140]) ).
thf(zip_derived_cl157,plain,
~ ( q @ '#sk11' ),
inference(demod,[status(thm)],[zip_derived_cl72,zip_derived_cl155]) ).
thf(zip_derived_cl173,plain,
~ ( rel_s4 @ '#sk4' @ '#sk11' ),
inference('sup-',[status(thm)],[zip_derived_cl172,zip_derived_cl157]) ).
thf(zip_derived_cl71,plain,
( ( rel_s4 @ '#sk4' @ '#sk11' )
| '#form10' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl155_018,plain,
~ '#form10',
inference(clc,[status(thm)],[zip_derived_cl153,zip_derived_cl140]) ).
thf(zip_derived_cl156,plain,
rel_s4 @ '#sk4' @ '#sk11',
inference(demod,[status(thm)],[zip_derived_cl71,zip_derived_cl155]) ).
thf(zip_derived_cl175,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl173,zip_derived_cl156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN045^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ZobRGlaF2A true
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 18:09:55 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.37 % Python version: Python 3.6.8
% 0.14/0.37 % Running in HO mode
% 0.23/0.69 % Total configuration time : 828
% 0.23/0.69 % Estimated wc time : 1656
% 0.23/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.23/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.23/0.78 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.23/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.23/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.26/0.80 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.26/0.81 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.26/0.81 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.26/0.81 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.26/0.83 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.46/0.94 % Solved by lams/20_acsne_simpl.sh.
% 1.46/0.94 % done 50 iterations in 0.086s
% 1.46/0.94 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.46/0.94 % SZS output start Refutation
% See solution above
% 1.46/0.95
% 1.46/0.95
% 1.58/0.95 % Terminating...
% 1.73/0.99 % Runner terminated.
% 1.73/1.00 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------