%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO064^4.003 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.jV8zmHbydK true
% Computer : n021.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 : Thu Oct 2 05:06:21 PM UTC 2025
% Result : Theorem 14.07s 2.43s
% Output : Refutation 14.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 32
% Syntax : Number of formulae : 211 ( 72 unt; 0 typ; 0 def)
% Number of atoms : 1217 ( 30 equ; 4 cnn)
% Maximal formula atoms : 21 ( 5 avg)
% Number of connectives : 2930 ( 296 ~; 434 |; 45 &;1735 @)
% ( 0 <=>; 234 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 27 usr; 11 con; 0-3 aty)
% ( 186 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 568 ( 246 ^; 322 !; 0 ?; 568 :)
% Comments :
%------------------------------------------------------------------------------
thf(iatom_type,type,
iatom: ( $i > $o ) > $i > $o ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(a2_type,type,
a2: $i > $o ).
thf(ivalid_type,type,
ivalid: ( $i > $o ) > $o ).
thf(a1_type,type,
a1: $i > $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf(irel_type,type,
irel: $i > $i > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ior_type,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(b_type,type,
b: $i > $o ).
thf(iimplies_type,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(a_type,type,
a: $i > $o ).
thf(iand_type,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(b2_type,type,
b2: $i > $o ).
thf('#sk6_type',type,
'#sk6': $i ).
thf('#sk5_type',type,
'#sk5': $i ).
thf(b1_type,type,
b1: $i > $o ).
thf('#sk9_type',type,
'#sk9': $i > $i ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(a3_type,type,
a3: $i > $o ).
thf('#sk7_type',type,
'#sk7': $i ).
thf('#sk8_type',type,
'#sk8': $i > $i ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ivalid,axiom,
( ivalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('0',plain,
( ivalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[ivalid]) ).
thf('1',plain,
( ivalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
define([status(thm)]) ).
thf(ior,axiom,
( ior
= ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [P: $i > $o,X: $i] :
! [Y: $i] :
( ( irel @ X @ Y )
=> ( P @ Y ) ) ) ) ).
thf('2',plain,
( mbox_s4
= ( ^ [P: $i > $o,X: $i] :
! [Y: $i] :
( ( irel @ X @ Y )
=> ( P @ Y ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox_s4]) ).
thf('3',plain,
( mbox_s4
= ( ^ [V_1: $i > $o,V_2: $i] :
! [X4: $i] :
( ( irel @ V_2 @ X4 )
=> ( V_1 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(mor,axiom,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ) ).
thf('4',plain,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
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('6',plain,
( ior
= ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ior,'3','5']) ).
thf('7',plain,
( ior
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mbox_s4 @ V_1 ) @ ( mbox_s4 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(iand,axiom,
( iand
= ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ) ).
thf(mand,axiom,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ) ).
thf('8',plain,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand]) ).
thf('9',plain,
( mand
= ( ^ [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,
( iand
= ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ),
inference(simplify_rw_rule,[status(thm)],[iand,'9']) ).
thf('11',plain,
( iand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf(iatom,axiom,
( iatom
= ( ^ [P: $i > $o] : P ) ) ).
thf('12',plain,
( iatom
= ( ^ [P: $i > $o] : P ) ),
inference(simplify_rw_rule,[status(thm)],[iatom]) ).
thf('13',plain,
( iatom
= ( ^ [V_1: $i > $o] : V_1 ) ),
define([status(thm)]) ).
thf(con,conjecture,
ivalid @ ( ior @ ( iatom @ a ) @ ( ior @ ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @ ( ior @ ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iand @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ! [X8: $i] :
( ( irel @ X4 @ X8 )
=> ( ! [X12: $i] :
( ( irel @ X8 @ X12 )
=> ( ! [X16: $i] :
( ( irel @ X12 @ X16 )
=> ( ( a3 @ X16 )
& ( b2 @ X16 ) ) )
| ! [X14: $i] :
( ( irel @ X12 @ X14 )
=> ( ( a2 @ X14 )
& ( b1 @ X14 ) ) ) ) )
| ! [X10: $i] :
( ( irel @ X8 @ X10 )
=> ( ( a1 @ X10 )
& ( b @ X10 ) ) ) ) )
| ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( a @ X6 ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ! [X8: $i] :
( ( irel @ X4 @ X8 )
=> ( ! [X12: $i] :
( ( irel @ X8 @ X12 )
=> ( ! [X16: $i] :
( ( irel @ X12 @ X16 )
=> ( ( a3 @ X16 )
& ( b2 @ X16 ) ) )
| ! [X14: $i] :
( ( irel @ X12 @ X14 )
=> ( ( a2 @ X14 )
& ( b1 @ X14 ) ) ) ) )
| ! [X10: $i] :
( ( irel @ X8 @ X10 )
=> ( ( a1 @ X10 )
& ( b @ X10 ) ) ) ) )
| ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( a @ X6 ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl6,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( a3 @ Y3 )
& ( b2 @ Y3 ) ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( a2 @ Y3 )
& ( b1 @ Y3 ) ) ) ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( a1 @ Y2 )
& ( b @ Y2 ) ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl25,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( a3 @ Y2 )
& ( b2 @ Y2 ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( a2 @ Y2 )
& ( b1 @ Y2 ) ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( a1 @ Y1 )
& ( b @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( a @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl27,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( a @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl29,plain,
~ ( ( irel @ '#sk1' @ '#sk3' )
=> ( a @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl32,plain,
irel @ '#sk1' @ '#sk3',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(axiom4,axiom,
ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i] :
( ! [X12: $i] :
( ( irel @ X4 @ X12 )
=> ( b @ X12 ) )
| ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( ! [X10: $i] :
( ( irel @ X6 @ X10 )
=> ( a @ X10 ) )
| ! [X8: $i] :
( ( irel @ X6 @ X8 )
=> ( b @ X8 ) ) ) ) ) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl14,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl15,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl16,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( b @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl17,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( b @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl18,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X2 @ X6 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( b @ Y0 ) ) ) ) )
| ( b @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl19,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X2 @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( b @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( b @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl20,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( b @ Y0 ) ) )
| ( b @ X4 )
| ~ ( irel @ X2 @ X4 )
| ~ ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl21,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( irel @ X6 @ X8 )
=> ( a @ X8 ) )
| ~ ( irel @ X2 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( b @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( b @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl22,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( irel @ X6 @ X8 )
| ( a @ X8 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( b @ Y0 ) ) )
| ( b @ X4 )
| ~ ( irel @ X2 @ X4 )
| ~ ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl23,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( irel @ X6 @ X10 )
=> ( b @ X10 ) )
| ~ ( irel @ X2 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( b @ X4 )
| ( a @ X8 )
| ~ ( irel @ X6 @ X8 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ~ ( irel @ X6 @ X10 )
| ( b @ X10 )
| ~ ( irel @ X6 @ X8 )
| ( a @ X8 )
| ( b @ X4 )
| ~ ( irel @ X2 @ X4 )
| ~ ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl123,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( irel @ X1 @ X1 )
| ~ ( irel @ X1 @ X0 )
| ( b @ X0 )
| ( a @ X2 )
| ~ ( irel @ X1 @ X2 )
| ( b @ X0 ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl125,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( irel @ X1 @ X2 )
| ( a @ X2 )
| ( b @ X0 )
| ~ ( irel @ X1 @ X0 )
| ~ ( irel @ X1 @ X1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl123]) ).
thf(refl_axiom,axiom,
! [X: $i] : ( irel @ X @ X ) ).
thf(zip_derived_cl0,plain,
( !!
@ ^ [Y0: $i] : ( irel @ Y0 @ Y0 ) ),
inference(cnf,[status(esa)],[refl_axiom]) ).
thf(zip_derived_cl8,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl137,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( irel @ X1 @ X2 )
| ( a @ X2 )
| ( b @ X0 )
| ~ ( irel @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl125,zip_derived_cl8]) ).
thf(zip_derived_cl414,plain,
! [X0: $i] :
( ~ ( irel @ '#sk1' @ X0 )
| ( b @ X0 )
| ( a @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl137]) ).
thf(zip_derived_cl33,plain,
~ ( a @ '#sk3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl432,plain,
! [X0: $i] :
( ~ ( irel @ '#sk1' @ X0 )
| ( b @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl414,zip_derived_cl33]) ).
thf(zip_derived_cl26,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( a3 @ Y2 )
& ( b2 @ Y2 ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( a2 @ Y2 )
& ( b1 @ Y2 ) ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( a1 @ Y1 )
& ( b @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl28,plain,
~ ( ( irel @ '#sk1' @ '#sk2' )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( a3 @ Y1 )
& ( b2 @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( a2 @ Y1 )
& ( b1 @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( a1 @ Y0 )
& ( b @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl31,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( a3 @ Y1 )
& ( b2 @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( a2 @ Y1 )
& ( b1 @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( a1 @ Y0 )
& ( b @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl34,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( a3 @ Y1 )
& ( b2 @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( a2 @ Y1 )
& ( b1 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl36,plain,
~ ( ( irel @ '#sk2' @ '#sk4' )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( a3 @ Y0 )
& ( b2 @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( a2 @ Y0 )
& ( b1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl39,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( a3 @ Y0 )
& ( b2 @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( a2 @ Y0 )
& ( b1 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl42,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( a3 @ Y0 )
& ( b2 @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl45,plain,
~ ( ( irel @ '#sk4' @ '#sk6' )
=> ( ( a3 @ '#sk6' )
& ( b2 @ '#sk6' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl42]) ).
thf(axiom1,axiom,
ivalid @ ( iatom @ a3 ) ).
thf(zf_stmt_3,axiom,
! [X4: $i] : ( a3 @ X4 ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] : ( a3 @ Y0 ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl7,plain,
! [X2: $i] : ( a3 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl47,plain,
~ ( ( irel @ '#sk4' @ '#sk6' )
=> ( $true
& ( b2 @ '#sk6' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl45,zip_derived_cl7]) ).
thf(zip_derived_cl48,plain,
~ ( ( irel @ '#sk4' @ '#sk6' )
=> ( b2 @ '#sk6' ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl49,plain,
irel @ '#sk4' @ '#sk6',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl43,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( a2 @ Y0 )
& ( b1 @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl46,plain,
~ ( ( irel @ '#sk4' @ '#sk7' )
=> ( ( a2 @ '#sk7' )
& ( b1 @ '#sk7' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl51,plain,
irel @ '#sk4' @ '#sk7',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(iimplies,axiom,
( iimplies
= ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
thf(mnot,axiom,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ) ).
thf('14',plain,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('15',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('16',plain,
( mimplies
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'5','15']) ).
thf('17',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
define([status(thm)]) ).
thf('18',plain,
( iimplies
= ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[iimplies,'3','17']) ).
thf('19',plain,
( iimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mimplies @ ( mbox_s4 @ V_1 ) @ ( mbox_s4 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(axiom2,axiom,
ivalid @ ( iimplies @ ( iatom @ b1 ) @ ( ior @ ( ior @ ( iatom @ b2 ) @ ( iatom @ a2 ) ) @ ( iatom @ b2 ) ) ) ).
thf(zf_stmt_4,axiom,
! [X4: $i] :
( ! [X8: $i] :
( ( irel @ X4 @ X8 )
=> ( ! [X16: $i] :
( ( irel @ X8 @ X16 )
=> ( b2 @ X16 ) )
| ! [X10: $i] :
( ( irel @ X8 @ X10 )
=> ( ! [X14: $i] :
( ( irel @ X10 @ X14 )
=> ( a2 @ X14 ) )
| ! [X12: $i] :
( ( irel @ X10 @ X12 )
=> ( b2 @ X12 ) ) ) ) ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( b1 @ X6 ) ) ) ).
thf(zip_derived_cl3,plain,
( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b2 @ Y3 ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl54,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl55,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl56,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl57,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl58,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl59,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X4 @ X6 )
=> ( b2 @ X6 ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl60,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ( b2 @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl61,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( irel @ X4 @ X8 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( b2 @ Y0 ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( b2 @ X6 )
| ~ ( irel @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl62,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( irel @ X4 @ X8 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( b2 @ Y0 ) ) )
| ~ ( irel @ X4 @ X6 )
| ( b2 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl63,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( b2 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( b2 @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X4 @ X8 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl64,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( irel @ X8 @ X10 )
=> ( a2 @ X10 ) )
| ~ ( irel @ X4 @ X8 )
| ~ ( irel @ X4 @ X6 )
| ( b2 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( b2 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl65,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ~ ( irel @ X8 @ X10 )
| ( a2 @ X10 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( b2 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( b2 @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X4 @ X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl66,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ( ( irel @ X8 @ X12 )
=> ( b2 @ X12 ) )
| ~ ( irel @ X4 @ X8 )
| ~ ( irel @ X4 @ X6 )
| ( b2 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a2 @ X10 )
| ~ ( irel @ X8 @ X10 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl67,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ~ ( irel @ X8 @ X12 )
| ( b2 @ X12 )
| ~ ( irel @ X8 @ X10 )
| ( a2 @ X10 )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( b2 @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X4 @ X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl68,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ~ ( ( irel @ X2 @ ( '#sk8' @ X2 ) )
=> ( b1 @ ( '#sk8' @ X2 ) ) )
| ~ ( irel @ X4 @ X8 )
| ~ ( irel @ X4 @ X6 )
| ( b2 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( a2 @ X10 )
| ~ ( irel @ X8 @ X10 )
| ( b2 @ X12 )
| ~ ( irel @ X8 @ X12 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl69,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ( irel @ X2 @ ( '#sk8' @ X2 ) )
| ~ ( irel @ X8 @ X12 )
| ( b2 @ X12 )
| ~ ( irel @ X8 @ X10 )
| ( a2 @ X10 )
| ~ ( irel @ X2 @ X4 )
| ( b2 @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X4 @ X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( irel @ X1 @ X1 )
| ~ ( irel @ X1 @ X0 )
| ( b2 @ X0 )
| ~ ( irel @ X2 @ X1 )
| ( a2 @ X3 )
| ~ ( irel @ X1 @ X3 )
| ( b2 @ X0 )
| ( irel @ X2 @ ( '#sk8' @ X2 ) ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( irel @ X2 @ ( '#sk8' @ X2 ) )
| ~ ( irel @ X1 @ X3 )
| ( a2 @ X3 )
| ~ ( irel @ X2 @ X1 )
| ( b2 @ X0 )
| ~ ( irel @ X1 @ X0 )
| ~ ( irel @ X1 @ X1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl173]) ).
thf(zip_derived_cl8_001,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl193,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( irel @ X2 @ ( '#sk8' @ X2 ) )
| ~ ( irel @ X1 @ X3 )
| ( a2 @ X3 )
| ~ ( irel @ X2 @ X1 )
| ( b2 @ X0 )
| ~ ( irel @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl177,zip_derived_cl8]) ).
thf(zip_derived_cl1091,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk4' @ X0 )
| ( b2 @ X0 )
| ~ ( irel @ X1 @ '#sk4' )
| ( a2 @ '#sk7' )
| ( irel @ X1 @ ( '#sk8' @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl193]) ).
thf(zip_derived_cl3066,plain,
! [X0: $i] :
( ( irel @ X0 @ ( '#sk8' @ X0 ) )
| ( a2 @ '#sk7' )
| ~ ( irel @ X0 @ '#sk4' )
| ( b2 @ '#sk6' ) ),
inference('sup-',[status(thm)],[zip_derived_cl49,zip_derived_cl1091]) ).
thf(zip_derived_cl50,plain,
~ ( b2 @ '#sk6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl3077,plain,
! [X0: $i] :
( ( irel @ X0 @ ( '#sk8' @ X0 ) )
| ( a2 @ '#sk7' )
| ~ ( irel @ X0 @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl3066,zip_derived_cl50]) ).
thf(zip_derived_cl52,plain,
~ ( ( a2 @ '#sk7' )
& ( b1 @ '#sk7' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl53,plain,
( ~ ( a2 @ '#sk7' )
| ~ ( b1 @ '#sk7' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl432_002,plain,
! [X0: $i] :
( ~ ( irel @ '#sk1' @ X0 )
| ( b @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl414,zip_derived_cl33]) ).
thf(zip_derived_cl38,plain,
irel @ '#sk2' @ '#sk4',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl51_003,plain,
irel @ '#sk4' @ '#sk7',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(trans_axiom,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ Y @ Z )
& ( irel @ X @ Y ) )
=> ( irel @ X @ Z ) ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( irel @ Y1 @ Y2 )
& ( irel @ Y0 @ Y1 ) )
=> ( irel @ Y0 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[trans_axiom]) ).
thf(zip_derived_cl9,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( irel @ Y0 @ Y1 )
& ( irel @ X2 @ Y0 ) )
=> ( irel @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl10,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( irel @ X4 @ Y0 )
& ( irel @ X2 @ X4 ) )
=> ( irel @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl11,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X4 @ X6 )
& ( irel @ X2 @ X4 ) )
=> ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl12,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( irel @ X4 @ X6 )
& ( irel @ X2 @ X4 ) )
| ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl13,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl88,plain,
! [X0: $i] :
( ( irel @ X0 @ '#sk7' )
| ~ ( irel @ X0 @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl13]) ).
thf(zip_derived_cl108,plain,
irel @ '#sk2' @ '#sk7',
inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl88]) ).
thf(zip_derived_cl35,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( a1 @ Y0 )
& ( b @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl37,plain,
~ ( ( irel @ '#sk2' @ '#sk5' )
=> ( ( a1 @ '#sk5' )
& ( b @ '#sk5' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl40,plain,
irel @ '#sk2' @ '#sk5',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(axiom3,axiom,
ivalid @ ( iimplies @ ( iatom @ b ) @ ( ior @ ( ior @ ( iatom @ b1 ) @ ( iatom @ a1 ) ) @ ( iatom @ b1 ) ) ) ).
thf(zf_stmt_5,axiom,
! [X4: $i] :
( ! [X8: $i] :
( ( irel @ X4 @ X8 )
=> ( ! [X16: $i] :
( ( irel @ X8 @ X16 )
=> ( b1 @ X16 ) )
| ! [X10: $i] :
( ( irel @ X8 @ X10 )
=> ( ! [X14: $i] :
( ( irel @ X10 @ X14 )
=> ( a1 @ X14 ) )
| ! [X12: $i] :
( ( irel @ X10 @ X12 )
=> ( b1 @ X12 ) ) ) ) ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( b @ X6 ) ) ) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b1 @ Y3 ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_5]) ).
thf(zip_derived_cl71,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl72,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl73,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl74,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl75,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl76,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X4 @ X6 )
=> ( b1 @ X6 ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl77,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ( b1 @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl78,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( irel @ X4 @ X8 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( b1 @ Y0 ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ( b1 @ X6 )
| ~ ( irel @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl79,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( irel @ X4 @ X8 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ~ ( irel @ X4 @ X6 )
| ( b1 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl80,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ( b1 @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X4 @ X8 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl81,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( irel @ X8 @ X10 )
=> ( a1 @ X10 ) )
| ~ ( irel @ X4 @ X8 )
| ~ ( irel @ X4 @ X6 )
| ( b1 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( b1 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl82,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ~ ( irel @ X8 @ X10 )
| ( a1 @ X10 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X8 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ( b1 @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X4 @ X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl83,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ( ( irel @ X8 @ X12 )
=> ( b1 @ X12 ) )
| ~ ( irel @ X4 @ X8 )
| ~ ( irel @ X4 @ X6 )
| ( b1 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a1 @ X10 )
| ~ ( irel @ X8 @ X10 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl84,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ~ ( irel @ X8 @ X12 )
| ( b1 @ X12 )
| ~ ( irel @ X8 @ X10 )
| ( a1 @ X10 )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ( b1 @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X4 @ X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl85,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ~ ( ( irel @ X2 @ ( '#sk9' @ X2 ) )
=> ( b @ ( '#sk9' @ X2 ) ) )
| ~ ( irel @ X4 @ X8 )
| ~ ( irel @ X4 @ X6 )
| ( b1 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( a1 @ X10 )
| ~ ( irel @ X8 @ X10 )
| ( b1 @ X12 )
| ~ ( irel @ X8 @ X12 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl86,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ( irel @ X2 @ ( '#sk9' @ X2 ) )
| ~ ( irel @ X8 @ X12 )
| ( b1 @ X12 )
| ~ ( irel @ X8 @ X10 )
| ( a1 @ X10 )
| ~ ( irel @ X2 @ X4 )
| ( b1 @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X4 @ X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( irel @ X1 @ X1 )
| ~ ( irel @ X1 @ X0 )
| ( b1 @ X0 )
| ~ ( irel @ X2 @ X1 )
| ( a1 @ X3 )
| ~ ( irel @ X1 @ X3 )
| ( b1 @ X0 )
| ( irel @ X2 @ ( '#sk9' @ X2 ) ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( irel @ X2 @ ( '#sk9' @ X2 ) )
| ~ ( irel @ X1 @ X3 )
| ( a1 @ X3 )
| ~ ( irel @ X2 @ X1 )
| ( b1 @ X0 )
| ~ ( irel @ X1 @ X0 )
| ~ ( irel @ X1 @ X1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl294]) ).
thf(zip_derived_cl8_004,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( irel @ X2 @ ( '#sk9' @ X2 ) )
| ~ ( irel @ X1 @ X3 )
| ( a1 @ X3 )
| ~ ( irel @ X2 @ X1 )
| ( b1 @ X0 )
| ~ ( irel @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl298,zip_derived_cl8]) ).
thf(zip_derived_cl4092,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk2' @ X0 )
| ( b1 @ X0 )
| ~ ( irel @ X1 @ '#sk2' )
| ( a1 @ '#sk5' )
| ( irel @ X1 @ ( '#sk9' @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl317]) ).
thf(zip_derived_cl41,plain,
~ ( ( a1 @ '#sk5' )
& ( b @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl44,plain,
( ~ ( a1 @ '#sk5' )
| ~ ( b @ '#sk5' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl432_005,plain,
! [X0: $i] :
( ~ ( irel @ '#sk1' @ X0 )
| ( b @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl414,zip_derived_cl33]) ).
thf(zip_derived_cl30,plain,
irel @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl40_006,plain,
irel @ '#sk2' @ '#sk5',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl13_007,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl90,plain,
! [X0: $i] :
( ( irel @ X0 @ '#sk5' )
| ~ ( irel @ X0 @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl13]) ).
thf(zip_derived_cl150,plain,
irel @ '#sk1' @ '#sk5',
inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl90]) ).
thf(zip_derived_cl436,plain,
b @ '#sk5',
inference('sup+',[status(thm)],[zip_derived_cl432,zip_derived_cl150]) ).
thf(zip_derived_cl462,plain,
~ ( a1 @ '#sk5' ),
inference(demod,[status(thm)],[zip_derived_cl44,zip_derived_cl436]) ).
thf(zip_derived_cl4126,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk2' @ X0 )
| ( b1 @ X0 )
| ~ ( irel @ X1 @ '#sk2' )
| ( irel @ X1 @ ( '#sk9' @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4092,zip_derived_cl462]) ).
thf(zip_derived_cl4848,plain,
! [X0: $i] :
( ( irel @ X0 @ ( '#sk9' @ X0 ) )
| ~ ( irel @ X0 @ '#sk2' )
| ( b1 @ '#sk7' ) ),
inference('sup-',[status(thm)],[zip_derived_cl108,zip_derived_cl4126]) ).
thf(zip_derived_cl4947,plain,
( ( b @ ( '#sk9' @ '#sk1' ) )
| ( b1 @ '#sk7' )
| ~ ( irel @ '#sk1' @ '#sk2' ) ),
inference('sup+',[status(thm)],[zip_derived_cl432,zip_derived_cl4848]) ).
thf(zip_derived_cl30_008,plain,
irel @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl5014,plain,
( ( b @ ( '#sk9' @ '#sk1' ) )
| ( b1 @ '#sk7' ) ),
inference(demod,[status(thm)],[zip_derived_cl4947,zip_derived_cl30]) ).
thf(zip_derived_cl108_009,plain,
irel @ '#sk2' @ '#sk7',
inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl88]) ).
thf(zip_derived_cl40_010,plain,
irel @ '#sk2' @ '#sk5',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl87,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ~ ( b @ ( '#sk9' @ X2 ) )
| ~ ( irel @ X8 @ X12 )
| ( b1 @ X12 )
| ~ ( irel @ X8 @ X10 )
| ( a1 @ X10 )
| ~ ( irel @ X2 @ X4 )
| ( b1 @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X4 @ X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( irel @ X1 @ X1 )
| ~ ( irel @ X1 @ X0 )
| ( b1 @ X0 )
| ~ ( irel @ X2 @ X1 )
| ( a1 @ X3 )
| ~ ( irel @ X1 @ X3 )
| ( b1 @ X0 )
| ~ ( b @ ( '#sk9' @ X2 ) ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( b @ ( '#sk9' @ X2 ) )
| ~ ( irel @ X1 @ X3 )
| ( a1 @ X3 )
| ~ ( irel @ X2 @ X1 )
| ( b1 @ X0 )
| ~ ( irel @ X1 @ X0 )
| ~ ( irel @ X1 @ X1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl342]) ).
thf(zip_derived_cl8_011,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( b @ ( '#sk9' @ X2 ) )
| ~ ( irel @ X1 @ X3 )
| ( a1 @ X3 )
| ~ ( irel @ X2 @ X1 )
| ( b1 @ X0 )
| ~ ( irel @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl345,zip_derived_cl8]) ).
thf(zip_derived_cl3822,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk2' @ X0 )
| ( b1 @ X0 )
| ~ ( irel @ X1 @ '#sk2' )
| ( a1 @ '#sk5' )
| ~ ( b @ ( '#sk9' @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl363]) ).
thf(zip_derived_cl462_012,plain,
~ ( a1 @ '#sk5' ),
inference(demod,[status(thm)],[zip_derived_cl44,zip_derived_cl436]) ).
thf(zip_derived_cl3857,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk2' @ X0 )
| ( b1 @ X0 )
| ~ ( irel @ X1 @ '#sk2' )
| ~ ( b @ ( '#sk9' @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3822,zip_derived_cl462]) ).
thf(zip_derived_cl3862,plain,
! [X0: $i] :
( ~ ( b @ ( '#sk9' @ X0 ) )
| ~ ( irel @ X0 @ '#sk2' )
| ( b1 @ '#sk7' ) ),
inference('sup-',[status(thm)],[zip_derived_cl108,zip_derived_cl3857]) ).
thf(zip_derived_cl30_013,plain,
irel @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl3892,plain,
( ( b1 @ '#sk7' )
| ~ ( b @ ( '#sk9' @ '#sk1' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3862,zip_derived_cl30]) ).
thf(zip_derived_cl5049,plain,
b1 @ '#sk7',
inference(clc,[status(thm)],[zip_derived_cl5014,zip_derived_cl3892]) ).
thf(zip_derived_cl5050,plain,
~ ( a2 @ '#sk7' ),
inference(demod,[status(thm)],[zip_derived_cl53,zip_derived_cl5049]) ).
thf(zip_derived_cl5057,plain,
! [X0: $i] :
( ( irel @ X0 @ ( '#sk8' @ X0 ) )
| ~ ( irel @ X0 @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl3077,zip_derived_cl5050]) ).
thf(zip_derived_cl4126_014,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk2' @ X0 )
| ( b1 @ X0 )
| ~ ( irel @ X1 @ '#sk2' )
| ( irel @ X1 @ ( '#sk9' @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4092,zip_derived_cl462]) ).
thf(zip_derived_cl5137,plain,
! [X0: $i] :
( ~ ( irel @ '#sk2' @ '#sk4' )
| ( irel @ X0 @ ( '#sk9' @ X0 ) )
| ~ ( irel @ X0 @ '#sk2' )
| ( b1 @ ( '#sk8' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl5057,zip_derived_cl4126]) ).
thf(zip_derived_cl38_015,plain,
irel @ '#sk2' @ '#sk4',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl49_016,plain,
irel @ '#sk4' @ '#sk6',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl51_017,plain,
irel @ '#sk4' @ '#sk7',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl70,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ~ ( b1 @ ( '#sk8' @ X2 ) )
| ~ ( irel @ X8 @ X12 )
| ( b2 @ X12 )
| ~ ( irel @ X8 @ X10 )
| ( a2 @ X10 )
| ~ ( irel @ X2 @ X4 )
| ( b2 @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X4 @ X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( irel @ X1 @ X1 )
| ~ ( irel @ X1 @ X0 )
| ( b2 @ X0 )
| ~ ( irel @ X2 @ X1 )
| ( a2 @ X3 )
| ~ ( irel @ X1 @ X3 )
| ( b2 @ X0 )
| ~ ( b1 @ ( '#sk8' @ X2 ) ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( b1 @ ( '#sk8' @ X2 ) )
| ~ ( irel @ X1 @ X3 )
| ( a2 @ X3 )
| ~ ( irel @ X2 @ X1 )
| ( b2 @ X0 )
| ~ ( irel @ X1 @ X0 )
| ~ ( irel @ X1 @ X1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl244]) ).
thf(zip_derived_cl8_018,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( b1 @ ( '#sk8' @ X2 ) )
| ~ ( irel @ X1 @ X3 )
| ( a2 @ X3 )
| ~ ( irel @ X2 @ X1 )
| ( b2 @ X0 )
| ~ ( irel @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl247,zip_derived_cl8]) ).
thf(zip_derived_cl935,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk4' @ X0 )
| ( b2 @ X0 )
| ~ ( irel @ X1 @ '#sk4' )
| ( a2 @ '#sk7' )
| ~ ( b1 @ ( '#sk8' @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl265]) ).
thf(zip_derived_cl1068,plain,
! [X0: $i] :
( ~ ( b1 @ ( '#sk8' @ X0 ) )
| ( a2 @ '#sk7' )
| ~ ( irel @ X0 @ '#sk4' )
| ( b2 @ '#sk6' ) ),
inference('sup-',[status(thm)],[zip_derived_cl49,zip_derived_cl935]) ).
thf(zip_derived_cl50_019,plain,
~ ( b2 @ '#sk6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl1076,plain,
! [X0: $i] :
( ~ ( b1 @ ( '#sk8' @ X0 ) )
| ( a2 @ '#sk7' )
| ~ ( irel @ X0 @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl1068,zip_derived_cl50]) ).
thf(zip_derived_cl38_020,plain,
irel @ '#sk2' @ '#sk4',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl1079,plain,
( ( a2 @ '#sk7' )
| ~ ( b1 @ ( '#sk8' @ '#sk2' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1076,zip_derived_cl38]) ).
thf(zip_derived_cl5050_021,plain,
~ ( a2 @ '#sk7' ),
inference(demod,[status(thm)],[zip_derived_cl53,zip_derived_cl5049]) ).
thf(zip_derived_cl5052,plain,
~ ( b1 @ ( '#sk8' @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl1079,zip_derived_cl5050]) ).
thf(zip_derived_cl5260,plain,
! [X0: $i] :
( ( irel @ X0 @ ( '#sk9' @ X0 ) )
| ~ ( irel @ X0 @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl5137,zip_derived_cl38,zip_derived_cl5052]) ).
thf(zip_derived_cl5377,plain,
( ( b @ ( '#sk9' @ '#sk1' ) )
| ~ ( irel @ '#sk1' @ '#sk2' ) ),
inference('sup+',[status(thm)],[zip_derived_cl432,zip_derived_cl5260]) ).
thf(zip_derived_cl3077_022,plain,
! [X0: $i] :
( ( irel @ X0 @ ( '#sk8' @ X0 ) )
| ( a2 @ '#sk7' )
| ~ ( irel @ X0 @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl3066,zip_derived_cl50]) ).
thf(zip_derived_cl3857_023,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk2' @ X0 )
| ( b1 @ X0 )
| ~ ( irel @ X1 @ '#sk2' )
| ~ ( b @ ( '#sk9' @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3822,zip_derived_cl462]) ).
thf(zip_derived_cl3868,plain,
! [X0: $i] :
( ~ ( irel @ '#sk2' @ '#sk4' )
| ( a2 @ '#sk7' )
| ~ ( b @ ( '#sk9' @ X0 ) )
| ~ ( irel @ X0 @ '#sk2' )
| ( b1 @ ( '#sk8' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3077,zip_derived_cl3857]) ).
thf(zip_derived_cl38_024,plain,
irel @ '#sk2' @ '#sk4',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl3883,plain,
! [X0: $i] :
( ( a2 @ '#sk7' )
| ~ ( b @ ( '#sk9' @ X0 ) )
| ~ ( irel @ X0 @ '#sk2' )
| ( b1 @ ( '#sk8' @ '#sk2' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3868,zip_derived_cl38]) ).
thf(zip_derived_cl1079_025,plain,
( ( a2 @ '#sk7' )
| ~ ( b1 @ ( '#sk8' @ '#sk2' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1076,zip_derived_cl38]) ).
thf(zip_derived_cl4231,plain,
! [X0: $i] :
( ~ ( irel @ X0 @ '#sk2' )
| ~ ( b @ ( '#sk9' @ X0 ) )
| ( a2 @ '#sk7' ) ),
inference(clc,[status(thm)],[zip_derived_cl3883,zip_derived_cl1079]) ).
thf(zip_derived_cl30_026,plain,
irel @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl4232,plain,
( ( a2 @ '#sk7' )
| ~ ( b @ ( '#sk9' @ '#sk1' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4231,zip_derived_cl30]) ).
thf(zip_derived_cl5050_027,plain,
~ ( a2 @ '#sk7' ),
inference(demod,[status(thm)],[zip_derived_cl53,zip_derived_cl5049]) ).
thf(zip_derived_cl5075,plain,
~ ( b @ ( '#sk9' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl4232,zip_derived_cl5050]) ).
thf(zip_derived_cl30_028,plain,
irel @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl5438,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl5377,zip_derived_cl5075,zip_derived_cl30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO064^4.003 : TPTP v9.2.0. Released v4.0.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.jV8zmHbydK true
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 17:51:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.35 % Running in HO mode
% 0.50/0.62 % Total configuration time : 828
% 0.50/0.62 % Estimated wc time : 1656
% 0.50/0.62 % Estimated cpu time (8 cpus) : 207.0
% 0.55/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.55/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.55/0.71 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.55/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.55/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.55/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.55/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 10.39/1.96 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 14.07/2.43 % Solved by lams/30_sp5.sh.
% 14.07/2.43 % done 1799 iterations in 1.574s
% 14.07/2.43 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 14.07/2.43 % SZS output start Refutation
% See solution above
% 14.07/2.43
% 14.07/2.43
% 14.07/2.43 % Terminating...
% 14.99/2.58 % Runner terminated.
% 14.99/2.59 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------