%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYN391^4 : 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.96MNryPcnA true
% Computer : n016.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 05:04:42 PM UTC 2025
% Result : Theorem 13.91s 2.34s
% Output : Refutation 13.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 26
% Syntax : Number of formulae : 160 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 876 ( 33 equ; 48 cnn)
% Maximal formula atoms : 45 ( 5 avg)
% Number of connectives : 2140 ( 230 ~; 233 |; 23 &;1330 @)
% ( 0 <=>; 186 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 18 usr; 5 con; 0-3 aty)
% ( 138 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 402 ( 201 ^; 201 !; 0 ?; 402 :)
% Comments :
%------------------------------------------------------------------------------
thf(iatom_type,type,
iatom: ( $i > $o ) > $i > $o ).
thf(ivalid_type,type,
ivalid: ( $i > $o ) > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(p2_type,type,
p2: $i > $o ).
thf('#sk4_type',type,
'#sk4': $i > $i ).
thf(irel_type,type,
irel: $i > $i > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
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(iimplies_type,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(p1_type,type,
p1: $i > $o ).
thf(iand_type,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk3_type',type,
'#sk3': $i > $i ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(inot_type,type,
inot: ( $i > $o ) > $i > $o ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
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_cl57,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl57_001,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl57_002,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl57_003,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl57_004,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
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(iimplies,axiom,
( iimplies
= ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( 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(mimplies,axiom,
( mimplies
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
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(mnot,axiom,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ) ).
thf('6',plain,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
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
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
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('10',plain,
( iimplies
= ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[iimplies,'3','9']) ).
thf('11',plain,
( iimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mimplies @ ( mbox_s4 @ V_1 ) @ ( mbox_s4 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(ior,axiom,
( ior
= ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
thf('12',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('13',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('14',plain,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand]) ).
thf('15',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('16',plain,
( iand
= ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ),
inference(simplify_rw_rule,[status(thm)],[iand,'15']) ).
thf('17',plain,
( iand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf(inot,axiom,
( inot
= ( ^ [P: $i > $o] : ( mnot @ ( mbox_s4 @ P ) ) ) ) ).
thf('18',plain,
( inot
= ( ^ [P: $i > $o] : ( mnot @ ( mbox_s4 @ P ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[inot,'3','7']) ).
thf('19',plain,
( inot
= ( ^ [V_1: $i > $o] : ( mnot @ ( mbox_s4 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(iatom,axiom,
( iatom
= ( ^ [P: $i > $o] : P ) ) ).
thf('20',plain,
( iatom
= ( ^ [P: $i > $o] : P ) ),
inference(simplify_rw_rule,[status(thm)],[iatom]) ).
thf('21',plain,
( iatom
= ( ^ [V_1: $i > $o] : V_1 ) ),
define([status(thm)]) ).
thf(pel9,conjecture,
ivalid @ ( iimplies @ ( iand @ ( ior @ ( iatom @ p1 ) @ ( iatom @ p2 ) ) @ ( iand @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( iatom @ p2 ) ) @ ( ior @ ( iatom @ p1 ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) @ ( inot @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ! [X24: $i] :
( ( irel @ X4 @ X24 )
=> ~ ! [X26: $i] :
( ( irel @ X24 @ X26 )
=> ( ! [X32: $i] :
( ( irel @ X26 @ X32 )
=> ~ ! [X34: $i] :
( ( irel @ X32 @ X34 )
=> ( p2 @ X34 ) ) )
| ! [X28: $i] :
( ( irel @ X26 @ X28 )
=> ~ ! [X30: $i] :
( ( irel @ X28 @ X30 )
=> ( p1 @ X30 ) ) ) ) ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( ( ! [X20: $i] :
( ( irel @ X6 @ X20 )
=> ~ ! [X22: $i] :
( ( irel @ X20 @ X22 )
=> ( p2 @ X22 ) ) )
| ! [X18: $i] :
( ( irel @ X6 @ X18 )
=> ( p1 @ X18 ) ) )
& ( ! [X16: $i] :
( ( irel @ X6 @ X16 )
=> ( p2 @ X16 ) )
| ! [X12: $i] :
( ( irel @ X6 @ X12 )
=> ~ ! [X14: $i] :
( ( irel @ X12 @ X14 )
=> ( p1 @ X14 ) ) ) )
& ( ! [X10: $i] :
( ( irel @ X6 @ X10 )
=> ( p2 @ X10 ) )
| ! [X8: $i] :
( ( irel @ X6 @ X8 )
=> ( p1 @ X8 ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ! [X24: $i] :
( ( irel @ X4 @ X24 )
=> ~ ! [X26: $i] :
( ( irel @ X24 @ X26 )
=> ( ! [X32: $i] :
( ( irel @ X26 @ X32 )
=> ~ ! [X34: $i] :
( ( irel @ X32 @ X34 )
=> ( p2 @ X34 ) ) )
| ! [X28: $i] :
( ( irel @ X26 @ X28 )
=> ~ ! [X30: $i] :
( ( irel @ X28 @ X30 )
=> ( p1 @ X30 ) ) ) ) ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( ( ! [X20: $i] :
( ( irel @ X6 @ X20 )
=> ~ ! [X22: $i] :
( ( irel @ X20 @ X22 )
=> ( p2 @ X22 ) ) )
| ! [X18: $i] :
( ( irel @ X6 @ X18 )
=> ( p1 @ X18 ) ) )
& ( ! [X16: $i] :
( ( irel @ X6 @ X16 )
=> ( p2 @ X16 ) )
| ! [X12: $i] :
( ( irel @ X6 @ X12 )
=> ~ ! [X14: $i] :
( ( irel @ X12 @ X14 )
=> ( p1 @ X14 ) ) ) )
& ( ! [X10: $i] :
( ( irel @ X6 @ X10 )
=> ( p2 @ X10 ) )
| ! [X8: $i] :
( ( irel @ X6 @ X8 )
=> ( p1 @ X8 ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( p2 @ Y4 ) ) ) ) ) )
| ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( p1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p2 @ Y3 ) ) ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p1 @ Y3 ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl5,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p2 @ Y3 ) ) ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl6,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p2 @ Y3 ) ) ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl8,plain,
~ ( ( irel @ '#sk1' @ '#sk2' )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl11,plain,
( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl13,plain,
! [X2: $i] :
( ( irel @ '#sk2' @ X2 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl17,plain,
! [X2: $i] :
( ~ ( irel @ '#sk2' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl21,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
| ~ ( irel @ '#sk2' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl25,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) )
| ~ ( irel @ '#sk2' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl29,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
| ~ ( irel @ '#sk2' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl33,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X4 @ ( '#sk3' @ X4 ) )
=> ( p2 @ ( '#sk3' @ X4 ) ) )
| ~ ( irel @ '#sk2' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl38,plain,
! [X2: $i,X4: $i] :
( ( irel @ X4 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
| ~ ( irel @ '#sk2' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl43,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X2 @ X6 )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) )
| ~ ( irel @ '#sk2' @ X2 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X4 @ ( '#sk3' @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl49,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X2 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( irel @ X4 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( irel @ '#sk2' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl51,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( irel @ X6 @ ( '#sk4' @ X6 ) )
=> ( p1 @ ( '#sk4' @ X6 ) ) )
| ~ ( irel @ '#sk2' @ X2 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X4 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl53,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( irel @ X6 @ ( '#sk4' @ X6 ) )
| ~ ( irel @ X2 @ X6 )
| ( irel @ X4 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( irel @ '#sk2' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl253,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk2' @ X0 )
| ~ ( irel @ X0 @ X1 )
| ( irel @ X1 @ ( '#sk3' @ X1 ) )
| ( irel @ X0 @ ( '#sk4' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl53]) ).
thf(zip_derived_cl376,plain,
! [X0: $i] :
( ( irel @ '#sk2' @ ( '#sk4' @ '#sk2' ) )
| ( irel @ X0 @ ( '#sk3' @ X0 ) )
| ~ ( irel @ '#sk2' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl253]) ).
thf(zip_derived_cl382,plain,
( ( irel @ '#sk2' @ ( '#sk3' @ '#sk2' ) )
| ( irel @ '#sk2' @ ( '#sk4' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl376]) ).
thf(zip_derived_cl10,plain,
irel @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl57_005,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl7,plain,
( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl9,plain,
! [X2: $i] :
( ( irel @ '#sk1' @ X2 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl12,plain,
! [X2: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl15,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl19,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl23,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( p2 @ X4 ) )
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl27,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( p2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl31,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X2 @ X6 )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ( p2 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl36,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X2 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( p2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl42,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( irel @ X6 @ ( '#sk4' @ X6 ) )
=> ( p1 @ ( '#sk4' @ X6 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ( p2 @ X4 )
| ~ ( irel @ X2 @ X4 )
| ~ ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl47,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( irel @ X6 @ ( '#sk4' @ X6 ) )
| ~ ( irel @ X2 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( p2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl217,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk1' @ X0 )
| ( p2 @ X1 )
| ~ ( irel @ X0 @ X1 )
| ( irel @ X0 @ ( '#sk4' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl47]) ).
thf(zip_derived_cl332,plain,
! [X0: $i] :
( ( irel @ '#sk2' @ ( '#sk4' @ '#sk2' ) )
| ~ ( irel @ '#sk2' @ X0 )
| ( p2 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl217]) ).
thf(zip_derived_cl405,plain,
( ( irel @ '#sk2' @ ( '#sk4' @ '#sk2' ) )
| ( p2 @ ( '#sk3' @ '#sk2' ) )
| ( irel @ '#sk2' @ ( '#sk4' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl382,zip_derived_cl332]) ).
thf(zip_derived_cl455,plain,
( ( p2 @ ( '#sk3' @ '#sk2' ) )
| ( irel @ '#sk2' @ ( '#sk4' @ '#sk2' ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl405]) ).
thf(zip_derived_cl57_006,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl57_007,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl39,plain,
! [X2: $i,X4: $i] :
( ~ ( p2 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
| ~ ( irel @ '#sk2' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl44,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X2 @ X6 )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) )
| ~ ( irel @ '#sk2' @ X2 )
| ~ ( irel @ X2 @ X4 )
| ~ ( p2 @ ( '#sk3' @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl50,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X2 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( p2 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( irel @ '#sk2' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl52,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( irel @ X6 @ ( '#sk4' @ X6 ) )
=> ( p1 @ ( '#sk4' @ X6 ) ) )
| ~ ( irel @ '#sk2' @ X2 )
| ~ ( irel @ X2 @ X4 )
| ~ ( p2 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl55,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( irel @ X6 @ ( '#sk4' @ X6 ) )
| ~ ( irel @ X2 @ X6 )
| ~ ( p2 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( irel @ '#sk2' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl301,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk2' @ X0 )
| ~ ( irel @ X0 @ X1 )
| ~ ( p2 @ ( '#sk3' @ X1 ) )
| ( irel @ X0 @ ( '#sk4' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl55]) ).
thf(zip_derived_cl512,plain,
! [X0: $i] :
( ( irel @ '#sk2' @ ( '#sk4' @ '#sk2' ) )
| ~ ( p2 @ ( '#sk3' @ X0 ) )
| ~ ( irel @ '#sk2' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl301]) ).
thf(zip_derived_cl520,plain,
( ( irel @ '#sk2' @ ( '#sk4' @ '#sk2' ) )
| ~ ( irel @ '#sk2' @ '#sk2' )
| ( irel @ '#sk2' @ ( '#sk4' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl455,zip_derived_cl512]) ).
thf(zip_derived_cl57_008,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl524,plain,
( ( irel @ '#sk2' @ ( '#sk4' @ '#sk2' ) )
| ( irel @ '#sk2' @ ( '#sk4' @ '#sk2' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl520,zip_derived_cl57]) ).
thf(zip_derived_cl525,plain,
irel @ '#sk2' @ ( '#sk4' @ '#sk2' ),
inference(simplify,[status(thm)],[zip_derived_cl524]) ).
thf(zip_derived_cl10_009,plain,
irel @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl14,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl18,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl22,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl26,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X4 @ ( '#sk3' @ X4 ) )
=> ( p2 @ ( '#sk3' @ X4 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl34,plain,
! [X2: $i,X4: $i] :
( ( irel @ X4 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl40,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X2 @ X6 )
=> ( p1 @ X6 ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X4 @ ( '#sk3' @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl45,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X2 @ X6 )
| ( p1 @ X6 )
| ( irel @ X4 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl145,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk1' @ X1 )
| ~ ( irel @ X1 @ X0 )
| ( irel @ X0 @ ( '#sk3' @ X0 ) )
| ( p1 @ X0 ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl310,plain,
! [X0: $i] :
( ( p1 @ X0 )
| ( irel @ X0 @ ( '#sk3' @ X0 ) )
| ~ ( irel @ '#sk2' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl145]) ).
thf(zip_derived_cl532,plain,
( ( irel @ ( '#sk4' @ '#sk2' ) @ ( '#sk3' @ ( '#sk4' @ '#sk2' ) ) )
| ( p1 @ ( '#sk4' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl525,zip_derived_cl310]) ).
thf(zip_derived_cl10_010,plain,
irel @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl525_011,plain,
irel @ '#sk2' @ ( '#sk4' @ '#sk2' ),
inference(simplify,[status(thm)],[zip_derived_cl524]) ).
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_cl104,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_cl105,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( irel @ X4 @ Y0 )
& ( irel @ X2 @ X4 ) )
=> ( irel @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl106,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X4 @ X6 )
& ( irel @ X2 @ X4 ) )
=> ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl107,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( irel @ X4 @ X6 )
& ( irel @ X2 @ X4 ) )
| ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl108,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl538,plain,
! [X0: $i] :
( ( irel @ X0 @ ( '#sk4' @ '#sk2' ) )
| ~ ( irel @ X0 @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl525,zip_derived_cl108]) ).
thf(zip_derived_cl579,plain,
irel @ '#sk1' @ ( '#sk4' @ '#sk2' ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl538]) ).
thf(zip_derived_cl57_012,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl16,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl20,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p2 @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( p2 @ X4 ) )
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl28,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( p2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl32,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X2 @ X6 )
=> ( p1 @ X6 ) )
| ~ ( irel @ '#sk1' @ X2 )
| ( p2 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl37,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X2 @ X6 )
| ( p1 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( p2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl77,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk1' @ X0 )
| ( p2 @ X1 )
| ~ ( irel @ X0 @ X1 )
| ( p1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl37]) ).
thf(zip_derived_cl603,plain,
! [X0: $i] :
( ( p1 @ ( '#sk4' @ '#sk2' ) )
| ~ ( irel @ ( '#sk4' @ '#sk2' ) @ X0 )
| ( p2 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl579,zip_derived_cl77]) ).
thf(zip_derived_cl853,plain,
( ( p1 @ ( '#sk4' @ '#sk2' ) )
| ( p2 @ ( '#sk3' @ ( '#sk4' @ '#sk2' ) ) )
| ( p1 @ ( '#sk4' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl532,zip_derived_cl603]) ).
thf(zip_derived_cl882,plain,
( ( p2 @ ( '#sk3' @ ( '#sk4' @ '#sk2' ) ) )
| ( p1 @ ( '#sk4' @ '#sk2' ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl853]) ).
thf(zip_derived_cl525_013,plain,
irel @ '#sk2' @ ( '#sk4' @ '#sk2' ),
inference(simplify,[status(thm)],[zip_derived_cl524]) ).
thf(zip_derived_cl525_014,plain,
irel @ '#sk2' @ ( '#sk4' @ '#sk2' ),
inference(simplify,[status(thm)],[zip_derived_cl524]) ).
thf(zip_derived_cl35,plain,
! [X2: $i,X4: $i] :
( ~ ( p2 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl41,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X2 @ X6 )
=> ( p1 @ X6 ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( irel @ X2 @ X4 )
| ~ ( p2 @ ( '#sk3' @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl46,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X2 @ X6 )
| ( p1 @ X6 )
| ~ ( p2 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl542,plain,
! [X0: $i] :
( ~ ( irel @ '#sk1' @ '#sk2' )
| ~ ( irel @ '#sk2' @ X0 )
| ~ ( p2 @ ( '#sk3' @ X0 ) )
| ( p1 @ ( '#sk4' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl525,zip_derived_cl46]) ).
thf(zip_derived_cl10_015,plain,
irel @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl565,plain,
! [X0: $i] :
( ~ ( irel @ '#sk2' @ X0 )
| ~ ( p2 @ ( '#sk3' @ X0 ) )
| ( p1 @ ( '#sk4' @ '#sk2' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl542,zip_derived_cl10]) ).
thf(zip_derived_cl653,plain,
( ( p1 @ ( '#sk4' @ '#sk2' ) )
| ~ ( p2 @ ( '#sk3' @ ( '#sk4' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl525,zip_derived_cl565]) ).
thf(zip_derived_cl904,plain,
p1 @ ( '#sk4' @ '#sk2' ),
inference(clc,[status(thm)],[zip_derived_cl882,zip_derived_cl653]) ).
thf(zip_derived_cl54,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( p1 @ ( '#sk4' @ X6 ) )
| ~ ( irel @ X2 @ X6 )
| ( irel @ X4 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( irel @ '#sk2' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl906,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk2' @ X0 )
| ~ ( irel @ X0 @ X1 )
| ( irel @ X1 @ ( '#sk3' @ X1 ) )
| ~ ( irel @ X0 @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl904,zip_derived_cl54]) ).
thf(zip_derived_cl1117,plain,
! [X0: $i] :
( ~ ( irel @ '#sk2' @ '#sk2' )
| ( irel @ X0 @ ( '#sk3' @ X0 ) )
| ~ ( irel @ '#sk2' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl906]) ).
thf(zip_derived_cl57_016,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl1122,plain,
! [X0: $i] :
( ( irel @ X0 @ ( '#sk3' @ X0 ) )
| ~ ( irel @ '#sk2' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1117,zip_derived_cl57]) ).
thf(zip_derived_cl1130,plain,
irel @ '#sk2' @ ( '#sk3' @ '#sk2' ),
inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl1122]) ).
thf(zip_derived_cl10_017,plain,
irel @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl904_018,plain,
p1 @ ( '#sk4' @ '#sk2' ),
inference(clc,[status(thm)],[zip_derived_cl882,zip_derived_cl653]) ).
thf(zip_derived_cl48,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( p1 @ ( '#sk4' @ X6 ) )
| ~ ( irel @ X2 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( p2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl907,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk1' @ X0 )
| ( p2 @ X1 )
| ~ ( irel @ X0 @ X1 )
| ~ ( irel @ X0 @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl904,zip_derived_cl48]) ).
thf(zip_derived_cl930,plain,
! [X0: $i] :
( ~ ( irel @ '#sk2' @ '#sk2' )
| ~ ( irel @ '#sk2' @ X0 )
| ( p2 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl907]) ).
thf(zip_derived_cl57_019,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl937,plain,
! [X0: $i] :
( ~ ( irel @ '#sk2' @ X0 )
| ( p2 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl930,zip_derived_cl57]) ).
thf(zip_derived_cl1140,plain,
p2 @ ( '#sk3' @ '#sk2' ),
inference('sup-',[status(thm)],[zip_derived_cl1130,zip_derived_cl937]) ).
thf(zip_derived_cl57_020,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl904_021,plain,
p1 @ ( '#sk4' @ '#sk2' ),
inference(clc,[status(thm)],[zip_derived_cl882,zip_derived_cl653]) ).
thf(zip_derived_cl56,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( p1 @ ( '#sk4' @ X6 ) )
| ~ ( irel @ X2 @ X6 )
| ~ ( p2 @ ( '#sk3' @ X4 ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( irel @ '#sk2' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl905,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk2' @ X0 )
| ~ ( irel @ X0 @ X1 )
| ~ ( p2 @ ( '#sk3' @ X1 ) )
| ~ ( irel @ X0 @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl904,zip_derived_cl56]) ).
thf(zip_derived_cl917,plain,
! [X0: $i] :
( ~ ( irel @ '#sk2' @ '#sk2' )
| ~ ( p2 @ ( '#sk3' @ X0 ) )
| ~ ( irel @ '#sk2' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl57,zip_derived_cl905]) ).
thf(zip_derived_cl57_022,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl922,plain,
! [X0: $i] :
( ~ ( p2 @ ( '#sk3' @ X0 ) )
| ~ ( irel @ '#sk2' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl917,zip_derived_cl57]) ).
thf(zip_derived_cl1185,plain,
~ ( irel @ '#sk2' @ '#sk2' ),
inference('sup-',[status(thm)],[zip_derived_cl1140,zip_derived_cl922]) ).
thf(zip_derived_cl57_023,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl1201,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl1185,zip_derived_cl57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SYN391^4 : TPTP v9.2.0. Released v4.0.0.
% 0.06/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.96MNryPcnA true
% 0.10/0.32 % Computer : n016.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Wed Oct 1 13:34:23 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Running portfolio for 300 s
% 0.10/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.32 % Number of cores: 8
% 0.10/0.32 % Python version: Python 3.6.8
% 0.10/0.32 % Running in HO mode
% 0.44/0.60 % Total configuration time : 828
% 0.44/0.60 % Estimated wc time : 1656
% 0.44/0.60 % Estimated cpu time (8 cpus) : 207.0
% 0.46/0.66 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.47/0.67 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.47/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.47/0.68 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.47/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.47/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.47/0.69 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.47/0.69 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.47/0.81 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 13.91/2.34 % Solved by lams/15_e_short1.sh.
% 13.91/2.34 % done 323 iterations in 1.596s
% 13.91/2.34 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 13.91/2.34 % SZS output start Refutation
% See solution above
% 13.91/2.35
% 13.91/2.35
% 13.91/2.35 % Terminating...
% 14.42/2.42 % Runner terminated.
% 14.42/2.44 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------