%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU469^1 : TPTP v9.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.9cPOmqBVDp 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 04:54:44 PM UTC 2025
% Result : Theorem 10.17s 1.85s
% Output : Refutation 10.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 17
% Syntax : Number of formulae : 115 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 684 ( 104 equ; 0 cnn)
% Maximal formula atoms : 33 ( 5 avg)
% Number of connectives : 2129 ( 77 ~; 150 |; 131 &;1296 @)
% ( 0 <=>; 184 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 168 ( 168 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 5 con; 0-3 aty)
% ( 291 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 446 ( 324 ^; 122 !; 0 ?; 446 :)
% Comments :
%------------------------------------------------------------------------------
thf(trc_type,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf('#sk164_type',type,
'#sk164': ( $i > $i > $o ) > $i ).
thf(subrel_type,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf('#sk66_type',type,
'#sk66': ( $i > $i > $o ) > $i ).
thf('#sk5_type',type,
'#sk5': $i > $i > $o ).
thf(refl_type,type,
refl: ( $i > $i > $o ) > $o ).
thf('#sk117_type',type,
'#sk117': ( $i > $i > $o ) > $i ).
thf('#form116_type',type,
'#form116': ( $i > $i > $o ) > $o ).
thf(tc_type,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(trans_type,type,
trans: ( $i > $i > $o ) > $o ).
thf('#sk213_type',type,
'#sk213': ( $i > $i > $o ) > $i ).
thf('#sk3_type',type,
'#sk3': $i ).
thf('#sk46_type',type,
'#sk46': ( $i > $i > $o ) > $i ).
thf('#sk2_type',type,
'#sk2': $i ).
thf('#sk4_type',type,
'#sk4': $i ).
thf(rc_type,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf('#sk1_type',type,
'#sk1': $i > $i > $o ).
thf(transitive_reflexive_closure,axiom,
( trc
= ( ^ [R: $i > $i > $o] : ( rc @ ( tc @ R ) ) ) ) ).
thf(transitive_closure,axiom,
( tc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
! [S: $i > $i > $o] :
( ( ( trans @ S )
& ( subrel @ R @ S ) )
=> ( S @ X @ Y ) ) ) ) ).
thf(transitive,axiom,
( trans
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Y )
& ( R @ Y @ Z ) )
=> ( R @ X @ Z ) ) ) ) ).
thf('0',plain,
( trans
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Y )
& ( R @ Y @ Z ) )
=> ( R @ X @ Z ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[transitive]) ).
thf('1',plain,
( trans
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i,X6: $i,X8: $i] :
( ( ( V_1 @ X4 @ X6 )
& ( V_1 @ X6 @ X8 ) )
=> ( V_1 @ X4 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(subrel,axiom,
( subrel
= ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ( S @ X @ Y ) ) ) ) ).
thf('2',plain,
( subrel
= ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ( S @ X @ Y ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[subrel]) ).
thf('3',plain,
( subrel
= ( ^ [V_1: $i > $i > $o,V_2: $i > $i > $o] :
! [X4: $i,X6: $i] :
( ( V_1 @ X4 @ X6 )
=> ( V_2 @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf('4',plain,
( tc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
! [S: $i > $i > $o] :
( ( ( trans @ S )
& ( subrel @ R @ S ) )
=> ( S @ X @ Y ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[transitive_closure,'1','3']) ).
thf('5',plain,
( tc
= ( ^ [V_1: $i > $i > $o,V_2: $i,V_3: $i] :
! [X4: $i > $i > $o] :
( ( ( trans @ X4 )
& ( subrel @ V_1 @ X4 ) )
=> ( X4 @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(reflexive_closure,axiom,
( rc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( X = Y )
| ( R @ X @ Y ) ) ) ) ).
thf('6',plain,
( rc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( X = Y )
| ( R @ X @ Y ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[reflexive_closure]) ).
thf('7',plain,
( rc
= ( ^ [V_1: $i > $i > $o,V_2: $i,V_3: $i] :
( ( V_2 = V_3 )
| ( V_1 @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('8',plain,
( trc
= ( ^ [R: $i > $i > $o] : ( rc @ ( tc @ R ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[transitive_reflexive_closure,'5','1','7','3']) ).
thf('9',plain,
( trc
= ( ^ [V_1: $i > $i > $o] : ( rc @ ( tc @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(reflexive,axiom,
( refl
= ( ^ [R: $i > $i > $o] :
! [X: $i] : ( R @ X @ X ) ) ) ).
thf('10',plain,
( refl
= ( ^ [R: $i > $i > $o] :
! [X: $i] : ( R @ X @ X ) ) ),
inference(simplify_rw_rule,[status(thm)],[reflexive]) ).
thf('11',plain,
( refl
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i] : ( V_1 @ X4 @ X4 ) ) ),
define([status(thm)]) ).
thf(transitive_reflexive_closure_is_transitive_reflexive,conjecture,
! [R: $i > $i > $o] :
( ( refl @ ( trc @ R ) )
& ( trans @ ( trc @ R ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i > $i > $o] :
( ! [X20: $i,X22: $i,X24: $i] :
( ( ( ! [X38: $i > $i > $o] :
( ( ! [X46: $i,X48: $i] :
( ( X4 @ X46 @ X48 )
=> ( X38 @ X46 @ X48 ) )
& ! [X40: $i,X42: $i,X44: $i] :
( ( ( X38 @ X42 @ X44 )
& ( X38 @ X40 @ X42 ) )
=> ( X38 @ X40 @ X44 ) ) )
=> ( X38 @ X22 @ X24 ) )
| ( X22 = X24 ) )
& ( ! [X26: $i > $i > $o] :
( ( ! [X34: $i,X36: $i] :
( ( X4 @ X34 @ X36 )
=> ( X26 @ X34 @ X36 ) )
& ! [X28: $i,X30: $i,X32: $i] :
( ( ( X26 @ X30 @ X32 )
& ( X26 @ X28 @ X30 ) )
=> ( X26 @ X28 @ X32 ) ) )
=> ( X26 @ X20 @ X22 ) )
| ( X20 = X22 ) ) )
=> ( ! [X50: $i > $i > $o] :
( ( ! [X58: $i,X60: $i] :
( ( X4 @ X58 @ X60 )
=> ( X50 @ X58 @ X60 ) )
& ! [X52: $i,X54: $i,X56: $i] :
( ( ( X50 @ X54 @ X56 )
& ( X50 @ X52 @ X54 ) )
=> ( X50 @ X52 @ X56 ) ) )
=> ( X50 @ X20 @ X24 ) )
| ( X20 = X24 ) ) )
& ! [X6: $i] :
( ! [X8: $i > $i > $o] :
( ( ! [X16: $i,X18: $i] :
( ( X4 @ X16 @ X18 )
=> ( X8 @ X16 @ X18 ) )
& ! [X10: $i,X12: $i,X14: $i] :
( ( ( X8 @ X12 @ X14 )
& ( X8 @ X10 @ X12 ) )
=> ( X8 @ X10 @ X14 ) ) )
=> ( X8 @ X6 @ X6 ) )
| ( X6 = X6 ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i > $i > $o] :
( ! [X20: $i,X22: $i,X24: $i] :
( ( ( ! [X38: $i > $i > $o] :
( ( ! [X46: $i,X48: $i] :
( ( X4 @ X46 @ X48 )
=> ( X38 @ X46 @ X48 ) )
& ! [X40: $i,X42: $i,X44: $i] :
( ( ( X38 @ X42 @ X44 )
& ( X38 @ X40 @ X42 ) )
=> ( X38 @ X40 @ X44 ) ) )
=> ( X38 @ X22 @ X24 ) )
| ( X22 = X24 ) )
& ( ! [X26: $i > $i > $o] :
( ( ! [X34: $i,X36: $i] :
( ( X4 @ X34 @ X36 )
=> ( X26 @ X34 @ X36 ) )
& ! [X28: $i,X30: $i,X32: $i] :
( ( ( X26 @ X30 @ X32 )
& ( X26 @ X28 @ X30 ) )
=> ( X26 @ X28 @ X32 ) ) )
=> ( X26 @ X20 @ X22 ) )
| ( X20 = X22 ) ) )
=> ( ! [X50: $i > $i > $o] :
( ( ! [X58: $i,X60: $i] :
( ( X4 @ X58 @ X60 )
=> ( X50 @ X58 @ X60 ) )
& ! [X52: $i,X54: $i,X56: $i] :
( ( ( X50 @ X54 @ X56 )
& ( X50 @ X52 @ X54 ) )
=> ( X50 @ X52 @ X56 ) ) )
=> ( X50 @ X20 @ X24 ) )
| ( X20 = X24 ) ) )
& ! [X6: $i] :
( ! [X8: $i > $i > $o] :
( ( ! [X16: $i,X18: $i] :
( ( X4 @ X16 @ X18 )
=> ( X8 @ X16 @ X18 ) )
& ! [X10: $i,X12: $i,X14: $i] :
( ( ( X8 @ X12 @ X14 )
& ( X8 @ X10 @ X12 ) )
=> ( X8 @ X10 @ X14 ) ) )
=> ( X8 @ X6 @ X6 ) )
| ( X6 = X6 ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: $i > $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( ( !!
@ ^ [Y4: $i > $i > $o] :
( ( ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( !!
@ ^ [Y7: $i] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( Y2 = Y3 ) )
& ( ( !!
@ ^ [Y4: $i > $i > $o] :
( ( ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( !!
@ ^ [Y7: $i] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) )
=> ( ( !!
@ ^ [Y4: $i > $i > $o] :
( ( ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( !!
@ ^ [Y7: $i] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
| ( Y1 = Y3 ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i > $i > $o] :
( ( ( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( ( Y0 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y1 ) ) )
| ( Y1 = Y1 ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( ( !!
@ ^ [Y4: $i > $i > $o] :
( ( ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( !!
@ ^ [Y7: $i] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( Y2 = Y3 ) )
& ( ( !!
@ ^ [Y4: $i > $i > $o] :
( ( ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( !!
@ ^ [Y7: $i] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) )
=> ( ( !!
@ ^ [Y4: $i > $i > $o] :
( ( ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( !!
@ ^ [Y7: $i] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
| ( Y1 = Y3 ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( ( !!
@ ^ [Y3: $i > $i > $o] :
( ( ( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) )
& ( ( !!
@ ^ [Y3: $i > $i > $o] :
( ( ( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y1 ) ) )
| ( Y0 = Y1 ) ) )
=> ( ( !!
@ ^ [Y3: $i > $i > $o] :
( ( ( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
| ( Y0 = Y2 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( ( !!
@ ^ [Y2: $i > $i > $o] :
( ( ( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( Y0 = Y1 ) )
& ( ( !!
@ ^ [Y2: $i > $i > $o] :
( ( ( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ '#sk2' @ Y0 ) ) )
| ( '#sk2' = Y0 ) ) )
=> ( ( !!
@ ^ [Y2: $i > $i > $o] :
( ( ( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( ( '#sk1' @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ '#sk2' @ Y1 ) ) )
| ( '#sk2' = Y1 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( ( ( !!
@ ^ [Y1: $i > $i > $o] :
( ( ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ '#sk3' @ Y0 ) ) )
| ( '#sk3' = Y0 ) )
& ( ( !!
@ ^ [Y1: $i > $i > $o] :
( ( ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ '#sk2' @ '#sk3' ) ) )
| ( '#sk2' = '#sk3' ) ) )
=> ( ( !!
@ ^ [Y1: $i > $i > $o] :
( ( ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ '#sk2' @ Y0 ) ) )
| ( '#sk2' = Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl5,plain,
~ ( ( ( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' ) )
& ( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk2' @ '#sk3' ) ) )
| ( '#sk2' = '#sk3' ) ) )
=> ( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk2' @ '#sk4' ) ) )
| ( '#sk2' = '#sk4' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl6,plain,
( ( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' ) )
& ( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk2' @ '#sk3' ) ) )
| ( '#sk2' = '#sk3' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl9,plain,
( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk2' @ '#sk3' ) ) )
| ( '#sk2' = '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl13,plain,
( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk2' @ '#sk3' ) ) )
| ( '#sk2' = '#sk3' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl20,plain,
( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk2' @ '#sk3' ) ) )
| ( '#sk2' = '#sk3' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl21,plain,
! [X2: $i > $i > $o] :
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) )
=> ( X2 @ '#sk2' @ '#sk3' ) )
| ( '#sk2' = '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl22,plain,
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk5' @ '#sk2' @ '#sk3' ) )
| ( '#sk2' = '#sk3' ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl163,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) )
| ( '#sk5' @ '#sk2' @ '#sk3' )
| ( '#sk2' = '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl164,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
| ( '#sk2' = '#sk3' )
| ( '#sk5' @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl163]) ).
thf(zip_derived_cl8,plain,
( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl12,plain,
( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl16,plain,
( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl17,plain,
! [X2: $i > $i > $o] :
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) )
=> ( X2 @ '#sk3' @ '#sk4' ) )
| ( '#sk3' = '#sk4' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl26,plain,
! [X2: $i > $i > $o] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) )
| ( X2 @ '#sk3' @ '#sk4' )
| ( '#sk3' = '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl30,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| ( '#sk3' = '#sk4' )
| ( X2 @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl34,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ ( '#sk46' @ X2 ) @ Y0 )
=> ( X2 @ ( '#sk46' @ X2 ) @ Y0 ) ) )
| ( X2 @ '#sk3' @ '#sk4' )
| ( '#sk3' = '#sk4' )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl38,plain,
! [X2: $i > $i > $o] :
( ~ ( ( '#sk1' @ ( '#sk46' @ X2 ) @ ( '#sk66' @ X2 ) )
=> ( X2 @ ( '#sk46' @ X2 ) @ ( '#sk66' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| ( '#sk3' = '#sk4' )
| ( X2 @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl42,plain,
! [X2: $i > $i > $o] :
( ( '#sk1' @ ( '#sk46' @ X2 ) @ ( '#sk66' @ X2 ) )
| ( X2 @ '#sk3' @ '#sk4' )
| ( '#sk3' = '#sk4' )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl47,plain,
! [X2: $i > $i > $o] :
( ( '#form116' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl165,plain,
( ~ ( '#form116' @ '#sk5' )
| ( '#sk5' @ '#sk2' @ '#sk3' )
| ( '#sk2' = '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl164,zip_derived_cl47]) ).
thf(zip_derived_cl166,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ ( '#sk46' @ '#sk5' ) @ Y0 )
=> ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ Y0 ) ) )
| ( '#sk2' = '#sk3' )
| ( '#sk5' @ '#sk2' @ '#sk3' )
| ~ ( '#form116' @ '#sk5' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl165]) ).
thf(zip_derived_cl167,plain,
( ~ ( ( '#sk1' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) )
=> ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) ) )
| ~ ( '#form116' @ '#sk5' )
| ( '#sk5' @ '#sk2' @ '#sk3' )
| ( '#sk2' = '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl166]) ).
thf(zip_derived_cl168,plain,
( ( '#sk1' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) )
| ( '#sk2' = '#sk3' )
| ( '#sk5' @ '#sk2' @ '#sk3' )
| ~ ( '#form116' @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl167]) ).
thf(zip_derived_cl7,plain,
~ ( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk2' @ '#sk4' ) ) )
| ( '#sk2' = '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl10,plain,
~ ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk2' @ '#sk4' ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl14,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk5' @ '#sk2' @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl24,plain,
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl28,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl32,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk5' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl36,plain,
! [X2: $i,X4: $i] :
( ( '#sk1' @ X2 @ X4 )
=> ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl40,plain,
! [X2: $i,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl170,plain,
( ~ ( '#form116' @ '#sk5' )
| ( '#sk5' @ '#sk2' @ '#sk3' )
| ( '#sk2' = '#sk3' )
| ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl168,zip_derived_cl40]) ).
thf(zip_derived_cl169,plain,
( ~ ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) )
| ( '#sk2' = '#sk3' )
| ( '#sk5' @ '#sk2' @ '#sk3' )
| ~ ( '#form116' @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl167]) ).
thf(zip_derived_cl196,plain,
( ( '#sk2' = '#sk3' )
| ( '#sk5' @ '#sk2' @ '#sk3' )
| ~ ( '#form116' @ '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl170,zip_derived_cl169]) ).
thf(zip_derived_cl17_001,plain,
! [X2: $i > $i > $o] :
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) )
=> ( X2 @ '#sk3' @ '#sk4' ) )
| ( '#sk3' = '#sk4' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl18,plain,
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk5' @ '#sk3' @ '#sk4' ) )
| ( '#sk3' = '#sk4' ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl92,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) )
| ( '#sk5' @ '#sk3' @ '#sk4' )
| ( '#sk3' = '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl93,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
| ( '#sk3' = '#sk4' )
| ( '#sk5' @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl47_002,plain,
! [X2: $i > $i > $o] :
( ( '#form116' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl94,plain,
( ~ ( '#form116' @ '#sk5' )
| ( '#sk5' @ '#sk3' @ '#sk4' )
| ( '#sk3' = '#sk4' )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl93,zip_derived_cl47]) ).
thf(zip_derived_cl95,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ ( '#sk46' @ '#sk5' ) @ Y0 )
=> ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ Y0 ) ) )
| ( '#sk3' = '#sk4' )
| ( '#sk5' @ '#sk3' @ '#sk4' )
| ~ ( '#form116' @ '#sk5' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl96,plain,
( ~ ( ( '#sk1' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) )
=> ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) ) )
| ~ ( '#form116' @ '#sk5' )
| ( '#sk5' @ '#sk3' @ '#sk4' )
| ( '#sk3' = '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl98,plain,
( ~ ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) )
| ( '#sk3' = '#sk4' )
| ( '#sk5' @ '#sk3' @ '#sk4' )
| ~ ( '#form116' @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl97,plain,
( ( '#sk1' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) )
| ( '#sk3' = '#sk4' )
| ( '#sk5' @ '#sk3' @ '#sk4' )
| ~ ( '#form116' @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl40_003,plain,
! [X2: $i,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl99,plain,
( ~ ( '#form116' @ '#sk5' )
| ( '#sk5' @ '#sk3' @ '#sk4' )
| ( '#sk3' = '#sk4' )
| ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl97,zip_derived_cl40]) ).
thf(zip_derived_cl160,plain,
( ~ ( '#form116' @ '#sk5' )
| ( '#sk5' @ '#sk3' @ '#sk4' )
| ( '#sk3' = '#sk4' ) ),
inference(clc,[status(thm)],[zip_derived_cl98,zip_derived_cl99]) ).
thf(zip_derived_cl29,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl33,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( '#sk5' @ Y0 @ Y1 )
& ( '#sk5' @ X2 @ Y0 ) )
=> ( '#sk5' @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl37,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( '#sk5' @ X4 @ Y0 )
& ( '#sk5' @ X2 @ X4 ) )
=> ( '#sk5' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl41,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( '#sk5' @ X4 @ X6 )
& ( '#sk5' @ X2 @ X4 ) )
=> ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl46,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( '#sk5' @ X4 @ X6 )
& ( '#sk5' @ X2 @ X4 ) )
| ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl53,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#sk5' @ X4 @ X6 )
| ~ ( '#sk5' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl161,plain,
! [X0: $i] :
( ( '#sk3' = '#sk4' )
| ~ ( '#form116' @ '#sk5' )
| ( '#sk5' @ X0 @ '#sk4' )
| ~ ( '#sk5' @ X0 @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl160,zip_derived_cl53]) ).
thf(zip_derived_cl205,plain,
( ~ ( '#form116' @ '#sk5' )
| ( '#sk2' = '#sk3' )
| ( '#sk5' @ '#sk2' @ '#sk4' )
| ~ ( '#form116' @ '#sk5' )
| ( '#sk3' = '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl196,zip_derived_cl161]) ).
thf(zip_derived_cl213,plain,
( ( '#sk3' = '#sk4' )
| ( '#sk5' @ '#sk2' @ '#sk4' )
| ( '#sk2' = '#sk3' )
| ~ ( '#form116' @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl205]) ).
thf(zip_derived_cl25,plain,
~ ( '#sk5' @ '#sk2' @ '#sk4' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl221,plain,
( ~ ( '#form116' @ '#sk5' )
| ( '#sk2' = '#sk3' )
| ( '#sk3' = '#sk4' ) ),
inference(clc,[status(thm)],[zip_derived_cl213,zip_derived_cl25]) ).
thf(zip_derived_cl47_004,plain,
! [X2: $i > $i > $o] :
( ( '#form116' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl48,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( X2 @ Y0 @ Y1 )
& ( X2 @ ( '#sk117' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk117' @ X2 ) @ Y1 ) ) ) )
| ( '#form116' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl54,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( ( X2 @ ( '#sk164' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk117' @ X2 ) @ ( '#sk164' @ X2 ) ) )
=> ( X2 @ ( '#sk117' @ X2 ) @ Y0 ) ) )
| ( '#form116' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl58,plain,
! [X2: $i > $i > $o] :
( ~ ( ( ( X2 @ ( '#sk164' @ X2 ) @ ( '#sk213' @ X2 ) )
& ( X2 @ ( '#sk117' @ X2 ) @ ( '#sk164' @ X2 ) ) )
=> ( X2 @ ( '#sk117' @ X2 ) @ ( '#sk213' @ X2 ) ) )
| ( '#form116' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl59,plain,
! [X2: $i > $i > $o] :
( ( ( X2 @ ( '#sk164' @ X2 ) @ ( '#sk213' @ X2 ) )
& ( X2 @ ( '#sk117' @ X2 ) @ ( '#sk164' @ X2 ) ) )
| ( '#form116' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl62,plain,
! [X2: $i > $i > $o] :
( ( X2 @ ( '#sk117' @ X2 ) @ ( '#sk164' @ X2 ) )
| ( '#form116' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl61,plain,
! [X2: $i > $i > $o] :
( ( X2 @ ( '#sk164' @ X2 ) @ ( '#sk213' @ X2 ) )
| ( '#form116' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl53_005,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#sk5' @ X4 @ X6 )
| ~ ( '#sk5' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl125,plain,
! [X0: $i] :
( ( '#form116' @ '#sk5' )
| ( '#sk5' @ X0 @ ( '#sk213' @ '#sk5' ) )
| ~ ( '#sk5' @ X0 @ ( '#sk164' @ '#sk5' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl53]) ).
thf(zip_derived_cl317,plain,
( ( '#form116' @ '#sk5' )
| ( '#sk5' @ ( '#sk117' @ '#sk5' ) @ ( '#sk213' @ '#sk5' ) )
| ( '#form116' @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl125]) ).
thf(zip_derived_cl321,plain,
( ( '#sk5' @ ( '#sk117' @ '#sk5' ) @ ( '#sk213' @ '#sk5' ) )
| ( '#form116' @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl317]) ).
thf(zip_derived_cl60,plain,
! [X2: $i > $i > $o] :
( ~ ( X2 @ ( '#sk117' @ X2 ) @ ( '#sk213' @ X2 ) )
| ( '#form116' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl322,plain,
'#form116' @ '#sk5',
inference(clc,[status(thm)],[zip_derived_cl321,zip_derived_cl60]) ).
thf(zip_derived_cl326,plain,
( ( '#sk2' = '#sk3' )
| ( '#sk3' = '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl221,zip_derived_cl322]) ).
thf(zip_derived_cl25_006,plain,
~ ( '#sk5' @ '#sk2' @ '#sk4' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl339,plain,
( ~ ( '#sk5' @ '#sk3' @ '#sk4' )
| ( '#sk3' = '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl326,zip_derived_cl25]) ).
thf(zip_derived_cl160_007,plain,
( ~ ( '#form116' @ '#sk5' )
| ( '#sk5' @ '#sk3' @ '#sk4' )
| ( '#sk3' = '#sk4' ) ),
inference(clc,[status(thm)],[zip_derived_cl98,zip_derived_cl99]) ).
thf(zip_derived_cl322_008,plain,
'#form116' @ '#sk5',
inference(clc,[status(thm)],[zip_derived_cl321,zip_derived_cl60]) ).
thf(zip_derived_cl323,plain,
( ( '#sk5' @ '#sk3' @ '#sk4' )
| ( '#sk3' = '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl160,zip_derived_cl322]) ).
thf(zip_derived_cl414,plain,
'#sk3' = '#sk4',
inference(clc,[status(thm)],[zip_derived_cl339,zip_derived_cl323]) ).
thf(zip_derived_cl25_009,plain,
~ ( '#sk5' @ '#sk2' @ '#sk4' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl416,plain,
~ ( '#sk5' @ '#sk2' @ '#sk3' ),
inference('sup-',[status(thm)],[zip_derived_cl414,zip_derived_cl25]) ).
thf(zip_derived_cl196_010,plain,
( ( '#sk2' = '#sk3' )
| ( '#sk5' @ '#sk2' @ '#sk3' )
| ~ ( '#form116' @ '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl170,zip_derived_cl169]) ).
thf(zip_derived_cl322_011,plain,
'#form116' @ '#sk5',
inference(clc,[status(thm)],[zip_derived_cl321,zip_derived_cl60]) ).
thf(zip_derived_cl325,plain,
( ( '#sk2' = '#sk3' )
| ( '#sk5' @ '#sk2' @ '#sk3' ) ),
inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl322]) ).
thf(zip_derived_cl414_012,plain,
'#sk3' = '#sk4',
inference(clc,[status(thm)],[zip_derived_cl339,zip_derived_cl323]) ).
thf(zip_derived_cl11,plain,
'#sk2' != '#sk4',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl15,plain,
'#sk2' != '#sk4',
inference('simplify nested equalities',[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl417,plain,
'#sk2' != '#sk3',
inference('sup-',[status(thm)],[zip_derived_cl414,zip_derived_cl15]) ).
thf(zip_derived_cl487,plain,
'#sk5' @ '#sk2' @ '#sk3',
inference('simplify_reflect-',[status(thm)],[zip_derived_cl325,zip_derived_cl417]) ).
thf(zip_derived_cl488,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl416,zip_derived_cl487]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU469^1 : TPTP v9.2.0. Released v3.6.0.
% 0.00/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.9cPOmqBVDp true
% 0.11/0.31 % Computer : n016.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Oct 1 16:04:53 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Running portfolio for 300 s
% 0.11/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.32 % Number of cores: 8
% 0.11/0.32 % Python version: Python 3.6.8
% 0.11/0.32 % Running in HO mode
% 0.48/0.61 % Total configuration time : 828
% 0.48/0.61 % Estimated wc time : 1656
% 0.48/0.61 % Estimated cpu time (8 cpus) : 207.0
% 0.49/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.49/0.69 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.49/0.69 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.49/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.49/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 10.17/1.85 % Solved by lams/35_full_unif4.sh.
% 10.17/1.85 % done 68 iterations in 1.090s
% 10.17/1.85 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 10.17/1.85 % SZS output start Refutation
% See solution above
% 10.17/1.85
% 10.17/1.85
% 10.17/1.85 % Terminating...
% 10.17/1.93 % Runner terminated.
% 10.17/1.94 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------