TSTP Solution File: SEU490^1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU490^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.i98ECqJrgA true
% Computer : n006.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 Aug 31 19:13:17 EDT 2023
% Result : Theorem 49.67s 7.04s
% Output : Refutation 49.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 66
% Syntax : Number of formulae : 201 ( 46 unt; 24 typ; 0 def)
% Number of atoms : 1407 ( 158 equ; 1 cnn)
% Maximal formula atoms : 64 ( 7 avg)
% Number of connectives : 5399 ( 164 ~; 299 |; 335 &;3325 @)
% ( 0 <=>; 464 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 485 ( 485 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 24 usr; 7 con; 0-4 aty)
% ( 795 !!; 17 ??; 0 @@+; 0 @@-)
% Number of variables : 1158 ( 875 ^; 276 !; 7 ?;1158 :)
% Comments :
%------------------------------------------------------------------------------
thf('#form133_type',type,
'#form133': ( $i > $i > $o ) > $o ).
thf(trc_type,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf('#sk1_type',type,
'#sk1': $i > $i > $o ).
thf('#sk278_type',type,
'#sk278': ( $i > $i > $o ) > $i ).
thf('#form307_type',type,
'#form307': ( $i > $i > $o ) > $o ).
thf(subrel_type,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(sc_type,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf('#sk13_type',type,
'#sk13': $i > $i > $i > $i > $o ).
thf('#sk134_type',type,
'#sk134': ( $i > $i > $o ) > $i ).
thf(cr_type,type,
cr: ( $i > $i > $o ) > $o ).
thf(trsc_type,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf('#sk3_type',type,
'#sk3': $i ).
thf('#sk2_type',type,
'#sk2': $i ).
thf('#sk191_type',type,
'#sk191': ( $i > $i > $o ) > $i ).
thf(tc_type,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(sconfl_type,type,
sconfl: ( $i > $i > $o ) > $o ).
thf('#sk14_type',type,
'#sk14': $i > $i > $i ).
thf('#sk77_type',type,
'#sk77': ( $i > $i > $o ) > $i ).
thf(join_type,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(trans_type,type,
trans: ( $i > $i > $o ) > $o ).
thf('#form65_type',type,
'#form65': $i > $o ).
thf(rc_type,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf('#form12_type',type,
'#form12': $o ).
thf('#sk56_type',type,
'#sk56': ( $i > $i > $o ) > $i ).
thf(church_rosser,axiom,
( cr
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( trsc @ R @ X @ Y )
=> ( join @ R @ X @ Y ) ) ) ) ).
thf(joinable,axiom,
( join
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
? [Z: $i] :
( ( trc @ R @ Y @ Z )
& ( trc @ R @ X @ Z ) ) ) ) ).
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('10',plain,
( join
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
? [Z: $i] :
( ( trc @ R @ Y @ Z )
& ( trc @ R @ X @ Z ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[joinable,'9','5','1','7','3']) ).
thf('11',plain,
( join
= ( ^ [V_1: $i > $i > $o,V_2: $i,V_3: $i] :
? [X4: $i] :
( ( trc @ V_1 @ V_3 @ X4 )
& ( trc @ V_1 @ V_2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(transitive_reflexive_symmetric_closure,axiom,
( trsc
= ( ^ [R: $i > $i > $o] : ( sc @ ( rc @ ( tc @ R ) ) ) ) ) ).
thf(symmetric_closure,axiom,
( sc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( R @ Y @ X )
| ( R @ X @ Y ) ) ) ) ).
thf('12',plain,
( sc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( R @ Y @ X )
| ( R @ X @ Y ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[symmetric_closure]) ).
thf('13',plain,
( sc
= ( ^ [V_1: $i > $i > $o,V_2: $i,V_3: $i] :
( ( V_1 @ V_3 @ V_2 )
| ( V_1 @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('14',plain,
( trsc
= ( ^ [R: $i > $i > $o] : ( sc @ ( rc @ ( tc @ R ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[transitive_reflexive_symmetric_closure,'5','1','13','7','3']) ).
thf('15',plain,
( trsc
= ( ^ [V_1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ V_1 ) ) ) ) ),
define([status(thm)]) ).
thf('16',plain,
( cr
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( trsc @ R @ X @ Y )
=> ( join @ R @ X @ Y ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[church_rosser,'11','15','9','5','1','13','7','3']) ).
thf('17',plain,
( cr
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i,X6: $i] :
( ( trsc @ V_1 @ X4 @ X6 )
=> ( join @ V_1 @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(semi_confluent,axiom,
( sconfl
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Z )
& ( trc @ R @ X @ Y ) )
=> ( join @ R @ Z @ Y ) ) ) ) ).
thf('18',plain,
( sconfl
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Z )
& ( trc @ R @ X @ Y ) )
=> ( join @ R @ Z @ Y ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[semi_confluent,'11','9','5','1','7','3']) ).
thf('19',plain,
( sconfl
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i,X6: $i,X8: $i] :
( ( ( V_1 @ X4 @ X8 )
& ( trc @ V_1 @ X4 @ X6 ) )
=> ( join @ V_1 @ X8 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(semi_confluence_implies_church_rosser,conjecture,
! [R: $i > $i > $o] :
( ( sconfl @ R )
=> ( cr @ R ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i > $i > $o] :
( ! [X6: $i,X8: $i,X10: $i] :
( ( ( ! [X12: $i > $i > $o] :
( ( ! [X20: $i,X22: $i] :
( ( X4 @ X20 @ X22 )
=> ( X12 @ X20 @ X22 ) )
& ! [X14: $i,X16: $i,X18: $i] :
( ( ( X12 @ X16 @ X18 )
& ( X12 @ X14 @ X16 ) )
=> ( X12 @ X14 @ X18 ) ) )
=> ( X12 @ X6 @ X8 ) )
| ( X6 = X8 ) )
& ( X4 @ X6 @ X10 ) )
=> ? [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 @ X10 @ X24 ) )
| ( X10 = 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 @ X8 @ X24 ) )
| ( X8 = X24 ) ) ) )
=> ! [X50: $i,X52: $i] :
( ( ! [X66: $i > $i > $o] :
( ( ! [X74: $i,X76: $i] :
( ( X4 @ X74 @ X76 )
=> ( X66 @ X74 @ X76 ) )
& ! [X68: $i,X70: $i,X72: $i] :
( ( ( X66 @ X70 @ X72 )
& ( X66 @ X68 @ X70 ) )
=> ( X66 @ X68 @ X72 ) ) )
=> ( X66 @ X50 @ X52 ) )
| ( X50 = X52 )
| ! [X54: $i > $i > $o] :
( ( ! [X62: $i,X64: $i] :
( ( X4 @ X62 @ X64 )
=> ( X54 @ X62 @ X64 ) )
& ! [X56: $i,X58: $i,X60: $i] :
( ( ( X54 @ X58 @ X60 )
& ( X54 @ X56 @ X58 ) )
=> ( X54 @ X56 @ X60 ) ) )
=> ( X54 @ X52 @ X50 ) )
| ( X52 = X50 ) )
=> ? [X78: $i] :
( ( ! [X92: $i > $i > $o] :
( ( ! [X100: $i,X102: $i] :
( ( X4 @ X100 @ X102 )
=> ( X92 @ X100 @ X102 ) )
& ! [X94: $i,X96: $i,X98: $i] :
( ( ( X92 @ X96 @ X98 )
& ( X92 @ X94 @ X96 ) )
=> ( X92 @ X94 @ X98 ) ) )
=> ( X92 @ X50 @ X78 ) )
| ( X50 = X78 ) )
& ( ! [X80: $i > $i > $o] :
( ( ! [X88: $i,X90: $i] :
( ( X4 @ X88 @ X90 )
=> ( X80 @ X88 @ X90 ) )
& ! [X82: $i,X84: $i,X86: $i] :
( ( ( X80 @ X84 @ X86 )
& ( X80 @ X82 @ X84 ) )
=> ( X80 @ X82 @ X86 ) ) )
=> ( X80 @ X52 @ X78 ) )
| ( X52 = X78 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i > $i > $o] :
( ! [X6: $i,X8: $i,X10: $i] :
( ( ( ! [X12: $i > $i > $o] :
( ( ! [X20: $i,X22: $i] :
( ( X4 @ X20 @ X22 )
=> ( X12 @ X20 @ X22 ) )
& ! [X14: $i,X16: $i,X18: $i] :
( ( ( X12 @ X16 @ X18 )
& ( X12 @ X14 @ X16 ) )
=> ( X12 @ X14 @ X18 ) ) )
=> ( X12 @ X6 @ X8 ) )
| ( X6 = X8 ) )
& ( X4 @ X6 @ X10 ) )
=> ? [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 @ X10 @ X24 ) )
| ( X10 = 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 @ X8 @ X24 ) )
| ( X8 = X24 ) ) ) )
=> ! [X50: $i,X52: $i] :
( ( ! [X66: $i > $i > $o] :
( ( ! [X74: $i,X76: $i] :
( ( X4 @ X74 @ X76 )
=> ( X66 @ X74 @ X76 ) )
& ! [X68: $i,X70: $i,X72: $i] :
( ( ( X66 @ X70 @ X72 )
& ( X66 @ X68 @ X70 ) )
=> ( X66 @ X68 @ X72 ) ) )
=> ( X66 @ X50 @ X52 ) )
| ( X50 = X52 )
| ! [X54: $i > $i > $o] :
( ( ! [X62: $i,X64: $i] :
( ( X4 @ X62 @ X64 )
=> ( X54 @ X62 @ X64 ) )
& ! [X56: $i,X58: $i,X60: $i] :
( ( ( X54 @ X58 @ X60 )
& ( X54 @ X56 @ X58 ) )
=> ( X54 @ X56 @ X60 ) ) )
=> ( X54 @ X52 @ X50 ) )
| ( X52 = X50 ) )
=> ? [X78: $i] :
( ( ! [X92: $i > $i > $o] :
( ( ! [X100: $i,X102: $i] :
( ( X4 @ X100 @ X102 )
=> ( X92 @ X100 @ X102 ) )
& ! [X94: $i,X96: $i,X98: $i] :
( ( ( X92 @ X96 @ X98 )
& ( X92 @ X94 @ X96 ) )
=> ( X92 @ X94 @ X98 ) ) )
=> ( X92 @ X50 @ X78 ) )
| ( X50 = X78 ) )
& ( ! [X80: $i > $i > $o] :
( ( ! [X88: $i,X90: $i] :
( ( X4 @ X88 @ X90 )
=> ( X80 @ X88 @ X90 ) )
& ! [X82: $i,X84: $i,X86: $i] :
( ( ( X80 @ X84 @ X86 )
& ( X80 @ X82 @ X84 ) )
=> ( X80 @ X82 @ X86 ) ) )
=> ( X80 @ X52 @ X78 ) )
| ( X52 = X78 ) ) ) ) ),
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 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) )
& ( Y0 @ Y1 @ Y3 ) )
=> ( ??
@ ^ [Y4: $i] :
( ( ( !!
@ ^ [Y5: $i > $i > $o] :
( ( ( !!
@ ^ [Y6: $i] :
( !!
@ ^ [Y7: $i] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: $i] :
( !!
@ ^ [Y7: $i] :
( !!
@ ^ [Y8: $i] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( Y3 = Y4 ) )
& ( ( !!
@ ^ [Y5: $i > $i > $o] :
( ( ( !!
@ ^ [Y6: $i] :
( !!
@ ^ [Y7: $i] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !!
@ ^ [Y6: $i] :
( !!
@ ^ [Y7: $i] :
( !!
@ ^ [Y8: $i] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) )
| ( Y2 = Y4 ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i > $i > $o] :
( ( ( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( ( Y0 @ 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] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( Y2 = Y1 ) )
=> ( ??
@ ^ [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 @ Y1 @ Y3 ) ) )
| ( Y1 = 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 @ Y2 @ Y3 ) ) )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,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 @ Y0 @ Y1 ) ) )
| ( Y0 = Y1 ) )
& ( '#sk1' @ Y0 @ Y2 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( ( !!
@ ^ [Y4: $i > $i > $o] :
( ( ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( '#sk1' @ 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] :
( ( '#sk1' @ 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 ) ) ) ) ) ) ) )
=> ( !!
@ ^ [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 @ Y1 @ Y0 ) ) )
| ( Y1 = Y0 ) )
=> ( ??
@ ^ [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 @ Y0 @ Y2 ) ) )
| ( Y0 = 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 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
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 @ Y1 @ Y0 ) ) )
| ( Y1 = Y0 ) )
=> ( ??
@ ^ [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 @ Y0 @ Y2 ) ) )
| ( Y0 = 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 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl5,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 @ '#sk2' @ Y0 ) ) )
| ( '#sk2' = 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 @ Y0 @ '#sk2' ) ) )
| ( Y0 = '#sk2' ) )
=> ( ??
@ ^ [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 @ '#sk2' @ Y1 ) ) )
| ( '#sk2' = 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 @ Y0 @ Y1 ) ) )
| ( Y0 = Y1 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
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' @ '#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 @ '#sk3' @ '#sk2' ) ) )
| ( '#sk3' = '#sk2' ) )
=> ( ??
@ ^ [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 @ '#sk2' @ Y0 ) ) )
| ( '#sk2' = 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 @ '#sk3' @ Y0 ) ) )
| ( '#sk3' = Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl10,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 @ '#sk2' @ Y0 ) ) )
| ( '#sk2' = 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 @ '#sk3' @ Y0 ) ) )
| ( '#sk3' = Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl13,plain,
! [X2: $i] :
~ ( ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk2' = X2 ) )
& ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk3' = X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl19,plain,
! [X2: $i] :
( ~ ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk2' = X2 ) )
| ~ ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk3' = X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl26,plain,
! [X2: $i] :
( ~ ( !!
@ ^ [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' @ X2 ) ) )
| ~ ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk3' = X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl36,plain,
! [X2: $i] :
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk2' @ X2 @ Y1 @ Y2 )
& ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk13' @ '#sk2' @ X2 @ '#sk2' @ X2 ) )
| ~ ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk3' = X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl47,plain,
! [X2: $i] :
( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk2' @ X2 @ Y1 @ Y2 )
& ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk3' = X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl59,plain,
! [X2: $i] :
( ( '#form65' @ X2 )
| ~ ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk3' = X2 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl61,plain,
! [X2: $i] :
( ( '#sk3' != X2 )
| ( '#form65' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl83,plain,
! [X2: $i] :
( ( '#sk3' != X2 )
| ( '#form65' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl84,plain,
'#form65' @ '#sk3',
inference(simplify,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl48,plain,
! [X2: $i] :
( ~ ( '#sk13' @ '#sk2' @ X2 @ '#sk2' @ X2 )
| ~ ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk3' = X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl59_001,plain,
! [X2: $i] :
( ( '#form65' @ X2 )
| ~ ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk3' = X2 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl63,plain,
! [X2: $i] :
( ~ ( '#form65' @ X2 )
| ~ ( '#sk13' @ '#sk2' @ X2 @ '#sk2' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl48,zip_derived_cl59]) ).
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' )
| ( !!
@ ^ [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' @ '#sk2' ) ) )
| ( '#sk3' = '#sk2' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
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 @ '#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 @ '#sk3' @ '#sk2' ) ) )
| ( '#sk3' = '#sk2' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl15,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' )
| ( !!
@ ^ [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' @ '#sk2' ) ) )
| ( '#sk3' = '#sk2' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl12]) ).
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' @ '#sk2' ) ) )
| ( '#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' @ '#sk3' ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl15]) ).
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' @ '#sk2' ) )
| ( !!
@ ^ [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_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl22,plain,
( ~ '#form12'
| ( !!
@ ^ [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' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl23,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' ) )
| ~ '#form12' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl35,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' )
| ~ '#form12' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl46,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 ) ) ) ) )
| ~ '#form12'
| ( X2 @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl58,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ ( '#sk56' @ X2 ) @ Y0 )
=> ( X2 @ ( '#sk56' @ X2 ) @ Y0 ) ) )
| ( X2 @ '#sk2' @ '#sk3' )
| ~ '#form12'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl79,plain,
! [X2: $i > $i > $o] :
( ~ ( ( '#sk1' @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) )
=> ( X2 @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| ~ '#form12'
| ( X2 @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl95,plain,
! [X2: $i > $i > $o] :
( ( '#form133' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl96,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( X2 @ Y0 @ Y1 )
& ( X2 @ ( '#sk134' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk134' @ X2 ) @ Y1 ) ) ) )
| ( '#form133' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl122,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( ( X2 @ ( '#sk191' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk134' @ X2 ) @ ( '#sk191' @ X2 ) ) )
=> ( X2 @ ( '#sk134' @ X2 ) @ Y0 ) ) )
| ( '#form133' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl137,plain,
! [X2: $i > $i > $o] :
( ~ ( ( ( X2 @ ( '#sk191' @ X2 ) @ ( '#sk278' @ X2 ) )
& ( X2 @ ( '#sk134' @ X2 ) @ ( '#sk191' @ X2 ) ) )
=> ( X2 @ ( '#sk134' @ X2 ) @ ( '#sk278' @ X2 ) ) )
| ( '#form133' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl122]) ).
thf(zip_derived_cl153,plain,
! [X2: $i > $i > $o] :
( ( ( X2 @ ( '#sk191' @ X2 ) @ ( '#sk278' @ X2 ) )
& ( X2 @ ( '#sk134' @ X2 ) @ ( '#sk191' @ X2 ) ) )
| ( '#form133' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl137]) ).
thf(zip_derived_cl164,plain,
! [X2: $i > $i > $o] :
( ( X2 @ ( '#sk191' @ X2 ) @ ( '#sk278' @ X2 ) )
| ( '#form133' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl165,plain,
! [X2: $i > $i > $o] :
( ( X2 @ ( '#sk134' @ X2 ) @ ( '#sk191' @ X2 ) )
| ( '#form133' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl154,plain,
! [X2: $i > $i > $o] :
( ~ ( X2 @ ( '#sk134' @ X2 ) @ ( '#sk278' @ X2 ) )
| ( '#form133' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl137]) ).
thf(zip_derived_cl47_002,plain,
! [X2: $i] :
( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk2' @ X2 @ Y1 @ Y2 )
& ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk3' = X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl59_003,plain,
! [X2: $i] :
( ( '#form65' @ X2 )
| ~ ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk3' = X2 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl62,plain,
! [X2: $i] :
( ~ ( '#form65' @ X2 )
| ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk2' @ X2 @ Y1 @ Y2 )
& ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl47,zip_derived_cl59]) ).
thf(zip_derived_cl80,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y1 ) ) ) )
| ~ ( '#form65' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl98,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X4 @ Y0 )
=> ( '#sk13' @ '#sk2' @ X2 @ X4 @ Y0 ) ) )
| ~ ( '#form65' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl123,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( '#sk1' @ X4 @ X6 )
=> ( '#sk13' @ '#sk2' @ X2 @ X4 @ X6 ) )
| ~ ( '#form65' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl98]) ).
thf(zip_derived_cl138,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#sk1' @ X4 @ X6 )
| ( '#sk13' @ '#sk2' @ X2 @ X4 @ X6 )
| ~ ( '#form65' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl123]) ).
thf(zip_derived_cl79_004,plain,
! [X2: $i > $i > $o] :
( ~ ( ( '#sk1' @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) )
=> ( X2 @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| ~ '#form12'
| ( X2 @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl95_005,plain,
! [X2: $i > $i > $o] :
( ( '#form133' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl97,plain,
! [X2: $i > $i > $o] :
( ~ ( '#form133' @ X2 )
| ( X2 @ '#sk2' @ '#sk3' )
| ~ '#form12'
| ~ ( ( '#sk1' @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) )
=> ( X2 @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl79,zip_derived_cl95]) ).
thf(zip_derived_cl121,plain,
! [X2: $i > $i > $o] :
( ~ ( X2 @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) )
| ~ '#form12'
| ( X2 @ '#sk2' @ '#sk3' )
| ~ ( '#form133' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl727,plain,
! [X0: $i > $i > $o] :
( ( ( X0 @ ( '#sk56' @ X0 ) @ ( '#sk77' @ X0 ) )
!= ( '#form133' @ X0 ) )
| ~ ( '#form133' @ X0 )
| ( X0 @ '#sk2' @ '#sk3' )
| ~ '#form12' ),
inference(eq_fact,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl735,plain,
! [X0: $i > $i > $o] :
( ~ ( X0 @ ( '#sk56' @ X0 ) @ ( '#sk77' @ X0 ) )
| ~ ( '#form133' @ X0 )
| ( X0 @ '#sk2' @ '#sk3' )
| ~ '#form12' ),
inference(local_rewriting,[status(thm)],[zip_derived_cl727]) ).
thf(zip_derived_cl17_006,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' @ '#sk2' ) )
| ( !!
@ ^ [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_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl185,plain,
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk3' @ '#sk2' @ Y1 @ Y2 )
& ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ '#sk3' @ '#sk2' ) )
| ( !!
@ ^ [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(triggered_bool_instantiation,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl27,plain,
! [X2: $i] :
( ( '#sk2' != X2 )
| ~ ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk3' = X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl37,plain,
! [X2: $i] :
( ( '#sk2' != X2 )
| ~ ( ( !!
@ ^ [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' @ X2 ) ) )
| ( '#sk3' = X2 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl38,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' @ '#sk2' ) ) )
| ( '#sk3' = '#sk2' ) ),
inference(simplify,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl39,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' @ '#sk2' ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl49,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk3' @ '#sk2' @ Y1 @ Y2 )
& ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ '#sk3' @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl65,plain,
~ ( '#sk13' @ '#sk3' @ '#sk2' @ '#sk3' @ '#sk2' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl259,plain,
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk3' @ '#sk2' @ Y1 @ Y2 )
& ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y2 ) ) ) ) ) )
=> $false )
| ( !!
@ ^ [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(demod,[status(thm)],[zip_derived_cl185,zip_derived_cl65]) ).
thf(zip_derived_cl40,plain,
'#sk3' != '#sk2',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl50,plain,
'#sk3' != '#sk2',
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl260,plain,
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk3' @ '#sk2' @ Y1 @ Y2 )
& ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y2 ) ) ) ) ) )
=> $false )
| ( !!
@ ^ [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' ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl259,zip_derived_cl50]) ).
thf(zip_derived_cl261,plain,
( ( (~)
@ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk3' @ '#sk2' @ Y1 @ Y2 )
& ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y2 ) ) ) ) ) ) )
| ( !!
@ ^ [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' ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl260]) ).
thf(zip_derived_cl262,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk3' @ '#sk2' @ Y1 @ Y2 )
& ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y2 ) ) ) ) ) )
| ( !!
@ ^ [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' ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl261]) ).
thf(zip_derived_cl22_007,plain,
( ~ '#form12'
| ( !!
@ ^ [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' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl263,plain,
( '#form12'
| ~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk3' @ '#sk2' @ Y1 @ Y2 )
& ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl262,zip_derived_cl22]) ).
thf(zip_derived_cl264,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk3' @ '#sk2' @ Y1 @ Y2 )
& ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y2 ) ) ) ) )
| '#form12' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl263]) ).
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 @ Y0 @ Y1 ) ) )
| ( Y0 = Y1 ) )
& ( '#sk1' @ Y0 @ Y2 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( ( !!
@ ^ [Y4: $i > $i > $o] :
( ( ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( '#sk1' @ 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] :
( ( '#sk1' @ 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(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
! [X2: $i] :
( !!
@ ^ [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 @ X2 @ Y0 ) ) )
| ( X2 = Y0 ) )
& ( '#sk1' @ X2 @ Y1 ) )
=> ( ??
@ ^ [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 @ Y2 ) ) )
| ( Y0 = Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl6,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [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 @ X2 @ X4 ) ) )
| ( X2 = X4 ) )
& ( '#sk1' @ X2 @ Y0 ) )
=> ( ??
@ ^ [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 @ X4 @ Y1 ) ) )
| ( X4 = Y1 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl8,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( ( !!
@ ^ [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 @ X2 @ X4 ) ) )
| ( X2 = X4 ) )
& ( '#sk1' @ X2 @ X6 ) )
=> ( ??
@ ^ [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 @ X6 @ Y0 ) ) )
| ( X6 = 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 @ X4 @ Y0 ) ) )
| ( X4 = Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl11,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( ( !!
@ ^ [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 @ X2 @ X4 ) ) )
| ( X2 = X4 ) )
& ( '#sk1' @ X2 @ X6 ) )
| ( ??
@ ^ [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 @ X6 @ Y0 ) ) )
| ( X6 = 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 @ X4 @ Y0 ) ) )
| ( X4 = Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl14,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( !!
@ ^ [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 @ X2 @ X4 ) ) )
| ( X2 = X4 ) )
| ~ ( '#sk1' @ X2 @ X6 )
| ( ??
@ ^ [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 @ X6 @ Y0 ) ) )
| ( X6 = 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 @ X4 @ Y0 ) ) )
| ( X4 = Y0 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl21,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( X2 != X4 )
| ( ??
@ ^ [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 @ X6 @ Y0 ) ) )
| ( X6 = 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 @ X4 @ Y0 ) ) )
| ( X4 = Y0 ) ) ) )
| ~ ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl31,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( X2 != X4 )
| ( ??
@ ^ [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 @ X6 @ Y0 ) ) )
| ( X6 = 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 @ X4 @ Y0 ) ) )
| ( X4 = Y0 ) ) ) )
| ~ ( '#sk1' @ X2 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl32,plain,
! [X4: $i,X6: $i] :
( ~ ( '#sk1' @ X4 @ X6 )
| ( ??
@ ^ [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 @ X6 @ Y0 ) ) )
| ( X6 = 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 @ X4 @ Y0 ) ) )
| ( X4 = Y0 ) ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl33,plain,
! [X4: $i,X6: $i] :
( ( ( ( !!
@ ^ [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 @ X6 @ ( '#sk14' @ X4 @ X6 ) ) ) )
| ( X6
= ( '#sk14' @ X4 @ X6 ) ) )
& ( ( !!
@ ^ [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 @ X4 @ ( '#sk14' @ X4 @ X6 ) ) ) )
| ( X4
= ( '#sk14' @ X4 @ X6 ) ) ) )
| ~ ( '#sk1' @ X4 @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl43,plain,
! [X4: $i,X6: $i] :
( ( !!
@ ^ [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 @ X6 @ ( '#sk14' @ X4 @ X6 ) ) ) )
| ( X6
= ( '#sk14' @ X4 @ X6 ) )
| ~ ( '#sk1' @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl55,plain,
! [X4: $i,X6: $i] :
( ( !!
@ ^ [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 @ X6 @ ( '#sk14' @ X4 @ X6 ) ) ) )
| ( X6
= ( '#sk14' @ X4 @ X6 ) )
| ~ ( '#sk1' @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl70,plain,
! [X4: $i,X6: $i] :
( ( !!
@ ^ [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 @ X6 @ ( '#sk14' @ X4 @ X6 ) ) ) )
| ( X6
= ( '#sk14' @ X4 @ X6 ) )
| ~ ( '#sk1' @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl71,plain,
! [X4: $i,X6: $i,X8: $i > $i > $o] :
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X8 @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X8 @ Y1 @ Y2 )
& ( X8 @ Y0 @ Y1 ) )
=> ( X8 @ Y0 @ Y2 ) ) ) ) ) )
=> ( X8 @ X6 @ ( '#sk14' @ X4 @ X6 ) ) )
| ~ ( '#sk1' @ X4 @ X6 )
| ( X6
= ( '#sk14' @ X4 @ X6 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl91,plain,
! [X4: $i,X6: $i,X8: $i > $i > $o] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X8 @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X8 @ Y1 @ Y2 )
& ( X8 @ Y0 @ Y1 ) )
=> ( X8 @ Y0 @ Y2 ) ) ) ) ) )
| ( X8 @ X6 @ ( '#sk14' @ X4 @ X6 ) )
| ( X6
= ( '#sk14' @ X4 @ X6 ) )
| ~ ( '#sk1' @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl116,plain,
! [X4: $i,X6: $i,X8: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X8 @ Y0 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X8 @ Y1 @ Y2 )
& ( X8 @ Y0 @ Y1 ) )
=> ( X8 @ Y0 @ Y2 ) ) ) ) )
| ~ ( '#sk1' @ X4 @ X6 )
| ( X6
= ( '#sk14' @ X4 @ X6 ) )
| ( X8 @ X6 @ ( '#sk14' @ X4 @ X6 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl64,plain,
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk3' @ '#sk2' @ Y1 @ Y2 )
& ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl86,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk3' @ '#sk2' @ Y1 @ Y2 )
& ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl103,plain,
! [X2: $i > $i > $o] :
( ~ ( '#form133' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl95_008,plain,
! [X2: $i > $i > $o] :
( ( '#form133' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl133,plain,
! [X4: $i,X6: $i,X8: $i > $i > $o] :
( ~ ( '#form133'
@ ^ [Y0: $i,Y1: $i] : ( X8 @ Y0 @ Y1 ) )
| ( X8 @ X6 @ ( '#sk14' @ X4 @ X6 ) )
| ( X6
= ( '#sk14' @ X4 @ X6 ) )
| ~ ( '#sk1' @ X4 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X8 @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl116,zip_derived_cl103,zip_derived_cl95]) ).
thf(zip_derived_cl147,plain,
! [X4: $i,X6: $i,X8: $i > $i > $o] :
( ~ ( '#form133' @ X8 )
| ( X8 @ X6 @ ( '#sk14' @ X4 @ X6 ) )
| ( X6
= ( '#sk14' @ X4 @ X6 ) )
| ~ ( '#sk1' @ X4 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X8 @ Y0 @ Y1 ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl133]) ).
thf(zip_derived_cl148,plain,
! [X8: $i > $i > $o] :
( ( '#form307' @ X8 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X8 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl265,plain,
( ~ ( '#form307' @ ( '#sk13' @ '#sk3' @ '#sk2' ) )
| '#form12'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk3' @ '#sk2' @ Y1 @ Y2 )
& ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y2 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl264,zip_derived_cl148]) ).
thf(zip_derived_cl103_009,plain,
! [X2: $i > $i > $o] :
( ~ ( '#form133' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl95_010,plain,
! [X2: $i > $i > $o] :
( ( '#form133' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl266,plain,
( ~ ( '#form133' @ ( '#sk13' @ '#sk3' @ '#sk2' ) )
| '#form12'
| ~ ( '#form307' @ ( '#sk13' @ '#sk3' @ '#sk2' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl265,zip_derived_cl103,zip_derived_cl95]) ).
thf(zip_derived_cl86_011,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk3' @ '#sk2' @ Y1 @ Y2 )
& ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl103_012,plain,
! [X2: $i > $i > $o] :
( ~ ( '#form133' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl95_013,plain,
! [X2: $i > $i > $o] :
( ( '#form133' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl105,plain,
'#form133' @ ( '#sk13' @ '#sk3' @ '#sk2' ),
inference(renaming,[status(thm)],[zip_derived_cl86,zip_derived_cl103,zip_derived_cl95]) ).
thf(zip_derived_cl267,plain,
( '#form12'
| ~ ( '#form307' @ ( '#sk13' @ '#sk3' @ '#sk2' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl266,zip_derived_cl105]) ).
thf(zip_derived_cl148_014,plain,
! [X8: $i > $i > $o] :
( ( '#form307' @ X8 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X8 @ Y0 @ Y1 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl149,plain,
! [X8: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ ( '#sk56' @ X8 ) @ Y0 )
=> ( X8 @ ( '#sk56' @ X8 ) @ Y0 ) ) )
| ( '#form307' @ X8 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl148]) ).
thf(zip_derived_cl162,plain,
! [X8: $i > $i > $o] :
( ~ ( ( '#sk1' @ ( '#sk56' @ X8 ) @ ( '#sk77' @ X8 ) )
=> ( X8 @ ( '#sk56' @ X8 ) @ ( '#sk77' @ X8 ) ) )
| ( '#form307' @ X8 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl149]) ).
thf(zip_derived_cl175,plain,
! [X8: $i > $i > $o] :
( ~ ( X8 @ ( '#sk56' @ X8 ) @ ( '#sk77' @ X8 ) )
| ( '#form307' @ X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl162]) ).
thf(zip_derived_cl85,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl102,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl127,plain,
! [X2: $i,X4: $i] :
( ( '#sk1' @ X2 @ X4 )
=> ( '#sk13' @ '#sk3' @ '#sk2' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl142,plain,
! [X2: $i,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk13' @ '#sk3' @ '#sk2' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl127]) ).
thf(zip_derived_cl571,plain,
( ( '#form307' @ ( '#sk13' @ '#sk3' @ '#sk2' ) )
| ~ ( '#sk1' @ ( '#sk56' @ ( '#sk13' @ '#sk3' @ '#sk2' ) ) @ ( '#sk77' @ ( '#sk13' @ '#sk3' @ '#sk2' ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl175,zip_derived_cl142]) ).
thf(zip_derived_cl174,plain,
! [X8: $i > $i > $o] :
( ( '#sk1' @ ( '#sk56' @ X8 ) @ ( '#sk77' @ X8 ) )
| ( '#form307' @ X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl162]) ).
thf(zip_derived_cl990,plain,
'#form307' @ ( '#sk13' @ '#sk3' @ '#sk2' ),
inference(clc,[status(thm)],[zip_derived_cl571,zip_derived_cl174]) ).
thf(zip_derived_cl991,plain,
'#form12',
inference(demod,[status(thm)],[zip_derived_cl267,zip_derived_cl990]) ).
thf(zip_derived_cl1075,plain,
! [X0: $i > $i > $o] :
( ~ ( X0 @ ( '#sk56' @ X0 ) @ ( '#sk77' @ X0 ) )
| ~ ( '#form133' @ X0 )
| ( X0 @ '#sk2' @ '#sk3' ) ),
inference(demod,[status(thm)],[zip_derived_cl735,zip_derived_cl991]) ).
thf(zip_derived_cl81,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk13' @ '#sk2' @ X2 @ Y1 @ Y2 )
& ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y1 ) )
=> ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y2 ) ) ) ) )
| ~ ( '#form65' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl99,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( '#sk13' @ '#sk2' @ X2 @ Y0 @ Y1 )
& ( '#sk13' @ '#sk2' @ X2 @ X4 @ Y0 ) )
=> ( '#sk13' @ '#sk2' @ X2 @ X4 @ Y1 ) ) ) )
| ~ ( '#form65' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl124,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( ( '#sk13' @ '#sk2' @ X2 @ X6 @ Y0 )
& ( '#sk13' @ '#sk2' @ X2 @ X4 @ X6 ) )
=> ( '#sk13' @ '#sk2' @ X2 @ X4 @ Y0 ) ) )
| ~ ( '#form65' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl139,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( ( '#sk13' @ '#sk2' @ X2 @ X6 @ X8 )
& ( '#sk13' @ '#sk2' @ X2 @ X4 @ X6 ) )
=> ( '#sk13' @ '#sk2' @ X2 @ X4 @ X8 ) )
| ~ ( '#form65' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl124]) ).
thf(zip_derived_cl155,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( ( '#sk13' @ '#sk2' @ X2 @ X6 @ X8 )
& ( '#sk13' @ '#sk2' @ X2 @ X4 @ X6 ) )
| ( '#sk13' @ '#sk2' @ X2 @ X4 @ X8 )
| ~ ( '#form65' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl139]) ).
thf(zip_derived_cl166,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( '#sk13' @ '#sk2' @ X2 @ X6 @ X8 )
| ~ ( '#sk13' @ '#sk2' @ X2 @ X4 @ X6 )
| ~ ( '#form65' @ X2 )
| ( '#sk13' @ '#sk2' @ X2 @ X4 @ X8 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl155]) ).
thf(zip_derived_cl105_015,plain,
'#form133' @ ( '#sk13' @ '#sk3' @ '#sk2' ),
inference(renaming,[status(thm)],[zip_derived_cl86,zip_derived_cl103,zip_derived_cl95]) ).
thf(zip_derived_cl120,plain,
! [X2: $i > $i > $o] :
( ( '#sk1' @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) )
| ~ '#form12'
| ( X2 @ '#sk2' @ '#sk3' )
| ~ ( '#form133' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl17_016,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' @ '#sk2' ) )
| ( !!
@ ^ [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_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl22_017,plain,
( ~ '#form12'
| ( !!
@ ^ [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' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl25,plain,
! [X2: $i > $i > $o] :
( '#form12'
| ( '#sk2' = '#sk3' )
| ( ( ( !!
@ ^ [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' @ '#sk2' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl17,zip_derived_cl22]) ).
thf(zip_derived_cl34,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' @ '#sk2' )
| ( '#sk2' = '#sk3' )
| '#form12' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl45,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 ) ) ) ) )
| '#form12'
| ( '#sk2' = '#sk3' )
| ( X2 @ '#sk3' @ '#sk2' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl57,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ ( '#sk56' @ X2 ) @ Y0 )
=> ( X2 @ ( '#sk56' @ X2 ) @ Y0 ) ) )
| ( X2 @ '#sk3' @ '#sk2' )
| ( '#sk2' = '#sk3' )
| '#form12'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl78,plain,
! [X2: $i > $i > $o] :
( ~ ( ( '#sk1' @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) )
=> ( X2 @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| '#form12'
| ( '#sk2' = '#sk3' )
| ( X2 @ '#sk3' @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl93,plain,
! [X2: $i > $i > $o] :
( ( '#sk1' @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) )
| ( X2 @ '#sk3' @ '#sk2' )
| ( '#sk2' = '#sk3' )
| '#form12'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl103_018,plain,
! [X2: $i > $i > $o] :
( ~ ( '#form133' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl95_019,plain,
! [X2: $i > $i > $o] :
( ( '#form133' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl118,plain,
! [X2: $i > $i > $o] :
( ~ ( '#form133'
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) )
| '#form12'
| ( '#sk2' = '#sk3' )
| ( X2 @ '#sk3' @ '#sk2' )
| ( '#sk1' @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl93,zip_derived_cl103,zip_derived_cl95]) ).
thf(zip_derived_cl135,plain,
! [X2: $i > $i > $o] :
( ~ ( '#form133' @ X2 )
| '#form12'
| ( '#sk2' = '#sk3' )
| ( X2 @ '#sk3' @ '#sk2' )
| ( '#sk1' @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl118]) ).
thf(zip_derived_cl50_020,plain,
'#sk3' != '#sk2',
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl212,plain,
! [X2: $i > $i > $o] :
( ~ ( '#form133' @ X2 )
| '#form12'
| ( X2 @ '#sk3' @ '#sk2' )
| ( '#sk1' @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl135,zip_derived_cl50]) ).
thf(zip_derived_cl65_021,plain,
~ ( '#sk13' @ '#sk3' @ '#sk2' @ '#sk3' @ '#sk2' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl142_022,plain,
! [X2: $i,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk13' @ '#sk3' @ '#sk2' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl127]) ).
thf(zip_derived_cl94,plain,
! [X2: $i > $i > $o] :
( ~ ( X2 @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) )
| ( X2 @ '#sk3' @ '#sk2' )
| ( '#sk2' = '#sk3' )
| '#form12'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl103_023,plain,
! [X2: $i > $i > $o] :
( ~ ( '#form133' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl95_024,plain,
! [X2: $i > $i > $o] :
( ( '#form133' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl119,plain,
! [X2: $i > $i > $o] :
( ~ ( '#form133'
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) )
| '#form12'
| ( '#sk2' = '#sk3' )
| ( X2 @ '#sk3' @ '#sk2' )
| ~ ( X2 @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl94,zip_derived_cl103,zip_derived_cl95]) ).
thf(zip_derived_cl136,plain,
! [X2: $i > $i > $o] :
( ~ ( '#form133' @ X2 )
| '#form12'
| ( '#sk2' = '#sk3' )
| ( X2 @ '#sk3' @ '#sk2' )
| ~ ( X2 @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl119]) ).
thf(zip_derived_cl50_025,plain,
'#sk3' != '#sk2',
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl228,plain,
! [X2: $i > $i > $o] :
( ~ ( '#form133' @ X2 )
| '#form12'
| ( X2 @ '#sk3' @ '#sk2' )
| ~ ( X2 @ ( '#sk56' @ X2 ) @ ( '#sk77' @ X2 ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl136,zip_derived_cl50]) ).
thf(zip_derived_cl6383,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl84,zip_derived_cl63,zip_derived_cl164,zip_derived_cl165,zip_derived_cl154,zip_derived_cl138,zip_derived_cl1075,zip_derived_cl166,zip_derived_cl105,zip_derived_cl120,zip_derived_cl212,zip_derived_cl65,zip_derived_cl142,zip_derived_cl228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU490^1 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.i98ECqJrgA true
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 23:18:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.20/0.66 % Total configuration time : 828
% 0.20/0.66 % Estimated wc time : 1656
% 0.20/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.57/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.57/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.57/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.79 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.59/0.82 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 49.67/7.04 % Solved by lams/20_acsne_simpl.sh.
% 49.67/7.04 % done 467 iterations in 6.136s
% 49.67/7.04 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 49.67/7.04 % SZS output start Refutation
% See solution above
% 49.67/7.04
% 49.67/7.04
% 49.67/7.04 % Terminating...
% 49.99/7.08 % Runner terminated.
% 49.99/7.10 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------