TSTP Solution File: SEU496^1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU496^1 : 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.RqBuZHUoVu 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 19:13:18 EDT 2023
% Result : Theorem 10.01s 1.91s
% Output : Refutation 10.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 41
% Syntax : Number of formulae : 140 ( 21 unt; 19 typ; 0 def)
% Number of atoms : 1105 ( 15 equ; 30 cnn)
% Maximal formula atoms : 52 ( 9 avg)
% Number of connectives : 4019 ( 150 ~; 113 |; 264 &;2405 @)
% ( 0 <=>; 404 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 312 ( 312 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 19 usr; 9 con; 0-3 aty)
% ( 683 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 865 ( 707 ^; 158 !; 0 ?; 865 :)
% Comments :
%------------------------------------------------------------------------------
thf('#sk7_type',type,
'#sk7': $i ).
thf(so_type,type,
so: ( $i > $i > $o ) > $o ).
thf(subrel_type,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf('#form6_type',type,
'#form6': $o ).
thf('#sk57_type',type,
'#sk57': ( $i > $i > $o ) > $i ).
thf('#sk136_type',type,
'#sk136': ( $i > $i > $o ) > $i ).
thf('#sk187_type',type,
'#sk187': ( $i > $i > $o ) > $i ).
thf(tc_type,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf('#sk93_type',type,
'#sk93': ( $i > $i > $o ) > $i ).
thf(trans_type,type,
trans: ( $i > $i > $o ) > $o ).
thf('#form135_type',type,
'#form135': ( $i > $i > $o ) > $o ).
thf('#sk5_type',type,
'#sk5': $i > $i > $o ).
thf(asymm_type,type,
asymm: ( $i > $i > $o ) > $o ).
thf('#sk16_type',type,
'#sk16': $i ).
thf('#sk248_type',type,
'#sk248': ( $i > $i > $o ) > $i ).
thf('#sk3_type',type,
'#sk3': $i ).
thf('#sk1_type',type,
'#sk1': $i > $i > $o ).
thf(strict_order,axiom,
( so
= ( ^ [R: $i > $i > $o] :
( ( asymm @ R )
& ( trans @ R ) ) ) ) ).
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(asymmetric,axiom,
( asymm
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ~ ( R @ Y @ X ) ) ) ) ).
thf('2',plain,
( asymm
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ~ ( R @ Y @ X ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[asymmetric]) ).
thf('3',plain,
( asymm
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i,X6: $i] :
( ( V_1 @ X4 @ X6 )
=> ~ ( V_1 @ X6 @ X4 ) ) ) ),
define([status(thm)]) ).
thf('4',plain,
( so
= ( ^ [R: $i > $i > $o] :
( ( asymm @ R )
& ( trans @ R ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[strict_order,'1','3']) ).
thf('5',plain,
( so
= ( ^ [V_1: $i > $i > $o] :
( ( asymm @ V_1 )
& ( trans @ V_1 ) ) ) ),
define([status(thm)]) ).
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(subrel,axiom,
( subrel
= ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
! [X: $i,Y: $i] :
( ( R @ X @ Y )
=> ( S @ X @ Y ) ) ) ) ).
thf('6',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('7',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('8',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','7']) ).
thf('9',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(transitive_closure_of_strict_order_is_strict_order,conjecture,
! [R: $i > $i > $o] :
( ( so @ R )
=> ( so @ ( tc @ R ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i > $i > $o] :
( ( ! [X10: $i,X12: $i,X14: $i] :
( ( ( X4 @ X12 @ X14 )
& ( X4 @ X10 @ X12 ) )
=> ( X4 @ X10 @ X14 ) )
& ! [X6: $i,X8: $i] :
( ( X4 @ X6 @ X8 )
=> ~ ( X4 @ X8 @ X6 ) ) )
=> ( ! [X44: $i,X46: $i,X48: $i] :
( ( ! [X62: $i > $i > $o] :
( ( ! [X70: $i,X72: $i] :
( ( X4 @ X70 @ X72 )
=> ( X62 @ X70 @ X72 ) )
& ! [X64: $i,X66: $i,X68: $i] :
( ( ( X62 @ X66 @ X68 )
& ( X62 @ X64 @ X66 ) )
=> ( X62 @ X64 @ X68 ) ) )
=> ( X62 @ X46 @ X48 ) )
& ! [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 @ X44 @ X46 ) ) )
=> ! [X74: $i > $i > $o] :
( ( ! [X82: $i,X84: $i] :
( ( X4 @ X82 @ X84 )
=> ( X74 @ X82 @ X84 ) )
& ! [X76: $i,X78: $i,X80: $i] :
( ( ( X74 @ X78 @ X80 )
& ( X74 @ X76 @ X78 ) )
=> ( X74 @ X76 @ X80 ) ) )
=> ( X74 @ X44 @ X48 ) ) )
& ! [X16: $i,X18: $i] :
( ! [X20: $i > $i > $o] :
( ( ! [X28: $i,X30: $i] :
( ( X4 @ X28 @ X30 )
=> ( X20 @ X28 @ X30 ) )
& ! [X22: $i,X24: $i,X26: $i] :
( ( ( X20 @ X24 @ X26 )
& ( X20 @ X22 @ X24 ) )
=> ( X20 @ X22 @ X26 ) ) )
=> ( X20 @ X16 @ X18 ) )
=> ~ ! [X32: $i > $i > $o] :
( ( ! [X40: $i,X42: $i] :
( ( X4 @ X40 @ X42 )
=> ( X32 @ X40 @ X42 ) )
& ! [X34: $i,X36: $i,X38: $i] :
( ( ( X32 @ X36 @ X38 )
& ( X32 @ X34 @ X36 ) )
=> ( X32 @ X34 @ X38 ) ) )
=> ( X32 @ X18 @ X16 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i > $i > $o] :
( ( ! [X10: $i,X12: $i,X14: $i] :
( ( ( X4 @ X12 @ X14 )
& ( X4 @ X10 @ X12 ) )
=> ( X4 @ X10 @ X14 ) )
& ! [X6: $i,X8: $i] :
( ( X4 @ X6 @ X8 )
=> ~ ( X4 @ X8 @ X6 ) ) )
=> ( ! [X44: $i,X46: $i,X48: $i] :
( ( ! [X62: $i > $i > $o] :
( ( ! [X70: $i,X72: $i] :
( ( X4 @ X70 @ X72 )
=> ( X62 @ X70 @ X72 ) )
& ! [X64: $i,X66: $i,X68: $i] :
( ( ( X62 @ X66 @ X68 )
& ( X62 @ X64 @ X66 ) )
=> ( X62 @ X64 @ X68 ) ) )
=> ( X62 @ X46 @ X48 ) )
& ! [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 @ X44 @ X46 ) ) )
=> ! [X74: $i > $i > $o] :
( ( ! [X82: $i,X84: $i] :
( ( X4 @ X82 @ X84 )
=> ( X74 @ X82 @ X84 ) )
& ! [X76: $i,X78: $i,X80: $i] :
( ( ( X74 @ X78 @ X80 )
& ( X74 @ X76 @ X78 ) )
=> ( X74 @ X76 @ X80 ) ) )
=> ( X74 @ X44 @ X48 ) ) )
& ! [X16: $i,X18: $i] :
( ! [X20: $i > $i > $o] :
( ( ! [X28: $i,X30: $i] :
( ( X4 @ X28 @ X30 )
=> ( X20 @ X28 @ X30 ) )
& ! [X22: $i,X24: $i,X26: $i] :
( ( ( X20 @ X24 @ X26 )
& ( X20 @ X22 @ X24 ) )
=> ( X20 @ X22 @ X26 ) ) )
=> ( X20 @ X16 @ X18 ) )
=> ~ ! [X32: $i > $i > $o] :
( ( ! [X40: $i,X42: $i] :
( ( X4 @ X40 @ X42 )
=> ( X32 @ X40 @ X42 ) )
& ! [X34: $i,X36: $i,X38: $i] :
( ( ( X32 @ X36 @ X38 )
& ( X32 @ X34 @ X36 ) )
=> ( X32 @ X34 @ X38 ) ) )
=> ( X32 @ X18 @ X16 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( (~) @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [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 ) ) )
& ( !!
@ ^ [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 ) ) ) )
=> ( !!
@ ^ [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: $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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( (~) @ ( '#sk1' @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !!
@ ^ [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 ) ) )
& ( !!
@ ^ [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 ) ) ) )
=> ( !!
@ ^ [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: $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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,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 ) ) )
& ( !!
@ ^ [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 ) ) ) )
=> ( !!
@ ^ [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: $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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,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 ) ) )
& ( !!
@ ^ [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 ) ) ) )
=> ( !!
@ ^ [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: $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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl9,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 ) ) )
& ( !!
@ ^ [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 ) ) ) )
=> ( !!
@ ^ [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 ) ) ) ) ) )
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl12,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 ) ) )
& ( !!
@ ^ [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' ) ) ) )
=> ( !!
@ ^ [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 ) ) ) ) )
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[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 @ '#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' ) ) ) )
=> ( !!
@ ^ [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' ) ) ) )
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl17,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' ) ) )
& ( !!
@ ^ [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' ) ) ) )
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21,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' ) ) )
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl21_001,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' ) ) )
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl26,plain,
( '#form6'
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl28,plain,
( ~ '#form6'
| ( !!
@ ^ [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(renaming,[status(thm)],[zip_derived_cl21,zip_derived_cl26]) ).
thf(zip_derived_cl31,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' ) )
| ~ '#form6' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl33,plain,
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk1' @ '#sk2' @ '#sk3' ) )
| ~ '#form6' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl147,plain,
( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
=> ( '#sk1' @ '#sk2' @ '#sk3' ) )
| ~ '#form6' ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl148,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
| ( '#sk1' @ '#sk2' @ '#sk3' )
| ~ '#form6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl147]) ).
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 @ '#sk3' @ '#sk4' ) ) )
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl17]) ).
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 @ '#sk3' @ '#sk4' ) )
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl26_002,plain,
( '#form6'
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl30,plain,
! [X2: $i > $i > $o] :
( ~ '#form6'
| ( ( ( !!
@ ^ [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' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl23,zip_derived_cl26]) ).
thf(zip_derived_cl37,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' )
| ~ '#form6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl43,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 ) ) ) ) )
| ~ '#form6'
| ( X2 @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl53,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ ( '#sk57' @ X2 ) @ Y0 )
=> ( X2 @ ( '#sk57' @ X2 ) @ Y0 ) ) )
| ( X2 @ '#sk3' @ '#sk4' )
| ~ '#form6'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl59,plain,
! [X2: $i > $i > $o] :
( ~ ( ( '#sk1' @ ( '#sk57' @ X2 ) @ ( '#sk93' @ X2 ) )
=> ( X2 @ ( '#sk57' @ X2 ) @ ( '#sk93' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| ~ '#form6'
| ( X2 @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl65,plain,
! [X2: $i > $i > $o] :
( ( '#form135' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl149,plain,
( ~ ( '#form135' @ '#sk1' )
| ~ '#form6'
| ( '#sk1' @ '#sk2' @ '#sk3' ) ),
inference(renaming,[status(thm)],[zip_derived_cl148,zip_derived_cl65]) ).
thf(zip_derived_cl23_003,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' ) )
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl25,plain,
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk1' @ '#sk3' @ '#sk4' ) )
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl204,plain,
( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
=> ( '#sk1' @ '#sk3' @ '#sk4' ) )
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl26_004,plain,
( '#form6'
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl205,plain,
( ~ '#form6'
| ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
=> ( '#sk1' @ '#sk3' @ '#sk4' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl204,zip_derived_cl26]) ).
thf(zip_derived_cl206,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
| ( '#sk1' @ '#sk3' @ '#sk4' )
| ~ '#form6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl205]) ).
thf(zip_derived_cl65_005,plain,
! [X2: $i > $i > $o] :
( ( '#form135' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl207,plain,
( ~ ( '#form135' @ '#sk1' )
| ~ '#form6'
| ( '#sk1' @ '#sk3' @ '#sk4' ) ),
inference(renaming,[status(thm)],[zip_derived_cl206,zip_derived_cl65]) ).
thf(zip_derived_cl2,plain,
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( (~) @ ( '#sk1' @ Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl7,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( '#sk1' @ Y0 @ Y1 )
& ( '#sk1' @ X2 @ Y0 ) )
=> ( '#sk1' @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl10,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( '#sk1' @ X4 @ Y0 )
& ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk1' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl13,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( '#sk1' @ X4 @ X6 )
& ( '#sk1' @ X2 @ X4 ) )
=> ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl16,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( '#sk1' @ X4 @ X6 )
& ( '#sk1' @ X2 @ X4 ) )
| ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl19,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#sk1' @ X4 @ X6 )
| ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl208,plain,
! [X0: $i] :
( ~ '#form6'
| ~ ( '#form135' @ '#sk1' )
| ( '#sk1' @ X0 @ '#sk4' )
| ~ ( '#sk1' @ X0 @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl207,zip_derived_cl19]) ).
thf(zip_derived_cl26_006,plain,
( '#form6'
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl27,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 @ '#sk7' @ 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 @ '#sk7' ) ) ) ) ) )
| '#form6' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl34,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 @ '#sk7' @ '#sk16' ) ) )
=> ( (~)
@ ( !!
@ ^ [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 @ '#sk16' @ '#sk7' ) ) ) ) )
| '#form6' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl40,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 @ '#sk16' @ '#sk7' ) ) )
| '#form6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl48,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 @ '#sk16' @ '#sk7' ) )
| '#form6' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl50,plain,
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk1' @ '#sk16' @ '#sk7' ) )
| '#form6' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl317,plain,
( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
=> ( '#sk1' @ '#sk16' @ '#sk7' ) )
| '#form6' ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl318,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
| ( '#sk1' @ '#sk16' @ '#sk7' )
| '#form6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl317]) ).
thf(zip_derived_cl65_007,plain,
! [X2: $i > $i > $o] :
( ( '#form135' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl319,plain,
( ~ ( '#form135' @ '#sk1' )
| '#form6'
| ( '#sk1' @ '#sk16' @ '#sk7' ) ),
inference(renaming,[status(thm)],[zip_derived_cl318,zip_derived_cl65]) ).
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 @ '#sk7' @ '#sk16' ) ) )
| '#form6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl34]) ).
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 ) ) ) ) ) )
=> ( X2 @ '#sk7' @ '#sk16' ) )
| '#form6' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl47,plain,
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk1' @ '#sk7' @ '#sk16' ) )
| '#form6' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl291,plain,
( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
=> ( '#sk1' @ '#sk7' @ '#sk16' ) )
| '#form6' ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl292,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk1' @ Y1 @ Y2 )
& ( '#sk1' @ Y0 @ Y1 ) )
=> ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
| ( '#sk1' @ '#sk7' @ '#sk16' )
| '#form6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl291]) ).
thf(zip_derived_cl65_008,plain,
! [X2: $i > $i > $o] :
( ( '#form135' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl293,plain,
( ~ ( '#form135' @ '#sk1' )
| '#form6'
| ( '#sk1' @ '#sk7' @ '#sk16' ) ),
inference(renaming,[status(thm)],[zip_derived_cl292,zip_derived_cl65]) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( (~) @ ( '#sk1' @ Y1 @ Y0 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl8,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( (~) @ ( '#sk1' @ Y0 @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl11,plain,
! [X2: $i,X4: $i] :
( ( '#sk1' @ X2 @ X4 )
=> ( (~) @ ( '#sk1' @ X4 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl14,plain,
! [X2: $i,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ~ ( '#sk1' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl296,plain,
( '#form6'
| ~ ( '#form135' @ '#sk1' )
| ~ ( '#sk1' @ '#sk16' @ '#sk7' ) ),
inference('sup-',[status(thm)],[zip_derived_cl293,zip_derived_cl14]) ).
thf(zip_derived_cl320,plain,
( '#form6'
| ~ ( '#form135' @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl319,zip_derived_cl296]) ).
thf(zip_derived_cl329,plain,
! [X0: $i] :
( ~ ( '#sk1' @ X0 @ '#sk3' )
| ( '#sk1' @ X0 @ '#sk4' )
| ~ ( '#form135' @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl208,zip_derived_cl320]) ).
thf(zip_derived_cl330,plain,
( ~ '#form6'
| ~ ( '#form135' @ '#sk1' )
| ~ ( '#form135' @ '#sk1' )
| ( '#sk1' @ '#sk2' @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl149,zip_derived_cl329]) ).
thf(zip_derived_cl337,plain,
( ( '#sk1' @ '#sk2' @ '#sk4' )
| ~ ( '#form135' @ '#sk1' )
| ~ '#form6' ),
inference(simplify,[status(thm)],[zip_derived_cl330]) ).
thf(zip_derived_cl320_009,plain,
( '#form6'
| ~ ( '#form135' @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl319,zip_derived_cl296]) ).
thf(zip_derived_cl343,plain,
( ~ ( '#form135' @ '#sk1' )
| ( '#sk1' @ '#sk2' @ '#sk4' ) ),
inference(clc,[status(thm)],[zip_derived_cl337,zip_derived_cl320]) ).
thf(zip_derived_cl18,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' ) ) )
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
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' @ '#sk4' ) )
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl26_010,plain,
( '#form6'
| ~ ( !!
@ ^ [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 ) ) )
=> ( (~)
@ ( !!
@ ^ [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 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl29,plain,
( ~ '#form6'
| ~ ( ( ( !!
@ ^ [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(renaming,[status(thm)],[zip_derived_cl22,zip_derived_cl26]) ).
thf(zip_derived_cl35,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 ) ) ) ) ) )
| ~ '#form6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl41,plain,
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
| ~ '#form6' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl51,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk5' @ X2 @ Y0 ) ) )
| ~ '#form6' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl57,plain,
! [X2: $i,X4: $i] :
( ( ( '#sk1' @ X2 @ X4 )
=> ( '#sk5' @ X2 @ X4 ) )
| ~ '#form6' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl63,plain,
! [X2: $i,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X4 )
| ~ '#form6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl345,plain,
( ~ ( '#form135' @ '#sk1' )
| ~ '#form6'
| ( '#sk5' @ '#sk2' @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl343,zip_derived_cl63]) ).
thf(zip_derived_cl320_011,plain,
( '#form6'
| ~ ( '#form135' @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl319,zip_derived_cl296]) ).
thf(zip_derived_cl358,plain,
( ( '#sk5' @ '#sk2' @ '#sk4' )
| ~ ( '#form135' @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl345,zip_derived_cl320]) ).
thf(zip_derived_cl36,plain,
( ~ ( '#sk5' @ '#sk2' @ '#sk4' )
| ~ '#form6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl359,plain,
( ~ ( '#form135' @ '#sk1' )
| ~ '#form6' ),
inference('sup-',[status(thm)],[zip_derived_cl358,zip_derived_cl36]) ).
thf(zip_derived_cl320_012,plain,
( '#form6'
| ~ ( '#form135' @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl319,zip_derived_cl296]) ).
thf(zip_derived_cl459,plain,
~ ( '#form135' @ '#sk1' ),
inference(clc,[status(thm)],[zip_derived_cl359,zip_derived_cl320]) ).
thf(zip_derived_cl65_013,plain,
! [X2: $i > $i > $o] :
( ( '#form135' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl66,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( X2 @ Y0 @ Y1 )
& ( X2 @ ( '#sk136' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk136' @ X2 ) @ Y1 ) ) ) )
| ( '#form135' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl74,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( ( X2 @ ( '#sk187' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk136' @ X2 ) @ ( '#sk187' @ X2 ) ) )
=> ( X2 @ ( '#sk136' @ X2 ) @ Y0 ) ) )
| ( '#form135' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl83,plain,
! [X2: $i > $i > $o] :
( ~ ( ( ( X2 @ ( '#sk187' @ X2 ) @ ( '#sk248' @ X2 ) )
& ( X2 @ ( '#sk136' @ X2 ) @ ( '#sk187' @ X2 ) ) )
=> ( X2 @ ( '#sk136' @ X2 ) @ ( '#sk248' @ X2 ) ) )
| ( '#form135' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl86,plain,
! [X2: $i > $i > $o] :
( ( ( X2 @ ( '#sk187' @ X2 ) @ ( '#sk248' @ X2 ) )
& ( X2 @ ( '#sk136' @ X2 ) @ ( '#sk187' @ X2 ) ) )
| ( '#form135' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl94,plain,
! [X2: $i > $i > $o] :
( ( X2 @ ( '#sk136' @ X2 ) @ ( '#sk187' @ X2 ) )
| ( '#form135' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl93,plain,
! [X2: $i > $i > $o] :
( ( X2 @ ( '#sk187' @ X2 ) @ ( '#sk248' @ X2 ) )
| ( '#form135' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl19_014,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#sk1' @ X4 @ X6 )
| ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl126,plain,
! [X0: $i] :
( ( '#form135' @ '#sk1' )
| ( '#sk1' @ X0 @ ( '#sk248' @ '#sk1' ) )
| ~ ( '#sk1' @ X0 @ ( '#sk187' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl19]) ).
thf(zip_derived_cl459_015,plain,
~ ( '#form135' @ '#sk1' ),
inference(clc,[status(thm)],[zip_derived_cl359,zip_derived_cl320]) ).
thf(zip_derived_cl562,plain,
! [X0: $i] :
( ( '#sk1' @ X0 @ ( '#sk248' @ '#sk1' ) )
| ~ ( '#sk1' @ X0 @ ( '#sk187' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl126,zip_derived_cl459]) ).
thf(zip_derived_cl563,plain,
( ( '#form135' @ '#sk1' )
| ( '#sk1' @ ( '#sk136' @ '#sk1' ) @ ( '#sk248' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl94,zip_derived_cl562]) ).
thf(zip_derived_cl459_016,plain,
~ ( '#form135' @ '#sk1' ),
inference(clc,[status(thm)],[zip_derived_cl359,zip_derived_cl320]) ).
thf(zip_derived_cl564,plain,
'#sk1' @ ( '#sk136' @ '#sk1' ) @ ( '#sk248' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl563,zip_derived_cl459]) ).
thf(zip_derived_cl87,plain,
! [X2: $i > $i > $o] :
( ~ ( X2 @ ( '#sk136' @ X2 ) @ ( '#sk248' @ X2 ) )
| ( '#form135' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl569,plain,
'#form135' @ '#sk1',
inference('sup-',[status(thm)],[zip_derived_cl564,zip_derived_cl87]) ).
thf(zip_derived_cl571,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl459,zip_derived_cl569]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU496^1 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.RqBuZHUoVu true
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 17:00:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.22/0.67 % Total configuration time : 828
% 0.22/0.67 % Estimated wc time : 1656
% 0.22/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 10.01/1.91 % Solved by lams/35_full_unif4.sh.
% 10.01/1.91 % done 98 iterations in 1.050s
% 10.01/1.91 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 10.01/1.91 % SZS output start Refutation
% See solution above
% 10.01/1.92
% 10.01/1.92
% 10.01/1.92 % Terminating...
% 10.53/2.05 % Runner terminated.
% 10.53/2.07 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------