TSTP Solution File: SEU473^1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU473^1 : 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.MDAdxOQfYO true
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:13:14 EDT 2023
% Result : Theorem 2.05s 1.28s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 42
% Syntax : Number of formulae : 154 ( 35 unt; 20 typ; 0 def)
% Number of atoms : 929 ( 78 equ; 2 cnn)
% Maximal formula atoms : 38 ( 6 avg)
% Number of connectives : 3032 ( 70 ~; 154 |; 179 &;1872 @)
% ( 0 <=>; 289 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 306 ( 306 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 6 con; 0-3 aty)
% ( 468 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 660 ( 510 ^; 150 !; 0 ?; 660 :)
% Comments :
%------------------------------------------------------------------------------
thf('#sk56_type',type,
'#sk56': ( $i > $i > $o ) > $i ).
thf('#sk76_type',type,
'#sk76': ( $i > $i > $o ) > $i ).
thf(subrel_type,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(sc_type,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(mono_type,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf('#sk5_type',type,
'#sk5': $i > $i > $o ).
thf('#sk223_type',type,
'#sk223': ( $i > $i > $o ) > $i ).
thf(trsc_type,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf('#form126_type',type,
'#form126': ( $i > $i > $o ) > $o ).
thf(tc_type,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf('#sk127_type',type,
'#sk127': ( $i > $i > $o ) > $i ).
thf('#sk174_type',type,
'#sk174': ( $i > $i > $o ) > $i ).
thf(trans_type,type,
trans: ( $i > $i > $o ) > $o ).
thf('#sk3_type',type,
'#sk3': $i ).
thf('#sk2_type',type,
'#sk2': $i > $i > $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf('#form15_type',type,
'#form15': $o ).
thf(rc_type,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf('#sk1_type',type,
'#sk1': $i > $i > $o ).
thf('#sk6_type',type,
'#sk6': $i > $i > $o ).
thf(transitive_reflexive_symmetric_closure,axiom,
( trsc
= ( ^ [R: $i > $i > $o] : ( sc @ ( 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(symmetric_closure,axiom,
( sc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( R @ Y @ X )
| ( R @ X @ Y ) ) ) ) ).
thf('6',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('7',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(reflexive_closure,axiom,
( rc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( X = Y )
| ( R @ X @ Y ) ) ) ) ).
thf('8',plain,
( rc
= ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
( ( X = Y )
| ( R @ X @ Y ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[reflexive_closure]) ).
thf('9',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('10',plain,
( trsc
= ( ^ [R: $i > $i > $o] : ( sc @ ( rc @ ( tc @ R ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[transitive_reflexive_symmetric_closure,'5','1','7','9','3']) ).
thf('11',plain,
( trsc
= ( ^ [V_1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ V_1 ) ) ) ) ),
define([status(thm)]) ).
thf(monotonic,axiom,
( mono
= ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
! [R: $i > $i > $o,S: $i > $i > $o] :
( ( subrel @ R @ S )
=> ( subrel @ ( F @ R ) @ ( F @ S ) ) ) ) ) ).
thf('12',plain,
( mono
= ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
! [R: $i > $i > $o,S: $i > $i > $o] :
( ( subrel @ R @ S )
=> ( subrel @ ( F @ R ) @ ( F @ S ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[monotonic,'3']) ).
thf('13',plain,
( mono
= ( ^ [V_1: ( $i > $i > $o ) > $i > $i > $o] :
! [X4: $i > $i > $o,X6: $i > $i > $o] :
( ( subrel @ X4 @ X6 )
=> ( subrel @ ( V_1 @ X4 ) @ ( V_1 @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(transitive_reflexive_symmetric_closure_op_is_monotonic,conjecture,
mono @ trsc ).
thf(zf_stmt_0,conjecture,
! [X4: $i > $i > $o,X6: $i > $i > $o] :
( ! [X8: $i,X10: $i] :
( ( X4 @ X8 @ X10 )
=> ( X6 @ X8 @ X10 ) )
=> ! [X12: $i,X14: $i] :
( ( ! [X28: $i > $i > $o] :
( ( ! [X36: $i,X38: $i] :
( ( X4 @ X36 @ X38 )
=> ( X28 @ X36 @ X38 ) )
& ! [X30: $i,X32: $i,X34: $i] :
( ( ( X28 @ X32 @ X34 )
& ( X28 @ X30 @ X32 ) )
=> ( X28 @ X30 @ X34 ) ) )
=> ( X28 @ X12 @ X14 ) )
| ( X12 = X14 )
| ! [X16: $i > $i > $o] :
( ( ! [X24: $i,X26: $i] :
( ( X4 @ X24 @ X26 )
=> ( X16 @ X24 @ X26 ) )
& ! [X18: $i,X20: $i,X22: $i] :
( ( ( X16 @ X20 @ X22 )
& ( X16 @ X18 @ X20 ) )
=> ( X16 @ X18 @ X22 ) ) )
=> ( X16 @ X14 @ X12 ) )
| ( X14 = X12 ) )
=> ( ! [X52: $i > $i > $o] :
( ( ! [X60: $i,X62: $i] :
( ( X6 @ X60 @ X62 )
=> ( X52 @ X60 @ X62 ) )
& ! [X54: $i,X56: $i,X58: $i] :
( ( ( X52 @ X56 @ X58 )
& ( X52 @ X54 @ X56 ) )
=> ( X52 @ X54 @ X58 ) ) )
=> ( X52 @ X12 @ X14 ) )
| ( X12 = X14 )
| ! [X40: $i > $i > $o] :
( ( ! [X48: $i,X50: $i] :
( ( X6 @ X48 @ X50 )
=> ( X40 @ X48 @ X50 ) )
& ! [X42: $i,X44: $i,X46: $i] :
( ( ( X40 @ X44 @ X46 )
& ( X40 @ X42 @ X44 ) )
=> ( X40 @ X42 @ X46 ) ) )
=> ( X40 @ X14 @ X12 ) )
| ( X14 = X12 ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i > $i > $o,X6: $i > $i > $o] :
( ! [X8: $i,X10: $i] :
( ( X4 @ X8 @ X10 )
=> ( X6 @ X8 @ X10 ) )
=> ! [X12: $i,X14: $i] :
( ( ! [X28: $i > $i > $o] :
( ( ! [X36: $i,X38: $i] :
( ( X4 @ X36 @ X38 )
=> ( X28 @ X36 @ X38 ) )
& ! [X30: $i,X32: $i,X34: $i] :
( ( ( X28 @ X32 @ X34 )
& ( X28 @ X30 @ X32 ) )
=> ( X28 @ X30 @ X34 ) ) )
=> ( X28 @ X12 @ X14 ) )
| ( X12 = X14 )
| ! [X16: $i > $i > $o] :
( ( ! [X24: $i,X26: $i] :
( ( X4 @ X24 @ X26 )
=> ( X16 @ X24 @ X26 ) )
& ! [X18: $i,X20: $i,X22: $i] :
( ( ( X16 @ X20 @ X22 )
& ( X16 @ X18 @ X20 ) )
=> ( X16 @ X18 @ X22 ) ) )
=> ( X16 @ X14 @ X12 ) )
| ( X14 = X12 ) )
=> ( ! [X52: $i > $i > $o] :
( ( ! [X60: $i,X62: $i] :
( ( X6 @ X60 @ X62 )
=> ( X52 @ X60 @ X62 ) )
& ! [X54: $i,X56: $i,X58: $i] :
( ( ( X52 @ X56 @ X58 )
& ( X52 @ X54 @ X56 ) )
=> ( X52 @ X54 @ X58 ) ) )
=> ( X52 @ X12 @ X14 ) )
| ( X12 = X14 )
| ! [X40: $i > $i > $o] :
( ( ! [X48: $i,X50: $i] :
( ( X6 @ X48 @ X50 )
=> ( X40 @ X48 @ X50 ) )
& ! [X42: $i,X44: $i,X46: $i] :
( ( ( X40 @ X44 @ X46 )
& ( X40 @ X42 @ X44 ) )
=> ( X40 @ X42 @ X46 ) ) )
=> ( X40 @ X14 @ X12 ) )
| ( X14 = X12 ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i > $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
=> ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( !!
@ ^ [Y4: $i > $i > $o] :
( ( ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( !!
@ ^ [Y7: $i] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( Y2 = Y3 )
| ( !!
@ ^ [Y4: $i > $i > $o] :
( ( ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( !!
@ ^ [Y7: $i] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( Y3 = Y2 ) )
=> ( ( !!
@ ^ [Y4: $i > $i > $o] :
( ( ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( Y1 @ 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] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( !!
@ ^ [Y7: $i] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( Y3 = Y2 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( !!
@ ^ [Y0: $i > $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i > $i > $o] :
( ( ( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 )
| ( !!
@ ^ [Y3: $i > $i > $o] :
( ( ( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( ( '#sk1' @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !!
@ ^ [Y4: $i] :
( !!
@ ^ [Y5: $i] :
( !!
@ ^ [Y6: $i] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( Y2 = Y1 ) )
=> ( ( !!
@ ^ [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 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk2' @ Y0 @ 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 ) ) )
| ( 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 > $i > $o] :
( ( ( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( ( '#sk2' @ 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] :
( ( '#sk2' @ 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 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,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 > $i > $o] :
( ( ( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( ( '#sk2' @ 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] :
( ( '#sk2' @ 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 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl6,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i > $i > $o] :
( ( ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ '#sk3' @ Y0 ) ) )
| ( '#sk3' = Y0 )
| ( !!
@ ^ [Y1: $i > $i > $o] :
( ( ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( '#sk1' @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ '#sk3' ) ) )
| ( Y0 = '#sk3' ) )
=> ( ( !!
@ ^ [Y1: $i > $i > $o] :
( ( ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( '#sk2' @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ '#sk3' @ Y0 ) ) )
| ( '#sk3' = Y0 )
| ( !!
@ ^ [Y1: $i > $i > $o] :
( ( ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( '#sk2' @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( !!
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ '#sk3' ) ) )
| ( Y0 = '#sk3' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl8,plain,
~ ( ( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' )
| ( !!
@ ^ [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 @ '#sk4' @ '#sk3' ) ) )
| ( '#sk4' = '#sk3' ) )
=> ( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk2' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' )
| ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk2' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk4' @ '#sk3' ) ) )
| ( '#sk4' = '#sk3' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl10,plain,
( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' )
| ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk4' @ '#sk3' ) ) )
| ( '#sk4' = '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl12,plain,
( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk1' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' )
| ( !!
@ ^ [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 @ '#sk4' @ '#sk3' ) ) )
| ( '#sk4' = '#sk3' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl10]) ).
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' ) ) )
| ( '#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 @ '#sk4' @ '#sk3' ) ) )
| ( '#sk4' = '#sk3' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl12]) ).
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 @ '#sk4' @ '#sk3' ) ) )
| ( '#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 @ '#sk3' @ '#sk4' ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl19,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 @ '#sk4' @ '#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' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl28,plain,
( ~ '#form15'
| ( !!
@ ^ [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' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl29,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' ) )
| ~ '#form15' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl31,plain,
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk5' @ '#sk3' @ '#sk4' ) )
| ~ '#form15' ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl11,plain,
~ ( ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk2' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' )
| ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk2' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk4' @ '#sk3' ) ) )
| ( '#sk4' = '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl13,plain,
~ ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk2' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk3' @ '#sk4' ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl23,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk5' @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl36,plain,
~ ( '#sk5' @ '#sk3' @ '#sk4' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl19_001,plain,
! [X2: $i > $i > $o] :
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( X2 @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) )
=> ( X2 @ '#sk4' @ '#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' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl25,plain,
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk6' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk6' @ Y1 @ Y2 )
& ( '#sk6' @ Y0 @ Y1 ) )
=> ( '#sk6' @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk6' @ '#sk4' @ '#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' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl15,plain,
~ ( !!
@ ^ [Y0: $i > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( '#sk2' @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ '#sk4' @ '#sk3' ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl26,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk6' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk6' @ Y1 @ Y2 )
& ( '#sk6' @ Y0 @ Y1 ) )
=> ( '#sk6' @ Y0 @ Y2 ) ) ) ) ) )
=> ( '#sk6' @ '#sk4' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl38,plain,
~ ( '#sk6' @ '#sk4' @ '#sk3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl254,plain,
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk6' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk6' @ Y1 @ Y2 )
& ( '#sk6' @ Y0 @ Y1 ) )
=> ( '#sk6' @ 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 @ '#sk3' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl25,zip_derived_cl38]) ).
thf(zip_derived_cl14,plain,
'#sk3' != '#sk4',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl24,plain,
'#sk3' != '#sk4',
inference('simplify nested equalities',[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl255,plain,
( ( ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk6' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk6' @ Y1 @ Y2 )
& ( '#sk6' @ Y0 @ Y1 ) )
=> ( '#sk6' @ 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 @ '#sk3' @ '#sk4' ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl254,zip_derived_cl24]) ).
thf(zip_derived_cl256,plain,
( ( (~)
@ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk6' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk6' @ Y1 @ Y2 )
& ( '#sk6' @ Y0 @ Y1 ) )
=> ( '#sk6' @ 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' @ '#sk4' ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl255]) ).
thf(zip_derived_cl257,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk6' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk6' @ Y1 @ Y2 )
& ( '#sk6' @ Y0 @ Y1 ) )
=> ( '#sk6' @ 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' @ '#sk4' ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl256]) ).
thf(zip_derived_cl28_002,plain,
( ~ '#form15'
| ( !!
@ ^ [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' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl258,plain,
( '#form15'
| ~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk6' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk6' @ Y1 @ Y2 )
& ( '#sk6' @ Y0 @ Y1 ) )
=> ( '#sk6' @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl257,zip_derived_cl28]) ).
thf(zip_derived_cl259,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk6' @ Y0 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk6' @ Y1 @ Y2 )
& ( '#sk6' @ Y0 @ Y1 ) )
=> ( '#sk6' @ Y0 @ Y2 ) ) ) ) )
| '#form15' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl258]) ).
thf(zip_derived_cl19_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 @ '#sk4' @ '#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' @ '#sk4' ) ) )
| ( '#sk3' = '#sk4' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl28_004,plain,
( ~ '#form15'
| ( !!
@ ^ [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' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl34,plain,
! [X2: $i > $i > $o] :
( '#form15'
| ( '#sk3' = '#sk4' )
| ( ( ( !!
@ ^ [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 @ '#sk4' @ '#sk3' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl19,zip_derived_cl28]) ).
thf(zip_derived_cl39,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 @ '#sk4' @ '#sk3' )
| ( '#sk3' = '#sk4' )
| '#form15' ),
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 ) ) ) ) )
| '#form15'
| ( '#sk3' = '#sk4' )
| ( X2 @ '#sk4' @ '#sk3' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl51,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ ( '#sk56' @ X2 ) @ Y0 )
=> ( X2 @ ( '#sk56' @ X2 ) @ Y0 ) ) )
| ( X2 @ '#sk4' @ '#sk3' )
| ( '#sk3' = '#sk4' )
| '#form15'
| ~ ( !!
@ ^ [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_cl57,plain,
! [X2: $i > $i > $o] :
( ~ ( ( '#sk1' @ ( '#sk56' @ X2 ) @ ( '#sk76' @ X2 ) )
=> ( X2 @ ( '#sk56' @ X2 ) @ ( '#sk76' @ X2 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) )
| '#form15'
| ( '#sk3' = '#sk4' )
| ( X2 @ '#sk4' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl63,plain,
! [X2: $i > $i > $o] :
( ( '#sk1' @ ( '#sk56' @ X2 ) @ ( '#sk76' @ X2 ) )
| ( X2 @ '#sk4' @ '#sk3' )
| ( '#sk3' = '#sk4' )
| '#form15'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl69,plain,
! [X2: $i > $i > $o] :
( ( '#form126' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl260,plain,
( ~ ( '#form126' @ '#sk6' )
| '#form15'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk6' @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl259,zip_derived_cl69]) ).
thf(zip_derived_cl69_005,plain,
! [X2: $i > $i > $o] :
( ( '#form126' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl70,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( X2 @ Y0 @ Y1 )
& ( X2 @ ( '#sk127' @ X2 ) @ Y0 ) )
=> ( X2 @ ( '#sk127' @ X2 ) @ Y1 ) ) ) )
| ( '#form126' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl77,plain,
! [X2: $i > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( ( X2 @ ( '#sk174' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk127' @ X2 ) @ ( '#sk174' @ X2 ) ) )
=> ( X2 @ ( '#sk127' @ X2 ) @ Y0 ) ) )
| ( '#form126' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl81,plain,
! [X2: $i > $i > $o] :
( ~ ( ( ( X2 @ ( '#sk174' @ X2 ) @ ( '#sk223' @ X2 ) )
& ( X2 @ ( '#sk127' @ X2 ) @ ( '#sk174' @ X2 ) ) )
=> ( X2 @ ( '#sk127' @ X2 ) @ ( '#sk223' @ X2 ) ) )
| ( '#form126' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl82,plain,
! [X2: $i > $i > $o] :
( ( ( X2 @ ( '#sk174' @ X2 ) @ ( '#sk223' @ X2 ) )
& ( X2 @ ( '#sk127' @ X2 ) @ ( '#sk174' @ X2 ) ) )
| ( '#form126' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl85,plain,
! [X2: $i > $i > $o] :
( ( X2 @ ( '#sk127' @ X2 ) @ ( '#sk174' @ X2 ) )
| ( '#form126' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl84,plain,
! [X2: $i > $i > $o] :
( ( X2 @ ( '#sk174' @ X2 ) @ ( '#sk223' @ X2 ) )
| ( '#form126' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl37,plain,
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk6' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk6' @ Y1 @ Y2 )
& ( '#sk6' @ Y0 @ Y1 ) )
=> ( '#sk6' @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl44,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk6' @ Y1 @ Y2 )
& ( '#sk6' @ Y0 @ Y1 ) )
=> ( '#sk6' @ Y0 @ Y2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl50,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( '#sk6' @ Y0 @ Y1 )
& ( '#sk6' @ X2 @ Y0 ) )
=> ( '#sk6' @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl56,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( '#sk6' @ X4 @ Y0 )
& ( '#sk6' @ X2 @ X4 ) )
=> ( '#sk6' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl62,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( '#sk6' @ X4 @ X6 )
& ( '#sk6' @ X2 @ X4 ) )
=> ( '#sk6' @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl68,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( '#sk6' @ X4 @ X6 )
& ( '#sk6' @ X2 @ X4 ) )
| ( '#sk6' @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl76,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#sk6' @ X4 @ X6 )
| ~ ( '#sk6' @ X2 @ X4 )
| ( '#sk6' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl138,plain,
! [X0: $i] :
( ( '#form126' @ '#sk6' )
| ( '#sk6' @ X0 @ ( '#sk223' @ '#sk6' ) )
| ~ ( '#sk6' @ X0 @ ( '#sk174' @ '#sk6' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl84,zip_derived_cl76]) ).
thf(zip_derived_cl225,plain,
( ( '#form126' @ '#sk6' )
| ( '#sk6' @ ( '#sk127' @ '#sk6' ) @ ( '#sk223' @ '#sk6' ) )
| ( '#form126' @ '#sk6' ) ),
inference('sup-',[status(thm)],[zip_derived_cl85,zip_derived_cl138]) ).
thf(zip_derived_cl231,plain,
( ( '#sk6' @ ( '#sk127' @ '#sk6' ) @ ( '#sk223' @ '#sk6' ) )
| ( '#form126' @ '#sk6' ) ),
inference(simplify,[status(thm)],[zip_derived_cl225]) ).
thf(zip_derived_cl83,plain,
! [X2: $i > $i > $o] :
( ~ ( X2 @ ( '#sk127' @ X2 ) @ ( '#sk223' @ X2 ) )
| ( '#form126' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl232,plain,
'#form126' @ '#sk6',
inference(clc,[status(thm)],[zip_derived_cl231,zip_derived_cl83]) ).
thf(zip_derived_cl261,plain,
( '#form15'
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk6' @ Y0 @ Y1 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl260,zip_derived_cl232]) ).
thf(zip_derived_cl262,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ ( '#sk56' @ '#sk6' ) @ Y0 )
=> ( '#sk6' @ ( '#sk56' @ '#sk6' ) @ Y0 ) ) )
| '#form15' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl261]) ).
thf(zip_derived_cl263,plain,
( ~ ( ( '#sk1' @ ( '#sk56' @ '#sk6' ) @ ( '#sk76' @ '#sk6' ) )
=> ( '#sk6' @ ( '#sk56' @ '#sk6' ) @ ( '#sk76' @ '#sk6' ) ) )
| '#form15' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl262]) ).
thf(zip_derived_cl264,plain,
( ( '#sk1' @ ( '#sk56' @ '#sk6' ) @ ( '#sk76' @ '#sk6' ) )
| '#form15' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl263]) ).
thf(zip_derived_cl3,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk2' @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl5,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ X2 @ Y0 )
=> ( '#sk2' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl7,plain,
! [X2: $i,X4: $i] :
( ( '#sk1' @ X2 @ X4 )
=> ( '#sk2' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl9,plain,
! [X2: $i,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk2' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl266,plain,
( '#form15'
| ( '#sk2' @ ( '#sk56' @ '#sk6' ) @ ( '#sk76' @ '#sk6' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl264,zip_derived_cl9]) ).
thf(zip_derived_cl43,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk6' @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl49,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( '#sk2' @ X2 @ Y0 )
=> ( '#sk6' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl55,plain,
! [X2: $i,X4: $i] :
( ( '#sk2' @ X2 @ X4 )
=> ( '#sk6' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl61,plain,
! [X2: $i,X4: $i] :
( ~ ( '#sk2' @ X2 @ X4 )
| ( '#sk6' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl272,plain,
( '#form15'
| ( '#sk6' @ ( '#sk56' @ '#sk6' ) @ ( '#sk76' @ '#sk6' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl266,zip_derived_cl61]) ).
thf(zip_derived_cl265,plain,
( ~ ( '#sk6' @ ( '#sk56' @ '#sk6' ) @ ( '#sk76' @ '#sk6' ) )
| '#form15' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl263]) ).
thf(zip_derived_cl276,plain,
'#form15',
inference(clc,[status(thm)],[zip_derived_cl272,zip_derived_cl265]) ).
thf(zip_derived_cl291,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 ) ) ) ) ) )
=> $false ),
inference(demod,[status(thm)],[zip_derived_cl31,zip_derived_cl36,zip_derived_cl276]) ).
thf(zip_derived_cl292,plain,
( (~)
@ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl291]) ).
thf(zip_derived_cl293,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl292]) ).
thf(zip_derived_cl294,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl293]) ).
thf(zip_derived_cl69_006,plain,
! [X2: $i > $i > $o] :
( ( '#form126' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( X2 @ Y1 @ Y2 )
& ( X2 @ Y0 @ Y1 ) )
=> ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl295,plain,
( ~ ( '#form126' @ '#sk5' )
| ~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl294,zip_derived_cl69]) ).
thf(zip_derived_cl85_007,plain,
! [X2: $i > $i > $o] :
( ( X2 @ ( '#sk127' @ X2 ) @ ( '#sk174' @ X2 ) )
| ( '#form126' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl84_008,plain,
! [X2: $i > $i > $o] :
( ( X2 @ ( '#sk174' @ X2 ) @ ( '#sk223' @ X2 ) )
| ( '#form126' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl35,plain,
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl42,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( '#sk5' @ Y1 @ Y2 )
& ( '#sk5' @ Y0 @ Y1 ) )
=> ( '#sk5' @ Y0 @ Y2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl48,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( '#sk5' @ Y0 @ Y1 )
& ( '#sk5' @ X2 @ Y0 ) )
=> ( '#sk5' @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl54,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( '#sk5' @ X4 @ Y0 )
& ( '#sk5' @ X2 @ X4 ) )
=> ( '#sk5' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl60,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( '#sk5' @ X4 @ X6 )
& ( '#sk5' @ X2 @ X4 ) )
=> ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl67,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( '#sk5' @ X4 @ X6 )
& ( '#sk5' @ X2 @ X4 ) )
| ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl75,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#sk5' @ X4 @ X6 )
| ~ ( '#sk5' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl132,plain,
! [X0: $i] :
( ( '#form126' @ '#sk5' )
| ( '#sk5' @ X0 @ ( '#sk223' @ '#sk5' ) )
| ~ ( '#sk5' @ X0 @ ( '#sk174' @ '#sk5' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl84,zip_derived_cl75]) ).
thf(zip_derived_cl221,plain,
( ( '#form126' @ '#sk5' )
| ( '#sk5' @ ( '#sk127' @ '#sk5' ) @ ( '#sk223' @ '#sk5' ) )
| ( '#form126' @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl85,zip_derived_cl132]) ).
thf(zip_derived_cl222,plain,
( ( '#sk5' @ ( '#sk127' @ '#sk5' ) @ ( '#sk223' @ '#sk5' ) )
| ( '#form126' @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl221]) ).
thf(zip_derived_cl83_009,plain,
! [X2: $i > $i > $o] :
( ~ ( X2 @ ( '#sk127' @ X2 ) @ ( '#sk223' @ X2 ) )
| ( '#form126' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl223,plain,
'#form126' @ '#sk5',
inference(clc,[status(thm)],[zip_derived_cl222,zip_derived_cl83]) ).
thf(zip_derived_cl296,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk1' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl295,zip_derived_cl223]) ).
thf(zip_derived_cl297,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( '#sk1' @ ( '#sk56' @ '#sk5' ) @ Y0 )
=> ( '#sk5' @ ( '#sk56' @ '#sk5' ) @ Y0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl296]) ).
thf(zip_derived_cl298,plain,
~ ( ( '#sk1' @ ( '#sk56' @ '#sk5' ) @ ( '#sk76' @ '#sk5' ) )
=> ( '#sk5' @ ( '#sk56' @ '#sk5' ) @ ( '#sk76' @ '#sk5' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl297]) ).
thf(zip_derived_cl300,plain,
~ ( '#sk5' @ ( '#sk56' @ '#sk5' ) @ ( '#sk76' @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl298]) ).
thf(zip_derived_cl299,plain,
'#sk1' @ ( '#sk56' @ '#sk5' ) @ ( '#sk76' @ '#sk5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl298]) ).
thf(zip_derived_cl9_010,plain,
! [X2: $i,X4: $i] :
( ~ ( '#sk1' @ X2 @ X4 )
| ( '#sk2' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl301,plain,
'#sk2' @ ( '#sk56' @ '#sk5' ) @ ( '#sk76' @ '#sk5' ),
inference('sup-',[status(thm)],[zip_derived_cl299,zip_derived_cl9]) ).
thf(zip_derived_cl41,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( '#sk2' @ Y0 @ Y1 )
=> ( '#sk5' @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl47,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( '#sk2' @ X2 @ Y0 )
=> ( '#sk5' @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl53,plain,
! [X2: $i,X4: $i] :
( ( '#sk2' @ X2 @ X4 )
=> ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl59,plain,
! [X2: $i,X4: $i] :
( ~ ( '#sk2' @ X2 @ X4 )
| ( '#sk5' @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl304,plain,
'#sk5' @ ( '#sk56' @ '#sk5' ) @ ( '#sk76' @ '#sk5' ),
inference('sup-',[status(thm)],[zip_derived_cl301,zip_derived_cl59]) ).
thf(zip_derived_cl309,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl300,zip_derived_cl304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU473^1 : 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.MDAdxOQfYO true
% 0.18/0.35 % Computer : n016.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Wed Aug 23 13:00:37 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.18/0.35 % Running portfolio for 300 s
% 0.18/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.35 % Number of cores: 8
% 0.18/0.35 % Python version: Python 3.6.8
% 0.18/0.35 % Running in HO mode
% 0.21/0.69 % Total configuration time : 828
% 0.21/0.69 % Estimated wc time : 1656
% 0.21/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.36/0.83 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.36/0.83 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.36/0.87 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 2.05/1.28 % Solved by lams/35_full_unif4.sh.
% 2.05/1.28 % done 69 iterations in 0.455s
% 2.05/1.28 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 2.05/1.28 % SZS output start Refutation
% See solution above
% 2.05/1.28
% 2.05/1.28
% 2.05/1.28 % Terminating...
% 2.16/1.45 % Runner terminated.
% 2.16/1.46 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------