%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ALG276^5 : TPTP v9.2.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Guh595FMWy true
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:28:33 PM UTC 2025
% Result : Theorem 4.69s 1.20s
% Output : Refutation 4.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 20
% Syntax : Number of formulae : 146 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 794 ( 373 equ; 0 cnn)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 2410 ( 166 ~; 163 |; 137 &;1636 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 19 usr; 10 con; 0-2 aty)
% ( 217 !!; 86 ??; 0 @@+; 0 @@-)
% Number of variables : 564 ( 330 ^; 216 !; 18 ?; 564 :)
% Comments :
%------------------------------------------------------------------------------
thf(g_type,type,
g: $tType ).
thf(cGRP_DIVISORS_type,type,
cGRP_DIVISORS: ( g > g > g ) > $o ).
thf('#sk10_type',type,
'#sk10': g ).
thf('#sk8_type',type,
'#sk8': g ).
thf(cGROUP4_type,type,
cGROUP4: ( g > g > g ) > $o ).
thf(cGRP_UNIT_type,type,
cGRP_UNIT: ( g > g > g ) > g > $o ).
thf('#sk2_type',type,
'#sk2': g ).
thf('#sk4_type',type,
'#sk4': g > g ).
thf('#sk6_type',type,
'#sk6': g > g > g ).
thf('#form3_type',type,
'#form3': $o ).
thf(cGRP_INVERSE_type,type,
cGRP_INVERSE: ( g > g > g ) > g > $o ).
thf('#sk5_type',type,
'#sk5': g > g > g ).
thf(cGRP_ASSOC_type,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf('#sk7_type',type,
'#sk7': g ).
thf('#sk1_type',type,
'#sk1': g > g > g ).
thf('#sk11_type',type,
'#sk11': g ).
thf(cGROUP1_type,type,
cGROUP1: ( g > g > g ) > g > $o ).
thf('#sk9_type',type,
'#sk9': g > g ).
thf('#sk13_type',type,
'#sk13': g > g ).
thf('#sk12_type',type,
'#sk12': g ).
thf(cGROUP4_def,axiom,
( cGROUP4
= ( ^ [Xf: g > g > g] :
( ( cGRP_ASSOC @ Xf )
& ( cGRP_DIVISORS @ Xf ) ) ) ) ).
thf(cGRP_DIVISORS_def,axiom,
( cGRP_DIVISORS
= ( ^ [Xf: g > g > g] :
! [Xa: g,Xb: g] :
( ? [Xy: g] :
( ( Xf @ Xy @ Xa )
= Xb )
& ? [Xx: g] :
( ( Xf @ Xa @ Xx )
= Xb ) ) ) ) ).
thf('0',plain,
( cGRP_DIVISORS
= ( ^ [Xf: g > g > g] :
! [Xa: g,Xb: g] :
( ? [Xy: g] :
( ( Xf @ Xy @ Xa )
= Xb )
& ? [Xx: g] :
( ( Xf @ Xa @ Xx )
= Xb ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[cGRP_DIVISORS_def]) ).
thf('1',plain,
( cGRP_DIVISORS
= ( ^ [V_1: g > g > g] :
! [X4: g,X6: g] :
( ? [X8: g] :
( ( V_1 @ X8 @ X4 )
= X6 )
& ? [X10: g] :
( ( V_1 @ X4 @ X10 )
= X6 ) ) ) ),
define([status(thm)]) ).
thf(cGRP_ASSOC_def,axiom,
( cGRP_ASSOC
= ( ^ [Xf: g > g > g] :
! [Xa: g,Xb: g,Xc: g] :
( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
= ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ) ).
thf('2',plain,
( cGRP_ASSOC
= ( ^ [Xf: g > g > g] :
! [Xa: g,Xb: g,Xc: g] :
( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
= ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[cGRP_ASSOC_def]) ).
thf('3',plain,
( cGRP_ASSOC
= ( ^ [V_1: g > g > g] :
! [X4: g,X6: g,X8: g] :
( ( V_1 @ ( V_1 @ X4 @ X6 ) @ X8 )
= ( V_1 @ X4 @ ( V_1 @ X6 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf('4',plain,
( cGROUP4
= ( ^ [Xf: g > g > g] :
( ( cGRP_ASSOC @ Xf )
& ( cGRP_DIVISORS @ Xf ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[cGROUP4_def,'1','3']) ).
thf('5',plain,
( cGROUP4
= ( ^ [V_1: g > g > g] :
( ( cGRP_ASSOC @ V_1 )
& ( cGRP_DIVISORS @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(cGROUP1_def,axiom,
( cGROUP1
= ( ^ [Xf: g > g > g,Xe: g] :
( ( cGRP_ASSOC @ Xf )
& ( cGRP_UNIT @ Xf @ Xe )
& ( cGRP_INVERSE @ Xf @ Xe ) ) ) ) ).
thf(cGRP_UNIT_def,axiom,
( cGRP_UNIT
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
( ( ( Xf @ Xa @ Xe )
= Xa )
& ( ( Xf @ Xe @ Xa )
= Xa ) ) ) ) ).
thf('6',plain,
( cGRP_UNIT
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
( ( ( Xf @ Xa @ Xe )
= Xa )
& ( ( Xf @ Xe @ Xa )
= Xa ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[cGRP_UNIT_def]) ).
thf('7',plain,
( cGRP_UNIT
= ( ^ [V_1: g > g > g,V_2: g] :
! [X4: g] :
( ( ( V_1 @ X4 @ V_2 )
= X4 )
& ( ( V_1 @ V_2 @ X4 )
= X4 ) ) ) ),
define([status(thm)]) ).
thf(cGRP_INVERSE_def,axiom,
( cGRP_INVERSE
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
? [Xb: g] :
( ( ( Xf @ Xb @ Xa )
= Xe )
& ( ( Xf @ Xa @ Xb )
= Xe ) ) ) ) ).
thf('8',plain,
( cGRP_INVERSE
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
? [Xb: g] :
( ( ( Xf @ Xb @ Xa )
= Xe )
& ( ( Xf @ Xa @ Xb )
= Xe ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[cGRP_INVERSE_def]) ).
thf('9',plain,
( cGRP_INVERSE
= ( ^ [V_1: g > g > g,V_2: g] :
! [X4: g] :
? [X6: g] :
( ( ( V_1 @ X6 @ X4 )
= V_2 )
& ( ( V_1 @ X4 @ X6 )
= V_2 ) ) ) ),
define([status(thm)]) ).
thf('10',plain,
( cGROUP1
= ( ^ [Xf: g > g > g,Xe: g] :
( ( cGRP_ASSOC @ Xf )
& ( cGRP_UNIT @ Xf @ Xe )
& ( cGRP_INVERSE @ Xf @ Xe ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[cGROUP1_def,'7','9','3']) ).
thf('11',plain,
( cGROUP1
= ( ^ [V_1: g > g > g,V_2: g] :
( ( cGRP_ASSOC @ V_1 )
& ( cGRP_UNIT @ V_1 @ V_2 )
& ( cGRP_INVERSE @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(cEQUIV_01_04,conjecture,
! [Xf: g > g > g] :
( ? [Xe: g] : ( cGROUP1 @ Xf @ Xe )
<=> ( cGROUP4 @ Xf ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: g > g > g] :
( ? [X6: g] :
( ! [X16: g] :
? [X18: g] :
( ( ( X4 @ X16 @ X18 )
= X6 )
& ( ( X4 @ X18 @ X16 )
= X6 ) )
& ! [X14: g] :
( ( ( X4 @ X6 @ X14 )
= X14 )
& ( ( X4 @ X14 @ X6 )
= X14 ) )
& ! [X8: g,X10: g,X12: g] :
( ( X4 @ ( X4 @ X8 @ X10 ) @ X12 )
= ( X4 @ X8 @ ( X4 @ X10 @ X12 ) ) ) )
<=> ( ! [X26: g,X28: g] :
( ? [X32: g] :
( ( X4 @ X26 @ X32 )
= X28 )
& ? [X30: g] :
( ( X4 @ X30 @ X26 )
= X28 ) )
& ! [X20: g,X22: g,X24: g] :
( ( X4 @ ( X4 @ X20 @ X22 ) @ X24 )
= ( X4 @ X20 @ ( X4 @ X22 @ X24 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: g > g > g] :
( ? [X6: g] :
( ! [X16: g] :
? [X18: g] :
( ( ( X4 @ X16 @ X18 )
= X6 )
& ( ( X4 @ X18 @ X16 )
= X6 ) )
& ! [X14: g] :
( ( ( X4 @ X6 @ X14 )
= X14 )
& ( ( X4 @ X14 @ X6 )
= X14 ) )
& ! [X8: g,X10: g,X12: g] :
( ( X4 @ ( X4 @ X8 @ X10 ) @ X12 )
= ( X4 @ X8 @ ( X4 @ X10 @ X12 ) ) ) )
<=> ( ! [X26: g,X28: g] :
( ? [X32: g] :
( ( X4 @ X26 @ X32 )
= X28 )
& ? [X30: g] :
( ( X4 @ X30 @ X26 )
= X28 ) )
& ! [X20: g,X22: g,X24: g] :
( ( X4 @ ( X4 @ X20 @ X22 ) @ X24 )
= ( X4 @ X20 @ ( X4 @ X22 @ X24 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: g > g > g] :
( ( ??
@ ^ [Y1: g] :
( ( !!
@ ^ [Y2: g] :
( ??
@ ^ [Y3: g] :
( ( ( Y0 @ Y2 @ Y3 )
= Y1 )
& ( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) )
& ( !!
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) )
& ( !!
@ ^ [Y2: g] :
( !!
@ ^ [Y3: g] :
( !!
@ ^ [Y4: g] :
( ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y4 )
= ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) )
<=> ( ( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( ??
@ ^ [Y3: g] :
( ( Y0 @ Y1 @ Y3 )
= Y2 ) )
& ( ??
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y1 )
= Y2 ) ) ) ) )
& ( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( !!
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ Y1 @ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( ( ??
@ ^ [Y0: g] :
( ( !!
@ ^ [Y1: g] :
( ??
@ ^ [Y2: g] :
( ( ( '#sk1' @ Y1 @ Y2 )
= Y0 )
& ( ( '#sk1' @ Y2 @ Y1 )
= Y0 ) ) ) )
& ( !!
@ ^ [Y1: g] :
( ( ( '#sk1' @ Y0 @ Y1 )
= Y1 )
& ( ( '#sk1' @ Y1 @ Y0 )
= Y1 ) ) )
& ( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( !!
@ ^ [Y3: g] :
( ( '#sk1' @ ( '#sk1' @ Y1 @ Y2 ) @ Y3 )
= ( '#sk1' @ Y1 @ ( '#sk1' @ Y2 @ Y3 ) ) ) ) ) ) ) )
<=> ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
( ( ??
@ ^ [Y0: g] :
( ( !!
@ ^ [Y1: g] :
( ??
@ ^ [Y2: g] :
( ( ( '#sk1' @ Y1 @ Y2 )
= Y0 )
& ( ( '#sk1' @ Y2 @ Y1 )
= Y0 ) ) ) )
& ( !!
@ ^ [Y1: g] :
( ( ( '#sk1' @ Y0 @ Y1 )
= Y1 )
& ( ( '#sk1' @ Y1 @ Y0 )
= Y1 ) ) )
& ( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( !!
@ ^ [Y3: g] :
( ( '#sk1' @ ( '#sk1' @ Y1 @ Y2 ) @ Y3 )
= ( '#sk1' @ Y1 @ ( '#sk1' @ Y2 @ Y3 ) ) ) ) ) ) ) )
!= ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
( ( ??
@ ^ [Y0: g] :
( ( !!
@ ^ [Y1: g] :
( ??
@ ^ [Y2: g] :
( ( ( '#sk1' @ Y1 @ Y2 )
= Y0 )
& ( ( '#sk1' @ Y2 @ Y1 )
= Y0 ) ) ) )
& ( !!
@ ^ [Y1: g] :
( ( ( '#sk1' @ Y0 @ Y1 )
= Y1 )
& ( ( '#sk1' @ Y1 @ Y0 )
= Y1 ) ) )
& ( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( !!
@ ^ [Y3: g] :
( ( '#sk1' @ ( '#sk1' @ Y1 @ Y2 ) @ Y3 )
= ( '#sk1' @ Y1 @ ( '#sk1' @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl5,plain,
( ( ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( ( '#sk1' @ Y0 @ Y1 )
= '#sk2' )
& ( ( '#sk1' @ Y1 @ Y0 )
= '#sk2' ) ) ) )
& ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ '#sk2' @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ '#sk2' )
= Y0 ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl6,plain,
( ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( ( '#sk1' @ Y0 @ Y1 )
= '#sk2' )
& ( ( '#sk1' @ Y1 @ Y0 )
= '#sk2' ) ) ) )
| ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl9,plain,
( ~ '#form3'
| ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl10,plain,
( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl18,plain,
! [X2: g] :
( ( !!
@ ^ [Y0: g] :
( ( ??
@ ^ [Y1: g] :
( ( '#sk1' @ X2 @ Y1 )
= Y0 ) )
& ( ??
@ ^ [Y1: g] :
( ( '#sk1' @ Y1 @ X2 )
= Y0 ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl23,plain,
! [X2: g,X4: g] :
( ( ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ X2 @ Y0 )
= X4 ) )
& ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ X2 )
= X4 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl30,plain,
! [X2: g,X4: g] :
( ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ X2 @ Y0 )
= X4 ) )
| ~ '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl38,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ X2 @ ( '#sk5' @ X2 @ X4 ) )
= X4 )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl41,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ X2 @ ( '#sk5' @ X2 @ X4 ) )
= X4 )
| ~ '#form3' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl31,plain,
! [X2: g,X4: g] :
( ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ X2 )
= X4 ) )
| ~ '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl39,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk6' @ X2 @ X4 ) @ X2 )
= X4 )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl42,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk6' @ X2 @ X4 ) @ X2 )
= X4 )
| ~ '#form3' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl8,plain,
( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl14,plain,
( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& $false ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl15,plain,
( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl16,plain,
! [X2: g] :
( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( '#sk1' @ ( '#sk1' @ X2 @ Y0 ) @ Y1 )
= ( '#sk1' @ X2 @ ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21,plain,
! [X2: g,X4: g] :
( !!
@ ^ [Y0: g] :
( ( '#sk1' @ ( '#sk1' @ X2 @ X4 ) @ Y0 )
= ( '#sk1' @ X2 @ ( '#sk1' @ X4 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl27,plain,
! [X2: g,X4: g,X6: g] :
( ( '#sk1' @ ( '#sk1' @ X2 @ X4 ) @ X6 )
= ( '#sk1' @ X2 @ ( '#sk1' @ X4 @ X6 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl35,plain,
! [X2: g,X4: g,X6: g] :
( ( '#sk1' @ ( '#sk1' @ X2 @ X4 ) @ X6 )
= ( '#sk1' @ X2 @ ( '#sk1' @ X4 @ X6 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl65,plain,
! [X0: g,X1: g,X2: g] :
( ( ( '#sk1' @ X0 @ X1 )
= ( '#sk1' @ ( '#sk6' @ X2 @ X0 ) @ ( '#sk1' @ X2 @ X1 ) ) )
| ~ '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl42,zip_derived_cl35]) ).
thf(zip_derived_cl284,plain,
! [X0: g,X1: g,X2: g] :
( ( ( '#sk1' @ X2 @ ( '#sk5' @ X1 @ X0 ) )
= ( '#sk1' @ ( '#sk6' @ X1 @ X2 ) @ X0 ) )
| ~ '#form3'
| ~ '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl65]) ).
thf(zip_derived_cl303,plain,
! [X0: g,X1: g,X2: g] :
( ~ '#form3'
| ( ( '#sk1' @ X2 @ ( '#sk5' @ X1 @ X0 ) )
= ( '#sk1' @ ( '#sk6' @ X1 @ X2 ) @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl284]) ).
thf(zip_derived_cl7,plain,
( ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ '#sk2' @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ '#sk2' )
= Y0 ) ) )
| ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl9_001,plain,
( ~ '#form3'
| ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl13,plain,
( '#form3'
| ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ '#sk2' @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ '#sk2' )
= Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl7,zip_derived_cl9]) ).
thf(zip_derived_cl20,plain,
! [X2: g] :
( ( ( ( '#sk1' @ '#sk2' @ X2 )
= X2 )
& ( ( '#sk1' @ X2 @ '#sk2' )
= X2 ) )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl25,plain,
! [X2: g] :
( ( ( '#sk1' @ '#sk2' @ X2 )
= X2 )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl33,plain,
! [X2: g] :
( ( ( '#sk1' @ '#sk2' @ X2 )
= X2 )
| '#form3' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl26,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ '#sk2' )
= X2 )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl34,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ '#sk2' )
= X2 )
| '#form3' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl6_002,plain,
( ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( ( '#sk1' @ Y0 @ Y1 )
= '#sk2' )
& ( ( '#sk1' @ Y1 @ Y0 )
= '#sk2' ) ) ) )
| ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl9_003,plain,
( ~ '#form3'
| ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl12,plain,
( '#form3'
| ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( ( '#sk1' @ Y0 @ Y1 )
= '#sk2' )
& ( ( '#sk1' @ Y1 @ Y0 )
= '#sk2' ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl6,zip_derived_cl9]) ).
thf(zip_derived_cl17,plain,
! [X2: g] :
( ( ??
@ ^ [Y0: g] :
( ( ( '#sk1' @ X2 @ Y0 )
= '#sk2' )
& ( ( '#sk1' @ Y0 @ X2 )
= '#sk2' ) ) )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl22,plain,
! [X2: g] :
( ( ( ( '#sk1' @ X2 @ ( '#sk4' @ X2 ) )
= '#sk2' )
& ( ( '#sk1' @ ( '#sk4' @ X2 ) @ X2 )
= '#sk2' ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl28,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ ( '#sk4' @ X2 ) )
= '#sk2' )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl36,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ ( '#sk4' @ X2 ) )
= '#sk2' )
| '#form3' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl35_004,plain,
! [X2: g,X4: g,X6: g] :
( ( '#sk1' @ ( '#sk1' @ X2 @ X4 ) @ X6 )
= ( '#sk1' @ X2 @ ( '#sk1' @ X4 @ X6 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl70,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ '#sk2' @ X0 )
= ( '#sk1' @ X1 @ ( '#sk1' @ ( '#sk4' @ X1 ) @ X0 ) ) )
| '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl36,zip_derived_cl35]) ).
thf(zip_derived_cl29,plain,
! [X2: g] :
( ( ( '#sk1' @ ( '#sk4' @ X2 ) @ X2 )
= '#sk2' )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl37,plain,
! [X2: g] :
( ( ( '#sk1' @ ( '#sk4' @ X2 ) @ X2 )
= '#sk2' )
| '#form3' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl35_005,plain,
! [X2: g,X4: g,X6: g] :
( ( '#sk1' @ ( '#sk1' @ X2 @ X4 ) @ X6 )
= ( '#sk1' @ X2 @ ( '#sk1' @ X4 @ X6 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl2_006,plain,
( ( ??
@ ^ [Y0: g] :
( ( !!
@ ^ [Y1: g] :
( ??
@ ^ [Y2: g] :
( ( ( '#sk1' @ Y1 @ Y2 )
= Y0 )
& ( ( '#sk1' @ Y2 @ Y1 )
= Y0 ) ) ) )
& ( !!
@ ^ [Y1: g] :
( ( ( '#sk1' @ Y0 @ Y1 )
= Y1 )
& ( ( '#sk1' @ Y1 @ Y0 )
= Y1 ) ) )
& ( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( !!
@ ^ [Y3: g] :
( ( '#sk1' @ ( '#sk1' @ Y1 @ Y2 ) @ Y3 )
= ( '#sk1' @ Y1 @ ( '#sk1' @ Y2 @ Y3 ) ) ) ) ) ) ) )
!= ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
( ~ ( ??
@ ^ [Y0: g] :
( ( !!
@ ^ [Y1: g] :
( ??
@ ^ [Y2: g] :
( ( ( '#sk1' @ Y1 @ Y2 )
= Y0 )
& ( ( '#sk1' @ Y2 @ Y1 )
= Y0 ) ) ) )
& ( !!
@ ^ [Y1: g] :
( ( ( '#sk1' @ Y0 @ Y1 )
= Y1 )
& ( ( '#sk1' @ Y1 @ Y0 )
= Y1 ) ) )
& ( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( !!
@ ^ [Y3: g] :
( ( '#sk1' @ ( '#sk1' @ Y1 @ Y2 ) @ Y3 )
= ( '#sk1' @ Y1 @ ( '#sk1' @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl89,plain,
( '#form3'
| ~ ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl90,plain,
( ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl93,plain,
( ~ ( !!
@ ^ [Y0: g] :
( ( ??
@ ^ [Y1: g] :
( ( '#sk1' @ '#sk7' @ Y1 )
= Y0 ) )
& ( ??
@ ^ [Y1: g] :
( ( '#sk1' @ Y1 @ '#sk7' )
= Y0 ) ) ) )
| '#form3'
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl95,plain,
( ~ ( ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ '#sk7' @ Y0 )
= '#sk8' ) )
& ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk7' )
= '#sk8' ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl97,plain,
( ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ '#sk7' @ Y0 )
= '#sk8' ) )
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk7' )
= '#sk8' ) )
| '#form3'
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl99,plain,
! [X2: g] :
( ( ( '#sk1' @ '#sk7' @ X2 )
!= '#sk8' )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| '#form3'
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk7' )
= '#sk8' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl101,plain,
! [X2: g] :
( ( ( '#sk1' @ '#sk7' @ X2 )
!= '#sk8' )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| '#form3'
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk7' )
= '#sk8' ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl102,plain,
! [X2: g] :
( ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( '#sk1' @ ( '#sk1' @ '#sk10' @ Y0 ) @ Y1 )
= ( '#sk1' @ '#sk10' @ ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk7' )
= '#sk8' ) )
| '#form3'
| ( ( '#sk1' @ '#sk7' @ X2 )
!= '#sk8' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl105,plain,
! [X2: g] :
( ~ ( !!
@ ^ [Y0: g] :
( ( '#sk1' @ ( '#sk1' @ '#sk10' @ '#sk11' ) @ Y0 )
= ( '#sk1' @ '#sk10' @ ( '#sk1' @ '#sk11' @ Y0 ) ) ) )
| ( ( '#sk1' @ '#sk7' @ X2 )
!= '#sk8' )
| '#form3'
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk7' )
= '#sk8' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl107,plain,
! [X2: g] :
( ( ( '#sk1' @ ( '#sk1' @ '#sk10' @ '#sk11' ) @ '#sk12' )
!= ( '#sk1' @ '#sk10' @ ( '#sk1' @ '#sk11' @ '#sk12' ) ) )
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk7' )
= '#sk8' ) )
| '#form3'
| ( ( '#sk1' @ '#sk7' @ X2 )
!= '#sk8' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl109,plain,
! [X2: g] :
( ( ( '#sk1' @ ( '#sk1' @ '#sk10' @ '#sk11' ) @ '#sk12' )
!= ( '#sk1' @ '#sk10' @ ( '#sk1' @ '#sk11' @ '#sk12' ) ) )
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk7' )
= '#sk8' ) )
| '#form3'
| ( ( '#sk1' @ '#sk7' @ X2 )
!= '#sk8' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl35_007,plain,
! [X2: g,X4: g,X6: g] :
( ( '#sk1' @ ( '#sk1' @ X2 @ X4 ) @ X6 )
= ( '#sk1' @ X2 @ ( '#sk1' @ X4 @ X6 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl110,plain,
! [X2: g] :
( ( ( '#sk1' @ '#sk10' @ ( '#sk1' @ '#sk11' @ '#sk12' ) )
!= ( '#sk1' @ '#sk10' @ ( '#sk1' @ '#sk11' @ '#sk12' ) ) )
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk7' )
= '#sk8' ) )
| '#form3'
| ( ( '#sk1' @ '#sk7' @ X2 )
!= '#sk8' ) ),
inference(demod,[status(thm)],[zip_derived_cl109,zip_derived_cl35]) ).
thf(zip_derived_cl111,plain,
! [X2: g] :
( ( ( '#sk1' @ '#sk7' @ X2 )
!= '#sk8' )
| '#form3'
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk7' )
= '#sk8' ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl112,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ X4 @ '#sk7' )
!= '#sk8' )
| '#form3'
| ( ( '#sk1' @ '#sk7' @ X2 )
!= '#sk8' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl117,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ X4 @ '#sk7' )
!= '#sk8' )
| '#form3'
| ( ( '#sk1' @ '#sk7' @ X2 )
!= '#sk8' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl123,plain,
! [X0: g,X1: g,X2: g] :
( ( ( '#sk1' @ X1 @ ( '#sk1' @ X0 @ '#sk7' ) )
!= '#sk8' )
| ( ( '#sk1' @ '#sk7' @ X2 )
!= '#sk8' )
| '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl117]) ).
thf(zip_derived_cl339,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ X0 @ '#sk2' )
!= '#sk8' )
| '#form3'
| '#form3'
| ( ( '#sk1' @ '#sk7' @ X1 )
!= '#sk8' ) ),
inference('sup-',[status(thm)],[zip_derived_cl37,zip_derived_cl123]) ).
thf(zip_derived_cl362,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ '#sk7' @ X1 )
!= '#sk8' )
| '#form3'
| ( ( '#sk1' @ X0 @ '#sk2' )
!= '#sk8' ) ),
inference(simplify,[status(thm)],[zip_derived_cl339]) ).
thf(zip_derived_cl469,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ '#sk2' @ X0 )
!= '#sk8' )
| '#form3'
| ( ( '#sk1' @ X1 @ '#sk2' )
!= '#sk8' )
| '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl70,zip_derived_cl362]) ).
thf(zip_derived_cl517,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ X1 @ '#sk2' )
!= '#sk8' )
| '#form3'
| ( ( '#sk1' @ '#sk2' @ X0 )
!= '#sk8' ) ),
inference(simplify,[status(thm)],[zip_derived_cl469]) ).
thf(zip_derived_cl1152,plain,
! [X0: g,X1: g] :
( ( X0 != '#sk8' )
| '#form3'
| ( ( '#sk1' @ '#sk2' @ X1 )
!= '#sk8' )
| '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl517]) ).
thf(zip_derived_cl1175,plain,
! [X1: g] :
( ( ( '#sk1' @ '#sk2' @ X1 )
!= '#sk8' )
| '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl1152]) ).
thf(zip_derived_cl1190,plain,
! [X0: g] :
( ( X0 != '#sk8' )
| '#form3'
| '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl33,zip_derived_cl1175]) ).
thf(zip_derived_cl1216,plain,
'#form3',
inference(simplify,[status(thm)],[zip_derived_cl1190]) ).
thf(zip_derived_cl1424,plain,
! [X0: g,X1: g,X2: g] :
( ( '#sk1' @ X2 @ ( '#sk5' @ X1 @ X0 ) )
= ( '#sk1' @ ( '#sk6' @ X1 @ X2 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl303,zip_derived_cl1216]) ).
thf(zip_derived_cl42_008,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk6' @ X2 @ X4 ) @ X2 )
= X4 )
| ~ '#form3' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl1216_009,plain,
'#form3',
inference(simplify,[status(thm)],[zip_derived_cl1190]) ).
thf(zip_derived_cl1238,plain,
! [X2: g,X4: g] :
( ( '#sk1' @ ( '#sk6' @ X2 @ X4 ) @ X2 )
= X4 ),
inference(demod,[status(thm)],[zip_derived_cl42,zip_derived_cl1216]) ).
thf(zip_derived_cl1425,plain,
! [X0: g,X1: g] :
( ( '#sk1' @ X1 @ ( '#sk5' @ X0 @ X0 ) )
= X1 ),
inference('sup+',[status(thm)],[zip_derived_cl1424,zip_derived_cl1238]) ).
thf(zip_derived_cl1424_010,plain,
! [X0: g,X1: g,X2: g] :
( ( '#sk1' @ X2 @ ( '#sk5' @ X1 @ X0 ) )
= ( '#sk1' @ ( '#sk6' @ X1 @ X2 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl303,zip_derived_cl1216]) ).
thf(zip_derived_cl1442,plain,
! [X0: g,X1: g,X2: g] :
( ( '#sk1' @ X0 @ ( '#sk5' @ X1 @ ( '#sk5' @ X2 @ X2 ) ) )
= ( '#sk6' @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1425,zip_derived_cl1424]) ).
thf(zip_derived_cl41_011,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ X2 @ ( '#sk5' @ X2 @ X4 ) )
= X4 )
| ~ '#form3' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl1216_012,plain,
'#form3',
inference(simplify,[status(thm)],[zip_derived_cl1190]) ).
thf(zip_derived_cl1237,plain,
! [X2: g,X4: g] :
( ( '#sk1' @ X2 @ ( '#sk5' @ X2 @ X4 ) )
= X4 ),
inference(demod,[status(thm)],[zip_derived_cl41,zip_derived_cl1216]) ).
thf(zip_derived_cl1529,plain,
! [X0: g,X1: g] :
( ( '#sk6' @ X0 @ X0 )
= ( '#sk5' @ X1 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1442,zip_derived_cl1237]) ).
thf(zip_derived_cl1238_013,plain,
! [X2: g,X4: g] :
( ( '#sk1' @ ( '#sk6' @ X2 @ X4 ) @ X2 )
= X4 ),
inference(demod,[status(thm)],[zip_derived_cl42,zip_derived_cl1216]) ).
thf(zip_derived_cl1564,plain,
! [X0: g,X1: g] :
( ( '#sk1' @ ( '#sk5' @ X0 @ X0 ) @ X1 )
= X1 ),
inference('sup+',[status(thm)],[zip_derived_cl1529,zip_derived_cl1238]) ).
thf(zip_derived_cl1442_014,plain,
! [X0: g,X1: g,X2: g] :
( ( '#sk1' @ X0 @ ( '#sk5' @ X1 @ ( '#sk5' @ X2 @ X2 ) ) )
= ( '#sk6' @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1425,zip_derived_cl1424]) ).
thf(zip_derived_cl1699,plain,
! [X0: g,X1: g,X2: g] :
( ( '#sk5' @ X1 @ ( '#sk5' @ X0 @ X0 ) )
= ( '#sk6' @ X1 @ ( '#sk5' @ X2 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1564,zip_derived_cl1442]) ).
thf(zip_derived_cl1237_015,plain,
! [X2: g,X4: g] :
( ( '#sk1' @ X2 @ ( '#sk5' @ X2 @ X4 ) )
= X4 ),
inference(demod,[status(thm)],[zip_derived_cl41,zip_derived_cl1216]) ).
thf(zip_derived_cl4_016,plain,
( ~ ( ??
@ ^ [Y0: g] :
( ( !!
@ ^ [Y1: g] :
( ??
@ ^ [Y2: g] :
( ( ( '#sk1' @ Y1 @ Y2 )
= Y0 )
& ( ( '#sk1' @ Y2 @ Y1 )
= Y0 ) ) ) )
& ( !!
@ ^ [Y1: g] :
( ( ( '#sk1' @ Y0 @ Y1 )
= Y1 )
& ( ( '#sk1' @ Y1 @ Y0 )
= Y1 ) ) )
& ( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( !!
@ ^ [Y3: g] :
( ( '#sk1' @ ( '#sk1' @ Y1 @ Y2 ) @ Y3 )
= ( '#sk1' @ Y1 @ ( '#sk1' @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl89_017,plain,
( '#form3'
| ~ ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl9_018,plain,
( ~ '#form3'
| ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl91,plain,
( ~ '#form3'
| ~ ( ??
@ ^ [Y0: g] :
( ( !!
@ ^ [Y1: g] :
( ??
@ ^ [Y2: g] :
( ( ( '#sk1' @ Y1 @ Y2 )
= Y0 )
& ( ( '#sk1' @ Y2 @ Y1 )
= Y0 ) ) ) )
& ( !!
@ ^ [Y1: g] :
( ( ( '#sk1' @ Y0 @ Y1 )
= Y1 )
& ( ( '#sk1' @ Y1 @ Y0 )
= Y1 ) ) )
& ( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( !!
@ ^ [Y3: g] :
( ( '#sk1' @ ( '#sk1' @ Y1 @ Y2 ) @ Y3 )
= ( '#sk1' @ Y1 @ ( '#sk1' @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl4,zip_derived_cl89,zip_derived_cl9]) ).
thf(zip_derived_cl92,plain,
! [X2: g] :
( ~ ( ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( ( '#sk1' @ Y0 @ Y1 )
= X2 )
& ( ( '#sk1' @ Y1 @ Y0 )
= X2 ) ) ) )
& ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ X2 @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ X2 )
= Y0 ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl94,plain,
! [X2: g] :
( ~ ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( ( '#sk1' @ Y0 @ Y1 )
= X2 )
& ( ( '#sk1' @ Y1 @ Y0 )
= X2 ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ X2 @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ X2 )
= Y0 ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl96,plain,
! [X2: g] :
( ~ ( ??
@ ^ [Y0: g] :
( ( ( '#sk1' @ ( '#sk9' @ X2 ) @ Y0 )
= X2 )
& ( ( '#sk1' @ Y0 @ ( '#sk9' @ X2 ) )
= X2 ) ) )
| ~ '#form3'
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ X2 @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ X2 )
= Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl98,plain,
! [X2: g,X4: g] :
( ~ ( ( ( '#sk1' @ ( '#sk9' @ X2 ) @ X4 )
= X2 )
& ( ( '#sk1' @ X4 @ ( '#sk9' @ X2 ) )
= X2 ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ X2 @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ X2 )
= Y0 ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl100,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk9' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ X4 @ ( '#sk9' @ X2 ) )
!= X2 )
| ~ '#form3'
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ X2 @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ X2 )
= Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl98]) ).
thf(zip_derived_cl103,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk9' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ X4 @ ( '#sk9' @ X2 ) )
!= X2 )
| ~ '#form3'
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ X2 @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ X2 )
= Y0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl104,plain,
! [X2: g,X4: g] :
( ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( '#sk1' @ ( '#sk1' @ '#sk10' @ Y0 ) @ Y1 )
= ( '#sk1' @ '#sk10' @ ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ X2 @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ X2 )
= Y0 ) ) )
| ~ '#form3'
| ( ( '#sk1' @ X4 @ ( '#sk9' @ X2 ) )
!= X2 )
| ( ( '#sk1' @ ( '#sk9' @ X2 ) @ X4 )
!= X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl106,plain,
! [X2: g,X4: g] :
( ~ ( !!
@ ^ [Y0: g] :
( ( '#sk1' @ ( '#sk1' @ '#sk10' @ '#sk11' ) @ Y0 )
= ( '#sk1' @ '#sk10' @ ( '#sk1' @ '#sk11' @ Y0 ) ) ) )
| ( ( '#sk1' @ ( '#sk9' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ X4 @ ( '#sk9' @ X2 ) )
!= X2 )
| ~ '#form3'
| ~ ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ X2 @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ X2 )
= Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl108,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk1' @ '#sk10' @ '#sk11' ) @ '#sk12' )
!= ( '#sk1' @ '#sk10' @ ( '#sk1' @ '#sk11' @ '#sk12' ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ X2 @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ X2 )
= Y0 ) ) )
| ~ '#form3'
| ( ( '#sk1' @ X4 @ ( '#sk9' @ X2 ) )
!= X2 )
| ( ( '#sk1' @ ( '#sk9' @ X2 ) @ X4 )
!= X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl113,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk1' @ '#sk10' @ '#sk11' ) @ '#sk12' )
!= ( '#sk1' @ '#sk10' @ ( '#sk1' @ '#sk11' @ '#sk12' ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ X2 @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ X2 )
= Y0 ) ) )
| ~ '#form3'
| ( ( '#sk1' @ X4 @ ( '#sk9' @ X2 ) )
!= X2 )
| ( ( '#sk1' @ ( '#sk9' @ X2 ) @ X4 )
!= X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl35_019,plain,
! [X2: g,X4: g,X6: g] :
( ( '#sk1' @ ( '#sk1' @ X2 @ X4 ) @ X6 )
= ( '#sk1' @ X2 @ ( '#sk1' @ X4 @ X6 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl114,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ '#sk10' @ ( '#sk1' @ '#sk11' @ '#sk12' ) )
!= ( '#sk1' @ '#sk10' @ ( '#sk1' @ '#sk11' @ '#sk12' ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ X2 @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ X2 )
= Y0 ) ) )
| ~ '#form3'
| ( ( '#sk1' @ X4 @ ( '#sk9' @ X2 ) )
!= X2 )
| ( ( '#sk1' @ ( '#sk9' @ X2 ) @ X4 )
!= X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl113,zip_derived_cl35]) ).
thf(zip_derived_cl115,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk9' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ X4 @ ( '#sk9' @ X2 ) )
!= X2 )
| ~ '#form3'
| ~ ( !!
@ ^ [Y0: g] :
( ( ( '#sk1' @ X2 @ Y0 )
= Y0 )
& ( ( '#sk1' @ Y0 @ X2 )
= Y0 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl116,plain,
! [X2: g,X4: g] :
( ~ ( ( ( '#sk1' @ X2 @ ( '#sk13' @ X2 ) )
= ( '#sk13' @ X2 ) )
& ( ( '#sk1' @ ( '#sk13' @ X2 ) @ X2 )
= ( '#sk13' @ X2 ) ) )
| ~ '#form3'
| ( ( '#sk1' @ X4 @ ( '#sk9' @ X2 ) )
!= X2 )
| ( ( '#sk1' @ ( '#sk9' @ X2 ) @ X4 )
!= X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl115]) ).
thf(zip_derived_cl118,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ X2 @ ( '#sk13' @ X2 ) )
!= ( '#sk13' @ X2 ) )
| ( ( '#sk1' @ ( '#sk13' @ X2 ) @ X2 )
!= ( '#sk13' @ X2 ) )
| ( ( '#sk1' @ ( '#sk9' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ X4 @ ( '#sk9' @ X2 ) )
!= X2 )
| ~ '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl119,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ X2 @ ( '#sk13' @ X2 ) )
!= ( '#sk13' @ X2 ) )
| ( ( '#sk1' @ ( '#sk13' @ X2 ) @ X2 )
!= ( '#sk13' @ X2 ) )
| ( ( '#sk1' @ ( '#sk9' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ X4 @ ( '#sk9' @ X2 ) )
!= X2 )
| ~ '#form3' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl118]) ).
thf(zip_derived_cl1216_020,plain,
'#form3',
inference(simplify,[status(thm)],[zip_derived_cl1190]) ).
thf(zip_derived_cl1375,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ X2 @ ( '#sk13' @ X2 ) )
!= ( '#sk13' @ X2 ) )
| ( ( '#sk1' @ ( '#sk13' @ X2 ) @ X2 )
!= ( '#sk13' @ X2 ) )
| ( ( '#sk1' @ ( '#sk9' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ X4 @ ( '#sk9' @ X2 ) )
!= X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl119,zip_derived_cl1216]) ).
thf(zip_derived_cl1376,plain,
! [X0: g,X1: g] :
( ( X0 != X1 )
| ( ( '#sk1' @ ( '#sk5' @ ( '#sk9' @ X1 ) @ X0 ) @ ( '#sk9' @ X1 ) )
!= X1 )
| ( ( '#sk1' @ ( '#sk13' @ X1 ) @ X1 )
!= ( '#sk13' @ X1 ) )
| ( ( '#sk1' @ X1 @ ( '#sk13' @ X1 ) )
!= ( '#sk13' @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1237,zip_derived_cl1375]) ).
thf(zip_derived_cl1378,plain,
! [X1: g] :
( ( ( '#sk1' @ X1 @ ( '#sk13' @ X1 ) )
!= ( '#sk13' @ X1 ) )
| ( ( '#sk1' @ ( '#sk13' @ X1 ) @ X1 )
!= ( '#sk13' @ X1 ) )
| ( ( '#sk1' @ ( '#sk5' @ ( '#sk9' @ X1 ) @ X1 ) @ ( '#sk9' @ X1 ) )
!= X1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1376]) ).
thf(zip_derived_cl2607,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ ( '#sk6' @ ( '#sk9' @ ( '#sk5' @ X1 @ X1 ) ) @ ( '#sk5' @ X0 @ X0 ) ) @ ( '#sk9' @ ( '#sk5' @ X1 @ X1 ) ) )
!= ( '#sk5' @ X1 @ X1 ) )
| ( ( '#sk1' @ ( '#sk13' @ ( '#sk5' @ X1 @ X1 ) ) @ ( '#sk5' @ X1 @ X1 ) )
!= ( '#sk13' @ ( '#sk5' @ X1 @ X1 ) ) )
| ( ( '#sk1' @ ( '#sk5' @ X1 @ X1 ) @ ( '#sk13' @ ( '#sk5' @ X1 @ X1 ) ) )
!= ( '#sk13' @ ( '#sk5' @ X1 @ X1 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1699,zip_derived_cl1378]) ).
thf(zip_derived_cl1424_021,plain,
! [X0: g,X1: g,X2: g] :
( ( '#sk1' @ X2 @ ( '#sk5' @ X1 @ X0 ) )
= ( '#sk1' @ ( '#sk6' @ X1 @ X2 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl303,zip_derived_cl1216]) ).
thf(zip_derived_cl1529_022,plain,
! [X0: g,X1: g] :
( ( '#sk6' @ X0 @ X0 )
= ( '#sk5' @ X1 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1442,zip_derived_cl1237]) ).
thf(zip_derived_cl1425_023,plain,
! [X0: g,X1: g] :
( ( '#sk1' @ X1 @ ( '#sk5' @ X0 @ X0 ) )
= X1 ),
inference('sup+',[status(thm)],[zip_derived_cl1424,zip_derived_cl1238]) ).
thf(zip_derived_cl1238_024,plain,
! [X2: g,X4: g] :
( ( '#sk1' @ ( '#sk6' @ X2 @ X4 ) @ X2 )
= X4 ),
inference(demod,[status(thm)],[zip_derived_cl42,zip_derived_cl1216]) ).
thf(zip_derived_cl1443,plain,
! [X0: g,X1: g] :
( ( '#sk6' @ ( '#sk5' @ X1 @ X1 ) @ X0 )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl1425,zip_derived_cl1238]) ).
thf(zip_derived_cl1560,plain,
! [X0: g,X1: g] :
( ( '#sk5' @ X0 @ X0 )
= ( '#sk5' @ X1 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1529,zip_derived_cl1443]) ).
thf(zip_derived_cl1564_025,plain,
! [X0: g,X1: g] :
( ( '#sk1' @ ( '#sk5' @ X0 @ X0 ) @ X1 )
= X1 ),
inference('sup+',[status(thm)],[zip_derived_cl1529,zip_derived_cl1238]) ).
thf(zip_derived_cl1425_026,plain,
! [X0: g,X1: g] :
( ( '#sk1' @ X1 @ ( '#sk5' @ X0 @ X0 ) )
= X1 ),
inference('sup+',[status(thm)],[zip_derived_cl1424,zip_derived_cl1238]) ).
thf(zip_derived_cl1564_027,plain,
! [X0: g,X1: g] :
( ( '#sk1' @ ( '#sk5' @ X0 @ X0 ) @ X1 )
= X1 ),
inference('sup+',[status(thm)],[zip_derived_cl1529,zip_derived_cl1238]) ).
thf(zip_derived_cl2736,plain,
! [X1: g] :
( ( ( '#sk5' @ X1 @ X1 )
!= ( '#sk5' @ X1 @ X1 ) )
| ( ( '#sk13' @ ( '#sk5' @ X1 @ X1 ) )
!= ( '#sk13' @ ( '#sk5' @ X1 @ X1 ) ) )
| ( ( '#sk13' @ ( '#sk5' @ X1 @ X1 ) )
!= ( '#sk13' @ ( '#sk5' @ X1 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2607,zip_derived_cl1424,zip_derived_cl1560,zip_derived_cl1564,zip_derived_cl1425,zip_derived_cl1564]) ).
thf(zip_derived_cl2737,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl2736]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG276^5 : TPTP v9.2.0. Bugfixed v5.3.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Guh595FMWy true
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 17:02:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.19/0.35 % Python version: Python 3.6.8
% 0.19/0.35 % Running in HO mode
% 0.55/0.67 % Total configuration time : 828
% 0.55/0.67 % Estimated wc time : 1656
% 0.55/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.55/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 4.69/1.20 % Solved by lams/20_acsne_simpl.sh.
% 4.69/1.20 % done 736 iterations in 0.408s
% 4.69/1.20 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.69/1.20 % SZS output start Refutation
% See solution above
% 4.69/1.21
% 4.69/1.21
% 4.69/1.21 % Terminating...
% 5.03/1.28 % Runner terminated.
% 5.03/1.28 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------