%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ALG274^5 : 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.FKtdgdJPUU true
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:28:33 PM UTC 2025
% Result : Theorem 4.24s 1.97s
% Output : Refutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 17
% Syntax : Number of formulae : 144 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 751 ( 340 equ; 0 cnn)
% Maximal formula atoms : 21 ( 5 avg)
% Number of connectives : 2230 ( 169 ~; 180 |; 83 &;1494 @)
% ( 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 : 24 ( 19 usr; 11 con; 0-2 aty)
% ( 209 !!; 90 ??; 0 @@+; 0 @@-)
% Number of variables : 586 ( 326 ^; 242 !; 18 ?; 586 :)
% Comments :
%------------------------------------------------------------------------------
thf(g_type,type,
g: $tType ).
thf(cGRP_DIVISORS_type,type,
cGRP_DIVISORS: ( g > g > g ) > $o ).
thf('#form10_type',type,
'#form10': $o ).
thf('#sk8_type',type,
'#sk8': g ).
thf(cGROUP4_type,type,
cGROUP4: ( g > g > g ) > $o ).
thf(cGRP_RIGHT_UNIT_type,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf('#sk2_type',type,
'#sk2': g > g ).
thf('#sk4_type',type,
'#sk4': g ).
thf('#sk6_type',type,
'#sk6': g ).
thf('#sk3_type',type,
'#sk3': g > g ).
thf(cGRP_RIGHT_INVERSE_type,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf('#sk5_type',type,
'#sk5': 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 > g ).
thf(cGROUP3_type,type,
cGROUP3: ( g > g > g ) > g > $o ).
thf('#sk9_type',type,
'#sk9': g ).
thf('#sk13_type',type,
'#sk13': g > g > g ).
thf('#sk12_type',type,
'#sk12': g > g > 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(cGROUP3_def,axiom,
( cGROUP3
= ( ^ [Xf: g > g > g,Xe: g] :
( ( cGRP_ASSOC @ Xf )
& ( cGRP_RIGHT_UNIT @ Xf @ Xe )
& ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) ) ) ) ).
thf(cGRP_RIGHT_UNIT_def,axiom,
( cGRP_RIGHT_UNIT
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
( ( Xf @ Xa @ Xe )
= Xa ) ) ) ).
thf('6',plain,
( cGRP_RIGHT_UNIT
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
( ( Xf @ Xa @ Xe )
= Xa ) ) ),
inference(simplify_rw_rule,[status(thm)],[cGRP_RIGHT_UNIT_def]) ).
thf('7',plain,
( cGRP_RIGHT_UNIT
= ( ^ [V_1: g > g > g,V_2: g] :
! [X4: g] :
( ( V_1 @ X4 @ V_2 )
= X4 ) ) ),
define([status(thm)]) ).
thf(cGRP_RIGHT_INVERSE_def,axiom,
( cGRP_RIGHT_INVERSE
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
? [Xb: g] :
( ( Xf @ Xa @ Xb )
= Xe ) ) ) ).
thf('8',plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Xf: g > g > g,Xe: g] :
! [Xa: g] :
? [Xb: g] :
( ( Xf @ Xa @ Xb )
= Xe ) ) ),
inference(simplify_rw_rule,[status(thm)],[cGRP_RIGHT_INVERSE_def]) ).
thf('9',plain,
( cGRP_RIGHT_INVERSE
= ( ^ [V_1: g > g > g,V_2: g] :
! [X4: g] :
? [X6: g] :
( ( V_1 @ X4 @ X6 )
= V_2 ) ) ),
define([status(thm)]) ).
thf('10',plain,
( cGROUP3
= ( ^ [Xf: g > g > g,Xe: g] :
( ( cGRP_ASSOC @ Xf )
& ( cGRP_RIGHT_UNIT @ Xf @ Xe )
& ( cGRP_RIGHT_INVERSE @ Xf @ Xe ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[cGROUP3_def,'7','9','3']) ).
thf('11',plain,
( cGROUP3
= ( ^ [V_1: g > g > g,V_2: g] :
( ( cGRP_ASSOC @ V_1 )
& ( cGRP_RIGHT_UNIT @ V_1 @ V_2 )
& ( cGRP_RIGHT_INVERSE @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(cEQUIV_03_04,conjecture,
! [Xf: g > g > g] :
( ? [Xe: g] : ( cGROUP3 @ Xf @ Xe )
<=> ( cGROUP4 @ Xf ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: g > g > g] :
( ? [X6: g] :
( ! [X16: g] :
? [X18: g] :
( ( X4 @ X16 @ X18 )
= X6 )
& ! [X14: g] :
( ( 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 )
& ! [X14: g] :
( ( 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 ) ) )
& ( !!
@ ^ [Y2: g] :
( ( 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 ) ) )
& ( !!
@ ^ [Y1: g] :
( ( '#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 ) ) )
& ( !!
@ ^ [Y1: g] :
( ( '#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 ) ) )
& ( !!
@ ^ [Y1: g] :
( ( '#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_cl25,plain,
( ( ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( '#sk1' @ Y0 @ Y1 )
= '#sk9' ) ) )
& ( !!
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk9' )
= 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_cl26,plain,
( ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( '#sk1' @ Y0 @ Y1 )
= '#sk9' ) ) )
| ( ( !!
@ ^ [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_cl25]) ).
thf(zip_derived_cl29,plain,
( ~ '#form10'
| ( ( !!
@ ^ [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_cl30,plain,
( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y0 @ Y2 )
= Y1 ) )
& ( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y2 @ Y0 )
= Y1 ) ) ) ) )
| ~ '#form10' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl38,plain,
! [X2: g] :
( ( !!
@ ^ [Y0: g] :
( ( ??
@ ^ [Y1: g] :
( ( '#sk1' @ X2 @ Y1 )
= Y0 ) )
& ( ??
@ ^ [Y1: g] :
( ( '#sk1' @ Y1 @ X2 )
= Y0 ) ) ) )
| ~ '#form10' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl43,plain,
! [X2: g,X4: g] :
( ( ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ X2 @ Y0 )
= X4 ) )
& ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ X2 )
= X4 ) ) )
| ~ '#form10' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl48,plain,
! [X2: g,X4: g] :
( ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ X2 @ Y0 )
= X4 ) )
| ~ '#form10' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl52,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ X2 @ ( '#sk12' @ X2 @ X4 ) )
= X4 )
| ~ '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl55,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ X2 @ ( '#sk12' @ X2 @ X4 ) )
= X4 )
| ~ '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl27,plain,
( ( !!
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk9' )
= 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_cl25]) ).
thf(zip_derived_cl29_001,plain,
( ~ '#form10'
| ( ( !!
@ ^ [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_cl33,plain,
( '#form10'
| ( !!
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk9' )
= Y0 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl27,zip_derived_cl29]) ).
thf(zip_derived_cl40,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ '#sk9' )
= X2 )
| '#form10' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl45,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ '#sk9' )
= X2 )
| '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl26_002,plain,
( ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( '#sk1' @ Y0 @ Y1 )
= '#sk9' ) ) )
| ( ( !!
@ ^ [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_cl25]) ).
thf(zip_derived_cl29_003,plain,
( ~ '#form10'
| ( ( !!
@ ^ [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_cl32,plain,
( '#form10'
| ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( '#sk1' @ Y0 @ Y1 )
= '#sk9' ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl26,zip_derived_cl29]) ).
thf(zip_derived_cl37,plain,
! [X2: g] :
( ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ X2 @ Y0 )
= '#sk9' ) )
| '#form10' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl42,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ ( '#sk11' @ X2 ) )
= '#sk9' )
| '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl47,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ ( '#sk11' @ X2 ) )
= '#sk9' )
| '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl47_004,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ ( '#sk11' @ X2 ) )
= '#sk9' )
| '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl28,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_cl25]) ).
thf(zip_derived_cl34,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_cl28]) ).
thf(zip_derived_cl35,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_cl34]) ).
thf(zip_derived_cl36,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_cl35]) ).
thf(zip_derived_cl41,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_cl36]) ).
thf(zip_derived_cl46,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_cl41]) ).
thf(zip_derived_cl51,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_cl46]) ).
thf(zip_derived_cl67,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ '#sk9' @ X0 )
= ( '#sk1' @ X1 @ ( '#sk1' @ ( '#sk11' @ X1 ) @ X0 ) ) )
| '#form10' ),
inference('sup+',[status(thm)],[zip_derived_cl47,zip_derived_cl51]) ).
thf(zip_derived_cl504,plain,
! [X0: g] :
( ( ( '#sk1' @ '#sk9' @ ( '#sk11' @ ( '#sk11' @ X0 ) ) )
= ( '#sk1' @ X0 @ '#sk9' ) )
| '#form10'
| '#form10' ),
inference('sup+',[status(thm)],[zip_derived_cl47,zip_derived_cl67]) ).
thf(zip_derived_cl535,plain,
! [X0: g] :
( '#form10'
| ( ( '#sk1' @ '#sk9' @ ( '#sk11' @ ( '#sk11' @ X0 ) ) )
= ( '#sk1' @ X0 @ '#sk9' ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl504]) ).
thf(zip_derived_cl45_005,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ '#sk9' )
= X2 )
| '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl51_006,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_cl46]) ).
thf(zip_derived_cl47_007,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ ( '#sk11' @ X2 ) )
= '#sk9' )
| '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl61,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ X1 @ ( '#sk1' @ X0 @ ( '#sk11' @ ( '#sk1' @ X1 @ X0 ) ) ) )
= '#sk9' )
| '#form10' ),
inference('sup+',[status(thm)],[zip_derived_cl51,zip_derived_cl47]) ).
thf(zip_derived_cl183,plain,
! [X0: g] :
( ( ( '#sk1' @ X0 @ ( '#sk1' @ '#sk9' @ ( '#sk11' @ X0 ) ) )
= '#sk9' )
| '#form10'
| '#form10' ),
inference('sup+',[status(thm)],[zip_derived_cl45,zip_derived_cl61]) ).
thf(zip_derived_cl205,plain,
! [X0: g] :
( '#form10'
| ( ( '#sk1' @ X0 @ ( '#sk1' @ '#sk9' @ ( '#sk11' @ X0 ) ) )
= '#sk9' ) ),
inference(simplify,[status(thm)],[zip_derived_cl183]) ).
thf(zip_derived_cl798,plain,
! [X0: g] :
( ( ( '#sk1' @ ( '#sk11' @ X0 ) @ ( '#sk1' @ X0 @ '#sk9' ) )
= '#sk9' )
| '#form10'
| '#form10' ),
inference('sup+',[status(thm)],[zip_derived_cl535,zip_derived_cl205]) ).
thf(zip_derived_cl810,plain,
! [X0: g] :
( '#form10'
| ( ( '#sk1' @ ( '#sk11' @ X0 ) @ ( '#sk1' @ X0 @ '#sk9' ) )
= '#sk9' ) ),
inference(simplify,[status(thm)],[zip_derived_cl798]) ).
thf(zip_derived_cl827,plain,
! [X0: g] :
( ( ( '#sk1' @ ( '#sk11' @ X0 ) @ X0 )
= '#sk9' )
| '#form10'
| '#form10' ),
inference('sup+',[status(thm)],[zip_derived_cl45,zip_derived_cl810]) ).
thf(zip_derived_cl839,plain,
! [X0: g] :
( '#form10'
| ( ( '#sk1' @ ( '#sk11' @ X0 ) @ X0 )
= '#sk9' ) ),
inference(simplify,[status(thm)],[zip_derived_cl827]) ).
thf(zip_derived_cl67_008,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ '#sk9' @ X0 )
= ( '#sk1' @ X1 @ ( '#sk1' @ ( '#sk11' @ X1 ) @ X0 ) ) )
| '#form10' ),
inference('sup+',[status(thm)],[zip_derived_cl47,zip_derived_cl51]) ).
thf(zip_derived_cl856,plain,
! [X0: g] :
( ( ( '#sk1' @ '#sk9' @ X0 )
= ( '#sk1' @ X0 @ '#sk9' ) )
| '#form10'
| '#form10' ),
inference('sup+',[status(thm)],[zip_derived_cl839,zip_derived_cl67]) ).
thf(zip_derived_cl892,plain,
! [X0: g] :
( '#form10'
| ( ( '#sk1' @ '#sk9' @ X0 )
= ( '#sk1' @ X0 @ '#sk9' ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl856]) ).
thf(zip_derived_cl45_009,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ '#sk9' )
= X2 )
| '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl1134,plain,
! [X0: g] :
( ( ( '#sk1' @ '#sk9' @ X0 )
= X0 )
| '#form10'
| '#form10' ),
inference('sup+',[status(thm)],[zip_derived_cl892,zip_derived_cl45]) ).
thf(zip_derived_cl1195,plain,
! [X0: g] :
( '#form10'
| ( ( '#sk1' @ '#sk9' @ X0 )
= X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1134]) ).
thf(zip_derived_cl45_010,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ '#sk9' )
= X2 )
| '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl67_011,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ '#sk9' @ X0 )
= ( '#sk1' @ X1 @ ( '#sk1' @ ( '#sk11' @ X1 ) @ X0 ) ) )
| '#form10' ),
inference('sup+',[status(thm)],[zip_derived_cl47,zip_derived_cl51]) ).
thf(zip_derived_cl839_012,plain,
! [X0: g] :
( '#form10'
| ( ( '#sk1' @ ( '#sk11' @ X0 ) @ X0 )
= '#sk9' ) ),
inference(simplify,[status(thm)],[zip_derived_cl827]) ).
thf(zip_derived_cl51_013,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_cl46]) ).
thf(zip_derived_cl47_014,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ ( '#sk11' @ X2 ) )
= '#sk9' )
| '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl2_015,plain,
( ( ??
@ ^ [Y0: g] :
( ( !!
@ ^ [Y1: g] :
( ??
@ ^ [Y2: g] :
( ( '#sk1' @ Y1 @ Y2 )
= Y0 ) ) )
& ( !!
@ ^ [Y1: g] :
( ( '#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 ) ) )
& ( !!
@ ^ [Y1: g] :
( ( '#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,
! [X2: g] :
( ~ ( ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( '#sk1' @ Y0 @ Y1 )
= X2 ) ) )
& ( !!
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ X2 )
= 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_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl6,plain,
! [X2: g] :
( ~ ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( '#sk1' @ Y0 @ Y1 )
= X2 ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ X2 )
= 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_and,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl7,plain,
! [X2: g] :
( ~ ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( '#sk1' @ Y0 @ Y1 )
= X2 ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ X2 )
= 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 ) ) ) ) )
& $true ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl8,plain,
! [X2: g] :
( ~ ( !!
@ ^ [Y0: g] :
( ??
@ ^ [Y1: g] :
( ( '#sk1' @ Y0 @ Y1 )
= X2 ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ X2 )
= 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 ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl9,plain,
! [X2: g] :
( ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ ( '#sk2' @ X2 ) @ Y0 )
= X2 ) )
| ~ ( !!
@ ^ [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 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ X2 )
= Y0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl10,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ X2 )
= 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 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl11,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ X2 )
= 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 ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl12,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ~ ( !!
@ ^ [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 ) ) ) ) ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl13,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ~ ( !!
@ ^ [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 ) ) ) ) ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl14,plain,
! [X2: g,X4: g] :
( ~ ( !!
@ ^ [Y0: g] :
( ( ??
@ ^ [Y1: g] :
( ( '#sk1' @ '#sk4' @ Y1 )
= Y0 ) )
& ( ??
@ ^ [Y1: g] :
( ( '#sk1' @ Y1 @ '#sk4' )
= Y0 ) ) ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl15,plain,
! [X2: g,X4: g] :
( ~ ( ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ '#sk4' @ Y0 )
= '#sk5' ) )
& ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk4' )
= '#sk5' ) ) )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl16,plain,
! [X2: g,X4: g] :
( ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ '#sk4' @ Y0 )
= '#sk5' ) )
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk4' )
= '#sk5' ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl17,plain,
! [X2: g,X4: g,X6: g] :
( ( ( '#sk1' @ '#sk4' @ X6 )
!= '#sk5' )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk4' )
= '#sk5' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl18,plain,
! [X2: g,X4: g,X6: g] :
( ( ( '#sk1' @ '#sk4' @ X6 )
!= '#sk5' )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
= ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk4' )
= '#sk5' ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl19,plain,
! [X2: g,X4: g,X6: g] :
( ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( '#sk1' @ ( '#sk1' @ '#sk6' @ Y0 ) @ Y1 )
= ( '#sk1' @ '#sk6' @ ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk4' )
= '#sk5' ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ( ( '#sk1' @ '#sk4' @ X6 )
!= '#sk5' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl20,plain,
! [X2: g,X4: g,X6: g] :
( ~ ( !!
@ ^ [Y0: g] :
( ( '#sk1' @ ( '#sk1' @ '#sk6' @ '#sk7' ) @ Y0 )
= ( '#sk1' @ '#sk6' @ ( '#sk1' @ '#sk7' @ Y0 ) ) ) )
| ( ( '#sk1' @ '#sk4' @ X6 )
!= '#sk5' )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk4' )
= '#sk5' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl21,plain,
! [X2: g,X4: g,X6: g] :
( ( ( '#sk1' @ ( '#sk1' @ '#sk6' @ '#sk7' ) @ '#sk8' )
!= ( '#sk1' @ '#sk6' @ ( '#sk1' @ '#sk7' @ '#sk8' ) ) )
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk4' )
= '#sk5' ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ( ( '#sk1' @ '#sk4' @ X6 )
!= '#sk5' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl22,plain,
! [X2: g,X4: g,X6: g] :
( ( ( '#sk1' @ ( '#sk1' @ '#sk6' @ '#sk7' ) @ '#sk8' )
!= ( '#sk1' @ '#sk6' @ ( '#sk1' @ '#sk7' @ '#sk8' ) ) )
| ~ ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ '#sk4' )
= '#sk5' ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ( ( '#sk1' @ '#sk4' @ X6 )
!= '#sk5' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl23,plain,
! [X2: g,X4: g,X6: g,X8: g] :
( ( ( '#sk1' @ X8 @ '#sk4' )
!= '#sk5' )
| ( ( '#sk1' @ '#sk4' @ X6 )
!= '#sk5' )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ ( '#sk1' @ '#sk6' @ '#sk7' ) @ '#sk8' )
!= ( '#sk1' @ '#sk6' @ ( '#sk1' @ '#sk7' @ '#sk8' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl24,plain,
! [X2: g,X4: g,X6: g,X8: g] :
( ( ( '#sk1' @ X8 @ '#sk4' )
!= '#sk5' )
| ( ( '#sk1' @ '#sk4' @ X6 )
!= '#sk5' )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ ( '#sk1' @ '#sk6' @ '#sk7' ) @ '#sk8' )
!= ( '#sk1' @ '#sk6' @ ( '#sk1' @ '#sk7' @ '#sk8' ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl51_016,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_cl46]) ).
thf(zip_derived_cl59,plain,
! [X2: g,X4: g,X6: g,X8: g] :
( ( ( '#sk1' @ X8 @ '#sk4' )
!= '#sk5' )
| ( ( '#sk1' @ '#sk4' @ X6 )
!= '#sk5' )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ '#sk6' @ ( '#sk1' @ '#sk7' @ '#sk8' ) )
!= ( '#sk1' @ '#sk6' @ ( '#sk1' @ '#sk7' @ '#sk8' ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl24,zip_derived_cl51]) ).
thf(zip_derived_cl60,plain,
! [X2: g,X4: g,X6: g,X8: g] :
( ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ( ( '#sk1' @ '#sk4' @ X6 )
!= '#sk5' )
| ( ( '#sk1' @ X8 @ '#sk4' )
!= '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl132,plain,
! [X0: g,X1: g,X2: g] :
( ( '#sk9' != X0 )
| '#form10'
| ( ( '#sk1' @ X1 @ '#sk4' )
!= '#sk5' )
| ( ( '#sk1' @ '#sk4' @ X2 )
!= '#sk5' )
| ( ( '#sk1' @ ( '#sk3' @ X0 ) @ X0 )
!= ( '#sk3' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl47,zip_derived_cl60]) ).
thf(zip_derived_cl141,plain,
! [X1: g,X2: g] :
( ( ( '#sk1' @ ( '#sk3' @ '#sk9' ) @ '#sk9' )
!= ( '#sk3' @ '#sk9' ) )
| ( ( '#sk1' @ '#sk4' @ X2 )
!= '#sk5' )
| ( ( '#sk1' @ X1 @ '#sk4' )
!= '#sk5' )
| '#form10' ),
inference(simplify,[status(thm)],[zip_derived_cl132]) ).
thf(zip_derived_cl45_017,plain,
! [X2: g] :
( ( ( '#sk1' @ X2 @ '#sk9' )
= X2 )
| '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl152,plain,
! [X1: g,X2: g] :
( '#form10'
| ( ( '#sk1' @ X1 @ '#sk4' )
!= '#sk5' )
| ( ( '#sk1' @ '#sk4' @ X2 )
!= '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl141,zip_derived_cl45]) ).
thf(zip_derived_cl154,plain,
! [X0: g,X1: g,X2: g] :
( ( ( '#sk1' @ X1 @ ( '#sk1' @ X0 @ '#sk4' ) )
!= '#sk5' )
| ( ( '#sk1' @ '#sk4' @ X2 )
!= '#sk5' )
| '#form10' ),
inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl152]) ).
thf(zip_derived_cl862,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ X0 @ '#sk9' )
!= '#sk5' )
| '#form10'
| '#form10'
| ( ( '#sk1' @ '#sk4' @ X1 )
!= '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl839,zip_derived_cl154]) ).
thf(zip_derived_cl898,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ '#sk4' @ X1 )
!= '#sk5' )
| '#form10'
| ( ( '#sk1' @ X0 @ '#sk9' )
!= '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl862]) ).
thf(zip_derived_cl1032,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ '#sk9' @ X0 )
!= '#sk5' )
| '#form10'
| ( ( '#sk1' @ X1 @ '#sk9' )
!= '#sk5' )
| '#form10' ),
inference('sup-',[status(thm)],[zip_derived_cl67,zip_derived_cl898]) ).
thf(zip_derived_cl1058,plain,
! [X0: g,X1: g] :
( ( ( '#sk1' @ X1 @ '#sk9' )
!= '#sk5' )
| '#form10'
| ( ( '#sk1' @ '#sk9' @ X0 )
!= '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1032]) ).
thf(zip_derived_cl1436,plain,
! [X0: g,X1: g] :
( ( X0 != '#sk5' )
| '#form10'
| ( ( '#sk1' @ '#sk9' @ X1 )
!= '#sk5' )
| '#form10' ),
inference('sup-',[status(thm)],[zip_derived_cl45,zip_derived_cl1058]) ).
thf(zip_derived_cl1451,plain,
! [X1: g] :
( ( ( '#sk1' @ '#sk9' @ X1 )
!= '#sk5' )
| '#form10' ),
inference(simplify,[status(thm)],[zip_derived_cl1436]) ).
thf(zip_derived_cl1461,plain,
! [X0: g] :
( ( X0 != '#sk5' )
| '#form10'
| '#form10' ),
inference('sup-',[status(thm)],[zip_derived_cl1195,zip_derived_cl1451]) ).
thf(zip_derived_cl1497,plain,
'#form10',
inference(simplify,[status(thm)],[zip_derived_cl1461]) ).
thf(zip_derived_cl1529,plain,
! [X2: g,X4: g] :
( ( '#sk1' @ X2 @ ( '#sk12' @ X2 @ X4 ) )
= X4 ),
inference(demod,[status(thm)],[zip_derived_cl55,zip_derived_cl1497]) ).
thf(zip_derived_cl49,plain,
! [X2: g,X4: g] :
( ( ??
@ ^ [Y0: g] :
( ( '#sk1' @ Y0 @ X2 )
= X4 ) )
| ~ '#form10' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl53,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk13' @ X2 @ X4 ) @ X2 )
= X4 )
| ~ '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl56,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk13' @ X2 @ X4 ) @ X2 )
= X4 )
| ~ '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl1497_018,plain,
'#form10',
inference(simplify,[status(thm)],[zip_derived_cl1461]) ).
thf(zip_derived_cl1530,plain,
! [X2: g,X4: g] :
( ( '#sk1' @ ( '#sk13' @ X2 @ X4 ) @ X2 )
= X4 ),
inference(demod,[status(thm)],[zip_derived_cl56,zip_derived_cl1497]) ).
thf(zip_derived_cl1529_019,plain,
! [X2: g,X4: g] :
( ( '#sk1' @ X2 @ ( '#sk12' @ X2 @ X4 ) )
= X4 ),
inference(demod,[status(thm)],[zip_derived_cl55,zip_derived_cl1497]) ).
thf(zip_derived_cl56_020,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ ( '#sk13' @ X2 @ X4 ) @ X2 )
= X4 )
| ~ '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl51_021,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_cl46]) ).
thf(zip_derived_cl64,plain,
! [X0: g,X1: g,X2: g] :
( ( ( '#sk1' @ X0 @ X1 )
= ( '#sk1' @ ( '#sk13' @ X2 @ X0 ) @ ( '#sk1' @ X2 @ X1 ) ) )
| ~ '#form10' ),
inference('sup+',[status(thm)],[zip_derived_cl56,zip_derived_cl51]) ).
thf(zip_derived_cl1497_022,plain,
'#form10',
inference(simplify,[status(thm)],[zip_derived_cl1461]) ).
thf(zip_derived_cl1531,plain,
! [X0: g,X1: g,X2: g] :
( ( '#sk1' @ X0 @ X1 )
= ( '#sk1' @ ( '#sk13' @ X2 @ X0 ) @ ( '#sk1' @ X2 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl64,zip_derived_cl1497]) ).
thf(zip_derived_cl1576,plain,
! [X0: g,X1: g,X2: g] :
( ( '#sk1' @ X2 @ ( '#sk12' @ X1 @ X0 ) )
= ( '#sk1' @ ( '#sk13' @ X1 @ X2 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1529,zip_derived_cl1531]) ).
thf(zip_derived_cl1530_023,plain,
! [X2: g,X4: g] :
( ( '#sk1' @ ( '#sk13' @ X2 @ X4 ) @ X2 )
= X4 ),
inference(demod,[status(thm)],[zip_derived_cl56,zip_derived_cl1497]) ).
thf(zip_derived_cl1699,plain,
! [X0: g,X1: g] :
( ( '#sk1' @ X1 @ ( '#sk12' @ X0 @ X0 ) )
= X1 ),
inference('sup+',[status(thm)],[zip_derived_cl1576,zip_derived_cl1530]) ).
thf(zip_derived_cl55_024,plain,
! [X2: g,X4: g] :
( ( ( '#sk1' @ X2 @ ( '#sk12' @ X2 @ X4 ) )
= X4 )
| ~ '#form10' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl51_025,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_cl46]) ).
thf(zip_derived_cl69,plain,
! [X0: g,X1: g,X2: g] :
( ( X0
= ( '#sk1' @ X2 @ ( '#sk1' @ X1 @ ( '#sk12' @ ( '#sk1' @ X2 @ X1 ) @ X0 ) ) ) )
| ~ '#form10' ),
inference('sup+',[status(thm)],[zip_derived_cl55,zip_derived_cl51]) ).
thf(zip_derived_cl60_026,plain,
! [X2: g,X4: g,X6: g,X8: g] :
( ( ( '#sk1' @ ( '#sk2' @ X2 ) @ X4 )
!= X2 )
| ( ( '#sk1' @ ( '#sk3' @ X2 ) @ X2 )
!= ( '#sk3' @ X2 ) )
| ( ( '#sk1' @ '#sk4' @ X6 )
!= '#sk5' )
| ( ( '#sk1' @ X8 @ '#sk4' )
!= '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl573,plain,
! [X0: g,X1: g,X3: g,X4: g] :
( ( X0 != X1 )
| ~ '#form10'
| ( ( '#sk1' @ X3 @ '#sk4' )
!= '#sk5' )
| ( ( '#sk1' @ '#sk4' @ X4 )
!= '#sk5' )
| ( ( '#sk1' @ ( '#sk3' @ X1 ) @ X1 )
!= ( '#sk3' @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl69,zip_derived_cl60]) ).
thf(zip_derived_cl646,plain,
! [X1: g,X3: g,X4: g] :
( ( ( '#sk1' @ ( '#sk3' @ X1 ) @ X1 )
!= ( '#sk3' @ X1 ) )
| ( ( '#sk1' @ '#sk4' @ X4 )
!= '#sk5' )
| ( ( '#sk1' @ X3 @ '#sk4' )
!= '#sk5' )
| ~ '#form10' ),
inference(simplify,[status(thm)],[zip_derived_cl573]) ).
thf(zip_derived_cl152_027,plain,
! [X1: g,X2: g] :
( '#form10'
| ( ( '#sk1' @ X1 @ '#sk4' )
!= '#sk5' )
| ( ( '#sk1' @ '#sk4' @ X2 )
!= '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl141,zip_derived_cl45]) ).
thf(zip_derived_cl713,plain,
! [X1: g,X3: g,X4: g] :
( ( ( '#sk1' @ X3 @ '#sk4' )
!= '#sk5' )
| ( ( '#sk1' @ '#sk4' @ X4 )
!= '#sk5' )
| ( ( '#sk1' @ ( '#sk3' @ X1 ) @ X1 )
!= ( '#sk3' @ X1 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl646,zip_derived_cl152]) ).
thf(zip_derived_cl1725,plain,
! [X0: g,X1: g,X2: g] :
( ( ( '#sk3' @ ( '#sk12' @ X0 @ X0 ) )
!= ( '#sk3' @ ( '#sk12' @ X0 @ X0 ) ) )
| ( ( '#sk1' @ '#sk4' @ X1 )
!= '#sk5' )
| ( ( '#sk1' @ X2 @ '#sk4' )
!= '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1699,zip_derived_cl713]) ).
thf(zip_derived_cl1742,plain,
! [X1: g,X2: g] :
( ( ( '#sk1' @ X2 @ '#sk4' )
!= '#sk5' )
| ( ( '#sk1' @ '#sk4' @ X1 )
!= '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1725]) ).
thf(zip_derived_cl1751,plain,
! [X0: g,X1: g] :
( ( X0 != '#sk5' )
| ( ( '#sk1' @ '#sk4' @ X1 )
!= '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1530,zip_derived_cl1742]) ).
thf(zip_derived_cl1757,plain,
! [X1: g] :
( ( '#sk1' @ '#sk4' @ X1 )
!= '#sk5' ),
inference(simplify,[status(thm)],[zip_derived_cl1751]) ).
thf(zip_derived_cl1760,plain,
! [X0: g] : ( X0 != '#sk5' ),
inference('sup-',[status(thm)],[zip_derived_cl1529,zip_derived_cl1757]) ).
thf(zip_derived_cl1767,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl1760]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.37 % Problem : ALG274^5 : TPTP v9.2.0. Bugfixed v5.3.0.
% 0.12/0.40 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.FKtdgdJPUU true
% 0.12/0.59 % Computer : n016.cluster.edu
% 0.12/0.59 % Model : x86_64 x86_64
% 0.12/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.59 % Memory : 8042.1875MB
% 0.12/0.59 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.59 % CPULimit : 300
% 0.12/0.59 % WCLimit : 300
% 0.12/0.59 % DateTime : Wed Oct 1 17:03:08 EDT 2025
% 0.17/0.60 % CPUTime :
% 0.17/0.60 % Running portfolio for 300 s
% 0.17/0.60 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.60 % Number of cores: 8
% 0.17/0.60 % Python version: Python 3.6.8
% 0.17/0.61 % Running in HO mode
% 0.18/0.90 % Total configuration time : 828
% 0.18/0.90 % Estimated wc time : 1656
% 0.18/0.90 % Estimated cpu time (8 cpus) : 207.0
% 0.18/1.11 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.18/1.11 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.18/1.14 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.39/1.19 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.39/1.22 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.48/1.24 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.48/1.26 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.48/1.27 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 4.24/1.97 % Solved by lams/30_sp5.sh.
% 4.24/1.97 % done 299 iterations in 0.541s
% 4.24/1.97 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.24/1.97 % SZS output start Refutation
% See solution above
% 4.24/1.98
% 4.24/1.98
% 4.24/1.98 % Terminating...
% 4.57/2.16 % Runner terminated.
% 4.57/2.20 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------