%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ALG269^3 : TPTP v9.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.lNARy0oRJo true
% Computer : n029.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 04:28:32 PM UTC 2025
% Result : Theorem 29.76s 9.19s
% Output : Refutation 29.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 39
% Syntax : Number of formulae : 173 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 1258 ( 117 equ; 0 cnn)
% Maximal formula atoms : 44 ( 7 avg)
% Number of connectives : 5719 ( 125 ~; 136 |; 0 &;4255 @)
% ( 39 <=>; 612 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 313 ( 313 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 38 usr; 14 con; 0-4 aty)
% ( 547 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 962 ( 655 ^; 303 !; 4 ?; 962 :)
% Comments :
%------------------------------------------------------------------------------
thf(subst_type,type,
subst: $tType ).
thf(term_type,type,
term: $tType ).
thf('#sk124_type',type,
'#sk124': ( term > $o ) > subst > term > term ).
thf(lam_type,type,
lam: term > term ).
thf('#sk225_type',type,
'#sk225': ( term > $o ) > term ).
thf('#sk30_type',type,
'#sk30': ( term > $o ) > term ).
thf('#sk251_type',type,
'#sk251': term ).
thf('#form632_type',type,
'#form632': ( term > $o ) > $o ).
thf(push_type,type,
push: term > subst > subst ).
thf('#form178_type',type,
'#form178': ( term > $o ) > $o ).
thf('#form234_type',type,
'#form234': ( term > $o ) > ( term > $o ) > $o ).
thf('#l_lift5555_type',type,
'#l_lift5555': term > $o ).
thf('#sk5_type',type,
'#sk5': ( term > $o ) > term > $o ).
thf(hoasinduction_p_and_p_prime_type,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(hoasap_type,type,
hoasap: subst > term > subst > term > term ).
thf(one_type,type,
one: term ).
thf(id_type,type,
id: subst ).
thf(comp_type,type,
comp: subst > subst > subst ).
thf(induction2_type,type,
induction2: $o ).
thf(axvarid_type,type,
axvarid: $o ).
thf(sh_type,type,
sh: subst ).
thf(hoasinduction_lthm_3_type,type,
hoasinduction_lthm_3: $o ).
thf('#sk417_type',type,
'#sk417': ( term > $o ) > term > term ).
thf('#form922_type',type,
'#form922': $o ).
thf(sub_type,type,
sub: term > subst > term ).
thf(hoasinduction_type,type,
hoasinduction: $o ).
thf(ap_type,type,
ap: term > term > term ).
thf('#sk31_type',type,
'#sk31': subst > term > subst > $o ).
thf(hoasinduction_lem3v2a_type,type,
hoasinduction_lem3v2a: $o ).
thf(var_type,type,
var: term > $o ).
thf('#sk372_type',type,
'#sk372': ( subst > term > term ) > subst ).
thf(hoaslam_type,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf('#sk500_type',type,
'#sk500': ( subst > term > term ) > term ).
thf('#sk405_type',type,
'#sk405': ( subst > term > term ) > term ).
thf(hoasinduction_lem0_type,type,
hoasinduction_lem0: $o ).
thf(hoasvar_type,type,
hoasvar: subst > term > subst > $o ).
thf('#sk294_type',type,
'#sk294': ( term > $o ) > ( term > $o ) > term ).
thf('#sk135_type',type,
'#sk135': ( term > $o ) > term ).
thf('#sk103_type',type,
'#sk103': ( term > $o ) > term ).
thf('#sk428_type',type,
'#sk428': ( subst > term > term ) > subst ).
thf(hoasinduction_lthm_3,axiom,
( hoasinduction_lthm_3
= ( hoasinduction_lem0
=> ( induction2
=> ( axvarid
=> ( hoasinduction_lem3v2a
=> hoasinduction ) ) ) ) ) ).
thf('0',plain,
( hoasinduction_lthm_3
= ( hoasinduction_lem0
=> ( induction2
=> ( axvarid
=> ( hoasinduction_lem3v2a
=> hoasinduction ) ) ) ) ),
define([status(thm)]) ).
thf(hoasinduction,axiom,
( hoasinduction
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] : ( P @ id @ A @ id ) ) ) ) ) ) ) ) ).
thf('1',plain,
( hoasinduction
= ( ! [X4: subst > term > subst > $o] :
( ! [X6: subst,X8: term,X10: subst,X12: subst] :
( ( X4 @ X6 @ X8 @ ( comp @ X12 @ X10 ) )
=> ( X4 @ ( comp @ X6 @ X12 ) @ ( sub @ X8 @ X12 ) @ X10 ) )
=> ( ! [X14: subst,X16: term,X18: subst,X20: subst] :
( ( X4 @ ( comp @ X14 @ X20 ) @ ( sub @ X16 @ X20 ) @ X18 )
=> ( X4 @ X14 @ X16 @ ( comp @ X20 @ X18 ) ) )
=> ( ! [X22: term] :
( ( hoasvar @ id @ X22 @ id )
=> ( X4 @ id @ X22 @ id ) )
=> ( ! [X24: term,X26: term] :
( ( X4 @ id @ X24 @ id )
=> ( ( X4 @ id @ X26 @ id )
=> ( X4 @ id @ ( hoasap @ id @ X24 @ id @ X26 ) @ id ) ) )
=> ( ! [X28: subst > term > term] :
( ! [X30: subst,X32: term,X34: subst] :
( ( sub @ ( X28 @ X30 @ X32 ) @ X34 )
= ( X28 @ ( comp @ X30 @ X34 ) @ ( sub @ X32 @ X34 ) ) )
=> ( ! [X36: term] :
( ( X4 @ id @ X36 @ id )
=> ( X4 @ id @ ( X28 @ id @ X36 ) @ id ) )
=> ( X4 @ id
@ ( hoaslam @ id
@ ^ [V_1: subst,V_2: term] : ( X28 @ V_1 @ V_2 ) )
@ id ) ) )
=> ! [X38: term] : ( X4 @ id @ X38 @ id ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(hoasinduction_lem3v2a,axiom,
( hoasinduction_lem3v2a
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ! [B: term] :
( ( Q @ B )
=> ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( Q @ ( lam @ A ) ) ) ) ) ) ) ).
thf('2',plain,
( hoasinduction_lem3v2a
= ( ! [X4: subst > term > subst > $o,X6: term > $o] :
( ! [X8: subst > term > term] :
( ! [X10: subst,X12: term,X14: subst] :
( ( sub @ ( X8 @ X10 @ X12 ) @ X14 )
= ( X8 @ ( comp @ X10 @ X14 ) @ ( sub @ X12 @ X14 ) ) )
=> ( ! [X16: term] :
( ( X4 @ id @ X16 @ id )
=> ( X4 @ id @ ( X8 @ id @ X16 ) @ id ) )
=> ( X4 @ id
@ ( hoaslam @ id
@ ^ [V_1: subst,V_2: term] : ( X8 @ V_1 @ V_2 ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X4 @ X6 )
=> ! [X18: term] :
( ! [X20: term] :
( ( X6 @ X20 )
=> ( X6 @ ( sub @ X18 @ ( push @ X20 @ id ) ) ) )
=> ( X6 @ ( lam @ X18 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(hoasinduction_lem0,axiom,
( hoasinduction_lem0
= ( ! [P: subst > term > subst > $o] :
? [Q: term > $o] : ( hoasinduction_p_and_p_prime @ P @ Q ) ) ) ).
thf('3',plain,
( hoasinduction_lem0
= ( ! [X4: subst > term > subst > $o] :
? [X6: term > $o] : ( hoasinduction_p_and_p_prime @ X4 @ X6 ) ) ),
define([status(thm)]) ).
thf(hoasinduction_p_and_p_prime,axiom,
( hoasinduction_p_and_p_prime
= ( ^ [P: subst > term > subst > $o,Q: term > $o] :
! [X: term] :
( ( Q @ X )
<=> ( P @ id @ X @ id ) ) ) ) ).
thf('4',plain,
( hoasinduction_p_and_p_prime
= ( ^ [P: subst > term > subst > $o,Q: term > $o] :
! [X: term] :
( ( Q @ X )
<=> ( P @ id @ X @ id ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[hoasinduction_p_and_p_prime]) ).
thf('5',plain,
( hoasinduction_p_and_p_prime
= ( ^ [V_1: subst > term > subst > $o,V_2: term > $o] :
! [X4: term] :
( ( V_2 @ X4 )
<=> ( V_1 @ id @ X4 @ id ) ) ) ),
define([status(thm)]) ).
thf(hoasvar,axiom,
( hoasvar
= ( ^ [M: subst,A: term,N: subst] : ( var @ ( sub @ A @ N ) ) ) ) ).
thf('6',plain,
( hoasvar
= ( ^ [M: subst,A: term,N: subst] : ( var @ ( sub @ A @ N ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[hoasvar]) ).
thf('7',plain,
( hoasvar
= ( ^ [V_1: subst,V_2: term,V_3: subst] : ( var @ ( sub @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(hoaslam,axiom,
( hoaslam
= ( ^ [M: subst,F: subst > term > term] : ( lam @ ( F @ sh @ one ) ) ) ) ).
thf('8',plain,
( hoaslam
= ( ^ [M: subst,F: subst > term > term] : ( lam @ ( F @ sh @ one ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[hoaslam]) ).
thf('9',plain,
( hoaslam
= ( ^ [V_1: subst,V_2: subst > term > term] : ( lam @ ( V_2 @ sh @ one ) ) ) ),
define([status(thm)]) ).
thf(hoasap,axiom,
( hoasap
= ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ) ).
thf('10',plain,
( hoasap
= ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ),
inference(simplify_rw_rule,[status(thm)],[hoasap]) ).
thf('11',plain,
( hoasap
= ( ^ [V_1: subst,V_2: term,V_3: subst,V_4: term] : ( ap @ ( sub @ V_2 @ V_3 ) @ V_4 ) ) ),
define([status(thm)]) ).
thf(induction2,axiom,
( induction2
= ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) ) ) ).
thf('12',plain,
( induction2
= ( ! [X4: term > $o] :
( ! [X6: term] :
( ( var @ X6 )
=> ( X4 @ X6 ) )
=> ( ! [X8: term,X10: term] :
( ( X4 @ X8 )
=> ( ( X4 @ X10 )
=> ( X4 @ ( ap @ X8 @ X10 ) ) ) )
=> ( ! [X12: term] :
( ! [X14: term] :
( ( X4 @ X14 )
=> ( X4 @ ( sub @ X12 @ ( push @ X14 @ id ) ) ) )
=> ( X4 @ ( lam @ X12 ) ) )
=> ! [X16: term] : ( X4 @ X16 ) ) ) ) ) ),
define([status(thm)]) ).
thf(axvarid,axiom,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ) ).
thf('13',plain,
( axvarid
= ( ! [X4: term] :
( ( sub @ X4 @ id )
= X4 ) ) ),
define([status(thm)]) ).
thf(thm,conjecture,
hoasinduction_lthm_3 ).
thf(zf_stmt_0,conjecture,
( ! [X4: subst > term > subst > $o] :
? [X6: term > $o] :
! [X8: term] :
( ( X6 @ X8 )
<=> ( X4 @ id @ X8 @ id ) )
=> ( ! [X10: term > $o] :
( ! [X12: term] :
( ( var @ X12 )
=> ( X10 @ X12 ) )
=> ( ! [X14: term,X16: term] :
( ( X10 @ X14 )
=> ( ( X10 @ X16 )
=> ( X10 @ ( ap @ X14 @ X16 ) ) ) )
=> ( ! [X18: term] :
( ! [X20: term] :
( ( X10 @ X20 )
=> ( X10 @ ( sub @ X18 @ ( push @ X20 @ id ) ) ) )
=> ( X10 @ ( lam @ X18 ) ) )
=> ! [X22: term] : ( X10 @ X22 ) ) ) )
=> ( ! [X24: term] :
( ( sub @ X24 @ id )
= X24 )
=> ( ! [X26: subst > term > subst > $o,X28: term > $o] :
( ! [X30: subst > term > term] :
( ! [X32: subst,X34: term,X36: subst] :
( ( sub @ ( X30 @ X32 @ X34 ) @ X36 )
= ( X30 @ ( comp @ X32 @ X36 ) @ ( sub @ X34 @ X36 ) ) )
=> ( ! [X38: term] :
( ( X26 @ id @ X38 @ id )
=> ( X26 @ id @ ( X30 @ id @ X38 ) @ id ) )
=> ( X26 @ id @ ( lam @ ( X30 @ sh @ one ) ) @ id ) ) )
=> ( ! [X40: term] :
( ( X28 @ X40 )
<=> ( X26 @ id @ X40 @ id ) )
=> ! [X42: term] :
( ! [X44: term] :
( ( X28 @ X44 )
=> ( X28 @ ( sub @ X42 @ ( push @ X44 @ id ) ) ) )
=> ( X28 @ ( lam @ X42 ) ) ) ) )
=> ! [X46: subst > term > subst > $o] :
( ! [X48: subst,X50: term,X52: subst,X54: subst] :
( ( X46 @ X48 @ X50 @ ( comp @ X54 @ X52 ) )
=> ( X46 @ ( comp @ X48 @ X54 ) @ ( sub @ X50 @ X54 ) @ X52 ) )
=> ( ! [X56: subst,X58: term,X60: subst,X62: subst] :
( ( X46 @ ( comp @ X56 @ X62 ) @ ( sub @ X58 @ X62 ) @ X60 )
=> ( X46 @ X56 @ X58 @ ( comp @ X62 @ X60 ) ) )
=> ( ! [X64: term] :
( ( var @ ( sub @ X64 @ id ) )
=> ( X46 @ id @ X64 @ id ) )
=> ( ! [X66: term,X68: term] :
( ( X46 @ id @ X66 @ id )
=> ( ( X46 @ id @ X68 @ id )
=> ( X46 @ id @ ( ap @ ( sub @ X66 @ id ) @ X68 ) @ id ) ) )
=> ( ! [X70: subst > term > term] :
( ! [X72: subst,X74: term,X76: subst] :
( ( sub @ ( X70 @ X72 @ X74 ) @ X76 )
= ( X70 @ ( comp @ X72 @ X76 ) @ ( sub @ X74 @ X76 ) ) )
=> ( ! [X78: term] :
( ( X46 @ id @ X78 @ id )
=> ( X46 @ id @ ( X70 @ id @ X78 ) @ id ) )
=> ( X46 @ id @ ( lam @ ( X70 @ sh @ one ) ) @ id ) ) )
=> ! [X80: term] : ( X46 @ id @ X80 @ id ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: subst > term > subst > $o] :
? [X6: term > $o] :
! [X8: term] :
( ( X6 @ X8 )
<=> ( X4 @ id @ X8 @ id ) )
=> ( ! [X10: term > $o] :
( ! [X12: term] :
( ( var @ X12 )
=> ( X10 @ X12 ) )
=> ( ! [X14: term,X16: term] :
( ( X10 @ X14 )
=> ( ( X10 @ X16 )
=> ( X10 @ ( ap @ X14 @ X16 ) ) ) )
=> ( ! [X18: term] :
( ! [X20: term] :
( ( X10 @ X20 )
=> ( X10 @ ( sub @ X18 @ ( push @ X20 @ id ) ) ) )
=> ( X10 @ ( lam @ X18 ) ) )
=> ! [X22: term] : ( X10 @ X22 ) ) ) )
=> ( ! [X24: term] :
( ( sub @ X24 @ id )
= X24 )
=> ( ! [X26: subst > term > subst > $o,X28: term > $o] :
( ! [X30: subst > term > term] :
( ! [X32: subst,X34: term,X36: subst] :
( ( sub @ ( X30 @ X32 @ X34 ) @ X36 )
= ( X30 @ ( comp @ X32 @ X36 ) @ ( sub @ X34 @ X36 ) ) )
=> ( ! [X38: term] :
( ( X26 @ id @ X38 @ id )
=> ( X26 @ id @ ( X30 @ id @ X38 ) @ id ) )
=> ( X26 @ id @ ( lam @ ( X30 @ sh @ one ) ) @ id ) ) )
=> ( ! [X40: term] :
( ( X28 @ X40 )
<=> ( X26 @ id @ X40 @ id ) )
=> ! [X42: term] :
( ! [X44: term] :
( ( X28 @ X44 )
=> ( X28 @ ( sub @ X42 @ ( push @ X44 @ id ) ) ) )
=> ( X28 @ ( lam @ X42 ) ) ) ) )
=> ! [X46: subst > term > subst > $o] :
( ! [X48: subst,X50: term,X52: subst,X54: subst] :
( ( X46 @ X48 @ X50 @ ( comp @ X54 @ X52 ) )
=> ( X46 @ ( comp @ X48 @ X54 ) @ ( sub @ X50 @ X54 ) @ X52 ) )
=> ( ! [X56: subst,X58: term,X60: subst,X62: subst] :
( ( X46 @ ( comp @ X56 @ X62 ) @ ( sub @ X58 @ X62 ) @ X60 )
=> ( X46 @ X56 @ X58 @ ( comp @ X62 @ X60 ) ) )
=> ( ! [X64: term] :
( ( var @ ( sub @ X64 @ id ) )
=> ( X46 @ id @ X64 @ id ) )
=> ( ! [X66: term,X68: term] :
( ( X46 @ id @ X66 @ id )
=> ( ( X46 @ id @ X68 @ id )
=> ( X46 @ id @ ( ap @ ( sub @ X66 @ id ) @ X68 ) @ id ) ) )
=> ( ! [X70: subst > term > term] :
( ! [X72: subst,X74: term,X76: subst] :
( ( sub @ ( X70 @ X72 @ X74 ) @ X76 )
= ( X70 @ ( comp @ X72 @ X76 ) @ ( sub @ X74 @ X76 ) ) )
=> ( ! [X78: term] :
( ( X46 @ id @ X78 @ id )
=> ( X46 @ id @ ( X70 @ id @ X78 ) @ id ) )
=> ( X46 @ id @ ( lam @ ( X70 @ sh @ one ) ) @ id ) ) )
=> ! [X80: term] : ( X46 @ id @ X80 @ id ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: subst > term > subst > $o] :
( ??
@ ^ [Y1: term > $o] :
( !!
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
<=> ( Y0 @ id @ Y2 @ id ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( !!
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !!
@ ^ [Y0: subst > term > subst > $o] :
( !!
@ ^ [Y1: term > $o] :
( ( !!
@ ^ [Y2: subst > term > term] :
( ( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: term] :
( !!
@ ^ [Y5: subst] :
( ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 )
= ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y3: term] :
( ( Y0 @ id @ Y3 @ id )
=> ( Y0 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y2 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
<=> ( Y0 @ id @ Y2 @ id ) ) )
=> ( !!
@ ^ [Y2: term] :
( ( !!
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: subst > term > subst > $o] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y2 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y3 )
=> ( Y0 @ Y1 @ Y2 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !!
@ ^ [Y1: subst > term > term] :
( ( !!
@ ^ [Y2: subst] :
( !!
@ ^ [Y3: term] :
( !!
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl2,plain,
~ ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( !!
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !!
@ ^ [Y0: subst > term > subst > $o] :
( !!
@ ^ [Y1: term > $o] :
( ( !!
@ ^ [Y2: subst > term > term] :
( ( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: term] :
( !!
@ ^ [Y5: subst] :
( ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 )
= ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y3: term] :
( ( Y0 @ id @ Y3 @ id )
=> ( Y0 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y2 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
<=> ( Y0 @ id @ Y2 @ id ) ) )
=> ( !!
@ ^ [Y2: term] :
( ( !!
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: subst > term > subst > $o] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y2 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y3 )
=> ( Y0 @ Y1 @ Y2 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !!
@ ^ [Y1: subst > term > term] :
( ( !!
@ ^ [Y2: subst] :
( !!
@ ^ [Y3: term] :
( !!
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl5,plain,
~ ( ( !!
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !!
@ ^ [Y0: subst > term > subst > $o] :
( !!
@ ^ [Y1: term > $o] :
( ( !!
@ ^ [Y2: subst > term > term] :
( ( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: term] :
( !!
@ ^ [Y5: subst] :
( ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 )
= ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y3: term] :
( ( Y0 @ id @ Y3 @ id )
=> ( Y0 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y2 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
<=> ( Y0 @ id @ Y2 @ id ) ) )
=> ( !!
@ ^ [Y2: term] :
( ( !!
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: subst > term > subst > $o] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y2 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y3 )
=> ( Y0 @ Y1 @ Y2 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !!
@ ^ [Y1: subst > term > term] :
( ( !!
@ ^ [Y2: subst] :
( !!
@ ^ [Y3: term] :
( !!
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl12,plain,
~ ( ( !!
@ ^ [Y0: subst > term > subst > $o] :
( !!
@ ^ [Y1: term > $o] :
( ( !!
@ ^ [Y2: subst > term > term] :
( ( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: term] :
( !!
@ ^ [Y5: subst] :
( ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 )
= ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y3: term] :
( ( Y0 @ id @ Y3 @ id )
=> ( Y0 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y2 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
<=> ( Y0 @ id @ Y2 @ id ) ) )
=> ( !!
@ ^ [Y2: term] :
( ( !!
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: subst > term > subst > $o] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y2 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y3 )
=> ( Y0 @ Y1 @ Y2 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !!
@ ^ [Y1: subst > term > term] :
( ( !!
@ ^ [Y2: subst] :
( !!
@ ^ [Y3: term] :
( !!
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl17,plain,
~ ( !!
@ ^ [Y0: subst > term > subst > $o] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y2 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y3 )
=> ( Y0 @ Y1 @ Y2 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !!
@ ^ [Y1: subst > term > term] :
( ( !!
@ ^ [Y2: subst] :
( !!
@ ^ [Y3: term] :
( !!
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl24,plain,
~ ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( !!
@ ^ [Y3: subst] :
( ( '#sk31' @ Y0 @ Y1 @ ( comp @ Y3 @ Y2 ) )
=> ( '#sk31' @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( !!
@ ^ [Y3: subst] :
( ( '#sk31' @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y1 @ Y3 ) @ Y2 )
=> ( '#sk31' @ Y0 @ Y1 @ ( comp @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( '#sk31' @ id @ Y0 @ id ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl32,plain,
~ ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( !!
@ ^ [Y3: subst] :
( ( '#sk31' @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y1 @ Y3 ) @ Y2 )
=> ( '#sk31' @ Y0 @ Y1 @ ( comp @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( '#sk31' @ id @ Y0 @ id ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl38,plain,
~ ( ( !!
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( '#sk31' @ id @ Y0 @ id ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl45,plain,
~ ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl54,plain,
~ ( ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl68,plain,
~ ( !!
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl83,plain,
~ ( '#sk31' @ id @ '#sk251' @ id ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( !!
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl9,plain,
! [X2: term > $o] :
( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X2 @ Y0 ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( X2 @ Y0 )
=> ( ( X2 @ Y1 )
=> ( X2 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl14,plain,
! [X2: term > $o] :
( ~ ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X2 @ Y0 ) ) )
| ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( X2 @ Y0 )
=> ( ( X2 @ Y1 )
=> ( X2 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl19,plain,
! [X2: term > $o] :
( ~ ( ( var @ ( '#sk30' @ X2 ) )
=> ( X2 @ ( '#sk30' @ X2 ) ) )
| ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( X2 @ Y0 )
=> ( ( X2 @ Y1 )
=> ( X2 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl26,plain,
! [X2: term > $o] :
( ~ ( X2 @ ( '#sk30' @ X2 ) )
| ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( X2 @ Y0 )
=> ( ( X2 @ Y1 )
=> ( X2 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl34,plain,
! [X2: term > $o] :
( ~ ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( X2 @ Y0 )
=> ( ( X2 @ Y1 )
=> ( X2 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) ) )
| ~ ( X2 @ ( '#sk30' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl40,plain,
! [X2: term > $o] :
( ~ ( !!
@ ^ [Y0: term] :
( ( X2 @ ( '#sk103' @ X2 ) )
=> ( ( X2 @ Y0 )
=> ( X2 @ ( ap @ ( '#sk103' @ X2 ) @ Y0 ) ) ) ) )
| ~ ( X2 @ ( '#sk30' @ X2 ) )
| ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl47,plain,
! [X2: term > $o] :
( ~ ( ( X2 @ ( '#sk103' @ X2 ) )
=> ( ( X2 @ ( '#sk135' @ X2 ) )
=> ( X2 @ ( ap @ ( '#sk103' @ X2 ) @ ( '#sk135' @ X2 ) ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) ) )
| ~ ( X2 @ ( '#sk30' @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl57,plain,
! [X2: term > $o] :
( ~ ( '#form178' @ X2 )
| ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl58,plain,
! [X2: term > $o] :
( ~ ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) )
| ~ ( '#form178' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl73,plain,
! [X2: term > $o] :
( ~ ( ( !!
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ ( '#sk225' @ X2 ) @ ( push @ Y0 @ id ) ) ) ) )
=> ( X2 @ ( lam @ ( '#sk225' @ X2 ) ) ) )
| ~ ( '#form178' @ X2 )
| ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl91,plain,
! [X2: term > $o] :
( ~ ( X2 @ ( lam @ ( '#sk225' @ X2 ) ) )
| ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) )
| ~ ( '#form178' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl101,plain,
! [X2: term > $o,X4: term] :
( ( X2 @ X4 )
| ~ ( '#form178' @ X2 )
| ~ ( X2 @ ( lam @ ( '#sk225' @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl90,plain,
! [X2: term > $o] :
( ( !!
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( sub @ ( '#sk225' @ X2 ) @ ( push @ Y0 @ id ) ) ) ) )
| ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) )
| ~ ( '#form178' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl100,plain,
! [X2: term > $o,X4: term] :
( ( ( X2 @ X4 )
=> ( X2 @ ( sub @ ( '#sk225' @ X2 ) @ ( push @ X4 @ id ) ) ) )
| ~ ( '#form178' @ X2 )
| ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl108,plain,
! [X2: term > $o,X4: term] :
( ~ ( X2 @ X4 )
| ( X2 @ ( sub @ ( '#sk225' @ X2 ) @ ( push @ X4 @ id ) ) )
| ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) )
| ~ ( '#form178' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl112,plain,
! [X2: term > $o,X4: term,X6: term] :
( ( X2 @ X6 )
| ~ ( '#form178' @ X2 )
| ( X2 @ ( sub @ ( '#sk225' @ X2 ) @ ( push @ X4 @ id ) ) )
| ~ ( X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl115,plain,
! [X0: term > $o,X1: term] :
( ~ ( X0 @ X1 )
| ~ ( '#form178' @ X0 )
| ( X0 @ ( sub @ ( '#sk225' @ X0 ) @ ( push @ X1 @ id ) ) ) ),
inference(condensation,[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl9_001,plain,
! [X2: term > $o] :
( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X2 @ Y0 ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( X2 @ Y0 )
=> ( ( X2 @ Y1 )
=> ( X2 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl10,plain,
! [X0: term > $o] :
( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk5' @ X0 @ Y0 ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk5' @ X0 @ Y0 ) ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl129,plain,
! [X0: term > $o] :
( ~ ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk5' @ X0 @ Y0 ) ) )
| ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk5' @ X0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl130,plain,
! [X0: term > $o] :
( ~ ( ( var @ ( '#sk30' @ ( '#sk5' @ X0 ) ) )
=> ( '#sk5' @ X0 @ ( '#sk30' @ ( '#sk5' @ X0 ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk5' @ X0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl129]) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: subst > term > subst > $o] :
( ??
@ ^ [Y1: term > $o] :
( !!
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
<=> ( Y0 @ id @ Y2 @ id ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
! [X2: subst > term > subst > $o] :
( ??
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
<=> ( X2 @ id @ Y1 @ id ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
! [X2: term > $o] :
( ??
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
<=> ( ^ [Y2: subst,Y3: term,Y4: subst] : ( X2 @ Y3 )
@ id
@ Y1
@ id ) ) ) ),
inference(prune_arg_fun,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl7,plain,
! [X2: term > $o] :
( ??
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
<=> ( X2 @ Y1 ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl8,plain,
! [X2: term > $o] :
( !!
@ ^ [Y0: term] :
( ( '#sk5' @ X2 @ Y0 )
<=> ( X2 @ Y0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl13,plain,
! [X2: term > $o,X4: term] :
( ( '#sk5' @ X2 @ X4 )
<=> ( X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl18,plain,
! [X2: term > $o,X4: term] :
( ( '#sk5' @ X2 @ X4 )
= ( X2 @ X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl131,plain,
! [X0: term > $o] :
( ~ ( ( '#sk5' @ var @ ( '#sk30' @ ( '#sk5' @ X0 ) ) )
=> ( '#sk5' @ X0 @ ( '#sk30' @ ( '#sk5' @ X0 ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk5' @ X0 @ Y0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl130,zip_derived_cl18]) ).
thf(zip_derived_cl133,plain,
! [X0: term > $o] :
( ~ ( '#sk5' @ X0 @ ( '#sk30' @ ( '#sk5' @ X0 ) ) )
| ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk5' @ X0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl131]) ).
thf(zip_derived_cl132,plain,
! [X0: term > $o] :
( ( '#sk5' @ var @ ( '#sk30' @ ( '#sk5' @ X0 ) ) )
| ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk5' @ X0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl131]) ).
thf(zip_derived_cl134,plain,
! [X0: term > $o] :
( ~ ( '#form632' @ X0 )
| ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk5' @ X0 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl137,plain,
! [X0: term > $o] :
( ( '#form632' @ X0 )
| ~ ( '#sk5' @ X0 @ ( '#sk30' @ ( '#sk5' @ X0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl133,zip_derived_cl134]) ).
thf(zip_derived_cl16,plain,
( !!
@ ^ [Y0: subst > term > subst > $o] :
( !!
@ ^ [Y1: term > $o] :
( ( !!
@ ^ [Y2: subst > term > term] :
( ( !!
@ ^ [Y3: subst] :
( !!
@ ^ [Y4: term] :
( !!
@ ^ [Y5: subst] :
( ( sub @ ( Y2 @ Y3 @ Y4 ) @ Y5 )
= ( Y2 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y3: term] :
( ( Y0 @ id @ Y3 @ id )
=> ( Y0 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y2 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
<=> ( Y0 @ id @ Y2 @ id ) ) )
=> ( !!
@ ^ [Y2: term] :
( ( !!
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y1 @ ( lam @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl21,plain,
! [X2: subst > term > subst > $o] :
( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: subst > term > term] :
( ( !!
@ ^ [Y2: subst] :
( !!
@ ^ [Y3: term] :
( !!
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( X2 @ id @ Y2 @ id )
=> ( X2 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( X2 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
<=> ( X2 @ id @ Y1 @ id ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( !!
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl22,plain,
( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: subst > term > term] :
( ( !!
@ ^ [Y2: subst] :
( !!
@ ^ [Y3: term] :
( !!
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( '#sk31' @ id @ Y2 @ id )
=> ( '#sk31' @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
<=> ( '#sk31' @ id @ Y1 @ id ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( !!
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl184,plain,
! [X2: term > $o] :
( ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( X2 @ Y0 )
<=> ( '#sk31' @ id @ Y0 @ id ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl186,plain,
! [X0: term > $o] :
( ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( '#sk5' @ X0 @ Y0 )
<=> ( '#sk31' @ id @ Y0 @ id ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl184]) ).
thf(zip_derived_cl214,plain,
! [X0: term > $o] :
( ~ ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( '#sk5' @ X0 @ Y0 )
<=> ( '#sk31' @ id @ Y0 @ id ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl186]) ).
thf(zip_derived_cl214_002,plain,
! [X0: term > $o] :
( ~ ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( '#sk5' @ X0 @ Y0 )
<=> ( '#sk31' @ id @ Y0 @ id ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl186]) ).
thf(zip_derived_cl215,plain,
( '#form922'
| ~ ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl217,plain,
! [X0: term > $o] :
( ~ '#form922'
| ( ( !!
@ ^ [Y0: term] :
( ( '#sk5' @ X0 @ Y0 )
<=> ( '#sk31' @ id @ Y0 @ id ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl214,zip_derived_cl215]) ).
thf(zip_derived_cl218,plain,
! [X0: term > $o] :
( ~ ( !!
@ ^ [Y0: term] :
( ( '#sk5' @ X0 @ Y0 )
<=> ( '#sk31' @ id @ Y0 @ id ) ) )
| ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) )
| ~ '#form922' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl217]) ).
thf(zip_derived_cl221,plain,
! [X0: term > $o] :
( ~ ( ( '#sk5' @ X0
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) ) )
<=> ( '#sk31' @ id
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) )
@ id ) )
| ~ '#form922'
| ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl218]) ).
thf(zip_derived_cl225,plain,
! [X0: term > $o] :
( ( ( '#sk5' @ X0
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) ) )
!= ( '#sk31' @ id
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) )
@ id ) )
| ~ '#form922'
| ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl221]) ).
thf(zip_derived_cl226,plain,
! [X0: term > $o,X2: term] :
( ( ( !!
@ ^ [Y0: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( '#sk5' @ X0 @ ( sub @ X2 @ ( push @ Y0 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ X2 ) ) )
| ~ '#form922'
| ( ( '#sk5' @ X0
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) ) )
!= ( '#sk31' @ id
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) )
@ id ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl225]) ).
thf(zip_derived_cl229,plain,
! [X0: term > $o,X2: term] :
( ~ ( !!
@ ^ [Y0: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( '#sk5' @ X0 @ ( sub @ X2 @ ( push @ Y0 @ id ) ) ) ) )
| ( '#sk5' @ X0 @ ( lam @ X2 ) )
| ( ( '#sk5' @ X0
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) ) )
!= ( '#sk31' @ id
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) )
@ id ) )
| ~ '#form922' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl226]) ).
thf(zip_derived_cl232,plain,
! [X0: term > $o,X2: term] :
( ~ ( ( '#sk5' @ X0 @ ( '#sk417' @ ( '#sk5' @ X0 ) @ X2 ) )
=> ( '#sk5' @ X0 @ ( sub @ X2 @ ( push @ ( '#sk417' @ ( '#sk5' @ X0 ) @ X2 ) @ id ) ) ) )
| ~ '#form922'
| ( ( '#sk5' @ X0
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) ) )
!= ( '#sk31' @ id
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) )
@ id ) )
| ( '#sk5' @ X0 @ ( lam @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl229]) ).
thf(zip_derived_cl234,plain,
! [X0: term > $o,X2: term] :
( ( '#sk5' @ X0 @ ( '#sk417' @ ( '#sk5' @ X0 ) @ X2 ) )
| ( '#sk5' @ X0 @ ( lam @ X2 ) )
| ( ( '#sk5' @ X0
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) ) )
!= ( '#sk31' @ id
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) )
@ id ) )
| ~ '#form922' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl232]) ).
thf(zip_derived_cl184_003,plain,
! [X2: term > $o] :
( ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( X2 @ Y0 )
<=> ( '#sk31' @ id @ Y0 @ id ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl187,plain,
! [X2: term > $o] :
( ~ ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( X2 @ Y0 )
<=> ( '#sk31' @ id @ Y0 @ id ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl184]) ).
thf(zip_derived_cl21_004,plain,
! [X2: subst > term > subst > $o] :
( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: subst > term > term] :
( ( !!
@ ^ [Y2: subst] :
( !!
@ ^ [Y3: term] :
( !!
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( X2 @ id @ Y2 @ id )
=> ( X2 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( X2 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
<=> ( X2 @ id @ Y1 @ id ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( !!
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl27,plain,
! [X2: term > $o] :
( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: subst > term > term] :
( ( !!
@ ^ [Y2: subst] :
( !!
@ ^ [Y3: term] :
( !!
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: term,Y5: subst] : ( X2 @ Y4 )
@ id
@ Y2
@ id )
=> ( ^ [Y3: subst,Y4: term,Y5: subst] : ( X2 @ Y4 )
@ id
@ ( Y1 @ id @ Y2 )
@ id ) ) )
=> ( ^ [Y2: subst,Y3: term,Y4: subst] : ( X2 @ Y3 )
@ id
@ ( lam @ ( Y1 @ sh @ one ) )
@ id ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
<=> ( ^ [Y2: subst,Y3: term,Y4: subst] : ( X2 @ Y3 )
@ id
@ Y1
@ id ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( !!
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) ) ) ) ),
inference(prune_arg_fun,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl28,plain,
! [X2: term > $o] :
( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: subst > term > term] :
( ( !!
@ ^ [Y2: subst] :
( !!
@ ^ [Y3: term] :
( !!
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y2: term] :
( ( X2 @ Y2 )
=> ( X2 @ ( Y1 @ id @ Y2 ) ) ) )
=> ( X2 @ ( lam @ ( Y1 @ sh @ one ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
<=> ( X2 @ Y1 ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( !!
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl29,plain,
! [X2: term > $o,X4: term > $o] :
( ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( Y0 @ id @ Y1 ) ) ) )
=> ( X2 @ ( lam @ ( Y0 @ sh @ one ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( X4 @ Y0 )
<=> ( X2 @ Y0 ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X4 @ Y1 )
=> ( X4 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X4 @ ( lam @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl35,plain,
! [X2: term > $o,X4: term > $o] :
( ~ ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( Y0 @ id @ Y1 ) ) ) )
=> ( X2 @ ( lam @ ( Y0 @ sh @ one ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( X4 @ Y0 )
<=> ( X2 @ Y0 ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X4 @ Y1 )
=> ( X4 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X4 @ ( lam @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl41,plain,
! [X2: term > $o,X4: term > $o] :
( ~ ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( sub @ ( '#sk124' @ X2 @ Y0 @ Y1 ) @ Y2 )
= ( '#sk124' @ X2 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( X2 @ Y0 )
=> ( X2 @ ( '#sk124' @ X2 @ id @ Y0 ) ) ) )
=> ( X2 @ ( lam @ ( '#sk124' @ X2 @ sh @ one ) ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( X4 @ Y0 )
<=> ( X2 @ Y0 ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X4 @ Y1 )
=> ( X4 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X4 @ ( lam @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl48,plain,
! [X2: term > $o,X4: term > $o] :
( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( sub @ ( '#sk124' @ X2 @ Y0 @ Y1 ) @ Y2 )
= ( '#sk124' @ X2 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( X4 @ Y0 )
<=> ( X2 @ Y0 ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X4 @ Y1 )
=> ( X4 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X4 @ ( lam @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl60,plain,
! [X2: term > $o,X4: term > $o,X6: subst] :
( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( sub @ ( '#sk124' @ X2 @ X6 @ Y0 ) @ Y1 )
= ( '#sk124' @ X2 @ ( comp @ X6 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( X4 @ Y0 )
<=> ( X2 @ Y0 ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X4 @ Y1 )
=> ( X4 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X4 @ ( lam @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl74,plain,
! [X2: term > $o,X4: term > $o] :
( ~ ( '#form234' @ X2 @ X4 )
| ( ( !!
@ ^ [Y0: term] :
( ( X4 @ Y0 )
<=> ( X2 @ Y0 ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X4 @ Y1 )
=> ( X4 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X4 @ ( lam @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl188,plain,
! [X2: term > $o] :
( ( '#form234'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ^ [Y0: term] : ( X2 @ Y0 ) )
| ~ ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl187,zip_derived_cl74]) ).
thf(zip_derived_cl189,plain,
! [X2: term > $o] :
( ( '#form234'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ X2 )
| ~ ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl188]) ).
thf(zip_derived_cl190,plain,
! [X2: term > $o] :
( ~ ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( sub
@ ( '#sk124'
@ ^ [Y3: term] : ( '#sk31' @ id @ Y3 @ id )
@ Y0
@ Y1 )
@ Y2 )
= ( '#sk124'
@ ^ [Y3: term] : ( '#sk31' @ id @ Y3 @ id )
@ ( comp @ Y0 @ Y2 )
@ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( '#sk31' @ id
@ ( '#sk124'
@ ^ [Y1: term] : ( '#sk31' @ id @ Y1 @ id )
@ id
@ Y0 )
@ id ) ) )
=> ( '#sk31' @ id
@ ( lam
@ ( '#sk124'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ sh
@ one ) )
@ id ) ) )
| ( '#form234'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl189]) ).
thf(zip_derived_cl192,plain,
! [X2: term > $o] :
( ~ ( ( !!
@ ^ [Y0: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( '#sk31' @ id
@ ( '#sk124'
@ ^ [Y1: term] : ( '#sk31' @ id @ Y1 @ id )
@ id
@ Y0 )
@ id ) ) )
=> ( '#sk31' @ id
@ ( lam
@ ( '#sk124'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ sh
@ one ) )
@ id ) )
| ( '#form234'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl190]) ).
thf(zip_derived_cl195,plain,
! [X2: term > $o] :
( ~ ( '#sk31' @ id
@ ( lam
@ ( '#sk124'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ sh
@ one ) )
@ id )
| ( '#form234'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl192]) ).
thf(zip_derived_cl4148,plain,
! [X3: term] :
( ( '#l_lift5555' @ X3 )
= ( '#sk31' @ id @ X3 @ id ) ),
define([status(thm)]) ).
thf(zip_derived_cl4148_005,plain,
! [X3: term] :
( ( '#l_lift5555' @ X3 )
= ( '#sk31' @ id @ X3 @ id ) ),
define([status(thm)]) ).
thf(zip_derived_cl4154,plain,
! [X0: term > $o,X2: term] :
( ( '#sk5' @ X0 @ ( '#sk417' @ ( '#sk5' @ X0 ) @ X2 ) )
| ( '#sk5' @ X0 @ ( lam @ X2 ) )
| ( ( '#sk5' @ X0 @ ( '#sk294' @ '#l_lift5555' @ ( '#sk5' @ X0 ) ) )
!= ( '#sk31' @ id @ ( '#sk294' @ '#l_lift5555' @ ( '#sk5' @ X0 ) ) @ id ) )
| ~ '#form922' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl234,zip_derived_cl4148,zip_derived_cl4148]) ).
thf(zip_derived_cl235,plain,
! [X0: term > $o,X2: term] :
( ~ ( '#sk5' @ X0 @ ( sub @ X2 @ ( push @ ( '#sk417' @ ( '#sk5' @ X0 ) @ X2 ) @ id ) ) )
| ( '#sk5' @ X0 @ ( lam @ X2 ) )
| ( ( '#sk5' @ X0
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) ) )
!= ( '#sk31' @ id
@ ( '#sk294'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( '#sk5' @ X0 ) )
@ id ) )
| ~ '#form922' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl232]) ).
thf(zip_derived_cl4148_006,plain,
! [X3: term] :
( ( '#l_lift5555' @ X3 )
= ( '#sk31' @ id @ X3 @ id ) ),
define([status(thm)]) ).
thf(zip_derived_cl4148_007,plain,
! [X3: term] :
( ( '#l_lift5555' @ X3 )
= ( '#sk31' @ id @ X3 @ id ) ),
define([status(thm)]) ).
thf(zip_derived_cl4155,plain,
! [X0: term > $o,X2: term] :
( ~ ( '#sk5' @ X0 @ ( sub @ X2 @ ( push @ ( '#sk417' @ ( '#sk5' @ X0 ) @ X2 ) @ id ) ) )
| ( '#sk5' @ X0 @ ( lam @ X2 ) )
| ( ( '#sk5' @ X0 @ ( '#sk294' @ '#l_lift5555' @ ( '#sk5' @ X0 ) ) )
!= ( '#sk31' @ id @ ( '#sk294' @ '#l_lift5555' @ ( '#sk5' @ X0 ) ) @ id ) )
| ~ '#form922' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl235,zip_derived_cl4148,zip_derived_cl4148]) ).
thf(zip_derived_cl132_008,plain,
! [X0: term > $o] :
( ( '#sk5' @ var @ ( '#sk30' @ ( '#sk5' @ X0 ) ) )
| ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk5' @ X0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl131]) ).
thf(zip_derived_cl134_009,plain,
! [X0: term > $o] :
( ~ ( '#form632' @ X0 )
| ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk5' @ X0 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl136,plain,
! [X0: term > $o] :
( ( '#form632' @ X0 )
| ( '#sk5' @ var @ ( '#sk30' @ ( '#sk5' @ X0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl132,zip_derived_cl134]) ).
thf(zip_derived_cl67,plain,
( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl82,plain,
! [X2: subst > term > term] :
( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( sub @ ( X2 @ Y0 @ Y1 ) @ Y2 )
= ( X2 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( '#sk31' @ id @ ( X2 @ id @ Y0 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl99,plain,
! [X2: subst > term > term] :
( ~ ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( sub @ ( X2 @ Y0 @ Y1 ) @ Y2 )
= ( X2 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( '#sk31' @ id @ ( X2 @ id @ Y0 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl107,plain,
! [X2: subst > term > term] :
( ~ ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( sub @ ( X2 @ ( '#sk372' @ X2 ) @ Y0 ) @ Y1 )
= ( X2 @ ( comp @ ( '#sk372' @ X2 ) @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( '#sk31' @ id @ ( X2 @ id @ Y0 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl111,plain,
! [X2: subst > term > term] :
( ~ ( !!
@ ^ [Y0: subst] :
( ( sub @ ( X2 @ ( '#sk372' @ X2 ) @ ( '#sk405' @ X2 ) ) @ Y0 )
= ( X2 @ ( comp @ ( '#sk372' @ X2 ) @ Y0 ) @ ( sub @ ( '#sk405' @ X2 ) @ Y0 ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( '#sk31' @ id @ ( X2 @ id @ Y0 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl114,plain,
! [X2: subst > term > term] :
( ( ( sub @ ( X2 @ ( '#sk372' @ X2 ) @ ( '#sk405' @ X2 ) ) @ ( '#sk428' @ X2 ) )
!= ( X2 @ ( comp @ ( '#sk372' @ X2 ) @ ( '#sk428' @ X2 ) ) @ ( sub @ ( '#sk405' @ X2 ) @ ( '#sk428' @ X2 ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( '#sk31' @ id @ ( X2 @ id @ Y0 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl118,plain,
! [X2: subst > term > term] :
( ( ( sub @ ( X2 @ ( '#sk372' @ X2 ) @ ( '#sk405' @ X2 ) ) @ ( '#sk428' @ X2 ) )
!= ( X2 @ ( comp @ ( '#sk372' @ X2 ) @ ( '#sk428' @ X2 ) ) @ ( sub @ ( '#sk405' @ X2 ) @ ( '#sk428' @ X2 ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( '#sk31' @ id @ ( X2 @ id @ Y0 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl119,plain,
! [X2: subst > term > term] :
( ~ ( !!
@ ^ [Y0: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( '#sk31' @ id @ ( X2 @ id @ Y0 ) @ id ) ) )
| ( '#sk31' @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id )
| ( ( sub @ ( X2 @ ( '#sk372' @ X2 ) @ ( '#sk405' @ X2 ) ) @ ( '#sk428' @ X2 ) )
!= ( X2 @ ( comp @ ( '#sk372' @ X2 ) @ ( '#sk428' @ X2 ) ) @ ( sub @ ( '#sk405' @ X2 ) @ ( '#sk428' @ X2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl118]) ).
thf(zip_derived_cl120,plain,
! [X2: subst > term > term] :
( ~ ( ( '#sk31' @ id @ ( '#sk500' @ X2 ) @ id )
=> ( '#sk31' @ id @ ( X2 @ id @ ( '#sk500' @ X2 ) ) @ id ) )
| ( ( sub @ ( X2 @ ( '#sk372' @ X2 ) @ ( '#sk405' @ X2 ) ) @ ( '#sk428' @ X2 ) )
!= ( X2 @ ( comp @ ( '#sk372' @ X2 ) @ ( '#sk428' @ X2 ) ) @ ( sub @ ( '#sk405' @ X2 ) @ ( '#sk428' @ X2 ) ) ) )
| ( '#sk31' @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl119]) ).
thf(zip_derived_cl121,plain,
! [X2: subst > term > term] :
( ( '#sk31' @ id @ ( '#sk500' @ X2 ) @ id )
| ( '#sk31' @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id )
| ( ( sub @ ( X2 @ ( '#sk372' @ X2 ) @ ( '#sk405' @ X2 ) ) @ ( '#sk428' @ X2 ) )
!= ( X2 @ ( comp @ ( '#sk372' @ X2 ) @ ( '#sk428' @ X2 ) ) @ ( sub @ ( '#sk405' @ X2 ) @ ( '#sk428' @ X2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl120]) ).
thf(zip_derived_cl215_010,plain,
( '#form922'
| ~ ( !!
@ ^ [Y0: subst > term > term] :
( ( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( '#sk31' @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl216,plain,
( ~ ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( sub
@ ( '#sk124'
@ ^ [Y3: term] : ( '#sk31' @ id @ Y3 @ id )
@ Y0
@ Y1 )
@ Y2 )
= ( '#sk124'
@ ^ [Y3: term] : ( '#sk31' @ id @ Y3 @ id )
@ ( comp @ Y0 @ Y2 )
@ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( '#sk31' @ id
@ ( '#sk124'
@ ^ [Y1: term] : ( '#sk31' @ id @ Y1 @ id )
@ id
@ Y0 )
@ id ) ) )
=> ( '#sk31' @ id
@ ( lam
@ ( '#sk124'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ sh
@ one ) )
@ id ) ) )
| '#form922' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl215]) ).
thf(zip_derived_cl220,plain,
( ~ ( ( !!
@ ^ [Y0: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( '#sk31' @ id
@ ( '#sk124'
@ ^ [Y1: term] : ( '#sk31' @ id @ Y1 @ id )
@ id
@ Y0 )
@ id ) ) )
=> ( '#sk31' @ id
@ ( lam
@ ( '#sk124'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ sh
@ one ) )
@ id ) )
| '#form922' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl216]) ).
thf(zip_derived_cl223,plain,
( ( !!
@ ^ [Y0: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( '#sk31' @ id
@ ( '#sk124'
@ ^ [Y1: term] : ( '#sk31' @ id @ Y1 @ id )
@ id
@ Y0 )
@ id ) ) )
| '#form922' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl220]) ).
thf(zip_derived_cl228,plain,
! [X2: term] :
( ( ( '#sk31' @ id @ X2 @ id )
=> ( '#sk31' @ id
@ ( '#sk124'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ id
@ X2 )
@ id ) )
| '#form922' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl223]) ).
thf(zip_derived_cl231,plain,
! [X2: term] :
( ~ ( '#sk31' @ id @ X2 @ id )
| ( '#sk31' @ id
@ ( '#sk124'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ id
@ X2 )
@ id )
| '#form922' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl228]) ).
thf(zip_derived_cl4148_011,plain,
! [X3: term] :
( ( '#l_lift5555' @ X3 )
= ( '#sk31' @ id @ X3 @ id ) ),
define([status(thm)]) ).
thf(zip_derived_cl4152,plain,
! [X2: term] :
( ~ ( '#sk31' @ id @ X2 @ id )
| ( '#sk31' @ id @ ( '#sk124' @ '#l_lift5555' @ id @ X2 ) @ id )
| '#form922' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl231,zip_derived_cl4148]) ).
thf(zip_derived_cl224,plain,
( ~ ( '#sk31' @ id
@ ( lam
@ ( '#sk124'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ sh
@ one ) )
@ id )
| '#form922' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl220]) ).
thf(zip_derived_cl4148_012,plain,
! [X3: term] :
( ( '#l_lift5555' @ X3 )
= ( '#sk31' @ id @ X3 @ id ) ),
define([status(thm)]) ).
thf(zip_derived_cl4151,plain,
( ~ ( '#sk31' @ id @ ( lam @ ( '#sk124' @ '#l_lift5555' @ sh @ one ) ) @ id )
| '#form922' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl224,zip_derived_cl4148]) ).
thf(zip_derived_cl219,plain,
( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( sub
@ ( '#sk124'
@ ^ [Y3: term] : ( '#sk31' @ id @ Y3 @ id )
@ Y0
@ Y1 )
@ Y2 )
= ( '#sk124'
@ ^ [Y3: term] : ( '#sk31' @ id @ Y3 @ id )
@ ( comp @ Y0 @ Y2 )
@ ( sub @ Y1 @ Y2 ) ) ) ) ) )
| '#form922' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl216]) ).
thf(zip_derived_cl222,plain,
! [X2: subst] :
( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( sub
@ ( '#sk124'
@ ^ [Y2: term] : ( '#sk31' @ id @ Y2 @ id )
@ X2
@ Y0 )
@ Y1 )
= ( '#sk124'
@ ^ [Y2: term] : ( '#sk31' @ id @ Y2 @ id )
@ ( comp @ X2 @ Y1 )
@ ( sub @ Y0 @ Y1 ) ) ) ) )
| '#form922' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl219]) ).
thf(zip_derived_cl227,plain,
! [X2: subst,X4: term] :
( ( !!
@ ^ [Y0: subst] :
( ( sub
@ ( '#sk124'
@ ^ [Y1: term] : ( '#sk31' @ id @ Y1 @ id )
@ X2
@ X4 )
@ Y0 )
= ( '#sk124'
@ ^ [Y1: term] : ( '#sk31' @ id @ Y1 @ id )
@ ( comp @ X2 @ Y0 )
@ ( sub @ X4 @ Y0 ) ) ) )
| '#form922' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl222]) ).
thf(zip_derived_cl230,plain,
! [X2: subst,X4: term,X6: subst] :
( ( ( sub
@ ( '#sk124'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ X2
@ X4 )
@ X6 )
= ( '#sk124'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( comp @ X2 @ X6 )
@ ( sub @ X4 @ X6 ) ) )
| '#form922' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl227]) ).
thf(zip_derived_cl233,plain,
! [X2: subst,X4: term,X6: subst] :
( ( ( sub
@ ( '#sk124'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ X2
@ X4 )
@ X6 )
= ( '#sk124'
@ ^ [Y0: term] : ( '#sk31' @ id @ Y0 @ id )
@ ( comp @ X2 @ X6 )
@ ( sub @ X4 @ X6 ) ) )
| '#form922' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl230]) ).
thf(zip_derived_cl4148_013,plain,
! [X3: term] :
( ( '#l_lift5555' @ X3 )
= ( '#sk31' @ id @ X3 @ id ) ),
define([status(thm)]) ).
thf(zip_derived_cl4148_014,plain,
! [X3: term] :
( ( '#l_lift5555' @ X3 )
= ( '#sk31' @ id @ X3 @ id ) ),
define([status(thm)]) ).
thf(zip_derived_cl4153,plain,
! [X2: subst,X4: term,X6: subst] :
( ( ( sub @ ( '#sk124' @ '#l_lift5555' @ X2 @ X4 ) @ X6 )
= ( '#sk124' @ '#l_lift5555' @ ( comp @ X2 @ X6 ) @ ( sub @ X4 @ X6 ) ) )
| '#form922' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl233,zip_derived_cl4148,zip_derived_cl4148]) ).
thf(zip_derived_cl44,plain,
( !!
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( '#sk31' @ id @ Y0 @ id ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl52,plain,
! [X2: term] :
( ( var @ ( sub @ X2 @ id ) )
=> ( '#sk31' @ id @ X2 @ id ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl65,plain,
! [X2: term] :
( ~ ( var @ ( sub @ X2 @ id ) )
| ( '#sk31' @ id @ X2 @ id ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl11,plain,
( !!
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl15,plain,
! [X2: term] :
( ( sub @ X2 @ id )
= X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl20,plain,
! [X2: term] :
( ( sub @ X2 @ id )
= X2 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl18_015,plain,
! [X2: term > $o,X4: term] :
( ( '#sk5' @ X2 @ X4 )
= ( X2 @ X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl126,plain,
! [X2: term] :
( ~ ( '#sk5' @ var @ X2 )
| ( '#sk31' @ id @ X2 @ id ) ),
inference(demod,[status(thm)],[zip_derived_cl65,zip_derived_cl20,zip_derived_cl18]) ).
thf(zip_derived_cl134_016,plain,
! [X0: term > $o] :
( ~ ( '#form632' @ X0 )
| ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk5' @ X0 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl135,plain,
! [X0: term > $o] :
( ~ ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
| ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( '#sk5' @ X0 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( '#sk5' @ X0 @ Y0 ) ) )
| ~ ( '#form632' @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl134]) ).
thf(zip_derived_cl57_017,plain,
! [X2: term > $o] :
( ~ ( '#form178' @ X2 )
| ( ( !!
@ ^ [Y0: term] :
( ( !!
@ ^ [Y1: term] :
( ( X2 @ Y1 )
=> ( X2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X2 @ ( lam @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: term] : ( X2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl138,plain,
! [X0: term > $o] :
( ( '#form178' @ ( '#sk5' @ X0 ) )
| ~ ( '#form632' @ X0 )
| ~ ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk5' @ X0 @ Y0 )
=> ( ( '#sk5' @ X0 @ Y1 )
=> ( '#sk5' @ X0 @ ( ap @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl135,zip_derived_cl57]) ).
thf(zip_derived_cl139,plain,
! [X0: term > $o] :
( ~ ( !!
@ ^ [Y0: term] :
( ( '#sk5' @ X0 @ ( '#sk103' @ ( '#sk5' @ X0 ) ) )
=> ( ( '#sk5' @ X0 @ Y0 )
=> ( '#sk5' @ X0 @ ( ap @ ( '#sk103' @ ( '#sk5' @ X0 ) ) @ Y0 ) ) ) ) )
| ~ ( '#form632' @ X0 )
| ( '#form178' @ ( '#sk5' @ X0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl138]) ).
thf(zip_derived_cl140,plain,
! [X0: term > $o] :
( ~ ( ( '#sk5' @ X0 @ ( '#sk103' @ ( '#sk5' @ X0 ) ) )
=> ( ( '#sk5' @ X0 @ ( '#sk135' @ ( '#sk5' @ X0 ) ) )
=> ( '#sk5' @ X0 @ ( ap @ ( '#sk103' @ ( '#sk5' @ X0 ) ) @ ( '#sk135' @ ( '#sk5' @ X0 ) ) ) ) ) )
| ( '#form178' @ ( '#sk5' @ X0 ) )
| ~ ( '#form632' @ X0 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl139]) ).
thf(zip_derived_cl141,plain,
! [X0: term > $o] :
( ( '#sk5' @ X0 @ ( '#sk103' @ ( '#sk5' @ X0 ) ) )
| ~ ( '#form632' @ X0 )
| ( '#form178' @ ( '#sk5' @ X0 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl140]) ).
thf(zip_derived_cl122,plain,
! [X2: subst > term > term] :
( ~ ( '#sk31' @ id @ ( X2 @ id @ ( '#sk500' @ X2 ) ) @ id )
| ( '#sk31' @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id )
| ( ( sub @ ( X2 @ ( '#sk372' @ X2 ) @ ( '#sk405' @ X2 ) ) @ ( '#sk428' @ X2 ) )
!= ( X2 @ ( comp @ ( '#sk372' @ X2 ) @ ( '#sk428' @ X2 ) ) @ ( sub @ ( '#sk405' @ X2 ) @ ( '#sk428' @ X2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl120]) ).
thf(zip_derived_cl142,plain,
! [X0: term > $o] :
( ~ ( ( '#sk5' @ X0 @ ( '#sk135' @ ( '#sk5' @ X0 ) ) )
=> ( '#sk5' @ X0 @ ( ap @ ( '#sk103' @ ( '#sk5' @ X0 ) ) @ ( '#sk135' @ ( '#sk5' @ X0 ) ) ) ) )
| ~ ( '#form632' @ X0 )
| ( '#form178' @ ( '#sk5' @ X0 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl140]) ).
thf(zip_derived_cl143,plain,
! [X0: term > $o] :
( ( '#sk5' @ X0 @ ( '#sk135' @ ( '#sk5' @ X0 ) ) )
| ( '#form178' @ ( '#sk5' @ X0 ) )
| ~ ( '#form632' @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl142]) ).
thf(zip_derived_cl4148_018,plain,
! [X3: term] :
( ( '#l_lift5555' @ X3 )
= ( '#sk31' @ id @ X3 @ id ) ),
define([status(thm)]) ).
thf(zip_derived_cl18_019,plain,
! [X2: term > $o,X4: term] :
( ( '#sk5' @ X2 @ X4 )
= ( X2 @ X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl53,plain,
( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( '#sk31' @ id @ Y0 @ id )
=> ( ( '#sk31' @ id @ Y1 @ id )
=> ( '#sk31' @ id @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl66,plain,
! [X2: term] :
( !!
@ ^ [Y0: term] :
( ( '#sk31' @ id @ X2 @ id )
=> ( ( '#sk31' @ id @ Y0 @ id )
=> ( '#sk31' @ id @ ( ap @ ( sub @ X2 @ id ) @ Y0 ) @ id ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl81,plain,
! [X2: term,X4: term] :
( ( '#sk31' @ id @ X2 @ id )
=> ( ( '#sk31' @ id @ X4 @ id )
=> ( '#sk31' @ id @ ( ap @ ( sub @ X2 @ id ) @ X4 ) @ id ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl98,plain,
! [X2: term,X4: term] :
( ~ ( '#sk31' @ id @ X2 @ id )
| ( ( '#sk31' @ id @ X4 @ id )
=> ( '#sk31' @ id @ ( ap @ ( sub @ X2 @ id ) @ X4 ) @ id ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl106,plain,
! [X2: term,X4: term] :
( ~ ( '#sk31' @ id @ X4 @ id )
| ( '#sk31' @ id @ ( ap @ ( sub @ X2 @ id ) @ X4 ) @ id )
| ~ ( '#sk31' @ id @ X2 @ id ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl98]) ).
thf(zip_derived_cl20_020,plain,
! [X2: term] :
( ( sub @ X2 @ id )
= X2 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl145,plain,
! [X2: term,X4: term] :
( ~ ( '#sk31' @ id @ X4 @ id )
| ( '#sk31' @ id @ ( ap @ X2 @ X4 ) @ id )
| ~ ( '#sk31' @ id @ X2 @ id ) ),
inference(demod,[status(thm)],[zip_derived_cl106,zip_derived_cl20]) ).
thf(zip_derived_cl144,plain,
! [X0: term > $o] :
( ~ ( '#sk5' @ X0 @ ( ap @ ( '#sk103' @ ( '#sk5' @ X0 ) ) @ ( '#sk135' @ ( '#sk5' @ X0 ) ) ) )
| ( '#form178' @ ( '#sk5' @ X0 ) )
| ~ ( '#form632' @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl142]) ).
thf(zip_derived_cl4166,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl83,zip_derived_cl101,zip_derived_cl115,zip_derived_cl137,zip_derived_cl4154,zip_derived_cl4155,zip_derived_cl136,zip_derived_cl121,zip_derived_cl4152,zip_derived_cl4151,zip_derived_cl4153,zip_derived_cl126,zip_derived_cl141,zip_derived_cl122,zip_derived_cl143,zip_derived_cl4148,zip_derived_cl18,zip_derived_cl145,zip_derived_cl144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.67 % Problem : ALG269^3 : TPTP v9.2.0. Bugfixed v5.2.0.
% 0.07/0.68 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.lNARy0oRJo true
% 0.08/1.07 % Computer : n029.cluster.edu
% 0.08/1.07 % Model : x86_64 x86_64
% 0.08/1.07 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/1.07 % Memory : 8042.1875MB
% 0.08/1.07 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/1.07 % CPULimit : 300
% 0.08/1.07 % WCLimit : 300
% 0.08/1.07 % DateTime : Wed Oct 1 17:00:54 EDT 2025
% 0.10/1.08 % CPUTime :
% 0.10/1.08 % Running portfolio for 300 s
% 0.10/1.08 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/1.09 % Number of cores: 8
% 0.10/1.11 % Python version: Python 3.6.8
% 0.10/1.12 % Running in HO mode
% 0.40/1.73 % Total configuration time : 828
% 0.40/1.73 % Estimated wc time : 1656
% 0.40/1.73 % Estimated cpu time (8 cpus) : 207.0
% 0.71/1.90 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.08/2.11 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.10/2.13 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.10/2.15 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.10/2.16 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.10/2.18 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.48/2.22 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.48/2.24 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.77/2.42 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 29.76/9.19 % Solved by lams/20_acsne_simpl.sh.
% 29.76/9.19 % done 218 iterations in 6.740s
% 29.76/9.19 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 29.76/9.19 % SZS output start Refutation
% See solution above
% 29.76/9.20
% 29.76/9.20
% 29.76/9.20 % Terminating...
% 30.09/9.43 % Runner terminated.
% 30.09/9.45 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------