%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM729^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.63GyPVdFoq 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 04:48:09 PM UTC 2025
% Result : Theorem 130.36s 17.12s
% Output : Refutation 130.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 98
% Syntax : Number of formulae : 133 ( 108 unt; 0 typ; 0 def)
% Number of atoms : 644 ( 331 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 2607 ( 186 ~; 20 |; 0 &;2382 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 13 con; 0-5 aty)
% Number of variables : 440 ( 322 ^; 118 !; 0 ?; 440 :)
% Comments :
%------------------------------------------------------------------------------
thf(pair1_type,type,
pair1: $i > $i > $i > $i ).
thf(n_1_type,type,
n_1: $i ).
thf(ind_type,type,
ind: $i > ( $i > $o ) > $i ).
thf(prop1_type,type,
prop1: $o > $i > $i > $i > $i > $o ).
thf(nat_type,type,
nat: $i ).
thf(lessis_type,type,
lessis: $i > $i > $o ).
thf(is_of_type,type,
is_of: $i > ( $i > $o ) > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(d_Sep_type,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(n_2_type,type,
n_2: $i ).
thf(n_fr_type,type,
n_fr: $i > $i > $i ).
thf('#l_lift7193_type',type,
'#l_lift7193': $i > $i > $i > $i ).
thf(d_Sigma_type,type,
d_Sigma: $i > ( $i > $i ) > $i ).
thf(ap_type,type,
ap: $i > $i > $i ).
thf(times_type,type,
times: $i > $i ).
thf(emptyset_type,type,
emptyset: $i ).
thf(sk__7_type,type,
sk__7: $i ).
thf(n_is_type,type,
n_is: $i > $i > $o ).
thf(n_1t_type,type,
n_1t: $i ).
thf(frac_type,type,
frac: $i ).
thf('#l_lift7192_type',type,
'#l_lift7192': $i > $i > $i > $i ).
thf(n_2t_type,type,
n_2t: $i ).
thf('#l_lift7190_type',type,
'#l_lift7190': $i > $o ).
thf(n_ts_type,type,
n_ts: $i > $i > $i ).
thf(n_eq_type,type,
n_eq: $i > $i > $o ).
thf(omega_type,type,
omega: $i ).
thf('#l_lift7188_type',type,
'#l_lift7188': $i > $i > $o ).
thf(all_of_type,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(num_type,type,
num: $i > $i ).
thf('#l_lift7191_type',type,
'#l_lift7191': $i > $o ).
thf(d_1to_type,type,
d_1to: $i > $i ).
thf(sk__6_type,type,
sk__6: $i ).
thf(ordsucc_type,type,
ordsucc: $i > $i ).
thf(outn_type,type,
outn: $i > $i > $i ).
thf(sk__5_type,type,
sk__5: $i ).
thf(first1_type,type,
first1: $i > $i > $i ).
thf(den_type,type,
den: $i > $i ).
thf(second1_type,type,
second1: $i > $i > $i ).
thf(e_is_type,type,
e_is: $i > $i > $i > $o ).
thf(ite_type,type,
ite: $o > $i > $i > $i > $i ).
thf(n_pl_type,type,
n_pl: $i > $i > $i ).
thf(def_n_eq,axiom,
( n_eq
= ( ^ [X0: $i,X1: $i] : ( n_is @ ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) ) ) ).
thf(def_den,axiom,
( den
= ( second1 @ nat ) ) ).
thf(def_second1,axiom,
( second1
= ( ^ [X0: $i,X1: $i] : ( ap @ X1 @ n_2t ) ) ) ).
thf('0',plain,
( second1
= ( ^ [X0: $i,X1: $i] : ( ap @ X1 @ n_2t ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_second1]) ).
thf('1',plain,
( second1
= ( ^ [V_1: $i,V_2: $i] : ( ap @ V_2 @ n_2t ) ) ),
define([status(thm)]) ).
thf(def_nat,axiom,
( nat
= ( d_Sep @ omega
@ ^ [X0: $i] : ( X0 != emptyset ) ) ) ).
thf('2',plain,
( nat
= ( d_Sep @ omega
@ ^ [X0: $i] : ( X0 != emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_nat]) ).
thf('3',plain,
( nat
= ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) ),
define([status(thm)]) ).
thf('4',plain,
( den
= ( second1 @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_den,'1','3']) ).
thf('5',plain,
( den
= ( second1 @ nat ) ),
define([status(thm)]) ).
thf(def_num,axiom,
( num
= ( first1 @ nat ) ) ).
thf(def_first1,axiom,
( first1
= ( ^ [X0: $i,X1: $i] : ( ap @ X1 @ n_1t ) ) ) ).
thf(def_n_1t,axiom,
( n_1t
= ( outn @ n_2 @ n_1 ) ) ).
thf(def_n_2,axiom,
( n_2
= ( n_pl @ n_1 @ n_1 ) ) ).
thf(def_n_1,axiom,
( n_1
= ( ordsucc @ emptyset ) ) ).
thf('6',plain,
( n_1
= ( ordsucc @ emptyset ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_1]) ).
thf('7',plain,
( n_1
= ( ordsucc @ emptyset ) ),
define([status(thm)]) ).
thf('8',plain,
( n_2
= ( n_pl @ n_1 @ n_1 ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_2,'7']) ).
thf('9',plain,
( n_2
= ( n_pl @ n_1 @ n_1 ) ),
define([status(thm)]) ).
thf('10',plain,
( n_1t
= ( outn @ n_2 @ n_1 ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_1t,'9','7']) ).
thf('11',plain,
( n_1t
= ( outn @ n_2 @ n_1 ) ),
define([status(thm)]) ).
thf('12',plain,
( first1
= ( ^ [X0: $i,X1: $i] : ( ap @ X1 @ n_1t ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_first1,'11','9','7']) ).
thf('13',plain,
( first1
= ( ^ [V_1: $i,V_2: $i] : ( ap @ V_2 @ n_1t ) ) ),
define([status(thm)]) ).
thf('14',plain,
( num
= ( first1 @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_num,'13','11','3']) ).
thf('15',plain,
( num
= ( first1 @ nat ) ),
define([status(thm)]) ).
thf(def_n_ts,axiom,
( n_ts
= ( ^ [X0: $i] : ( ap @ ( times @ X0 ) ) ) ) ).
thf('16',plain,
( n_ts
= ( ^ [X0: $i] : ( ap @ ( times @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_ts]) ).
thf('17',plain,
( n_ts
= ( ^ [V_1: $i] : ( ap @ ( times @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(def_n_is,axiom,
( n_is
= ( e_is @ nat ) ) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ) ).
thf('18',plain,
( e_is
= ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_e_is]) ).
thf('19',plain,
( e_is
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( V_2 = V_3 ) ) ),
define([status(thm)]) ).
thf('20',plain,
( n_is
= ( e_is @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_is,'3','19']) ).
thf('21',plain,
( n_is
= ( e_is @ nat ) ),
define([status(thm)]) ).
thf('22',plain,
( n_eq
= ( ^ [X0: $i,X1: $i] : ( n_is @ ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_eq,'5','15','1','13','11','9','17','7','21','3','19']) ).
thf('23',plain,
( n_eq
= ( ^ [V_1: $i,V_2: $i] : ( n_is @ ( n_ts @ ( num @ V_1 ) @ ( den @ V_2 ) ) @ ( n_ts @ ( num @ V_2 ) @ ( den @ V_1 ) ) ) ) ),
define([status(thm)]) ).
thf(def_n_fr,axiom,
( n_fr
= ( pair1 @ nat ) ) ).
thf(def_pair1,axiom,
( pair1
= ( ^ [X0: $i,X1: $i,X2: $i] :
( d_Sigma @ ( d_1to @ n_2 )
@ ^ [X3: $i] : ( ite @ ( e_is @ ( d_1to @ n_2 ) @ X3 @ n_1t ) @ X0 @ X1 @ X2 ) ) ) ) ).
thf(def_d_1to,axiom,
( d_1to
= ( ^ [X0: $i] :
( d_Sep @ nat
@ ^ [X1: $i] : ( lessis @ X1 @ X0 ) ) ) ) ).
thf('24',plain,
( d_1to
= ( ^ [X0: $i] :
( d_Sep @ nat
@ ^ [X1: $i] : ( lessis @ X1 @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_1to,'3']) ).
thf('25',plain,
( d_1to
= ( ^ [V_1: $i] :
( d_Sep @ nat
@ ^ [V_2: $i] : ( lessis @ V_2 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(def_ite,axiom,
( ite
= ( ^ [X0: $o,X1: $i,X2: $i,X3: $i] : ( ind @ X1 @ ( prop1 @ X0 @ X1 @ X2 @ X3 ) ) ) ) ).
thf('26',plain,
( ite
= ( ^ [X0: $o,X1: $i,X2: $i,X3: $i] : ( ind @ X1 @ ( prop1 @ X0 @ X1 @ X2 @ X3 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_ite]) ).
thf('27',plain,
( ite
= ( ^ [V_1: $o,V_2: $i,V_3: $i,V_4: $i] : ( ind @ V_2 @ ( prop1 @ V_1 @ V_2 @ V_3 @ V_4 ) ) ) ),
define([status(thm)]) ).
thf('28',plain,
( pair1
= ( ^ [X0: $i,X1: $i,X2: $i] :
( d_Sigma @ ( d_1to @ n_2 )
@ ^ [X3: $i] : ( ite @ ( e_is @ ( d_1to @ n_2 ) @ X3 @ n_1t ) @ X0 @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_pair1,'11','9','25','7','3','27','19']) ).
thf('29',plain,
( pair1
= ( ^ [V_1: $i,V_2: $i,V_3: $i] :
( d_Sigma @ ( d_1to @ n_2 )
@ ^ [V_4: $i] : ( ite @ ( e_is @ ( d_1to @ n_2 ) @ V_4 @ n_1t ) @ V_1 @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('30',plain,
( n_fr
= ( pair1 @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_fr,'29','11','9','25','7','3','27','19']) ).
thf('31',plain,
( n_fr
= ( pair1 @ nat ) ),
define([status(thm)]) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ) ).
thf('32',plain,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_all_of]) ).
thf('33',plain,
( all_of
= ( ^ [V_1: $i > $o,V_2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ V_1 )
=> ( V_2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(satz40c,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] : ( n_eq @ ( n_fr @ ( n_ts @ X0 @ X2 ) @ ( n_ts @ X1 @ X2 ) ) @ ( n_fr @ X0 @ X1 ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( is_of @ X4
@ ^ [V_1: $i] :
( in @ V_1
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
=> ! [X6: $i] :
( ( is_of @ X6
@ ^ [V_3: $i] :
( in @ V_3
@ ( d_Sep @ omega
@ ^ [V_4: $i] : ( V_4 != emptyset ) ) ) )
=> ! [X8: $i] :
( ( is_of @ X8
@ ^ [V_5: $i] :
( in @ V_5
@ ( d_Sep @ omega
@ ^ [V_6: $i] : ( V_6 != emptyset ) ) ) )
=> ( ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_7: $i] : ( V_7 != emptyset ) )
@ ^ [V_8: $i] : ( lessis @ V_8 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_9: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_10: $i] : ( V_10 != emptyset ) )
@ ( prop1
@ ( V_9
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_11: $i] : ( V_11 != emptyset ) )
@ ( ap @ ( times @ X4 ) @ X8 )
@ ( ap @ ( times @ X6 ) @ X8 ) ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_12: $i] : ( V_12 != emptyset ) )
@ ^ [V_13: $i] : ( lessis @ V_13 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_14: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_15: $i] : ( V_15 != emptyset ) )
@ ( prop1
@ ( V_14
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_16: $i] : ( V_16 != emptyset ) )
@ X4
@ X6 ) ) )
@ n_2t ) )
= ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_17: $i] : ( V_17 != emptyset ) )
@ ^ [V_18: $i] : ( lessis @ V_18 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_19: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_20: $i] : ( V_20 != emptyset ) )
@ ( prop1
@ ( V_19
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_21: $i] : ( V_21 != emptyset ) )
@ X4
@ X6 ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_22: $i] : ( V_22 != emptyset ) )
@ ^ [V_23: $i] : ( lessis @ V_23 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_24: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_25: $i] : ( V_25 != emptyset ) )
@ ( prop1
@ ( V_24
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_26: $i] : ( V_26 != emptyset ) )
@ ( ap @ ( times @ X4 ) @ X8 )
@ ( ap @ ( times @ X6 ) @ X8 ) ) ) )
@ n_2t ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( is_of @ X4
@ ^ [V_1: $i] :
( in @ V_1
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
=> ! [X6: $i] :
( ( is_of @ X6
@ ^ [V_3: $i] :
( in @ V_3
@ ( d_Sep @ omega
@ ^ [V_4: $i] : ( V_4 != emptyset ) ) ) )
=> ! [X8: $i] :
( ( is_of @ X8
@ ^ [V_5: $i] :
( in @ V_5
@ ( d_Sep @ omega
@ ^ [V_6: $i] : ( V_6 != emptyset ) ) ) )
=> ( ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_7: $i] : ( V_7 != emptyset ) )
@ ^ [V_8: $i] : ( lessis @ V_8 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_9: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_10: $i] : ( V_10 != emptyset ) )
@ ( prop1
@ ( V_9
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_11: $i] : ( V_11 != emptyset ) )
@ ( ap @ ( times @ X4 ) @ X8 )
@ ( ap @ ( times @ X6 ) @ X8 ) ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_12: $i] : ( V_12 != emptyset ) )
@ ^ [V_13: $i] : ( lessis @ V_13 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_14: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_15: $i] : ( V_15 != emptyset ) )
@ ( prop1
@ ( V_14
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_16: $i] : ( V_16 != emptyset ) )
@ X4
@ X6 ) ) )
@ n_2t ) )
= ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_17: $i] : ( V_17 != emptyset ) )
@ ^ [V_18: $i] : ( lessis @ V_18 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_19: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_20: $i] : ( V_20 != emptyset ) )
@ ( prop1
@ ( V_19
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_21: $i] : ( V_21 != emptyset ) )
@ X4
@ X6 ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_22: $i] : ( V_22 != emptyset ) )
@ ^ [V_23: $i] : ( lessis @ V_23 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_24: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_25: $i] : ( V_25 != emptyset ) )
@ ( prop1
@ ( V_24
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_26: $i] : ( V_26 != emptyset ) )
@ ( ap @ ( times @ X4 ) @ X8 )
@ ( ap @ ( times @ X6 ) @ X8 ) ) ) )
@ n_2t ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl136,plain,
( is_of @ sk__6
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(refis,axiom,
! [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ X0 )
@ ^ [X1: $i] : ( e_is @ X0 @ X1 @ X1 ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i,X6: $i] :
( ( is_of @ X6
@ ^ [V_1: $i] : ( in @ V_1 @ X4 ) )
=> ( X6 = X6 ) ) ).
thf(zip_derived_cl13,plain,
! [X0: $i,X1: $i] :
( $true
| ~ ( is_of @ X0
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl7408,plain,
! [X1: $i,X2: $i] :
( ( '#l_lift7188' @ X1 @ X2 )
= ( in @ X2 @ X1 ) ),
define([status(thm)]) ).
thf(n_ax4,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( n_is @ ( ordsucc @ X0 ) @ ( ordsucc @ X1 ) )
=> ( n_is @ X0 @ X1 ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i] :
( ( is_of @ X4
@ ^ [V_1: $i] :
( in @ V_1
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
=> ! [X6: $i] :
( ( is_of @ X6
@ ^ [V_3: $i] :
( in @ V_3
@ ( d_Sep @ omega
@ ^ [V_4: $i] : ( V_4 != emptyset ) ) ) )
=> ( ( ( ordsucc @ X4 )
= ( ordsucc @ X6 ) )
=> ( X4 = X6 ) ) ) ) ).
thf(zip_derived_cl17,plain,
! [X0: $i,X1: $i] :
( ~ ( is_of @ X0
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ( X1 = X0 )
| ( ( ordsucc @ X1 )
!= ( ordsucc @ X0 ) )
| ~ ( is_of @ X1
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl7414,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7538,plain,
is_of @ sk__6 @ ( '#l_lift7188' @ ( d_Sep @ omega @ '#l_lift7190' ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl136,zip_derived_cl7408,zip_derived_cl7414]) ).
thf(zip_derived_cl133,plain,
( is_of @ sk__5
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl7408_001,plain,
! [X1: $i,X2: $i] :
( ( '#l_lift7188' @ X1 @ X2 )
= ( in @ X2 @ X1 ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_002,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7535,plain,
is_of @ sk__5 @ ( '#l_lift7188' @ ( d_Sep @ omega @ '#l_lift7190' ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl133,zip_derived_cl7408,zip_derived_cl7414]) ).
thf(zip_derived_cl134,plain,
( is_of @ sk__7
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl7408_003,plain,
! [X1: $i,X2: $i] :
( ( '#l_lift7188' @ X1 @ X2 )
= ( in @ X2 @ X1 ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_004,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7536,plain,
is_of @ sk__7 @ ( '#l_lift7188' @ ( d_Sep @ omega @ '#l_lift7190' ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl134,zip_derived_cl7408,zip_derived_cl7414]) ).
thf(zip_derived_cl135,plain,
( ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( ap @ ( times @ sk__5 ) @ sk__7 )
@ ( ap @ ( times @ sk__6 ) @ sk__7 ) ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ sk__5
@ sk__6 ) ) )
@ n_2t ) )
!= ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ sk__5
@ sk__6 ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( ap @ ( times @ sk__5 ) @ sk__7 )
@ ( ap @ ( times @ sk__6 ) @ sk__7 ) ) ) )
@ n_2t ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl7414_005,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(satz40,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ frac )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_eq @ X0 @ ( n_fr @ ( n_ts @ ( num @ X0 ) @ X1 ) @ ( n_ts @ ( den @ X0 ) @ X1 ) ) ) ) ) ).
thf(zf_stmt_4,axiom,
! [X4: $i] :
( ( is_of @ X4
@ ^ [V_1: $i] : ( in @ V_1 @ frac ) )
=> ! [X6: $i] :
( ( is_of @ X6
@ ^ [V_2: $i] :
( in @ V_2
@ ( d_Sep @ omega
@ ^ [V_3: $i] : ( V_3 != emptyset ) ) ) )
=> ( ( ap @ ( times @ ( ap @ X4 @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_4: $i] : ( V_4 != emptyset ) )
@ ^ [V_5: $i] : ( lessis @ V_5 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_6: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_7: $i] : ( V_7 != emptyset ) )
@ ( prop1
@ ( V_6
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_8: $i] : ( V_8 != emptyset ) )
@ ( ap @ ( times @ ( ap @ X4 @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) ) @ X6 )
@ ( ap @ ( times @ ( ap @ X4 @ n_2t ) ) @ X6 ) ) ) )
@ n_2t ) )
= ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_9: $i] : ( V_9 != emptyset ) )
@ ^ [V_10: $i] : ( lessis @ V_10 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_11: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_12: $i] : ( V_12 != emptyset ) )
@ ( prop1
@ ( V_11
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_13: $i] : ( V_13 != emptyset ) )
@ ( ap @ ( times @ ( ap @ X4 @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) ) @ X6 )
@ ( ap @ ( times @ ( ap @ X4 @ n_2t ) ) @ X6 ) ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap @ X4 @ n_2t ) ) ) ) ) ).
thf(zip_derived_cl130,plain,
! [X0: $i,X1: $i] :
( ~ ( is_of @ X0
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ( ( ap @ ( times @ ( ap @ X1 @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( ap @ ( times @ ( ap @ X1 @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) ) @ X0 )
@ ( ap @ ( times @ ( ap @ X1 @ n_2t ) ) @ X0 ) ) ) )
@ n_2t ) )
= ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( ap @ ( times @ ( ap @ X1 @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) ) @ X0 )
@ ( ap @ ( times @ ( ap @ X1 @ n_2t ) ) @ X0 ) ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap @ X1 @ n_2t ) ) )
| ~ ( is_of @ X1
@ ^ [Y0: $i] : ( in @ Y0 @ frac ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl7528,plain,
! [X2: $i] :
( ( '#l_lift7191' @ X2 )
= ( lessis @ X2 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ),
define([status(thm)]) ).
thf(satz40b,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] : ( n_eq @ ( n_fr @ X0 @ X1 ) @ ( n_fr @ ( n_ts @ X0 @ X2 ) @ ( n_ts @ X1 @ X2 ) ) ) ) ) ) ).
thf(zf_stmt_5,axiom,
! [X4: $i] :
( ( is_of @ X4
@ ^ [V_1: $i] :
( in @ V_1
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
=> ! [X6: $i] :
( ( is_of @ X6
@ ^ [V_3: $i] :
( in @ V_3
@ ( d_Sep @ omega
@ ^ [V_4: $i] : ( V_4 != emptyset ) ) ) )
=> ! [X8: $i] :
( ( is_of @ X8
@ ^ [V_5: $i] :
( in @ V_5
@ ( d_Sep @ omega
@ ^ [V_6: $i] : ( V_6 != emptyset ) ) ) )
=> ( ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_7: $i] : ( V_7 != emptyset ) )
@ ^ [V_8: $i] : ( lessis @ V_8 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_9: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_10: $i] : ( V_10 != emptyset ) )
@ ( prop1
@ ( V_9
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_11: $i] : ( V_11 != emptyset ) )
@ X4
@ X6 ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_12: $i] : ( V_12 != emptyset ) )
@ ^ [V_13: $i] : ( lessis @ V_13 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_14: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_15: $i] : ( V_15 != emptyset ) )
@ ( prop1
@ ( V_14
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_16: $i] : ( V_16 != emptyset ) )
@ ( ap @ ( times @ X4 ) @ X8 )
@ ( ap @ ( times @ X6 ) @ X8 ) ) ) )
@ n_2t ) )
= ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_17: $i] : ( V_17 != emptyset ) )
@ ^ [V_18: $i] : ( lessis @ V_18 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_19: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_20: $i] : ( V_20 != emptyset ) )
@ ( prop1
@ ( V_19
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_21: $i] : ( V_21 != emptyset ) )
@ ( ap @ ( times @ X4 ) @ X8 )
@ ( ap @ ( times @ X6 ) @ X8 ) ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [V_22: $i] : ( V_22 != emptyset ) )
@ ^ [V_23: $i] : ( lessis @ V_23 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [V_24: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [V_25: $i] : ( V_25 != emptyset ) )
@ ( prop1
@ ( V_24
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [V_26: $i] : ( V_26 != emptyset ) )
@ X4
@ X6 ) ) )
@ n_2t ) ) ) ) ) ) ).
thf(zip_derived_cl132,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( is_of @ X0
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ( ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ X1
@ X0 ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( ap @ ( times @ X1 ) @ X2 )
@ ( ap @ ( times @ X0 ) @ X2 ) ) ) )
@ n_2t ) )
= ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( ap @ ( times @ X1 ) @ X2 )
@ ( ap @ ( times @ X0 ) @ X2 ) ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ X1
@ X0 ) ) )
@ n_2t ) ) )
| ~ ( is_of @ X2
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ~ ( is_of @ X1
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_5]) ).
thf(zip_derived_cl7532,plain,
! [X0: $i,X1: $i,X3: $i] :
( ( '#l_lift7193' @ X0 @ X1 @ X3 )
= ( ind @ ( d_Sep @ omega @ '#l_lift7190' )
@ ( prop1
@ ( X3
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega @ '#l_lift7190' )
@ X1
@ X0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_006,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_007,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_008,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7528_009,plain,
! [X2: $i] :
( ( '#l_lift7191' @ X2 )
= ( lessis @ X2 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7532_010,plain,
! [X0: $i,X1: $i,X3: $i] :
( ( '#l_lift7193' @ X0 @ X1 @ X3 )
= ( ind @ ( d_Sep @ omega @ '#l_lift7190' )
@ ( prop1
@ ( X3
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega @ '#l_lift7190' )
@ X1
@ X0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_011,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_012,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_013,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7528_014,plain,
! [X2: $i] :
( ( '#l_lift7191' @ X2 )
= ( lessis @ X2 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7532_015,plain,
! [X0: $i,X1: $i,X3: $i] :
( ( '#l_lift7193' @ X0 @ X1 @ X3 )
= ( ind @ ( d_Sep @ omega @ '#l_lift7190' )
@ ( prop1
@ ( X3
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega @ '#l_lift7190' )
@ X1
@ X0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_016,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_017,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_018,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7528_019,plain,
! [X2: $i] :
( ( '#l_lift7191' @ X2 )
= ( lessis @ X2 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7532_020,plain,
! [X0: $i,X1: $i,X3: $i] :
( ( '#l_lift7193' @ X0 @ X1 @ X3 )
= ( ind @ ( d_Sep @ omega @ '#l_lift7190' )
@ ( prop1
@ ( X3
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega @ '#l_lift7190' )
@ X1
@ X0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_021,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_022,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7537,plain,
( ( ap @ ( times @ ( ap @ ( d_Sigma @ ( d_Sep @ ( d_Sep @ omega @ '#l_lift7190' ) @ '#l_lift7191' ) @ ( '#l_lift7193' @ ( ap @ ( times @ sk__6 ) @ sk__7 ) @ ( ap @ ( times @ sk__5 ) @ sk__7 ) ) ) @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) ) @ ( ap @ ( d_Sigma @ ( d_Sep @ ( d_Sep @ omega @ '#l_lift7190' ) @ '#l_lift7191' ) @ ( '#l_lift7193' @ sk__6 @ sk__5 ) ) @ n_2t ) )
!= ( ap @ ( times @ ( ap @ ( d_Sigma @ ( d_Sep @ ( d_Sep @ omega @ '#l_lift7190' ) @ '#l_lift7191' ) @ ( '#l_lift7193' @ sk__6 @ sk__5 ) ) @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) ) @ ( ap @ ( d_Sigma @ ( d_Sep @ ( d_Sep @ omega @ '#l_lift7190' ) @ '#l_lift7191' ) @ ( '#l_lift7193' @ ( ap @ ( times @ sk__6 ) @ sk__7 ) @ ( ap @ ( times @ sk__5 ) @ sk__7 ) ) ) @ n_2t ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl135,zip_derived_cl7414,zip_derived_cl7528,zip_derived_cl7532,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7528,zip_derived_cl7532,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7528,zip_derived_cl7532,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7528,zip_derived_cl7532,zip_derived_cl7414,zip_derived_cl7414]) ).
thf(zip_derived_cl132_023,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( is_of @ X0
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ( ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ X1
@ X0 ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( ap @ ( times @ X1 ) @ X2 )
@ ( ap @ ( times @ X0 ) @ X2 ) ) ) )
@ n_2t ) )
= ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( ap @ ( times @ X1 ) @ X2 )
@ ( ap @ ( times @ X0 ) @ X2 ) ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ X1
@ X0 ) ) )
@ n_2t ) ) )
| ~ ( is_of @ X2
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ~ ( is_of @ X1
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_5]) ).
thf(zip_derived_cl7408_024,plain,
! [X1: $i,X2: $i] :
( ( '#l_lift7188' @ X1 @ X2 )
= ( in @ X2 @ X1 ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_025,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_026,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7528_027,plain,
! [X2: $i] :
( ( '#l_lift7191' @ X2 )
= ( lessis @ X2 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_028,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_029,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_030,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7528_031,plain,
! [X2: $i] :
( ( '#l_lift7191' @ X2 )
= ( lessis @ X2 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7532_032,plain,
! [X0: $i,X1: $i,X3: $i] :
( ( '#l_lift7193' @ X0 @ X1 @ X3 )
= ( ind @ ( d_Sep @ omega @ '#l_lift7190' )
@ ( prop1
@ ( X3
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega @ '#l_lift7190' )
@ X1
@ X0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_033,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_034,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_035,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7528_036,plain,
! [X2: $i] :
( ( '#l_lift7191' @ X2 )
= ( lessis @ X2 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7532_037,plain,
! [X0: $i,X1: $i,X3: $i] :
( ( '#l_lift7193' @ X0 @ X1 @ X3 )
= ( ind @ ( d_Sep @ omega @ '#l_lift7190' )
@ ( prop1
@ ( X3
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega @ '#l_lift7190' )
@ X1
@ X0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_038,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_039,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_040,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7528_041,plain,
! [X2: $i] :
( ( '#l_lift7191' @ X2 )
= ( lessis @ X2 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7532_042,plain,
! [X0: $i,X1: $i,X3: $i] :
( ( '#l_lift7193' @ X0 @ X1 @ X3 )
= ( ind @ ( d_Sep @ omega @ '#l_lift7190' )
@ ( prop1
@ ( X3
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega @ '#l_lift7190' )
@ X1
@ X0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_043,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_044,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7408_045,plain,
! [X1: $i,X2: $i] :
( ( '#l_lift7188' @ X1 @ X2 )
= ( in @ X2 @ X1 ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_046,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl7408_047,plain,
! [X1: $i,X2: $i] :
( ( '#l_lift7188' @ X1 @ X2 )
= ( in @ X2 @ X1 ) ),
define([status(thm)]) ).
thf(zip_derived_cl7414_048,plain,
! [X2: $i] :
( ( '#l_lift7190' @ X2 )
= ( X2 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl132_049,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( is_of @ X0
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ( ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ X1
@ X0 ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( ap @ ( times @ X1 ) @ X2 )
@ ( ap @ ( times @ X0 ) @ X2 ) ) ) )
@ n_2t ) )
= ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( ap @ ( times @ X1 ) @ X2 )
@ ( ap @ ( times @ X0 ) @ X2 ) ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ X1
@ X0 ) ) )
@ n_2t ) ) )
| ~ ( is_of @ X2
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ~ ( is_of @ X1
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_5]) ).
thf(zip_derived_cl130_050,plain,
! [X0: $i,X1: $i] :
( ~ ( is_of @ X0
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ( ( ap @ ( times @ ( ap @ X1 @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( ap @ ( times @ ( ap @ X1 @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) ) @ X0 )
@ ( ap @ ( times @ ( ap @ X1 @ n_2t ) ) @ X0 ) ) ) )
@ n_2t ) )
= ( ap
@ ( times
@ ( ap
@ ( d_Sigma
@ ( d_Sep
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] : ( lessis @ Y0 @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) ) )
@ ^ [Y0: $i] :
( ind
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( prop1
@ ( Y0
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) )
@ ( ap @ ( times @ ( ap @ X1 @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) ) @ X0 )
@ ( ap @ ( times @ ( ap @ X1 @ n_2t ) ) @ X0 ) ) ) )
@ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) )
@ ( ap @ X1 @ n_2t ) ) )
| ~ ( is_of @ X1
@ ^ [Y0: $i] : ( in @ Y0 @ frac ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl7529,plain,
! [X0: $i,X1: $i,X3: $i] :
( ( '#l_lift7192' @ X0 @ X1 @ X3 )
= ( ind @ ( d_Sep @ omega @ '#l_lift7190' )
@ ( prop1
@ ( X3
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega @ '#l_lift7190' )
@ ( ap @ ( times @ ( ap @ X1 @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) ) @ X0 )
@ ( ap @ ( times @ ( ap @ X1 @ n_2t ) ) @ X0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7533,plain,
! [X0: $i,X1: $i] :
( ( '#l_lift7193' @ ( ap @ ( times @ ( ap @ X0 @ n_2t ) ) @ X1 ) @ ( ap @ ( times @ ( ap @ X0 @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) ) @ X1 ) )
= ( '#l_lift7192' @ X1 @ X0 ) ),
define([status(thm)]) ).
thf(zip_derived_cl7532_051,plain,
! [X0: $i,X1: $i,X3: $i] :
( ( '#l_lift7193' @ X0 @ X1 @ X3 )
= ( ind @ ( d_Sep @ omega @ '#l_lift7190' )
@ ( prop1
@ ( X3
= ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) )
@ ( d_Sep @ omega @ '#l_lift7190' )
@ X1
@ X0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7534,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( is_of @ X0 @ ( '#l_lift7188' @ ( d_Sep @ omega @ '#l_lift7190' ) ) )
| ( ( ap @ ( times @ ( ap @ ( d_Sigma @ ( d_Sep @ ( d_Sep @ omega @ '#l_lift7190' ) @ '#l_lift7191' ) @ ( '#l_lift7193' @ X0 @ X1 ) ) @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) ) @ ( ap @ ( d_Sigma @ ( d_Sep @ ( d_Sep @ omega @ '#l_lift7190' ) @ '#l_lift7191' ) @ ( '#l_lift7193' @ ( ap @ ( times @ X0 ) @ X2 ) @ ( ap @ ( times @ X1 ) @ X2 ) ) ) @ n_2t ) )
= ( ap @ ( times @ ( ap @ ( d_Sigma @ ( d_Sep @ ( d_Sep @ omega @ '#l_lift7190' ) @ '#l_lift7191' ) @ ( '#l_lift7193' @ ( ap @ ( times @ X0 ) @ X2 ) @ ( ap @ ( times @ X1 ) @ X2 ) ) ) @ ( outn @ ( n_pl @ ( ordsucc @ emptyset ) @ ( ordsucc @ emptyset ) ) @ ( ordsucc @ emptyset ) ) ) ) @ ( ap @ ( d_Sigma @ ( d_Sep @ ( d_Sep @ omega @ '#l_lift7190' ) @ '#l_lift7191' ) @ ( '#l_lift7193' @ X0 @ X1 ) ) @ n_2t ) ) )
| ~ ( is_of @ X2 @ ( '#l_lift7188' @ ( d_Sep @ omega @ '#l_lift7190' ) ) )
| ~ ( is_of @ X1 @ ( '#l_lift7188' @ ( d_Sep @ omega @ '#l_lift7190' ) ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl132,zip_derived_cl7408,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7528,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7528,zip_derived_cl7532,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7528,zip_derived_cl7532,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7528,zip_derived_cl7532,zip_derived_cl7414,zip_derived_cl7414,zip_derived_cl7408,zip_derived_cl7414,zip_derived_cl7408,zip_derived_cl7414,zip_derived_cl7533,zip_derived_cl7532]) ).
thf(zip_derived_cl7557,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl7538,zip_derived_cl7535,zip_derived_cl7536,zip_derived_cl7537,zip_derived_cl7534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM729^4 : TPTP v9.2.0. Released v7.1.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.63GyPVdFoq true
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 16:16:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.19/0.34 % Python version: Python 3.6.8
% 0.19/0.35 % Running in HO mode
% 0.49/0.59 % Total configuration time : 828
% 0.49/0.59 % Estimated wc time : 1656
% 0.49/0.59 % Estimated cpu time (8 cpus) : 207.0
% 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.49/0.70 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.49/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.49/0.70 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.49/0.70 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.50/0.71 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 130.36/17.12 % Solved by lams/40_c.s.sh.
% 130.36/17.12 % done 536 iterations in 16.396s
% 130.36/17.12 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 130.36/17.12 % SZS output start Refutation
% See solution above
% 130.53/17.13
% 130.53/17.13
% 130.53/17.13 % Terminating...
% 130.53/17.23 % Runner terminated.
% 130.53/17.24 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------