%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM728^4 : 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.8wGaYdCPIl true
% Computer : n006.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 04:48:08 PM UTC 2025
% Result : Theorem 73.19s 9.85s
% Output : Refutation 73.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM728^4 : TPTP v9.2.0. Released v7.1.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.8wGaYdCPIl true
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 16:17:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in HO mode
% 0.59/0.69 % Total configuration time : 828
% 0.59/0.69 % Estimated wc time : 1656
% 0.59/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.60/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.60/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.60/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.60/0.79 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.60/0.79 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.61/0.81 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.61/0.81 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.62/0.84 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 73.19/9.85 % Solved by lams/40_b.comb.sh.
% 73.19/9.85 % done 442 iterations in 9.003s
% 73.19/9.85 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 73.19/9.85 % SZS output start Refutation
% 73.19/9.85 thf(pair1_type, type, pair1: $i > $i > $i > $i).
% 73.19/9.85 thf(n_1_type, type, n_1: $i).
% 73.19/9.85 thf('#sk2_type', type, '#sk2': $i).
% 73.19/9.85 thf(nat_type, type, nat: $i).
% 73.19/9.85 thf(lessis_type, type, lessis: $i > $i > $o).
% 73.19/9.85 thf(is_of_type, type, is_of: $i > ($i > $o) > $o).
% 73.19/9.85 thf(in_type, type, in: $i > $i > $o).
% 73.19/9.85 thf('#sk3_type', type, '#sk3': $i).
% 73.19/9.85 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i).
% 73.19/9.85 thf(n_2_type, type, n_2: $i).
% 73.19/9.85 thf(n_fr_type, type, n_fr: $i > $i > $i).
% 73.19/9.85 thf(d_Sigma_type, type, d_Sigma: $i > ($i > $i) > $i).
% 73.19/9.85 thf(ap_type, type, ap: $i > $i > $i).
% 73.19/9.85 thf(times_type, type, times: $i > $i).
% 73.19/9.85 thf(emptyset_type, type, emptyset: $i).
% 73.19/9.85 thf(n_is_type, type, n_is: $i > $i > $o).
% 73.19/9.85 thf(n_1t_type, type, n_1t: $i).
% 73.19/9.85 thf(frac_type, type, frac: $i).
% 73.19/9.85 thf(n_2t_type, type, n_2t: $i).
% 73.19/9.85 thf(n_ts_type, type, n_ts: $i > $i > $i).
% 73.19/9.85 thf(n_eq_type, type, n_eq: $i > $i > $o).
% 73.19/9.85 thf(omega_type, type, omega: $i).
% 73.19/9.85 thf(pair1type_type, type, pair1type: $i > $i).
% 73.19/9.85 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o).
% 73.19/9.85 thf(num_type, type, num: $i > $i).
% 73.19/9.85 thf(d_1to_type, type, d_1to: $i > $i).
% 73.19/9.85 thf(ordsucc_type, type, ordsucc: $i > $i).
% 73.19/9.85 thf(outn_type, type, outn: $i > $i > $i).
% 73.19/9.85 thf(first1_type, type, first1: $i > $i > $i).
% 73.19/9.85 thf(den_type, type, den: $i > $i).
% 73.19/9.85 thf(second1_type, type, second1: $i > $i > $i).
% 73.19/9.85 thf(e_is_type, type, e_is: $i > $i > $i > $o).
% 73.19/9.85 thf(ite_type, type, ite: $o > $i > $i > $i > $i).
% 73.19/9.85 thf(n_pl_type, type, n_pl: $i > $i > $i).
% 73.19/9.85 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 73.19/9.85 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 73.19/9.85 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 73.19/9.85 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 73.19/9.85 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 73.19/9.85 thf(satz40, axiom,
% 73.19/9.85 (all_of @
% 73.19/9.85 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 73.19/9.85 ( ^[X0:$i]:
% 73.19/9.85 ( all_of @
% 73.19/9.85 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 73.19/9.85 ( ^[X1:$i]:
% 73.19/9.85 ( n_eq @
% 73.19/9.85 X0 @
% 73.19/9.85 ( n_fr @
% 73.19/9.85 ( n_ts @ ( num @ X0 ) @ X1 ) @ ( n_ts @ ( den @ X0 ) @ X1 ) ) ) ) ) ))).
% 73.19/9.85 thf(zip_derived_cl289, plain,
% 73.19/9.85 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 73.19/9.85 (^[Y0 : $i]:
% 73.19/9.85 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 73.19/9.85 (^[Y1 : $i]:
% 73.19/9.85 (n_eq @ Y0 @
% 73.19/9.85 (n_fr @ (n_ts @ (num @ Y0) @ Y1) @ (n_ts @ (den @ Y0) @ Y1)))))))),
% 73.19/9.85 inference('cnf', [status(esa)], [satz40])).
% 73.19/9.85 thf(zip_derived_cl290, plain,
% 73.19/9.85 ( (all_of @ ((('#C') @ in @ frac)) @
% 73.19/9.85 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#B') @ n_eq)) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#S') @
% 73.19/9.85 ((('#B') @ ((('#B') @ n_fr)) @
% 73.19/9.85 ((('#B') @ n_ts @ num)))))) @
% 73.19/9.85 ((('#B') @ n_ts @ den)))))))))),
% 73.19/9.85 inference('lams2combs', [status(thm)], [zip_derived_cl289])).
% 73.19/9.85 thf(def_nat, axiom,(( nat ) =
% 73.19/9.85 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))).
% 73.19/9.85 thf('0', plain,
% 73.19/9.85 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )),
% 73.19/9.85 define([status(thm)])).
% 73.19/9.85 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))).
% 73.19/9.85 thf('1', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])).
% 73.19/9.85 thf(zip_derived_cl873, plain,
% 73.19/9.85 ( (all_of @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 73.19/9.85 ((('#B') @ (all_of @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#B') @ n_eq)) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#S') @
% 73.19/9.85 ((('#B') @ ((('#B') @ n_fr)) @
% 73.19/9.85 ((('#B') @ n_ts @ num)))))) @
% 73.19/9.85 ((('#B') @ n_ts @ den)))))))))),
% 73.19/9.85 inference('rw', [status(thm)], [zip_derived_cl290, '0', '1'])).
% 73.19/9.85 thf(def_all_of, axiom, (all_of @ X0 @ X1) =>
% 73.19/9.85 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))).
% 73.19/9.85 thf('2', plain,
% 73.19/9.85 (![X0:( $i > $o ),X1:( $i > $o )]:
% 73.19/9.85 ( ( all_of @ X0 @ X1 ) <=>
% 73.19/9.85 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )),
% 73.19/9.85 inference('rw.lit', [status(esa)], [def_all_of])).
% 73.19/9.85 thf(zip_derived_cl874, plain,
% 73.19/9.85 ( (((!!) @ (^[Y0 : $i]:
% 73.19/9.85 (((is_of @ Y0 @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @
% 73.19/9.85 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) =>
% 73.19/9.85 ((('#B') @ (all_of @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset)))))) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#B') @ n_eq)) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#S') @
% 73.19/9.85 ((('#B') @ ((('#B') @ n_fr)) @
% 73.19/9.85 ((('#B') @ n_ts @ num)))))) @
% 73.19/9.85 ((('#B') @ n_ts @ den)))))) @
% 73.19/9.85 Y0)))))))),
% 73.19/9.85 inference('rw_clause', [status(thm)], [zip_derived_cl873, '2'])).
% 73.19/9.85 thf(zip_derived_cl875, plain,
% 73.19/9.85 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.19/9.85 ((('#C') @ is_of @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset)))))))))) @
% 73.19/9.85 ((('#B') @ (all_of @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#B') @ n_eq)) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#S') @
% 73.19/9.85 ((('#B') @ ((('#B') @ n_fr)) @
% 73.19/9.85 ((('#B') @ n_ts @ num)))))) @
% 73.19/9.85 ((('#B') @ n_ts @ den))))))))))))),
% 73.19/9.85 inference('comb-normalize', [status(thm)], [zip_derived_cl874])).
% 73.19/9.85 thf(zip_derived_cl876, plain,
% 73.19/9.85 (![X2 : $i]:
% 73.19/9.85 (((is_of @ X2 @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) =>
% 73.19/9.85 (all_of @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 ((('#B') @ (n_eq @ X2) @
% 73.19/9.85 ((('#S') @ ((('#B') @ n_fr @ (n_ts @ (num @ X2)))) @
% 73.19/9.85 (n_ts @ (den @ X2)))))))))),
% 73.19/9.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl875])).
% 73.19/9.85 thf(def_n_1, axiom,(( n_1 ) = ((ordsucc @ emptyset)))).
% 73.19/9.85 thf('3', plain, (( n_1 ) = ( ordsucc @ emptyset )), define([status(thm)])).
% 73.19/9.85 thf(def_n_2, axiom,(( n_2 ) = ((n_pl @ n_1 @ n_1)))).
% 73.19/9.85 thf('4', plain, (( n_2 ) = ( n_pl @ n_1 @ n_1 )), define([status(thm)])).
% 73.19/9.85 thf(def_n_1t, axiom,(( n_1t ) = ((outn @ n_2 @ n_1)))).
% 73.19/9.85 thf('5', plain, (( n_1t ) = ( outn @ n_2 @ n_1 )), define([status(thm)])).
% 73.19/9.85 thf(def_n_2t, axiom,(( n_2t ) = ((outn @ n_2 @ n_2)))).
% 73.19/9.85 thf('6', plain, (( n_2t ) = ( outn @ n_2 @ n_2 )), define([status(thm)])).
% 73.19/9.85 thf(def_first1, axiom,(( first1 @ (X1)@ (X0)) = ((ap @ X0 @ n_1t)))).
% 73.19/9.85 thf('7', plain,
% 73.19/9.85 (![X1:$i,X0:$i]: ( ( first1 @ X1 @ X0 ) = ( ap @ X0 @ n_1t ) )),
% 73.19/9.85 define([status(thm)])).
% 73.19/9.85 thf(def_second1, axiom,(( second1 @ (X1)@ (X0)) = ((ap @ X0 @ n_2t)))).
% 73.19/9.85 thf('8', plain,
% 73.19/9.85 (![X1:$i,X0:$i]: ( ( second1 @ X1 @ X0 ) = ( ap @ X0 @ n_2t ) )),
% 73.19/9.85 define([status(thm)])).
% 73.19/9.85 thf(def_num, axiom,(( num @ (X0)) = ((first1 @ nat @ X0)))).
% 73.19/9.85 thf('9', plain, (![X0:$i]: ( ( num @ X0 ) = ( first1 @ nat @ X0 ) )),
% 73.19/9.85 define([status(thm)])).
% 73.19/9.85 thf(def_den, axiom,(( den @ (X0)) = ((second1 @ nat @ X0)))).
% 73.19/9.85 thf('10', plain, (![X0:$i]: ( ( den @ X0 ) = ( second1 @ nat @ X0 ) )),
% 73.19/9.85 define([status(thm)])).
% 73.19/9.85 thf(zip_derived_cl877, plain,
% 73.19/9.85 (![X2 : $i]:
% 73.19/9.85 (((is_of @ X2 @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) =>
% 73.19/9.85 (all_of @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 ((('#B') @ (n_eq @ X2) @
% 73.19/9.85 ((('#S') @ ((('#B') @ n_fr @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ X2 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ X2 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))))))))),
% 73.19/9.85 inference('rw', [status(thm)],
% 73.19/9.85 [zip_derived_cl876, '0', '3', '4', '5', '6', '7', '8', '9',
% 73.19/9.85 '10'])).
% 73.19/9.85 thf(zip_derived_cl878, plain,
% 73.19/9.85 (![X2 : $i]:
% 73.19/9.85 (~ (is_of @ X2 @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))
% 73.19/9.85 | (all_of @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 ((('#B') @ (n_eq @ X2) @
% 73.19/9.85 ((('#S') @ ((('#B') @ n_fr @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ X2 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ X2 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))))))))),
% 73.19/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl877])).
% 73.19/9.85 thf(zip_derived_cl879, plain,
% 73.19/9.85 (![X0 : $i]:
% 73.19/9.85 ( (((!!) @ (^[Y0 : $i]:
% 73.19/9.85 (((is_of @ Y0 @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 73.19/9.85 ((('#B') @ (n_eq @ X0) @
% 73.19/9.85 ((('#S') @ ((('#B') @ n_fr @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset))))))) @
% 73.19/9.85 Y0)))))))
% 73.19/9.85 | ~ (is_of @ X0 @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))),
% 73.19/9.85 inference('rw_clause', [status(thm)], [zip_derived_cl878, '2'])).
% 73.19/9.85 thf(zip_derived_cl880, plain,
% 73.19/9.85 (![X0 : $i]:
% 73.19/9.85 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.19/9.85 ((('#C') @ is_of @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))))))) @
% 73.19/9.85 ((('#B') @ (n_eq @ X0) @
% 73.19/9.85 ((('#S') @ ((('#B') @ n_fr @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)))))))))))))
% 73.19/9.85 | ~ (is_of @ X0 @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))),
% 73.19/9.85 inference('comb-normalize', [status(thm)], [zip_derived_cl879])).
% 73.19/9.85 thf(zip_derived_cl881, plain,
% 73.19/9.85 (![X0 : $i, X2 : $i]:
% 73.19/9.85 ( (((is_of @ X2 @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 73.19/9.85 (n_eq @ X0 @
% 73.19/9.85 (n_fr @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset))) @
% 73.19/9.85 X2) @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 73.19/9.85 X2)))))
% 73.19/9.85 | ~ (is_of @ X0 @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))),
% 73.19/9.85 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl880])).
% 73.19/9.85 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))).
% 73.19/9.85 thf('11', plain,
% 73.19/9.85 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )),
% 73.19/9.85 define([status(thm)])).
% 73.19/9.85 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))).
% 73.19/9.85 thf('12', plain,
% 73.19/9.85 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )),
% 73.19/9.85 define([status(thm)])).
% 73.19/9.85 thf(def_n_ts, axiom,(( n_ts @ (X0)@ (X1)) = ((ap @ (times @ X0) @ X1)))).
% 73.19/9.85 thf('13', plain,
% 73.19/9.85 (![X1:$i,X0:$i]: ( ( n_ts @ X0 @ X1 ) = ( ap @ ( times @ X0 ) @ X1 ) )),
% 73.19/9.85 define([status(thm)])).
% 73.19/9.85 thf(def_d_1to, axiom,(( d_1to @ (X0)) =
% 73.19/9.85 ((d_Sep @ nat @ (^[Y0 : $i]: (lessis @ Y0 @ X0)))))).
% 73.19/9.85 thf('14', plain,
% 73.19/9.85 (![X0:$i]:
% 73.19/9.85 ( ( d_1to @ X0 ) =
% 73.19/9.85 ( d_Sep @ nat @ ( ^[V_1:$i]: ( lessis @ V_1 @ X0 ) ) ) )),
% 73.19/9.85 define([status(thm)])).
% 73.19/9.85 thf(def_pair1, axiom,(( pair1 @ (X0)@ (X1)@ (X2)) =
% 73.19/9.85 ((d_Sigma @ (d_1to @ n_2) @
% 73.19/9.85 (^[Y0 : $i]: (ite @ (e_is @ (d_1to @ n_2) @ Y0 @ n_1t) @ X0 @ X1 @ X2)))))).
% 73.19/9.85 thf('15', plain,
% 73.19/9.85 (![X2:$i,X1:$i,X0:$i]:
% 73.19/9.85 ( ( pair1 @ X0 @ X1 @ X2 ) =
% 73.19/9.85 ( d_Sigma @
% 73.19/9.85 ( d_1to @ n_2 ) @
% 73.19/9.85 ( ^[V_1:$i]:
% 73.19/9.85 ( ite @ ( e_is @ ( d_1to @ n_2 ) @ V_1 @ n_1t ) @ X0 @ X1 @ X2 ) ) ) )),
% 73.19/9.85 define([status(thm)])).
% 73.19/9.85 thf(def_n_fr, axiom,(( n_fr @ (X0)@ (X1)) = ((pair1 @ nat @ X0 @ X1)))).
% 73.19/9.85 thf('16', plain,
% 73.19/9.85 (![X1:$i,X0:$i]: ( ( n_fr @ X0 @ X1 ) = ( pair1 @ nat @ X0 @ X1 ) )),
% 73.19/9.85 define([status(thm)])).
% 73.19/9.85 thf(def_n_eq, axiom,(( n_eq @ (X0)@ (X1)) =
% 73.19/9.85 ((n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @
% 73.19/9.85 (n_ts @ (num @ X1) @ (den @ X0)))))).
% 73.19/9.85 thf('17', plain,
% 73.19/9.85 (![X1:$i,X0:$i]:
% 73.19/9.85 ( ( n_eq @ X0 @ X1 ) =
% 73.19/9.85 ( n_is @
% 73.19/9.85 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @
% 73.19/9.85 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )),
% 73.19/9.85 define([status(thm)])).
% 73.19/9.85 thf(zip_derived_cl882, plain,
% 73.19/9.85 (![X0 : $i, X2 : $i]:
% 73.19/9.85 ( (((is_of @ X2 @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 73.19/9.85 (((ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @
% 73.19/9.85 emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 X2))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 X2)))) @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) =
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @
% 73.19/9.85 emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 X2))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 X2)))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))))))
% 73.19/9.85 | ~ (is_of @ X0 @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))),
% 73.19/9.85 inference('rw', [status(thm)],
% 73.19/9.85 [zip_derived_cl881, '11', '0', '12', '3', '13', '13', '13',
% 73.19/9.85 '13', '14', '4', '5', '6', '15', '7', '7', '8', '8', '16',
% 73.19/9.85 '9', '9', '10', '10', '17'])).
% 73.19/9.85 thf(zip_derived_cl883, plain,
% 73.19/9.85 (![X0 : $i, X2 : $i]:
% 73.19/9.85 (~ (is_of @ X2 @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 73.19/9.85 | (((ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @
% 73.19/9.85 emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 X2))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 X2)))) @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) =
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @
% 73.19/9.85 emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 X2))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 X2)))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))))
% 73.19/9.85 | ~ (is_of @ X0 @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))),
% 73.19/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl882])).
% 73.19/9.85 thf(zip_derived_cl884, plain,
% 73.19/9.85 (![X0 : $i, X2 : $i]:
% 73.19/9.85 (~ (is_of @ X2 @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))
% 73.19/9.85 | ((ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @
% 73.19/9.85 emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 X2))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 X2)))) @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))
% 73.19/9.85 = (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 omega @
% 73.19/9.85 ((
% 73.19/9.85 ('#C') @ (
% 73.19/9.85 !=) @
% 73.19/9.85 emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (
% 73.19/9.85 n_pl @
% 73.19/9.85 (
% 73.19/9.85 ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (
% 73.19/9.85 ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 X2))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 X2)))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @ X0 @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))
% 73.19/9.85 | ~ (is_of @ X0 @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))),
% 73.19/9.85 inference('simplify nested equalities', [status(thm)],
% 73.19/9.85 [zip_derived_cl883])).
% 73.19/9.85 thf(satz40a, conjecture,
% 73.19/9.85 (all_of @
% 73.19/9.85 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 73.19/9.85 ( ^[X0:$i]:
% 73.19/9.85 ( all_of @
% 73.19/9.85 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 73.19/9.85 ( ^[X1:$i]:
% 73.19/9.85 ( n_eq @
% 73.19/9.85 ( n_fr @
% 73.19/9.85 ( n_ts @ ( num @ X0 ) @ X1 ) @ ( n_ts @ ( den @ X0 ) @ X1 ) ) @
% 73.19/9.85 X0 ) ) ) ))).
% 73.19/9.85 thf(zf_stmt_0, negated_conjecture,
% 73.19/9.85 (~( all_of @
% 73.19/9.85 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @
% 73.19/9.85 ( ^[X0:$i]:
% 73.19/9.85 ( all_of @
% 73.19/9.85 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @
% 73.19/9.85 ( ^[X1:$i]:
% 73.19/9.85 ( n_eq @
% 73.19/9.85 ( n_fr @
% 73.19/9.85 ( n_ts @ ( num @ X0 ) @ X1 ) @ ( n_ts @ ( den @ X0 ) @ X1 ) ) @
% 73.19/9.85 X0 ) ) ) ) )),
% 73.19/9.85 inference('cnf.neg', [status(esa)], [satz40a])).
% 73.19/9.85 thf(zip_derived_cl291, plain,
% 73.19/9.85 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @
% 73.19/9.85 (^[Y0 : $i]:
% 73.19/9.85 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @
% 73.19/9.85 (^[Y1 : $i]:
% 73.19/9.85 (n_eq @
% 73.19/9.85 (n_fr @ (n_ts @ (num @ Y0) @ Y1) @ (n_ts @ (den @ Y0) @ Y1)) @
% 73.19/9.85 Y0)))))),
% 73.19/9.85 inference('cnf', [status(esa)], [zf_stmt_0])).
% 73.19/9.85 thf(zip_derived_cl292, plain,
% 73.19/9.85 (~ (all_of @ ((('#C') @ in @ frac)) @
% 73.19/9.85 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#C') @
% 73.19/9.85 ((('#B') @ ((('#B') @ n_eq)) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#S') @
% 73.19/9.85 ((('#B') @ ((('#B') @ n_fr)) @
% 73.19/9.85 ((('#B') @ n_ts @ num)))))) @
% 73.19/9.85 ((('#B') @ n_ts @ den)))))))) @
% 73.19/9.85 ('#I'))))))),
% 73.19/9.85 inference('lams2combs', [status(thm)], [zip_derived_cl291])).
% 73.19/9.85 thf(zip_derived_cl460, plain,
% 73.19/9.85 (~ (all_of @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 73.19/9.85 ((('#B') @ (all_of @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#C') @
% 73.19/9.85 ((('#B') @ ((('#B') @ n_eq)) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#S') @
% 73.19/9.85 ((('#B') @ ((('#B') @ n_fr)) @
% 73.19/9.85 ((('#B') @ n_ts @ num)))))) @
% 73.19/9.85 ((('#B') @ n_ts @ den)))))))) @
% 73.19/9.85 ('#I'))))))),
% 73.19/9.85 inference('rw', [status(thm)], [zip_derived_cl292, '0', '1'])).
% 73.19/9.85 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) =>
% 73.19/9.85 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))).
% 73.19/9.85 thf('18', plain,
% 73.19/9.85 (![X0:( $i > $o ),X1:( $i > $o )]:
% 73.19/9.85 ( ( ~( all_of @ X0 @ X1 ) ) <=>
% 73.19/9.85 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )),
% 73.19/9.85 inference('rw.lit', [status(esa)], [def_all_of])).
% 73.19/9.85 thf(zip_derived_cl461, plain,
% 73.19/9.85 (~ (((!!) @ (^[Y0 : $i]:
% 73.19/9.85 (((is_of @ Y0 @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @
% 73.19/9.85 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) =>
% 73.19/9.85 ((('#B') @ (all_of @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset)))))) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#C') @
% 73.19/9.85 ((('#B') @ ((('#B') @ n_eq)) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#S') @
% 73.19/9.85 ((('#B') @ ((('#B') @ n_fr)) @
% 73.19/9.85 ((('#B') @ n_ts @ num)))))) @
% 73.19/9.85 ((('#B') @ n_ts @ den)))))))) @
% 73.19/9.85 ('#I'))) @
% 73.19/9.85 Y0)))))))),
% 73.19/9.85 inference('rw_clause', [status(thm)], [zip_derived_cl460, '18'])).
% 73.19/9.85 thf(zip_derived_cl462, plain,
% 73.19/9.85 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.19/9.85 ((('#C') @ is_of @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset)))))))))) @
% 73.19/9.85 ((('#B') @ (all_of @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#C') @
% 73.19/9.85 ((('#B') @ ((('#B') @ n_eq)) @
% 73.19/9.85 ((('#S') @ ((('#B') @ ('#S') @
% 73.19/9.85 ((('#B') @ ((('#B') @ n_fr)) @
% 73.19/9.85 ((('#B') @ n_ts @ num)))))) @
% 73.19/9.85 ((('#B') @ n_ts @ den)))))))) @
% 73.19/9.85 ('#I')))))))))),
% 73.19/9.85 inference('comb-normalize', [status(thm)], [zip_derived_cl461])).
% 73.19/9.85 thf(zip_derived_cl463, plain,
% 73.19/9.85 (~ (((is_of @ '#sk2' @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) =>
% 73.19/9.85 (all_of @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#B') @ n_eq @
% 73.19/9.85 ((('#S') @ ((('#B') @ n_fr @ (n_ts @ (num @ '#sk2')))) @
% 73.19/9.85 (n_ts @ (den @ '#sk2')))))) @
% 73.19/9.85 '#sk2')))))),
% 73.19/9.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl462])).
% 73.19/9.85 thf(zip_derived_cl464, plain,
% 73.19/9.85 (~ (((is_of @ '#sk2' @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) =>
% 73.19/9.85 (all_of @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#B') @ n_eq @
% 73.19/9.85 ((('#S') @ ((('#B') @ n_fr @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset))))))))) @
% 73.19/9.85 '#sk2')))))),
% 73.19/9.85 inference('rw', [status(thm)],
% 73.19/9.85 [zip_derived_cl463, '0', '3', '4', '5', '6', '7', '8', '9',
% 73.19/9.85 '10'])).
% 73.19/9.85 thf(zip_derived_cl466, plain,
% 73.19/9.85 (~ (all_of @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#B') @ n_eq @
% 73.19/9.85 ((('#S') @ ((('#B') @ n_fr @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))))) @
% 73.19/9.85 '#sk2')))),
% 73.19/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl464])).
% 73.19/9.85 thf(zip_derived_cl467, plain,
% 73.19/9.85 (~ (((!!) @ (^[Y0 : $i]:
% 73.19/9.85 (((is_of @ Y0 @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 73.19/9.85 ((('#C') @ ((('#B') @ n_eq @
% 73.19/9.85 ((('#S') @ ((('#B') @ n_fr @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset))))))))) @
% 73.19/9.85 '#sk2' @ Y0)))))))),
% 73.19/9.85 inference('rw_clause', [status(thm)], [zip_derived_cl466, '18'])).
% 73.19/9.85 thf(zip_derived_cl468, plain,
% 73.19/9.85 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 73.19/9.85 ((('#C') @ is_of @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))))))) @
% 73.19/9.85 ((('#C') @ ((('#B') @ n_eq @
% 73.19/9.85 ((('#S') @ ((('#B') @ n_fr @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset))))))))) @
% 73.19/9.85 '#sk2'))))))),
% 73.19/9.85 inference('comb-normalize', [status(thm)], [zip_derived_cl467])).
% 73.19/9.85 thf(zip_derived_cl469, plain,
% 73.19/9.85 (~ (((is_of @ '#sk3' @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 73.19/9.85 (n_eq @
% 73.19/9.85 (n_fr @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset))) @
% 73.19/9.85 '#sk3') @
% 73.19/9.85 (n_ts @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @
% 73.19/9.85 '#sk3')) @
% 73.19/9.85 '#sk2')))),
% 73.19/9.85 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl468])).
% 73.19/9.85 thf(zip_derived_cl470, plain,
% 73.19/9.85 (~ (((is_of @ '#sk3' @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) =>
% 73.19/9.85 (((ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @
% 73.19/9.85 emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 '#sk3'))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 '#sk3')))) @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) =
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @
% 73.19/9.85 emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 '#sk3'))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 '#sk3')))) @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))))))),
% 73.19/9.85 inference('rw', [status(thm)],
% 73.19/9.85 [zip_derived_cl469, '11', '0', '12', '3', '13', '13', '13',
% 73.19/9.85 '13', '14', '4', '5', '6', '15', '7', '7', '8', '8', '16',
% 73.19/9.85 '9', '9', '10', '10', '17'])).
% 73.19/9.85 thf(zip_derived_cl472, plain,
% 73.19/9.85 (~ (((ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 '#sk3'))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 '#sk3')))) @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) =
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 '#sk3'))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 '#sk3')))) @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))))),
% 73.19/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl470])).
% 73.19/9.85 thf(zip_derived_cl473, plain,
% 73.19/9.85 (((ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 '#sk3'))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 '#sk3')))) @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))
% 73.19/9.85 != (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @
% 73.19/9.85 emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 '#sk3'))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 '#sk3')))) @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))),
% 73.19/9.85 inference('simplify nested equalities', [status(thm)],
% 73.19/9.85 [zip_derived_cl472])).
% 73.19/9.85 thf(zip_derived_cl5600, plain,
% 73.19/9.85 ((((ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 '#sk3'))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 '#sk3')))) @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))
% 73.19/9.85 != (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @
% 73.19/9.85 emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 '#sk3'))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 '#sk3')))) @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))
% 73.19/9.85 | ~ (is_of @ '#sk2' @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))
% 73.19/9.85 | ~ (is_of @ '#sk3' @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 73.19/9.85 inference('sup-', [status(thm)], [zip_derived_cl884, zip_derived_cl473])).
% 73.19/9.85 thf(zip_derived_cl465, plain,
% 73.19/9.85 ( (is_of @ '#sk2' @
% 73.19/9.85 ((('#C') @ in @
% 73.19/9.85 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))),
% 73.19/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl464])).
% 73.19/9.85 thf(zip_derived_cl471, plain,
% 73.19/9.85 ( (is_of @ '#sk3' @
% 73.19/9.85 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))),
% 73.19/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl470])).
% 73.19/9.85 thf(zip_derived_cl6036, plain,
% 73.19/9.85 (((ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 '#sk3'))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 '#sk3')))) @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))
% 73.19/9.85 != (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (d_Sigma @
% 73.19/9.85 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @
% 73.19/9.85 ((('#C') @ (e_is @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 (d_Sep @
% 73.19/9.85 omega @
% 73.19/9.85 ((('#C') @ (
% 73.19/9.85 !=) @
% 73.19/9.85 emptyset))) @
% 73.19/9.85 ((('#C') @ lessis @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset) @
% 73.19/9.85 (ordsucc @
% 73.19/9.85 emptyset)))))) @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @
% 73.19/9.85 (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))))) @
% 73.19/9.85 (d_Sep @ omega @
% 73.19/9.85 ((('#C') @ (!=) @ emptyset))))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @
% 73.19/9.85 (ordsucc @ emptyset)) @
% 73.19/9.85 (ordsucc @ emptyset)))) @
% 73.19/9.85 '#sk3'))) @
% 73.19/9.85 (ap @
% 73.19/9.85 (times @
% 73.19/9.85 (ap @ '#sk2' @
% 73.19/9.85 (outn @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @
% 73.19/9.85 '#sk3')))) @
% 73.19/9.85 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @
% 73.19/9.85 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))),
% 73.19/9.85 inference('demod', [status(thm)],
% 73.19/9.85 [zip_derived_cl5600, zip_derived_cl465, zip_derived_cl471])).
% 73.19/9.85 thf(zip_derived_cl6037, plain, ($false),
% 73.19/9.85 inference('simplify', [status(thm)], [zip_derived_cl6036])).
% 73.19/9.85
% 73.19/9.85 % SZS output end Refutation
% 73.19/9.85
% 73.19/9.85
% 73.19/9.85 % Terminating...
% 73.19/9.91 % Runner terminated.
% 73.19/9.93 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------