0.03/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Ln06PVU0MF true 0.12/0.32 % Computer : n004.cluster.edu 0.12/0.32 % Model : x86_64 x86_64 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.32 % Memory : 8042.1875MB 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.32 % CPULimit : 1920 0.12/0.32 % WCLimit : 240 0.12/0.32 % DateTime : Wed Jul 30 08:24:04 EDT 2025 0.12/0.32 % CPUTime : 0.12/0.32 % Running portfolio for 1920 s 0.12/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.32 % Number of cores: 8 0.12/0.32 % Python version: Python 3.6.8 0.12/0.33 % Running in HO mode 0.53/0.66 % Total configuration time : 828 0.53/0.66 % Estimated wc time : 1656 0.53/0.66 % Estimated cpu time (8 cpus) : 207.0 0.53/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.53/0.69 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.53/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 66.77/9.07 % Solved by lams/40_b.comb.sh. 66.77/9.07 % done 491 iterations in 8.284s 66.77/9.07 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 66.77/9.07 % SZS output start Refutation 66.77/9.07 thf(emptyset_type, type, emptyset: $i). 66.77/9.07 thf(n_2t_type, type, n_2t: $i). 66.77/9.07 thf(times_type, type, times: $i > $i). 66.77/9.07 thf(lessis_type, type, lessis: $i > $i > $o). 66.77/9.07 thf('#sk2_type', type, '#sk2': $i). 66.77/9.07 thf(ite_type, type, ite: $o > $i > $i > $i > $i). 66.77/9.07 thf('#sk1_type', type, '#sk1': $i). 66.77/9.07 thf(n_2_type, type, n_2: $i). 66.77/9.07 thf(d_Sigma_type, type, d_Sigma: $i > ($i > $i) > $i). 66.77/9.07 thf(omega_type, type, omega: $i). 66.77/9.07 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 66.77/9.07 thf(in_type, type, in: $i > $i > $o). 66.77/9.07 thf(pair1_type, type, pair1: $i > $i > $i > $i). 66.77/9.07 thf(d_1to_type, type, d_1to: $i > $i). 66.77/9.07 thf(den_type, type, den: $i > $i). 66.77/9.07 thf(n_1_type, type, n_1: $i). 66.77/9.07 thf(n_1t_type, type, n_1t: $i). 66.77/9.07 thf(first1_type, type, first1: $i > $i > $i). 66.77/9.07 thf(n_fr_type, type, n_fr: $i > $i > $i). 66.77/9.07 thf(e_is_type, type, e_is: $i > $i > $i > $o). 66.77/9.07 thf(ap_type, type, ap: $i > $i > $i). 66.77/9.07 thf(nat_type, type, nat: $i). 66.77/9.07 thf(d_Sep_type, type, d_Sep: $i > ($i > $o) > $i). 66.77/9.07 thf(second1_type, type, second1: $i > $i > $i). 66.77/9.07 thf(outn_type, type, outn: $i > $i > $i). 66.77/9.07 thf(frac_type, type, frac: $i). 66.77/9.07 thf(n_ts_type, type, n_ts: $i > $i > $i). 66.77/9.07 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 66.77/9.07 thf(n_eq_type, type, n_eq: $i > $i > $o). 66.77/9.07 thf(n_is_type, type, n_is: $i > $i > $o). 66.77/9.07 thf(ordsucc_type, type, ordsucc: $i > $i). 66.77/9.07 thf(n_pl_type, type, n_pl: $i > $i > $i). 66.77/9.07 thf(num_type, type, num: $i > $i). 66.77/9.07 thf(pair1type_type, type, pair1type: $i > $i). 66.77/9.07 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 66.77/9.07 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 66.77/9.07 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 66.77/9.07 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 66.77/9.07 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 66.77/9.07 thf(satz40, axiom, 66.77/9.07 (all_of @ 66.77/9.07 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 66.77/9.07 ( ^[X0:$i]: 66.77/9.07 ( all_of @ 66.77/9.07 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 66.77/9.07 ( ^[X1:$i]: 66.77/9.07 ( n_eq @ 66.77/9.07 X0 @ 66.77/9.07 ( n_fr @ 66.77/9.07 ( n_ts @ ( num @ X0 ) @ X1 ) @ ( n_ts @ ( den @ X0 ) @ X1 ) ) ) ) ) ))). 66.77/9.07 thf(zip_derived_cl207, plain, 66.77/9.07 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 66.77/9.07 (^[Y0 : $i]: 66.77/9.07 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 66.77/9.07 (^[Y1 : $i]: 66.77/9.07 (n_eq @ Y0 @ 66.77/9.07 (n_fr @ (n_ts @ (num @ Y0) @ Y1) @ (n_ts @ (den @ Y0) @ Y1)))))))), 66.77/9.07 inference('cnf', [status(esa)], [satz40])). 66.77/9.07 thf(zip_derived_cl208, plain, 66.77/9.07 ( (all_of @ ((('#C') @ in @ frac)) @ 66.77/9.07 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#B') @ n_eq)) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#S') @ 66.77/9.07 ((('#B') @ ((('#B') @ n_fr)) @ 66.77/9.07 ((('#B') @ n_ts @ num)))))) @ 66.77/9.07 ((('#B') @ n_ts @ den)))))))))), 66.77/9.07 inference('lams2combs', [status(thm)], [zip_derived_cl207])). 66.77/9.07 thf(def_nat, axiom,(( nat ) = 66.77/9.07 ((d_Sep @ omega @ (^[Y0 : $i]: (((Y0) != (emptyset)))))))). 66.77/9.07 thf('0', plain, 66.77/9.07 (( nat ) = ( d_Sep @ omega @ ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) ) )), 66.77/9.07 define([status(thm)])). 66.77/9.07 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))). 66.77/9.07 thf('1', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])). 66.77/9.07 thf(zip_derived_cl843, plain, 66.77/9.07 ( (all_of @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 66.77/9.07 ((('#B') @ (all_of @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#B') @ n_eq)) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#S') @ 66.77/9.07 ((('#B') @ ((('#B') @ n_fr)) @ 66.77/9.07 ((('#B') @ n_ts @ num)))))) @ 66.77/9.07 ((('#B') @ n_ts @ den)))))))))), 66.77/9.07 inference('rw', [status(thm)], [zip_derived_cl208, '0', '1'])). 66.77/9.07 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 66.77/9.07 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 66.77/9.07 thf('2', plain, 66.77/9.07 (![X0:( $i > $o ),X1:( $i > $o )]: 66.77/9.07 ( ( all_of @ X0 @ X1 ) <=> 66.77/9.07 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 66.77/9.07 inference('rw.lit', [status(esa)], [def_all_of])). 66.77/9.07 thf(zip_derived_cl844, plain, 66.77/9.07 ( (((!!) @ (^[Y0 : $i]: 66.77/9.07 (((is_of @ Y0 @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ 66.77/9.07 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) => 66.77/9.07 ((('#B') @ (all_of @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (d_Sep @ omega @ 66.77/9.07 ((('#C') @ (!=) @ emptyset)))))) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#B') @ n_eq)) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#S') @ 66.77/9.07 ((('#B') @ ((('#B') @ n_fr)) @ 66.77/9.07 ((('#B') @ n_ts @ num)))))) @ 66.77/9.07 ((('#B') @ n_ts @ den)))))) @ 66.77/9.07 Y0)))))))), 66.77/9.07 inference('rw_clause', [status(thm)], [zip_derived_cl843, '2'])). 66.77/9.07 thf(zip_derived_cl845, plain, 66.77/9.07 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 66.77/9.07 ((('#C') @ is_of @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ 66.77/9.07 (d_Sep @ omega @ 66.77/9.07 ((('#C') @ (!=) @ emptyset)))))))))) @ 66.77/9.07 ((('#B') @ (all_of @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#B') @ n_eq)) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#S') @ 66.77/9.07 ((('#B') @ ((('#B') @ n_fr)) @ 66.77/9.07 ((('#B') @ n_ts @ num)))))) @ 66.77/9.07 ((('#B') @ n_ts @ den))))))))))))), 66.77/9.07 inference('comb-normalize', [status(thm)], [zip_derived_cl844])). 66.77/9.07 thf(zip_derived_cl846, plain, 66.77/9.07 (![X2 : $i]: 66.77/9.07 (((is_of @ X2 @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) => 66.77/9.07 (all_of @ 66.77/9.07 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.07 ((('#B') @ (n_eq @ X2) @ 66.77/9.07 ((('#S') @ ((('#B') @ n_fr @ (n_ts @ (num @ X2)))) @ 66.77/9.07 (n_ts @ (den @ X2)))))))))), 66.77/9.07 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl845])). 66.77/9.07 thf(def_n_1, axiom,(( n_1 ) = ((ordsucc @ emptyset)))). 66.77/9.07 thf('3', plain, (( n_1 ) = ( ordsucc @ emptyset )), define([status(thm)])). 66.77/9.07 thf(def_n_2, axiom,(( n_2 ) = ((n_pl @ n_1 @ n_1)))). 66.77/9.07 thf('4', plain, (( n_2 ) = ( n_pl @ n_1 @ n_1 )), define([status(thm)])). 66.77/9.07 thf(def_n_1t, axiom,(( n_1t ) = ((outn @ n_2 @ n_1)))). 66.77/9.07 thf('5', plain, (( n_1t ) = ( outn @ n_2 @ n_1 )), define([status(thm)])). 66.77/9.07 thf(def_n_2t, axiom,(( n_2t ) = ((outn @ n_2 @ n_2)))). 66.77/9.07 thf('6', plain, (( n_2t ) = ( outn @ n_2 @ n_2 )), define([status(thm)])). 66.77/9.07 thf(def_first1, axiom,(( first1 @ (X1)@ (X0)) = ((ap @ X0 @ n_1t)))). 66.77/9.07 thf('7', plain, 66.77/9.07 (![X1:$i,X0:$i]: ( ( first1 @ X1 @ X0 ) = ( ap @ X0 @ n_1t ) )), 66.77/9.07 define([status(thm)])). 66.77/9.07 thf(def_second1, axiom,(( second1 @ (X1)@ (X0)) = ((ap @ X0 @ n_2t)))). 66.77/9.07 thf('8', plain, 66.77/9.07 (![X1:$i,X0:$i]: ( ( second1 @ X1 @ X0 ) = ( ap @ X0 @ n_2t ) )), 66.77/9.07 define([status(thm)])). 66.77/9.07 thf(def_num, axiom,(( num @ (X0)) = ((first1 @ nat @ X0)))). 66.77/9.07 thf('9', plain, (![X0:$i]: ( ( num @ X0 ) = ( first1 @ nat @ X0 ) )), 66.77/9.07 define([status(thm)])). 66.77/9.07 thf(def_den, axiom,(( den @ (X0)) = ((second1 @ nat @ X0)))). 66.77/9.07 thf('10', plain, (![X0:$i]: ( ( den @ X0 ) = ( second1 @ nat @ X0 ) )), 66.77/9.07 define([status(thm)])). 66.77/9.07 thf(zip_derived_cl847, plain, 66.77/9.07 (![X2 : $i]: 66.77/9.07 (((is_of @ X2 @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) => 66.77/9.07 (all_of @ 66.77/9.07 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.07 ((('#B') @ (n_eq @ X2) @ 66.77/9.07 ((('#S') @ ((('#B') @ n_fr @ 66.77/9.07 (n_ts @ 66.77/9.07 (ap @ X2 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))))) @ 66.77/9.07 (n_ts @ 66.77/9.07 (ap @ X2 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))))))))), 66.77/9.07 inference('rw', [status(thm)], 66.77/9.07 [zip_derived_cl846, '0', '3', '4', '5', '6', '7', '8', '9', 66.77/9.07 '10'])). 66.77/9.07 thf(zip_derived_cl848, plain, 66.77/9.07 (![X2 : $i]: 66.77/9.07 (~ (is_of @ X2 @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) 66.77/9.07 | (all_of @ 66.77/9.07 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.07 ((('#B') @ (n_eq @ X2) @ 66.77/9.07 ((('#S') @ ((('#B') @ n_fr @ 66.77/9.07 (n_ts @ 66.77/9.07 (ap @ X2 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))))) @ 66.77/9.07 (n_ts @ 66.77/9.07 (ap @ X2 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))))))))), 66.77/9.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl847])). 66.77/9.07 thf(zip_derived_cl849, plain, 66.77/9.07 (![X0 : $i]: 66.77/9.07 ( (((!!) @ (^[Y0 : $i]: 66.77/9.07 (((is_of @ Y0 @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 66.77/9.07 ((('#B') @ (n_eq @ X0) @ 66.77/9.07 ((('#S') @ ((('#B') @ n_fr @ 66.77/9.07 (n_ts @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))))) @ 66.77/9.07 (n_ts @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset))))))) @ 66.77/9.07 Y0))))))) 66.77/9.07 | ~ (is_of @ X0 @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))), 66.77/9.07 inference('rw_clause', [status(thm)], [zip_derived_cl848, '2'])). 66.77/9.07 thf(zip_derived_cl850, plain, 66.77/9.07 (![X0 : $i]: 66.77/9.07 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 66.77/9.07 ((('#C') @ is_of @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (d_Sep @ omega @ 66.77/9.07 ((('#C') @ (!=) @ emptyset))))))))) @ 66.77/9.07 ((('#B') @ (n_eq @ X0) @ 66.77/9.07 ((('#S') @ ((('#B') @ n_fr @ 66.77/9.07 (n_ts @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))))) @ 66.77/9.07 (n_ts @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset))))))))))))) 66.77/9.07 | ~ (is_of @ X0 @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))), 66.77/9.07 inference('comb-normalize', [status(thm)], [zip_derived_cl849])). 66.77/9.07 thf(zip_derived_cl851, plain, 66.77/9.07 (![X0 : $i, X2 : $i]: 66.77/9.07 ( (((is_of @ X2 @ 66.77/9.07 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 66.77/9.07 (n_eq @ X0 @ 66.77/9.07 (n_fr @ 66.77/9.07 (n_ts @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset))) @ 66.77/9.07 X2) @ 66.77/9.07 (n_ts @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @ 66.77/9.07 X2))))) 66.77/9.07 | ~ (is_of @ X0 @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))), 66.77/9.07 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl850])). 66.77/9.07 thf(def_e_is, axiom,(( e_is @ (X2)@ (X0)@ (X1)) = ((((X0) = (X1)))))). 66.77/9.07 thf('11', plain, 66.77/9.07 (![X2:$i,X1:$i,X0:$i]: ( ( e_is @ X2 @ X0 @ X1 ) = ( ( X0 ) = ( X1 ) ) )), 66.77/9.07 define([status(thm)])). 66.77/9.07 thf(def_n_is, axiom,(( n_is @ (X0)@ (X1)) = ((e_is @ nat @ X0 @ X1)))). 66.77/9.07 thf('12', plain, 66.77/9.07 (![X1:$i,X0:$i]: ( ( n_is @ X0 @ X1 ) = ( e_is @ nat @ X0 @ X1 ) )), 66.77/9.07 define([status(thm)])). 66.77/9.07 thf(def_n_ts, axiom,(( n_ts @ (X0)@ (X1)) = ((ap @ (times @ X0) @ X1)))). 66.77/9.07 thf('13', plain, 66.77/9.07 (![X1:$i,X0:$i]: ( ( n_ts @ X0 @ X1 ) = ( ap @ ( times @ X0 ) @ X1 ) )), 66.77/9.07 define([status(thm)])). 66.77/9.07 thf(def_d_1to, axiom,(( d_1to @ (X0)) = 66.77/9.07 ((d_Sep @ nat @ (^[Y0 : $i]: (lessis @ Y0 @ X0)))))). 66.77/9.07 thf('14', plain, 66.77/9.07 (![X0:$i]: 66.77/9.07 ( ( d_1to @ X0 ) = 66.77/9.07 ( d_Sep @ nat @ ( ^[V_1:$i]: ( lessis @ V_1 @ X0 ) ) ) )), 66.77/9.07 define([status(thm)])). 66.77/9.07 thf(def_pair1, axiom,(( pair1 @ (X0)@ (X1)@ (X2)) = 66.77/9.07 ((d_Sigma @ (d_1to @ n_2) @ 66.77/9.07 (^[Y0 : $i]: (ite @ (e_is @ (d_1to @ n_2) @ Y0 @ n_1t) @ X0 @ X1 @ X2)))))). 66.77/9.07 thf('15', plain, 66.77/9.07 (![X2:$i,X1:$i,X0:$i]: 66.77/9.07 ( ( pair1 @ X0 @ X1 @ X2 ) = 66.77/9.07 ( d_Sigma @ 66.77/9.07 ( d_1to @ n_2 ) @ 66.77/9.07 ( ^[V_1:$i]: 66.77/9.07 ( ite @ ( e_is @ ( d_1to @ n_2 ) @ V_1 @ n_1t ) @ X0 @ X1 @ X2 ) ) ) )), 66.77/9.07 define([status(thm)])). 66.77/9.07 thf(def_n_fr, axiom,(( n_fr @ (X0)@ (X1)) = ((pair1 @ nat @ X0 @ X1)))). 66.77/9.07 thf('16', plain, 66.77/9.07 (![X1:$i,X0:$i]: ( ( n_fr @ X0 @ X1 ) = ( pair1 @ nat @ X0 @ X1 ) )), 66.77/9.07 define([status(thm)])). 66.77/9.07 thf(def_n_eq, axiom,(( n_eq @ (X0)@ (X1)) = 66.77/9.07 ((n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @ 66.77/9.07 (n_ts @ (num @ X1) @ (den @ X0)))))). 66.77/9.07 thf('17', plain, 66.77/9.07 (![X1:$i,X0:$i]: 66.77/9.07 ( ( n_eq @ X0 @ X1 ) = 66.77/9.07 ( n_is @ 66.77/9.07 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 66.77/9.07 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 66.77/9.07 define([status(thm)])). 66.77/9.07 thf(zip_derived_cl852, plain, 66.77/9.07 (![X0 : $i, X2 : $i]: 66.77/9.07 ( (((is_of @ X2 @ 66.77/9.07 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 66.77/9.07 (((ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))) @ 66.77/9.07 (ap @ 66.77/9.07 (d_Sigma @ 66.77/9.07 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.07 ((('#C') @ lessis @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.07 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.07 ((('#C') @ (e_is @ 66.77/9.07 (d_Sep @ 66.77/9.07 (d_Sep @ 66.77/9.07 omega @ 66.77/9.07 ((('#C') @ ( 66.77/9.07 !=) @ 66.77/9.07 emptyset))) @ 66.77/9.07 ((('#C') @ lessis @ 66.77/9.07 (n_pl @ 66.77/9.07 (ordsucc @ 66.77/9.07 emptyset) @ 66.77/9.07 (ordsucc @ 66.77/9.07 emptyset)))))) @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ 66.77/9.07 (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))))) @ 66.77/9.07 (d_Sep @ omega @ 66.77/9.07 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))) @ 66.77/9.07 X2))) @ 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.07 X2)))) @ 66.77/9.07 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) = 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ 66.77/9.07 (d_Sigma @ 66.77/9.07 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.07 ((('#C') @ lessis @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.07 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.07 ((('#C') @ (e_is @ 66.77/9.07 (d_Sep @ 66.77/9.07 (d_Sep @ 66.77/9.07 omega @ 66.77/9.07 ((('#C') @ ( 66.77/9.07 !=) @ 66.77/9.07 emptyset))) @ 66.77/9.07 ((('#C') @ lessis @ 66.77/9.07 (n_pl @ 66.77/9.07 (ordsucc @ 66.77/9.07 emptyset) @ 66.77/9.07 (ordsucc @ 66.77/9.07 emptyset)))))) @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ 66.77/9.07 (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))))) @ 66.77/9.07 (d_Sep @ omega @ 66.77/9.07 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))) @ 66.77/9.07 X2))) @ 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.07 X2)))) @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))) @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))))) 66.77/9.07 | ~ (is_of @ X0 @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))), 66.77/9.07 inference('rw', [status(thm)], 66.77/9.07 [zip_derived_cl851, '11', '0', '12', '3', '13', '13', '13', 66.77/9.07 '13', '14', '4', '5', '6', '15', '7', '7', '8', '8', '16', 66.77/9.07 '9', '9', '10', '10', '17'])). 66.77/9.07 thf(zip_derived_cl853, plain, 66.77/9.07 (![X0 : $i, X2 : $i]: 66.77/9.07 (~ (is_of @ X2 @ 66.77/9.07 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 66.77/9.07 | (((ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))) @ 66.77/9.07 (ap @ 66.77/9.07 (d_Sigma @ 66.77/9.07 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.07 ((('#C') @ lessis @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.07 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.07 ((('#C') @ (e_is @ 66.77/9.07 (d_Sep @ 66.77/9.07 (d_Sep @ 66.77/9.07 omega @ 66.77/9.07 ((('#C') @ ( 66.77/9.07 !=) @ 66.77/9.07 emptyset))) @ 66.77/9.07 ((('#C') @ lessis @ 66.77/9.07 (n_pl @ 66.77/9.07 (ordsucc @ 66.77/9.07 emptyset) @ 66.77/9.07 (ordsucc @ 66.77/9.07 emptyset)))))) @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ 66.77/9.07 (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))))) @ 66.77/9.07 (d_Sep @ omega @ 66.77/9.07 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))) @ 66.77/9.07 X2))) @ 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.07 X2)))) @ 66.77/9.07 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) = 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ 66.77/9.07 (d_Sigma @ 66.77/9.07 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.07 ((('#C') @ lessis @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.07 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.07 ((('#C') @ (e_is @ 66.77/9.07 (d_Sep @ 66.77/9.07 (d_Sep @ 66.77/9.07 omega @ 66.77/9.07 ((('#C') @ ( 66.77/9.07 !=) @ 66.77/9.07 emptyset))) @ 66.77/9.07 ((('#C') @ lessis @ 66.77/9.07 (n_pl @ 66.77/9.07 (ordsucc @ 66.77/9.07 emptyset) @ 66.77/9.07 (ordsucc @ 66.77/9.07 emptyset)))))) @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ 66.77/9.07 (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))))) @ 66.77/9.07 (d_Sep @ omega @ 66.77/9.07 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))) @ 66.77/9.07 X2))) @ 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.07 X2)))) @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))) @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))) 66.77/9.07 | ~ (is_of @ X0 @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))), 66.77/9.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl852])). 66.77/9.07 thf(zip_derived_cl854, plain, 66.77/9.07 (![X0 : $i, X2 : $i]: 66.77/9.07 (~ (is_of @ X2 @ 66.77/9.07 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) 66.77/9.07 | ((ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))) @ 66.77/9.07 (ap @ 66.77/9.07 (d_Sigma @ 66.77/9.07 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.07 ((('#C') @ lessis @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.07 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.07 ((('#C') @ (e_is @ 66.77/9.07 (d_Sep @ 66.77/9.07 (d_Sep @ 66.77/9.07 omega @ 66.77/9.07 ((('#C') @ ( 66.77/9.07 !=) @ 66.77/9.07 emptyset))) @ 66.77/9.07 ((('#C') @ lessis @ 66.77/9.07 (n_pl @ 66.77/9.07 (ordsucc @ 66.77/9.07 emptyset) @ 66.77/9.07 (ordsucc @ 66.77/9.07 emptyset)))))) @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ 66.77/9.07 (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))))) @ 66.77/9.07 (d_Sep @ omega @ 66.77/9.07 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))) @ 66.77/9.07 X2))) @ 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.07 X2)))) @ 66.77/9.07 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) 66.77/9.07 = (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ 66.77/9.07 (d_Sigma @ 66.77/9.07 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.07 ((('#C') @ lessis @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.07 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.07 ((('#C') @ (e_is @ 66.77/9.07 (d_Sep @ 66.77/9.07 (d_Sep @ 66.77/9.07 omega @ 66.77/9.07 (( 66.77/9.07 ('#C') @ ( 66.77/9.07 !=) @ 66.77/9.07 emptyset))) @ 66.77/9.07 ((('#C') @ lessis @ 66.77/9.07 ( 66.77/9.07 n_pl @ 66.77/9.07 ( 66.77/9.07 ordsucc @ 66.77/9.07 emptyset) @ 66.77/9.07 ( 66.77/9.07 ordsucc @ 66.77/9.07 emptyset)))))) @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ 66.77/9.07 (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))))) @ 66.77/9.07 (d_Sep @ omega @ 66.77/9.07 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))) @ 66.77/9.07 X2))) @ 66.77/9.07 (ap @ 66.77/9.07 (times @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.07 X2)))) @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))) @ 66.77/9.07 (ap @ X0 @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))) 66.77/9.07 | ~ (is_of @ X0 @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))))), 66.77/9.07 inference('simplify nested equalities', [status(thm)], 66.77/9.07 [zip_derived_cl853])). 66.77/9.07 thf(satz40a, conjecture, 66.77/9.07 (all_of @ 66.77/9.07 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 66.77/9.07 ( ^[X0:$i]: 66.77/9.07 ( all_of @ 66.77/9.07 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 66.77/9.07 ( ^[X1:$i]: 66.77/9.07 ( n_eq @ 66.77/9.07 ( n_fr @ 66.77/9.07 ( n_ts @ ( num @ X0 ) @ X1 ) @ ( n_ts @ ( den @ X0 ) @ X1 ) ) @ 66.77/9.07 X0 ) ) ) ))). 66.77/9.07 thf(zf_stmt_0, negated_conjecture, 66.77/9.07 (~( all_of @ 66.77/9.07 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 66.77/9.07 ( ^[X0:$i]: 66.77/9.07 ( all_of @ 66.77/9.07 ( ^[X1:$i]: ( in @ X1 @ nat ) ) @ 66.77/9.07 ( ^[X1:$i]: 66.77/9.07 ( n_eq @ 66.77/9.07 ( n_fr @ 66.77/9.07 ( n_ts @ ( num @ X0 ) @ X1 ) @ ( n_ts @ ( den @ X0 ) @ X1 ) ) @ 66.77/9.07 X0 ) ) ) ) )), 66.77/9.07 inference('cnf.neg', [status(esa)], [satz40a])). 66.77/9.07 thf(zip_derived_cl291, plain, 66.77/9.07 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 66.77/9.07 (^[Y0 : $i]: 66.77/9.07 (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ 66.77/9.07 (^[Y1 : $i]: 66.77/9.07 (n_eq @ 66.77/9.07 (n_fr @ (n_ts @ (num @ Y0) @ Y1) @ (n_ts @ (den @ Y0) @ Y1)) @ 66.77/9.07 Y0)))))), 66.77/9.07 inference('cnf', [status(esa)], [zf_stmt_0])). 66.77/9.07 thf(zip_derived_cl292, plain, 66.77/9.07 (~ (all_of @ ((('#C') @ in @ frac)) @ 66.77/9.07 ((('#B') @ (all_of @ ((('#C') @ in @ nat))) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#C') @ 66.77/9.07 ((('#B') @ ((('#B') @ n_eq)) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#S') @ 66.77/9.07 ((('#B') @ ((('#B') @ n_fr)) @ 66.77/9.07 ((('#B') @ n_ts @ num)))))) @ 66.77/9.07 ((('#B') @ n_ts @ den)))))))) @ 66.77/9.07 ('#I'))))))), 66.77/9.07 inference('lams2combs', [status(thm)], [zip_derived_cl291])). 66.77/9.07 thf(zip_derived_cl446, plain, 66.77/9.07 (~ (all_of @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 66.77/9.07 ((('#B') @ (all_of @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#C') @ 66.77/9.07 ((('#B') @ ((('#B') @ n_eq)) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#S') @ 66.77/9.07 ((('#B') @ ((('#B') @ n_fr)) @ 66.77/9.07 ((('#B') @ n_ts @ num)))))) @ 66.77/9.07 ((('#B') @ n_ts @ den)))))))) @ 66.77/9.07 ('#I'))))))), 66.77/9.07 inference('rw', [status(thm)], [zip_derived_cl292, '0', '1'])). 66.77/9.07 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 66.77/9.07 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 66.77/9.07 thf('18', plain, 66.77/9.07 (![X0:( $i > $o ),X1:( $i > $o )]: 66.77/9.07 ( ( ~( all_of @ X0 @ X1 ) ) <=> 66.77/9.07 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 66.77/9.07 inference('rw.lit', [status(esa)], [def_all_of])). 66.77/9.07 thf(zip_derived_cl447, plain, 66.77/9.07 (~ (((!!) @ (^[Y0 : $i]: 66.77/9.07 (((is_of @ Y0 @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ 66.77/9.07 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) => 66.77/9.07 ((('#B') @ (all_of @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (d_Sep @ omega @ 66.77/9.07 ((('#C') @ (!=) @ emptyset)))))) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#C') @ 66.77/9.07 ((('#B') @ ((('#B') @ n_eq)) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#S') @ 66.77/9.07 ((('#B') @ ((('#B') @ n_fr)) @ 66.77/9.07 ((('#B') @ n_ts @ num)))))) @ 66.77/9.07 ((('#B') @ n_ts @ den)))))))) @ 66.77/9.07 ('#I'))) @ 66.77/9.07 Y0)))))))), 66.77/9.07 inference('rw_clause', [status(thm)], [zip_derived_cl446, '18'])). 66.77/9.07 thf(zip_derived_cl448, plain, 66.77/9.07 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 66.77/9.07 ((('#C') @ is_of @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ 66.77/9.07 (d_Sep @ omega @ 66.77/9.07 ((('#C') @ (!=) @ emptyset)))))))))) @ 66.77/9.07 ((('#B') @ (all_of @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#C') @ 66.77/9.07 ((('#B') @ ((('#B') @ n_eq)) @ 66.77/9.07 ((('#S') @ ((('#B') @ ('#S') @ 66.77/9.07 ((('#B') @ ((('#B') @ n_fr)) @ 66.77/9.07 ((('#B') @ n_ts @ num)))))) @ 66.77/9.07 ((('#B') @ n_ts @ den)))))))) @ 66.77/9.07 ('#I')))))))))), 66.77/9.07 inference('comb-normalize', [status(thm)], [zip_derived_cl447])). 66.77/9.07 thf(zip_derived_cl449, plain, 66.77/9.07 (~ (((is_of @ '#sk1' @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) => 66.77/9.07 (all_of @ 66.77/9.07 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.07 ((('#C') @ ((('#B') @ n_eq @ 66.77/9.07 ((('#S') @ ((('#B') @ n_fr @ (n_ts @ (num @ '#sk1')))) @ 66.77/9.07 (n_ts @ (den @ '#sk1')))))) @ 66.77/9.07 '#sk1')))))), 66.77/9.07 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl448])). 66.77/9.07 thf(zip_derived_cl450, plain, 66.77/9.07 (~ (((is_of @ '#sk1' @ 66.77/9.07 ((('#C') @ in @ 66.77/9.07 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) => 66.77/9.07 (all_of @ 66.77/9.07 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.07 ((('#C') @ ((('#B') @ n_eq @ 66.77/9.07 ((('#S') @ ((('#B') @ n_fr @ 66.77/9.07 (n_ts @ 66.77/9.07 (ap @ '#sk1' @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (ordsucc @ emptyset)))))) @ 66.77/9.07 (n_ts @ 66.77/9.07 (ap @ '#sk1' @ 66.77/9.07 (outn @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.07 (ordsucc @ emptyset)) @ 66.77/9.07 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset))))))))) @ 66.77/9.08 '#sk1')))))), 66.77/9.08 inference('rw', [status(thm)], 66.77/9.08 [zip_derived_cl449, '0', '3', '4', '5', '6', '7', '8', '9', 66.77/9.08 '10'])). 66.77/9.08 thf(zip_derived_cl452, plain, 66.77/9.08 (~ (all_of @ 66.77/9.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.08 ((('#C') @ ((('#B') @ n_eq @ 66.77/9.08 ((('#S') @ ((('#B') @ n_fr @ 66.77/9.08 (n_ts @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))))) @ 66.77/9.08 (n_ts @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))))) @ 66.77/9.08 '#sk1')))), 66.77/9.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl450])). 66.77/9.08 thf(zip_derived_cl453, plain, 66.77/9.08 (~ (((!!) @ (^[Y0 : $i]: 66.77/9.08 (((is_of @ Y0 @ 66.77/9.08 ((('#C') @ in @ 66.77/9.08 (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 66.77/9.08 ((('#C') @ ((('#B') @ n_eq @ 66.77/9.08 ((('#S') @ ((('#B') @ n_fr @ 66.77/9.08 (n_ts @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))))) @ 66.77/9.08 (n_ts @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset))))))))) @ 66.77/9.08 '#sk1' @ Y0)))))))), 66.77/9.08 inference('rw_clause', [status(thm)], [zip_derived_cl452, '18'])). 66.77/9.08 thf(zip_derived_cl454, plain, 66.77/9.08 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 66.77/9.08 ((('#C') @ is_of @ 66.77/9.08 ((('#C') @ in @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ (!=) @ emptyset))))))))) @ 66.77/9.08 ((('#C') @ ((('#B') @ n_eq @ 66.77/9.08 ((('#S') @ ((('#B') @ n_fr @ 66.77/9.08 (n_ts @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))))) @ 66.77/9.08 (n_ts @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset))))))))) @ 66.77/9.08 '#sk1'))))))), 66.77/9.08 inference('comb-normalize', [status(thm)], [zip_derived_cl453])). 66.77/9.08 thf(zip_derived_cl455, plain, 66.77/9.08 (~ (((is_of @ '#sk2' @ 66.77/9.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 66.77/9.08 (n_eq @ 66.77/9.08 (n_fr @ 66.77/9.08 (n_ts @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset))) @ 66.77/9.08 '#sk2') @ 66.77/9.08 (n_ts @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))) @ 66.77/9.08 '#sk2')) @ 66.77/9.08 '#sk1')))), 66.77/9.08 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl454])). 66.77/9.08 thf(zip_derived_cl456, plain, 66.77/9.08 (~ (((is_of @ '#sk2' @ 66.77/9.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))) => 66.77/9.08 (((ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ 66.77/9.08 (d_Sigma @ 66.77/9.08 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.08 ((('#C') @ (e_is @ 66.77/9.08 (d_Sep @ 66.77/9.08 (d_Sep @ 66.77/9.08 omega @ 66.77/9.08 ((('#C') @ ( 66.77/9.08 !=) @ 66.77/9.08 emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset) @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset)))))) @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))))) @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 '#sk2'))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 '#sk2')))) @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) = 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 (ap @ 66.77/9.08 (d_Sigma @ 66.77/9.08 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.08 ((('#C') @ (e_is @ 66.77/9.08 (d_Sep @ 66.77/9.08 (d_Sep @ 66.77/9.08 omega @ 66.77/9.08 ((('#C') @ ( 66.77/9.08 !=) @ 66.77/9.08 emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset) @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset)))))) @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))))) @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 '#sk2'))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 '#sk2')))) @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))))))), 66.77/9.08 inference('rw', [status(thm)], 66.77/9.08 [zip_derived_cl455, '11', '0', '12', '3', '13', '13', '13', 66.77/9.08 '13', '14', '4', '5', '6', '15', '7', '7', '8', '8', '16', 66.77/9.08 '9', '9', '10', '10', '17'])). 66.77/9.08 thf(zip_derived_cl458, plain, 66.77/9.08 (~ (((ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ 66.77/9.08 (d_Sigma @ 66.77/9.08 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.08 ((('#C') @ (e_is @ 66.77/9.08 (d_Sep @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ ( 66.77/9.08 !=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset) @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset)))))) @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))))) @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 '#sk2'))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 '#sk2')))) @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) = 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 (ap @ 66.77/9.08 (d_Sigma @ 66.77/9.08 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.08 ((('#C') @ (e_is @ 66.77/9.08 (d_Sep @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ ( 66.77/9.08 !=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset) @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset)))))) @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))))) @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 '#sk2'))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 '#sk2')))) @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))))), 66.77/9.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl456])). 66.77/9.08 thf(zip_derived_cl459, plain, 66.77/9.08 (((ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ 66.77/9.08 (d_Sigma @ 66.77/9.08 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.08 ((('#C') @ (e_is @ 66.77/9.08 (d_Sep @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ ( 66.77/9.08 !=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset) @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset)))))) @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))))) @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 '#sk2'))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 '#sk2')))) @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) 66.77/9.08 != (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 (ap @ 66.77/9.08 (d_Sigma @ 66.77/9.08 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.08 ((('#C') @ (e_is @ 66.77/9.08 (d_Sep @ 66.77/9.08 (d_Sep @ 66.77/9.08 omega @ 66.77/9.08 ((('#C') @ ( 66.77/9.08 !=) @ 66.77/9.08 emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset) @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset)))))) @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))))) @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 '#sk2'))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 '#sk2')))) @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))), 66.77/9.08 inference('simplify nested equalities', [status(thm)], 66.77/9.08 [zip_derived_cl458])). 66.77/9.08 thf(zip_derived_cl7807, plain, 66.77/9.08 ((((ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 (ap @ 66.77/9.08 (d_Sigma @ 66.77/9.08 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.08 ((('#C') @ (e_is @ 66.77/9.08 (d_Sep @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ ( 66.77/9.08 !=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset) @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset)))))) @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))))) @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 '#sk2'))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 '#sk2')))) @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) 66.77/9.08 != (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 (ap @ 66.77/9.08 (d_Sigma @ 66.77/9.08 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.08 ((('#C') @ (e_is @ 66.77/9.08 (d_Sep @ 66.77/9.08 (d_Sep @ 66.77/9.08 omega @ 66.77/9.08 ((('#C') @ ( 66.77/9.08 !=) @ 66.77/9.08 emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset) @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset)))))) @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))))) @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 '#sk2'))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 '#sk2')))) @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)))))) 66.77/9.08 | ~ (is_of @ '#sk1' @ 66.77/9.08 ((('#C') @ in @ 66.77/9.08 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))) 66.77/9.08 | ~ (is_of @ '#sk2' @ 66.77/9.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 66.77/9.08 inference('sup-', [status(thm)], [zip_derived_cl854, zip_derived_cl459])). 66.77/9.08 thf(zip_derived_cl451, plain, 66.77/9.08 ( (is_of @ '#sk1' @ 66.77/9.08 ((('#C') @ in @ 66.77/9.08 (pair1type @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset)))))))), 66.77/9.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl450])). 66.77/9.08 thf(zip_derived_cl457, plain, 66.77/9.08 ( (is_of @ '#sk2' @ 66.77/9.08 ((('#C') @ in @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))))))), 66.77/9.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl456])). 66.77/9.08 thf(zip_derived_cl8082, plain, 66.77/9.08 (((ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 (ap @ 66.77/9.08 (d_Sigma @ 66.77/9.08 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.08 ((('#C') @ (e_is @ 66.77/9.08 (d_Sep @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ ( 66.77/9.08 !=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset) @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset)))))) @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))))) @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 '#sk2'))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 '#sk2')))) @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) 66.77/9.08 != (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 (ap @ 66.77/9.08 (d_Sigma @ 66.77/9.08 (d_Sep @ (d_Sep @ omega @ ((('#C') @ (!=) @ emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 ((('#C') @ ((('#C') @ ((('#C') @ ((('#B') @ ite @ 66.77/9.08 ((('#C') @ (e_is @ 66.77/9.08 (d_Sep @ 66.77/9.08 (d_Sep @ 66.77/9.08 omega @ 66.77/9.08 ((('#C') @ ( 66.77/9.08 !=) @ 66.77/9.08 emptyset))) @ 66.77/9.08 ((('#C') @ lessis @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset) @ 66.77/9.08 (ordsucc @ 66.77/9.08 emptyset)))))) @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ 66.77/9.08 (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))))) @ 66.77/9.08 (d_Sep @ omega @ 66.77/9.08 ((('#C') @ (!=) @ emptyset))))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ 66.77/9.08 (ordsucc @ emptyset)) @ 66.77/9.08 (ordsucc @ emptyset)))) @ 66.77/9.08 '#sk2'))) @ 66.77/9.08 (ap @ 66.77/9.08 (times @ 66.77/9.08 (ap @ '#sk1' @ 66.77/9.08 (outn @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))) @ 66.77/9.08 '#sk2')))) @ 66.77/9.08 (outn @ (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset)) @ 66.77/9.08 (n_pl @ (ordsucc @ emptyset) @ (ordsucc @ emptyset))))))), 66.77/9.08 inference('demod', [status(thm)], 66.77/9.08 [zip_derived_cl7807, zip_derived_cl451, zip_derived_cl457])). 66.77/9.08 thf(zip_derived_cl8083, plain, ($false), 66.77/9.08 inference('simplify', [status(thm)], [zip_derived_cl8082])). 66.77/9.08 66.77/9.08 % SZS output end Refutation 66.77/9.08 66.77/9.08 66.77/9.08 % Terminating... 67.44/9.17 % Runner terminated. 67.44/9.18 % Zipperpin 1.5 exiting 67.44/9.18 EOF