0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.hUC2i08ehp true 0.15/0.36 % Computer : n004.cluster.edu 0.15/0.36 % Model : x86_64 x86_64 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.36 % Memory : 8042.1875MB 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.36 % CPULimit : 960 0.15/0.36 % WCLimit : 120 0.15/0.36 % DateTime : Tue Aug 9 07:55:35 EDT 2022 0.15/0.36 % CPUTime : 0.15/0.36 % Running portfolio for 960 s 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.15/0.36 % Number of cores: 8 0.15/0.36 % Python version: Python 3.6.8 0.15/0.36 % Running in HO mode 0.52/0.65 % Total configuration time : 828 0.52/0.65 % Estimated wc time : 1656 0.52/0.65 % Estimated cpu time (8 cpus) : 207.0 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.52/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.52/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.52/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.52/0.75 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.52/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.52/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.52/0.75 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 116.98/15.36 % Solved by lams/40_b.comb.sh. 116.98/15.36 % running E: timeout 28 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.hUC2i08ehp/e_inputf04e3a --cpu-limit=26 --auto-schedule -s -p 116.98/15.36 % done 331 iterations in 14.524s 116.98/15.36 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 116.98/15.36 % SZS output start Refutation 116.98/15.36 thf(n_1t_type, type, n_1t: $i). 116.98/15.36 thf('#sk4_type', type, '#sk4': $i). 116.98/15.36 thf('#sk5_type', type, '#sk5': $i). 116.98/15.36 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 116.98/15.36 thf(moreq_type, type, moreq: $i > $i > $o). 116.98/15.36 thf(n_is_type, type, n_is: $i > $i > $o). 116.98/15.36 thf(ap_type, type, ap: $i > $i > $i). 116.98/15.36 thf(num_type, type, num: $i > $i). 116.98/15.36 thf(n_eq_type, type, n_eq: $i > $i > $o). 116.98/15.36 thf(l_or_type, type, l_or: $o > $o > $o). 116.98/15.36 thf(n_ts_type, type, n_ts: $i > $i > $i). 116.98/15.36 thf(frac_type, type, frac: $i). 116.98/15.36 thf(in_type, type, in: $i > $i > $o). 116.98/15.36 thf(second1_type, type, second1: $i > $i > $i). 116.98/15.36 thf(lessf_type, type, lessf: $i > $i > $o). 116.98/15.36 thf(imp_type, type, imp: $o > $o > $o). 116.98/15.36 thf('#sk3_type', type, '#sk3': $i). 116.98/15.36 thf('#ty_enc6_type', type, '#ty_enc6': ($i > $i > $o) > $i > $i > $o). 116.98/15.36 thf(moref_type, type, moref: $i > $i > $o). 116.98/15.36 thf(first1_type, type, first1: $i > $i > $i). 116.98/15.36 thf(nat_type, type, nat: $i). 116.98/15.36 thf(l_some_type, type, l_some: $i > ($i > $o) > $o). 116.98/15.36 thf(lesseq_type, type, lesseq: $i > $i > $o). 116.98/15.36 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 116.98/15.36 thf(den_type, type, den: $i > $i). 116.98/15.36 thf(n_some_type, type, n_some: ($i > $o) > $o). 116.98/15.36 thf(ordsucc_type, type, ordsucc: $i > $i). 116.98/15.36 thf(iii_type, type, iii: $i > $i > $o). 116.98/15.36 thf(n_2t_type, type, n_2t: $i). 116.98/15.36 thf(pair1type_type, type, pair1type: $i > $i). 116.98/15.36 thf(d_29_ii_type, type, d_29_ii: $i > $i > $o). 116.98/15.36 thf(d_not_type, type, d_not: $o > $o). 116.98/15.36 thf('#sk2_type', type, '#sk2': $i). 116.98/15.36 thf(diffprop_type, type, diffprop: $i > $i > $i > $o). 116.98/15.36 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 116.98/15.36 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 116.98/15.36 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 116.98/15.36 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 116.98/15.36 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 116.98/15.36 thf(satz41h, axiom, 116.98/15.36 (all_of @ 116.98/15.36 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 116.98/15.36 ( ^[X0:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 116.98/15.36 ( ^[X1:$i]: ( ( lessf @ X0 @ X1 ) => ( d_not @ ( moreq @ X0 @ X1 ) ) ) ) ) ))). 116.98/15.36 thf(zip_derived_cl12, plain, 116.98/15.36 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 116.98/15.36 (^[Y0 : $i]: 116.98/15.36 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 116.98/15.36 (^[Y1 : $i]: (((lessf @ Y0 @ Y1) => (d_not @ (moreq @ Y0 @ Y1))))))))), 116.98/15.36 inference('cnf', [status(esa)], [satz41h])). 116.98/15.36 thf(zip_derived_cl13, plain, 116.98/15.36 ( (all_of @ ((('#C') @ in @ frac)) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))))), 116.98/15.36 inference('lams2combs', [status(thm)], [zip_derived_cl12])). 116.98/15.36 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))). 116.98/15.36 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])). 116.98/15.36 thf(zip_derived_cl514, plain, 116.98/15.36 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))))), 116.98/15.36 inference('rw', [status(thm)], [zip_derived_cl13, '0'])). 116.98/15.36 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 116.98/15.36 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 116.98/15.36 thf('1', plain, 116.98/15.36 (![X0:( $i > $o ),X1:( $i > $o )]: 116.98/15.36 ( ( all_of @ X0 @ X1 ) <=> 116.98/15.36 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 116.98/15.36 inference('rw.lit', [status(esa)], [def_all_of])). 116.98/15.36 thf(zip_derived_cl515, plain, 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ d_not)) @ moreq)))) @ 116.98/15.36 Y0)))))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl514, '1'])). 116.98/15.36 thf(zip_derived_cl516, plain, 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ d_not)) @ moreq))))))))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl515])). 116.98/15.36 thf(zip_derived_cl517, plain, 116.98/15.36 (![X2 : $i]: 116.98/15.36 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ 116.98/15.36 ((('#B') @ d_not @ (moreq @ X2))))))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl516])). 116.98/15.36 thf(zip_derived_cl518, plain, 116.98/15.36 (![X2 : $i]: 116.98/15.36 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ 116.98/15.36 ((('#B') @ d_not @ (moreq @ X2)))))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl517])). 116.98/15.36 thf(zip_derived_cl519, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X0))) @ 116.98/15.36 ((('#B') @ d_not @ (moreq @ X0))) @ Y0))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl518, '1'])). 116.98/15.36 thf(zip_derived_cl520, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X0))) @ 116.98/15.36 ((('#B') @ d_not @ (moreq @ X0))))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl519])). 116.98/15.36 thf(zip_derived_cl521, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((lessf @ X0 @ X2) => (d_not @ (moreq @ X0 @ X2)))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl520])). 116.98/15.36 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 116.98/15.36 thf('2', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 116.98/15.36 thf('3', plain, 116.98/15.36 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(def_n_some, axiom,(( n_some @ (X0)) = ((l_some @ nat @ X0)))). 116.98/15.36 thf('4', plain, 116.98/15.36 (![X0:( $i > $o )]: ( ( n_some @ X0 ) = ( l_some @ nat @ X0 ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(def_d_29_ii, axiom,(( d_29_ii @ (X0)@ (X1)) = 116.98/15.36 ((n_some @ (diffprop @ X0 @ X1))))). 116.98/15.36 thf('5', plain, 116.98/15.36 (![X1:$i,X0:$i]: 116.98/15.36 ( ( d_29_ii @ X0 @ X1 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(def_iii, axiom,(( iii @ (X1)@ (X0)) = ((n_some @ (diffprop @ X0 @ X1))))). 116.98/15.36 thf('6', plain, 116.98/15.36 (![X1:$i,X0:$i]: 116.98/15.36 ( ( iii @ X1 @ X0 ) = ( n_some @ ( diffprop @ X0 @ X1 ) ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(def_first1, axiom,(( first1 @ (X1)@ (X0)) = ((ap @ X0 @ n_1t)))). 116.98/15.36 thf('7', plain, 116.98/15.36 (![X1:$i,X0:$i]: ( ( first1 @ X1 @ X0 ) = ( ap @ X0 @ n_1t ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(def_second1, axiom,(( second1 @ (X1)@ (X0)) = ((ap @ X0 @ n_2t)))). 116.98/15.36 thf('8', plain, 116.98/15.36 (![X1:$i,X0:$i]: ( ( second1 @ X1 @ X0 ) = ( ap @ X0 @ n_2t ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(def_num, axiom,(( num @ (X0)) = ((first1 @ nat @ X0)))). 116.98/15.36 thf('9', plain, (![X0:$i]: ( ( num @ X0 ) = ( first1 @ nat @ X0 ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(def_den, axiom,(( den @ (X0)) = ((second1 @ nat @ X0)))). 116.98/15.36 thf('10', plain, (![X0:$i]: ( ( den @ X0 ) = ( second1 @ nat @ X0 ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(def_n_eq, axiom,(( n_eq @ (X0)@ (X1)) = 116.98/15.36 ((n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @ 116.98/15.36 (n_ts @ (num @ X1) @ (den @ X0)))))). 116.98/15.36 thf('11', plain, 116.98/15.36 (![X1:$i,X0:$i]: 116.98/15.36 ( ( n_eq @ X0 @ X1 ) = 116.98/15.36 ( n_is @ 116.98/15.36 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 116.98/15.36 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(def_moref, axiom,(( moref @ (X0)@ (X1)) = 116.98/15.36 ((d_29_ii @ (n_ts @ (num @ X0) @ (den @ X1)) @ 116.98/15.36 (n_ts @ (num @ X1) @ (den @ X0)))))). 116.98/15.36 thf('12', plain, 116.98/15.36 (![X1:$i,X0:$i]: 116.98/15.36 ( ( moref @ X0 @ X1 ) = 116.98/15.36 ( d_29_ii @ 116.98/15.36 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 116.98/15.36 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(def_lessf, axiom,(( lessf @ (X0)@ (X1)) = 116.98/15.36 ((iii @ (n_ts @ (num @ X0) @ (den @ X1)) @ (n_ts @ (num @ X1) @ (den @ X0)))))). 116.98/15.36 thf('13', plain, 116.98/15.36 (![X1:$i,X0:$i]: 116.98/15.36 ( ( lessf @ X0 @ X1 ) = 116.98/15.36 ( iii @ 116.98/15.36 ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ 116.98/15.36 ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(def_moreq, axiom,(( moreq @ (X0)@ (X1)) = 116.98/15.36 ((l_or @ (moref @ X0 @ X1) @ (n_eq @ X0 @ X1))))). 116.98/15.36 thf('14', plain, 116.98/15.36 (![X1:$i,X0:$i]: 116.98/15.36 ( ( moreq @ X0 @ X1 ) = 116.98/15.36 ( l_or @ ( moref @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(zip_derived_cl522, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))) => 116.98/15.36 (imp @ 116.98/15.36 (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw', [status(thm)], 116.98/15.36 [zip_derived_cl521, '2', '2', '3', '4', '4', '5', '6', '7', 116.98/15.36 '7', '8', '8', '9', '9', '10', '10', '11', '12', '13', '14'])). 116.98/15.36 thf(zip_derived_cl523, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (((l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))) => 116.98/15.36 (imp @ 116.98/15.36 (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl522])). 116.98/15.36 thf(zip_derived_cl524, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 (~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))) 116.98/15.36 | (imp @ 116.98/15.36 (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl523])). 116.98/15.36 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 116.98/15.36 thf('15', plain, 116.98/15.36 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 116.98/15.36 inference('rw.lit', [status(esa)], [def_imp])). 116.98/15.36 thf(zip_derived_cl525, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (((imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) => 116.98/15.36 ($false))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl524, '15'])). 116.98/15.36 thf(zip_derived_cl526, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (((~) @ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 116.98/15.36 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl525])). 116.98/15.36 thf(zip_derived_cl527, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 116.98/15.36 inference('simplify nested equalities', [status(thm)], 116.98/15.36 [zip_derived_cl526])). 116.98/15.36 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 116.98/15.36 thf('16', plain, 116.98/15.36 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 116.98/15.36 inference('rw.lit', [status(esa)], [def_imp])). 116.98/15.36 thf(zip_derived_cl528, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (((imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)) => (n_is @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl527, '16'])). 116.98/15.36 thf(zip_derived_cl529, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])). 116.98/15.36 thf(zip_derived_cl531, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (((l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) => 116.98/15.36 ($false))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl529, '15'])). 116.98/15.36 thf(zip_derived_cl532, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (((~) @ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl531])). 116.98/15.36 thf(zip_derived_cl533, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('simplify nested equalities', [status(thm)], 116.98/15.36 [zip_derived_cl532])). 116.98/15.36 thf(zip_derived_cl8847, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl533])). 116.98/15.36 thf(satz46, conjecture, 116.98/15.36 (all_of @ 116.98/15.36 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 116.98/15.36 ( ^[X0:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 116.98/15.36 ( ^[X1:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 116.98/15.36 ( ^[X2:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 116.98/15.36 ( ^[X3:$i]: 116.98/15.36 ( ( moreq @ X0 @ X1 ) => 116.98/15.36 ( ( n_eq @ X0 @ X2 ) => 116.98/15.36 ( ( n_eq @ X1 @ X3 ) => ( moreq @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 116.98/15.36 thf(zf_stmt_0, negated_conjecture, 116.98/15.36 (~( all_of @ 116.98/15.36 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 116.98/15.36 ( ^[X0:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 116.98/15.36 ( ^[X1:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 116.98/15.36 ( ^[X2:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 116.98/15.36 ( ^[X3:$i]: 116.98/15.36 ( ( moreq @ X0 @ X1 ) => 116.98/15.36 ( ( n_eq @ X0 @ X2 ) => 116.98/15.36 ( ( n_eq @ X1 @ X3 ) => ( moreq @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) )), 116.98/15.36 inference('cnf.neg', [status(esa)], [satz46])). 116.98/15.36 thf(zip_derived_cl282, plain, 116.98/15.36 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 116.98/15.36 (^[Y0 : $i]: 116.98/15.36 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 116.98/15.36 (^[Y1 : $i]: 116.98/15.36 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 116.98/15.36 (^[Y2 : $i]: 116.98/15.36 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 116.98/15.36 (^[Y3 : $i]: 116.98/15.36 (((moreq @ Y0 @ Y1) => 116.98/15.36 (((n_eq @ Y0 @ Y2) => 116.98/15.36 (((n_eq @ Y1 @ Y3) => (moreq @ Y2 @ Y3)))))))))))))))), 116.98/15.36 inference('cnf', [status(esa)], [zf_stmt_0])). 116.98/15.36 thf(zip_derived_cl283, plain, 116.98/15.36 (~ (all_of @ ((('#C') @ in @ frac)) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 moreq)))))))))))))), 116.98/15.36 inference('lams2combs', [status(thm)], [zip_derived_cl282])). 116.98/15.36 thf(zip_derived_cl1352, plain, 116.98/15.36 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ 116.98/15.36 (pair1type @ nat)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 moreq)))))))))))))), 116.98/15.36 inference('rw', [status(thm)], [zip_derived_cl283, '0'])). 116.98/15.36 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 116.98/15.36 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 116.98/15.36 thf('17', plain, 116.98/15.36 (![X0:( $i > $o ),X1:( $i > $o )]: 116.98/15.36 ( ( ~( all_of @ X0 @ X1 ) ) <=> 116.98/15.36 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 116.98/15.36 inference('rw.lit', [status(esa)], [def_all_of])). 116.98/15.36 thf(zip_derived_cl1353, plain, 116.98/15.36 (~ (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ 116.98/15.36 (pair1type @ nat)))))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ 116.98/15.36 (pair1type @ nat)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 moreq)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 n_eq)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 n_eq)))))) @ 116.98/15.36 moreq)))))))))) @ 116.98/15.36 Y0)))))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl1352, '17'])). 116.98/15.36 thf(zip_derived_cl1354, plain, 116.98/15.36 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat)))))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ 116.98/15.36 (pair1type @ nat)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 n_eq)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 n_eq)))))) @ 116.98/15.36 moreq))))))))))))))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl1353])). 116.98/15.36 thf(zip_derived_cl1355, plain, 116.98/15.36 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat)))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 moreq)))))))))))))), 116.98/15.36 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1354])). 116.98/15.36 thf(zip_derived_cl1357, plain, 116.98/15.36 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 moreq)))))))))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1355])). 116.98/15.36 thf(zip_derived_cl1358, plain, 116.98/15.36 (~ (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ 116.98/15.36 (pair1type @ nat)))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ 116.98/15.36 (n_eq @ '#sk2'))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 n_eq)))))) @ 116.98/15.36 moreq)))))))) @ 116.98/15.36 Y0)))))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl1357, '17'])). 116.98/15.36 thf(zip_derived_cl1359, plain, 116.98/15.36 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat)))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (moreq @ '#sk2'))))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ 116.98/15.36 (n_eq @ '#sk2'))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 moreq))))))))))))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl1358])). 116.98/15.36 thf(zip_derived_cl1360, plain, 116.98/15.36 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (((=>) @ (moreq @ '#sk2' @ '#sk3'))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))))) @ 116.98/15.36 moreq)))))))))))), 116.98/15.36 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1359])). 116.98/15.36 thf(zip_derived_cl1361, plain, 116.98/15.36 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))))) @ 116.98/15.36 moreq)))))))))))), 116.98/15.36 inference('rw', [status(thm)], 116.98/15.36 [zip_derived_cl1360, '2', '3', '4', '5', '7', '7', '8', '8', 116.98/15.36 '9', '9', '10', '10', '11', '12', '14'])). 116.98/15.36 thf(zip_derived_cl1363, plain, 116.98/15.36 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))))) @ 116.98/15.36 moreq)))))))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])). 116.98/15.36 thf(zip_derived_cl1364, plain, 116.98/15.36 (~ (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ 116.98/15.36 (ap @ '#sk2' @ 116.98/15.36 n_1t) @ 116.98/15.36 (ap @ '#sk3' @ 116.98/15.36 n_2t)) @ 116.98/15.36 (n_ts @ 116.98/15.36 (ap @ '#sk3' @ 116.98/15.36 n_1t) @ 116.98/15.36 (ap @ '#sk2' @ 116.98/15.36 n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ 116.98/15.36 (n_ts @ 116.98/15.36 (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ 116.98/15.36 (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 (n_eq @ '#sk3'))))) @ 116.98/15.36 moreq)))))) @ 116.98/15.36 Y0)))))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl1363, '17'])). 116.98/15.36 thf(zip_derived_cl1365, plain, 116.98/15.36 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (((=>) @ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ 116.98/15.36 (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ 116.98/15.36 (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ 116.98/15.36 (n_ts @ 116.98/15.36 (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ 116.98/15.36 (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ '#sk2'))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 (n_eq @ '#sk3'))))) @ 116.98/15.36 moreq))))))))))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl1364])). 116.98/15.36 thf(zip_derived_cl1366, plain, 116.98/15.36 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (((=>) @ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_eq @ '#sk2' @ '#sk4'))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @ 116.98/15.36 (moreq @ '#sk4'))))))))))), 116.98/15.36 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1365])). 116.98/15.36 thf(zip_derived_cl1367, plain, 116.98/15.36 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (((=>) @ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk4' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @ 116.98/15.36 (moreq @ '#sk4'))))))))))), 116.98/15.36 inference('rw', [status(thm)], 116.98/15.36 [zip_derived_cl1366, '7', '7', '8', '8', '9', '9', '10', '10', 116.98/15.36 '11'])). 116.98/15.36 thf(zip_derived_cl1369, plain, 116.98/15.36 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (((=>) @ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk4' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @ (moreq @ '#sk4'))))))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1367])). 116.98/15.36 thf(zip_derived_cl1370, plain, 116.98/15.36 (~ (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (((=>) @ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk4' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @ 116.98/15.36 (moreq @ '#sk4'))))) @ 116.98/15.36 Y0)))))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl1369, '17'])). 116.98/15.36 thf(zip_derived_cl1371, plain, 116.98/15.36 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (((=>) @ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t)))))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ 116.98/15.36 (ap @ '#sk4' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ 116.98/15.36 (ap @ '#sk2' @ n_2t))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ '#sk3'))) @ 116.98/15.36 (moreq @ '#sk4')))))))))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl1370])). 116.98/15.36 thf(zip_derived_cl1372, plain, 116.98/15.36 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t))) => 116.98/15.36 (((n_eq @ '#sk3' @ '#sk5') => (moreq @ '#sk4' @ '#sk5')))))))))), 116.98/15.36 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1371])). 116.98/15.36 thf(zip_derived_cl1373, plain, 116.98/15.36 (~ (((is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t))) => 116.98/15.36 (((n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t))) => 116.98/15.36 (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))))))), 116.98/15.36 inference('rw', [status(thm)], 116.98/15.36 [zip_derived_cl1372, '2', '3', '4', '5', '7', '7', '7', '8', 116.98/15.36 '8', '8', '9', '9', '9', '10', '10', '10', '11', '11', '12', 116.98/15.36 '14'])). 116.98/15.36 thf(zip_derived_cl1375, plain, 116.98/15.36 (~ (((imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t))) => (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1373])). 116.98/15.36 thf(zip_derived_cl1377, plain, 116.98/15.36 (~ (((n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t))) => (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1375])). 116.98/15.36 thf(zip_derived_cl1380, plain, 116.98/15.36 (~ (((n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t))) => (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])). 116.98/15.36 thf(zip_derived_cl1383, plain, 116.98/15.36 (~ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1380])). 116.98/15.36 thf(zip_derived_cl1385, plain, 116.98/15.36 (~ (((imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 116.98/15.36 ($false)) => (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl1383, '16'])). 116.98/15.36 thf(zip_derived_cl1388, plain, 116.98/15.36 ( (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) @ 116.98/15.36 ($false))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1385])). 116.98/15.36 thf(zip_derived_cl1390, plain, 116.98/15.36 ( (((l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))) => 116.98/15.36 ($false)))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl1388, '15'])). 116.98/15.36 thf(zip_derived_cl1391, plain, 116.98/15.36 ( (((~) @ (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))))), 116.98/15.36 inference('simplify boolean subterms', [status(thm)], 116.98/15.36 [zip_derived_cl1390])). 116.98/15.36 thf(zip_derived_cl1392, plain, 116.98/15.36 (~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t))))), 116.98/15.36 inference('simplify nested equalities', [status(thm)], 116.98/15.36 [zip_derived_cl1391])). 116.98/15.36 thf(ordsucc_inj, axiom, 116.98/15.36 (![X0:$i,X1:$i]: 116.98/15.36 ( ( ( ordsucc @ X0 ) = ( ordsucc @ X1 ) ) => ( ( X0 ) = ( X1 ) ) ))). 116.98/15.36 thf(zip_derived_cl0, plain, 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((!!) @ (^[Y1 : $i]: 116.98/15.36 (((((ordsucc @ Y0) = (ordsucc @ Y1))) => 116.98/15.36 (((Y0) = (Y1)))))))))))), 116.98/15.36 inference('cnf', [status(esa)], [ordsucc_inj])). 116.98/15.36 thf(zip_derived_cl1, plain, 116.98/15.36 ( (((!!) @ ((('#B') @ (!!) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=) @ ordsucc)))) @ 116.98/15.36 ordsucc)))))) @ 116.98/15.36 (=)))))))), 116.98/15.36 inference('lams2combs', [status(thm)], [zip_derived_cl0])). 116.98/15.36 thf(zip_derived_cl354, plain, 116.98/15.36 (![X2 : $i]: 116.98/15.36 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#B') @ ((($i) = (ordsucc @ X2))) @ ordsucc)))) @ 116.98/15.36 ((($i) = (X2)))))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 116.98/15.36 thf(zip_derived_cl355, plain, 116.98/15.36 (![X2 : $i, X4 : $i]: 116.98/15.36 (((((ordsucc @ X2) = (ordsucc @ X4))) => (((X2) = (X4)))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl354])). 116.98/15.36 thf(zip_derived_cl356, plain, 116.98/15.36 (![X2 : $i, X4 : $i]: 116.98/15.36 (~ (((ordsucc @ X2) = (ordsucc @ X4))) | (((X2) = (X4))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl355])). 116.98/15.36 thf(zip_derived_cl357, plain, 116.98/15.36 (![X2 : $i, X4 : $i]: 116.98/15.36 (((ordsucc @ X2) != (ordsucc @ X4)) | ((X2) = (X4)))), 116.98/15.36 inference('simplify nested equalities', [status(thm)], 116.98/15.36 [zip_derived_cl356])). 116.98/15.36 thf(zip_derived_cl1368, plain, 116.98/15.36 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1367])). 116.98/15.36 thf(zip_derived_cl2687, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (is_of @ '#sk4' @ ((('#C') @ in @ X0))) 116.98/15.36 | ((ordsucc @ X0) != (ordsucc @ (pair1type @ nat))))), 116.98/15.36 inference('sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl1368])). 116.98/15.36 thf(zip_derived_cl8928, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (is_of @ '#sk4' @ ('#ty_enc6' @ in @ X0)) 116.98/15.36 | ((ordsucc @ X0) != (ordsucc @ (pair1type @ nat))))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl2687])). 116.98/15.36 thf(satz45, axiom, 116.98/15.36 (all_of @ 116.98/15.36 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 116.98/15.36 ( ^[X0:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 116.98/15.36 ( ^[X1:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 116.98/15.36 ( ^[X2:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X3:$i]: ( in @ X3 @ frac ) ) @ 116.98/15.36 ( ^[X3:$i]: 116.98/15.36 ( ( lessf @ X0 @ X1 ) => 116.98/15.36 ( ( n_eq @ X0 @ X2 ) => 116.98/15.36 ( ( n_eq @ X1 @ X3 ) => ( lessf @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ))). 116.98/15.36 thf(zip_derived_cl192, plain, 116.98/15.36 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 116.98/15.36 (^[Y0 : $i]: 116.98/15.36 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 116.98/15.36 (^[Y1 : $i]: 116.98/15.36 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 116.98/15.36 (^[Y2 : $i]: 116.98/15.36 (all_of @ (^[Y3 : $i]: (in @ Y3 @ frac)) @ 116.98/15.36 (^[Y3 : $i]: 116.98/15.36 (((lessf @ Y0 @ Y1) => 116.98/15.36 (((n_eq @ Y0 @ Y2) => 116.98/15.36 (((n_eq @ Y1 @ Y3) => (lessf @ Y2 @ Y3)))))))))))))))), 116.98/15.36 inference('cnf', [status(esa)], [satz45])). 116.98/15.36 thf(zip_derived_cl193, plain, 116.98/15.36 ( (all_of @ ((('#C') @ in @ frac)) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 lessf)))))))))))))), 116.98/15.36 inference('lams2combs', [status(thm)], [zip_derived_cl192])). 116.98/15.36 thf(zip_derived_cl2543, plain, 116.98/15.36 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ 116.98/15.36 (pair1type @ nat)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 lessf)))))))))))))), 116.98/15.36 inference('rw', [status(thm)], [zip_derived_cl193, '0'])). 116.98/15.36 thf(zip_derived_cl2544, plain, 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ 116.98/15.36 (pair1type @ nat)))))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ 116.98/15.36 (pair1type @ nat)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 lessf)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 n_eq)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 n_eq)))))) @ 116.98/15.36 lessf)))))))))) @ 116.98/15.36 Y0)))))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl2543, '1'])). 116.98/15.36 thf(zip_derived_cl2545, plain, 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat)))))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ 116.98/15.36 (pair1type @ nat)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ lessf)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 lessf))))))))))))))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl2544])). 116.98/15.36 thf(zip_derived_cl2546, plain, 116.98/15.36 (![X2 : $i]: 116.98/15.36 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat)))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (lessf @ X2))))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 lessf)))))))))))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2545])). 116.98/15.36 thf(zip_derived_cl2547, plain, 116.98/15.36 (![X2 : $i]: 116.98/15.36 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat)))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (lessf @ X2))))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ X2))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 lessf))))))))))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2546])). 116.98/15.36 thf(zip_derived_cl2548, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ 116.98/15.36 (pair1type @ nat)))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (lessf @ X0))))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ 116.98/15.36 (n_eq @ X0))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 n_eq)))))) @ 116.98/15.36 lessf)))))))) @ 116.98/15.36 Y0))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl2547, '1'])). 116.98/15.36 thf(zip_derived_cl2549, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ 116.98/15.36 (pair1type @ nat)))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (lessf @ X0))))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ 116.98/15.36 (n_eq @ X0))))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 n_eq)))))) @ 116.98/15.36 lessf)))))))))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl2548])). 116.98/15.36 thf(zip_derived_cl2550, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (((=>) @ (lessf @ X0 @ X2))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 116.98/15.36 lessf))))))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2549])). 116.98/15.36 thf(zip_derived_cl2551, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ 116.98/15.36 (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ 116.98/15.36 (ap @ X2 @ n_2t)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X0))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 116.98/15.36 lessf))))))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw', [status(thm)], 116.98/15.36 [zip_derived_cl2550, '4', '6', '7', '7', '8', '8', '9', '9', 116.98/15.36 '10', '10', '13'])). 116.98/15.36 thf(zip_derived_cl2552, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ 116.98/15.36 (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ 116.98/15.36 (ap @ X2 @ n_2t)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 116.98/15.36 lessf))))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2551])). 116.98/15.36 thf(zip_derived_cl2553, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ 116.98/15.36 (ap @ X1 @ n_1t) @ 116.98/15.36 (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ 116.98/15.36 (ap @ X0 @ n_1t) @ 116.98/15.36 (ap @ X1 @ n_2t)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 (n_eq @ X1))))) @ 116.98/15.36 lessf)))))) @ 116.98/15.36 Y0))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl2552, '1'])). 116.98/15.36 thf(zip_derived_cl2554, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (((=>) @ (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ 116.98/15.36 (ap @ X1 @ n_1t) @ 116.98/15.36 (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ 116.98/15.36 (ap @ X0 @ n_1t) @ 116.98/15.36 (ap @ X1 @ n_2t)))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 116.98/15.36 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))))) @ 116.98/15.36 lessf)))))))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl2553])). 116.98/15.36 thf(zip_derived_cl2555, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X3 : $i]: 116.98/15.36 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (((=>) @ (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_eq @ X0 @ X3))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3)))))))))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2554])). 116.98/15.36 thf(zip_derived_cl2556, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X3 : $i]: 116.98/15.36 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (((=>) @ (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_is @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3)))))))))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw', [status(thm)], 116.98/15.36 [zip_derived_cl2555, '7', '7', '8', '8', '9', '9', '10', '10', 116.98/15.36 '11'])). 116.98/15.36 thf(zip_derived_cl2557, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X3 : $i]: 116.98/15.36 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (((=>) @ (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_is @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ 116.98/15.36 (ap @ X3 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X3 @ n_1t) @ 116.98/15.36 (ap @ X0 @ n_2t))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ (lessf @ X3)))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2556])). 116.98/15.36 thf(zip_derived_cl2558, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X2 : $i]: 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (((=>) @ (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ 116.98/15.36 (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ 116.98/15.36 (ap @ X0 @ n_2t)))))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_is @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ 116.98/15.36 (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ 116.98/15.36 (ap @ X1 @ n_2t))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 116.98/15.36 (lessf @ X2))))) @ 116.98/15.36 Y0))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl2557, '1'])). 116.98/15.36 thf(zip_derived_cl2559, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X2 : $i]: 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (((=>) @ (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ 116.98/15.36 (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ 116.98/15.36 (ap @ X0 @ n_2t)))))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_is @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ 116.98/15.36 (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ 116.98/15.36 (ap @ X1 @ n_2t))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 116.98/15.36 (lessf @ X2))))))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl2558])). 116.98/15.36 thf(zip_derived_cl2560, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 116.98/15.36 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 116.98/15.36 (((n_eq @ X0 @ X4) => (lessf @ X2 @ X4))))))))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2559])). 116.98/15.36 thf(zip_derived_cl2561, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 116.98/15.36 ( (((is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 116.98/15.36 nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))))))))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw', [status(thm)], 116.98/15.36 [zip_derived_cl2560, '4', '6', '7', '7', '7', '8', '8', '8', 116.98/15.36 '9', '9', '9', '10', '10', '10', '11', '13'])). 116.98/15.36 thf(zip_derived_cl2562, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 116.98/15.36 (~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (((l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 116.98/15.36 nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2561])). 116.98/15.36 thf(zip_derived_cl2563, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 116.98/15.36 (~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 116.98/15.36 nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2562])). 116.98/15.36 thf(zip_derived_cl2564, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))) 116.98/15.36 | (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) => (l_some @ 116.98/15.36 nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))))) 116.98/15.36 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2563])). 116.98/15.36 thf(zip_derived_cl2565, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) 116.98/15.36 | (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X4 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2564])). 116.98/15.36 thf(zip_derived_cl8922, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X4 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X0 @ n_2t))) 116.98/15.36 | (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X4 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X4 @ n_2t)))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (is_of @ X4 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X1 @ n_2t))))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl2565])). 116.98/15.36 thf(satz41d, axiom, 116.98/15.36 (all_of @ 116.98/15.36 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 116.98/15.36 ( ^[X0:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 116.98/15.36 ( ^[X1:$i]: 116.98/15.36 ( ( lesseq @ X0 @ X1 ) => ( d_not @ ( moref @ X0 @ X1 ) ) ) ) ) ))). 116.98/15.36 thf(zip_derived_cl40, plain, 116.98/15.36 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 116.98/15.36 (^[Y0 : $i]: 116.98/15.36 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 116.98/15.36 (^[Y1 : $i]: (((lesseq @ Y0 @ Y1) => (d_not @ (moref @ Y0 @ Y1))))))))), 116.98/15.36 inference('cnf', [status(esa)], [satz41d])). 116.98/15.36 thf(zip_derived_cl41, plain, 116.98/15.36 ( (all_of @ ((('#C') @ in @ frac)) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ d_not)) @ moref)))))))), 116.98/15.36 inference('lams2combs', [status(thm)], [zip_derived_cl40])). 116.98/15.36 thf(zip_derived_cl570, plain, 116.98/15.36 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ d_not)) @ moref)))))))), 116.98/15.36 inference('rw', [status(thm)], [zip_derived_cl41, '0'])). 116.98/15.36 thf(zip_derived_cl571, plain, 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ d_not)) @ moref)))) @ 116.98/15.36 Y0)))))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl570, '1'])). 116.98/15.36 thf(zip_derived_cl572, plain, 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ d_not)) @ moref))))))))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl571])). 116.98/15.36 thf(zip_derived_cl573, plain, 116.98/15.36 (![X2 : $i]: 116.98/15.36 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ X2))) @ 116.98/15.36 ((('#B') @ d_not @ (moref @ X2))))))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl572])). 116.98/15.36 thf(zip_derived_cl574, plain, 116.98/15.36 (![X2 : $i]: 116.98/15.36 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ X2))) @ 116.98/15.36 ((('#B') @ d_not @ (moref @ X2)))))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl573])). 116.98/15.36 thf(zip_derived_cl575, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ X0))) @ 116.98/15.36 ((('#B') @ d_not @ (moref @ X0))) @ Y0))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl574, '1'])). 116.98/15.36 thf(zip_derived_cl576, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ X0))) @ 116.98/15.36 ((('#B') @ d_not @ (moref @ X0))))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl575])). 116.98/15.36 thf(zip_derived_cl577, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((lesseq @ X0 @ X2) => (d_not @ (moref @ X0 @ X2)))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl576])). 116.98/15.36 thf(def_lesseq, axiom,(( lesseq @ (X0)@ (X1)) = 116.98/15.36 ((l_or @ (lessf @ X0 @ X1) @ (n_eq @ X0 @ X1))))). 116.98/15.36 thf('18', plain, 116.98/15.36 (![X1:$i,X0:$i]: 116.98/15.36 ( ( lesseq @ X0 @ X1 ) = 116.98/15.36 ( l_or @ ( lessf @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )), 116.98/15.36 define([status(thm)])). 116.98/15.36 thf(zip_derived_cl578, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) => 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw', [status(thm)], 116.98/15.36 [zip_derived_cl577, '2', '2', '3', '4', '4', '5', '6', '7', 116.98/15.36 '7', '8', '8', '9', '9', '10', '10', '11', '12', '13', '18'])). 116.98/15.36 thf(zip_derived_cl579, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (((imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) => 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])). 116.98/15.36 thf(zip_derived_cl580, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 (~ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl579])). 116.98/15.36 thf(zip_derived_cl581, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (((imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)) => (n_is @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl580, '16'])). 116.98/15.36 thf(zip_derived_cl582, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (((l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) => 116.98/15.36 ($false))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (((imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)) => (n_is @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl581, '15'])). 116.98/15.36 thf(zip_derived_cl583, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (((~) @ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (((imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)) => (n_is @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))))))), 116.98/15.36 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl582])). 116.98/15.36 thf(zip_derived_cl584, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (((imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)) => (n_is @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))))))), 116.98/15.36 inference('simplify nested equalities', [status(thm)], 116.98/15.36 [zip_derived_cl583])). 116.98/15.36 thf(zip_derived_cl586, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl584])). 116.98/15.36 thf(zip_derived_cl8849, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))) 116.98/15.36 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl586])). 116.98/15.36 thf(zip_derived_cl357, plain, 116.98/15.36 (![X2 : $i, X4 : $i]: 116.98/15.36 (((ordsucc @ X2) != (ordsucc @ X4)) | ((X2) = (X4)))), 116.98/15.36 inference('simplify nested equalities', [status(thm)], 116.98/15.36 [zip_derived_cl356])). 116.98/15.36 thf(zip_derived_cl1374, plain, 116.98/15.36 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1373])). 116.98/15.36 thf(zip_derived_cl2702, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (is_of @ '#sk5' @ ((('#C') @ in @ X0))) 116.98/15.36 | ((ordsucc @ X0) != (ordsucc @ (pair1type @ nat))))), 116.98/15.36 inference('sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl1374])). 116.98/15.36 thf(zip_derived_cl8924, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (is_of @ '#sk5' @ ('#ty_enc6' @ in @ X0)) 116.98/15.36 | ((ordsucc @ X0) != (ordsucc @ (pair1type @ nat))))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl2702])). 116.98/15.36 thf(satz41j, axiom, 116.98/15.36 (all_of @ 116.98/15.36 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 116.98/15.36 ( ^[X0:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 116.98/15.36 ( ^[X1:$i]: ( ( d_not @ ( moreq @ X0 @ X1 ) ) => ( lessf @ X0 @ X1 ) ) ) ) ))). 116.98/15.36 thf(zip_derived_cl124, plain, 116.98/15.36 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 116.98/15.36 (^[Y0 : $i]: 116.98/15.36 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 116.98/15.36 (^[Y1 : $i]: (((d_not @ (moreq @ Y0 @ Y1)) => (lessf @ Y0 @ Y1)))))))), 116.98/15.36 inference('cnf', [status(esa)], [satz41j])). 116.98/15.36 thf(zip_derived_cl125, plain, 116.98/15.36 ( (all_of @ ((('#C') @ in @ frac)) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))) @ 116.98/15.36 lessf)))))), 116.98/15.36 inference('lams2combs', [status(thm)], [zip_derived_cl124])). 116.98/15.36 thf(zip_derived_cl675, plain, 116.98/15.36 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))) @ 116.98/15.36 lessf)))))), 116.98/15.36 inference('rw', [status(thm)], [zip_derived_cl125, '0'])). 116.98/15.36 thf(zip_derived_cl676, plain, 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))) @ 116.98/15.36 lessf)) @ 116.98/15.36 Y0)))))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl675, '1'])). 116.98/15.36 thf(zip_derived_cl677, plain, 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))) @ 116.98/15.36 lessf))))))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl676])). 116.98/15.36 thf(zip_derived_cl678, plain, 116.98/15.36 (![X2 : $i]: 116.98/15.36 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (moreq @ X2))))) @ 116.98/15.36 (lessf @ X2))))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl677])). 116.98/15.36 thf(zip_derived_cl679, plain, 116.98/15.36 (![X2 : $i]: 116.98/15.36 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (moreq @ X2))))) @ 116.98/15.36 (lessf @ X2)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl678])). 116.98/15.36 thf(zip_derived_cl680, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#B') @ d_not @ (moreq @ X0))))) @ 116.98/15.36 (lessf @ X0) @ Y0))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl679, '1'])). 116.98/15.36 thf(zip_derived_cl681, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#B') @ d_not @ (moreq @ X0))))) @ 116.98/15.36 (lessf @ X0))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl680])). 116.98/15.36 thf(zip_derived_cl682, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((d_not @ (moreq @ X0 @ X2)) => (lessf @ X0 @ X2))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl681])). 116.98/15.36 thf(zip_derived_cl683, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((imp @ 116.98/15.36 (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)) => (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw', [status(thm)], 116.98/15.36 [zip_derived_cl682, '2', '2', '3', '4', '4', '5', '6', '7', 116.98/15.36 '7', '8', '8', '9', '9', '10', '10', '11', '12', '13', '14'])). 116.98/15.36 thf(zip_derived_cl684, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (((imp @ 116.98/15.36 (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)) => (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl683])). 116.98/15.36 thf(zip_derived_cl685, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 (~ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)))) @ 116.98/15.36 ($false)) 116.98/15.36 | (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl684])). 116.98/15.36 thf(zip_derived_cl686, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (((imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) => 116.98/15.36 ($false))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl685, '16'])). 116.98/15.36 thf(zip_derived_cl687, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (((~) @ (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 116.98/15.36 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl686])). 116.98/15.36 thf(zip_derived_cl688, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 116.98/15.36 inference('simplify nested equalities', [status(thm)], 116.98/15.36 [zip_derived_cl687])). 116.98/15.36 thf(zip_derived_cl689, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (((imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)) => (n_is @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))))) 116.98/15.36 | (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl688, '15'])). 116.98/15.36 thf(zip_derived_cl690, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) @ 116.98/15.36 ($false)) 116.98/15.36 | (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl689])). 116.98/15.36 thf(zip_derived_cl691, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (((l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) => 116.98/15.36 ($false))) 116.98/15.36 | (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl690, '16'])). 116.98/15.36 thf(zip_derived_cl692, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (((~) @ (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))))) 116.98/15.36 | (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))))), 116.98/15.36 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl691])). 116.98/15.36 thf(zip_derived_cl693, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) 116.98/15.36 | (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))))), 116.98/15.36 inference('simplify nested equalities', [status(thm)], 116.98/15.36 [zip_derived_cl692])). 116.98/15.36 thf(zip_derived_cl8854, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)))) 116.98/15.36 | (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))) 116.98/15.36 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl693])). 116.98/15.36 thf(zip_derived_cl1389, plain, 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk4' @ n_2t)))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1385])). 116.98/15.36 thf(zip_derived_cl1379, plain, 116.98/15.36 ( (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])). 116.98/15.36 thf(satz38, axiom, 116.98/15.36 (all_of @ 116.98/15.36 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 116.98/15.36 ( ^[X0:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 116.98/15.36 ( ^[X1:$i]: ( ( n_eq @ X0 @ X1 ) => ( n_eq @ X1 @ X0 ) ) ) ) ))). 116.98/15.36 thf(zip_derived_cl92, plain, 116.98/15.36 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 116.98/15.36 (^[Y0 : $i]: 116.98/15.36 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 116.98/15.36 (^[Y1 : $i]: (((n_eq @ Y0 @ Y1) => (n_eq @ Y1 @ Y0)))))))), 116.98/15.36 inference('cnf', [status(esa)], [satz38])). 116.98/15.36 thf(zip_derived_cl93, plain, 116.98/15.36 ( (all_of @ ((('#C') @ in @ frac)) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 116.98/15.36 ((('#C') @ n_eq)))))))), 116.98/15.36 inference('lams2combs', [status(thm)], [zip_derived_cl92])). 116.98/15.36 thf(zip_derived_cl403, plain, 116.98/15.36 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 116.98/15.36 ((('#C') @ n_eq)))))))), 116.98/15.36 inference('rw', [status(thm)], [zip_derived_cl93, '0'])). 116.98/15.36 thf(zip_derived_cl404, plain, 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 116.98/15.36 ((('#C') @ n_eq)))) @ 116.98/15.36 Y0)))))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl403, '1'])). 116.98/15.36 thf(zip_derived_cl405, plain, 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 116.98/15.36 ((('#C') @ n_eq))))))))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl404])). 116.98/15.36 thf(zip_derived_cl406, plain, 116.98/15.36 (![X2 : $i]: 116.98/15.36 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ ((('#C') @ n_eq @ X2)))))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl405])). 116.98/15.36 thf(zip_derived_cl407, plain, 116.98/15.36 (![X2 : $i]: 116.98/15.36 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ 116.98/15.36 ((('#C') @ n_eq @ X2))))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl406])). 116.98/15.36 thf(zip_derived_cl408, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 116.98/15.36 ((('#C') @ n_eq @ X0)) @ Y0))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl407, '1'])). 116.98/15.36 thf(zip_derived_cl409, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X0))) @ 116.98/15.36 ((('#C') @ n_eq @ X0)))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl408])). 116.98/15.36 thf(zip_derived_cl410, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((n_eq @ X0 @ X2) => (n_eq @ X2 @ X0))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl409])). 116.98/15.36 thf(zip_derived_cl411, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) => (n_is @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw', [status(thm)], 116.98/15.36 [zip_derived_cl410, '7', '7', '8', '8', '9', '9', '10', '10', 116.98/15.36 '11', '11'])). 116.98/15.36 thf(zip_derived_cl412, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) => (n_is @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl411])). 116.98/15.36 thf(zip_derived_cl413, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl412])). 116.98/15.36 thf(zip_derived_cl3366, plain, 116.98/15.36 ((~ (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t))))), 116.98/15.36 inference('sup-', [status(thm)], [zip_derived_cl1379, zip_derived_cl413])). 116.98/15.36 thf(zip_derived_cl1368, plain, 116.98/15.36 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1367])). 116.98/15.36 thf(zip_derived_cl1356, plain, 116.98/15.36 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1355])). 116.98/15.36 thf(zip_derived_cl3404, plain, 116.98/15.36 ( (n_is @ (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)))), 116.98/15.36 inference('demod', [status(thm)], 116.98/15.36 [zip_derived_cl3366, zip_derived_cl1368, zip_derived_cl1356])). 116.98/15.36 thf(zip_derived_cl1376, plain, 116.98/15.36 ( (imp @ 116.98/15.36 (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) @ 116.98/15.36 (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1375])). 116.98/15.36 thf(zip_derived_cl1378, plain, 116.98/15.36 ( (((imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) => (n_is @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl1376, '15'])). 116.98/15.36 thf(zip_derived_cl1381, plain, 116.98/15.36 ((~ (imp @ 116.98/15.36 (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) @ 116.98/15.36 ($false)) 116.98/15.36 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1378])). 116.98/15.36 thf(zip_derived_cl1384, plain, 116.98/15.36 ((~ (((l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) => 116.98/15.36 ($false))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl1381, '16'])). 116.98/15.36 thf(zip_derived_cl1386, plain, 116.98/15.36 ((~ (((~) @ (l_some @ nat @ 116.98/15.36 (diffprop @ 116.98/15.36 (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))), 116.98/15.36 inference('simplify boolean subterms', [status(thm)], 116.98/15.36 [zip_derived_cl1384])). 116.98/15.36 thf(zip_derived_cl1387, plain, 116.98/15.36 (( (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t)))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk2' @ n_2t))))), 116.98/15.36 inference('simplify nested equalities', [status(thm)], 116.98/15.36 [zip_derived_cl1386])). 116.98/15.36 thf(zip_derived_cl1382, plain, 116.98/15.36 ( (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t)))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1380])). 116.98/15.36 thf(zip_derived_cl413, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl412])). 116.98/15.36 thf(zip_derived_cl3367, plain, 116.98/15.36 ((~ (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t))))), 116.98/15.36 inference('sup-', [status(thm)], [zip_derived_cl1382, zip_derived_cl413])). 116.98/15.36 thf(zip_derived_cl1374, plain, 116.98/15.36 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1373])). 116.98/15.36 thf(zip_derived_cl1362, plain, 116.98/15.36 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])). 116.98/15.36 thf(zip_derived_cl3405, plain, 116.98/15.36 ( (n_is @ (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)))), 116.98/15.36 inference('demod', [status(thm)], 116.98/15.36 [zip_derived_cl3367, zip_derived_cl1374, zip_derived_cl1362])). 116.98/15.36 thf(zip_derived_cl357, plain, 116.98/15.36 (![X2 : $i, X4 : $i]: 116.98/15.36 (((ordsucc @ X2) != (ordsucc @ X4)) | ((X2) = (X4)))), 116.98/15.36 inference('simplify nested equalities', [status(thm)], 116.98/15.36 [zip_derived_cl356])). 116.98/15.36 thf(zip_derived_cl1356, plain, 116.98/15.36 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1355])). 116.98/15.36 thf(zip_derived_cl2685, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (is_of @ '#sk2' @ ((('#C') @ in @ X0))) 116.98/15.36 | ((ordsucc @ X0) != (ordsucc @ (pair1type @ nat))))), 116.98/15.36 inference('sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl1356])). 116.98/15.36 thf(zip_derived_cl8930, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (is_of @ '#sk2' @ ('#ty_enc6' @ in @ X0)) 116.98/15.36 | ((ordsucc @ X0) != (ordsucc @ (pair1type @ nat))))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl2685])). 116.98/15.36 thf(zip_derived_cl1374, plain, 116.98/15.36 ( (is_of @ '#sk5' @ ((('#C') @ in @ (pair1type @ nat))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1373])). 116.98/15.36 thf(zip_derived_cl8890, plain, 116.98/15.36 ( (is_of @ '#sk5' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl1374])). 116.98/15.36 thf(zip_derived_cl1362, plain, 116.98/15.36 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])). 116.98/15.36 thf(zip_derived_cl8888, plain, 116.98/15.36 ( (is_of @ '#sk3' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl1362])). 116.98/15.36 thf(zip_derived_cl1382, plain, 116.98/15.36 ( (n_is @ (n_ts @ (ap @ '#sk3' @ n_1t) @ (ap @ '#sk5' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk5' @ n_1t) @ (ap @ '#sk3' @ n_2t)))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1380])). 116.98/15.36 thf(zip_derived_cl530, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])). 116.98/15.36 thf(zip_derived_cl8846, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t))) 116.98/15.36 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (l_some @ nat @ 116.98/15.36 (diffprop @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t)))))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl530])). 116.98/15.36 thf(zip_derived_cl357, plain, 116.98/15.36 (![X2 : $i, X4 : $i]: 116.98/15.36 (((ordsucc @ X2) != (ordsucc @ X4)) | ((X2) = (X4)))), 116.98/15.36 inference('simplify nested equalities', [status(thm)], 116.98/15.36 [zip_derived_cl356])). 116.98/15.36 thf(zip_derived_cl1362, plain, 116.98/15.36 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])). 116.98/15.36 thf(zip_derived_cl2686, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (is_of @ '#sk3' @ ((('#C') @ in @ X0))) 116.98/15.36 | ((ordsucc @ X0) != (ordsucc @ (pair1type @ nat))))), 116.98/15.36 inference('sup+', [status(thm)], [zip_derived_cl357, zip_derived_cl1362])). 116.98/15.36 thf(zip_derived_cl8929, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (is_of @ '#sk3' @ ('#ty_enc6' @ in @ X0)) 116.98/15.36 | ((ordsucc @ X0) != (ordsucc @ (pair1type @ nat))))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl2686])). 116.98/15.36 thf(zip_derived_cl1368, plain, 116.98/15.36 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1367])). 116.98/15.36 thf(zip_derived_cl8889, plain, 116.98/15.36 ( (is_of @ '#sk4' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl1368])). 116.98/15.36 thf(zip_derived_cl1356, plain, 116.98/15.36 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1355])). 116.98/15.36 thf(zip_derived_cl8887, plain, 116.98/15.36 ( (is_of @ '#sk2' @ ('#ty_enc6' @ in @ (pair1type @ nat)))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl1356])). 116.98/15.36 thf(zip_derived_cl1379, plain, 116.98/15.36 ( (n_is @ (n_ts @ (ap @ '#sk2' @ n_1t) @ (ap @ '#sk4' @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ '#sk4' @ n_1t) @ (ap @ '#sk2' @ n_2t)))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])). 116.98/15.36 thf(zip_derived_cl413, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl412])). 116.98/15.36 thf(zip_derived_cl8841, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t))) 116.98/15.36 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (is_of @ X2 @ ('#ty_enc6' @ in @ (pair1type @ nat))))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl413])). 116.98/15.36 thf(satz39, axiom, 116.98/15.36 (all_of @ 116.98/15.36 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 116.98/15.36 ( ^[X0:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 116.98/15.36 ( ^[X1:$i]: 116.98/15.36 ( all_of @ 116.98/15.36 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 116.98/15.36 ( ^[X2:$i]: 116.98/15.36 ( ( n_eq @ X0 @ X1 ) => 116.98/15.36 ( ( n_eq @ X1 @ X2 ) => ( n_eq @ X0 @ X2 ) ) ) ) ) ) ) ))). 116.98/15.36 thf(zip_derived_cl122, plain, 116.98/15.36 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 116.98/15.36 (^[Y0 : $i]: 116.98/15.36 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 116.98/15.36 (^[Y1 : $i]: 116.98/15.36 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 116.98/15.36 (^[Y2 : $i]: 116.98/15.36 (((n_eq @ Y0 @ Y1) => 116.98/15.36 (((n_eq @ Y1 @ Y2) => (n_eq @ Y0 @ Y2)))))))))))), 116.98/15.36 inference('cnf', [status(esa)], [satz39])). 116.98/15.36 thf(zip_derived_cl123, plain, 116.98/15.36 ( (all_of @ ((('#C') @ in @ frac)) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 n_eq)))))))))), 116.98/15.36 inference('lams2combs', [status(thm)], [zip_derived_cl122])). 116.98/15.36 thf(zip_derived_cl1171, plain, 116.98/15.36 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 n_eq)))))))))), 116.98/15.36 inference('rw', [status(thm)], [zip_derived_cl123, '0'])). 116.98/15.36 thf(zip_derived_cl1172, plain, 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ 116.98/15.36 (pair1type @ nat)))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 n_eq)))))) @ 116.98/15.36 n_eq)))))) @ 116.98/15.36 Y0)))))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl1171, '1'])). 116.98/15.36 thf(zip_derived_cl1173, plain, 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat)))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ ('#B'))) @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))))) @ 116.98/15.36 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ 116.98/15.36 n_eq)))))) @ 116.98/15.36 n_eq))))))))))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl1172])). 116.98/15.36 thf(zip_derived_cl1174, plain, 116.98/15.36 (![X2 : $i]: 116.98/15.36 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 116.98/15.36 (n_eq @ X2))))))))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1173])). 116.98/15.36 thf(zip_derived_cl1175, plain, 116.98/15.36 (![X2 : $i]: 116.98/15.36 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (n_eq @ X2))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 116.98/15.36 (n_eq @ X2)))))))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])). 116.98/15.36 thf(zip_derived_cl1176, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 116.98/15.36 (n_eq @ X0))))) @ 116.98/15.36 Y0))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl1175, '1'])). 116.98/15.36 thf(zip_derived_cl1177, plain, 116.98/15.36 (![X0 : $i]: 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 116.98/15.36 ((('#S') @ ((('#B') @ ('#B') @ 116.98/15.36 ((('#B') @ (=>) @ (n_eq @ X0))))) @ 116.98/15.36 ((('#C') @ ((('#B') @ ('#S') @ 116.98/15.36 ((('#B') @ ((('#B') @ (=>))) @ n_eq)))) @ 116.98/15.36 (n_eq @ X0))))))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl1176])). 116.98/15.36 thf(zip_derived_cl1178, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_eq @ X0 @ X2))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ (n_eq @ X0)))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1177])). 116.98/15.36 thf(zip_derived_cl1179, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_is @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ (n_eq @ X0)))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw', [status(thm)], 116.98/15.36 [zip_derived_cl1178, '7', '7', '8', '8', '9', '9', '10', '10', 116.98/15.36 '11'])). 116.98/15.36 thf(zip_derived_cl1180, plain, 116.98/15.36 (![X0 : $i, X2 : $i]: 116.98/15.36 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_is @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X2 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X2 @ n_1t) @ (ap @ X0 @ n_2t))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X2))) @ (n_eq @ X0)))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1179])). 116.98/15.36 thf(zip_derived_cl1181, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (((!!) @ (^[Y0 : $i]: 116.98/15.36 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 ((('#B') @ (((=>) @ (n_is @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ 116.98/15.36 (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ 116.98/15.36 (ap @ X0 @ n_2t))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ 116.98/15.36 (n_eq @ X0))) @ 116.98/15.36 Y0))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw_clause', [status(thm)], [zip_derived_cl1180, '1'])). 116.98/15.36 thf(zip_derived_cl1182, plain, 116.98/15.36 (![X0 : $i, X1 : $i]: 116.98/15.36 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 116.98/15.36 ((('#C') @ is_of @ 116.98/15.36 ((('#C') @ in @ (pair1type @ nat))))))) @ 116.98/15.36 ((('#B') @ (((=>) @ (n_is @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ 116.98/15.36 (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ 116.98/15.36 (ap @ X0 @ n_2t))))) @ 116.98/15.36 ((('#S') @ ((('#B') @ (=>) @ (n_eq @ X1))) @ 116.98/15.36 (n_eq @ X0))))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('comb-normalize', [status(thm)], [zip_derived_cl1181])). 116.98/15.36 thf(zip_derived_cl1183, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X3 : $i]: 116.98/15.36 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))) => 116.98/15.36 (((n_eq @ X1 @ X3) => (n_eq @ X0 @ X3))))))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1182])). 116.98/15.36 thf(zip_derived_cl1184, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X3 : $i]: 116.98/15.36 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t))) => (n_is @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))))))))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('rw', [status(thm)], 116.98/15.36 [zip_derived_cl1183, '7', '7', '7', '8', '8', '8', '9', '9', 116.98/15.36 '9', '10', '10', '10', '11', '11'])). 116.98/15.36 thf(zip_derived_cl1185, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X3 : $i]: 116.98/15.36 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | (((n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))) => 116.98/15.36 (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t))) => (n_is @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))))))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1184])). 116.98/15.36 thf(zip_derived_cl1186, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X3 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))) 116.98/15.36 | (((n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t))) => (n_is @ 116.98/15.36 (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1185])). 116.98/15.36 thf(zip_derived_cl1187, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X3 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))) 116.98/15.36 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 116.98/15.36 | ~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))))), 116.98/15.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1186])). 116.98/15.36 thf(zip_derived_cl8879, plain, 116.98/15.36 (![X0 : $i, X1 : $i, X3 : $i]: 116.98/15.36 (~ (n_is @ (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X3 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X1 @ n_2t))) 116.98/15.36 | (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X3 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X3 @ n_1t) @ (ap @ X0 @ n_2t))) 116.98/15.36 | ~ (is_of @ X3 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (is_of @ X0 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (is_of @ X1 @ ('#ty_enc6' @ in @ (pair1type @ nat))) 116.98/15.36 | ~ (n_is @ (n_ts @ (ap @ X0 @ n_1t) @ (ap @ X1 @ n_2t)) @ 116.98/15.36 (n_ts @ (ap @ X1 @ n_1t) @ (ap @ X0 @ n_2t))))), 116.98/15.36 inference('remove_ty_args', [status(thm)], [zip_derived_cl1187])). 116.98/15.36 thf(zip_derived_cl8942, plain, ($false), 116.98/15.36 inference('eprover', [status(thm)], 116.98/15.36 [zip_derived_cl8847, zip_derived_cl1392, zip_derived_cl8928, 116.98/15.36 zip_derived_cl8922, zip_derived_cl8849, zip_derived_cl8924, 116.98/15.36 zip_derived_cl8854, zip_derived_cl1389, zip_derived_cl3404, 116.98/15.36 zip_derived_cl1387, zip_derived_cl3405, zip_derived_cl8930, 116.98/15.36 zip_derived_cl8890, zip_derived_cl8888, zip_derived_cl1382, 116.98/15.36 zip_derived_cl8846, zip_derived_cl8929, zip_derived_cl8889, 116.98/15.36 zip_derived_cl8887, zip_derived_cl1379, zip_derived_cl8841, 116.98/15.36 zip_derived_cl8879])). 116.98/15.36 116.98/15.36 % SZS output end Refutation 116.98/15.36 116.98/15.36 116.98/15.36 % Terminating... 116.98/15.40 % Runner terminated. 116.98/15.41 % Zipperpin 1.5 exiting 116.98/15.41 EOF