0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.YpgN9Bl7xp true 0.14/0.35 % Computer : n007.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 960 0.14/0.35 % WCLimit : 120 0.14/0.35 % DateTime : Tue Aug 9 07:39:12 EDT 2022 0.14/0.36 % CPUTime : 0.14/0.36 % Running portfolio for 960 s 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.36 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.51/0.65 % Total configuration time : 828 0.51/0.65 % Estimated wc time : 1656 0.51/0.65 % Estimated cpu time (8 cpus) : 207.0 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 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/40_c_ic.sh running for 80s 0.52/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.52/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.52/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.52/0.74 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.52/0.75 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 97.31/12.93 % Solved by lams/40_b.comb.sh. 97.31/12.93 % running E: timeout 28 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.YpgN9Bl7xp/e_inputdaa2a6 --cpu-limit=26 --auto-schedule -s -p 97.31/12.93 % done 347 iterations in 12.097s 97.31/12.93 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 97.31/12.93 % SZS output start Refutation 97.31/12.93 thf('#ty_enc5_type', type, '#ty_enc5': ($i > $i > $o) > $i > $i > $o). 97.31/12.93 thf(all_of_type, type, all_of: ($i > $o) > ($i > $o) > $o). 97.31/12.93 thf(moreq_type, type, moreq: $i > $i > $o). 97.31/12.93 thf(n_eq_type, type, n_eq: $i > $i > $o). 97.31/12.93 thf(l_or_type, type, l_or: $o > $o > $o). 97.31/12.93 thf(frac_type, type, frac: $i). 97.31/12.93 thf(in_type, type, in: $i > $i > $o). 97.31/12.93 thf(lessf_type, type, lessf: $i > $i > $o). 97.31/12.93 thf(imp_type, type, imp: $o > $o > $o). 97.31/12.93 thf('#sk2_type', type, '#sk2': $i). 97.31/12.93 thf(moref_type, type, moref: $i > $i > $o). 97.31/12.93 thf(nat_type, type, nat: $i). 97.31/12.93 thf(lesseq_type, type, lesseq: $i > $i > $o). 97.31/12.93 thf(is_of_type, type, is_of: $i > ($i > $o) > $o). 97.31/12.93 thf('#sk4_type', type, '#sk4': $i). 97.31/12.93 thf('#sk3_type', type, '#sk3': $i). 97.31/12.93 thf(pair1type_type, type, pair1type: $i > $i). 97.31/12.93 thf(d_not_type, type, d_not: $o > $o). 97.31/12.93 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 97.31/12.93 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 97.31/12.93 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 97.31/12.93 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 97.31/12.93 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 97.31/12.93 thf(satz51d, axiom, 97.31/12.93 (all_of @ 97.31/12.93 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.31/12.93 ( ^[X0:$i]: 97.31/12.93 ( all_of @ 97.31/12.93 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.31/12.93 ( ^[X1:$i]: 97.31/12.93 ( all_of @ 97.31/12.93 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 97.31/12.93 ( ^[X2:$i]: 97.31/12.93 ( ( moref @ X0 @ X1 ) => 97.31/12.93 ( ( moreq @ X1 @ X2 ) => ( moref @ X0 @ X2 ) ) ) ) ) ) ) ))). 97.31/12.93 thf(zip_derived_cl12, plain, 97.31/12.93 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.31/12.93 (^[Y0 : $i]: 97.31/12.93 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.31/12.93 (^[Y1 : $i]: 97.31/12.93 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 97.31/12.93 (^[Y2 : $i]: 97.31/12.93 (((moref @ Y0 @ Y1) => 97.31/12.93 (((moreq @ Y1 @ Y2) => (moref @ Y0 @ Y2)))))))))))), 97.31/12.93 inference('cnf', [status(esa)], [satz51d])). 97.31/12.93 thf(zip_derived_cl13, plain, 97.31/12.93 ( (all_of @ ((('#C') @ in @ frac)) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ ('#B'))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 97.31/12.93 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 97.31/12.93 moref)))))))))), 97.31/12.93 inference('lams2combs', [status(thm)], [zip_derived_cl12])). 97.31/12.93 thf(def_frac, axiom,(( frac ) = ((pair1type @ nat)))). 97.31/12.93 thf('0', plain, (( frac ) = ( pair1type @ nat )), define([status(thm)])). 97.31/12.93 thf(zip_derived_cl1217, plain, 97.31/12.93 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ ('#B'))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 97.31/12.93 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 97.31/12.93 moref)))))))))), 97.31/12.93 inference('rw', [status(thm)], [zip_derived_cl13, '0'])). 97.31/12.93 thf(def_all_of, axiom, (all_of @ X0 @ X1) => 97.31/12.93 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) = ($true))). 97.31/12.93 thf('1', plain, 97.31/12.93 (![X0:( $i > $o ),X1:( $i > $o )]: 97.31/12.93 ( ( all_of @ X0 @ X1 ) <=> 97.31/12.93 ( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) )), 97.31/12.93 inference('rw.lit', [status(esa)], [def_all_of])). 97.31/12.93 thf(zip_derived_cl1218, plain, 97.31/12.93 ( (((!!) @ (^[Y0 : $i]: 97.31/12.93 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (all_of @ 97.31/12.93 ((('#C') @ in @ 97.31/12.93 (pair1type @ nat)))))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ ('#B'))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 97.31/12.93 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ 97.31/12.93 moreq)))))) @ 97.31/12.93 moref)))))) @ 97.31/12.93 Y0)))))))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl1217, '1'])). 97.31/12.93 thf(zip_derived_cl1219, plain, 97.31/12.93 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.93 ((('#C') @ is_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ ('#B'))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 97.31/12.93 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ 97.31/12.93 moreq)))))) @ 97.31/12.93 moref))))))))))))), 97.31/12.93 inference('comb-normalize', [status(thm)], [zip_derived_cl1218])). 97.31/12.93 thf(zip_derived_cl1220, plain, 97.31/12.93 (![X2 : $i]: 97.31/12.93 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (moref @ X2))))) @ 97.31/12.93 ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 97.31/12.93 (moref @ X2))))))))))), 97.31/12.93 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1219])). 97.31/12.93 thf(zip_derived_cl1221, plain, 97.31/12.93 (![X2 : $i]: 97.31/12.93 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (moref @ X2))))) @ 97.31/12.93 ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 97.31/12.93 (moref @ X2)))))))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1220])). 97.31/12.93 thf(zip_derived_cl1222, plain, 97.31/12.93 (![X0 : $i]: 97.31/12.93 ( (((!!) @ (^[Y0 : $i]: 97.31/12.93 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 ((('#B') @ (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#B') @ 97.31/12.93 ((('#B') @ (=>) @ (moref @ X0))))) @ 97.31/12.93 ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 97.31/12.93 (moref @ X0))))) @ 97.31/12.93 Y0))))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl1221, '1'])). 97.31/12.93 thf(zip_derived_cl1223, plain, 97.31/12.93 (![X0 : $i]: 97.31/12.93 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.93 ((('#C') @ is_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#B') @ 97.31/12.93 ((('#B') @ (=>) @ (moref @ X0))))) @ 97.31/12.93 ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moreq)))) @ 97.31/12.93 (moref @ X0))))))))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('comb-normalize', [status(thm)], [zip_derived_cl1222])). 97.31/12.93 thf(zip_derived_cl1224, plain, 97.31/12.93 (![X0 : $i, X2 : $i]: 97.31/12.93 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (((=>) @ (moref @ X0 @ X2))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X2))) @ (moref @ X0)))))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1223])). 97.31/12.93 thf(zip_derived_cl1225, plain, 97.31/12.93 (![X0 : $i, X2 : $i]: 97.31/12.93 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (((=>) @ (moref @ X0 @ X2))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X2))) @ (moref @ X0)))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1224])). 97.31/12.93 thf(zip_derived_cl1226, plain, 97.31/12.93 (![X0 : $i, X1 : $i]: 97.31/12.93 ( (((!!) @ (^[Y0 : $i]: 97.31/12.93 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 ((('#B') @ (((=>) @ (moref @ X0 @ X1))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X1))) @ 97.31/12.93 (moref @ X0))) @ 97.31/12.93 Y0))))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl1225, '1'])). 97.31/12.93 thf(zip_derived_cl1227, plain, 97.31/12.93 (![X0 : $i, X1 : $i]: 97.31/12.93 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.93 ((('#C') @ is_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.93 ((('#B') @ (((=>) @ (moref @ X0 @ X1))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ (moreq @ X1))) @ 97.31/12.93 (moref @ X0))))))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('comb-normalize', [status(thm)], [zip_derived_cl1226])). 97.31/12.93 thf(zip_derived_cl1228, plain, 97.31/12.93 (![X0 : $i, X1 : $i, X3 : $i]: 97.31/12.93 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 (((moref @ X0 @ X1) => (((moreq @ X1 @ X3) => (moref @ X0 @ X3))))))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1227])). 97.31/12.93 thf(def_d_not, axiom,(( d_not @ (X0)) = ((imp @ X0 @ ($false))))). 97.31/12.93 thf('2', plain, (![X0:$o]: ( ( d_not @ X0 ) = ( imp @ X0 @ $false ) )), 97.31/12.93 define([status(thm)])). 97.31/12.93 thf(def_l_or, axiom,(( l_or @ (X0)@ (X1)) = ((imp @ (d_not @ X0) @ X1)))). 97.31/12.93 thf('3', plain, 97.31/12.93 (![X1:$o,X0:$o]: ( ( l_or @ X0 @ X1 ) = ( imp @ ( d_not @ X0 ) @ X1 ) )), 97.31/12.93 define([status(thm)])). 97.31/12.93 thf(def_moreq, axiom,(( moreq @ (X0)@ (X1)) = 97.31/12.93 ((l_or @ (moref @ X0 @ X1) @ (n_eq @ X0 @ X1))))). 97.31/12.93 thf('4', plain, 97.31/12.93 (![X1:$i,X0:$i]: 97.31/12.93 ( ( moreq @ X0 @ X1 ) = 97.31/12.93 ( l_or @ ( moref @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )), 97.31/12.93 define([status(thm)])). 97.31/12.93 thf(zip_derived_cl1229, plain, 97.31/12.93 (![X0 : $i, X1 : $i, X3 : $i]: 97.31/12.93 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 (((moref @ X0 @ X1) => 97.31/12.93 (((imp @ (imp @ (moref @ X1 @ X3) @ ($false)) @ 97.31/12.93 (n_eq @ X1 @ X3)) => (moref @ X0 @ X3))))))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('rw', [status(thm)], [zip_derived_cl1228, '2', '3', '4'])). 97.31/12.93 thf(zip_derived_cl1230, plain, 97.31/12.93 (![X0 : $i, X1 : $i, X3 : $i]: 97.31/12.93 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (((moref @ X0 @ X1) => 97.31/12.93 (((imp @ (imp @ (moref @ X1 @ X3) @ ($false)) @ 97.31/12.93 (n_eq @ X1 @ X3)) => (moref @ X0 @ X3))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1229])). 97.31/12.93 thf(zip_derived_cl1231, plain, 97.31/12.93 (![X0 : $i, X1 : $i, X3 : $i]: 97.31/12.93 (~ (moref @ X0 @ X1) 97.31/12.93 | (((imp @ (imp @ (moref @ X1 @ X3) @ ($false)) @ 97.31/12.93 (n_eq @ X1 @ X3)) => (moref @ X0 @ X3))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1230])). 97.31/12.93 thf(zip_derived_cl1232, plain, 97.31/12.93 (![X0 : $i, X1 : $i, X3 : $i]: 97.31/12.93 (~ (imp @ (imp @ (moref @ X1 @ X3) @ ($false)) @ (n_eq @ X1 @ X3)) 97.31/12.93 | (moref @ X0 @ X3) 97.31/12.93 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (moref @ X0 @ X1))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1231])). 97.31/12.93 thf(def_imp, axiom, ~ (imp @ X0 @ X1) => ((((X0) => (X1))) != ($true))). 97.31/12.93 thf('5', plain, 97.31/12.93 (![X0:$o,X1:$o]: ( ( ~( imp @ X0 @ X1 ) ) <=> ( ~( ( X0 ) => ( X1 ) ) ) )), 97.31/12.93 inference('rw.lit', [status(esa)], [def_imp])). 97.31/12.93 thf(zip_derived_cl1233, plain, 97.31/12.93 (![X0 : $i, X1 : $i, X2 : $i]: 97.31/12.93 (~ (((imp @ (moref @ X0 @ X2) @ ($false)) => (n_eq @ X0 @ X2))) 97.31/12.93 | ~ (moref @ X1 @ X0) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (moref @ X1 @ X2))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl1232, '5'])). 97.31/12.93 thf(zip_derived_cl1234, plain, 97.31/12.93 (![X0 : $i, X1 : $i, X2 : $i]: 97.31/12.93 ( (imp @ (moref @ X0 @ X2) @ ($false)) 97.31/12.93 | (moref @ X1 @ X2) 97.31/12.93 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (moref @ X1 @ X0))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1233])). 97.31/12.93 thf(def_imp, axiom, (imp @ X0 @ X1) => ((((X0) => (X1))) = ($true))). 97.31/12.93 thf('6', plain, 97.31/12.93 (![X0:$o,X1:$o]: ( ( imp @ X0 @ X1 ) <=> ( ( X0 ) => ( X1 ) ) )), 97.31/12.93 inference('rw.lit', [status(esa)], [def_imp])). 97.31/12.93 thf(zip_derived_cl1236, plain, 97.31/12.93 (![X0 : $i, X1 : $i, X2 : $i]: 97.31/12.93 ( (((moref @ X0 @ X2) => ($false))) 97.31/12.93 | ~ (moref @ X1 @ X0) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (moref @ X1 @ X2))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl1234, '6'])). 97.31/12.93 thf(zip_derived_cl1237, plain, 97.31/12.93 (![X0 : $i, X1 : $i, X2 : $i]: 97.31/12.93 ( (((~) @ (moref @ X0 @ X2))) 97.31/12.93 | ~ (moref @ X1 @ X0) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (moref @ X1 @ X2))), 97.31/12.93 inference('simplify boolean subterms', [status(thm)], 97.31/12.93 [zip_derived_cl1236])). 97.31/12.93 thf(zip_derived_cl1238, plain, 97.31/12.93 (![X0 : $i, X1 : $i, X2 : $i]: 97.31/12.93 (~ (moref @ X0 @ X2) 97.31/12.93 | ~ (moref @ X1 @ X0) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (moref @ X1 @ X2))), 97.31/12.93 inference('simplify nested equalities', [status(thm)], 97.31/12.93 [zip_derived_cl1237])). 97.31/12.93 thf(zip_derived_cl7087, plain, 97.31/12.93 (![X0 : $i, X1 : $i, X2 : $i]: 97.31/12.93 (~ (moref @ X0 @ X2) 97.31/12.93 | ~ (moref @ X1 @ X0) 97.31/12.93 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.31/12.93 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.31/12.93 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.31/12.93 | (moref @ X1 @ X2))), 97.31/12.93 inference('remove_ty_args', [status(thm)], [zip_derived_cl1238])). 97.31/12.93 thf(satz52, conjecture, 97.31/12.93 (all_of @ 97.31/12.93 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.31/12.93 ( ^[X0:$i]: 97.31/12.93 ( all_of @ 97.31/12.93 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.31/12.93 ( ^[X1:$i]: 97.31/12.93 ( all_of @ 97.31/12.93 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 97.31/12.93 ( ^[X2:$i]: 97.31/12.93 ( ( lesseq @ X0 @ X1 ) => 97.31/12.93 ( ( lesseq @ X1 @ X2 ) => ( lesseq @ X0 @ X2 ) ) ) ) ) ) ) ))). 97.31/12.93 thf(zf_stmt_0, negated_conjecture, 97.31/12.93 (~( all_of @ 97.31/12.93 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.31/12.93 ( ^[X0:$i]: 97.31/12.93 ( all_of @ 97.31/12.93 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.31/12.93 ( ^[X1:$i]: 97.31/12.93 ( all_of @ 97.31/12.93 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 97.31/12.93 ( ^[X2:$i]: 97.31/12.93 ( ( lesseq @ X0 @ X1 ) => 97.31/12.93 ( ( lesseq @ X1 @ X2 ) => ( lesseq @ X0 @ X2 ) ) ) ) ) ) ) ) )), 97.31/12.93 inference('cnf.neg', [status(esa)], [satz52])). 97.31/12.93 thf(zip_derived_cl292, plain, 97.31/12.93 (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.31/12.93 (^[Y0 : $i]: 97.31/12.93 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.31/12.93 (^[Y1 : $i]: 97.31/12.93 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 97.31/12.93 (^[Y2 : $i]: 97.31/12.93 (((lesseq @ Y0 @ Y1) => 97.31/12.93 (((lesseq @ Y1 @ Y2) => (lesseq @ Y0 @ Y2)))))))))))), 97.31/12.93 inference('cnf', [status(esa)], [zf_stmt_0])). 97.31/12.93 thf(zip_derived_cl293, plain, 97.31/12.93 (~ (all_of @ ((('#C') @ in @ frac)) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ ('#B'))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 97.31/12.93 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 97.31/12.93 lesseq)))))))))), 97.31/12.93 inference('lams2combs', [status(thm)], [zip_derived_cl292])). 97.31/12.93 thf(zip_derived_cl480, plain, 97.31/12.93 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ ('#B'))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 97.31/12.93 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 97.31/12.93 lesseq)))))))))), 97.31/12.93 inference('rw', [status(thm)], [zip_derived_cl293, '0'])). 97.31/12.93 thf(def_all_of, axiom, ~ (all_of @ X0 @ X1) => 97.31/12.93 ((((!!) @ (^[Y0 : $i]: (((is_of @ Y0 @ X0) => (X1 @ Y0)))))) != ($true))). 97.31/12.93 thf('7', plain, 97.31/12.93 (![X0:( $i > $o ),X1:( $i > $o )]: 97.31/12.93 ( ( ~( all_of @ X0 @ X1 ) ) <=> 97.31/12.93 ( ~( ![X6:$i]: ( ( is_of @ X6 @ X0 ) => ( X1 @ X6 ) ) ) ) )), 97.31/12.93 inference('rw.lit', [status(esa)], [def_all_of])). 97.31/12.93 thf(zip_derived_cl481, plain, 97.31/12.93 (~ (((!!) @ (^[Y0 : $i]: 97.31/12.93 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (all_of @ 97.31/12.93 ((('#C') @ in @ 97.31/12.93 (pair1type @ nat)))))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ ('#B'))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 97.31/12.93 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ 97.31/12.93 lesseq)))))) @ 97.31/12.93 lesseq)))))) @ 97.31/12.93 Y0)))))))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl480, '7'])). 97.31/12.93 thf(zip_derived_cl482, plain, 97.31/12.93 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.93 ((('#C') @ is_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ ('#B'))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))))) @ 97.31/12.93 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ 97.31/12.93 lesseq)))))) @ 97.31/12.93 lesseq))))))))))))), 97.31/12.93 inference('comb-normalize', [status(thm)], [zip_derived_cl481])). 97.31/12.93 thf(zip_derived_cl483, plain, 97.31/12.93 (~ (((is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#B') @ 97.31/12.93 ((('#B') @ (=>) @ (lesseq @ '#sk2'))))) @ 97.31/12.93 ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 97.31/12.93 (lesseq @ '#sk2'))))))))))), 97.31/12.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl482])). 97.31/12.93 thf(zip_derived_cl485, plain, 97.31/12.93 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#B') @ 97.31/12.93 ((('#B') @ (=>) @ (lesseq @ '#sk2'))))) @ 97.31/12.93 ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 97.31/12.93 (lesseq @ '#sk2'))))))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl483])). 97.31/12.93 thf(zip_derived_cl486, plain, 97.31/12.93 (~ (((!!) @ (^[Y0 : $i]: 97.31/12.93 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#B') @ 97.31/12.93 ((('#B') @ (=>) @ (lesseq @ '#sk2'))))) @ 97.31/12.93 ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 97.31/12.93 (lesseq @ '#sk2'))))) @ 97.31/12.93 Y0)))))))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl485, '7'])). 97.31/12.93 thf(zip_derived_cl487, plain, 97.31/12.93 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.93 ((('#C') @ is_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#B') @ 97.31/12.93 ((('#B') @ (=>) @ (lesseq @ '#sk2'))))) @ 97.31/12.93 ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ lesseq)))) @ 97.31/12.93 (lesseq @ '#sk2')))))))))))), 97.31/12.93 inference('comb-normalize', [status(thm)], [zip_derived_cl486])). 97.31/12.93 thf(zip_derived_cl488, plain, 97.31/12.93 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (((=>) @ (lesseq @ '#sk2' @ '#sk3'))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 97.31/12.93 (lesseq @ '#sk2'))))))))), 97.31/12.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl487])). 97.31/12.93 thf(def_lesseq, axiom,(( lesseq @ (X0)@ (X1)) = 97.31/12.93 ((l_or @ (lessf @ X0 @ X1) @ (n_eq @ X0 @ X1))))). 97.31/12.93 thf('8', plain, 97.31/12.93 (![X1:$i,X0:$i]: 97.31/12.93 ( ( lesseq @ X0 @ X1 ) = 97.31/12.93 ( l_or @ ( lessf @ X0 @ X1 ) @ ( n_eq @ X0 @ X1 ) ) )), 97.31/12.93 define([status(thm)])). 97.31/12.93 thf(zip_derived_cl489, plain, 97.31/12.93 (~ (((is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (((=>) @ (imp @ 97.31/12.93 (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk2' @ '#sk3')))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 97.31/12.93 (lesseq @ '#sk2'))))))))), 97.31/12.93 inference('rw', [status(thm)], [zip_derived_cl488, '2', '3', '8'])). 97.31/12.93 thf(zip_derived_cl491, plain, 97.31/12.93 (~ (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (((=>) @ (imp @ 97.31/12.93 (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk2' @ '#sk3')))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 97.31/12.93 (lesseq @ '#sk2'))))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl489])). 97.31/12.93 thf(zip_derived_cl492, plain, 97.31/12.93 (~ (((!!) @ (^[Y0 : $i]: 97.31/12.93 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 ((('#B') @ (((=>) @ (imp @ 97.31/12.93 (imp @ (lessf @ '#sk2' @ '#sk3') @ 97.31/12.93 ($false)) @ 97.31/12.93 (n_eq @ '#sk2' @ '#sk3')))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 97.31/12.93 (lesseq @ '#sk2'))) @ 97.31/12.93 Y0)))))))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl491, '7'])). 97.31/12.93 thf(zip_derived_cl493, plain, 97.31/12.93 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.93 ((('#C') @ is_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.93 ((('#B') @ (((=>) @ (imp @ 97.31/12.93 (imp @ (lessf @ '#sk2' @ '#sk3') @ 97.31/12.93 ($false)) @ 97.31/12.93 (n_eq @ '#sk2' @ '#sk3')))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ (lesseq @ '#sk3'))) @ 97.31/12.93 (lesseq @ '#sk2')))))))))), 97.31/12.93 inference('comb-normalize', [status(thm)], [zip_derived_cl492])). 97.31/12.93 thf(zip_derived_cl494, plain, 97.31/12.93 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 (((imp @ (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk2' @ '#sk3')) => 97.31/12.93 (((lesseq @ '#sk3' @ '#sk4') => (lesseq @ '#sk2' @ '#sk4')))))))), 97.31/12.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl493])). 97.31/12.93 thf(zip_derived_cl495, plain, 97.31/12.93 (~ (((is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 (((imp @ (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk2' @ '#sk3')) => 97.31/12.93 (((imp @ (imp @ (lessf @ '#sk3' @ '#sk4') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk3' @ '#sk4')) => (imp @ 97.31/12.93 (imp @ (lessf @ '#sk2' @ '#sk4') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk2' @ '#sk4'))))))))), 97.31/12.93 inference('rw', [status(thm)], 97.31/12.93 [zip_derived_cl494, '2', '2', '3', '3', '8', '8'])). 97.31/12.93 thf(zip_derived_cl497, plain, 97.31/12.93 (~ (((imp @ (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk2' @ '#sk3')) => 97.31/12.93 (((imp @ (imp @ (lessf @ '#sk3' @ '#sk4') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk3' @ '#sk4')) => (imp @ 97.31/12.93 (imp @ (lessf @ '#sk2' @ '#sk4') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk2' @ '#sk4'))))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl495])). 97.31/12.93 thf(zip_derived_cl499, plain, 97.31/12.93 (~ (((imp @ (imp @ (lessf @ '#sk3' @ '#sk4') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk3' @ '#sk4')) => (imp @ 97.31/12.93 (imp @ (lessf @ '#sk2' @ '#sk4') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk2' @ '#sk4'))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl497])). 97.31/12.93 thf(zip_derived_cl502, plain, 97.31/12.93 (~ (imp @ (imp @ (lessf @ '#sk2' @ '#sk4') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk2' @ '#sk4'))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl499])). 97.31/12.93 thf(zip_derived_cl505, plain, 97.31/12.93 (~ (((imp @ (lessf @ '#sk2' @ '#sk4') @ ($false)) => (n_eq @ '#sk2' @ 97.31/12.93 '#sk4')))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl502, '5'])). 97.31/12.93 thf(zip_derived_cl509, plain, (~ (n_eq @ '#sk2' @ '#sk4')), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl505])). 97.31/12.93 thf(zip_derived_cl501, plain, 97.31/12.93 ( (imp @ (imp @ (lessf @ '#sk3' @ '#sk4') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk3' @ '#sk4'))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl499])). 97.31/12.93 thf(zip_derived_cl504, plain, 97.31/12.93 ( (((imp @ (lessf @ '#sk3' @ '#sk4') @ ($false)) => (n_eq @ '#sk3' @ 97.31/12.93 '#sk4')))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl501, '6'])). 97.31/12.93 thf(zip_derived_cl507, plain, 97.31/12.93 ((~ (imp @ (lessf @ '#sk3' @ '#sk4') @ ($false)) 97.31/12.93 | (n_eq @ '#sk3' @ '#sk4'))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl504])). 97.31/12.93 thf(zip_derived_cl512, plain, 97.31/12.93 ((~ (((lessf @ '#sk3' @ '#sk4') => ($false))) | (n_eq @ '#sk3' @ '#sk4'))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl507, '5'])). 97.31/12.93 thf(zip_derived_cl514, plain, 97.31/12.93 ((~ (((~) @ (lessf @ '#sk3' @ '#sk4'))) | (n_eq @ '#sk3' @ '#sk4'))), 97.31/12.93 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl512])). 97.31/12.93 thf(zip_derived_cl515, plain, 97.31/12.93 (( (lessf @ '#sk3' @ '#sk4') | (n_eq @ '#sk3' @ '#sk4'))), 97.31/12.93 inference('simplify nested equalities', [status(thm)], 97.31/12.93 [zip_derived_cl514])). 97.31/12.93 thf(zip_derived_cl498, plain, 97.31/12.93 ( (imp @ (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) @ 97.31/12.93 (n_eq @ '#sk2' @ '#sk3'))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl497])). 97.31/12.93 thf(zip_derived_cl500, plain, 97.31/12.93 ( (((imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) => (n_eq @ '#sk2' @ 97.31/12.93 '#sk3')))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl498, '6'])). 97.31/12.93 thf(zip_derived_cl503, plain, 97.31/12.93 ((~ (imp @ (lessf @ '#sk2' @ '#sk3') @ ($false)) 97.31/12.93 | (n_eq @ '#sk2' @ '#sk3'))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl500])). 97.31/12.93 thf(zip_derived_cl506, plain, 97.31/12.93 ((~ (((lessf @ '#sk2' @ '#sk3') => ($false))) | (n_eq @ '#sk2' @ '#sk3'))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl503, '5'])). 97.31/12.93 thf(zip_derived_cl510, plain, 97.31/12.93 ((~ (((~) @ (lessf @ '#sk2' @ '#sk3'))) | (n_eq @ '#sk2' @ '#sk3'))), 97.31/12.93 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl506])). 97.31/12.93 thf(zip_derived_cl511, plain, 97.31/12.93 (( (lessf @ '#sk2' @ '#sk3') | (n_eq @ '#sk2' @ '#sk3'))), 97.31/12.93 inference('simplify nested equalities', [status(thm)], 97.31/12.93 [zip_derived_cl510])). 97.31/12.93 thf(zip_derived_cl508, plain, 97.31/12.93 ( (imp @ (lessf @ '#sk2' @ '#sk4') @ ($false))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl505])). 97.31/12.93 thf(zip_derived_cl513, plain, ( (((lessf @ '#sk2' @ '#sk4') => ($false)))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl508, '6'])). 97.31/12.93 thf(zip_derived_cl516, plain, ( (((~) @ (lessf @ '#sk2' @ '#sk4')))), 97.31/12.93 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl513])). 97.31/12.93 thf(zip_derived_cl517, plain, (~ (lessf @ '#sk2' @ '#sk4')), 97.31/12.93 inference('simplify nested equalities', [status(thm)], 97.31/12.93 [zip_derived_cl516])). 97.31/12.93 thf(zip_derived_cl484, plain, 97.31/12.93 ( (is_of @ '#sk2' @ ((('#C') @ in @ (pair1type @ nat))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl483])). 97.31/12.93 thf(zip_derived_cl7046, plain, 97.31/12.93 ( (is_of @ '#sk2' @ ('#ty_enc5' @ in @ (pair1type @ nat)))), 97.31/12.93 inference('remove_ty_args', [status(thm)], [zip_derived_cl484])). 97.31/12.93 thf(satz41j, axiom, 97.31/12.93 (all_of @ 97.31/12.93 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.31/12.93 ( ^[X0:$i]: 97.31/12.93 ( all_of @ 97.31/12.93 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.31/12.93 ( ^[X1:$i]: ( ( d_not @ ( moreq @ X0 @ X1 ) ) => ( lessf @ X0 @ X1 ) ) ) ) ))). 97.31/12.93 thf(zip_derived_cl96, plain, 97.31/12.93 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.31/12.93 (^[Y0 : $i]: 97.31/12.93 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.31/12.93 (^[Y1 : $i]: (((d_not @ (moreq @ Y0 @ Y1)) => (lessf @ Y0 @ Y1)))))))), 97.31/12.93 inference('cnf', [status(esa)], [satz41j])). 97.31/12.93 thf(zip_derived_cl97, plain, 97.31/12.93 ( (all_of @ ((('#C') @ in @ frac)) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ 97.31/12.93 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))) @ 97.31/12.93 lessf)))))), 97.31/12.93 inference('lams2combs', [status(thm)], [zip_derived_cl96])). 97.31/12.93 thf(zip_derived_cl692, plain, 97.31/12.93 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ 97.31/12.93 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))) @ 97.31/12.93 lessf)))))), 97.31/12.93 inference('rw', [status(thm)], [zip_derived_cl97, '0'])). 97.31/12.93 thf(zip_derived_cl693, plain, 97.31/12.93 ( (((!!) @ (^[Y0 : $i]: 97.31/12.93 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ 97.31/12.93 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))) @ 97.31/12.93 lessf)) @ 97.31/12.93 Y0)))))))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl692, '1'])). 97.31/12.93 thf(zip_derived_cl694, plain, 97.31/12.93 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.93 ((('#C') @ is_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ 97.31/12.93 ((('#B') @ ((('#B') @ d_not)) @ moreq)))))) @ 97.31/12.93 lessf))))))))), 97.31/12.93 inference('comb-normalize', [status(thm)], [zip_derived_cl693])). 97.31/12.93 thf(zip_derived_cl695, plain, 97.31/12.93 (![X2 : $i]: 97.31/12.93 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (moreq @ X2))))) @ 97.31/12.93 (lessf @ X2))))))), 97.31/12.93 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl694])). 97.31/12.93 thf(zip_derived_cl696, plain, 97.31/12.93 (![X2 : $i]: 97.31/12.93 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ ((('#B') @ d_not @ (moreq @ X2))))) @ 97.31/12.93 (lessf @ X2)))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl695])). 97.31/12.93 thf(zip_derived_cl697, plain, 97.31/12.93 (![X0 : $i]: 97.31/12.93 ( (((!!) @ (^[Y0 : $i]: 97.31/12.93 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ 97.31/12.93 ((('#B') @ d_not @ (moreq @ X0))))) @ 97.31/12.93 (lessf @ X0) @ Y0))))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl696, '1'])). 97.31/12.93 thf(zip_derived_cl698, plain, 97.31/12.93 (![X0 : $i]: 97.31/12.93 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.93 ((('#C') @ is_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ 97.31/12.93 ((('#B') @ d_not @ (moreq @ X0))))) @ 97.31/12.93 (lessf @ X0))))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('comb-normalize', [status(thm)], [zip_derived_cl697])). 97.31/12.93 thf(zip_derived_cl699, plain, 97.31/12.93 (![X0 : $i, X2 : $i]: 97.31/12.93 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 (((d_not @ (moreq @ X0 @ X2)) => (lessf @ X0 @ X2))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl698])). 97.31/12.93 thf(zip_derived_cl700, plain, 97.31/12.93 (![X0 : $i, X2 : $i]: 97.31/12.93 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 (((imp @ 97.31/12.93 (imp @ (imp @ (moref @ X0 @ X2) @ ($false)) @ (n_eq @ X0 @ X2)) @ 97.31/12.93 ($false)) => (lessf @ X0 @ X2))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('rw', [status(thm)], [zip_derived_cl699, '2', '2', '3', '4'])). 97.31/12.93 thf(zip_derived_cl701, plain, 97.31/12.93 (![X0 : $i, X2 : $i]: 97.31/12.93 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (((imp @ 97.31/12.93 (imp @ (imp @ (moref @ X0 @ X2) @ ($false)) @ (n_eq @ X0 @ X2)) @ 97.31/12.93 ($false)) => (lessf @ X0 @ X2))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl700])). 97.31/12.93 thf(zip_derived_cl702, plain, 97.31/12.93 (![X0 : $i, X2 : $i]: 97.31/12.93 (~ (imp @ 97.31/12.93 (imp @ (imp @ (moref @ X0 @ X2) @ ($false)) @ (n_eq @ X0 @ X2)) @ 97.31/12.93 ($false)) 97.31/12.93 | (lessf @ X0 @ X2) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl701])). 97.31/12.93 thf(zip_derived_cl703, plain, 97.31/12.93 (![X0 : $i, X1 : $i]: 97.31/12.93 (~ (((imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @ 97.31/12.93 (n_eq @ X1 @ X0)) => ($false))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (lessf @ X1 @ X0))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl702, '5'])). 97.31/12.93 thf(zip_derived_cl704, plain, 97.31/12.93 (![X0 : $i, X1 : $i]: 97.31/12.93 (~ (((~) @ (imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @ 97.31/12.93 (n_eq @ X1 @ X0)))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (lessf @ X1 @ X0))), 97.31/12.93 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl703])). 97.31/12.93 thf(zip_derived_cl705, plain, 97.31/12.93 (![X0 : $i, X1 : $i]: 97.31/12.93 ( (imp @ (imp @ (moref @ X1 @ X0) @ ($false)) @ (n_eq @ X1 @ X0)) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (lessf @ X1 @ X0))), 97.31/12.93 inference('simplify nested equalities', [status(thm)], 97.31/12.93 [zip_derived_cl704])). 97.31/12.93 thf(zip_derived_cl706, plain, 97.31/12.93 (![X0 : $i, X1 : $i]: 97.31/12.93 ( (((imp @ (moref @ X1 @ X0) @ ($false)) => (n_eq @ X1 @ X0))) 97.31/12.93 | (lessf @ X1 @ X0) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl705, '6'])). 97.31/12.93 thf(zip_derived_cl707, plain, 97.31/12.93 (![X0 : $i, X1 : $i]: 97.31/12.93 (~ (imp @ (moref @ X1 @ X0) @ ($false)) 97.31/12.93 | (n_eq @ X1 @ X0) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (lessf @ X1 @ X0))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl706])). 97.31/12.93 thf(zip_derived_cl708, plain, 97.31/12.93 (![X0 : $i, X1 : $i]: 97.31/12.93 (~ (((moref @ X1 @ X0) => ($false))) 97.31/12.93 | (lessf @ X1 @ X0) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (n_eq @ X1 @ X0))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl707, '5'])). 97.31/12.93 thf(zip_derived_cl709, plain, 97.31/12.93 (![X0 : $i, X1 : $i]: 97.31/12.93 (~ (((~) @ (moref @ X1 @ X0))) 97.31/12.93 | (lessf @ X1 @ X0) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (n_eq @ X1 @ X0))), 97.31/12.93 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl708])). 97.31/12.93 thf(zip_derived_cl710, plain, 97.31/12.93 (![X0 : $i, X1 : $i]: 97.31/12.93 ( (moref @ X1 @ X0) 97.31/12.93 | (lessf @ X1 @ X0) 97.31/12.93 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (n_eq @ X1 @ X0))), 97.31/12.93 inference('simplify nested equalities', [status(thm)], 97.31/12.93 [zip_derived_cl709])). 97.31/12.93 thf(zip_derived_cl7061, plain, 97.31/12.93 (![X0 : $i, X1 : $i]: 97.31/12.93 ( (moref @ X1 @ X0) 97.31/12.93 | (lessf @ X1 @ X0) 97.31/12.93 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.31/12.93 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.31/12.93 | (n_eq @ X1 @ X0))), 97.31/12.93 inference('remove_ty_args', [status(thm)], [zip_derived_cl710])). 97.31/12.93 thf(zip_derived_cl496, plain, 97.31/12.93 ( (is_of @ '#sk4' @ ((('#C') @ in @ (pair1type @ nat))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl495])). 97.31/12.93 thf(zip_derived_cl7048, plain, 97.31/12.93 ( (is_of @ '#sk4' @ ('#ty_enc5' @ in @ (pair1type @ nat)))), 97.31/12.93 inference('remove_ty_args', [status(thm)], [zip_derived_cl496])). 97.31/12.93 thf(satz51c, axiom, 97.31/12.93 (all_of @ 97.31/12.93 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.31/12.93 ( ^[X0:$i]: 97.31/12.93 ( all_of @ 97.31/12.93 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.31/12.93 ( ^[X1:$i]: 97.31/12.93 ( all_of @ 97.31/12.93 ( ^[X2:$i]: ( in @ X2 @ frac ) ) @ 97.31/12.93 ( ^[X2:$i]: 97.31/12.93 ( ( moreq @ X0 @ X1 ) => 97.31/12.93 ( ( moref @ X1 @ X2 ) => ( moref @ X0 @ X2 ) ) ) ) ) ) ) ))). 97.31/12.93 thf(zip_derived_cl130, plain, 97.31/12.93 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.31/12.93 (^[Y0 : $i]: 97.31/12.93 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.31/12.93 (^[Y1 : $i]: 97.31/12.93 (all_of @ (^[Y2 : $i]: (in @ Y2 @ frac)) @ 97.31/12.93 (^[Y2 : $i]: 97.31/12.93 (((moreq @ Y0 @ Y1) => 97.31/12.93 (((moref @ Y1 @ Y2) => (moref @ Y0 @ Y2)))))))))))), 97.31/12.93 inference('cnf', [status(esa)], [satz51c])). 97.31/12.93 thf(zip_derived_cl131, plain, 97.31/12.93 ( (all_of @ ((('#C') @ in @ frac)) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ frac))))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ ('#B'))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 97.31/12.93 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 97.31/12.93 moref)))))))))), 97.31/12.93 inference('lams2combs', [status(thm)], [zip_derived_cl130])). 97.31/12.93 thf(zip_derived_cl1381, plain, 97.31/12.93 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ ('#B'))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 97.31/12.93 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moref)))))) @ 97.31/12.93 moref)))))))))), 97.31/12.93 inference('rw', [status(thm)], [zip_derived_cl131, '0'])). 97.31/12.93 thf(zip_derived_cl1382, plain, 97.31/12.93 ( (((!!) @ (^[Y0 : $i]: 97.31/12.93 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (all_of @ 97.31/12.93 ((('#C') @ in @ 97.31/12.93 (pair1type @ nat)))))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ ('#B'))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 97.31/12.93 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ 97.31/12.93 moref)))))) @ 97.31/12.93 moref)))))) @ 97.31/12.93 Y0)))))))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl1381, '1'])). 97.31/12.93 thf(zip_derived_cl1383, plain, 97.31/12.93 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.93 ((('#C') @ is_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat)))))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ ('#B'))) @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moreq)))))) @ 97.31/12.93 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ 97.31/12.93 moref)))))) @ 97.31/12.93 moref))))))))))))), 97.31/12.93 inference('comb-normalize', [status(thm)], [zip_derived_cl1382])). 97.31/12.93 thf(zip_derived_cl1384, plain, 97.31/12.93 (![X2 : $i]: 97.31/12.93 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (moreq @ X2))))) @ 97.31/12.93 ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 97.31/12.93 (moref @ X2))))))))))), 97.31/12.93 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1383])). 97.31/12.93 thf(zip_derived_cl1385, plain, 97.31/12.93 (![X2 : $i]: 97.31/12.93 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ (moreq @ X2))))) @ 97.31/12.93 ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 97.31/12.93 (moref @ X2)))))))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1384])). 97.31/12.93 thf(zip_derived_cl1386, plain, 97.31/12.93 (![X0 : $i]: 97.31/12.93 ( (((!!) @ (^[Y0 : $i]: 97.31/12.93 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 ((('#B') @ (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#B') @ 97.31/12.93 ((('#B') @ (=>) @ (moreq @ X0))))) @ 97.31/12.93 ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 97.31/12.93 (moref @ X0))))) @ 97.31/12.93 Y0))))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('rw_clause', [status(thm)], [zip_derived_cl1385, '1'])). 97.31/12.93 thf(zip_derived_cl1387, plain, 97.31/12.93 (![X0 : $i]: 97.31/12.93 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.93 ((('#C') @ is_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.93 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ ('#B') @ 97.31/12.93 ((('#B') @ (=>) @ (moreq @ X0))))) @ 97.31/12.93 ((('#C') @ ((('#B') @ ('#S') @ 97.31/12.93 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 97.31/12.93 (moref @ X0))))))))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('comb-normalize', [status(thm)], [zip_derived_cl1386])). 97.31/12.93 thf(zip_derived_cl1388, plain, 97.31/12.93 (![X0 : $i, X2 : $i]: 97.31/12.93 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (((=>) @ (moreq @ X0 @ X2))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ (moref @ X0)))))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1387])). 97.31/12.93 thf(zip_derived_cl1389, plain, 97.31/12.93 (![X0 : $i, X2 : $i]: 97.31/12.93 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.31/12.93 ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (((=>) @ (imp @ (imp @ (moref @ X0 @ X2) @ ($false)) @ 97.31/12.93 (n_eq @ X0 @ X2)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ (moref @ X0)))))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('rw', [status(thm)], [zip_derived_cl1388, '2', '3', '4'])). 97.31/12.93 thf(zip_derived_cl1390, plain, 97.31/12.93 (![X0 : $i, X2 : $i]: 97.31/12.93 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.93 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.93 ((('#B') @ (((=>) @ (imp @ 97.31/12.93 (imp @ (moref @ X0 @ X2) @ ($false)) @ 97.31/12.93 (n_eq @ X0 @ X2)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ (moref @ X0)))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1389])). 97.31/12.93 thf(zip_derived_cl1391, plain, 97.31/12.93 (![X0 : $i, X1 : $i]: 97.31/12.93 ( (((!!) @ (^[Y0 : $i]: 97.31/12.93 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.93 ((('#B') @ (((=>) @ (imp @ 97.31/12.93 (imp @ (moref @ X0 @ X1) @ 97.31/12.93 ($false)) @ 97.31/12.93 (n_eq @ X0 @ X1)))) @ 97.31/12.93 ((('#S') @ ((('#B') @ (=>) @ (moref @ X1))) @ 97.31/12.93 (moref @ X0))) @ 97.31/12.93 Y0))))))) 97.31/12.93 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('rw_clause', [status(thm)], [zip_derived_cl1390, '1'])). 97.31/12.94 thf(zip_derived_cl1392, plain, 97.31/12.94 (![X0 : $i, X1 : $i]: 97.31/12.94 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.94 ((('#C') @ is_of @ 97.31/12.94 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.94 ((('#B') @ (((=>) @ (imp @ 97.31/12.94 (imp @ (moref @ X0 @ X1) @ ($false)) @ 97.31/12.94 (n_eq @ X0 @ X1)))) @ 97.31/12.94 ((('#S') @ ((('#B') @ (=>) @ (moref @ X1))) @ 97.31/12.94 (moref @ X0))))))))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('comb-normalize', [status(thm)], [zip_derived_cl1391])). 97.31/12.94 thf(zip_derived_cl1393, plain, 97.31/12.94 (![X0 : $i, X1 : $i, X3 : $i]: 97.31/12.94 ( (((is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.94 (((imp @ (imp @ (moref @ X0 @ X1) @ ($false)) @ 97.31/12.94 (n_eq @ X0 @ X1)) => (((moref @ X1 @ X3) => (moref @ X0 @ X3))))))) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1392])). 97.31/12.94 thf(zip_derived_cl1394, plain, 97.31/12.94 (![X0 : $i, X1 : $i, X3 : $i]: 97.31/12.94 (~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | (((imp @ (imp @ (moref @ X0 @ X1) @ ($false)) @ 97.31/12.94 (n_eq @ X0 @ X1)) => (((moref @ X1 @ X3) => (moref @ X0 @ X3))))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1393])). 97.31/12.94 thf(zip_derived_cl1395, plain, 97.31/12.94 (![X0 : $i, X1 : $i, X3 : $i]: 97.31/12.94 (~ (imp @ (imp @ (moref @ X0 @ X1) @ ($false)) @ (n_eq @ X0 @ X1)) 97.31/12.94 | (((moref @ X1 @ X3) => (moref @ X0 @ X3))) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X3 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1394])). 97.31/12.94 thf(zip_derived_cl1396, plain, 97.31/12.94 (![X0 : $i, X1 : $i, X2 : $i]: 97.31/12.94 (~ (((imp @ (moref @ X1 @ X2) @ ($false)) => (n_eq @ X1 @ X2))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | (((moref @ X2 @ X0) => (moref @ X1 @ X0))))), 97.31/12.94 inference('rw_clause', [status(thm)], [zip_derived_cl1395, '5'])). 97.31/12.94 thf(zip_derived_cl1398, plain, 97.31/12.94 (![X0 : $i, X1 : $i, X2 : $i]: 97.31/12.94 (~ (n_eq @ X1 @ X2) 97.31/12.94 | (((moref @ X2 @ X0) => (moref @ X1 @ X0))) 97.31/12.94 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])). 97.31/12.94 thf(zip_derived_cl1400, plain, 97.31/12.94 (![X0 : $i, X1 : $i, X2 : $i]: 97.31/12.94 (~ (moref @ X2 @ X0) 97.31/12.94 | (moref @ X1 @ X0) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (n_eq @ X1 @ X2))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1398])). 97.31/12.94 thf(zip_derived_cl7095, plain, 97.31/12.94 (![X0 : $i, X1 : $i, X2 : $i]: 97.31/12.94 (~ (moref @ X2 @ X0) 97.31/12.94 | (moref @ X1 @ X0) 97.31/12.94 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.31/12.94 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.31/12.94 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.31/12.94 | ~ (n_eq @ X1 @ X2))), 97.31/12.94 inference('remove_ty_args', [status(thm)], [zip_derived_cl1400])). 97.31/12.94 thf(zip_derived_cl490, plain, 97.31/12.94 ( (is_of @ '#sk3' @ ((('#C') @ in @ (pair1type @ nat))))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl489])). 97.31/12.94 thf(zip_derived_cl7047, plain, 97.31/12.94 ( (is_of @ '#sk3' @ ('#ty_enc5' @ in @ (pair1type @ nat)))), 97.31/12.94 inference('remove_ty_args', [status(thm)], [zip_derived_cl490])). 97.31/12.94 thf(satz43, axiom, 97.31/12.94 (all_of @ 97.31/12.94 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.31/12.94 ( ^[X0:$i]: 97.31/12.94 ( all_of @ 97.31/12.94 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.31/12.94 ( ^[X1:$i]: ( ( lessf @ X0 @ X1 ) => ( moref @ X1 @ X0 ) ) ) ) ))). 97.31/12.94 thf(zip_derived_cl180, plain, 97.31/12.94 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.31/12.94 (^[Y0 : $i]: 97.31/12.94 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.31/12.94 (^[Y1 : $i]: (((lessf @ Y0 @ Y1) => (moref @ Y1 @ Y0)))))))), 97.31/12.94 inference('cnf', [status(esa)], [satz43])). 97.31/12.94 thf(zip_derived_cl181, plain, 97.31/12.94 ( (all_of @ ((('#C') @ in @ frac)) @ 97.31/12.94 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.31/12.94 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.94 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 97.31/12.94 ((('#C') @ moref)))))))), 97.31/12.94 inference('lams2combs', [status(thm)], [zip_derived_cl180])). 97.31/12.94 thf(zip_derived_cl518, plain, 97.31/12.94 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.94 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.94 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.94 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 97.31/12.94 ((('#C') @ moref)))))))), 97.31/12.94 inference('rw', [status(thm)], [zip_derived_cl181, '0'])). 97.31/12.94 thf(zip_derived_cl519, plain, 97.31/12.94 ( (((!!) @ (^[Y0 : $i]: 97.31/12.94 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.94 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.94 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.94 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 97.31/12.94 ((('#C') @ moref)))) @ 97.31/12.94 Y0)))))))), 97.31/12.94 inference('rw_clause', [status(thm)], [zip_derived_cl518, '1'])). 97.31/12.94 thf(zip_derived_cl520, plain, 97.31/12.94 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.94 ((('#C') @ is_of @ 97.31/12.94 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.94 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.94 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.94 ((('#B') @ ((('#B') @ (=>))) @ lessf)))) @ 97.31/12.94 ((('#C') @ moref))))))))))), 97.31/12.94 inference('comb-normalize', [status(thm)], [zip_derived_cl519])). 97.31/12.94 thf(zip_derived_cl521, plain, 97.31/12.94 (![X2 : $i]: 97.31/12.94 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.31/12.94 ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.94 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ 97.31/12.94 ((('#C') @ moref @ X2)))))))), 97.31/12.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl520])). 97.31/12.94 thf(zip_derived_cl522, plain, 97.31/12.94 (![X2 : $i]: 97.31/12.94 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.94 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X2))) @ 97.31/12.94 ((('#C') @ moref @ X2))))))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl521])). 97.31/12.94 thf(zip_derived_cl523, plain, 97.31/12.94 (![X0 : $i]: 97.31/12.94 ( (((!!) @ (^[Y0 : $i]: 97.31/12.94 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.94 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X0))) @ 97.31/12.94 ((('#C') @ moref @ X0)) @ Y0))))))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('rw_clause', [status(thm)], [zip_derived_cl522, '1'])). 97.31/12.94 thf(zip_derived_cl524, plain, 97.31/12.94 (![X0 : $i]: 97.31/12.94 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.94 ((('#C') @ is_of @ 97.31/12.94 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.94 ((('#S') @ ((('#B') @ (=>) @ (lessf @ X0))) @ 97.31/12.94 ((('#C') @ moref @ X0)))))))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('comb-normalize', [status(thm)], [zip_derived_cl523])). 97.31/12.94 thf(zip_derived_cl525, plain, 97.31/12.94 (![X0 : $i, X2 : $i]: 97.31/12.94 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.94 (((lessf @ X0 @ X2) => (moref @ X2 @ X0))))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl524])). 97.31/12.94 thf(zip_derived_cl526, plain, 97.31/12.94 (![X0 : $i, X2 : $i]: 97.31/12.94 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | (((lessf @ X0 @ X2) => (moref @ X2 @ X0))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl525])). 97.31/12.94 thf(zip_derived_cl527, plain, 97.31/12.94 (![X0 : $i, X2 : $i]: 97.31/12.94 (~ (lessf @ X0 @ X2) 97.31/12.94 | (moref @ X2 @ X0) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl526])). 97.31/12.94 thf(zip_derived_cl7049, plain, 97.31/12.94 (![X0 : $i, X2 : $i]: 97.31/12.94 (~ (lessf @ X0 @ X2) 97.31/12.94 | (moref @ X2 @ X0) 97.31/12.94 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.31/12.94 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))))), 97.31/12.94 inference('remove_ty_args', [status(thm)], [zip_derived_cl527])). 97.31/12.94 thf(satz42, axiom, 97.31/12.94 (all_of @ 97.31/12.94 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.31/12.94 ( ^[X0:$i]: 97.31/12.94 ( all_of @ 97.31/12.94 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.31/12.94 ( ^[X1:$i]: ( ( moref @ X0 @ X1 ) => ( lessf @ X1 @ X0 ) ) ) ) ))). 97.31/12.94 thf(zip_derived_cl288, plain, 97.31/12.94 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.31/12.94 (^[Y0 : $i]: 97.31/12.94 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.31/12.94 (^[Y1 : $i]: (((moref @ Y0 @ Y1) => (lessf @ Y1 @ Y0)))))))), 97.31/12.94 inference('cnf', [status(esa)], [satz42])). 97.31/12.94 thf(zip_derived_cl289, plain, 97.31/12.94 ( (all_of @ ((('#C') @ in @ frac)) @ 97.31/12.94 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.31/12.94 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.94 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 97.31/12.94 ((('#C') @ lessf)))))))), 97.31/12.94 inference('lams2combs', [status(thm)], [zip_derived_cl288])). 97.31/12.94 thf(zip_derived_cl604, plain, 97.31/12.94 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.94 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.94 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.94 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 97.31/12.94 ((('#C') @ lessf)))))))), 97.31/12.94 inference('rw', [status(thm)], [zip_derived_cl289, '0'])). 97.31/12.94 thf(zip_derived_cl605, plain, 97.31/12.94 ( (((!!) @ (^[Y0 : $i]: 97.31/12.94 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.94 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.94 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.94 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 97.31/12.94 ((('#C') @ lessf)))) @ 97.31/12.94 Y0)))))))), 97.31/12.94 inference('rw_clause', [status(thm)], [zip_derived_cl604, '1'])). 97.31/12.94 thf(zip_derived_cl606, plain, 97.31/12.94 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.94 ((('#C') @ is_of @ 97.31/12.94 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.94 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.94 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.94 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 97.31/12.94 ((('#C') @ lessf))))))))))), 97.31/12.94 inference('comb-normalize', [status(thm)], [zip_derived_cl605])). 97.31/12.94 thf(zip_derived_cl607, plain, 97.31/12.94 (![X2 : $i]: 97.31/12.94 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.31/12.94 ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.94 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 97.31/12.94 ((('#C') @ lessf @ X2)))))))), 97.31/12.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl606])). 97.31/12.94 thf(zip_derived_cl608, plain, 97.31/12.94 (![X2 : $i]: 97.31/12.94 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.94 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 97.31/12.94 ((('#C') @ lessf @ X2))))))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl607])). 97.31/12.94 thf(zip_derived_cl609, plain, 97.31/12.94 (![X0 : $i]: 97.31/12.94 ( (((!!) @ (^[Y0 : $i]: 97.31/12.94 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.94 ((('#S') @ ((('#B') @ (=>) @ (moref @ X0))) @ 97.31/12.94 ((('#C') @ lessf @ X0)) @ Y0))))))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('rw_clause', [status(thm)], [zip_derived_cl608, '1'])). 97.31/12.94 thf(zip_derived_cl610, plain, 97.31/12.94 (![X0 : $i]: 97.31/12.94 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.94 ((('#C') @ is_of @ 97.31/12.94 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.94 ((('#S') @ ((('#B') @ (=>) @ (moref @ X0))) @ 97.31/12.94 ((('#C') @ lessf @ X0)))))))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('comb-normalize', [status(thm)], [zip_derived_cl609])). 97.31/12.94 thf(zip_derived_cl611, plain, 97.31/12.94 (![X0 : $i, X2 : $i]: 97.31/12.94 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.94 (((moref @ X0 @ X2) => (lessf @ X2 @ X0))))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl610])). 97.31/12.94 thf(zip_derived_cl612, plain, 97.31/12.94 (![X0 : $i, X2 : $i]: 97.31/12.94 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | (((moref @ X0 @ X2) => (lessf @ X2 @ X0))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl611])). 97.31/12.94 thf(zip_derived_cl613, plain, 97.31/12.94 (![X0 : $i, X2 : $i]: 97.31/12.94 (~ (moref @ X0 @ X2) 97.31/12.94 | (lessf @ X2 @ X0) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl612])). 97.31/12.94 thf(zip_derived_cl7055, plain, 97.31/12.94 (![X0 : $i, X2 : $i]: 97.31/12.94 (~ (moref @ X0 @ X2) 97.31/12.94 | (lessf @ X2 @ X0) 97.31/12.94 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.31/12.94 | ~ (is_of @ X2 @ ('#ty_enc5' @ in @ (pair1type @ nat))))), 97.31/12.94 inference('remove_ty_args', [status(thm)], [zip_derived_cl613])). 97.31/12.94 thf(satz41g, axiom, 97.31/12.94 (all_of @ 97.31/12.94 ( ^[X0:$i]: ( in @ X0 @ frac ) ) @ 97.31/12.94 ( ^[X0:$i]: 97.31/12.94 ( all_of @ 97.31/12.94 ( ^[X1:$i]: ( in @ X1 @ frac ) ) @ 97.31/12.94 ( ^[X1:$i]: 97.31/12.94 ( ( moref @ X0 @ X1 ) => ( d_not @ ( lesseq @ X0 @ X1 ) ) ) ) ) ))). 97.31/12.94 thf(zip_derived_cl54, plain, 97.31/12.94 ( (all_of @ (^[Y0 : $i]: (in @ Y0 @ frac)) @ 97.31/12.94 (^[Y0 : $i]: 97.31/12.94 (all_of @ (^[Y1 : $i]: (in @ Y1 @ frac)) @ 97.31/12.94 (^[Y1 : $i]: (((moref @ Y0 @ Y1) => (d_not @ (lesseq @ Y0 @ Y1))))))))), 97.31/12.94 inference('cnf', [status(esa)], [satz41g])). 97.31/12.94 thf(zip_derived_cl55, plain, 97.31/12.94 ( (all_of @ ((('#C') @ in @ frac)) @ 97.31/12.94 ((('#B') @ (all_of @ ((('#C') @ in @ frac))) @ 97.31/12.94 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.94 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 97.31/12.94 ((('#B') @ ((('#B') @ d_not)) @ lesseq)))))))), 97.31/12.94 inference('lams2combs', [status(thm)], [zip_derived_cl54])). 97.31/12.94 thf(zip_derived_cl615, plain, 97.31/12.94 ( (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.94 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.94 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.94 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 97.31/12.94 ((('#B') @ ((('#B') @ d_not)) @ lesseq)))))))), 97.31/12.94 inference('rw', [status(thm)], [zip_derived_cl55, '0'])). 97.31/12.94 thf(zip_derived_cl616, plain, 97.31/12.94 ( (((!!) @ (^[Y0 : $i]: 97.31/12.94 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.94 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.94 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.94 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 97.31/12.94 ((('#B') @ ((('#B') @ d_not)) @ lesseq)))) @ 97.31/12.94 Y0)))))))), 97.31/12.94 inference('rw_clause', [status(thm)], [zip_derived_cl615, '1'])). 97.31/12.94 thf(zip_derived_cl617, plain, 97.31/12.94 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.94 ((('#C') @ is_of @ 97.31/12.94 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.94 ((('#B') @ (all_of @ ((('#C') @ in @ (pair1type @ nat)))) @ 97.31/12.94 ((('#S') @ ((('#B') @ ('#S') @ 97.31/12.94 ((('#B') @ ((('#B') @ (=>))) @ moref)))) @ 97.31/12.94 ((('#B') @ ((('#B') @ d_not)) @ lesseq))))))))))), 97.31/12.94 inference('comb-normalize', [status(thm)], [zip_derived_cl616])). 97.31/12.94 thf(zip_derived_cl618, plain, 97.31/12.94 (![X2 : $i]: 97.31/12.94 (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => (all_of @ 97.31/12.94 ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.94 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 97.31/12.94 ((('#B') @ d_not @ (lesseq @ X2))))))))), 97.31/12.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl617])). 97.31/12.94 thf(zip_derived_cl619, plain, 97.31/12.94 (![X2 : $i]: 97.31/12.94 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | (all_of @ ((('#C') @ in @ (pair1type @ nat))) @ 97.31/12.94 ((('#S') @ ((('#B') @ (=>) @ (moref @ X2))) @ 97.31/12.94 ((('#B') @ d_not @ (lesseq @ X2)))))))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl618])). 97.31/12.94 thf(zip_derived_cl620, plain, 97.31/12.94 (![X0 : $i]: 97.31/12.94 ( (((!!) @ (^[Y0 : $i]: 97.31/12.94 (((is_of @ Y0 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.94 ((('#S') @ ((('#B') @ (=>) @ (moref @ X0))) @ 97.31/12.94 ((('#B') @ d_not @ (lesseq @ X0))) @ Y0))))))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('rw_clause', [status(thm)], [zip_derived_cl619, '1'])). 97.31/12.94 thf(zip_derived_cl621, plain, 97.31/12.94 (![X0 : $i]: 97.31/12.94 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 97.31/12.94 ((('#C') @ is_of @ 97.31/12.94 ((('#C') @ in @ (pair1type @ nat))))))) @ 97.31/12.94 ((('#S') @ ((('#B') @ (=>) @ (moref @ X0))) @ 97.31/12.94 ((('#B') @ d_not @ (lesseq @ X0))))))))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('comb-normalize', [status(thm)], [zip_derived_cl620])). 97.31/12.94 thf(zip_derived_cl622, plain, 97.31/12.94 (![X0 : $i, X2 : $i]: 97.31/12.94 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.94 (((moref @ X0 @ X2) => (d_not @ (lesseq @ X0 @ X2)))))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl621])). 97.31/12.94 thf(zip_derived_cl623, plain, 97.31/12.94 (![X0 : $i, X2 : $i]: 97.31/12.94 ( (((is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) => 97.31/12.94 (((moref @ X0 @ X2) => (imp @ 97.31/12.94 (imp @ (imp @ (lessf @ X0 @ X2) @ ($false)) @ (n_eq @ X0 @ X2)) @ 97.31/12.94 ($false)))))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('rw', [status(thm)], [zip_derived_cl622, '2', '2', '3', '8'])). 97.31/12.94 thf(zip_derived_cl624, plain, 97.31/12.94 (![X0 : $i, X2 : $i]: 97.31/12.94 (~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | (((moref @ X0 @ X2) => (imp @ 97.31/12.94 (imp @ (imp @ (lessf @ X0 @ X2) @ ($false)) @ (n_eq @ X0 @ X2)) @ 97.31/12.94 ($false)))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl623])). 97.31/12.94 thf(zip_derived_cl625, plain, 97.31/12.94 (![X0 : $i, X2 : $i]: 97.31/12.94 (~ (moref @ X0 @ X2) 97.31/12.94 | (imp @ 97.31/12.94 (imp @ (imp @ (lessf @ X0 @ X2) @ ($false)) @ (n_eq @ X0 @ X2)) @ 97.31/12.94 ($false)) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X2 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl624])). 97.31/12.94 thf(zip_derived_cl626, plain, 97.31/12.94 (![X0 : $i, X1 : $i]: 97.31/12.94 ( (((imp @ (imp @ (lessf @ X1 @ X0) @ ($false)) @ (n_eq @ X1 @ X0)) => 97.31/12.94 ($false))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (moref @ X1 @ X0))), 97.31/12.94 inference('rw_clause', [status(thm)], [zip_derived_cl625, '6'])). 97.31/12.94 thf(zip_derived_cl627, plain, 97.31/12.94 (![X0 : $i, X1 : $i]: 97.31/12.94 ( (((~) @ (imp @ (imp @ (lessf @ X1 @ X0) @ ($false)) @ 97.31/12.94 (n_eq @ X1 @ X0)))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (moref @ X1 @ X0))), 97.31/12.94 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl626])). 97.31/12.94 thf(zip_derived_cl628, plain, 97.31/12.94 (![X0 : $i, X1 : $i]: 97.31/12.94 (~ (imp @ (imp @ (lessf @ X1 @ X0) @ ($false)) @ (n_eq @ X1 @ X0)) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (moref @ X1 @ X0))), 97.31/12.94 inference('simplify nested equalities', [status(thm)], 97.31/12.94 [zip_derived_cl627])). 97.31/12.94 thf(zip_derived_cl629, plain, 97.31/12.94 (![X0 : $i, X1 : $i]: 97.31/12.94 (~ (((imp @ (lessf @ X1 @ X0) @ ($false)) => (n_eq @ X1 @ X0))) 97.31/12.94 | ~ (moref @ X1 @ X0) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('rw_clause', [status(thm)], [zip_derived_cl628, '5'])). 97.31/12.94 thf(zip_derived_cl631, plain, 97.31/12.94 (![X0 : $i, X1 : $i]: 97.31/12.94 (~ (n_eq @ X1 @ X0) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (moref @ X1 @ X0))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl629])). 97.31/12.94 thf(zip_derived_cl7056, plain, 97.31/12.94 (![X0 : $i, X1 : $i]: 97.31/12.94 (~ (n_eq @ X1 @ X0) 97.31/12.94 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.31/12.94 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.31/12.94 | ~ (moref @ X1 @ X0))), 97.31/12.94 inference('remove_ty_args', [status(thm)], [zip_derived_cl631])). 97.31/12.94 thf(zip_derived_cl630, plain, 97.31/12.94 (![X0 : $i, X1 : $i]: 97.31/12.94 ( (imp @ (lessf @ X1 @ X0) @ ($false)) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (moref @ X1 @ X0))), 97.31/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl629])). 97.31/12.94 thf(zip_derived_cl632, plain, 97.31/12.94 (![X0 : $i, X1 : $i]: 97.31/12.94 ( (((lessf @ X1 @ X0) => ($false))) 97.31/12.94 | ~ (moref @ X1 @ X0) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('rw_clause', [status(thm)], [zip_derived_cl630, '6'])). 97.31/12.94 thf(zip_derived_cl633, plain, 97.31/12.94 (![X0 : $i, X1 : $i]: 97.31/12.94 ( (((~) @ (lessf @ X1 @ X0))) 97.31/12.94 | ~ (moref @ X1 @ X0) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl632])). 97.31/12.94 thf(zip_derived_cl634, plain, 97.31/12.94 (![X0 : $i, X1 : $i]: 97.31/12.94 (~ (lessf @ X1 @ X0) 97.31/12.94 | ~ (moref @ X1 @ X0) 97.31/12.94 | ~ (is_of @ X1 @ ((('#C') @ in @ (pair1type @ nat)))) 97.31/12.94 | ~ (is_of @ X0 @ ((('#C') @ in @ (pair1type @ nat)))))), 97.31/12.94 inference('simplify nested equalities', [status(thm)], 97.31/12.94 [zip_derived_cl633])). 97.31/12.94 thf(zip_derived_cl7057, plain, 97.31/12.94 (![X0 : $i, X1 : $i]: 97.31/12.94 (~ (lessf @ X1 @ X0) 97.31/12.94 | ~ (moref @ X1 @ X0) 97.31/12.94 | ~ (is_of @ X1 @ ('#ty_enc5' @ in @ (pair1type @ nat))) 97.31/12.94 | ~ (is_of @ X0 @ ('#ty_enc5' @ in @ (pair1type @ nat))))), 97.31/12.94 inference('remove_ty_args', [status(thm)], [zip_derived_cl634])). 97.31/12.94 thf(zip_derived_cl7154, plain, ($false), 97.31/12.94 inference('eprover', [status(thm)], 97.31/12.94 [zip_derived_cl7087, zip_derived_cl509, zip_derived_cl515, 97.31/12.94 zip_derived_cl511, zip_derived_cl517, zip_derived_cl7046, 97.31/12.94 zip_derived_cl7061, zip_derived_cl7048, zip_derived_cl7095, 97.31/12.94 zip_derived_cl7047, zip_derived_cl7049, zip_derived_cl7055, 97.31/12.94 zip_derived_cl7056, zip_derived_cl7057])). 97.31/12.94 97.31/12.94 % SZS output end Refutation 97.31/12.94 97.31/12.94 97.31/12.94 % Terminating... 97.97/13.02 % Runner terminated. 98.02/13.03 % Zipperpin 1.5 exiting 98.02/13.03 EOF