0.06/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.8PrzRRh7XX true 0.12/0.33 % Computer : n025.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 960 0.12/0.33 % WCLimit : 120 0.12/0.33 % DateTime : Tue Aug 9 06:33:26 EDT 2022 0.12/0.33 % CPUTime : 0.12/0.33 % Running portfolio for 960 s 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.33 % Number of cores: 8 0.12/0.34 % Python version: Python 3.6.8 0.12/0.34 % Running in HO mode 0.48/0.63 % Total configuration time : 828 0.48/0.63 % Estimated wc time : 1656 0.48/0.63 % Estimated cpu time (8 cpus) : 207.0 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.52/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 51.84/7.14 % Solved by lams/20_acsne_simpl.sh. 51.84/7.14 % done 709 iterations in 6.198s 51.84/7.14 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 51.84/7.14 % SZS output start Refutation 51.84/7.14 thf(term_type, type, term: $tType). 51.84/7.14 thf(subst_type, type, subst: $tType). 51.84/7.14 thf(axmap_type, type, axmap: $o). 51.84/7.14 thf(axclos_type, type, axclos: $o). 51.84/7.14 thf(lam_type, type, lam: term > term). 51.84/7.14 thf(lamnotap_type, type, lamnotap: $o). 51.84/7.14 thf('#form109_type', type, '#form109': (term > $o) > $o). 51.84/7.14 thf(axvarcons_type, type, axvarcons: $o). 51.84/7.14 thf(push_type, type, push: term > subst > subst). 51.84/7.14 thf(axshiftcons_type, type, axshiftcons: $o). 51.84/7.14 thf('#sk53_type', type, '#sk53': term > $o). 51.84/7.14 thf(axapp_type, type, axapp: $o). 51.84/7.14 thf(shinj_type, type, shinj: $o). 51.84/7.14 thf(induction2_gthm_type, type, induction2_gthm: $o). 51.84/7.14 thf(one_type, type, one: term). 51.84/7.14 thf(id_type, type, id: subst). 51.84/7.14 thf(comp_type, type, comp: subst > subst > subst). 51.84/7.14 thf('#sk46_type', type, '#sk46': (term > $o) > term). 51.84/7.14 thf(induction2_type, type, induction2: $o). 51.84/7.14 thf(axvarid_type, type, axvarid: $o). 51.84/7.14 thf(axvarshift_type, type, axvarshift: $o). 51.84/7.14 thf(induction2lem_type, type, induction2lem: $o). 51.84/7.14 thf(sh_type, type, sh: subst). 51.84/7.14 thf(laminj_type, type, laminj: $o). 51.84/7.14 thf(ulamvarind_type, type, ulamvarind: $o). 51.84/7.14 thf(apinj2_type, type, apinj2: $o). 51.84/7.14 thf('#sk186_type', type, '#sk186': term). 51.84/7.14 thf(ulamvarsh_type, type, ulamvarsh: $o). 51.84/7.14 thf(lamnotvar_type, type, lamnotvar: $o). 51.84/7.14 thf(apnotvar_type, type, apnotvar: $o). 51.84/7.14 thf(pushprop_type, type, pushprop: $o). 51.84/7.14 thf(sub_type, type, sub: term > subst > term). 51.84/7.14 thf(apinj1_type, type, apinj1: $o). 51.84/7.14 thf(axidl_type, type, axidl: $o). 51.84/7.14 thf(ap_type, type, ap: term > term > term). 51.84/7.14 thf(var_type, type, var: term > $o). 51.84/7.14 thf(axassoc_type, type, axassoc: $o). 51.84/7.14 thf('#sk252_type', type, '#sk252': term > term). 51.84/7.14 thf(axidr_type, type, axidr: $o). 51.84/7.14 thf(axabs_type, type, axabs: $o). 51.84/7.14 thf(ulamvar1_type, type, ulamvar1: $o). 51.84/7.14 thf(induction_type, type, induction: $o). 51.84/7.14 thf(axscons_type, type, axscons: $o). 51.84/7.14 thf('#sk177_type', type, '#sk177': (term > $o) > term). 51.84/7.14 thf(induction2_gthm, axiom, induction2_gthm = 51.84/7.14 (( axapp ) => 51.84/7.14 ( ( axvarcons ) => 51.84/7.14 ( ( axvarid ) => 51.84/7.14 ( ( axabs ) => 51.84/7.14 ( ( axclos ) => 51.84/7.14 ( ( axidl ) => 51.84/7.14 ( ( axshiftcons ) => 51.84/7.14 ( ( axassoc ) => 51.84/7.14 ( ( axmap ) => 51.84/7.14 ( ( axidr ) => 51.84/7.14 ( ( axvarshift ) => 51.84/7.14 ( ( axscons ) => 51.84/7.14 ( ( ulamvar1 ) => 51.84/7.14 ( ( ulamvarsh ) => 51.84/7.14 ( ( ulamvarind ) => 51.84/7.14 ( ( apinj1 ) => 51.84/7.14 ( ( apinj2 ) => 51.84/7.14 ( ( laminj ) => 51.84/7.14 ( ( shinj ) => 51.84/7.14 ( ( lamnotap ) => 51.84/7.14 ( ( apnotvar ) => 51.84/7.14 ( ( lamnotvar ) => 51.84/7.14 ( ( induction ) => 51.84/7.14 ( ( pushprop ) => 51.84/7.14 ( ( induction2lem ) => 51.84/7.14 ( induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 51.84/7.14 thf('0', plain, 51.84/7.14 (( induction2_gthm ) = 51.84/7.14 ( ( axapp ) => 51.84/7.14 ( ( axvarcons ) => 51.84/7.14 ( ( axvarid ) => 51.84/7.14 ( ( axabs ) => 51.84/7.14 ( ( axclos ) => 51.84/7.14 ( ( axidl ) => 51.84/7.14 ( ( axshiftcons ) => 51.84/7.14 ( ( axassoc ) => 51.84/7.14 ( ( axmap ) => 51.84/7.14 ( ( axidr ) => 51.84/7.14 ( ( axvarshift ) => 51.84/7.14 ( ( axscons ) => 51.84/7.14 ( ( ulamvar1 ) => 51.84/7.14 ( ( ulamvarsh ) => 51.84/7.14 ( ( ulamvarind ) => 51.84/7.14 ( ( apinj1 ) => 51.84/7.14 ( ( apinj2 ) => 51.84/7.14 ( ( laminj ) => 51.84/7.14 ( ( shinj ) => 51.84/7.14 ( ( lamnotap ) => 51.84/7.14 ( ( apnotvar ) => 51.84/7.14 ( ( lamnotvar ) => 51.84/7.14 ( ( induction ) => 51.84/7.14 ( ( pushprop ) => 51.84/7.14 ( ( induction2lem ) => 51.84/7.14 ( induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(induction2, axiom, induction2 = 51.84/7.14 (![P:( term > $o )]: 51.84/7.14 ( ( ![A:term]: ( ( var @ A ) => ( P @ A ) ) ) => 51.84/7.14 ( ( ![A:term,B:term]: 51.84/7.14 ( ( P @ A ) => ( ( P @ B ) => ( P @ ( ap @ A @ B ) ) ) ) ) => 51.84/7.14 ( ( ![A:term]: 51.84/7.14 ( ( ![B:term]: 51.84/7.14 ( ( P @ B ) => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) => 51.84/7.14 ( P @ ( lam @ A ) ) ) ) => 51.84/7.14 ( ![A:term]: ( P @ A ) ) ) ) ))). 51.84/7.14 thf('1', plain, 51.84/7.14 (( induction2 ) = 51.84/7.14 ( ![X4:( term > $o )]: 51.84/7.14 ( ( ![X6:term]: ( ( var @ X6 ) => ( X4 @ X6 ) ) ) => 51.84/7.14 ( ( ![X8:term,X10:term]: 51.84/7.14 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( X4 @ ( ap @ X8 @ X10 ) ) ) ) ) => 51.84/7.14 ( ( ![X12:term]: 51.84/7.14 ( ( ![X14:term]: 51.84/7.14 ( ( X4 @ X14 ) => 51.84/7.14 ( X4 @ ( sub @ X12 @ ( push @ X14 @ id ) ) ) ) ) => 51.84/7.14 ( X4 @ ( lam @ X12 ) ) ) ) => 51.84/7.14 ( ![X16:term]: ( X4 @ X16 ) ) ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(induction2lem, axiom, induction2lem = 51.84/7.14 (![P:( term > $o )]: 51.84/7.14 ( ( ![A:term,B:term]: 51.84/7.14 ( ( P @ A ) => ( ( P @ B ) => ( P @ ( ap @ A @ B ) ) ) ) ) => 51.84/7.14 ( ( ![A:term]: 51.84/7.14 ( ( ![B:term]: 51.84/7.14 ( ( P @ B ) => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) => 51.84/7.14 ( P @ ( lam @ A ) ) ) ) => 51.84/7.14 ( ![A:term,M:subst]: 51.84/7.14 ( ( ![B:term]: ( ( var @ B ) => ( P @ ( sub @ B @ M ) ) ) ) => 51.84/7.14 ( P @ ( sub @ A @ M ) ) ) ) ) ))). 51.84/7.14 thf('2', plain, 51.84/7.14 (( induction2lem ) = 51.84/7.14 ( ![X4:( term > $o )]: 51.84/7.14 ( ( ![X6:term,X8:term]: 51.84/7.14 ( ( X4 @ X6 ) => ( ( X4 @ X8 ) => ( X4 @ ( ap @ X6 @ X8 ) ) ) ) ) => 51.84/7.14 ( ( ![X10:term]: 51.84/7.14 ( ( ![X12:term]: 51.84/7.14 ( ( X4 @ X12 ) => 51.84/7.14 ( X4 @ ( sub @ X10 @ ( push @ X12 @ id ) ) ) ) ) => 51.84/7.14 ( X4 @ ( lam @ X10 ) ) ) ) => 51.84/7.14 ( ![X14:term,X16:subst]: 51.84/7.14 ( ( ![X18:term]: 51.84/7.14 ( ( var @ X18 ) => ( X4 @ ( sub @ X18 @ X16 ) ) ) ) => 51.84/7.14 ( X4 @ ( sub @ X14 @ X16 ) ) ) ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(pushprop, axiom, pushprop = 51.84/7.14 (![P:( term > $o ),A:term,M:subst]: 51.84/7.14 ( ( ![B:term]: ( ( var @ B ) => ( P @ ( sub @ B @ M ) ) ) ) => 51.84/7.14 ( ( P @ A ) => 51.84/7.14 ( ![B:term]: ( ( var @ B ) => ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ))). 51.84/7.14 thf('3', plain, 51.84/7.14 (( pushprop ) = 51.84/7.14 ( ![X4:( term > $o ),X6:term,X8:subst]: 51.84/7.14 ( ( ![X10:term]: ( ( var @ X10 ) => ( X4 @ ( sub @ X10 @ X8 ) ) ) ) => 51.84/7.14 ( ( X4 @ X6 ) => 51.84/7.14 ( ![X12:term]: 51.84/7.14 ( ( var @ X12 ) => ( X4 @ ( sub @ X12 @ ( push @ X6 @ X8 ) ) ) ) ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(induction, axiom, induction = 51.84/7.14 (![P:( term > $o )]: 51.84/7.14 ( ( ![A:term]: ( ( var @ A ) => ( P @ A ) ) ) => 51.84/7.14 ( ( ![A:term,B:term]: 51.84/7.14 ( ( P @ A ) => ( ( P @ B ) => ( P @ ( ap @ A @ B ) ) ) ) ) => 51.84/7.14 ( ( ![A:term]: ( ( P @ A ) => ( P @ ( lam @ A ) ) ) ) => 51.84/7.14 ( ![A:term]: ( P @ A ) ) ) ) ))). 51.84/7.14 thf('4', plain, 51.84/7.14 (( induction ) = 51.84/7.14 ( ![X4:( term > $o )]: 51.84/7.14 ( ( ![X6:term]: ( ( var @ X6 ) => ( X4 @ X6 ) ) ) => 51.84/7.14 ( ( ![X8:term,X10:term]: 51.84/7.14 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( X4 @ ( ap @ X8 @ X10 ) ) ) ) ) => 51.84/7.14 ( ( ![X12:term]: ( ( X4 @ X12 ) => ( X4 @ ( lam @ X12 ) ) ) ) => 51.84/7.14 ( ![X14:term]: ( X4 @ X14 ) ) ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(lamnotvar, axiom, lamnotvar = (![A:term]: ( ~( var @ ( lam @ A ) ) ))). 51.84/7.14 thf('5', plain, 51.84/7.14 (( lamnotvar ) = ( ![X4:term]: ( ~( var @ ( lam @ X4 ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(apnotvar, axiom, apnotvar = 51.84/7.14 (![A:term,B:term]: ( ~( var @ ( ap @ A @ B ) ) ))). 51.84/7.14 thf('6', plain, 51.84/7.14 (( apnotvar ) = ( ![X4:term,X6:term]: ( ~( var @ ( ap @ X4 @ X6 ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(lamnotap, axiom, lamnotap = 51.84/7.14 (![A:term,B:term,C:term]: ( ( lam @ A ) != ( ap @ B @ C ) ))). 51.84/7.14 thf('7', plain, 51.84/7.14 (( lamnotap ) = 51.84/7.14 ( ![X4:term,X6:term,X8:term]: ( ( lam @ X4 ) != ( ap @ X6 @ X8 ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(shinj, axiom, shinj = 51.84/7.14 (![A:term,B:term]: 51.84/7.14 ( ( ( sub @ A @ sh ) = ( sub @ B @ sh ) ) => ( ( A ) = ( B ) ) ))). 51.84/7.14 thf('8', plain, 51.84/7.14 (( shinj ) = 51.84/7.14 ( ![X4:term,X6:term]: 51.84/7.14 ( ( ( sub @ X4 @ sh ) = ( sub @ X6 @ sh ) ) => ( ( X4 ) = ( X6 ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(laminj, axiom, laminj = 51.84/7.14 (![A:term,B:term]: ( ( ( lam @ A ) = ( lam @ B ) ) => ( ( A ) = ( B ) ) ))). 51.84/7.14 thf('9', plain, 51.84/7.14 (( laminj ) = 51.84/7.14 ( ![X4:term,X6:term]: 51.84/7.14 ( ( ( lam @ X4 ) = ( lam @ X6 ) ) => ( ( X4 ) = ( X6 ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(apinj2, axiom, apinj2 = 51.84/7.14 (![A:term,B:term,C:term,D:term]: 51.84/7.14 ( ( ( ap @ A @ C ) = ( ap @ B @ D ) ) => ( ( C ) = ( D ) ) ))). 51.84/7.14 thf('10', plain, 51.84/7.14 (( apinj2 ) = 51.84/7.14 ( ![X4:term,X6:term,X8:term,X10:term]: 51.84/7.14 ( ( ( ap @ X4 @ X8 ) = ( ap @ X6 @ X10 ) ) => ( ( X8 ) = ( X10 ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(apinj1, axiom, apinj1 = 51.84/7.14 (![A:term,B:term,C:term,D:term]: 51.84/7.14 ( ( ( ap @ A @ C ) = ( ap @ B @ D ) ) => ( ( A ) = ( B ) ) ))). 51.84/7.14 thf('11', plain, 51.84/7.14 (( apinj1 ) = 51.84/7.14 ( ![X4:term,X6:term,X8:term,X10:term]: 51.84/7.14 ( ( ( ap @ X4 @ X8 ) = ( ap @ X6 @ X10 ) ) => ( ( X4 ) = ( X6 ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(ulamvarind, axiom, ulamvarind = 51.84/7.14 (![P:( term > $o )]: 51.84/7.14 ( ( P @ one ) => 51.84/7.14 ( ( ![A:term]: 51.84/7.14 ( ( var @ A ) => ( ( P @ A ) => ( P @ ( sub @ A @ sh ) ) ) ) ) => 51.84/7.14 ( ![A:term]: ( ( var @ A ) => ( P @ A ) ) ) ) ))). 51.84/7.14 thf('12', plain, 51.84/7.14 (( ulamvarind ) = 51.84/7.14 ( ![X4:( term > $o )]: 51.84/7.14 ( ( X4 @ one ) => 51.84/7.14 ( ( ![X6:term]: 51.84/7.14 ( ( var @ X6 ) => ( ( X4 @ X6 ) => ( X4 @ ( sub @ X6 @ sh ) ) ) ) ) => 51.84/7.14 ( ![X8:term]: ( ( var @ X8 ) => ( X4 @ X8 ) ) ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(ulamvarsh, axiom, ulamvarsh = 51.84/7.14 (![A:term]: ( ( var @ A ) => ( var @ ( sub @ A @ sh ) ) ))). 51.84/7.14 thf('13', plain, 51.84/7.14 (( ulamvarsh ) = 51.84/7.14 ( ![X4:term]: ( ( var @ X4 ) => ( var @ ( sub @ X4 @ sh ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(ulamvar1, axiom,(( ulamvar1 ) = (var @ one))). 51.84/7.14 thf('14', plain, (( ulamvar1 ) = ( var @ one )), 51.84/7.14 inference('simplify_rw_rule', [status(thm)], [ulamvar1])). 51.84/7.14 thf('15', plain, (( ulamvar1 ) = ( var @ one )), define([status(thm)])). 51.84/7.14 thf(axscons, axiom, axscons = 51.84/7.14 (![M:subst]: ( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) = ( M ) ))). 51.84/7.14 thf('16', plain, 51.84/7.14 (( axscons ) = 51.84/7.14 ( ![X4:subst]: 51.84/7.14 ( ( push @ ( sub @ one @ X4 ) @ ( comp @ sh @ X4 ) ) = ( X4 ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(axvarshift, axiom, axvarshift = (( push @ one @ sh ) = ( id ))). 51.84/7.14 thf('17', plain, (( axvarshift ) = ( ( push @ one @ sh ) = ( id ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(axidr, axiom, axidr = (![M:subst]: ( ( comp @ M @ id ) = ( M ) ))). 51.84/7.14 thf('18', plain, 51.84/7.14 (( axidr ) = ( ![X4:subst]: ( ( comp @ X4 @ id ) = ( X4 ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(axmap, axiom, axmap = 51.84/7.14 (![A:term,M:subst,N:subst]: 51.84/7.14 ( ( comp @ ( push @ A @ M ) @ N ) = 51.84/7.14 ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ))). 51.84/7.14 thf('19', plain, 51.84/7.14 (( axmap ) = 51.84/7.14 ( ![X4:term,X6:subst,X8:subst]: 51.84/7.14 ( ( comp @ ( push @ X4 @ X6 ) @ X8 ) = 51.84/7.14 ( push @ ( sub @ X4 @ X8 ) @ ( comp @ X6 @ X8 ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(axassoc, axiom, axassoc = 51.84/7.14 (![M:subst,N:subst,K:subst]: 51.84/7.14 ( ( comp @ ( comp @ M @ N ) @ K ) = ( comp @ M @ ( comp @ N @ K ) ) ))). 51.84/7.14 thf('20', plain, 51.84/7.14 (( axassoc ) = 51.84/7.14 ( ![X4:subst,X6:subst,X8:subst]: 51.84/7.14 ( ( comp @ ( comp @ X4 @ X6 ) @ X8 ) = 51.84/7.14 ( comp @ X4 @ ( comp @ X6 @ X8 ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(axshiftcons, axiom, axshiftcons = 51.84/7.14 (![A:term,M:subst]: ( ( comp @ sh @ ( push @ A @ M ) ) = ( M ) ))). 51.84/7.14 thf('21', plain, 51.84/7.14 (( axshiftcons ) = 51.84/7.14 ( ![X4:term,X6:subst]: ( ( comp @ sh @ ( push @ X4 @ X6 ) ) = ( X6 ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(axidl, axiom, axidl = (![M:subst]: ( ( comp @ id @ M ) = ( M ) ))). 51.84/7.14 thf('22', plain, 51.84/7.14 (( axidl ) = ( ![X4:subst]: ( ( comp @ id @ X4 ) = ( X4 ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(axclos, axiom, axclos = 51.84/7.14 (![A:term,M:subst,N:subst]: 51.84/7.14 ( ( sub @ ( sub @ A @ M ) @ N ) = ( sub @ A @ ( comp @ M @ N ) ) ))). 51.84/7.14 thf('23', plain, 51.84/7.14 (( axclos ) = 51.84/7.14 ( ![X4:term,X6:subst,X8:subst]: 51.84/7.14 ( ( sub @ ( sub @ X4 @ X6 ) @ X8 ) = ( sub @ X4 @ ( comp @ X6 @ X8 ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(axabs, axiom, axabs = 51.84/7.14 (![A:term,M:subst]: 51.84/7.14 ( ( sub @ ( lam @ A ) @ M ) = 51.84/7.14 ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ))). 51.84/7.14 thf('24', plain, 51.84/7.14 (( axabs ) = 51.84/7.14 ( ![X4:term,X6:subst]: 51.84/7.14 ( ( sub @ ( lam @ X4 ) @ X6 ) = 51.84/7.14 ( lam @ ( sub @ X4 @ ( push @ one @ ( comp @ X6 @ sh ) ) ) ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(axvarid, axiom, axvarid = (![A:term]: ( ( sub @ A @ id ) = ( A ) ))). 51.84/7.14 thf('25', plain, 51.84/7.14 (( axvarid ) = ( ![X4:term]: ( ( sub @ X4 @ id ) = ( X4 ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(axvarcons, axiom, axvarcons = 51.84/7.14 (![A:term,M:subst]: ( ( sub @ one @ ( push @ A @ M ) ) = ( A ) ))). 51.84/7.14 thf('26', plain, 51.84/7.14 (( axvarcons ) = 51.84/7.14 ( ![X4:term,X6:subst]: ( ( sub @ one @ ( push @ X4 @ X6 ) ) = ( X4 ) ) )), 51.84/7.14 define([status(thm)])). 51.84/7.14 thf(axapp, axiom, axapp = 51.84/7.14 (![A:term,B:term,M:subst]: 51.84/7.14 ( ( sub @ ( ap @ A @ B ) @ M ) = 51.84/7.14 ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ))). 51.84/7.14 thf('27', plain, 51.84/7.14 (( axapp ) = 51.84/7.14 ( ![X4:term,X6:term,X8:subst]: 51.84/7.14 ( ( sub @ ( ap @ X4 @ X6 ) @ X8 ) = 51.84/7.14 ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) ) )), 51.84/7.14 define([status(thm)])).thf(thm, conjecture, (induction2_gthm)). 51.84/7.14 thf(zf_stmt_0, conjecture, 51.84/7.14 (( ![X4:term,X6:term,X8:subst]: 51.84/7.14 ( ( sub @ ( ap @ X4 @ X6 ) @ X8 ) = 51.84/7.14 ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) ) ) => 51.84/7.14 ( ( ![X10:term,X12:subst]: 51.84/7.14 ( ( sub @ one @ ( push @ X10 @ X12 ) ) = ( X10 ) ) ) => 51.84/7.14 ( ( ![X14:term]: ( ( sub @ X14 @ id ) = ( X14 ) ) ) => 51.84/7.14 ( ( ![X16:term,X18:subst]: 51.84/7.14 ( ( sub @ ( lam @ X16 ) @ X18 ) = 51.84/7.14 ( lam @ ( sub @ X16 @ ( push @ one @ ( comp @ X18 @ sh ) ) ) ) ) ) => 51.84/7.14 ( ( ![X20:term,X22:subst,X24:subst]: 51.84/7.14 ( ( sub @ ( sub @ X20 @ X22 ) @ X24 ) = 51.84/7.14 ( sub @ X20 @ ( comp @ X22 @ X24 ) ) ) ) => 51.84/7.14 ( ( ![X26:subst]: ( ( comp @ id @ X26 ) = ( X26 ) ) ) => 51.84/7.14 ( ( ![X28:term,X30:subst]: 51.84/7.14 ( ( comp @ sh @ ( push @ X28 @ X30 ) ) = ( X30 ) ) ) => 51.84/7.14 ( ( ![X32:subst,X34:subst,X36:subst]: 51.84/7.14 ( ( comp @ ( comp @ X32 @ X34 ) @ X36 ) = 51.84/7.14 ( comp @ X32 @ ( comp @ X34 @ X36 ) ) ) ) => 51.84/7.14 ( ( ![X38:term,X40:subst,X42:subst]: 51.84/7.14 ( ( comp @ ( push @ X38 @ X40 ) @ X42 ) = 51.84/7.14 ( push @ ( sub @ X38 @ X42 ) @ ( comp @ X40 @ X42 ) ) ) ) => 51.84/7.14 ( ( ![X44:subst]: ( ( comp @ X44 @ id ) = ( X44 ) ) ) => 51.84/7.14 ( ( ( push @ one @ sh ) = ( id ) ) => 51.84/7.14 ( ( ![X46:subst]: 51.84/7.14 ( ( push @ 51.84/7.14 ( sub @ one @ X46 ) @ ( comp @ sh @ X46 ) ) = 51.84/7.14 ( X46 ) ) ) => 51.84/7.14 ( ( var @ one ) => 51.84/7.14 ( ( ![X48:term]: 51.84/7.14 ( ( var @ X48 ) => 51.84/7.14 ( var @ ( sub @ X48 @ sh ) ) ) ) => 51.84/7.14 ( ( ![X50:( term > $o )]: 51.84/7.14 ( ( X50 @ one ) => 51.84/7.14 ( ( ![X52:term]: 51.84/7.14 ( ( var @ X52 ) => 51.84/7.14 ( ( X50 @ X52 ) => 51.84/7.14 ( X50 @ ( sub @ X52 @ sh ) ) ) ) ) => 51.84/7.14 ( ![X54:term]: 51.84/7.14 ( ( var @ X54 ) => ( X50 @ X54 ) ) ) ) ) ) => 51.84/7.14 ( ( ![X56:term,X58:term,X60:term,X62:term]: 51.84/7.14 ( ( ( ap @ X56 @ X60 ) = 51.84/7.14 ( ap @ X58 @ X62 ) ) => 51.84/7.14 ( ( X56 ) = ( X58 ) ) ) ) => 51.84/7.14 ( ( ![X64:term,X66:term,X68:term,X70:term]: 51.84/7.14 ( ( ( ap @ X64 @ X68 ) = 51.84/7.14 ( ap @ X66 @ X70 ) ) => 51.84/7.14 ( ( X68 ) = ( X70 ) ) ) ) => 51.84/7.14 ( ( ![X72:term,X74:term]: 51.84/7.14 ( ( ( lam @ X72 ) = ( lam @ X74 ) ) => 51.84/7.14 ( ( X72 ) = ( X74 ) ) ) ) => 51.84/7.14 ( ( ![X76:term,X78:term]: 51.84/7.14 ( ( ( sub @ X76 @ sh ) = 51.84/7.14 ( sub @ X78 @ sh ) ) => 51.84/7.14 ( ( X76 ) = ( X78 ) ) ) ) => 51.84/7.14 ( ( ![X80:term,X82:term,X84:term]: 51.84/7.14 ( ( lam @ X80 ) != 51.84/7.14 ( ap @ X82 @ X84 ) ) ) => 51.84/7.14 ( ( ![X86:term,X88:term]: 51.84/7.14 ( ~( var @ ( ap @ X86 @ X88 ) ) ) ) => 51.84/7.14 ( ( ![X90:term]: 51.84/7.14 ( ~( var @ ( lam @ X90 ) ) ) ) => 51.84/7.14 ( ( ![X92:( term > $o )]: 51.84/7.14 ( ( ![X94:term]: 51.84/7.14 ( ( var @ X94 ) => 51.84/7.14 ( X92 @ X94 ) ) ) => 51.84/7.14 ( ( ![X96:term,X98:term]: 51.84/7.14 ( ( X92 @ X96 ) => 51.84/7.14 ( ( X92 @ X98 ) => 51.84/7.14 ( X92 @ 51.84/7.14 ( ap @ X96 @ X98 ) ) ) ) ) => 51.84/7.14 ( ( ![X100:term]: 51.84/7.14 ( ( X92 @ X100 ) => 51.84/7.14 ( X92 @ 51.84/7.14 ( lam @ X100 ) ) ) ) => 51.84/7.14 ( ![X102:term]: 51.84/7.14 ( X92 @ X102 ) ) ) ) ) ) => 51.84/7.14 ( ( ![X104:( term > $o ), 51.84/7.14 X106:term,X108:subst]: 51.84/7.14 ( ( ![X110:term]: 51.84/7.14 ( ( var @ X110 ) => 51.84/7.14 ( X104 @ 51.84/7.14 ( sub @ 51.84/7.14 X110 @ X108 ) ) ) ) => 51.84/7.14 ( ( X104 @ X106 ) => 51.84/7.14 ( ![X112:term]: 51.84/7.14 ( ( var @ X112 ) => 51.84/7.14 ( X104 @ 51.84/7.14 ( sub @ 51.84/7.14 X112 @ 51.84/7.14 ( push @ 51.84/7.14 X106 @ X108 ) ) ) ) ) ) ) ) => 51.84/7.14 ( ( ![X114:( term > $o )]: 51.84/7.14 ( ( ![X116:term, 51.84/7.14 X118:term]: 51.84/7.14 ( ( X114 @ X116 ) => 51.84/7.14 ( ( X114 @ X118 ) => 51.84/7.14 ( X114 @ 51.84/7.14 ( ap @ 51.84/7.14 X116 @ X118 ) ) ) ) ) => 51.84/7.14 ( ( ![X120:term]: 51.84/7.14 ( ( ![X122:term]: 51.84/7.14 ( ( X114 @ 51.84/7.14 X122 ) => 51.84/7.14 ( X114 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 X120 @ 51.84/7.14 ( 51.84/7.14 push @ 51.84/7.14 X122 @ id ) ) ) ) ) => 51.84/7.14 ( X114 @ 51.84/7.14 ( lam @ X120 ) ) ) ) => 51.84/7.14 ( ![X124:term, 51.84/7.14 X126:subst]: 51.84/7.14 ( ( ![X128:term]: 51.84/7.14 ( ( var @ X128 ) => 51.84/7.14 ( X114 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 X128 @ 51.84/7.14 X126 ) ) ) ) => 51.84/7.14 ( X114 @ 51.84/7.14 ( sub @ 51.84/7.14 X124 @ X126 ) ) ) ) ) ) ) => 51.84/7.14 ( ![X130:( term > $o )]: 51.84/7.14 ( ( ![X132:term]: 51.84/7.14 ( ( var @ X132 ) => 51.84/7.14 ( X130 @ X132 ) ) ) => 51.84/7.14 ( ( ![X134:term, 51.84/7.14 X136:term]: 51.84/7.14 ( ( X130 @ X134 ) => 51.84/7.14 ( ( X130 @ X136 ) => 51.84/7.14 ( X130 @ 51.84/7.14 ( ap @ 51.84/7.14 X134 @ 51.84/7.14 X136 ) ) ) ) ) => 51.84/7.14 ( ( ![X138:term]: 51.84/7.14 ( ( ![X140:term]: 51.84/7.14 ( ( 51.84/7.14 X130 @ 51.84/7.14 X140 ) => 51.84/7.14 ( 51.84/7.14 X130 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 X138 @ 51.84/7.14 ( 51.84/7.14 push @ 51.84/7.14 X140 @ id ) ) ) ) ) => 51.84/7.14 ( X130 @ 51.84/7.14 ( lam @ X138 ) ) ) ) => 51.84/7.14 ( ![X142:term]: 51.84/7.14 ( X130 @ X142 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 51.84/7.14 thf(zf_stmt_1, negated_conjecture, 51.84/7.14 (~( ( ![X4:term,X6:term,X8:subst]: 51.84/7.14 ( ( sub @ ( ap @ X4 @ X6 ) @ X8 ) = 51.84/7.14 ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) ) ) => 51.84/7.14 ( ( ![X10:term,X12:subst]: 51.84/7.14 ( ( sub @ one @ ( push @ X10 @ X12 ) ) = ( X10 ) ) ) => 51.84/7.14 ( ( ![X14:term]: ( ( sub @ X14 @ id ) = ( X14 ) ) ) => 51.84/7.14 ( ( ![X16:term,X18:subst]: 51.84/7.14 ( ( sub @ ( lam @ X16 ) @ X18 ) = 51.84/7.14 ( lam @ ( sub @ X16 @ ( push @ one @ ( comp @ X18 @ sh ) ) ) ) ) ) => 51.84/7.14 ( ( ![X20:term,X22:subst,X24:subst]: 51.84/7.14 ( ( sub @ ( sub @ X20 @ X22 ) @ X24 ) = 51.84/7.14 ( sub @ X20 @ ( comp @ X22 @ X24 ) ) ) ) => 51.84/7.14 ( ( ![X26:subst]: ( ( comp @ id @ X26 ) = ( X26 ) ) ) => 51.84/7.14 ( ( ![X28:term,X30:subst]: 51.84/7.14 ( ( comp @ sh @ ( push @ X28 @ X30 ) ) = ( X30 ) ) ) => 51.84/7.14 ( ( ![X32:subst,X34:subst,X36:subst]: 51.84/7.14 ( ( comp @ ( comp @ X32 @ X34 ) @ X36 ) = 51.84/7.14 ( comp @ X32 @ ( comp @ X34 @ X36 ) ) ) ) => 51.84/7.14 ( ( ![X38:term,X40:subst,X42:subst]: 51.84/7.14 ( ( comp @ ( push @ X38 @ X40 ) @ X42 ) = 51.84/7.14 ( push @ ( sub @ X38 @ X42 ) @ ( comp @ X40 @ X42 ) ) ) ) => 51.84/7.14 ( ( ![X44:subst]: ( ( comp @ X44 @ id ) = ( X44 ) ) ) => 51.84/7.14 ( ( ( push @ one @ sh ) = ( id ) ) => 51.84/7.14 ( ( ![X46:subst]: 51.84/7.14 ( ( push @ 51.84/7.14 ( sub @ one @ X46 ) @ ( comp @ sh @ X46 ) ) = 51.84/7.14 ( X46 ) ) ) => 51.84/7.14 ( ( var @ one ) => 51.84/7.14 ( ( ![X48:term]: 51.84/7.14 ( ( var @ X48 ) => 51.84/7.14 ( var @ ( sub @ X48 @ sh ) ) ) ) => 51.84/7.14 ( ( ![X50:( term > $o )]: 51.84/7.14 ( ( X50 @ one ) => 51.84/7.14 ( ( ![X52:term]: 51.84/7.14 ( ( var @ X52 ) => 51.84/7.14 ( ( X50 @ X52 ) => 51.84/7.14 ( X50 @ ( sub @ X52 @ sh ) ) ) ) ) => 51.84/7.14 ( ![X54:term]: 51.84/7.14 ( ( var @ X54 ) => ( X50 @ X54 ) ) ) ) ) ) => 51.84/7.14 ( ( ![X56:term,X58:term,X60:term,X62:term]: 51.84/7.14 ( ( ( ap @ X56 @ X60 ) = 51.84/7.14 ( ap @ X58 @ X62 ) ) => 51.84/7.14 ( ( X56 ) = ( X58 ) ) ) ) => 51.84/7.14 ( ( ![X64:term,X66:term,X68:term,X70:term]: 51.84/7.14 ( ( ( ap @ X64 @ X68 ) = 51.84/7.14 ( ap @ X66 @ X70 ) ) => 51.84/7.14 ( ( X68 ) = ( X70 ) ) ) ) => 51.84/7.14 ( ( ![X72:term,X74:term]: 51.84/7.14 ( ( ( lam @ X72 ) = ( lam @ X74 ) ) => 51.84/7.14 ( ( X72 ) = ( X74 ) ) ) ) => 51.84/7.14 ( ( ![X76:term,X78:term]: 51.84/7.14 ( ( ( sub @ X76 @ sh ) = 51.84/7.14 ( sub @ X78 @ sh ) ) => 51.84/7.14 ( ( X76 ) = ( X78 ) ) ) ) => 51.84/7.14 ( ( ![X80:term,X82:term,X84:term]: 51.84/7.14 ( ( lam @ X80 ) != 51.84/7.14 ( ap @ X82 @ X84 ) ) ) => 51.84/7.14 ( ( ![X86:term,X88:term]: 51.84/7.14 ( ~( var @ ( ap @ X86 @ X88 ) ) ) ) => 51.84/7.14 ( ( ![X90:term]: 51.84/7.14 ( ~( var @ ( lam @ X90 ) ) ) ) => 51.84/7.14 ( ( ![X92:( term > $o )]: 51.84/7.14 ( ( ![X94:term]: 51.84/7.14 ( ( var @ X94 ) => 51.84/7.14 ( X92 @ X94 ) ) ) => 51.84/7.14 ( ( ![X96:term,X98:term]: 51.84/7.14 ( ( X92 @ X96 ) => 51.84/7.14 ( ( X92 @ X98 ) => 51.84/7.14 ( X92 @ 51.84/7.14 ( ap @ 51.84/7.14 X96 @ X98 ) ) ) ) ) => 51.84/7.14 ( ( ![X100:term]: 51.84/7.14 ( ( X92 @ X100 ) => 51.84/7.14 ( X92 @ 51.84/7.14 ( lam @ X100 ) ) ) ) => 51.84/7.14 ( ![X102:term]: 51.84/7.14 ( X92 @ X102 ) ) ) ) ) ) => 51.84/7.14 ( ( ![X104:( term > $o ), 51.84/7.14 X106:term,X108:subst]: 51.84/7.14 ( ( ![X110:term]: 51.84/7.14 ( ( var @ X110 ) => 51.84/7.14 ( X104 @ 51.84/7.14 ( sub @ 51.84/7.14 X110 @ X108 ) ) ) ) => 51.84/7.14 ( ( X104 @ X106 ) => 51.84/7.14 ( ![X112:term]: 51.84/7.14 ( ( var @ X112 ) => 51.84/7.14 ( X104 @ 51.84/7.14 ( sub @ 51.84/7.14 X112 @ 51.84/7.14 ( push @ 51.84/7.14 X106 @ 51.84/7.14 X108 ) ) ) ) ) ) ) ) => 51.84/7.14 ( ( ![X114:( term > $o )]: 51.84/7.14 ( ( ![X116:term, 51.84/7.14 X118:term]: 51.84/7.14 ( ( X114 @ X116 ) => 51.84/7.14 ( ( X114 @ X118 ) => 51.84/7.14 ( X114 @ 51.84/7.14 ( ap @ 51.84/7.14 X116 @ 51.84/7.14 X118 ) ) ) ) ) => 51.84/7.14 ( ( ![X120:term]: 51.84/7.14 ( ( ![X122:term]: 51.84/7.14 ( ( 51.84/7.14 X114 @ 51.84/7.14 X122 ) => 51.84/7.14 ( 51.84/7.14 X114 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 X120 @ 51.84/7.14 ( 51.84/7.14 push @ 51.84/7.14 X122 @ id ) ) ) ) ) => 51.84/7.14 ( X114 @ 51.84/7.14 ( lam @ 51.84/7.14 X120 ) ) ) ) => 51.84/7.14 ( ![X124:term, 51.84/7.14 X126:subst]: 51.84/7.14 ( ( ![X128:term]: 51.84/7.14 ( ( 51.84/7.14 var @ 51.84/7.14 X128 ) => 51.84/7.14 ( 51.84/7.14 X114 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 X128 @ 51.84/7.14 X126 ) ) ) ) => 51.84/7.14 ( X114 @ 51.84/7.14 ( sub @ 51.84/7.14 X124 @ 51.84/7.14 X126 ) ) ) ) ) ) ) => 51.84/7.14 ( ![X130:( term > $o )]: 51.84/7.14 ( ( ![X132:term]: 51.84/7.14 ( ( var @ X132 ) => 51.84/7.14 ( X130 @ X132 ) ) ) => 51.84/7.14 ( ( ![X134:term, 51.84/7.14 X136:term]: 51.84/7.14 ( ( X130 @ X134 ) => 51.84/7.14 ( ( X130 @ 51.84/7.14 X136 ) => 51.84/7.14 ( X130 @ 51.84/7.14 ( 51.84/7.14 ap @ 51.84/7.14 X134 @ 51.84/7.14 X136 ) ) ) ) ) => 51.84/7.14 ( ( ![X138:term]: 51.84/7.14 ( ( ![ 51.84/7.14 X140:term]: 51.84/7.14 ( 51.84/7.14 ( 51.84/7.14 X130 @ 51.84/7.14 X140 ) => 51.84/7.14 ( 51.84/7.14 X130 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 X138 @ 51.84/7.14 ( 51.84/7.14 push @ 51.84/7.14 X140 @ id ) ) ) ) ) => 51.84/7.14 ( X130 @ 51.84/7.14 ( 51.84/7.14 lam @ 51.84/7.14 X138 ) ) ) ) => 51.84/7.14 ( ![X142:term]: 51.84/7.14 ( X130 @ X142 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 51.84/7.14 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 51.84/7.14 thf(zip_derived_cl0, plain, 51.84/7.14 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (((!!) @ (^[Y2 : subst]: 51.84/7.14 (((sub @ (ap @ Y0 @ Y1) @ Y2) = 51.84/7.14 (ap @ (sub @ Y0 @ Y2) @ 51.84/7.14 (sub @ Y1 @ Y2))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((sub @ one @ (push @ Y0 @ Y1)) = (Y0))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((sub @ (lam @ Y0) @ Y1) = (lam @ 51.84/7.14 (sub @ Y0 @ 51.84/7.14 (push @ one @ (comp @ Y1 @ sh)))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((!!) @ (^[Y2 : subst]: 51.84/7.14 (((sub @ 51.84/7.14 (sub @ Y0 @ Y1) @ 51.84/7.14 Y2) = (sub @ Y0 @ 51.84/7.14 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((comp @ sh @ 51.84/7.14 (push @ Y0 @ Y1)) = (Y1))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((!!) @ (^[Y2 : subst]: 51.84/7.14 (((comp @ 51.84/7.14 (comp @ Y0 @ Y1) @ 51.84/7.14 Y2) = (comp @ 51.84/7.14 Y0 @ 51.84/7.14 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((!!) @ (^[Y2 : subst]: 51.84/7.14 (((comp @ 51.84/7.14 (push @ Y0 @ 51.84/7.14 Y1) @ 51.84/7.14 Y2) = (push @ 51.84/7.14 (sub @ Y0 @ Y2) @ 51.84/7.14 (comp @ Y1 @ 51.84/7.14 Y2))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: 51.84/7.14 (((comp @ Y0 @ id) = (Y0)))))) => 51.84/7.14 (((((push @ one @ sh) = (id))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: 51.84/7.14 (((push @ (sub @ one @ Y0) @ 51.84/7.14 (comp @ sh @ Y0)) = (Y0)))))) => 51.84/7.14 (((var @ one) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((var @ Y0) => (var @ 51.84/7.14 (sub @ Y0 @ sh))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (((Y0 @ one) => 51.84/7.14 (((((!!) @ (^[Y1 : term]: 51.84/7.14 (((var @ 51.84/7.14 Y1) => 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (Y0 @ 51.84/7.14 (sub @ 51.84/7.14 Y1 @ sh))))))))) => 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (((var @ 51.84/7.14 Y1) => 51.84/7.14 (Y0 @ Y1))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (ap @ 51.84/7.14 Y0 @ 51.84/7.14 Y2) = 51.84/7.14 (ap @ 51.84/7.14 Y1 @ Y3))) => 51.84/7.14 (( 51.84/7.14 (Y0) = 51.84/7.14 (Y1))))))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (ap @ 51.84/7.14 Y0 @ 51.84/7.14 Y2) = 51.84/7.14 (ap @ 51.84/7.14 Y1 @ Y3))) => 51.84/7.14 (( 51.84/7.14 (Y2) = 51.84/7.14 (Y3))))))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (lam @ 51.84/7.14 Y0) = 51.84/7.14 (lam @ 51.84/7.14 Y1))) => 51.84/7.14 (( 51.84/7.14 (Y0) = 51.84/7.14 (Y1))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (sub @ 51.84/7.14 Y0 @ 51.84/7.14 sh) = 51.84/7.14 (sub @ 51.84/7.14 Y1 @ sh))) => 51.84/7.14 (( 51.84/7.14 (Y0) = 51.84/7.14 (Y1))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (lam @ 51.84/7.14 Y0) != 51.84/7.14 (ap @ 51.84/7.14 Y1 @ Y2)))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (((~) @ ( 51.84/7.14 var @ 51.84/7.14 (ap @ 51.84/7.14 Y0 @ Y1)))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((~) @ ( 51.84/7.14 var @ 51.84/7.14 (lam @ Y0))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (((( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y1) => 51.84/7.14 (Y0 @ Y1)))))) => 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 ap @ 51.84/7.14 Y1 @ Y2)))))))))))) => 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 lam @ Y1))))))) => 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (Y0 @ Y1))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : subst]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y3) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y3 @ Y2))))))) => 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y3) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y3 @ 51.84/7.14 ( 51.84/7.14 push @ 51.84/7.14 Y1 @ Y2))))))))))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 ap @ 51.84/7.14 Y1 @ Y2)))))))))))) => 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y1 @ 51.84/7.14 ( 51.84/7.14 push @ 51.84/7.14 Y2 @ id)))))))) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 lam @ Y1))))))) => 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : subst]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y3) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y3 @ Y2))))))) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y1 @ Y2))))))))))))))))) => 51.84/7.14 (((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y1) => 51.84/7.14 (Y0 @ Y1)))))) => 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 ap @ 51.84/7.14 Y1 @ Y2)))))))))))) => 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y1 @ 51.84/7.14 ( 51.84/7.14 push @ 51.84/7.14 Y2 @ id)))))))) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 lam @ Y1))))))) => 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 51.84/7.14 inference('cnf', [status(esa)], [zf_stmt_1])). 51.84/7.14 thf(zip_derived_cl2, plain, 51.84/7.14 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((sub @ one @ (push @ Y0 @ Y1)) = (Y0))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((sub @ (lam @ Y0) @ Y1) = (lam @ 51.84/7.14 (sub @ Y0 @ 51.84/7.14 (push @ one @ (comp @ Y1 @ sh)))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((!!) @ (^[Y2 : subst]: 51.84/7.14 (((sub @ 51.84/7.14 (sub @ Y0 @ Y1) @ Y2) = 51.84/7.14 (sub @ Y0 @ 51.84/7.14 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((comp @ sh @ (push @ Y0 @ Y1)) = 51.84/7.14 (Y1))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((!!) @ (^[Y2 : subst]: 51.84/7.14 (((comp @ 51.84/7.14 (comp @ Y0 @ Y1) @ 51.84/7.14 Y2) = (comp @ 51.84/7.14 Y0 @ 51.84/7.14 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((!!) @ (^[Y2 : subst]: 51.84/7.14 (((comp @ 51.84/7.14 (push @ Y0 @ Y1) @ 51.84/7.14 Y2) = (push @ 51.84/7.14 (sub @ Y0 @ Y2) @ 51.84/7.14 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 51.84/7.14 (((((push @ one @ sh) = (id))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: 51.84/7.14 (((push @ (sub @ one @ Y0) @ 51.84/7.14 (comp @ sh @ Y0)) = (Y0)))))) => 51.84/7.14 (((var @ one) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((var @ Y0) => (var @ 51.84/7.14 (sub @ Y0 @ sh))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (((Y0 @ one) => 51.84/7.14 (((((!!) @ (^[Y1 : term]: 51.84/7.14 (((var @ 51.84/7.14 Y1) => 51.84/7.14 (((Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (Y0 @ 51.84/7.14 (sub @ 51.84/7.14 Y1 @ sh))))))))) => 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (((var @ 51.84/7.14 Y1) => 51.84/7.14 (Y0 @ Y1))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (ap @ 51.84/7.14 Y0 @ 51.84/7.14 Y2) = 51.84/7.14 (ap @ 51.84/7.14 Y1 @ Y3))) => 51.84/7.14 (( 51.84/7.14 (Y0) = 51.84/7.14 (Y1))))))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (ap @ 51.84/7.14 Y0 @ 51.84/7.14 Y2) = 51.84/7.14 (ap @ 51.84/7.14 Y1 @ Y3))) => 51.84/7.14 (( 51.84/7.14 (Y2) = 51.84/7.14 (Y3))))))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (((( 51.84/7.14 (lam @ 51.84/7.14 Y0) = 51.84/7.14 (lam @ Y1))) => 51.84/7.14 (( 51.84/7.14 (Y0) = 51.84/7.14 (Y1))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (sub @ 51.84/7.14 Y0 @ 51.84/7.14 sh) = 51.84/7.14 (sub @ 51.84/7.14 Y1 @ sh))) => 51.84/7.14 (( 51.84/7.14 (Y0) = 51.84/7.14 (Y1))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (lam @ 51.84/7.14 Y0) != 51.84/7.14 (ap @ 51.84/7.14 Y1 @ Y2)))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (((~) @ ( 51.84/7.14 var @ 51.84/7.14 (ap @ Y0 @ 51.84/7.14 Y1)))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((~) @ ( 51.84/7.14 var @ 51.84/7.14 (lam @ Y0))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (((((!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y1) => 51.84/7.14 (Y0 @ Y1)))))) => 51.84/7.14 (((( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 ap @ 51.84/7.14 Y1 @ Y2)))))))))))) => 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 lam @ Y1))))))) => 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (Y0 @ Y1))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : subst]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y3) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y3 @ Y2))))))) => 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y3) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y3 @ 51.84/7.14 ( 51.84/7.14 push @ 51.84/7.14 Y1 @ Y2))))))))))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 ap @ 51.84/7.14 Y1 @ Y2)))))))))))) => 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y1 @ 51.84/7.14 ( 51.84/7.14 push @ 51.84/7.14 Y2 @ id)))))))) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 lam @ Y1))))))) => 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : subst]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y3) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y3 @ Y2))))))) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y1 @ Y2))))))))))))))))) => 51.84/7.14 (((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y1) => 51.84/7.14 (Y0 @ Y1)))))) => 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 ap @ 51.84/7.14 Y1 @ Y2)))))))))))) => 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y1 @ 51.84/7.14 ( 51.84/7.14 push @ 51.84/7.14 Y2 @ id)))))))) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 lam @ Y1))))))) => 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 51.84/7.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 51.84/7.14 thf(zip_derived_cl5, plain, 51.84/7.14 (~ (((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((sub @ (lam @ Y0) @ Y1) = (lam @ 51.84/7.14 (sub @ Y0 @ 51.84/7.14 (push @ one @ (comp @ Y1 @ sh)))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((!!) @ (^[Y2 : subst]: 51.84/7.14 (((sub @ (sub @ Y0 @ Y1) @ 51.84/7.14 Y2) = (sub @ Y0 @ 51.84/7.14 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((comp @ sh @ (push @ Y0 @ Y1)) = 51.84/7.14 (Y1))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((!!) @ (^[Y2 : subst]: 51.84/7.14 (((comp @ 51.84/7.14 (comp @ Y0 @ Y1) @ 51.84/7.14 Y2) = (comp @ Y0 @ 51.84/7.14 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((!!) @ (^[Y2 : subst]: 51.84/7.14 (((comp @ 51.84/7.14 (push @ Y0 @ Y1) @ 51.84/7.14 Y2) = (push @ 51.84/7.14 (sub @ Y0 @ Y2) @ 51.84/7.14 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 51.84/7.14 (((((push @ one @ sh) = (id))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: 51.84/7.14 (((push @ (sub @ one @ Y0) @ 51.84/7.14 (comp @ sh @ Y0)) = (Y0)))))) => 51.84/7.14 (((var @ one) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((var @ Y0) => (var @ 51.84/7.14 (sub @ Y0 @ sh))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (((Y0 @ one) => 51.84/7.14 (((((!!) @ (^[Y1 : term]: 51.84/7.14 (((var @ Y1) => 51.84/7.14 (((Y0 @ Y1) => 51.84/7.14 (Y0 @ 51.84/7.14 (sub @ Y1 @ 51.84/7.14 sh))))))))) => 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (((var @ Y1) => 51.84/7.14 (Y0 @ Y1))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (ap @ 51.84/7.14 Y0 @ 51.84/7.14 Y2) = 51.84/7.14 (ap @ 51.84/7.14 Y1 @ Y3))) => 51.84/7.14 (( 51.84/7.14 (Y0) = 51.84/7.14 (Y1))))))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (ap @ 51.84/7.14 Y0 @ 51.84/7.14 Y2) = 51.84/7.14 (ap @ 51.84/7.14 Y1 @ Y3))) => 51.84/7.14 (( 51.84/7.14 (Y2) = 51.84/7.14 (Y3))))))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (((((lam @ 51.84/7.14 Y0) = 51.84/7.14 (lam @ Y1))) => 51.84/7.14 (((Y0) = 51.84/7.14 (Y1))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (((( 51.84/7.14 (sub @ 51.84/7.14 Y0 @ sh) = 51.84/7.14 (sub @ 51.84/7.14 Y1 @ sh))) => 51.84/7.14 (( 51.84/7.14 (Y0) = 51.84/7.14 (Y1))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (lam @ 51.84/7.14 Y0) != 51.84/7.14 (ap @ 51.84/7.14 Y1 @ Y2)))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (~) @ ( 51.84/7.14 var @ 51.84/7.14 ( 51.84/7.14 ap @ 51.84/7.14 Y0 @ Y1)))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((~) @ (var @ 51.84/7.14 ( 51.84/7.14 lam @ Y0))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (((((!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y1) => 51.84/7.14 (Y0 @ Y1)))))) => 51.84/7.14 (((((!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 ap @ 51.84/7.14 Y1 @ Y2)))))))))))) => 51.84/7.14 (((( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 lam @ Y1))))))) => 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (Y0 @ Y1))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (((!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : subst]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y3) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y3 @ Y2))))))) => 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y3) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y3 @ 51.84/7.14 ( 51.84/7.14 push @ 51.84/7.14 Y1 @ Y2))))))))))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (((( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 ap @ 51.84/7.14 Y1 @ Y2)))))))))))) => 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y1 @ 51.84/7.14 ( 51.84/7.14 push @ 51.84/7.14 Y2 @ id)))))))) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 lam @ Y1))))))) => 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : subst]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y3 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y3) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y3 @ Y2))))))) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y1 @ Y2))))))))))))))))) => 51.84/7.14 (((!!) @ (^[Y0 : term > $o]: 51.84/7.14 (((( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (var @ 51.84/7.14 Y1) => 51.84/7.14 (Y0 @ Y1)))))) => 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y1) => 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 ap @ 51.84/7.14 Y1 @ Y2)))))))))))) => 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (( 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y2 : term]: 51.84/7.14 (( 51.84/7.14 (Y0 @ 51.84/7.14 Y2) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 sub @ 51.84/7.14 Y1 @ 51.84/7.14 ( 51.84/7.14 push @ 51.84/7.14 Y2 @ id)))))))) => 51.84/7.14 (Y0 @ 51.84/7.14 ( 51.84/7.14 lam @ Y1))))))) => 51.84/7.14 (( 51.84/7.14 (!!) @ ( 51.84/7.14 ^[Y1 : term]: 51.84/7.14 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 51.84/7.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 51.84/7.14 thf(zip_derived_cl9, plain, 51.84/7.14 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((sub @ (lam @ Y0) @ Y1) = (lam @ 51.84/7.14 (sub @ Y0 @ 51.84/7.14 (push @ one @ (comp @ Y1 @ sh)))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((!!) @ (^[Y2 : subst]: 51.84/7.14 (((sub @ (sub @ Y0 @ Y1) @ 51.84/7.14 Y2) = (sub @ Y0 @ 51.84/7.14 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((comp @ sh @ (push @ Y0 @ Y1)) = 51.84/7.14 (Y1))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : subst]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((!!) @ (^[Y2 : subst]: 51.84/7.14 (((comp @ 51.84/7.14 (comp @ Y0 @ Y1) @ 51.84/7.14 Y2) = (comp @ Y0 @ 51.84/7.14 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.14 (((((!!) @ (^[Y0 : term]: 51.84/7.14 (((!!) @ (^[Y1 : subst]: 51.84/7.14 (((!!) @ (^[Y2 : subst]: 51.84/7.14 (((comp @ 51.84/7.14 (push @ Y0 @ Y1) @ 51.84/7.14 Y2) = (push @ 51.84/7.15 (sub @ Y0 @ Y2) @ 51.84/7.15 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 51.84/7.15 (((((push @ one @ sh) = (id))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: 51.84/7.15 (((push @ (sub @ one @ Y0) @ 51.84/7.15 (comp @ sh @ Y0)) = (Y0)))))) => 51.84/7.15 (((var @ one) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((var @ Y0) => (var @ 51.84/7.15 (sub @ Y0 @ sh))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((Y0 @ one) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (Y0 @ 51.84/7.15 (sub @ Y1 @ sh))))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ 51.84/7.15 Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y0) = 51.84/7.15 (Y1))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ 51.84/7.15 Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y2) = 51.84/7.15 (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = 51.84/7.15 (lam @ Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ 51.84/7.15 Y0 @ sh) = 51.84/7.15 (sub @ 51.84/7.15 Y1 @ sh))) => 51.84/7.15 (((Y0) = 51.84/7.15 (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (lam @ 51.84/7.15 Y0) != 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (~) @ ( 51.84/7.15 var @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y0 @ Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((~) @ (var @ 51.84/7.15 (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ Y2))))))))))))))))) => 51.84/7.15 (((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 51.84/7.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 51.84/7.15 thf(zip_derived_cl14, plain, 51.84/7.15 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : subst]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((sub @ (sub @ Y0 @ Y1) @ Y2) = 51.84/7.15 (sub @ Y0 @ (comp @ Y1 @ Y2))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : subst]: 51.84/7.15 (((comp @ sh @ (push @ Y0 @ Y1)) = (Y1))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: 51.84/7.15 (((!!) @ (^[Y1 : subst]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((comp @ 51.84/7.15 (comp @ Y0 @ Y1) @ Y2) = 51.84/7.15 (comp @ Y0 @ 51.84/7.15 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : subst]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((comp @ 51.84/7.15 (push @ Y0 @ Y1) @ 51.84/7.15 Y2) = (push @ 51.84/7.15 (sub @ Y0 @ Y2) @ 51.84/7.15 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 51.84/7.15 (((((push @ one @ sh) = (id))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: 51.84/7.15 (((push @ (sub @ one @ Y0) @ 51.84/7.15 (comp @ sh @ Y0)) = (Y0)))))) => 51.84/7.15 (((var @ one) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((var @ Y0) => (var @ 51.84/7.15 (sub @ Y0 @ sh))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((Y0 @ one) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (Y0 @ 51.84/7.15 (sub @ Y1 @ sh))))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ 51.84/7.15 Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y0) = 51.84/7.15 (Y1))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ 51.84/7.15 Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y2) = 51.84/7.15 (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = 51.84/7.15 (lam @ Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ Y0 @ 51.84/7.15 sh) = 51.84/7.15 (sub @ Y1 @ 51.84/7.15 sh))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (lam @ 51.84/7.15 Y0) != 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((~) @ ( 51.84/7.15 var @ 51.84/7.15 (ap @ 51.84/7.15 Y0 @ Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((~) @ (var @ 51.84/7.15 (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ Y2))))))))))))))))) => 51.84/7.15 (((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 51.84/7.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 51.84/7.15 thf(zip_derived_cl20, plain, 51.84/7.15 (~ (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : subst]: 51.84/7.15 (((comp @ sh @ (push @ Y0 @ Y1)) = (Y1))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: 51.84/7.15 (((!!) @ (^[Y1 : subst]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((comp @ 51.84/7.15 (comp @ Y0 @ Y1) @ Y2) = 51.84/7.15 (comp @ Y0 @ 51.84/7.15 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : subst]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((comp @ 51.84/7.15 (push @ Y0 @ Y1) @ Y2) = 51.84/7.15 (push @ 51.84/7.15 (sub @ Y0 @ Y2) @ 51.84/7.15 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 51.84/7.15 (((((push @ one @ sh) = (id))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: 51.84/7.15 (((push @ (sub @ one @ Y0) @ 51.84/7.15 (comp @ sh @ Y0)) = (Y0)))))) => 51.84/7.15 (((var @ one) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((Y0 @ one) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (Y0 @ 51.84/7.15 (sub @ Y1 @ sh))))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ 51.84/7.15 Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ 51.84/7.15 Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y0) = 51.84/7.15 (Y1))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ 51.84/7.15 Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y2) = 51.84/7.15 (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = 51.84/7.15 (lam @ Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ Y0 @ 51.84/7.15 sh) = (sub @ 51.84/7.15 Y1 @ sh))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (((lam @ 51.84/7.15 Y0) != 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((~) @ ( 51.84/7.15 var @ 51.84/7.15 (ap @ Y0 @ 51.84/7.15 Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((~) @ (var @ 51.84/7.15 (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ Y2))))))))))))))))) => 51.84/7.15 (((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))), 51.84/7.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 51.84/7.15 thf(zip_derived_cl24, plain, 51.84/7.15 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : subst]: 51.84/7.15 (((comp @ sh @ (push @ Y0 @ Y1)) = (Y1))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: 51.84/7.15 (((!!) @ (^[Y1 : subst]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((comp @ (comp @ Y0 @ Y1) @ 51.84/7.15 Y2) = (comp @ Y0 @ 51.84/7.15 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : subst]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((comp @ 51.84/7.15 (push @ Y0 @ Y1) @ Y2) = 51.84/7.15 (push @ (sub @ Y0 @ Y2) @ 51.84/7.15 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 51.84/7.15 (((((push @ one @ sh) = (id))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: 51.84/7.15 (((push @ (sub @ one @ Y0) @ 51.84/7.15 (comp @ sh @ Y0)) = (Y0)))))) => 51.84/7.15 (((var @ one) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((Y0 @ one) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (((Y0 @ Y1) => (Y0 @ 51.84/7.15 (sub @ Y1 @ sh))))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ 51.84/7.15 Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ 51.84/7.15 Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y0) = 51.84/7.15 (Y1))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ 51.84/7.15 Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y2) = 51.84/7.15 (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = 51.84/7.15 (lam @ Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ Y0 @ 51.84/7.15 sh) = (sub @ 51.84/7.15 Y1 @ sh))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (((lam @ 51.84/7.15 Y0) != 51.84/7.15 (ap @ Y1 @ 51.84/7.15 Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((~) @ ( 51.84/7.15 var @ 51.84/7.15 (ap @ Y0 @ Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ Y2))))))))))))))))) => 51.84/7.15 (((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))), 51.84/7.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 51.84/7.15 thf(zip_derived_cl29, plain, 51.84/7.15 (~ (((((!!) @ (^[Y0 : subst]: 51.84/7.15 (((!!) @ (^[Y1 : subst]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((comp @ (comp @ Y0 @ Y1) @ 51.84/7.15 Y2) = (comp @ Y0 @ 51.84/7.15 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : subst]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((comp @ (push @ Y0 @ Y1) @ 51.84/7.15 Y2) = (push @ 51.84/7.15 (sub @ Y0 @ Y2) @ 51.84/7.15 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 51.84/7.15 (((((push @ one @ sh) = (id))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: 51.84/7.15 (((push @ (sub @ one @ Y0) @ (comp @ sh @ Y0)) = 51.84/7.15 (Y0)))))) => 51.84/7.15 (((var @ one) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((Y0 @ one) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (((Y0 @ Y1) => (Y0 @ 51.84/7.15 (sub @ Y1 @ sh))))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (((( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y0) = 51.84/7.15 (Y1))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ 51.84/7.15 Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y2) = 51.84/7.15 (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = (lam @ 51.84/7.15 Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ Y0 @ sh) = 51.84/7.15 (sub @ Y1 @ sh))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (lam @ 51.84/7.15 Y0) != 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((~) @ (var @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y0 @ Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ Y2))))))))))))))))) => 51.84/7.15 (((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))), 51.84/7.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 51.84/7.15 thf(zip_derived_cl34, plain, 51.84/7.15 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : subst]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((comp @ (push @ Y0 @ Y1) @ 51.84/7.15 Y2) = (push @ 51.84/7.15 (sub @ Y0 @ Y2) @ 51.84/7.15 (comp @ Y1 @ Y2))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 51.84/7.15 (((((push @ one @ sh) = (id))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: 51.84/7.15 (((push @ (sub @ one @ Y0) @ (comp @ sh @ Y0)) = 51.84/7.15 (Y0)))))) => 51.84/7.15 (((var @ one) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((Y0 @ one) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (((Y0 @ Y1) => (Y0 @ 51.84/7.15 (sub @ Y1 @ sh))))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (((((ap @ 51.84/7.15 Y0 @ Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (((Y0) = 51.84/7.15 (Y1))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (((( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y2) = 51.84/7.15 (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = (lam @ 51.84/7.15 Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ Y0 @ sh) = 51.84/7.15 (sub @ Y1 @ sh))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (lam @ 51.84/7.15 Y0) != 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((~) @ (var @ 51.84/7.15 (ap @ Y0 @ 51.84/7.15 Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ Y2))))))))))))))))) => 51.84/7.15 (((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y1 : term]: 51.84/7.15 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))), 51.84/7.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl29])). 51.84/7.15 thf(zip_derived_cl39, plain, 51.84/7.15 (~ (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 51.84/7.15 (((((push @ one @ sh) = (id))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: 51.84/7.15 (((push @ (sub @ one @ Y0) @ (comp @ sh @ Y0)) = 51.84/7.15 (Y0)))))) => 51.84/7.15 (((var @ one) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((Y0 @ one) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (((Y0 @ Y1) => (Y0 @ 51.84/7.15 (sub @ Y1 @ sh))))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ 51.84/7.15 Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y0) = 51.84/7.15 (Y1))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (((((ap @ 51.84/7.15 Y0 @ Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (((Y2) = 51.84/7.15 (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = (lam @ Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ Y0 @ sh) = 51.84/7.15 (sub @ Y1 @ sh))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((lam @ 51.84/7.15 Y0) != 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((~) @ (var @ 51.84/7.15 (ap @ Y0 @ Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (((( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ Y2))))))))))))))))) => 51.84/7.15 (((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))), 51.84/7.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 51.84/7.15 thf(zip_derived_cl44, plain, 51.84/7.15 (~ (((((push @ one @ sh) = (id))) => 51.84/7.15 (((((!!) @ (^[Y0 : subst]: 51.84/7.15 (((push @ (sub @ one @ Y0) @ (comp @ sh @ Y0)) = (Y0)))))) => 51.84/7.15 (((var @ one) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((Y0 @ one) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (((Y0 @ Y1) => (Y0 @ 51.84/7.15 (sub @ Y1 @ sh))))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ 51.84/7.15 Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y0) = 51.84/7.15 (Y1))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ 51.84/7.15 Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y2) = 51.84/7.15 (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = (lam @ Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ Y0 @ sh) = 51.84/7.15 (sub @ Y1 @ sh))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((lam @ 51.84/7.15 Y0) != 51.84/7.15 (ap @ Y1 @ 51.84/7.15 Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((~) @ (var @ 51.84/7.15 (ap @ Y0 @ Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (((Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (((Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ Y2))))))))))))))))) => 51.84/7.15 (((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ 51.84/7.15 Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))), 51.84/7.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 51.84/7.15 thf(zip_derived_cl49, plain, 51.84/7.15 (~ (((((!!) @ (^[Y0 : subst]: 51.84/7.15 (((push @ (sub @ one @ Y0) @ (comp @ sh @ Y0)) = (Y0)))))) => 51.84/7.15 (((var @ one) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((Y0 @ one) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (((Y0 @ Y1) => (Y0 @ 51.84/7.15 (sub @ Y1 @ sh))))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (((( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y0) = 51.84/7.15 (Y1))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ 51.84/7.15 Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y2) = 51.84/7.15 (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = (lam @ Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ Y0 @ sh) = (sub @ 51.84/7.15 Y1 @ sh))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((lam @ Y0) != 51.84/7.15 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((~) @ (var @ 51.84/7.15 (ap @ Y0 @ Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (((Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (((Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ Y2))))))))))))))))) => 51.84/7.15 (((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))), 51.84/7.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 51.84/7.15 thf(zip_derived_cl55, plain, 51.84/7.15 (~ (((var @ one) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((Y0 @ one) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (((Y0 @ Y1) => (Y0 @ 51.84/7.15 (sub @ Y1 @ sh))))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (((((ap @ 51.84/7.15 Y0 @ Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (((Y0) = 51.84/7.15 (Y1))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (((( 51.84/7.15 (ap @ 51.84/7.15 Y0 @ Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (( 51.84/7.15 (Y2) = 51.84/7.15 (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = (lam @ Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ Y0 @ sh) = (sub @ 51.84/7.15 Y1 @ sh))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((lam @ Y0) != 51.84/7.15 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((~) @ (var @ 51.84/7.15 (ap @ Y0 @ Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ 51.84/7.15 Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (((Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (((( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (sub @ 51.84/7.15 Y1 @ Y2))))))))))))))))) => 51.84/7.15 (((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (((Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))))), 51.84/7.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 51.84/7.15 thf(zip_derived_cl59, plain, 51.84/7.15 (~ (((((!!) @ (^[Y0 : term]: (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((Y0 @ one) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (((Y0 @ Y1) => (Y0 @ 51.84/7.15 (sub @ Y1 @ sh))))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (((((ap @ Y0 @ 51.84/7.15 Y2) = (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (((Y0) = (Y1))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (((((ap @ 51.84/7.15 Y0 @ Y2) = 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (((Y2) = 51.84/7.15 (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = (lam @ Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ Y0 @ sh) = (sub @ Y1 @ 51.84/7.15 sh))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((lam @ Y0) != 51.84/7.15 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ 51.84/7.15 Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (Y0 @ (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (((Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : subst]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (sub @ Y1 @ 51.84/7.15 Y2))))))))))))))))) => 51.84/7.15 (((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (((Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1)))))))))))))))))))))))))))))))))))))), 51.84/7.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 51.84/7.15 thf(zip_derived_cl62, plain, 51.84/7.15 (~ (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((Y0 @ one) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => 51.84/7.15 (((Y0 @ Y1) => (Y0 @ (sub @ Y1 @ sh))))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (((((ap @ Y0 @ 51.84/7.15 Y2) = (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (((Y0) = (Y1))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (((((ap @ Y0 @ 51.84/7.15 Y2) = (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (((Y2) = (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = (lam @ Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ Y0 @ sh) = (sub @ Y1 @ 51.84/7.15 sh))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((lam @ Y0) != (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((Y0 @ Y1) => (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (((Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (((Y0 @ Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (sub @ Y1 @ 51.84/7.15 (push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ Y2))))))))))))))))) => 51.84/7.15 (((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ 51.84/7.15 Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (((Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1)))))))))))))))))))))))))))))))))))), 51.84/7.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl59])). 51.84/7.15 thf(zip_derived_cl65, plain, 51.84/7.15 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (((((ap @ Y0 @ Y2) = 51.84/7.15 (ap @ Y1 @ Y3))) => 51.84/7.15 (((Y0) = (Y1))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (((((ap @ Y0 @ 51.84/7.15 Y2) = (ap @ 51.84/7.15 Y1 @ Y3))) => 51.84/7.15 (((Y2) = (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = (lam @ Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ Y0 @ sh) = (sub @ Y1 @ sh))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((lam @ Y0) != (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (((Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((Y0 @ Y1) => (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (( 51.84/7.15 (( 51.84/7.15 (!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y1 @ Y2))))))))))))))))) => 51.84/7.15 (((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ 51.84/7.15 Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y1) => 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y2 : term]: 51.84/7.15 (((Y0 @ Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (sub @ Y1 @ 51.84/7.15 (push @ 51.84/7.15 Y2 @ id)))))))) => 51.84/7.15 (Y0 @ (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (Y0 @ Y1)))))))))))))))))))))))))))))))))), 51.84/7.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 51.84/7.15 thf(zip_derived_cl69, plain, 51.84/7.15 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((!!) @ (^[Y3 : term]: 51.84/7.15 (((((ap @ Y0 @ Y2) = 51.84/7.15 (ap @ Y1 @ Y3))) => 51.84/7.15 (((Y2) = (Y3))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((lam @ Y0) = (lam @ Y1))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((((sub @ Y0 @ sh) = (sub @ Y1 @ sh))) => 51.84/7.15 (((Y0) = (Y1))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((lam @ Y0) != (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (((Y0 @ Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (ap @ Y1 @ 51.84/7.15 Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((Y0 @ Y1) => (Y0 @ 51.84/7.15 (lam @ Y1))))))) => 51.84/7.15 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : subst]: 51.84/7.15 (((((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (((var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 (sub @ 51.84/7.15 Y3 @ Y2))))))) => 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (((!!) @ ( 51.84/7.15 ^[Y3 : term]: 51.84/7.15 (( 51.84/7.15 (var @ 51.84/7.15 Y3) => 51.84/7.15 (Y0 @ 51.84/7.15 ( 51.84/7.15 sub @ 51.84/7.15 Y3 @ 51.84/7.15 ( 51.84/7.15 push @ 51.84/7.15 Y1 @ Y2))))))))))))))))))))) => 51.84/7.15 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((!!) @ (^[Y2 : term]: 51.84/7.15 (((Y0 @ Y1) => 51.84/7.15 (((Y0 @ 51.84/7.15 Y2) => 51.84/7.15 (Y0 @ 51.84/7.15 (ap @ 51.84/7.15 Y1 @ Y2)))))))))))) => 51.84/7.15 (((((!!) @ (^[Y1 : term]: 51.84/7.15 (((((!!) @ (^[Y2 : term]: 51.84/7.15 (( 51.84/7.15 (Y0 @ 51.84/7.16 Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 ( 51.84/7.16 sub @ 51.84/7.16 Y1 @ 51.84/7.16 ( 51.84/7.16 push @ 51.84/7.16 Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((( 51.84/7.16 (!!) @ ( 51.84/7.16 ^[Y3 : term]: 51.84/7.16 (( 51.84/7.16 (var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 ( 51.84/7.16 sub @ 51.84/7.16 Y3 @ Y2))))))) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ 51.84/7.16 Y1 @ Y2))))))))))))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ 51.84/7.16 Y1) => 51.84/7.16 (( 51.84/7.16 (Y0 @ 51.84/7.16 Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (ap @ 51.84/7.16 Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (( 51.84/7.16 (Y0 @ 51.84/7.16 Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 ( 51.84/7.16 sub @ 51.84/7.16 Y1 @ 51.84/7.16 ( 51.84/7.16 push @ 51.84/7.16 Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))))))))))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])). 51.84/7.16 thf(zip_derived_cl73, plain, 51.84/7.16 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((((lam @ Y0) = (lam @ Y1))) => 51.84/7.16 (((Y0) = (Y1))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((((sub @ Y0 @ sh) = (sub @ Y1 @ sh))) => 51.84/7.16 (((Y0) = (Y1))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((lam @ Y0) != (ap @ Y1 @ 51.84/7.16 Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((Y0 @ Y1) => (Y0 @ 51.84/7.16 (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ ( 51.84/7.16 ^[Y3 : term]: 51.84/7.16 (((var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y3 @ 51.84/7.16 Y2))))))) => 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((!!) @ ( 51.84/7.16 ^[Y3 : term]: 51.84/7.16 (((var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ 51.84/7.16 Y3 @ 51.84/7.16 ( 51.84/7.16 push @ 51.84/7.16 Y1 @ Y2))))))))))))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (ap @ Y1 @ 51.84/7.16 Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ 51.84/7.16 Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ 51.84/7.16 Y1 @ 51.84/7.16 ( 51.84/7.16 push @ 51.84/7.16 Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ ( 51.84/7.16 ^[Y3 : term]: 51.84/7.16 (( 51.84/7.16 (var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 ( 51.84/7.16 sub @ 51.84/7.16 Y3 @ Y2))))))) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 Y2))))))))))))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ 51.84/7.16 Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (ap @ 51.84/7.16 Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (( 51.84/7.16 (Y0 @ 51.84/7.16 Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 ( 51.84/7.16 sub @ 51.84/7.16 Y1 @ 51.84/7.16 ( 51.84/7.16 push @ 51.84/7.16 Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))))))))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])). 51.84/7.16 thf(zip_derived_cl78, plain, 51.84/7.16 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((((sub @ Y0 @ sh) = (sub @ Y1 @ sh))) => 51.84/7.16 (((Y0) = (Y1))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((lam @ Y0) != (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((Y0 @ Y1) => (Y0 @ 51.84/7.16 (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ (^[Y3 : term]: 51.84/7.16 (( 51.84/7.16 (var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 ( 51.84/7.16 sub @ 51.84/7.16 Y3 @ Y2))))))) => 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((!!) @ ( 51.84/7.16 ^[Y3 : term]: 51.84/7.16 (((var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y3 @ 51.84/7.16 (push @ 51.84/7.16 Y1 @ Y2))))))))))))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ 51.84/7.16 Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ ( 51.84/7.16 ^[Y3 : term]: 51.84/7.16 (( 51.84/7.16 (var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 ( 51.84/7.16 sub @ 51.84/7.16 Y3 @ Y2))))))) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y1 @ Y2))))))))))))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (ap @ Y1 @ 51.84/7.16 Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ 51.84/7.16 Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ 51.84/7.16 Y1 @ 51.84/7.16 ( 51.84/7.16 push @ 51.84/7.16 Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))))))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 51.84/7.16 thf(zip_derived_cl84, plain, 51.84/7.16 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((lam @ Y0) != (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((Y0 @ Y1) => (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ (^[Y3 : term]: 51.84/7.16 (( 51.84/7.16 (var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 ( 51.84/7.16 sub @ 51.84/7.16 Y3 @ Y2))))))) => 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((!!) @ (^[Y3 : term]: 51.84/7.16 (( 51.84/7.16 (var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 ( 51.84/7.16 sub @ 51.84/7.16 Y3 @ 51.84/7.16 ( 51.84/7.16 push @ 51.84/7.16 Y1 @ Y2))))))))))))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ Y2 @ 51.84/7.16 id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ ( 51.84/7.16 ^[Y3 : term]: 51.84/7.16 (((var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ 51.84/7.16 Y3 @ Y2))))))) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y1 @ Y2))))))))))))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ 51.84/7.16 Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 51.84/7.16 thf(zip_derived_cl92, plain, 51.84/7.16 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((Y0 @ Y1) => (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ (^[Y3 : term]: 51.84/7.16 (((var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ 51.84/7.16 Y3 @ Y2))))))) => 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((!!) @ (^[Y3 : term]: 51.84/7.16 (( 51.84/7.16 (var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 ( 51.84/7.16 sub @ 51.84/7.16 Y3 @ 51.84/7.16 ( 51.84/7.16 push @ 51.84/7.16 Y1 @ Y2))))))))))))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ ( 51.84/7.16 ^[Y3 : term]: 51.84/7.16 (((var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y3 @ 51.84/7.16 Y2))))))) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y1 @ Y2))))))))))))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ Y2 @ 51.84/7.16 id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl84])). 51.84/7.16 thf(zip_derived_cl102, plain, 51.84/7.16 (~ (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((Y0 @ Y1) => (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ (^[Y3 : term]: 51.84/7.16 (((var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y3 @ 51.84/7.16 Y2))))))) => 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((!!) @ (^[Y3 : term]: 51.84/7.16 (((var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ 51.84/7.16 Y3 @ 51.84/7.16 ( 51.84/7.16 push @ 51.84/7.16 Y1 @ Y2))))))))))))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ (^[Y3 : term]: 51.84/7.16 (( 51.84/7.16 (var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 ( 51.84/7.16 sub @ 51.84/7.16 Y3 @ Y2))))))) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y1 @ Y2))))))))))))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 51.84/7.16 thf(zip_derived_cl113, plain, 51.84/7.16 (~ (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((Y0 @ Y1) => (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ (^[Y3 : term]: 51.84/7.16 (((var @ Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y3 @ Y2))))))) => 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((!!) @ (^[Y3 : term]: 51.84/7.16 (((var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y3 @ 51.84/7.16 (push @ 51.84/7.16 Y1 @ Y2))))))))))))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ (^[Y3 : term]: 51.84/7.16 (( 51.84/7.16 (var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 ( 51.84/7.16 sub @ 51.84/7.16 Y3 @ Y2))))))) => 51.84/7.16 (Y0 @ (sub @ Y1 @ Y2))))))))))))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])). 51.84/7.16 thf(zip_derived_cl122, plain, 51.84/7.16 (~ (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ (^[Y3 : term]: 51.84/7.16 (((var @ Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y3 @ Y2))))))) => 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((!!) @ (^[Y3 : term]: 51.84/7.16 (((var @ Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y3 @ 51.84/7.16 (push @ Y1 @ 51.84/7.16 Y2))))))))))))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ (^[Y3 : term]: 51.84/7.16 (((var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ 51.84/7.16 Y3 @ Y2))))))) => 51.84/7.16 (Y0 @ (sub @ Y1 @ Y2))))))))))))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 51.84/7.16 thf(zip_derived_cl126, plain, 51.84/7.16 (~ (((((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ (^[Y3 : term]: 51.84/7.16 (((var @ 51.84/7.16 Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y3 @ 51.84/7.16 Y2))))))) => 51.84/7.16 (Y0 @ (sub @ Y1 @ Y2))))))))))))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl122])). 51.84/7.16 thf(zip_derived_cl130, plain, 51.84/7.16 (~ (((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl126])). 51.84/7.16 thf(zip_derived_cl138, plain, 51.84/7.16 (~ (((((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk53' @ Y0)))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y0) => 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (ap @ Y0 @ Y1)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 51.84/7.16 ('#sk53' @ (lam @ Y0))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term]: ('#sk53' @ Y0))))))))))), 51.84/7.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl130])). 51.84/7.16 thf(zip_derived_cl144, plain, 51.84/7.16 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y0) => 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (ap @ Y0 @ Y1)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 51.84/7.16 ('#sk53' @ (lam @ Y0))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term]: ('#sk53' @ Y0))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl138])). 51.84/7.16 thf(zip_derived_cl153, plain, 51.84/7.16 (~ (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 51.84/7.16 ('#sk53' @ (lam @ Y0))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term]: ('#sk53' @ Y0))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 51.84/7.16 thf(zip_derived_cl164, plain, (~ (((!!) @ (^[Y0 : term]: ('#sk53' @ Y0))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl153])). 51.84/7.16 thf(zip_derived_cl176, plain, (~ ('#sk53' @ '#sk186')), 51.84/7.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl164])). 51.84/7.16 thf(zip_derived_cl143, plain, 51.84/7.16 ( (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk53' @ Y0))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl138])). 51.84/7.16 thf(zip_derived_cl151, plain, 51.84/7.16 (![X2 : term]: (((var @ X2) => ('#sk53' @ X2)))), 51.84/7.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl143])). 51.84/7.16 thf(zip_derived_cl159, plain, 51.84/7.16 (![X2 : term]: (~ (var @ X2) | ('#sk53' @ X2))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl151])). 51.84/7.16 thf(zip_derived_cl8, plain, 51.84/7.16 ( (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 51.84/7.16 thf(zip_derived_cl12, plain, (![X2 : term]: (((sub @ X2 @ id) = (X2)))), 51.84/7.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 51.84/7.16 thf(zip_derived_cl17, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))), 51.84/7.16 inference('simplify nested equalities', [status(thm)], [zip_derived_cl12])). 51.84/7.16 thf(zip_derived_cl129, plain, 51.84/7.16 ( (((!!) @ (^[Y0 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y1) => 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (ap @ Y1 @ Y2)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((Y0 @ Y2) => (Y0 @ 51.84/7.16 (sub @ Y1 @ 51.84/7.16 (push @ Y2 @ id)))))))) => 51.84/7.16 (Y0 @ (lam @ Y1))))))) => 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((!!) @ (^[Y2 : subst]: 51.84/7.16 (((((!!) @ (^[Y3 : term]: 51.84/7.16 (((var @ Y3) => 51.84/7.16 (Y0 @ 51.84/7.16 (sub @ Y3 @ Y2))))))) => 51.84/7.16 (Y0 @ (sub @ Y1 @ Y2)))))))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl126])). 51.84/7.16 thf(zip_derived_cl133, plain, 51.84/7.16 (![X2 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((X2 @ Y0) => 51.84/7.16 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((X2 @ Y1) => (X2 @ 51.84/7.16 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 51.84/7.16 (X2 @ (lam @ Y0))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : subst]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((var @ Y2) => (X2 @ 51.84/7.16 (sub @ Y2 @ Y1))))))) => 51.84/7.16 (X2 @ (sub @ Y0 @ Y1))))))))))))))), 51.84/7.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl129])). 51.84/7.16 thf(zip_derived_cl134, plain, 51.84/7.16 ( (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y0) => 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (ap @ Y0 @ Y1)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 51.84/7.16 ('#sk53' @ (lam @ Y0))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : subst]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((var @ Y2) => ('#sk53' @ 51.84/7.16 (sub @ Y2 @ Y1))))))) => 51.84/7.16 ('#sk53' @ (sub @ Y0 @ Y1))))))))))))))), 51.84/7.16 inference('triggered_bool_instantiation', [status(thm)], 51.84/7.16 [zip_derived_cl133])). 51.84/7.16 thf(zip_derived_cl274, plain, 51.84/7.16 ((~ (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y0) => 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (ap @ Y0 @ Y1)))))))))))) 51.84/7.16 | (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 51.84/7.16 ('#sk53' @ (lam @ Y0))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : subst]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((var @ Y2) => ('#sk53' @ 51.84/7.16 (sub @ Y2 @ Y1))))))) => 51.84/7.16 ('#sk53' @ (sub @ Y0 @ Y1)))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl134])). 51.84/7.16 thf(zip_derived_cl152, plain, 51.84/7.16 ( (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y0) => 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (ap @ Y0 @ Y1))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 51.84/7.16 thf(zip_derived_cl160, plain, 51.84/7.16 (![X2 : term > $o]: 51.84/7.16 (~ ('#form109' @ X2) 51.84/7.16 | (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((X2 @ Y0) => 51.84/7.16 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 51.84/7.16 define([status(thm)])). 51.84/7.16 thf(zip_derived_cl133, plain, 51.84/7.16 (![X2 : term > $o]: 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((X2 @ Y0) => 51.84/7.16 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((X2 @ Y1) => (X2 @ 51.84/7.16 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 51.84/7.16 (X2 @ (lam @ Y0))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : subst]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((var @ Y2) => (X2 @ 51.84/7.16 (sub @ Y2 @ Y1))))))) => 51.84/7.16 (X2 @ (sub @ Y0 @ Y1))))))))))))))), 51.84/7.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl129])). 51.84/7.16 thf(zip_derived_cl142, plain, 51.84/7.16 (![X2 : term > $o]: 51.84/7.16 (~ (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((X2 @ Y0) => 51.84/7.16 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) 51.84/7.16 | (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((X2 @ Y1) => (X2 @ 51.84/7.16 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 51.84/7.16 (X2 @ (lam @ Y0))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : subst]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((var @ Y2) => (X2 @ 51.84/7.16 (sub @ Y2 @ Y1))))))) => 51.84/7.16 (X2 @ (sub @ Y0 @ Y1)))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl133])). 51.84/7.16 thf(zip_derived_cl148, plain, 51.84/7.16 (![X2 : term > $o]: 51.84/7.16 ( ('#form109' @ X2) 51.84/7.16 | ~ (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((X2 @ Y0) => 51.84/7.16 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 51.84/7.16 define([status(thm)])). 51.84/7.16 thf(zip_derived_cl275, plain, 51.84/7.16 ((~ ('#form109' @ '#sk53') 51.84/7.16 | (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 51.84/7.16 ('#sk53' @ (lam @ Y0))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : subst]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((var @ Y2) => ('#sk53' @ 51.84/7.16 (sub @ Y2 @ Y1))))))) => 51.84/7.16 ('#sk53' @ (sub @ Y0 @ Y1)))))))))))))), 51.84/7.16 inference('renaming', [status(thm)], 51.84/7.16 [zip_derived_cl274, zip_derived_cl160, zip_derived_cl148])). 51.84/7.16 thf(zip_derived_cl152, plain, 51.84/7.16 ( (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y0) => 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (ap @ Y0 @ Y1))))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 51.84/7.16 thf(zip_derived_cl160, plain, 51.84/7.16 (![X2 : term > $o]: 51.84/7.16 (~ ('#form109' @ X2) 51.84/7.16 | (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((X2 @ Y0) => 51.84/7.16 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 51.84/7.16 define([status(thm)])). 51.84/7.16 thf(zip_derived_cl148, plain, 51.84/7.16 (![X2 : term > $o]: 51.84/7.16 ( ('#form109' @ X2) 51.84/7.16 | ~ (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : term]: 51.84/7.16 (((X2 @ Y0) => 51.84/7.16 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 51.84/7.16 define([status(thm)])). 51.84/7.16 thf(zip_derived_cl162, plain, ( ('#form109' @ '#sk53')), 51.84/7.16 inference('renaming', [status(thm)], 51.84/7.16 [zip_derived_cl152, zip_derived_cl160, zip_derived_cl148])). 51.84/7.16 thf(zip_derived_cl276, plain, 51.84/7.16 ( (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 51.84/7.16 ('#sk53' @ (lam @ Y0))))))) => 51.84/7.16 (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : subst]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((var @ Y2) => ('#sk53' @ 51.84/7.16 (sub @ Y2 @ Y1))))))) => 51.84/7.16 ('#sk53' @ (sub @ Y0 @ Y1))))))))))))), 51.84/7.16 inference('demod', [status(thm)], [zip_derived_cl275, zip_derived_cl162])). 51.84/7.16 thf(zip_derived_cl277, plain, 51.84/7.16 ((~ (((!!) @ (^[Y0 : term]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 51.84/7.16 ('#sk53' @ (lam @ Y0))))))) 51.84/7.16 | (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : subst]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((var @ Y2) => ('#sk53' @ 51.84/7.16 (sub @ Y2 @ Y1))))))) => 51.84/7.16 ('#sk53' @ (sub @ Y0 @ Y1)))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl276])). 51.84/7.16 thf(zip_derived_cl278, plain, 51.84/7.16 ((~ (((((!!) @ (^[Y0 : term]: 51.84/7.16 ((('#sk53' @ Y0) => ('#sk53' @ 51.84/7.16 (sub @ ('#sk177' @ '#sk53') @ (push @ Y0 @ id)))))))) => 51.84/7.16 ('#sk53' @ (lam @ ('#sk177' @ '#sk53'))))) 51.84/7.16 | (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : subst]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((var @ Y2) => ('#sk53' @ 51.84/7.16 (sub @ Y2 @ Y1))))))) => 51.84/7.16 ('#sk53' @ (sub @ Y0 @ Y1)))))))))))), 51.84/7.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl277])). 51.84/7.16 thf(zip_derived_cl280, plain, 51.84/7.16 ((~ ('#sk53' @ (lam @ ('#sk177' @ '#sk53'))) 51.84/7.16 | (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : subst]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((var @ Y2) => ('#sk53' @ 51.84/7.16 (sub @ Y2 @ Y1))))))) => 51.84/7.16 ('#sk53' @ (sub @ Y0 @ Y1)))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl278])). 51.84/7.16 thf(zip_derived_cl282, plain, 51.84/7.16 (![X2 : term]: 51.84/7.16 ( (((!!) @ (^[Y0 : subst]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((var @ Y1) => ('#sk53' @ 51.84/7.16 (sub @ Y1 @ Y0))))))) => 51.84/7.16 ('#sk53' @ (sub @ X2 @ Y0))))))) 51.84/7.16 | ~ ('#sk53' @ (lam @ ('#sk177' @ '#sk53'))))), 51.84/7.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl280])). 51.84/7.16 thf(zip_derived_cl284, plain, 51.84/7.16 (![X2 : term, X4 : subst]: 51.84/7.16 ( (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((var @ Y0) => ('#sk53' @ (sub @ Y0 @ X4))))))) => 51.84/7.16 ('#sk53' @ (sub @ X2 @ X4)))) 51.84/7.16 | ~ ('#sk53' @ (lam @ ('#sk177' @ '#sk53'))))), 51.84/7.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl282])). 51.84/7.16 thf(zip_derived_cl286, plain, 51.84/7.16 (![X2 : term, X4 : subst]: 51.84/7.16 (~ (((!!) @ (^[Y0 : term]: 51.84/7.16 (((var @ Y0) => ('#sk53' @ (sub @ Y0 @ X4))))))) 51.84/7.16 | ('#sk53' @ (sub @ X2 @ X4)) 51.84/7.16 | ~ ('#sk53' @ (lam @ ('#sk177' @ '#sk53'))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl284])). 51.84/7.16 thf(zip_derived_cl288, plain, 51.84/7.16 (![X2 : term, X4 : subst]: 51.84/7.16 (~ (((var @ 51.84/7.16 ('#sk46' @ (^[Y0 : term]: ('#sk53' @ (sub @ Y0 @ X4))))) => 51.84/7.16 ('#sk53' @ 51.84/7.16 (sub @ ('#sk46' @ (^[Y0 : term]: ('#sk53' @ (sub @ Y0 @ X4)))) @ 51.84/7.16 X4)))) 51.84/7.16 | ~ ('#sk53' @ (lam @ ('#sk177' @ '#sk53'))) 51.84/7.16 | ('#sk53' @ (sub @ X2 @ X4)))), 51.84/7.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl286])). 51.84/7.16 thf(zip_derived_cl291, plain, 51.84/7.16 (![X2 : term, X4 : subst]: 51.84/7.16 (~ ('#sk53' @ 51.84/7.16 (sub @ ('#sk46' @ (^[Y0 : term]: ('#sk53' @ (sub @ Y0 @ X4)))) @ 51.84/7.16 X4)) 51.84/7.16 | ('#sk53' @ (sub @ X2 @ X4)) 51.84/7.16 | ~ ('#sk53' @ (lam @ ('#sk177' @ '#sk53'))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl288])). 51.84/7.16 thf(zip_derived_cl163, plain, 51.84/7.16 ( (((!!) @ (^[Y0 : term]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 ((('#sk53' @ Y1) => ('#sk53' @ 51.84/7.16 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 51.84/7.16 ('#sk53' @ (lam @ Y0)))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl153])). 51.84/7.16 thf(zip_derived_cl175, plain, 51.84/7.16 (![X2 : term]: 51.84/7.16 (((((!!) @ (^[Y0 : term]: 51.84/7.16 ((('#sk53' @ Y0) => ('#sk53' @ 51.84/7.16 (sub @ X2 @ (push @ Y0 @ id)))))))) => 51.84/7.16 ('#sk53' @ (lam @ X2))))), 51.84/7.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl163])). 51.84/7.16 thf(zip_derived_cl186, plain, 51.84/7.16 (![X2 : term]: 51.84/7.16 (~ (((!!) @ (^[Y0 : term]: 51.84/7.16 ((('#sk53' @ Y0) => ('#sk53' @ 51.84/7.16 (sub @ X2 @ (push @ Y0 @ id)))))))) 51.84/7.16 | ('#sk53' @ (lam @ X2)))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])). 51.84/7.16 thf(zip_derived_cl196, plain, 51.84/7.16 (![X2 : term]: 51.84/7.16 (~ ((('#sk53' @ ('#sk252' @ X2)) => ('#sk53' @ 51.84/7.16 (sub @ X2 @ (push @ ('#sk252' @ X2) @ id))))) 51.84/7.16 | ('#sk53' @ (lam @ X2)))), 51.84/7.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl186])). 51.84/7.16 thf(zip_derived_cl205, plain, 51.84/7.16 (![X2 : term]: ( ('#sk53' @ ('#sk252' @ X2)) | ('#sk53' @ (lam @ X2)))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl196])). 51.84/7.16 thf(zip_derived_cl206, plain, 51.84/7.16 (![X2 : term]: 51.84/7.16 (~ ('#sk53' @ (sub @ X2 @ (push @ ('#sk252' @ X2) @ id))) 51.84/7.16 | ('#sk53' @ (lam @ X2)))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl196])). 51.84/7.16 thf(zip_derived_cl279, plain, 51.84/7.16 (( (((!!) @ (^[Y0 : term]: 51.84/7.16 ((('#sk53' @ Y0) => ('#sk53' @ 51.84/7.16 (sub @ ('#sk177' @ '#sk53') @ (push @ Y0 @ id)))))))) 51.84/7.16 | (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : subst]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((var @ Y2) => ('#sk53' @ 51.84/7.16 (sub @ Y2 @ Y1))))))) => 51.84/7.16 ('#sk53' @ (sub @ Y0 @ Y1)))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl278])). 51.84/7.16 thf(zip_derived_cl281, plain, 51.84/7.16 (![X2 : term]: 51.84/7.16 ( ((('#sk53' @ X2) => ('#sk53' @ 51.84/7.16 (sub @ ('#sk177' @ '#sk53') @ (push @ X2 @ id))))) 51.84/7.16 | (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : subst]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((var @ Y2) => ('#sk53' @ 51.84/7.16 (sub @ Y2 @ Y1))))))) => 51.84/7.16 ('#sk53' @ (sub @ Y0 @ Y1)))))))))))), 51.84/7.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl279])). 51.84/7.16 thf(zip_derived_cl283, plain, 51.84/7.16 (![X2 : term]: 51.84/7.16 (~ ('#sk53' @ X2) 51.84/7.16 | ('#sk53' @ (sub @ ('#sk177' @ '#sk53') @ (push @ X2 @ id))) 51.84/7.16 | (((!!) @ (^[Y0 : term]: 51.84/7.16 (((!!) @ (^[Y1 : subst]: 51.84/7.16 (((((!!) @ (^[Y2 : term]: 51.84/7.16 (((var @ Y2) => ('#sk53' @ 51.84/7.16 (sub @ Y2 @ Y1))))))) => 51.84/7.16 ('#sk53' @ (sub @ Y0 @ Y1)))))))))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl281])). 51.84/7.16 thf(zip_derived_cl285, plain, 51.84/7.16 (![X2 : term, X4 : term]: 51.84/7.16 ( (((!!) @ (^[Y0 : subst]: 51.84/7.16 (((((!!) @ (^[Y1 : term]: 51.84/7.16 (((var @ Y1) => ('#sk53' @ 51.84/7.16 (sub @ Y1 @ Y0))))))) => 51.84/7.16 ('#sk53' @ (sub @ X4 @ Y0))))))) 51.84/7.16 | ('#sk53' @ (sub @ ('#sk177' @ '#sk53') @ (push @ X2 @ id))) 51.84/7.16 | ~ ('#sk53' @ X2))), 51.84/7.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl283])). 51.84/7.16 thf(zip_derived_cl287, plain, 51.84/7.16 (![X2 : term, X4 : term, X6 : subst]: 51.84/7.16 ( (((((!!) @ (^[Y0 : term]: 51.84/7.16 (((var @ Y0) => ('#sk53' @ (sub @ Y0 @ X6))))))) => 51.84/7.16 ('#sk53' @ (sub @ X4 @ X6)))) 51.84/7.16 | ~ ('#sk53' @ X2) 51.84/7.16 | ('#sk53' @ (sub @ ('#sk177' @ '#sk53') @ (push @ X2 @ id))))), 51.84/7.16 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl285])). 51.84/7.16 thf(zip_derived_cl289, plain, 51.84/7.16 (![X2 : term, X4 : term, X6 : subst]: 51.84/7.16 (~ (((!!) @ (^[Y0 : term]: 51.84/7.16 (((var @ Y0) => ('#sk53' @ (sub @ Y0 @ X6))))))) 51.84/7.16 | ('#sk53' @ (sub @ X4 @ X6)) 51.84/7.16 | ('#sk53' @ (sub @ ('#sk177' @ '#sk53') @ (push @ X2 @ id))) 51.84/7.16 | ~ ('#sk53' @ X2))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl287])). 51.84/7.16 thf(zip_derived_cl292, plain, 51.84/7.16 (![X2 : term, X4 : term, X6 : subst]: 51.84/7.16 (~ (((var @ 51.84/7.16 ('#sk46' @ (^[Y0 : term]: ('#sk53' @ (sub @ Y0 @ X6))))) => 51.84/7.16 ('#sk53' @ 51.84/7.16 (sub @ ('#sk46' @ (^[Y0 : term]: ('#sk53' @ (sub @ Y0 @ X6)))) @ 51.84/7.16 X6)))) 51.84/7.16 | ~ ('#sk53' @ X2) 51.84/7.16 | ('#sk53' @ (sub @ ('#sk177' @ '#sk53') @ (push @ X2 @ id))) 51.84/7.16 | ('#sk53' @ (sub @ X4 @ X6)))), 51.84/7.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl289])). 51.84/7.16 thf(zip_derived_cl294, plain, 51.84/7.16 (![X2 : term, X4 : term, X6 : subst]: 51.84/7.16 (~ ('#sk53' @ 51.84/7.16 (sub @ ('#sk46' @ (^[Y0 : term]: ('#sk53' @ (sub @ Y0 @ X6)))) @ 51.84/7.16 X6)) 51.84/7.16 | ('#sk53' @ (sub @ X4 @ X6)) 51.84/7.16 | ('#sk53' @ (sub @ ('#sk177' @ '#sk53') @ (push @ X2 @ id))) 51.84/7.16 | ~ ('#sk53' @ X2))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl292])). 51.84/7.16 thf(zip_derived_cl290, plain, 51.84/7.16 (![X2 : term, X4 : subst]: 51.84/7.16 ( (var @ ('#sk46' @ (^[Y0 : term]: ('#sk53' @ (sub @ Y0 @ X4))))) 51.84/7.16 | ('#sk53' @ (sub @ X2 @ X4)) 51.84/7.16 | ~ ('#sk53' @ (lam @ ('#sk177' @ '#sk53'))))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl288])). 51.84/7.16 thf(zip_derived_cl293, plain, 51.84/7.16 (![X2 : term, X4 : term, X6 : subst]: 51.84/7.16 ( (var @ ('#sk46' @ (^[Y0 : term]: ('#sk53' @ (sub @ Y0 @ X6))))) 51.84/7.16 | ('#sk53' @ (sub @ X4 @ X6)) 51.84/7.16 | ('#sk53' @ (sub @ ('#sk177' @ '#sk53') @ (push @ X2 @ id))) 51.84/7.16 | ~ ('#sk53' @ X2))), 51.84/7.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl292])). 51.84/7.16 thf(zip_derived_cl12183, plain, ($false), 51.84/7.16 inference('eprover', [status(thm)], 51.84/7.16 [zip_derived_cl176, zip_derived_cl159, zip_derived_cl17, 51.84/7.16 zip_derived_cl291, zip_derived_cl205, zip_derived_cl206, 51.84/7.16 zip_derived_cl294, zip_derived_cl290, zip_derived_cl293])). 51.84/7.16 51.84/7.16 % SZS output end Refutation 51.84/7.16 51.84/7.16 51.84/7.16 % Terminating... 51.84/7.16 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 52.34/7.26 % Runner terminated. 52.34/7.29 % Zipperpin 1.5 exiting 52.34/7.30 EOF