0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.29iIFLwSBl true 0.16/0.36 % Computer : n021.cluster.edu 0.16/0.36 % Model : x86_64 x86_64 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.36 % Memory : 8042.1875MB 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.36 % CPULimit : 1200 0.16/0.36 % WCLimit : 120 0.16/0.36 % DateTime : Tue Jul 13 14:30:26 EDT 2021 0.16/0.36 % CPUTime : 0.16/0.36 % Running portfolio for 120 s 0.16/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.16/0.36 % Number of cores: 8 0.16/0.37 % Python version: Python 3.6.8 0.16/0.37 % Running in HO mode 0.56/0.68 % Total configuration time : 828 0.56/0.68 % Estimated wc time : 983 0.56/0.68 % Estimated cpu time (8 cpus) : 122.875 0.56/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.58/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.58/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.58/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.58/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.58/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.58/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 0.58/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.58/0.84 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 53s 31.89/4.69 % Solved by lams/20_acsne_simpl.sh. 31.89/4.69 % running E: timeout 13 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.29iIFLwSBl/e_inputfed46b --cpu-limit=11 --auto -s -p 31.89/4.69 % done 464 iterations in 3.808s 31.89/4.69 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 31.89/4.69 % SZS output start Refutation 31.89/4.69 thf(term_type, type, term: $tType). 31.89/4.69 thf(subst_type, type, subst: $tType). 31.89/4.69 thf(lamnotvar_type, type, lamnotvar: $o). 31.89/4.69 thf(apnotvar_type, type, apnotvar: $o). 31.89/4.69 thf(ap_type, type, ap: term > term > term). 31.89/4.69 thf(axapp_type, type, axapp: $o). 31.89/4.69 thf('#sk49_type', type, '#sk49': subst). 31.89/4.69 thf(var_type, type, var: term > $o). 31.89/4.69 thf(sh_type, type, sh: subst). 31.89/4.69 thf(shinj_type, type, shinj: $o). 31.89/4.69 thf(laminj_type, type, laminj: $o). 31.89/4.69 thf(sub_type, type, sub: term > subst > term). 31.89/4.69 thf(push_type, type, push: term > subst > subst). 31.89/4.69 thf(ulamvarsh_type, type, ulamvarsh: $o). 31.89/4.69 thf(id_type, type, id: subst). 31.89/4.69 thf(axassoc_type, type, axassoc: $o). 31.89/4.69 thf(axvarid_type, type, axvarid: $o). 31.89/4.69 thf('#sk48_type', type, '#sk48': (term > $o) > term). 31.89/4.69 thf(apinj1_type, type, apinj1: $o). 31.89/4.69 thf(axabs_type, type, axabs: $o). 31.89/4.69 thf(induction_type, type, induction: $o). 31.89/4.69 thf(lamnotap_type, type, lamnotap: $o). 31.89/4.69 thf(axidr_type, type, axidr: $o). 31.89/4.69 thf(pushprop_type, type, pushprop: $o). 31.89/4.69 thf(lam_type, type, lam: term > term). 31.89/4.69 thf('#sk30_type', type, '#sk30': term > $o). 31.89/4.69 thf(apinj2_type, type, apinj2: $o). 31.89/4.69 thf(one_type, type, one: term). 31.89/4.69 thf(axshiftcons_type, type, axshiftcons: $o). 31.89/4.69 thf(axvarshift_type, type, axvarshift: $o). 31.89/4.69 thf('#sk39_type', type, '#sk39': term). 31.89/4.69 thf(comp_type, type, comp: subst > subst > subst). 31.89/4.69 thf(ulamvar1_type, type, ulamvar1: $o). 31.89/4.69 thf(axclos_type, type, axclos: $o). 31.89/4.69 thf(axvarcons_type, type, axvarcons: $o). 31.89/4.69 thf(axidl_type, type, axidl: $o). 31.89/4.69 thf('#l_lift9963_type', type, '#l_lift9963': term > $o). 31.89/4.69 thf('#sk10_type', type, '#sk10': (term > $o) > term). 31.89/4.69 thf(pushprop_gthm_type, type, pushprop_gthm: $o). 31.89/4.69 thf(axscons_type, type, axscons: $o). 31.89/4.69 thf(ulamvarind_type, type, ulamvarind: $o). 31.89/4.69 thf(axmap_type, type, axmap: $o). 31.89/4.69 thf(pushprop_gthm, axiom, pushprop_gthm = 31.89/4.69 (( axapp ) => 31.89/4.69 ( ( axvarcons ) => 31.89/4.69 ( ( axvarid ) => 31.89/4.69 ( ( axabs ) => 31.89/4.69 ( ( axclos ) => 31.89/4.69 ( ( axidl ) => 31.89/4.69 ( ( axshiftcons ) => 31.89/4.69 ( ( axassoc ) => 31.89/4.69 ( ( axmap ) => 31.89/4.69 ( ( axidr ) => 31.89/4.69 ( ( axvarshift ) => 31.89/4.69 ( ( axscons ) => 31.89/4.69 ( ( ulamvar1 ) => 31.89/4.69 ( ( ulamvarsh ) => 31.89/4.69 ( ( ulamvarind ) => 31.89/4.69 ( ( apinj1 ) => 31.89/4.69 ( ( apinj2 ) => 31.89/4.69 ( ( laminj ) => 31.89/4.69 ( ( shinj ) => 31.89/4.69 ( ( lamnotap ) => 31.89/4.69 ( ( apnotvar ) => 31.89/4.69 ( ( lamnotvar ) => 31.89/4.69 ( ( induction ) => ( pushprop ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 31.89/4.69 thf('0', plain, 31.89/4.69 (( pushprop_gthm ) = 31.89/4.69 ( ( axapp ) => 31.89/4.69 ( ( axvarcons ) => 31.89/4.69 ( ( axvarid ) => 31.89/4.69 ( ( axabs ) => 31.89/4.69 ( ( axclos ) => 31.89/4.69 ( ( axidl ) => 31.89/4.69 ( ( axshiftcons ) => 31.89/4.69 ( ( axassoc ) => 31.89/4.69 ( ( axmap ) => 31.89/4.69 ( ( axidr ) => 31.89/4.69 ( ( axvarshift ) => 31.89/4.69 ( ( axscons ) => 31.89/4.69 ( ( ulamvar1 ) => 31.89/4.69 ( ( ulamvarsh ) => 31.89/4.69 ( ( ulamvarind ) => 31.89/4.69 ( ( apinj1 ) => 31.89/4.69 ( ( apinj2 ) => 31.89/4.69 ( ( laminj ) => 31.89/4.69 ( ( shinj ) => 31.89/4.69 ( ( lamnotap ) => 31.89/4.69 ( ( apnotvar ) => 31.89/4.69 ( ( lamnotvar ) => 31.89/4.69 ( ( induction ) => 31.89/4.69 ( pushprop ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(pushprop, axiom, pushprop = 31.89/4.69 (![P:( term > $o ),A:term,M:subst]: 31.89/4.69 ( ( ![B:term]: ( ( var @ B ) => ( P @ ( sub @ B @ M ) ) ) ) => 31.89/4.69 ( ( P @ A ) => 31.89/4.69 ( ![B:term]: ( ( var @ B ) => ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ))). 31.89/4.69 thf('1', plain, 31.89/4.69 (( pushprop ) = 31.89/4.69 ( ![X4:( term > $o ),X6:term,X8:subst]: 31.89/4.69 ( ( ![X10:term]: ( ( var @ X10 ) => ( X4 @ ( sub @ X10 @ X8 ) ) ) ) => 31.89/4.69 ( ( X4 @ X6 ) => 31.89/4.69 ( ![X12:term]: 31.89/4.69 ( ( var @ X12 ) => ( X4 @ ( sub @ X12 @ ( push @ X6 @ X8 ) ) ) ) ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(induction, axiom, induction = 31.89/4.69 (![P:( term > $o )]: 31.89/4.69 ( ( ![A:term]: ( ( var @ A ) => ( P @ A ) ) ) => 31.89/4.69 ( ( ![A:term,B:term]: 31.89/4.69 ( ( P @ A ) => ( ( P @ B ) => ( P @ ( ap @ A @ B ) ) ) ) ) => 31.89/4.69 ( ( ![A:term]: ( ( P @ A ) => ( P @ ( lam @ A ) ) ) ) => 31.89/4.69 ( ![A:term]: ( P @ A ) ) ) ) ))). 31.89/4.69 thf('2', plain, 31.89/4.69 (( induction ) = 31.89/4.69 ( ![X4:( term > $o )]: 31.89/4.69 ( ( ![X6:term]: ( ( var @ X6 ) => ( X4 @ X6 ) ) ) => 31.89/4.69 ( ( ![X8:term,X10:term]: 31.89/4.69 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( X4 @ ( ap @ X8 @ X10 ) ) ) ) ) => 31.89/4.69 ( ( ![X12:term]: ( ( X4 @ X12 ) => ( X4 @ ( lam @ X12 ) ) ) ) => 31.89/4.69 ( ![X14:term]: ( X4 @ X14 ) ) ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(lamnotvar, axiom, lamnotvar = (![A:term]: ( ~( var @ ( lam @ A ) ) ))). 31.89/4.69 thf('3', plain, 31.89/4.69 (( lamnotvar ) = ( ![X4:term]: ( ~( var @ ( lam @ X4 ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(apnotvar, axiom, apnotvar = 31.89/4.69 (![A:term,B:term]: ( ~( var @ ( ap @ A @ B ) ) ))). 31.89/4.69 thf('4', plain, 31.89/4.69 (( apnotvar ) = ( ![X4:term,X6:term]: ( ~( var @ ( ap @ X4 @ X6 ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(lamnotap, axiom, lamnotap = 31.89/4.69 (![A:term,B:term,C:term]: ( ( lam @ A ) != ( ap @ B @ C ) ))). 31.89/4.69 thf('5', plain, 31.89/4.69 (( lamnotap ) = 31.89/4.69 ( ![X4:term,X6:term,X8:term]: ( ( lam @ X4 ) != ( ap @ X6 @ X8 ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(shinj, axiom, shinj = 31.89/4.69 (![A:term,B:term]: 31.89/4.69 ( ( ( sub @ A @ sh ) = ( sub @ B @ sh ) ) => ( ( A ) = ( B ) ) ))). 31.89/4.69 thf('6', plain, 31.89/4.69 (( shinj ) = 31.89/4.69 ( ![X4:term,X6:term]: 31.89/4.69 ( ( ( sub @ X4 @ sh ) = ( sub @ X6 @ sh ) ) => ( ( X4 ) = ( X6 ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(laminj, axiom, laminj = 31.89/4.69 (![A:term,B:term]: ( ( ( lam @ A ) = ( lam @ B ) ) => ( ( A ) = ( B ) ) ))). 31.89/4.69 thf('7', plain, 31.89/4.69 (( laminj ) = 31.89/4.69 ( ![X4:term,X6:term]: 31.89/4.69 ( ( ( lam @ X4 ) = ( lam @ X6 ) ) => ( ( X4 ) = ( X6 ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(apinj2, axiom, apinj2 = 31.89/4.69 (![A:term,B:term,C:term,D:term]: 31.89/4.69 ( ( ( ap @ A @ C ) = ( ap @ B @ D ) ) => ( ( C ) = ( D ) ) ))). 31.89/4.69 thf('8', plain, 31.89/4.69 (( apinj2 ) = 31.89/4.69 ( ![X4:term,X6:term,X8:term,X10:term]: 31.89/4.69 ( ( ( ap @ X4 @ X8 ) = ( ap @ X6 @ X10 ) ) => ( ( X8 ) = ( X10 ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(apinj1, axiom, apinj1 = 31.89/4.69 (![A:term,B:term,C:term,D:term]: 31.89/4.69 ( ( ( ap @ A @ C ) = ( ap @ B @ D ) ) => ( ( A ) = ( B ) ) ))). 31.89/4.69 thf('9', plain, 31.89/4.69 (( apinj1 ) = 31.89/4.69 ( ![X4:term,X6:term,X8:term,X10:term]: 31.89/4.69 ( ( ( ap @ X4 @ X8 ) = ( ap @ X6 @ X10 ) ) => ( ( X4 ) = ( X6 ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(ulamvarind, axiom, ulamvarind = 31.89/4.69 (![P:( term > $o )]: 31.89/4.69 ( ( P @ one ) => 31.89/4.69 ( ( ![A:term]: 31.89/4.69 ( ( var @ A ) => ( ( P @ A ) => ( P @ ( sub @ A @ sh ) ) ) ) ) => 31.89/4.69 ( ![A:term]: ( ( var @ A ) => ( P @ A ) ) ) ) ))). 31.89/4.69 thf('10', plain, 31.89/4.69 (( ulamvarind ) = 31.89/4.69 ( ![X4:( term > $o )]: 31.89/4.69 ( ( X4 @ one ) => 31.89/4.69 ( ( ![X6:term]: 31.89/4.69 ( ( var @ X6 ) => ( ( X4 @ X6 ) => ( X4 @ ( sub @ X6 @ sh ) ) ) ) ) => 31.89/4.69 ( ![X8:term]: ( ( var @ X8 ) => ( X4 @ X8 ) ) ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(ulamvarsh, axiom, ulamvarsh = 31.89/4.69 (![A:term]: ( ( var @ A ) => ( var @ ( sub @ A @ sh ) ) ))). 31.89/4.69 thf('11', plain, 31.89/4.69 (( ulamvarsh ) = 31.89/4.69 ( ![X4:term]: ( ( var @ X4 ) => ( var @ ( sub @ X4 @ sh ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(ulamvar1, axiom,(( ulamvar1 ) = (var @ one))). 31.89/4.69 thf('12', plain, (( ulamvar1 ) = ( var @ one )), 31.89/4.69 inference('simplify_rw_rule', [status(thm)], [ulamvar1])). 31.89/4.69 thf('13', plain, (( ulamvar1 ) = ( var @ one )), define([status(thm)])). 31.89/4.69 thf(axscons, axiom, axscons = 31.89/4.69 (![M:subst]: ( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) = ( M ) ))). 31.89/4.69 thf('14', plain, 31.89/4.69 (( axscons ) = 31.89/4.69 ( ![X4:subst]: 31.89/4.69 ( ( push @ ( sub @ one @ X4 ) @ ( comp @ sh @ X4 ) ) = ( X4 ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(axvarshift, axiom, axvarshift = (( push @ one @ sh ) = ( id ))). 31.89/4.69 thf('15', plain, (( axvarshift ) = ( ( push @ one @ sh ) = ( id ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(axidr, axiom, axidr = (![M:subst]: ( ( comp @ M @ id ) = ( M ) ))). 31.89/4.69 thf('16', plain, 31.89/4.69 (( axidr ) = ( ![X4:subst]: ( ( comp @ X4 @ id ) = ( X4 ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(axmap, axiom, axmap = 31.89/4.69 (![A:term,M:subst,N:subst]: 31.89/4.69 ( ( comp @ ( push @ A @ M ) @ N ) = 31.89/4.69 ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ))). 31.89/4.69 thf('17', plain, 31.89/4.69 (( axmap ) = 31.89/4.69 ( ![X4:term,X6:subst,X8:subst]: 31.89/4.69 ( ( comp @ ( push @ X4 @ X6 ) @ X8 ) = 31.89/4.69 ( push @ ( sub @ X4 @ X8 ) @ ( comp @ X6 @ X8 ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(axassoc, axiom, axassoc = 31.89/4.69 (![M:subst,N:subst,K:subst]: 31.89/4.69 ( ( comp @ ( comp @ M @ N ) @ K ) = ( comp @ M @ ( comp @ N @ K ) ) ))). 31.89/4.69 thf('18', plain, 31.89/4.69 (( axassoc ) = 31.89/4.69 ( ![X4:subst,X6:subst,X8:subst]: 31.89/4.69 ( ( comp @ ( comp @ X4 @ X6 ) @ X8 ) = 31.89/4.69 ( comp @ X4 @ ( comp @ X6 @ X8 ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(axshiftcons, axiom, axshiftcons = 31.89/4.69 (![A:term,M:subst]: ( ( comp @ sh @ ( push @ A @ M ) ) = ( M ) ))). 31.89/4.69 thf('19', plain, 31.89/4.69 (( axshiftcons ) = 31.89/4.69 ( ![X4:term,X6:subst]: ( ( comp @ sh @ ( push @ X4 @ X6 ) ) = ( X6 ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(axidl, axiom, axidl = (![M:subst]: ( ( comp @ id @ M ) = ( M ) ))). 31.89/4.69 thf('20', plain, 31.89/4.69 (( axidl ) = ( ![X4:subst]: ( ( comp @ id @ X4 ) = ( X4 ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(axclos, axiom, axclos = 31.89/4.69 (![A:term,M:subst,N:subst]: 31.89/4.69 ( ( sub @ ( sub @ A @ M ) @ N ) = ( sub @ A @ ( comp @ M @ N ) ) ))). 31.89/4.69 thf('21', plain, 31.89/4.69 (( axclos ) = 31.89/4.69 ( ![X4:term,X6:subst,X8:subst]: 31.89/4.69 ( ( sub @ ( sub @ X4 @ X6 ) @ X8 ) = ( sub @ X4 @ ( comp @ X6 @ X8 ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(axabs, axiom, axabs = 31.89/4.69 (![A:term,M:subst]: 31.89/4.69 ( ( sub @ ( lam @ A ) @ M ) = 31.89/4.69 ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ))). 31.89/4.69 thf('22', plain, 31.89/4.69 (( axabs ) = 31.89/4.69 ( ![X4:term,X6:subst]: 31.89/4.69 ( ( sub @ ( lam @ X4 ) @ X6 ) = 31.89/4.69 ( lam @ ( sub @ X4 @ ( push @ one @ ( comp @ X6 @ sh ) ) ) ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(axvarid, axiom, axvarid = (![A:term]: ( ( sub @ A @ id ) = ( A ) ))). 31.89/4.69 thf('23', plain, 31.89/4.69 (( axvarid ) = ( ![X4:term]: ( ( sub @ X4 @ id ) = ( X4 ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(axvarcons, axiom, axvarcons = 31.89/4.69 (![A:term,M:subst]: ( ( sub @ one @ ( push @ A @ M ) ) = ( A ) ))). 31.89/4.69 thf('24', plain, 31.89/4.69 (( axvarcons ) = 31.89/4.69 ( ![X4:term,X6:subst]: ( ( sub @ one @ ( push @ X4 @ X6 ) ) = ( X4 ) ) )), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(axapp, axiom, axapp = 31.89/4.69 (![A:term,B:term,M:subst]: 31.89/4.69 ( ( sub @ ( ap @ A @ B ) @ M ) = 31.89/4.69 ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ))). 31.89/4.69 thf('25', plain, 31.89/4.69 (( axapp ) = 31.89/4.69 ( ![X4:term,X6:term,X8:subst]: 31.89/4.69 ( ( sub @ ( ap @ X4 @ X6 ) @ X8 ) = 31.89/4.69 ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) ) )), 31.89/4.69 define([status(thm)])).thf(thm, conjecture, (pushprop_gthm)). 31.89/4.69 thf(zf_stmt_0, conjecture, 31.89/4.69 (( ![X4:term,X6:term,X8:subst]: 31.89/4.69 ( ( sub @ ( ap @ X4 @ X6 ) @ X8 ) = 31.89/4.69 ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) ) ) => 31.89/4.69 ( ( ![X10:term,X12:subst]: 31.89/4.69 ( ( sub @ one @ ( push @ X10 @ X12 ) ) = ( X10 ) ) ) => 31.89/4.69 ( ( ![X14:term]: ( ( sub @ X14 @ id ) = ( X14 ) ) ) => 31.89/4.69 ( ( ![X16:term,X18:subst]: 31.89/4.69 ( ( sub @ ( lam @ X16 ) @ X18 ) = 31.89/4.69 ( lam @ ( sub @ X16 @ ( push @ one @ ( comp @ X18 @ sh ) ) ) ) ) ) => 31.89/4.69 ( ( ![X20:term,X22:subst,X24:subst]: 31.89/4.69 ( ( sub @ ( sub @ X20 @ X22 ) @ X24 ) = 31.89/4.69 ( sub @ X20 @ ( comp @ X22 @ X24 ) ) ) ) => 31.89/4.69 ( ( ![X26:subst]: ( ( comp @ id @ X26 ) = ( X26 ) ) ) => 31.89/4.69 ( ( ![X28:term,X30:subst]: 31.89/4.69 ( ( comp @ sh @ ( push @ X28 @ X30 ) ) = ( X30 ) ) ) => 31.89/4.69 ( ( ![X32:subst,X34:subst,X36:subst]: 31.89/4.69 ( ( comp @ ( comp @ X32 @ X34 ) @ X36 ) = 31.89/4.69 ( comp @ X32 @ ( comp @ X34 @ X36 ) ) ) ) => 31.89/4.69 ( ( ![X38:term,X40:subst,X42:subst]: 31.89/4.69 ( ( comp @ ( push @ X38 @ X40 ) @ X42 ) = 31.89/4.69 ( push @ ( sub @ X38 @ X42 ) @ ( comp @ X40 @ X42 ) ) ) ) => 31.89/4.69 ( ( ![X44:subst]: ( ( comp @ X44 @ id ) = ( X44 ) ) ) => 31.89/4.69 ( ( ( push @ one @ sh ) = ( id ) ) => 31.89/4.69 ( ( ![X46:subst]: 31.89/4.69 ( ( push @ 31.89/4.69 ( sub @ one @ X46 ) @ ( comp @ sh @ X46 ) ) = 31.89/4.69 ( X46 ) ) ) => 31.89/4.69 ( ( var @ one ) => 31.89/4.69 ( ( ![X48:term]: 31.89/4.69 ( ( var @ X48 ) => 31.89/4.69 ( var @ ( sub @ X48 @ sh ) ) ) ) => 31.89/4.69 ( ( ![X50:( term > $o )]: 31.89/4.69 ( ( X50 @ one ) => 31.89/4.69 ( ( ![X52:term]: 31.89/4.69 ( ( var @ X52 ) => 31.89/4.69 ( ( X50 @ X52 ) => 31.89/4.69 ( X50 @ ( sub @ X52 @ sh ) ) ) ) ) => 31.89/4.69 ( ![X54:term]: 31.89/4.69 ( ( var @ X54 ) => ( X50 @ X54 ) ) ) ) ) ) => 31.89/4.69 ( ( ![X56:term,X58:term,X60:term,X62:term]: 31.89/4.69 ( ( ( ap @ X56 @ X60 ) = 31.89/4.69 ( ap @ X58 @ X62 ) ) => 31.89/4.69 ( ( X56 ) = ( X58 ) ) ) ) => 31.89/4.69 ( ( ![X64:term,X66:term,X68:term,X70:term]: 31.89/4.69 ( ( ( ap @ X64 @ X68 ) = 31.89/4.69 ( ap @ X66 @ X70 ) ) => 31.89/4.69 ( ( X68 ) = ( X70 ) ) ) ) => 31.89/4.69 ( ( ![X72:term,X74:term]: 31.89/4.69 ( ( ( lam @ X72 ) = ( lam @ X74 ) ) => 31.89/4.69 ( ( X72 ) = ( X74 ) ) ) ) => 31.89/4.69 ( ( ![X76:term,X78:term]: 31.89/4.69 ( ( ( sub @ X76 @ sh ) = 31.89/4.69 ( sub @ X78 @ sh ) ) => 31.89/4.69 ( ( X76 ) = ( X78 ) ) ) ) => 31.89/4.69 ( ( ![X80:term,X82:term,X84:term]: 31.89/4.69 ( ( lam @ X80 ) != 31.89/4.69 ( ap @ X82 @ X84 ) ) ) => 31.89/4.69 ( ( ![X86:term,X88:term]: 31.89/4.69 ( ~( var @ ( ap @ X86 @ X88 ) ) ) ) => 31.89/4.69 ( ( ![X90:term]: 31.89/4.69 ( ~( var @ ( lam @ X90 ) ) ) ) => 31.89/4.69 ( ( ![X92:( term > $o )]: 31.89/4.69 ( ( ![X94:term]: 31.89/4.69 ( ( var @ X94 ) => 31.89/4.69 ( X92 @ X94 ) ) ) => 31.89/4.69 ( ( ![X96:term,X98:term]: 31.89/4.69 ( ( X92 @ X96 ) => 31.89/4.69 ( ( X92 @ X98 ) => 31.89/4.69 ( X92 @ 31.89/4.69 ( ap @ X96 @ X98 ) ) ) ) ) => 31.89/4.69 ( ( ![X100:term]: 31.89/4.69 ( ( X92 @ X100 ) => 31.89/4.69 ( X92 @ 31.89/4.69 ( lam @ X100 ) ) ) ) => 31.89/4.69 ( ![X102:term]: 31.89/4.69 ( X92 @ X102 ) ) ) ) ) ) => 31.89/4.69 ( ![X104:( term > $o ), 31.89/4.69 X106:term,X108:subst]: 31.89/4.69 ( ( ![X110:term]: 31.89/4.69 ( ( var @ X110 ) => 31.89/4.69 ( X104 @ 31.89/4.69 ( sub @ X110 @ X108 ) ) ) ) => 31.89/4.69 ( ( X104 @ X106 ) => 31.89/4.69 ( ![X112:term]: 31.89/4.69 ( ( var @ X112 ) => 31.89/4.69 ( X104 @ 31.89/4.69 ( sub @ 31.89/4.69 X112 @ 31.89/4.69 ( push @ 31.89/4.69 X106 @ X108 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 31.89/4.69 thf(zf_stmt_1, negated_conjecture, 31.89/4.69 (~( ( ![X4:term,X6:term,X8:subst]: 31.89/4.69 ( ( sub @ ( ap @ X4 @ X6 ) @ X8 ) = 31.89/4.69 ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) ) ) => 31.89/4.69 ( ( ![X10:term,X12:subst]: 31.89/4.69 ( ( sub @ one @ ( push @ X10 @ X12 ) ) = ( X10 ) ) ) => 31.89/4.69 ( ( ![X14:term]: ( ( sub @ X14 @ id ) = ( X14 ) ) ) => 31.89/4.69 ( ( ![X16:term,X18:subst]: 31.89/4.69 ( ( sub @ ( lam @ X16 ) @ X18 ) = 31.89/4.69 ( lam @ ( sub @ X16 @ ( push @ one @ ( comp @ X18 @ sh ) ) ) ) ) ) => 31.89/4.69 ( ( ![X20:term,X22:subst,X24:subst]: 31.89/4.69 ( ( sub @ ( sub @ X20 @ X22 ) @ X24 ) = 31.89/4.69 ( sub @ X20 @ ( comp @ X22 @ X24 ) ) ) ) => 31.89/4.69 ( ( ![X26:subst]: ( ( comp @ id @ X26 ) = ( X26 ) ) ) => 31.89/4.69 ( ( ![X28:term,X30:subst]: 31.89/4.69 ( ( comp @ sh @ ( push @ X28 @ X30 ) ) = ( X30 ) ) ) => 31.89/4.69 ( ( ![X32:subst,X34:subst,X36:subst]: 31.89/4.69 ( ( comp @ ( comp @ X32 @ X34 ) @ X36 ) = 31.89/4.69 ( comp @ X32 @ ( comp @ X34 @ X36 ) ) ) ) => 31.89/4.69 ( ( ![X38:term,X40:subst,X42:subst]: 31.89/4.69 ( ( comp @ ( push @ X38 @ X40 ) @ X42 ) = 31.89/4.69 ( push @ ( sub @ X38 @ X42 ) @ ( comp @ X40 @ X42 ) ) ) ) => 31.89/4.69 ( ( ![X44:subst]: ( ( comp @ X44 @ id ) = ( X44 ) ) ) => 31.89/4.69 ( ( ( push @ one @ sh ) = ( id ) ) => 31.89/4.69 ( ( ![X46:subst]: 31.89/4.69 ( ( push @ 31.89/4.69 ( sub @ one @ X46 ) @ ( comp @ sh @ X46 ) ) = 31.89/4.69 ( X46 ) ) ) => 31.89/4.69 ( ( var @ one ) => 31.89/4.69 ( ( ![X48:term]: 31.89/4.69 ( ( var @ X48 ) => 31.89/4.69 ( var @ ( sub @ X48 @ sh ) ) ) ) => 31.89/4.69 ( ( ![X50:( term > $o )]: 31.89/4.69 ( ( X50 @ one ) => 31.89/4.69 ( ( ![X52:term]: 31.89/4.69 ( ( var @ X52 ) => 31.89/4.69 ( ( X50 @ X52 ) => 31.89/4.69 ( X50 @ ( sub @ X52 @ sh ) ) ) ) ) => 31.89/4.69 ( ![X54:term]: 31.89/4.69 ( ( var @ X54 ) => ( X50 @ X54 ) ) ) ) ) ) => 31.89/4.69 ( ( ![X56:term,X58:term,X60:term,X62:term]: 31.89/4.69 ( ( ( ap @ X56 @ X60 ) = 31.89/4.69 ( ap @ X58 @ X62 ) ) => 31.89/4.69 ( ( X56 ) = ( X58 ) ) ) ) => 31.89/4.69 ( ( ![X64:term,X66:term,X68:term,X70:term]: 31.89/4.69 ( ( ( ap @ X64 @ X68 ) = 31.89/4.69 ( ap @ X66 @ X70 ) ) => 31.89/4.69 ( ( X68 ) = ( X70 ) ) ) ) => 31.89/4.69 ( ( ![X72:term,X74:term]: 31.89/4.69 ( ( ( lam @ X72 ) = ( lam @ X74 ) ) => 31.89/4.69 ( ( X72 ) = ( X74 ) ) ) ) => 31.89/4.69 ( ( ![X76:term,X78:term]: 31.89/4.69 ( ( ( sub @ X76 @ sh ) = 31.89/4.69 ( sub @ X78 @ sh ) ) => 31.89/4.69 ( ( X76 ) = ( X78 ) ) ) ) => 31.89/4.69 ( ( ![X80:term,X82:term,X84:term]: 31.89/4.69 ( ( lam @ X80 ) != 31.89/4.69 ( ap @ X82 @ X84 ) ) ) => 31.89/4.69 ( ( ![X86:term,X88:term]: 31.89/4.69 ( ~( var @ ( ap @ X86 @ X88 ) ) ) ) => 31.89/4.69 ( ( ![X90:term]: 31.89/4.69 ( ~( var @ ( lam @ X90 ) ) ) ) => 31.89/4.69 ( ( ![X92:( term > $o )]: 31.89/4.69 ( ( ![X94:term]: 31.89/4.69 ( ( var @ X94 ) => 31.89/4.69 ( X92 @ X94 ) ) ) => 31.89/4.69 ( ( ![X96:term,X98:term]: 31.89/4.69 ( ( X92 @ X96 ) => 31.89/4.69 ( ( X92 @ X98 ) => 31.89/4.69 ( X92 @ 31.89/4.69 ( ap @ 31.89/4.69 X96 @ X98 ) ) ) ) ) => 31.89/4.69 ( ( ![X100:term]: 31.89/4.69 ( ( X92 @ X100 ) => 31.89/4.69 ( X92 @ 31.89/4.69 ( lam @ X100 ) ) ) ) => 31.89/4.69 ( ![X102:term]: 31.89/4.69 ( X92 @ X102 ) ) ) ) ) ) => 31.89/4.69 ( ![X104:( term > $o ), 31.89/4.69 X106:term,X108:subst]: 31.89/4.69 ( ( ![X110:term]: 31.89/4.69 ( ( var @ X110 ) => 31.89/4.69 ( X104 @ 31.89/4.69 ( sub @ 31.89/4.69 X110 @ X108 ) ) ) ) => 31.89/4.69 ( ( X104 @ X106 ) => 31.89/4.69 ( ![X112:term]: 31.89/4.69 ( ( var @ X112 ) => 31.89/4.69 ( X104 @ 31.89/4.69 ( sub @ 31.89/4.69 X112 @ 31.89/4.69 ( push @ 31.89/4.69 X106 @ X108 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 31.89/4.69 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 31.89/4.69 thf(zip_derived_cl0, plain, 31.89/4.69 (~ (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((sub @ (ap @ Y0 @ Y1) @ Y2) = 31.89/4.69 (ap @ (sub @ Y0 @ Y2) @ 31.89/4.69 (sub @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((sub @ one @ (push @ Y0 @ Y1)) = (Y0))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((sub @ (lam @ Y0) @ Y1) = (lam @ 31.89/4.69 (sub @ Y0 @ 31.89/4.69 (push @ one @ (comp @ Y1 @ sh)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((sub @ 31.89/4.69 (sub @ Y0 @ Y1) @ 31.89/4.69 Y2) = (sub @ Y0 @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((comp @ sh @ 31.89/4.69 (push @ Y0 @ Y1)) = (Y1))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((comp @ 31.89/4.69 (comp @ Y0 @ Y1) @ 31.89/4.69 Y2) = (comp @ 31.89/4.69 Y0 @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((comp @ 31.89/4.69 (push @ Y0 @ 31.89/4.69 Y1) @ 31.89/4.69 Y2) = (push @ 31.89/4.69 (sub @ Y0 @ Y2) @ 31.89/4.69 (comp @ Y1 @ 31.89/4.69 Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((comp @ Y0 @ id) = (Y0)))))) => 31.89/4.69 (((((push @ one @ sh) = (id))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((push @ (sub @ one @ Y0) @ 31.89/4.69 (comp @ sh @ Y0)) = (Y0)))))) => 31.89/4.69 (((var @ one) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => (var @ 31.89/4.69 (sub @ Y0 @ sh))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((Y0 @ one) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ 31.89/4.69 Y1) => 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ 31.89/4.69 Y1 @ sh))))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ Y1))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (ap @ 31.89/4.69 Y0 @ 31.89/4.69 Y2) = 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y3))) => 31.89/4.69 (( 31.89/4.69 (Y0) = 31.89/4.69 (Y1))))))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (ap @ 31.89/4.69 Y0 @ 31.89/4.69 Y2) = 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y3))) => 31.89/4.69 (( 31.89/4.69 (Y2) = 31.89/4.69 (Y3))))))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (lam @ 31.89/4.69 Y0) = 31.89/4.69 (lam @ 31.89/4.69 Y1))) => 31.89/4.69 (( 31.89/4.69 (Y0) = 31.89/4.69 (Y1))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (sub @ 31.89/4.69 Y0 @ 31.89/4.69 sh) = 31.89/4.69 (sub @ 31.89/4.69 Y1 @ sh))) => 31.89/4.69 (( 31.89/4.69 (Y0) = 31.89/4.69 (Y1))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (lam @ 31.89/4.69 Y0) != 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (((~) @ ( 31.89/4.69 var @ 31.89/4.69 (ap @ 31.89/4.69 Y0 @ Y1)))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((~) @ ( 31.89/4.69 var @ 31.89/4.69 (lam @ Y0))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ Y1)))))) => 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y2) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 lam @ Y1))))))) => 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (Y0 @ Y1))))))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y2 : subst]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ Y2))))))) => 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ 31.89/4.69 ( 31.89/4.69 push @ 31.89/4.69 Y1 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 31.89/4.69 inference('cnf', [status(esa)], [zf_stmt_1])). 31.89/4.69 thf(zip_derived_cl2, plain, 31.89/4.69 (~ (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((sub @ one @ (push @ Y0 @ Y1)) = (Y0))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((sub @ (lam @ Y0) @ Y1) = (lam @ 31.89/4.69 (sub @ Y0 @ 31.89/4.69 (push @ one @ (comp @ Y1 @ sh)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((sub @ 31.89/4.69 (sub @ Y0 @ Y1) @ Y2) = 31.89/4.69 (sub @ Y0 @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((comp @ sh @ (push @ Y0 @ Y1)) = 31.89/4.69 (Y1))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((comp @ 31.89/4.69 (comp @ Y0 @ Y1) @ 31.89/4.69 Y2) = (comp @ 31.89/4.69 Y0 @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((comp @ 31.89/4.69 (push @ Y0 @ Y1) @ 31.89/4.69 Y2) = (push @ 31.89/4.69 (sub @ Y0 @ Y2) @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 31.89/4.69 (((((push @ one @ sh) = (id))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((push @ (sub @ one @ Y0) @ 31.89/4.69 (comp @ sh @ Y0)) = (Y0)))))) => 31.89/4.69 (((var @ one) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => (var @ 31.89/4.69 (sub @ Y0 @ sh))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((Y0 @ one) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ 31.89/4.69 Y1) => 31.89/4.69 (((Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ 31.89/4.69 Y1 @ sh))))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ Y1))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (ap @ 31.89/4.69 Y0 @ 31.89/4.69 Y2) = 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y3))) => 31.89/4.69 (( 31.89/4.69 (Y0) = 31.89/4.69 (Y1))))))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (ap @ 31.89/4.69 Y0 @ 31.89/4.69 Y2) = 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y3))) => 31.89/4.69 (( 31.89/4.69 (Y2) = 31.89/4.69 (Y3))))))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((( 31.89/4.69 (lam @ 31.89/4.69 Y0) = 31.89/4.69 (lam @ Y1))) => 31.89/4.69 (( 31.89/4.69 (Y0) = 31.89/4.69 (Y1))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (sub @ 31.89/4.69 Y0 @ 31.89/4.69 sh) = 31.89/4.69 (sub @ 31.89/4.69 Y1 @ sh))) => 31.89/4.69 (( 31.89/4.69 (Y0) = 31.89/4.69 (Y1))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (lam @ 31.89/4.69 Y0) != 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (((~) @ ( 31.89/4.69 var @ 31.89/4.69 (ap @ Y0 @ 31.89/4.69 Y1)))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((~) @ ( 31.89/4.69 var @ 31.89/4.69 (lam @ Y0))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ Y1)))))) => 31.89/4.69 (((( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y2) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 lam @ Y1))))))) => 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (Y0 @ Y1))))))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y2 : subst]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ Y2))))))) => 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ 31.89/4.69 ( 31.89/4.69 push @ 31.89/4.69 Y1 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 31.89/4.69 thf(zip_derived_cl5, plain, 31.89/4.69 (~ (((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((sub @ (lam @ Y0) @ Y1) = (lam @ 31.89/4.69 (sub @ Y0 @ 31.89/4.69 (push @ one @ (comp @ Y1 @ sh)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((sub @ (sub @ Y0 @ Y1) @ 31.89/4.69 Y2) = (sub @ Y0 @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((comp @ sh @ (push @ Y0 @ Y1)) = 31.89/4.69 (Y1))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((comp @ 31.89/4.69 (comp @ Y0 @ Y1) @ 31.89/4.69 Y2) = (comp @ Y0 @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((comp @ 31.89/4.69 (push @ Y0 @ Y1) @ 31.89/4.69 Y2) = (push @ 31.89/4.69 (sub @ Y0 @ Y2) @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 31.89/4.69 (((((push @ one @ sh) = (id))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((push @ (sub @ one @ Y0) @ 31.89/4.69 (comp @ sh @ Y0)) = (Y0)))))) => 31.89/4.69 (((var @ one) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => (var @ 31.89/4.69 (sub @ Y0 @ sh))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((Y0 @ one) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ Y1 @ 31.89/4.69 sh))))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => 31.89/4.69 (Y0 @ Y1))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (ap @ 31.89/4.69 Y0 @ 31.89/4.69 Y2) = 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y3))) => 31.89/4.69 (( 31.89/4.69 (Y0) = 31.89/4.69 (Y1))))))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (ap @ 31.89/4.69 Y0 @ 31.89/4.69 Y2) = 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y3))) => 31.89/4.69 (( 31.89/4.69 (Y2) = 31.89/4.69 (Y3))))))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((((lam @ 31.89/4.69 Y0) = 31.89/4.69 (lam @ Y1))) => 31.89/4.69 (((Y0) = 31.89/4.69 (Y1))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((( 31.89/4.69 (sub @ 31.89/4.69 Y0 @ sh) = 31.89/4.69 (sub @ 31.89/4.69 Y1 @ sh))) => 31.89/4.69 (( 31.89/4.69 (Y0) = 31.89/4.69 (Y1))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (lam @ 31.89/4.69 Y0) != 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (~) @ ( 31.89/4.69 var @ 31.89/4.69 ( 31.89/4.69 ap @ 31.89/4.69 Y0 @ Y1)))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((~) @ (var @ 31.89/4.69 ( 31.89/4.69 lam @ Y0))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ Y1)))))) => 31.89/4.69 (((((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y2) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (((( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 lam @ Y1))))))) => 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (Y0 @ Y1))))))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y2 : subst]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ Y2))))))) => 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ 31.89/4.69 ( 31.89/4.69 push @ 31.89/4.69 Y1 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 31.89/4.69 thf(zip_derived_cl9, plain, 31.89/4.69 (~ (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((sub @ (lam @ Y0) @ Y1) = (lam @ 31.89/4.69 (sub @ Y0 @ 31.89/4.69 (push @ one @ (comp @ Y1 @ sh)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((sub @ (sub @ Y0 @ Y1) @ 31.89/4.69 Y2) = (sub @ Y0 @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((comp @ sh @ (push @ Y0 @ Y1)) = 31.89/4.69 (Y1))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((comp @ 31.89/4.69 (comp @ Y0 @ Y1) @ 31.89/4.69 Y2) = (comp @ Y0 @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((comp @ 31.89/4.69 (push @ Y0 @ Y1) @ 31.89/4.69 Y2) = (push @ 31.89/4.69 (sub @ Y0 @ Y2) @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 31.89/4.69 (((((push @ one @ sh) = (id))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((push @ (sub @ one @ Y0) @ 31.89/4.69 (comp @ sh @ Y0)) = (Y0)))))) => 31.89/4.69 (((var @ one) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => (var @ 31.89/4.69 (sub @ Y0 @ sh))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((Y0 @ one) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ Y1 @ sh))))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => 31.89/4.69 (Y0 @ Y1))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (ap 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(( 31.89/4.69 (lam @ 31.89/4.69 Y0) != 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (~) @ ( 31.89/4.69 var @ 31.89/4.69 ( 31.89/4.69 ap @ 31.89/4.69 Y0 @ Y1)))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((~) @ (var @ 31.89/4.69 (lam @ Y0))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (((var @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ Y1)))))) => 31.89/4.69 (((((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y2) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 lam @ Y1))))))) => 31.89/4.69 (((!!) @ ( 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31.89/4.69 (sub @ Y0 @ (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((comp @ sh @ (push @ Y0 @ Y1)) = (Y1))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((comp @ 31.89/4.69 (comp @ Y0 @ Y1) @ Y2) = 31.89/4.69 (comp @ Y0 @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((comp @ 31.89/4.69 (push @ Y0 @ Y1) @ 31.89/4.69 Y2) = (push @ 31.89/4.69 (sub @ Y0 @ Y2) @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 31.89/4.69 (((((push @ one @ sh) = (id))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((push @ (sub @ one @ Y0) @ 31.89/4.69 (comp @ sh @ Y0)) = (Y0)))))) => 31.89/4.69 (((var @ one) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => (var @ 31.89/4.69 (sub @ Y0 @ sh))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((Y0 @ one) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ Y1 @ sh))))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => 31.89/4.69 (Y0 @ Y1))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (ap @ 31.89/4.69 Y0 @ 31.89/4.69 Y2) = 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y3))) => 31.89/4.69 (( 31.89/4.69 (Y0) = 31.89/4.69 (Y1))))))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (ap @ 31.89/4.69 Y0 @ 31.89/4.69 Y2) = 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y3))) => 31.89/4.69 (( 31.89/4.69 (Y2) = 31.89/4.69 (Y3))))))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((((lam @ Y0) = 31.89/4.69 (lam @ Y1))) => 31.89/4.69 (((Y0) = (Y1))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((((sub @ Y0 @ 31.89/4.69 sh) = 31.89/4.69 (sub @ Y1 @ 31.89/4.69 sh))) => 31.89/4.69 (((Y0) = (Y1))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (lam @ 31.89/4.69 Y0) != 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((~) @ ( 31.89/4.69 var @ 31.89/4.69 (ap @ 31.89/4.69 Y0 @ Y1)))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((~) @ (var @ 31.89/4.69 (lam @ Y0))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (((var @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ Y1)))))) => 31.89/4.69 (((((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y2) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 lam @ Y1))))))) => 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (Y0 @ Y1))))))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y2 : subst]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ Y2))))))) => 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ 31.89/4.69 ( 31.89/4.69 push @ 31.89/4.69 Y1 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 31.89/4.69 thf(zip_derived_cl20, plain, 31.89/4.69 (~ (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((comp @ sh @ (push @ Y0 @ Y1)) = (Y1))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((comp @ 31.89/4.69 (comp @ Y0 @ Y1) @ Y2) = 31.89/4.69 (comp @ Y0 @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ 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: term]: 31.89/4.69 (((lam @ 31.89/4.69 Y0) != 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((~) @ ( 31.89/4.69 var @ 31.89/4.69 (ap @ Y0 @ 31.89/4.69 Y1)))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((~) @ (var @ 31.89/4.69 (lam @ Y0))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ Y1)))))) => 31.89/4.69 (((((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y2 : term]: 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y2) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (((Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (Y0 @ 31.89/4.69 (lam @ Y1))))))) => 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y1 : term]: 31.89/4.69 (Y0 @ Y1))))))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y2 : subst]: 31.89/4.69 (( 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ Y2))))))) => 31.89/4.69 (( 31.89/4.69 (Y0 @ 31.89/4.69 Y1) => 31.89/4.69 (( 31.89/4.69 (!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ 31.89/4.69 ( 31.89/4.69 push @ 31.89/4.69 Y1 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 31.89/4.69 thf(zip_derived_cl24, plain, 31.89/4.69 (~ (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((comp @ sh @ (push @ Y0 @ Y1)) = (Y1))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((comp @ (comp @ Y0 @ Y1) @ 31.89/4.69 Y2) = (comp @ Y0 @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((comp @ 31.89/4.69 (push @ Y0 @ Y1) @ Y2) = 31.89/4.69 (push @ (sub @ Y0 @ Y2) @ 31.89/4.69 (comp @ Y1 @ Y2))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 31.89/4.69 (((((push @ one @ sh) = (id))) => 31.89/4.69 (((((!!) @ (^[Y0 : subst]: 31.89/4.69 (((push @ (sub @ one @ Y0) @ 31.89/4.69 (comp @ sh @ Y0)) = (Y0)))))) => 31.89/4.69 (((var @ one) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((Y0 @ one) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => 31.89/4.69 (((Y0 @ Y1) => (Y0 @ 31.89/4.69 (sub @ Y1 @ sh))))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: 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=> 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => (Y0 @ Y1)))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((Y0 @ 31.89/4.69 Y2) => 31.89/4.69 (Y0 @ 31.89/4.69 (ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((Y0 @ Y1) => (Y0 @ 31.89/4.69 (lam @ Y1))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((((!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (((var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ 31.89/4.69 Y3 @ Y2))))))) => 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ 31.89/4.69 ( 31.89/4.69 push @ 31.89/4.69 Y1 @ Y2)))))))))))))))))))))))))))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 31.89/4.69 thf(zip_derived_cl69, plain, 31.89/4.69 (~ (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (((!!) @ (^[Y3 : term]: 31.89/4.69 (((((ap @ Y0 @ Y2) = 31.89/4.69 (ap @ Y1 @ Y3))) => 31.89/4.69 (((Y2) = (Y3))))))))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((((lam @ Y0) = (lam @ Y1))) => 31.89/4.69 (((Y0) = (Y1))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((((sub @ Y0 @ sh) = (sub @ Y1 @ sh))) => 31.89/4.69 (((Y0) = (Y1))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (((lam @ Y0) != (ap @ 31.89/4.69 Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => (Y0 @ Y1)))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((Y0 @ Y2) => 31.89/4.69 (Y0 @ 31.89/4.69 (ap @ Y1 @ 31.89/4.69 Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((Y0 @ Y1) => (Y0 @ 31.89/4.69 (lam @ Y1))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((((!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (((var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ Y3 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Y1)))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => (Y0 @ Y1)))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((Y0 @ Y2) => 31.89/4.69 (Y0 @ 31.89/4.69 (ap @ Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((Y0 @ Y1) => (Y0 @ 31.89/4.69 (lam @ Y1))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((((!!) @ (^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ Y2))))))) => 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((!!) @ ( 31.89/4.69 ^[Y3 : term]: 31.89/4.69 (((var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ Y3 @ 31.89/4.69 (push @ 31.89/4.69 Y1 @ Y2)))))))))))))))))))))))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])). 31.89/4.69 thf(zip_derived_cl78, plain, 31.89/4.69 (~ (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((((sub @ Y0 @ sh) = (sub @ Y1 @ sh))) => 31.89/4.69 (((Y0) = (Y1))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (((lam @ Y0) != (ap @ Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => (Y0 @ Y1)))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((Y0 @ Y2) => 31.89/4.69 (Y0 @ 31.89/4.69 (ap @ Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((Y0 @ Y1) => (Y0 @ 31.89/4.69 (lam @ Y1))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((((!!) @ (^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ Y2))))))) => 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((!!) @ (^[Y3 : term]: 31.89/4.69 (( 31.89/4.69 (var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ 31.89/4.69 ( 31.89/4.69 push @ 31.89/4.69 Y1 @ Y2)))))))))))))))))))))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 31.89/4.69 thf(zip_derived_cl84, plain, 31.89/4.69 (~ (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (((lam @ Y0) != (ap @ Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ 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(Y0 @ 31.89/4.69 ( 31.89/4.69 sub @ 31.89/4.69 Y3 @ 31.89/4.69 ( 31.89/4.69 push @ 31.89/4.69 Y1 @ Y2)))))))))))))))))))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 31.89/4.69 thf(zip_derived_cl92, plain, 31.89/4.69 (~ (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : term]: (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => (Y0 @ Y1)))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((Y0 @ Y2) => (Y0 @ 31.89/4.69 (ap @ Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((Y0 @ Y1) => (Y0 @ (lam @ Y1))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((((!!) @ (^[Y3 : term]: 31.89/4.69 (((var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ Y3 @ 31.89/4.69 Y2))))))) => 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((!!) @ (^[Y3 : term]: 31.89/4.69 (((var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ 31.89/4.69 Y3 @ 31.89/4.69 ( 31.89/4.69 push @ 31.89/4.69 Y1 @ Y2)))))))))))))))))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl84])). 31.89/4.69 thf(zip_derived_cl102, plain, 31.89/4.69 (~ (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 31.89/4.69 (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((Y0 @ Y2) => (Y0 @ 31.89/4.69 (ap @ Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((Y0 @ Y1) => (Y0 @ (lam @ Y1))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((((!!) @ (^[Y3 : term]: 31.89/4.69 (((var @ Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ Y3 @ Y2))))))) => 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((!!) @ (^[Y3 : term]: 31.89/4.69 (((var @ 31.89/4.69 Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ Y3 @ 31.89/4.69 (push @ 31.89/4.69 Y1 @ Y2)))))))))))))))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 31.89/4.69 thf(zip_derived_cl113, plain, 31.89/4.69 (~ (((((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((Y0 @ Y2) => (Y0 @ 31.89/4.69 (ap @ Y1 @ Y2)))))))))))) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((Y0 @ Y1) => (Y0 @ (lam @ Y1))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((((!!) @ (^[Y3 : term]: 31.89/4.69 (((var @ Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ Y3 @ Y2))))))) => 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((!!) @ (^[Y3 : term]: 31.89/4.69 (((var @ Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ Y3 @ 31.89/4.69 (push @ Y1 @ 31.89/4.69 Y2)))))))))))))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])). 31.89/4.69 thf(zip_derived_cl122, plain, 31.89/4.69 (~ (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((((!!) @ (^[Y3 : term]: 31.89/4.69 (((var @ Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ Y3 @ Y2))))))) => 31.89/4.69 (((Y0 @ Y1) => 31.89/4.69 (((!!) @ (^[Y3 : term]: 31.89/4.69 (((var @ Y3) => 31.89/4.69 (Y0 @ 31.89/4.69 (sub @ Y3 @ 31.89/4.69 (push @ Y1 @ Y2)))))))))))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 31.89/4.69 thf(zip_derived_cl127, plain, 31.89/4.69 (~ (((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((((!!) @ (^[Y2 : term]: 31.89/4.69 (((var @ Y2) => ('#sk30' @ 31.89/4.69 (sub @ Y2 @ Y1))))))) => 31.89/4.69 ((('#sk30' @ Y0) => 31.89/4.69 (((!!) @ (^[Y2 : term]: 31.89/4.69 (((var @ Y2) => ('#sk30' @ 31.89/4.69 (sub @ Y2 @ (push @ Y0 @ Y1))))))))))))))))))), 31.89/4.69 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl122])). 31.89/4.69 thf(zip_derived_cl129, plain, 31.89/4.69 (~ (((!!) @ (^[Y0 : subst]: 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => ('#sk30' @ (sub @ Y1 @ Y0))))))) => 31.89/4.69 ((('#sk30' @ '#sk39') => 31.89/4.69 (((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => ('#sk30' @ 31.89/4.69 (sub @ Y1 @ (push @ '#sk39' @ Y0)))))))))))))))), 31.89/4.69 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl127])). 31.89/4.69 thf(zip_derived_cl131, plain, 31.89/4.69 (~ (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ (sub @ Y0 @ '#sk49'))))))) => 31.89/4.69 ((('#sk30' @ '#sk39') => 31.89/4.69 (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))))))))))), 31.89/4.69 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl129])). 31.89/4.69 thf(zip_derived_cl135, plain, 31.89/4.69 (~ ((('#sk30' @ '#sk39') => 31.89/4.69 (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl131])). 31.89/4.69 thf(zip_derived_cl140, plain, 31.89/4.69 (~ (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl135])). 31.89/4.69 thf(zip_derived_cl144, plain, 31.89/4.69 (~ (((var @ 31.89/4.69 ('#sk48' @ 31.89/4.69 (^[Y0 : term]: ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49')))))) => 31.89/4.69 ('#sk30' @ 31.89/4.69 (sub @ 31.89/4.69 ('#sk48' @ 31.89/4.69 (^[Y0 : term]: ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))) @ 31.89/4.69 (push @ '#sk39' @ '#sk49')))))), 31.89/4.69 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl140])). 31.89/4.69 thf(zip_derived_cl147, plain, 31.89/4.69 ( (var @ 31.89/4.69 ('#sk48' @ 31.89/4.69 (^[Y0 : term]: ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 31.89/4.69 thf(zip_derived_cl147, plain, 31.89/4.69 ( (var @ 31.89/4.69 ('#sk48' @ 31.89/4.69 (^[Y0 : term]: ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 31.89/4.69 thf(zip_derived_cl8801, plain, 31.89/4.69 (![X1 : term]: 31.89/4.69 (('#l_lift9963' @ X1) 31.89/4.69 = ('#sk30' @ (sub @ X1 @ (push @ '#sk39' @ '#sk49'))))), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(zip_derived_cl8802, plain, ( (var @ ('#sk48' @ '#l_lift9963'))), 31.89/4.69 inference('lambda_lifting', [status(thm)], 31.89/4.69 [zip_derived_cl147, zip_derived_cl8801])). 31.89/4.69 thf(zip_derived_cl148, plain, 31.89/4.69 (~ ('#sk30' @ 31.89/4.69 (sub @ 31.89/4.69 ('#sk48' @ 31.89/4.69 (^[Y0 : term]: ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))) @ 31.89/4.69 (push @ '#sk39' @ '#sk49')))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 31.89/4.69 thf(zip_derived_cl8801, plain, 31.89/4.69 (![X1 : term]: 31.89/4.69 (('#l_lift9963' @ X1) 31.89/4.69 = ('#sk30' @ (sub @ X1 @ (push @ '#sk39' @ '#sk49'))))), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(zip_derived_cl8803, plain, 31.89/4.69 (~ ('#sk30' @ 31.89/4.69 (sub @ ('#sk48' @ '#l_lift9963') @ (push @ '#sk39' @ '#sk49')))), 31.89/4.69 inference('lambda_lifting', [status(thm)], 31.89/4.69 [zip_derived_cl148, zip_derived_cl8801])). 31.89/4.69 thf(zip_derived_cl134, plain, 31.89/4.69 ( (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ (sub @ Y0 @ '#sk49')))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl131])). 31.89/4.69 thf(zip_derived_cl138, plain, 31.89/4.69 (![X2 : term]: (((var @ X2) => ('#sk30' @ (sub @ X2 @ '#sk49'))))), 31.89/4.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl134])). 31.89/4.69 thf(zip_derived_cl143, plain, 31.89/4.69 (![X2 : term]: (~ (var @ X2) | ('#sk30' @ (sub @ X2 @ '#sk49')))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl138])). 31.89/4.69 thf(zip_derived_cl64, plain, 31.89/4.69 ( (((!!) @ (^[Y0 : term > $o]: 31.89/4.69 (((Y0 @ one) => 31.89/4.69 (((((!!) @ (^[Y1 : term]: 31.89/4.69 (((var @ Y1) => 31.89/4.69 (((Y0 @ Y1) => (Y0 @ (sub @ Y1 @ sh))))))))) => 31.89/4.69 (((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 31.89/4.69 thf(zip_derived_cl67, plain, 31.89/4.69 (![X2 : term > $o]: 31.89/4.69 (((X2 @ one) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => 31.89/4.69 (((X2 @ Y0) => (X2 @ (sub @ Y0 @ sh))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0))))))))))), 31.89/4.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 31.89/4.69 thf(zip_derived_cl171, plain, 31.89/4.69 ( ((('#sk30' @ (sub @ one @ (push @ '#sk39' @ '#sk49'))) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => 31.89/4.69 ((('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))) => 31.89/4.69 ('#sk30' @ 31.89/4.69 (sub @ (sub @ Y0 @ sh) @ (push @ '#sk39' @ '#sk49')))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))))))))))), 31.89/4.69 inference('triggered_bool_instantiation', [status(thm)], 31.89/4.69 [zip_derived_cl67])). 31.89/4.69 thf(zip_derived_cl4, plain, 31.89/4.69 ( (((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((sub @ one @ (push @ Y0 @ Y1)) = (Y0)))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 31.89/4.69 thf(zip_derived_cl7, plain, 31.89/4.69 (![X2 : term]: 31.89/4.69 (((!!) @ (^[Y0 : subst]: (((sub @ one @ (push @ X2 @ Y0)) = (X2))))))), 31.89/4.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 31.89/4.69 thf(zip_derived_cl11, plain, 31.89/4.69 (![X2 : term, X4 : subst]: (((sub @ one @ (push @ X2 @ X4)) = (X2)))), 31.89/4.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 31.89/4.69 thf(zip_derived_cl16, plain, 31.89/4.69 (![X2 : term, X4 : subst]: ((sub @ one @ (push @ X2 @ X4)) = (X2))), 31.89/4.69 inference('simplify nested equalities', [status(thm)], [zip_derived_cl11])). 31.89/4.69 thf(zip_derived_cl139, plain, ( ('#sk30' @ '#sk39')), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl135])). 31.89/4.69 thf(zip_derived_cl205, plain, 31.89/4.69 ( ((($true) => 31.89/4.69 (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => 31.89/4.69 ((('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))) => 31.89/4.69 ('#sk30' @ 31.89/4.69 (sub @ (sub @ Y0 @ sh) @ (push @ '#sk39' @ '#sk49')))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))))))))))), 31.89/4.69 inference('demod', [status(thm)], 31.89/4.69 [zip_derived_cl171, zip_derived_cl16, zip_derived_cl139])). 31.89/4.69 thf(zip_derived_cl206, plain, 31.89/4.69 ( (((((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => 31.89/4.69 ((('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))) => 31.89/4.69 ('#sk30' @ 31.89/4.69 (sub @ (sub @ Y0 @ sh) @ (push @ '#sk39' @ '#sk49')))))))))) => 31.89/4.69 (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))))))))), 31.89/4.69 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl205])). 31.89/4.69 thf(zip_derived_cl207, plain, 31.89/4.69 ((~ (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => 31.89/4.69 ((('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))) => 31.89/4.69 ('#sk30' @ 31.89/4.69 (sub @ (sub @ Y0 @ sh) @ (push @ '#sk39' @ '#sk49')))))))))) 31.89/4.69 | (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49')))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])). 31.89/4.69 thf(zip_derived_cl208, plain, 31.89/4.69 ((~ (((var @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49')))))) => 31.89/4.69 ((('#sk30' @ 31.89/4.69 (sub @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: 31.89/4.69 ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))) @ 31.89/4.69 (push @ '#sk39' @ '#sk49'))) => 31.89/4.69 ('#sk30' @ 31.89/4.69 (sub @ 31.89/4.69 (sub @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: 31.89/4.69 ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))) @ 31.89/4.69 sh) @ 31.89/4.69 (push @ '#sk39' @ '#sk49'))))))) 31.89/4.69 | (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49')))))))))), 31.89/4.69 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl207])). 31.89/4.69 thf(zip_derived_cl19, plain, 31.89/4.69 ( (((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((!!) @ (^[Y2 : subst]: 31.89/4.69 (((sub @ (sub @ Y0 @ Y1) @ Y2) = 31.89/4.69 (sub @ Y0 @ (comp @ Y1 @ Y2)))))))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 31.89/4.69 thf(zip_derived_cl22, plain, 31.89/4.69 (![X2 : term]: 31.89/4.69 (((!!) @ (^[Y0 : subst]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((sub @ (sub @ X2 @ Y0) @ Y1) = (sub @ X2 @ 31.89/4.69 (comp @ Y0 @ Y1))))))))))), 31.89/4.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 31.89/4.69 thf(zip_derived_cl26, plain, 31.89/4.69 (![X2 : term, X4 : subst]: 31.89/4.69 (((!!) @ (^[Y0 : subst]: 31.89/4.69 (((sub @ (sub @ X2 @ X4) @ Y0) = (sub @ X2 @ 31.89/4.69 (comp @ X4 @ Y0)))))))), 31.89/4.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 31.89/4.69 thf(zip_derived_cl30, plain, 31.89/4.69 (![X2 : term, X4 : subst, X6 : subst]: 31.89/4.69 (((sub @ (sub @ X2 @ X4) @ X6) = (sub @ X2 @ (comp @ X4 @ X6))))), 31.89/4.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 31.89/4.69 thf(zip_derived_cl35, plain, 31.89/4.69 (![X2 : term, X4 : subst, X6 : subst]: 31.89/4.69 ((sub @ (sub @ X2 @ X4) @ X6) = (sub @ X2 @ (comp @ X4 @ X6)))), 31.89/4.69 inference('simplify nested equalities', [status(thm)], [zip_derived_cl30])). 31.89/4.69 thf(zip_derived_cl28, plain, 31.89/4.69 ( (((!!) @ (^[Y0 : term]: 31.89/4.69 (((!!) @ (^[Y1 : subst]: 31.89/4.69 (((comp @ sh @ (push @ Y0 @ Y1)) = (Y1)))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 31.89/4.69 thf(zip_derived_cl32, plain, 31.89/4.69 (![X2 : term]: 31.89/4.69 (((!!) @ (^[Y0 : subst]: (((comp @ sh @ (push @ X2 @ Y0)) = (Y0))))))), 31.89/4.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 31.89/4.69 thf(zip_derived_cl36, plain, 31.89/4.69 (![X2 : term, X4 : subst]: (((comp @ sh @ (push @ X2 @ X4)) = (X4)))), 31.89/4.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 31.89/4.69 thf(zip_derived_cl40, plain, 31.89/4.69 (![X2 : term, X4 : subst]: ((comp @ sh @ (push @ X2 @ X4)) = (X4))), 31.89/4.69 inference('simplify nested equalities', [status(thm)], [zip_derived_cl36])). 31.89/4.69 thf(zip_derived_cl209, plain, 31.89/4.69 ((~ (((var @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49')))))) => 31.89/4.69 ((('#sk30' @ 31.89/4.69 (sub @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: 31.89/4.69 ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))) @ 31.89/4.69 (push @ '#sk39' @ '#sk49'))) => 31.89/4.69 ('#sk30' @ 31.89/4.69 (sub @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: 31.89/4.69 ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))) @ 31.89/4.69 '#sk49')))))) 31.89/4.69 | (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49')))))))))), 31.89/4.69 inference('demod', [status(thm)], 31.89/4.69 [zip_derived_cl208, zip_derived_cl35, zip_derived_cl40])). 31.89/4.69 thf(zip_derived_cl211, plain, 31.89/4.69 ((~ ((('#sk30' @ 31.89/4.69 (sub @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: 31.89/4.69 ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))) @ 31.89/4.69 (push @ '#sk39' @ '#sk49'))) => 31.89/4.69 ('#sk30' @ 31.89/4.69 (sub @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: 31.89/4.69 ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))) @ 31.89/4.69 '#sk49')))) 31.89/4.69 | (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49')))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl209])). 31.89/4.69 thf(zip_derived_cl214, plain, 31.89/4.69 ((~ ('#sk30' @ 31.89/4.69 (sub @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))) @ 31.89/4.69 '#sk49')) 31.89/4.69 | (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49')))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl211])). 31.89/4.69 thf(zip_derived_cl217, plain, 31.89/4.69 (![X2 : term]: 31.89/4.69 ( (((var @ X2) => ('#sk30' @ (sub @ X2 @ (push @ '#sk39' @ '#sk49'))))) 31.89/4.69 | ~ ('#sk30' @ 31.89/4.69 (sub @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: 31.89/4.69 ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))) @ 31.89/4.69 '#sk49')))), 31.89/4.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl214])). 31.89/4.69 thf(zip_derived_cl219, plain, 31.89/4.69 (![X2 : term]: 31.89/4.69 (~ (var @ X2) 31.89/4.69 | ('#sk30' @ (sub @ X2 @ (push @ '#sk39' @ '#sk49'))) 31.89/4.69 | ~ ('#sk30' @ 31.89/4.69 (sub @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: 31.89/4.69 ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49'))))) @ 31.89/4.69 '#sk49')))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl217])). 31.89/4.69 thf(zip_derived_cl8801, plain, 31.89/4.69 (![X1 : term]: 31.89/4.69 (('#l_lift9963' @ X1) 31.89/4.69 = ('#sk30' @ (sub @ X1 @ (push @ '#sk39' @ '#sk49'))))), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(zip_derived_cl8806, plain, 31.89/4.69 (![X2 : term]: 31.89/4.69 (~ (var @ X2) 31.89/4.69 | ('#sk30' @ (sub @ X2 @ (push @ '#sk39' @ '#sk49'))) 31.89/4.69 | ~ ('#sk30' @ (sub @ ('#sk10' @ '#l_lift9963') @ '#sk49')))), 31.89/4.69 inference('lambda_lifting', [status(thm)], 31.89/4.69 [zip_derived_cl219, zip_derived_cl8801])). 31.89/4.69 thf(zip_derived_cl210, plain, 31.89/4.69 (( (var @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49')))))) 31.89/4.69 | (((!!) @ (^[Y0 : term]: 31.89/4.69 (((var @ Y0) => ('#sk30' @ 31.89/4.69 (sub @ Y0 @ (push @ '#sk39' @ '#sk49')))))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl209])). 31.89/4.69 thf(zip_derived_cl212, plain, 31.89/4.69 (![X2 : term]: 31.89/4.69 ( (((var @ X2) => ('#sk30' @ (sub @ X2 @ (push @ '#sk39' @ '#sk49'))))) 31.89/4.69 | (var @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: 31.89/4.69 ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49')))))))), 31.89/4.69 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl210])). 31.89/4.69 thf(zip_derived_cl215, plain, 31.89/4.69 (![X2 : term]: 31.89/4.69 (~ (var @ X2) 31.89/4.69 | ('#sk30' @ (sub @ X2 @ (push @ '#sk39' @ '#sk49'))) 31.89/4.69 | (var @ 31.89/4.69 ('#sk10' @ 31.89/4.69 (^[Y0 : term]: 31.89/4.69 ('#sk30' @ (sub @ Y0 @ (push @ '#sk39' @ '#sk49')))))))), 31.89/4.69 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl212])). 31.89/4.69 thf(zip_derived_cl8801, plain, 31.89/4.69 (![X1 : term]: 31.89/4.69 (('#l_lift9963' @ X1) 31.89/4.69 = ('#sk30' @ (sub @ X1 @ (push @ '#sk39' @ '#sk49'))))), 31.89/4.69 define([status(thm)])). 31.89/4.69 thf(zip_derived_cl8804, plain, 31.89/4.69 (![X2 : term]: 31.89/4.69 (~ (var @ X2) 31.89/4.69 | ('#sk30' @ (sub @ X2 @ (push @ '#sk39' @ '#sk49'))) 31.89/4.69 | (var @ ('#sk10' @ '#l_lift9963')))), 31.89/4.69 inference('lambda_lifting', [status(thm)], 31.89/4.69 [zip_derived_cl215, zip_derived_cl8801])). 31.89/4.69 thf(zip_derived_cl8812, plain, ($false), 31.89/4.69 inference('eprover', [status(thm)], 31.89/4.69 [zip_derived_cl8802, zip_derived_cl8803, zip_derived_cl143, 31.89/4.69 zip_derived_cl8806, zip_derived_cl8804])). 31.89/4.69 31.89/4.69 % SZS output end Refutation 31.89/4.69 31.89/4.69 31.89/4.69 % Terminating... 32.60/4.80 % Runner terminated. 32.60/4.81 % Zipperpin 1.5 exiting 32.60/4.81 EOF