0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.eHkTg7U9am true 0.14/0.36 % Computer : n017.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 1200 0.14/0.36 % WCLimit : 120 0.14/0.36 % DateTime : Tue Jul 13 12:57:02 EDT 2021 0.14/0.36 % CPUTime : 0.14/0.36 % Running portfolio for 120 s 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.36 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.54/0.67 % Total configuration time : 828 0.54/0.67 % Estimated wc time : 983 0.54/0.67 % Estimated cpu time (8 cpus) : 122.875 0.54/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.54/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 0.54/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 53s 67.71/9.24 % Solved by lams/30_b.l.sh. 67.71/9.24 % running E: timeout 14 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.eHkTg7U9am/e_inpute7150b --cpu-limit=12 --auto -s -p 67.71/9.24 % done 554 iterations in 8.358s 67.71/9.24 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 67.71/9.24 % SZS output start Refutation 67.71/9.24 thf(subst_type, type, subst: $tType). 67.71/9.24 thf(term_type, type, term: $tType). 67.71/9.24 thf(lamnotvar_type, type, lamnotvar: $o). 67.71/9.24 thf(apnotvar_type, type, apnotvar: $o). 67.71/9.24 thf(ap_type, type, ap: term > term > term). 67.71/9.24 thf('#sk186_type', type, '#sk186': (term > $o) > term). 67.71/9.24 thf(axapp_type, type, axapp: $o). 67.71/9.24 thf('#sk127_type', type, '#sk127': (term > $o) > subst > term). 67.71/9.24 thf(var_type, type, var: term > $o). 67.71/9.24 thf(sh_type, type, sh: subst). 67.71/9.24 thf('#sk110_type', type, '#sk110': (term > $o) > term). 67.71/9.24 thf(shinj_type, type, shinj: $o). 67.71/9.24 thf(laminj_type, type, laminj: $o). 67.71/9.24 thf('#form140_type', type, '#form140': (term > $o) > $o). 67.71/9.24 thf(induction2_gthm_type, type, induction2_gthm: $o). 67.71/9.24 thf('#sk53_type', type, '#sk53': term > $o). 67.71/9.24 thf(sub_type, type, sub: term > subst > term). 67.71/9.24 thf(push_type, type, push: term > subst > subst). 67.71/9.24 thf(ulamvarsh_type, type, ulamvarsh: $o). 67.71/9.24 thf(id_type, type, id: subst). 67.71/9.24 thf(axassoc_type, type, axassoc: $o). 67.71/9.24 thf('#sk217_type', type, '#sk217': term > term). 67.71/9.24 thf(axvarid_type, type, axvarid: $o). 67.71/9.24 thf(apinj1_type, type, apinj1: $o). 67.71/9.24 thf('#sk167_type', type, '#sk167': term). 67.71/9.24 thf(axabs_type, type, axabs: $o). 67.71/9.24 thf(induction_type, type, induction: $o). 67.71/9.24 thf(lamnotap_type, type, lamnotap: $o). 67.71/9.24 thf(axidr_type, type, axidr: $o). 67.71/9.24 thf(pushprop_type, type, pushprop: $o). 67.71/9.24 thf(lam_type, type, lam: term > term). 67.71/9.24 thf(apinj2_type, type, apinj2: $o). 67.71/9.24 thf(one_type, type, one: term). 67.71/9.24 thf(axshiftcons_type, type, axshiftcons: $o). 67.71/9.24 thf(axvarshift_type, type, axvarshift: $o). 67.71/9.24 thf(ulamvar1_type, type, ulamvar1: $o). 67.71/9.24 thf(axclos_type, type, axclos: $o). 67.71/9.24 thf(axvarcons_type, type, axvarcons: $o). 67.71/9.24 thf(induction2_type, type, induction2: $o). 67.71/9.24 thf(axidl_type, type, axidl: $o). 67.71/9.24 thf(induction2lem_type, type, induction2lem: $o). 67.71/9.24 thf('#sk141_type', type, '#sk141': (term > $o) > term). 67.71/9.24 thf('#form233_type', type, '#form233': (term > $o) > $o). 67.71/9.24 thf(axscons_type, type, axscons: $o). 67.71/9.24 thf(ulamvarind_type, type, ulamvarind: $o). 67.71/9.24 thf(axmap_type, type, axmap: $o). 67.71/9.24 thf(thm, conjecture, (induction2_gthm)). 67.71/9.24 thf(zf_stmt_0, negated_conjecture, (~( induction2_gthm )), 67.71/9.24 inference('cnf.neg', [status(esa)], [thm])). 67.71/9.24 thf(zip_derived_cl0, plain, (~ (induction2_gthm)), 67.71/9.24 inference('cnf', [status(esa)], [zf_stmt_0])). 67.71/9.24 thf(induction2_gthm, axiom, ~ (induction2_gthm) => 67.71/9.24 ((((axapp) => 67.71/9.24 (((axvarcons) => 67.71/9.24 (((axvarid) => 67.71/9.24 (((axabs) => 67.71/9.24 (((axclos) => 67.71/9.24 (((axidl) => 67.71/9.24 (((axshiftcons) => 67.71/9.24 (((axassoc) => 67.71/9.24 (((axmap) => 67.71/9.24 (((axidr) => 67.71/9.24 (((axvarshift) => 67.71/9.24 (((axscons) => 67.71/9.24 (((ulamvar1) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => 67.71/9.24 (induction2))))))))))))))))))))))))))))))))))))))))))))))))))) 67.71/9.24 != ($true))). 67.71/9.24 thf('0', plain, 67.71/9.24 (( ~( induction2_gthm ) ) <=> 67.71/9.24 ( ~( ( axapp ) => 67.71/9.24 ( ( axvarcons ) => 67.71/9.24 ( ( axvarid ) => 67.71/9.24 ( ( axabs ) => 67.71/9.24 ( ( axclos ) => 67.71/9.24 ( ( axidl ) => 67.71/9.24 ( ( axshiftcons ) => 67.71/9.24 ( ( axassoc ) => 67.71/9.24 ( ( axmap ) => 67.71/9.24 ( ( axidr ) => 67.71/9.24 ( ( axvarshift ) => 67.71/9.24 ( ( axscons ) => 67.71/9.24 ( ( ulamvar1 ) => 67.71/9.24 ( ( ulamvarsh ) => 67.71/9.24 ( ( ulamvarind ) => 67.71/9.24 ( ( apinj1 ) => 67.71/9.24 ( ( apinj2 ) => 67.71/9.24 ( ( laminj ) => 67.71/9.24 ( ( shinj ) => 67.71/9.24 ( ( lamnotap ) => 67.71/9.24 ( ( apnotvar ) => 67.71/9.24 ( ( lamnotvar ) => 67.71/9.24 ( ( induction ) => 67.71/9.24 ( ( pushprop ) => 67.71/9.24 ( ( induction2lem ) => 67.71/9.24 ( induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 67.71/9.24 inference('rw.lit', [status(esa)], [induction2_gthm])). 67.71/9.24 thf(zip_derived_cl1, plain, 67.71/9.24 (~ (((axapp) => 67.71/9.24 (((axvarcons) => 67.71/9.24 (((axvarid) => 67.71/9.24 (((axabs) => 67.71/9.24 (((axclos) => 67.71/9.24 (((axidl) => 67.71/9.24 (((axshiftcons) => 67.71/9.24 (((axassoc) => 67.71/9.24 (((axmap) => 67.71/9.24 (((axidr) => 67.71/9.24 (((axvarshift) => 67.71/9.24 (((axscons) => 67.71/9.24 (((ulamvar1) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => 67.71/9.24 (induction2)))))))))))))))))))))))))))))))))))))))))))))))))))), 67.71/9.24 inference('rw_clause', [status(thm)], [zip_derived_cl0, '0'])). 67.71/9.24 thf(axvarshift, axiom,(( axvarshift ) = ((((push @ one @ sh) = (id)))))). 67.71/9.24 thf('1', plain, (( axvarshift ) = ( ( push @ one @ sh ) = ( id ) )), 67.71/9.24 define([status(thm)])). 67.71/9.24 thf(ulamvar1, axiom,(( ulamvar1 ) = ((var @ one)))). 67.71/9.24 thf('2', plain, (( ulamvar1 ) = ( var @ one )), define([status(thm)])). 67.71/9.24 thf(zip_derived_cl2, plain, 67.71/9.24 (~ (((axapp) => 67.71/9.24 (((axvarcons) => 67.71/9.24 (((axvarid) => 67.71/9.24 (((axabs) => 67.71/9.24 (((axclos) => 67.71/9.24 (((axidl) => 67.71/9.24 (((axshiftcons) => 67.71/9.24 (((axassoc) => 67.71/9.24 (((axmap) => 67.71/9.24 (((axidr) => 67.71/9.24 (((((push @ one @ sh) = (id))) => 67.71/9.24 (((axscons) => 67.71/9.24 (((var @ one) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => 67.71/9.24 (induction2)))))))))))))))))))))))))))))))))))))))))))))))))))), 67.71/9.24 inference('rw', [status(thm)], [zip_derived_cl1, '1', '2'])). 67.71/9.24 thf(zip_derived_cl4, plain, 67.71/9.24 (~ (((axvarcons) => 67.71/9.24 (((axvarid) => 67.71/9.24 (((axabs) => 67.71/9.24 (((axclos) => 67.71/9.24 (((axidl) => 67.71/9.24 (((axshiftcons) => 67.71/9.24 (((axassoc) => 67.71/9.24 (((axmap) => 67.71/9.24 (((axidr) => 67.71/9.24 (((((push @ one @ sh) = (id))) => 67.71/9.24 (((axscons) => 67.71/9.24 (((var @ one) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => 67.71/9.24 (induction2)))))))))))))))))))))))))))))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 67.71/9.24 thf(zip_derived_cl7, plain, 67.71/9.24 (~ (((axvarid) => 67.71/9.24 (((axabs) => 67.71/9.24 (((axclos) => 67.71/9.24 (((axidl) => 67.71/9.24 (((axshiftcons) => 67.71/9.24 (((axassoc) => 67.71/9.24 (((axmap) => 67.71/9.24 (((axidr) => 67.71/9.24 (((((push @ one @ sh) = (id))) => 67.71/9.24 (((axscons) => 67.71/9.24 (((var @ one) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => 67.71/9.24 (induction2)))))))))))))))))))))))))))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 67.71/9.24 thf(zip_derived_cl11, plain, 67.71/9.24 (~ (((axabs) => 67.71/9.24 (((axclos) => 67.71/9.24 (((axidl) => 67.71/9.24 (((axshiftcons) => 67.71/9.24 (((axassoc) => 67.71/9.24 (((axmap) => 67.71/9.24 (((axidr) => 67.71/9.24 (((((push @ one @ sh) = (id))) => 67.71/9.24 (((axscons) => 67.71/9.24 (((var @ one) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => 67.71/9.24 (induction2)))))))))))))))))))))))))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 67.71/9.24 thf(zip_derived_cl16, plain, 67.71/9.24 (~ (((axclos) => 67.71/9.24 (((axidl) => 67.71/9.24 (((axshiftcons) => 67.71/9.24 (((axassoc) => 67.71/9.24 (((axmap) => 67.71/9.24 (((axidr) => 67.71/9.24 (((((push @ one @ sh) = (id))) => 67.71/9.24 (((axscons) => 67.71/9.24 (((var @ one) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => 67.71/9.24 (induction2)))))))))))))))))))))))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 67.71/9.24 thf(zip_derived_cl22, plain, 67.71/9.24 (~ (((axidl) => 67.71/9.24 (((axshiftcons) => 67.71/9.24 (((axassoc) => 67.71/9.24 (((axmap) => 67.71/9.24 (((axidr) => 67.71/9.24 (((((push @ one @ sh) = (id))) => 67.71/9.24 (((axscons) => 67.71/9.24 (((var @ one) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => 67.71/9.24 (induction2)))))))))))))))))))))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 67.71/9.24 thf(zip_derived_cl29, plain, 67.71/9.24 (~ (((axshiftcons) => 67.71/9.24 (((axassoc) => 67.71/9.24 (((axmap) => 67.71/9.24 (((axidr) => 67.71/9.24 (((((push @ one @ sh) = (id))) => 67.71/9.24 (((axscons) => 67.71/9.24 (((var @ one) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => (induction2)))))))))))))))))))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 67.71/9.24 thf(zip_derived_cl34, plain, 67.71/9.24 (~ (((axassoc) => 67.71/9.24 (((axmap) => 67.71/9.24 (((axidr) => 67.71/9.24 (((((push @ one @ sh) = (id))) => 67.71/9.24 (((axscons) => 67.71/9.24 (((var @ one) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => (induction2)))))))))))))))))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl29])). 67.71/9.24 thf(zip_derived_cl40, plain, 67.71/9.24 (~ (((axmap) => 67.71/9.24 (((axidr) => 67.71/9.24 (((((push @ one @ sh) = (id))) => 67.71/9.24 (((axscons) => 67.71/9.24 (((var @ one) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => (induction2)))))))))))))))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 67.71/9.24 thf(zip_derived_cl46, plain, 67.71/9.24 (~ (((axidr) => 67.71/9.24 (((((push @ one @ sh) = (id))) => 67.71/9.24 (((axscons) => 67.71/9.24 (((var @ one) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => (induction2)))))))))))))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 67.71/9.24 thf(zip_derived_cl52, plain, 67.71/9.24 (~ (((((push @ one @ sh) = (id))) => 67.71/9.24 (((axscons) => 67.71/9.24 (((var @ one) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => (induction2)))))))))))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])). 67.71/9.24 thf(zip_derived_cl58, plain, 67.71/9.24 (~ (((axscons) => 67.71/9.24 (((var @ one) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => (induction2)))))))))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 67.71/9.24 thf(zip_derived_cl64, plain, 67.71/9.24 (~ (((var @ one) => 67.71/9.24 (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => (induction2)))))))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 67.71/9.24 thf(zip_derived_cl70, plain, 67.71/9.24 (~ (((ulamvarsh) => 67.71/9.24 (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => 67.71/9.24 (((induction2lem) => (induction2)))))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])). 67.71/9.24 thf(zip_derived_cl74, plain, 67.71/9.24 (~ (((ulamvarind) => 67.71/9.24 (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => (((induction2lem) => (induction2)))))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl70])). 67.71/9.24 thf(zip_derived_cl78, plain, 67.71/9.24 (~ (((apinj1) => 67.71/9.24 (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => (((induction2lem) => (induction2)))))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 67.71/9.24 thf(zip_derived_cl82, plain, 67.71/9.24 (~ (((apinj2) => 67.71/9.24 (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => (((induction2lem) => (induction2)))))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 67.71/9.24 thf(zip_derived_cl87, plain, 67.71/9.24 (~ (((laminj) => 67.71/9.24 (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => (((induction2lem) => (induction2)))))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 67.71/9.24 thf(zip_derived_cl92, plain, 67.71/9.24 (~ (((shinj) => 67.71/9.24 (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => (((induction2lem) => (induction2)))))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 67.71/9.24 thf(zip_derived_cl98, plain, 67.71/9.24 (~ (((lamnotap) => 67.71/9.24 (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => (((induction2lem) => (induction2)))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 67.71/9.24 thf(zip_derived_cl105, plain, 67.71/9.24 (~ (((apnotvar) => 67.71/9.24 (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => (((induction2lem) => (induction2)))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl98])). 67.71/9.24 thf(zip_derived_cl114, plain, 67.71/9.24 (~ (((lamnotvar) => 67.71/9.24 (((induction) => 67.71/9.24 (((pushprop) => (((induction2lem) => (induction2)))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 67.71/9.24 thf(zip_derived_cl125, plain, 67.71/9.24 (~ (((induction) => (((pushprop) => (((induction2lem) => (induction2)))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])). 67.71/9.24 thf(zip_derived_cl137, plain, 67.71/9.24 (~ (((pushprop) => (((induction2lem) => (induction2)))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])). 67.71/9.24 thf(zip_derived_cl147, plain, (~ (((induction2lem) => (induction2)))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 67.71/9.24 thf(zip_derived_cl152, plain, (~ (induction2)), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl147])). 67.71/9.24 thf(induction2, axiom, ~ (induction2) => 67.71/9.24 ((((!!) @ (^[Y0 : term > $o]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((!!) @ (^[Y2 : term]: 67.71/9.24 (((Y0 @ Y1) => 67.71/9.24 (((Y0 @ Y2) => (Y0 @ 67.71/9.24 (ap @ Y1 @ Y2)))))))))))) => 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((Y0 @ Y2) => (Y0 @ 67.71/9.24 (sub @ Y1 @ (push @ Y2 @ id)))))))) => 67.71/9.24 (Y0 @ (lam @ Y1))))))) => 67.71/9.24 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) 67.71/9.24 != ($true))). 67.71/9.24 thf('3', plain, 67.71/9.24 (( ~( induction2 ) ) <=> 67.71/9.24 ( ~( ![X5:( term > $o )]: 67.71/9.24 ( ( ![X7:term]: ( ( var @ X7 ) => ( X5 @ X7 ) ) ) => 67.71/9.24 ( ( ![X9:term,X11:term]: 67.71/9.24 ( ( X5 @ X9 ) => 67.71/9.24 ( ( X5 @ X11 ) => ( X5 @ ( ap @ X9 @ X11 ) ) ) ) ) => 67.71/9.24 ( ( ![X13:term]: 67.71/9.24 ( ( ![X15:term]: 67.71/9.24 ( ( X5 @ X15 ) => 67.71/9.24 ( X5 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) ) => 67.71/9.24 ( X5 @ ( lam @ X13 ) ) ) ) => 67.71/9.24 ( ![X17:term]: ( X5 @ X17 ) ) ) ) ) ) )), 67.71/9.24 inference('rw.lit', [status(esa)], [induction2])). 67.71/9.24 thf(zip_derived_cl156, plain, 67.71/9.24 (~ (((!!) @ (^[Y0 : term > $o]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((!!) @ (^[Y2 : term]: 67.71/9.24 (((Y0 @ Y1) => 67.71/9.24 (((Y0 @ Y2) => (Y0 @ 67.71/9.24 (ap @ Y1 @ Y2)))))))))))) => 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((Y0 @ Y2) => (Y0 @ 67.71/9.24 (sub @ Y1 @ 67.71/9.24 (push @ Y2 @ id)))))))) => 67.71/9.24 (Y0 @ (lam @ Y1))))))) => 67.71/9.24 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))), 67.71/9.24 inference('rw_clause', [status(thm)], [zip_derived_cl152, '3'])). 67.71/9.24 thf(zip_derived_cl160, plain, 67.71/9.24 (~ (((((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk53' @ Y0)))))) => 67.71/9.24 (((((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : term]: 67.71/9.24 ((('#sk53' @ Y0) => 67.71/9.24 ((('#sk53' @ Y1) => ('#sk53' @ 67.71/9.24 (ap @ Y0 @ Y1)))))))))))) => 67.71/9.24 (((((!!) @ (^[Y0 : term]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 ((('#sk53' @ Y1) => ('#sk53' @ 67.71/9.24 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 67.71/9.24 ('#sk53' @ (lam @ Y0))))))) => 67.71/9.24 (((!!) @ (^[Y0 : term]: ('#sk53' @ Y0))))))))))), 67.71/9.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl156])). 67.71/9.24 thf(zip_derived_cl166, plain, 67.71/9.24 (~ (((((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : term]: 67.71/9.24 ((('#sk53' @ Y0) => 67.71/9.24 ((('#sk53' @ Y1) => ('#sk53' @ 67.71/9.24 (ap @ Y0 @ Y1)))))))))))) => 67.71/9.24 (((((!!) @ (^[Y0 : term]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 ((('#sk53' @ Y1) => ('#sk53' @ 67.71/9.24 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 67.71/9.24 ('#sk53' @ (lam @ Y0))))))) => 67.71/9.24 (((!!) @ (^[Y0 : term]: ('#sk53' @ Y0))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl160])). 67.71/9.24 thf(zip_derived_cl175, plain, 67.71/9.24 (~ (((((!!) @ (^[Y0 : term]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 ((('#sk53' @ Y1) => ('#sk53' @ 67.71/9.24 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 67.71/9.24 ('#sk53' @ (lam @ Y0))))))) => 67.71/9.24 (((!!) @ (^[Y0 : term]: ('#sk53' @ Y0))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl166])). 67.71/9.24 thf(zip_derived_cl185, plain, (~ (((!!) @ (^[Y0 : term]: ('#sk53' @ Y0))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])). 67.71/9.24 thf(zip_derived_cl194, plain, (~ ('#sk53' @ '#sk167')), 67.71/9.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl185])). 67.71/9.24 thf(zip_derived_cl151, plain, ( (induction2lem)), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl147])). 67.71/9.24 thf(induction2lem, axiom, (induction2lem) => 67.71/9.24 ((((!!) @ (^[Y0 : term > $o]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((!!) @ (^[Y2 : term]: 67.71/9.24 (((Y0 @ Y1) => 67.71/9.24 (((Y0 @ Y2) => (Y0 @ 67.71/9.24 (ap @ Y1 @ Y2)))))))))))) => 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((Y0 @ Y2) => (Y0 @ 67.71/9.24 (sub @ Y1 @ (push @ Y2 @ id)))))))) => 67.71/9.24 (Y0 @ (lam @ Y1))))))) => 67.71/9.24 (((!!) @ (^[Y1 : term]: 67.71/9.24 (((!!) @ (^[Y2 : subst]: 67.71/9.24 (((((!!) @ (^[Y3 : term]: 67.71/9.24 (((var @ Y3) => 67.71/9.24 (Y0 @ 67.71/9.24 (sub @ Y3 @ Y2))))))) => 67.71/9.24 (Y0 @ (sub @ Y1 @ Y2))))))))))))))))) 67.71/9.24 = ($true))). 67.71/9.24 thf('4', plain, 67.71/9.24 (( induction2lem ) <=> 67.71/9.24 ( ![X5:( term > $o )]: 67.71/9.24 ( ( ![X7:term,X9:term]: 67.71/9.24 ( ( X5 @ X7 ) => ( ( X5 @ X9 ) => ( X5 @ ( ap @ X7 @ X9 ) ) ) ) ) => 67.71/9.24 ( ( ![X11:term]: 67.71/9.24 ( ( ![X13:term]: 67.71/9.24 ( ( X5 @ X13 ) => 67.71/9.24 ( X5 @ ( sub @ X11 @ ( push @ X13 @ id ) ) ) ) ) => 67.71/9.24 ( X5 @ ( lam @ X11 ) ) ) ) => 67.71/9.24 ( ![X15:term,X17:subst]: 67.71/9.24 ( ( ![X19:term]: 67.71/9.24 ( ( var @ X19 ) => ( X5 @ ( sub @ X19 @ X17 ) ) ) ) => 67.71/9.24 ( X5 @ ( sub @ X15 @ X17 ) ) ) ) ) ) )), 67.71/9.24 inference('rw.lit', [status(esa)], [induction2lem])). 67.71/9.24 thf(zip_derived_cl155, plain, 67.71/9.24 ( (((!!) @ (^[Y0 : term > $o]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((!!) @ (^[Y2 : term]: 67.71/9.24 (((Y0 @ Y1) => 67.71/9.24 (((Y0 @ Y2) => (Y0 @ 67.71/9.24 (ap @ Y1 @ Y2)))))))))))) => 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((Y0 @ Y2) => (Y0 @ 67.71/9.24 (sub @ Y1 @ 67.71/9.24 (push @ Y2 @ id)))))))) => 67.71/9.24 (Y0 @ (lam @ Y1))))))) => 67.71/9.24 (((!!) @ (^[Y1 : term]: 67.71/9.24 (((!!) @ (^[Y2 : subst]: 67.71/9.24 (((((!!) @ (^[Y3 : term]: 67.71/9.24 (((var @ Y3) => 67.71/9.24 (Y0 @ 67.71/9.24 (sub @ Y3 @ Y2))))))) => 67.71/9.24 (Y0 @ (sub @ Y1 @ Y2)))))))))))))))))), 67.71/9.24 inference('rw_clause', [status(thm)], [zip_derived_cl151, '4'])). 67.71/9.24 thf(zip_derived_cl159, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (((((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : term]: 67.71/9.24 (((X2 @ Y0) => 67.71/9.24 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 67.71/9.24 (((((!!) @ (^[Y0 : term]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((X2 @ Y1) => (X2 @ 67.71/9.24 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 67.71/9.24 (X2 @ (lam @ Y0))))))) => 67.71/9.24 (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : subst]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((var @ Y2) => (X2 @ 67.71/9.24 (sub @ Y2 @ Y1))))))) => 67.71/9.24 (X2 @ (sub @ Y0 @ Y1))))))))))))))), 67.71/9.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl155])). 67.71/9.24 thf(zip_derived_cl164, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (~ (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : term]: 67.71/9.24 (((X2 @ Y0) => 67.71/9.24 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) 67.71/9.24 | (((((!!) @ (^[Y0 : term]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((X2 @ Y1) => (X2 @ 67.71/9.24 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 67.71/9.24 (X2 @ (lam @ Y0))))))) => 67.71/9.24 (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : subst]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((var @ Y2) => (X2 @ 67.71/9.24 (sub @ Y2 @ Y1))))))) => 67.71/9.24 (X2 @ (sub @ Y0 @ Y1)))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 67.71/9.24 thf(zip_derived_cl172, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (~ (((!!) @ (^[Y0 : term]: 67.71/9.24 (((X2 @ ('#sk110' @ X2)) => 67.71/9.24 (((X2 @ Y0) => (X2 @ (ap @ ('#sk110' @ X2) @ Y0))))))))) 67.71/9.24 | (((((!!) @ (^[Y0 : term]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((X2 @ Y1) => (X2 @ 67.71/9.24 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 67.71/9.24 (X2 @ (lam @ Y0))))))) => 67.71/9.24 (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : subst]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((var @ Y2) => (X2 @ 67.71/9.24 (sub @ Y2 @ Y1))))))) => 67.71/9.24 (X2 @ (sub @ Y0 @ Y1)))))))))))))), 67.71/9.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl164])). 67.71/9.24 thf(zip_derived_cl172, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (~ (((!!) @ (^[Y0 : term]: 67.71/9.24 (((X2 @ ('#sk110' @ X2)) => 67.71/9.24 (((X2 @ Y0) => (X2 @ (ap @ ('#sk110' @ X2) @ Y0))))))))) 67.71/9.24 | (((((!!) @ (^[Y0 : term]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((X2 @ Y1) => (X2 @ 67.71/9.24 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 67.71/9.24 (X2 @ (lam @ Y0))))))) => 67.71/9.24 (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : subst]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((var @ Y2) => (X2 @ 67.71/9.24 (sub @ Y2 @ Y1))))))) => 67.71/9.24 (X2 @ (sub @ Y0 @ Y1)))))))))))))), 67.71/9.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl164])). 67.71/9.24 thf(zip_derived_cl179, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 ( ('#form140' @ X2) 67.71/9.24 | ~ (((!!) @ (^[Y0 : term]: 67.71/9.24 (((X2 @ ('#sk110' @ X2)) => 67.71/9.24 (((X2 @ Y0) => (X2 @ (ap @ ('#sk110' @ X2) @ Y0))))))))))), 67.71/9.24 define([status(thm)])). 67.71/9.24 thf(zip_derived_cl181, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (~ ('#form140' @ X2) 67.71/9.24 | (((((!!) @ (^[Y0 : term]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((X2 @ Y1) => (X2 @ 67.71/9.24 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 67.71/9.24 (X2 @ (lam @ Y0))))))) => 67.71/9.24 (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : subst]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((var @ Y2) => (X2 @ 67.71/9.24 (sub @ Y2 @ Y1))))))) => 67.71/9.24 (X2 @ (sub @ Y0 @ Y1)))))))))))))), 67.71/9.24 inference('renaming', [status(thm)], 67.71/9.24 [zip_derived_cl172, zip_derived_cl179])). 67.71/9.24 thf(zip_derived_cl189, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (~ (((!!) @ (^[Y0 : term]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((X2 @ Y1) => (X2 @ 67.71/9.24 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 67.71/9.24 (X2 @ (lam @ Y0))))))) 67.71/9.24 | (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : subst]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((var @ Y2) => (X2 @ 67.71/9.24 (sub @ Y2 @ Y1))))))) => 67.71/9.24 (X2 @ (sub @ Y0 @ Y1)))))))))) 67.71/9.24 | ~ ('#form140' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl181])). 67.71/9.24 thf(zip_derived_cl198, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (~ (((((!!) @ (^[Y0 : term]: 67.71/9.24 (((X2 @ Y0) => (X2 @ 67.71/9.24 (sub @ ('#sk186' @ X2) @ (push @ Y0 @ id)))))))) => 67.71/9.24 (X2 @ (lam @ ('#sk186' @ X2))))) 67.71/9.24 | ~ ('#form140' @ X2) 67.71/9.24 | (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : subst]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((var @ Y2) => (X2 @ 67.71/9.24 (sub @ Y2 @ Y1))))))) => 67.71/9.24 (X2 @ (sub @ Y0 @ Y1)))))))))))), 67.71/9.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl189])). 67.71/9.24 thf(zip_derived_cl206, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 ( (((!!) @ (^[Y0 : term]: 67.71/9.24 (((X2 @ Y0) => (X2 @ 67.71/9.24 (sub @ ('#sk186' @ X2) @ (push @ Y0 @ id)))))))) 67.71/9.24 | (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : subst]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((var @ Y2) => (X2 @ 67.71/9.24 (sub @ Y2 @ Y1))))))) => 67.71/9.24 (X2 @ (sub @ Y0 @ Y1)))))))))) 67.71/9.24 | ~ ('#form140' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl198])). 67.71/9.24 thf(zip_derived_cl214, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (~ ('#form233' @ X2) 67.71/9.24 | (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : subst]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((var @ Y2) => (X2 @ 67.71/9.24 (sub @ Y2 @ Y1))))))) => 67.71/9.24 (X2 @ (sub @ Y0 @ Y1)))))))))))), 67.71/9.24 define([status(thm)])). 67.71/9.24 thf(zip_derived_cl215, plain, 67.71/9.24 (![X2 : term > $o, X4 : term]: 67.71/9.24 ( (((!!) @ (^[Y0 : subst]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 (((var @ Y1) => (X2 @ (sub @ Y1 @ Y0))))))) => 67.71/9.24 (X2 @ (sub @ X4 @ Y0))))))) 67.71/9.24 | ~ ('#form233' @ X2))), 67.71/9.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl214])). 67.71/9.24 thf(zip_derived_cl223, plain, 67.71/9.24 (![X2 : term > $o, X4 : term, X6 : subst]: 67.71/9.24 ( (((((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ (sub @ Y0 @ X6))))))) => 67.71/9.24 (X2 @ (sub @ X4 @ X6)))) 67.71/9.24 | ~ ('#form233' @ X2))), 67.71/9.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl215])). 67.71/9.24 thf(zip_derived_cl226, plain, 67.71/9.24 (![X2 : term > $o, X4 : term, X6 : subst]: 67.71/9.24 (~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ (sub @ Y0 @ X6))))))) 67.71/9.24 | (X2 @ (sub @ X4 @ X6)) 67.71/9.24 | ~ ('#form233' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl223])). 67.71/9.24 thf(zip_derived_cl227, plain, 67.71/9.24 (![X2 : term > $o, X4 : term, X6 : subst]: 67.71/9.24 (~ (((var @ ('#sk127' @ X2 @ X6)) => (X2 @ 67.71/9.24 (sub @ ('#sk127' @ X2 @ X6) @ X6)))) 67.71/9.24 | ~ ('#form233' @ X2) 67.71/9.24 | (X2 @ (sub @ X4 @ X6)))), 67.71/9.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl226])). 67.71/9.24 thf(zip_derived_cl228, plain, 67.71/9.24 (![X2 : term > $o, X4 : term, X6 : subst]: 67.71/9.24 ( (var @ ('#sk127' @ X2 @ X6)) 67.71/9.24 | (X2 @ (sub @ X4 @ X6)) 67.71/9.24 | ~ ('#form233' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl227])). 67.71/9.24 thf(zip_derived_cl165, plain, 67.71/9.24 ( (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk53' @ Y0))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl160])). 67.71/9.24 thf(zip_derived_cl173, plain, 67.71/9.24 (![X2 : term]: (((var @ X2) => ('#sk53' @ X2)))), 67.71/9.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl165])). 67.71/9.24 thf(zip_derived_cl182, plain, 67.71/9.24 (![X2 : term]: (~ (var @ X2) | ('#sk53' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])). 67.71/9.24 thf(zip_derived_cl10, plain, ( (axvarid)), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 67.71/9.24 thf(axvarid, axiom, (axvarid) => 67.71/9.24 ((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) = ($true))). 67.71/9.24 thf('5', plain, 67.71/9.24 (( axvarid ) <=> ( ![X5:term]: ( ( sub @ X5 @ id ) = ( X5 ) ) )), 67.71/9.24 inference('rw.lit', [status(esa)], [axvarid])). 67.71/9.24 thf(zip_derived_cl14, plain, 67.71/9.24 ( (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0))))))), 67.71/9.24 inference('rw_clause', [status(thm)], [zip_derived_cl10, '5'])). 67.71/9.24 thf(zip_derived_cl19, plain, (![X2 : term]: (((sub @ X2 @ id) = (X2)))), 67.71/9.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 67.71/9.24 thf(zip_derived_cl25, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))), 67.71/9.24 inference('simplify nested equalities', [status(thm)], [zip_derived_cl19])). 67.71/9.24 thf(zip_derived_cl207, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (~ (X2 @ (lam @ ('#sk186' @ X2))) 67.71/9.24 | (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : subst]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((var @ Y2) => (X2 @ 67.71/9.24 (sub @ Y2 @ Y1))))))) => 67.71/9.24 (X2 @ (sub @ Y0 @ Y1)))))))))) 67.71/9.24 | ~ ('#form140' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl198])). 67.71/9.24 thf(zip_derived_cl214, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (~ ('#form233' @ X2) 67.71/9.24 | (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : subst]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((var @ Y2) => (X2 @ 67.71/9.24 (sub @ Y2 @ Y1))))))) => 67.71/9.24 (X2 @ (sub @ Y0 @ Y1)))))))))))), 67.71/9.24 define([status(thm)])). 67.71/9.24 thf(zip_derived_cl217, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 ( ('#form233' @ X2) 67.71/9.24 | ~ ('#form140' @ X2) 67.71/9.24 | ~ (X2 @ (lam @ ('#sk186' @ X2))))), 67.71/9.24 inference('renaming', [status(thm)], 67.71/9.24 [zip_derived_cl207, zip_derived_cl214])). 67.71/9.24 thf(zip_derived_cl229, plain, 67.71/9.24 (![X2 : term > $o, X4 : term, X6 : subst]: 67.71/9.24 (~ (X2 @ (sub @ ('#sk127' @ X2 @ X6) @ X6)) 67.71/9.24 | (X2 @ (sub @ X4 @ X6)) 67.71/9.24 | ~ ('#form233' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl227])). 67.71/9.24 thf(zip_derived_cl184, plain, 67.71/9.24 ( (((!!) @ (^[Y0 : term]: 67.71/9.24 (((((!!) @ (^[Y1 : term]: 67.71/9.24 ((('#sk53' @ Y1) => ('#sk53' @ 67.71/9.24 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 67.71/9.24 ('#sk53' @ (lam @ Y0)))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])). 67.71/9.24 thf(zip_derived_cl193, plain, 67.71/9.24 (![X2 : term]: 67.71/9.24 (((((!!) @ (^[Y0 : term]: 67.71/9.24 ((('#sk53' @ Y0) => ('#sk53' @ 67.71/9.24 (sub @ X2 @ (push @ Y0 @ id)))))))) => 67.71/9.24 ('#sk53' @ (lam @ X2))))), 67.71/9.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl184])). 67.71/9.24 thf(zip_derived_cl202, plain, 67.71/9.24 (![X2 : term]: 67.71/9.24 (~ (((!!) @ (^[Y0 : term]: 67.71/9.24 ((('#sk53' @ Y0) => ('#sk53' @ 67.71/9.24 (sub @ X2 @ (push @ Y0 @ id)))))))) 67.71/9.24 | ('#sk53' @ (lam @ X2)))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl193])). 67.71/9.24 thf(zip_derived_cl209, plain, 67.71/9.24 (![X2 : term]: 67.71/9.24 (~ ((('#sk53' @ ('#sk217' @ X2)) => ('#sk53' @ 67.71/9.24 (sub @ X2 @ (push @ ('#sk217' @ X2) @ id))))) 67.71/9.24 | ('#sk53' @ (lam @ X2)))), 67.71/9.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl202])). 67.71/9.24 thf(zip_derived_cl218, plain, 67.71/9.24 (![X2 : term]: ( ('#sk53' @ ('#sk217' @ X2)) | ('#sk53' @ (lam @ X2)))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl209])). 67.71/9.24 thf(zip_derived_cl179, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 ( ('#form140' @ X2) 67.71/9.24 | ~ (((!!) @ (^[Y0 : term]: 67.71/9.24 (((X2 @ ('#sk110' @ X2)) => 67.71/9.24 (((X2 @ Y0) => (X2 @ (ap @ ('#sk110' @ X2) @ Y0))))))))))), 67.71/9.24 define([status(thm)])). 67.71/9.24 thf(zip_derived_cl180, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (~ (((X2 @ ('#sk110' @ X2)) => 67.71/9.24 (((X2 @ ('#sk141' @ X2)) => (X2 @ 67.71/9.24 (ap @ ('#sk110' @ X2) @ ('#sk141' @ X2))))))) 67.71/9.24 | ('#form140' @ X2))), 67.71/9.24 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl179])). 67.71/9.24 thf(zip_derived_cl191, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (~ (((X2 @ ('#sk141' @ X2)) => (X2 @ 67.71/9.24 (ap @ ('#sk110' @ X2) @ ('#sk141' @ X2))))) 67.71/9.24 | ('#form140' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl180])). 67.71/9.24 thf(zip_derived_cl200, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (~ (X2 @ (ap @ ('#sk110' @ X2) @ ('#sk141' @ X2))) 67.71/9.24 | ('#form140' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])). 67.71/9.24 thf(zip_derived_cl174, plain, 67.71/9.24 ( (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : term]: 67.71/9.24 ((('#sk53' @ Y0) => 67.71/9.24 ((('#sk53' @ Y1) => ('#sk53' @ 67.71/9.24 (ap @ Y0 @ Y1))))))))))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl166])). 67.71/9.24 thf(zip_derived_cl183, plain, 67.71/9.24 (![X2 : term]: 67.71/9.24 (((!!) @ (^[Y0 : term]: 67.71/9.24 ((('#sk53' @ X2) => 67.71/9.24 ((('#sk53' @ Y0) => ('#sk53' @ (ap @ X2 @ Y0)))))))))), 67.71/9.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl174])). 67.71/9.24 thf(zip_derived_cl192, plain, 67.71/9.24 (![X2 : term, X4 : term]: 67.71/9.24 ((('#sk53' @ X2) => ((('#sk53' @ X4) => ('#sk53' @ (ap @ X2 @ X4))))))), 67.71/9.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl183])). 67.71/9.24 thf(zip_derived_cl201, plain, 67.71/9.24 (![X2 : term, X4 : term]: 67.71/9.24 (~ ('#sk53' @ X2) | ((('#sk53' @ X4) => ('#sk53' @ (ap @ X2 @ X4)))))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl192])). 67.71/9.24 thf(zip_derived_cl208, plain, 67.71/9.24 (![X2 : term, X4 : term]: 67.71/9.24 (~ ('#sk53' @ X4) | ('#sk53' @ (ap @ X2 @ X4)) | ~ ('#sk53' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl201])). 67.71/9.24 thf(zip_derived_cl2753, plain, 67.71/9.24 (( ('#form140' @ '#sk53') 67.71/9.24 | ~ ('#sk53' @ ('#sk110' @ '#sk53')) 67.71/9.24 | ~ ('#sk53' @ ('#sk141' @ '#sk53')))), 67.71/9.24 inference('sup+', [status(thm)], [zip_derived_cl200, zip_derived_cl208])). 67.71/9.24 thf(zip_derived_cl190, plain, 67.71/9.24 (![X2 : term > $o]: ( (X2 @ ('#sk110' @ X2)) | ('#form140' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl180])). 67.71/9.24 thf(zip_derived_cl2768, plain, 67.71/9.24 ((~ ('#sk53' @ ('#sk141' @ '#sk53')) | ('#form140' @ '#sk53'))), 67.71/9.24 inference('clc', [status(thm)], [zip_derived_cl2753, zip_derived_cl190])). 67.71/9.24 thf(zip_derived_cl199, plain, 67.71/9.24 (![X2 : term > $o]: ( (X2 @ ('#sk141' @ X2)) | ('#form140' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])). 67.71/9.24 thf(zip_derived_cl2769, plain, ( ('#form140' @ '#sk53')), 67.71/9.24 inference('clc', [status(thm)], [zip_derived_cl2768, zip_derived_cl199])). 67.71/9.24 thf(zip_derived_cl219, plain, 67.71/9.24 (![X2 : term]: 67.71/9.24 (~ ('#sk53' @ (sub @ X2 @ (push @ ('#sk217' @ X2) @ id))) 67.71/9.24 | ('#sk53' @ (lam @ X2)))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl209])). 67.71/9.24 thf(zip_derived_cl206, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 ( (((!!) @ (^[Y0 : term]: 67.71/9.24 (((X2 @ Y0) => (X2 @ 67.71/9.24 (sub @ ('#sk186' @ X2) @ (push @ Y0 @ id)))))))) 67.71/9.24 | (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : subst]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((var @ Y2) => (X2 @ 67.71/9.24 (sub @ Y2 @ Y1))))))) => 67.71/9.24 (X2 @ (sub @ Y0 @ Y1)))))))))) 67.71/9.24 | ~ ('#form140' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl198])). 67.71/9.24 thf(zip_derived_cl214, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 (~ ('#form233' @ X2) 67.71/9.24 | (((!!) @ (^[Y0 : term]: 67.71/9.24 (((!!) @ (^[Y1 : subst]: 67.71/9.24 (((((!!) @ (^[Y2 : term]: 67.71/9.24 (((var @ Y2) => (X2 @ 67.71/9.24 (sub @ Y2 @ Y1))))))) => 67.71/9.24 (X2 @ (sub @ Y0 @ Y1)))))))))))), 67.71/9.24 define([status(thm)])). 67.71/9.24 thf(zip_derived_cl216, plain, 67.71/9.24 (![X2 : term > $o]: 67.71/9.24 ( ('#form233' @ X2) 67.71/9.24 | ~ ('#form140' @ X2) 67.71/9.24 | (((!!) @ (^[Y0 : term]: 67.71/9.24 (((X2 @ Y0) => (X2 @ 67.71/9.24 (sub @ ('#sk186' @ X2) @ (push @ Y0 @ id)))))))))), 67.71/9.24 inference('renaming', [status(thm)], 67.71/9.24 [zip_derived_cl206, zip_derived_cl214])). 67.71/9.24 thf(zip_derived_cl222, plain, 67.71/9.24 (![X2 : term > $o, X4 : term]: 67.71/9.24 ( (((X2 @ X4) => (X2 @ (sub @ ('#sk186' @ X2) @ (push @ X4 @ id))))) 67.71/9.24 | ~ ('#form140' @ X2) 67.71/9.24 | ('#form233' @ X2))), 67.71/9.24 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl216])). 67.71/9.24 thf(zip_derived_cl225, plain, 67.71/9.24 (![X2 : term > $o, X4 : term]: 67.71/9.24 (~ (X2 @ X4) 67.71/9.24 | (X2 @ (sub @ ('#sk186' @ X2) @ (push @ X4 @ id))) 67.71/9.24 | ('#form233' @ X2) 67.71/9.24 | ~ ('#form140' @ X2))), 67.71/9.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])). 67.71/9.24 thf(zip_derived_cl11694, plain, ($false), 67.71/9.24 inference('eprover', [status(thm)], 67.71/9.24 [zip_derived_cl194, zip_derived_cl228, zip_derived_cl182, 67.71/9.24 zip_derived_cl25, zip_derived_cl217, zip_derived_cl229, 67.71/9.24 zip_derived_cl218, zip_derived_cl2769, zip_derived_cl219, 67.71/9.24 zip_derived_cl225])). 67.71/9.24 67.71/9.24 % SZS output end Refutation 67.71/9.24 67.71/9.24 67.71/9.24 % Terminating... 67.71/9.28 % Runner terminated. 67.71/9.28 % Zipperpin 1.5 exiting 67.71/9.29 EOF