0.05/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ZQCDCWiZtT true 0.12/0.32 % Computer : n005.cluster.edu 0.12/0.32 % Model : x86_64 x86_64 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.32 % Memory : 8042.1875MB 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.32 % CPULimit : 960 0.12/0.32 % WCLimit : 120 0.12/0.32 % DateTime : Tue Aug 9 06:24:34 EDT 2022 0.12/0.32 % CPUTime : 0.12/0.32 % Running portfolio for 960 s 0.12/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.12/0.32 % Number of cores: 8 0.12/0.32 % Python version: Python 3.6.8 0.12/0.33 % Running in HO mode 0.43/0.59 % Total configuration time : 828 0.43/0.59 % Estimated wc time : 1656 0.43/0.59 % Estimated cpu time (8 cpus) : 207.0 0.45/0.67 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.45/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.45/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.45/0.68 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.45/0.68 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.45/0.68 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.47/0.68 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.47/0.68 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.47/0.74 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 114.13/15.02 % Solved by lams/30_b.l.sh. 114.13/15.02 % running E: timeout 14 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.ZQCDCWiZtT/e_input7c7dab --cpu-limit=12 --auto -s -p 114.13/15.02 % done 614 iterations in 14.205s 114.13/15.02 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 114.13/15.02 % SZS output start Refutation 114.13/15.02 thf(subst_type, type, subst: $tType). 114.13/15.02 thf(term_type, type, term: $tType). 114.13/15.02 thf(lamnotvar_type, type, lamnotvar: $o). 114.13/15.02 thf(apnotvar_type, type, apnotvar: $o). 114.13/15.02 thf(ap_type, type, ap: term > term > term). 114.13/15.02 thf('#sk186_type', type, '#sk186': (term > $o) > term). 114.13/15.02 thf(axapp_type, type, axapp: $o). 114.13/15.02 thf('#sk127_type', type, '#sk127': (term > $o) > subst > term). 114.13/15.02 thf(var_type, type, var: term > $o). 114.13/15.02 thf(sh_type, type, sh: subst). 114.13/15.02 thf('#sk110_type', type, '#sk110': (term > $o) > term). 114.13/15.02 thf(shinj_type, type, shinj: $o). 114.13/15.02 thf(laminj_type, type, laminj: $o). 114.13/15.02 thf('#form140_type', type, '#form140': (term > $o) > $o). 114.13/15.02 thf(induction2_gthm_type, type, induction2_gthm: $o). 114.13/15.02 thf('#sk53_type', type, '#sk53': term > $o). 114.13/15.02 thf(sub_type, type, sub: term > subst > term). 114.13/15.02 thf(push_type, type, push: term > subst > subst). 114.13/15.02 thf(ulamvarsh_type, type, ulamvarsh: $o). 114.13/15.02 thf(id_type, type, id: subst). 114.13/15.02 thf(axassoc_type, type, axassoc: $o). 114.13/15.02 thf('#sk217_type', type, '#sk217': term > term). 114.13/15.02 thf(axvarid_type, type, axvarid: $o). 114.13/15.02 thf(apinj1_type, type, apinj1: $o). 114.13/15.02 thf('#sk167_type', type, '#sk167': term). 114.13/15.02 thf(axabs_type, type, axabs: $o). 114.13/15.02 thf(induction_type, type, induction: $o). 114.13/15.02 thf(lamnotap_type, type, lamnotap: $o). 114.13/15.02 thf(axidr_type, type, axidr: $o). 114.13/15.02 thf(pushprop_type, type, pushprop: $o). 114.13/15.02 thf(lam_type, type, lam: term > term). 114.13/15.02 thf(apinj2_type, type, apinj2: $o). 114.13/15.02 thf(one_type, type, one: term). 114.13/15.02 thf(axshiftcons_type, type, axshiftcons: $o). 114.13/15.02 thf(axvarshift_type, type, axvarshift: $o). 114.13/15.02 thf(ulamvar1_type, type, ulamvar1: $o). 114.13/15.02 thf(axclos_type, type, axclos: $o). 114.13/15.02 thf(axvarcons_type, type, axvarcons: $o). 114.13/15.02 thf(induction2_type, type, induction2: $o). 114.13/15.02 thf(axidl_type, type, axidl: $o). 114.13/15.02 thf(induction2lem_type, type, induction2lem: $o). 114.13/15.02 thf('#sk141_type', type, '#sk141': (term > $o) > term). 114.13/15.02 thf('#form233_type', type, '#form233': (term > $o) > $o). 114.13/15.02 thf(axscons_type, type, axscons: $o). 114.13/15.02 thf(ulamvarind_type, type, ulamvarind: $o). 114.13/15.02 thf(axmap_type, type, axmap: $o). 114.13/15.02 thf(thm, conjecture, (induction2_gthm)). 114.13/15.02 thf(zf_stmt_0, negated_conjecture, (~( induction2_gthm )), 114.13/15.02 inference('cnf.neg', [status(esa)], [thm])). 114.13/15.02 thf(zip_derived_cl0, plain, (~ (induction2_gthm)), 114.13/15.02 inference('cnf', [status(esa)], [zf_stmt_0])). 114.13/15.02 thf(induction2_gthm, axiom, ~ (induction2_gthm) => 114.13/15.02 ((((axapp) => 114.13/15.02 (((axvarcons) => 114.13/15.02 (((axvarid) => 114.13/15.02 (((axabs) => 114.13/15.02 (((axclos) => 114.13/15.02 (((axidl) => 114.13/15.02 (((axshiftcons) => 114.13/15.02 (((axassoc) => 114.13/15.02 (((axmap) => 114.13/15.02 (((axidr) => 114.13/15.02 (((axvarshift) => 114.13/15.02 (((axscons) => 114.13/15.02 (((ulamvar1) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => 114.13/15.02 (induction2))))))))))))))))))))))))))))))))))))))))))))))))))) 114.13/15.02 != ($true))). 114.13/15.02 thf('0', plain, 114.13/15.02 (( ~( induction2_gthm ) ) <=> 114.13/15.02 ( ~( ( axapp ) => 114.13/15.02 ( ( axvarcons ) => 114.13/15.02 ( ( axvarid ) => 114.13/15.02 ( ( axabs ) => 114.13/15.02 ( ( axclos ) => 114.13/15.02 ( ( axidl ) => 114.13/15.02 ( ( axshiftcons ) => 114.13/15.02 ( ( axassoc ) => 114.13/15.02 ( ( axmap ) => 114.13/15.02 ( ( axidr ) => 114.13/15.02 ( ( axvarshift ) => 114.13/15.02 ( ( axscons ) => 114.13/15.02 ( ( ulamvar1 ) => 114.13/15.02 ( ( ulamvarsh ) => 114.13/15.02 ( ( ulamvarind ) => 114.13/15.02 ( ( apinj1 ) => 114.13/15.02 ( ( apinj2 ) => 114.13/15.02 ( ( laminj ) => 114.13/15.02 ( ( shinj ) => 114.13/15.02 ( ( lamnotap ) => 114.13/15.02 ( ( apnotvar ) => 114.13/15.02 ( ( lamnotvar ) => 114.13/15.02 ( ( induction ) => 114.13/15.02 ( ( pushprop ) => 114.13/15.02 ( ( induction2lem ) => 114.13/15.02 ( induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 114.13/15.02 inference('rw.lit', [status(esa)], [induction2_gthm])). 114.13/15.02 thf(zip_derived_cl1, plain, 114.13/15.02 (~ (((axapp) => 114.13/15.02 (((axvarcons) => 114.13/15.02 (((axvarid) => 114.13/15.02 (((axabs) => 114.13/15.02 (((axclos) => 114.13/15.02 (((axidl) => 114.13/15.02 (((axshiftcons) => 114.13/15.02 (((axassoc) => 114.13/15.02 (((axmap) => 114.13/15.02 (((axidr) => 114.13/15.02 (((axvarshift) => 114.13/15.02 (((axscons) => 114.13/15.02 (((ulamvar1) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => 114.13/15.02 (induction2)))))))))))))))))))))))))))))))))))))))))))))))))))), 114.13/15.02 inference('rw_clause', [status(thm)], [zip_derived_cl0, '0'])). 114.13/15.02 thf(axvarshift, axiom,(( axvarshift ) = ((((push @ one @ sh) = (id)))))). 114.13/15.02 thf('1', plain, (( axvarshift ) = ( ( push @ one @ sh ) = ( id ) )), 114.13/15.02 define([status(thm)])). 114.13/15.02 thf(ulamvar1, axiom,(( ulamvar1 ) = ((var @ one)))). 114.13/15.02 thf('2', plain, (( ulamvar1 ) = ( var @ one )), define([status(thm)])). 114.13/15.02 thf(zip_derived_cl2, plain, 114.13/15.02 (~ (((axapp) => 114.13/15.02 (((axvarcons) => 114.13/15.02 (((axvarid) => 114.13/15.02 (((axabs) => 114.13/15.02 (((axclos) => 114.13/15.02 (((axidl) => 114.13/15.02 (((axshiftcons) => 114.13/15.02 (((axassoc) => 114.13/15.02 (((axmap) => 114.13/15.02 (((axidr) => 114.13/15.02 (((((push @ one @ sh) = (id))) => 114.13/15.02 (((axscons) => 114.13/15.02 (((var @ one) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => 114.13/15.02 (induction2)))))))))))))))))))))))))))))))))))))))))))))))))))), 114.13/15.02 inference('rw', [status(thm)], [zip_derived_cl1, '1', '2'])). 114.13/15.02 thf(zip_derived_cl4, plain, 114.13/15.02 (~ (((axvarcons) => 114.13/15.02 (((axvarid) => 114.13/15.02 (((axabs) => 114.13/15.02 (((axclos) => 114.13/15.02 (((axidl) => 114.13/15.02 (((axshiftcons) => 114.13/15.02 (((axassoc) => 114.13/15.02 (((axmap) => 114.13/15.02 (((axidr) => 114.13/15.02 (((((push @ one @ sh) = (id))) => 114.13/15.02 (((axscons) => 114.13/15.02 (((var @ one) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => 114.13/15.02 (induction2)))))))))))))))))))))))))))))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 114.13/15.02 thf(zip_derived_cl7, plain, 114.13/15.02 (~ (((axvarid) => 114.13/15.02 (((axabs) => 114.13/15.02 (((axclos) => 114.13/15.02 (((axidl) => 114.13/15.02 (((axshiftcons) => 114.13/15.02 (((axassoc) => 114.13/15.02 (((axmap) => 114.13/15.02 (((axidr) => 114.13/15.02 (((((push @ one @ sh) = (id))) => 114.13/15.02 (((axscons) => 114.13/15.02 (((var @ one) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => 114.13/15.02 (induction2)))))))))))))))))))))))))))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 114.13/15.02 thf(zip_derived_cl11, plain, 114.13/15.02 (~ (((axabs) => 114.13/15.02 (((axclos) => 114.13/15.02 (((axidl) => 114.13/15.02 (((axshiftcons) => 114.13/15.02 (((axassoc) => 114.13/15.02 (((axmap) => 114.13/15.02 (((axidr) => 114.13/15.02 (((((push @ one @ sh) = (id))) => 114.13/15.02 (((axscons) => 114.13/15.02 (((var @ one) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => 114.13/15.02 (induction2)))))))))))))))))))))))))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 114.13/15.02 thf(zip_derived_cl16, plain, 114.13/15.02 (~ (((axclos) => 114.13/15.02 (((axidl) => 114.13/15.02 (((axshiftcons) => 114.13/15.02 (((axassoc) => 114.13/15.02 (((axmap) => 114.13/15.02 (((axidr) => 114.13/15.02 (((((push @ one @ sh) = (id))) => 114.13/15.02 (((axscons) => 114.13/15.02 (((var @ one) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => 114.13/15.02 (induction2)))))))))))))))))))))))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 114.13/15.02 thf(zip_derived_cl22, plain, 114.13/15.02 (~ (((axidl) => 114.13/15.02 (((axshiftcons) => 114.13/15.02 (((axassoc) => 114.13/15.02 (((axmap) => 114.13/15.02 (((axidr) => 114.13/15.02 (((((push @ one @ sh) = (id))) => 114.13/15.02 (((axscons) => 114.13/15.02 (((var @ one) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => 114.13/15.02 (induction2)))))))))))))))))))))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 114.13/15.02 thf(zip_derived_cl29, plain, 114.13/15.02 (~ (((axshiftcons) => 114.13/15.02 (((axassoc) => 114.13/15.02 (((axmap) => 114.13/15.02 (((axidr) => 114.13/15.02 (((((push @ one @ sh) = (id))) => 114.13/15.02 (((axscons) => 114.13/15.02 (((var @ one) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => (induction2)))))))))))))))))))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 114.13/15.02 thf(zip_derived_cl34, plain, 114.13/15.02 (~ (((axassoc) => 114.13/15.02 (((axmap) => 114.13/15.02 (((axidr) => 114.13/15.02 (((((push @ one @ sh) = (id))) => 114.13/15.02 (((axscons) => 114.13/15.02 (((var @ one) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => (induction2)))))))))))))))))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl29])). 114.13/15.02 thf(zip_derived_cl40, plain, 114.13/15.02 (~ (((axmap) => 114.13/15.02 (((axidr) => 114.13/15.02 (((((push @ one @ sh) = (id))) => 114.13/15.02 (((axscons) => 114.13/15.02 (((var @ one) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => (induction2)))))))))))))))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 114.13/15.02 thf(zip_derived_cl46, plain, 114.13/15.02 (~ (((axidr) => 114.13/15.02 (((((push @ one @ sh) = (id))) => 114.13/15.02 (((axscons) => 114.13/15.02 (((var @ one) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => (induction2)))))))))))))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 114.13/15.02 thf(zip_derived_cl52, plain, 114.13/15.02 (~ (((((push @ one @ sh) = (id))) => 114.13/15.02 (((axscons) => 114.13/15.02 (((var @ one) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => (induction2)))))))))))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])). 114.13/15.02 thf(zip_derived_cl58, plain, 114.13/15.02 (~ (((axscons) => 114.13/15.02 (((var @ one) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => (induction2)))))))))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 114.13/15.02 thf(zip_derived_cl64, plain, 114.13/15.02 (~ (((var @ one) => 114.13/15.02 (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => (induction2)))))))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])). 114.13/15.02 thf(zip_derived_cl70, plain, 114.13/15.02 (~ (((ulamvarsh) => 114.13/15.02 (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => 114.13/15.02 (((induction2lem) => (induction2)))))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])). 114.13/15.02 thf(zip_derived_cl74, plain, 114.13/15.02 (~ (((ulamvarind) => 114.13/15.02 (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => (((induction2lem) => (induction2)))))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl70])). 114.13/15.02 thf(zip_derived_cl78, plain, 114.13/15.02 (~ (((apinj1) => 114.13/15.02 (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => (((induction2lem) => (induction2)))))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 114.13/15.02 thf(zip_derived_cl82, plain, 114.13/15.02 (~ (((apinj2) => 114.13/15.02 (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => (((induction2lem) => (induction2)))))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 114.13/15.02 thf(zip_derived_cl87, plain, 114.13/15.02 (~ (((laminj) => 114.13/15.02 (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => (((induction2lem) => (induction2)))))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 114.13/15.02 thf(zip_derived_cl92, plain, 114.13/15.02 (~ (((shinj) => 114.13/15.02 (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => (((induction2lem) => (induction2)))))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 114.13/15.02 thf(zip_derived_cl98, plain, 114.13/15.02 (~ (((lamnotap) => 114.13/15.02 (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => (((induction2lem) => (induction2)))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 114.13/15.02 thf(zip_derived_cl105, plain, 114.13/15.02 (~ (((apnotvar) => 114.13/15.02 (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => (((induction2lem) => (induction2)))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl98])). 114.13/15.02 thf(zip_derived_cl114, plain, 114.13/15.02 (~ (((lamnotvar) => 114.13/15.02 (((induction) => 114.13/15.02 (((pushprop) => (((induction2lem) => (induction2)))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 114.13/15.02 thf(zip_derived_cl125, plain, 114.13/15.02 (~ (((induction) => (((pushprop) => (((induction2lem) => (induction2)))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])). 114.13/15.02 thf(zip_derived_cl137, plain, 114.13/15.02 (~ (((pushprop) => (((induction2lem) => (induction2)))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])). 114.13/15.02 thf(zip_derived_cl147, plain, (~ (((induction2lem) => (induction2)))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 114.13/15.02 thf(zip_derived_cl152, plain, (~ (induction2)), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl147])). 114.13/15.02 thf(induction2, axiom, ~ (induction2) => 114.13/15.02 ((((!!) @ (^[Y0 : term > $o]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((!!) @ (^[Y2 : term]: 114.13/15.02 (((Y0 @ Y1) => 114.13/15.02 (((Y0 @ Y2) => (Y0 @ 114.13/15.02 (ap @ Y1 @ Y2)))))))))))) => 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((Y0 @ Y2) => (Y0 @ 114.13/15.02 (sub @ Y1 @ (push @ Y2 @ id)))))))) => 114.13/15.02 (Y0 @ (lam @ Y1))))))) => 114.13/15.02 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) 114.13/15.02 != ($true))). 114.13/15.02 thf('3', plain, 114.13/15.02 (( ~( induction2 ) ) <=> 114.13/15.02 ( ~( ![X5:( term > $o )]: 114.13/15.02 ( ( ![X7:term]: ( ( var @ X7 ) => ( X5 @ X7 ) ) ) => 114.13/15.02 ( ( ![X9:term,X11:term]: 114.13/15.02 ( ( X5 @ X9 ) => 114.13/15.02 ( ( X5 @ X11 ) => ( X5 @ ( ap @ X9 @ X11 ) ) ) ) ) => 114.13/15.02 ( ( ![X13:term]: 114.13/15.02 ( ( ![X15:term]: 114.13/15.02 ( ( X5 @ X15 ) => 114.13/15.02 ( X5 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) ) => 114.13/15.02 ( X5 @ ( lam @ X13 ) ) ) ) => 114.13/15.02 ( ![X17:term]: ( X5 @ X17 ) ) ) ) ) ) )), 114.13/15.02 inference('rw.lit', [status(esa)], [induction2])). 114.13/15.02 thf(zip_derived_cl156, plain, 114.13/15.02 (~ (((!!) @ (^[Y0 : term > $o]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((!!) @ (^[Y2 : term]: 114.13/15.02 (((Y0 @ Y1) => 114.13/15.02 (((Y0 @ Y2) => (Y0 @ 114.13/15.02 (ap @ Y1 @ Y2)))))))))))) => 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((Y0 @ Y2) => (Y0 @ 114.13/15.02 (sub @ Y1 @ 114.13/15.02 (push @ Y2 @ id)))))))) => 114.13/15.02 (Y0 @ (lam @ Y1))))))) => 114.13/15.02 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))), 114.13/15.02 inference('rw_clause', [status(thm)], [zip_derived_cl152, '3'])). 114.13/15.02 thf(zip_derived_cl160, plain, 114.13/15.02 (~ (((((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk53' @ Y0)))))) => 114.13/15.02 (((((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : term]: 114.13/15.02 ((('#sk53' @ Y0) => 114.13/15.02 ((('#sk53' @ Y1) => ('#sk53' @ 114.13/15.02 (ap @ Y0 @ Y1)))))))))))) => 114.13/15.02 (((((!!) @ (^[Y0 : term]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 ((('#sk53' @ Y1) => ('#sk53' @ 114.13/15.02 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 114.13/15.02 ('#sk53' @ (lam @ Y0))))))) => 114.13/15.02 (((!!) @ (^[Y0 : term]: ('#sk53' @ Y0))))))))))), 114.13/15.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl156])). 114.13/15.02 thf(zip_derived_cl166, plain, 114.13/15.02 (~ (((((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : term]: 114.13/15.02 ((('#sk53' @ Y0) => 114.13/15.02 ((('#sk53' @ Y1) => ('#sk53' @ 114.13/15.02 (ap @ Y0 @ Y1)))))))))))) => 114.13/15.02 (((((!!) @ (^[Y0 : term]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 ((('#sk53' @ Y1) => ('#sk53' @ 114.13/15.02 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 114.13/15.02 ('#sk53' @ (lam @ Y0))))))) => 114.13/15.02 (((!!) @ (^[Y0 : term]: ('#sk53' @ Y0))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl160])). 114.13/15.02 thf(zip_derived_cl175, plain, 114.13/15.02 (~ (((((!!) @ (^[Y0 : term]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 ((('#sk53' @ Y1) => ('#sk53' @ 114.13/15.02 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 114.13/15.02 ('#sk53' @ (lam @ Y0))))))) => 114.13/15.02 (((!!) @ (^[Y0 : term]: ('#sk53' @ Y0))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl166])). 114.13/15.02 thf(zip_derived_cl185, plain, (~ (((!!) @ (^[Y0 : term]: ('#sk53' @ Y0))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])). 114.13/15.02 thf(zip_derived_cl194, plain, (~ ('#sk53' @ '#sk167')), 114.13/15.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl185])). 114.13/15.02 thf(zip_derived_cl151, plain, ( (induction2lem)), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl147])). 114.13/15.02 thf(induction2lem, axiom, (induction2lem) => 114.13/15.02 ((((!!) @ (^[Y0 : term > $o]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((!!) @ (^[Y2 : term]: 114.13/15.02 (((Y0 @ Y1) => 114.13/15.02 (((Y0 @ Y2) => (Y0 @ 114.13/15.02 (ap @ Y1 @ Y2)))))))))))) => 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((Y0 @ Y2) => (Y0 @ 114.13/15.02 (sub @ Y1 @ (push @ Y2 @ id)))))))) => 114.13/15.02 (Y0 @ (lam @ Y1))))))) => 114.13/15.02 (((!!) @ (^[Y1 : term]: 114.13/15.02 (((!!) @ (^[Y2 : subst]: 114.13/15.02 (((((!!) @ (^[Y3 : term]: 114.13/15.02 (((var @ Y3) => 114.13/15.02 (Y0 @ 114.13/15.02 (sub @ Y3 @ Y2))))))) => 114.13/15.02 (Y0 @ (sub @ Y1 @ Y2))))))))))))))))) 114.13/15.02 = ($true))). 114.13/15.02 thf('4', plain, 114.13/15.02 (( induction2lem ) <=> 114.13/15.02 ( ![X5:( term > $o )]: 114.13/15.02 ( ( ![X7:term,X9:term]: 114.13/15.02 ( ( X5 @ X7 ) => ( ( X5 @ X9 ) => ( X5 @ ( ap @ X7 @ X9 ) ) ) ) ) => 114.13/15.02 ( ( ![X11:term]: 114.13/15.02 ( ( ![X13:term]: 114.13/15.02 ( ( X5 @ X13 ) => 114.13/15.02 ( X5 @ ( sub @ X11 @ ( push @ X13 @ id ) ) ) ) ) => 114.13/15.02 ( X5 @ ( lam @ X11 ) ) ) ) => 114.13/15.02 ( ![X15:term,X17:subst]: 114.13/15.02 ( ( ![X19:term]: 114.13/15.02 ( ( var @ X19 ) => ( X5 @ ( sub @ X19 @ X17 ) ) ) ) => 114.13/15.02 ( X5 @ ( sub @ X15 @ X17 ) ) ) ) ) ) )), 114.13/15.02 inference('rw.lit', [status(esa)], [induction2lem])). 114.13/15.02 thf(zip_derived_cl155, plain, 114.13/15.02 ( (((!!) @ (^[Y0 : term > $o]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((!!) @ (^[Y2 : term]: 114.13/15.02 (((Y0 @ Y1) => 114.13/15.02 (((Y0 @ Y2) => (Y0 @ 114.13/15.02 (ap @ Y1 @ Y2)))))))))))) => 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((Y0 @ Y2) => (Y0 @ 114.13/15.02 (sub @ Y1 @ 114.13/15.02 (push @ Y2 @ id)))))))) => 114.13/15.02 (Y0 @ (lam @ Y1))))))) => 114.13/15.02 (((!!) @ (^[Y1 : term]: 114.13/15.02 (((!!) @ (^[Y2 : subst]: 114.13/15.02 (((((!!) @ (^[Y3 : term]: 114.13/15.02 (((var @ Y3) => 114.13/15.02 (Y0 @ 114.13/15.02 (sub @ Y3 @ Y2))))))) => 114.13/15.02 (Y0 @ (sub @ Y1 @ Y2)))))))))))))))))), 114.13/15.02 inference('rw_clause', [status(thm)], [zip_derived_cl151, '4'])). 114.13/15.02 thf(zip_derived_cl159, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (((((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : term]: 114.13/15.02 (((X2 @ Y0) => 114.13/15.02 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 114.13/15.02 (((((!!) @ (^[Y0 : term]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((X2 @ Y1) => (X2 @ 114.13/15.02 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 114.13/15.02 (X2 @ (lam @ Y0))))))) => 114.13/15.02 (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : subst]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((var @ Y2) => (X2 @ 114.13/15.02 (sub @ Y2 @ Y1))))))) => 114.13/15.02 (X2 @ (sub @ Y0 @ Y1))))))))))))))), 114.13/15.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl155])). 114.13/15.02 thf(zip_derived_cl164, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (~ (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : term]: 114.13/15.02 (((X2 @ Y0) => 114.13/15.02 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) 114.13/15.02 | (((((!!) @ (^[Y0 : term]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((X2 @ Y1) => (X2 @ 114.13/15.02 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 114.13/15.02 (X2 @ (lam @ Y0))))))) => 114.13/15.02 (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : subst]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((var @ Y2) => (X2 @ 114.13/15.02 (sub @ Y2 @ Y1))))))) => 114.13/15.02 (X2 @ (sub @ Y0 @ Y1)))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 114.13/15.02 thf(zip_derived_cl172, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (~ (((!!) @ (^[Y0 : term]: 114.13/15.02 (((X2 @ ('#sk110' @ X2)) => 114.13/15.02 (((X2 @ Y0) => (X2 @ (ap @ ('#sk110' @ X2) @ Y0))))))))) 114.13/15.02 | (((((!!) @ (^[Y0 : term]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((X2 @ Y1) => (X2 @ 114.13/15.02 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 114.13/15.02 (X2 @ (lam @ Y0))))))) => 114.13/15.02 (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : subst]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((var @ Y2) => (X2 @ 114.13/15.02 (sub @ Y2 @ Y1))))))) => 114.13/15.02 (X2 @ (sub @ Y0 @ Y1)))))))))))))), 114.13/15.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl164])). 114.13/15.02 thf(zip_derived_cl172, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (~ (((!!) @ (^[Y0 : term]: 114.13/15.02 (((X2 @ ('#sk110' @ X2)) => 114.13/15.02 (((X2 @ Y0) => (X2 @ (ap @ ('#sk110' @ X2) @ Y0))))))))) 114.13/15.02 | (((((!!) @ (^[Y0 : term]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((X2 @ Y1) => (X2 @ 114.13/15.02 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 114.13/15.02 (X2 @ (lam @ Y0))))))) => 114.13/15.02 (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : subst]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((var @ Y2) => (X2 @ 114.13/15.02 (sub @ Y2 @ Y1))))))) => 114.13/15.02 (X2 @ (sub @ Y0 @ Y1)))))))))))))), 114.13/15.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl164])). 114.13/15.02 thf(zip_derived_cl179, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 ( ('#form140' @ X2) 114.13/15.02 | ~ (((!!) @ (^[Y0 : term]: 114.13/15.02 (((X2 @ ('#sk110' @ X2)) => 114.13/15.02 (((X2 @ Y0) => (X2 @ (ap @ ('#sk110' @ X2) @ Y0))))))))))), 114.13/15.02 define([status(thm)])). 114.13/15.02 thf(zip_derived_cl181, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (~ ('#form140' @ X2) 114.13/15.02 | (((((!!) @ (^[Y0 : term]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((X2 @ Y1) => (X2 @ 114.13/15.02 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 114.13/15.02 (X2 @ (lam @ Y0))))))) => 114.13/15.02 (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : subst]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((var @ Y2) => (X2 @ 114.13/15.02 (sub @ Y2 @ Y1))))))) => 114.13/15.02 (X2 @ (sub @ Y0 @ Y1)))))))))))))), 114.13/15.02 inference('renaming', [status(thm)], 114.13/15.02 [zip_derived_cl172, zip_derived_cl179])). 114.13/15.02 thf(zip_derived_cl189, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (~ (((!!) @ (^[Y0 : term]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((X2 @ Y1) => (X2 @ 114.13/15.02 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 114.13/15.02 (X2 @ (lam @ Y0))))))) 114.13/15.02 | (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : subst]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((var @ Y2) => (X2 @ 114.13/15.02 (sub @ Y2 @ Y1))))))) => 114.13/15.02 (X2 @ (sub @ Y0 @ Y1)))))))))) 114.13/15.02 | ~ ('#form140' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl181])). 114.13/15.02 thf(zip_derived_cl198, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (~ (((((!!) @ (^[Y0 : term]: 114.13/15.02 (((X2 @ Y0) => (X2 @ 114.13/15.02 (sub @ ('#sk186' @ X2) @ (push @ Y0 @ id)))))))) => 114.13/15.02 (X2 @ (lam @ ('#sk186' @ X2))))) 114.13/15.02 | ~ ('#form140' @ X2) 114.13/15.02 | (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : subst]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((var @ Y2) => (X2 @ 114.13/15.02 (sub @ Y2 @ Y1))))))) => 114.13/15.02 (X2 @ (sub @ Y0 @ Y1)))))))))))), 114.13/15.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl189])). 114.13/15.02 thf(zip_derived_cl206, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 ( (((!!) @ (^[Y0 : term]: 114.13/15.02 (((X2 @ Y0) => (X2 @ 114.13/15.02 (sub @ ('#sk186' @ X2) @ (push @ Y0 @ id)))))))) 114.13/15.02 | (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : subst]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((var @ Y2) => (X2 @ 114.13/15.02 (sub @ Y2 @ Y1))))))) => 114.13/15.02 (X2 @ (sub @ Y0 @ Y1)))))))))) 114.13/15.02 | ~ ('#form140' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl198])). 114.13/15.02 thf(zip_derived_cl214, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (~ ('#form233' @ X2) 114.13/15.02 | (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : subst]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((var @ Y2) => (X2 @ 114.13/15.02 (sub @ Y2 @ Y1))))))) => 114.13/15.02 (X2 @ (sub @ Y0 @ Y1)))))))))))), 114.13/15.02 define([status(thm)])). 114.13/15.02 thf(zip_derived_cl215, plain, 114.13/15.02 (![X2 : term > $o, X4 : term]: 114.13/15.02 ( (((!!) @ (^[Y0 : subst]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 (((var @ Y1) => (X2 @ (sub @ Y1 @ Y0))))))) => 114.13/15.02 (X2 @ (sub @ X4 @ Y0))))))) 114.13/15.02 | ~ ('#form233' @ X2))), 114.13/15.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl214])). 114.13/15.02 thf(zip_derived_cl223, plain, 114.13/15.02 (![X2 : term > $o, X4 : term, X6 : subst]: 114.13/15.02 ( (((((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ (sub @ Y0 @ X6))))))) => 114.13/15.02 (X2 @ (sub @ X4 @ X6)))) 114.13/15.02 | ~ ('#form233' @ X2))), 114.13/15.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl215])). 114.13/15.02 thf(zip_derived_cl226, plain, 114.13/15.02 (![X2 : term > $o, X4 : term, X6 : subst]: 114.13/15.02 (~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ (sub @ Y0 @ X6))))))) 114.13/15.02 | (X2 @ (sub @ X4 @ X6)) 114.13/15.02 | ~ ('#form233' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl223])). 114.13/15.02 thf(zip_derived_cl227, plain, 114.13/15.02 (![X2 : term > $o, X4 : term, X6 : subst]: 114.13/15.02 (~ (((var @ ('#sk127' @ X2 @ X6)) => (X2 @ 114.13/15.02 (sub @ ('#sk127' @ X2 @ X6) @ X6)))) 114.13/15.02 | ~ ('#form233' @ X2) 114.13/15.02 | (X2 @ (sub @ X4 @ X6)))), 114.13/15.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl226])). 114.13/15.02 thf(zip_derived_cl228, plain, 114.13/15.02 (![X2 : term > $o, X4 : term, X6 : subst]: 114.13/15.02 ( (var @ ('#sk127' @ X2 @ X6)) 114.13/15.02 | (X2 @ (sub @ X4 @ X6)) 114.13/15.02 | ~ ('#form233' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl227])). 114.13/15.02 thf(zip_derived_cl165, plain, 114.13/15.02 ( (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk53' @ Y0))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl160])). 114.13/15.02 thf(zip_derived_cl173, plain, 114.13/15.02 (![X2 : term]: (((var @ X2) => ('#sk53' @ X2)))), 114.13/15.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl165])). 114.13/15.02 thf(zip_derived_cl182, plain, 114.13/15.02 (![X2 : term]: (~ (var @ X2) | ('#sk53' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])). 114.13/15.02 thf(zip_derived_cl10, plain, ( (axvarid)), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 114.13/15.02 thf(axvarid, axiom, (axvarid) => 114.13/15.02 ((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) = ($true))). 114.13/15.02 thf('5', plain, 114.13/15.02 (( axvarid ) <=> ( ![X5:term]: ( ( sub @ X5 @ id ) = ( X5 ) ) )), 114.13/15.02 inference('rw.lit', [status(esa)], [axvarid])). 114.13/15.02 thf(zip_derived_cl14, plain, 114.13/15.02 ( (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0))))))), 114.13/15.02 inference('rw_clause', [status(thm)], [zip_derived_cl10, '5'])). 114.13/15.02 thf(zip_derived_cl19, plain, (![X2 : term]: (((sub @ X2 @ id) = (X2)))), 114.13/15.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 114.13/15.02 thf(zip_derived_cl25, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))), 114.13/15.02 inference('simplify nested equalities', [status(thm)], [zip_derived_cl19])). 114.13/15.02 thf(zip_derived_cl207, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (~ (X2 @ (lam @ ('#sk186' @ X2))) 114.13/15.02 | (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : subst]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((var @ Y2) => (X2 @ 114.13/15.02 (sub @ Y2 @ Y1))))))) => 114.13/15.02 (X2 @ (sub @ Y0 @ Y1)))))))))) 114.13/15.02 | ~ ('#form140' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl198])). 114.13/15.02 thf(zip_derived_cl214, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (~ ('#form233' @ X2) 114.13/15.02 | (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : subst]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((var @ Y2) => (X2 @ 114.13/15.02 (sub @ Y2 @ Y1))))))) => 114.13/15.02 (X2 @ (sub @ Y0 @ Y1)))))))))))), 114.13/15.02 define([status(thm)])). 114.13/15.02 thf(zip_derived_cl217, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 ( ('#form233' @ X2) 114.13/15.02 | ~ ('#form140' @ X2) 114.13/15.02 | ~ (X2 @ (lam @ ('#sk186' @ X2))))), 114.13/15.02 inference('renaming', [status(thm)], 114.13/15.02 [zip_derived_cl207, zip_derived_cl214])). 114.13/15.02 thf(zip_derived_cl229, plain, 114.13/15.02 (![X2 : term > $o, X4 : term, X6 : subst]: 114.13/15.02 (~ (X2 @ (sub @ ('#sk127' @ X2 @ X6) @ X6)) 114.13/15.02 | (X2 @ (sub @ X4 @ X6)) 114.13/15.02 | ~ ('#form233' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl227])). 114.13/15.02 thf(zip_derived_cl184, plain, 114.13/15.02 ( (((!!) @ (^[Y0 : term]: 114.13/15.02 (((((!!) @ (^[Y1 : term]: 114.13/15.02 ((('#sk53' @ Y1) => ('#sk53' @ 114.13/15.02 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 114.13/15.02 ('#sk53' @ (lam @ Y0)))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])). 114.13/15.02 thf(zip_derived_cl193, plain, 114.13/15.02 (![X2 : term]: 114.13/15.02 (((((!!) @ (^[Y0 : term]: 114.13/15.02 ((('#sk53' @ Y0) => ('#sk53' @ 114.13/15.02 (sub @ X2 @ (push @ Y0 @ id)))))))) => 114.13/15.02 ('#sk53' @ (lam @ X2))))), 114.13/15.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl184])). 114.13/15.02 thf(zip_derived_cl202, plain, 114.13/15.02 (![X2 : term]: 114.13/15.02 (~ (((!!) @ (^[Y0 : term]: 114.13/15.02 ((('#sk53' @ Y0) => ('#sk53' @ 114.13/15.02 (sub @ X2 @ (push @ Y0 @ id)))))))) 114.13/15.02 | ('#sk53' @ (lam @ X2)))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl193])). 114.13/15.02 thf(zip_derived_cl209, plain, 114.13/15.02 (![X2 : term]: 114.13/15.02 (~ ((('#sk53' @ ('#sk217' @ X2)) => ('#sk53' @ 114.13/15.02 (sub @ X2 @ (push @ ('#sk217' @ X2) @ id))))) 114.13/15.02 | ('#sk53' @ (lam @ X2)))), 114.13/15.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl202])). 114.13/15.02 thf(zip_derived_cl218, plain, 114.13/15.02 (![X2 : term]: ( ('#sk53' @ ('#sk217' @ X2)) | ('#sk53' @ (lam @ X2)))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl209])). 114.13/15.02 thf(zip_derived_cl179, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 ( ('#form140' @ X2) 114.13/15.02 | ~ (((!!) @ (^[Y0 : term]: 114.13/15.02 (((X2 @ ('#sk110' @ X2)) => 114.13/15.02 (((X2 @ Y0) => (X2 @ (ap @ ('#sk110' @ X2) @ Y0))))))))))), 114.13/15.02 define([status(thm)])). 114.13/15.02 thf(zip_derived_cl180, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (~ (((X2 @ ('#sk110' @ X2)) => 114.13/15.02 (((X2 @ ('#sk141' @ X2)) => (X2 @ 114.13/15.02 (ap @ ('#sk110' @ X2) @ ('#sk141' @ X2))))))) 114.13/15.02 | ('#form140' @ X2))), 114.13/15.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl179])). 114.13/15.02 thf(zip_derived_cl191, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (~ (((X2 @ ('#sk141' @ X2)) => (X2 @ 114.13/15.02 (ap @ ('#sk110' @ X2) @ ('#sk141' @ X2))))) 114.13/15.02 | ('#form140' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl180])). 114.13/15.02 thf(zip_derived_cl200, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (~ (X2 @ (ap @ ('#sk110' @ X2) @ ('#sk141' @ X2))) 114.13/15.02 | ('#form140' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])). 114.13/15.02 thf(zip_derived_cl174, plain, 114.13/15.02 ( (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : term]: 114.13/15.02 ((('#sk53' @ Y0) => 114.13/15.02 ((('#sk53' @ Y1) => ('#sk53' @ 114.13/15.02 (ap @ Y0 @ Y1))))))))))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl166])). 114.13/15.02 thf(zip_derived_cl183, plain, 114.13/15.02 (![X2 : term]: 114.13/15.02 (((!!) @ (^[Y0 : term]: 114.13/15.02 ((('#sk53' @ X2) => 114.13/15.02 ((('#sk53' @ Y0) => ('#sk53' @ (ap @ X2 @ Y0)))))))))), 114.13/15.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl174])). 114.13/15.02 thf(zip_derived_cl192, plain, 114.13/15.02 (![X2 : term, X4 : term]: 114.13/15.02 ((('#sk53' @ X2) => ((('#sk53' @ X4) => ('#sk53' @ (ap @ X2 @ X4))))))), 114.13/15.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl183])). 114.13/15.02 thf(zip_derived_cl201, plain, 114.13/15.02 (![X2 : term, X4 : term]: 114.13/15.02 (~ ('#sk53' @ X2) | ((('#sk53' @ X4) => ('#sk53' @ (ap @ X2 @ X4)))))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl192])). 114.13/15.02 thf(zip_derived_cl208, plain, 114.13/15.02 (![X2 : term, X4 : term]: 114.13/15.02 (~ ('#sk53' @ X4) | ('#sk53' @ (ap @ X2 @ X4)) | ~ ('#sk53' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl201])). 114.13/15.02 thf(zip_derived_cl2753, plain, 114.13/15.02 (( ('#form140' @ '#sk53') 114.13/15.02 | ~ ('#sk53' @ ('#sk110' @ '#sk53')) 114.13/15.02 | ~ ('#sk53' @ ('#sk141' @ '#sk53')))), 114.13/15.02 inference('sup+', [status(thm)], [zip_derived_cl200, zip_derived_cl208])). 114.13/15.02 thf(zip_derived_cl190, plain, 114.13/15.02 (![X2 : term > $o]: ( (X2 @ ('#sk110' @ X2)) | ('#form140' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl180])). 114.13/15.02 thf(zip_derived_cl2768, plain, 114.13/15.02 ((~ ('#sk53' @ ('#sk141' @ '#sk53')) | ('#form140' @ '#sk53'))), 114.13/15.02 inference('clc', [status(thm)], [zip_derived_cl2753, zip_derived_cl190])). 114.13/15.02 thf(zip_derived_cl199, plain, 114.13/15.02 (![X2 : term > $o]: ( (X2 @ ('#sk141' @ X2)) | ('#form140' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])). 114.13/15.02 thf(zip_derived_cl2769, plain, ( ('#form140' @ '#sk53')), 114.13/15.02 inference('clc', [status(thm)], [zip_derived_cl2768, zip_derived_cl199])). 114.13/15.02 thf(zip_derived_cl219, plain, 114.13/15.02 (![X2 : term]: 114.13/15.02 (~ ('#sk53' @ (sub @ X2 @ (push @ ('#sk217' @ X2) @ id))) 114.13/15.02 | ('#sk53' @ (lam @ X2)))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl209])). 114.13/15.02 thf(zip_derived_cl206, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 ( (((!!) @ (^[Y0 : term]: 114.13/15.02 (((X2 @ Y0) => (X2 @ 114.13/15.02 (sub @ ('#sk186' @ X2) @ (push @ Y0 @ id)))))))) 114.13/15.02 | (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : subst]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((var @ Y2) => (X2 @ 114.13/15.02 (sub @ Y2 @ Y1))))))) => 114.13/15.02 (X2 @ (sub @ Y0 @ Y1)))))))))) 114.13/15.02 | ~ ('#form140' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl198])). 114.13/15.02 thf(zip_derived_cl214, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 (~ ('#form233' @ X2) 114.13/15.02 | (((!!) @ (^[Y0 : term]: 114.13/15.02 (((!!) @ (^[Y1 : subst]: 114.13/15.02 (((((!!) @ (^[Y2 : term]: 114.13/15.02 (((var @ Y2) => (X2 @ 114.13/15.02 (sub @ Y2 @ Y1))))))) => 114.13/15.02 (X2 @ (sub @ Y0 @ Y1)))))))))))), 114.13/15.02 define([status(thm)])). 114.13/15.02 thf(zip_derived_cl216, plain, 114.13/15.02 (![X2 : term > $o]: 114.13/15.02 ( ('#form233' @ X2) 114.13/15.02 | ~ ('#form140' @ X2) 114.13/15.02 | (((!!) @ (^[Y0 : term]: 114.13/15.02 (((X2 @ Y0) => (X2 @ 114.13/15.02 (sub @ ('#sk186' @ X2) @ (push @ Y0 @ id)))))))))), 114.13/15.02 inference('renaming', [status(thm)], 114.13/15.02 [zip_derived_cl206, zip_derived_cl214])). 114.13/15.02 thf(zip_derived_cl222, plain, 114.13/15.02 (![X2 : term > $o, X4 : term]: 114.13/15.02 ( (((X2 @ X4) => (X2 @ (sub @ ('#sk186' @ X2) @ (push @ X4 @ id))))) 114.13/15.02 | ~ ('#form140' @ X2) 114.13/15.02 | ('#form233' @ X2))), 114.13/15.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl216])). 114.13/15.02 thf(zip_derived_cl225, plain, 114.13/15.02 (![X2 : term > $o, X4 : term]: 114.13/15.02 (~ (X2 @ X4) 114.13/15.02 | (X2 @ (sub @ ('#sk186' @ X2) @ (push @ X4 @ id))) 114.13/15.02 | ('#form233' @ X2) 114.13/15.02 | ~ ('#form140' @ X2))), 114.13/15.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])). 114.13/15.02 thf(zip_derived_cl12614, plain, ($false), 114.13/15.02 inference('eprover', [status(thm)], 114.13/15.02 [zip_derived_cl194, zip_derived_cl228, zip_derived_cl182, 114.13/15.02 zip_derived_cl25, zip_derived_cl217, zip_derived_cl229, 114.13/15.02 zip_derived_cl218, zip_derived_cl2769, zip_derived_cl219, 114.13/15.02 zip_derived_cl225])). 114.13/15.02 114.13/15.02 % SZS output end Refutation 114.13/15.02 114.13/15.02 114.13/15.02 % Terminating... 114.43/15.16 % Runner terminated. 114.43/15.17 % Zipperpin 1.5 exiting 114.43/15.17 EOF