%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ALG263^3 : TPTP v9.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.vuH6v8YuN2 true
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:28:29 PM UTC 2025
% Result : Theorem 1.39s 1.06s
% Output : Refutation 1.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG263^3 : TPTP v9.2.0. Bugfixed v5.2.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.vuH6v8YuN2 true
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 17:03:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35 % Number of cores: 8
% 0.12/0.35 % Python version: Python 3.6.8
% 0.12/0.35 % Running in HO mode
% 0.61/0.62 % Total configuration time : 828
% 0.61/0.62 % Estimated wc time : 1656
% 0.61/0.62 % Estimated cpu time (8 cpus) : 207.0
% 0.87/0.68 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.87/0.69 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.87/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.28/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.28/0.71 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.28/0.71 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.28/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.28/0.73 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.34/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.39/1.06 % Solved by lams/30_b.l.sh.
% 1.39/1.06 % done 14 iterations in 0.225s
% 1.39/1.06 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.39/1.06 % SZS output start Refutation
% 1.39/1.06 thf(subst_type, type, subst: $tType).
% 1.39/1.06 thf(term_type, type, term: $tType).
% 1.39/1.06 thf(axmap_type, type, axmap: $o).
% 1.39/1.06 thf(axclos_type, type, axclos: $o).
% 1.39/1.06 thf(lamnotap_type, type, lamnotap: $o).
% 1.39/1.06 thf(axvarcons_type, type, axvarcons: $o).
% 1.39/1.06 thf('#sk46_type', type, '#sk46': (term > $o) > term).
% 1.39/1.06 thf(substmonoid_type, type, substmonoid: $o).
% 1.39/1.06 thf(push_type, type, push: term > subst > subst).
% 1.39/1.06 thf('#sk422_type', type, '#sk422': subst > term > subst > $o).
% 1.39/1.06 thf(axshiftcons_type, type, axshiftcons: $o).
% 1.39/1.06 thf(hoasinduction_lem1v2_type, type, hoasinduction_lem1v2: $o).
% 1.39/1.06 thf(hoasapinj1_type, type, hoasapinj1: $o).
% 1.39/1.06 thf(hoasinduction_p_and_p_prime_type, type, hoasinduction_p_and_p_prime:
% 1.39/1.06 (subst > term > subst > $o) > (term > $o) > $o).
% 1.39/1.06 thf(axapp_type, type, axapp: $o).
% 1.39/1.06 thf(shinj_type, type, shinj: $o).
% 1.39/1.06 thf(hoaslaminj_type, type, hoaslaminj: $o).
% 1.39/1.06 thf(one_type, type, one: term).
% 1.39/1.06 thf(id_type, type, id: subst).
% 1.39/1.06 thf(comp_type, type, comp: subst > subst > subst).
% 1.39/1.06 thf(hoaslamnotap_type, type, hoaslamnotap: $o).
% 1.39/1.06 thf(induction2_type, type, induction2: $o).
% 1.39/1.06 thf(axvarid_type, type, axvarid: $o).
% 1.39/1.06 thf(axvarshift_type, type, axvarshift: $o).
% 1.39/1.06 thf(induction2lem_type, type, induction2lem: $o).
% 1.39/1.06 thf(sh_type, type, sh: subst).
% 1.39/1.06 thf(laminj_type, type, laminj: $o).
% 1.39/1.06 thf(ulamvarind_type, type, ulamvarind: $o).
% 1.39/1.06 thf(apinj2_type, type, apinj2: $o).
% 1.39/1.06 thf(ulamvarsh_type, type, ulamvarsh: $o).
% 1.39/1.06 thf(lamnotvar_type, type, lamnotvar: $o).
% 1.39/1.06 thf(apnotvar_type, type, apnotvar: $o).
% 1.39/1.06 thf(pushprop_type, type, pushprop: $o).
% 1.39/1.06 thf(sub_type, type, sub: term > subst > term).
% 1.39/1.06 thf(apinj1_type, type, apinj1: $o).
% 1.39/1.06 thf(axidl_type, type, axidl: $o).
% 1.39/1.06 thf(termmset_type, type, termmset: $o).
% 1.39/1.06 thf(hoasapinj2_type, type, hoasapinj2: $o).
% 1.39/1.06 thf('#sk459_type', type, '#sk459': term > $o).
% 1.39/1.06 thf(hoasapnotvar_type, type, hoasapnotvar: $o).
% 1.39/1.06 thf(var_type, type, var: term > $o).
% 1.39/1.06 thf(axassoc_type, type, axassoc: $o).
% 1.39/1.06 thf(hoaslamnotvar_type, type, hoaslamnotvar: $o).
% 1.39/1.06 thf(axidr_type, type, axidr: $o).
% 1.39/1.06 thf(axabs_type, type, axabs: $o).
% 1.39/1.06 thf(hoasvar_type, type, hoasvar: subst > term > subst > $o).
% 1.39/1.06 thf(ulamvar1_type, type, ulamvar1: $o).
% 1.39/1.06 thf(hoasinduction_lem1v2_gthm_type, type, hoasinduction_lem1v2_gthm: $o).
% 1.39/1.06 thf(induction_type, type, induction: $o).
% 1.39/1.06 thf(axscons_type, type, axscons: $o).
% 1.39/1.06 thf(thm, conjecture, (hoasinduction_lem1v2_gthm)).
% 1.39/1.06 thf(zf_stmt_0, negated_conjecture, (~( hoasinduction_lem1v2_gthm )),
% 1.39/1.06 inference('cnf.neg', [status(esa)], [thm])).
% 1.39/1.06 thf(zip_derived_cl0, plain, (~ (hoasinduction_lem1v2_gthm)),
% 1.39/1.06 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.39/1.06 thf(hoasinduction_lem1v2_gthm, axiom, ~ (hoasinduction_lem1v2_gthm) =>
% 1.39/1.06 ((((axapp) =>
% 1.39/1.06 (((axvarcons) =>
% 1.39/1.06 (((axvarid) =>
% 1.39/1.06 (((axabs) =>
% 1.39/1.06 (((axclos) =>
% 1.39/1.06 (((axidl) =>
% 1.39/1.06 (((axshiftcons) =>
% 1.39/1.06 (((axassoc) =>
% 1.39/1.06 (((axmap) =>
% 1.39/1.06 (((axidr) =>
% 1.39/1.06 (((axvarshift) =>
% 1.39/1.06 (((axscons) =>
% 1.39/1.06 (((ulamvar1) =>
% 1.39/1.06 (((ulamvarsh) =>
% 1.39/1.06 (((ulamvarind) =>
% 1.39/1.06 (((apinj1) =>
% 1.39/1.06 (((apinj2) =>
% 1.39/1.06 (((laminj) =>
% 1.39/1.06 (((shinj) =>
% 1.39/1.06 (((lamnotap) =>
% 1.39/1.06 (((apnotvar) =>
% 1.39/1.06 (((lamnotvar) =>
% 1.39/1.06 (((induction) =>
% 1.39/1.06 (((pushprop) =>
% 1.39/1.06 (((induction2lem) =>
% 1.39/1.06 (((induction2) =>
% 1.39/1.06 (((substmonoid) =>
% 1.39/1.06 (((termmset) =>
% 1.39/1.06 (((hoasapinj1) =>
% 1.39/1.06 (((hoasapinj2) =>
% 1.39/1.06 (((hoaslaminj) =>
% 1.39/1.06 (((hoaslamnotap) =>
% 1.39/1.06 ((
% 1.39/1.06 (hoaslamnotvar) =>
% 1.39/1.06 ((
% 1.39/1.06 (hoasapnotvar) =>
% 1.39/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.39/1.06 != ($true))).
% 1.39/1.06 thf('0', plain,
% 1.39/1.06 (( ~( hoasinduction_lem1v2_gthm ) ) <=>
% 1.39/1.06 ( ~( ( axapp ) =>
% 1.39/1.06 ( ( axvarcons ) =>
% 1.39/1.06 ( ( axvarid ) =>
% 1.39/1.06 ( ( axabs ) =>
% 1.39/1.06 ( ( axclos ) =>
% 1.39/1.06 ( ( axidl ) =>
% 1.39/1.06 ( ( axshiftcons ) =>
% 1.39/1.06 ( ( axassoc ) =>
% 1.39/1.06 ( ( axmap ) =>
% 1.39/1.06 ( ( axidr ) =>
% 1.39/1.06 ( ( axvarshift ) =>
% 1.39/1.06 ( ( axscons ) =>
% 1.39/1.06 ( ( ulamvar1 ) =>
% 1.39/1.06 ( ( ulamvarsh ) =>
% 1.39/1.06 ( ( ulamvarind ) =>
% 1.39/1.06 ( ( apinj1 ) =>
% 1.39/1.06 ( ( apinj2 ) =>
% 1.39/1.06 ( ( laminj ) =>
% 1.39/1.06 ( ( shinj ) =>
% 1.39/1.06 ( ( lamnotap ) =>
% 1.39/1.06 ( ( apnotvar ) =>
% 1.39/1.06 ( ( lamnotvar ) =>
% 1.39/1.06 ( ( induction ) =>
% 1.39/1.06 ( ( pushprop ) =>
% 1.39/1.06 ( ( induction2lem ) =>
% 1.39/1.06 ( ( induction2 ) =>
% 1.39/1.06 ( ( substmonoid ) =>
% 1.39/1.06 ( ( termmset ) =>
% 1.39/1.06 ( ( hoasapinj1 ) =>
% 1.39/1.06 ( (
% 1.39/1.06 hoasapinj2 ) =>
% 1.39/1.06 (
% 1.39/1.06 (
% 1.39/1.06 hoaslaminj ) =>
% 1.39/1.06 (
% 1.39/1.06 (
% 1.39/1.06 hoaslamnotap ) =>
% 1.39/1.06 (
% 1.39/1.06 (
% 1.39/1.06 hoaslamnotvar ) =>
% 1.39/1.06 (
% 1.39/1.06 (
% 1.39/1.06 hoasapnotvar ) =>
% 1.39/1.06 (
% 1.39/1.06 hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 1.39/1.06 inference('rw.lit', [status(esa)], [hoasinduction_lem1v2_gthm])).
% 1.39/1.06 thf(zip_derived_cl1, plain,
% 1.39/1.06 (~ (((axapp) =>
% 1.39/1.06 (((axvarcons) =>
% 1.39/1.06 (((axvarid) =>
% 1.39/1.06 (((axabs) =>
% 1.39/1.06 (((axclos) =>
% 1.39/1.06 (((axidl) =>
% 1.39/1.06 (((axshiftcons) =>
% 1.39/1.06 (((axassoc) =>
% 1.39/1.06 (((axmap) =>
% 1.39/1.06 (((axidr) =>
% 1.39/1.06 (((axvarshift) =>
% 1.39/1.06 (((axscons) =>
% 1.39/1.06 (((ulamvar1) =>
% 1.39/1.06 (((ulamvarsh) =>
% 1.39/1.06 (((ulamvarind) =>
% 1.39/1.06 (((apinj1) =>
% 1.39/1.06 (((apinj2) =>
% 1.39/1.06 (((laminj) =>
% 1.39/1.06 (((shinj) =>
% 1.39/1.06 (((lamnotap) =>
% 1.39/1.06 (((apnotvar) =>
% 1.39/1.06 (((lamnotvar) =>
% 1.39/1.06 (((induction) =>
% 1.39/1.06 (((pushprop) =>
% 1.39/1.06 (((induction2lem) =>
% 1.39/1.06 (((induction2) =>
% 1.39/1.06 (((substmonoid) =>
% 1.39/1.06 (((termmset) =>
% 1.39/1.06 (((hoasapinj1) =>
% 1.39/1.06 (((hoasapinj2) =>
% 1.39/1.06 ((
% 1.39/1.06 (hoaslaminj) =>
% 1.39/1.06 ((
% 1.39/1.06 (hoaslamnotap) =>
% 1.39/1.06 ((
% 1.39/1.06 (hoaslamnotvar) =>
% 1.39/1.06 ((
% 1.39/1.06 (hoasapnotvar) =>
% 1.39/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.39/1.06 inference('rw_clause', [status(thm)], [zip_derived_cl0, '0'])).
% 1.39/1.06 thf(axvarshift, axiom,(( axvarshift ) = ((((push @ one @ sh) = (id)))))).
% 1.39/1.06 thf('1', plain, (( axvarshift ) = ( ( push @ one @ sh ) = ( id ) )),
% 1.39/1.06 define([status(thm)])).
% 1.39/1.06 thf(ulamvar1, axiom,(( ulamvar1 ) = ((var @ one)))).
% 1.39/1.06 thf('2', plain, (( ulamvar1 ) = ( var @ one )), define([status(thm)])).
% 1.39/1.06 thf(zip_derived_cl2, plain,
% 1.39/1.06 (~ (((axapp) =>
% 1.39/1.06 (((axvarcons) =>
% 1.39/1.06 (((axvarid) =>
% 1.39/1.06 (((axabs) =>
% 1.39/1.06 (((axclos) =>
% 1.39/1.06 (((axidl) =>
% 1.39/1.06 (((axshiftcons) =>
% 1.39/1.06 (((axassoc) =>
% 1.39/1.06 (((axmap) =>
% 1.39/1.06 (((axidr) =>
% 1.39/1.06 (((((push @ one @ sh) = (id))) =>
% 1.39/1.06 (((axscons) =>
% 1.39/1.06 (((var @ one) =>
% 1.39/1.06 (((ulamvarsh) =>
% 1.39/1.06 (((ulamvarind) =>
% 1.39/1.06 (((apinj1) =>
% 1.39/1.06 (((apinj2) =>
% 1.39/1.06 (((laminj) =>
% 1.39/1.06 (((shinj) =>
% 1.39/1.06 (((lamnotap) =>
% 1.39/1.06 (((apnotvar) =>
% 1.39/1.06 (((lamnotvar) =>
% 1.39/1.06 (((induction) =>
% 1.39/1.06 (((pushprop) =>
% 1.39/1.06 (((induction2lem) =>
% 1.39/1.06 (((induction2) =>
% 1.39/1.06 (((substmonoid) =>
% 1.39/1.06 (((termmset) =>
% 1.39/1.06 (((hoasapinj1) =>
% 1.39/1.06 (((hoasapinj2) =>
% 1.39/1.06 ((
% 1.39/1.06 (hoaslaminj) =>
% 1.39/1.06 ((
% 1.39/1.06 (hoaslamnotap) =>
% 1.39/1.06 ((
% 1.39/1.06 (hoaslamnotvar) =>
% 1.39/1.06 ((
% 1.39/1.06 (hoasapnotvar) =>
% 1.39/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.39/1.06 inference('rw', [status(thm)], [zip_derived_cl1, '1', '2'])).
% 1.39/1.06 thf(zip_derived_cl4, plain,
% 1.39/1.06 (~ (((axvarcons) =>
% 1.39/1.06 (((axvarid) =>
% 1.39/1.06 (((axabs) =>
% 1.39/1.06 (((axclos) =>
% 1.39/1.06 (((axidl) =>
% 1.39/1.06 (((axshiftcons) =>
% 1.39/1.06 (((axassoc) =>
% 1.39/1.06 (((axmap) =>
% 1.39/1.06 (((axidr) =>
% 1.39/1.06 (((((push @ one @ sh) = (id))) =>
% 1.39/1.06 (((axscons) =>
% 1.39/1.06 (((var @ one) =>
% 1.39/1.06 (((ulamvarsh) =>
% 1.39/1.06 (((ulamvarind) =>
% 1.39/1.06 (((apinj1) =>
% 1.39/1.06 (((apinj2) =>
% 1.39/1.06 (((laminj) =>
% 1.39/1.06 (((shinj) =>
% 1.39/1.06 (((lamnotap) =>
% 1.39/1.06 (((apnotvar) =>
% 1.39/1.06 (((lamnotvar) =>
% 1.39/1.06 (((induction) =>
% 1.39/1.06 (((pushprop) =>
% 1.39/1.06 (((induction2lem) =>
% 1.39/1.06 (((induction2) =>
% 1.39/1.06 (((substmonoid) =>
% 1.39/1.06 (((termmset) =>
% 1.39/1.06 (((hoasapinj1) =>
% 1.39/1.06 (((hoasapinj2) =>
% 1.39/1.06 (((hoaslaminj) =>
% 1.39/1.06 ((
% 1.39/1.06 (hoaslamnotap) =>
% 1.39/1.06 ((
% 1.39/1.06 (hoaslamnotvar) =>
% 1.39/1.06 ((
% 1.39/1.06 (hoasapnotvar) =>
% 1.39/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.39/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])).
% 1.39/1.06 thf(zip_derived_cl7, plain,
% 1.39/1.06 (~ (((axvarid) =>
% 1.39/1.06 (((axabs) =>
% 1.39/1.06 (((axclos) =>
% 1.39/1.06 (((axidl) =>
% 1.39/1.06 (((axshiftcons) =>
% 1.39/1.06 (((axassoc) =>
% 1.39/1.06 (((axmap) =>
% 1.39/1.06 (((axidr) =>
% 1.39/1.06 (((((push @ one @ sh) = (id))) =>
% 1.39/1.06 (((axscons) =>
% 1.39/1.06 (((var @ one) =>
% 1.39/1.06 (((ulamvarsh) =>
% 1.39/1.06 (((ulamvarind) =>
% 1.39/1.06 (((apinj1) =>
% 1.39/1.06 (((apinj2) =>
% 1.39/1.06 (((laminj) =>
% 1.39/1.06 (((shinj) =>
% 1.39/1.06 (((lamnotap) =>
% 1.39/1.06 (((apnotvar) =>
% 1.39/1.06 (((lamnotvar) =>
% 1.39/1.06 (((induction) =>
% 1.39/1.06 (((pushprop) =>
% 1.39/1.06 (((induction2lem) =>
% 1.39/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 ((
% 1.66/1.06 (hoaslamnotvar) =>
% 1.66/1.06 ((
% 1.66/1.06 (hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])).
% 1.66/1.06 thf(zip_derived_cl11, plain,
% 1.66/1.06 (~ (((axabs) =>
% 1.66/1.06 (((axclos) =>
% 1.66/1.06 (((axidl) =>
% 1.66/1.06 (((axshiftcons) =>
% 1.66/1.06 (((axassoc) =>
% 1.66/1.06 (((axmap) =>
% 1.66/1.06 (((axidr) =>
% 1.66/1.06 (((((push @ one @ sh) = (id))) =>
% 1.66/1.06 (((axscons) =>
% 1.66/1.06 (((var @ one) =>
% 1.66/1.06 (((ulamvarsh) =>
% 1.66/1.06 (((ulamvarind) =>
% 1.66/1.06 (((apinj1) =>
% 1.66/1.06 (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 ((
% 1.66/1.06 (hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 1.66/1.06 thf(zip_derived_cl16, plain,
% 1.66/1.06 (~ (((axclos) =>
% 1.66/1.06 (((axidl) =>
% 1.66/1.06 (((axshiftcons) =>
% 1.66/1.06 (((axassoc) =>
% 1.66/1.06 (((axmap) =>
% 1.66/1.06 (((axidr) =>
% 1.66/1.06 (((((push @ one @ sh) = (id))) =>
% 1.66/1.06 (((axscons) =>
% 1.66/1.06 (((var @ one) =>
% 1.66/1.06 (((ulamvarsh) =>
% 1.66/1.06 (((ulamvarind) =>
% 1.66/1.06 (((apinj1) =>
% 1.66/1.06 (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])).
% 1.66/1.06 thf(zip_derived_cl22, plain,
% 1.66/1.06 (~ (((axidl) =>
% 1.66/1.06 (((axshiftcons) =>
% 1.66/1.06 (((axassoc) =>
% 1.66/1.06 (((axmap) =>
% 1.66/1.06 (((axidr) =>
% 1.66/1.06 (((((push @ one @ sh) = (id))) =>
% 1.66/1.06 (((axscons) =>
% 1.66/1.06 (((var @ one) =>
% 1.66/1.06 (((ulamvarsh) =>
% 1.66/1.06 (((ulamvarind) =>
% 1.66/1.06 (((apinj1) =>
% 1.66/1.06 (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])).
% 1.66/1.06 thf(zip_derived_cl29, plain,
% 1.66/1.06 (~ (((axshiftcons) =>
% 1.66/1.06 (((axassoc) =>
% 1.66/1.06 (((axmap) =>
% 1.66/1.06 (((axidr) =>
% 1.66/1.06 (((((push @ one @ sh) = (id))) =>
% 1.66/1.06 (((axscons) =>
% 1.66/1.06 (((var @ one) =>
% 1.66/1.06 (((ulamvarsh) =>
% 1.66/1.06 (((ulamvarind) =>
% 1.66/1.06 (((apinj1) =>
% 1.66/1.06 (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])).
% 1.66/1.06 thf(zip_derived_cl34, plain,
% 1.66/1.06 (~ (((axassoc) =>
% 1.66/1.06 (((axmap) =>
% 1.66/1.06 (((axidr) =>
% 1.66/1.06 (((((push @ one @ sh) = (id))) =>
% 1.66/1.06 (((axscons) =>
% 1.66/1.06 (((var @ one) =>
% 1.66/1.06 (((ulamvarsh) =>
% 1.66/1.06 (((ulamvarind) =>
% 1.66/1.06 (((apinj1) =>
% 1.66/1.06 (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl29])).
% 1.66/1.06 thf(zip_derived_cl40, plain,
% 1.66/1.06 (~ (((axmap) =>
% 1.66/1.06 (((axidr) =>
% 1.66/1.06 (((((push @ one @ sh) = (id))) =>
% 1.66/1.06 (((axscons) =>
% 1.66/1.06 (((var @ one) =>
% 1.66/1.06 (((ulamvarsh) =>
% 1.66/1.06 (((ulamvarind) =>
% 1.66/1.06 (((apinj1) =>
% 1.66/1.06 (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 1.66/1.06 thf(zip_derived_cl46, plain,
% 1.66/1.06 (~ (((axidr) =>
% 1.66/1.06 (((((push @ one @ sh) = (id))) =>
% 1.66/1.06 (((axscons) =>
% 1.66/1.06 (((var @ one) =>
% 1.66/1.06 (((ulamvarsh) =>
% 1.66/1.06 (((ulamvarind) =>
% 1.66/1.06 (((apinj1) =>
% 1.66/1.06 (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
% 1.66/1.06 thf(zip_derived_cl52, plain,
% 1.66/1.06 (~ (((((push @ one @ sh) = (id))) =>
% 1.66/1.06 (((axscons) =>
% 1.66/1.06 (((var @ one) =>
% 1.66/1.06 (((ulamvarsh) =>
% 1.66/1.06 (((ulamvarind) =>
% 1.66/1.06 (((apinj1) =>
% 1.66/1.06 (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 1.66/1.06 thf(zip_derived_cl58, plain,
% 1.66/1.06 (~ (((axscons) =>
% 1.66/1.06 (((var @ one) =>
% 1.66/1.06 (((ulamvarsh) =>
% 1.66/1.06 (((ulamvarind) =>
% 1.66/1.06 (((apinj1) =>
% 1.66/1.06 (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
% 1.66/1.06 thf(zip_derived_cl64, plain,
% 1.66/1.06 (~ (((var @ one) =>
% 1.66/1.06 (((ulamvarsh) =>
% 1.66/1.06 (((ulamvarind) =>
% 1.66/1.06 (((apinj1) =>
% 1.66/1.06 (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])).
% 1.66/1.06 thf(zip_derived_cl70, plain,
% 1.66/1.06 (~ (((ulamvarsh) =>
% 1.66/1.06 (((ulamvarind) =>
% 1.66/1.06 (((apinj1) =>
% 1.66/1.06 (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 1.66/1.06 thf(zip_derived_cl74, plain,
% 1.66/1.06 (~ (((ulamvarind) =>
% 1.66/1.06 (((apinj1) =>
% 1.66/1.06 (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl70])).
% 1.66/1.06 thf(zip_derived_cl78, plain,
% 1.66/1.06 (~ (((apinj1) =>
% 1.66/1.06 (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])).
% 1.66/1.06 thf(zip_derived_cl82, plain,
% 1.66/1.06 (~ (((apinj2) =>
% 1.66/1.06 (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])).
% 1.66/1.06 thf(zip_derived_cl87, plain,
% 1.66/1.06 (~ (((laminj) =>
% 1.66/1.06 (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])).
% 1.66/1.06 thf(zip_derived_cl92, plain,
% 1.66/1.06 (~ (((shinj) =>
% 1.66/1.06 (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) =>
% 1.66/1.06 (hoasinduction_lem1v2)))))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])).
% 1.66/1.06 thf(zip_derived_cl98, plain,
% 1.66/1.06 (~ (((lamnotap) =>
% 1.66/1.06 (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) => (hoasinduction_lem1v2)))))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])).
% 1.66/1.06 thf(zip_derived_cl105, plain,
% 1.66/1.06 (~ (((apnotvar) =>
% 1.66/1.06 (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) => (hoasinduction_lem1v2)))))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl98])).
% 1.66/1.06 thf(zip_derived_cl114, plain,
% 1.66/1.06 (~ (((lamnotvar) =>
% 1.66/1.06 (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) => (hoasinduction_lem1v2)))))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])).
% 1.66/1.06 thf(zip_derived_cl125, plain,
% 1.66/1.06 (~ (((induction) =>
% 1.66/1.06 (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) => (hoasinduction_lem1v2)))))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])).
% 1.66/1.06 thf(zip_derived_cl137, plain,
% 1.66/1.06 (~ (((pushprop) =>
% 1.66/1.06 (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) => (hoasinduction_lem1v2)))))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])).
% 1.66/1.06 thf(zip_derived_cl147, plain,
% 1.66/1.06 (~ (((induction2lem) =>
% 1.66/1.06 (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) => (hoasinduction_lem1v2)))))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])).
% 1.66/1.06 thf(zip_derived_cl152, plain,
% 1.66/1.06 (~ (((induction2) =>
% 1.66/1.06 (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) => (hoasinduction_lem1v2)))))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl147])).
% 1.66/1.06 thf(zip_derived_cl157, plain,
% 1.66/1.06 (~ (((substmonoid) =>
% 1.66/1.06 (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) => (hoasinduction_lem1v2)))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl152])).
% 1.66/1.06 thf(zip_derived_cl163, plain,
% 1.66/1.06 (~ (((termmset) =>
% 1.66/1.06 (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) => (hoasinduction_lem1v2)))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl157])).
% 1.66/1.06 thf(zip_derived_cl171, plain,
% 1.66/1.06 (~ (((hoasapinj1) =>
% 1.66/1.06 (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) => (hoasinduction_lem1v2)))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl163])).
% 1.66/1.06 thf(zip_derived_cl184, plain,
% 1.66/1.06 (~ (((hoasapinj2) =>
% 1.66/1.06 (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) =>
% 1.66/1.06 (((hoasapnotvar) => (hoasinduction_lem1v2)))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl171])).
% 1.66/1.06 thf(zip_derived_cl199, plain,
% 1.66/1.06 (~ (((hoaslaminj) =>
% 1.66/1.06 (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) => (((hoasapnotvar) => (hoasinduction_lem1v2)))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl184])).
% 1.66/1.06 thf(zip_derived_cl216, plain,
% 1.66/1.06 (~ (((hoaslamnotap) =>
% 1.66/1.06 (((hoaslamnotvar) => (((hoasapnotvar) => (hoasinduction_lem1v2)))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl199])).
% 1.66/1.06 thf(zip_derived_cl234, plain,
% 1.66/1.06 (~ (((hoaslamnotvar) => (((hoasapnotvar) => (hoasinduction_lem1v2)))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl216])).
% 1.66/1.06 thf(zip_derived_cl250, plain,
% 1.66/1.06 (~ (((hoasapnotvar) => (hoasinduction_lem1v2)))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl234])).
% 1.66/1.06 thf(zip_derived_cl270, plain, (~ (hoasinduction_lem1v2)),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl250])).
% 1.66/1.06 thf(hoasinduction_lem1v2, axiom, ~ (hoasinduction_lem1v2) =>
% 1.66/1.06 ((((!!) @ (^[Y0 : subst > term > subst > $o]:
% 1.66/1.06 (((!!) @ (^[Y1 : term > $o]:
% 1.66/1.06 (((((!!) @ (^[Y2 : subst]:
% 1.66/1.06 (((!!) @ (^[Y3 : term]:
% 1.66/1.06 (((!!) @ (^[Y4 : subst]:
% 1.66/1.06 (((!!) @ (
% 1.66/1.06 ^[Y5 : subst]:
% 1.66/1.06 ((
% 1.66/1.06 (Y0 @
% 1.66/1.06 Y2 @
% 1.66/1.06 Y3 @
% 1.66/1.06 (
% 1.66/1.06 comp @
% 1.66/1.06 Y5 @ Y4)) =>
% 1.66/1.06 (Y0 @
% 1.66/1.06 (
% 1.66/1.06 comp @
% 1.66/1.06 Y2 @ Y5) @
% 1.66/1.06 (
% 1.66/1.06 sub @
% 1.66/1.06 Y3 @ Y5) @
% 1.66/1.06 Y4))))))))))))))) =>
% 1.66/1.06 (((((!!) @ (^[Y2 : subst]:
% 1.66/1.06 (((!!) @ (^[Y3 : term]:
% 1.66/1.06 (((!!) @ (^[Y4 : subst]:
% 1.66/1.06 ((
% 1.66/1.06 (!!) @ (
% 1.66/1.06 ^[Y5 : subst]:
% 1.66/1.06 ((
% 1.66/1.06 (Y0 @
% 1.66/1.06 (
% 1.66/1.06 comp @
% 1.66/1.06 Y2 @ Y5) @
% 1.66/1.06 (
% 1.66/1.06 sub @
% 1.66/1.06 Y3 @ Y5) @
% 1.66/1.06 Y4) =>
% 1.66/1.06 (Y0 @
% 1.66/1.06 Y2 @
% 1.66/1.06 Y3 @
% 1.66/1.06 (
% 1.66/1.06 comp @
% 1.66/1.06 Y5 @ Y4)))))))))))))))) =>
% 1.66/1.06 (((((!!) @ (^[Y2 : term]:
% 1.66/1.06 (((hoasvar @ id @ Y2 @ id) =>
% 1.66/1.06 (Y0 @ id @ Y2 @ id)))))) =>
% 1.66/1.06 (((hoasinduction_p_and_p_prime @ Y0 @ Y1) =>
% 1.66/1.06 (((!!) @ (^[Y2 : term]:
% 1.66/1.06 (((var @ Y2) => (Y1 @ Y2))))))))))))))))))))
% 1.66/1.06 != ($true))).
% 1.66/1.06 thf('3', plain,
% 1.66/1.06 (( ~( hoasinduction_lem1v2 ) ) <=>
% 1.66/1.06 ( ~( ![X5:( subst > term > subst > $o ),X7:( term > $o )]:
% 1.66/1.06 ( ( ![X9:subst,X11:term,X13:subst,X15:subst]:
% 1.66/1.06 ( ( X5 @ X9 @ X11 @ ( comp @ X15 @ X13 ) ) =>
% 1.66/1.06 ( X5 @ ( comp @ X9 @ X15 ) @ ( sub @ X11 @ X15 ) @ X13 ) ) ) =>
% 1.66/1.06 ( ( ![X17:subst,X19:term,X21:subst,X23:subst]:
% 1.66/1.06 ( ( X5 @ ( comp @ X17 @ X23 ) @ ( sub @ X19 @ X23 ) @ X21 ) =>
% 1.66/1.06 ( X5 @ X17 @ X19 @ ( comp @ X23 @ X21 ) ) ) ) =>
% 1.66/1.06 ( ( ![X25:term]:
% 1.66/1.06 ( ( hoasvar @ id @ X25 @ id ) => ( X5 @ id @ X25 @ id ) ) ) =>
% 1.66/1.06 ( ( hoasinduction_p_and_p_prime @ X5 @ X7 ) =>
% 1.66/1.06 ( ![X27:term]: ( ( var @ X27 ) => ( X7 @ X27 ) ) ) ) ) ) ) ) )),
% 1.66/1.06 inference('rw.lit', [status(esa)], [hoasinduction_lem1v2])).
% 1.66/1.06 thf(zip_derived_cl286, plain,
% 1.66/1.06 (~ (((!!) @ (^[Y0 : subst > term > subst > $o]:
% 1.66/1.06 (((!!) @ (^[Y1 : term > $o]:
% 1.66/1.06 (((((!!) @ (^[Y2 : subst]:
% 1.66/1.06 (((!!) @ (^[Y3 : term]:
% 1.66/1.06 (((!!) @ (^[Y4 : subst]:
% 1.66/1.06 ((
% 1.66/1.06 (!!) @ (
% 1.66/1.06 ^[Y5 : subst]:
% 1.66/1.06 ((
% 1.66/1.06 (Y0 @
% 1.66/1.06 Y2 @
% 1.66/1.06 Y3 @
% 1.66/1.06 (
% 1.66/1.06 comp @
% 1.66/1.06 Y5 @ Y4)) =>
% 1.66/1.06 (Y0 @
% 1.66/1.06 (
% 1.66/1.06 comp @
% 1.66/1.06 Y2 @ Y5) @
% 1.66/1.06 (
% 1.66/1.06 sub @
% 1.66/1.06 Y3 @ Y5) @
% 1.66/1.06 Y4))))))))))))))) =>
% 1.66/1.06 (((((!!) @ (^[Y2 : subst]:
% 1.66/1.06 (((!!) @ (^[Y3 : term]:
% 1.66/1.06 (((!!) @ (
% 1.66/1.06 ^[Y4 : subst]:
% 1.66/1.06 (((!!) @ (
% 1.66/1.06 ^[Y5 : subst]:
% 1.66/1.06 ((
% 1.66/1.06 (Y0 @
% 1.66/1.06 (
% 1.66/1.06 comp @
% 1.66/1.06 Y2 @ Y5) @
% 1.66/1.06 (
% 1.66/1.06 sub @
% 1.66/1.06 Y3 @ Y5) @
% 1.66/1.06 Y4) =>
% 1.66/1.06 (Y0 @
% 1.66/1.06 Y2 @
% 1.66/1.06 Y3 @
% 1.66/1.06 (
% 1.66/1.06 comp @
% 1.66/1.06 Y5 @ Y4)))))))))))))))) =>
% 1.66/1.06 (((((!!) @ (^[Y2 : term]:
% 1.66/1.06 (((hoasvar @ id @ Y2 @
% 1.66/1.06 id) => (Y0 @ id @ Y2 @ id)))))) =>
% 1.66/1.06 (((hoasinduction_p_and_p_prime @ Y0 @
% 1.66/1.06 Y1) =>
% 1.66/1.06 (((!!) @ (^[Y2 : term]:
% 1.66/1.06 (((var @ Y2) => (Y1 @ Y2))))))))))))))))))))),
% 1.66/1.06 inference('rw_clause', [status(thm)], [zip_derived_cl270, '3'])).
% 1.66/1.06 thf(zip_derived_cl299, plain,
% 1.66/1.06 (~ (((!!) @ (^[Y0 : term > $o]:
% 1.66/1.06 (((((!!) @ (^[Y1 : subst]:
% 1.66/1.06 (((!!) @ (^[Y2 : term]:
% 1.66/1.06 (((!!) @ (^[Y3 : subst]:
% 1.66/1.06 (((!!) @ (^[Y4 : subst]:
% 1.66/1.06 ((
% 1.66/1.06 ('#sk422' @
% 1.66/1.06 Y1 @
% 1.66/1.06 Y2 @
% 1.66/1.06 (
% 1.66/1.06 comp @
% 1.66/1.06 Y4 @ Y3)) =>
% 1.66/1.06 ('#sk422' @
% 1.66/1.06 (
% 1.66/1.06 comp @
% 1.66/1.06 Y1 @ Y4) @
% 1.66/1.06 (
% 1.66/1.06 sub @
% 1.66/1.06 Y2 @ Y4) @
% 1.66/1.06 Y3))))))))))))))) =>
% 1.66/1.06 (((((!!) @ (^[Y1 : subst]:
% 1.66/1.06 (((!!) @ (^[Y2 : term]:
% 1.66/1.06 (((!!) @ (^[Y3 : subst]:
% 1.66/1.06 (((!!) @ (
% 1.66/1.06 ^[Y4 : subst]:
% 1.66/1.06 ((('#sk422' @
% 1.66/1.06 (comp @
% 1.66/1.06 Y1 @ Y4) @
% 1.66/1.06 (sub @ Y2 @
% 1.66/1.06 Y4) @
% 1.66/1.06 Y3) =>
% 1.66/1.06 ('#sk422' @
% 1.66/1.06 Y1 @ Y2 @
% 1.66/1.06 (comp @
% 1.66/1.06 Y4 @ Y3)))))))))))))))) =>
% 1.66/1.06 (((((!!) @ (^[Y1 : term]:
% 1.66/1.06 (((hoasvar @ id @ Y1 @ id) =>
% 1.66/1.06 ('#sk422' @ id @ Y1 @ id)))))) =>
% 1.66/1.06 (((hoasinduction_p_and_p_prime @ '#sk422' @ Y0) =>
% 1.66/1.06 (((!!) @ (^[Y1 : term]:
% 1.66/1.06 (((var @ Y1) => (Y0 @ Y1)))))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl286])).
% 1.66/1.06 thf(zip_derived_cl308, plain,
% 1.66/1.06 (~ (((((!!) @ (^[Y0 : subst]:
% 1.66/1.06 (((!!) @ (^[Y1 : term]:
% 1.66/1.06 (((!!) @ (^[Y2 : subst]:
% 1.66/1.06 (((!!) @ (^[Y3 : subst]:
% 1.66/1.06 ((('#sk422' @ Y0 @
% 1.66/1.06 Y1 @
% 1.66/1.06 (comp @ Y3 @ Y2)) =>
% 1.66/1.06 ('#sk422' @
% 1.66/1.06 (comp @ Y0 @ Y3) @
% 1.66/1.06 (sub @ Y1 @ Y3) @
% 1.66/1.06 Y2))))))))))))))) =>
% 1.66/1.06 (((((!!) @ (^[Y0 : subst]:
% 1.66/1.06 (((!!) @ (^[Y1 : term]:
% 1.66/1.06 (((!!) @ (^[Y2 : subst]:
% 1.66/1.06 (((!!) @ (^[Y3 : subst]:
% 1.66/1.06 ((('#sk422' @
% 1.66/1.06 (comp @ Y0 @ Y3) @
% 1.66/1.06 (sub @ Y1 @ Y3) @
% 1.66/1.06 Y2) =>
% 1.66/1.06 ('#sk422' @
% 1.66/1.06 Y0 @ Y1 @
% 1.66/1.06 (comp @ Y3 @ Y2)))))))))))))))) =>
% 1.66/1.06 (((((!!) @ (^[Y0 : term]:
% 1.66/1.06 (((hoasvar @ id @ Y0 @ id) => ('#sk422' @ id @ Y0 @
% 1.66/1.06 id)))))) =>
% 1.66/1.06 (((hoasinduction_p_and_p_prime @ '#sk422' @ '#sk459') =>
% 1.66/1.06 (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk459' @ Y0))))))))))))))),
% 1.66/1.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl299])).
% 1.66/1.06 thf(zip_derived_cl319, plain,
% 1.66/1.06 (~ (((((!!) @ (^[Y0 : subst]:
% 1.66/1.06 (((!!) @ (^[Y1 : term]:
% 1.66/1.06 (((!!) @ (^[Y2 : subst]:
% 1.66/1.06 (((!!) @ (^[Y3 : subst]:
% 1.66/1.06 ((('#sk422' @
% 1.66/1.06 (comp @ Y0 @ Y3) @
% 1.66/1.06 (sub @ Y1 @ Y3) @
% 1.66/1.06 Y2) =>
% 1.66/1.06 ('#sk422' @ Y0 @
% 1.66/1.06 Y1 @
% 1.66/1.06 (comp @ Y3 @ Y2)))))))))))))))) =>
% 1.66/1.06 (((((!!) @ (^[Y0 : term]:
% 1.66/1.06 (((hoasvar @ id @ Y0 @ id) => ('#sk422' @ id @ Y0 @
% 1.66/1.06 id)))))) =>
% 1.66/1.06 (((hoasinduction_p_and_p_prime @ '#sk422' @ '#sk459') =>
% 1.66/1.06 (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk459' @ Y0))))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl308])).
% 1.66/1.06 thf(zip_derived_cl328, plain,
% 1.66/1.06 (~ (((((!!) @ (^[Y0 : term]:
% 1.66/1.06 (((hoasvar @ id @ Y0 @ id) => ('#sk422' @ id @ Y0 @ id)))))) =>
% 1.66/1.06 (((hoasinduction_p_and_p_prime @ '#sk422' @ '#sk459') =>
% 1.66/1.06 (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk459' @ Y0))))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl319])).
% 1.66/1.06 thf(zip_derived_cl336, plain,
% 1.66/1.06 (~ (((hoasinduction_p_and_p_prime @ '#sk422' @ '#sk459') =>
% 1.66/1.06 (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk459' @ Y0))))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl328])).
% 1.66/1.06 thf(zip_derived_cl345, plain,
% 1.66/1.06 (~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk459' @ Y0))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl336])).
% 1.66/1.06 thf(zip_derived_cl352, plain,
% 1.66/1.06 (~ (((var @ ('#sk46' @ '#sk459')) => ('#sk459' @ ('#sk46' @ '#sk459'))))),
% 1.66/1.06 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl345])).
% 1.66/1.06 thf(zip_derived_cl359, plain, (~ ('#sk459' @ ('#sk46' @ '#sk459'))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl352])).
% 1.66/1.06 thf(zip_derived_cl358, plain, ( (var @ ('#sk46' @ '#sk459'))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl352])).
% 1.66/1.06 thf(zip_derived_cl335, plain,
% 1.66/1.06 ( (((!!) @ (^[Y0 : term]:
% 1.66/1.06 (((hoasvar @ id @ Y0 @ id) => ('#sk422' @ id @ Y0 @ id))))))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl328])).
% 1.66/1.06 thf(zip_derived_cl343, plain,
% 1.66/1.06 (![X2 : term]: (((hoasvar @ id @ X2 @ id) => ('#sk422' @ id @ X2 @ id)))),
% 1.66/1.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl335])).
% 1.66/1.06 thf(hoasvar, axiom,(( hoasvar @ (X2)@ (X0)@ (X1)) =
% 1.66/1.06 ((var @ (sub @ X0 @ X1))))).
% 1.66/1.06 thf('4', plain,
% 1.66/1.06 (![X2:subst,X1:subst,X0:term]:
% 1.66/1.06 ( ( hoasvar @ X2 @ X0 @ X1 ) = ( var @ ( sub @ X0 @ X1 ) ) )),
% 1.66/1.06 define([status(thm)])).
% 1.66/1.06 thf(zip_derived_cl349, plain,
% 1.66/1.06 (![X2 : term]: (((var @ (sub @ X2 @ id)) => ('#sk422' @ id @ X2 @ id)))),
% 1.66/1.06 inference('rw', [status(thm)], [zip_derived_cl343, '4'])).
% 1.66/1.06 thf(zip_derived_cl350, plain,
% 1.66/1.06 (![X2 : term]: (~ (var @ (sub @ X2 @ id)) | ('#sk422' @ id @ X2 @ id))),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl349])).
% 1.66/1.06 thf(zip_derived_cl10, plain, ( (axvarid)),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 1.66/1.06 thf(axvarid, axiom, (axvarid) =>
% 1.66/1.06 ((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) = ($true))).
% 1.66/1.06 thf('5', plain,
% 1.66/1.06 (( axvarid ) <=> ( ![X5:term]: ( ( sub @ X5 @ id ) = ( X5 ) ) )),
% 1.66/1.06 inference('rw.lit', [status(esa)], [axvarid])).
% 1.66/1.06 thf(zip_derived_cl14, plain,
% 1.66/1.06 ( (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0))))))),
% 1.66/1.06 inference('rw_clause', [status(thm)], [zip_derived_cl10, '5'])).
% 1.66/1.06 thf(zip_derived_cl19, plain, (![X2 : term]: (((sub @ X2 @ id) = (X2)))),
% 1.66/1.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])).
% 1.66/1.06 thf(zip_derived_cl25, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))),
% 1.66/1.06 inference('simplify nested equalities', [status(thm)], [zip_derived_cl19])).
% 1.66/1.06 thf(zip_derived_cl344, plain,
% 1.66/1.06 ( (hoasinduction_p_and_p_prime @ '#sk422' @ '#sk459')),
% 1.66/1.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl336])).
% 1.66/1.06 thf(hoasinduction_p_and_p_prime, axiom,
% 1.66/1.06 (hoasinduction_p_and_p_prime @ X0 @ X1) =>
% 1.66/1.06 ((((!!) @ (^[Y0 : term]: (((X1 @ Y0) <=> (X0 @ id @ Y0 @ id)))))) = ($true))).
% 1.66/1.06 thf('6', plain,
% 1.66/1.06 (![X0:( subst > term > subst > $o ),X1:( term > $o )]:
% 1.66/1.06 ( ( hoasinduction_p_and_p_prime @ X0 @ X1 ) <=>
% 1.66/1.06 ( ![X6:term]: ( ( X1 @ X6 ) <=> ( X0 @ id @ X6 @ id ) ) ) )),
% 1.66/1.06 inference('rw.lit', [status(esa)], [hoasinduction_p_and_p_prime])).
% 1.66/1.06 thf(zip_derived_cl351, plain,
% 1.66/1.06 ( (((!!) @ (^[Y0 : term]:
% 1.66/1.06 ((('#sk459' @ Y0) <=> ('#sk422' @ id @ Y0 @ id))))))),
% 1.66/1.06 inference('rw_clause', [status(thm)], [zip_derived_cl344, '6'])).
% 1.66/1.06 thf(zip_derived_cl357, plain,
% 1.66/1.06 (![X2 : term]: ((('#sk459' @ X2) <=> ('#sk422' @ id @ X2 @ id)))),
% 1.66/1.06 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl351])).
% 1.66/1.06 thf(zip_derived_cl363, plain,
% 1.66/1.06 (![X2 : term]: (('#sk459' @ X2) = ('#sk422' @ id @ X2 @ id))),
% 1.66/1.06 inference('simplify nested equalities', [status(thm)],
% 1.66/1.06 [zip_derived_cl357])).
% 1.66/1.06 thf(zip_derived_cl369, plain,
% 1.66/1.06 (![X2 : term]: (~ (var @ X2) | ('#sk459' @ X2))),
% 1.66/1.06 inference('demod', [status(thm)],
% 1.66/1.06 [zip_derived_cl350, zip_derived_cl25, zip_derived_cl363])).
% 1.66/1.06 thf(zip_derived_cl383, plain, ( ('#sk459' @ ('#sk46' @ '#sk459'))),
% 1.66/1.06 inference('sup-', [status(thm)], [zip_derived_cl358, zip_derived_cl369])).
% 1.66/1.06 thf(zip_derived_cl393, plain, ($false),
% 1.66/1.06 inference('demod', [status(thm)], [zip_derived_cl359, zip_derived_cl383])).
% 1.66/1.06
% 1.66/1.06 % SZS output end Refutation
% 1.66/1.06
% 1.66/1.06
% 1.66/1.06 % Terminating...
% 1.66/1.16 % Runner terminated.
% 1.82/1.17 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------