%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ALG264^3 : 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.ARMHLmQzDf true
% Computer : n031.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 04:28:30 PM UTC 2025
% Result : Theorem 8.69s 1.75s
% Output : Refutation 8.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG264^3 : 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.ARMHLmQzDf true
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 17:03:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.36 % Running in HO mode
% 0.57/0.68 % Total configuration time : 828
% 0.57/0.68 % Estimated wc time : 1656
% 0.57/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.57/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.57/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.57/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 8.69/1.75 % Solved by lams/40_b.comb.sh.
% 8.69/1.75 % done 57 iterations in 0.956s
% 8.69/1.75 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 8.69/1.75 % SZS output start Refutation
% 8.69/1.75 thf(subst_type, type, subst: $tType).
% 8.69/1.75 thf(term_type, type, term: $tType).
% 8.69/1.75 thf(axmap_type, type, axmap: $o).
% 8.69/1.75 thf(axclos_type, type, axclos: $o).
% 8.69/1.75 thf(lamnotap_type, type, lamnotap: $o).
% 8.69/1.75 thf(axvarcons_type, type, axvarcons: $o).
% 8.69/1.75 thf(substmonoid_type, type, substmonoid: $o).
% 8.69/1.75 thf('#sk3_type', type, '#sk3': (term > $o) > term).
% 8.69/1.75 thf(push_type, type, push: term > subst > subst).
% 8.69/1.75 thf(axshiftcons_type, type, axshiftcons: $o).
% 8.69/1.75 thf(hoasapinj1_type, type, hoasapinj1: $o).
% 8.69/1.75 thf(hoasinduction_p_and_p_prime_type, type, hoasinduction_p_and_p_prime:
% 8.69/1.75 (subst > term > subst > $o) > (term > $o) > $o).
% 8.69/1.75 thf(axapp_type, type, axapp: $o).
% 8.69/1.75 thf(shinj_type, type, shinj: $o).
% 8.69/1.75 thf(hoasap_type, type, hoasap: subst > term > subst > term > term).
% 8.69/1.75 thf(hoaslaminj_type, type, hoaslaminj: $o).
% 8.69/1.75 thf(one_type, type, one: term).
% 8.69/1.75 thf(id_type, type, id: subst).
% 8.69/1.75 thf(comp_type, type, comp: subst > subst > subst).
% 8.69/1.75 thf(hoaslamnotap_type, type, hoaslamnotap: $o).
% 8.69/1.75 thf(induction2_type, type, induction2: $o).
% 8.69/1.75 thf(axvarid_type, type, axvarid: $o).
% 8.69/1.75 thf(axvarshift_type, type, axvarshift: $o).
% 8.69/1.75 thf(induction2lem_type, type, induction2lem: $o).
% 8.69/1.75 thf(sh_type, type, sh: subst).
% 8.69/1.75 thf(hoasinduction_lem2v2_type, type, hoasinduction_lem2v2: $o).
% 8.69/1.75 thf(laminj_type, type, laminj: $o).
% 8.69/1.75 thf(ulamvarind_type, type, ulamvarind: $o).
% 8.69/1.75 thf(apinj2_type, type, apinj2: $o).
% 8.69/1.75 thf(ulamvarsh_type, type, ulamvarsh: $o).
% 8.69/1.75 thf(lamnotvar_type, type, lamnotvar: $o).
% 8.69/1.75 thf(apnotvar_type, type, apnotvar: $o).
% 8.69/1.75 thf(pushprop_type, type, pushprop: $o).
% 8.69/1.75 thf(sub_type, type, sub: term > subst > term).
% 8.69/1.75 thf(apinj1_type, type, apinj1: $o).
% 8.69/1.75 thf('#sk10_type', type, '#sk10': subst > term > subst > $o).
% 8.69/1.75 thf('#sk12_type', type, '#sk12': term > $o).
% 8.69/1.75 thf(axidl_type, type, axidl: $o).
% 8.69/1.75 thf(ap_type, type, ap: term > term > term).
% 8.69/1.75 thf(termmset_type, type, termmset: $o).
% 8.69/1.75 thf(hoasapinj2_type, type, hoasapinj2: $o).
% 8.69/1.75 thf('#sk5_type', type, '#sk5': (term > $o) > term).
% 8.69/1.75 thf(hoasapnotvar_type, type, hoasapnotvar: $o).
% 8.69/1.75 thf(var_type, type, var: term > $o).
% 8.69/1.75 thf(axassoc_type, type, axassoc: $o).
% 8.69/1.75 thf(hoaslamnotvar_type, type, hoaslamnotvar: $o).
% 8.69/1.75 thf(axidr_type, type, axidr: $o).
% 8.69/1.75 thf(axabs_type, type, axabs: $o).
% 8.69/1.75 thf(hoasinduction_lem2v2_gthm_type, type, hoasinduction_lem2v2_gthm: $o).
% 8.69/1.75 thf(ulamvar1_type, type, ulamvar1: $o).
% 8.69/1.75 thf(induction_type, type, induction: $o).
% 8.69/1.75 thf(axscons_type, type, axscons: $o).
% 8.69/1.75 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 8.69/1.75 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 8.69/1.75 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 8.69/1.75 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 8.69/1.75 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 8.69/1.75 thf(thm, conjecture, (hoasinduction_lem2v2_gthm)).
% 8.69/1.75 thf(zf_stmt_0, negated_conjecture, (~( hoasinduction_lem2v2_gthm )),
% 8.69/1.75 inference('cnf.neg', [status(esa)], [thm])).
% 8.69/1.75 thf(zip_derived_cl0, plain, (~ (hoasinduction_lem2v2_gthm)),
% 8.69/1.75 inference('cnf', [status(esa)], [zf_stmt_0])).
% 8.69/1.75 thf(hoasinduction_lem2v2_gthm, axiom, ~ (hoasinduction_lem2v2_gthm) =>
% 8.69/1.75 ((((axapp) =>
% 8.69/1.75 (((axvarcons) =>
% 8.69/1.75 (((axvarid) =>
% 8.69/1.75 (((axabs) =>
% 8.69/1.75 (((axclos) =>
% 8.69/1.75 (((axidl) =>
% 8.69/1.75 (((axshiftcons) =>
% 8.69/1.75 (((axassoc) =>
% 8.69/1.75 (((axmap) =>
% 8.69/1.75 (((axidr) =>
% 8.69/1.75 (((axvarshift) =>
% 8.69/1.75 (((axscons) =>
% 8.69/1.75 (((ulamvar1) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoaslamnotvar) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 8.69/1.75 != ($true))).
% 8.69/1.75 thf('0', plain,
% 8.69/1.75 (( ~( hoasinduction_lem2v2_gthm ) ) <=>
% 8.69/1.75 ( ~( ( axapp ) =>
% 8.69/1.75 ( ( axvarcons ) =>
% 8.69/1.75 ( ( axvarid ) =>
% 8.69/1.75 ( ( axabs ) =>
% 8.69/1.75 ( ( axclos ) =>
% 8.69/1.75 ( ( axidl ) =>
% 8.69/1.75 ( ( axshiftcons ) =>
% 8.69/1.75 ( ( axassoc ) =>
% 8.69/1.75 ( ( axmap ) =>
% 8.69/1.75 ( ( axidr ) =>
% 8.69/1.75 ( ( axvarshift ) =>
% 8.69/1.75 ( ( axscons ) =>
% 8.69/1.75 ( ( ulamvar1 ) =>
% 8.69/1.75 ( ( ulamvarsh ) =>
% 8.69/1.75 ( ( ulamvarind ) =>
% 8.69/1.75 ( ( apinj1 ) =>
% 8.69/1.75 ( ( apinj2 ) =>
% 8.69/1.75 ( ( laminj ) =>
% 8.69/1.75 ( ( shinj ) =>
% 8.69/1.75 ( ( lamnotap ) =>
% 8.69/1.75 ( ( apnotvar ) =>
% 8.69/1.75 ( ( lamnotvar ) =>
% 8.69/1.75 ( ( induction ) =>
% 8.69/1.75 ( ( pushprop ) =>
% 8.69/1.75 ( ( induction2lem ) =>
% 8.69/1.75 ( ( induction2 ) =>
% 8.69/1.75 ( ( substmonoid ) =>
% 8.69/1.75 ( ( termmset ) =>
% 8.69/1.75 ( ( hoasapinj1 ) =>
% 8.69/1.75 ( (
% 8.69/1.75 hoasapinj2 ) =>
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 hoaslaminj ) =>
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 hoaslamnotap ) =>
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 hoaslamnotvar ) =>
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 hoasapnotvar ) =>
% 8.69/1.75 (
% 8.69/1.75 hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 8.69/1.75 inference('rw.lit', [status(esa)], [hoasinduction_lem2v2_gthm])).
% 8.69/1.75 thf(zip_derived_cl1, plain,
% 8.69/1.75 (~ (((axapp) =>
% 8.69/1.75 (((axvarcons) =>
% 8.69/1.75 (((axvarid) =>
% 8.69/1.75 (((axabs) =>
% 8.69/1.75 (((axclos) =>
% 8.69/1.75 (((axidl) =>
% 8.69/1.75 (((axshiftcons) =>
% 8.69/1.75 (((axassoc) =>
% 8.69/1.75 (((axmap) =>
% 8.69/1.75 (((axidr) =>
% 8.69/1.75 (((axvarshift) =>
% 8.69/1.75 (((axscons) =>
% 8.69/1.75 (((ulamvar1) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoaslaminj) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoaslamnotap) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoaslamnotvar) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('rw_clause', [status(thm)], [zip_derived_cl0, '0'])).
% 8.69/1.75 thf(axvarshift, axiom,(( axvarshift ) = ((((push @ one @ sh) = (id)))))).
% 8.69/1.75 thf('1', plain, (( axvarshift ) = ( ( push @ one @ sh ) = ( id ) )),
% 8.69/1.75 define([status(thm)])).
% 8.69/1.75 thf(ulamvar1, axiom,(( ulamvar1 ) = ((var @ one)))).
% 8.69/1.75 thf('2', plain, (( ulamvar1 ) = ( var @ one )), define([status(thm)])).
% 8.69/1.75 thf(zip_derived_cl2, plain,
% 8.69/1.75 (~ (((axapp) =>
% 8.69/1.75 (((axvarcons) =>
% 8.69/1.75 (((axvarid) =>
% 8.69/1.75 (((axabs) =>
% 8.69/1.75 (((axclos) =>
% 8.69/1.75 (((axidl) =>
% 8.69/1.75 (((axshiftcons) =>
% 8.69/1.75 (((axassoc) =>
% 8.69/1.75 (((axmap) =>
% 8.69/1.75 (((axidr) =>
% 8.69/1.75 (((((push @ one @ sh) = (id))) =>
% 8.69/1.75 (((axscons) =>
% 8.69/1.75 (((var @ one) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoaslaminj) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoaslamnotap) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoaslamnotvar) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('rw', [status(thm)], [zip_derived_cl1, '1', '2'])).
% 8.69/1.75 thf(zip_derived_cl4, plain,
% 8.69/1.75 (~ (((axvarcons) =>
% 8.69/1.75 (((axvarid) =>
% 8.69/1.75 (((axabs) =>
% 8.69/1.75 (((axclos) =>
% 8.69/1.75 (((axidl) =>
% 8.69/1.75 (((axshiftcons) =>
% 8.69/1.75 (((axassoc) =>
% 8.69/1.75 (((axmap) =>
% 8.69/1.75 (((axidr) =>
% 8.69/1.75 (((((push @ one @ sh) = (id))) =>
% 8.69/1.75 (((axscons) =>
% 8.69/1.75 (((var @ one) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoaslamnotap) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoaslamnotvar) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])).
% 8.69/1.75 thf(zip_derived_cl7, plain,
% 8.69/1.75 (~ (((axvarid) =>
% 8.69/1.75 (((axabs) =>
% 8.69/1.75 (((axclos) =>
% 8.69/1.75 (((axidl) =>
% 8.69/1.75 (((axshiftcons) =>
% 8.69/1.75 (((axassoc) =>
% 8.69/1.75 (((axmap) =>
% 8.69/1.75 (((axidr) =>
% 8.69/1.75 (((((push @ one @ sh) = (id))) =>
% 8.69/1.75 (((axscons) =>
% 8.69/1.75 (((var @ one) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoaslamnotvar) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])).
% 8.69/1.75 thf(zip_derived_cl12, plain,
% 8.69/1.75 (~ (((axabs) =>
% 8.69/1.75 (((axclos) =>
% 8.69/1.75 (((axidl) =>
% 8.69/1.75 (((axshiftcons) =>
% 8.69/1.75 (((axassoc) =>
% 8.69/1.75 (((axmap) =>
% 8.69/1.75 (((axidr) =>
% 8.69/1.75 (((((push @ one @ sh) = (id))) =>
% 8.69/1.75 (((axscons) =>
% 8.69/1.75 (((var @ one) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 ((
% 8.69/1.75 (hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 8.69/1.75 thf(zip_derived_cl18, plain,
% 8.69/1.75 (~ (((axclos) =>
% 8.69/1.75 (((axidl) =>
% 8.69/1.75 (((axshiftcons) =>
% 8.69/1.75 (((axassoc) =>
% 8.69/1.75 (((axmap) =>
% 8.69/1.75 (((axidr) =>
% 8.69/1.75 (((((push @ one @ sh) = (id))) =>
% 8.69/1.75 (((axscons) =>
% 8.69/1.75 (((var @ one) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])).
% 8.69/1.75 thf(zip_derived_cl25, plain,
% 8.69/1.75 (~ (((axidl) =>
% 8.69/1.75 (((axshiftcons) =>
% 8.69/1.75 (((axassoc) =>
% 8.69/1.75 (((axmap) =>
% 8.69/1.75 (((axidr) =>
% 8.69/1.75 (((((push @ one @ sh) = (id))) =>
% 8.69/1.75 (((axscons) =>
% 8.69/1.75 (((var @ one) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])).
% 8.69/1.75 thf(zip_derived_cl33, plain,
% 8.69/1.75 (~ (((axshiftcons) =>
% 8.69/1.75 (((axassoc) =>
% 8.69/1.75 (((axmap) =>
% 8.69/1.75 (((axidr) =>
% 8.69/1.75 (((((push @ one @ sh) = (id))) =>
% 8.69/1.75 (((axscons) =>
% 8.69/1.75 (((var @ one) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 8.69/1.75 thf(zip_derived_cl39, plain,
% 8.69/1.75 (~ (((axassoc) =>
% 8.69/1.75 (((axmap) =>
% 8.69/1.75 (((axidr) =>
% 8.69/1.75 (((((push @ one @ sh) = (id))) =>
% 8.69/1.75 (((axscons) =>
% 8.69/1.75 (((var @ one) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 8.69/1.75 thf(zip_derived_cl46, plain,
% 8.69/1.75 (~ (((axmap) =>
% 8.69/1.75 (((axidr) =>
% 8.69/1.75 (((((push @ one @ sh) = (id))) =>
% 8.69/1.75 (((axscons) =>
% 8.69/1.75 (((var @ one) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])).
% 8.69/1.75 thf(zip_derived_cl53, plain,
% 8.69/1.75 (~ (((axidr) =>
% 8.69/1.75 (((((push @ one @ sh) = (id))) =>
% 8.69/1.75 (((axscons) =>
% 8.69/1.75 (((var @ one) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 8.69/1.75 thf(zip_derived_cl60, plain,
% 8.69/1.75 (~ (((((push @ one @ sh) = (id))) =>
% 8.69/1.75 (((axscons) =>
% 8.69/1.75 (((var @ one) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])).
% 8.69/1.75 thf(zip_derived_cl67, plain,
% 8.69/1.75 (~ (((axscons) =>
% 8.69/1.75 (((var @ one) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl60])).
% 8.69/1.75 thf(zip_derived_cl74, plain,
% 8.69/1.75 (~ (((var @ one) =>
% 8.69/1.75 (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])).
% 8.69/1.75 thf(zip_derived_cl80, plain,
% 8.69/1.75 (~ (((ulamvarsh) =>
% 8.69/1.75 (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])).
% 8.69/1.75 thf(zip_derived_cl85, plain,
% 8.69/1.75 (~ (((ulamvarind) =>
% 8.69/1.75 (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])).
% 8.69/1.75 thf(zip_derived_cl89, plain,
% 8.69/1.75 (~ (((apinj1) =>
% 8.69/1.75 (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])).
% 8.69/1.75 thf(zip_derived_cl94, plain,
% 8.69/1.75 (~ (((apinj2) =>
% 8.69/1.75 (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])).
% 8.69/1.75 thf(zip_derived_cl100, plain,
% 8.69/1.75 (~ (((laminj) =>
% 8.69/1.75 (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl94])).
% 8.69/1.75 thf(zip_derived_cl106, plain,
% 8.69/1.75 (~ (((shinj) =>
% 8.69/1.75 (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) =>
% 8.69/1.75 (hoasinduction_lem2v2)))))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])).
% 8.69/1.75 thf(zip_derived_cl113, plain,
% 8.69/1.75 (~ (((lamnotap) =>
% 8.69/1.75 (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) => (hoasinduction_lem2v2)))))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl106])).
% 8.69/1.75 thf(zip_derived_cl121, plain,
% 8.69/1.75 (~ (((apnotvar) =>
% 8.69/1.75 (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) => (hoasinduction_lem2v2)))))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])).
% 8.69/1.75 thf(zip_derived_cl131, plain,
% 8.69/1.75 (~ (((lamnotvar) =>
% 8.69/1.75 (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) => (hoasinduction_lem2v2)))))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl121])).
% 8.69/1.75 thf(zip_derived_cl143, plain,
% 8.69/1.75 (~ (((induction) =>
% 8.69/1.75 (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) => (hoasinduction_lem2v2)))))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl131])).
% 8.69/1.75 thf(zip_derived_cl156, plain,
% 8.69/1.75 (~ (((pushprop) =>
% 8.69/1.75 (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) => (hoasinduction_lem2v2)))))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl143])).
% 8.69/1.75 thf(zip_derived_cl167, plain,
% 8.69/1.75 (~ (((induction2lem) =>
% 8.69/1.75 (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) => (hoasinduction_lem2v2)))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl156])).
% 8.69/1.75 thf(zip_derived_cl173, plain,
% 8.69/1.75 (~ (((induction2) =>
% 8.69/1.75 (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) => (hoasinduction_lem2v2)))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl167])).
% 8.69/1.75 thf(zip_derived_cl179, plain,
% 8.69/1.75 (~ (((substmonoid) =>
% 8.69/1.75 (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) => (hoasinduction_lem2v2)))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])).
% 8.69/1.75 thf(zip_derived_cl186, plain,
% 8.69/1.75 (~ (((termmset) =>
% 8.69/1.75 (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) => (hoasinduction_lem2v2)))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])).
% 8.69/1.75 thf(zip_derived_cl195, plain,
% 8.69/1.75 (~ (((hoasapinj1) =>
% 8.69/1.75 (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) => (hoasinduction_lem2v2)))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl186])).
% 8.69/1.75 thf(zip_derived_cl207, plain,
% 8.69/1.75 (~ (((hoasapinj2) =>
% 8.69/1.75 (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) =>
% 8.69/1.75 (((hoasapnotvar) => (hoasinduction_lem2v2)))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl195])).
% 8.69/1.75 thf(zip_derived_cl221, plain,
% 8.69/1.75 (~ (((hoaslaminj) =>
% 8.69/1.75 (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) => (((hoasapnotvar) => (hoasinduction_lem2v2)))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl207])).
% 8.69/1.75 thf(zip_derived_cl239, plain,
% 8.69/1.75 (~ (((hoaslamnotap) =>
% 8.69/1.75 (((hoaslamnotvar) => (((hoasapnotvar) => (hoasinduction_lem2v2)))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl221])).
% 8.69/1.75 thf(zip_derived_cl259, plain,
% 8.69/1.75 (~ (((hoaslamnotvar) => (((hoasapnotvar) => (hoasinduction_lem2v2)))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl239])).
% 8.69/1.75 thf(zip_derived_cl281, plain,
% 8.69/1.75 (~ (((hoasapnotvar) => (hoasinduction_lem2v2)))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl259])).
% 8.69/1.75 thf(zip_derived_cl306, plain, (~ (hoasinduction_lem2v2)),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl281])).
% 8.69/1.75 thf(hoasinduction_lem2v2, axiom, ~ (hoasinduction_lem2v2) =>
% 8.69/1.75 ((((!!) @ (^[Y0 : subst > term > subst > $o]:
% 8.69/1.75 (((!!) @ (^[Y1 : term > $o]:
% 8.69/1.75 (((((!!) @ (^[Y2 : subst]:
% 8.69/1.75 (((!!) @ (^[Y3 : term]:
% 8.69/1.75 (((!!) @ (^[Y4 : subst]:
% 8.69/1.75 (((!!) @ (
% 8.69/1.75 ^[Y5 : subst]:
% 8.69/1.75 ((
% 8.69/1.75 (Y0 @
% 8.69/1.75 Y2 @
% 8.69/1.75 Y3 @
% 8.69/1.75 (
% 8.69/1.75 comp @
% 8.69/1.75 Y5 @ Y4)) =>
% 8.69/1.75 (Y0 @
% 8.69/1.75 (
% 8.69/1.75 comp @
% 8.69/1.75 Y2 @ Y5) @
% 8.69/1.75 (
% 8.69/1.75 sub @
% 8.69/1.75 Y3 @ Y5) @
% 8.69/1.75 Y4))))))))))))))) =>
% 8.69/1.75 (((((!!) @ (^[Y2 : subst]:
% 8.69/1.75 (((!!) @ (^[Y3 : term]:
% 8.69/1.75 (((!!) @ (^[Y4 : subst]:
% 8.69/1.75 ((
% 8.69/1.75 (!!) @ (
% 8.69/1.75 ^[Y5 : subst]:
% 8.69/1.75 ((
% 8.69/1.75 (Y0 @
% 8.69/1.75 (
% 8.69/1.75 comp @
% 8.69/1.75 Y2 @ Y5) @
% 8.69/1.75 (
% 8.69/1.75 sub @
% 8.69/1.75 Y3 @ Y5) @
% 8.69/1.75 Y4) =>
% 8.69/1.75 (Y0 @
% 8.69/1.75 Y2 @
% 8.69/1.75 Y3 @
% 8.69/1.75 (
% 8.69/1.75 comp @
% 8.69/1.75 Y5 @ Y4)))))))))))))))) =>
% 8.69/1.75 (((((!!) @ (^[Y2 : term]:
% 8.69/1.75 (((!!) @ (^[Y3 : term]:
% 8.69/1.75 (((Y0 @ id @ Y2 @
% 8.69/1.75 id) =>
% 8.69/1.75 (((Y0 @ id @ Y3 @
% 8.69/1.75 id) => (Y0 @
% 8.69/1.75 id @
% 8.69/1.75 (hoasap @ id @
% 8.69/1.75 Y2 @ id @ Y3) @
% 8.69/1.75 id))))))))))) =>
% 8.69/1.75 (((hoasinduction_p_and_p_prime @ Y0 @ Y1) =>
% 8.69/1.75 (((!!) @ (^[Y2 : term]:
% 8.69/1.75 (((!!) @ (^[Y3 : term]:
% 8.69/1.75 (((Y1 @ Y2) =>
% 8.69/1.75 (((Y1 @ Y3) =>
% 8.69/1.75 (Y1 @
% 8.69/1.75 (ap @ Y2 @ Y3))))))))))))))))))))))))))
% 8.69/1.75 != ($true))).
% 8.69/1.75 thf('3', plain,
% 8.69/1.75 (( ~( hoasinduction_lem2v2 ) ) <=>
% 8.69/1.75 ( ~( ![X5:( subst > term > subst > $o ),X7:( term > $o )]:
% 8.69/1.75 ( ( ![X9:subst,X11:term,X13:subst,X15:subst]:
% 8.69/1.75 ( ( X5 @ X9 @ X11 @ ( comp @ X15 @ X13 ) ) =>
% 8.69/1.75 ( X5 @ ( comp @ X9 @ X15 ) @ ( sub @ X11 @ X15 ) @ X13 ) ) ) =>
% 8.69/1.75 ( ( ![X17:subst,X19:term,X21:subst,X23:subst]:
% 8.69/1.75 ( ( X5 @ ( comp @ X17 @ X23 ) @ ( sub @ X19 @ X23 ) @ X21 ) =>
% 8.69/1.75 ( X5 @ X17 @ X19 @ ( comp @ X23 @ X21 ) ) ) ) =>
% 8.69/1.75 ( ( ![X25:term,X27:term]:
% 8.69/1.75 ( ( X5 @ id @ X25 @ id ) =>
% 8.69/1.75 ( ( X5 @ id @ X27 @ id ) =>
% 8.69/1.75 ( X5 @ id @ ( hoasap @ id @ X25 @ id @ X27 ) @ id ) ) ) ) =>
% 8.69/1.75 ( ( hoasinduction_p_and_p_prime @ X5 @ X7 ) =>
% 8.69/1.75 ( ![X29:term,X31:term]:
% 8.69/1.75 ( ( X7 @ X29 ) =>
% 8.69/1.75 ( ( X7 @ X31 ) => ( X7 @ ( ap @ X29 @ X31 ) ) ) ) ) ) ) ) ) ) )),
% 8.69/1.75 inference('rw.lit', [status(esa)], [hoasinduction_lem2v2])).
% 8.69/1.75 thf(zip_derived_cl335, plain,
% 8.69/1.75 (~ (((!!) @ (^[Y0 : subst > term > subst > $o]:
% 8.69/1.75 (((!!) @ (^[Y1 : term > $o]:
% 8.69/1.75 (((((!!) @ (^[Y2 : subst]:
% 8.69/1.75 (((!!) @ (^[Y3 : term]:
% 8.69/1.75 (((!!) @ (^[Y4 : subst]:
% 8.69/1.75 ((
% 8.69/1.75 (!!) @ (
% 8.69/1.75 ^[Y5 : subst]:
% 8.69/1.75 ((
% 8.69/1.75 (Y0 @
% 8.69/1.75 Y2 @
% 8.69/1.75 Y3 @
% 8.69/1.75 (
% 8.69/1.75 comp @
% 8.69/1.75 Y5 @ Y4)) =>
% 8.69/1.75 (Y0 @
% 8.69/1.75 (
% 8.69/1.75 comp @
% 8.69/1.75 Y2 @ Y5) @
% 8.69/1.75 (
% 8.69/1.75 sub @
% 8.69/1.75 Y3 @ Y5) @
% 8.69/1.75 Y4))))))))))))))) =>
% 8.69/1.75 (((((!!) @ (^[Y2 : subst]:
% 8.69/1.75 (((!!) @ (^[Y3 : term]:
% 8.69/1.75 (((!!) @ (
% 8.69/1.75 ^[Y4 : subst]:
% 8.69/1.75 (((!!) @ (
% 8.69/1.75 ^[Y5 : subst]:
% 8.69/1.75 ((
% 8.69/1.75 (Y0 @
% 8.69/1.75 (
% 8.69/1.75 comp @
% 8.69/1.75 Y2 @ Y5) @
% 8.69/1.75 (
% 8.69/1.75 sub @
% 8.69/1.75 Y3 @ Y5) @
% 8.69/1.75 Y4) =>
% 8.69/1.75 (Y0 @
% 8.69/1.75 Y2 @
% 8.69/1.75 Y3 @
% 8.69/1.75 (
% 8.69/1.75 comp @
% 8.69/1.75 Y5 @ Y4)))))))))))))))) =>
% 8.69/1.75 (((((!!) @ (^[Y2 : term]:
% 8.69/1.75 (((!!) @ (^[Y3 : term]:
% 8.69/1.75 (((Y0 @ id @
% 8.69/1.75 Y2 @ id) =>
% 8.69/1.75 (((Y0 @ id @
% 8.69/1.75 Y3 @ id) =>
% 8.69/1.75 (Y0 @ id @
% 8.69/1.75 (hoasap @
% 8.69/1.75 id @ Y2 @
% 8.69/1.75 id @ Y3) @
% 8.69/1.75 id))))))))))) =>
% 8.69/1.75 (((hoasinduction_p_and_p_prime @ Y0 @
% 8.69/1.75 Y1) =>
% 8.69/1.75 (((!!) @ (^[Y2 : term]:
% 8.69/1.75 (((!!) @ (^[Y3 : term]:
% 8.69/1.75 (((Y1 @ Y2) =>
% 8.69/1.75 (((Y1 @
% 8.69/1.75 Y3) =>
% 8.69/1.75 (Y1 @
% 8.69/1.75 (ap @
% 8.69/1.75 Y2 @ Y3))))))))))))))))))))))))))),
% 8.69/1.75 inference('rw_clause', [status(thm)], [zip_derived_cl306, '3'])).
% 8.69/1.75 thf(zip_derived_cl369, plain,
% 8.69/1.75 (~ (((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ (=>) @
% 8.69/1.75 ((('#B') @ (!!) @
% 8.69/1.75 ((('#B') @ ((('#B') @ (!!))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (
% 8.69/1.75 (('#B') @ (!!))))))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#S') @
% 8.69/1.75 ((('#B') @ ((('#B') @ (
% 8.69/1.75 '#S'))) @
% 8.69/1.75 ((('#B') @ ((
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#S'))))) @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 '#S'))))))) @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 =>))))))))) @
% 8.69/1.75 ((('#C') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 '#C') @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 '#C'))) @
% 8.69/1.75 ((
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#B'))))) @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#B'))))))))))) @
% 8.69/1.75 ((('#C') @ comp)))))))))))))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (
% 8.69/1.75 '#C'))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#C') @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ ('#B'))) @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 '#S'))) @
% 8.69/1.75 ((('#C') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 '#B') @
% 8.69/1.75 ('#B'))) @
% 8.69/1.75 comp)))))))) @
% 8.69/1.75 sub)))))))))))))))))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ (=>) @
% 8.69/1.75 ((('#B') @ (!!) @
% 8.69/1.75 ((('#B') @ ((('#B') @ (!!))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 !!))))))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#S') @
% 8.69/1.75 ((('#B') @ ((
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#S'))) @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 (('#B') @ ('#S'))))) @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 '#S'))))))) @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 =>))))))))) @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 '#C'))))) @
% 8.69/1.75 ((('#C') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#C') @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#B'))) @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#S'))) @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#C') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#B') @
% 8.69/1.75 (
% 8.69/1.75 '#B'))) @
% 8.69/1.75 comp)))))))) @
% 8.69/1.75 sub)))))))))))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#C') @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ ('#C'))) @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 '#B'))))) @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 '#B'))))))))))) @
% 8.69/1.75 ((('#C') @ comp)))))))))))))))))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ (=>) @
% 8.69/1.75 ((('#B') @ (!!) @
% 8.69/1.75 ((('#B') @ ((('#B') @ (!!))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#S') @
% 8.69/1.75 ((('#B') @ ((('#B') @ (
% 8.69/1.75 '#B'))) @
% 8.69/1.75 ((('#B') @ ((
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 =>))) @
% 8.69/1.75 ((('#C') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 '#C') @
% 8.69/1.75 ((('#C') @ (
% 8.69/1.75 '#I') @ id)))) @
% 8.69/1.75 id)))))))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ ('#S') @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ (=>))) @
% 8.69/1.75 ((('#C') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 '#C') @
% 8.69/1.75 ((('#C') @ (
% 8.69/1.75 '#I') @ id)))) @
% 8.69/1.75 id)))))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#C') @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ ('#C'))) @
% 8.69/1.75 ((('#C') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 '#B') @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 '#B') @
% 8.69/1.75 ((('#C') @ (
% 8.69/1.75 '#I') @ id)))))) @
% 8.69/1.75 ((('#C') @ (
% 8.69/1.75 hoasap @ id) @
% 8.69/1.75 id)))))))) @
% 8.69/1.75 id)))))))))))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#S') @
% 8.69/1.75 ((('#B') @ ((('#B') @ (=>))) @
% 8.69/1.75 hoasinduction_p_and_p_prime)))) @
% 8.69/1.75 ((('#B') @ (!!) @
% 8.69/1.75 ((('#B') @ ((('#B') @ (!!))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#S') @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#B'))) @
% 8.69/1.75 ((('#B') @ (=>))))))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ ('#S') @
% 8.69/1.75 ((('#B') @ (=>))))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#B') @ ('#B'))) @
% 8.69/1.75 ap))))))))))))))))))))))),
% 8.69/1.75 inference('comb-normalize', [status(thm)], [zip_derived_cl335])).
% 8.69/1.75 thf(zip_derived_cl370, plain,
% 8.69/1.75 (~ (((!!) @ ((('#B') @ (((=>) @ (((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#B') @ ((('#B') @ (!!))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ (
% 8.69/1.75 (('#B') @ (!!))))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ (
% 8.69/1.75 '#S') @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 '#S'))) @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#S'))))) @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 =>))))))) @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#C') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#C') @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#B'))) @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#B'))) @
% 8.69/1.75 '#sk10')))))) @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#C') @ comp)))))))))))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ (
% 8.69/1.75 '#C'))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ (
% 8.69/1.75 '#B') @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#S') @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ '#sk10')) @
% 8.69/1.75 comp)))))) @
% 8.69/1.75 sub)))))))))))))))) @
% 8.69/1.75 ((('#B') @ (((=>) @ (((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#B') @ ((('#B') @ (!!))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 !!))))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ (
% 8.69/1.75 '#S') @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#S'))) @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#S'))))) @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 =>))))))) @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#C'))) @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#C') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#B') @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#S') @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ '#sk10')) @
% 8.69/1.75 comp)))))) @
% 8.69/1.75 sub)))))))))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ (
% 8.69/1.75 '#C') @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#B'))) @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#B'))) @
% 8.69/1.75 '#sk10')))))) @
% 8.69/1.75 ((('#C') @ comp)))))))))))))))) @
% 8.69/1.75 ((('#B') @ (((=>) @ (((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#S') @ ((('#B') @ (
% 8.69/1.75 '#B') @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 =>) @
% 8.69/1.75 ((('#C') @ (
% 8.69/1.75 '#sk10' @
% 8.69/1.75 id) @ id)))))) @
% 8.69/1.75 ((('#B') @ ((('#S') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 =>) @
% 8.69/1.75 ((
% 8.69/1.75 ('#C') @ (
% 8.69/1.75 '#sk10' @
% 8.69/1.75 id) @ id)))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ (
% 8.69/1.75 '#C') @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 (
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#sk10' @
% 8.69/1.75 id))) @
% 8.69/1.75 (
% 8.69/1.75 (
% 8.69/1.75 ('#C') @ (
% 8.69/1.75 hoasap @
% 8.69/1.75 id) @ id)))))) @
% 8.69/1.75 id)))))))))))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ (=>) @
% 8.69/1.75 (hoasinduction_p_and_p_prime @ '#sk10'))) @
% 8.69/1.75 ((('#B') @ (!!) @
% 8.69/1.75 ((('#B') @ ((('#B') @ (!!))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#S') @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#B'))) @
% 8.69/1.75 ((('#B') @ (=>))))))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ ('#S') @
% 8.69/1.75 ((('#B') @ (=>))))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#B') @ ('#B'))) @ ap))))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl369])).
% 8.69/1.75 thf(zip_derived_cl400, plain,
% 8.69/1.75 (~ (((((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#B') @ ((('#B') @ (!!))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#S') @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#S'))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (
% 8.69/1.75 '#S'))))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 =>))))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#C') @
% 8.69/1.75 ((('#B') @ ((
% 8.69/1.75 ('#B') @ (
% 8.69/1.75 '#B'))) @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ ('#B'))) @
% 8.69/1.75 '#sk10')))))) @
% 8.69/1.75 ((('#C') @ comp)))))))))))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#C'))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ ('#S') @
% 8.69/1.75 ((('#B') @ ((('#B') @ '#sk10')) @
% 8.69/1.75 comp)))))) @
% 8.69/1.75 sub)))))))))))))) =>
% 8.69/1.75 (((((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#B') @ ((('#B') @ (!!))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#S') @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#S'))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (
% 8.69/1.75 '#S'))))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 =>))))))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#C'))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ (
% 8.69/1.75 '#B') @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 '#S') @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ '#sk10')) @
% 8.69/1.75 comp)))))) @
% 8.69/1.75 sub)))))))))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#C') @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#B'))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#B'))) @
% 8.69/1.75 '#sk10')))))) @
% 8.69/1.75 ((('#C') @ comp)))))))))))))) =>
% 8.69/1.75 (((((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ (=>) @
% 8.69/1.75 ((('#C') @ ('#sk10' @ id) @ id)))))) @
% 8.69/1.75 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 8.69/1.75 ((('#C') @ ('#sk10' @ id) @
% 8.69/1.75 id)))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#C') @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#sk10' @ id))) @
% 8.69/1.75 ((('#C') @ (hoasap @ id) @ id)))))) @
% 8.69/1.75 id)))))))))) =>
% 8.69/1.75 (((hoasinduction_p_and_p_prime @ '#sk10' @ '#sk12') =>
% 8.69/1.75 (((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ (=>) @ '#sk12')))) @
% 8.69/1.75 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ '#sk12')))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ '#sk12')) @ ap))))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl370])).
% 8.69/1.75 thf(zip_derived_cl427, plain,
% 8.69/1.75 (~ (((((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#B') @ ((('#B') @ (!!))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#S') @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#S'))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (
% 8.69/1.75 '#S'))))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ((('#B') @ (
% 8.69/1.75 (('#B') @ (
% 8.69/1.75 =>))))))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#C'))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 '#S') @
% 8.69/1.75 ((('#B') @ (
% 8.69/1.75 (('#B') @ '#sk10')) @
% 8.69/1.75 comp)))))) @
% 8.69/1.75 sub)))))))))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#C') @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#B'))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#B'))) @
% 8.69/1.75 '#sk10')))))) @
% 8.69/1.75 ((('#C') @ comp)))))))))))))) =>
% 8.69/1.75 (((((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ (=>) @
% 8.69/1.75 ((('#C') @ ('#sk10' @ id) @ id)))))) @
% 8.69/1.75 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 8.69/1.75 ((('#C') @ ('#sk10' @ id) @
% 8.69/1.75 id)))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#C') @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#sk10' @ id))) @
% 8.69/1.75 ((('#C') @ (hoasap @ id) @ id)))))) @
% 8.69/1.75 id)))))))))) =>
% 8.69/1.75 (((hoasinduction_p_and_p_prime @ '#sk10' @ '#sk12') =>
% 8.69/1.75 (((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ (=>) @ '#sk12')))) @
% 8.69/1.75 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ '#sk12')))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ '#sk12')) @ ap))))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
% 8.69/1.75 thf(zip_derived_cl454, plain,
% 8.69/1.75 (~ (((((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ (=>) @
% 8.69/1.75 ((('#C') @ ('#sk10' @ id) @ id)))))) @
% 8.69/1.75 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 8.69/1.75 ((('#C') @ ('#sk10' @ id) @ id)))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#C') @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#sk10' @ id))) @
% 8.69/1.75 ((('#C') @ (hoasap @ id) @ id)))))) @
% 8.69/1.75 id)))))))))) =>
% 8.69/1.75 (((hoasinduction_p_and_p_prime @ '#sk10' @ '#sk12') =>
% 8.69/1.75 (((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ (=>) @ '#sk12')))) @
% 8.69/1.75 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ '#sk12')))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ '#sk12')) @ ap))))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl427])).
% 8.69/1.75 thf(zip_derived_cl480, plain,
% 8.69/1.75 (~ (((hoasinduction_p_and_p_prime @ '#sk10' @ '#sk12') =>
% 8.69/1.75 (((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ (=>) @ '#sk12')))) @
% 8.69/1.75 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ '#sk12')))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ '#sk12')) @ ap))))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl454])).
% 8.69/1.75 thf(zip_derived_cl500, plain,
% 8.69/1.75 (~ (((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @ ((('#B') @ (=>) @ '#sk12')))) @
% 8.69/1.75 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ '#sk12')))) @
% 8.69/1.75 ((('#B') @ ((('#B') @ '#sk12')) @ ap))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl480])).
% 8.69/1.75 thf(zip_derived_cl516, plain,
% 8.69/1.75 (~ (((!!) @ ((('#B') @ (((=>) @ ('#sk12' @ ('#sk3' @ '#sk12')))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ (=>) @ '#sk12')) @
% 8.69/1.75 ((('#B') @ '#sk12' @ (ap @ ('#sk3' @ '#sk12'))))))))))),
% 8.69/1.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl500])).
% 8.69/1.75 thf(zip_derived_cl529, plain,
% 8.69/1.75 (~ ((('#sk12' @ ('#sk3' @ '#sk12')) =>
% 8.69/1.75 ((('#sk12' @ ('#sk5' @ '#sk12')) => ('#sk12' @
% 8.69/1.75 (ap @ ('#sk3' @ '#sk12') @ ('#sk5' @ '#sk12')))))))),
% 8.69/1.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl516])).
% 8.69/1.75 thf(zip_derived_cl536, plain,
% 8.69/1.75 (~ ((('#sk12' @ ('#sk5' @ '#sk12')) => ('#sk12' @
% 8.69/1.75 (ap @ ('#sk3' @ '#sk12') @ ('#sk5' @ '#sk12')))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl529])).
% 8.69/1.75 thf(zip_derived_cl539, plain,
% 8.69/1.75 (~ ('#sk12' @ (ap @ ('#sk3' @ '#sk12') @ ('#sk5' @ '#sk12')))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl536])).
% 8.69/1.75 thf(zip_derived_cl479, plain,
% 8.69/1.75 ( (((!!) @ ((('#B') @ (!!) @
% 8.69/1.75 ((('#S') @ ((('#B') @ ('#B') @
% 8.69/1.75 ((('#B') @ (=>) @
% 8.69/1.75 ((('#C') @ ('#sk10' @ id) @ id)))))) @
% 8.69/1.75 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 8.69/1.75 ((('#C') @ ('#sk10' @ id) @ id)))))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#C') @
% 8.69/1.75 ((('#B') @ ((('#B') @ ('#sk10' @ id))) @
% 8.69/1.75 ((('#C') @ (hoasap @ id) @ id)))))) @
% 8.69/1.75 id))))))))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl454])).
% 8.69/1.75 thf(zip_derived_cl498, plain,
% 8.69/1.75 (![X2 : term]:
% 8.69/1.75 (((!!) @ ((('#B') @ (((=>) @ ('#sk10' @ id @ X2 @ id))) @
% 8.69/1.75 ((('#S') @ ((('#B') @ (=>) @
% 8.69/1.75 ((('#C') @ ('#sk10' @ id) @ id)))) @
% 8.69/1.75 ((('#C') @ ((('#B') @ ('#sk10' @ id) @
% 8.69/1.75 (hoasap @ id @ X2 @ id))) @
% 8.69/1.75 id))))))))),
% 8.69/1.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl479])).
% 8.69/1.75 thf(zip_derived_cl514, plain,
% 8.69/1.75 (![X2 : term, X4 : term]:
% 8.69/1.75 ((('#sk10' @ id @ X2 @ id) =>
% 8.69/1.75 ((('#sk10' @ id @ X4 @ id) => ('#sk10' @ id @
% 8.69/1.75 (hoasap @ id @ X2 @ id @ X4) @ id)))))),
% 8.69/1.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl498])).
% 8.69/1.75 thf(hoasap, axiom,(( hoasap @ (X3)@ (X0)@ (X1)@ (X2)) =
% 8.69/1.75 ((ap @ (sub @ X0 @ X1) @ X2)))).
% 8.69/1.75 thf('4', plain,
% 8.69/1.75 (![X3:subst,X2:term,X1:subst,X0:term]:
% 8.69/1.75 ( ( hoasap @ X3 @ X0 @ X1 @ X2 ) = ( ap @ ( sub @ X0 @ X1 ) @ X2 ) )),
% 8.69/1.75 define([status(thm)])).
% 8.69/1.75 thf(zip_derived_cl525, plain,
% 8.69/1.75 (![X2 : term, X4 : term]:
% 8.69/1.75 ((('#sk10' @ id @ X2 @ id) =>
% 8.69/1.75 ((('#sk10' @ id @ X4 @ id) => ('#sk10' @ id @
% 8.69/1.75 (ap @ (sub @ X2 @ id) @ X4) @ id)))))),
% 8.69/1.75 inference('rw', [status(thm)], [zip_derived_cl514, '4'])).
% 8.69/1.75 thf(zip_derived_cl526, plain,
% 8.69/1.75 (![X2 : term, X4 : term]:
% 8.69/1.75 (~ ('#sk10' @ id @ X2 @ id)
% 8.69/1.75 | ((('#sk10' @ id @ X4 @ id) => ('#sk10' @ id @
% 8.69/1.75 (ap @ (sub @ X2 @ id) @ X4) @ id))))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl525])).
% 8.69/1.75 thf(zip_derived_cl533, plain,
% 8.69/1.75 (![X2 : term, X4 : term]:
% 8.69/1.75 (~ ('#sk10' @ id @ X4 @ id)
% 8.69/1.75 | ('#sk10' @ id @ (ap @ (sub @ X2 @ id) @ X4) @ id)
% 8.69/1.75 | ~ ('#sk10' @ id @ X2 @ id))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl526])).
% 8.69/1.75 thf(zip_derived_cl499, plain,
% 8.69/1.75 ( (hoasinduction_p_and_p_prime @ '#sk10' @ '#sk12')),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl480])).
% 8.69/1.75 thf(hoasinduction_p_and_p_prime, axiom,
% 8.69/1.75 (hoasinduction_p_and_p_prime @ X0 @ X1) =>
% 8.69/1.75 ((((!!) @ (^[Y0 : term]: (((X1 @ Y0) <=> (X0 @ id @ Y0 @ id)))))) = ($true))).
% 8.69/1.75 thf('5', plain,
% 8.69/1.75 (![X0:( subst > term > subst > $o ),X1:( term > $o )]:
% 8.69/1.75 ( ( hoasinduction_p_and_p_prime @ X0 @ X1 ) <=>
% 8.69/1.75 ( ![X6:term]: ( ( X1 @ X6 ) <=> ( X0 @ id @ X6 @ id ) ) ) )),
% 8.69/1.75 inference('rw.lit', [status(esa)], [hoasinduction_p_and_p_prime])).
% 8.69/1.75 thf(zip_derived_cl515, plain,
% 8.69/1.75 ( (((!!) @ (^[Y0 : term]: ((('#sk12' @ Y0) <=> ('#sk10' @ id @ Y0 @ id))))))),
% 8.69/1.75 inference('rw_clause', [status(thm)], [zip_derived_cl499, '5'])).
% 8.69/1.75 thf(zip_derived_cl527, plain,
% 8.69/1.75 ( (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ '#sk12')) @
% 8.69/1.75 ((('#C') @ ('#sk10' @ id) @ id))))))),
% 8.69/1.75 inference('comb-normalize', [status(thm)], [zip_derived_cl515])).
% 8.69/1.75 thf(zip_derived_cl528, plain,
% 8.69/1.75 (![X2 : term]: ((('#sk12' @ X2) <=> ('#sk10' @ id @ X2 @ id)))),
% 8.69/1.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl527])).
% 8.69/1.75 thf(zip_derived_cl534, plain,
% 8.69/1.75 (![X2 : term]: (('#sk12' @ X2) = ('#sk10' @ id @ X2 @ id))),
% 8.69/1.75 inference('simplify nested equalities', [status(thm)],
% 8.69/1.75 [zip_derived_cl528])).
% 8.69/1.75 thf(zip_derived_cl11, plain, ( (axvarid)),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 8.69/1.75 thf(axvarid, axiom, (axvarid) =>
% 8.69/1.75 ((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) = ($true))).
% 8.69/1.75 thf('6', plain,
% 8.69/1.75 (( axvarid ) <=> ( ![X5:term]: ( ( sub @ X5 @ id ) = ( X5 ) ) )),
% 8.69/1.75 inference('rw.lit', [status(esa)], [axvarid])).
% 8.69/1.75 thf(zip_derived_cl16, plain,
% 8.69/1.75 ( (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0))))))),
% 8.69/1.75 inference('rw_clause', [status(thm)], [zip_derived_cl11, '6'])).
% 8.69/1.75 thf(zip_derived_cl21, plain,
% 8.69/1.75 ( (((!!) @ ((('#S') @ ((('#B') @ (=) @ ((('#C') @ sub @ id)))) @ ('#I')))))),
% 8.69/1.75 inference('comb-normalize', [status(thm)], [zip_derived_cl16])).
% 8.69/1.75 thf(zip_derived_cl22, plain, (![X2 : term]: (((sub @ X2 @ id) = (X2)))),
% 8.69/1.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])).
% 8.69/1.75 thf(zip_derived_cl28, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))),
% 8.69/1.75 inference('simplify nested equalities', [status(thm)], [zip_derived_cl22])).
% 8.69/1.75 thf(zip_derived_cl534, plain,
% 8.69/1.75 (![X2 : term]: (('#sk12' @ X2) = ('#sk10' @ id @ X2 @ id))),
% 8.69/1.75 inference('simplify nested equalities', [status(thm)],
% 8.69/1.75 [zip_derived_cl528])).
% 8.69/1.75 thf(zip_derived_cl534, plain,
% 8.69/1.75 (![X2 : term]: (('#sk12' @ X2) = ('#sk10' @ id @ X2 @ id))),
% 8.69/1.75 inference('simplify nested equalities', [status(thm)],
% 8.69/1.75 [zip_derived_cl528])).
% 8.69/1.75 thf(zip_derived_cl547, plain,
% 8.69/1.75 (![X2 : term, X4 : term]:
% 8.69/1.75 (~ ('#sk12' @ X4) | ('#sk12' @ (ap @ X2 @ X4)) | ~ ('#sk12' @ X2))),
% 8.69/1.75 inference('demod', [status(thm)],
% 8.69/1.75 [zip_derived_cl533, zip_derived_cl534, zip_derived_cl28,
% 8.69/1.75 zip_derived_cl534, zip_derived_cl534])).
% 8.69/1.75 thf(zip_derived_cl1103, plain,
% 8.69/1.75 ((~ ('#sk12' @ ('#sk3' @ '#sk12')) | ~ ('#sk12' @ ('#sk5' @ '#sk12')))),
% 8.69/1.75 inference('sup+', [status(thm)], [zip_derived_cl539, zip_derived_cl547])).
% 8.69/1.75 thf(zip_derived_cl535, plain, ( ('#sk12' @ ('#sk3' @ '#sk12'))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl529])).
% 8.69/1.75 thf(zip_derived_cl538, plain, ( ('#sk12' @ ('#sk5' @ '#sk12'))),
% 8.69/1.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl536])).
% 8.69/1.75 thf(zip_derived_cl1113, plain, ($false),
% 8.69/1.75 inference('demod', [status(thm)],
% 8.69/1.75 [zip_derived_cl1103, zip_derived_cl535, zip_derived_cl538])).
% 8.69/1.75
% 8.69/1.75 % SZS output end Refutation
% 8.69/1.75
% 8.69/1.75
% 8.69/1.75 % Terminating...
% 9.80/1.88 % Runner terminated.
% 9.80/1.89 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------