TSTP Solution File: ALG257^1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ALG257^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Qf1W8XMDEi true
% Computer : n002.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 : Wed Aug 30 17:12:31 EDT 2023
% Result : Theorem 9.11s 1.82s
% Output : Refutation 9.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : ALG257^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.14/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Qf1W8XMDEi true
% 0.16/0.37 % Computer : n002.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon Aug 28 03:56:49 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.16/0.37 % Running portfolio for 300 s
% 0.16/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.37 % Number of cores: 8
% 0.16/0.38 % Python version: Python 3.6.8
% 0.16/0.38 % Running in HO mode
% 0.24/0.70 % Total configuration time : 828
% 0.24/0.71 % Estimated wc time : 1656
% 0.24/0.71 % Estimated cpu time (8 cpus) : 207.0
% 0.24/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.24/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.20/0.79 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.37/0.79 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.37/0.80 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.37/0.83 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.51/0.84 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.51/0.84 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.53/0.89 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 9.11/1.82 % Solved by lams/40_b.comb.sh.
% 9.11/1.82 % done 116 iterations in 0.962s
% 9.11/1.82 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 9.11/1.82 % SZS output start Refutation
% 9.11/1.82 thf(subst_type, type, subst: $tType).
% 9.11/1.82 thf(term_type, type, term: $tType).
% 9.11/1.82 thf(axmap_type, type, axmap: $o).
% 9.11/1.82 thf(axclos_type, type, axclos: $o).
% 9.11/1.82 thf(lamnotap_type, type, lamnotap: $o).
% 9.11/1.82 thf(axvarcons_type, type, axvarcons: $o).
% 9.11/1.82 thf(substmonoid_type, type, substmonoid: $o).
% 9.11/1.82 thf('#sk6_type', type, '#sk6': term).
% 9.11/1.82 thf(push_type, type, push: term > subst > subst).
% 9.11/1.82 thf(axshiftcons_type, type, axshiftcons: $o).
% 9.11/1.82 thf(hoasapinj1_type, type, hoasapinj1: $o).
% 9.11/1.82 thf(axapp_type, type, axapp: $o).
% 9.11/1.82 thf(shinj_type, type, shinj: $o).
% 9.11/1.82 thf(hoasap_type, type, hoasap: subst > term > subst > term > term).
% 9.11/1.82 thf('#sk7_type', type, '#sk7': term).
% 9.11/1.82 thf(one_type, type, one: term).
% 9.11/1.82 thf(id_type, type, id: subst).
% 9.11/1.82 thf(induction2_type, type, induction2: $o).
% 9.11/1.82 thf(axvarid_type, type, axvarid: $o).
% 9.11/1.82 thf(axvarshift_type, type, axvarshift: $o).
% 9.11/1.82 thf('#sk11_type', type, '#sk11': term).
% 9.11/1.82 thf(induction2lem_type, type, induction2lem: $o).
% 9.11/1.82 thf(sh_type, type, sh: subst).
% 9.11/1.82 thf(laminj_type, type, laminj: $o).
% 9.11/1.82 thf(ulamvarind_type, type, ulamvarind: $o).
% 9.11/1.82 thf(apinj2_type, type, apinj2: $o).
% 9.11/1.82 thf(ulamvarsh_type, type, ulamvarsh: $o).
% 9.11/1.82 thf(lamnotvar_type, type, lamnotvar: $o).
% 9.11/1.82 thf(apnotvar_type, type, apnotvar: $o).
% 9.11/1.82 thf(hoasapinj2_gthm_type, type, hoasapinj2_gthm: $o).
% 9.11/1.82 thf(pushprop_type, type, pushprop: $o).
% 9.11/1.82 thf(sub_type, type, sub: term > subst > term).
% 9.11/1.82 thf(apinj1_type, type, apinj1: $o).
% 9.11/1.82 thf(axidl_type, type, axidl: $o).
% 9.11/1.82 thf(ap_type, type, ap: term > term > term).
% 9.11/1.82 thf(termmset_type, type, termmset: $o).
% 9.11/1.82 thf(hoasapinj2_type, type, hoasapinj2: $o).
% 9.11/1.82 thf(var_type, type, var: term > $o).
% 9.11/1.82 thf(axassoc_type, type, axassoc: $o).
% 9.11/1.82 thf(axidr_type, type, axidr: $o).
% 9.11/1.82 thf(axabs_type, type, axabs: $o).
% 9.11/1.82 thf(ulamvar1_type, type, ulamvar1: $o).
% 9.11/1.82 thf(induction_type, type, induction: $o).
% 9.11/1.82 thf(axscons_type, type, axscons: $o).
% 9.11/1.82 thf('#sk9_type', type, '#sk9': term).
% 9.11/1.82 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 9.11/1.82 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 9.11/1.82 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 9.11/1.82 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 9.11/1.82 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 9.11/1.82 thf(thm, conjecture, (hoasapinj2_gthm)).
% 9.11/1.82 thf(zf_stmt_0, negated_conjecture, (~( hoasapinj2_gthm )),
% 9.11/1.82 inference('cnf.neg', [status(esa)], [thm])).
% 9.11/1.82 thf(zip_derived_cl0, plain, (~ (hoasapinj2_gthm)),
% 9.11/1.82 inference('cnf', [status(esa)], [zf_stmt_0])).
% 9.11/1.82 thf(hoasapinj2_gthm, axiom, ~ (hoasapinj2_gthm) =>
% 9.11/1.82 ((((axapp) =>
% 9.11/1.82 (((axvarcons) =>
% 9.11/1.82 (((axvarid) =>
% 9.11/1.82 (((axabs) =>
% 9.11/1.82 (((axclos) =>
% 9.11/1.82 (((axidl) =>
% 9.11/1.82 (((axshiftcons) =>
% 9.11/1.82 (((axassoc) =>
% 9.11/1.82 (((axmap) =>
% 9.11/1.82 (((axidr) =>
% 9.11/1.82 (((axvarshift) =>
% 9.11/1.82 (((axscons) =>
% 9.11/1.82 (((ulamvar1) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) =>
% 9.11/1.82 (hoasapinj2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 9.11/1.82 != ($true))).
% 9.11/1.82 thf('0', plain,
% 9.11/1.82 (( ~( hoasapinj2_gthm ) ) <=>
% 9.11/1.82 ( ~( ( axapp ) =>
% 9.11/1.82 ( ( axvarcons ) =>
% 9.11/1.82 ( ( axvarid ) =>
% 9.11/1.82 ( ( axabs ) =>
% 9.11/1.82 ( ( axclos ) =>
% 9.11/1.82 ( ( axidl ) =>
% 9.11/1.82 ( ( axshiftcons ) =>
% 9.11/1.82 ( ( axassoc ) =>
% 9.11/1.82 ( ( axmap ) =>
% 9.11/1.82 ( ( axidr ) =>
% 9.11/1.82 ( ( axvarshift ) =>
% 9.11/1.82 ( ( axscons ) =>
% 9.11/1.82 ( ( ulamvar1 ) =>
% 9.11/1.82 ( ( ulamvarsh ) =>
% 9.11/1.82 ( ( ulamvarind ) =>
% 9.11/1.82 ( ( apinj1 ) =>
% 9.11/1.82 ( ( apinj2 ) =>
% 9.11/1.82 ( ( laminj ) =>
% 9.11/1.82 ( ( shinj ) =>
% 9.11/1.82 ( ( lamnotap ) =>
% 9.11/1.82 ( ( apnotvar ) =>
% 9.11/1.82 ( ( lamnotvar ) =>
% 9.11/1.82 ( ( induction ) =>
% 9.11/1.82 ( ( pushprop ) =>
% 9.11/1.82 ( ( induction2lem ) =>
% 9.11/1.82 ( ( induction2 ) =>
% 9.11/1.82 ( ( substmonoid ) =>
% 9.11/1.82 ( ( termmset ) =>
% 9.11/1.82 ( ( hoasapinj1 ) =>
% 9.11/1.82 ( hoasapinj2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 9.11/1.82 inference('rw.lit', [status(esa)], [hoasapinj2_gthm])).
% 9.11/1.82 thf(zip_derived_cl1, plain,
% 9.11/1.82 (~ (((axapp) =>
% 9.11/1.82 (((axvarcons) =>
% 9.11/1.82 (((axvarid) =>
% 9.11/1.82 (((axabs) =>
% 9.11/1.82 (((axclos) =>
% 9.11/1.82 (((axidl) =>
% 9.11/1.82 (((axshiftcons) =>
% 9.11/1.82 (((axassoc) =>
% 9.11/1.82 (((axmap) =>
% 9.11/1.82 (((axidr) =>
% 9.11/1.82 (((axvarshift) =>
% 9.11/1.82 (((axscons) =>
% 9.11/1.82 (((ulamvar1) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) =>
% 9.11/1.82 (hoasapinj2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('rw_clause', [status(thm)], [zip_derived_cl0, '0'])).
% 9.11/1.82 thf(axvarshift, axiom,(( axvarshift ) = ((((push @ one @ sh) = (id)))))).
% 9.11/1.82 thf('1', plain, (( axvarshift ) = ( ( push @ one @ sh ) = ( id ) )),
% 9.11/1.82 define([status(thm)])).
% 9.11/1.82 thf(ulamvar1, axiom,(( ulamvar1 ) = ((var @ one)))).
% 9.11/1.82 thf('2', plain, (( ulamvar1 ) = ( var @ one )), define([status(thm)])).
% 9.11/1.82 thf(zip_derived_cl2, plain,
% 9.11/1.82 (~ (((axapp) =>
% 9.11/1.82 (((axvarcons) =>
% 9.11/1.82 (((axvarid) =>
% 9.11/1.82 (((axabs) =>
% 9.11/1.82 (((axclos) =>
% 9.11/1.82 (((axidl) =>
% 9.11/1.82 (((axshiftcons) =>
% 9.11/1.82 (((axassoc) =>
% 9.11/1.82 (((axmap) =>
% 9.11/1.82 (((axidr) =>
% 9.11/1.82 (((((push @ one @ sh) = (id))) =>
% 9.11/1.82 (((axscons) =>
% 9.11/1.82 (((var @ one) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) =>
% 9.11/1.82 (hoasapinj2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('rw', [status(thm)], [zip_derived_cl1, '1', '2'])).
% 9.11/1.82 thf(zip_derived_cl4, plain,
% 9.11/1.82 (~ (((axvarcons) =>
% 9.11/1.82 (((axvarid) =>
% 9.11/1.82 (((axabs) =>
% 9.11/1.82 (((axclos) =>
% 9.11/1.82 (((axidl) =>
% 9.11/1.82 (((axshiftcons) =>
% 9.11/1.82 (((axassoc) =>
% 9.11/1.82 (((axmap) =>
% 9.11/1.82 (((axidr) =>
% 9.11/1.82 (((((push @ one @ sh) = (id))) =>
% 9.11/1.82 (((axscons) =>
% 9.11/1.82 (((var @ one) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) =>
% 9.11/1.82 (hoasapinj2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])).
% 9.11/1.82 thf(zip_derived_cl7, plain,
% 9.11/1.82 (~ (((axvarid) =>
% 9.11/1.82 (((axabs) =>
% 9.11/1.82 (((axclos) =>
% 9.11/1.82 (((axidl) =>
% 9.11/1.82 (((axshiftcons) =>
% 9.11/1.82 (((axassoc) =>
% 9.11/1.82 (((axmap) =>
% 9.11/1.82 (((axidr) =>
% 9.11/1.82 (((((push @ one @ sh) = (id))) =>
% 9.11/1.82 (((axscons) =>
% 9.11/1.82 (((var @ one) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) =>
% 9.11/1.82 (hoasapinj2)))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])).
% 9.11/1.82 thf(zip_derived_cl12, plain,
% 9.11/1.82 (~ (((axabs) =>
% 9.11/1.82 (((axclos) =>
% 9.11/1.82 (((axidl) =>
% 9.11/1.82 (((axshiftcons) =>
% 9.11/1.82 (((axassoc) =>
% 9.11/1.82 (((axmap) =>
% 9.11/1.82 (((axidr) =>
% 9.11/1.82 (((((push @ one @ sh) = (id))) =>
% 9.11/1.82 (((axscons) =>
% 9.11/1.82 (((var @ one) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) =>
% 9.11/1.82 (hoasapinj2)))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 9.11/1.82 thf(zip_derived_cl18, plain,
% 9.11/1.82 (~ (((axclos) =>
% 9.11/1.82 (((axidl) =>
% 9.11/1.82 (((axshiftcons) =>
% 9.11/1.82 (((axassoc) =>
% 9.11/1.82 (((axmap) =>
% 9.11/1.82 (((axidr) =>
% 9.11/1.82 (((((push @ one @ sh) = (id))) =>
% 9.11/1.82 (((axscons) =>
% 9.11/1.82 (((var @ one) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) =>
% 9.11/1.82 (hoasapinj2)))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])).
% 9.11/1.82 thf(zip_derived_cl25, plain,
% 9.11/1.82 (~ (((axidl) =>
% 9.11/1.82 (((axshiftcons) =>
% 9.11/1.82 (((axassoc) =>
% 9.11/1.82 (((axmap) =>
% 9.11/1.82 (((axidr) =>
% 9.11/1.82 (((((push @ one @ sh) = (id))) =>
% 9.11/1.82 (((axscons) =>
% 9.11/1.82 (((var @ one) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) =>
% 9.11/1.82 (hoasapinj2)))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])).
% 9.11/1.82 thf(zip_derived_cl33, plain,
% 9.11/1.82 (~ (((axshiftcons) =>
% 9.11/1.82 (((axassoc) =>
% 9.11/1.82 (((axmap) =>
% 9.11/1.82 (((axidr) =>
% 9.11/1.82 (((((push @ one @ sh) = (id))) =>
% 9.11/1.82 (((axscons) =>
% 9.11/1.82 (((var @ one) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) =>
% 9.11/1.82 (hoasapinj2)))))))))))))))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 9.11/1.82 thf(zip_derived_cl39, plain,
% 9.11/1.82 (~ (((axassoc) =>
% 9.11/1.82 (((axmap) =>
% 9.11/1.82 (((axidr) =>
% 9.11/1.82 (((((push @ one @ sh) = (id))) =>
% 9.11/1.82 (((axscons) =>
% 9.11/1.82 (((var @ one) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) =>
% 9.11/1.82 (hoasapinj2)))))))))))))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 9.11/1.82 thf(zip_derived_cl46, plain,
% 9.11/1.82 (~ (((axmap) =>
% 9.11/1.82 (((axidr) =>
% 9.11/1.82 (((((push @ one @ sh) = (id))) =>
% 9.11/1.82 (((axscons) =>
% 9.11/1.82 (((var @ one) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) => (hoasapinj2)))))))))))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])).
% 9.11/1.82 thf(zip_derived_cl53, plain,
% 9.11/1.82 (~ (((axidr) =>
% 9.11/1.82 (((((push @ one @ sh) = (id))) =>
% 9.11/1.82 (((axscons) =>
% 9.11/1.82 (((var @ one) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) => (hoasapinj2)))))))))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 9.11/1.82 thf(zip_derived_cl60, plain,
% 9.11/1.82 (~ (((((push @ one @ sh) = (id))) =>
% 9.11/1.82 (((axscons) =>
% 9.11/1.82 (((var @ one) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) => (hoasapinj2)))))))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])).
% 9.11/1.82 thf(zip_derived_cl67, plain,
% 9.11/1.82 (~ (((axscons) =>
% 9.11/1.82 (((var @ one) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) => (hoasapinj2)))))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl60])).
% 9.11/1.82 thf(zip_derived_cl74, plain,
% 9.11/1.82 (~ (((var @ one) =>
% 9.11/1.82 (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) => (hoasapinj2)))))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])).
% 9.11/1.82 thf(zip_derived_cl80, plain,
% 9.11/1.82 (~ (((ulamvarsh) =>
% 9.11/1.82 (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) => (hoasapinj2)))))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])).
% 9.11/1.82 thf(zip_derived_cl85, plain,
% 9.11/1.82 (~ (((ulamvarind) =>
% 9.11/1.82 (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) => (hoasapinj2)))))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl80])).
% 9.11/1.82 thf(zip_derived_cl89, plain,
% 9.11/1.82 (~ (((apinj1) =>
% 9.11/1.82 (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) =>
% 9.11/1.82 (((hoasapinj1) => (hoasapinj2)))))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])).
% 9.11/1.82 thf(zip_derived_cl94, plain,
% 9.11/1.82 (~ (((apinj2) =>
% 9.11/1.82 (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) => (((hoasapinj1) => (hoasapinj2)))))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])).
% 9.11/1.82 thf(zip_derived_cl100, plain,
% 9.11/1.82 (~ (((laminj) =>
% 9.11/1.82 (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) => (((hoasapinj1) => (hoasapinj2)))))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl94])).
% 9.11/1.82 thf(zip_derived_cl106, plain,
% 9.11/1.82 (~ (((shinj) =>
% 9.11/1.82 (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) => (((hoasapinj1) => (hoasapinj2)))))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])).
% 9.11/1.82 thf(zip_derived_cl113, plain,
% 9.11/1.82 (~ (((lamnotap) =>
% 9.11/1.82 (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) => (((hoasapinj1) => (hoasapinj2)))))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl106])).
% 9.11/1.82 thf(zip_derived_cl121, plain,
% 9.11/1.82 (~ (((apnotvar) =>
% 9.11/1.82 (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) => (((hoasapinj1) => (hoasapinj2)))))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])).
% 9.11/1.82 thf(zip_derived_cl131, plain,
% 9.11/1.82 (~ (((lamnotvar) =>
% 9.11/1.82 (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) => (((hoasapinj1) => (hoasapinj2)))))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl121])).
% 9.11/1.82 thf(zip_derived_cl143, plain,
% 9.11/1.82 (~ (((induction) =>
% 9.11/1.82 (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) => (((hoasapinj1) => (hoasapinj2)))))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl131])).
% 9.11/1.82 thf(zip_derived_cl156, plain,
% 9.11/1.82 (~ (((pushprop) =>
% 9.11/1.82 (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) => (((hoasapinj1) => (hoasapinj2)))))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl143])).
% 9.11/1.82 thf(zip_derived_cl167, plain,
% 9.11/1.82 (~ (((induction2lem) =>
% 9.11/1.82 (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) => (((hoasapinj1) => (hoasapinj2)))))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl156])).
% 9.11/1.82 thf(zip_derived_cl173, plain,
% 9.11/1.82 (~ (((induction2) =>
% 9.11/1.82 (((substmonoid) =>
% 9.11/1.82 (((termmset) => (((hoasapinj1) => (hoasapinj2)))))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl167])).
% 9.11/1.82 thf(zip_derived_cl179, plain,
% 9.11/1.82 (~ (((substmonoid) => (((termmset) => (((hoasapinj1) => (hoasapinj2)))))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])).
% 9.11/1.82 thf(zip_derived_cl186, plain,
% 9.11/1.82 (~ (((termmset) => (((hoasapinj1) => (hoasapinj2)))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])).
% 9.11/1.82 thf(zip_derived_cl195, plain, (~ (((hoasapinj1) => (hoasapinj2)))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl186])).
% 9.11/1.82 thf(zip_derived_cl207, plain, (~ (hoasapinj2)),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl195])).
% 9.11/1.82 thf(hoasapinj2, axiom, ~ (hoasapinj2) =>
% 9.11/1.82 ((((!!) @ (^[Y0 : term]:
% 9.11/1.82 (((!!) @ (^[Y1 : term]:
% 9.11/1.82 (((!!) @ (^[Y2 : term]:
% 9.11/1.82 (((!!) @ (^[Y3 : term]:
% 9.11/1.82 (((((hoasap @ id @ Y0 @
% 9.11/1.82 id @ Y2) = (hoasap @
% 9.11/1.82 id @ Y1 @ id @ Y3))) =>
% 9.11/1.82 (((Y2) = (Y3)))))))))))))))))
% 9.11/1.82 != ($true))).
% 9.11/1.82 thf('3', plain,
% 9.11/1.82 (( ~( hoasapinj2 ) ) <=>
% 9.11/1.82 ( ~( ![X5:term,X7:term,X9:term,X11:term]:
% 9.11/1.82 ( ( ( hoasap @ id @ X5 @ id @ X9 ) =
% 9.11/1.82 ( hoasap @ id @ X7 @ id @ X11 ) ) =>
% 9.11/1.82 ( ( X9 ) = ( X11 ) ) ) ) )),
% 9.11/1.82 inference('rw.lit', [status(esa)], [hoasapinj2])).
% 9.11/1.82 thf(zip_derived_cl220, plain,
% 9.11/1.82 (~ (((!!) @ (^[Y0 : term]:
% 9.11/1.82 (((!!) @ (^[Y1 : term]:
% 9.11/1.82 (((!!) @ (^[Y2 : term]:
% 9.11/1.82 (((!!) @ (^[Y3 : term]:
% 9.11/1.82 (((((hoasap @ id @
% 9.11/1.82 Y0 @ id @ Y2) =
% 9.11/1.82 (hoasap @ id @
% 9.11/1.82 Y1 @ id @ Y3))) =>
% 9.11/1.82 (((Y2) = (Y3)))))))))))))))))),
% 9.11/1.82 inference('rw_clause', [status(thm)], [zip_derived_cl207, '3'])).
% 9.11/1.82 thf(zip_derived_cl236, plain,
% 9.11/1.82 (~ (((!!) @ ((('#B') @ (!!) @
% 9.11/1.82 ((('#B') @ ((('#B') @ (!!))) @
% 9.11/1.82 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 9.11/1.82 ((('#C') @ ((('#B') @ ('#C') @
% 9.11/1.82 ((('#B') @ ((('#B') @ ('#S'))) @
% 9.11/1.82 ((('#B') @ ((('#B') @ ((('#B') @ ('#S'))))) @
% 9.11/1.82 ((('#B') @ ((('#B') @ ((('#B') @ (
% 9.11/1.82 (('#B') @ (=>))))))) @
% 9.11/1.82 ((('#C') @ ((('#B') @ ('#B') @
% 9.11/1.82 ((('#B') @ ('#C') @
% 9.11/1.82 ((('#B') @ ((
% 9.11/1.82 ('#B') @ (
% 9.11/1.82 '#B'))) @
% 9.11/1.82 ((('#B') @ (
% 9.11/1.82 (('#B') @ (=))) @
% 9.11/1.82 ((('#C') @ (
% 9.11/1.82 hoasap @ id) @
% 9.11/1.82 id)))))))))) @
% 9.11/1.82 ((('#C') @ (hoasap @ id) @ id)))))))))))) @
% 9.11/1.82 (=)))))))))))),
% 9.11/1.82 inference('comb-normalize', [status(thm)], [zip_derived_cl220])).
% 9.11/1.82 thf(zip_derived_cl237, plain,
% 9.11/1.82 (~ (((!!) @ ((('#B') @ (!!) @
% 9.11/1.82 ((('#B') @ ((('#B') @ (!!))) @
% 9.11/1.82 ((('#C') @ ((('#B') @ ('#S') @
% 9.11/1.82 ((('#B') @ ((('#B') @ ('#S'))) @
% 9.11/1.82 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 9.11/1.82 ((('#B') @ ((('#C') @ ((('#B') @ (
% 9.11/1.82 '#B') @
% 9.11/1.82 ((('#B') @ (
% 9.11/1.82 =) @
% 9.11/1.82 (hoasap @
% 9.11/1.82 id @
% 9.11/1.82 '#sk6' @ id))))))) @
% 9.11/1.82 ((('#C') @ (hoasap @ id) @ id)))))))))) @
% 9.11/1.82 (=)))))))))),
% 9.11/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl236])).
% 9.11/1.82 thf(zip_derived_cl253, plain,
% 9.11/1.82 (~ (((!!) @ ((('#B') @ (!!) @
% 9.11/1.82 ((('#S') @ ((('#B') @ ('#S') @
% 9.11/1.82 ((('#B') @ ((('#B') @ (=>))) @
% 9.11/1.82 ((('#C') @ ((('#B') @ ('#B') @
% 9.11/1.82 ((('#B') @ (=) @
% 9.11/1.82 (hoasap @ id @ '#sk6' @ id))))) @
% 9.11/1.82 (hoasap @ id @ '#sk7' @ id))))))) @
% 9.11/1.82 (=)))))))),
% 9.11/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl237])).
% 9.11/1.82 thf(zip_derived_cl270, plain,
% 9.11/1.82 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 9.11/1.82 ((('#B') @ (((term) = (hoasap @ id @ '#sk6' @
% 9.11/1.82 id @ '#sk9'))) @
% 9.11/1.82 (hoasap @ id @ '#sk7' @ id))))) @
% 9.11/1.82 (((term) = ('#sk9')))))))),
% 9.11/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl253])).
% 9.11/1.82 thf(hoasap, axiom,(( hoasap @ (X3)@ (X0)@ (X1)@ (X2)) =
% 9.11/1.82 ((ap @ (sub @ X0 @ X1) @ X2)))).
% 9.11/1.82 thf('4', plain,
% 9.11/1.82 (![X3:subst,X2:term,X1:subst,X0:term]:
% 9.11/1.82 ( ( hoasap @ X3 @ X0 @ X1 @ X2 ) = ( ap @ ( sub @ X0 @ X1 ) @ X2 ) )),
% 9.11/1.82 define([status(thm)])).
% 9.11/1.82 thf(zip_derived_cl288, plain,
% 9.11/1.82 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 9.11/1.82 ((('#B') @ (((term) = (ap @
% 9.11/1.82 (sub @ '#sk6' @ id) @ '#sk9'))) @
% 9.11/1.82 (hoasap @ id @ '#sk7' @ id))))) @
% 9.11/1.82 (((term) = ('#sk9')))))))),
% 9.11/1.82 inference('rw', [status(thm)], [zip_derived_cl270, '4'])).
% 9.11/1.82 thf(zip_derived_cl289, plain,
% 9.11/1.82 (~ (((((ap @ (sub @ '#sk6' @ id) @ '#sk9') = (hoasap @ id @ '#sk7' @
% 9.11/1.82 id @ '#sk11'))) =>
% 9.11/1.82 ((('#sk9') = ('#sk11')))))),
% 9.11/1.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl288])).
% 9.11/1.82 thf(zip_derived_cl310, plain,
% 9.11/1.82 (~ (((((ap @ (sub @ '#sk6' @ id) @ '#sk9') = (ap @ (sub @ '#sk7' @ id) @
% 9.11/1.82 '#sk11'))) =>
% 9.11/1.82 ((('#sk9') = ('#sk11')))))),
% 9.11/1.82 inference('rw', [status(thm)], [zip_derived_cl289, '4'])).
% 9.11/1.82 thf(zip_derived_cl311, plain,
% 9.11/1.82 ( (((ap @ (sub @ '#sk6' @ id) @ '#sk9') = (ap @ (sub @ '#sk7' @ id) @
% 9.11/1.82 '#sk11')))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl310])).
% 9.11/1.82 thf(zip_derived_cl338, plain,
% 9.11/1.82 (((ap @ (sub @ '#sk6' @ id) @ '#sk9')
% 9.11/1.82 = (ap @ (sub @ '#sk7' @ id) @ '#sk11'))),
% 9.11/1.82 inference('simplify nested equalities', [status(thm)],
% 9.11/1.82 [zip_derived_cl311])).
% 9.11/1.82 thf(zip_derived_cl11, plain, ( (axvarid)),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 9.11/1.82 thf(axvarid, axiom, (axvarid) =>
% 9.11/1.82 ((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) = ($true))).
% 9.11/1.82 thf('5', plain,
% 9.11/1.82 (( axvarid ) <=> ( ![X5:term]: ( ( sub @ X5 @ id ) = ( X5 ) ) )),
% 9.11/1.82 inference('rw.lit', [status(esa)], [axvarid])).
% 9.11/1.82 thf(zip_derived_cl16, plain,
% 9.11/1.82 ( (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0))))))),
% 9.11/1.82 inference('rw_clause', [status(thm)], [zip_derived_cl11, '5'])).
% 9.11/1.82 thf(zip_derived_cl21, plain,
% 9.11/1.82 ( (((!!) @ ((('#S') @ ((('#B') @ (=) @ ((('#C') @ sub @ id)))) @ ('#I')))))),
% 9.11/1.82 inference('comb-normalize', [status(thm)], [zip_derived_cl16])).
% 9.11/1.82 thf(zip_derived_cl22, plain, (![X2 : term]: (((sub @ X2 @ id) = (X2)))),
% 9.11/1.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])).
% 9.11/1.82 thf(zip_derived_cl28, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))),
% 9.11/1.82 inference('simplify nested equalities', [status(thm)], [zip_derived_cl22])).
% 9.11/1.82 thf(zip_derived_cl28, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))),
% 9.11/1.82 inference('simplify nested equalities', [status(thm)], [zip_derived_cl22])).
% 9.11/1.82 thf(zip_derived_cl448, plain,
% 9.11/1.82 (((ap @ '#sk6' @ '#sk9') = (ap @ '#sk7' @ '#sk11'))),
% 9.11/1.82 inference('demod', [status(thm)],
% 9.11/1.82 [zip_derived_cl338, zip_derived_cl28, zip_derived_cl28])).
% 9.11/1.82 thf(zip_derived_cl99, plain, ( (apinj2)),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl94])).
% 9.11/1.82 thf(apinj2, axiom, (apinj2) =>
% 9.11/1.82 ((((!!) @ (^[Y0 : term]:
% 9.11/1.82 (((!!) @ (^[Y1 : term]:
% 9.11/1.82 (((!!) @ (^[Y2 : term]:
% 9.11/1.82 (((!!) @ (^[Y3 : term]:
% 9.11/1.82 (((((ap @ Y0 @ Y2) =
% 9.11/1.82 (ap @ Y1 @ Y3))) =>
% 9.11/1.82 (((Y2) = (Y3)))))))))))))))))
% 9.11/1.82 = ($true))).
% 9.11/1.82 thf('6', plain,
% 9.11/1.82 (( apinj2 ) <=>
% 9.11/1.82 ( ![X5:term,X7:term,X9:term,X11:term]:
% 9.11/1.82 ( ( ( ap @ X5 @ X9 ) = ( ap @ X7 @ X11 ) ) => ( ( X9 ) = ( X11 ) ) ) )),
% 9.11/1.82 inference('rw.lit', [status(esa)], [apinj2])).
% 9.11/1.82 thf(zip_derived_cl104, plain,
% 9.11/1.82 ( (((!!) @ (^[Y0 : term]:
% 9.11/1.82 (((!!) @ (^[Y1 : term]:
% 9.11/1.82 (((!!) @ (^[Y2 : term]:
% 9.11/1.82 (((!!) @ (^[Y3 : term]:
% 9.11/1.82 (((((ap @ Y0 @ Y2) =
% 9.11/1.82 (ap @ Y1 @ Y3))) =>
% 9.11/1.82 (((Y2) = (Y3)))))))))))))))))),
% 9.11/1.82 inference('rw_clause', [status(thm)], [zip_derived_cl99, '6'])).
% 9.11/1.82 thf(zip_derived_cl109, plain,
% 9.11/1.82 ( (((!!) @ ((('#B') @ (!!) @
% 9.11/1.82 ((('#B') @ ((('#B') @ (!!))) @
% 9.11/1.82 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 9.11/1.82 ((('#C') @ ((('#B') @ ('#C') @
% 9.11/1.82 ((('#B') @ ((('#B') @ ('#S'))) @
% 9.11/1.82 ((('#B') @ ((('#B') @ ((('#B') @ ('#S'))))) @
% 9.11/1.82 ((('#B') @ ((('#B') @ ((('#B') @ (
% 9.11/1.82 (('#B') @ (=>))))))) @
% 9.11/1.82 ((('#C') @ ((('#B') @ ('#B') @
% 9.11/1.82 ((('#B') @ ('#C') @
% 9.11/1.82 ((('#B') @ ((('#B') @ (
% 9.11/1.82 '#B'))) @
% 9.11/1.82 ((('#B') @ (
% 9.11/1.82 (('#B') @ (=))) @
% 9.11/1.82 ap)))))))) @
% 9.11/1.82 ap)))))))))) @
% 9.11/1.82 (=)))))))))))),
% 9.11/1.82 inference('comb-normalize', [status(thm)], [zip_derived_cl104])).
% 9.11/1.82 thf(zip_derived_cl110, plain,
% 9.11/1.82 (![X2 : term]:
% 9.11/1.82 (((!!) @ ((('#B') @ (!!) @
% 9.11/1.82 ((('#B') @ ((('#B') @ (!!))) @
% 9.11/1.82 ((('#C') @ ((('#B') @ ('#S') @
% 9.11/1.82 ((('#B') @ ((('#B') @ ('#S'))) @
% 9.11/1.82 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 9.11/1.82 ((('#B') @ ((('#C') @ ((('#B') @ (
% 9.11/1.82 '#B') @
% 9.11/1.82 ((('#B') @ (
% 9.11/1.82 =) @
% 9.11/1.82 (ap @ X2))))))) @
% 9.11/1.82 ap)))))))) @
% 9.11/1.82 (=)))))))))),
% 9.11/1.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl109])).
% 9.11/1.82 thf(zip_derived_cl116, plain,
% 9.11/1.82 (![X2 : term, X4 : term]:
% 9.11/1.82 (((!!) @ ((('#B') @ (!!) @
% 9.11/1.82 ((('#S') @ ((('#B') @ ('#S') @
% 9.11/1.82 ((('#B') @ ((('#B') @ (=>))) @
% 9.11/1.82 ((('#C') @ ((('#B') @ ('#B') @
% 9.11/1.82 ((('#B') @ (=) @ (ap @ X2))))) @
% 9.11/1.82 (ap @ X4))))))) @
% 9.11/1.82 (=)))))))),
% 9.11/1.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl110])).
% 9.11/1.82 thf(zip_derived_cl125, plain,
% 9.11/1.82 (![X2 : term, X4 : term, X6 : term]:
% 9.11/1.82 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 9.11/1.82 ((('#B') @ (((term) = (ap @ X2 @ X6))) @
% 9.11/1.82 (ap @ X4))))) @
% 9.11/1.82 (((term) = (X6)))))))),
% 9.11/1.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl116])).
% 9.11/1.82 thf(zip_derived_cl136, plain,
% 9.11/1.82 (![X2 : term, X4 : term, X6 : term, X8 : term]:
% 9.11/1.82 (((((ap @ X2 @ X6) = (ap @ X4 @ X8))) => (((X6) = (X8)))))),
% 9.11/1.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl125])).
% 9.11/1.82 thf(zip_derived_cl148, plain,
% 9.11/1.82 (![X2 : term, X4 : term, X6 : term, X8 : term]:
% 9.11/1.82 (~ (((ap @ X2 @ X6) = (ap @ X4 @ X8))) | (((X6) = (X8))))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl136])).
% 9.11/1.82 thf(zip_derived_cl159, plain,
% 9.11/1.82 (![X2 : term, X4 : term, X6 : term, X8 : term]:
% 9.11/1.82 (((ap @ X2 @ X6) != (ap @ X4 @ X8)) | ((X6) = (X8)))),
% 9.11/1.82 inference('simplify nested equalities', [status(thm)],
% 9.11/1.82 [zip_derived_cl148])).
% 9.11/1.82 thf(zip_derived_cl901, plain,
% 9.11/1.82 (![X0 : term, X1 : term]:
% 9.11/1.82 (((ap @ '#sk7' @ '#sk11') != (ap @ X1 @ X0)) | (('#sk9') = (X0)))),
% 9.11/1.82 inference('sup-', [status(thm)], [zip_derived_cl448, zip_derived_cl159])).
% 9.11/1.82 thf(zip_derived_cl1551, plain, ((('#sk9') = ('#sk11'))),
% 9.11/1.82 inference('eq_res', [status(thm)], [zip_derived_cl901])).
% 9.11/1.82 thf(zip_derived_cl312, plain, (~ ((('#sk9') = ('#sk11')))),
% 9.11/1.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl310])).
% 9.11/1.82 thf(zip_derived_cl339, plain, ((('#sk9') != ('#sk11'))),
% 9.11/1.82 inference('simplify nested equalities', [status(thm)],
% 9.11/1.82 [zip_derived_cl312])).
% 9.11/1.82 thf(zip_derived_cl1552, plain, ($false),
% 9.11/1.82 inference('simplify_reflect-', [status(thm)],
% 9.11/1.82 [zip_derived_cl1551, zip_derived_cl339])).
% 9.11/1.82
% 9.11/1.82 % SZS output end Refutation
% 9.11/1.82
% 9.11/1.82
% 9.11/1.82 % Terminating...
% 9.54/1.91 % Runner terminated.
% 9.54/1.91 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------