TSTP Solution File: GEG005^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : GEG005^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ggqOvVz3oj true

% Computer : n029.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 22:42:13 EDT 2023

% Result   : Theorem 18.82s 3.18s
% Output   : Refutation 18.82s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEG005^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ggqOvVz3oj true
% 0.14/0.34  % Computer : n029.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Mon Aug 28 01:18:56 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  % Running portfolio for 300 s
% 0.14/0.34  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34  % Number of cores: 8
% 0.14/0.35  % Python version: Python 3.6.8
% 0.14/0.35  % Running in HO mode
% 0.21/0.61  % Total configuration time : 828
% 0.21/0.61  % Estimated wc time : 1656
% 0.21/0.61  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.72  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.72  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.76  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.71/0.82  % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 18.82/3.18  % Solved by lams/30_b.l.sh.
% 18.82/3.18  % done 575 iterations in 2.358s
% 18.82/3.18  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 18.82/3.18  % SZS output start Refutation
% 18.82/3.18  thf(reg_type, type, reg: $tType).
% 18.82/3.18  thf('#form13_type', type, '#form13': reg > $o).
% 18.82/3.18  thf('#sk9_type', type, '#sk9': reg > reg).
% 18.82/3.18  thf(mbox_type, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 18.82/3.18  thf(paris_type, type, paris: reg).
% 18.82/3.18  thf(ntpp_type, type, ntpp: reg > reg > $o).
% 18.82/3.18  thf(a_type, type, a: $i > $i > $o).
% 18.82/3.18  thf(pp_type, type, pp: reg > reg > $o).
% 18.82/3.18  thf(fool_type, type, fool: $i > $i > $o).
% 18.82/3.18  thf('#sk1_type', type, '#sk1': $i).
% 18.82/3.18  thf(france_type, type, france: reg).
% 18.82/3.18  thf(mnot_type, type, mnot: ($i > $o) > $i > $o).
% 18.82/3.18  thf('#sk12_type', type, '#sk12': reg > reg).
% 18.82/3.18  thf(po_type, type, po: reg > reg > $o).
% 18.82/3.18  thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 18.82/3.18  thf('#sk2_type', type, '#sk2': $i).
% 18.82/3.18  thf(ec_type, type, ec: reg > reg > $o).
% 18.82/3.18  thf('#sk5_type', type, '#sk5': reg).
% 18.82/3.18  thf(o_type, type, o: reg > reg > $o).
% 18.82/3.18  thf('#sk26_type', type, '#sk26': ($i > $o) > $i > $i).
% 18.82/3.18  thf(c_type, type, c: reg > reg > $o).
% 18.82/3.18  thf(p_type, type, p: reg > reg > $o).
% 18.82/3.18  thf(catalunya_type, type, catalunya: reg).
% 18.82/3.18  thf(spain_type, type, spain: reg).
% 18.82/3.18  thf(tpp_type, type, tpp: reg > reg > $o).
% 18.82/3.18  thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 18.82/3.18  thf(mforall_prop_type, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 18.82/3.18  thf(mvalid_type, type, mvalid: ($i > $o) > $o).
% 18.82/3.18  thf(ax2, axiom,
% 18.82/3.18    (mvalid @ ( mbox @ fool @ ( ^[X:$i]: ( ec @ spain @ france ) ) ))).
% 18.82/3.18  thf(zip_derived_cl6, plain,
% 18.82/3.18      ( (mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france))))),
% 18.82/3.18      inference('cnf', [status(esa)], [ax2])).
% 18.82/3.18  thf(mvalid, axiom, (mvalid @ X0) =>
% 18.82/3.18    ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))).
% 18.82/3.18  thf('0', plain,
% 18.82/3.18      (![X0:( $i > $o )]: ( ( mvalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [mvalid])).
% 18.82/3.18  thf(zip_derived_cl89, plain,
% 18.82/3.18      ( (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                    (mbox @ fool @ (^[Y1 : $i]: (ec @ spain @ france)) @ Y0))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl6, '0'])).
% 18.82/3.18  thf(zip_derived_cl90, plain,
% 18.82/3.18      (![X2 : $i]:  (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france)) @ X2)),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl89])).
% 18.82/3.18  thf(mbox, axiom, (mbox @ X0 @ X1 @ X2) =>
% 18.82/3.18    ((((!!) @ (^[Y0 : $i]: (((((~) @ (X0 @ X2 @ Y0))) | (X1 @ Y0)))))) =
% 18.82/3.18     ($true))).
% 18.82/3.18  thf('1', plain,
% 18.82/3.18      (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 18.82/3.18       ( ( mbox @ X0 @ X1 @ X2 ) <=>
% 18.82/3.18         ( ![X7:$i]: ( ( ~( X0 @ X2 @ X7 ) ) | ( X1 @ X7 ) ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [mbox])).
% 18.82/3.18  thf(zip_derived_cl91, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18          (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                      (((((~) @ (fool @ X0 @ Y0))) |
% 18.82/3.18                        ((^[Y1 : $i]: (ec @ spain @ france)) @ Y0))))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl90, '1'])).
% 18.82/3.18  thf(zip_derived_cl92, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18          (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                      (((((~) @ (fool @ X0 @ Y0))) | (ec @ spain @ france))))))),
% 18.82/3.18      inference('ho_norm', [status(thm)], [zip_derived_cl91])).
% 18.82/3.18  thf(zip_derived_cl93, plain,
% 18.82/3.18      (![X0 : $i, X2 : $i]:
% 18.82/3.18          (((((~) @ (fool @ X0 @ X2))) | (ec @ spain @ france)))),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl92])).
% 18.82/3.18  thf(zip_derived_cl94, plain,
% 18.82/3.18      (![X0 : $i, X2 : $i]: (~ (fool @ X0 @ X2) |  (ec @ spain @ france))),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl93])).
% 18.82/3.18  thf(ec, axiom, (ec @ X0 @ X1) =>
% 18.82/3.18    ((((((~) @ (o @ X0 @ X1))) & (c @ X0 @ X1))) = ($true))).
% 18.82/3.18  thf('2', plain,
% 18.82/3.18      (![X0:reg,X1:reg]:
% 18.82/3.18       ( ( ec @ X0 @ X1 ) <=> ( ( c @ X0 @ X1 ) & ( ~( o @ X0 @ X1 ) ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [ec])).
% 18.82/3.18  thf(zip_derived_cl95, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]:
% 18.82/3.18         ( (((((~) @ (o @ spain @ france))) & (c @ spain @ france)))
% 18.82/3.18          | ~ (fool @ X1 @ X0))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl94, '2'])).
% 18.82/3.18  thf(zip_derived_cl96, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]: (~ (o @ spain @ france) | ~ (fool @ X1 @ X0))),
% 18.82/3.18      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl95])).
% 18.82/3.18  thf(o, axiom, ~ (o @ X0 @ X1) =>
% 18.82/3.18    ((((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ X1)))))) != ($true))).
% 18.82/3.18  thf('3', plain,
% 18.82/3.18      (![X0:reg,X1:reg]:
% 18.82/3.18       ( ( ~( o @ X0 @ X1 ) ) <=>
% 18.82/3.18         ( ~( ?[X6:reg]: ( ( p @ X6 @ X0 ) & ( p @ X6 @ X1 ) ) ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [o])).
% 18.82/3.18  thf(zip_derived_cl98, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]:
% 18.82/3.18         (~ (((??) @ (^[Y0 : reg]: (((p @ Y0 @ spain) & (p @ Y0 @ france))))))
% 18.82/3.18          | ~ (fool @ X1 @ X0))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl96, '3'])).
% 18.82/3.18  thf(zip_derived_cl99, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X3 : reg]:
% 18.82/3.18         (~ (((p @ X3 @ spain) & (p @ X3 @ france))) | ~ (fool @ X1 @ X0))),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl98])).
% 18.82/3.18  thf(zip_derived_cl100, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X3 : reg]:
% 18.82/3.18         (~ (p @ X3 @ spain) | ~ (p @ X3 @ france) | ~ (fool @ X1 @ X0))),
% 18.82/3.18      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl99])).
% 18.82/3.18  thf(p, axiom, ~ (p @ X0 @ X1) =>
% 18.82/3.18    ((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ X1)))))) != ($true))).
% 18.82/3.18  thf('4', plain,
% 18.82/3.18      (![X0:reg,X1:reg]:
% 18.82/3.18       ( ( ~( p @ X0 @ X1 ) ) <=>
% 18.82/3.18         ( ~( ![X6:reg]: ( ( c @ X6 @ X0 ) => ( c @ X6 @ X1 ) ) ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [p])).
% 18.82/3.18  thf(zip_derived_cl101, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X2 : reg]:
% 18.82/3.18         (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain))))))
% 18.82/3.18          | ~ (fool @ X1 @ X0)
% 18.82/3.18          | ~ (p @ X2 @ france))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl100, '4'])).
% 18.82/3.18  thf(zip_derived_cl102, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X2 : reg]:
% 18.82/3.18         (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ france))))))
% 18.82/3.18          | ~ (fool @ X1 @ X0)
% 18.82/3.18          | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl101, '4'])).
% 18.82/3.18  thf(zip_derived_cl103, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X2 : reg]:
% 18.82/3.18         (~ (((c @ ('#sk12' @ X2) @ X2) => (c @ ('#sk12' @ X2) @ france)))
% 18.82/3.18          | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain))))))
% 18.82/3.18          | ~ (fool @ X1 @ X0))),
% 18.82/3.18      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl102])).
% 18.82/3.18  thf(zip_derived_cl104, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X2 : reg]:
% 18.82/3.18         ( (c @ ('#sk12' @ X2) @ X2)
% 18.82/3.18          | ~ (fool @ X1 @ X0)
% 18.82/3.18          | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 18.82/3.18      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])).
% 18.82/3.18  thf(zip_derived_cl104, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X2 : reg]:
% 18.82/3.18         ( (c @ ('#sk12' @ X2) @ X2)
% 18.82/3.18          | ~ (fool @ X1 @ X0)
% 18.82/3.18          | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 18.82/3.18      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])).
% 18.82/3.18  thf(zip_derived_cl106, plain,
% 18.82/3.18      (![X2 : reg]:
% 18.82/3.18         ( ('#form13' @ X2)
% 18.82/3.18          | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 18.82/3.18      define([status(thm)])).
% 18.82/3.18  thf(zip_derived_cl108, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X2 : reg]:
% 18.82/3.18         (~ ('#form13' @ X2) | ~ (fool @ X1 @ X0) |  (c @ ('#sk12' @ X2) @ X2))),
% 18.82/3.18      inference('renaming', [status(thm)],
% 18.82/3.18                [zip_derived_cl104, zip_derived_cl106])).
% 18.82/3.18  thf(ax3, axiom,
% 18.82/3.18    (mvalid @ ( mbox @ a @ ( ^[X:$i]: ( ntpp @ paris @ france ) ) ))).
% 18.82/3.18  thf(zip_derived_cl7, plain,
% 18.82/3.18      ( (mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france))))),
% 18.82/3.18      inference('cnf', [status(esa)], [ax3])).
% 18.82/3.18  thf(zip_derived_cl112, plain,
% 18.82/3.18      ( (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                    (mbox @ a @ (^[Y1 : $i]: (ntpp @ paris @ france)) @ Y0))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl7, '0'])).
% 18.82/3.18  thf(zip_derived_cl113, plain,
% 18.82/3.18      (![X2 : $i]:  (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)) @ X2)),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl112])).
% 18.82/3.18  thf(zip_derived_cl114, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18          (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                      (((((~) @ (a @ X0 @ Y0))) |
% 18.82/3.18                        ((^[Y1 : $i]: (ntpp @ paris @ france)) @ Y0))))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl113, '1'])).
% 18.82/3.18  thf(zip_derived_cl115, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18          (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                      (((((~) @ (a @ X0 @ Y0))) | (ntpp @ paris @ france))))))),
% 18.82/3.18      inference('ho_norm', [status(thm)], [zip_derived_cl114])).
% 18.82/3.18  thf(zip_derived_cl116, plain,
% 18.82/3.18      (![X0 : $i, X2 : $i]:
% 18.82/3.18          (((((~) @ (a @ X0 @ X2))) | (ntpp @ paris @ france)))),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl115])).
% 18.82/3.18  thf(zip_derived_cl117, plain,
% 18.82/3.18      (![X0 : $i, X2 : $i]: (~ (a @ X0 @ X2) |  (ntpp @ paris @ france))),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl116])).
% 18.82/3.18  thf(ntpp, axiom, (ntpp @ X0 @ X1) =>
% 18.82/3.18    ((((((~) @ (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ X0) & (ec @ Y0 @ X1)))))))) &
% 18.82/3.18       (pp @ X0 @ X1)))
% 18.82/3.18     = ($true))).
% 18.82/3.18  thf('5', plain,
% 18.82/3.18      (![X0:reg,X1:reg]:
% 18.82/3.18       ( ( ntpp @ X0 @ X1 ) <=>
% 18.82/3.18         ( ( pp @ X0 @ X1 ) & 
% 18.82/3.18           ( ~( ?[X6:reg]: ( ( ec @ X6 @ X0 ) & ( ec @ X6 @ X1 ) ) ) ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [ntpp])).
% 18.82/3.18  thf(zip_derived_cl118, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]:
% 18.82/3.18         ( (((((~) @ (((??) @ (^[Y0 : reg]:
% 18.82/3.18                                 (((ec @ Y0 @ paris) & (ec @ Y0 @ france)))))))) &
% 18.82/3.18             (pp @ paris @ france)))
% 18.82/3.18          | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl117, '5'])).
% 18.82/3.18  thf(zip_derived_cl120, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]: ( (pp @ paris @ france) | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl118])).
% 18.82/3.18  thf(pp, axiom, (pp @ X0 @ X1) =>
% 18.82/3.18    ((((((~) @ (p @ X1 @ X0))) & (p @ X0 @ X1))) = ($true))).
% 18.82/3.18  thf('6', plain,
% 18.82/3.18      (![X0:reg,X1:reg]:
% 18.82/3.18       ( ( pp @ X0 @ X1 ) <=> ( ( p @ X0 @ X1 ) & ( ~( p @ X1 @ X0 ) ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [pp])).
% 18.82/3.18  thf(zip_derived_cl122, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]:
% 18.82/3.18         ( (((((~) @ (p @ france @ paris))) & (p @ paris @ france)))
% 18.82/3.18          | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl120, '6'])).
% 18.82/3.18  thf(zip_derived_cl125, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]: ( (p @ paris @ france) | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl122])).
% 18.82/3.18  thf(p, axiom, (p @ X0 @ X1) =>
% 18.82/3.18    ((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ X1)))))) = ($true))).
% 18.82/3.18  thf('7', plain,
% 18.82/3.18      (![X0:reg,X1:reg]:
% 18.82/3.18       ( ( p @ X0 @ X1 ) <=>
% 18.82/3.18         ( ![X6:reg]: ( ( c @ X6 @ X0 ) => ( c @ X6 @ X1 ) ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [p])).
% 18.82/3.18  thf(zip_derived_cl128, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]:
% 18.82/3.18         ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ paris) => (c @ Y0 @ france))))))
% 18.82/3.18          | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl125, '7'])).
% 18.82/3.18  thf(zip_derived_cl131, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X3 : reg]:
% 18.82/3.18         ( (((c @ X3 @ paris) => (c @ X3 @ france))) | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl128])).
% 18.82/3.18  thf(zip_derived_cl135, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X3 : reg]:
% 18.82/3.18         (~ (c @ X3 @ paris) |  (c @ X3 @ france) | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl131])).
% 18.82/3.18  thf(con, conjecture,
% 18.82/3.18    (mvalid @ ( mbox @ a @ ( ^[X:$i]: ( ~( po @ catalunya @ paris ) ) ) ))).
% 18.82/3.18  thf(zf_stmt_0, negated_conjecture,
% 18.82/3.18    (~( mvalid @ ( mbox @ a @ ( ^[X:$i]: ( ~( po @ catalunya @ paris ) ) ) ) )),
% 18.82/3.18    inference('cnf.neg', [status(esa)], [con])).
% 18.82/3.18  thf(zip_derived_cl8, plain,
% 18.82/3.18      (~ (mvalid @ 
% 18.82/3.18          (mbox @ a @ (^[Y0 : $i]: (((~) @ (po @ catalunya @ paris))))))),
% 18.82/3.18      inference('cnf', [status(esa)], [zf_stmt_0])).
% 18.82/3.18  thf(mvalid, axiom, ~ (mvalid @ X0) =>
% 18.82/3.18    ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))).
% 18.82/3.18  thf('8', plain,
% 18.82/3.18      (![X0:( $i > $o )]:
% 18.82/3.18       ( ( ~( mvalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [mvalid])).
% 18.82/3.18  thf(zip_derived_cl9, plain,
% 18.82/3.18      (~ (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                     (mbox @ a @ 
% 18.82/3.18                      (^[Y1 : $i]: (((~) @ (po @ catalunya @ paris)))) @ Y0))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl8, '8'])).
% 18.82/3.18  thf(zip_derived_cl10, plain,
% 18.82/3.18      (~ (mbox @ a @ (^[Y0 : $i]: (((~) @ (po @ catalunya @ paris)))) @ '#sk1')),
% 18.82/3.18      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl9])).
% 18.82/3.18  thf(mbox, axiom, ~ (mbox @ X0 @ X1 @ X2) =>
% 18.82/3.18    ((((!!) @ (^[Y0 : $i]: (((((~) @ (X0 @ X2 @ Y0))) | (X1 @ Y0)))))) !=
% 18.82/3.18     ($true))).
% 18.82/3.18  thf('9', plain,
% 18.82/3.18      (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 18.82/3.18       ( ( ~( mbox @ X0 @ X1 @ X2 ) ) <=>
% 18.82/3.18         ( ~( ![X7:$i]: ( ( ~( X0 @ X2 @ X7 ) ) | ( X1 @ X7 ) ) ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [mbox])).
% 18.82/3.18  thf(zip_derived_cl11, plain,
% 18.82/3.18      (~ (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                     (((((~) @ (a @ '#sk1' @ Y0))) |
% 18.82/3.18                       ((^[Y1 : $i]: (((~) @ (po @ catalunya @ paris)))) @ Y0))))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl10, '9'])).
% 18.82/3.18  thf(zip_derived_cl12, plain,
% 18.82/3.18      (~ (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                     (((((~) @ (a @ '#sk1' @ Y0))) |
% 18.82/3.18                       (((~) @ (po @ catalunya @ paris))))))))),
% 18.82/3.18      inference('ho_norm', [status(thm)], [zip_derived_cl11])).
% 18.82/3.18  thf(zip_derived_cl13, plain,
% 18.82/3.18      (~ (((((~) @ (a @ '#sk1' @ '#sk2'))) | (((~) @ (po @ catalunya @ paris)))))),
% 18.82/3.18      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])).
% 18.82/3.18  thf(zip_derived_cl14, plain, ( (a @ '#sk1' @ '#sk2')),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl13])).
% 18.82/3.18  thf(zip_derived_cl859, plain,
% 18.82/3.18      (![X0 : reg]: ( (c @ X0 @ france) | ~ (c @ X0 @ paris))),
% 18.82/3.18      inference('sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl14])).
% 18.82/3.18  thf(zip_derived_cl15, plain, ( (po @ catalunya @ paris)),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl13])).
% 18.82/3.18  thf(po, axiom, (po @ X0 @ X1) =>
% 18.82/3.18    ((((((~) @ (p @ X1 @ X0))) & (((~) @ (p @ X0 @ X1))) & (o @ X0 @ X1))) =
% 18.82/3.18     ($true))).
% 18.82/3.18  thf('10', plain,
% 18.82/3.18      (![X0:reg,X1:reg]:
% 18.82/3.18       ( ( po @ X0 @ X1 ) <=>
% 18.82/3.18         ( ( o @ X0 @ X1 ) & ( ~( p @ X0 @ X1 ) ) & ( ~( p @ X1 @ X0 ) ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [po])).
% 18.82/3.18  thf(zip_derived_cl16, plain,
% 18.82/3.18      ( (((((~) @ (p @ paris @ catalunya))) & 
% 18.82/3.18          (((~) @ (p @ catalunya @ paris))) & (o @ catalunya @ paris)))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl15, '10'])).
% 18.82/3.18  thf(zip_derived_cl19, plain, ( (o @ catalunya @ paris)),
% 18.82/3.18      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl16])).
% 18.82/3.18  thf(o, axiom, (o @ X0 @ X1) =>
% 18.82/3.18    ((((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ X1)))))) = ($true))).
% 18.82/3.18  thf('11', plain,
% 18.82/3.18      (![X0:reg,X1:reg]:
% 18.82/3.18       ( ( o @ X0 @ X1 ) <=>
% 18.82/3.18         ( ?[X6:reg]: ( ( p @ X6 @ X0 ) & ( p @ X6 @ X1 ) ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [o])).
% 18.82/3.18  thf(zip_derived_cl22, plain,
% 18.82/3.18      ( (((??) @ (^[Y0 : reg]: (((p @ Y0 @ catalunya) & (p @ Y0 @ paris))))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl19, '11'])).
% 18.82/3.18  thf(zip_derived_cl25, plain,
% 18.82/3.18      ( (((p @ '#sk5' @ catalunya) & (p @ '#sk5' @ paris)))),
% 18.82/3.18      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl22])).
% 18.82/3.18  thf(zip_derived_cl31, plain, ( (p @ '#sk5' @ paris)),
% 18.82/3.18      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])).
% 18.82/3.18  thf(zip_derived_cl33, plain,
% 18.82/3.18      ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ '#sk5') => (c @ Y0 @ paris))))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl31, '7'])).
% 18.82/3.18  thf(zip_derived_cl35, plain,
% 18.82/3.18      (![X2 : reg]:  (((c @ X2 @ '#sk5') => (c @ X2 @ paris)))),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])).
% 18.82/3.18  thf(zip_derived_cl37, plain,
% 18.82/3.18      (![X2 : reg]: (~ (c @ X2 @ '#sk5') |  (c @ X2 @ paris))),
% 18.82/3.18      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])).
% 18.82/3.18  thf(zip_derived_cl3103, plain,
% 18.82/3.18      (![X0 : reg]: ( (c @ X0 @ france) | ~ (c @ X0 @ '#sk5'))),
% 18.82/3.18      inference('sup+', [status(thm)], [zip_derived_cl859, zip_derived_cl37])).
% 18.82/3.18  thf(t_axiom_for_fool, axiom,
% 18.82/3.18    (mvalid @
% 18.82/3.18     ( mforall_prop @
% 18.82/3.18       ( ^[A:( $i > $o )]: ( mimplies @ ( mbox @ fool @ A ) @ A ) ) ))).
% 18.82/3.18  thf(zip_derived_cl2, plain,
% 18.82/3.18      ( (mvalid @ 
% 18.82/3.18         (mforall_prop @ 
% 18.82/3.18          (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0))))),
% 18.82/3.18      inference('cnf', [status(esa)], [t_axiom_for_fool])).
% 18.82/3.18  thf(zip_derived_cl166, plain,
% 18.82/3.18      ( (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                    (mforall_prop @ 
% 18.82/3.18                     (^[Y1 : $i > $o]: (mimplies @ (mbox @ fool @ Y1) @ Y1)) @ 
% 18.82/3.18                     Y0))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl2, '0'])).
% 18.82/3.18  thf(zip_derived_cl167, plain,
% 18.82/3.18      (![X2 : $i]:
% 18.82/3.18          (mforall_prop @ 
% 18.82/3.18           (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0)) @ X2)),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl166])).
% 18.82/3.18  thf(mforall_prop, axiom, (mforall_prop @ X0 @ X1) =>
% 18.82/3.18    ((((!!) @ (^[Y0 : $i > $o]: (X0 @ Y0 @ X1)))) = ($true))).
% 18.82/3.18  thf('12', plain,
% 18.82/3.18      (![X0:( ( $i > $o ) > $i > $o ),X1:$i]:
% 18.82/3.18       ( ( mforall_prop @ X0 @ X1 ) <=> ( ![X6:( $i > $o )]: ( X0 @ X6 @ X1 ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [mforall_prop])).
% 18.82/3.18  thf(zip_derived_cl168, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18          (((!!) @ (^[Y0 : $i > $o]:
% 18.82/3.18                      ((^[Y1 : $i > $o]: (mimplies @ (mbox @ fool @ Y1) @ Y1)) @ 
% 18.82/3.18                       Y0 @ X0))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl167, '12'])).
% 18.82/3.18  thf(zip_derived_cl169, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18          (((!!) @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0 @ X0))))),
% 18.82/3.18      inference('ho_norm', [status(thm)], [zip_derived_cl168])).
% 18.82/3.18  thf(zip_derived_cl170, plain,
% 18.82/3.18      (![X0 : $i, X2 : $i > $o]:  (mimplies @ (mbox @ fool @ X2) @ X2 @ X0)),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl169])).
% 18.82/3.18  thf(mimplies, axiom,(( mimplies @ (X0)@ (X1)@ (X2)) =
% 18.82/3.18    ((mor @ (mnot @ X0) @ X1 @ X2)))).
% 18.82/3.18  thf('13', plain,
% 18.82/3.18      (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 18.82/3.18       ( ( mimplies @ X0 @ X1 @ X2 ) = ( mor @ ( mnot @ X0 ) @ X1 @ X2 ) )),
% 18.82/3.18      define([status(thm)])).
% 18.82/3.18  thf(zip_derived_cl171, plain,
% 18.82/3.18      (![X0 : $i, X2 : $i > $o]:  (mor @ (mnot @ (mbox @ fool @ X2)) @ X2 @ X0)),
% 18.82/3.18      inference('rw', [status(thm)], [zip_derived_cl170, '13'])).
% 18.82/3.18  thf(mor, axiom, (mor @ X0 @ X1 @ X2) =>
% 18.82/3.18    ((((X1 @ X2) | (X0 @ X2))) = ($true))).
% 18.82/3.18  thf('14', plain,
% 18.82/3.18      (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 18.82/3.18       ( ( mor @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) | ( X1 @ X2 ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [mor])).
% 18.82/3.18  thf(zip_derived_cl172, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]:
% 18.82/3.18          (((X0 @ X1) | (mnot @ (mbox @ fool @ X0) @ X1)))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl171, '14'])).
% 18.82/3.18  thf(zip_derived_cl173, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]:
% 18.82/3.18         ( (X0 @ X1) |  (mnot @ (mbox @ fool @ X0) @ X1))),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl172])).
% 18.82/3.18  thf(mnot, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))).
% 18.82/3.18  thf('15', plain,
% 18.82/3.18      (![X0:( $i > $o ),X1:$i]: ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [mnot])).
% 18.82/3.18  thf(zip_derived_cl174, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]: (~ (mbox @ fool @ X0 @ X1) |  (X0 @ X1))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl173, '15'])).
% 18.82/3.18  thf(zip_derived_cl175, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]:
% 18.82/3.18         (~ (((!!) @ (^[Y0 : $i]: (((((~) @ (fool @ X1 @ Y0))) | (X0 @ Y0))))))
% 18.82/3.18          |  (X0 @ X1))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl174, '9'])).
% 18.82/3.18  thf(zip_derived_cl176, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]:
% 18.82/3.18         (~ (((((~) @ (fool @ X1 @ ('#sk26' @ X0 @ X1)))) | (X0 @ 
% 18.82/3.18              ('#sk26' @ X0 @ X1))))
% 18.82/3.18          |  (X0 @ X1))),
% 18.82/3.18      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl175])).
% 18.82/3.18  thf(zip_derived_cl178, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]: (~ (X0 @ ('#sk26' @ X0 @ X1)) |  (X0 @ X1))),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl176])).
% 18.82/3.18  thf(zip_derived_cl313, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18         (~ ((^[Y0 : $i]: (((X0) != (Y0)))) @ 
% 18.82/3.18             ('#sk26' @ (^[Y0 : $i]: (((X0) != (Y0)))) @ X0))
% 18.82/3.18          |  ((^[Y0 : $i]: (((X0) != (Y0)))) @ X0))),
% 18.82/3.18      inference('elim_leibniz_eq_+', [status(thm)], [zip_derived_cl178])).
% 18.82/3.18  thf(zip_derived_cl323, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18         (~ (((X0) != ('#sk26' @ ((($i) != (X0))) @ X0))) |  (((X0) != (X0))))),
% 18.82/3.18      inference('ho_norm', [status(thm)], [zip_derived_cl313])).
% 18.82/3.18  thf(zip_derived_cl324, plain,
% 18.82/3.18      (![X0 : $i]: ~ (((X0) != ('#sk26' @ ((($i) != (X0))) @ X0)))),
% 18.82/3.18      inference('simplify boolean subterms', [status(thm)], [zip_derived_cl323])).
% 18.82/3.18  thf(zip_derived_cl325, plain,
% 18.82/3.18      (![X0 : $i]: ((X0) = ('#sk26' @ ((($i) != (X0))) @ X0))),
% 18.82/3.18      inference('simplify nested equalities', [status(thm)],
% 18.82/3.18                [zip_derived_cl324])).
% 18.82/3.18  thf(zip_derived_cl177, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]:
% 18.82/3.18         ( (fool @ X1 @ ('#sk26' @ X0 @ X1)) |  (X0 @ X1))),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl176])).
% 18.82/3.18  thf(zip_derived_cl1042, plain,
% 18.82/3.18      (![X0 : $i]: ( (fool @ X0 @ X0) |  (((X0) != (X0))))),
% 18.82/3.18      inference('sup+', [status(thm)], [zip_derived_cl325, zip_derived_cl177])).
% 18.82/3.18  thf(zip_derived_cl1067, plain, (![X0 : $i]:  (fool @ X0 @ X0)),
% 18.82/3.18      inference('simplify boolean subterms', [status(thm)],
% 18.82/3.18                [zip_derived_cl1042])).
% 18.82/3.18  thf(zip_derived_cl105, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X2 : reg]:
% 18.82/3.18         (~ (c @ ('#sk12' @ X2) @ france)
% 18.82/3.18          | ~ (fool @ X1 @ X0)
% 18.82/3.18          | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 18.82/3.18      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])).
% 18.82/3.18  thf(zip_derived_cl106, plain,
% 18.82/3.18      (![X2 : reg]:
% 18.82/3.18         ( ('#form13' @ X2)
% 18.82/3.18          | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 18.82/3.18      define([status(thm)])).
% 18.82/3.18  thf(zip_derived_cl109, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X2 : reg]:
% 18.82/3.18         (~ ('#form13' @ X2)
% 18.82/3.18          | ~ (fool @ X1 @ X0)
% 18.82/3.18          | ~ (c @ ('#sk12' @ X2) @ france))),
% 18.82/3.18      inference('renaming', [status(thm)],
% 18.82/3.18                [zip_derived_cl105, zip_derived_cl106])).
% 18.82/3.18  thf(zip_derived_cl1253, plain,
% 18.82/3.18      (![X1 : reg]: (~ (c @ ('#sk12' @ X1) @ france) | ~ ('#form13' @ X1))),
% 18.82/3.18      inference('sup-', [status(thm)], [zip_derived_cl1067, zip_derived_cl109])).
% 18.82/3.18  thf(zip_derived_cl5038, plain,
% 18.82/3.18      (![X0 : reg]: (~ (c @ ('#sk12' @ X0) @ '#sk5') | ~ ('#form13' @ X0))),
% 18.82/3.18      inference('sup-', [status(thm)], [zip_derived_cl3103, zip_derived_cl1253])).
% 18.82/3.18  thf(zip_derived_cl5073, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]:
% 18.82/3.18         (~ (fool @ X1 @ X0) | ~ ('#form13' @ '#sk5') | ~ ('#form13' @ '#sk5'))),
% 18.82/3.18      inference('sup-', [status(thm)], [zip_derived_cl108, zip_derived_cl5038])).
% 18.82/3.18  thf(ax1, axiom,
% 18.82/3.18    (mvalid @ ( mbox @ a @ ( ^[X:$i]: ( tpp @ catalunya @ spain ) ) ))).
% 18.82/3.18  thf(zip_derived_cl5, plain,
% 18.82/3.18      ( (mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain))))),
% 18.82/3.18      inference('cnf', [status(esa)], [ax1])).
% 18.82/3.18  thf(zip_derived_cl38, plain,
% 18.82/3.18      ( (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                    (mbox @ a @ (^[Y1 : $i]: (tpp @ catalunya @ spain)) @ Y0))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl5, '0'])).
% 18.82/3.18  thf(zip_derived_cl39, plain,
% 18.82/3.18      (![X2 : $i]:  (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)) @ X2)),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])).
% 18.82/3.18  thf(zip_derived_cl40, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18          (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                      (((((~) @ (a @ X0 @ Y0))) |
% 18.82/3.18                        ((^[Y1 : $i]: (tpp @ catalunya @ spain)) @ Y0))))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl39, '1'])).
% 18.82/3.18  thf(zip_derived_cl41, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18          (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                      (((((~) @ (a @ X0 @ Y0))) | (tpp @ catalunya @ spain))))))),
% 18.82/3.18      inference('ho_norm', [status(thm)], [zip_derived_cl40])).
% 18.82/3.18  thf(zip_derived_cl42, plain,
% 18.82/3.18      (![X0 : $i, X2 : $i]:
% 18.82/3.18          (((((~) @ (a @ X0 @ X2))) | (tpp @ catalunya @ spain)))),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])).
% 18.82/3.18  thf(zip_derived_cl43, plain,
% 18.82/3.18      (![X0 : $i, X2 : $i]: (~ (a @ X0 @ X2) |  (tpp @ catalunya @ spain))),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])).
% 18.82/3.18  thf(tpp, axiom, (tpp @ X0 @ X1) =>
% 18.82/3.18    ((((((??) @ (^[Y0 : reg]: (((ec @ Y0 @ X0) & (ec @ Y0 @ X1)))))) & (pp @ 
% 18.82/3.18       X0 @ X1)))
% 18.82/3.18     = ($true))).
% 18.82/3.18  thf('16', plain,
% 18.82/3.18      (![X0:reg,X1:reg]:
% 18.82/3.18       ( ( tpp @ X0 @ X1 ) <=>
% 18.82/3.18         ( ( pp @ X0 @ X1 ) & 
% 18.82/3.18           ( ?[X6:reg]: ( ( ec @ X6 @ X0 ) & ( ec @ X6 @ X1 ) ) ) ) )),
% 18.82/3.18      inference('rw.lit', [status(esa)], [tpp])).
% 18.82/3.18  thf(zip_derived_cl44, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]:
% 18.82/3.18         ( (((((??) @ (^[Y0 : reg]:
% 18.82/3.18                         (((ec @ Y0 @ catalunya) & (ec @ Y0 @ spain)))))) &
% 18.82/3.18             (pp @ catalunya @ spain)))
% 18.82/3.18          | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl43, '16'])).
% 18.82/3.18  thf(zip_derived_cl46, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]: ( (pp @ catalunya @ spain) | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl44])).
% 18.82/3.18  thf(zip_derived_cl48, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]:
% 18.82/3.18         ( (((((~) @ (p @ spain @ catalunya))) & (p @ catalunya @ spain)))
% 18.82/3.18          | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl46, '6'])).
% 18.82/3.18  thf(zip_derived_cl52, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]: ( (p @ catalunya @ spain) | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl48])).
% 18.82/3.18  thf(zip_derived_cl56, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i]:
% 18.82/3.18         ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ catalunya) => (c @ Y0 @ spain))))))
% 18.82/3.18          | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl52, '7'])).
% 18.82/3.18  thf(zip_derived_cl62, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X3 : reg]:
% 18.82/3.18         ( (((c @ X3 @ catalunya) => (c @ X3 @ spain))) | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl56])).
% 18.82/3.18  thf(zip_derived_cl67, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i, X3 : reg]:
% 18.82/3.18         (~ (c @ X3 @ catalunya) |  (c @ X3 @ spain) | ~ (a @ X1 @ X0))),
% 18.82/3.18      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])).
% 18.82/3.18  thf(zip_derived_cl14, plain, ( (a @ '#sk1' @ '#sk2')),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl13])).
% 18.82/3.18  thf(zip_derived_cl259, plain,
% 18.82/3.18      (![X0 : reg]: ( (c @ X0 @ spain) | ~ (c @ X0 @ catalunya))),
% 18.82/3.18      inference('sup+', [status(thm)], [zip_derived_cl67, zip_derived_cl14])).
% 18.82/3.18  thf(zip_derived_cl106, plain,
% 18.82/3.18      (![X2 : reg]:
% 18.82/3.18         ( ('#form13' @ X2)
% 18.82/3.18          | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 18.82/3.18      define([status(thm)])).
% 18.82/3.18  thf(zip_derived_cl107, plain,
% 18.82/3.18      (![X2 : reg]:
% 18.82/3.18         (~ (((c @ ('#sk9' @ X2) @ X2) => (c @ ('#sk9' @ X2) @ spain)))
% 18.82/3.18          |  ('#form13' @ X2))),
% 18.82/3.18      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl106])).
% 18.82/3.18  thf(zip_derived_cl111, plain,
% 18.82/3.18      (![X2 : reg]: (~ (c @ ('#sk9' @ X2) @ spain) |  ('#form13' @ X2))),
% 18.82/3.18      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])).
% 18.82/3.18  thf(zip_derived_cl271, plain,
% 18.82/3.18      (![X0 : reg]: (~ (c @ ('#sk9' @ X0) @ catalunya) |  ('#form13' @ X0))),
% 18.82/3.18      inference('sup-', [status(thm)], [zip_derived_cl259, zip_derived_cl111])).
% 18.82/3.18  thf(zip_derived_cl30, plain, ( (p @ '#sk5' @ catalunya)),
% 18.82/3.18      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])).
% 18.82/3.18  thf(zip_derived_cl32, plain,
% 18.82/3.18      ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ '#sk5') => (c @ Y0 @ catalunya))))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl30, '7'])).
% 18.82/3.18  thf(zip_derived_cl34, plain,
% 18.82/3.18      (![X2 : reg]:  (((c @ X2 @ '#sk5') => (c @ X2 @ catalunya)))),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])).
% 18.82/3.18  thf(zip_derived_cl36, plain,
% 18.82/3.18      (![X2 : reg]: (~ (c @ X2 @ '#sk5') |  (c @ X2 @ catalunya))),
% 18.82/3.18      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 18.82/3.18  thf(zip_derived_cl275, plain,
% 18.82/3.18      (![X0 : reg]: ( ('#form13' @ X0) | ~ (c @ ('#sk9' @ X0) @ '#sk5'))),
% 18.82/3.18      inference('sup+', [status(thm)], [zip_derived_cl271, zip_derived_cl36])).
% 18.82/3.18  thf(zip_derived_cl110, plain,
% 18.82/3.18      (![X2 : reg]: ( (c @ ('#sk9' @ X2) @ X2) |  ('#form13' @ X2))),
% 18.82/3.18      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])).
% 18.82/3.18  thf(zip_derived_cl647, plain,
% 18.82/3.18      (( ('#form13' @ '#sk5') |  ('#form13' @ '#sk5'))),
% 18.82/3.18      inference('sup+', [status(thm)], [zip_derived_cl275, zip_derived_cl110])).
% 18.82/3.18  thf(zip_derived_cl661, plain, ( ('#form13' @ '#sk5')),
% 18.82/3.18      inference('simplify', [status(thm)], [zip_derived_cl647])).
% 18.82/3.18  thf(zip_derived_cl661, plain, ( ('#form13' @ '#sk5')),
% 18.82/3.18      inference('simplify', [status(thm)], [zip_derived_cl647])).
% 18.82/3.18  thf(zip_derived_cl5088, plain, (![X0 : $i, X1 : $i]: ~ (fool @ X1 @ X0)),
% 18.82/3.18      inference('demod', [status(thm)],
% 18.82/3.18                [zip_derived_cl5073, zip_derived_cl661, zip_derived_cl661])).
% 18.82/3.18  thf(i_axiom_for_fool_a, axiom,
% 18.82/3.18    (mvalid @
% 18.82/3.18     ( mforall_prop @
% 18.82/3.18       ( ^[Phi:( $i > $o )]:
% 18.82/3.18         ( mimplies @ ( mbox @ fool @ Phi ) @ ( mbox @ a @ Phi ) ) ) ))).
% 18.82/3.18  thf(zip_derived_cl4, plain,
% 18.82/3.18      ( (mvalid @ 
% 18.82/3.18         (mforall_prop @ 
% 18.82/3.18          (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ (mbox @ a @ Y0)))))),
% 18.82/3.18      inference('cnf', [status(esa)], [i_axiom_for_fool_a])).
% 18.82/3.18  thf(zip_derived_cl179, plain,
% 18.82/3.18      ( (((!!) @ (^[Y0 : $i]:
% 18.82/3.18                    (mforall_prop @ 
% 18.82/3.18                     (^[Y1 : $i > $o]:
% 18.82/3.18                        (mimplies @ (mbox @ fool @ Y1) @ (mbox @ a @ Y1))) @ 
% 18.82/3.18                     Y0))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl4, '0'])).
% 18.82/3.18  thf(zip_derived_cl180, plain,
% 18.82/3.18      (![X2 : $i]:
% 18.82/3.18          (mforall_prop @ 
% 18.82/3.18           (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ (mbox @ a @ Y0))) @ 
% 18.82/3.18           X2)),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl179])).
% 18.82/3.18  thf(zip_derived_cl181, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18          (((!!) @ (^[Y0 : $i > $o]:
% 18.82/3.18                      ((^[Y1 : $i > $o]:
% 18.82/3.18                          (mimplies @ (mbox @ fool @ Y1) @ (mbox @ a @ Y1))) @ 
% 18.82/3.18                       Y0 @ X0))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl180, '12'])).
% 18.82/3.18  thf(zip_derived_cl182, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18          (((!!) @ (^[Y0 : $i > $o]:
% 18.82/3.18                      (mimplies @ (mbox @ fool @ Y0) @ (mbox @ a @ Y0) @ X0))))),
% 18.82/3.18      inference('ho_norm', [status(thm)], [zip_derived_cl181])).
% 18.82/3.18  thf(zip_derived_cl183, plain,
% 18.82/3.18      (![X0 : $i, X2 : $i > $o]:
% 18.82/3.18          (mimplies @ (mbox @ fool @ X2) @ (mbox @ a @ X2) @ X0)),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl182])).
% 18.82/3.18  thf(zip_derived_cl184, plain,
% 18.82/3.18      (![X0 : $i, X2 : $i > $o]:
% 18.82/3.18          (mor @ (mnot @ (mbox @ fool @ X2)) @ (mbox @ a @ X2) @ X0)),
% 18.82/3.18      inference('rw', [status(thm)], [zip_derived_cl183, '13'])).
% 18.82/3.18  thf(zip_derived_cl185, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]:
% 18.82/3.18          (((mbox @ a @ X0 @ X1) | (mnot @ (mbox @ fool @ X0) @ X1)))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl184, '14'])).
% 18.82/3.18  thf(zip_derived_cl186, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]:
% 18.82/3.18         ( (mbox @ a @ X0 @ X1) |  (mnot @ (mbox @ fool @ X0) @ X1))),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl185])).
% 18.82/3.18  thf(zip_derived_cl187, plain,
% 18.82/3.18      (![X0 : $i, X1 : $i > $o]:
% 18.82/3.18         ( (((!!) @ (^[Y0 : $i]: (((((~) @ (a @ X0 @ Y0))) | (X1 @ Y0))))))
% 18.82/3.18          |  (mnot @ (mbox @ fool @ X1) @ X0))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl186, '1'])).
% 18.82/3.18  thf(zip_derived_cl188, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]:
% 18.82/3.18         (~ (mbox @ fool @ X0 @ X1)
% 18.82/3.18          |  (((!!) @ (^[Y0 : $i]: (((((~) @ (a @ X1 @ Y0))) | (X0 @ Y0)))))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl187, '15'])).
% 18.82/3.18  thf(zip_derived_cl189, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]:
% 18.82/3.18         (~ (((!!) @ (^[Y0 : $i]: (((((~) @ (fool @ X1 @ Y0))) | (X0 @ Y0))))))
% 18.82/3.18          |  (((!!) @ (^[Y0 : $i]: (((((~) @ (a @ X1 @ Y0))) | (X0 @ Y0)))))))),
% 18.82/3.18      inference('rw_clause', [status(thm)], [zip_derived_cl188, '9'])).
% 18.82/3.18  thf(zip_derived_cl190, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]:
% 18.82/3.18         (~ (((((~) @ (fool @ X1 @ ('#sk26' @ X0 @ X1)))) | (X0 @ 
% 18.82/3.18              ('#sk26' @ X0 @ X1))))
% 18.82/3.18          |  (((!!) @ (^[Y0 : $i]: (((((~) @ (a @ X1 @ Y0))) | (X0 @ Y0)))))))),
% 18.82/3.18      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl189])).
% 18.82/3.18  thf(zip_derived_cl192, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]:
% 18.82/3.18         (~ (X0 @ ('#sk26' @ X0 @ X1))
% 18.82/3.18          |  (((!!) @ (^[Y0 : $i]: (((((~) @ (a @ X1 @ Y0))) | (X0 @ Y0)))))))),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl190])).
% 18.82/3.18  thf(zip_derived_cl194, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i, X3 : $i]:
% 18.82/3.18         ( (((((~) @ (a @ X1 @ X3))) | (X0 @ X3)))
% 18.82/3.18          | ~ (X0 @ ('#sk26' @ X0 @ X1)))),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl192])).
% 18.82/3.18  thf(zip_derived_cl196, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i, X3 : $i]:
% 18.82/3.18         (~ (a @ X1 @ X3) |  (X0 @ X3) | ~ (X0 @ ('#sk26' @ X0 @ X1)))),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl194])).
% 18.82/3.18  thf(zip_derived_cl14, plain, ( (a @ '#sk1' @ '#sk2')),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl13])).
% 18.82/3.18  thf(zip_derived_cl1327, plain,
% 18.82/3.18      (![X0 : $i > $o]: (~ (X0 @ ('#sk26' @ X0 @ '#sk1')) |  (X0 @ '#sk2'))),
% 18.82/3.18      inference('sup+', [status(thm)], [zip_derived_cl196, zip_derived_cl14])).
% 18.82/3.18  thf(zip_derived_cl3303, plain,
% 18.82/3.18      ((~ ((^[Y0 : $i]: ((('#sk2') != (Y0)))) @ 
% 18.82/3.18           ('#sk26' @ (^[Y0 : $i]: ((('#sk2') != (Y0)))) @ '#sk1'))
% 18.82/3.18        |  ((^[Y0 : $i]: ((('#sk2') != (Y0)))) @ '#sk2'))),
% 18.82/3.18      inference('elim_leibniz_eq_+', [status(thm)], [zip_derived_cl1327])).
% 18.82/3.18  thf(zip_derived_cl3313, plain,
% 18.82/3.18      ((~ ((('#sk2') != ('#sk26' @ ((($i) != ('#sk2'))) @ '#sk1')))
% 18.82/3.18        |  ((('#sk2') != ('#sk2'))))),
% 18.82/3.18      inference('ho_norm', [status(thm)], [zip_derived_cl3303])).
% 18.82/3.18  thf(zip_derived_cl3314, plain,
% 18.82/3.18      (~ ((('#sk2') != ('#sk26' @ ((($i) != ('#sk2'))) @ '#sk1')))),
% 18.82/3.18      inference('simplify boolean subterms', [status(thm)],
% 18.82/3.18                [zip_derived_cl3313])).
% 18.82/3.18  thf(zip_derived_cl3315, plain,
% 18.82/3.18      ((('#sk2') = ('#sk26' @ ((($i) != ('#sk2'))) @ '#sk1'))),
% 18.82/3.18      inference('simplify nested equalities', [status(thm)],
% 18.82/3.18                [zip_derived_cl3314])).
% 18.82/3.18  thf(zip_derived_cl191, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i]:
% 18.82/3.18         ( (fool @ X1 @ ('#sk26' @ X0 @ X1))
% 18.82/3.18          |  (((!!) @ (^[Y0 : $i]: (((((~) @ (a @ X1 @ Y0))) | (X0 @ Y0)))))))),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl190])).
% 18.82/3.18  thf(zip_derived_cl193, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i, X3 : $i]:
% 18.82/3.18         ( (((((~) @ (a @ X1 @ X3))) | (X0 @ X3)))
% 18.82/3.18          |  (fool @ X1 @ ('#sk26' @ X0 @ X1)))),
% 18.82/3.18      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl191])).
% 18.82/3.18  thf(zip_derived_cl195, plain,
% 18.82/3.18      (![X0 : $i > $o, X1 : $i, X3 : $i]:
% 18.82/3.18         (~ (a @ X1 @ X3) |  (X0 @ X3) |  (fool @ X1 @ ('#sk26' @ X0 @ X1)))),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl193])).
% 18.82/3.18  thf(zip_derived_cl3768, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18         ( (fool @ '#sk1' @ '#sk2')
% 18.82/3.18          |  ((('#sk2') != (X0)))
% 18.82/3.18          | ~ (a @ '#sk1' @ X0))),
% 18.82/3.18      inference('sup+', [status(thm)], [zip_derived_cl3315, zip_derived_cl195])).
% 18.82/3.18  thf(zip_derived_cl3786, plain,
% 18.82/3.18      (![X0 : $i]:
% 18.82/3.18         ( (fool @ '#sk1' @ '#sk2') | (('#sk2') != (X0)) | ~ (a @ '#sk1' @ X0))),
% 18.82/3.18      inference('simplify nested equalities', [status(thm)],
% 18.82/3.18                [zip_derived_cl3768])).
% 18.82/3.18  thf(zip_derived_cl3787, plain,
% 18.82/3.18      ((~ (a @ '#sk1' @ '#sk2') |  (fool @ '#sk1' @ '#sk2'))),
% 18.82/3.18      inference('simplify', [status(thm)], [zip_derived_cl3786])).
% 18.82/3.18  thf(zip_derived_cl14, plain, ( (a @ '#sk1' @ '#sk2')),
% 18.82/3.18      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl13])).
% 18.82/3.18  thf(zip_derived_cl4370, plain, ( (fool @ '#sk1' @ '#sk2')),
% 18.82/3.18      inference('demod', [status(thm)], [zip_derived_cl3787, zip_derived_cl14])).
% 18.82/3.18  thf(zip_derived_cl5101, plain, ($false),
% 18.82/3.18      inference('sup+', [status(thm)], [zip_derived_cl5088, zip_derived_cl4370])).
% 18.82/3.18  
% 18.82/3.18  % SZS output end Refutation
% 18.82/3.18  
% 18.82/3.18  
% 18.82/3.18  % Terminating...
% 20.77/3.36  % Runner terminated.
% 20.77/3.36  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------