%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GEG010^1 : TPTP v9.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.G5SYFHBkpO 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 : Thu Oct 2 04:33:31 PM UTC 2025
% Result : Theorem 40.94s 5.79s
% Output : Refutation 40.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GEG010^1 : TPTP v9.2.0. Released v4.1.0.
% 0.04/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.G5SYFHBkpO true
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Wed Oct 1 11:14:38 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % Running portfolio for 300 s
% 0.14/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % Number of cores: 8
% 0.14/0.37 % Python version: Python 3.6.8
% 0.14/0.37 % Running in HO mode
% 0.58/0.64 % Total configuration time : 828
% 0.58/0.64 % Estimated wc time : 1656
% 0.58/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.58/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.58/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.58/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.58/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.59/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.59/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 0.59/0.81 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 40.94/5.79 % Solved by lams/30_b.l.sh.
% 40.94/5.79 % done 614 iterations in 4.954s
% 40.94/5.79 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 40.94/5.79 % SZS output start Refutation
% 40.94/5.79 thf(reg_type, type, reg: $tType).
% 40.94/5.79 thf('#form8_type', type, '#form8': reg > $o).
% 40.94/5.79 thf(mbox_type, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 40.94/5.79 thf('#sk21_type', type, '#sk21': ($i > $o) > $i > $i).
% 40.94/5.79 thf(paris_type, type, paris: reg).
% 40.94/5.79 thf(ntpp_type, type, ntpp: reg > reg > $o).
% 40.94/5.79 thf(a_type, type, a: $i > $i > $o).
% 40.94/5.79 thf(pp_type, type, pp: reg > reg > $o).
% 40.94/5.79 thf(fool_type, type, fool: $i > $i > $o).
% 40.94/5.79 thf(france_type, type, france: reg).
% 40.94/5.79 thf(mnot_type, type, mnot: ($i > $o) > $i > $o).
% 40.94/5.79 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 40.94/5.79 thf(ec_type, type, ec: reg > reg > $o).
% 40.94/5.79 thf('#sk4_type', type, '#sk4': reg > reg).
% 40.94/5.79 thf(o_type, type, o: reg > reg > $o).
% 40.94/5.79 thf(c_type, type, c: reg > reg > $o).
% 40.94/5.79 thf('#sk7_type', type, '#sk7': reg > reg).
% 40.94/5.79 thf('#sk28_type', type, '#sk28': reg).
% 40.94/5.79 thf(p_type, type, p: reg > reg > $o).
% 40.94/5.79 thf(catalunya_type, type, catalunya: reg).
% 40.94/5.79 thf(spain_type, type, spain: reg).
% 40.94/5.79 thf('#sk27_type', type, '#sk27': $i).
% 40.94/5.79 thf(tpp_type, type, tpp: reg > reg > $o).
% 40.94/5.79 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 40.94/5.79 thf(mforall_prop_type, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 40.94/5.79 thf('#sk26_type', type, '#sk26': $i).
% 40.94/5.79 thf(mvalid_type, type, mvalid: ($i > $o) > $o).
% 40.94/5.79 thf(t_axiom_for_fool, axiom,
% 40.94/5.79 (mvalid @
% 40.94/5.79 ( mforall_prop @
% 40.94/5.79 ( ^[A:( $i > $o )]: ( mimplies @ ( mbox @ fool @ A ) @ A ) ) ))).
% 40.94/5.79 thf(zip_derived_cl2, plain,
% 40.94/5.79 ( (mvalid @
% 40.94/5.79 (mforall_prop @
% 40.94/5.79 (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0))))),
% 40.94/5.79 inference('cnf', [status(esa)], [t_axiom_for_fool])).
% 40.94/5.79 thf(mvalid, axiom, (mvalid @ X0) =>
% 40.94/5.79 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))).
% 40.94/5.79 thf('0', plain,
% 40.94/5.79 (![X0:( $i > $o )]: ( ( mvalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [mvalid])).
% 40.94/5.79 thf(zip_derived_cl134, plain,
% 40.94/5.79 ( (((!!) @ (^[Y0 : $i]:
% 40.94/5.79 (mforall_prop @
% 40.94/5.79 (^[Y1 : $i > $o]: (mimplies @ (mbox @ fool @ Y1) @ Y1)) @
% 40.94/5.79 Y0))))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl2, '0'])).
% 40.94/5.79 thf(zip_derived_cl135, plain,
% 40.94/5.79 (![X2 : $i]:
% 40.94/5.79 (mforall_prop @
% 40.94/5.79 (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0)) @ X2)),
% 40.94/5.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl134])).
% 40.94/5.79 thf(mforall_prop, axiom, (mforall_prop @ X0 @ X1) =>
% 40.94/5.79 ((((!!) @ (^[Y0 : $i > $o]: (X0 @ Y0 @ X1)))) = ($true))).
% 40.94/5.79 thf('1', plain,
% 40.94/5.79 (![X0:( ( $i > $o ) > $i > $o ),X1:$i]:
% 40.94/5.79 ( ( mforall_prop @ X0 @ X1 ) <=> ( ![X6:( $i > $o )]: ( X0 @ X6 @ X1 ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [mforall_prop])).
% 40.94/5.79 thf(zip_derived_cl136, plain,
% 40.94/5.79 (![X0 : $i]:
% 40.94/5.79 (((!!) @ (^[Y0 : $i > $o]:
% 40.94/5.79 ((^[Y1 : $i > $o]: (mimplies @ (mbox @ fool @ Y1) @ Y1)) @
% 40.94/5.79 Y0 @ X0))))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl135, '1'])).
% 40.94/5.79 thf(zip_derived_cl137, plain,
% 40.94/5.79 (![X0 : $i]:
% 40.94/5.79 (((!!) @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0 @ X0))))),
% 40.94/5.79 inference('ho_norm', [status(thm)], [zip_derived_cl136])).
% 40.94/5.79 thf(zip_derived_cl138, plain,
% 40.94/5.79 (![X0 : $i, X2 : $i > $o]: (mimplies @ (mbox @ fool @ X2) @ X2 @ X0)),
% 40.94/5.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl137])).
% 40.94/5.79 thf(mimplies, axiom,(( mimplies @ (X0)@ (X1)@ (X2)) =
% 40.94/5.79 ((mor @ (mnot @ X0) @ X1 @ X2)))).
% 40.94/5.79 thf('2', plain,
% 40.94/5.79 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 40.94/5.79 ( ( mimplies @ X0 @ X1 @ X2 ) = ( mor @ ( mnot @ X0 ) @ X1 @ X2 ) )),
% 40.94/5.79 define([status(thm)])).
% 40.94/5.79 thf(zip_derived_cl139, plain,
% 40.94/5.79 (![X0 : $i, X2 : $i > $o]: (mor @ (mnot @ (mbox @ fool @ X2)) @ X2 @ X0)),
% 40.94/5.79 inference('rw', [status(thm)], [zip_derived_cl138, '2'])).
% 40.94/5.79 thf(mor, axiom, (mor @ X0 @ X1 @ X2) =>
% 40.94/5.79 ((((X1 @ X2) | (X0 @ X2))) = ($true))).
% 40.94/5.79 thf('3', plain,
% 40.94/5.79 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 40.94/5.79 ( ( mor @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) | ( X1 @ X2 ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [mor])).
% 40.94/5.79 thf(zip_derived_cl140, plain,
% 40.94/5.79 (![X0 : $i > $o, X1 : $i]:
% 40.94/5.79 (((X0 @ X1) | (mnot @ (mbox @ fool @ X0) @ X1)))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl139, '3'])).
% 40.94/5.79 thf(zip_derived_cl141, plain,
% 40.94/5.79 (![X0 : $i > $o, X1 : $i]:
% 40.94/5.79 ( (X0 @ X1) | (mnot @ (mbox @ fool @ X0) @ X1))),
% 40.94/5.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl140])).
% 40.94/5.79 thf(mnot, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))).
% 40.94/5.79 thf('4', plain,
% 40.94/5.79 (![X0:( $i > $o ),X1:$i]: ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [mnot])).
% 40.94/5.79 thf(zip_derived_cl142, plain,
% 40.94/5.79 (![X0 : $i > $o, X1 : $i]: (~ (mbox @ fool @ X0 @ X1) | (X0 @ X1))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl141, '4'])).
% 40.94/5.79 thf(mbox, axiom, ~ (mbox @ X0 @ X1 @ X2) =>
% 40.94/5.79 ((((!!) @ (^[Y0 : $i]: (((((~) @ (X0 @ X2 @ Y0))) | (X1 @ Y0)))))) !=
% 40.94/5.79 ($true))).
% 40.94/5.79 thf('5', plain,
% 40.94/5.79 (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 40.94/5.79 ( ( ~( mbox @ X0 @ X1 @ X2 ) ) <=>
% 40.94/5.79 ( ~( ![X7:$i]: ( ( ~( X0 @ X2 @ X7 ) ) | ( X1 @ X7 ) ) ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [mbox])).
% 40.94/5.79 thf(zip_derived_cl143, plain,
% 40.94/5.79 (![X0 : $i > $o, X1 : $i]:
% 40.94/5.79 (~ (((!!) @ (^[Y0 : $i]: (((((~) @ (fool @ X1 @ Y0))) | (X0 @ Y0))))))
% 40.94/5.79 | (X0 @ X1))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl142, '5'])).
% 40.94/5.79 thf(zip_derived_cl144, plain,
% 40.94/5.79 (![X0 : $i > $o, X1 : $i]:
% 40.94/5.79 (~ (((((~) @ (fool @ X1 @ ('#sk21' @ X0 @ X1)))) | (X0 @
% 40.94/5.79 ('#sk21' @ X0 @ X1))))
% 40.94/5.79 | (X0 @ X1))),
% 40.94/5.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl143])).
% 40.94/5.79 thf(zip_derived_cl146, plain,
% 40.94/5.79 (![X0 : $i > $o, X1 : $i]: (~ (X0 @ ('#sk21' @ X0 @ X1)) | (X0 @ X1))),
% 40.94/5.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl144])).
% 40.94/5.79 thf(zip_derived_cl258, plain,
% 40.94/5.79 (![X0 : $i]:
% 40.94/5.79 (~ ((^[Y0 : $i]: (((X0) != (Y0)))) @
% 40.94/5.79 ('#sk21' @ (^[Y0 : $i]: (((X0) != (Y0)))) @ X0))
% 40.94/5.79 | ((^[Y0 : $i]: (((X0) != (Y0)))) @ X0))),
% 40.94/5.79 inference('elim_leibniz_eq_+', [status(thm)], [zip_derived_cl146])).
% 40.94/5.79 thf(zip_derived_cl268, plain,
% 40.94/5.79 (![X0 : $i]:
% 40.94/5.79 (~ (((X0) != ('#sk21' @ ((($i) != (X0))) @ X0))) | (((X0) != (X0))))),
% 40.94/5.79 inference('ho_norm', [status(thm)], [zip_derived_cl258])).
% 40.94/5.79 thf(zip_derived_cl269, plain,
% 40.94/5.79 (![X0 : $i]: ~ (((X0) != ('#sk21' @ ((($i) != (X0))) @ X0)))),
% 40.94/5.79 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl268])).
% 40.94/5.79 thf(zip_derived_cl270, plain,
% 40.94/5.79 (![X0 : $i]: ((X0) = ('#sk21' @ ((($i) != (X0))) @ X0))),
% 40.94/5.79 inference('simplify nested equalities', [status(thm)],
% 40.94/5.79 [zip_derived_cl269])).
% 40.94/5.79 thf(zip_derived_cl145, plain,
% 40.94/5.79 (![X0 : $i > $o, X1 : $i]:
% 40.94/5.79 ( (fool @ X1 @ ('#sk21' @ X0 @ X1)) | (X0 @ X1))),
% 40.94/5.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl144])).
% 40.94/5.79 thf(zip_derived_cl2107, plain,
% 40.94/5.79 (![X0 : $i]: ( (fool @ X0 @ X0) | (((X0) != (X0))))),
% 40.94/5.79 inference('sup+', [status(thm)], [zip_derived_cl270, zip_derived_cl145])).
% 40.94/5.79 thf(zip_derived_cl2121, plain, (![X0 : $i]: (fool @ X0 @ X0)),
% 40.94/5.79 inference('simplify boolean subterms', [status(thm)],
% 40.94/5.79 [zip_derived_cl2107])).
% 40.94/5.79 thf(ax2, axiom,
% 40.94/5.79 (mvalid @ ( mbox @ fool @ ( ^[X:$i]: ( ec @ spain @ france ) ) ))).
% 40.94/5.79 thf(zip_derived_cl6, plain,
% 40.94/5.79 ( (mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france))))),
% 40.94/5.79 inference('cnf', [status(esa)], [ax2])).
% 40.94/5.79 thf(zip_derived_cl60, plain,
% 40.94/5.79 ( (((!!) @ (^[Y0 : $i]:
% 40.94/5.79 (mbox @ fool @ (^[Y1 : $i]: (ec @ spain @ france)) @ Y0))))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl6, '0'])).
% 40.94/5.79 thf(zip_derived_cl61, plain,
% 40.94/5.79 (![X2 : $i]: (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france)) @ X2)),
% 40.94/5.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl60])).
% 40.94/5.79 thf(mbox, axiom, (mbox @ X0 @ X1 @ X2) =>
% 40.94/5.79 ((((!!) @ (^[Y0 : $i]: (((((~) @ (X0 @ X2 @ Y0))) | (X1 @ Y0)))))) =
% 40.94/5.79 ($true))).
% 40.94/5.79 thf('6', plain,
% 40.94/5.79 (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 40.94/5.79 ( ( mbox @ X0 @ X1 @ X2 ) <=>
% 40.94/5.79 ( ![X7:$i]: ( ( ~( X0 @ X2 @ X7 ) ) | ( X1 @ X7 ) ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [mbox])).
% 40.94/5.79 thf(zip_derived_cl62, plain,
% 40.94/5.79 (![X0 : $i]:
% 40.94/5.79 (((!!) @ (^[Y0 : $i]:
% 40.94/5.79 (((((~) @ (fool @ X0 @ Y0))) |
% 40.94/5.79 ((^[Y1 : $i]: (ec @ spain @ france)) @ Y0))))))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl61, '6'])).
% 40.94/5.79 thf(zip_derived_cl63, plain,
% 40.94/5.79 (![X0 : $i]:
% 40.94/5.79 (((!!) @ (^[Y0 : $i]:
% 40.94/5.79 (((((~) @ (fool @ X0 @ Y0))) | (ec @ spain @ france))))))),
% 40.94/5.79 inference('ho_norm', [status(thm)], [zip_derived_cl62])).
% 40.94/5.79 thf(zip_derived_cl64, plain,
% 40.94/5.79 (![X0 : $i, X2 : $i]:
% 40.94/5.79 (((((~) @ (fool @ X0 @ X2))) | (ec @ spain @ france)))),
% 40.94/5.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])).
% 40.94/5.79 thf(zip_derived_cl65, plain,
% 40.94/5.79 (![X0 : $i, X2 : $i]: (~ (fool @ X0 @ X2) | (ec @ spain @ france))),
% 40.94/5.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])).
% 40.94/5.79 thf(ec, axiom, (ec @ X0 @ X1) =>
% 40.94/5.79 ((((((~) @ (o @ X0 @ X1))) & (c @ X0 @ X1))) = ($true))).
% 40.94/5.79 thf('7', plain,
% 40.94/5.79 (![X0:reg,X1:reg]:
% 40.94/5.79 ( ( ec @ X0 @ X1 ) <=> ( ( c @ X0 @ X1 ) & ( ~( o @ X0 @ X1 ) ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [ec])).
% 40.94/5.79 thf(zip_derived_cl66, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i]:
% 40.94/5.79 ( (((((~) @ (o @ spain @ france))) & (c @ spain @ france)))
% 40.94/5.79 | ~ (fool @ X1 @ X0))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl65, '7'])).
% 40.94/5.79 thf(zip_derived_cl67, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i]: (~ (o @ spain @ france) | ~ (fool @ X1 @ X0))),
% 40.94/5.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl66])).
% 40.94/5.79 thf(o, axiom, ~ (o @ X0 @ X1) =>
% 40.94/5.79 ((((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ X1)))))) != ($true))).
% 40.94/5.79 thf('8', plain,
% 40.94/5.79 (![X0:reg,X1:reg]:
% 40.94/5.79 ( ( ~( o @ X0 @ X1 ) ) <=>
% 40.94/5.79 ( ~( ?[X6:reg]: ( ( p @ X6 @ X0 ) & ( p @ X6 @ X1 ) ) ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [o])).
% 40.94/5.79 thf(zip_derived_cl69, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i]:
% 40.94/5.79 (~ (((??) @ (^[Y0 : reg]: (((p @ Y0 @ spain) & (p @ Y0 @ france))))))
% 40.94/5.79 | ~ (fool @ X1 @ X0))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl67, '8'])).
% 40.94/5.79 thf(zip_derived_cl70, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X3 : reg]:
% 40.94/5.79 (~ (((p @ X3 @ spain) & (p @ X3 @ france))) | ~ (fool @ X1 @ X0))),
% 40.94/5.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl69])).
% 40.94/5.79 thf(zip_derived_cl71, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X3 : reg]:
% 40.94/5.79 (~ (p @ X3 @ spain) | ~ (p @ X3 @ france) | ~ (fool @ X1 @ X0))),
% 40.94/5.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl70])).
% 40.94/5.79 thf(p, axiom, ~ (p @ X0 @ X1) =>
% 40.94/5.79 ((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ X1)))))) != ($true))).
% 40.94/5.79 thf('9', plain,
% 40.94/5.79 (![X0:reg,X1:reg]:
% 40.94/5.79 ( ( ~( p @ X0 @ X1 ) ) <=>
% 40.94/5.79 ( ~( ![X6:reg]: ( ( c @ X6 @ X0 ) => ( c @ X6 @ X1 ) ) ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [p])).
% 40.94/5.79 thf(zip_derived_cl72, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X2 : reg]:
% 40.94/5.79 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain))))))
% 40.94/5.79 | ~ (fool @ X1 @ X0)
% 40.94/5.79 | ~ (p @ X2 @ france))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl71, '9'])).
% 40.94/5.79 thf(zip_derived_cl73, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X2 : reg]:
% 40.94/5.79 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ france))))))
% 40.94/5.79 | ~ (fool @ X1 @ X0)
% 40.94/5.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl72, '9'])).
% 40.94/5.79 thf(zip_derived_cl74, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X2 : reg]:
% 40.94/5.79 (~ (((c @ ('#sk7' @ X2) @ X2) => (c @ ('#sk7' @ X2) @ france)))
% 40.94/5.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain))))))
% 40.94/5.79 | ~ (fool @ X1 @ X0))),
% 40.94/5.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl73])).
% 40.94/5.79 thf(zip_derived_cl75, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X2 : reg]:
% 40.94/5.79 ( (c @ ('#sk7' @ X2) @ X2)
% 40.94/5.79 | ~ (fool @ X1 @ X0)
% 40.94/5.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 40.94/5.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])).
% 40.94/5.79 thf(zip_derived_cl75, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X2 : reg]:
% 40.94/5.79 ( (c @ ('#sk7' @ X2) @ X2)
% 40.94/5.79 | ~ (fool @ X1 @ X0)
% 40.94/5.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 40.94/5.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])).
% 40.94/5.79 thf(zip_derived_cl77, plain,
% 40.94/5.79 (![X2 : reg]:
% 40.94/5.79 ( ('#form8' @ X2)
% 40.94/5.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 40.94/5.79 define([status(thm)])).
% 40.94/5.79 thf(zip_derived_cl79, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X2 : reg]:
% 40.94/5.79 (~ ('#form8' @ X2) | ~ (fool @ X1 @ X0) | (c @ ('#sk7' @ X2) @ X2))),
% 40.94/5.79 inference('renaming', [status(thm)], [zip_derived_cl75, zip_derived_cl77])).
% 40.94/5.79 thf(zip_derived_cl2247, plain,
% 40.94/5.79 (![X1 : reg]: ( (c @ ('#sk7' @ X1) @ X1) | ~ ('#form8' @ X1))),
% 40.94/5.79 inference('sup-', [status(thm)], [zip_derived_cl2121, zip_derived_cl79])).
% 40.94/5.79 thf(ax3, axiom,
% 40.94/5.79 (mvalid @ ( mbox @ a @ ( ^[X:$i]: ( ntpp @ paris @ france ) ) ))).
% 40.94/5.79 thf(zip_derived_cl7, plain,
% 40.94/5.79 ( (mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france))))),
% 40.94/5.79 inference('cnf', [status(esa)], [ax3])).
% 40.94/5.79 thf(zip_derived_cl83, plain,
% 40.94/5.79 ( (((!!) @ (^[Y0 : $i]:
% 40.94/5.79 (mbox @ a @ (^[Y1 : $i]: (ntpp @ paris @ france)) @ Y0))))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl7, '0'])).
% 40.94/5.79 thf(zip_derived_cl84, plain,
% 40.94/5.79 (![X2 : $i]: (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)) @ X2)),
% 40.94/5.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl83])).
% 40.94/5.79 thf(zip_derived_cl85, plain,
% 40.94/5.79 (![X0 : $i]:
% 40.94/5.79 (((!!) @ (^[Y0 : $i]:
% 40.94/5.79 (((((~) @ (a @ X0 @ Y0))) |
% 40.94/5.79 ((^[Y1 : $i]: (ntpp @ paris @ france)) @ Y0))))))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl84, '6'])).
% 40.94/5.79 thf(zip_derived_cl86, plain,
% 40.94/5.79 (![X0 : $i]:
% 40.94/5.79 (((!!) @ (^[Y0 : $i]:
% 40.94/5.79 (((((~) @ (a @ X0 @ Y0))) | (ntpp @ paris @ france))))))),
% 40.94/5.79 inference('ho_norm', [status(thm)], [zip_derived_cl85])).
% 40.94/5.79 thf(zip_derived_cl87, plain,
% 40.94/5.79 (![X0 : $i, X2 : $i]:
% 40.94/5.79 (((((~) @ (a @ X0 @ X2))) | (ntpp @ paris @ france)))),
% 40.94/5.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])).
% 40.94/5.79 thf(zip_derived_cl88, plain,
% 40.94/5.79 (![X0 : $i, X2 : $i]: (~ (a @ X0 @ X2) | (ntpp @ paris @ france))),
% 40.94/5.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl87])).
% 40.94/5.79 thf(ntpp, axiom, (ntpp @ X0 @ X1) =>
% 40.94/5.79 ((((((~) @ (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ X0) & (ec @ Y0 @ X1)))))))) &
% 40.94/5.79 (pp @ X0 @ X1)))
% 40.94/5.79 = ($true))).
% 40.94/5.79 thf('10', plain,
% 40.94/5.79 (![X0:reg,X1:reg]:
% 40.94/5.79 ( ( ntpp @ X0 @ X1 ) <=>
% 40.94/5.79 ( ( pp @ X0 @ X1 ) &
% 40.94/5.79 ( ~( ?[X6:reg]: ( ( ec @ X6 @ X0 ) & ( ec @ X6 @ X1 ) ) ) ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [ntpp])).
% 40.94/5.79 thf(zip_derived_cl89, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i]:
% 40.94/5.79 ( (((((~) @ (((??) @ (^[Y0 : reg]:
% 40.94/5.79 (((ec @ Y0 @ paris) & (ec @ Y0 @ france)))))))) &
% 40.94/5.79 (pp @ paris @ france)))
% 40.94/5.79 | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl88, '10'])).
% 40.94/5.79 thf(zip_derived_cl91, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i]: ( (pp @ paris @ france) | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl89])).
% 40.94/5.79 thf(pp, axiom, (pp @ X0 @ X1) =>
% 40.94/5.79 ((((((~) @ (p @ X1 @ X0))) & (p @ X0 @ X1))) = ($true))).
% 40.94/5.79 thf('11', plain,
% 40.94/5.79 (![X0:reg,X1:reg]:
% 40.94/5.79 ( ( pp @ X0 @ X1 ) <=> ( ( p @ X0 @ X1 ) & ( ~( p @ X1 @ X0 ) ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [pp])).
% 40.94/5.79 thf(zip_derived_cl93, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i]:
% 40.94/5.79 ( (((((~) @ (p @ france @ paris))) & (p @ paris @ france)))
% 40.94/5.79 | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl91, '11'])).
% 40.94/5.79 thf(zip_derived_cl96, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i]: ( (p @ paris @ france) | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl93])).
% 40.94/5.79 thf(p, axiom, (p @ X0 @ X1) =>
% 40.94/5.79 ((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ X1)))))) = ($true))).
% 40.94/5.79 thf('12', plain,
% 40.94/5.79 (![X0:reg,X1:reg]:
% 40.94/5.79 ( ( p @ X0 @ X1 ) <=>
% 40.94/5.79 ( ![X6:reg]: ( ( c @ X6 @ X0 ) => ( c @ X6 @ X1 ) ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [p])).
% 40.94/5.79 thf(zip_derived_cl99, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i]:
% 40.94/5.79 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ paris) => (c @ Y0 @ france))))))
% 40.94/5.79 | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl96, '12'])).
% 40.94/5.79 thf(zip_derived_cl102, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X3 : reg]:
% 40.94/5.79 ( (((c @ X3 @ paris) => (c @ X3 @ france))) | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl99])).
% 40.94/5.79 thf(zip_derived_cl106, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X3 : reg]:
% 40.94/5.79 (~ (c @ X3 @ paris) | (c @ X3 @ france) | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])).
% 40.94/5.79 thf(con, conjecture,
% 40.94/5.79 (mvalid @
% 40.94/5.79 ( mbox @
% 40.94/5.79 a @
% 40.94/5.79 ( ^[X:$i]:
% 40.94/5.79 ( ![Z:reg]: ( ( p @ Z @ catalunya ) => ( ~( p @ Z @ paris ) ) ) ) ) ))).
% 40.94/5.79 thf(zf_stmt_0, negated_conjecture,
% 40.94/5.79 (~( mvalid @
% 40.94/5.79 ( mbox @
% 40.94/5.79 a @
% 40.94/5.79 ( ^[X:$i]:
% 40.94/5.79 ( ![Z:reg]: ( ( p @ Z @ catalunya ) => ( ~( p @ Z @ paris ) ) ) ) ) ) )),
% 40.94/5.79 inference('cnf.neg', [status(esa)], [con])).
% 40.94/5.79 thf(zip_derived_cl8, plain,
% 40.94/5.79 (~ (mvalid @
% 40.94/5.79 (mbox @ a @
% 40.94/5.79 (^[Y0 : $i]:
% 40.94/5.79 (((!!) @ (^[Y1 : reg]:
% 40.94/5.79 (((p @ Y1 @ catalunya) => (((~) @ (p @ Y1 @ paris)))))))))))),
% 40.94/5.79 inference('cnf', [status(esa)], [zf_stmt_0])).
% 40.94/5.79 thf(mvalid, axiom, ~ (mvalid @ X0) =>
% 40.94/5.79 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))).
% 40.94/5.79 thf('13', plain,
% 40.94/5.79 (![X0:( $i > $o )]:
% 40.94/5.79 ( ( ~( mvalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [mvalid])).
% 40.94/5.79 thf(zip_derived_cl150, plain,
% 40.94/5.79 (~ (((!!) @ (^[Y0 : $i]:
% 40.94/5.79 (mbox @ a @
% 40.94/5.79 (^[Y1 : $i]:
% 40.94/5.79 (((!!) @ (^[Y2 : reg]:
% 40.94/5.79 (((p @ Y2 @ catalunya) =>
% 40.94/5.79 (((~) @ (p @ Y2 @ paris))))))))) @
% 40.94/5.79 Y0))))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl8, '13'])).
% 40.94/5.79 thf(zip_derived_cl151, plain,
% 40.94/5.79 (~ (mbox @ a @
% 40.94/5.79 (^[Y0 : $i]:
% 40.94/5.79 (((!!) @ (^[Y1 : reg]:
% 40.94/5.79 (((p @ Y1 @ catalunya) => (((~) @ (p @ Y1 @ paris))))))))) @
% 40.94/5.79 '#sk26')),
% 40.94/5.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl150])).
% 40.94/5.79 thf(zip_derived_cl152, plain,
% 40.94/5.79 (~ (((!!) @ (^[Y0 : $i]:
% 40.94/5.79 (((((~) @ (a @ '#sk26' @ Y0))) |
% 40.94/5.79 ((^[Y1 : $i]:
% 40.94/5.79 (((!!) @ (^[Y2 : reg]:
% 40.94/5.79 (((p @ Y2 @ catalunya) =>
% 40.94/5.79 (((~) @ (p @ Y2 @ paris))))))))) @
% 40.94/5.79 Y0))))))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl151, '5'])).
% 40.94/5.79 thf(zip_derived_cl153, plain,
% 40.94/5.79 (~ (((!!) @ (^[Y0 : $i]:
% 40.94/5.79 (((((~) @ (a @ '#sk26' @ Y0))) |
% 40.94/5.79 (((!!) @ (^[Y1 : reg]:
% 40.94/5.79 (((p @ Y1 @ catalunya) =>
% 40.94/5.79 (((~) @ (p @ Y1 @ paris)))))))))))))),
% 40.94/5.79 inference('ho_norm', [status(thm)], [zip_derived_cl152])).
% 40.94/5.79 thf(zip_derived_cl154, plain,
% 40.94/5.79 (~ (((((~) @ (a @ '#sk26' @ '#sk27'))) |
% 40.94/5.79 (((!!) @ (^[Y0 : reg]:
% 40.94/5.79 (((p @ Y0 @ catalunya) => (((~) @ (p @ Y0 @ paris))))))))))),
% 40.94/5.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl153])).
% 40.94/5.79 thf(zip_derived_cl155, plain, ( (a @ '#sk26' @ '#sk27')),
% 40.94/5.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl154])).
% 40.94/5.79 thf(zip_derived_cl1659, plain,
% 40.94/5.79 (![X0 : reg]: ( (c @ X0 @ france) | ~ (c @ X0 @ paris))),
% 40.94/5.79 inference('sup+', [status(thm)], [zip_derived_cl106, zip_derived_cl155])).
% 40.94/5.79 thf(zip_derived_cl156, plain,
% 40.94/5.79 (~ (((!!) @ (^[Y0 : reg]:
% 40.94/5.79 (((p @ Y0 @ catalunya) => (((~) @ (p @ Y0 @ paris))))))))),
% 40.94/5.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl154])).
% 40.94/5.79 thf(zip_derived_cl157, plain,
% 40.94/5.79 (~ (((p @ '#sk28' @ catalunya) => (((~) @ (p @ '#sk28' @ paris)))))),
% 40.94/5.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl156])).
% 40.94/5.79 thf(zip_derived_cl159, plain, ( (p @ '#sk28' @ paris)),
% 40.94/5.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl157])).
% 40.94/5.79 thf(zip_derived_cl161, plain,
% 40.94/5.79 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ '#sk28') => (c @ Y0 @ paris))))))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl159, '12'])).
% 40.94/5.79 thf(zip_derived_cl163, plain,
% 40.94/5.79 (![X2 : reg]: (((c @ X2 @ '#sk28') => (c @ X2 @ paris)))),
% 40.94/5.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl161])).
% 40.94/5.79 thf(zip_derived_cl165, plain,
% 40.94/5.79 (![X2 : reg]: (~ (c @ X2 @ '#sk28') | (c @ X2 @ paris))),
% 40.94/5.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl163])).
% 40.94/5.79 thf(zip_derived_cl3459, plain,
% 40.94/5.79 (![X0 : reg]: ( (c @ X0 @ france) | ~ (c @ X0 @ '#sk28'))),
% 40.94/5.79 inference('sup+', [status(thm)], [zip_derived_cl1659, zip_derived_cl165])).
% 40.94/5.79 thf(zip_derived_cl2121, plain, (![X0 : $i]: (fool @ X0 @ X0)),
% 40.94/5.79 inference('simplify boolean subterms', [status(thm)],
% 40.94/5.79 [zip_derived_cl2107])).
% 40.94/5.79 thf(zip_derived_cl76, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X2 : reg]:
% 40.94/5.79 (~ (c @ ('#sk7' @ X2) @ france)
% 40.94/5.79 | ~ (fool @ X1 @ X0)
% 40.94/5.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 40.94/5.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])).
% 40.94/5.79 thf(zip_derived_cl77, plain,
% 40.94/5.79 (![X2 : reg]:
% 40.94/5.79 ( ('#form8' @ X2)
% 40.94/5.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 40.94/5.79 define([status(thm)])).
% 40.94/5.79 thf(zip_derived_cl80, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X2 : reg]:
% 40.94/5.79 (~ ('#form8' @ X2)
% 40.94/5.79 | ~ (fool @ X1 @ X0)
% 40.94/5.79 | ~ (c @ ('#sk7' @ X2) @ france))),
% 40.94/5.79 inference('renaming', [status(thm)], [zip_derived_cl76, zip_derived_cl77])).
% 40.94/5.79 thf(zip_derived_cl2246, plain,
% 40.94/5.79 (![X1 : reg]: (~ (c @ ('#sk7' @ X1) @ france) | ~ ('#form8' @ X1))),
% 40.94/5.79 inference('sup-', [status(thm)], [zip_derived_cl2121, zip_derived_cl80])).
% 40.94/5.79 thf(zip_derived_cl9649, plain,
% 40.94/5.79 (![X0 : reg]: (~ (c @ ('#sk7' @ X0) @ '#sk28') | ~ ('#form8' @ X0))),
% 40.94/5.79 inference('sup-', [status(thm)], [zip_derived_cl3459, zip_derived_cl2246])).
% 40.94/5.79 thf(zip_derived_cl9694, plain,
% 40.94/5.79 ((~ ('#form8' @ '#sk28') | ~ ('#form8' @ '#sk28'))),
% 40.94/5.79 inference('sup-', [status(thm)], [zip_derived_cl2247, zip_derived_cl9649])).
% 40.94/5.79 thf(ax1, axiom,
% 40.94/5.79 (mvalid @ ( mbox @ a @ ( ^[X:$i]: ( tpp @ catalunya @ spain ) ) ))).
% 40.94/5.79 thf(zip_derived_cl5, plain,
% 40.94/5.79 ( (mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain))))),
% 40.94/5.79 inference('cnf', [status(esa)], [ax1])).
% 40.94/5.79 thf(zip_derived_cl10, plain,
% 40.94/5.79 ( (((!!) @ (^[Y0 : $i]:
% 40.94/5.79 (mbox @ a @ (^[Y1 : $i]: (tpp @ catalunya @ spain)) @ Y0))))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl5, '0'])).
% 40.94/5.79 thf(zip_derived_cl11, plain,
% 40.94/5.79 (![X2 : $i]: (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)) @ X2)),
% 40.94/5.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])).
% 40.94/5.79 thf(zip_derived_cl12, plain,
% 40.94/5.79 (![X0 : $i]:
% 40.94/5.79 (((!!) @ (^[Y0 : $i]:
% 40.94/5.79 (((((~) @ (a @ X0 @ Y0))) |
% 40.94/5.79 ((^[Y1 : $i]: (tpp @ catalunya @ spain)) @ Y0))))))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl11, '6'])).
% 40.94/5.79 thf(zip_derived_cl13, plain,
% 40.94/5.79 (![X0 : $i]:
% 40.94/5.79 (((!!) @ (^[Y0 : $i]:
% 40.94/5.79 (((((~) @ (a @ X0 @ Y0))) | (tpp @ catalunya @ spain))))))),
% 40.94/5.79 inference('ho_norm', [status(thm)], [zip_derived_cl12])).
% 40.94/5.79 thf(zip_derived_cl14, plain,
% 40.94/5.79 (![X0 : $i, X2 : $i]:
% 40.94/5.79 (((((~) @ (a @ X0 @ X2))) | (tpp @ catalunya @ spain)))),
% 40.94/5.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])).
% 40.94/5.79 thf(zip_derived_cl15, plain,
% 40.94/5.79 (![X0 : $i, X2 : $i]: (~ (a @ X0 @ X2) | (tpp @ catalunya @ spain))),
% 40.94/5.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl14])).
% 40.94/5.79 thf(tpp, axiom, (tpp @ X0 @ X1) =>
% 40.94/5.79 ((((((??) @ (^[Y0 : reg]: (((ec @ Y0 @ X0) & (ec @ Y0 @ X1)))))) & (pp @
% 40.94/5.79 X0 @ X1)))
% 40.94/5.79 = ($true))).
% 40.94/5.79 thf('14', plain,
% 40.94/5.79 (![X0:reg,X1:reg]:
% 40.94/5.79 ( ( tpp @ X0 @ X1 ) <=>
% 40.94/5.79 ( ( pp @ X0 @ X1 ) &
% 40.94/5.79 ( ?[X6:reg]: ( ( ec @ X6 @ X0 ) & ( ec @ X6 @ X1 ) ) ) ) )),
% 40.94/5.79 inference('rw.lit', [status(esa)], [tpp])).
% 40.94/5.79 thf(zip_derived_cl16, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i]:
% 40.94/5.79 ( (((((??) @ (^[Y0 : reg]:
% 40.94/5.79 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ spain)))))) &
% 40.94/5.79 (pp @ catalunya @ spain)))
% 40.94/5.79 | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl15, '14'])).
% 40.94/5.79 thf(zip_derived_cl18, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i]: ( (pp @ catalunya @ spain) | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl16])).
% 40.94/5.79 thf(zip_derived_cl20, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i]:
% 40.94/5.79 ( (((((~) @ (p @ spain @ catalunya))) & (p @ catalunya @ spain)))
% 40.94/5.79 | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl18, '11'])).
% 40.94/5.79 thf(zip_derived_cl24, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i]: ( (p @ catalunya @ spain) | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl20])).
% 40.94/5.79 thf(zip_derived_cl28, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i]:
% 40.94/5.79 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ catalunya) => (c @ Y0 @ spain))))))
% 40.94/5.79 | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl24, '12'])).
% 40.94/5.79 thf(zip_derived_cl34, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X3 : reg]:
% 40.94/5.79 ( (((c @ X3 @ catalunya) => (c @ X3 @ spain))) | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])).
% 40.94/5.79 thf(zip_derived_cl39, plain,
% 40.94/5.79 (![X0 : $i, X1 : $i, X3 : reg]:
% 40.94/5.79 (~ (c @ X3 @ catalunya) | (c @ X3 @ spain) | ~ (a @ X1 @ X0))),
% 40.94/5.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 40.94/5.79 thf(zip_derived_cl155, plain, ( (a @ '#sk26' @ '#sk27')),
% 40.94/5.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl154])).
% 40.94/5.79 thf(zip_derived_cl234, plain,
% 40.94/5.79 (![X0 : reg]: ( (c @ X0 @ spain) | ~ (c @ X0 @ catalunya))),
% 40.94/5.79 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl155])).
% 40.94/5.79 thf(zip_derived_cl77, plain,
% 40.94/5.79 (![X2 : reg]:
% 40.94/5.79 ( ('#form8' @ X2)
% 40.94/5.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 40.94/5.79 define([status(thm)])).
% 40.94/5.79 thf(zip_derived_cl78, plain,
% 40.94/5.79 (![X2 : reg]:
% 40.94/5.79 (~ (((c @ ('#sk4' @ X2) @ X2) => (c @ ('#sk4' @ X2) @ spain)))
% 40.94/5.79 | ('#form8' @ X2))),
% 40.94/5.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl77])).
% 40.94/5.79 thf(zip_derived_cl82, plain,
% 40.94/5.79 (![X2 : reg]: (~ (c @ ('#sk4' @ X2) @ spain) | ('#form8' @ X2))),
% 40.94/5.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])).
% 40.94/5.79 thf(zip_derived_cl936, plain,
% 40.94/5.79 (![X0 : reg]: (~ (c @ ('#sk4' @ X0) @ catalunya) | ('#form8' @ X0))),
% 40.94/5.79 inference('sup-', [status(thm)], [zip_derived_cl234, zip_derived_cl82])).
% 40.94/5.79 thf(zip_derived_cl158, plain, ( (p @ '#sk28' @ catalunya)),
% 40.94/5.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl157])).
% 40.94/5.79 thf(zip_derived_cl160, plain,
% 40.94/5.79 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ '#sk28') => (c @ Y0 @ catalunya))))))),
% 40.94/5.79 inference('rw_clause', [status(thm)], [zip_derived_cl158, '12'])).
% 40.94/5.79 thf(zip_derived_cl162, plain,
% 40.94/5.79 (![X2 : reg]: (((c @ X2 @ '#sk28') => (c @ X2 @ catalunya)))),
% 40.94/5.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl160])).
% 40.94/5.79 thf(zip_derived_cl164, plain,
% 40.94/5.79 (![X2 : reg]: (~ (c @ X2 @ '#sk28') | (c @ X2 @ catalunya))),
% 40.94/5.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl162])).
% 40.94/5.79 thf(zip_derived_cl979, plain,
% 40.94/5.79 (![X0 : reg]: ( ('#form8' @ X0) | ~ (c @ ('#sk4' @ X0) @ '#sk28'))),
% 40.94/5.79 inference('sup+', [status(thm)], [zip_derived_cl936, zip_derived_cl164])).
% 40.94/5.79 thf(zip_derived_cl81, plain,
% 40.94/5.79 (![X2 : reg]: ( (c @ ('#sk4' @ X2) @ X2) | ('#form8' @ X2))),
% 40.94/5.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])).
% 40.94/5.79 thf(zip_derived_cl1293, plain,
% 40.94/5.79 (( ('#form8' @ '#sk28') | ('#form8' @ '#sk28'))),
% 40.94/5.79 inference('sup+', [status(thm)], [zip_derived_cl979, zip_derived_cl81])).
% 40.94/5.79 thf(zip_derived_cl1313, plain, ( ('#form8' @ '#sk28')),
% 40.94/5.79 inference('simplify', [status(thm)], [zip_derived_cl1293])).
% 40.94/5.79 thf(zip_derived_cl1313, plain, ( ('#form8' @ '#sk28')),
% 40.94/5.79 inference('simplify', [status(thm)], [zip_derived_cl1293])).
% 40.94/5.79 thf(zip_derived_cl9712, plain, ($false),
% 40.94/5.79 inference('demod', [status(thm)],
% 40.94/5.79 [zip_derived_cl9694, zip_derived_cl1313, zip_derived_cl1313])).
% 40.94/5.79
% 40.94/5.79 % SZS output end Refutation
% 40.94/5.79
% 40.94/5.79
% 40.94/5.79 % Terminating...
% 41.54/5.88 % Runner terminated.
% 41.54/5.88 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------