TSTP Solution File: GEG020^1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GEG020^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.UbBiBX9vDg true
% Computer : n028.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 22:42:16 EDT 2023
% Result : Theorem 107.12s 14.53s
% Output : Refutation 107.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GEG020^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.UbBiBX9vDg true
% 0.14/0.36 % Computer : n028.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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 01:17:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.22/0.64 % Total configuration time : 828
% 0.22/0.64 % Estimated wc time : 1656
% 0.22/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 3.81/1.39 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 107.12/14.53 % Solved by lams/30_b.l.sh.
% 107.12/14.53 % done 1604 iterations in 13.646s
% 107.12/14.53 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 107.12/14.53 % SZS output start Refutation
% 107.12/14.53 thf(reg_type, type, reg: $tType).
% 107.12/14.53 thf('#form12_type', type, '#form12': reg > $o).
% 107.12/14.53 thf('#sk8_type', type, '#sk8': reg > reg).
% 107.12/14.53 thf('#sk89_type', type, '#sk89': $i).
% 107.12/14.53 thf(mbox_type, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 107.12/14.53 thf('#sk90_type', type, '#sk90': $i).
% 107.12/14.53 thf(paris_type, type, paris: reg).
% 107.12/14.53 thf(ntpp_type, type, ntpp: reg > reg > $o).
% 107.12/14.53 thf(a_type, type, a: $i > $i > $o).
% 107.12/14.53 thf(pp_type, type, pp: reg > reg > $o).
% 107.12/14.53 thf('#form10_type', type, '#form10': reg > $o).
% 107.12/14.53 thf(fool_type, type, fool: $i > $i > $o).
% 107.12/14.53 thf('#sk91_type', type, '#sk91': reg).
% 107.12/14.53 thf('#form94_type', type, '#form94': reg > $o).
% 107.12/14.53 thf(france_type, type, france: reg).
% 107.12/14.53 thf('#sk92_type', type, '#sk92': reg).
% 107.12/14.53 thf('#sk11_type', type, '#sk11': reg > reg).
% 107.12/14.53 thf('#sk93_type', type, '#sk93': reg > reg).
% 107.12/14.53 thf(ec_type, type, ec: reg > reg > $o).
% 107.12/14.53 thf('#sk4_type', type, '#sk4': reg > reg).
% 107.12/14.53 thf(o_type, type, o: reg > reg > $o).
% 107.12/14.53 thf(c_type, type, c: reg > reg > $o).
% 107.12/14.53 thf(p_type, type, p: reg > reg > $o).
% 107.12/14.53 thf(catalunya_type, type, catalunya: reg).
% 107.12/14.53 thf(spain_type, type, spain: reg).
% 107.12/14.53 thf('#sk9_type', type, '#sk9': reg > reg).
% 107.12/14.53 thf(tpp_type, type, tpp: reg > reg > $o).
% 107.12/14.53 thf(mvalid_type, type, mvalid: ($i > $o) > $o).
% 107.12/14.53 thf(con, conjecture,
% 107.12/14.53 (mvalid @
% 107.12/14.53 ( mbox @
% 107.12/14.53 a @
% 107.12/14.53 ( ^[X:$i]:
% 107.12/14.53 ( ![Z:reg]:
% 107.12/14.53 ( ( ( o @ Z @ catalunya ) | ( o @ Z @ paris ) ) =>
% 107.12/14.53 ( ( o @ Z @ france ) | ( o @ Z @ spain ) ) ) ) ) ))).
% 107.12/14.53 thf(zf_stmt_0, negated_conjecture,
% 107.12/14.53 (~( mvalid @
% 107.12/14.53 ( mbox @
% 107.12/14.53 a @
% 107.12/14.53 ( ^[X:$i]:
% 107.12/14.53 ( ![Z:reg]:
% 107.12/14.53 ( ( ( o @ Z @ catalunya ) | ( o @ Z @ paris ) ) =>
% 107.12/14.53 ( ( o @ Z @ france ) | ( o @ Z @ spain ) ) ) ) ) ) )),
% 107.12/14.53 inference('cnf.neg', [status(esa)], [con])).
% 107.12/14.53 thf(zip_derived_cl8, plain,
% 107.12/14.53 (~ (mvalid @
% 107.12/14.53 (mbox @ a @
% 107.12/14.53 (^[Y0 : $i]:
% 107.12/14.53 (((!!) @ (^[Y1 : reg]:
% 107.12/14.53 (((((o @ Y1 @ catalunya) | (o @ Y1 @ paris))) =>
% 107.12/14.53 (((o @ Y1 @ france) | (o @ Y1 @ spain)))))))))))),
% 107.12/14.53 inference('cnf', [status(esa)], [zf_stmt_0])).
% 107.12/14.53 thf(mvalid, axiom, ~ (mvalid @ X0) =>
% 107.12/14.53 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))).
% 107.12/14.53 thf('0', plain,
% 107.12/14.53 (![X0:( $i > $o )]:
% 107.12/14.53 ( ( ~( mvalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )),
% 107.12/14.53 inference('rw.lit', [status(esa)], [mvalid])).
% 107.12/14.53 thf(zip_derived_cl192, plain,
% 107.12/14.53 (~ (((!!) @ (^[Y0 : $i]:
% 107.12/14.53 (mbox @ a @
% 107.12/14.53 (^[Y1 : $i]:
% 107.12/14.53 (((!!) @ (^[Y2 : reg]:
% 107.12/14.53 (((((o @ Y2 @ catalunya) | (o @ Y2 @
% 107.12/14.53 paris))) =>
% 107.12/14.53 (((o @ Y2 @ france) | (o @ Y2 @ spain))))))))) @
% 107.12/14.53 Y0))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl8, '0'])).
% 107.12/14.53 thf(zip_derived_cl193, plain,
% 107.12/14.53 (~ (mbox @ a @
% 107.12/14.53 (^[Y0 : $i]:
% 107.12/14.53 (((!!) @ (^[Y1 : reg]:
% 107.12/14.53 (((((o @ Y1 @ catalunya) | (o @ Y1 @ paris))) =>
% 107.12/14.53 (((o @ Y1 @ france) | (o @ Y1 @ spain))))))))) @
% 107.12/14.53 '#sk89')),
% 107.12/14.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl192])).
% 107.12/14.53 thf(mbox, axiom, ~ (mbox @ X0 @ X1 @ X2) =>
% 107.12/14.53 ((((!!) @ (^[Y0 : $i]: (((((~) @ (X0 @ X2 @ Y0))) | (X1 @ Y0)))))) !=
% 107.12/14.53 ($true))).
% 107.12/14.53 thf('1', plain,
% 107.12/14.53 (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 107.12/14.53 ( ( ~( mbox @ X0 @ X1 @ X2 ) ) <=>
% 107.12/14.53 ( ~( ![X7:$i]: ( ( ~( X0 @ X2 @ X7 ) ) | ( X1 @ X7 ) ) ) ) )),
% 107.12/14.53 inference('rw.lit', [status(esa)], [mbox])).
% 107.12/14.53 thf(zip_derived_cl194, plain,
% 107.12/14.53 (~ (((!!) @ (^[Y0 : $i]:
% 107.12/14.53 (((((~) @ (a @ '#sk89' @ Y0))) |
% 107.12/14.53 ((^[Y1 : $i]:
% 107.12/14.53 (((!!) @ (^[Y2 : reg]:
% 107.12/14.53 (((((o @ Y2 @ catalunya) | (o @ Y2 @
% 107.12/14.53 paris))) =>
% 107.12/14.53 (((o @ Y2 @ france) | (o @ Y2 @ spain))))))))) @
% 107.12/14.53 Y0))))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl193, '1'])).
% 107.12/14.53 thf(zip_derived_cl195, plain,
% 107.12/14.53 (~ (((!!) @ (^[Y0 : $i]:
% 107.12/14.53 (((((~) @ (a @ '#sk89' @ Y0))) |
% 107.12/14.53 (((!!) @ (^[Y1 : reg]:
% 107.12/14.53 (((((o @ Y1 @ catalunya) | (o @ Y1 @ paris))) =>
% 107.12/14.53 (((o @ Y1 @ france) | (o @ Y1 @ spain)))))))))))))),
% 107.12/14.53 inference('ho_norm', [status(thm)], [zip_derived_cl194])).
% 107.12/14.53 thf(zip_derived_cl196, plain,
% 107.12/14.53 (~ (((((~) @ (a @ '#sk89' @ '#sk90'))) |
% 107.12/14.53 (((!!) @ (^[Y0 : reg]:
% 107.12/14.53 (((((o @ Y0 @ catalunya) | (o @ Y0 @ paris))) =>
% 107.12/14.53 (((o @ Y0 @ france) | (o @ Y0 @ spain))))))))))),
% 107.12/14.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl195])).
% 107.12/14.53 thf(zip_derived_cl197, plain, ( (a @ '#sk89' @ '#sk90')),
% 107.12/14.53 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl196])).
% 107.12/14.53 thf(zip_derived_cl198, plain,
% 107.12/14.53 (~ (((!!) @ (^[Y0 : reg]:
% 107.12/14.53 (((((o @ Y0 @ catalunya) | (o @ Y0 @ paris))) =>
% 107.12/14.53 (((o @ Y0 @ france) | (o @ Y0 @ spain))))))))),
% 107.12/14.53 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl196])).
% 107.12/14.53 thf(zip_derived_cl199, plain,
% 107.12/14.53 (~ (((((o @ '#sk91' @ catalunya) | (o @ '#sk91' @ paris))) =>
% 107.12/14.53 (((o @ '#sk91' @ france) | (o @ '#sk91' @ spain)))))),
% 107.12/14.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl198])).
% 107.12/14.53 thf(zip_derived_cl201, plain,
% 107.12/14.53 (~ (((o @ '#sk91' @ france) | (o @ '#sk91' @ spain)))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl199])).
% 107.12/14.53 thf(zip_derived_cl203, plain, (~ (o @ '#sk91' @ france)),
% 107.12/14.53 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl201])).
% 107.12/14.53 thf(o, axiom, ~ (o @ X0 @ X1) =>
% 107.12/14.53 ((((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ X1)))))) != ($true))).
% 107.12/14.53 thf('2', plain,
% 107.12/14.53 (![X0:reg,X1:reg]:
% 107.12/14.53 ( ( ~( o @ X0 @ X1 ) ) <=>
% 107.12/14.53 ( ~( ?[X6:reg]: ( ( p @ X6 @ X0 ) & ( p @ X6 @ X1 ) ) ) ) )),
% 107.12/14.53 inference('rw.lit', [status(esa)], [o])).
% 107.12/14.53 thf(zip_derived_cl206, plain,
% 107.12/14.53 (~ (((??) @ (^[Y0 : reg]: (((p @ Y0 @ '#sk91') & (p @ Y0 @ france))))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl203, '2'])).
% 107.12/14.53 thf(zip_derived_cl209, plain,
% 107.12/14.53 (![X2 : reg]: ~ (((p @ X2 @ '#sk91') & (p @ X2 @ france)))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl206])).
% 107.12/14.53 thf(zip_derived_cl212, plain,
% 107.12/14.53 (![X2 : reg]: (~ (p @ X2 @ '#sk91') | ~ (p @ X2 @ france))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl209])).
% 107.12/14.53 thf(p, axiom, ~ (p @ X0 @ X1) =>
% 107.12/14.53 ((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ X1)))))) != ($true))).
% 107.12/14.53 thf('3', plain,
% 107.12/14.53 (![X0:reg,X1:reg]:
% 107.12/14.53 ( ( ~( p @ X0 @ X1 ) ) <=>
% 107.12/14.53 ( ~( ![X6:reg]: ( ( c @ X6 @ X0 ) => ( c @ X6 @ X1 ) ) ) ) )),
% 107.12/14.53 inference('rw.lit', [status(esa)], [p])).
% 107.12/14.53 thf(zip_derived_cl215, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91'))))))
% 107.12/14.53 | ~ (p @ X0 @ france))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl212, '3'])).
% 107.12/14.53 thf(zip_derived_cl218, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ france))))))
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91')))))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl215, '3'])).
% 107.12/14.53 thf(zip_derived_cl222, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 (~ (((c @ ('#sk11' @ X0) @ X0) => (c @ ('#sk11' @ X0) @ france)))
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91')))))))),
% 107.12/14.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl218])).
% 107.12/14.53 thf(zip_derived_cl227, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 (~ (c @ ('#sk11' @ X0) @ france)
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91')))))))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
% 107.12/14.53 thf(zip_derived_cl226, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 ( (c @ ('#sk11' @ X0) @ X0)
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91')))))))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
% 107.12/14.53 thf(zip_derived_cl231, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 ( ('#form94' @ X0)
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91')))))))),
% 107.12/14.53 define([status(thm)])).
% 107.12/14.53 thf(zip_derived_cl234, plain,
% 107.12/14.53 (![X0 : reg]: (~ ('#form94' @ X0) | ~ (c @ ('#sk11' @ X0) @ france))),
% 107.12/14.53 inference('renaming', [status(thm)],
% 107.12/14.53 [zip_derived_cl227, zip_derived_cl231])).
% 107.12/14.53 thf(ax3, axiom,
% 107.12/14.53 (mvalid @ ( mbox @ a @ ( ^[X:$i]: ( ntpp @ paris @ france ) ) ))).
% 107.12/14.53 thf(zip_derived_cl7, plain,
% 107.12/14.53 ( (mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france))))),
% 107.12/14.53 inference('cnf', [status(esa)], [ax3])).
% 107.12/14.53 thf(mvalid, axiom, (mvalid @ X0) =>
% 107.12/14.53 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))).
% 107.12/14.53 thf('4', plain,
% 107.12/14.53 (![X0:( $i > $o )]: ( ( mvalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )),
% 107.12/14.53 inference('rw.lit', [status(esa)], [mvalid])).
% 107.12/14.53 thf(zip_derived_cl60, plain,
% 107.12/14.53 ( (((!!) @ (^[Y0 : $i]:
% 107.12/14.53 (mbox @ a @ (^[Y1 : $i]: (ntpp @ paris @ france)) @ Y0))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl7, '4'])).
% 107.12/14.53 thf(zip_derived_cl61, plain,
% 107.12/14.53 (![X2 : $i]: (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)) @ X2)),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl60])).
% 107.12/14.53 thf(mbox, axiom, (mbox @ X0 @ X1 @ X2) =>
% 107.12/14.53 ((((!!) @ (^[Y0 : $i]: (((((~) @ (X0 @ X2 @ Y0))) | (X1 @ Y0)))))) =
% 107.12/14.53 ($true))).
% 107.12/14.53 thf('5', plain,
% 107.12/14.53 (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 107.12/14.53 ( ( mbox @ X0 @ X1 @ X2 ) <=>
% 107.12/14.53 ( ![X7:$i]: ( ( ~( X0 @ X2 @ X7 ) ) | ( X1 @ X7 ) ) ) )),
% 107.12/14.53 inference('rw.lit', [status(esa)], [mbox])).
% 107.12/14.53 thf(zip_derived_cl62, plain,
% 107.12/14.53 (![X0 : $i]:
% 107.12/14.53 (((!!) @ (^[Y0 : $i]:
% 107.12/14.53 (((((~) @ (a @ X0 @ Y0))) |
% 107.12/14.53 ((^[Y1 : $i]: (ntpp @ paris @ france)) @ Y0))))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl61, '5'])).
% 107.12/14.53 thf(zip_derived_cl63, plain,
% 107.12/14.53 (![X0 : $i]:
% 107.12/14.53 (((!!) @ (^[Y0 : $i]:
% 107.12/14.53 (((((~) @ (a @ X0 @ Y0))) | (ntpp @ paris @ france))))))),
% 107.12/14.53 inference('ho_norm', [status(thm)], [zip_derived_cl62])).
% 107.12/14.53 thf(zip_derived_cl64, plain,
% 107.12/14.53 (![X0 : $i, X2 : $i]:
% 107.12/14.53 (((((~) @ (a @ X0 @ X2))) | (ntpp @ paris @ france)))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])).
% 107.12/14.53 thf(zip_derived_cl65, plain,
% 107.12/14.53 (![X0 : $i, X2 : $i]: (~ (a @ X0 @ X2) | (ntpp @ paris @ france))),
% 107.12/14.53 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])).
% 107.12/14.53 thf(ntpp, axiom, (ntpp @ X0 @ X1) =>
% 107.12/14.53 ((((((~) @ (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ X0) & (ec @ Y0 @ X1)))))))) &
% 107.12/14.53 (pp @ X0 @ X1)))
% 107.12/14.53 = ($true))).
% 107.12/14.53 thf('6', plain,
% 107.12/14.53 (![X0:reg,X1:reg]:
% 107.12/14.53 ( ( ntpp @ X0 @ X1 ) <=>
% 107.12/14.53 ( ( pp @ X0 @ X1 ) &
% 107.12/14.53 ( ~( ?[X6:reg]: ( ( ec @ X6 @ X0 ) & ( ec @ X6 @ X1 ) ) ) ) ) )),
% 107.12/14.53 inference('rw.lit', [status(esa)], [ntpp])).
% 107.12/14.53 thf(zip_derived_cl66, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]:
% 107.12/14.53 ( (((((~) @ (((??) @ (^[Y0 : reg]:
% 107.12/14.53 (((ec @ Y0 @ paris) & (ec @ Y0 @ france)))))))) &
% 107.12/14.53 (pp @ paris @ france)))
% 107.12/14.53 | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl65, '6'])).
% 107.12/14.53 thf(zip_derived_cl68, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]: ( (pp @ paris @ france) | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl66])).
% 107.12/14.53 thf(pp, axiom, (pp @ X0 @ X1) =>
% 107.12/14.53 ((((((~) @ (p @ X1 @ X0))) & (p @ X0 @ X1))) = ($true))).
% 107.12/14.53 thf('7', plain,
% 107.12/14.53 (![X0:reg,X1:reg]:
% 107.12/14.53 ( ( pp @ X0 @ X1 ) <=> ( ( p @ X0 @ X1 ) & ( ~( p @ X1 @ X0 ) ) ) )),
% 107.12/14.53 inference('rw.lit', [status(esa)], [pp])).
% 107.12/14.53 thf(zip_derived_cl70, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]:
% 107.12/14.53 ( (((((~) @ (p @ france @ paris))) & (p @ paris @ france)))
% 107.12/14.53 | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl68, '7'])).
% 107.12/14.53 thf(zip_derived_cl73, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]: ( (p @ paris @ france) | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl70])).
% 107.12/14.53 thf(p, axiom, (p @ X0 @ X1) =>
% 107.12/14.53 ((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ X1)))))) = ($true))).
% 107.12/14.53 thf('8', plain,
% 107.12/14.53 (![X0:reg,X1:reg]:
% 107.12/14.53 ( ( p @ X0 @ X1 ) <=>
% 107.12/14.53 ( ![X6:reg]: ( ( c @ X6 @ X0 ) => ( c @ X6 @ X1 ) ) ) )),
% 107.12/14.53 inference('rw.lit', [status(esa)], [p])).
% 107.12/14.53 thf(zip_derived_cl76, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]:
% 107.12/14.53 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ paris) => (c @ Y0 @ france))))))
% 107.12/14.53 | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl73, '8'])).
% 107.12/14.53 thf(zip_derived_cl79, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X3 : reg]:
% 107.12/14.53 ( (((c @ X3 @ paris) => (c @ X3 @ france))) | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl76])).
% 107.12/14.53 thf(zip_derived_cl83, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X3 : reg]:
% 107.12/14.53 (~ (c @ X3 @ paris) | (c @ X3 @ france) | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 107.12/14.53 thf(ax2, axiom,
% 107.12/14.53 (mvalid @ ( mbox @ fool @ ( ^[X:$i]: ( ec @ spain @ france ) ) ))).
% 107.12/14.53 thf(zip_derived_cl6, plain,
% 107.12/14.53 ( (mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france))))),
% 107.12/14.53 inference('cnf', [status(esa)], [ax2])).
% 107.12/14.53 thf(zip_derived_cl111, plain,
% 107.12/14.53 ( (((!!) @ (^[Y0 : $i]:
% 107.12/14.53 (mbox @ fool @ (^[Y1 : $i]: (ec @ spain @ france)) @ Y0))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl6, '4'])).
% 107.12/14.53 thf(zip_derived_cl112, plain,
% 107.12/14.53 (![X2 : $i]: (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france)) @ X2)),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl111])).
% 107.12/14.53 thf(zip_derived_cl113, plain,
% 107.12/14.53 (![X0 : $i]:
% 107.12/14.53 (((!!) @ (^[Y0 : $i]:
% 107.12/14.53 (((((~) @ (fool @ X0 @ Y0))) |
% 107.12/14.53 ((^[Y1 : $i]: (ec @ spain @ france)) @ Y0))))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl112, '5'])).
% 107.12/14.53 thf(zip_derived_cl114, plain,
% 107.12/14.53 (![X0 : $i]:
% 107.12/14.53 (((!!) @ (^[Y0 : $i]:
% 107.12/14.53 (((((~) @ (fool @ X0 @ Y0))) | (ec @ spain @ france))))))),
% 107.12/14.53 inference('ho_norm', [status(thm)], [zip_derived_cl113])).
% 107.12/14.53 thf(zip_derived_cl115, plain,
% 107.12/14.53 (![X0 : $i, X2 : $i]:
% 107.12/14.53 (((((~) @ (fool @ X0 @ X2))) | (ec @ spain @ france)))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl114])).
% 107.12/14.53 thf(zip_derived_cl116, plain,
% 107.12/14.53 (![X0 : $i, X2 : $i]: (~ (fool @ X0 @ X2) | (ec @ spain @ france))),
% 107.12/14.53 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl115])).
% 107.12/14.53 thf(ec, axiom, (ec @ X0 @ X1) =>
% 107.12/14.53 ((((((~) @ (o @ X0 @ X1))) & (c @ X0 @ X1))) = ($true))).
% 107.12/14.53 thf('9', plain,
% 107.12/14.53 (![X0:reg,X1:reg]:
% 107.12/14.53 ( ( ec @ X0 @ X1 ) <=> ( ( c @ X0 @ X1 ) & ( ~( o @ X0 @ X1 ) ) ) )),
% 107.12/14.53 inference('rw.lit', [status(esa)], [ec])).
% 107.12/14.53 thf(zip_derived_cl117, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]:
% 107.12/14.53 ( (((((~) @ (o @ spain @ france))) & (c @ spain @ france)))
% 107.12/14.53 | ~ (fool @ X1 @ X0))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl116, '9'])).
% 107.12/14.53 thf(zip_derived_cl118, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]: (~ (o @ spain @ france) | ~ (fool @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl117])).
% 107.12/14.53 thf(zip_derived_cl120, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]:
% 107.12/14.53 (~ (((??) @ (^[Y0 : reg]: (((p @ Y0 @ spain) & (p @ Y0 @ france))))))
% 107.12/14.53 | ~ (fool @ X1 @ X0))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl118, '2'])).
% 107.12/14.53 thf(zip_derived_cl121, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X3 : reg]:
% 107.12/14.53 (~ (((p @ X3 @ spain) & (p @ X3 @ france))) | ~ (fool @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl120])).
% 107.12/14.53 thf(zip_derived_cl122, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X3 : reg]:
% 107.12/14.53 (~ (p @ X3 @ spain) | ~ (p @ X3 @ france) | ~ (fool @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl121])).
% 107.12/14.53 thf(zip_derived_cl123, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X2 : reg]:
% 107.12/14.53 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain))))))
% 107.12/14.53 | ~ (fool @ X1 @ X0)
% 107.12/14.53 | ~ (p @ X2 @ france))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl122, '3'])).
% 107.12/14.53 thf(zip_derived_cl124, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X2 : reg]:
% 107.12/14.53 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ france))))))
% 107.12/14.53 | ~ (fool @ X1 @ X0)
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl123, '3'])).
% 107.12/14.53 thf(zip_derived_cl125, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X2 : reg]:
% 107.12/14.53 (~ (((c @ ('#sk11' @ X2) @ X2) => (c @ ('#sk11' @ X2) @ france)))
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain))))))
% 107.12/14.53 | ~ (fool @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl124])).
% 107.12/14.53 thf(zip_derived_cl126, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X2 : reg]:
% 107.12/14.53 ( (c @ ('#sk11' @ X2) @ X2)
% 107.12/14.53 | ~ (fool @ X1 @ X0)
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])).
% 107.12/14.53 thf(zip_derived_cl128, plain,
% 107.12/14.53 (![X2 : reg]:
% 107.12/14.53 ( ('#form12' @ X2)
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 107.12/14.53 define([status(thm)])).
% 107.12/14.53 thf(zip_derived_cl129, plain,
% 107.12/14.53 (![X2 : reg]:
% 107.12/14.53 (~ (((c @ ('#sk4' @ X2) @ X2) => (c @ ('#sk4' @ X2) @ spain)))
% 107.12/14.53 | ('#form12' @ X2))),
% 107.12/14.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl128])).
% 107.12/14.53 thf(zip_derived_cl133, plain,
% 107.12/14.53 (![X2 : reg]: (~ (c @ ('#sk4' @ X2) @ spain) | ('#form12' @ X2))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl129])).
% 107.12/14.53 thf(zip_derived_cl231, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 ( ('#form94' @ X0)
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91')))))))),
% 107.12/14.53 define([status(thm)])).
% 107.12/14.53 thf(zip_derived_cl232, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 (~ (((c @ ('#sk93' @ X0) @ X0) => (c @ ('#sk93' @ X0) @ '#sk91')))
% 107.12/14.53 | ('#form94' @ X0))),
% 107.12/14.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl231])).
% 107.12/14.53 thf(zip_derived_cl239, plain,
% 107.12/14.53 (![X0 : reg]: ( (c @ ('#sk93' @ X0) @ X0) | ('#form94' @ X0))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl232])).
% 107.12/14.53 thf(zip_derived_cl240, plain,
% 107.12/14.53 (![X0 : reg]: (~ (c @ ('#sk93' @ X0) @ '#sk91') | ('#form94' @ X0))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl232])).
% 107.12/14.53 thf(zip_derived_cl226, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 ( (c @ ('#sk11' @ X0) @ X0)
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91')))))))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
% 107.12/14.53 thf(zip_derived_cl231, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 ( ('#form94' @ X0)
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91')))))))),
% 107.12/14.53 define([status(thm)])).
% 107.12/14.53 thf(zip_derived_cl233, plain,
% 107.12/14.53 (![X0 : reg]: (~ ('#form94' @ X0) | (c @ ('#sk11' @ X0) @ X0))),
% 107.12/14.53 inference('renaming', [status(thm)],
% 107.12/14.53 [zip_derived_cl226, zip_derived_cl231])).
% 107.12/14.53 thf(zip_derived_cl67, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]:
% 107.12/14.53 (~ (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ paris) & (ec @ Y0 @ france))))))
% 107.12/14.53 | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl66])).
% 107.12/14.53 thf(zip_derived_cl69, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X3 : reg]:
% 107.12/14.53 (~ (((ec @ X3 @ paris) & (ec @ X3 @ france))) | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl67])).
% 107.12/14.53 thf(zip_derived_cl71, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X3 : reg]:
% 107.12/14.53 (~ (ec @ X3 @ paris) | ~ (ec @ X3 @ france) | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])).
% 107.12/14.53 thf(ec, axiom, ~ (ec @ X0 @ X1) =>
% 107.12/14.53 ((((c @ X0 @ X1) & (((~) @ (o @ X0 @ X1))))) != ($true))).
% 107.12/14.53 thf('10', plain,
% 107.12/14.53 (![X0:reg,X1:reg]:
% 107.12/14.53 ( ( ~( ec @ X0 @ X1 ) ) <=>
% 107.12/14.53 ( ~( ( c @ X0 @ X1 ) & ( ~( o @ X0 @ X1 ) ) ) ) )),
% 107.12/14.53 inference('rw.lit', [status(esa)], [ec])).
% 107.12/14.53 thf(zip_derived_cl74, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X2 : reg]:
% 107.12/14.53 (~ (((c @ X2 @ paris) & (((~) @ (o @ X2 @ paris)))))
% 107.12/14.53 | ~ (a @ X1 @ X0)
% 107.12/14.53 | ~ (ec @ X2 @ france))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl71, '10'])).
% 107.12/14.53 thf(zip_derived_cl77, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X2 : reg]:
% 107.12/14.53 (~ (((c @ X2 @ france) & (((~) @ (o @ X2 @ france)))))
% 107.12/14.53 | ~ (a @ X1 @ X0)
% 107.12/14.53 | ~ (((c @ X2 @ paris) & (((~) @ (o @ X2 @ paris))))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl74, '10'])).
% 107.12/14.53 thf(zip_derived_cl80, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X2 : reg]:
% 107.12/14.53 (~ (c @ X2 @ france)
% 107.12/14.53 | (o @ X2 @ france)
% 107.12/14.53 | ~ (((c @ X2 @ paris) & (((~) @ (o @ X2 @ paris)))))
% 107.12/14.53 | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl77])).
% 107.12/14.53 thf(o, axiom, (o @ X0 @ X1) =>
% 107.12/14.53 ((((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ X1)))))) = ($true))).
% 107.12/14.53 thf('11', plain,
% 107.12/14.53 (![X0:reg,X1:reg]:
% 107.12/14.53 ( ( o @ X0 @ X1 ) <=>
% 107.12/14.53 ( ?[X6:reg]: ( ( p @ X6 @ X0 ) & ( p @ X6 @ X1 ) ) ) )),
% 107.12/14.53 inference('rw.lit', [status(esa)], [o])).
% 107.12/14.53 thf(zip_derived_cl84, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X2 : reg]:
% 107.12/14.53 ( (((??) @ (^[Y0 : reg]: (((p @ Y0 @ X2) & (p @ Y0 @ france))))))
% 107.12/14.53 | ~ (a @ X1 @ X0)
% 107.12/14.53 | ~ (((c @ X2 @ paris) & (((~) @ (o @ X2 @ paris)))))
% 107.12/14.53 | ~ (c @ X2 @ france))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl80, '11'])).
% 107.12/14.53 thf(zip_derived_cl85, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X2 : reg]:
% 107.12/14.53 ( (((p @ ('#sk8' @ X2) @ X2) & (p @ ('#sk8' @ X2) @ france)))
% 107.12/14.53 | ~ (c @ X2 @ france)
% 107.12/14.53 | ~ (((c @ X2 @ paris) & (((~) @ (o @ X2 @ paris)))))
% 107.12/14.53 | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl84])).
% 107.12/14.53 thf(zip_derived_cl86, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X2 : reg]:
% 107.12/14.53 ( (p @ ('#sk8' @ X2) @ X2)
% 107.12/14.53 | ~ (a @ X1 @ X0)
% 107.12/14.53 | ~ (((c @ X2 @ paris) & (((~) @ (o @ X2 @ paris)))))
% 107.12/14.53 | ~ (c @ X2 @ france))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl85])).
% 107.12/14.53 thf(zip_derived_cl88, plain,
% 107.12/14.53 (![X0 : reg, X1 : $i, X2 : $i]:
% 107.12/14.53 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ ('#sk8' @ X0)) => (c @ Y0 @ X0))))))
% 107.12/14.53 | ~ (c @ X0 @ france)
% 107.12/14.53 | ~ (((c @ X0 @ paris) & (((~) @ (o @ X0 @ paris)))))
% 107.12/14.53 | ~ (a @ X2 @ X1))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl86, '8'])).
% 107.12/14.53 thf(zip_derived_cl90, plain,
% 107.12/14.53 (![X0 : reg, X1 : $i, X2 : $i, X4 : reg]:
% 107.12/14.53 ( (((c @ X4 @ ('#sk8' @ X0)) => (c @ X4 @ X0)))
% 107.12/14.53 | ~ (a @ X2 @ X1)
% 107.12/14.53 | ~ (((c @ X0 @ paris) & (((~) @ (o @ X0 @ paris)))))
% 107.12/14.53 | ~ (c @ X0 @ france))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl88])).
% 107.12/14.53 thf(zip_derived_cl92, plain,
% 107.12/14.53 (![X0 : reg, X1 : $i, X2 : $i, X4 : reg]:
% 107.12/14.53 (~ (c @ X4 @ ('#sk8' @ X0))
% 107.12/14.53 | (c @ X4 @ X0)
% 107.12/14.53 | ~ (c @ X0 @ france)
% 107.12/14.53 | ~ (((c @ X0 @ paris) & (((~) @ (o @ X0 @ paris)))))
% 107.12/14.53 | ~ (a @ X2 @ X1))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl90])).
% 107.12/14.53 thf(zip_derived_cl94, plain,
% 107.12/14.53 (![X0 : reg, X1 : $i, X2 : $i, X4 : reg]:
% 107.12/14.53 (~ (c @ X0 @ paris)
% 107.12/14.53 | (o @ X0 @ paris)
% 107.12/14.53 | ~ (a @ X2 @ X1)
% 107.12/14.53 | ~ (c @ X0 @ france)
% 107.12/14.53 | (c @ X4 @ X0)
% 107.12/14.53 | ~ (c @ X4 @ ('#sk8' @ X0)))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl92])).
% 107.12/14.53 thf(zip_derived_cl96, plain,
% 107.12/14.53 (![X0 : reg, X1 : reg, X2 : $i, X3 : $i]:
% 107.12/14.53 ( (((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ paris))))))
% 107.12/14.53 | ~ (c @ X1 @ ('#sk8' @ X0))
% 107.12/14.53 | (c @ X1 @ X0)
% 107.12/14.53 | ~ (c @ X0 @ france)
% 107.12/14.53 | ~ (a @ X3 @ X2)
% 107.12/14.53 | ~ (c @ X0 @ paris))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl94, '11'])).
% 107.12/14.53 thf(zip_derived_cl98, plain,
% 107.12/14.53 (![X0 : reg, X1 : reg, X2 : $i, X3 : $i]:
% 107.12/14.53 ( (((p @ ('#sk9' @ X0) @ X0) & (p @ ('#sk9' @ X0) @ paris)))
% 107.12/14.53 | ~ (c @ X0 @ paris)
% 107.12/14.53 | ~ (a @ X3 @ X2)
% 107.12/14.53 | ~ (c @ X0 @ france)
% 107.12/14.53 | (c @ X1 @ X0)
% 107.12/14.53 | ~ (c @ X1 @ ('#sk8' @ X0)))),
% 107.12/14.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])).
% 107.12/14.53 thf(zip_derived_cl100, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 (~ ('#form10' @ X0)
% 107.12/14.53 | (((p @ ('#sk9' @ X0) @ X0) & (p @ ('#sk9' @ X0) @ paris))))),
% 107.12/14.53 define([status(thm)])).
% 107.12/14.53 thf(zip_derived_cl102, plain,
% 107.12/14.53 (![X0 : reg]: ( (p @ ('#sk9' @ X0) @ paris) | ~ ('#form10' @ X0))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl100])).
% 107.12/14.53 thf(zip_derived_cl106, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 ( (((!!) @ (^[Y0 : reg]:
% 107.12/14.53 (((c @ Y0 @ ('#sk9' @ X0)) => (c @ Y0 @ paris))))))
% 107.12/14.53 | ~ ('#form10' @ X0))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl102, '8'])).
% 107.12/14.53 thf(zip_derived_cl108, plain,
% 107.12/14.53 (![X0 : reg, X2 : reg]:
% 107.12/14.53 ( (((c @ X2 @ ('#sk9' @ X0)) => (c @ X2 @ paris)))
% 107.12/14.53 | ~ ('#form10' @ X0))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl106])).
% 107.12/14.53 thf(zip_derived_cl110, plain,
% 107.12/14.53 (![X0 : reg, X2 : reg]:
% 107.12/14.53 (~ (c @ X2 @ ('#sk9' @ X0)) | (c @ X2 @ paris) | ~ ('#form10' @ X0))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])).
% 107.12/14.53 thf(zip_derived_cl101, plain,
% 107.12/14.53 (![X0 : reg]: ( (p @ ('#sk9' @ X0) @ X0) | ~ ('#form10' @ X0))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl100])).
% 107.12/14.53 thf(zip_derived_cl105, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ ('#sk9' @ X0)) => (c @ Y0 @ X0))))))
% 107.12/14.53 | ~ ('#form10' @ X0))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl101, '8'])).
% 107.12/14.53 thf(zip_derived_cl107, plain,
% 107.12/14.53 (![X0 : reg, X2 : reg]:
% 107.12/14.53 ( (((c @ X2 @ ('#sk9' @ X0)) => (c @ X2 @ X0))) | ~ ('#form10' @ X0))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl105])).
% 107.12/14.53 thf(zip_derived_cl109, plain,
% 107.12/14.53 (![X0 : reg, X2 : reg]:
% 107.12/14.53 (~ (c @ X2 @ ('#sk9' @ X0)) | (c @ X2 @ X0) | ~ ('#form10' @ X0))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])).
% 107.12/14.53 thf(zip_derived_cl132, plain,
% 107.12/14.53 (![X2 : reg]: ( (c @ ('#sk4' @ X2) @ X2) | ('#form12' @ X2))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl129])).
% 107.12/14.53 thf(ax1, axiom,
% 107.12/14.53 (mvalid @ ( mbox @ a @ ( ^[X:$i]: ( tpp @ catalunya @ spain ) ) ))).
% 107.12/14.53 thf(zip_derived_cl5, plain,
% 107.12/14.53 ( (mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain))))),
% 107.12/14.53 inference('cnf', [status(esa)], [ax1])).
% 107.12/14.53 thf(zip_derived_cl10, plain,
% 107.12/14.53 ( (((!!) @ (^[Y0 : $i]:
% 107.12/14.53 (mbox @ a @ (^[Y1 : $i]: (tpp @ catalunya @ spain)) @ Y0))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl5, '4'])).
% 107.12/14.53 thf(zip_derived_cl11, plain,
% 107.12/14.53 (![X2 : $i]: (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)) @ X2)),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])).
% 107.12/14.53 thf(zip_derived_cl12, plain,
% 107.12/14.53 (![X0 : $i]:
% 107.12/14.53 (((!!) @ (^[Y0 : $i]:
% 107.12/14.53 (((((~) @ (a @ X0 @ Y0))) |
% 107.12/14.53 ((^[Y1 : $i]: (tpp @ catalunya @ spain)) @ Y0))))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl11, '5'])).
% 107.12/14.53 thf(zip_derived_cl13, plain,
% 107.12/14.53 (![X0 : $i]:
% 107.12/14.53 (((!!) @ (^[Y0 : $i]:
% 107.12/14.53 (((((~) @ (a @ X0 @ Y0))) | (tpp @ catalunya @ spain))))))),
% 107.12/14.53 inference('ho_norm', [status(thm)], [zip_derived_cl12])).
% 107.12/14.53 thf(zip_derived_cl14, plain,
% 107.12/14.53 (![X0 : $i, X2 : $i]:
% 107.12/14.53 (((((~) @ (a @ X0 @ X2))) | (tpp @ catalunya @ spain)))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])).
% 107.12/14.53 thf(zip_derived_cl15, plain,
% 107.12/14.53 (![X0 : $i, X2 : $i]: (~ (a @ X0 @ X2) | (tpp @ catalunya @ spain))),
% 107.12/14.53 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl14])).
% 107.12/14.53 thf(tpp, axiom, (tpp @ X0 @ X1) =>
% 107.12/14.53 ((((((??) @ (^[Y0 : reg]: (((ec @ Y0 @ X0) & (ec @ Y0 @ X1)))))) & (pp @
% 107.12/14.53 X0 @ X1)))
% 107.12/14.53 = ($true))).
% 107.12/14.53 thf('12', plain,
% 107.12/14.53 (![X0:reg,X1:reg]:
% 107.12/14.53 ( ( tpp @ X0 @ X1 ) <=>
% 107.12/14.53 ( ( pp @ X0 @ X1 ) &
% 107.12/14.53 ( ?[X6:reg]: ( ( ec @ X6 @ X0 ) & ( ec @ X6 @ X1 ) ) ) ) )),
% 107.12/14.53 inference('rw.lit', [status(esa)], [tpp])).
% 107.12/14.53 thf(zip_derived_cl16, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]:
% 107.12/14.53 ( (((((??) @ (^[Y0 : reg]:
% 107.12/14.53 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ spain)))))) &
% 107.12/14.53 (pp @ catalunya @ spain)))
% 107.12/14.53 | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl15, '12'])).
% 107.12/14.53 thf(zip_derived_cl18, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]: ( (pp @ catalunya @ spain) | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl16])).
% 107.12/14.53 thf(zip_derived_cl20, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]:
% 107.12/14.53 ( (((((~) @ (p @ spain @ catalunya))) & (p @ catalunya @ spain)))
% 107.12/14.53 | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl18, '7'])).
% 107.12/14.53 thf(zip_derived_cl24, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]: ( (p @ catalunya @ spain) | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl20])).
% 107.12/14.53 thf(zip_derived_cl28, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i]:
% 107.12/14.53 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ catalunya) => (c @ Y0 @ spain))))))
% 107.12/14.53 | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl24, '8'])).
% 107.12/14.53 thf(zip_derived_cl34, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X3 : reg]:
% 107.12/14.53 ( (((c @ X3 @ catalunya) => (c @ X3 @ spain))) | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])).
% 107.12/14.53 thf(zip_derived_cl39, plain,
% 107.12/14.53 (![X0 : $i, X1 : $i, X3 : reg]:
% 107.12/14.53 (~ (c @ X3 @ catalunya) | (c @ X3 @ spain) | ~ (a @ X1 @ X0))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 107.12/14.53 thf(zip_derived_cl200, plain,
% 107.12/14.53 ( (((o @ '#sk91' @ catalunya) | (o @ '#sk91' @ paris)))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl199])).
% 107.12/14.53 thf(zip_derived_cl202, plain,
% 107.12/14.53 (( (o @ '#sk91' @ catalunya) | (o @ '#sk91' @ paris))),
% 107.12/14.53 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl200])).
% 107.12/14.53 thf(zip_derived_cl205, plain,
% 107.12/14.53 (( (((??) @ (^[Y0 : reg]: (((p @ Y0 @ '#sk91') & (p @ Y0 @ catalunya))))))
% 107.12/14.53 | (o @ '#sk91' @ paris))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl202, '11'])).
% 107.12/14.53 thf(zip_derived_cl208, plain,
% 107.12/14.53 (( (((??) @ (^[Y0 : reg]: (((p @ Y0 @ '#sk91') & (p @ Y0 @ paris))))))
% 107.12/14.53 | (((??) @ (^[Y0 : reg]: (((p @ Y0 @ '#sk91') & (p @ Y0 @ catalunya)))))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl205, '11'])).
% 107.12/14.53 thf(zip_derived_cl211, plain,
% 107.12/14.53 (( (((p @ ('#sk9' @ '#sk91') @ '#sk91') & (p @ ('#sk9' @ '#sk91') @
% 107.12/14.53 paris)))
% 107.12/14.53 | (((??) @ (^[Y0 : reg]: (((p @ Y0 @ '#sk91') & (p @ Y0 @ catalunya)))))))),
% 107.12/14.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl208])).
% 107.12/14.53 thf(zip_derived_cl100, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 (~ ('#form10' @ X0)
% 107.12/14.53 | (((p @ ('#sk9' @ X0) @ X0) & (p @ ('#sk9' @ X0) @ paris))))),
% 107.12/14.53 define([status(thm)])).
% 107.12/14.53 thf(zip_derived_cl214, plain,
% 107.12/14.53 (( ('#form10' @ '#sk91')
% 107.12/14.53 | (((??) @ (^[Y0 : reg]: (((p @ Y0 @ '#sk91') & (p @ Y0 @ catalunya)))))))),
% 107.12/14.53 inference('renaming', [status(thm)],
% 107.12/14.53 [zip_derived_cl211, zip_derived_cl100])).
% 107.12/14.53 thf(zip_derived_cl217, plain,
% 107.12/14.53 (( (((p @ '#sk92' @ '#sk91') & (p @ '#sk92' @ catalunya)))
% 107.12/14.53 | ('#form10' @ '#sk91'))),
% 107.12/14.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl214])).
% 107.12/14.53 thf(zip_derived_cl221, plain,
% 107.12/14.53 (( (p @ '#sk92' @ catalunya) | ('#form10' @ '#sk91'))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl217])).
% 107.12/14.53 thf(zip_derived_cl225, plain,
% 107.12/14.53 (( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ '#sk92') => (c @ Y0 @ catalunya))))))
% 107.12/14.53 | ('#form10' @ '#sk91'))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl221, '8'])).
% 107.12/14.53 thf(zip_derived_cl230, plain,
% 107.12/14.53 (![X2 : reg]:
% 107.12/14.53 ( (((c @ X2 @ '#sk92') => (c @ X2 @ catalunya)))
% 107.12/14.53 | ('#form10' @ '#sk91'))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl225])).
% 107.12/14.53 thf(zip_derived_cl238, plain,
% 107.12/14.53 (![X2 : reg]:
% 107.12/14.53 (~ (c @ X2 @ '#sk92') | (c @ X2 @ catalunya) | ('#form10' @ '#sk91'))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl230])).
% 107.12/14.53 thf(zip_derived_cl204, plain, (~ (o @ '#sk91' @ spain)),
% 107.12/14.53 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl201])).
% 107.12/14.53 thf(zip_derived_cl207, plain,
% 107.12/14.53 (~ (((??) @ (^[Y0 : reg]: (((p @ Y0 @ '#sk91') & (p @ Y0 @ spain))))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl204, '2'])).
% 107.12/14.53 thf(zip_derived_cl210, plain,
% 107.12/14.53 (![X2 : reg]: ~ (((p @ X2 @ '#sk91') & (p @ X2 @ spain)))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl207])).
% 107.12/14.53 thf(zip_derived_cl213, plain,
% 107.12/14.53 (![X2 : reg]: (~ (p @ X2 @ '#sk91') | ~ (p @ X2 @ spain))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl210])).
% 107.12/14.53 thf(zip_derived_cl216, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91'))))))
% 107.12/14.53 | ~ (p @ X0 @ spain))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl213, '3'])).
% 107.12/14.53 thf(zip_derived_cl219, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ spain))))))
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91')))))))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl216, '3'])).
% 107.12/14.53 thf(zip_derived_cl128, plain,
% 107.12/14.53 (![X2 : reg]:
% 107.12/14.53 ( ('#form12' @ X2)
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 107.12/14.53 define([status(thm)])).
% 107.12/14.53 thf(zip_derived_cl223, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 (~ ('#form12' @ X0)
% 107.12/14.53 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91')))))))),
% 107.12/14.53 inference('renaming', [status(thm)],
% 107.12/14.53 [zip_derived_cl219, zip_derived_cl128])).
% 107.12/14.53 thf(zip_derived_cl228, plain,
% 107.12/14.53 (![X0 : reg]:
% 107.12/14.53 (~ (((c @ ('#sk93' @ X0) @ X0) => (c @ ('#sk93' @ X0) @ '#sk91')))
% 107.12/14.53 | ~ ('#form12' @ X0))),
% 107.12/14.53 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl223])).
% 107.12/14.53 thf(zip_derived_cl236, plain,
% 107.12/14.53 (![X0 : reg]: (~ (c @ ('#sk93' @ X0) @ '#sk91') | ~ ('#form12' @ X0))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl228])).
% 107.12/14.53 thf(zip_derived_cl235, plain,
% 107.12/14.53 (![X0 : reg]: ( (c @ ('#sk93' @ X0) @ X0) | ~ ('#form12' @ X0))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl228])).
% 107.12/14.53 thf(zip_derived_cl220, plain,
% 107.12/14.53 (( (p @ '#sk92' @ '#sk91') | ('#form10' @ '#sk91'))),
% 107.12/14.53 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl217])).
% 107.12/14.53 thf(zip_derived_cl224, plain,
% 107.12/14.53 (( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ '#sk92') => (c @ Y0 @ '#sk91'))))))
% 107.12/14.53 | ('#form10' @ '#sk91'))),
% 107.12/14.53 inference('rw_clause', [status(thm)], [zip_derived_cl220, '8'])).
% 107.12/14.53 thf(zip_derived_cl229, plain,
% 107.12/14.53 (![X2 : reg]:
% 107.12/14.53 ( (((c @ X2 @ '#sk92') => (c @ X2 @ '#sk91')))
% 107.12/14.53 | ('#form10' @ '#sk91'))),
% 107.12/14.53 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl224])).
% 107.12/14.53 thf(zip_derived_cl237, plain,
% 107.12/14.53 (![X2 : reg]:
% 107.12/14.53 (~ (c @ X2 @ '#sk92') | (c @ X2 @ '#sk91') | ('#form10' @ '#sk91'))),
% 107.12/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl229])).
% 107.12/14.53 thf(zip_derived_cl20079, plain, ($false),
% 107.12/14.53 inference('eprover', [status(thm)],
% 107.12/14.53 [zip_derived_cl197, zip_derived_cl234, zip_derived_cl83,
% 107.12/14.53 zip_derived_cl133, zip_derived_cl239, zip_derived_cl240,
% 107.12/14.53 zip_derived_cl233, zip_derived_cl110, zip_derived_cl109,
% 107.12/14.53 zip_derived_cl132, zip_derived_cl39, zip_derived_cl238,
% 107.12/14.53 zip_derived_cl236, zip_derived_cl235, zip_derived_cl237])).
% 107.12/14.53
% 107.12/14.53 % SZS output end Refutation
% 107.12/14.53
% 107.12/14.53
% 107.12/14.53 % Terminating...
% 107.12/14.59 % Runner terminated.
% 107.12/14.60 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------