TSTP Solution File: GEG012^1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GEG012^1 : 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.6NaVzJ0Bzq 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 22:42:15 EDT 2023
% Result : Theorem 108.10s 14.78s
% Output : Refutation 108.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEG012^1 : 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.6NaVzJ0Bzq true
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 01:18:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.21/0.66 % Total configuration time : 828
% 0.21/0.66 % Estimated wc time : 1656
% 0.21/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.34/0.80 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.34/0.81 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 108.10/14.78 % Solved by lams/30_b.l.sh.
% 108.10/14.78 % done 2323 iterations in 13.862s
% 108.10/14.78 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 108.10/14.78 % SZS output start Refutation
% 108.10/14.78 thf(reg_type, type, reg: $tType).
% 108.10/14.78 thf('#form12_type', type, '#form12': reg > $o).
% 108.10/14.78 thf('#sk98_type', type, '#sk98': reg > reg).
% 108.10/14.78 thf('#sk8_type', type, '#sk8': reg > reg).
% 108.10/14.78 thf('#sk89_type', type, '#sk89': $i).
% 108.10/14.78 thf(mbox_type, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 108.10/14.78 thf('#sk90_type', type, '#sk90': $i).
% 108.10/14.78 thf(paris_type, type, paris: reg).
% 108.10/14.78 thf(ntpp_type, type, ntpp: reg > reg > $o).
% 108.10/14.78 thf('#sk100_type', type, '#sk100': reg).
% 108.10/14.78 thf(a_type, type, a: $i > $i > $o).
% 108.10/14.78 thf(pp_type, type, pp: reg > reg > $o).
% 108.10/14.78 thf('#sk101_type', type, '#sk101': reg).
% 108.10/14.78 thf(fool_type, type, fool: $i > $i > $o).
% 108.10/14.78 thf('#sk107_type', type, '#sk107': reg > reg).
% 108.10/14.78 thf('#sk91_type', type, '#sk91': reg).
% 108.10/14.78 thf('#form108_type', type, '#form108': reg > $o).
% 108.10/14.78 thf('#form94_type', type, '#form94': $o).
% 108.10/14.78 thf(france_type, type, france: reg).
% 108.10/14.78 thf('#form104_type', type, '#form104': reg > $o).
% 108.10/14.78 thf('#form92_type', type, '#form92': $o).
% 108.10/14.78 thf('#sk102_type', type, '#sk102': reg > reg).
% 108.10/14.78 thf('#sk11_type', type, '#sk11': reg > reg).
% 108.10/14.78 thf('#sk105_type', type, '#sk105': reg > reg).
% 108.10/14.78 thf('#sk93_type', type, '#sk93': reg).
% 108.10/14.78 thf(ec_type, type, ec: reg > reg > $o).
% 108.10/14.78 thf('#sk4_type', type, '#sk4': reg > reg).
% 108.10/14.78 thf('#form96_type', type, '#form96': reg > $o).
% 108.10/14.78 thf(o_type, type, o: reg > reg > $o).
% 108.10/14.78 thf('#sk97_type', type, '#sk97': reg).
% 108.10/14.78 thf('#form99_type', type, '#form99': $o).
% 108.10/14.78 thf('#sk3_type', type, '#sk3': reg > reg).
% 108.10/14.78 thf(c_type, type, c: reg > reg > $o).
% 108.10/14.78 thf('#sk2_type', type, '#sk2': reg).
% 108.10/14.78 thf('#sk7_type', type, '#sk7': reg).
% 108.10/14.78 thf(p_type, type, p: reg > reg > $o).
% 108.10/14.78 thf(catalunya_type, type, catalunya: reg).
% 108.10/14.78 thf('#sk95_type', type, '#sk95': reg > reg).
% 108.10/14.78 thf('#sk103_type', type, '#sk103': reg > reg).
% 108.10/14.78 thf(spain_type, type, spain: reg).
% 108.10/14.78 thf(tpp_type, type, tpp: reg > reg > $o).
% 108.10/14.78 thf('#form106_type', type, '#form106': reg > $o).
% 108.10/14.78 thf(mvalid_type, type, mvalid: ($i > $o) > $o).
% 108.10/14.78 thf(con, conjecture,
% 108.10/14.78 (mvalid @
% 108.10/14.78 ( mbox @
% 108.10/14.78 a @
% 108.10/14.78 ( ^[X:$i]:
% 108.10/14.78 ( ![X:reg]:
% 108.10/14.78 ( ( ( ntpp @ spain @ X ) & ( ntpp @ france @ X ) ) =>
% 108.10/14.78 ( ( ntpp @ catalunya @ X ) & ( ntpp @ paris @ X ) ) ) ) ) ))).
% 108.10/14.78 thf(zf_stmt_0, negated_conjecture,
% 108.10/14.78 (~( mvalid @
% 108.10/14.78 ( mbox @
% 108.10/14.78 a @
% 108.10/14.78 ( ^[X:$i]:
% 108.10/14.78 ( ![X:reg]:
% 108.10/14.78 ( ( ( ntpp @ spain @ X ) & ( ntpp @ france @ X ) ) =>
% 108.10/14.78 ( ( ntpp @ catalunya @ X ) & ( ntpp @ paris @ X ) ) ) ) ) ) )),
% 108.10/14.78 inference('cnf.neg', [status(esa)], [con])).
% 108.10/14.78 thf(zip_derived_cl8, plain,
% 108.10/14.78 (~ (mvalid @
% 108.10/14.78 (mbox @ a @
% 108.10/14.78 (^[Y0 : $i]:
% 108.10/14.78 (((!!) @ (^[Y1 : reg]:
% 108.10/14.78 (((((ntpp @ spain @ Y1) & (ntpp @ france @ Y1))) =>
% 108.10/14.78 (((ntpp @ catalunya @ Y1) & (ntpp @ paris @ Y1)))))))))))),
% 108.10/14.78 inference('cnf', [status(esa)], [zf_stmt_0])).
% 108.10/14.78 thf(mvalid, axiom, ~ (mvalid @ X0) =>
% 108.10/14.78 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))).
% 108.10/14.78 thf('0', plain,
% 108.10/14.78 (![X0:( $i > $o )]:
% 108.10/14.78 ( ( ~( mvalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [mvalid])).
% 108.10/14.78 thf(zip_derived_cl192, plain,
% 108.10/14.78 (~ (((!!) @ (^[Y0 : $i]:
% 108.10/14.78 (mbox @ a @
% 108.10/14.78 (^[Y1 : $i]:
% 108.10/14.78 (((!!) @ (^[Y2 : reg]:
% 108.10/14.78 (((((ntpp @ spain @ Y2) & (ntpp @
% 108.10/14.78 france @ Y2))) =>
% 108.10/14.78 (((ntpp @ catalunya @ Y2) & (ntpp @
% 108.10/14.78 paris @ Y2))))))))) @
% 108.10/14.78 Y0))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl8, '0'])).
% 108.10/14.78 thf(zip_derived_cl193, plain,
% 108.10/14.78 (~ (mbox @ a @
% 108.10/14.78 (^[Y0 : $i]:
% 108.10/14.78 (((!!) @ (^[Y1 : reg]:
% 108.10/14.78 (((((ntpp @ spain @ Y1) & (ntpp @ france @ Y1))) =>
% 108.10/14.78 (((ntpp @ catalunya @ Y1) & (ntpp @ paris @ Y1))))))))) @
% 108.10/14.78 '#sk89')),
% 108.10/14.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl192])).
% 108.10/14.78 thf(mbox, axiom, ~ (mbox @ X0 @ X1 @ X2) =>
% 108.10/14.78 ((((!!) @ (^[Y0 : $i]: (((((~) @ (X0 @ X2 @ Y0))) | (X1 @ Y0)))))) !=
% 108.10/14.78 ($true))).
% 108.10/14.78 thf('1', plain,
% 108.10/14.78 (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 108.10/14.78 ( ( ~( mbox @ X0 @ X1 @ X2 ) ) <=>
% 108.10/14.78 ( ~( ![X7:$i]: ( ( ~( X0 @ X2 @ X7 ) ) | ( X1 @ X7 ) ) ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [mbox])).
% 108.10/14.78 thf(zip_derived_cl194, plain,
% 108.10/14.78 (~ (((!!) @ (^[Y0 : $i]:
% 108.10/14.78 (((((~) @ (a @ '#sk89' @ Y0))) |
% 108.10/14.78 ((^[Y1 : $i]:
% 108.10/14.78 (((!!) @ (^[Y2 : reg]:
% 108.10/14.78 (((((ntpp @ spain @ Y2) & (ntpp @
% 108.10/14.78 france @ Y2))) =>
% 108.10/14.78 (((ntpp @ catalunya @ Y2) & (ntpp @
% 108.10/14.78 paris @ Y2))))))))) @
% 108.10/14.78 Y0))))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl193, '1'])).
% 108.10/14.78 thf(zip_derived_cl195, plain,
% 108.10/14.78 (~ (((!!) @ (^[Y0 : $i]:
% 108.10/14.78 (((((~) @ (a @ '#sk89' @ Y0))) |
% 108.10/14.78 (((!!) @ (^[Y1 : reg]:
% 108.10/14.78 (((((ntpp @ spain @ Y1) & (ntpp @ france @
% 108.10/14.78 Y1))) =>
% 108.10/14.78 (((ntpp @ catalunya @ Y1) & (ntpp @
% 108.10/14.78 paris @ Y1)))))))))))))),
% 108.10/14.78 inference('ho_norm', [status(thm)], [zip_derived_cl194])).
% 108.10/14.78 thf(zip_derived_cl196, plain,
% 108.10/14.78 (~ (((((~) @ (a @ '#sk89' @ '#sk90'))) |
% 108.10/14.78 (((!!) @ (^[Y0 : reg]:
% 108.10/14.78 (((((ntpp @ spain @ Y0) & (ntpp @ france @ Y0))) =>
% 108.10/14.78 (((ntpp @ catalunya @ Y0) & (ntpp @ paris @ Y0))))))))))),
% 108.10/14.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl195])).
% 108.10/14.78 thf(zip_derived_cl198, plain,
% 108.10/14.78 (~ (((!!) @ (^[Y0 : reg]:
% 108.10/14.78 (((((ntpp @ spain @ Y0) & (ntpp @ france @ Y0))) =>
% 108.10/14.78 (((ntpp @ catalunya @ Y0) & (ntpp @ paris @ Y0))))))))),
% 108.10/14.78 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl196])).
% 108.10/14.78 thf(zip_derived_cl199, plain,
% 108.10/14.78 (~ (((((ntpp @ spain @ '#sk91') & (ntpp @ france @ '#sk91'))) =>
% 108.10/14.78 (((ntpp @ catalunya @ '#sk91') & (ntpp @ paris @ '#sk91')))))),
% 108.10/14.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl198])).
% 108.10/14.78 thf(zip_derived_cl201, plain,
% 108.10/14.78 (~ (((ntpp @ catalunya @ '#sk91') & (ntpp @ paris @ '#sk91')))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl199])).
% 108.10/14.78 thf(zip_derived_cl204, plain,
% 108.10/14.78 ((~ (ntpp @ catalunya @ '#sk91') | ~ (ntpp @ paris @ '#sk91'))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl201])).
% 108.10/14.78 thf(ntpp, axiom, ~ (ntpp @ X0 @ X1) =>
% 108.10/14.78 ((((pp @ X0 @ X1) &
% 108.10/14.78 (((~) @ (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ X0) & (ec @ Y0 @ X1))))))))))
% 108.10/14.78 != ($true))).
% 108.10/14.78 thf('2', plain,
% 108.10/14.78 (![X0:reg,X1:reg]:
% 108.10/14.78 ( ( ~( ntpp @ X0 @ X1 ) ) <=>
% 108.10/14.78 ( ~( ( pp @ X0 @ X1 ) &
% 108.10/14.78 ( ~( ?[X6:reg]: ( ( ec @ X6 @ X0 ) & ( ec @ X6 @ X1 ) ) ) ) ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [ntpp])).
% 108.10/14.78 thf(zip_derived_cl207, plain,
% 108.10/14.78 ((~ (((pp @ catalunya @ '#sk91') &
% 108.10/14.78 (((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91'))))))))))
% 108.10/14.78 | ~ (ntpp @ paris @ '#sk91'))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl204, '2'])).
% 108.10/14.78 thf(zip_derived_cl212, plain,
% 108.10/14.78 ((~ (((pp @ paris @ '#sk91') &
% 108.10/14.78 (((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ paris) & (ec @ Y0 @ '#sk91'))))))))))
% 108.10/14.78 | ~ (((pp @ catalunya @ '#sk91') &
% 108.10/14.78 (((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91')))))))))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl207, '2'])).
% 108.10/14.78 thf(zip_derived_cl217, plain,
% 108.10/14.78 ((~ (pp @ paris @ '#sk91')
% 108.10/14.78 | (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ paris) & (ec @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ~ (((pp @ catalunya @ '#sk91') &
% 108.10/14.78 (((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91')))))))))))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl212])).
% 108.10/14.78 thf(pp, axiom, ~ (pp @ X0 @ X1) =>
% 108.10/14.78 ((((p @ X0 @ X1) & (((~) @ (p @ X1 @ X0))))) != ($true))).
% 108.10/14.78 thf('3', plain,
% 108.10/14.78 (![X0:reg,X1:reg]:
% 108.10/14.78 ( ( ~( pp @ X0 @ X1 ) ) <=>
% 108.10/14.78 ( ~( ( p @ X0 @ X1 ) & ( ~( p @ X1 @ X0 ) ) ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [pp])).
% 108.10/14.78 thf(zip_derived_cl224, plain,
% 108.10/14.78 ((~ (((p @ paris @ '#sk91') & (((~) @ (p @ '#sk91' @ paris)))))
% 108.10/14.78 | ~ (((pp @ catalunya @ '#sk91') &
% 108.10/14.78 (((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91'))))))))))
% 108.10/14.78 | (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ paris) & (ec @ Y0 @ '#sk91')))))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl217, '3'])).
% 108.10/14.78 thf(zip_derived_cl231, plain,
% 108.10/14.78 ((~ (p @ paris @ '#sk91')
% 108.10/14.78 | (p @ '#sk91' @ paris)
% 108.10/14.78 | (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ paris) & (ec @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ~ (((pp @ catalunya @ '#sk91') &
% 108.10/14.78 (((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91')))))))))))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl224])).
% 108.10/14.78 thf(zip_derived_cl231, plain,
% 108.10/14.78 ((~ (p @ paris @ '#sk91')
% 108.10/14.78 | (p @ '#sk91' @ paris)
% 108.10/14.78 | (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ paris) & (ec @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ~ (((pp @ catalunya @ '#sk91') &
% 108.10/14.78 (((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91')))))))))))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl224])).
% 108.10/14.78 thf(zip_derived_cl238, plain,
% 108.10/14.78 ((~ ('#form92')
% 108.10/14.78 | (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ paris) & (ec @ Y0 @ '#sk91')))))))),
% 108.10/14.78 define([status(thm)])).
% 108.10/14.78 thf(zip_derived_cl240, plain,
% 108.10/14.78 (( ('#form92')
% 108.10/14.78 | ~ (((pp @ catalunya @ '#sk91') &
% 108.10/14.78 (((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91'))))))))))
% 108.10/14.78 | (p @ '#sk91' @ paris)
% 108.10/14.78 | ~ (p @ paris @ '#sk91'))),
% 108.10/14.78 inference('renaming', [status(thm)],
% 108.10/14.78 [zip_derived_cl231, zip_derived_cl238])).
% 108.10/14.78 thf(zip_derived_cl240, plain,
% 108.10/14.78 (( ('#form92')
% 108.10/14.78 | ~ (((pp @ catalunya @ '#sk91') &
% 108.10/14.78 (((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91'))))))))))
% 108.10/14.78 | (p @ '#sk91' @ paris)
% 108.10/14.78 | ~ (p @ paris @ '#sk91'))),
% 108.10/14.78 inference('renaming', [status(thm)],
% 108.10/14.78 [zip_derived_cl231, zip_derived_cl238])).
% 108.10/14.78 thf(zip_derived_cl247, plain,
% 108.10/14.78 (( ('#form94')
% 108.10/14.78 | ~ (((pp @ catalunya @ '#sk91') &
% 108.10/14.78 (((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91')))))))))))),
% 108.10/14.78 define([status(thm)])).
% 108.10/14.78 thf(zip_derived_cl249, plain,
% 108.10/14.78 ((~ ('#form94')
% 108.10/14.78 | ~ (p @ paris @ '#sk91')
% 108.10/14.78 | (p @ '#sk91' @ paris)
% 108.10/14.78 | ('#form92'))),
% 108.10/14.78 inference('renaming', [status(thm)],
% 108.10/14.78 [zip_derived_cl240, zip_derived_cl247])).
% 108.10/14.78 thf(p, axiom, ~ (p @ X0 @ X1) =>
% 108.10/14.78 ((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ X1)))))) != ($true))).
% 108.10/14.78 thf('4', plain,
% 108.10/14.78 (![X0:reg,X1:reg]:
% 108.10/14.78 ( ( ~( p @ X0 @ X1 ) ) <=>
% 108.10/14.78 ( ~( ![X6:reg]: ( ( c @ X6 @ X0 ) => ( c @ X6 @ X1 ) ) ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [p])).
% 108.10/14.78 thf(zip_derived_cl254, plain,
% 108.10/14.78 ((~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ paris) => (c @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ('#form92')
% 108.10/14.78 | (p @ '#sk91' @ paris)
% 108.10/14.78 | ~ ('#form94'))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl249, '4'])).
% 108.10/14.78 thf(p, axiom, (p @ X0 @ X1) =>
% 108.10/14.78 ((((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ X1)))))) = ($true))).
% 108.10/14.78 thf('5', plain,
% 108.10/14.78 (![X0:reg,X1:reg]:
% 108.10/14.78 ( ( p @ X0 @ X1 ) <=>
% 108.10/14.78 ( ![X6:reg]: ( ( c @ X6 @ X0 ) => ( c @ X6 @ X1 ) ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [p])).
% 108.10/14.78 thf(zip_derived_cl260, plain,
% 108.10/14.78 (( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ '#sk91') => (c @ Y0 @ paris))))))
% 108.10/14.78 | ~ ('#form94')
% 108.10/14.78 | ('#form92')
% 108.10/14.78 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ paris) => (c @ Y0 @ '#sk91')))))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl254, '5'])).
% 108.10/14.78 thf(zip_derived_cl271, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 ( (((c @ X2 @ '#sk91') => (c @ X2 @ paris)))
% 108.10/14.78 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ paris) => (c @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ('#form92')
% 108.10/14.78 | ~ ('#form94'))),
% 108.10/14.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl260])).
% 108.10/14.78 thf(zip_derived_cl279, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 (~ (c @ X2 @ '#sk91')
% 108.10/14.78 | (c @ X2 @ paris)
% 108.10/14.78 | ~ ('#form94')
% 108.10/14.78 | ('#form92')
% 108.10/14.78 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ paris) => (c @ Y0 @ '#sk91')))))))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl271])).
% 108.10/14.78 thf(zip_derived_cl287, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 (~ (((c @ '#sk97' @ paris) => (c @ '#sk97' @ '#sk91')))
% 108.10/14.78 | ('#form92')
% 108.10/14.78 | ~ ('#form94')
% 108.10/14.78 | (c @ X2 @ paris)
% 108.10/14.78 | ~ (c @ X2 @ '#sk91'))),
% 108.10/14.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl279])).
% 108.10/14.78 thf(zip_derived_cl296, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 (~ (c @ '#sk97' @ '#sk91')
% 108.10/14.78 | ~ (c @ X2 @ '#sk91')
% 108.10/14.78 | (c @ X2 @ paris)
% 108.10/14.78 | ~ ('#form94')
% 108.10/14.78 | ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl287])).
% 108.10/14.78 thf(zip_derived_cl197, plain, ( (a @ '#sk89' @ '#sk90')),
% 108.10/14.78 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl196])).
% 108.10/14.78 thf(ax3, axiom,
% 108.10/14.78 (mvalid @ ( mbox @ a @ ( ^[X:$i]: ( ntpp @ paris @ france ) ) ))).
% 108.10/14.78 thf(zip_derived_cl7, plain,
% 108.10/14.78 ( (mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france))))),
% 108.10/14.78 inference('cnf', [status(esa)], [ax3])).
% 108.10/14.78 thf(mvalid, axiom, (mvalid @ X0) =>
% 108.10/14.78 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))).
% 108.10/14.78 thf('6', plain,
% 108.10/14.78 (![X0:( $i > $o )]: ( ( mvalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [mvalid])).
% 108.10/14.78 thf(zip_derived_cl60, plain,
% 108.10/14.78 ( (((!!) @ (^[Y0 : $i]:
% 108.10/14.78 (mbox @ a @ (^[Y1 : $i]: (ntpp @ paris @ france)) @ Y0))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl7, '6'])).
% 108.10/14.78 thf(zip_derived_cl61, plain,
% 108.10/14.78 (![X2 : $i]: (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)) @ X2)),
% 108.10/14.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl60])).
% 108.10/14.78 thf(mbox, axiom, (mbox @ X0 @ X1 @ X2) =>
% 108.10/14.78 ((((!!) @ (^[Y0 : $i]: (((((~) @ (X0 @ X2 @ Y0))) | (X1 @ Y0)))))) =
% 108.10/14.78 ($true))).
% 108.10/14.78 thf('7', plain,
% 108.10/14.78 (![X0:( $i > $i > $o ),X1:( $i > $o ),X2:$i]:
% 108.10/14.78 ( ( mbox @ X0 @ X1 @ X2 ) <=>
% 108.10/14.78 ( ![X7:$i]: ( ( ~( X0 @ X2 @ X7 ) ) | ( X1 @ X7 ) ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [mbox])).
% 108.10/14.78 thf(zip_derived_cl62, plain,
% 108.10/14.78 (![X0 : $i]:
% 108.10/14.78 (((!!) @ (^[Y0 : $i]:
% 108.10/14.78 (((((~) @ (a @ X0 @ Y0))) |
% 108.10/14.78 ((^[Y1 : $i]: (ntpp @ paris @ france)) @ Y0))))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl61, '7'])).
% 108.10/14.78 thf(zip_derived_cl63, plain,
% 108.10/14.78 (![X0 : $i]:
% 108.10/14.78 (((!!) @ (^[Y0 : $i]:
% 108.10/14.78 (((((~) @ (a @ X0 @ Y0))) | (ntpp @ paris @ france))))))),
% 108.10/14.78 inference('ho_norm', [status(thm)], [zip_derived_cl62])).
% 108.10/14.78 thf(zip_derived_cl64, plain,
% 108.10/14.78 (![X0 : $i, X2 : $i]:
% 108.10/14.78 (((((~) @ (a @ X0 @ X2))) | (ntpp @ paris @ france)))),
% 108.10/14.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])).
% 108.10/14.78 thf(zip_derived_cl65, plain,
% 108.10/14.78 (![X0 : $i, X2 : $i]: (~ (a @ X0 @ X2) | (ntpp @ paris @ france))),
% 108.10/14.78 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])).
% 108.10/14.78 thf(ntpp, axiom, (ntpp @ X0 @ X1) =>
% 108.10/14.78 ((((((~) @ (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ X0) & (ec @ Y0 @ X1)))))))) &
% 108.10/14.78 (pp @ X0 @ X1)))
% 108.10/14.78 = ($true))).
% 108.10/14.78 thf('8', plain,
% 108.10/14.78 (![X0:reg,X1:reg]:
% 108.10/14.78 ( ( ntpp @ X0 @ X1 ) <=>
% 108.10/14.78 ( ( pp @ X0 @ X1 ) &
% 108.10/14.78 ( ~( ?[X6:reg]: ( ( ec @ X6 @ X0 ) & ( ec @ X6 @ X1 ) ) ) ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [ntpp])).
% 108.10/14.78 thf(zip_derived_cl66, plain,
% 108.10/14.78 (![X0 : $i, X1 : $i]:
% 108.10/14.78 ( (((((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ paris) & (ec @ Y0 @ france)))))))) &
% 108.10/14.78 (pp @ paris @ france)))
% 108.10/14.78 | ~ (a @ X1 @ X0))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl65, '8'])).
% 108.10/14.78 thf(zip_derived_cl68, plain,
% 108.10/14.78 (![X0 : $i, X1 : $i]: ( (pp @ paris @ france) | ~ (a @ X1 @ X0))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl66])).
% 108.10/14.78 thf(pp, axiom, (pp @ X0 @ X1) =>
% 108.10/14.78 ((((((~) @ (p @ X1 @ X0))) & (p @ X0 @ X1))) = ($true))).
% 108.10/14.78 thf('9', plain,
% 108.10/14.78 (![X0:reg,X1:reg]:
% 108.10/14.78 ( ( pp @ X0 @ X1 ) <=> ( ( p @ X0 @ X1 ) & ( ~( p @ X1 @ X0 ) ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [pp])).
% 108.10/14.78 thf(zip_derived_cl70, plain,
% 108.10/14.78 (![X0 : $i, X1 : $i]:
% 108.10/14.78 ( (((((~) @ (p @ france @ paris))) & (p @ paris @ france)))
% 108.10/14.78 | ~ (a @ X1 @ X0))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl68, '9'])).
% 108.10/14.78 thf(zip_derived_cl72, plain,
% 108.10/14.78 (![X0 : $i, X1 : $i]: (~ (p @ france @ paris) | ~ (a @ X1 @ X0))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl70])).
% 108.10/14.78 thf(zip_derived_cl75, plain,
% 108.10/14.78 (![X0 : $i, X1 : $i]:
% 108.10/14.78 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ france) => (c @ Y0 @ paris))))))
% 108.10/14.78 | ~ (a @ X1 @ X0))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl72, '4'])).
% 108.10/14.78 thf(zip_derived_cl78, plain,
% 108.10/14.78 (![X0 : $i, X1 : $i]:
% 108.10/14.78 (~ (((c @ '#sk7' @ france) => (c @ '#sk7' @ paris))) | ~ (a @ X1 @ X0))),
% 108.10/14.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl75])).
% 108.10/14.78 thf(zip_derived_cl82, plain,
% 108.10/14.78 (![X0 : $i, X1 : $i]: (~ (c @ '#sk7' @ paris) | ~ (a @ X1 @ X0))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])).
% 108.10/14.78 thf(zip_derived_cl377, plain, (~ (c @ '#sk7' @ paris)),
% 108.10/14.78 inference('sup-', [status(thm)], [zip_derived_cl197, zip_derived_cl82])).
% 108.10/14.78 thf(zip_derived_cl81, plain,
% 108.10/14.78 (![X0 : $i, X1 : $i]: ( (c @ '#sk7' @ france) | ~ (a @ X1 @ X0))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])).
% 108.10/14.78 thf(zip_derived_cl197, plain, ( (a @ '#sk89' @ '#sk90')),
% 108.10/14.78 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl196])).
% 108.10/14.78 thf(zip_derived_cl397, plain, ( (c @ '#sk7' @ france)),
% 108.10/14.78 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl197])).
% 108.10/14.78 thf(zip_derived_cl295, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 ( (c @ '#sk97' @ paris)
% 108.10/14.78 | ~ (c @ X2 @ '#sk91')
% 108.10/14.78 | (c @ X2 @ paris)
% 108.10/14.78 | ~ ('#form94')
% 108.10/14.78 | ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl287])).
% 108.10/14.78 thf(zip_derived_cl238, plain,
% 108.10/14.78 ((~ ('#form92')
% 108.10/14.78 | (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ paris) & (ec @ Y0 @ '#sk91')))))))),
% 108.10/14.78 define([status(thm)])).
% 108.10/14.78 thf(zip_derived_cl239, plain,
% 108.10/14.78 (( (((ec @ '#sk93' @ paris) & (ec @ '#sk93' @ '#sk91'))) | ~ ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl238])).
% 108.10/14.78 thf(zip_derived_cl250, plain, (( (ec @ '#sk93' @ paris) | ~ ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl239])).
% 108.10/14.78 thf(ec, axiom, (ec @ X0 @ X1) =>
% 108.10/14.78 ((((((~) @ (o @ X0 @ X1))) & (c @ X0 @ X1))) = ($true))).
% 108.10/14.78 thf('10', plain,
% 108.10/14.78 (![X0:reg,X1:reg]:
% 108.10/14.78 ( ( ec @ X0 @ X1 ) <=> ( ( c @ X0 @ X1 ) & ( ~( o @ X0 @ X1 ) ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [ec])).
% 108.10/14.78 thf(zip_derived_cl256, plain,
% 108.10/14.78 (( (((((~) @ (o @ '#sk93' @ paris))) & (c @ '#sk93' @ paris)))
% 108.10/14.78 | ~ ('#form92'))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl250, '10'])).
% 108.10/14.78 thf(zip_derived_cl263, plain, (( (c @ '#sk93' @ paris) | ~ ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl256])).
% 108.10/14.78 thf(zip_derived_cl200, plain,
% 108.10/14.78 ( (((ntpp @ spain @ '#sk91') & (ntpp @ france @ '#sk91')))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl199])).
% 108.10/14.78 thf(zip_derived_cl203, plain, ( (ntpp @ france @ '#sk91')),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl200])).
% 108.10/14.78 thf(zip_derived_cl206, plain,
% 108.10/14.78 ( (((((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ france) & (ec @ Y0 @ '#sk91')))))))) &
% 108.10/14.78 (pp @ france @ '#sk91')))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl203, '8'])).
% 108.10/14.78 thf(zip_derived_cl211, plain, ( (pp @ france @ '#sk91')),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl206])).
% 108.10/14.78 thf(zip_derived_cl216, plain,
% 108.10/14.78 ( (((((~) @ (p @ '#sk91' @ france))) & (p @ france @ '#sk91')))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl211, '9'])).
% 108.10/14.78 thf(zip_derived_cl223, plain, ( (p @ france @ '#sk91')),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl216])).
% 108.10/14.78 thf(zip_derived_cl230, plain,
% 108.10/14.78 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ france) => (c @ Y0 @ '#sk91'))))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl223, '5'])).
% 108.10/14.78 thf(zip_derived_cl237, plain,
% 108.10/14.78 (![X2 : reg]: (((c @ X2 @ france) => (c @ X2 @ '#sk91')))),
% 108.10/14.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl230])).
% 108.10/14.78 thf(zip_derived_cl246, plain,
% 108.10/14.78 (![X2 : reg]: (~ (c @ X2 @ france) | (c @ X2 @ '#sk91'))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl237])).
% 108.10/14.78 thf(zip_derived_cl247, plain,
% 108.10/14.78 (( ('#form94')
% 108.10/14.78 | ~ (((pp @ catalunya @ '#sk91') &
% 108.10/14.78 (((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91')))))))))))),
% 108.10/14.78 define([status(thm)])).
% 108.10/14.78 thf(zip_derived_cl248, plain,
% 108.10/14.78 ((~ (pp @ catalunya @ '#sk91')
% 108.10/14.78 | (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ('#form94'))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl247])).
% 108.10/14.78 thf(zip_derived_cl255, plain,
% 108.10/14.78 ((~ (((p @ catalunya @ '#sk91') & (((~) @ (p @ '#sk91' @ catalunya)))))
% 108.10/14.78 | ('#form94')
% 108.10/14.78 | (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91')))))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl248, '3'])).
% 108.10/14.78 thf(zip_derived_cl261, plain,
% 108.10/14.78 ((~ (p @ catalunya @ '#sk91')
% 108.10/14.78 | (p @ '#sk91' @ catalunya)
% 108.10/14.78 | (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ('#form94'))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl255])).
% 108.10/14.78 thf(zip_derived_cl272, plain,
% 108.10/14.78 ((~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ catalunya) => (c @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ('#form94')
% 108.10/14.78 | (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91'))))))
% 108.10/14.78 | (p @ '#sk91' @ catalunya))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl261, '4'])).
% 108.10/14.78 thf(zip_derived_cl280, plain,
% 108.10/14.78 (( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ '#sk91') => (c @ Y0 @ catalunya))))))
% 108.10/14.78 | (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ('#form94')
% 108.10/14.78 | ~ (((!!) @ (^[Y0 : reg]:
% 108.10/14.78 (((c @ Y0 @ catalunya) => (c @ Y0 @ '#sk91')))))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl272, '5'])).
% 108.10/14.78 thf(zip_derived_cl288, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 ( (((c @ X2 @ '#sk91') => (c @ X2 @ catalunya)))
% 108.10/14.78 | ~ (((!!) @ (^[Y0 : reg]:
% 108.10/14.78 (((c @ Y0 @ catalunya) => (c @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ('#form94')
% 108.10/14.78 | (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91')))))))),
% 108.10/14.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl280])).
% 108.10/14.78 thf(zip_derived_cl288, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 ( (((c @ X2 @ '#sk91') => (c @ X2 @ catalunya)))
% 108.10/14.78 | ~ (((!!) @ (^[Y0 : reg]:
% 108.10/14.78 (((c @ Y0 @ catalunya) => (c @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ('#form94')
% 108.10/14.78 | (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91')))))))),
% 108.10/14.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl280])).
% 108.10/14.78 thf(zip_derived_cl297, plain,
% 108.10/14.78 ((~ ('#form99')
% 108.10/14.78 | (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91')))))))),
% 108.10/14.78 define([status(thm)])).
% 108.10/14.78 thf(zip_derived_cl299, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 ( ('#form99')
% 108.10/14.78 | ('#form94')
% 108.10/14.78 | ~ (((!!) @ (^[Y0 : reg]:
% 108.10/14.78 (((c @ Y0 @ catalunya) => (c @ Y0 @ '#sk91'))))))
% 108.10/14.78 | (((c @ X2 @ '#sk91') => (c @ X2 @ catalunya))))),
% 108.10/14.78 inference('renaming', [status(thm)],
% 108.10/14.78 [zip_derived_cl288, zip_derived_cl297])).
% 108.10/14.78 thf(zip_derived_cl306, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 (~ (((c @ '#sk101' @ catalunya) => (c @ '#sk101' @ '#sk91')))
% 108.10/14.78 | (((c @ X2 @ '#sk91') => (c @ X2 @ catalunya)))
% 108.10/14.78 | ('#form94')
% 108.10/14.78 | ('#form99'))),
% 108.10/14.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl299])).
% 108.10/14.78 thf(zip_derived_cl316, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 (~ (c @ '#sk101' @ '#sk91')
% 108.10/14.78 | ('#form99')
% 108.10/14.78 | ('#form94')
% 108.10/14.78 | (((c @ X2 @ '#sk91') => (c @ X2 @ catalunya))))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl306])).
% 108.10/14.78 thf(zip_derived_cl328, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 (~ (c @ X2 @ '#sk91')
% 108.10/14.78 | (c @ X2 @ catalunya)
% 108.10/14.78 | ('#form94')
% 108.10/14.78 | ('#form99')
% 108.10/14.78 | ~ (c @ '#sk101' @ '#sk91'))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl316])).
% 108.10/14.78 thf(zip_derived_cl262, plain, ((~ (o @ '#sk93' @ paris) | ~ ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl256])).
% 108.10/14.78 thf(o, axiom, ~ (o @ X0 @ X1) =>
% 108.10/14.78 ((((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ X1)))))) != ($true))).
% 108.10/14.78 thf('11', plain,
% 108.10/14.78 (![X0:reg,X1:reg]:
% 108.10/14.78 ( ( ~( o @ X0 @ X1 ) ) <=>
% 108.10/14.78 ( ~( ?[X6:reg]: ( ( p @ X6 @ X0 ) & ( p @ X6 @ X1 ) ) ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [o])).
% 108.10/14.78 thf(zip_derived_cl273, plain,
% 108.10/14.78 ((~ (((??) @ (^[Y0 : reg]: (((p @ Y0 @ '#sk93') & (p @ Y0 @ paris))))))
% 108.10/14.78 | ~ ('#form92'))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl262, '11'])).
% 108.10/14.78 thf(zip_derived_cl281, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 (~ (((p @ X2 @ '#sk93') & (p @ X2 @ paris))) | ~ ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl273])).
% 108.10/14.78 thf(zip_derived_cl289, plain,
% 108.10/14.78 (![X2 : reg]: (~ (p @ X2 @ '#sk93') | ~ (p @ X2 @ paris) | ~ ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl281])).
% 108.10/14.78 thf(zip_derived_cl300, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk93'))))))
% 108.10/14.78 | ~ ('#form92')
% 108.10/14.78 | ~ (p @ X0 @ paris))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl289, '4'])).
% 108.10/14.78 thf(zip_derived_cl309, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ paris))))))
% 108.10/14.78 | ~ ('#form92')
% 108.10/14.78 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk93')))))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl300, '4'])).
% 108.10/14.78 thf(zip_derived_cl319, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (((c @ ('#sk102' @ X0) @ X0) => (c @ ('#sk102' @ X0) @ paris)))
% 108.10/14.78 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk93'))))))
% 108.10/14.78 | ~ ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl309])).
% 108.10/14.78 thf(zip_derived_cl333, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( ('#form104' @ X0)
% 108.10/14.78 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk93')))))))),
% 108.10/14.78 define([status(thm)])).
% 108.10/14.78 thf(zip_derived_cl334, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (((c @ ('#sk105' @ X0) @ X0) => (c @ ('#sk105' @ X0) @ '#sk93')))
% 108.10/14.78 | ('#form104' @ X0))),
% 108.10/14.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl333])).
% 108.10/14.78 thf(zip_derived_cl345, plain,
% 108.10/14.78 (![X0 : reg]: ( (c @ ('#sk105' @ X0) @ X0) | ('#form104' @ X0))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl334])).
% 108.10/14.78 thf(zip_derived_cl346, plain,
% 108.10/14.78 (![X0 : reg]: (~ (c @ ('#sk105' @ X0) @ '#sk93') | ('#form104' @ X0))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl334])).
% 108.10/14.78 thf(zip_derived_cl251, plain, (( (ec @ '#sk93' @ '#sk91') | ~ ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl239])).
% 108.10/14.78 thf(zip_derived_cl257, plain,
% 108.10/14.78 (( (((((~) @ (o @ '#sk93' @ '#sk91'))) & (c @ '#sk93' @ '#sk91')))
% 108.10/14.78 | ~ ('#form92'))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl251, '10'])).
% 108.10/14.78 thf(zip_derived_cl264, plain, ((~ (o @ '#sk93' @ '#sk91') | ~ ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl257])).
% 108.10/14.78 thf(zip_derived_cl274, plain,
% 108.10/14.78 ((~ (((??) @ (^[Y0 : reg]: (((p @ Y0 @ '#sk93') & (p @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ~ ('#form92'))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl264, '11'])).
% 108.10/14.78 thf(zip_derived_cl282, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 (~ (((p @ X2 @ '#sk93') & (p @ X2 @ '#sk91'))) | ~ ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl274])).
% 108.10/14.78 thf(zip_derived_cl290, plain,
% 108.10/14.78 (![X2 : reg]:
% 108.10/14.78 (~ (p @ X2 @ '#sk93') | ~ (p @ X2 @ '#sk91') | ~ ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl282])).
% 108.10/14.78 thf(zip_derived_cl301, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk93'))))))
% 108.10/14.78 | ~ ('#form92')
% 108.10/14.78 | ~ (p @ X0 @ '#sk91'))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl290, '4'])).
% 108.10/14.78 thf(zip_derived_cl310, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ~ ('#form92')
% 108.10/14.78 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk93')))))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl301, '4'])).
% 108.10/14.78 thf(zip_derived_cl320, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (((c @ ('#sk103' @ X0) @ X0) => (c @ ('#sk103' @ X0) @ '#sk91')))
% 108.10/14.78 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk93'))))))
% 108.10/14.78 | ~ ('#form92'))),
% 108.10/14.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl310])).
% 108.10/14.78 thf(zip_derived_cl333, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( ('#form104' @ X0)
% 108.10/14.78 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk93')))))))),
% 108.10/14.78 define([status(thm)])).
% 108.10/14.78 thf(zip_derived_cl336, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ ('#form104' @ X0)
% 108.10/14.78 | ~ ('#form92')
% 108.10/14.78 | ~ (((c @ ('#sk103' @ X0) @ X0) => (c @ ('#sk103' @ X0) @ '#sk91'))))),
% 108.10/14.78 inference('renaming', [status(thm)],
% 108.10/14.78 [zip_derived_cl320, zip_derived_cl333])).
% 108.10/14.78 thf(zip_derived_cl348, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (c @ ('#sk103' @ X0) @ '#sk91')
% 108.10/14.78 | ~ ('#form92')
% 108.10/14.78 | ~ ('#form104' @ X0))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl336])).
% 108.10/14.78 thf(zip_derived_cl73, plain,
% 108.10/14.78 (![X0 : $i, X1 : $i]: ( (p @ paris @ france) | ~ (a @ X1 @ X0))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl70])).
% 108.10/14.78 thf(zip_derived_cl76, plain,
% 108.10/14.78 (![X0 : $i, X1 : $i]:
% 108.10/14.78 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ paris) => (c @ Y0 @ france))))))
% 108.10/14.78 | ~ (a @ X1 @ X0))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl73, '5'])).
% 108.10/14.78 thf(zip_derived_cl79, plain,
% 108.10/14.78 (![X0 : $i, X1 : $i, X3 : reg]:
% 108.10/14.78 ( (((c @ X3 @ paris) => (c @ X3 @ france))) | ~ (a @ X1 @ X0))),
% 108.10/14.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl76])).
% 108.10/14.78 thf(zip_derived_cl83, plain,
% 108.10/14.78 (![X0 : $i, X1 : $i, X3 : reg]:
% 108.10/14.78 (~ (c @ X3 @ paris) | (c @ X3 @ france) | ~ (a @ X1 @ X0))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 108.10/14.78 thf(zip_derived_cl210, plain,
% 108.10/14.78 (~ (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ france) & (ec @ Y0 @ '#sk91'))))))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl206])).
% 108.10/14.78 thf(zip_derived_cl215, plain,
% 108.10/14.78 (![X2 : reg]: ~ (((ec @ X2 @ france) & (ec @ X2 @ '#sk91')))),
% 108.10/14.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl210])).
% 108.10/14.78 thf(zip_derived_cl221, plain,
% 108.10/14.78 (![X2 : reg]: (~ (ec @ X2 @ france) | ~ (ec @ X2 @ '#sk91'))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl215])).
% 108.10/14.78 thf(ec, axiom, ~ (ec @ X0 @ X1) =>
% 108.10/14.78 ((((c @ X0 @ X1) & (((~) @ (o @ X0 @ X1))))) != ($true))).
% 108.10/14.78 thf('12', plain,
% 108.10/14.78 (![X0:reg,X1:reg]:
% 108.10/14.78 ( ( ~( ec @ X0 @ X1 ) ) <=>
% 108.10/14.78 ( ~( ( c @ X0 @ X1 ) & ( ~( o @ X0 @ X1 ) ) ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [ec])).
% 108.10/14.78 thf(zip_derived_cl228, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (((c @ X0 @ france) & (((~) @ (o @ X0 @ france)))))
% 108.10/14.78 | ~ (ec @ X0 @ '#sk91'))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl221, '12'])).
% 108.10/14.78 thf(zip_derived_cl235, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (((c @ X0 @ '#sk91') & (((~) @ (o @ X0 @ '#sk91')))))
% 108.10/14.78 | ~ (((c @ X0 @ france) & (((~) @ (o @ X0 @ france))))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl228, '12'])).
% 108.10/14.78 thf(zip_derived_cl243, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (c @ X0 @ '#sk91')
% 108.10/14.78 | (o @ X0 @ '#sk91')
% 108.10/14.78 | ~ (((c @ X0 @ france) & (((~) @ (o @ X0 @ france))))))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl235])).
% 108.10/14.78 thf(o, axiom, (o @ X0 @ X1) =>
% 108.10/14.78 ((((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ X1)))))) = ($true))).
% 108.10/14.78 thf('13', plain,
% 108.10/14.78 (![X0:reg,X1:reg]:
% 108.10/14.78 ( ( o @ X0 @ X1 ) <=>
% 108.10/14.78 ( ?[X6:reg]: ( ( p @ X6 @ X0 ) & ( p @ X6 @ X1 ) ) ) )),
% 108.10/14.78 inference('rw.lit', [status(esa)], [o])).
% 108.10/14.78 thf(zip_derived_cl253, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( (((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ~ (((c @ X0 @ france) & (((~) @ (o @ X0 @ france)))))
% 108.10/14.78 | ~ (c @ X0 @ '#sk91'))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl243, '13'])).
% 108.10/14.78 thf(zip_derived_cl259, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( (((p @ ('#sk95' @ X0) @ X0) & (p @ ('#sk95' @ X0) @ '#sk91')))
% 108.10/14.78 | ~ (c @ X0 @ '#sk91')
% 108.10/14.78 | ~ (((c @ X0 @ france) & (((~) @ (o @ X0 @ france))))))),
% 108.10/14.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl253])).
% 108.10/14.78 thf(zip_derived_cl202, plain, ( (ntpp @ spain @ '#sk91')),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl200])).
% 108.10/14.78 thf(zip_derived_cl205, plain,
% 108.10/14.78 ( (((((~) @ (((??) @ (^[Y0 : reg]:
% 108.10/14.78 (((ec @ Y0 @ spain) & (ec @ Y0 @ '#sk91')))))))) &
% 108.10/14.78 (pp @ spain @ '#sk91')))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl202, '8'])).
% 108.10/14.78 thf(zip_derived_cl208, plain,
% 108.10/14.78 (~ (((??) @ (^[Y0 : reg]: (((ec @ Y0 @ spain) & (ec @ Y0 @ '#sk91'))))))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl205])).
% 108.10/14.78 thf(zip_derived_cl213, plain,
% 108.10/14.78 (![X2 : reg]: ~ (((ec @ X2 @ spain) & (ec @ X2 @ '#sk91')))),
% 108.10/14.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl208])).
% 108.10/14.78 thf(zip_derived_cl218, plain,
% 108.10/14.78 (![X2 : reg]: (~ (ec @ X2 @ spain) | ~ (ec @ X2 @ '#sk91'))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl213])).
% 108.10/14.78 thf(zip_derived_cl225, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (((c @ X0 @ spain) & (((~) @ (o @ X0 @ spain)))))
% 108.10/14.78 | ~ (ec @ X0 @ '#sk91'))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl218, '12'])).
% 108.10/14.78 thf(zip_derived_cl232, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (((c @ X0 @ '#sk91') & (((~) @ (o @ X0 @ '#sk91')))))
% 108.10/14.78 | ~ (((c @ X0 @ spain) & (((~) @ (o @ X0 @ spain))))))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl225, '12'])).
% 108.10/14.78 thf(zip_derived_cl241, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (c @ X0 @ '#sk91')
% 108.10/14.78 | (o @ X0 @ '#sk91')
% 108.10/14.78 | ~ (((c @ X0 @ spain) & (((~) @ (o @ X0 @ spain))))))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl232])).
% 108.10/14.78 thf(zip_derived_cl252, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( (((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ '#sk91'))))))
% 108.10/14.78 | ~ (((c @ X0 @ spain) & (((~) @ (o @ X0 @ spain)))))
% 108.10/14.78 | ~ (c @ X0 @ '#sk91'))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl241, '13'])).
% 108.10/14.78 thf(zip_derived_cl258, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( (((p @ ('#sk95' @ X0) @ X0) & (p @ ('#sk95' @ X0) @ '#sk91')))
% 108.10/14.78 | ~ (c @ X0 @ '#sk91')
% 108.10/14.78 | ~ (((c @ X0 @ spain) & (((~) @ (o @ X0 @ spain))))))),
% 108.10/14.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl252])).
% 108.10/14.78 thf(zip_derived_cl266, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ ('#form96' @ X0)
% 108.10/14.78 | (((p @ ('#sk95' @ X0) @ X0) & (p @ ('#sk95' @ X0) @ '#sk91'))))),
% 108.10/14.78 define([status(thm)])).
% 108.10/14.78 thf(zip_derived_cl270, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( ('#form96' @ X0)
% 108.10/14.78 | ~ (((c @ X0 @ france) & (((~) @ (o @ X0 @ france)))))
% 108.10/14.78 | ~ (c @ X0 @ '#sk91'))),
% 108.10/14.78 inference('renaming', [status(thm)],
% 108.10/14.78 [zip_derived_cl259, zip_derived_cl266])).
% 108.10/14.78 thf(zip_derived_cl278, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 (~ (c @ X0 @ france)
% 108.10/14.78 | (o @ X0 @ france)
% 108.10/14.78 | ~ (c @ X0 @ '#sk91')
% 108.10/14.78 | ('#form96' @ X0))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl270])).
% 108.10/14.78 thf(zip_derived_cl286, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( (((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ france))))))
% 108.10/14.78 | ('#form96' @ X0)
% 108.10/14.78 | ~ (c @ X0 @ '#sk91')
% 108.10/14.78 | ~ (c @ X0 @ france))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl278, '13'])).
% 108.10/14.78 thf(zip_derived_cl294, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( (((p @ ('#sk8' @ X0) @ X0) & (p @ ('#sk8' @ X0) @ france)))
% 108.10/14.78 | ~ (c @ X0 @ france)
% 108.10/14.78 | ~ (c @ X0 @ '#sk91')
% 108.10/14.78 | ('#form96' @ X0))),
% 108.10/14.78 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl286])).
% 108.10/14.78 thf(zip_derived_cl304, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( (p @ ('#sk8' @ X0) @ X0)
% 108.10/14.78 | ('#form96' @ X0)
% 108.10/14.78 | ~ (c @ X0 @ '#sk91')
% 108.10/14.78 | ~ (c @ X0 @ france))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl294])).
% 108.10/14.78 thf(zip_derived_cl313, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ ('#sk8' @ X0)) => (c @ Y0 @ X0))))))
% 108.10/14.78 | ~ (c @ X0 @ france)
% 108.10/14.78 | ~ (c @ X0 @ '#sk91')
% 108.10/14.78 | ('#form96' @ X0))),
% 108.10/14.78 inference('rw_clause', [status(thm)], [zip_derived_cl304, '5'])).
% 108.10/14.78 thf(zip_derived_cl325, plain,
% 108.10/14.78 (![X0 : reg, X2 : reg]:
% 108.10/14.78 ( (((c @ X2 @ ('#sk8' @ X0)) => (c @ X2 @ X0)))
% 108.10/14.78 | ('#form96' @ X0)
% 108.10/14.78 | ~ (c @ X0 @ '#sk91')
% 108.10/14.78 | ~ (c @ X0 @ france))),
% 108.10/14.78 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl313])).
% 108.10/14.78 thf(zip_derived_cl339, plain,
% 108.10/14.78 (![X0 : reg, X2 : reg]:
% 108.10/14.78 (~ (c @ X2 @ ('#sk8' @ X0))
% 108.10/14.78 | (c @ X2 @ X0)
% 108.10/14.78 | ~ (c @ X0 @ france)
% 108.10/14.78 | ~ (c @ X0 @ '#sk91')
% 108.10/14.78 | ('#form96' @ X0))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])).
% 108.10/14.78 thf(zip_derived_cl246, plain,
% 108.10/14.78 (![X2 : reg]: (~ (c @ X2 @ france) | (c @ X2 @ '#sk91'))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl237])).
% 108.10/14.78 thf(zip_derived_cl375, plain,
% 108.10/14.78 (![X0 : reg, X2 : reg]:
% 108.10/14.78 ( ('#form96' @ X0)
% 108.10/14.78 | ~ (c @ X0 @ france)
% 108.10/14.78 | (c @ X2 @ X0)
% 108.10/14.78 | ~ (c @ X2 @ ('#sk8' @ X0)))),
% 108.10/14.78 inference('clc', [status(thm)], [zip_derived_cl339, zip_derived_cl246])).
% 108.10/14.78 thf(zip_derived_cl347, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( (c @ ('#sk103' @ X0) @ X0) | ~ ('#form92') | ~ ('#form104' @ X0))),
% 108.10/14.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl336])).
% 108.10/14.78 thf(zip_derived_cl305, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( (p @ ('#sk8' @ X0) @ france)
% 108.10/14.78 | ('#form96' @ X0)
% 108.10/14.78 | ~ (c @ X0 @ '#sk91')
% 108.10/14.78 | ~ (c @ X0 @ france))),
% 108.10/14.78 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl294])).
% 108.10/14.78 thf(zip_derived_cl314, plain,
% 108.10/14.78 (![X0 : reg]:
% 108.10/14.78 ( (((!!) @ (^[Y0 : reg]:
% 108.10/14.78 (((c @ Y0 @ ('#sk8' @ X0)) => (c @ Y0 @ france))))))
% 108.10/14.78 | ~ (c @ X0 @ france)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ('#form96' @ X0))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl305, '5'])).
% 108.10/14.79 thf(zip_derived_cl326, plain,
% 108.10/14.79 (![X0 : reg, X2 : reg]:
% 108.10/14.79 ( (((c @ X2 @ ('#sk8' @ X0)) => (c @ X2 @ france)))
% 108.10/14.79 | ('#form96' @ X0)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ~ (c @ X0 @ france))),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl314])).
% 108.10/14.79 thf(zip_derived_cl340, plain,
% 108.10/14.79 (![X0 : reg, X2 : reg]:
% 108.10/14.79 (~ (c @ X2 @ ('#sk8' @ X0))
% 108.10/14.79 | (c @ X2 @ france)
% 108.10/14.79 | ~ (c @ X0 @ france)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ('#form96' @ X0))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl326])).
% 108.10/14.79 thf(zip_derived_cl246, plain,
% 108.10/14.79 (![X2 : reg]: (~ (c @ X2 @ france) | (c @ X2 @ '#sk91'))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl237])).
% 108.10/14.79 thf(zip_derived_cl373, plain,
% 108.10/14.79 (![X0 : reg, X2 : reg]:
% 108.10/14.79 ( ('#form96' @ X0)
% 108.10/14.79 | ~ (c @ X0 @ france)
% 108.10/14.79 | (c @ X2 @ france)
% 108.10/14.79 | ~ (c @ X2 @ ('#sk8' @ X0)))),
% 108.10/14.79 inference('clc', [status(thm)], [zip_derived_cl340, zip_derived_cl246])).
% 108.10/14.79 thf(zip_derived_cl258, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( (((p @ ('#sk95' @ X0) @ X0) & (p @ ('#sk95' @ X0) @ '#sk91')))
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ~ (((c @ X0 @ spain) & (((~) @ (o @ X0 @ spain))))))),
% 108.10/14.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl252])).
% 108.10/14.79 thf(zip_derived_cl266, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 (~ ('#form96' @ X0)
% 108.10/14.79 | (((p @ ('#sk95' @ X0) @ X0) & (p @ ('#sk95' @ X0) @ '#sk91'))))),
% 108.10/14.79 define([status(thm)])).
% 108.10/14.79 thf(zip_derived_cl269, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( ('#form96' @ X0)
% 108.10/14.79 | ~ (((c @ X0 @ spain) & (((~) @ (o @ X0 @ spain)))))
% 108.10/14.79 | ~ (c @ X0 @ '#sk91'))),
% 108.10/14.79 inference('renaming', [status(thm)],
% 108.10/14.79 [zip_derived_cl258, zip_derived_cl266])).
% 108.10/14.79 thf(zip_derived_cl275, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 (~ (c @ X0 @ spain)
% 108.10/14.79 | (o @ X0 @ spain)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ('#form96' @ X0))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl269])).
% 108.10/14.79 thf(zip_derived_cl283, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( (((??) @ (^[Y0 : reg]: (((p @ Y0 @ X0) & (p @ Y0 @ spain))))))
% 108.10/14.79 | ('#form96' @ X0)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ~ (c @ X0 @ spain))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl275, '13'])).
% 108.10/14.79 thf(zip_derived_cl291, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( (((p @ ('#sk98' @ X0) @ X0) & (p @ ('#sk98' @ X0) @ spain)))
% 108.10/14.79 | ~ (c @ X0 @ spain)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ('#form96' @ X0))),
% 108.10/14.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl283])).
% 108.10/14.79 thf(zip_derived_cl303, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( (p @ ('#sk98' @ X0) @ spain)
% 108.10/14.79 | ('#form96' @ X0)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ~ (c @ X0 @ spain))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl291])).
% 108.10/14.79 thf(zip_derived_cl312, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( (((!!) @ (^[Y0 : reg]:
% 108.10/14.79 (((c @ Y0 @ ('#sk98' @ X0)) => (c @ Y0 @ spain))))))
% 108.10/14.79 | ~ (c @ X0 @ spain)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ('#form96' @ X0))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl303, '5'])).
% 108.10/14.79 thf(zip_derived_cl312, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( (((!!) @ (^[Y0 : reg]:
% 108.10/14.79 (((c @ Y0 @ ('#sk98' @ X0)) => (c @ Y0 @ spain))))))
% 108.10/14.79 | ~ (c @ X0 @ spain)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ('#form96' @ X0))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl303, '5'])).
% 108.10/14.79 thf(zip_derived_cl322, plain,
% 108.10/14.79 (![X2 : reg]:
% 108.10/14.79 (~ ('#form12' @ X2)
% 108.10/14.79 | (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 108.10/14.79 define([status(thm)])).
% 108.10/14.79 thf(ax2, axiom,
% 108.10/14.79 (mvalid @ ( mbox @ fool @ ( ^[X:$i]: ( ec @ spain @ france ) ) ))).
% 108.10/14.79 thf(zip_derived_cl6, plain,
% 108.10/14.79 ( (mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france))))),
% 108.10/14.79 inference('cnf', [status(esa)], [ax2])).
% 108.10/14.79 thf(zip_derived_cl111, plain,
% 108.10/14.79 ( (((!!) @ (^[Y0 : $i]:
% 108.10/14.79 (mbox @ fool @ (^[Y1 : $i]: (ec @ spain @ france)) @ Y0))))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl6, '6'])).
% 108.10/14.79 thf(zip_derived_cl112, plain,
% 108.10/14.79 (![X2 : $i]: (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france)) @ X2)),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl111])).
% 108.10/14.79 thf(zip_derived_cl113, plain,
% 108.10/14.79 (![X0 : $i]:
% 108.10/14.79 (((!!) @ (^[Y0 : $i]:
% 108.10/14.79 (((((~) @ (fool @ X0 @ Y0))) |
% 108.10/14.79 ((^[Y1 : $i]: (ec @ spain @ france)) @ Y0))))))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl112, '7'])).
% 108.10/14.79 thf(zip_derived_cl114, plain,
% 108.10/14.79 (![X0 : $i]:
% 108.10/14.79 (((!!) @ (^[Y0 : $i]:
% 108.10/14.79 (((((~) @ (fool @ X0 @ Y0))) | (ec @ spain @ france))))))),
% 108.10/14.79 inference('ho_norm', [status(thm)], [zip_derived_cl113])).
% 108.10/14.79 thf(zip_derived_cl115, plain,
% 108.10/14.79 (![X0 : $i, X2 : $i]:
% 108.10/14.79 (((((~) @ (fool @ X0 @ X2))) | (ec @ spain @ france)))),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl114])).
% 108.10/14.79 thf(zip_derived_cl116, plain,
% 108.10/14.79 (![X0 : $i, X2 : $i]: (~ (fool @ X0 @ X2) | (ec @ spain @ france))),
% 108.10/14.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl115])).
% 108.10/14.79 thf(zip_derived_cl117, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i]:
% 108.10/14.79 ( (((((~) @ (o @ spain @ france))) & (c @ spain @ france)))
% 108.10/14.79 | ~ (fool @ X1 @ X0))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl116, '10'])).
% 108.10/14.79 thf(zip_derived_cl118, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i]: (~ (o @ spain @ france) | ~ (fool @ X1 @ X0))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl117])).
% 108.10/14.79 thf(zip_derived_cl120, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i]:
% 108.10/14.79 (~ (((??) @ (^[Y0 : reg]: (((p @ Y0 @ spain) & (p @ Y0 @ france))))))
% 108.10/14.79 | ~ (fool @ X1 @ X0))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl118, '11'])).
% 108.10/14.79 thf(zip_derived_cl121, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i, X3 : reg]:
% 108.10/14.79 (~ (((p @ X3 @ spain) & (p @ X3 @ france))) | ~ (fool @ X1 @ X0))),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl120])).
% 108.10/14.79 thf(zip_derived_cl122, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i, X3 : reg]:
% 108.10/14.79 (~ (p @ X3 @ spain) | ~ (p @ X3 @ france) | ~ (fool @ X1 @ X0))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl121])).
% 108.10/14.79 thf(zip_derived_cl123, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i, X2 : reg]:
% 108.10/14.79 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain))))))
% 108.10/14.79 | ~ (fool @ X1 @ X0)
% 108.10/14.79 | ~ (p @ X2 @ france))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl122, '4'])).
% 108.10/14.79 thf(zip_derived_cl124, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i, X2 : reg]:
% 108.10/14.79 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ france))))))
% 108.10/14.79 | ~ (fool @ X1 @ X0)
% 108.10/14.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl123, '4'])).
% 108.10/14.79 thf(zip_derived_cl125, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i, X2 : reg]:
% 108.10/14.79 (~ (((c @ ('#sk11' @ X2) @ X2) => (c @ ('#sk11' @ X2) @ france)))
% 108.10/14.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain))))))
% 108.10/14.79 | ~ (fool @ X1 @ X0))),
% 108.10/14.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl124])).
% 108.10/14.79 thf(zip_derived_cl126, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i, X2 : reg]:
% 108.10/14.79 ( (c @ ('#sk11' @ X2) @ X2)
% 108.10/14.79 | ~ (fool @ X1 @ X0)
% 108.10/14.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])).
% 108.10/14.79 thf(zip_derived_cl128, plain,
% 108.10/14.79 (![X2 : reg]:
% 108.10/14.79 ( ('#form12' @ X2)
% 108.10/14.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 108.10/14.79 define([status(thm)])).
% 108.10/14.79 thf(zip_derived_cl324, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( ('#form12' @ ('#sk98' @ X0))
% 108.10/14.79 | ('#form96' @ X0)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ~ (c @ X0 @ spain))),
% 108.10/14.79 inference('renaming', [status(thm)],
% 108.10/14.79 [zip_derived_cl312, zip_derived_cl322, zip_derived_cl128])).
% 108.10/14.79 thf(zip_derived_cl209, plain, ( (pp @ spain @ '#sk91')),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl205])).
% 108.10/14.79 thf(zip_derived_cl214, plain,
% 108.10/14.79 ( (((((~) @ (p @ '#sk91' @ spain))) & (p @ spain @ '#sk91')))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl209, '9'])).
% 108.10/14.79 thf(zip_derived_cl220, plain, ( (p @ spain @ '#sk91')),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl214])).
% 108.10/14.79 thf(zip_derived_cl227, plain,
% 108.10/14.79 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ spain) => (c @ Y0 @ '#sk91'))))))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl220, '5'])).
% 108.10/14.79 thf(zip_derived_cl234, plain,
% 108.10/14.79 (![X2 : reg]: (((c @ X2 @ spain) => (c @ X2 @ '#sk91')))),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl227])).
% 108.10/14.79 thf(zip_derived_cl242, plain,
% 108.10/14.79 (![X2 : reg]: (~ (c @ X2 @ spain) | (c @ X2 @ '#sk91'))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl234])).
% 108.10/14.79 thf(zip_derived_cl371, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 (~ (c @ X0 @ spain)
% 108.10/14.79 | ('#form96' @ X0)
% 108.10/14.79 | ('#form12' @ ('#sk98' @ X0)))),
% 108.10/14.79 inference('clc', [status(thm)], [zip_derived_cl324, zip_derived_cl242])).
% 108.10/14.79 thf(zip_derived_cl197, plain, ( (a @ '#sk89' @ '#sk90')),
% 108.10/14.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl196])).
% 108.10/14.79 thf(zip_derived_cl197, plain, ( (a @ '#sk89' @ '#sk90')),
% 108.10/14.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl196])).
% 108.10/14.79 thf(ax1, axiom,
% 108.10/14.79 (mvalid @ ( mbox @ a @ ( ^[X:$i]: ( tpp @ catalunya @ spain ) ) ))).
% 108.10/14.79 thf(zip_derived_cl5, plain,
% 108.10/14.79 ( (mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain))))),
% 108.10/14.79 inference('cnf', [status(esa)], [ax1])).
% 108.10/14.79 thf(zip_derived_cl10, plain,
% 108.10/14.79 ( (((!!) @ (^[Y0 : $i]:
% 108.10/14.79 (mbox @ a @ (^[Y1 : $i]: (tpp @ catalunya @ spain)) @ Y0))))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl5, '6'])).
% 108.10/14.79 thf(zip_derived_cl11, plain,
% 108.10/14.79 (![X2 : $i]: (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)) @ X2)),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])).
% 108.10/14.79 thf(zip_derived_cl12, plain,
% 108.10/14.79 (![X0 : $i]:
% 108.10/14.79 (((!!) @ (^[Y0 : $i]:
% 108.10/14.79 (((((~) @ (a @ X0 @ Y0))) |
% 108.10/14.79 ((^[Y1 : $i]: (tpp @ catalunya @ spain)) @ Y0))))))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl11, '7'])).
% 108.10/14.79 thf(zip_derived_cl13, plain,
% 108.10/14.79 (![X0 : $i]:
% 108.10/14.79 (((!!) @ (^[Y0 : $i]:
% 108.10/14.79 (((((~) @ (a @ X0 @ Y0))) | (tpp @ catalunya @ spain))))))),
% 108.10/14.79 inference('ho_norm', [status(thm)], [zip_derived_cl12])).
% 108.10/14.79 thf(zip_derived_cl14, plain,
% 108.10/14.79 (![X0 : $i, X2 : $i]:
% 108.10/14.79 (((((~) @ (a @ X0 @ X2))) | (tpp @ catalunya @ spain)))),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])).
% 108.10/14.79 thf(zip_derived_cl15, plain,
% 108.10/14.79 (![X0 : $i, X2 : $i]: (~ (a @ X0 @ X2) | (tpp @ catalunya @ spain))),
% 108.10/14.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl14])).
% 108.10/14.79 thf(tpp, axiom, (tpp @ X0 @ X1) =>
% 108.10/14.79 ((((((??) @ (^[Y0 : reg]: (((ec @ Y0 @ X0) & (ec @ Y0 @ X1)))))) & (pp @
% 108.10/14.79 X0 @ X1)))
% 108.10/14.79 = ($true))).
% 108.10/14.79 thf('14', plain,
% 108.10/14.79 (![X0:reg,X1:reg]:
% 108.10/14.79 ( ( tpp @ X0 @ X1 ) <=>
% 108.10/14.79 ( ( pp @ X0 @ X1 ) &
% 108.10/14.79 ( ?[X6:reg]: ( ( ec @ X6 @ X0 ) & ( ec @ X6 @ X1 ) ) ) ) )),
% 108.10/14.79 inference('rw.lit', [status(esa)], [tpp])).
% 108.10/14.79 thf(zip_derived_cl16, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i]:
% 108.10/14.79 ( (((((??) @ (^[Y0 : reg]:
% 108.10/14.79 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ spain)))))) &
% 108.10/14.79 (pp @ catalunya @ spain)))
% 108.10/14.79 | ~ (a @ X1 @ X0))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl15, '14'])).
% 108.10/14.79 thf(zip_derived_cl18, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i]: ( (pp @ catalunya @ spain) | ~ (a @ X1 @ X0))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl16])).
% 108.10/14.79 thf(zip_derived_cl20, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i]:
% 108.10/14.79 ( (((((~) @ (p @ spain @ catalunya))) & (p @ catalunya @ spain)))
% 108.10/14.79 | ~ (a @ X1 @ X0))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl18, '9'])).
% 108.10/14.79 thf(zip_derived_cl23, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i]: (~ (p @ spain @ catalunya) | ~ (a @ X1 @ X0))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl20])).
% 108.10/14.79 thf(zip_derived_cl27, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i]:
% 108.10/14.79 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))))
% 108.10/14.79 | ~ (a @ X1 @ X0))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl23, '4'])).
% 108.10/14.79 thf(zip_derived_cl33, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i]:
% 108.10/14.79 (~ (((c @ '#sk2' @ spain) => (c @ '#sk2' @ catalunya)))
% 108.10/14.79 | ~ (a @ X1 @ X0))),
% 108.10/14.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl27])).
% 108.10/14.79 thf(zip_derived_cl38, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i]: (~ (c @ '#sk2' @ catalunya) | ~ (a @ X1 @ X0))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 108.10/14.79 thf(zip_derived_cl378, plain, (~ (c @ '#sk2' @ catalunya)),
% 108.10/14.79 inference('sup-', [status(thm)], [zip_derived_cl197, zip_derived_cl38])).
% 108.10/14.79 thf(zip_derived_cl37, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i]: ( (c @ '#sk2' @ spain) | ~ (a @ X1 @ X0))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 108.10/14.79 thf(zip_derived_cl197, plain, ( (a @ '#sk89' @ '#sk90')),
% 108.10/14.79 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl196])).
% 108.10/14.79 thf(zip_derived_cl393, plain, ( (c @ '#sk2' @ spain)),
% 108.10/14.79 inference('sup+', [status(thm)], [zip_derived_cl37, zip_derived_cl197])).
% 108.10/14.79 thf(zip_derived_cl297, plain,
% 108.10/14.79 ((~ ('#form99')
% 108.10/14.79 | (((??) @ (^[Y0 : reg]:
% 108.10/14.79 (((ec @ Y0 @ catalunya) & (ec @ Y0 @ '#sk91')))))))),
% 108.10/14.79 define([status(thm)])).
% 108.10/14.79 thf(zip_derived_cl298, plain,
% 108.10/14.79 (( (((ec @ '#sk100' @ catalunya) & (ec @ '#sk100' @ '#sk91')))
% 108.10/14.79 | ~ ('#form99'))),
% 108.10/14.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl297])).
% 108.10/14.79 thf(zip_derived_cl307, plain,
% 108.10/14.79 (( (ec @ '#sk100' @ catalunya) | ~ ('#form99'))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl298])).
% 108.10/14.79 thf(zip_derived_cl317, plain,
% 108.10/14.79 (( (((((~) @ (o @ '#sk100' @ catalunya))) & (c @ '#sk100' @ catalunya)))
% 108.10/14.79 | ~ ('#form99'))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl307, '10'])).
% 108.10/14.79 thf(zip_derived_cl330, plain,
% 108.10/14.79 (( (c @ '#sk100' @ catalunya) | ~ ('#form99'))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl317])).
% 108.10/14.79 thf(zip_derived_cl128, plain,
% 108.10/14.79 (![X2 : reg]:
% 108.10/14.79 ( ('#form12' @ X2)
% 108.10/14.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 108.10/14.79 define([status(thm)])).
% 108.10/14.79 thf(zip_derived_cl129, plain,
% 108.10/14.79 (![X2 : reg]:
% 108.10/14.79 (~ (((c @ ('#sk4' @ X2) @ X2) => (c @ ('#sk4' @ X2) @ spain)))
% 108.10/14.79 | ('#form12' @ X2))),
% 108.10/14.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl128])).
% 108.10/14.79 thf(zip_derived_cl132, plain,
% 108.10/14.79 (![X2 : reg]: ( (c @ ('#sk4' @ X2) @ X2) | ('#form12' @ X2))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl129])).
% 108.10/14.79 thf(zip_derived_cl315, plain,
% 108.10/14.79 (![X2 : reg]:
% 108.10/14.79 ( (c @ '#sk101' @ catalunya)
% 108.10/14.79 | ('#form99')
% 108.10/14.79 | ('#form94')
% 108.10/14.79 | (((c @ X2 @ '#sk91') => (c @ X2 @ catalunya))))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl306])).
% 108.10/14.79 thf(zip_derived_cl327, plain,
% 108.10/14.79 (![X2 : reg]:
% 108.10/14.79 (~ (c @ X2 @ '#sk91')
% 108.10/14.79 | (c @ X2 @ catalunya)
% 108.10/14.79 | ('#form94')
% 108.10/14.79 | ('#form99')
% 108.10/14.79 | (c @ '#sk101' @ catalunya))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl315])).
% 108.10/14.79 thf(zip_derived_cl329, plain,
% 108.10/14.79 ((~ (o @ '#sk100' @ catalunya) | ~ ('#form99'))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl317])).
% 108.10/14.79 thf(zip_derived_cl341, plain,
% 108.10/14.79 ((~ (((??) @ (^[Y0 : reg]: (((p @ Y0 @ '#sk100') & (p @ Y0 @ catalunya))))))
% 108.10/14.79 | ~ ('#form99'))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl329, '11'])).
% 108.10/14.79 thf(zip_derived_cl349, plain,
% 108.10/14.79 (![X2 : reg]:
% 108.10/14.79 (~ (((p @ X2 @ '#sk100') & (p @ X2 @ catalunya))) | ~ ('#form99'))),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl341])).
% 108.10/14.79 thf(zip_derived_cl351, plain,
% 108.10/14.79 (![X2 : reg]:
% 108.10/14.79 (~ (p @ X2 @ '#sk100') | ~ (p @ X2 @ catalunya) | ~ ('#form99'))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl349])).
% 108.10/14.79 thf(zip_derived_cl353, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk100'))))))
% 108.10/14.79 | ~ ('#form99')
% 108.10/14.79 | ~ (p @ X0 @ catalunya))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl351, '4'])).
% 108.10/14.79 thf(zip_derived_cl355, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ catalunya))))))
% 108.10/14.79 | ~ ('#form99')
% 108.10/14.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk100')))))))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl353, '4'])).
% 108.10/14.79 thf(zip_derived_cl357, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 (~ (((c @ ('#sk3' @ X0) @ X0) => (c @ ('#sk3' @ X0) @ catalunya)))
% 108.10/14.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk100'))))))
% 108.10/14.79 | ~ ('#form99'))),
% 108.10/14.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl355])).
% 108.10/14.79 thf(zip_derived_cl359, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( ('#form106' @ X0)
% 108.10/14.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk100')))))))),
% 108.10/14.79 define([status(thm)])).
% 108.10/14.79 thf(zip_derived_cl360, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 (~ (((c @ ('#sk107' @ X0) @ X0) => (c @ ('#sk107' @ X0) @ '#sk100')))
% 108.10/14.79 | ('#form106' @ X0))),
% 108.10/14.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl359])).
% 108.10/14.79 thf(zip_derived_cl368, plain,
% 108.10/14.79 (![X0 : reg]: ( (c @ ('#sk107' @ X0) @ X0) | ('#form106' @ X0))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl360])).
% 108.10/14.79 thf(zip_derived_cl369, plain,
% 108.10/14.79 (![X0 : reg]: (~ (c @ ('#sk107' @ X0) @ '#sk100') | ('#form106' @ X0))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl360])).
% 108.10/14.79 thf(zip_derived_cl308, plain, (( (ec @ '#sk100' @ '#sk91') | ~ ('#form99'))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl298])).
% 108.10/14.79 thf(zip_derived_cl318, plain,
% 108.10/14.79 (( (((((~) @ (o @ '#sk100' @ '#sk91'))) & (c @ '#sk100' @ '#sk91')))
% 108.10/14.79 | ~ ('#form99'))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl308, '10'])).
% 108.10/14.79 thf(zip_derived_cl331, plain, ((~ (o @ '#sk100' @ '#sk91') | ~ ('#form99'))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl318])).
% 108.10/14.79 thf(zip_derived_cl342, plain,
% 108.10/14.79 ((~ (((??) @ (^[Y0 : reg]: (((p @ Y0 @ '#sk100') & (p @ Y0 @ '#sk91'))))))
% 108.10/14.79 | ~ ('#form99'))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl331, '11'])).
% 108.10/14.79 thf(zip_derived_cl350, plain,
% 108.10/14.79 (![X2 : reg]:
% 108.10/14.79 (~ (((p @ X2 @ '#sk100') & (p @ X2 @ '#sk91'))) | ~ ('#form99'))),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl342])).
% 108.10/14.79 thf(zip_derived_cl352, plain,
% 108.10/14.79 (![X2 : reg]:
% 108.10/14.79 (~ (p @ X2 @ '#sk100') | ~ (p @ X2 @ '#sk91') | ~ ('#form99'))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl350])).
% 108.10/14.79 thf(zip_derived_cl354, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk100'))))))
% 108.10/14.79 | ~ ('#form99')
% 108.10/14.79 | ~ (p @ X0 @ '#sk91'))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl352, '4'])).
% 108.10/14.79 thf(zip_derived_cl356, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 (~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk91'))))))
% 108.10/14.79 | ~ ('#form99')
% 108.10/14.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk100')))))))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl354, '4'])).
% 108.10/14.79 thf(zip_derived_cl358, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 (~ (((c @ ('#sk103' @ X0) @ X0) => (c @ ('#sk103' @ X0) @ '#sk91')))
% 108.10/14.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk100'))))))
% 108.10/14.79 | ~ ('#form99'))),
% 108.10/14.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl356])).
% 108.10/14.79 thf(zip_derived_cl358, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 (~ (((c @ ('#sk103' @ X0) @ X0) => (c @ ('#sk103' @ X0) @ '#sk91')))
% 108.10/14.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk100'))))))
% 108.10/14.79 | ~ ('#form99'))),
% 108.10/14.79 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl356])).
% 108.10/14.79 thf(zip_derived_cl362, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( ('#form108' @ X0)
% 108.10/14.79 | ~ (((c @ ('#sk103' @ X0) @ X0) => (c @ ('#sk103' @ X0) @ '#sk91'))))),
% 108.10/14.79 define([status(thm)])).
% 108.10/14.79 thf(zip_derived_cl365, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 (~ ('#form108' @ X0)
% 108.10/14.79 | ~ ('#form99')
% 108.10/14.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk100')))))))),
% 108.10/14.79 inference('renaming', [status(thm)],
% 108.10/14.79 [zip_derived_cl358, zip_derived_cl362])).
% 108.10/14.79 thf(zip_derived_cl359, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( ('#form106' @ X0)
% 108.10/14.79 | ~ (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X0) => (c @ Y0 @ '#sk100')))))))),
% 108.10/14.79 define([status(thm)])).
% 108.10/14.79 thf(zip_derived_cl370, plain,
% 108.10/14.79 (![X0 : reg]: (~ ('#form106' @ X0) | ~ ('#form99') | ~ ('#form108' @ X0))),
% 108.10/14.79 inference('renaming', [status(thm)],
% 108.10/14.79 [zip_derived_cl365, zip_derived_cl359])).
% 108.10/14.79 thf(zip_derived_cl302, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( (p @ ('#sk98' @ X0) @ X0)
% 108.10/14.79 | ('#form96' @ X0)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ~ (c @ X0 @ spain))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl291])).
% 108.10/14.79 thf(zip_derived_cl311, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( (((!!) @ (^[Y0 : reg]:
% 108.10/14.79 (((c @ Y0 @ ('#sk98' @ X0)) => (c @ Y0 @ X0))))))
% 108.10/14.79 | ~ (c @ X0 @ spain)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ('#form96' @ X0))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl302, '5'])).
% 108.10/14.79 thf(zip_derived_cl321, plain,
% 108.10/14.79 (![X0 : reg, X2 : reg]:
% 108.10/14.79 ( (((c @ X2 @ ('#sk98' @ X0)) => (c @ X2 @ X0)))
% 108.10/14.79 | ('#form96' @ X0)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ~ (c @ X0 @ spain))),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl311])).
% 108.10/14.79 thf(zip_derived_cl337, plain,
% 108.10/14.79 (![X0 : reg, X2 : reg]:
% 108.10/14.79 (~ (c @ X2 @ ('#sk98' @ X0))
% 108.10/14.79 | (c @ X2 @ X0)
% 108.10/14.79 | ~ (c @ X0 @ spain)
% 108.10/14.79 | ~ (c @ X0 @ '#sk91')
% 108.10/14.79 | ('#form96' @ X0))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl321])).
% 108.10/14.79 thf(zip_derived_cl242, plain,
% 108.10/14.79 (![X2 : reg]: (~ (c @ X2 @ spain) | (c @ X2 @ '#sk91'))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl234])).
% 108.10/14.79 thf(zip_derived_cl374, plain,
% 108.10/14.79 (![X0 : reg, X2 : reg]:
% 108.10/14.79 ( ('#form96' @ X0)
% 108.10/14.79 | ~ (c @ X0 @ spain)
% 108.10/14.79 | (c @ X2 @ X0)
% 108.10/14.79 | ~ (c @ X2 @ ('#sk98' @ X0)))),
% 108.10/14.79 inference('clc', [status(thm)], [zip_derived_cl337, zip_derived_cl242])).
% 108.10/14.79 thf(zip_derived_cl362, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( ('#form108' @ X0)
% 108.10/14.79 | ~ (((c @ ('#sk103' @ X0) @ X0) => (c @ ('#sk103' @ X0) @ '#sk91'))))),
% 108.10/14.79 define([status(thm)])).
% 108.10/14.79 thf(zip_derived_cl363, plain,
% 108.10/14.79 (![X0 : reg]: ( (c @ ('#sk103' @ X0) @ X0) | ('#form108' @ X0))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])).
% 108.10/14.79 thf(zip_derived_cl133, plain,
% 108.10/14.79 (![X2 : reg]: (~ (c @ ('#sk4' @ X2) @ spain) | ('#form12' @ X2))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl129])).
% 108.10/14.79 thf(zip_derived_cl24, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i]: ( (p @ catalunya @ spain) | ~ (a @ X1 @ X0))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl20])).
% 108.10/14.79 thf(zip_derived_cl28, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i]:
% 108.10/14.79 ( (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ catalunya) => (c @ Y0 @ spain))))))
% 108.10/14.79 | ~ (a @ X1 @ X0))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl24, '5'])).
% 108.10/14.79 thf(zip_derived_cl34, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i, X3 : reg]:
% 108.10/14.79 ( (((c @ X3 @ catalunya) => (c @ X3 @ spain))) | ~ (a @ X1 @ X0))),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])).
% 108.10/14.79 thf(zip_derived_cl39, plain,
% 108.10/14.79 (![X0 : $i, X1 : $i, X3 : reg]:
% 108.10/14.79 (~ (c @ X3 @ catalunya) | (c @ X3 @ spain) | ~ (a @ X1 @ X0))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 108.10/14.79 thf(zip_derived_cl242, plain,
% 108.10/14.79 (![X2 : reg]: (~ (c @ X2 @ spain) | (c @ X2 @ '#sk91'))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl234])).
% 108.10/14.79 thf(zip_derived_cl266, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 (~ ('#form96' @ X0)
% 108.10/14.79 | (((p @ ('#sk95' @ X0) @ X0) & (p @ ('#sk95' @ X0) @ '#sk91'))))),
% 108.10/14.79 define([status(thm)])).
% 108.10/14.79 thf(zip_derived_cl267, plain,
% 108.10/14.79 (![X0 : reg]: ( (p @ ('#sk95' @ X0) @ X0) | ~ ('#form96' @ X0))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl266])).
% 108.10/14.79 thf(zip_derived_cl276, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( (((!!) @ (^[Y0 : reg]:
% 108.10/14.79 (((c @ Y0 @ ('#sk95' @ X0)) => (c @ Y0 @ X0))))))
% 108.10/14.79 | ~ ('#form96' @ X0))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl267, '5'])).
% 108.10/14.79 thf(zip_derived_cl284, plain,
% 108.10/14.79 (![X0 : reg, X2 : reg]:
% 108.10/14.79 ( (((c @ X2 @ ('#sk95' @ X0)) => (c @ X2 @ X0))) | ~ ('#form96' @ X0))),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl276])).
% 108.10/14.79 thf(zip_derived_cl292, plain,
% 108.10/14.79 (![X0 : reg, X2 : reg]:
% 108.10/14.79 (~ (c @ X2 @ ('#sk95' @ X0)) | (c @ X2 @ X0) | ~ ('#form96' @ X0))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl284])).
% 108.10/14.79 thf(zip_derived_cl364, plain,
% 108.10/14.79 (![X0 : reg]: (~ (c @ ('#sk103' @ X0) @ '#sk91') | ('#form108' @ X0))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])).
% 108.10/14.79 thf(zip_derived_cl268, plain,
% 108.10/14.79 (![X0 : reg]: ( (p @ ('#sk95' @ X0) @ '#sk91') | ~ ('#form96' @ X0))),
% 108.10/14.79 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl266])).
% 108.10/14.79 thf(zip_derived_cl277, plain,
% 108.10/14.79 (![X0 : reg]:
% 108.10/14.79 ( (((!!) @ (^[Y0 : reg]:
% 108.10/14.79 (((c @ Y0 @ ('#sk95' @ X0)) => (c @ Y0 @ '#sk91'))))))
% 108.10/14.79 | ~ ('#form96' @ X0))),
% 108.10/14.79 inference('rw_clause', [status(thm)], [zip_derived_cl268, '5'])).
% 108.10/14.79 thf(zip_derived_cl285, plain,
% 108.10/14.79 (![X0 : reg, X2 : reg]:
% 108.10/14.79 ( (((c @ X2 @ ('#sk95' @ X0)) => (c @ X2 @ '#sk91')))
% 108.10/14.79 | ~ ('#form96' @ X0))),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl277])).
% 108.10/14.79 thf(zip_derived_cl293, plain,
% 108.10/14.79 (![X0 : reg, X2 : reg]:
% 108.10/14.79 (~ (c @ X2 @ ('#sk95' @ X0))
% 108.10/14.79 | (c @ X2 @ '#sk91')
% 108.10/14.79 | ~ ('#form96' @ X0))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl285])).
% 108.10/14.79 thf(zip_derived_cl322, plain,
% 108.10/14.79 (![X2 : reg]:
% 108.10/14.79 (~ ('#form12' @ X2)
% 108.10/14.79 | (((!!) @ (^[Y0 : reg]: (((c @ Y0 @ X2) => (c @ Y0 @ spain)))))))),
% 108.10/14.79 define([status(thm)])).
% 108.10/14.79 thf(zip_derived_cl323, plain,
% 108.10/14.79 (![X2 : reg, X4 : reg]:
% 108.10/14.79 ( (((c @ X4 @ X2) => (c @ X4 @ spain))) | ~ ('#form12' @ X2))),
% 108.10/14.79 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl322])).
% 108.10/14.79 thf(zip_derived_cl338, plain,
% 108.10/14.79 (![X2 : reg, X4 : reg]:
% 108.10/14.79 (~ (c @ X4 @ X2) | (c @ X4 @ spain) | ~ ('#form12' @ X2))),
% 108.10/14.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl323])).
% 108.10/14.79 thf(zip_derived_cl23278, plain, ($false),
% 108.10/14.79 inference('eprover', [status(thm)],
% 108.10/14.79 [zip_derived_cl296, zip_derived_cl377, zip_derived_cl397,
% 108.10/14.79 zip_derived_cl295, zip_derived_cl263, zip_derived_cl246,
% 108.10/14.79 zip_derived_cl328, zip_derived_cl345, zip_derived_cl346,
% 108.10/14.79 zip_derived_cl348, zip_derived_cl83, zip_derived_cl375,
% 108.10/14.79 zip_derived_cl347, zip_derived_cl373, zip_derived_cl371,
% 108.10/14.79 zip_derived_cl197, zip_derived_cl378, zip_derived_cl393,
% 108.10/14.79 zip_derived_cl330, zip_derived_cl132, zip_derived_cl327,
% 108.10/14.79 zip_derived_cl368, zip_derived_cl369, zip_derived_cl370,
% 108.10/14.79 zip_derived_cl374, zip_derived_cl363, zip_derived_cl133,
% 108.10/14.79 zip_derived_cl39, zip_derived_cl242, zip_derived_cl292,
% 108.10/14.79 zip_derived_cl364, zip_derived_cl293, zip_derived_cl338])).
% 108.10/14.79
% 108.10/14.79 % SZS output end Refutation
% 108.10/14.79
% 108.10/14.79
% 108.10/14.79 % Terminating...
% 110.55/14.86 % Runner terminated.
% 110.55/14.88 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------