%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : PHI006^4 : TPTP v9.2.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.V6tAMNgciA true
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:49:04 PM UTC 2025
% Result : Theorem 5.42s 1.32s
% Output : Refutation 5.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : PHI006^4 : TPTP v9.2.0. Released v6.4.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.V6tAMNgciA true
% 0.15/0.35 % Computer : n018.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Oct 1 16:57:08 EDT 2025
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.35 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in HO mode
% 0.58/0.68 % Total configuration time : 828
% 0.58/0.68 % Estimated wc time : 1656
% 0.58/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.59/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.59/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.59/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.59/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.60/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.60/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 0.60/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.60/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.60/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.60/0.78 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 0.60/0.84 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s
% 0.60/0.84 % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s
% 5.42/1.32 % Solved by lams/40_b.comb.sh.
% 5.42/1.32 % done 78 iterations in 0.497s
% 5.42/1.32 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 5.42/1.32 % SZS output start Refutation
% 5.42/1.32 thf(mu_type, type, mu: $tType).
% 5.42/1.32 thf('#sk1_type', type, '#sk1': (mu > $i > $o) > (mu > $i > $o) > $i).
% 5.42/1.32 thf(mexists_ind_type, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 5.42/1.32 thf('#sk2_type', type, '#sk2': (mu > $i > $o) > (mu > $i > $o) > mu).
% 5.42/1.32 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 5.42/1.32 thf(mnot_type, type, mnot: ($i > $o) > $i > $o).
% 5.42/1.32 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 5.42/1.32 thf(mbox_type, type, mbox: ($i > $o) > $i > $o).
% 5.42/1.32 thf(mvalid_type, type, mvalid: ($i > $o) > $o).
% 5.42/1.32 thf(necessary_existence_type, type, necessary_existence: mu > $i > $o).
% 5.42/1.32 thf('#sk3_type', type, '#sk3': (mu > $i > $o) > $i > mu).
% 5.42/1.32 thf(mforall_indset_type, type, mforall_indset: ((mu > $i > $o) > $i > $o) >
% 5.42/1.32 $i > $o).
% 5.42/1.32 thf('#sk4_type', type, '#sk4': (mu > $i > $o) > mu > $i > $o).
% 5.42/1.32 thf(essence_type, type, essence: (mu > $i > $o) > mu > $i > $o).
% 5.42/1.32 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 5.42/1.32 thf(god_type, type, god: mu > $i > $o).
% 5.42/1.32 thf(positive_type, type, positive: (mu > $i > $o) > $i > $o).
% 5.42/1.32 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 5.42/1.32 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 5.42/1.32 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 5.42/1.32 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 5.42/1.32 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 5.42/1.32 thf(axA1a, axiom,
% 5.42/1.32 (mvalid @
% 5.42/1.32 ( mforall_indset @
% 5.42/1.32 ( ^[Phi:( mu > $i > $o )]:
% 5.42/1.32 ( mimplies @
% 5.42/1.32 ( positive @ ( ^[X:mu]: ( mnot @ ( Phi @ X ) ) ) ) @
% 5.42/1.32 ( mnot @ ( positive @ Phi ) ) ) ) ))).
% 5.42/1.32 thf(zip_derived_cl0, plain,
% 5.42/1.32 ( (mvalid @
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 (^[Y0 : mu > $i > $o]:
% 5.42/1.32 (mimplies @ (positive @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))) @
% 5.42/1.32 (mnot @ (positive @ Y0))))))),
% 5.42/1.32 inference('cnf', [status(esa)], [axA1a])).
% 5.42/1.32 thf(zip_derived_cl1, plain,
% 5.42/1.32 ( (mvalid @
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#B') @ positive @ ((('#B') @ mnot)))))) @
% 5.42/1.32 ((('#B') @ mnot @ positive))))))),
% 5.42/1.32 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 5.42/1.32 thf(mvalid, axiom, (mvalid @ X0) =>
% 5.42/1.32 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))).
% 5.42/1.32 thf('0', plain,
% 5.42/1.32 (![X0:( $i > $o )]: ( ( mvalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )),
% 5.42/1.32 inference('rw.lit', [status(esa)], [mvalid])).
% 5.42/1.32 thf(zip_derived_cl28, plain,
% 5.42/1.32 ( (((!!) @ (^[Y0 : $i]:
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#B') @ positive @ ((('#B') @ mnot)))))) @
% 5.42/1.32 ((('#B') @ mnot @ positive)))) @
% 5.42/1.32 Y0))))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl1, '0'])).
% 5.42/1.32 thf(zip_derived_cl29, plain,
% 5.42/1.32 ( (((!!) @ (mforall_indset @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#B') @ positive @ ((('#B') @ mnot)))))) @
% 5.42/1.32 ((('#B') @ mnot @ positive)))))))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl28])).
% 5.42/1.32 thf(zip_derived_cl30, plain,
% 5.42/1.32 (![X2 : $i]:
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#B') @ positive @ ((('#B') @ mnot)))))) @
% 5.42/1.32 ((('#B') @ mnot @ positive)))) @
% 5.42/1.32 X2)),
% 5.42/1.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl29])).
% 5.42/1.32 thf(mforall_indset, axiom, (mforall_indset @ X0 @ X1) =>
% 5.42/1.32 ((((!!) @ (^[Y0 : mu > $i > $o]: (X0 @ Y0 @ X1)))) = ($true))).
% 5.42/1.32 thf('1', plain,
% 5.42/1.32 (![X0:( ( mu > $i > $o ) > $i > $o ),X1:$i]:
% 5.42/1.32 ( ( mforall_indset @ X0 @ X1 ) <=>
% 5.42/1.32 ( ![X6:( mu > $i > $o )]: ( X0 @ X6 @ X1 ) ) )),
% 5.42/1.32 inference('rw.lit', [status(esa)], [mforall_indset])).
% 5.42/1.32 thf(zip_derived_cl31, plain,
% 5.42/1.32 (![X0 : $i]:
% 5.42/1.32 (((!!) @ (^[Y0 : mu > $i > $o]:
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#B') @ positive @ ((('#B') @ mnot)))))) @
% 5.42/1.32 ((('#B') @ mnot @ positive)) @ Y0 @ X0)))))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl30, '1'])).
% 5.42/1.32 thf(zip_derived_cl32, plain,
% 5.42/1.32 (![X0 : $i]:
% 5.42/1.32 (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#B') @ positive @
% 5.42/1.32 ((('#B') @ mnot)))))) @
% 5.42/1.32 ((('#B') @ mnot @ positive)))) @
% 5.42/1.32 X0))))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl31])).
% 5.42/1.32 thf(zip_derived_cl33, plain,
% 5.42/1.32 (![X0 : $i, X2 : mu > $i > $o]:
% 5.42/1.32 (mimplies @ (positive @ ((('#B') @ mnot @ X2))) @
% 5.42/1.32 (mnot @ (positive @ X2)) @ X0)),
% 5.42/1.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])).
% 5.42/1.32 thf(mimplies, axiom, (mimplies @ X0 @ X1 @ X2) =>
% 5.42/1.32 ((((X0 @ X2) => (X1 @ X2))) = ($true))).
% 5.42/1.32 thf('2', plain,
% 5.42/1.32 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 5.42/1.32 ( ( mimplies @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) => ( X1 @ X2 ) ) )),
% 5.42/1.32 inference('rw.lit', [status(esa)], [mimplies])).
% 5.42/1.32 thf(zip_derived_cl34, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (((positive @ ((('#B') @ mnot @ X0)) @ X1) => (mnot @
% 5.42/1.32 (positive @ X0) @ X1)))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl33, '2'])).
% 5.42/1.32 thf(zip_derived_cl35, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (~ (positive @ ((('#B') @ mnot @ X0)) @ X1)
% 5.42/1.32 | (mnot @ (positive @ X0) @ X1))),
% 5.42/1.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 5.42/1.32 thf(mnot, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))).
% 5.42/1.32 thf('3', plain,
% 5.42/1.32 (![X0:( $i > $o ),X1:$i]: ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )),
% 5.42/1.32 inference('rw.lit', [status(esa)], [mnot])).
% 5.42/1.32 thf(zip_derived_cl36, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o]:
% 5.42/1.32 (~ (positive @ X1 @ X0) | ~ (positive @ ((('#B') @ mnot @ X1)) @ X0))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl35, '3'])).
% 5.42/1.32 thf(axA4, axiom,
% 5.42/1.32 (mvalid @
% 5.42/1.32 ( mforall_indset @
% 5.42/1.32 ( ^[Phi:( mu > $i > $o )]:
% 5.42/1.32 ( mimplies @ ( positive @ Phi ) @ ( mbox @ ( positive @ Phi ) ) ) ) ))).
% 5.42/1.32 thf(zip_derived_cl7, plain,
% 5.42/1.32 ( (mvalid @
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 (^[Y0 : mu > $i > $o]:
% 5.42/1.32 (mimplies @ (positive @ Y0) @ (mbox @ (positive @ Y0))))))),
% 5.42/1.32 inference('cnf', [status(esa)], [axA4])).
% 5.42/1.32 thf(zip_derived_cl8, plain,
% 5.42/1.32 ( (mvalid @
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ positive)) @
% 5.42/1.32 ((('#B') @ mbox @ positive))))))),
% 5.42/1.32 inference('lams2combs', [status(thm)], [zip_derived_cl7])).
% 5.42/1.32 thf(zip_derived_cl17, plain,
% 5.42/1.32 ( (((!!) @ (^[Y0 : $i]:
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ positive)) @
% 5.42/1.32 ((('#B') @ mbox @ positive)))) @
% 5.42/1.32 Y0))))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl8, '0'])).
% 5.42/1.32 thf(zip_derived_cl18, plain,
% 5.42/1.32 ( (((!!) @ (mforall_indset @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ positive)) @
% 5.42/1.32 ((('#B') @ mbox @ positive)))))))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl17])).
% 5.42/1.32 thf(zip_derived_cl19, plain,
% 5.42/1.32 (![X2 : $i]:
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ positive)) @
% 5.42/1.32 ((('#B') @ mbox @ positive)))) @
% 5.42/1.32 X2)),
% 5.42/1.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])).
% 5.42/1.32 thf(zip_derived_cl20, plain,
% 5.42/1.32 (![X0 : $i]:
% 5.42/1.32 (((!!) @ (^[Y0 : mu > $i > $o]:
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ positive)) @
% 5.42/1.32 ((('#B') @ mbox @ positive)) @ Y0 @ X0)))))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl19, '1'])).
% 5.42/1.32 thf(zip_derived_cl21, plain,
% 5.42/1.32 (![X0 : $i]:
% 5.42/1.32 (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @ positive)) @
% 5.42/1.32 ((('#B') @ mbox @ positive)))) @
% 5.42/1.32 X0))))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl20])).
% 5.42/1.32 thf(zip_derived_cl22, plain,
% 5.42/1.32 (![X0 : $i, X2 : mu > $i > $o]:
% 5.42/1.32 (mimplies @ (positive @ X2) @ (mbox @ (positive @ X2)) @ X0)),
% 5.42/1.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])).
% 5.42/1.32 thf(zip_derived_cl23, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (((positive @ X0 @ X1) => (mbox @ (positive @ X0) @ X1)))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl22, '2'])).
% 5.42/1.32 thf(zip_derived_cl24, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (~ (positive @ X0 @ X1) | (mbox @ (positive @ X0) @ X1))),
% 5.42/1.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])).
% 5.42/1.32 thf(mbox, axiom, (mbox @ X0 @ X1) =>
% 5.42/1.32 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))).
% 5.42/1.32 thf('4', plain,
% 5.42/1.32 (![X0:( $i > $o ),X1:$i]:
% 5.42/1.32 ( ( mbox @ X0 @ X1 ) <=> ( ![X6:$i]: ( X0 @ X6 ) ) )),
% 5.42/1.32 inference('rw.lit', [status(esa)], [mbox])).
% 5.42/1.32 thf(zip_derived_cl25, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o]:
% 5.42/1.32 ( (((!!) @ (^[Y0 : $i]: (positive @ X1 @ Y0))))
% 5.42/1.32 | ~ (positive @ X1 @ X0))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl24, '4'])).
% 5.42/1.32 thf(zip_derived_cl26, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o]:
% 5.42/1.32 ( (((!!) @ (positive @ X1))) | ~ (positive @ X1 @ X0))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl25])).
% 5.42/1.32 thf(zip_derived_cl27, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o, X3 : $i]:
% 5.42/1.32 ( (positive @ X1 @ X3) | ~ (positive @ X1 @ X0))),
% 5.42/1.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])).
% 5.42/1.32 thf(zip_derived_cl77, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o, X2 : $i]:
% 5.42/1.32 (~ (positive @ ((('#B') @ mnot @ X1)) @ X0) | ~ (positive @ X1 @ X2))),
% 5.42/1.32 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl27])).
% 5.42/1.32 thf(axA5, axiom, (mvalid @ ( positive @ necessary_existence ))).
% 5.42/1.32 thf(zip_derived_cl9, plain, ( (mvalid @ (positive @ necessary_existence))),
% 5.42/1.32 inference('cnf', [status(esa)], [axA5])).
% 5.42/1.32 thf(zip_derived_cl14, plain,
% 5.42/1.32 ( (((!!) @ (^[Y0 : $i]: (positive @ necessary_existence @ Y0))))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl9, '0'])).
% 5.42/1.32 thf(zip_derived_cl15, plain, ( (((!!) @ (positive @ necessary_existence)))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl14])).
% 5.42/1.32 thf(zip_derived_cl16, plain,
% 5.42/1.32 (![X2 : $i]: (positive @ necessary_existence @ X2)),
% 5.42/1.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])).
% 5.42/1.32 thf(zip_derived_cl185, plain,
% 5.42/1.32 (![X1 : $i]: ~ (positive @ ((('#B') @ mnot @ necessary_existence)) @ X1)),
% 5.42/1.32 inference('sup+', [status(thm)], [zip_derived_cl77, zip_derived_cl16])).
% 5.42/1.32 thf(axA2, axiom,
% 5.42/1.32 (mvalid @
% 5.42/1.32 ( mforall_indset @
% 5.42/1.32 ( ^[Phi:( mu > $i > $o )]:
% 5.42/1.32 ( mforall_indset @
% 5.42/1.32 ( ^[Psi:( mu > $i > $o )]:
% 5.42/1.32 ( mimplies @
% 5.42/1.32 ( mand @
% 5.42/1.32 ( positive @ Phi ) @
% 5.42/1.32 ( mbox @
% 5.42/1.32 ( mforall_ind @
% 5.42/1.32 ( ^[X:mu]: ( mimplies @ ( Phi @ X ) @ ( Psi @ X ) ) ) ) ) ) @
% 5.42/1.32 ( positive @ Psi ) ) ) ) ) ))).
% 5.42/1.32 thf(zip_derived_cl4, plain,
% 5.42/1.32 ( (mvalid @
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 (^[Y0 : mu > $i > $o]:
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 (^[Y1 : mu > $i > $o]:
% 5.42/1.32 (mimplies @
% 5.42/1.32 (mand @ (positive @ Y0) @
% 5.42/1.32 (mbox @
% 5.42/1.32 (mforall_ind @
% 5.42/1.32 (^[Y2 : mu]: (mimplies @ (Y0 @ Y2) @ (Y1 @ Y2)))))) @
% 5.42/1.32 (positive @ Y1)))))))),
% 5.42/1.32 inference('cnf', [status(esa)], [axA2])).
% 5.42/1.32 thf(zip_derived_cl5, plain,
% 5.42/1.32 ( (mvalid @
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 ((('#B') @ mforall_indset @
% 5.42/1.32 ((('#C') @ ((('#B') @ ('#S') @
% 5.42/1.32 ((('#B') @ ((('#B') @ mimplies)) @
% 5.42/1.32 ((('#S') @ ((('#B') @ ('#B') @
% 5.42/1.32 ((('#B') @ mand @ positive)))) @
% 5.42/1.32 ((('#B') @ ((('#B') @ mbox)) @
% 5.42/1.32 ((('#B') @ ((('#B') @ mforall_ind)) @
% 5.42/1.32 ((('#B') @ ('#S') @ ((('#B') @ mimplies)))))))))))))) @
% 5.42/1.32 positive))))))),
% 5.42/1.32 inference('lams2combs', [status(thm)], [zip_derived_cl4])).
% 5.42/1.32 thf(zip_derived_cl46, plain,
% 5.42/1.32 ( (((!!) @ (^[Y0 : $i]:
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 ((('#B') @ mforall_indset @
% 5.42/1.32 ((('#C') @ ((('#B') @ ('#S') @
% 5.42/1.32 ((('#B') @ ((('#B') @ mimplies)) @
% 5.42/1.32 ((('#S') @ ((('#B') @ ('#B') @
% 5.42/1.32 ((('#B') @ mand @ positive)))) @
% 5.42/1.32 ((('#B') @ ((('#B') @ mbox)) @
% 5.42/1.32 ((('#B') @ ((('#B') @ mforall_ind)) @
% 5.42/1.32 ((('#B') @ ('#S') @
% 5.42/1.32 ((('#B') @ mimplies)))))))))))))) @
% 5.42/1.32 positive)))) @
% 5.42/1.32 Y0))))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl5, '0'])).
% 5.42/1.32 thf(zip_derived_cl47, plain,
% 5.42/1.32 ( (((!!) @ (mforall_indset @
% 5.42/1.32 ((('#B') @ mforall_indset @
% 5.42/1.32 ((('#C') @ ((('#B') @ ('#S') @
% 5.42/1.32 ((('#B') @ ((('#B') @ mimplies)) @
% 5.42/1.32 ((('#S') @ ((('#B') @ ('#B') @
% 5.42/1.32 ((('#B') @ mand @ positive)))) @
% 5.42/1.32 ((('#B') @ ((('#B') @ mbox)) @
% 5.42/1.32 ((('#B') @ ((('#B') @ mforall_ind)) @
% 5.42/1.32 ((('#B') @ ('#S') @
% 5.42/1.32 ((('#B') @ mimplies)))))))))))))) @
% 5.42/1.32 positive)))))))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl46])).
% 5.42/1.32 thf(zip_derived_cl48, plain,
% 5.42/1.32 (![X2 : $i]:
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 ((('#B') @ mforall_indset @
% 5.42/1.32 ((('#C') @ ((('#B') @ ('#S') @
% 5.42/1.32 ((('#B') @ ((('#B') @ mimplies)) @
% 5.42/1.32 ((('#S') @ ((('#B') @ ('#B') @
% 5.42/1.32 ((('#B') @ mand @ positive)))) @
% 5.42/1.32 ((('#B') @ ((('#B') @ mbox)) @
% 5.42/1.32 ((('#B') @ ((('#B') @ mforall_ind)) @
% 5.42/1.32 ((('#B') @ ('#S') @ ((('#B') @ mimplies)))))))))))))) @
% 5.42/1.32 positive)))) @
% 5.42/1.32 X2)),
% 5.42/1.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])).
% 5.42/1.32 thf(zip_derived_cl49, plain,
% 5.42/1.32 (![X0 : $i]:
% 5.42/1.32 (((!!) @ (^[Y0 : mu > $i > $o]:
% 5.42/1.32 ((('#B') @ mforall_indset @
% 5.42/1.32 ((('#C') @ ((('#B') @ ('#S') @
% 5.42/1.32 ((('#B') @ ((('#B') @ mimplies)) @
% 5.42/1.32 ((('#S') @ ((('#B') @ ('#B') @
% 5.42/1.32 ((('#B') @ mand @ positive)))) @
% 5.42/1.32 ((('#B') @ ((('#B') @ mbox)) @
% 5.42/1.32 ((('#B') @ ((('#B') @ mforall_ind)) @
% 5.42/1.32 ((('#B') @ ('#S') @
% 5.42/1.32 ((('#B') @ mimplies)))))))))))))) @
% 5.42/1.32 positive)) @
% 5.42/1.32 Y0 @ X0)))))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl48, '1'])).
% 5.42/1.32 thf(zip_derived_cl50, plain,
% 5.42/1.32 (![X0 : $i]:
% 5.42/1.32 (((!!) @ ((('#C') @ ((('#B') @ mforall_indset @
% 5.42/1.32 ((('#C') @ ((('#B') @ ('#S') @
% 5.42/1.32 ((('#B') @ ((('#B') @ mimplies)) @
% 5.42/1.32 ((('#S') @ ((('#B') @ ('#B') @
% 5.42/1.32 ((('#B') @ mand @
% 5.42/1.32 positive)))) @
% 5.42/1.32 ((('#B') @ ((('#B') @ mbox)) @
% 5.42/1.32 ((('#B') @ ((('#B') @ mforall_ind)) @
% 5.42/1.32 ((('#B') @ ('#S') @
% 5.42/1.32 ((('#B') @ mimplies)))))))))))))) @
% 5.42/1.32 positive)))) @
% 5.42/1.32 X0))))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl49])).
% 5.42/1.32 thf(zip_derived_cl51, plain,
% 5.42/1.32 (![X0 : $i, X2 : mu > $i > $o]:
% 5.42/1.32 (mforall_indset @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#B') @ (mand @ (positive @ X2)) @
% 5.42/1.32 ((('#B') @ mbox @
% 5.42/1.32 ((('#B') @ mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X2)))))))))))) @
% 5.42/1.32 positive)) @
% 5.42/1.32 X0)),
% 5.42/1.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl50])).
% 5.42/1.32 thf(zip_derived_cl52, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (((!!) @ (^[Y0 : mu > $i > $o]:
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#B') @ (mand @ (positive @ X0)) @
% 5.42/1.32 ((('#B') @ mbox @
% 5.42/1.32 ((('#B') @ mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)))))))))))) @
% 5.42/1.32 positive @ Y0 @ X1)))))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl51, '1'])).
% 5.42/1.32 thf(zip_derived_cl53, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#B') @ (mand @ (positive @ X0)) @
% 5.42/1.32 ((('#B') @ mbox @
% 5.42/1.32 ((('#B') @ mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 X0)))))))))))) @
% 5.42/1.32 positive)) @
% 5.42/1.32 X1))))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl52])).
% 5.42/1.32 thf(zip_derived_cl54, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i, X3 : mu > $i > $o]:
% 5.42/1.32 (mimplies @
% 5.42/1.32 (mand @ (positive @ X0) @
% 5.42/1.32 (mbox @
% 5.42/1.32 (mforall_ind @ ((('#S') @ ((('#B') @ mimplies @ X0)) @ X3))))) @
% 5.42/1.32 (positive @ X3) @ X1)),
% 5.42/1.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl53])).
% 5.42/1.32 thf(zip_derived_cl55, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i, X2 : mu > $i > $o]:
% 5.42/1.32 (((mand @ (positive @ X2) @
% 5.42/1.32 (mbox @
% 5.42/1.32 (mforall_ind @ ((('#S') @ ((('#B') @ mimplies @ X2)) @ X0)))) @
% 5.42/1.32 X1) => (positive @ X0 @ X1)))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl54, '2'])).
% 5.42/1.32 thf(zip_derived_cl56, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i, X2 : mu > $i > $o]:
% 5.42/1.32 (~ (mand @ (positive @ X2) @
% 5.42/1.32 (mbox @
% 5.42/1.32 (mforall_ind @ ((('#S') @ ((('#B') @ mimplies @ X2)) @ X0)))) @
% 5.42/1.32 X1)
% 5.42/1.32 | (positive @ X0 @ X1))),
% 5.42/1.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])).
% 5.42/1.32 thf(mand, axiom, ~ (mand @ X0 @ X1 @ X2) =>
% 5.42/1.32 ((((X0 @ X2) & (X1 @ X2))) != ($true))).
% 5.42/1.32 thf('5', plain,
% 5.42/1.32 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 5.42/1.32 ( ( ~( mand @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X0 @ X2 ) & ( X1 @ X2 ) ) ) )),
% 5.42/1.32 inference('rw.lit', [status(esa)], [mand])).
% 5.42/1.32 thf(zip_derived_cl57, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 5.42/1.32 (~ (((positive @ X2 @ X0) & (mbox @
% 5.42/1.32 (mforall_ind @ ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1))) @
% 5.42/1.32 X0)))
% 5.42/1.32 | (positive @ X1 @ X0))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl56, '5'])).
% 5.42/1.32 thf(zip_derived_cl58, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 5.42/1.32 (~ (positive @ X2 @ X0)
% 5.42/1.32 | ~ (mbox @
% 5.42/1.32 (mforall_ind @ ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1))) @
% 5.42/1.32 X0)
% 5.42/1.32 | (positive @ X1 @ X0))),
% 5.42/1.32 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl57])).
% 5.42/1.32 thf(mbox, axiom, ~ (mbox @ X0 @ X1) =>
% 5.42/1.32 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))).
% 5.42/1.32 thf('6', plain,
% 5.42/1.32 (![X0:( $i > $o ),X1:$i]:
% 5.42/1.32 ( ( ~( mbox @ X0 @ X1 ) ) <=> ( ~( ![X6:$i]: ( X0 @ X6 ) ) ) )),
% 5.42/1.32 inference('rw.lit', [status(esa)], [mbox])).
% 5.42/1.32 thf(zip_derived_cl59, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 5.42/1.32 (~ (((!!) @ (^[Y0 : $i]:
% 5.42/1.32 (mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1)) @ Y0))))
% 5.42/1.32 | (positive @ X1 @ X0)
% 5.42/1.32 | ~ (positive @ X2 @ X0))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl58, '6'])).
% 5.42/1.32 thf(zip_derived_cl60, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 5.42/1.32 (~ (((!!) @ (mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1)))))
% 5.42/1.32 | (positive @ X1 @ X0)
% 5.42/1.32 | ~ (positive @ X2 @ X0))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl59])).
% 5.42/1.32 thf(zip_derived_cl61, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 5.42/1.32 (~ (mforall_ind @ ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1)) @
% 5.42/1.32 ('#sk1' @ X1 @ X2))
% 5.42/1.32 | ~ (positive @ X2 @ X0)
% 5.42/1.32 | (positive @ X1 @ X0))),
% 5.42/1.32 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])).
% 5.42/1.32 thf(mforall_ind, axiom, ~ (mforall_ind @ X0 @ X1) =>
% 5.42/1.32 ((((!!) @ (^[Y0 : mu]: (X0 @ Y0 @ X1)))) != ($true))).
% 5.42/1.32 thf('7', plain,
% 5.42/1.32 (![X0:( mu > $i > $o ),X1:$i]:
% 5.42/1.32 ( ( ~( mforall_ind @ X0 @ X1 ) ) <=> ( ~( ![X6:mu]: ( X0 @ X6 @ X1 ) ) ) )),
% 5.42/1.32 inference('rw.lit', [status(esa)], [mforall_ind])).
% 5.42/1.32 thf(zip_derived_cl62, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 5.42/1.32 (~ (((!!) @ (^[Y0 : mu]:
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1 @ Y0 @
% 5.42/1.32 ('#sk1' @ X1 @ X2))))))
% 5.42/1.32 | (positive @ X1 @ X0)
% 5.42/1.32 | ~ (positive @ X2 @ X0))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl61, '7'])).
% 5.42/1.32 thf(zip_derived_cl63, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 5.42/1.32 (~ (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @ X2)) @ X1)) @
% 5.42/1.32 ('#sk1' @ X1 @ X2)))))
% 5.42/1.32 | (positive @ X1 @ X0)
% 5.42/1.32 | ~ (positive @ X2 @ X0))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl62])).
% 5.42/1.32 thf(zip_derived_cl64, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 5.42/1.32 (~ (mimplies @ (X2 @ ('#sk2' @ X1 @ X2)) @
% 5.42/1.32 (X1 @ ('#sk2' @ X1 @ X2)) @ ('#sk1' @ X1 @ X2))
% 5.42/1.32 | ~ (positive @ X2 @ X0)
% 5.42/1.32 | (positive @ X1 @ X0))),
% 5.42/1.32 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl63])).
% 5.42/1.32 thf(mimplies, axiom, ~ (mimplies @ X0 @ X1 @ X2) =>
% 5.42/1.32 ((((X0 @ X2) => (X1 @ X2))) != ($true))).
% 5.42/1.32 thf('8', plain,
% 5.42/1.32 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 5.42/1.32 ( ( ~( mimplies @ X0 @ X1 @ X2 ) ) <=>
% 5.42/1.32 ( ~( ( X0 @ X2 ) => ( X1 @ X2 ) ) ) )),
% 5.42/1.32 inference('rw.lit', [status(esa)], [mimplies])).
% 5.42/1.32 thf(zip_derived_cl65, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 5.42/1.32 (~ (((X2 @ ('#sk2' @ X1 @ X2) @ ('#sk1' @ X1 @ X2)) => (X1 @
% 5.42/1.32 ('#sk2' @ X1 @ X2) @ ('#sk1' @ X1 @ X2))))
% 5.42/1.32 | (positive @ X1 @ X0)
% 5.42/1.32 | ~ (positive @ X2 @ X0))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl64, '8'])).
% 5.42/1.32 thf(zip_derived_cl67, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o, X2 : mu > $i > $o]:
% 5.42/1.32 (~ (X1 @ ('#sk2' @ X1 @ X2) @ ('#sk1' @ X1 @ X2))
% 5.42/1.32 | ~ (positive @ X2 @ X0)
% 5.42/1.32 | (positive @ X1 @ X0))),
% 5.42/1.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])).
% 5.42/1.32 thf(axA3, axiom, (mvalid @ ( positive @ god ))).
% 5.42/1.32 thf(zip_derived_cl6, plain, ( (mvalid @ (positive @ god))),
% 5.42/1.32 inference('cnf', [status(esa)], [axA3])).
% 5.42/1.32 thf(zip_derived_cl11, plain,
% 5.42/1.32 ( (((!!) @ (^[Y0 : $i]: (positive @ god @ Y0))))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl6, '0'])).
% 5.42/1.32 thf(zip_derived_cl12, plain, ( (((!!) @ (positive @ god)))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl11])).
% 5.42/1.32 thf(zip_derived_cl13, plain, (![X2 : $i]: (positive @ god @ X2)),
% 5.42/1.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])).
% 5.42/1.32 thf(zip_derived_cl96, plain,
% 5.42/1.32 (![X0 : $i, X1 : mu > $i > $o]:
% 5.42/1.32 ( (positive @ X1 @ X0)
% 5.42/1.32 | ~ (X1 @ ('#sk2' @ X1 @ god) @ ('#sk1' @ X1 @ god)))),
% 5.42/1.32 inference('sup+', [status(thm)], [zip_derived_cl67, zip_derived_cl13])).
% 5.42/1.32 thf(zip_derived_cl371, plain,
% 5.42/1.32 (~ ((('#B') @ mnot @ necessary_existence @
% 5.42/1.32 ('#sk2' @ ((('#B') @ mnot @ necessary_existence)) @ god) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god)))),
% 5.42/1.32 inference('sup+', [status(thm)], [zip_derived_cl185, zip_derived_cl96])).
% 5.42/1.32 thf(zip_derived_cl386, plain,
% 5.42/1.32 (~ (mnot @
% 5.42/1.32 (necessary_existence @
% 5.42/1.32 ('#sk2' @ ((('#B') @ mnot @ necessary_existence)) @ god)) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl371])).
% 5.42/1.32 thf(mnot, axiom, ~ (mnot @ X0 @ X1) => ((X0 @ X1) = ($true))).
% 5.42/1.32 thf('9', plain,
% 5.42/1.32 (![X0:( $i > $o ),X1:$i]: ( ( ~( mnot @ X0 @ X1 ) ) <=> ( X0 @ X1 ) )),
% 5.42/1.32 inference('rw.lit', [status(esa)], [mnot])).
% 5.42/1.32 thf(zip_derived_cl739, plain,
% 5.42/1.32 ( (necessary_existence @
% 5.42/1.32 ('#sk2' @ ((('#B') @ mnot @ necessary_existence)) @ god) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl386, '9'])).
% 5.42/1.32 thf(defD3, axiom,(( necessary_existence @ (X0)@ (X1)) =
% 5.42/1.32 ((mforall_indset @
% 5.42/1.32 (^[Y0 : mu > $i > $o]:
% 5.42/1.32 (mimplies @ (essence @ Y0 @ X0) @
% 5.42/1.32 (mbox @ (mexists_ind @ (^[Y1 : mu]: (Y0 @ Y1)))))) @
% 5.42/1.32 X1)))).
% 5.42/1.32 thf('10', plain,
% 5.42/1.32 (![X1:$i,X0:mu]:
% 5.42/1.32 ( ( necessary_existence @ X0 @ X1 ) =
% 5.42/1.32 ( mforall_indset @
% 5.42/1.32 ( ^[V_1:( mu > $i > $o )]:
% 5.42/1.32 ( mimplies @
% 5.42/1.32 ( essence @ V_1 @ X0 ) @
% 5.42/1.32 ( mbox @ ( mexists_ind @ ( ^[V_2:mu]: ( V_1 @ V_2 ) ) ) ) ) ) @
% 5.42/1.32 X1 ) )),
% 5.42/1.32 define([status(thm)])).
% 5.42/1.32 thf(zip_derived_cl740, plain,
% 5.42/1.32 ( (mforall_indset @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#C') @ essence @
% 5.42/1.32 ('#sk2' @ ((('#B') @ mnot @ necessary_existence)) @ god))))) @
% 5.42/1.32 ((('#B') @ mbox @ mexists_ind)))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god))),
% 5.42/1.32 inference('rw', [status(thm)], [zip_derived_cl739, '10'])).
% 5.42/1.32 thf(zip_derived_cl741, plain,
% 5.42/1.32 ( (((!!) @ (^[Y0 : mu > $i > $o]:
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#C') @ essence @
% 5.42/1.32 ('#sk2' @
% 5.42/1.32 ((('#B') @ mnot @ necessary_existence)) @
% 5.42/1.32 god))))) @
% 5.42/1.32 ((('#B') @ mbox @ mexists_ind)) @ Y0 @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god))))))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl740, '1'])).
% 5.42/1.32 thf(zip_derived_cl742, plain,
% 5.42/1.32 ( (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#C') @ essence @
% 5.42/1.32 ('#sk2' @
% 5.42/1.32 ((('#B') @ mnot @
% 5.42/1.32 necessary_existence)) @
% 5.42/1.32 god))))) @
% 5.42/1.32 ((('#B') @ mbox @ mexists_ind)))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god)))))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl741])).
% 5.42/1.32 thf(zip_derived_cl743, plain,
% 5.42/1.32 (![X2 : mu > $i > $o]:
% 5.42/1.32 (mimplies @
% 5.42/1.32 (essence @ X2 @
% 5.42/1.32 ('#sk2' @ ((('#B') @ mnot @ necessary_existence)) @ god)) @
% 5.42/1.32 (mbox @ (mexists_ind @ X2)) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god))),
% 5.42/1.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl742])).
% 5.42/1.32 thf(zip_derived_cl744, plain,
% 5.42/1.32 (![X0 : mu > $i > $o]:
% 5.42/1.32 (((essence @ X0 @
% 5.42/1.32 ('#sk2' @ ((('#B') @ mnot @ necessary_existence)) @ god) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god)) =>
% 5.42/1.32 (mbox @ (mexists_ind @ X0) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god))))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl743, '2'])).
% 5.42/1.32 thf(defD2, axiom,(( essence @ (X1)@ (X0)@ (X2)) =
% 5.42/1.32 ((mforall_indset @
% 5.42/1.32 (^[Y0 : mu > $i > $o]:
% 5.42/1.32 (mimplies @ (Y0 @ X0) @
% 5.42/1.32 (mbox @
% 5.42/1.32 (mforall_ind @ (^[Y1 : mu]: (mimplies @ (X1 @ Y1) @ (Y0 @ Y1))))))) @
% 5.42/1.32 X2)))).
% 5.42/1.32 thf('11', plain,
% 5.42/1.32 (![X2:$i,X1:( mu > $i > $o ),X0:mu]:
% 5.42/1.32 ( ( essence @ X1 @ X0 @ X2 ) =
% 5.42/1.32 ( mforall_indset @
% 5.42/1.32 ( ^[V_1:( mu > $i > $o )]:
% 5.42/1.32 ( mimplies @
% 5.42/1.32 ( V_1 @ X0 ) @
% 5.42/1.32 ( mbox @
% 5.42/1.32 ( mforall_ind @
% 5.42/1.32 ( ^[V_2:mu]: ( mimplies @ ( X1 @ V_2 ) @ ( V_1 @ V_2 ) ) ) ) ) ) ) @
% 5.42/1.32 X2 ) )),
% 5.42/1.32 define([status(thm)])).
% 5.42/1.32 thf(zip_derived_cl745, plain,
% 5.42/1.32 (![X0 : mu > $i > $o]:
% 5.42/1.32 (((mforall_indset @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#C') @ ('#I') @
% 5.42/1.32 ('#sk2' @ ((('#B') @ mnot @ necessary_existence)) @
% 5.42/1.32 god))))) @
% 5.42/1.32 ((('#B') @ mbox @
% 5.42/1.32 ((('#B') @ mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)))))))))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god)) =>
% 5.42/1.32 (mbox @ (mexists_ind @ X0) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god))))),
% 5.42/1.32 inference('rw', [status(thm)], [zip_derived_cl744, '11'])).
% 5.42/1.32 thf(zip_derived_cl746, plain,
% 5.42/1.32 (![X0 : mu > $i > $o]:
% 5.42/1.32 (~ (mforall_indset @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#C') @ ('#I') @
% 5.42/1.32 ('#sk2' @
% 5.42/1.32 ((('#B') @ mnot @ necessary_existence)) @ god))))) @
% 5.42/1.32 ((('#B') @ mbox @
% 5.42/1.32 ((('#B') @ mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)))))))))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god))
% 5.42/1.32 | (mbox @ (mexists_ind @ X0) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god)))),
% 5.42/1.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl745])).
% 5.42/1.32 thf(mforall_indset, axiom, ~ (mforall_indset @ X0 @ X1) =>
% 5.42/1.32 ((((!!) @ (^[Y0 : mu > $i > $o]: (X0 @ Y0 @ X1)))) != ($true))).
% 5.42/1.32 thf('12', plain,
% 5.42/1.32 (![X0:( ( mu > $i > $o ) > $i > $o ),X1:$i]:
% 5.42/1.32 ( ( ~( mforall_indset @ X0 @ X1 ) ) <=>
% 5.42/1.32 ( ~( ![X6:( mu > $i > $o )]: ( X0 @ X6 @ X1 ) ) ) )),
% 5.42/1.32 inference('rw.lit', [status(esa)], [mforall_indset])).
% 5.42/1.32 thf(zip_derived_cl747, plain,
% 5.42/1.32 (![X0 : mu > $i > $o]:
% 5.42/1.32 (~ (((!!) @ (^[Y0 : mu > $i > $o]:
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#C') @ ('#I') @
% 5.42/1.32 ('#sk2' @
% 5.42/1.32 ((('#B') @ mnot @ necessary_existence)) @
% 5.42/1.32 god))))) @
% 5.42/1.32 ((('#B') @ mbox @
% 5.42/1.32 ((('#B') @ mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)))))))) @
% 5.42/1.32 Y0 @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @
% 5.42/1.32 god))))))
% 5.42/1.32 | (mbox @ (mexists_ind @ X0) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god)))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl746, '12'])).
% 5.42/1.32 thf(zip_derived_cl748, plain,
% 5.42/1.32 (![X0 : mu > $i > $o]:
% 5.42/1.32 (~ (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#C') @ ('#I') @
% 5.42/1.32 ('#sk2' @
% 5.42/1.32 ((('#B') @ mnot @
% 5.42/1.32 necessary_existence)) @
% 5.42/1.32 god))))) @
% 5.42/1.32 ((('#B') @ mbox @
% 5.42/1.32 ((('#B') @ mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)))))))))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god)))))
% 5.42/1.32 | (mbox @ (mexists_ind @ X0) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god)))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl747])).
% 5.42/1.32 thf(zip_derived_cl749, plain,
% 5.42/1.32 (![X0 : mu > $i > $o]:
% 5.42/1.32 ( (((!!) @ (^[Y0 : $i]: (mexists_ind @ X0 @ Y0))))
% 5.42/1.32 | ~ (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#C') @ ('#I') @
% 5.42/1.32 ('#sk2' @
% 5.42/1.32 ((('#B') @ mnot @
% 5.42/1.32 necessary_existence)) @
% 5.42/1.32 god))))) @
% 5.42/1.32 ((('#B') @ mbox @
% 5.42/1.32 ((('#B') @ mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)))))))))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @
% 5.42/1.32 god))))))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl748, '4'])).
% 5.42/1.32 thf(zip_derived_cl750, plain,
% 5.42/1.32 (![X0 : mu > $i > $o]:
% 5.42/1.32 ( (((!!) @ (mexists_ind @ X0)))
% 5.42/1.32 | ~ (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#C') @ ('#I') @
% 5.42/1.32 ('#sk2' @
% 5.42/1.32 ((('#B') @ mnot @
% 5.42/1.32 necessary_existence)) @
% 5.42/1.32 god))))) @
% 5.42/1.32 ((('#B') @ mbox @
% 5.42/1.32 ((('#B') @ mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)))))))))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @
% 5.42/1.32 god))))))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl749])).
% 5.42/1.32 thf(zip_derived_cl751, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X2 : $i]:
% 5.42/1.32 ( (mexists_ind @ X0 @ X2)
% 5.42/1.32 | ~ (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#C') @ ('#I') @
% 5.42/1.32 ('#sk2' @
% 5.42/1.32 ((('#B') @ mnot @
% 5.42/1.32 necessary_existence)) @
% 5.42/1.32 god))))) @
% 5.42/1.32 ((('#B') @ mbox @
% 5.42/1.32 ((('#B') @ mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)))))))))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @
% 5.42/1.32 god))))))),
% 5.42/1.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl750])).
% 5.42/1.32 thf(mexists_ind, axiom, (mexists_ind @ X0 @ X1) =>
% 5.42/1.32 ((((??) @ (^[Y0 : mu]: (X0 @ Y0 @ X1)))) = ($true))).
% 5.42/1.32 thf('13', plain,
% 5.42/1.32 (![X0:( mu > $i > $o ),X1:$i]:
% 5.42/1.32 ( ( mexists_ind @ X0 @ X1 ) <=> ( ?[X6:mu]: ( X0 @ X6 @ X1 ) ) )),
% 5.42/1.32 inference('rw.lit', [status(esa)], [mexists_ind])).
% 5.42/1.32 thf(zip_derived_cl752, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 ( (((??) @ (^[Y0 : mu]: (X0 @ Y0 @ X1))))
% 5.42/1.32 | ~ (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#C') @ ('#I') @
% 5.42/1.32 ('#sk2' @
% 5.42/1.32 ((('#B') @ mnot @
% 5.42/1.32 necessary_existence)) @
% 5.42/1.32 god))))) @
% 5.42/1.32 ((('#B') @ mbox @
% 5.42/1.32 ((('#B') @ mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)))))))))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @
% 5.42/1.32 god))))))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl751, '13'])).
% 5.42/1.32 thf(zip_derived_cl753, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 ( (((??) @ ((('#C') @ X0 @ X1))))
% 5.42/1.32 | ~ (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#C') @ ('#I') @
% 5.42/1.32 ('#sk2' @
% 5.42/1.32 ((('#B') @ mnot @
% 5.42/1.32 necessary_existence)) @
% 5.42/1.32 god))))) @
% 5.42/1.32 ((('#B') @ mbox @
% 5.42/1.32 ((('#B') @ mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)))))))))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @
% 5.42/1.32 god))))))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl752])).
% 5.42/1.32 thf(zip_derived_cl754, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 ( (X0 @ ('#sk3' @ X0 @ X1) @ X1)
% 5.42/1.32 | ~ (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @
% 5.42/1.32 ((('#C') @ ('#I') @
% 5.42/1.32 ('#sk2' @
% 5.42/1.32 ((('#B') @ mnot @
% 5.42/1.32 necessary_existence)) @
% 5.42/1.32 god))))) @
% 5.42/1.32 ((('#B') @ mbox @
% 5.42/1.32 ((('#B') @ mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)))))))))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @
% 5.42/1.32 god))))))),
% 5.42/1.32 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl753])).
% 5.42/1.32 thf(zip_derived_cl755, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (~ (mimplies @
% 5.42/1.32 ('#sk4' @ X0 @
% 5.42/1.32 ('#sk2' @ ((('#B') @ mnot @ necessary_existence)) @ god)) @
% 5.42/1.32 (mbox @
% 5.42/1.32 (mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)) @ ('#sk4' @ X0))))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god))
% 5.42/1.32 | (X0 @ ('#sk3' @ X0 @ X1) @ X1))),
% 5.42/1.32 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl754])).
% 5.42/1.32 thf(zip_derived_cl756, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (~ ((('#sk4' @ X0 @
% 5.42/1.32 ('#sk2' @ ((('#B') @ mnot @ necessary_existence)) @ god) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god)) =>
% 5.42/1.32 (mbox @
% 5.42/1.32 (mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)) @ ('#sk4' @ X0)))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god))))
% 5.42/1.32 | (X0 @ ('#sk3' @ X0 @ X1) @ X1))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl755, '8'])).
% 5.42/1.32 thf(zip_derived_cl758, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (~ (mbox @
% 5.42/1.32 (mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)) @ ('#sk4' @ X0)))) @
% 5.42/1.32 ('#sk1' @ ((('#B') @ mnot @ necessary_existence)) @ god))
% 5.42/1.32 | (X0 @ ('#sk3' @ X0 @ X1) @ X1))),
% 5.42/1.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl756])).
% 5.42/1.32 thf(zip_derived_cl759, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (~ (((!!) @ (^[Y0 : $i]:
% 5.42/1.32 (mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)) @ ('#sk4' @ X0))) @
% 5.42/1.32 Y0))))
% 5.42/1.32 | (X0 @ ('#sk3' @ X0 @ X1) @ X1))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl758, '6'])).
% 5.42/1.32 thf(zip_derived_cl760, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (~ (((!!) @ (mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)) @ ('#sk4' @ X0))))))
% 5.42/1.32 | (X0 @ ('#sk3' @ X0 @ X1) @ X1))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl759])).
% 5.42/1.32 thf(zip_derived_cl761, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (~ (mforall_ind @
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)) @ ('#sk4' @ X0))) @
% 5.42/1.32 ('#sk1' @ ('#sk4' @ X0) @ X0))
% 5.42/1.32 | (X0 @ ('#sk3' @ X0 @ X1) @ X1))),
% 5.42/1.32 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl760])).
% 5.42/1.32 thf(zip_derived_cl762, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (~ (((!!) @ (^[Y0 : mu]:
% 5.42/1.32 ((('#S') @ ((('#B') @ mimplies @ X0)) @
% 5.42/1.32 ('#sk4' @ X0) @ Y0 @ ('#sk1' @ ('#sk4' @ X0) @ X0))))))
% 5.42/1.32 | (X0 @ ('#sk3' @ X0 @ X1) @ X1))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl761, '7'])).
% 5.42/1.32 thf(zip_derived_cl763, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (~ (((!!) @ ((('#C') @ ((('#S') @ ((('#B') @ mimplies @ X0)) @
% 5.42/1.32 ('#sk4' @ X0))) @
% 5.42/1.32 ('#sk1' @ ('#sk4' @ X0) @ X0)))))
% 5.42/1.32 | (X0 @ ('#sk3' @ X0 @ X1) @ X1))),
% 5.42/1.32 inference('comb-normalize', [status(thm)], [zip_derived_cl762])).
% 5.42/1.32 thf(zip_derived_cl764, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (~ (mimplies @ (X0 @ ('#sk2' @ ('#sk4' @ X0) @ X0)) @
% 5.42/1.32 ('#sk4' @ X0 @ ('#sk2' @ ('#sk4' @ X0) @ X0)) @
% 5.42/1.32 ('#sk1' @ ('#sk4' @ X0) @ X0))
% 5.42/1.32 | (X0 @ ('#sk3' @ X0 @ X1) @ X1))),
% 5.42/1.32 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl763])).
% 5.42/1.32 thf(zip_derived_cl765, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 (~ (((X0 @ ('#sk2' @ ('#sk4' @ X0) @ X0) @
% 5.42/1.32 ('#sk1' @ ('#sk4' @ X0) @ X0)) => ('#sk4' @ X0 @
% 5.42/1.32 ('#sk2' @ ('#sk4' @ X0) @ X0) @ ('#sk1' @ ('#sk4' @ X0) @ X0))))
% 5.42/1.32 | (X0 @ ('#sk3' @ X0 @ X1) @ X1))),
% 5.42/1.32 inference('rw_clause', [status(thm)], [zip_derived_cl764, '8'])).
% 5.42/1.32 thf(zip_derived_cl766, plain,
% 5.42/1.32 (![X0 : mu > $i > $o, X1 : $i]:
% 5.42/1.32 ( (X0 @ ('#sk2' @ ('#sk4' @ X0) @ X0) @ ('#sk1' @ ('#sk4' @ X0) @ X0))
% 5.42/1.32 | (X0 @ ('#sk3' @ X0 @ X1) @ X1))),
% 5.42/1.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl765])).
% 5.42/1.32 thf(zip_derived_cl768, plain, ($false),
% 5.42/1.32 inference('flex_resolve', [status(thm)], [zip_derived_cl766])).
% 5.42/1.32
% 5.42/1.32 % SZS output end Refutation
% 5.42/1.32
% 5.42/1.32
% 5.42/1.32 % Terminating...
% 5.83/1.38 % Runner terminated.
% 5.83/1.40 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------