%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET575^7 : TPTP v9.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.b5XjBNXFFM true
% Computer : n013.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 04:52:15 PM UTC 2025
% Result : Theorem 113.99s 14.95s
% Output : Refutation 113.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET575^7 : TPTP v9.2.0. Released v5.5.0.
% 0.03/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.b5XjBNXFFM true
% 0.13/0.34 % Computer : n013.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 : Wed Oct 1 12:57:23 EDT 2025
% 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
% 0.55/0.69 % Total configuration time : 828
% 0.55/0.69 % Estimated wc time : 1656
% 0.55/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.57/0.82 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 8.54/1.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 113.99/14.95 % Solved by lams/30_b.l.sh.
% 113.99/14.95 % done 2555 iterations in 14.065s
% 113.99/14.95 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 113.99/14.95 % SZS output start Refutation
% 113.99/14.95 thf(mu_type, type, mu: $tType).
% 113.99/14.95 thf(member_type, type, member: mu > mu > $i > $o).
% 113.99/14.95 thf(rel_s4_type, type, rel_s4: $i > $i > $o).
% 113.99/14.95 thf('#sk13_type', type, '#sk13': $i > mu > mu > mu).
% 113.99/14.95 thf(mreflexive_type, type, mreflexive: ($i > $i > $o) > $o).
% 113.99/14.95 thf('#sk2_type', type, '#sk2': $i).
% 113.99/14.95 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 113.99/14.95 thf('#sk10_type', type, '#sk10': mu > $i).
% 113.99/14.95 thf('#form12_type', type, '#form12': $i > mu > mu > $o).
% 113.99/14.95 thf('#sk11_type', type, '#sk11': mu > mu > $i > $i).
% 113.99/14.95 thf(mnot_type, type, mnot: ($i > $o) > $i > $o).
% 113.99/14.95 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 113.99/14.95 thf('#sk8_type', type, '#sk8': mu > $i).
% 113.99/14.95 thf('#form9_type', type, '#form9': mu > $o).
% 113.99/14.95 thf('#sk4_type', type, '#sk4': mu).
% 113.99/14.95 thf('#sk3_type', type, '#sk3': $i).
% 113.99/14.95 thf(mexists_ind_type, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 113.99/14.95 thf('#sk7_type', type, '#sk7': $i).
% 113.99/14.95 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 113.99/14.95 thf(mtransitive_type, type, mtransitive: ($i > $i > $o) > $o).
% 113.99/14.95 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o).
% 113.99/14.95 thf(exists_in_world_type, type, exists_in_world: mu > $i > $o).
% 113.99/14.95 thf('#sk6_type', type, '#sk6': mu).
% 113.99/14.95 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 113.99/14.95 thf(intersect_type, type, intersect: mu > mu > $i > $o).
% 113.99/14.95 thf(mvalid_type, type, mvalid: ($i > $o) > $o).
% 113.99/14.95 thf('#sk5_type', type, '#sk5': $i).
% 113.99/14.95 thf(prove_th15, conjecture,
% 113.99/14.95 (mvalid @
% 113.99/14.95 ( mbox_s4 @
% 113.99/14.95 ( mforall_ind @
% 113.99/14.95 ( ^[B:mu]:
% 113.99/14.95 ( mbox_s4 @
% 113.99/14.95 ( mforall_ind @
% 113.99/14.95 ( ^[C:mu]:
% 113.99/14.95 ( mbox_s4 @
% 113.99/14.95 ( mimplies @
% 113.99/14.95 ( mbox_s4 @ ( intersect @ B @ C ) ) @
% 113.99/14.95 ( mexists_ind @
% 113.99/14.95 ( ^[D:mu]:
% 113.99/14.95 ( mand @
% 113.99/14.95 ( mbox_s4 @ ( member @ D @ B ) ) @
% 113.99/14.95 ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 113.99/14.95 thf(zf_stmt_0, negated_conjecture,
% 113.99/14.95 (~( mvalid @
% 113.99/14.95 ( mbox_s4 @
% 113.99/14.95 ( mforall_ind @
% 113.99/14.95 ( ^[B:mu]:
% 113.99/14.95 ( mbox_s4 @
% 113.99/14.95 ( mforall_ind @
% 113.99/14.95 ( ^[C:mu]:
% 113.99/14.95 ( mbox_s4 @
% 113.99/14.95 ( mimplies @
% 113.99/14.95 ( mbox_s4 @ ( intersect @ B @ C ) ) @
% 113.99/14.95 ( mexists_ind @
% 113.99/14.95 ( ^[D:mu]:
% 113.99/14.95 ( mand @
% 113.99/14.95 ( mbox_s4 @ ( member @ D @ B ) ) @
% 113.99/14.95 ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 113.99/14.95 inference('cnf.neg', [status(esa)], [prove_th15])).
% 113.99/14.95 thf(zip_derived_cl6, plain,
% 113.99/14.95 (~ (mvalid @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))))))))))))),
% 113.99/14.95 inference('cnf', [status(esa)], [zf_stmt_0])).
% 113.99/14.95 thf(mvalid, axiom, ~ (mvalid @ X0) =>
% 113.99/14.95 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))).
% 113.99/14.95 thf('0', plain,
% 113.99/14.95 (![X0:( $i > $o )]:
% 113.99/14.95 ( ( ~( mvalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )),
% 113.99/14.95 inference('rw.lit', [status(esa)], [mvalid])).
% 113.99/14.95 thf(zip_derived_cl17, plain,
% 113.99/14.95 (~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y1 @ Y2)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y3 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y3 @ Y2)))))))))))) @
% 113.99/14.95 Y0))))),
% 113.99/14.95 inference('rw_clause', [status(thm)], [zip_derived_cl6, '0'])).
% 113.99/14.95 thf(zip_derived_cl18, plain,
% 113.99/14.95 (~ (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1)))))))))))) @
% 113.99/14.95 '#sk2')),
% 113.99/14.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl17])).
% 113.99/14.95 thf(mbox_s4, axiom, ~ (mbox_s4 @ X0 @ X1) =>
% 113.99/14.95 ((((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X1 @ Y0))) | (X0 @ Y0)))))) !=
% 113.99/14.95 ($true))).
% 113.99/14.95 thf('1', plain,
% 113.99/14.95 (![X0:( $i > $o ),X1:$i]:
% 113.99/14.95 ( ( ~( mbox_s4 @ X0 @ X1 ) ) <=>
% 113.99/14.95 ( ~( ![X6:$i]: ( ( ~( rel_s4 @ X1 @ X6 ) ) | ( X0 @ X6 ) ) ) ) )),
% 113.99/14.95 inference('rw.lit', [status(esa)], [mbox_s4])).
% 113.99/14.95 thf(zip_derived_cl19, plain,
% 113.99/14.95 (~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.95 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y1 @ Y2)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y3 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y3 @ Y2))))))))))) @
% 113.99/14.95 Y0))))))),
% 113.99/14.95 inference('rw_clause', [status(thm)], [zip_derived_cl18, '1'])).
% 113.99/14.95 thf(zip_derived_cl20, plain,
% 113.99/14.95 (~ (((((~) @ (rel_s4 @ '#sk2' @ '#sk3'))) | (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))))))))) @
% 113.99/14.95 '#sk3')))),
% 113.99/14.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])).
% 113.99/14.95 thf(zip_derived_cl22, plain,
% 113.99/14.95 (~ (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))))))))) @
% 113.99/14.95 '#sk3')),
% 113.99/14.95 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])).
% 113.99/14.95 thf(mforall_ind, axiom, ~ (mforall_ind @ X0 @ X1) =>
% 113.99/14.95 ((((!!) @ (^[Y0 : mu]: (((exists_in_world @ Y0 @ X1) => (X0 @ Y0 @ X1))))))
% 113.99/14.95 != ($true))).
% 113.99/14.95 thf('2', plain,
% 113.99/14.95 (![X0:( mu > $i > $o ),X1:$i]:
% 113.99/14.95 ( ( ~( mforall_ind @ X0 @ X1 ) ) <=>
% 113.99/14.95 ( ~( ![X6:mu]: ( ( exists_in_world @ X6 @ X1 ) => ( X0 @ X6 @ X1 ) ) ) ) )),
% 113.99/14.95 inference('rw.lit', [status(esa)], [mforall_ind])).
% 113.99/14.95 thf(zip_derived_cl23, plain,
% 113.99/14.95 (~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.95 (((exists_in_world @ Y0 @ '#sk3') =>
% 113.99/14.95 ((^[Y1 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y1 @ Y2)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y3 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y3 @ Y2))))))))))) @
% 113.99/14.95 Y0 @ '#sk3'))))))),
% 113.99/14.95 inference('rw_clause', [status(thm)], [zip_derived_cl22, '2'])).
% 113.99/14.95 thf(zip_derived_cl24, plain,
% 113.99/14.95 (~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.95 (((exists_in_world @ Y0 @ '#sk3') => (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))))))) @
% 113.99/14.95 '#sk3'))))))),
% 113.99/14.95 inference('ho_norm', [status(thm)], [zip_derived_cl23])).
% 113.99/14.95 thf(zip_derived_cl25, plain,
% 113.99/14.95 (~ (((exists_in_world @ '#sk4' @ '#sk3') => (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0))))))))) @
% 113.99/14.95 '#sk3')))),
% 113.99/14.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl24])).
% 113.99/14.95 thf(zip_derived_cl27, plain,
% 113.99/14.95 (~ (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0))))))))) @
% 113.99/14.95 '#sk3')),
% 113.99/14.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 113.99/14.95 thf(zip_derived_cl28, plain,
% 113.99/14.95 (~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.95 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ '#sk4')) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1)))))))) @
% 113.99/14.95 Y0))))))),
% 113.99/14.95 inference('rw_clause', [status(thm)], [zip_derived_cl27, '1'])).
% 113.99/14.95 thf(zip_derived_cl29, plain,
% 113.99/14.95 (~ (((((~) @ (rel_s4 @ '#sk3' @ '#sk5'))) | (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0)))))))) @
% 113.99/14.95 '#sk5')))),
% 113.99/14.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])).
% 113.99/14.95 thf(zip_derived_cl31, plain,
% 113.99/14.95 (~ (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0)))))))) @
% 113.99/14.95 '#sk5')),
% 113.99/14.95 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])).
% 113.99/14.95 thf(zip_derived_cl32, plain,
% 113.99/14.95 (~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.95 (((exists_in_world @ Y0 @ '#sk5') =>
% 113.99/14.95 ((^[Y1 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mbox_s4 @ (intersect @ '#sk4' @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ '#sk4')) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1)))))))) @
% 113.99/14.95 Y0 @ '#sk5'))))))),
% 113.99/14.95 inference('rw_clause', [status(thm)], [zip_derived_cl31, '2'])).
% 113.99/14.95 thf(zip_derived_cl33, plain,
% 113.99/14.95 (~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.95 (((exists_in_world @ Y0 @ '#sk5') => (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0)))))) @
% 113.99/14.95 '#sk5'))))))),
% 113.99/14.95 inference('ho_norm', [status(thm)], [zip_derived_cl32])).
% 113.99/14.95 thf(zip_derived_cl34, plain,
% 113.99/14.95 (~ (((exists_in_world @ '#sk6' @ '#sk5') => (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @
% 113.99/14.95 (mbox_s4 @ (member @ Y0 @ '#sk6')))))) @
% 113.99/14.95 '#sk5')))),
% 113.99/14.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl33])).
% 113.99/14.95 thf(zip_derived_cl36, plain,
% 113.99/14.95 (~ (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @
% 113.99/14.95 (mbox_s4 @ (member @ Y0 @ '#sk6')))))) @
% 113.99/14.95 '#sk5')),
% 113.99/14.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 113.99/14.95 thf(zip_derived_cl37, plain,
% 113.99/14.95 (~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.95 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (mimplies @
% 113.99/14.95 (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ '#sk6'))))) @
% 113.99/14.95 Y0))))))),
% 113.99/14.95 inference('rw_clause', [status(thm)], [zip_derived_cl36, '1'])).
% 113.99/14.95 thf(zip_derived_cl38, plain,
% 113.99/14.95 (~ (((((~) @ (rel_s4 @ '#sk5' @ '#sk7'))) | (mimplies @
% 113.99/14.95 (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @
% 113.99/14.95 (mbox_s4 @ (member @ Y0 @ '#sk6'))))) @
% 113.99/14.95 '#sk7')))),
% 113.99/14.95 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl37])).
% 113.99/14.95 thf(mimplies, axiom,(( mimplies @ (X0)@ (X1)@ (X2)) =
% 113.99/14.95 ((mor @ (mnot @ X0) @ X1 @ X2)))).
% 113.99/14.95 thf('3', plain,
% 113.99/14.95 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 113.99/14.95 ( ( mimplies @ X0 @ X1 @ X2 ) = ( mor @ ( mnot @ X0 ) @ X1 @ X2 ) )),
% 113.99/14.95 define([status(thm)])).
% 113.99/14.95 thf(zip_derived_cl39, plain,
% 113.99/14.95 (~ (((((~) @ (rel_s4 @ '#sk5' @ '#sk7'))) | (mor @
% 113.99/14.95 (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6'))) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @
% 113.99/14.95 (mbox_s4 @ (member @ Y0 @ '#sk6'))))) @
% 113.99/14.95 '#sk7')))),
% 113.99/14.95 inference('rw', [status(thm)], [zip_derived_cl38, '3'])).
% 113.99/14.95 thf(zip_derived_cl40, plain, ( (rel_s4 @ '#sk5' @ '#sk7')),
% 113.99/14.95 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])).
% 113.99/14.95 thf(zip_derived_cl26, plain, ( (exists_in_world @ '#sk4' @ '#sk3')),
% 113.99/14.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 113.99/14.95 thf(a1, axiom, (mreflexive @ rel_s4)).
% 113.99/14.95 thf(zip_derived_cl1, plain, ( (mreflexive @ rel_s4)),
% 113.99/14.95 inference('cnf', [status(esa)], [a1])).
% 113.99/14.95 thf(mreflexive, axiom, (mreflexive @ X0) =>
% 113.99/14.95 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0 @ Y0)))) = ($true))).
% 113.99/14.95 thf('4', plain,
% 113.99/14.95 (![X0:( $i > $i > $o )]:
% 113.99/14.95 ( ( mreflexive @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 @ X5 ) ) )),
% 113.99/14.95 inference('rw.lit', [status(esa)], [mreflexive])).
% 113.99/14.95 thf(zip_derived_cl7, plain, ( (((!!) @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))),
% 113.99/14.95 inference('rw_clause', [status(thm)], [zip_derived_cl1, '4'])).
% 113.99/14.95 thf(zip_derived_cl8, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)),
% 113.99/14.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])).
% 113.99/14.95 thf(zip_derived_cl35, plain, ( (exists_in_world @ '#sk6' @ '#sk5')),
% 113.99/14.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 113.99/14.95 thf(intersect_defn, axiom,
% 113.99/14.95 (mvalid @
% 113.99/14.95 ( mbox_s4 @
% 113.99/14.95 ( mforall_ind @
% 113.99/14.95 ( ^[B:mu]:
% 113.99/14.95 ( mbox_s4 @
% 113.99/14.95 ( mforall_ind @
% 113.99/14.95 ( ^[C:mu]:
% 113.99/14.95 ( mand @
% 113.99/14.95 ( mbox_s4 @
% 113.99/14.95 ( mimplies @
% 113.99/14.95 ( mbox_s4 @ ( intersect @ B @ C ) ) @
% 113.99/14.95 ( mexists_ind @
% 113.99/14.95 ( ^[D:mu]:
% 113.99/14.95 ( mand @
% 113.99/14.95 ( mbox_s4 @ ( member @ D @ B ) ) @
% 113.99/14.95 ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) ) ) @
% 113.99/14.95 ( mbox_s4 @
% 113.99/14.95 ( mimplies @
% 113.99/14.95 ( mexists_ind @
% 113.99/14.95 ( ^[D:mu]:
% 113.99/14.95 ( mand @
% 113.99/14.95 ( mbox_s4 @ ( member @ D @ B ) ) @
% 113.99/14.95 ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) @
% 113.99/14.95 ( mbox_s4 @ ( intersect @ B @ C ) ) ) ) ) ) ) ) ) ) ))).
% 113.99/14.95 thf(zip_derived_cl4, plain,
% 113.99/14.95 ( (mvalid @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y0 @ Y1))))))))))))),
% 113.99/14.95 inference('cnf', [status(esa)], [intersect_defn])).
% 113.99/14.95 thf(mvalid, axiom, (mvalid @ X0) =>
% 113.99/14.95 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))).
% 113.99/14.95 thf('5', plain,
% 113.99/14.95 (![X0:( $i > $o )]: ( ( mvalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )),
% 113.99/14.95 inference('rw.lit', [status(esa)], [mvalid])).
% 113.99/14.95 thf(zip_derived_cl110, plain,
% 113.99/14.95 ( (((!!) @ (^[Y0 : $i]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y1 @ Y2)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y3 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y3 @ Y2))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y3 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y3 @ Y2))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y1 @ Y2)))))))))) @
% 113.99/14.95 Y0))))),
% 113.99/14.95 inference('rw_clause', [status(thm)], [zip_derived_cl4, '5'])).
% 113.99/14.95 thf(zip_derived_cl111, plain,
% 113.99/14.95 (![X2 : $i]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y0 @ Y1)))))))))) @
% 113.99/14.95 X2)),
% 113.99/14.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl110])).
% 113.99/14.95 thf(mbox_s4, axiom, (mbox_s4 @ X0 @ X1) =>
% 113.99/14.95 ((((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X1 @ Y0))) | (X0 @ Y0)))))) =
% 113.99/14.95 ($true))).
% 113.99/14.95 thf('6', plain,
% 113.99/14.95 (![X0:( $i > $o ),X1:$i]:
% 113.99/14.95 ( ( mbox_s4 @ X0 @ X1 ) <=>
% 113.99/14.95 ( ![X6:$i]: ( ( ~( rel_s4 @ X1 @ X6 ) ) | ( X0 @ X6 ) ) ) )),
% 113.99/14.95 inference('rw.lit', [status(esa)], [mbox_s4])).
% 113.99/14.95 thf(zip_derived_cl112, plain,
% 113.99/14.95 (![X0 : $i]:
% 113.99/14.95 (((!!) @ (^[Y0 : $i]:
% 113.99/14.95 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y1 @ Y2)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y3 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @ (member @ Y3 @ Y1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y3 @ Y2))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y3 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @ (member @ Y3 @ Y1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y3 @ Y2))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y1 @ Y2))))))))) @
% 113.99/14.95 Y0))))))),
% 113.99/14.95 inference('rw_clause', [status(thm)], [zip_derived_cl111, '6'])).
% 113.99/14.95 thf(zip_derived_cl113, plain,
% 113.99/14.95 (![X0 : $i, X2 : $i]:
% 113.99/14.95 (((((~) @ (rel_s4 @ X0 @ X2))) | (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y0 @ Y1))))))))) @
% 113.99/14.95 X2)))),
% 113.99/14.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl112])).
% 113.99/14.95 thf(zip_derived_cl114, plain,
% 113.99/14.95 (![X0 : $i, X2 : $i]:
% 113.99/14.95 (~ (rel_s4 @ X0 @ X2)
% 113.99/14.95 | (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y0 @ Y1))))))))) @
% 113.99/14.95 X2))),
% 113.99/14.95 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl113])).
% 113.99/14.95 thf(mforall_ind, axiom, (mforall_ind @ X0 @ X1) =>
% 113.99/14.95 ((((!!) @ (^[Y0 : mu]: (((exists_in_world @ Y0 @ X1) => (X0 @ Y0 @ X1))))))
% 113.99/14.95 = ($true))).
% 113.99/14.95 thf('7', plain,
% 113.99/14.95 (![X0:( mu > $i > $o ),X1:$i]:
% 113.99/14.95 ( ( mforall_ind @ X0 @ X1 ) <=>
% 113.99/14.95 ( ![X6:mu]: ( ( exists_in_world @ X6 @ X1 ) => ( X0 @ X6 @ X1 ) ) ) )),
% 113.99/14.95 inference('rw.lit', [status(esa)], [mforall_ind])).
% 113.99/14.95 thf(zip_derived_cl115, plain,
% 113.99/14.95 (![X0 : $i, X1 : $i]:
% 113.99/14.95 ( (((!!) @ (^[Y0 : mu]:
% 113.99/14.95 (((exists_in_world @ Y0 @ X0) =>
% 113.99/14.95 ((^[Y1 : mu]:
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y1 @ Y2)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y3 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @ (member @ Y3 @ Y1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y3 @ Y2))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y3 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @ (member @ Y3 @ Y1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y3 @ Y2))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y1 @ Y2))))))))) @
% 113.99/14.95 Y0 @ X0))))))
% 113.99/14.95 | ~ (rel_s4 @ X1 @ X0))),
% 113.99/14.95 inference('rw_clause', [status(thm)], [zip_derived_cl114, '7'])).
% 113.99/14.95 thf(zip_derived_cl116, plain,
% 113.99/14.95 (![X0 : $i, X1 : $i]:
% 113.99/14.95 ( (((!!) @ (^[Y0 : mu]:
% 113.99/14.95 (((exists_in_world @ Y0 @ X0) => (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ Y0 @ Y1))))))) @
% 113.99/14.95 X0))))))
% 113.99/14.95 | ~ (rel_s4 @ X1 @ X0))),
% 113.99/14.95 inference('ho_norm', [status(thm)], [zip_derived_cl115])).
% 113.99/14.95 thf(zip_derived_cl117, plain,
% 113.99/14.95 (![X0 : $i, X1 : $i, X3 : mu]:
% 113.99/14.95 ( (((exists_in_world @ X3 @ X0) => (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ X3 @ Y0)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ X3 @ Y0))))))) @
% 113.99/14.95 X0)))
% 113.99/14.95 | ~ (rel_s4 @ X1 @ X0))),
% 113.99/14.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl116])).
% 113.99/14.95 thf(zip_derived_cl118, plain,
% 113.99/14.95 (![X0 : $i, X1 : $i, X3 : mu]:
% 113.99/14.95 (~ (exists_in_world @ X3 @ X0)
% 113.99/14.95 | (mbox_s4 @
% 113.99/14.95 (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ X3 @ Y0)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ X3 @ Y0))))))) @
% 113.99/14.95 X0)
% 113.99/14.95 | ~ (rel_s4 @ X1 @ X0))),
% 113.99/14.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl117])).
% 113.99/14.95 thf(zip_derived_cl119, plain,
% 113.99/14.95 (![X0 : $i, X1 : $i, X2 : mu]:
% 113.99/14.95 ( (((!!) @ (^[Y0 : $i]:
% 113.99/14.95 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ X2 @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ X2)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ X2)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ X2 @ Y1)))))) @
% 113.99/14.95 Y0))))))
% 113.99/14.95 | ~ (rel_s4 @ X1 @ X0)
% 113.99/14.95 | ~ (exists_in_world @ X2 @ X0))),
% 113.99/14.95 inference('rw_clause', [status(thm)], [zip_derived_cl118, '6'])).
% 113.99/14.95 thf(zip_derived_cl120, plain,
% 113.99/14.95 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]:
% 113.99/14.95 ( (((((~) @ (rel_s4 @ X0 @ X4))) | (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ X2 @ Y0)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ X2 @ Y0)))))) @
% 113.99/14.95 X4)))
% 113.99/14.95 | ~ (exists_in_world @ X2 @ X0)
% 113.99/14.95 | ~ (rel_s4 @ X1 @ X0))),
% 113.99/14.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl119])).
% 113.99/14.95 thf(zip_derived_cl121, plain,
% 113.99/14.95 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]:
% 113.99/14.95 (~ (rel_s4 @ X0 @ X4)
% 113.99/14.95 | (mforall_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ X2 @ Y0)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ X2 @ Y0)))))) @
% 113.99/14.95 X4)
% 113.99/14.95 | ~ (rel_s4 @ X1 @ X0)
% 113.99/14.95 | ~ (exists_in_world @ X2 @ X0))),
% 113.99/14.95 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl120])).
% 113.99/14.95 thf(zip_derived_cl122, plain,
% 113.99/14.95 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i]:
% 113.99/14.95 ( (((!!) @ (^[Y0 : mu]:
% 113.99/14.95 (((exists_in_world @ Y0 @ X3) =>
% 113.99/14.95 ((^[Y1 : mu]:
% 113.99/14.95 (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ X1 @ Y1)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ X1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y2 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y2 @ X1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y2 @ Y1))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ X1 @ Y1)))))) @
% 113.99/14.95 Y0 @ X3))))))
% 113.99/14.95 | ~ (exists_in_world @ X1 @ X0)
% 113.99/14.95 | ~ (rel_s4 @ X2 @ X0)
% 113.99/14.95 | ~ (rel_s4 @ X0 @ X3))),
% 113.99/14.95 inference('rw_clause', [status(thm)], [zip_derived_cl121, '7'])).
% 113.99/14.95 thf(zip_derived_cl123, plain,
% 113.99/14.95 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i]:
% 113.99/14.95 ( (((!!) @ (^[Y0 : mu]:
% 113.99/14.95 (((exists_in_world @ Y0 @ X3) => (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ X1 @ Y0)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ X1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y1 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y1 @ X1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y1 @ Y0))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ X1 @ Y0)))) @
% 113.99/14.95 X3))))))
% 113.99/14.95 | ~ (exists_in_world @ X1 @ X0)
% 113.99/14.95 | ~ (rel_s4 @ X2 @ X0)
% 113.99/14.95 | ~ (rel_s4 @ X0 @ X3))),
% 113.99/14.95 inference('ho_norm', [status(thm)], [zip_derived_cl122])).
% 113.99/14.95 thf(zip_derived_cl124, plain,
% 113.99/14.95 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i, X5 : mu]:
% 113.99/14.95 ( (((exists_in_world @ X5 @ X3) => (mand @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ X1 @ X5)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y0 @ X5))))))) @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y0 @ X5))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ X1 @ X5)))) @
% 113.99/14.95 X3)))
% 113.99/14.95 | ~ (rel_s4 @ X0 @ X3)
% 113.99/14.95 | ~ (rel_s4 @ X2 @ X0)
% 113.99/14.95 | ~ (exists_in_world @ X1 @ X0))),
% 113.99/14.95 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl123])).
% 113.99/14.95 thf(mand, axiom,(( mand @ (X0)@ (X1)@ (X2)) =
% 113.99/14.95 ((mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)) @ X2)))).
% 113.99/14.95 thf('8', plain,
% 113.99/14.95 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]:
% 113.99/14.95 ( ( mand @ X0 @ X1 @ X2 ) =
% 113.99/14.95 ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) @ X2 ) )),
% 113.99/14.95 define([status(thm)])).
% 113.99/14.95 thf(zip_derived_cl125, plain,
% 113.99/14.95 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i, X5 : mu]:
% 113.99/14.95 ( (((exists_in_world @ X5 @ X3) => (mnot @
% 113.99/14.95 (mor @
% 113.99/14.95 (mnot @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ X1 @ X5)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y0 @ X5)))))))) @
% 113.99/14.95 (mnot @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y0 @ X5))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ X1 @ X5)))))) @
% 113.99/14.95 X3)))
% 113.99/14.95 | ~ (rel_s4 @ X0 @ X3)
% 113.99/14.95 | ~ (rel_s4 @ X2 @ X0)
% 113.99/14.95 | ~ (exists_in_world @ X1 @ X0))),
% 113.99/14.95 inference('rw', [status(thm)], [zip_derived_cl124, '8'])).
% 113.99/14.95 thf(zip_derived_cl126, plain,
% 113.99/14.95 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i, X5 : mu]:
% 113.99/14.95 (~ (exists_in_world @ X5 @ X3)
% 113.99/14.95 | (mnot @
% 113.99/14.95 (mor @
% 113.99/14.95 (mnot @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @ (mbox_s4 @ (intersect @ X1 @ X5)) @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y0 @ X5)))))))) @
% 113.99/14.95 (mnot @
% 113.99/14.95 (mbox_s4 @
% 113.99/14.95 (mimplies @
% 113.99/14.95 (mexists_ind @
% 113.99/14.95 (^[Y0 : mu]:
% 113.99/14.95 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @
% 113.99/14.95 (mbox_s4 @ (member @ Y0 @ X5))))) @
% 113.99/14.95 (mbox_s4 @ (intersect @ X1 @ X5)))))) @
% 113.99/14.95 X3)
% 113.99/14.95 | ~ (exists_in_world @ X1 @ X0)
% 113.99/14.95 | ~ (rel_s4 @ X2 @ X0)
% 113.99/14.95 | ~ (rel_s4 @ X0 @ X3))),
% 113.99/14.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])).
% 113.99/14.95 thf(mnot, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))).
% 113.99/14.95 thf('9', plain,
% 113.99/14.95 (![X0:( $i > $o ),X1:$i]: ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )),
% 113.99/14.96 inference('rw.lit', [status(esa)], [mnot])).
% 113.99/14.96 thf(zip_derived_cl127, plain,
% 113.99/14.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu]:
% 113.99/14.96 (~ (mor @
% 113.99/14.96 (mnot @
% 113.99/14.96 (mbox_s4 @
% 113.99/14.96 (mimplies @ (mbox_s4 @ (intersect @ X3 @ X4)) @
% 113.99/14.96 (mexists_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X4)))))))) @
% 113.99/14.96 (mnot @
% 113.99/14.96 (mbox_s4 @
% 113.99/14.96 (mimplies @
% 113.99/14.96 (mexists_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X4))))) @
% 113.99/14.96 (mbox_s4 @ (intersect @ X3 @ X4))))) @
% 113.99/14.96 X0)
% 113.99/14.96 | ~ (rel_s4 @ X1 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X2 @ X1)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X1)
% 113.99/14.96 | ~ (exists_in_world @ X4 @ X0))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl126, '9'])).
% 113.99/14.96 thf(mor, axiom, ~ (mor @ X0 @ X1 @ X2) =>
% 113.99/14.96 ((((X1 @ X2) | (X0 @ X2))) != ($true))).
% 113.99/14.96 thf('10', plain,
% 113.99/14.96 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 113.99/14.96 ( ( ~( mor @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X1 @ X2 ) | ( X0 @ X2 ) ) ) )),
% 113.99/14.96 inference('rw.lit', [status(esa)], [mor])).
% 113.99/14.96 thf(zip_derived_cl128, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i]:
% 113.99/14.96 (~ (((mnot @
% 113.99/14.96 (mbox_s4 @
% 113.99/14.96 (mimplies @
% 113.99/14.96 (mexists_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))))) @
% 113.99/14.96 (mbox_s4 @ (intersect @ X3 @ X1)))) @
% 113.99/14.96 X0) | (mnot @
% 113.99/14.96 (mbox_s4 @
% 113.99/14.96 (mimplies @ (mbox_s4 @ (intersect @ X3 @ X1)) @
% 113.99/14.96 (mexists_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))))))) @
% 113.99/14.96 X0)))
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X2)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X2)
% 113.99/14.96 | ~ (rel_s4 @ X2 @ X0))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl127, '10'])).
% 113.99/14.96 thf(zip_derived_cl130, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i]:
% 113.99/14.96 (~ (mnot @
% 113.99/14.96 (mbox_s4 @
% 113.99/14.96 (mimplies @ (mbox_s4 @ (intersect @ X3 @ X1)) @
% 113.99/14.96 (mexists_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))))))) @
% 113.99/14.96 X0)
% 113.99/14.96 | ~ (rel_s4 @ X2 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X2)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X2)
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X0))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl128])).
% 113.99/14.96 thf(mnot, axiom, ~ (mnot @ X0 @ X1) => ((X0 @ X1) = ($true))).
% 113.99/14.96 thf('11', plain,
% 113.99/14.96 (![X0:( $i > $o ),X1:$i]: ( ( ~( mnot @ X0 @ X1 ) ) <=> ( X0 @ X1 ) )),
% 113.99/14.96 inference('rw.lit', [status(esa)], [mnot])).
% 113.99/14.96 thf(zip_derived_cl132, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i]:
% 113.99/14.96 ( (mbox_s4 @
% 113.99/14.96 (mimplies @ (mbox_s4 @ (intersect @ X3 @ X1)) @
% 113.99/14.96 (mexists_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1)))))) @
% 113.99/14.96 X0)
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X2)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X2)
% 113.99/14.96 | ~ (rel_s4 @ X2 @ X0))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl130, '11'])).
% 113.99/14.96 thf(zip_derived_cl134, plain,
% 113.99/14.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu]:
% 113.99/14.96 ( (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mimplies @
% 113.99/14.96 (mbox_s4 @ (intersect @ X3 @ X4)) @
% 113.99/14.96 (mexists_ind @
% 113.99/14.96 (^[Y1 : mu]:
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y1 @ X4))))) @
% 113.99/14.96 Y0))))))
% 113.99/14.96 | ~ (rel_s4 @ X1 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X2 @ X1)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X1)
% 113.99/14.96 | ~ (exists_in_world @ X4 @ X0))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl132, '6'])).
% 113.99/14.96 thf(zip_derived_cl136, plain,
% 113.99/14.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu, X6 : $i]:
% 113.99/14.96 ( (((((~) @ (rel_s4 @ X0 @ X6))) | (mimplies @
% 113.99/14.96 (mbox_s4 @ (intersect @ X3 @ X4)) @
% 113.99/14.96 (mexists_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X4))))) @
% 113.99/14.96 X6)))
% 113.99/14.96 | ~ (exists_in_world @ X4 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X1)
% 113.99/14.96 | ~ (rel_s4 @ X2 @ X1)
% 113.99/14.96 | ~ (rel_s4 @ X1 @ X0))),
% 113.99/14.96 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl134])).
% 113.99/14.96 thf(zip_derived_cl139, plain,
% 113.99/14.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu, X6 : $i]:
% 113.99/14.96 ( (((((~) @ (rel_s4 @ X0 @ X6))) | (mor @
% 113.99/14.96 (mnot @ (mbox_s4 @ (intersect @ X3 @ X4))) @
% 113.99/14.96 (mexists_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X4))))) @
% 113.99/14.96 X6)))
% 113.99/14.96 | ~ (exists_in_world @ X4 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X1)
% 113.99/14.96 | ~ (rel_s4 @ X2 @ X1)
% 113.99/14.96 | ~ (rel_s4 @ X1 @ X0))),
% 113.99/14.96 inference('rw', [status(thm)], [zip_derived_cl136, '3'])).
% 113.99/14.96 thf(zip_derived_cl140, plain,
% 113.99/14.96 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu, X6 : $i]:
% 113.99/14.96 (~ (rel_s4 @ X0 @ X6)
% 113.99/14.96 | (mor @ (mnot @ (mbox_s4 @ (intersect @ X3 @ X4))) @
% 113.99/14.96 (mexists_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X4))))) @
% 113.99/14.96 X6)
% 113.99/14.96 | ~ (rel_s4 @ X1 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X2 @ X1)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X1)
% 113.99/14.96 | ~ (exists_in_world @ X4 @ X0))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl139])).
% 113.99/14.96 thf(mor, axiom, (mor @ X0 @ X1 @ X2) =>
% 113.99/14.96 ((((X1 @ X2) | (X0 @ X2))) = ($true))).
% 113.99/14.96 thf('12', plain,
% 113.99/14.96 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]:
% 113.99/14.96 ( ( mor @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) | ( X1 @ X2 ) ) )),
% 113.99/14.96 inference('rw.lit', [status(esa)], [mor])).
% 113.99/14.96 thf(zip_derived_cl142, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]:
% 113.99/14.96 ( (((mexists_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1)))) @
% 113.99/14.96 X5) | (mnot @ (mbox_s4 @ (intersect @ X3 @ X1)) @ X5)))
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X2)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X2)
% 113.99/14.96 | ~ (rel_s4 @ X2 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X0 @ X5))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl140, '12'])).
% 113.99/14.96 thf(mexists_ind, axiom,(( mexists_ind @ (X0)@ (X1)) =
% 113.99/14.96 ((mnot @ (mforall_ind @ (^[Y0 : mu]: (mnot @ (X0 @ Y0)))) @ X1)))).
% 113.99/14.96 thf('13', plain,
% 113.99/14.96 (![X1:$i,X0:( mu > $i > $o )]:
% 113.99/14.96 ( ( mexists_ind @ X0 @ X1 ) =
% 113.99/14.96 ( mnot @ ( mforall_ind @ ( ^[V_1:mu]: ( mnot @ ( X0 @ V_1 ) ) ) ) @ X1 ) )),
% 113.99/14.96 define([status(thm)])).
% 113.99/14.96 thf(zip_derived_cl144, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]:
% 113.99/14.96 ( (((mnot @
% 113.99/14.96 (mforall_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1)))))) @
% 113.99/14.96 X5) | (mnot @ (mbox_s4 @ (intersect @ X3 @ X1)) @ X5)))
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X2)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X2)
% 113.99/14.96 | ~ (rel_s4 @ X2 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X0 @ X5))),
% 113.99/14.96 inference('rw', [status(thm)], [zip_derived_cl142, '13'])).
% 113.99/14.96 thf(zip_derived_cl145, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]:
% 113.99/14.96 ( (mnot @
% 113.99/14.96 (mforall_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1)))))) @
% 113.99/14.96 X5)
% 113.99/14.96 | (mnot @ (mbox_s4 @ (intersect @ X3 @ X1)) @ X5)
% 113.99/14.96 | ~ (rel_s4 @ X0 @ X5)
% 113.99/14.96 | ~ (rel_s4 @ X2 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X2)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X2)
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X0))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl144])).
% 113.99/14.96 thf(zip_derived_cl147, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]:
% 113.99/14.96 (~ (mforall_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))))) @
% 113.99/14.96 X5)
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X2)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X2)
% 113.99/14.96 | ~ (rel_s4 @ X2 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X0 @ X5)
% 113.99/14.96 | (mnot @ (mbox_s4 @ (intersect @ X3 @ X1)) @ X5))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl145, '9'])).
% 113.99/14.96 thf(zip_derived_cl149, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]:
% 113.99/14.96 (~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((exists_in_world @ Y0 @ X0) =>
% 113.99/14.96 ((^[Y1 : mu]:
% 113.99/14.96 (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y1 @ X1))))) @
% 113.99/14.96 Y0 @ X0))))))
% 113.99/14.96 | (mnot @ (mbox_s4 @ (intersect @ X2 @ X1)) @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X3 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X3)
% 113.99/14.96 | ~ (rel_s4 @ X5 @ X4)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X4)
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X3))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl147, '2'])).
% 113.99/14.96 thf(zip_derived_cl152, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]:
% 113.99/14.96 (~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((exists_in_world @ Y0 @ X0) => (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))) @
% 113.99/14.96 X0))))))
% 113.99/14.96 | (mnot @ (mbox_s4 @ (intersect @ X2 @ X1)) @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X3 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X3)
% 113.99/14.96 | ~ (rel_s4 @ X5 @ X4)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X4)
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X3))),
% 113.99/14.96 inference('ho_norm', [status(thm)], [zip_derived_cl149])).
% 113.99/14.96 thf(zip_derived_cl153, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]:
% 113.99/14.96 (~ (mbox_s4 @ (intersect @ X3 @ X1) @ X5)
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X2)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X2)
% 113.99/14.96 | ~ (rel_s4 @ X2 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X0 @ X5)
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((exists_in_world @ Y0 @ X5) => (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))) @
% 113.99/14.96 X5)))))))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl152, '9'])).
% 113.99/14.96 thf(zip_derived_cl155, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]:
% 113.99/14.96 (~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ X0 @ Y0))) | (intersect @ X2 @
% 113.99/14.96 X1 @ Y0))))))
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((exists_in_world @ Y0 @ X0) => (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))) @
% 113.99/14.96 X0))))))
% 113.99/14.96 | ~ (rel_s4 @ X3 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X3)
% 113.99/14.96 | ~ (rel_s4 @ X5 @ X4)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X4)
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X3))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl153, '1'])).
% 113.99/14.96 thf(zip_derived_cl158, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]:
% 113.99/14.96 (~ (((((~) @ (rel_s4 @ X0 @ ('#sk11' @ X2 @ X1 @ X0)))) |
% 113.99/14.96 (intersect @ X2 @ X1 @ ('#sk11' @ X2 @ X1 @ X0))))
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X3)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X4)
% 113.99/14.96 | ~ (rel_s4 @ X5 @ X4)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X3)
% 113.99/14.96 | ~ (rel_s4 @ X3 @ X0)
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((exists_in_world @ Y0 @ X0) => (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))) @
% 113.99/14.96 X0)))))))),
% 113.99/14.96 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl155])).
% 113.99/14.96 thf(zip_derived_cl160, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]:
% 113.99/14.96 ( (rel_s4 @ X0 @ ('#sk11' @ X2 @ X1 @ X0))
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((exists_in_world @ Y0 @ X0) => (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))) @
% 113.99/14.96 X0))))))
% 113.99/14.96 | ~ (rel_s4 @ X3 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X3)
% 113.99/14.96 | ~ (rel_s4 @ X5 @ X4)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X4)
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X3))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl158])).
% 113.99/14.96 thf(zip_derived_cl163, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu]:
% 113.99/14.96 ( ('#form12' @ X0 @ X1 @ X2)
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((exists_in_world @ Y0 @ X0) => (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))) @
% 113.99/14.96 X0)))))))),
% 113.99/14.96 define([status(thm)])).
% 113.99/14.96 thf(zip_derived_cl164, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu]:
% 113.99/14.96 (~ (((exists_in_world @ ('#sk13' @ X0 @ X1 @ X2) @ X0) => (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ ('#sk13' @ X0 @ X1 @ X2) @ X2)) @
% 113.99/14.96 (mbox_s4 @ (member @ ('#sk13' @ X0 @ X1 @ X2) @ X1))) @
% 113.99/14.96 X0)))
% 113.99/14.96 | ('#form12' @ X0 @ X1 @ X2))),
% 113.99/14.96 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl163])).
% 113.99/14.96 thf(zip_derived_cl169, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu]:
% 113.99/14.96 ( (exists_in_world @ ('#sk13' @ X0 @ X1 @ X2) @ X0)
% 113.99/14.96 | ('#form12' @ X0 @ X1 @ X2))),
% 113.99/14.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])).
% 113.99/14.96 thf(zip_derived_cl160, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]:
% 113.99/14.96 ( (rel_s4 @ X0 @ ('#sk11' @ X2 @ X1 @ X0))
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((exists_in_world @ Y0 @ X0) => (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))) @
% 113.99/14.96 X0))))))
% 113.99/14.96 | ~ (rel_s4 @ X3 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X3)
% 113.99/14.96 | ~ (rel_s4 @ X5 @ X4)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X4)
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X3))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl158])).
% 113.99/14.96 thf(zip_derived_cl163, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu]:
% 113.99/14.96 ( ('#form12' @ X0 @ X1 @ X2)
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((exists_in_world @ Y0 @ X0) => (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))) @
% 113.99/14.96 X0)))))))),
% 113.99/14.96 define([status(thm)])).
% 113.99/14.96 thf(zip_derived_cl165, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]:
% 113.99/14.96 (~ ('#form12' @ X0 @ X1 @ X2)
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X3)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X4)
% 113.99/14.96 | ~ (rel_s4 @ X5 @ X4)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X3)
% 113.99/14.96 | ~ (rel_s4 @ X3 @ X0)
% 113.99/14.96 | (rel_s4 @ X0 @ ('#sk11' @ X2 @ X1 @ X0)))),
% 113.99/14.96 inference('renaming', [status(thm)],
% 113.99/14.96 [zip_derived_cl160, zip_derived_cl163])).
% 113.99/14.96 thf(zip_derived_cl1292, plain,
% 113.99/14.96 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu]:
% 113.99/14.96 ( (rel_s4 @ X1 @ ('#sk11' @ X3 @ X2 @ X1))
% 113.99/14.96 | ~ (rel_s4 @ X0 @ X1)
% 113.99/14.96 | ~ (rel_s4 @ X0 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X0)
% 113.99/14.96 | ~ ('#form12' @ X1 @ X2 @ X3))),
% 113.99/14.96 inference('eq_fact', [status(thm)], [zip_derived_cl165])).
% 113.99/14.96 thf(zip_derived_cl8, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)),
% 113.99/14.96 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])).
% 113.99/14.96 thf(zip_derived_cl1400, plain,
% 113.99/14.96 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu]:
% 113.99/14.96 ( (rel_s4 @ X1 @ ('#sk11' @ X3 @ X2 @ X1))
% 113.99/14.96 | ~ (rel_s4 @ X0 @ X1)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X0)
% 113.99/14.96 | ~ ('#form12' @ X1 @ X2 @ X3))),
% 113.99/14.96 inference('demod', [status(thm)], [zip_derived_cl1292, zip_derived_cl8])).
% 113.99/14.96 thf(zip_derived_cl41, plain,
% 113.99/14.96 (~ (mor @ (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6'))) @
% 113.99/14.96 (mexists_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ '#sk6'))))) @
% 113.99/14.96 '#sk7')),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])).
% 113.99/14.96 thf(zip_derived_cl42, plain,
% 113.99/14.96 (~ (((mexists_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ '#sk6')))) @
% 113.99/14.96 '#sk7') | (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @
% 113.99/14.96 '#sk7')))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl41, '10'])).
% 113.99/14.96 thf(zip_derived_cl43, plain,
% 113.99/14.96 (~ (((mnot @
% 113.99/14.96 (mforall_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ '#sk6')))))) @
% 113.99/14.96 '#sk7') | (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @
% 113.99/14.96 '#sk7')))),
% 113.99/14.96 inference('rw', [status(thm)], [zip_derived_cl42, '13'])).
% 113.99/14.96 thf(zip_derived_cl45, plain,
% 113.99/14.96 (~ (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ '#sk7')),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])).
% 113.99/14.96 thf(zip_derived_cl47, plain,
% 113.99/14.96 ( (mbox_s4 @ (intersect @ '#sk4' @ '#sk6') @ '#sk7')),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl45, '11'])).
% 113.99/14.96 thf(zip_derived_cl49, plain,
% 113.99/14.96 ( (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (intersect @ '#sk4' @
% 113.99/14.96 '#sk6' @ Y0))))))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl47, '6'])).
% 113.99/14.96 thf(zip_derived_cl52, plain,
% 113.99/14.96 (![X2 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ '#sk7' @ X2))) | (intersect @ '#sk4' @ '#sk6' @
% 113.99/14.96 X2)))),
% 113.99/14.96 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl49])).
% 113.99/14.96 thf(zip_derived_cl54, plain,
% 113.99/14.96 (![X2 : $i]:
% 113.99/14.96 (~ (rel_s4 @ '#sk7' @ X2) | (intersect @ '#sk4' @ '#sk6' @ X2))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])).
% 113.99/14.96 thf(zip_derived_cl161, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]:
% 113.99/14.96 (~ (intersect @ X2 @ X1 @ ('#sk11' @ X2 @ X1 @ X0))
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((exists_in_world @ Y0 @ X0) => (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))) @
% 113.99/14.96 X0))))))
% 113.99/14.96 | ~ (rel_s4 @ X3 @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X3)
% 113.99/14.96 | ~ (rel_s4 @ X5 @ X4)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X4)
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X3))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl158])).
% 113.99/14.96 thf(zip_derived_cl163, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu]:
% 113.99/14.96 ( ('#form12' @ X0 @ X1 @ X2)
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((exists_in_world @ Y0 @ X0) => (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ X1))) @
% 113.99/14.96 X0)))))))),
% 113.99/14.96 define([status(thm)])).
% 113.99/14.96 thf(zip_derived_cl166, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]:
% 113.99/14.96 (~ ('#form12' @ X0 @ X1 @ X2)
% 113.99/14.96 | ~ (exists_in_world @ X1 @ X3)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X4)
% 113.99/14.96 | ~ (rel_s4 @ X5 @ X4)
% 113.99/14.96 | ~ (rel_s4 @ X4 @ X3)
% 113.99/14.96 | ~ (rel_s4 @ X3 @ X0)
% 113.99/14.96 | ~ (intersect @ X2 @ X1 @ ('#sk11' @ X2 @ X1 @ X0)))),
% 113.99/14.96 inference('renaming', [status(thm)],
% 113.99/14.96 [zip_derived_cl161, zip_derived_cl163])).
% 113.99/14.96 thf(zip_derived_cl1511, plain,
% 113.99/14.96 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu]:
% 113.99/14.96 (~ (intersect @ X3 @ X2 @ ('#sk11' @ X3 @ X2 @ X1))
% 113.99/14.96 | ~ (rel_s4 @ X0 @ X1)
% 113.99/14.96 | ~ (rel_s4 @ X0 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X0)
% 113.99/14.96 | ~ ('#form12' @ X1 @ X2 @ X3))),
% 113.99/14.96 inference('eq_fact', [status(thm)], [zip_derived_cl166])).
% 113.99/14.96 thf(zip_derived_cl8, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)),
% 113.99/14.96 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])).
% 113.99/14.96 thf(zip_derived_cl1596, plain,
% 113.99/14.96 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu]:
% 113.99/14.96 (~ (intersect @ X3 @ X2 @ ('#sk11' @ X3 @ X2 @ X1))
% 113.99/14.96 | ~ (rel_s4 @ X0 @ X1)
% 113.99/14.96 | ~ (exists_in_world @ X3 @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X0)
% 113.99/14.96 | ~ ('#form12' @ X1 @ X2 @ X3))),
% 113.99/14.96 inference('demod', [status(thm)], [zip_derived_cl1511, zip_derived_cl8])).
% 113.99/14.96 thf(cumulative_ax, axiom,
% 113.99/14.96 (![X:mu,V:$i,W:$i]:
% 113.99/14.96 ( ( ( rel_s4 @ V @ W ) & ( exists_in_world @ X @ V ) ) =>
% 113.99/14.96 ( exists_in_world @ X @ W ) ))).
% 113.99/14.96 thf(zip_derived_cl3, plain,
% 113.99/14.96 ( (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((!!) @ (^[Y1 : $i]:
% 113.99/14.96 (((!!) @ (^[Y2 : $i]:
% 113.99/14.96 (((((rel_s4 @ Y1 @ Y2) &
% 113.99/14.96 (exists_in_world @ Y0 @ Y1))) =>
% 113.99/14.96 (exists_in_world @ Y0 @ Y2))))))))))))),
% 113.99/14.96 inference('cnf', [status(esa)], [cumulative_ax])).
% 113.99/14.96 thf(zip_derived_cl105, plain,
% 113.99/14.96 (![X2 : mu]:
% 113.99/14.96 (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((!!) @ (^[Y1 : $i]:
% 113.99/14.96 (((((rel_s4 @ Y0 @ Y1) & (exists_in_world @
% 113.99/14.96 X2 @ Y0))) =>
% 113.99/14.96 (exists_in_world @ X2 @ Y1)))))))))),
% 113.99/14.96 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])).
% 113.99/14.96 thf(zip_derived_cl106, plain,
% 113.99/14.96 (![X2 : mu, X4 : $i]:
% 113.99/14.96 (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((rel_s4 @ X4 @ Y0) & (exists_in_world @ X2 @ X4))) =>
% 113.99/14.96 (exists_in_world @ X2 @ Y0))))))),
% 113.99/14.96 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl105])).
% 113.99/14.96 thf(zip_derived_cl107, plain,
% 113.99/14.96 (![X2 : mu, X4 : $i, X6 : $i]:
% 113.99/14.96 (((((rel_s4 @ X4 @ X6) & (exists_in_world @ X2 @ X4))) =>
% 113.99/14.96 (exists_in_world @ X2 @ X6)))),
% 113.99/14.96 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl106])).
% 113.99/14.96 thf(zip_derived_cl108, plain,
% 113.99/14.96 (![X2 : mu, X4 : $i, X6 : $i]:
% 113.99/14.96 (~ (((rel_s4 @ X4 @ X6) & (exists_in_world @ X2 @ X4)))
% 113.99/14.96 | (exists_in_world @ X2 @ X6))),
% 113.99/14.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])).
% 113.99/14.96 thf(zip_derived_cl109, plain,
% 113.99/14.96 (![X2 : mu, X4 : $i, X6 : $i]:
% 113.99/14.96 (~ (rel_s4 @ X4 @ X6)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X4)
% 113.99/14.96 | (exists_in_world @ X2 @ X6))),
% 113.99/14.96 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl108])).
% 113.99/14.96 thf(zip_derived_cl30, plain, ( (rel_s4 @ '#sk3' @ '#sk5')),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])).
% 113.99/14.96 thf(zip_derived_cl1082, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 ( (exists_in_world @ X0 @ '#sk5') | ~ (exists_in_world @ X0 @ '#sk3'))),
% 113.99/14.96 inference('sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl30])).
% 113.99/14.96 thf(a2, axiom, (mtransitive @ rel_s4)).
% 113.99/14.96 thf(zip_derived_cl2, plain, ( (mtransitive @ rel_s4)),
% 113.99/14.96 inference('cnf', [status(esa)], [a2])).
% 113.99/14.96 thf(mtransitive, axiom, (mtransitive @ X0) =>
% 113.99/14.96 ((((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((!!) @ (^[Y1 : $i]:
% 113.99/14.96 (((!!) @ (^[Y2 : $i]:
% 113.99/14.96 (((((X0 @ Y1 @ Y2) & (X0 @ Y0 @ Y1))) =>
% 113.99/14.96 (X0 @ Y0 @ Y2))))))))))))
% 113.99/14.96 = ($true))).
% 113.99/14.96 thf('14', plain,
% 113.99/14.96 (![X0:( $i > $i > $o )]:
% 113.99/14.96 ( ( mtransitive @ X0 ) <=>
% 113.99/14.96 ( ![X5:$i,X7:$i,X9:$i]:
% 113.99/14.96 ( ( ( X0 @ X7 @ X9 ) & ( X0 @ X5 @ X7 ) ) => ( X0 @ X5 @ X9 ) ) ) )),
% 113.99/14.96 inference('rw.lit', [status(esa)], [mtransitive])).
% 113.99/14.96 thf(zip_derived_cl9, plain,
% 113.99/14.96 ( (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((!!) @ (^[Y1 : $i]:
% 113.99/14.96 (((!!) @ (^[Y2 : $i]:
% 113.99/14.96 (((((rel_s4 @ Y1 @ Y2) & (rel_s4 @
% 113.99/14.96 Y0 @ Y1))) =>
% 113.99/14.96 (rel_s4 @ Y0 @ Y2))))))))))))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl2, '14'])).
% 113.99/14.96 thf(zip_derived_cl10, plain,
% 113.99/14.96 (![X2 : $i]:
% 113.99/14.96 (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((!!) @ (^[Y1 : $i]:
% 113.99/14.96 (((((rel_s4 @ Y0 @ Y1) & (rel_s4 @ X2 @ Y0))) =>
% 113.99/14.96 (rel_s4 @ X2 @ Y1)))))))))),
% 113.99/14.96 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])).
% 113.99/14.96 thf(zip_derived_cl11, plain,
% 113.99/14.96 (![X2 : $i, X4 : $i]:
% 113.99/14.96 (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((rel_s4 @ X4 @ Y0) & (rel_s4 @ X2 @ X4))) =>
% 113.99/14.96 (rel_s4 @ X2 @ Y0))))))),
% 113.99/14.96 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])).
% 113.99/14.96 thf(zip_derived_cl12, plain,
% 113.99/14.96 (![X2 : $i, X4 : $i, X6 : $i]:
% 113.99/14.96 (((((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) => (rel_s4 @ X2 @ X6)))),
% 113.99/14.96 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])).
% 113.99/14.96 thf(zip_derived_cl13, plain,
% 113.99/14.96 (![X2 : $i, X4 : $i, X6 : $i]:
% 113.99/14.96 (~ (((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) | (rel_s4 @ X2 @ X6))),
% 113.99/14.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])).
% 113.99/14.96 thf(zip_derived_cl14, plain,
% 113.99/14.96 (![X2 : $i, X4 : $i, X6 : $i]:
% 113.99/14.96 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))),
% 113.99/14.96 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl13])).
% 113.99/14.96 thf(zip_derived_cl44, plain,
% 113.99/14.96 (~ (mnot @
% 113.99/14.96 (mforall_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ '#sk6')))))) @
% 113.99/14.96 '#sk7')),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])).
% 113.99/14.96 thf(zip_derived_cl46, plain,
% 113.99/14.96 ( (mforall_ind @
% 113.99/14.96 (^[Y0 : mu]:
% 113.99/14.96 (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ '#sk6'))))) @
% 113.99/14.96 '#sk7')),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl44, '11'])).
% 113.99/14.96 thf(zip_derived_cl48, plain,
% 113.99/14.96 ( (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((exists_in_world @ Y0 @ '#sk7') =>
% 113.99/14.96 ((^[Y1 : mu]:
% 113.99/14.96 (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @
% 113.99/14.96 (mbox_s4 @ (member @ Y1 @ '#sk6'))))) @
% 113.99/14.96 Y0 @ '#sk7'))))))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl46, '7'])).
% 113.99/14.96 thf(zip_derived_cl50, plain,
% 113.99/14.96 ( (((!!) @ (^[Y0 : mu]:
% 113.99/14.96 (((exists_in_world @ Y0 @ '#sk7') => (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @
% 113.99/14.96 (mbox_s4 @ (member @ Y0 @ '#sk6'))) @
% 113.99/14.96 '#sk7'))))))),
% 113.99/14.96 inference('ho_norm', [status(thm)], [zip_derived_cl48])).
% 113.99/14.96 thf(zip_derived_cl51, plain,
% 113.99/14.96 (![X2 : mu]:
% 113.99/14.96 (((exists_in_world @ X2 @ '#sk7') => (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ X2 @ '#sk4')) @
% 113.99/14.96 (mbox_s4 @ (member @ X2 @ '#sk6'))) @
% 113.99/14.96 '#sk7')))),
% 113.99/14.96 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl50])).
% 113.99/14.96 thf(zip_derived_cl53, plain,
% 113.99/14.96 (![X2 : mu]:
% 113.99/14.96 (~ (exists_in_world @ X2 @ '#sk7')
% 113.99/14.96 | (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ X2 @ '#sk4')) @
% 113.99/14.96 (mbox_s4 @ (member @ X2 @ '#sk6'))) @
% 113.99/14.96 '#sk7'))),
% 113.99/14.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])).
% 113.99/14.96 thf(zip_derived_cl55, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 (~ (mand @ (mbox_s4 @ (member @ X0 @ '#sk4')) @
% 113.99/14.96 (mbox_s4 @ (member @ X0 @ '#sk6')) @ '#sk7')
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7'))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl53, '9'])).
% 113.99/14.96 thf(zip_derived_cl56, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 (~ (mnot @
% 113.99/14.96 (mor @ (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4'))) @
% 113.99/14.96 (mnot @ (mbox_s4 @ (member @ X0 @ '#sk6')))) @
% 113.99/14.96 '#sk7')
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7'))),
% 113.99/14.96 inference('rw', [status(thm)], [zip_derived_cl55, '8'])).
% 113.99/14.96 thf(zip_derived_cl57, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 ( (mor @ (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4'))) @
% 113.99/14.96 (mnot @ (mbox_s4 @ (member @ X0 @ '#sk6'))) @ '#sk7')
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7'))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl56, '11'])).
% 113.99/14.96 thf(zip_derived_cl58, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 ( (((mnot @ (mbox_s4 @ (member @ X0 @ '#sk6')) @ '#sk7') | (mnot @
% 113.99/14.96 (mbox_s4 @ (member @ X0 @ '#sk4')) @ '#sk7')))
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7'))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl57, '12'])).
% 113.99/14.96 thf(zip_derived_cl59, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 ( (mnot @ (mbox_s4 @ (member @ X0 @ '#sk6')) @ '#sk7')
% 113.99/14.96 | (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4')) @ '#sk7')
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7'))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl58])).
% 113.99/14.96 thf(zip_derived_cl60, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 (~ (mbox_s4 @ (member @ X0 @ '#sk6') @ '#sk7')
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7')
% 113.99/14.96 | (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4')) @ '#sk7'))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl59, '9'])).
% 113.99/14.96 thf(zip_derived_cl61, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 (~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @
% 113.99/14.96 '#sk6' @ Y0))))))
% 113.99/14.96 | (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4')) @ '#sk7')
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7'))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl60, '1'])).
% 113.99/14.96 thf(zip_derived_cl62, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 (~ (mbox_s4 @ (member @ X0 @ '#sk4') @ '#sk7')
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7')
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @
% 113.99/14.96 '#sk6' @ Y0)))))))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl61, '9'])).
% 113.99/14.96 thf(zip_derived_cl63, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 (~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @
% 113.99/14.96 '#sk4' @ Y0))))))
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @
% 113.99/14.96 '#sk6' @ Y0))))))
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7'))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl62, '1'])).
% 113.99/14.96 thf(zip_derived_cl64, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 (~ (((((~) @ (rel_s4 @ '#sk7' @ ('#sk8' @ X0)))) | (member @ X0 @
% 113.99/14.96 '#sk4' @ ('#sk8' @ X0))))
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7')
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @
% 113.99/14.96 '#sk6' @ Y0)))))))),
% 113.99/14.96 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl63])).
% 113.99/14.96 thf(zip_derived_cl65, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 ( (rel_s4 @ '#sk7' @ ('#sk8' @ X0))
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @
% 113.99/14.96 '#sk6' @ Y0))))))
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7'))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])).
% 113.99/14.96 thf(zip_derived_cl67, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 ( ('#form9' @ X0)
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @
% 113.99/14.96 '#sk6' @ Y0)))))))),
% 113.99/14.96 define([status(thm)])).
% 113.99/14.96 thf(zip_derived_cl68, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 (~ (((((~) @ (rel_s4 @ '#sk7' @ ('#sk10' @ X0)))) | (member @ X0 @
% 113.99/14.96 '#sk6' @ ('#sk10' @ X0))))
% 113.99/14.96 | ('#form9' @ X0))),
% 113.99/14.96 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl67])).
% 113.99/14.96 thf(zip_derived_cl71, plain,
% 113.99/14.96 (![X0 : mu]: ( (rel_s4 @ '#sk7' @ ('#sk10' @ X0)) | ('#form9' @ X0))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl68])).
% 113.99/14.96 thf(zip_derived_cl211, plain,
% 113.99/14.96 (![X0 : mu, X1 : $i]:
% 113.99/14.96 ( (rel_s4 @ X1 @ ('#sk10' @ X0))
% 113.99/14.96 | ~ (rel_s4 @ X1 @ '#sk7')
% 113.99/14.96 | ('#form9' @ X0))),
% 113.99/14.96 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl71])).
% 113.99/14.96 thf(zip_derived_cl170, plain,
% 113.99/14.96 (![X0 : $i, X1 : mu, X2 : mu]:
% 113.99/14.96 (~ (mnot @
% 113.99/14.96 (mand @ (mbox_s4 @ (member @ ('#sk13' @ X0 @ X1 @ X2) @ X2)) @
% 113.99/14.96 (mbox_s4 @ (member @ ('#sk13' @ X0 @ X1 @ X2) @ X1))) @
% 113.99/14.96 X0)
% 113.99/14.96 | ('#form12' @ X0 @ X1 @ X2))),
% 113.99/14.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])).
% 113.99/14.96 thf(zip_derived_cl172, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i]:
% 113.99/14.96 ( (mand @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0)) @
% 113.99/14.96 (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1)) @ X2)
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl170, '11'])).
% 113.99/14.96 thf(zip_derived_cl174, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i]:
% 113.99/14.96 ( (mnot @
% 113.99/14.96 (mor @
% 113.99/14.96 (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0))) @
% 113.99/14.96 (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1)))) @
% 113.99/14.96 X2)
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('rw', [status(thm)], [zip_derived_cl172, '8'])).
% 113.99/14.96 thf(zip_derived_cl175, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i]:
% 113.99/14.96 (~ (mor @
% 113.99/14.96 (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0))) @
% 113.99/14.96 (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1))) @ X2)
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl174, '9'])).
% 113.99/14.96 thf(zip_derived_cl177, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i]:
% 113.99/14.96 (~ (((mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1)) @
% 113.99/14.96 X2) | (mnot @
% 113.99/14.96 (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0)) @ X2)))
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl175, '10'])).
% 113.99/14.96 thf(zip_derived_cl179, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i]:
% 113.99/14.96 (~ (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1)) @ X2)
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl177])).
% 113.99/14.96 thf(zip_derived_cl182, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i]:
% 113.99/14.96 ( (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1) @ X2)
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl179, '11'])).
% 113.99/14.96 thf(zip_derived_cl185, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i]:
% 113.99/14.96 ( (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ X2 @ Y0))) | (member @
% 113.99/14.96 ('#sk13' @ X2 @ X1 @ X0) @ X1 @ Y0))))))
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl182, '6'])).
% 113.99/14.96 thf(zip_derived_cl188, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i, X4 : $i]:
% 113.99/14.96 ( (((((~) @ (rel_s4 @ X2 @ X4))) | (member @
% 113.99/14.96 ('#sk13' @ X2 @ X1 @ X0) @ X1 @ X4)))
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl185])).
% 113.99/14.96 thf(zip_derived_cl192, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i, X4 : $i]:
% 113.99/14.96 (~ (rel_s4 @ X2 @ X4)
% 113.99/14.96 | (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1 @ X4)
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl188])).
% 113.99/14.96 thf(zip_derived_cl72, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 (~ (member @ X0 @ '#sk6' @ ('#sk10' @ X0)) | ('#form9' @ X0))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl68])).
% 113.99/14.96 thf(zip_derived_cl1729, plain,
% 113.99/14.96 (![X0 : mu, X1 : $i]:
% 113.99/14.96 ( ('#form12' @ X1 @ '#sk6' @ X0)
% 113.99/14.96 | ~ (rel_s4 @ X1 @ ('#sk10' @ ('#sk13' @ X1 @ '#sk6' @ X0)))
% 113.99/14.96 | ('#form9' @ ('#sk13' @ X1 @ '#sk6' @ X0)))),
% 113.99/14.96 inference('sup-', [status(thm)], [zip_derived_cl192, zip_derived_cl72])).
% 113.99/14.96 thf(zip_derived_cl65, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 ( (rel_s4 @ '#sk7' @ ('#sk8' @ X0))
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @
% 113.99/14.96 '#sk6' @ Y0))))))
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7'))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])).
% 113.99/14.96 thf(zip_derived_cl67, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 ( ('#form9' @ X0)
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @
% 113.99/14.96 '#sk6' @ Y0)))))))),
% 113.99/14.96 define([status(thm)])).
% 113.99/14.96 thf(zip_derived_cl69, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 (~ ('#form9' @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7')
% 113.99/14.96 | (rel_s4 @ '#sk7' @ ('#sk8' @ X0)))),
% 113.99/14.96 inference('renaming', [status(thm)], [zip_derived_cl65, zip_derived_cl67])).
% 113.99/14.96 thf(zip_derived_cl180, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i]:
% 113.99/14.96 (~ (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0)) @ X2)
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl177])).
% 113.99/14.96 thf(zip_derived_cl183, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i]:
% 113.99/14.96 ( (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0) @ X2)
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl180, '11'])).
% 113.99/14.96 thf(zip_derived_cl186, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i]:
% 113.99/14.96 ( (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ X2 @ Y0))) | (member @
% 113.99/14.96 ('#sk13' @ X2 @ X1 @ X0) @ X0 @ Y0))))))
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('rw_clause', [status(thm)], [zip_derived_cl183, '6'])).
% 113.99/14.96 thf(zip_derived_cl189, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i, X4 : $i]:
% 113.99/14.96 ( (((((~) @ (rel_s4 @ X2 @ X4))) | (member @
% 113.99/14.96 ('#sk13' @ X2 @ X1 @ X0) @ X0 @ X4)))
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl186])).
% 113.99/14.96 thf(zip_derived_cl193, plain,
% 113.99/14.96 (![X0 : mu, X1 : mu, X2 : $i, X4 : $i]:
% 113.99/14.96 (~ (rel_s4 @ X2 @ X4)
% 113.99/14.96 | (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0 @ X4)
% 113.99/14.96 | ('#form12' @ X2 @ X1 @ X0))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl189])).
% 113.99/14.96 thf(zip_derived_cl66, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 (~ (member @ X0 @ '#sk4' @ ('#sk8' @ X0))
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @
% 113.99/14.96 '#sk6' @ Y0))))))
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7'))),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])).
% 113.99/14.96 thf(zip_derived_cl67, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 ( ('#form9' @ X0)
% 113.99/14.96 | ~ (((!!) @ (^[Y0 : $i]:
% 113.99/14.96 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @
% 113.99/14.96 '#sk6' @ Y0)))))))),
% 113.99/14.96 define([status(thm)])).
% 113.99/14.96 thf(zip_derived_cl70, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 (~ ('#form9' @ X0)
% 113.99/14.96 | ~ (exists_in_world @ X0 @ '#sk7')
% 113.99/14.96 | ~ (member @ X0 @ '#sk4' @ ('#sk8' @ X0)))),
% 113.99/14.96 inference('renaming', [status(thm)], [zip_derived_cl66, zip_derived_cl67])).
% 113.99/14.96 thf(zip_derived_cl1874, plain,
% 113.99/14.96 (![X0 : mu, X1 : $i]:
% 113.99/14.96 ( ('#form12' @ X1 @ X0 @ '#sk4')
% 113.99/14.96 | ~ (rel_s4 @ X1 @ ('#sk8' @ ('#sk13' @ X1 @ X0 @ '#sk4')))
% 113.99/14.96 | ~ (exists_in_world @ ('#sk13' @ X1 @ X0 @ '#sk4') @ '#sk7')
% 113.99/14.96 | ~ ('#form9' @ ('#sk13' @ X1 @ X0 @ '#sk4')))),
% 113.99/14.96 inference('sup-', [status(thm)], [zip_derived_cl193, zip_derived_cl70])).
% 113.99/14.96 thf(zip_derived_cl109, plain,
% 113.99/14.96 (![X2 : mu, X4 : $i, X6 : $i]:
% 113.99/14.96 (~ (rel_s4 @ X4 @ X6)
% 113.99/14.96 | ~ (exists_in_world @ X2 @ X4)
% 113.99/14.96 | (exists_in_world @ X2 @ X6))),
% 113.99/14.96 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl108])).
% 113.99/14.96 thf(zip_derived_cl40, plain, ( (rel_s4 @ '#sk5' @ '#sk7')),
% 113.99/14.96 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])).
% 113.99/14.96 thf(zip_derived_cl1078, plain,
% 113.99/14.96 (![X0 : mu]:
% 113.99/14.96 ( (exists_in_world @ X0 @ '#sk7') | ~ (exists_in_world @ X0 @ '#sk5'))),
% 113.99/14.96 inference('sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl40])).
% 113.99/14.96 thf(zip_derived_cl39080, plain, ($false),
% 113.99/14.96 inference('eprover', [status(thm)],
% 113.99/14.96 [zip_derived_cl40, zip_derived_cl26, zip_derived_cl8,
% 113.99/14.96 zip_derived_cl35, zip_derived_cl169, zip_derived_cl1400,
% 113.99/14.96 zip_derived_cl54, zip_derived_cl1596, zip_derived_cl1082,
% 113.99/14.96 zip_derived_cl211, zip_derived_cl1729, zip_derived_cl69,
% 113.99/14.96 zip_derived_cl1874, zip_derived_cl1078])).
% 113.99/14.96
% 113.99/14.96 % SZS output end Refutation
% 113.99/14.96
% 113.99/14.96
% 113.99/14.96 % Terminating...
% 114.16/15.01 % Runner terminated.
% 114.16/15.02 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------