0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.uD3niQnSbO 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 : 1920 0.15/0.35 % WCLimit : 240 0.15/0.35 % DateTime : Wed Jul 30 03:03:04 EDT 2025 0.15/0.35 % CPUTime : 0.15/0.35 % Running portfolio for 1920 s 0.15/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.15/0.36 % Number of cores: 8 0.15/0.36 % Python version: Python 3.6.8 0.15/0.36 % Running in HO mode 0.57/0.65 % Total configuration time : 828 0.57/0.65 % Estimated wc time : 1656 0.57/0.65 % Estimated cpu time (8 cpus) : 207.0 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.59/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.59/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.59/0.80 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.59/0.80 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.59/0.81 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.59/0.81 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.61/0.97 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 15.52/2.64 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s 114.44/15.10 % Solved by lams/30_b.l.sh. 114.44/15.10 % done 1423 iterations in 13.988s 114.44/15.10 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 114.44/15.10 % SZS output start Refutation 114.44/15.10 thf(mu_type, type, mu: $tType). 114.44/15.10 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 114.44/15.10 thf(mreflexive_type, type, mreflexive: ($i > $i > $o) > $o). 114.44/15.10 thf(mexists_ind_type, type, mexists_ind: (mu > $i > $o) > $i > $o). 114.44/15.10 thf(member_type, type, member: mu > mu > $i > $o). 114.44/15.10 thf(rel_s4_type, type, rel_s4: $i > $i > $o). 114.44/15.10 thf('#sk13_type', type, '#sk13': $i > mu > mu > mu). 114.44/15.10 thf('#sk2_type', type, '#sk2': $i). 114.44/15.10 thf('#sk10_type', type, '#sk10': mu > $i). 114.44/15.10 thf('#form12_type', type, '#form12': $i > mu > mu > $o). 114.44/15.10 thf('#sk11_type', type, '#sk11': mu > mu > $i > $i). 114.44/15.10 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 114.44/15.10 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 114.44/15.10 thf('#sk8_type', type, '#sk8': mu > $i). 114.44/15.10 thf('#form9_type', type, '#form9': mu > $o). 114.44/15.10 thf('#sk4_type', type, '#sk4': mu). 114.44/15.10 thf('#sk3_type', type, '#sk3': $i). 114.44/15.10 thf(mtransitive_type, type, mtransitive: ($i > $i > $o) > $o). 114.44/15.10 thf('#sk7_type', type, '#sk7': $i). 114.44/15.10 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 114.44/15.10 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o). 114.44/15.10 thf(exists_in_world_type, type, exists_in_world: mu > $i > $o). 114.44/15.10 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o). 114.44/15.10 thf('#sk6_type', type, '#sk6': mu). 114.44/15.10 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 114.44/15.10 thf(intersect_type, type, intersect: mu > mu > $i > $o). 114.44/15.10 thf('#sk5_type', type, '#sk5': $i). 114.44/15.10 thf(prove_th15, conjecture, 114.44/15.10 (mvalid @ 114.44/15.10 ( mbox_s4 @ 114.44/15.10 ( mforall_ind @ 114.44/15.10 ( ^[B:mu]: 114.44/15.10 ( mbox_s4 @ 114.44/15.10 ( mforall_ind @ 114.44/15.10 ( ^[C:mu]: 114.44/15.10 ( mbox_s4 @ 114.44/15.10 ( mimplies @ 114.44/15.10 ( mbox_s4 @ ( intersect @ B @ C ) ) @ 114.44/15.10 ( mexists_ind @ 114.44/15.10 ( ^[D:mu]: 114.44/15.10 ( mand @ 114.44/15.10 ( mbox_s4 @ ( member @ D @ B ) ) @ 114.44/15.10 ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) ) ) ) ) ) ) ) ))). 114.44/15.10 thf(zf_stmt_0, negated_conjecture, 114.44/15.10 (~( mvalid @ 114.44/15.10 ( mbox_s4 @ 114.44/15.10 ( mforall_ind @ 114.44/15.10 ( ^[B:mu]: 114.44/15.10 ( mbox_s4 @ 114.44/15.10 ( mforall_ind @ 114.44/15.10 ( ^[C:mu]: 114.44/15.10 ( mbox_s4 @ 114.44/15.10 ( mimplies @ 114.44/15.10 ( mbox_s4 @ ( intersect @ B @ C ) ) @ 114.44/15.10 ( mexists_ind @ 114.44/15.10 ( ^[D:mu]: 114.44/15.10 ( mand @ 114.44/15.10 ( mbox_s4 @ ( member @ D @ B ) ) @ 114.44/15.10 ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) ) ) ) ) ) ) ) ) )), 114.44/15.10 inference('cnf.neg', [status(esa)], [prove_th15])). 114.44/15.10 thf(zip_derived_cl6, plain, 114.44/15.10 (~ (mvalid @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))))))))))))), 114.44/15.10 inference('cnf', [status(esa)], [zf_stmt_0])). 114.44/15.10 thf(mvalid, axiom, ~ (mvalid @ X0) => 114.44/15.10 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))). 114.44/15.10 thf('0', plain, 114.44/15.10 (![X0:( $i > $o )]: 114.44/15.10 ( ( ~( mvalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )), 114.44/15.10 inference('rw.lit', [status(esa)], [mvalid])). 114.44/15.10 thf(zip_derived_cl17, plain, 114.44/15.10 (~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mbox_s4 @ (intersect @ Y1 @ Y2)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y3 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y3 @ Y2)))))))))))) @ 114.44/15.10 Y0))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl6, '0'])). 114.44/15.10 thf(zip_derived_cl18, plain, 114.44/15.10 (~ (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1)))))))))))) @ 114.44/15.10 '#sk2')), 114.44/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl17])). 114.44/15.10 thf(mbox_s4, axiom, ~ (mbox_s4 @ X0 @ X1) => 114.44/15.10 ((((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X1 @ Y0))) | (X0 @ Y0)))))) != 114.44/15.10 ($true))). 114.44/15.10 thf('1', plain, 114.44/15.10 (![X0:( $i > $o ),X1:$i]: 114.44/15.10 ( ( ~( mbox_s4 @ X0 @ X1 ) ) <=> 114.44/15.10 ( ~( ![X6:$i]: ( ( ~( rel_s4 @ X1 @ X6 ) ) | ( X0 @ X6 ) ) ) ) )), 114.44/15.10 inference('rw.lit', [status(esa)], [mbox_s4])). 114.44/15.10 thf(zip_derived_cl19, plain, 114.44/15.10 (~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mbox_s4 @ (intersect @ Y1 @ Y2)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y3 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y3 @ Y2))))))))))) @ 114.44/15.10 Y0))))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl18, '1'])). 114.44/15.10 thf(zip_derived_cl20, plain, 114.44/15.10 (~ (((((~) @ (rel_s4 @ '#sk2' @ '#sk3'))) | (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))))))))) @ 114.44/15.10 '#sk3')))), 114.44/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 114.44/15.10 thf(zip_derived_cl22, plain, 114.44/15.10 (~ (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))))))))) @ 114.44/15.10 '#sk3')), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 114.44/15.10 thf(mforall_ind, axiom, ~ (mforall_ind @ X0 @ X1) => 114.44/15.10 ((((!!) @ (^[Y0 : mu]: (((exists_in_world @ Y0 @ X1) => (X0 @ Y0 @ X1)))))) 114.44/15.10 != ($true))). 114.44/15.10 thf('2', plain, 114.44/15.10 (![X0:( mu > $i > $o ),X1:$i]: 114.44/15.10 ( ( ~( mforall_ind @ X0 @ X1 ) ) <=> 114.44/15.10 ( ~( ![X6:mu]: ( ( exists_in_world @ X6 @ X1 ) => ( X0 @ X6 @ X1 ) ) ) ) )), 114.44/15.10 inference('rw.lit', [status(esa)], [mforall_ind])). 114.44/15.10 thf(zip_derived_cl23, plain, 114.44/15.10 (~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ '#sk3') => 114.44/15.10 ((^[Y1 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mbox_s4 @ (intersect @ Y1 @ Y2)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y3 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y3 @ Y2))))))))))) @ 114.44/15.10 Y0 @ '#sk3'))))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl22, '2'])). 114.44/15.10 thf(zip_derived_cl24, plain, 114.44/15.10 (~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ '#sk3') => (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))))))) @ 114.44/15.10 '#sk3'))))))), 114.44/15.10 inference('ho_norm', [status(thm)], [zip_derived_cl23])). 114.44/15.10 thf(zip_derived_cl25, plain, 114.44/15.10 (~ (((exists_in_world @ '#sk4' @ '#sk3') => (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0))))))))) @ 114.44/15.10 '#sk3')))), 114.44/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl24])). 114.44/15.10 thf(zip_derived_cl27, plain, 114.44/15.10 (~ (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0))))))))) @ 114.44/15.10 '#sk3')), 114.44/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 114.44/15.10 thf(zip_derived_cl28, plain, 114.44/15.10 (~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1)))))))) @ 114.44/15.10 Y0))))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl27, '1'])). 114.44/15.10 thf(zip_derived_cl29, plain, 114.44/15.10 (~ (((((~) @ (rel_s4 @ '#sk3' @ '#sk5'))) | (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0)))))))) @ 114.44/15.10 '#sk5')))), 114.44/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])). 114.44/15.10 thf(zip_derived_cl31, plain, 114.44/15.10 (~ (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0)))))))) @ 114.44/15.10 '#sk5')), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 114.44/15.10 thf(zip_derived_cl32, plain, 114.44/15.10 (~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ '#sk5') => 114.44/15.10 ((^[Y1 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mbox_s4 @ (intersect @ '#sk4' @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1)))))))) @ 114.44/15.10 Y0 @ '#sk5'))))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl31, '2'])). 114.44/15.10 thf(zip_derived_cl33, plain, 114.44/15.10 (~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ '#sk5') => (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0)))))) @ 114.44/15.10 '#sk5'))))))), 114.44/15.10 inference('ho_norm', [status(thm)], [zip_derived_cl32])). 114.44/15.10 thf(zip_derived_cl34, plain, 114.44/15.10 (~ (((exists_in_world @ '#sk6' @ '#sk5') => (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ '#sk6')))))) @ 114.44/15.10 '#sk5')))), 114.44/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl33])). 114.44/15.10 thf(zip_derived_cl36, plain, 114.44/15.10 (~ (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ '#sk6')))))) @ 114.44/15.10 '#sk5')), 114.44/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 114.44/15.10 thf(zip_derived_cl37, plain, 114.44/15.10 (~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (mimplies @ 114.44/15.10 (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ '#sk6'))))) @ 114.44/15.10 Y0))))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl36, '1'])). 114.44/15.10 thf(zip_derived_cl38, plain, 114.44/15.10 (~ (((((~) @ (rel_s4 @ '#sk5' @ '#sk7'))) | (mimplies @ 114.44/15.10 (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ '#sk6'))))) @ 114.44/15.10 '#sk7')))), 114.44/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl37])). 114.44/15.10 thf(mimplies, axiom,(( mimplies @ (X0)@ (X1)@ (X2)) = 114.44/15.10 ((mor @ (mnot @ X0) @ X1 @ X2)))). 114.44/15.10 thf('3', plain, 114.44/15.10 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]: 114.44/15.10 ( ( mimplies @ X0 @ X1 @ X2 ) = ( mor @ ( mnot @ X0 ) @ X1 @ X2 ) )), 114.44/15.10 define([status(thm)])). 114.44/15.10 thf(zip_derived_cl39, plain, 114.44/15.10 (~ (((((~) @ (rel_s4 @ '#sk5' @ '#sk7'))) | (mor @ 114.44/15.10 (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6'))) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ '#sk6'))))) @ 114.44/15.10 '#sk7')))), 114.44/15.10 inference('rw', [status(thm)], [zip_derived_cl38, '3'])). 114.44/15.10 thf(zip_derived_cl40, plain, ( (rel_s4 @ '#sk5' @ '#sk7')), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 114.44/15.10 thf(zip_derived_cl26, plain, ( (exists_in_world @ '#sk4' @ '#sk3')), 114.44/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 114.44/15.10 thf(a1, axiom, (mreflexive @ rel_s4)). 114.44/15.10 thf(zip_derived_cl2, plain, ( (mreflexive @ rel_s4)), 114.44/15.10 inference('cnf', [status(esa)], [a1])). 114.44/15.10 thf(mreflexive, axiom, (mreflexive @ X0) => 114.44/15.10 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0 @ Y0)))) = ($true))). 114.44/15.10 thf('4', plain, 114.44/15.10 (![X0:( $i > $i > $o )]: 114.44/15.10 ( ( mreflexive @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 @ X5 ) ) )), 114.44/15.10 inference('rw.lit', [status(esa)], [mreflexive])). 114.44/15.10 thf(zip_derived_cl13, plain, ( (((!!) @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl2, '4'])). 114.44/15.10 thf(zip_derived_cl14, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 114.44/15.10 thf(zip_derived_cl35, plain, ( (exists_in_world @ '#sk6' @ '#sk5')), 114.44/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 114.44/15.10 thf(intersect_defn, axiom, 114.44/15.10 (mvalid @ 114.44/15.10 ( mbox_s4 @ 114.44/15.10 ( mforall_ind @ 114.44/15.10 ( ^[B:mu]: 114.44/15.10 ( mbox_s4 @ 114.44/15.10 ( mforall_ind @ 114.44/15.10 ( ^[C:mu]: 114.44/15.10 ( mand @ 114.44/15.10 ( mbox_s4 @ 114.44/15.10 ( mimplies @ 114.44/15.10 ( mbox_s4 @ ( intersect @ B @ C ) ) @ 114.44/15.10 ( mexists_ind @ 114.44/15.10 ( ^[D:mu]: 114.44/15.10 ( mand @ 114.44/15.10 ( mbox_s4 @ ( member @ D @ B ) ) @ 114.44/15.10 ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) ) ) @ 114.44/15.10 ( mbox_s4 @ 114.44/15.10 ( mimplies @ 114.44/15.10 ( mexists_ind @ 114.44/15.10 ( ^[D:mu]: 114.44/15.10 ( mand @ 114.44/15.10 ( mbox_s4 @ ( member @ D @ B ) ) @ 114.44/15.10 ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) @ 114.44/15.10 ( mbox_s4 @ ( intersect @ B @ C ) ) ) ) ) ) ) ) ) ) ))). 114.44/15.10 thf(zip_derived_cl5, plain, 114.44/15.10 ( (mvalid @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ Y0 @ Y1))))))))))))), 114.44/15.10 inference('cnf', [status(esa)], [intersect_defn])). 114.44/15.10 thf(mvalid, axiom, (mvalid @ X0) => 114.44/15.10 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))). 114.44/15.10 thf('5', plain, 114.44/15.10 (![X0:( $i > $o )]: ( ( mvalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )), 114.44/15.10 inference('rw.lit', [status(esa)], [mvalid])). 114.44/15.10 thf(zip_derived_cl110, plain, 114.44/15.10 ( (((!!) @ (^[Y0 : $i]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mbox_s4 @ (intersect @ Y1 @ Y2)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y3 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y3 @ Y2))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y3 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y3 @ Y2))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ Y1 @ Y2)))))))))) @ 114.44/15.10 Y0))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl5, '5'])). 114.44/15.10 thf(zip_derived_cl111, plain, 114.44/15.10 (![X2 : $i]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ Y0 @ Y1)))))))))) @ 114.44/15.10 X2)), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl110])). 114.44/15.10 thf(mbox_s4, axiom, (mbox_s4 @ X0 @ X1) => 114.44/15.10 ((((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X1 @ Y0))) | (X0 @ Y0)))))) = 114.44/15.10 ($true))). 114.44/15.10 thf('6', plain, 114.44/15.10 (![X0:( $i > $o ),X1:$i]: 114.44/15.10 ( ( mbox_s4 @ X0 @ X1 ) <=> 114.44/15.10 ( ![X6:$i]: ( ( ~( rel_s4 @ X1 @ X6 ) ) | ( X0 @ X6 ) ) ) )), 114.44/15.10 inference('rw.lit', [status(esa)], [mbox_s4])). 114.44/15.10 thf(zip_derived_cl112, plain, 114.44/15.10 (![X0 : $i]: 114.44/15.10 (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mbox_s4 @ (intersect @ Y1 @ Y2)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y3 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ (member @ Y3 @ Y1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y3 @ Y2))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y3 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ (member @ Y3 @ Y1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y3 @ Y2))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ Y1 @ Y2))))))))) @ 114.44/15.10 Y0))))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl111, '6'])). 114.44/15.10 thf(zip_derived_cl113, plain, 114.44/15.10 (![X0 : $i, X2 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ X0 @ X2))) | (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ Y0 @ Y1))))))))) @ 114.44/15.10 X2)))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl112])). 114.44/15.10 thf(zip_derived_cl114, plain, 114.44/15.10 (![X0 : $i, X2 : $i]: 114.44/15.10 (~ (rel_s4 @ X0 @ X2) 114.44/15.10 | (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ Y0 @ Y1))))))))) @ 114.44/15.10 X2))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl113])). 114.44/15.10 thf(mforall_ind, axiom, (mforall_ind @ X0 @ X1) => 114.44/15.10 ((((!!) @ (^[Y0 : mu]: (((exists_in_world @ Y0 @ X1) => (X0 @ Y0 @ X1)))))) 114.44/15.10 = ($true))). 114.44/15.10 thf('7', plain, 114.44/15.10 (![X0:( mu > $i > $o ),X1:$i]: 114.44/15.10 ( ( mforall_ind @ X0 @ X1 ) <=> 114.44/15.10 ( ![X6:mu]: ( ( exists_in_world @ X6 @ X1 ) => ( X0 @ X6 @ X1 ) ) ) )), 114.44/15.10 inference('rw.lit', [status(esa)], [mforall_ind])). 114.44/15.10 thf(zip_derived_cl115, plain, 114.44/15.10 (![X0 : $i, X1 : $i]: 114.44/15.10 ( (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X0) => 114.44/15.10 ((^[Y1 : mu]: 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mbox_s4 @ (intersect @ Y1 @ Y2)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y3 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ (member @ Y3 @ Y1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y3 @ Y2))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y3 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ (member @ Y3 @ Y1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y3 @ Y2))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ Y1 @ Y2))))))))) @ 114.44/15.10 Y0 @ X0)))))) 114.44/15.10 | ~ (rel_s4 @ X1 @ X0))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl114, '7'])). 114.44/15.10 thf(zip_derived_cl116, plain, 114.44/15.10 (![X0 : $i, X1 : $i]: 114.44/15.10 ( (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X0) => (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ Y0 @ Y1))))))) @ 114.44/15.10 X0)))))) 114.44/15.10 | ~ (rel_s4 @ X1 @ X0))), 114.44/15.10 inference('ho_norm', [status(thm)], [zip_derived_cl115])). 114.44/15.10 thf(zip_derived_cl117, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X3 : mu]: 114.44/15.10 ( (((exists_in_world @ X3 @ X0) => (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X3 @ Y0)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ X3 @ Y0))))))) @ 114.44/15.10 X0))) 114.44/15.10 | ~ (rel_s4 @ X1 @ X0))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl116])). 114.44/15.10 thf(zip_derived_cl118, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X3 : mu]: 114.44/15.10 (~ (exists_in_world @ X3 @ X0) 114.44/15.10 | (mbox_s4 @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X3 @ Y0)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ X3 @ Y0))))))) @ 114.44/15.10 X0) 114.44/15.10 | ~ (rel_s4 @ X1 @ X0))), 114.44/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl117])). 114.44/15.10 thf(zip_derived_cl119, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X2 : mu]: 114.44/15.10 ( (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X2 @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ X2 @ Y1)))))) @ 114.44/15.10 Y0)))))) 114.44/15.10 | ~ (rel_s4 @ X1 @ X0) 114.44/15.10 | ~ (exists_in_world @ X2 @ X0))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl118, '6'])). 114.44/15.10 thf(zip_derived_cl120, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]: 114.44/15.10 ( (((((~) @ (rel_s4 @ X0 @ X4))) | (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X2 @ Y0)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ X2 @ Y0)))))) @ 114.44/15.10 X4))) 114.44/15.10 | ~ (exists_in_world @ X2 @ X0) 114.44/15.10 | ~ (rel_s4 @ X1 @ X0))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl119])). 114.44/15.10 thf(zip_derived_cl121, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]: 114.44/15.10 (~ (rel_s4 @ X0 @ X4) 114.44/15.10 | (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X2 @ Y0)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ X2 @ Y0)))))) @ 114.44/15.10 X4) 114.44/15.10 | ~ (rel_s4 @ X1 @ X0) 114.44/15.10 | ~ (exists_in_world @ X2 @ X0))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl120])). 114.44/15.10 thf(zip_derived_cl122, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i]: 114.44/15.10 ( (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X3) => 114.44/15.10 ((^[Y1 : mu]: 114.44/15.10 (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X1 @ Y1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ X1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y2 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y2 @ X1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ X1 @ Y1)))))) @ 114.44/15.10 Y0 @ X3)))))) 114.44/15.10 | ~ (exists_in_world @ X1 @ X0) 114.44/15.10 | ~ (rel_s4 @ X2 @ X0) 114.44/15.10 | ~ (rel_s4 @ X0 @ X3))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl121, '7'])). 114.44/15.10 thf(zip_derived_cl123, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i]: 114.44/15.10 ( (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X3) => (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X1 @ Y0)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ X1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ X1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ Y0))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ X1 @ Y0)))) @ 114.44/15.10 X3)))))) 114.44/15.10 | ~ (exists_in_world @ X1 @ X0) 114.44/15.10 | ~ (rel_s4 @ X2 @ X0) 114.44/15.10 | ~ (rel_s4 @ X0 @ X3))), 114.44/15.10 inference('ho_norm', [status(thm)], [zip_derived_cl122])). 114.44/15.10 thf(zip_derived_cl124, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i, X5 : mu]: 114.44/15.10 ( (((exists_in_world @ X5 @ X3) => (mand @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X1 @ X5)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X5))))))) @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X5))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ X1 @ X5)))) @ 114.44/15.10 X3))) 114.44/15.10 | ~ (rel_s4 @ X0 @ X3) 114.44/15.10 | ~ (rel_s4 @ X2 @ X0) 114.44/15.10 | ~ (exists_in_world @ X1 @ X0))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl123])). 114.44/15.10 thf(mand, axiom,(( mand @ (X0)@ (X1)@ (X2)) = 114.44/15.10 ((mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)) @ X2)))). 114.44/15.10 thf('8', plain, 114.44/15.10 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]: 114.44/15.10 ( ( mand @ X0 @ X1 @ X2 ) = 114.44/15.10 ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) @ X2 ) )), 114.44/15.10 define([status(thm)])). 114.44/15.10 thf(zip_derived_cl125, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i, X5 : mu]: 114.44/15.10 ( (((exists_in_world @ X5 @ X3) => (mnot @ 114.44/15.10 (mor @ 114.44/15.10 (mnot @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X1 @ X5)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X5)))))))) @ 114.44/15.10 (mnot @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X5))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ X1 @ X5)))))) @ 114.44/15.10 X3))) 114.44/15.10 | ~ (rel_s4 @ X0 @ X3) 114.44/15.10 | ~ (rel_s4 @ X2 @ X0) 114.44/15.10 | ~ (exists_in_world @ X1 @ X0))), 114.44/15.10 inference('rw', [status(thm)], [zip_derived_cl124, '8'])). 114.44/15.10 thf(zip_derived_cl126, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i, X5 : mu]: 114.44/15.10 (~ (exists_in_world @ X5 @ X3) 114.44/15.10 | (mnot @ 114.44/15.10 (mor @ 114.44/15.10 (mnot @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X1 @ X5)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X5)))))))) @ 114.44/15.10 (mnot @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X5))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ X1 @ X5)))))) @ 114.44/15.10 X3) 114.44/15.10 | ~ (exists_in_world @ X1 @ X0) 114.44/15.10 | ~ (rel_s4 @ X2 @ X0) 114.44/15.10 | ~ (rel_s4 @ X0 @ X3))), 114.44/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])). 114.44/15.10 thf(mnot, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))). 114.44/15.10 thf('9', plain, 114.44/15.10 (![X0:( $i > $o ),X1:$i]: ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )), 114.44/15.10 inference('rw.lit', [status(esa)], [mnot])). 114.44/15.10 thf(zip_derived_cl127, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu]: 114.44/15.10 (~ (mor @ 114.44/15.10 (mnot @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X3 @ X4)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X4)))))))) @ 114.44/15.10 (mnot @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X4))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ X3 @ X4))))) @ 114.44/15.10 X0) 114.44/15.10 | ~ (rel_s4 @ X1 @ X0) 114.44/15.10 | ~ (rel_s4 @ X2 @ X1) 114.44/15.10 | ~ (exists_in_world @ X3 @ X1) 114.44/15.10 | ~ (exists_in_world @ X4 @ X0))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl126, '9'])). 114.44/15.10 thf(mor, axiom, ~ (mor @ X0 @ X1 @ X2) => 114.44/15.10 ((((X1 @ X2) | (X0 @ X2))) != ($true))). 114.44/15.10 thf('10', plain, 114.44/15.10 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]: 114.44/15.10 ( ( ~( mor @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X1 @ X2 ) | ( X0 @ X2 ) ) ) )), 114.44/15.10 inference('rw.lit', [status(esa)], [mor])). 114.44/15.10 thf(zip_derived_cl128, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i]: 114.44/15.10 (~ (((mnot @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))))) @ 114.44/15.10 (mbox_s4 @ (intersect @ X3 @ X1)))) @ 114.44/15.10 X0) | (mnot @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X3 @ X1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))))))) @ 114.44/15.10 X0))) 114.44/15.10 | ~ (exists_in_world @ X1 @ X0) 114.44/15.10 | ~ (exists_in_world @ X3 @ X2) 114.44/15.10 | ~ (rel_s4 @ X4 @ X2) 114.44/15.10 | ~ (rel_s4 @ X2 @ X0))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl127, '10'])). 114.44/15.10 thf(zip_derived_cl130, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i]: 114.44/15.10 (~ (mnot @ 114.44/15.10 (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X3 @ X1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))))))) @ 114.44/15.10 X0) 114.44/15.10 | ~ (rel_s4 @ X2 @ X0) 114.44/15.10 | ~ (rel_s4 @ X4 @ X2) 114.44/15.10 | ~ (exists_in_world @ X3 @ X2) 114.44/15.10 | ~ (exists_in_world @ X1 @ X0))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl128])). 114.44/15.10 thf(mnot, axiom, ~ (mnot @ X0 @ X1) => ((X0 @ X1) = ($true))). 114.44/15.10 thf('11', plain, 114.44/15.10 (![X0:( $i > $o ),X1:$i]: ( ( ~( mnot @ X0 @ X1 ) ) <=> ( X0 @ X1 ) )), 114.44/15.10 inference('rw.lit', [status(esa)], [mnot])). 114.44/15.10 thf(zip_derived_cl132, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i]: 114.44/15.10 ( (mbox_s4 @ 114.44/15.10 (mimplies @ (mbox_s4 @ (intersect @ X3 @ X1)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1)))))) @ 114.44/15.10 X0) 114.44/15.10 | ~ (exists_in_world @ X1 @ X0) 114.44/15.10 | ~ (exists_in_world @ X3 @ X2) 114.44/15.10 | ~ (rel_s4 @ X4 @ X2) 114.44/15.10 | ~ (rel_s4 @ X2 @ X0))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl130, '11'])). 114.44/15.10 thf(zip_derived_cl134, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu]: 114.44/15.10 ( (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mimplies @ 114.44/15.10 (mbox_s4 @ (intersect @ X3 @ X4)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y1 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ X4))))) @ 114.44/15.10 Y0)))))) 114.44/15.10 | ~ (rel_s4 @ X1 @ X0) 114.44/15.10 | ~ (rel_s4 @ X2 @ X1) 114.44/15.10 | ~ (exists_in_world @ X3 @ X1) 114.44/15.10 | ~ (exists_in_world @ X4 @ X0))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl132, '6'])). 114.44/15.10 thf(zip_derived_cl136, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu, X6 : $i]: 114.44/15.10 ( (((((~) @ (rel_s4 @ X0 @ X6))) | (mimplies @ 114.44/15.10 (mbox_s4 @ (intersect @ X3 @ X4)) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X4))))) @ 114.44/15.10 X6))) 114.44/15.10 | ~ (exists_in_world @ X4 @ X0) 114.44/15.10 | ~ (exists_in_world @ X3 @ X1) 114.44/15.10 | ~ (rel_s4 @ X2 @ X1) 114.44/15.10 | ~ (rel_s4 @ X1 @ X0))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl134])). 114.44/15.10 thf(zip_derived_cl139, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu, X6 : $i]: 114.44/15.10 ( (((((~) @ (rel_s4 @ X0 @ X6))) | (mor @ 114.44/15.10 (mnot @ (mbox_s4 @ (intersect @ X3 @ X4))) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X4))))) @ 114.44/15.10 X6))) 114.44/15.10 | ~ (exists_in_world @ X4 @ X0) 114.44/15.10 | ~ (exists_in_world @ X3 @ X1) 114.44/15.10 | ~ (rel_s4 @ X2 @ X1) 114.44/15.10 | ~ (rel_s4 @ X1 @ X0))), 114.44/15.10 inference('rw', [status(thm)], [zip_derived_cl136, '3'])). 114.44/15.10 thf(zip_derived_cl140, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu, X6 : $i]: 114.44/15.10 (~ (rel_s4 @ X0 @ X6) 114.44/15.10 | (mor @ (mnot @ (mbox_s4 @ (intersect @ X3 @ X4))) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X4))))) @ 114.44/15.10 X6) 114.44/15.10 | ~ (rel_s4 @ X1 @ X0) 114.44/15.10 | ~ (rel_s4 @ X2 @ X1) 114.44/15.10 | ~ (exists_in_world @ X3 @ X1) 114.44/15.10 | ~ (exists_in_world @ X4 @ X0))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl139])). 114.44/15.10 thf(mor, axiom, (mor @ X0 @ X1 @ X2) => 114.44/15.10 ((((X1 @ X2) | (X0 @ X2))) = ($true))). 114.44/15.10 thf('12', plain, 114.44/15.10 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]: 114.44/15.10 ( ( mor @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) | ( X1 @ X2 ) ) )), 114.44/15.10 inference('rw.lit', [status(esa)], [mor])). 114.44/15.10 thf(zip_derived_cl142, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]: 114.44/15.10 ( (((mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1)))) @ 114.44/15.10 X5) | (mnot @ (mbox_s4 @ (intersect @ X3 @ X1)) @ X5))) 114.44/15.10 | ~ (exists_in_world @ X1 @ X0) 114.44/15.10 | ~ (exists_in_world @ X3 @ X2) 114.44/15.10 | ~ (rel_s4 @ X4 @ X2) 114.44/15.10 | ~ (rel_s4 @ X2 @ X0) 114.44/15.10 | ~ (rel_s4 @ X0 @ X5))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl140, '12'])). 114.44/15.10 thf(mexists_ind, axiom,(( mexists_ind @ (X0)@ (X1)) = 114.44/15.10 ((mnot @ (mforall_ind @ (^[Y0 : mu]: (mnot @ (X0 @ Y0)))) @ X1)))). 114.44/15.10 thf('13', plain, 114.44/15.10 (![X1:$i,X0:( mu > $i > $o )]: 114.44/15.10 ( ( mexists_ind @ X0 @ X1 ) = 114.44/15.10 ( mnot @ ( mforall_ind @ ( ^[V_1:mu]: ( mnot @ ( X0 @ V_1 ) ) ) ) @ X1 ) )), 114.44/15.10 define([status(thm)])). 114.44/15.10 thf(zip_derived_cl144, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]: 114.44/15.10 ( (((mnot @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1)))))) @ 114.44/15.10 X5) | (mnot @ (mbox_s4 @ (intersect @ X3 @ X1)) @ X5))) 114.44/15.10 | ~ (exists_in_world @ X1 @ X0) 114.44/15.10 | ~ (exists_in_world @ X3 @ X2) 114.44/15.10 | ~ (rel_s4 @ X4 @ X2) 114.44/15.10 | ~ (rel_s4 @ X2 @ X0) 114.44/15.10 | ~ (rel_s4 @ X0 @ X5))), 114.44/15.10 inference('rw', [status(thm)], [zip_derived_cl142, '13'])). 114.44/15.10 thf(zip_derived_cl145, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]: 114.44/15.10 ( (mnot @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1)))))) @ 114.44/15.10 X5) 114.44/15.10 | (mnot @ (mbox_s4 @ (intersect @ X3 @ X1)) @ X5) 114.44/15.10 | ~ (rel_s4 @ X0 @ X5) 114.44/15.10 | ~ (rel_s4 @ X2 @ X0) 114.44/15.10 | ~ (rel_s4 @ X4 @ X2) 114.44/15.10 | ~ (exists_in_world @ X3 @ X2) 114.44/15.10 | ~ (exists_in_world @ X1 @ X0))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl144])). 114.44/15.10 thf(zip_derived_cl147, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]: 114.44/15.10 (~ (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))))) @ 114.44/15.10 X5) 114.44/15.10 | ~ (exists_in_world @ X1 @ X0) 114.44/15.10 | ~ (exists_in_world @ X3 @ X2) 114.44/15.10 | ~ (rel_s4 @ X4 @ X2) 114.44/15.10 | ~ (rel_s4 @ X2 @ X0) 114.44/15.10 | ~ (rel_s4 @ X0 @ X5) 114.44/15.10 | (mnot @ (mbox_s4 @ (intersect @ X3 @ X1)) @ X5))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl145, '9'])). 114.44/15.10 thf(zip_derived_cl149, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 114.44/15.10 (~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X0) => 114.44/15.10 ((^[Y1 : mu]: 114.44/15.10 (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ X1))))) @ 114.44/15.10 Y0 @ X0)))))) 114.44/15.10 | (mnot @ (mbox_s4 @ (intersect @ X2 @ X1)) @ X0) 114.44/15.10 | ~ (rel_s4 @ X3 @ X0) 114.44/15.10 | ~ (rel_s4 @ X4 @ X3) 114.44/15.10 | ~ (rel_s4 @ X5 @ X4) 114.44/15.10 | ~ (exists_in_world @ X2 @ X4) 114.44/15.10 | ~ (exists_in_world @ X1 @ X3))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl147, '2'])). 114.44/15.10 thf(zip_derived_cl152, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 114.44/15.10 (~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X0) => (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))) @ 114.44/15.10 X0)))))) 114.44/15.10 | (mnot @ (mbox_s4 @ (intersect @ X2 @ X1)) @ X0) 114.44/15.10 | ~ (rel_s4 @ X3 @ X0) 114.44/15.10 | ~ (rel_s4 @ X4 @ X3) 114.44/15.10 | ~ (rel_s4 @ X5 @ X4) 114.44/15.10 | ~ (exists_in_world @ X2 @ X4) 114.44/15.10 | ~ (exists_in_world @ X1 @ X3))), 114.44/15.10 inference('ho_norm', [status(thm)], [zip_derived_cl149])). 114.44/15.10 thf(zip_derived_cl153, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]: 114.44/15.10 (~ (mbox_s4 @ (intersect @ X3 @ X1) @ X5) 114.44/15.10 | ~ (exists_in_world @ X1 @ X0) 114.44/15.10 | ~ (exists_in_world @ X3 @ X2) 114.44/15.10 | ~ (rel_s4 @ X4 @ X2) 114.44/15.10 | ~ (rel_s4 @ X2 @ X0) 114.44/15.10 | ~ (rel_s4 @ X0 @ X5) 114.44/15.10 | ~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X5) => (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))) @ 114.44/15.10 X5)))))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl152, '9'])). 114.44/15.10 thf(zip_derived_cl155, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 114.44/15.10 (~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ X0 @ Y0))) | (intersect @ X2 @ 114.44/15.10 X1 @ Y0)))))) 114.44/15.10 | ~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X0) => (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))) @ 114.44/15.10 X0)))))) 114.44/15.10 | ~ (rel_s4 @ X3 @ X0) 114.44/15.10 | ~ (rel_s4 @ X4 @ X3) 114.44/15.10 | ~ (rel_s4 @ X5 @ X4) 114.44/15.10 | ~ (exists_in_world @ X2 @ X4) 114.44/15.10 | ~ (exists_in_world @ X1 @ X3))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl153, '1'])). 114.44/15.10 thf(zip_derived_cl158, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 114.44/15.10 (~ (((((~) @ (rel_s4 @ X0 @ ('#sk11' @ X2 @ X1 @ X0)))) | 114.44/15.10 (intersect @ X2 @ X1 @ ('#sk11' @ X2 @ X1 @ X0)))) 114.44/15.10 | ~ (exists_in_world @ X1 @ X3) 114.44/15.10 | ~ (exists_in_world @ X2 @ X4) 114.44/15.10 | ~ (rel_s4 @ X5 @ X4) 114.44/15.10 | ~ (rel_s4 @ X4 @ X3) 114.44/15.10 | ~ (rel_s4 @ X3 @ X0) 114.44/15.10 | ~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X0) => (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))) @ 114.44/15.10 X0)))))))), 114.44/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl155])). 114.44/15.10 thf(zip_derived_cl160, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 114.44/15.10 ( (rel_s4 @ X0 @ ('#sk11' @ X2 @ X1 @ X0)) 114.44/15.10 | ~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X0) => (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))) @ 114.44/15.10 X0)))))) 114.44/15.10 | ~ (rel_s4 @ X3 @ X0) 114.44/15.10 | ~ (rel_s4 @ X4 @ X3) 114.44/15.10 | ~ (rel_s4 @ X5 @ X4) 114.44/15.10 | ~ (exists_in_world @ X2 @ X4) 114.44/15.10 | ~ (exists_in_world @ X1 @ X3))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl158])). 114.44/15.10 thf(zip_derived_cl163, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu]: 114.44/15.10 ( ('#form12' @ X0 @ X1 @ X2) 114.44/15.10 | ~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X0) => (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))) @ 114.44/15.10 X0)))))))), 114.44/15.10 define([status(thm)])). 114.44/15.10 thf(zip_derived_cl164, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu]: 114.44/15.10 (~ (((exists_in_world @ ('#sk13' @ X0 @ X1 @ X2) @ X0) => (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ ('#sk13' @ X0 @ X1 @ X2) @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ ('#sk13' @ X0 @ X1 @ X2) @ X1))) @ 114.44/15.10 X0))) 114.44/15.10 | ('#form12' @ X0 @ X1 @ X2))), 114.44/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl163])). 114.44/15.10 thf(zip_derived_cl169, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu]: 114.44/15.10 ( (exists_in_world @ ('#sk13' @ X0 @ X1 @ X2) @ X0) 114.44/15.10 | ('#form12' @ X0 @ X1 @ X2))), 114.44/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 114.44/15.10 thf(zip_derived_cl160, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 114.44/15.10 ( (rel_s4 @ X0 @ ('#sk11' @ X2 @ X1 @ X0)) 114.44/15.10 | ~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X0) => (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))) @ 114.44/15.10 X0)))))) 114.44/15.10 | ~ (rel_s4 @ X3 @ X0) 114.44/15.10 | ~ (rel_s4 @ X4 @ X3) 114.44/15.10 | ~ (rel_s4 @ X5 @ X4) 114.44/15.10 | ~ (exists_in_world @ X2 @ X4) 114.44/15.10 | ~ (exists_in_world @ X1 @ X3))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl158])). 114.44/15.10 thf(zip_derived_cl163, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu]: 114.44/15.10 ( ('#form12' @ X0 @ X1 @ X2) 114.44/15.10 | ~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X0) => (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))) @ 114.44/15.10 X0)))))))), 114.44/15.10 define([status(thm)])). 114.44/15.10 thf(zip_derived_cl165, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 114.44/15.10 (~ ('#form12' @ X0 @ X1 @ X2) 114.44/15.10 | ~ (exists_in_world @ X1 @ X3) 114.44/15.10 | ~ (exists_in_world @ X2 @ X4) 114.44/15.10 | ~ (rel_s4 @ X5 @ X4) 114.44/15.10 | ~ (rel_s4 @ X4 @ X3) 114.44/15.10 | ~ (rel_s4 @ X3 @ X0) 114.44/15.10 | (rel_s4 @ X0 @ ('#sk11' @ X2 @ X1 @ X0)))), 114.44/15.10 inference('renaming', [status(thm)], 114.44/15.10 [zip_derived_cl160, zip_derived_cl163])). 114.44/15.10 thf(zip_derived_cl1292, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu]: 114.44/15.10 ( (rel_s4 @ X1 @ ('#sk11' @ X3 @ X2 @ X1)) 114.44/15.10 | ~ (rel_s4 @ X0 @ X1) 114.44/15.10 | ~ (rel_s4 @ X0 @ X0) 114.44/15.10 | ~ (exists_in_world @ X3 @ X0) 114.44/15.10 | ~ (exists_in_world @ X2 @ X0) 114.44/15.10 | ~ ('#form12' @ X1 @ X2 @ X3))), 114.44/15.10 inference('eq_fact', [status(thm)], [zip_derived_cl165])). 114.44/15.10 thf(zip_derived_cl14, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 114.44/15.10 thf(zip_derived_cl1400, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu]: 114.44/15.10 ( (rel_s4 @ X1 @ ('#sk11' @ X3 @ X2 @ X1)) 114.44/15.10 | ~ (rel_s4 @ X0 @ X1) 114.44/15.10 | ~ (exists_in_world @ X3 @ X0) 114.44/15.10 | ~ (exists_in_world @ X2 @ X0) 114.44/15.10 | ~ ('#form12' @ X1 @ X2 @ X3))), 114.44/15.10 inference('demod', [status(thm)], [zip_derived_cl1292, zip_derived_cl14])). 114.44/15.10 thf(zip_derived_cl41, plain, 114.44/15.10 (~ (mor @ (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6'))) @ 114.44/15.10 (mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ '#sk6'))))) @ 114.44/15.10 '#sk7')), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 114.44/15.10 thf(zip_derived_cl42, plain, 114.44/15.10 (~ (((mexists_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ '#sk6')))) @ 114.44/15.10 '#sk7') | (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ 114.44/15.10 '#sk7')))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl41, '10'])). 114.44/15.10 thf(zip_derived_cl43, plain, 114.44/15.10 (~ (((mnot @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ '#sk6')))))) @ 114.44/15.10 '#sk7') | (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ 114.44/15.10 '#sk7')))), 114.44/15.10 inference('rw', [status(thm)], [zip_derived_cl42, '13'])). 114.44/15.10 thf(zip_derived_cl45, plain, 114.44/15.10 (~ (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ '#sk7')), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 114.44/15.10 thf(zip_derived_cl47, plain, 114.44/15.10 ( (mbox_s4 @ (intersect @ '#sk4' @ '#sk6') @ '#sk7')), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl45, '11'])). 114.44/15.10 thf(zip_derived_cl49, plain, 114.44/15.10 ( (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (intersect @ '#sk4' @ 114.44/15.10 '#sk6' @ Y0))))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl47, '6'])). 114.44/15.10 thf(zip_derived_cl52, plain, 114.44/15.10 (![X2 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk7' @ X2))) | (intersect @ '#sk4' @ '#sk6' @ 114.44/15.10 X2)))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl49])). 114.44/15.10 thf(zip_derived_cl54, plain, 114.44/15.10 (![X2 : $i]: 114.44/15.10 (~ (rel_s4 @ '#sk7' @ X2) | (intersect @ '#sk4' @ '#sk6' @ X2))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 114.44/15.10 thf(zip_derived_cl161, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 114.44/15.10 (~ (intersect @ X2 @ X1 @ ('#sk11' @ X2 @ X1 @ X0)) 114.44/15.10 | ~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X0) => (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))) @ 114.44/15.10 X0)))))) 114.44/15.10 | ~ (rel_s4 @ X3 @ X0) 114.44/15.10 | ~ (rel_s4 @ X4 @ X3) 114.44/15.10 | ~ (rel_s4 @ X5 @ X4) 114.44/15.10 | ~ (exists_in_world @ X2 @ X4) 114.44/15.10 | ~ (exists_in_world @ X1 @ X3))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl158])). 114.44/15.10 thf(zip_derived_cl163, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu]: 114.44/15.10 ( ('#form12' @ X0 @ X1 @ X2) 114.44/15.10 | ~ (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ X0) => (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ X1))) @ 114.44/15.10 X0)))))))), 114.44/15.10 define([status(thm)])). 114.44/15.10 thf(zip_derived_cl166, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 114.44/15.10 (~ ('#form12' @ X0 @ X1 @ X2) 114.44/15.10 | ~ (exists_in_world @ X1 @ X3) 114.44/15.10 | ~ (exists_in_world @ X2 @ X4) 114.44/15.10 | ~ (rel_s4 @ X5 @ X4) 114.44/15.10 | ~ (rel_s4 @ X4 @ X3) 114.44/15.10 | ~ (rel_s4 @ X3 @ X0) 114.44/15.10 | ~ (intersect @ X2 @ X1 @ ('#sk11' @ X2 @ X1 @ X0)))), 114.44/15.10 inference('renaming', [status(thm)], 114.44/15.10 [zip_derived_cl161, zip_derived_cl163])). 114.44/15.10 thf(zip_derived_cl1511, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu]: 114.44/15.10 (~ (intersect @ X3 @ X2 @ ('#sk11' @ X3 @ X2 @ X1)) 114.44/15.10 | ~ (rel_s4 @ X0 @ X1) 114.44/15.10 | ~ (rel_s4 @ X0 @ X0) 114.44/15.10 | ~ (exists_in_world @ X3 @ X0) 114.44/15.10 | ~ (exists_in_world @ X2 @ X0) 114.44/15.10 | ~ ('#form12' @ X1 @ X2 @ X3))), 114.44/15.10 inference('eq_fact', [status(thm)], [zip_derived_cl166])). 114.44/15.10 thf(zip_derived_cl14, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 114.44/15.10 thf(zip_derived_cl1596, plain, 114.44/15.10 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu]: 114.44/15.10 (~ (intersect @ X3 @ X2 @ ('#sk11' @ X3 @ X2 @ X1)) 114.44/15.10 | ~ (rel_s4 @ X0 @ X1) 114.44/15.10 | ~ (exists_in_world @ X3 @ X0) 114.44/15.10 | ~ (exists_in_world @ X2 @ X0) 114.44/15.10 | ~ ('#form12' @ X1 @ X2 @ X3))), 114.44/15.10 inference('demod', [status(thm)], [zip_derived_cl1511, zip_derived_cl14])). 114.44/15.10 thf(cumulative_ax, axiom, 114.44/15.10 (![X:mu,V:$i,W:$i]: 114.44/15.10 ( ( ( rel_s4 @ V @ W ) & ( exists_in_world @ X @ V ) ) => 114.44/15.10 ( exists_in_world @ X @ W ) ))). 114.44/15.10 thf(zip_derived_cl3, plain, 114.44/15.10 ( (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((!!) @ (^[Y1 : $i]: 114.44/15.10 (((!!) @ (^[Y2 : $i]: 114.44/15.10 (((((rel_s4 @ Y1 @ Y2) & 114.44/15.10 (exists_in_world @ Y0 @ Y1))) => 114.44/15.10 (exists_in_world @ Y0 @ Y2))))))))))))), 114.44/15.10 inference('cnf', [status(esa)], [cumulative_ax])). 114.44/15.10 thf(zip_derived_cl105, plain, 114.44/15.10 (![X2 : mu]: 114.44/15.10 (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((!!) @ (^[Y1 : $i]: 114.44/15.10 (((((rel_s4 @ Y0 @ Y1) & (exists_in_world @ 114.44/15.10 X2 @ Y0))) => 114.44/15.10 (exists_in_world @ X2 @ Y1)))))))))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 114.44/15.10 thf(zip_derived_cl106, plain, 114.44/15.10 (![X2 : mu, X4 : $i]: 114.44/15.10 (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((rel_s4 @ X4 @ Y0) & (exists_in_world @ X2 @ X4))) => 114.44/15.10 (exists_in_world @ X2 @ Y0))))))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl105])). 114.44/15.10 thf(zip_derived_cl107, plain, 114.44/15.10 (![X2 : mu, X4 : $i, X6 : $i]: 114.44/15.10 (((((rel_s4 @ X4 @ X6) & (exists_in_world @ X2 @ X4))) => 114.44/15.10 (exists_in_world @ X2 @ X6)))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl106])). 114.44/15.10 thf(zip_derived_cl108, plain, 114.44/15.10 (![X2 : mu, X4 : $i, X6 : $i]: 114.44/15.10 (~ (((rel_s4 @ X4 @ X6) & (exists_in_world @ X2 @ X4))) 114.44/15.10 | (exists_in_world @ X2 @ X6))), 114.44/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 114.44/15.10 thf(zip_derived_cl109, plain, 114.44/15.10 (![X2 : mu, X4 : $i, X6 : $i]: 114.44/15.10 (~ (rel_s4 @ X4 @ X6) 114.44/15.10 | ~ (exists_in_world @ X2 @ X4) 114.44/15.10 | (exists_in_world @ X2 @ X6))), 114.44/15.10 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl108])). 114.44/15.10 thf(zip_derived_cl30, plain, ( (rel_s4 @ '#sk3' @ '#sk5')), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 114.44/15.10 thf(zip_derived_cl1082, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 ( (exists_in_world @ X0 @ '#sk5') | ~ (exists_in_world @ X0 @ '#sk3'))), 114.44/15.10 inference('sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl30])). 114.44/15.10 thf(a2, axiom, (mtransitive @ rel_s4)). 114.44/15.10 thf(zip_derived_cl1, plain, ( (mtransitive @ rel_s4)), 114.44/15.10 inference('cnf', [status(esa)], [a2])). 114.44/15.10 thf(mtransitive, axiom, (mtransitive @ X0) => 114.44/15.10 ((((!!) @ (^[Y0 : $i]: 114.44/15.10 (((!!) @ (^[Y1 : $i]: 114.44/15.10 (((!!) @ (^[Y2 : $i]: 114.44/15.10 (((((X0 @ Y1 @ Y2) & (X0 @ Y0 @ Y1))) => 114.44/15.10 (X0 @ Y0 @ Y2)))))))))))) 114.44/15.10 = ($true))). 114.44/15.10 thf('14', plain, 114.44/15.10 (![X0:( $i > $i > $o )]: 114.44/15.10 ( ( mtransitive @ X0 ) <=> 114.44/15.10 ( ![X5:$i,X7:$i,X9:$i]: 114.44/15.10 ( ( ( X0 @ X7 @ X9 ) & ( X0 @ X5 @ X7 ) ) => ( X0 @ X5 @ X9 ) ) ) )), 114.44/15.10 inference('rw.lit', [status(esa)], [mtransitive])). 114.44/15.10 thf(zip_derived_cl7, plain, 114.44/15.10 ( (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((!!) @ (^[Y1 : $i]: 114.44/15.10 (((!!) @ (^[Y2 : $i]: 114.44/15.10 (((((rel_s4 @ Y1 @ Y2) & (rel_s4 @ 114.44/15.10 Y0 @ Y1))) => 114.44/15.10 (rel_s4 @ Y0 @ Y2))))))))))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl1, '14'])). 114.44/15.10 thf(zip_derived_cl8, plain, 114.44/15.10 (![X2 : $i]: 114.44/15.10 (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((!!) @ (^[Y1 : $i]: 114.44/15.10 (((((rel_s4 @ Y0 @ Y1) & (rel_s4 @ X2 @ Y0))) => 114.44/15.10 (rel_s4 @ X2 @ Y1)))))))))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 114.44/15.10 thf(zip_derived_cl9, plain, 114.44/15.10 (![X2 : $i, X4 : $i]: 114.44/15.10 (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((rel_s4 @ X4 @ Y0) & (rel_s4 @ X2 @ X4))) => 114.44/15.10 (rel_s4 @ X2 @ Y0))))))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 114.44/15.10 thf(zip_derived_cl10, plain, 114.44/15.10 (![X2 : $i, X4 : $i, X6 : $i]: 114.44/15.10 (((((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) => (rel_s4 @ X2 @ X6)))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 114.44/15.10 thf(zip_derived_cl11, plain, 114.44/15.10 (![X2 : $i, X4 : $i, X6 : $i]: 114.44/15.10 (~ (((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) | (rel_s4 @ X2 @ X6))), 114.44/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10])). 114.44/15.10 thf(zip_derived_cl12, plain, 114.44/15.10 (![X2 : $i, X4 : $i, X6 : $i]: 114.44/15.10 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))), 114.44/15.10 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl11])). 114.44/15.10 thf(zip_derived_cl44, plain, 114.44/15.10 (~ (mnot @ 114.44/15.10 (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ '#sk6')))))) @ 114.44/15.10 '#sk7')), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 114.44/15.10 thf(zip_derived_cl46, plain, 114.44/15.10 ( (mforall_ind @ 114.44/15.10 (^[Y0 : mu]: 114.44/15.10 (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ '#sk6'))))) @ 114.44/15.10 '#sk7')), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl44, '11'])). 114.44/15.10 thf(zip_derived_cl48, plain, 114.44/15.10 ( (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ '#sk7') => 114.44/15.10 ((^[Y1 : mu]: 114.44/15.10 (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y1 @ '#sk6'))))) @ 114.44/15.10 Y0 @ '#sk7'))))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl46, '7'])). 114.44/15.10 thf(zip_derived_cl50, plain, 114.44/15.10 ( (((!!) @ (^[Y0 : mu]: 114.44/15.10 (((exists_in_world @ Y0 @ '#sk7') => (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ Y0 @ '#sk6'))) @ 114.44/15.10 '#sk7'))))))), 114.44/15.10 inference('ho_norm', [status(thm)], [zip_derived_cl48])). 114.44/15.10 thf(zip_derived_cl51, plain, 114.44/15.10 (![X2 : mu]: 114.44/15.10 (((exists_in_world @ X2 @ '#sk7') => (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ X2 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ X2 @ '#sk6'))) @ 114.44/15.10 '#sk7')))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl50])). 114.44/15.10 thf(zip_derived_cl53, plain, 114.44/15.10 (![X2 : mu]: 114.44/15.10 (~ (exists_in_world @ X2 @ '#sk7') 114.44/15.10 | (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ X2 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ X2 @ '#sk6'))) @ 114.44/15.10 '#sk7'))), 114.44/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 114.44/15.10 thf(zip_derived_cl55, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 (~ (mand @ (mbox_s4 @ (member @ X0 @ '#sk4')) @ 114.44/15.10 (mbox_s4 @ (member @ X0 @ '#sk6')) @ '#sk7') 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7'))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl53, '9'])). 114.44/15.10 thf(zip_derived_cl56, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 (~ (mnot @ 114.44/15.10 (mor @ (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4'))) @ 114.44/15.10 (mnot @ (mbox_s4 @ (member @ X0 @ '#sk6')))) @ 114.44/15.10 '#sk7') 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7'))), 114.44/15.10 inference('rw', [status(thm)], [zip_derived_cl55, '8'])). 114.44/15.10 thf(zip_derived_cl57, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 ( (mor @ (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4'))) @ 114.44/15.10 (mnot @ (mbox_s4 @ (member @ X0 @ '#sk6'))) @ '#sk7') 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7'))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl56, '11'])). 114.44/15.10 thf(zip_derived_cl58, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 ( (((mnot @ (mbox_s4 @ (member @ X0 @ '#sk6')) @ '#sk7') | (mnot @ 114.44/15.10 (mbox_s4 @ (member @ X0 @ '#sk4')) @ '#sk7'))) 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7'))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl57, '12'])). 114.44/15.10 thf(zip_derived_cl59, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 ( (mnot @ (mbox_s4 @ (member @ X0 @ '#sk6')) @ '#sk7') 114.44/15.10 | (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4')) @ '#sk7') 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7'))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl58])). 114.44/15.10 thf(zip_derived_cl60, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 (~ (mbox_s4 @ (member @ X0 @ '#sk6') @ '#sk7') 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7') 114.44/15.10 | (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4')) @ '#sk7'))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl59, '9'])). 114.44/15.10 thf(zip_derived_cl61, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 (~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 114.44/15.10 '#sk6' @ Y0)))))) 114.44/15.10 | (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4')) @ '#sk7') 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7'))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl60, '1'])). 114.44/15.10 thf(zip_derived_cl62, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 (~ (mbox_s4 @ (member @ X0 @ '#sk4') @ '#sk7') 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7') 114.44/15.10 | ~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 114.44/15.10 '#sk6' @ Y0)))))))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl61, '9'])). 114.44/15.10 thf(zip_derived_cl63, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 (~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 114.44/15.10 '#sk4' @ Y0)))))) 114.44/15.10 | ~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 114.44/15.10 '#sk6' @ Y0)))))) 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7'))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl62, '1'])). 114.44/15.10 thf(zip_derived_cl64, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 (~ (((((~) @ (rel_s4 @ '#sk7' @ ('#sk8' @ X0)))) | (member @ X0 @ 114.44/15.10 '#sk4' @ ('#sk8' @ X0)))) 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7') 114.44/15.10 | ~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 114.44/15.10 '#sk6' @ Y0)))))))), 114.44/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl63])). 114.44/15.10 thf(zip_derived_cl65, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 ( (rel_s4 @ '#sk7' @ ('#sk8' @ X0)) 114.44/15.10 | ~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 114.44/15.10 '#sk6' @ Y0)))))) 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7'))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])). 114.44/15.10 thf(zip_derived_cl67, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 ( ('#form9' @ X0) 114.44/15.10 | ~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 114.44/15.10 '#sk6' @ Y0)))))))), 114.44/15.10 define([status(thm)])). 114.44/15.10 thf(zip_derived_cl68, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 (~ (((((~) @ (rel_s4 @ '#sk7' @ ('#sk10' @ X0)))) | (member @ X0 @ 114.44/15.10 '#sk6' @ ('#sk10' @ X0)))) 114.44/15.10 | ('#form9' @ X0))), 114.44/15.10 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl67])). 114.44/15.10 thf(zip_derived_cl71, plain, 114.44/15.10 (![X0 : mu]: ( (rel_s4 @ '#sk7' @ ('#sk10' @ X0)) | ('#form9' @ X0))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl68])). 114.44/15.10 thf(zip_derived_cl211, plain, 114.44/15.10 (![X0 : mu, X1 : $i]: 114.44/15.10 ( (rel_s4 @ X1 @ ('#sk10' @ X0)) 114.44/15.10 | ~ (rel_s4 @ X1 @ '#sk7') 114.44/15.10 | ('#form9' @ X0))), 114.44/15.10 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl71])). 114.44/15.10 thf(zip_derived_cl170, plain, 114.44/15.10 (![X0 : $i, X1 : mu, X2 : mu]: 114.44/15.10 (~ (mnot @ 114.44/15.10 (mand @ (mbox_s4 @ (member @ ('#sk13' @ X0 @ X1 @ X2) @ X2)) @ 114.44/15.10 (mbox_s4 @ (member @ ('#sk13' @ X0 @ X1 @ X2) @ X1))) @ 114.44/15.10 X0) 114.44/15.10 | ('#form12' @ X0 @ X1 @ X2))), 114.44/15.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 114.44/15.10 thf(zip_derived_cl172, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i]: 114.44/15.10 ( (mand @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0)) @ 114.44/15.10 (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1)) @ X2) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl170, '11'])). 114.44/15.10 thf(zip_derived_cl174, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i]: 114.44/15.10 ( (mnot @ 114.44/15.10 (mor @ 114.44/15.10 (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0))) @ 114.44/15.10 (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1)))) @ 114.44/15.10 X2) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('rw', [status(thm)], [zip_derived_cl172, '8'])). 114.44/15.10 thf(zip_derived_cl175, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i]: 114.44/15.10 (~ (mor @ 114.44/15.10 (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0))) @ 114.44/15.10 (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1))) @ X2) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl174, '9'])). 114.44/15.10 thf(zip_derived_cl177, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i]: 114.44/15.10 (~ (((mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1)) @ 114.44/15.10 X2) | (mnot @ 114.44/15.10 (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0)) @ X2))) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl175, '10'])). 114.44/15.10 thf(zip_derived_cl179, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i]: 114.44/15.10 (~ (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1)) @ X2) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl177])). 114.44/15.10 thf(zip_derived_cl182, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i]: 114.44/15.10 ( (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1) @ X2) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl179, '11'])). 114.44/15.10 thf(zip_derived_cl185, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i]: 114.44/15.10 ( (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ X2 @ Y0))) | (member @ 114.44/15.10 ('#sk13' @ X2 @ X1 @ X0) @ X1 @ Y0)))))) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl182, '6'])). 114.44/15.10 thf(zip_derived_cl188, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i, X4 : $i]: 114.44/15.10 ( (((((~) @ (rel_s4 @ X2 @ X4))) | (member @ 114.44/15.10 ('#sk13' @ X2 @ X1 @ X0) @ X1 @ X4))) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl185])). 114.44/15.10 thf(zip_derived_cl192, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i, X4 : $i]: 114.44/15.10 (~ (rel_s4 @ X2 @ X4) 114.44/15.10 | (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1 @ X4) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl188])). 114.44/15.10 thf(zip_derived_cl72, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 (~ (member @ X0 @ '#sk6' @ ('#sk10' @ X0)) | ('#form9' @ X0))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl68])). 114.44/15.10 thf(zip_derived_cl1729, plain, 114.44/15.10 (![X0 : mu, X1 : $i]: 114.44/15.10 ( ('#form12' @ X1 @ '#sk6' @ X0) 114.44/15.10 | ~ (rel_s4 @ X1 @ ('#sk10' @ ('#sk13' @ X1 @ '#sk6' @ X0))) 114.44/15.10 | ('#form9' @ ('#sk13' @ X1 @ '#sk6' @ X0)))), 114.44/15.10 inference('sup-', [status(thm)], [zip_derived_cl192, zip_derived_cl72])). 114.44/15.10 thf(zip_derived_cl65, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 ( (rel_s4 @ '#sk7' @ ('#sk8' @ X0)) 114.44/15.10 | ~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 114.44/15.10 '#sk6' @ Y0)))))) 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7'))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])). 114.44/15.10 thf(zip_derived_cl67, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 ( ('#form9' @ X0) 114.44/15.10 | ~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 114.44/15.10 '#sk6' @ Y0)))))))), 114.44/15.10 define([status(thm)])). 114.44/15.10 thf(zip_derived_cl69, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 (~ ('#form9' @ X0) 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7') 114.44/15.10 | (rel_s4 @ '#sk7' @ ('#sk8' @ X0)))), 114.44/15.10 inference('renaming', [status(thm)], [zip_derived_cl65, zip_derived_cl67])). 114.44/15.10 thf(zip_derived_cl180, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i]: 114.44/15.10 (~ (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0)) @ X2) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl177])). 114.44/15.10 thf(zip_derived_cl183, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i]: 114.44/15.10 ( (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0) @ X2) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl180, '11'])). 114.44/15.10 thf(zip_derived_cl186, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i]: 114.44/15.10 ( (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ X2 @ Y0))) | (member @ 114.44/15.10 ('#sk13' @ X2 @ X1 @ X0) @ X0 @ Y0)))))) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('rw_clause', [status(thm)], [zip_derived_cl183, '6'])). 114.44/15.10 thf(zip_derived_cl189, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i, X4 : $i]: 114.44/15.10 ( (((((~) @ (rel_s4 @ X2 @ X4))) | (member @ 114.44/15.10 ('#sk13' @ X2 @ X1 @ X0) @ X0 @ X4))) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl186])). 114.44/15.10 thf(zip_derived_cl193, plain, 114.44/15.10 (![X0 : mu, X1 : mu, X2 : $i, X4 : $i]: 114.44/15.10 (~ (rel_s4 @ X2 @ X4) 114.44/15.10 | (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0 @ X4) 114.44/15.10 | ('#form12' @ X2 @ X1 @ X0))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl189])). 114.44/15.10 thf(zip_derived_cl66, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 (~ (member @ X0 @ '#sk4' @ ('#sk8' @ X0)) 114.44/15.10 | ~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 114.44/15.10 '#sk6' @ Y0)))))) 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7'))), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])). 114.44/15.10 thf(zip_derived_cl67, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 ( ('#form9' @ X0) 114.44/15.10 | ~ (((!!) @ (^[Y0 : $i]: 114.44/15.10 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 114.44/15.10 '#sk6' @ Y0)))))))), 114.44/15.10 define([status(thm)])). 114.44/15.10 thf(zip_derived_cl70, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 (~ ('#form9' @ X0) 114.44/15.10 | ~ (exists_in_world @ X0 @ '#sk7') 114.44/15.10 | ~ (member @ X0 @ '#sk4' @ ('#sk8' @ X0)))), 114.44/15.10 inference('renaming', [status(thm)], [zip_derived_cl66, zip_derived_cl67])). 114.44/15.10 thf(zip_derived_cl1874, plain, 114.44/15.10 (![X0 : mu, X1 : $i]: 114.44/15.10 ( ('#form12' @ X1 @ X0 @ '#sk4') 114.44/15.10 | ~ (rel_s4 @ X1 @ ('#sk8' @ ('#sk13' @ X1 @ X0 @ '#sk4'))) 114.44/15.10 | ~ (exists_in_world @ ('#sk13' @ X1 @ X0 @ '#sk4') @ '#sk7') 114.44/15.10 | ~ ('#form9' @ ('#sk13' @ X1 @ X0 @ '#sk4')))), 114.44/15.10 inference('sup-', [status(thm)], [zip_derived_cl193, zip_derived_cl70])). 114.44/15.10 thf(zip_derived_cl109, plain, 114.44/15.10 (![X2 : mu, X4 : $i, X6 : $i]: 114.44/15.10 (~ (rel_s4 @ X4 @ X6) 114.44/15.10 | ~ (exists_in_world @ X2 @ X4) 114.44/15.10 | (exists_in_world @ X2 @ X6))), 114.44/15.10 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl108])). 114.44/15.10 thf(zip_derived_cl40, plain, ( (rel_s4 @ '#sk5' @ '#sk7')), 114.44/15.10 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 114.44/15.10 thf(zip_derived_cl1078, plain, 114.44/15.10 (![X0 : mu]: 114.44/15.10 ( (exists_in_world @ X0 @ '#sk7') | ~ (exists_in_world @ X0 @ '#sk5'))), 114.44/15.10 inference('sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl40])). 114.44/15.10 thf(zip_derived_cl25321, plain, ($false), 114.44/15.10 inference('eprover', [status(thm)], 114.44/15.10 [zip_derived_cl40, zip_derived_cl26, zip_derived_cl14, 114.44/15.10 zip_derived_cl35, zip_derived_cl169, zip_derived_cl1400, 114.44/15.10 zip_derived_cl54, zip_derived_cl1596, zip_derived_cl1082, 114.44/15.10 zip_derived_cl211, zip_derived_cl1729, zip_derived_cl69, 114.44/15.10 zip_derived_cl1874, zip_derived_cl1078])). 114.44/15.10 114.44/15.10 % SZS output end Refutation 114.44/15.10 114.44/15.10 114.44/15.10 % Terminating... 115.21/15.22 % Runner terminated. 115.21/15.24 % Zipperpin 1.5 exiting 115.21/15.25 EOF