0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.ByHGRKNwFO true 0.13/0.34 % Computer : n003.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 : 1200 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Jul 13 10:47:39 EDT 2021 0.13/0.35 % CPUTime : 0.13/0.35 % Running portfolio for 120 s 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.35 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.52/0.66 % Total configuration time : 828 0.52/0.66 % Estimated wc time : 983 0.52/0.66 % Estimated cpu time (8 cpus) : 122.875 0.54/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.55/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.55/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.55/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 0.56/0.88 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 53s 7.72/1.63 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 33s 132.99/17.82 % Solved by lams/30_b.l.sh. 132.99/17.82 % running E: timeout 14 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.ByHGRKNwFO/e_input06e3e9 --cpu-limit=12 --auto -s -p 132.99/17.82 % done 1175 iterations in 16.854s 132.99/17.82 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 132.99/17.82 % SZS output start Refutation 132.99/17.82 thf(mu_type, type, mu: $tType). 132.99/17.82 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 132.99/17.82 thf(mreflexive_type, type, mreflexive: ($i > $i > $o) > $o). 132.99/17.82 thf('#sk13_type', type, '#sk13': $i > mu > mu > mu). 132.99/17.82 thf('#form12_type', type, '#form12': $i > mu > mu > $o). 132.99/17.82 thf('#form9_type', type, '#form9': mu > $o). 132.99/17.82 thf('#sk11_type', type, '#sk11': mu > mu > $i > $i). 132.99/17.82 thf('#sk10_type', type, '#sk10': mu > $i). 132.99/17.82 thf('#sk7_type', type, '#sk7': $i). 132.99/17.82 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 132.99/17.82 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 132.99/17.82 thf('#sk8_type', type, '#sk8': mu > $i). 132.99/17.82 thf('#sk3_type', type, '#sk3': $i). 132.99/17.82 thf('#sk2_type', type, '#sk2': $i). 132.99/17.82 thf(mtransitive_type, type, mtransitive: ($i > $i > $o) > $o). 132.99/17.82 thf('#sk6_type', type, '#sk6': mu). 132.99/17.82 thf(intersect_type, type, intersect: mu > mu > $i > $o). 132.99/17.82 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o). 132.99/17.82 thf(rel_s4_type, type, rel_s4: $i > $i > $o). 132.99/17.82 thf(mexists_ind_type, type, mexists_ind: (mu > $i > $o) > $i > $o). 132.99/17.82 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 132.99/17.82 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 132.99/17.82 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o). 132.99/17.82 thf(exists_in_world_type, type, exists_in_world: mu > $i > $o). 132.99/17.82 thf('#sk5_type', type, '#sk5': $i). 132.99/17.82 thf(member_type, type, member: mu > mu > $i > $o). 132.99/17.82 thf('#sk4_type', type, '#sk4': mu). 132.99/17.82 thf(prove_th15, conjecture, 132.99/17.82 (mvalid @ 132.99/17.82 ( mbox_s4 @ 132.99/17.82 ( mforall_ind @ 132.99/17.82 ( ^[B:mu]: 132.99/17.82 ( mbox_s4 @ 132.99/17.82 ( mforall_ind @ 132.99/17.82 ( ^[C:mu]: 132.99/17.82 ( mbox_s4 @ 132.99/17.82 ( mimplies @ 132.99/17.82 ( mbox_s4 @ ( intersect @ B @ C ) ) @ 132.99/17.82 ( mexists_ind @ 132.99/17.82 ( ^[D:mu]: 132.99/17.82 ( mand @ 132.99/17.82 ( mbox_s4 @ ( member @ D @ B ) ) @ 132.99/17.82 ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) ) ) ) ) ) ) ) ))). 132.99/17.82 thf(zf_stmt_0, negated_conjecture, 132.99/17.82 (~( mvalid @ 132.99/17.82 ( mbox_s4 @ 132.99/17.82 ( mforall_ind @ 132.99/17.82 ( ^[B:mu]: 132.99/17.82 ( mbox_s4 @ 132.99/17.82 ( mforall_ind @ 132.99/17.82 ( ^[C:mu]: 132.99/17.82 ( mbox_s4 @ 132.99/17.82 ( mimplies @ 132.99/17.82 ( mbox_s4 @ ( intersect @ B @ C ) ) @ 132.99/17.82 ( mexists_ind @ 132.99/17.82 ( ^[D:mu]: 132.99/17.82 ( mand @ 132.99/17.82 ( mbox_s4 @ ( member @ D @ B ) ) @ 132.99/17.82 ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) ) ) ) ) ) ) ) ) )), 132.99/17.82 inference('cnf.neg', [status(esa)], [prove_th15])). 132.99/17.82 thf(zip_derived_cl6, plain, 132.99/17.82 (~ (mvalid @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))))))))))))), 132.99/17.82 inference('cnf', [status(esa)], [zf_stmt_0])). 132.99/17.82 thf(mvalid, axiom, ~ (mvalid @ X0) => 132.99/17.82 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))). 132.99/17.82 thf('0', plain, 132.99/17.82 (![X0:( $i > $o )]: 132.99/17.82 ( ( ~( mvalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )), 132.99/17.82 inference('rw.lit', [status(esa)], [mvalid])). 132.99/17.82 thf(zip_derived_cl17, plain, 132.99/17.82 (~ (((!!) @ (^[Y0 : $i]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mbox_s4 @ (intersect @ Y1 @ Y2)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y3 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y3 @ Y2)))))))))))) @ 132.99/17.82 Y0))))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl6, '0'])). 132.99/17.82 thf(zip_derived_cl18, plain, 132.99/17.82 (~ (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1)))))))))))) @ 132.99/17.82 '#sk2')), 132.99/17.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl17])). 132.99/17.82 thf(mbox_s4, axiom, ~ (mbox_s4 @ X0 @ X1) => 132.99/17.82 ((((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X1 @ Y0))) | (X0 @ Y0)))))) != 132.99/17.82 ($true))). 132.99/17.82 thf('1', plain, 132.99/17.82 (![X0:( $i > $o ),X1:$i]: 132.99/17.82 ( ( ~( mbox_s4 @ X0 @ X1 ) ) <=> 132.99/17.82 ( ~( ![X6:$i]: ( ( ~( rel_s4 @ X1 @ X6 ) ) | ( X0 @ X6 ) ) ) ) )), 132.99/17.82 inference('rw.lit', [status(esa)], [mbox_s4])). 132.99/17.82 thf(zip_derived_cl19, plain, 132.99/17.82 (~ (((!!) @ (^[Y0 : $i]: 132.99/17.82 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mbox_s4 @ (intersect @ Y1 @ Y2)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y3 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y3 @ Y2))))))))))) @ 132.99/17.82 Y0))))))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl18, '1'])). 132.99/17.82 thf(zip_derived_cl20, plain, 132.99/17.82 (~ (((((~) @ (rel_s4 @ '#sk2' @ '#sk3'))) | (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))))))))) @ 132.99/17.82 '#sk3')))), 132.99/17.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl19])). 132.99/17.82 thf(zip_derived_cl22, plain, 132.99/17.82 (~ (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))))))))) @ 132.99/17.82 '#sk3')), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl20])). 132.99/17.82 thf(mforall_ind, axiom, ~ (mforall_ind @ X0 @ X1) => 132.99/17.82 ((((!!) @ (^[Y0 : mu]: (((exists_in_world @ Y0 @ X1) => (X0 @ Y0 @ X1)))))) 132.99/17.82 != ($true))). 132.99/17.82 thf('2', plain, 132.99/17.82 (![X0:( mu > $i > $o ),X1:$i]: 132.99/17.82 ( ( ~( mforall_ind @ X0 @ X1 ) ) <=> 132.99/17.82 ( ~( ![X6:mu]: ( ( exists_in_world @ X6 @ X1 ) => ( X0 @ X6 @ X1 ) ) ) ) )), 132.99/17.82 inference('rw.lit', [status(esa)], [mforall_ind])). 132.99/17.82 thf(zip_derived_cl23, plain, 132.99/17.82 (~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ '#sk3') => 132.99/17.82 ((^[Y1 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mbox_s4 @ (intersect @ Y1 @ Y2)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y3 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y3 @ Y2))))))))))) @ 132.99/17.82 Y0 @ '#sk3'))))))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl22, '2'])). 132.99/17.82 thf(zip_derived_cl24, plain, 132.99/17.82 (~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ '#sk3') => (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))))))) @ 132.99/17.82 '#sk3'))))))), 132.99/17.82 inference('ho_norm', [status(thm)], [zip_derived_cl23])). 132.99/17.82 thf(zip_derived_cl25, plain, 132.99/17.82 (~ (((exists_in_world @ '#sk4' @ '#sk3') => (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0))))))))) @ 132.99/17.82 '#sk3')))), 132.99/17.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl24])). 132.99/17.82 thf(zip_derived_cl27, plain, 132.99/17.82 (~ (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0))))))))) @ 132.99/17.82 '#sk3')), 132.99/17.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 132.99/17.82 thf(zip_derived_cl28, plain, 132.99/17.82 (~ (((!!) @ (^[Y0 : $i]: 132.99/17.82 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1)))))))) @ 132.99/17.82 Y0))))))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl27, '1'])). 132.99/17.82 thf(zip_derived_cl29, plain, 132.99/17.82 (~ (((((~) @ (rel_s4 @ '#sk3' @ '#sk5'))) | (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0)))))))) @ 132.99/17.82 '#sk5')))), 132.99/17.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])). 132.99/17.82 thf(zip_derived_cl31, plain, 132.99/17.82 (~ (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0)))))))) @ 132.99/17.82 '#sk5')), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 132.99/17.82 thf(zip_derived_cl32, plain, 132.99/17.82 (~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ '#sk5') => 132.99/17.82 ((^[Y1 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mbox_s4 @ (intersect @ '#sk4' @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1)))))))) @ 132.99/17.82 Y0 @ '#sk5'))))))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl31, '2'])). 132.99/17.82 thf(zip_derived_cl33, plain, 132.99/17.82 (~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ '#sk5') => (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ Y0)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0)))))) @ 132.99/17.82 '#sk5'))))))), 132.99/17.82 inference('ho_norm', [status(thm)], [zip_derived_cl32])). 132.99/17.82 thf(zip_derived_cl34, plain, 132.99/17.82 (~ (((exists_in_world @ '#sk6' @ '#sk5') => (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ '#sk6')))))) @ 132.99/17.82 '#sk5')))), 132.99/17.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl33])). 132.99/17.82 thf(zip_derived_cl36, plain, 132.99/17.82 (~ (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ '#sk6')))))) @ 132.99/17.82 '#sk5')), 132.99/17.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 132.99/17.82 thf(zip_derived_cl37, plain, 132.99/17.82 (~ (((!!) @ (^[Y0 : $i]: 132.99/17.82 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (mimplies @ 132.99/17.82 (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ '#sk6'))))) @ 132.99/17.82 Y0))))))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl36, '1'])). 132.99/17.82 thf(zip_derived_cl38, plain, 132.99/17.82 (~ (((((~) @ (rel_s4 @ '#sk5' @ '#sk7'))) | (mimplies @ 132.99/17.82 (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ '#sk6'))))) @ 132.99/17.82 '#sk7')))), 132.99/17.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl37])). 132.99/17.82 thf(mimplies, axiom,(( mimplies @ (X0)@ (X1)@ (X2)) = 132.99/17.82 ((mor @ (mnot @ X0) @ X1 @ X2)))). 132.99/17.82 thf('3', plain, 132.99/17.82 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]: 132.99/17.82 ( ( mimplies @ X0 @ X1 @ X2 ) = ( mor @ ( mnot @ X0 ) @ X1 @ X2 ) )), 132.99/17.82 define([status(thm)])). 132.99/17.82 thf(zip_derived_cl39, plain, 132.99/17.82 (~ (((((~) @ (rel_s4 @ '#sk5' @ '#sk7'))) | (mor @ 132.99/17.82 (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6'))) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ '#sk6'))))) @ 132.99/17.82 '#sk7')))), 132.99/17.82 inference('rw', [status(thm)], [zip_derived_cl38, '3'])). 132.99/17.82 thf(zip_derived_cl40, plain, ( (rel_s4 @ '#sk5' @ '#sk7')), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 132.99/17.82 thf(zip_derived_cl26, plain, ( (exists_in_world @ '#sk4' @ '#sk3')), 132.99/17.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 132.99/17.82 thf(zip_derived_cl35, plain, ( (exists_in_world @ '#sk6' @ '#sk5')), 132.99/17.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 132.99/17.82 thf(a1, axiom, (mreflexive @ rel_s4)). 132.99/17.82 thf(zip_derived_cl2, plain, ( (mreflexive @ rel_s4)), 132.99/17.82 inference('cnf', [status(esa)], [a1])). 132.99/17.82 thf(mreflexive, axiom, (mreflexive @ X0) => 132.99/17.82 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0 @ Y0)))) = ($true))). 132.99/17.82 thf('4', plain, 132.99/17.82 (![X0:( $i > $i > $o )]: 132.99/17.82 ( ( mreflexive @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 @ X5 ) ) )), 132.99/17.82 inference('rw.lit', [status(esa)], [mreflexive])). 132.99/17.82 thf(zip_derived_cl13, plain, ( (((!!) @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl2, '4'])). 132.99/17.82 thf(zip_derived_cl14, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 132.99/17.82 thf(a2, axiom, (mtransitive @ rel_s4)). 132.99/17.82 thf(zip_derived_cl1, plain, ( (mtransitive @ rel_s4)), 132.99/17.82 inference('cnf', [status(esa)], [a2])). 132.99/17.82 thf(mtransitive, axiom, (mtransitive @ X0) => 132.99/17.82 ((((!!) @ (^[Y0 : $i]: 132.99/17.82 (((!!) @ (^[Y1 : $i]: 132.99/17.82 (((!!) @ (^[Y2 : $i]: 132.99/17.82 (((((X0 @ Y1 @ Y2) & (X0 @ Y0 @ Y1))) => 132.99/17.82 (X0 @ Y0 @ Y2)))))))))))) 132.99/17.82 = ($true))). 132.99/17.82 thf('5', plain, 132.99/17.82 (![X0:( $i > $i > $o )]: 132.99/17.82 ( ( mtransitive @ X0 ) <=> 132.99/17.82 ( ![X5:$i,X7:$i,X9:$i]: 132.99/17.82 ( ( ( X0 @ X7 @ X9 ) & ( X0 @ X5 @ X7 ) ) => ( X0 @ X5 @ X9 ) ) ) )), 132.99/17.82 inference('rw.lit', [status(esa)], [mtransitive])). 132.99/17.82 thf(zip_derived_cl7, plain, 132.99/17.82 ( (((!!) @ (^[Y0 : $i]: 132.99/17.82 (((!!) @ (^[Y1 : $i]: 132.99/17.82 (((!!) @ (^[Y2 : $i]: 132.99/17.82 (((((rel_s4 @ Y1 @ Y2) & (rel_s4 @ 132.99/17.82 Y0 @ Y1))) => 132.99/17.82 (rel_s4 @ Y0 @ Y2))))))))))))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl1, '5'])). 132.99/17.82 thf(zip_derived_cl8, plain, 132.99/17.82 (![X2 : $i]: 132.99/17.82 (((!!) @ (^[Y0 : $i]: 132.99/17.82 (((!!) @ (^[Y1 : $i]: 132.99/17.82 (((((rel_s4 @ Y0 @ Y1) & (rel_s4 @ X2 @ Y0))) => 132.99/17.82 (rel_s4 @ X2 @ Y1)))))))))), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 132.99/17.82 thf(zip_derived_cl9, plain, 132.99/17.82 (![X2 : $i, X4 : $i]: 132.99/17.82 (((!!) @ (^[Y0 : $i]: 132.99/17.82 (((((rel_s4 @ X4 @ Y0) & (rel_s4 @ X2 @ X4))) => 132.99/17.82 (rel_s4 @ X2 @ Y0))))))), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 132.99/17.82 thf(zip_derived_cl10, plain, 132.99/17.82 (![X2 : $i, X4 : $i, X6 : $i]: 132.99/17.82 (((((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) => (rel_s4 @ X2 @ X6)))), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 132.99/17.82 thf(zip_derived_cl11, plain, 132.99/17.82 (![X2 : $i, X4 : $i, X6 : $i]: 132.99/17.82 (~ (((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) | (rel_s4 @ X2 @ X6))), 132.99/17.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10])). 132.99/17.82 thf(zip_derived_cl12, plain, 132.99/17.82 (![X2 : $i, X4 : $i, X6 : $i]: 132.99/17.82 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))), 132.99/17.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl11])). 132.99/17.82 thf(zip_derived_cl40, plain, ( (rel_s4 @ '#sk5' @ '#sk7')), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 132.99/17.82 thf(zip_derived_cl206, plain, 132.99/17.82 (![X0 : $i]: ( (rel_s4 @ '#sk5' @ X0) | ~ (rel_s4 @ '#sk7' @ X0))), 132.99/17.82 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl40])). 132.99/17.82 thf(cumulative_ax, axiom, 132.99/17.82 (![X:mu,V:$i,W:$i]: 132.99/17.82 ( ( ( exists_in_world @ X @ V ) & ( rel_s4 @ V @ W ) ) => 132.99/17.82 ( exists_in_world @ X @ W ) ))). 132.99/17.82 thf(zip_derived_cl3, plain, 132.99/17.82 ( (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((!!) @ (^[Y1 : $i]: 132.99/17.82 (((!!) @ (^[Y2 : $i]: 132.99/17.82 (((((exists_in_world @ Y0 @ Y1) & 132.99/17.82 (rel_s4 @ Y1 @ Y2))) => 132.99/17.82 (exists_in_world @ Y0 @ Y2))))))))))))), 132.99/17.82 inference('cnf', [status(esa)], [cumulative_ax])). 132.99/17.82 thf(zip_derived_cl105, plain, 132.99/17.82 (![X2 : mu]: 132.99/17.82 (((!!) @ (^[Y0 : $i]: 132.99/17.82 (((!!) @ (^[Y1 : $i]: 132.99/17.82 (((((exists_in_world @ X2 @ Y0) & (rel_s4 @ 132.99/17.82 Y0 @ Y1))) => 132.99/17.82 (exists_in_world @ X2 @ Y1)))))))))), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 132.99/17.82 thf(zip_derived_cl106, plain, 132.99/17.82 (![X2 : mu, X4 : $i]: 132.99/17.82 (((!!) @ (^[Y0 : $i]: 132.99/17.82 (((((exists_in_world @ X2 @ X4) & (rel_s4 @ X4 @ Y0))) => 132.99/17.82 (exists_in_world @ X2 @ Y0))))))), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl105])). 132.99/17.82 thf(zip_derived_cl107, plain, 132.99/17.82 (![X2 : mu, X4 : $i, X6 : $i]: 132.99/17.82 (((((exists_in_world @ X2 @ X4) & (rel_s4 @ X4 @ X6))) => 132.99/17.82 (exists_in_world @ X2 @ X6)))), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl106])). 132.99/17.82 thf(zip_derived_cl108, plain, 132.99/17.82 (![X2 : mu, X4 : $i, X6 : $i]: 132.99/17.82 (~ (((exists_in_world @ X2 @ X4) & (rel_s4 @ X4 @ X6))) 132.99/17.82 | (exists_in_world @ X2 @ X6))), 132.99/17.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl107])). 132.99/17.82 thf(zip_derived_cl109, plain, 132.99/17.82 (![X2 : mu, X4 : $i, X6 : $i]: 132.99/17.82 (~ (exists_in_world @ X2 @ X4) 132.99/17.82 | ~ (rel_s4 @ X4 @ X6) 132.99/17.82 | (exists_in_world @ X2 @ X6))), 132.99/17.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl108])). 132.99/17.82 thf(zip_derived_cl41, plain, 132.99/17.82 (~ (mor @ (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6'))) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ '#sk6'))))) @ 132.99/17.82 '#sk7')), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 132.99/17.82 thf(mor, axiom, ~ (mor @ X0 @ X1 @ X2) => 132.99/17.82 ((((X1 @ X2) | (X0 @ X2))) != ($true))). 132.99/17.82 thf('6', plain, 132.99/17.82 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]: 132.99/17.82 ( ( ~( mor @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X1 @ X2 ) | ( X0 @ X2 ) ) ) )), 132.99/17.82 inference('rw.lit', [status(esa)], [mor])). 132.99/17.82 thf(zip_derived_cl42, plain, 132.99/17.82 (~ (((mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ '#sk6')))) @ 132.99/17.82 '#sk7') | (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ 132.99/17.82 '#sk7')))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl41, '6'])). 132.99/17.82 thf(mexists_ind, axiom,(( mexists_ind @ (X0)@ (X1)) = 132.99/17.82 ((mnot @ (mforall_ind @ (^[Y0 : mu]: (mnot @ (X0 @ Y0)))) @ X1)))). 132.99/17.82 thf('7', plain, 132.99/17.82 (![X1:$i,X0:( mu > $i > $o )]: 132.99/17.82 ( ( mexists_ind @ X0 @ X1 ) = 132.99/17.82 ( mnot @ ( mforall_ind @ ( ^[V_1:mu]: ( mnot @ ( X0 @ V_1 ) ) ) ) @ X1 ) )), 132.99/17.82 define([status(thm)])). 132.99/17.82 thf(zip_derived_cl43, plain, 132.99/17.82 (~ (((mnot @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ '#sk6')))))) @ 132.99/17.82 '#sk7') | (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ 132.99/17.82 '#sk7')))), 132.99/17.82 inference('rw', [status(thm)], [zip_derived_cl42, '7'])). 132.99/17.82 thf(zip_derived_cl45, plain, 132.99/17.82 (~ (mnot @ (mbox_s4 @ (intersect @ '#sk4' @ '#sk6')) @ '#sk7')), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 132.99/17.82 thf(mnot, axiom, ~ (mnot @ X0 @ X1) => ((X0 @ X1) = ($true))). 132.99/17.82 thf('8', plain, 132.99/17.82 (![X0:( $i > $o ),X1:$i]: ( ( ~( mnot @ X0 @ X1 ) ) <=> ( X0 @ X1 ) )), 132.99/17.82 inference('rw.lit', [status(esa)], [mnot])). 132.99/17.82 thf(zip_derived_cl47, plain, 132.99/17.82 ( (mbox_s4 @ (intersect @ '#sk4' @ '#sk6') @ '#sk7')), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl45, '8'])). 132.99/17.82 thf(mbox_s4, axiom, (mbox_s4 @ X0 @ X1) => 132.99/17.82 ((((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X1 @ Y0))) | (X0 @ Y0)))))) = 132.99/17.82 ($true))). 132.99/17.82 thf('9', plain, 132.99/17.82 (![X0:( $i > $o ),X1:$i]: 132.99/17.82 ( ( mbox_s4 @ X0 @ X1 ) <=> 132.99/17.82 ( ![X6:$i]: ( ( ~( rel_s4 @ X1 @ X6 ) ) | ( X0 @ X6 ) ) ) )), 132.99/17.82 inference('rw.lit', [status(esa)], [mbox_s4])). 132.99/17.82 thf(zip_derived_cl49, plain, 132.99/17.82 ( (((!!) @ (^[Y0 : $i]: 132.99/17.82 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (intersect @ '#sk4' @ 132.99/17.82 '#sk6' @ Y0))))))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl47, '9'])). 132.99/17.82 thf(zip_derived_cl52, plain, 132.99/17.82 (![X2 : $i]: 132.99/17.82 (((((~) @ (rel_s4 @ '#sk7' @ X2))) | (intersect @ '#sk4' @ '#sk6' @ 132.99/17.82 X2)))), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl49])). 132.99/17.82 thf(zip_derived_cl54, plain, 132.99/17.82 (![X2 : $i]: 132.99/17.82 (~ (rel_s4 @ '#sk7' @ X2) | (intersect @ '#sk4' @ '#sk6' @ X2))), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 132.99/17.82 thf(intersect_defn, axiom, 132.99/17.82 (mvalid @ 132.99/17.82 ( mbox_s4 @ 132.99/17.82 ( mforall_ind @ 132.99/17.82 ( ^[B:mu]: 132.99/17.82 ( mbox_s4 @ 132.99/17.82 ( mforall_ind @ 132.99/17.82 ( ^[C:mu]: 132.99/17.82 ( mand @ 132.99/17.82 ( mbox_s4 @ 132.99/17.82 ( mimplies @ 132.99/17.82 ( mbox_s4 @ ( intersect @ B @ C ) ) @ 132.99/17.82 ( mexists_ind @ 132.99/17.82 ( ^[D:mu]: 132.99/17.82 ( mand @ 132.99/17.82 ( mbox_s4 @ ( member @ D @ B ) ) @ 132.99/17.82 ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) ) ) @ 132.99/17.82 ( mbox_s4 @ 132.99/17.82 ( mimplies @ 132.99/17.82 ( mexists_ind @ 132.99/17.82 ( ^[D:mu]: 132.99/17.82 ( mand @ 132.99/17.82 ( mbox_s4 @ ( member @ D @ B ) ) @ 132.99/17.82 ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) @ 132.99/17.82 ( mbox_s4 @ ( intersect @ B @ C ) ) ) ) ) ) ) ) ) ) ))). 132.99/17.82 thf(zip_derived_cl4, plain, 132.99/17.82 ( (mvalid @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ Y0 @ Y1))))))))))))), 132.99/17.82 inference('cnf', [status(esa)], [intersect_defn])). 132.99/17.82 thf(mvalid, axiom, (mvalid @ X0) => 132.99/17.82 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) = ($true))). 132.99/17.82 thf('10', plain, 132.99/17.82 (![X0:( $i > $o )]: ( ( mvalid @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 ) ) )), 132.99/17.82 inference('rw.lit', [status(esa)], [mvalid])). 132.99/17.82 thf(zip_derived_cl110, plain, 132.99/17.82 ( (((!!) @ (^[Y0 : $i]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mbox_s4 @ (intersect @ Y1 @ Y2)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y3 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y3 @ Y2))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y3 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y3 @ Y1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y3 @ Y2))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ Y1 @ Y2)))))))))) @ 132.99/17.82 Y0))))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl4, '10'])). 132.99/17.82 thf(zip_derived_cl111, plain, 132.99/17.82 (![X2 : $i]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ Y0 @ Y1)))))))))) @ 132.99/17.82 X2)), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl110])). 132.99/17.82 thf(zip_derived_cl112, plain, 132.99/17.82 (![X0 : $i]: 132.99/17.82 (((!!) @ (^[Y0 : $i]: 132.99/17.82 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mbox_s4 @ (intersect @ Y1 @ Y2)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y3 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ (member @ Y3 @ Y1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y3 @ Y2))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y3 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ (member @ Y3 @ Y1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y3 @ Y2))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ Y1 @ Y2))))))))) @ 132.99/17.82 Y0))))))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl111, '9'])). 132.99/17.82 thf(zip_derived_cl113, plain, 132.99/17.82 (![X0 : $i, X2 : $i]: 132.99/17.82 (((((~) @ (rel_s4 @ X0 @ X2))) | (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ Y0 @ Y1))))))))) @ 132.99/17.82 X2)))), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl112])). 132.99/17.82 thf(zip_derived_cl114, plain, 132.99/17.82 (![X0 : $i, X2 : $i]: 132.99/17.82 (~ (rel_s4 @ X0 @ X2) 132.99/17.82 | (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ Y0 @ Y1))))))))) @ 132.99/17.82 X2))), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl113])). 132.99/17.82 thf(mforall_ind, axiom, (mforall_ind @ X0 @ X1) => 132.99/17.82 ((((!!) @ (^[Y0 : mu]: (((exists_in_world @ Y0 @ X1) => (X0 @ Y0 @ X1)))))) 132.99/17.82 = ($true))). 132.99/17.82 thf('11', plain, 132.99/17.82 (![X0:( mu > $i > $o ),X1:$i]: 132.99/17.82 ( ( mforall_ind @ X0 @ X1 ) <=> 132.99/17.82 ( ![X6:mu]: ( ( exists_in_world @ X6 @ X1 ) => ( X0 @ X6 @ X1 ) ) ) )), 132.99/17.82 inference('rw.lit', [status(esa)], [mforall_ind])). 132.99/17.82 thf(zip_derived_cl115, plain, 132.99/17.82 (![X0 : $i, X1 : $i]: 132.99/17.82 ( (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X0) => 132.99/17.82 ((^[Y1 : mu]: 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mbox_s4 @ (intersect @ Y1 @ Y2)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y3 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ (member @ Y3 @ Y1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y3 @ Y2))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y3 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ (member @ Y3 @ Y1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y3 @ Y2))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ Y1 @ Y2))))))))) @ 132.99/17.82 Y0 @ X0)))))) 132.99/17.82 | ~ (rel_s4 @ X1 @ X0))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl114, '11'])). 132.99/17.82 thf(zip_derived_cl116, plain, 132.99/17.82 (![X0 : $i, X1 : $i]: 132.99/17.82 ( (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X0) => (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ Y0 @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ Y0)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ Y0 @ Y1))))))) @ 132.99/17.82 X0)))))) 132.99/17.82 | ~ (rel_s4 @ X1 @ X0))), 132.99/17.82 inference('ho_norm', [status(thm)], [zip_derived_cl115])). 132.99/17.82 thf(zip_derived_cl117, plain, 132.99/17.82 (![X0 : $i, X1 : $i, X3 : mu]: 132.99/17.82 ( (((exists_in_world @ X3 @ X0) => (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X3 @ Y0)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ X3 @ Y0))))))) @ 132.99/17.82 X0))) 132.99/17.82 | ~ (rel_s4 @ X1 @ X0))), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl116])). 132.99/17.82 thf(zip_derived_cl118, plain, 132.99/17.82 (![X0 : $i, X1 : $i, X3 : mu]: 132.99/17.82 (~ (exists_in_world @ X3 @ X0) 132.99/17.82 | (mbox_s4 @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X3 @ Y0)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ X3 @ Y0))))))) @ 132.99/17.82 X0) 132.99/17.82 | ~ (rel_s4 @ X1 @ X0))), 132.99/17.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl117])). 132.99/17.82 thf(zip_derived_cl119, plain, 132.99/17.82 (![X0 : $i, X1 : $i, X2 : mu]: 132.99/17.82 ( (((!!) @ (^[Y0 : $i]: 132.99/17.82 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X2 @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ X2 @ Y1)))))) @ 132.99/17.82 Y0)))))) 132.99/17.82 | ~ (rel_s4 @ X1 @ X0) 132.99/17.82 | ~ (exists_in_world @ X2 @ X0))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl118, '9'])). 132.99/17.82 thf(zip_derived_cl120, plain, 132.99/17.82 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]: 132.99/17.82 ( (((((~) @ (rel_s4 @ X0 @ X4))) | (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X2 @ Y0)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ X2 @ Y0)))))) @ 132.99/17.82 X4))) 132.99/17.82 | ~ (exists_in_world @ X2 @ X0) 132.99/17.82 | ~ (rel_s4 @ X1 @ X0))), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl119])). 132.99/17.82 thf(zip_derived_cl121, plain, 132.99/17.82 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]: 132.99/17.82 (~ (rel_s4 @ X0 @ X4) 132.99/17.82 | (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X2 @ Y0)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ X2 @ Y0)))))) @ 132.99/17.82 X4) 132.99/17.82 | ~ (rel_s4 @ X1 @ X0) 132.99/17.82 | ~ (exists_in_world @ X2 @ X0))), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl120])). 132.99/17.82 thf(zip_derived_cl122, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i]: 132.99/17.82 ( (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X3) => 132.99/17.82 ((^[Y1 : mu]: 132.99/17.82 (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X1 @ Y1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ X1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y2 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y2 @ X1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y2 @ Y1))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ X1 @ Y1)))))) @ 132.99/17.82 Y0 @ X3)))))) 132.99/17.82 | ~ (exists_in_world @ X1 @ X0) 132.99/17.82 | ~ (rel_s4 @ X2 @ X0) 132.99/17.82 | ~ (rel_s4 @ X0 @ X3))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl121, '11'])). 132.99/17.82 thf(zip_derived_cl123, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i]: 132.99/17.82 ( (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X3) => (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X1 @ Y0)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ X1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ X1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ Y0))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ X1 @ Y0)))) @ 132.99/17.82 X3)))))) 132.99/17.82 | ~ (exists_in_world @ X1 @ X0) 132.99/17.82 | ~ (rel_s4 @ X2 @ X0) 132.99/17.82 | ~ (rel_s4 @ X0 @ X3))), 132.99/17.82 inference('ho_norm', [status(thm)], [zip_derived_cl122])). 132.99/17.82 thf(zip_derived_cl124, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i, X5 : mu]: 132.99/17.82 ( (((exists_in_world @ X5 @ X3) => (mand @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X1 @ X5)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X5))))))) @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X5))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ X1 @ X5)))) @ 132.99/17.82 X3))) 132.99/17.82 | ~ (rel_s4 @ X0 @ X3) 132.99/17.82 | ~ (rel_s4 @ X2 @ X0) 132.99/17.82 | ~ (exists_in_world @ X1 @ X0))), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl123])). 132.99/17.82 thf(mand, axiom,(( mand @ (X0)@ (X1)@ (X2)) = 132.99/17.82 ((mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)) @ X2)))). 132.99/17.82 thf('12', plain, 132.99/17.82 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]: 132.99/17.82 ( ( mand @ X0 @ X1 @ X2 ) = 132.99/17.82 ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) @ X2 ) )), 132.99/17.82 define([status(thm)])). 132.99/17.82 thf(zip_derived_cl125, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i, X5 : mu]: 132.99/17.82 ( (((exists_in_world @ X5 @ X3) => (mnot @ 132.99/17.82 (mor @ 132.99/17.82 (mnot @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X1 @ X5)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X5)))))))) @ 132.99/17.82 (mnot @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X5))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ X1 @ X5)))))) @ 132.99/17.82 X3))) 132.99/17.82 | ~ (rel_s4 @ X0 @ X3) 132.99/17.82 | ~ (rel_s4 @ X2 @ X0) 132.99/17.82 | ~ (exists_in_world @ X1 @ X0))), 132.99/17.82 inference('rw', [status(thm)], [zip_derived_cl124, '12'])). 132.99/17.82 thf(zip_derived_cl126, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : $i, X3 : $i, X5 : mu]: 132.99/17.82 (~ (exists_in_world @ X5 @ X3) 132.99/17.82 | (mnot @ 132.99/17.82 (mor @ 132.99/17.82 (mnot @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X1 @ X5)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X5)))))))) @ 132.99/17.82 (mnot @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X1)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X5))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ X1 @ X5)))))) @ 132.99/17.82 X3) 132.99/17.82 | ~ (exists_in_world @ X1 @ X0) 132.99/17.82 | ~ (rel_s4 @ X2 @ X0) 132.99/17.82 | ~ (rel_s4 @ X0 @ X3))), 132.99/17.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])). 132.99/17.82 thf(mnot, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))). 132.99/17.82 thf('13', plain, 132.99/17.82 (![X0:( $i > $o ),X1:$i]: ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )), 132.99/17.82 inference('rw.lit', [status(esa)], [mnot])). 132.99/17.82 thf(zip_derived_cl127, plain, 132.99/17.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu]: 132.99/17.82 (~ (mor @ 132.99/17.82 (mnot @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X3 @ X4)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X4)))))))) @ 132.99/17.82 (mnot @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X4))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ X3 @ X4))))) @ 132.99/17.82 X0) 132.99/17.82 | ~ (rel_s4 @ X1 @ X0) 132.99/17.82 | ~ (rel_s4 @ X2 @ X1) 132.99/17.82 | ~ (exists_in_world @ X3 @ X1) 132.99/17.82 | ~ (exists_in_world @ X4 @ X0))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl126, '13'])). 132.99/17.82 thf(zip_derived_cl128, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i]: 132.99/17.82 (~ (((mnot @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1))))) @ 132.99/17.82 (mbox_s4 @ (intersect @ X3 @ X1)))) @ 132.99/17.82 X0) | (mnot @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X3 @ X1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1))))))) @ 132.99/17.82 X0))) 132.99/17.82 | ~ (exists_in_world @ X1 @ X0) 132.99/17.82 | ~ (exists_in_world @ X3 @ X2) 132.99/17.82 | ~ (rel_s4 @ X4 @ X2) 132.99/17.82 | ~ (rel_s4 @ X2 @ X0))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl127, '6'])). 132.99/17.82 thf(zip_derived_cl130, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i]: 132.99/17.82 (~ (mnot @ 132.99/17.82 (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X3 @ X1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1))))))) @ 132.99/17.82 X0) 132.99/17.82 | ~ (rel_s4 @ X2 @ X0) 132.99/17.82 | ~ (rel_s4 @ X4 @ X2) 132.99/17.82 | ~ (exists_in_world @ X3 @ X2) 132.99/17.82 | ~ (exists_in_world @ X1 @ X0))), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl128])). 132.99/17.82 thf(zip_derived_cl132, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i]: 132.99/17.82 ( (mbox_s4 @ 132.99/17.82 (mimplies @ (mbox_s4 @ (intersect @ X3 @ X1)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1)))))) @ 132.99/17.82 X0) 132.99/17.82 | ~ (exists_in_world @ X1 @ X0) 132.99/17.82 | ~ (exists_in_world @ X3 @ X2) 132.99/17.82 | ~ (rel_s4 @ X4 @ X2) 132.99/17.82 | ~ (rel_s4 @ X2 @ X0))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl130, '8'])). 132.99/17.82 thf(zip_derived_cl134, plain, 132.99/17.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu]: 132.99/17.82 ( (((!!) @ (^[Y0 : $i]: 132.99/17.82 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mimplies @ 132.99/17.82 (mbox_s4 @ (intersect @ X3 @ X4)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y1 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ X4))))) @ 132.99/17.82 Y0)))))) 132.99/17.82 | ~ (rel_s4 @ X1 @ X0) 132.99/17.82 | ~ (rel_s4 @ X2 @ X1) 132.99/17.82 | ~ (exists_in_world @ X3 @ X1) 132.99/17.82 | ~ (exists_in_world @ X4 @ X0))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl132, '9'])). 132.99/17.82 thf(zip_derived_cl136, plain, 132.99/17.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu, X6 : $i]: 132.99/17.82 ( (((((~) @ (rel_s4 @ X0 @ X6))) | (mimplies @ 132.99/17.82 (mbox_s4 @ (intersect @ X3 @ X4)) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X4))))) @ 132.99/17.82 X6))) 132.99/17.82 | ~ (exists_in_world @ X4 @ X0) 132.99/17.82 | ~ (exists_in_world @ X3 @ X1) 132.99/17.82 | ~ (rel_s4 @ X2 @ X1) 132.99/17.82 | ~ (rel_s4 @ X1 @ X0))), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl134])). 132.99/17.82 thf(zip_derived_cl139, plain, 132.99/17.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu, X6 : $i]: 132.99/17.82 ( (((((~) @ (rel_s4 @ X0 @ X6))) | (mor @ 132.99/17.82 (mnot @ (mbox_s4 @ (intersect @ X3 @ X4))) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X4))))) @ 132.99/17.82 X6))) 132.99/17.82 | ~ (exists_in_world @ X4 @ X0) 132.99/17.82 | ~ (exists_in_world @ X3 @ X1) 132.99/17.82 | ~ (rel_s4 @ X2 @ X1) 132.99/17.82 | ~ (rel_s4 @ X1 @ X0))), 132.99/17.82 inference('rw', [status(thm)], [zip_derived_cl136, '3'])). 132.99/17.82 thf(zip_derived_cl140, plain, 132.99/17.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : mu, X4 : mu, X6 : $i]: 132.99/17.82 (~ (rel_s4 @ X0 @ X6) 132.99/17.82 | (mor @ (mnot @ (mbox_s4 @ (intersect @ X3 @ X4))) @ 132.99/17.82 (mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X4))))) @ 132.99/17.82 X6) 132.99/17.82 | ~ (rel_s4 @ X1 @ X0) 132.99/17.82 | ~ (rel_s4 @ X2 @ X1) 132.99/17.82 | ~ (exists_in_world @ X3 @ X1) 132.99/17.82 | ~ (exists_in_world @ X4 @ X0))), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl139])). 132.99/17.82 thf(mor, axiom, (mor @ X0 @ X1 @ X2) => 132.99/17.82 ((((X1 @ X2) | (X0 @ X2))) = ($true))). 132.99/17.82 thf('14', plain, 132.99/17.82 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]: 132.99/17.82 ( ( mor @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) | ( X1 @ X2 ) ) )), 132.99/17.82 inference('rw.lit', [status(esa)], [mor])). 132.99/17.82 thf(zip_derived_cl142, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]: 132.99/17.82 ( (((mexists_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1)))) @ 132.99/17.82 X5) | (mnot @ (mbox_s4 @ (intersect @ X3 @ X1)) @ X5))) 132.99/17.82 | ~ (exists_in_world @ X1 @ X0) 132.99/17.82 | ~ (exists_in_world @ X3 @ X2) 132.99/17.82 | ~ (rel_s4 @ X4 @ X2) 132.99/17.82 | ~ (rel_s4 @ X2 @ X0) 132.99/17.82 | ~ (rel_s4 @ X0 @ X5))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl140, '14'])). 132.99/17.82 thf(zip_derived_cl144, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]: 132.99/17.82 ( (((mnot @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1)))))) @ 132.99/17.82 X5) | (mnot @ (mbox_s4 @ (intersect @ X3 @ X1)) @ X5))) 132.99/17.82 | ~ (exists_in_world @ X1 @ X0) 132.99/17.82 | ~ (exists_in_world @ X3 @ X2) 132.99/17.82 | ~ (rel_s4 @ X4 @ X2) 132.99/17.82 | ~ (rel_s4 @ X2 @ X0) 132.99/17.82 | ~ (rel_s4 @ X0 @ X5))), 132.99/17.82 inference('rw', [status(thm)], [zip_derived_cl142, '7'])). 132.99/17.82 thf(zip_derived_cl145, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]: 132.99/17.82 ( (mnot @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1)))))) @ 132.99/17.82 X5) 132.99/17.82 | (mnot @ (mbox_s4 @ (intersect @ X3 @ X1)) @ X5) 132.99/17.82 | ~ (rel_s4 @ X0 @ X5) 132.99/17.82 | ~ (rel_s4 @ X2 @ X0) 132.99/17.82 | ~ (rel_s4 @ X4 @ X2) 132.99/17.82 | ~ (exists_in_world @ X3 @ X2) 132.99/17.82 | ~ (exists_in_world @ X1 @ X0))), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl144])). 132.99/17.82 thf(zip_derived_cl147, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]: 132.99/17.82 (~ (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1))))) @ 132.99/17.82 X5) 132.99/17.82 | ~ (exists_in_world @ X1 @ X0) 132.99/17.82 | ~ (exists_in_world @ X3 @ X2) 132.99/17.82 | ~ (rel_s4 @ X4 @ X2) 132.99/17.82 | ~ (rel_s4 @ X2 @ X0) 132.99/17.82 | ~ (rel_s4 @ X0 @ X5) 132.99/17.82 | (mnot @ (mbox_s4 @ (intersect @ X3 @ X1)) @ X5))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl145, '13'])). 132.99/17.82 thf(zip_derived_cl149, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 132.99/17.82 (~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X0) => 132.99/17.82 ((^[Y1 : mu]: 132.99/17.82 (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ X1))))) @ 132.99/17.82 Y0 @ X0)))))) 132.99/17.82 | (mnot @ (mbox_s4 @ (intersect @ X2 @ X1)) @ X0) 132.99/17.82 | ~ (rel_s4 @ X3 @ X0) 132.99/17.82 | ~ (rel_s4 @ X4 @ X3) 132.99/17.82 | ~ (rel_s4 @ X5 @ X4) 132.99/17.82 | ~ (exists_in_world @ X2 @ X4) 132.99/17.82 | ~ (exists_in_world @ X1 @ X3))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl147, '2'])). 132.99/17.82 thf(zip_derived_cl152, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 132.99/17.82 (~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X0) => (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1))) @ 132.99/17.82 X0)))))) 132.99/17.82 | (mnot @ (mbox_s4 @ (intersect @ X2 @ X1)) @ X0) 132.99/17.82 | ~ (rel_s4 @ X3 @ X0) 132.99/17.82 | ~ (rel_s4 @ X4 @ X3) 132.99/17.82 | ~ (rel_s4 @ X5 @ X4) 132.99/17.82 | ~ (exists_in_world @ X2 @ X4) 132.99/17.82 | ~ (exists_in_world @ X1 @ X3))), 132.99/17.82 inference('ho_norm', [status(thm)], [zip_derived_cl149])). 132.99/17.82 thf(zip_derived_cl153, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : $i, X3 : mu, X4 : $i, X5 : $i]: 132.99/17.82 (~ (mbox_s4 @ (intersect @ X3 @ X1) @ X5) 132.99/17.82 | ~ (exists_in_world @ X1 @ X0) 132.99/17.82 | ~ (exists_in_world @ X3 @ X2) 132.99/17.82 | ~ (rel_s4 @ X4 @ X2) 132.99/17.82 | ~ (rel_s4 @ X2 @ X0) 132.99/17.82 | ~ (rel_s4 @ X0 @ X5) 132.99/17.82 | ~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X5) => (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X3)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1))) @ 132.99/17.82 X5)))))))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl152, '13'])). 132.99/17.82 thf(zip_derived_cl155, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 132.99/17.82 (~ (((!!) @ (^[Y0 : $i]: 132.99/17.82 (((((~) @ (rel_s4 @ X0 @ Y0))) | (intersect @ X2 @ 132.99/17.82 X1 @ Y0)))))) 132.99/17.82 | ~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X0) => (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1))) @ 132.99/17.82 X0)))))) 132.99/17.82 | ~ (rel_s4 @ X3 @ X0) 132.99/17.82 | ~ (rel_s4 @ X4 @ X3) 132.99/17.82 | ~ (rel_s4 @ X5 @ X4) 132.99/17.82 | ~ (exists_in_world @ X2 @ X4) 132.99/17.82 | ~ (exists_in_world @ X1 @ X3))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl153, '1'])). 132.99/17.82 thf(zip_derived_cl158, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 132.99/17.82 (~ (((((~) @ (rel_s4 @ X0 @ ('#sk11' @ X2 @ X1 @ X0)))) | 132.99/17.82 (intersect @ X2 @ X1 @ ('#sk11' @ X2 @ X1 @ X0)))) 132.99/17.82 | ~ (exists_in_world @ X1 @ X3) 132.99/17.82 | ~ (exists_in_world @ X2 @ X4) 132.99/17.82 | ~ (rel_s4 @ X5 @ X4) 132.99/17.82 | ~ (rel_s4 @ X4 @ X3) 132.99/17.82 | ~ (rel_s4 @ X3 @ X0) 132.99/17.82 | ~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X0) => (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1))) @ 132.99/17.82 X0)))))))), 132.99/17.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl155])). 132.99/17.82 thf(zip_derived_cl161, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 132.99/17.82 (~ (intersect @ X2 @ X1 @ ('#sk11' @ X2 @ X1 @ X0)) 132.99/17.82 | ~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X0) => (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1))) @ 132.99/17.82 X0)))))) 132.99/17.82 | ~ (rel_s4 @ X3 @ X0) 132.99/17.82 | ~ (rel_s4 @ X4 @ X3) 132.99/17.82 | ~ (rel_s4 @ X5 @ X4) 132.99/17.82 | ~ (exists_in_world @ X2 @ X4) 132.99/17.82 | ~ (exists_in_world @ X1 @ X3))), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl158])). 132.99/17.82 thf(zip_derived_cl160, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 132.99/17.82 ( (rel_s4 @ X0 @ ('#sk11' @ X2 @ X1 @ X0)) 132.99/17.82 | ~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X0) => (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1))) @ 132.99/17.82 X0)))))) 132.99/17.82 | ~ (rel_s4 @ X3 @ X0) 132.99/17.82 | ~ (rel_s4 @ X4 @ X3) 132.99/17.82 | ~ (rel_s4 @ X5 @ X4) 132.99/17.82 | ~ (exists_in_world @ X2 @ X4) 132.99/17.82 | ~ (exists_in_world @ X1 @ X3))), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl158])). 132.99/17.82 thf(zip_derived_cl163, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : mu]: 132.99/17.82 ( ('#form12' @ X0 @ X1 @ X2) 132.99/17.82 | ~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X0) => (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1))) @ 132.99/17.82 X0)))))))), 132.99/17.82 define([status(thm)])). 132.99/17.82 thf(zip_derived_cl166, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 132.99/17.82 (~ ('#form12' @ X0 @ X1 @ X2) 132.99/17.82 | ~ (exists_in_world @ X1 @ X3) 132.99/17.82 | ~ (exists_in_world @ X2 @ X4) 132.99/17.82 | ~ (rel_s4 @ X5 @ X4) 132.99/17.82 | ~ (rel_s4 @ X4 @ X3) 132.99/17.82 | ~ (rel_s4 @ X3 @ X0) 132.99/17.82 | ~ (intersect @ X2 @ X1 @ ('#sk11' @ X2 @ X1 @ X0)))), 132.99/17.82 inference('renaming', [status(thm)], 132.99/17.82 [zip_derived_cl161, zip_derived_cl163])). 132.99/17.82 thf(zip_derived_cl160, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 132.99/17.82 ( (rel_s4 @ X0 @ ('#sk11' @ X2 @ X1 @ X0)) 132.99/17.82 | ~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X0) => (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1))) @ 132.99/17.82 X0)))))) 132.99/17.82 | ~ (rel_s4 @ X3 @ X0) 132.99/17.82 | ~ (rel_s4 @ X4 @ X3) 132.99/17.82 | ~ (rel_s4 @ X5 @ X4) 132.99/17.82 | ~ (exists_in_world @ X2 @ X4) 132.99/17.82 | ~ (exists_in_world @ X1 @ X3))), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl158])). 132.99/17.82 thf(zip_derived_cl163, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : mu]: 132.99/17.82 ( ('#form12' @ X0 @ X1 @ X2) 132.99/17.82 | ~ (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ X0) => (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ X1))) @ 132.99/17.82 X0)))))))), 132.99/17.82 define([status(thm)])). 132.99/17.82 thf(zip_derived_cl165, plain, 132.99/17.82 (![X0 : $i, X1 : mu, X2 : mu, X3 : $i, X4 : $i, X5 : $i]: 132.99/17.82 (~ ('#form12' @ X0 @ X1 @ X2) 132.99/17.82 | ~ (exists_in_world @ X1 @ X3) 132.99/17.82 | ~ (exists_in_world @ X2 @ X4) 132.99/17.82 | ~ (rel_s4 @ X5 @ X4) 132.99/17.82 | ~ (rel_s4 @ X4 @ X3) 132.99/17.82 | ~ (rel_s4 @ X3 @ X0) 132.99/17.82 | (rel_s4 @ X0 @ ('#sk11' @ X2 @ X1 @ X0)))), 132.99/17.82 inference('renaming', [status(thm)], 132.99/17.82 [zip_derived_cl160, zip_derived_cl163])). 132.99/17.82 thf(zip_derived_cl1315, plain, 132.99/17.82 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu]: 132.99/17.82 ( (rel_s4 @ X1 @ ('#sk11' @ X3 @ X2 @ X1)) 132.99/17.82 | ~ (rel_s4 @ X0 @ X1) 132.99/17.82 | ~ (rel_s4 @ X0 @ X0) 132.99/17.82 | ~ (exists_in_world @ X3 @ X0) 132.99/17.82 | ~ (exists_in_world @ X2 @ X0) 132.99/17.82 | ~ ('#form12' @ X1 @ X2 @ X3))), 132.99/17.82 inference('eq_fact', [status(thm)], [zip_derived_cl165])). 132.99/17.82 thf(zip_derived_cl14, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 132.99/17.82 thf(zip_derived_cl1424, plain, 132.99/17.82 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu]: 132.99/17.82 ( (rel_s4 @ X1 @ ('#sk11' @ X3 @ X2 @ X1)) 132.99/17.82 | ~ (rel_s4 @ X0 @ X1) 132.99/17.82 | ~ (exists_in_world @ X3 @ X0) 132.99/17.82 | ~ (exists_in_world @ X2 @ X0) 132.99/17.82 | ~ ('#form12' @ X1 @ X2 @ X3))), 132.99/17.82 inference('demod', [status(thm)], [zip_derived_cl1315, zip_derived_cl14])). 132.99/17.82 thf(zip_derived_cl109, plain, 132.99/17.82 (![X2 : mu, X4 : $i, X6 : $i]: 132.99/17.82 (~ (exists_in_world @ X2 @ X4) 132.99/17.82 | ~ (rel_s4 @ X4 @ X6) 132.99/17.82 | (exists_in_world @ X2 @ X6))), 132.99/17.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl108])). 132.99/17.82 thf(zip_derived_cl30, plain, ( (rel_s4 @ '#sk3' @ '#sk5')), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 132.99/17.82 thf(zip_derived_cl1099, plain, 132.99/17.82 (![X0 : mu]: 132.99/17.82 ( (exists_in_world @ X0 @ '#sk5') | ~ (exists_in_world @ X0 @ '#sk3'))), 132.99/17.82 inference('sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl30])). 132.99/17.82 thf(zip_derived_cl109, plain, 132.99/17.82 (![X2 : mu, X4 : $i, X6 : $i]: 132.99/17.82 (~ (exists_in_world @ X2 @ X4) 132.99/17.82 | ~ (rel_s4 @ X4 @ X6) 132.99/17.82 | (exists_in_world @ X2 @ X6))), 132.99/17.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl108])). 132.99/17.82 thf(zip_derived_cl40, plain, ( (rel_s4 @ '#sk5' @ '#sk7')), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 132.99/17.82 thf(zip_derived_cl1095, plain, 132.99/17.82 (![X0 : mu]: 132.99/17.82 ( (exists_in_world @ X0 @ '#sk7') | ~ (exists_in_world @ X0 @ '#sk5'))), 132.99/17.82 inference('sup+', [status(thm)], [zip_derived_cl109, zip_derived_cl40])). 132.99/17.82 thf(zip_derived_cl44, plain, 132.99/17.82 (~ (mnot @ 132.99/17.82 (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ '#sk6')))))) @ 132.99/17.82 '#sk7')), 132.99/17.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 132.99/17.82 thf(zip_derived_cl46, plain, 132.99/17.82 ( (mforall_ind @ 132.99/17.82 (^[Y0 : mu]: 132.99/17.82 (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ '#sk6'))))) @ 132.99/17.82 '#sk7')), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl44, '8'])). 132.99/17.82 thf(zip_derived_cl48, plain, 132.99/17.82 ( (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ '#sk7') => 132.99/17.82 ((^[Y1 : mu]: 132.99/17.82 (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y1 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y1 @ '#sk6'))))) @ 132.99/17.82 Y0 @ '#sk7'))))))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl46, '11'])). 132.99/17.82 thf(zip_derived_cl50, plain, 132.99/17.82 ( (((!!) @ (^[Y0 : mu]: 132.99/17.82 (((exists_in_world @ Y0 @ '#sk7') => (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ Y0 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ Y0 @ '#sk6'))) @ 132.99/17.82 '#sk7'))))))), 132.99/17.82 inference('ho_norm', [status(thm)], [zip_derived_cl48])). 132.99/17.82 thf(zip_derived_cl51, plain, 132.99/17.82 (![X2 : mu]: 132.99/17.82 (((exists_in_world @ X2 @ '#sk7') => (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ X2 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ X2 @ '#sk6'))) @ 132.99/17.82 '#sk7')))), 132.99/17.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl50])). 132.99/17.82 thf(zip_derived_cl53, plain, 132.99/17.82 (![X2 : mu]: 132.99/17.82 (~ (exists_in_world @ X2 @ '#sk7') 132.99/17.82 | (mnot @ 132.99/17.82 (mand @ (mbox_s4 @ (member @ X2 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ X2 @ '#sk6'))) @ 132.99/17.82 '#sk7'))), 132.99/17.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 132.99/17.82 thf(zip_derived_cl55, plain, 132.99/17.82 (![X0 : mu]: 132.99/17.82 (~ (mand @ (mbox_s4 @ (member @ X0 @ '#sk4')) @ 132.99/17.82 (mbox_s4 @ (member @ X0 @ '#sk6')) @ '#sk7') 132.99/17.82 | ~ (exists_in_world @ X0 @ '#sk7'))), 132.99/17.82 inference('rw_clause', [status(thm)], [zip_derived_cl53, '13'])). 132.99/17.82 thf(zip_derived_cl56, plain, 132.99/17.82 (![X0 : mu]: 132.99/17.82 (~ (mnot @ 132.99/17.82 (mor @ (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4'))) @ 132.99/17.82 (mnot @ (mbox_s4 @ (member @ X0 @ '#sk6')))) @ 132.99/17.82 '#sk7') 132.99/17.82 | ~ (exists_in_world @ X0 @ '#sk7'))), 132.99/17.82 inference('rw', [status(thm)], [zip_derived_cl55, '12'])). 132.99/17.82 thf(zip_derived_cl57, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 ( (mor @ (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4'))) @ 132.99/17.83 (mnot @ (mbox_s4 @ (member @ X0 @ '#sk6'))) @ '#sk7') 132.99/17.83 | ~ (exists_in_world @ X0 @ '#sk7'))), 132.99/17.83 inference('rw_clause', [status(thm)], [zip_derived_cl56, '8'])). 132.99/17.83 thf(zip_derived_cl58, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 ( (((mnot @ (mbox_s4 @ (member @ X0 @ '#sk6')) @ '#sk7') | (mnot @ 132.99/17.83 (mbox_s4 @ (member @ X0 @ '#sk4')) @ '#sk7'))) 132.99/17.83 | ~ (exists_in_world @ X0 @ '#sk7'))), 132.99/17.83 inference('rw_clause', [status(thm)], [zip_derived_cl57, '14'])). 132.99/17.83 thf(zip_derived_cl59, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 ( (mnot @ (mbox_s4 @ (member @ X0 @ '#sk6')) @ '#sk7') 132.99/17.83 | (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4')) @ '#sk7') 132.99/17.83 | ~ (exists_in_world @ X0 @ '#sk7'))), 132.99/17.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl58])). 132.99/17.83 thf(zip_derived_cl60, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 (~ (mbox_s4 @ (member @ X0 @ '#sk6') @ '#sk7') 132.99/17.83 | ~ (exists_in_world @ X0 @ '#sk7') 132.99/17.83 | (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4')) @ '#sk7'))), 132.99/17.83 inference('rw_clause', [status(thm)], [zip_derived_cl59, '13'])). 132.99/17.83 thf(zip_derived_cl61, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 (~ (((!!) @ (^[Y0 : $i]: 132.99/17.83 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 132.99/17.83 '#sk6' @ Y0)))))) 132.99/17.83 | (mnot @ (mbox_s4 @ (member @ X0 @ '#sk4')) @ '#sk7') 132.99/17.83 | ~ (exists_in_world @ X0 @ '#sk7'))), 132.99/17.83 inference('rw_clause', [status(thm)], [zip_derived_cl60, '1'])). 132.99/17.83 thf(zip_derived_cl62, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 (~ (mbox_s4 @ (member @ X0 @ '#sk4') @ '#sk7') 132.99/17.83 | ~ (exists_in_world @ X0 @ '#sk7') 132.99/17.83 | ~ (((!!) @ (^[Y0 : $i]: 132.99/17.83 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 132.99/17.83 '#sk6' @ Y0)))))))), 132.99/17.83 inference('rw_clause', [status(thm)], [zip_derived_cl61, '13'])). 132.99/17.83 thf(zip_derived_cl63, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 (~ (((!!) @ (^[Y0 : $i]: 132.99/17.83 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 132.99/17.83 '#sk4' @ Y0)))))) 132.99/17.83 | ~ (((!!) @ (^[Y0 : $i]: 132.99/17.83 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 132.99/17.83 '#sk6' @ Y0)))))) 132.99/17.83 | ~ (exists_in_world @ X0 @ '#sk7'))), 132.99/17.83 inference('rw_clause', [status(thm)], [zip_derived_cl62, '1'])). 132.99/17.83 thf(zip_derived_cl64, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 (~ (((((~) @ (rel_s4 @ '#sk7' @ ('#sk8' @ X0)))) | (member @ X0 @ 132.99/17.83 '#sk4' @ ('#sk8' @ X0)))) 132.99/17.83 | ~ (exists_in_world @ X0 @ '#sk7') 132.99/17.83 | ~ (((!!) @ (^[Y0 : $i]: 132.99/17.83 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 132.99/17.83 '#sk6' @ Y0)))))))), 132.99/17.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl63])). 132.99/17.83 thf(zip_derived_cl66, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 (~ (member @ X0 @ '#sk4' @ ('#sk8' @ X0)) 132.99/17.83 | ~ (((!!) @ (^[Y0 : $i]: 132.99/17.83 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 132.99/17.83 '#sk6' @ Y0)))))) 132.99/17.83 | ~ (exists_in_world @ X0 @ '#sk7'))), 132.99/17.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])). 132.99/17.83 thf(zip_derived_cl65, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 ( (rel_s4 @ '#sk7' @ ('#sk8' @ X0)) 132.99/17.83 | ~ (((!!) @ (^[Y0 : $i]: 132.99/17.83 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 132.99/17.83 '#sk6' @ Y0)))))) 132.99/17.83 | ~ (exists_in_world @ X0 @ '#sk7'))), 132.99/17.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])). 132.99/17.83 thf(zip_derived_cl67, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 ( ('#form9' @ X0) 132.99/17.83 | ~ (((!!) @ (^[Y0 : $i]: 132.99/17.83 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 132.99/17.83 '#sk6' @ Y0)))))))), 132.99/17.83 define([status(thm)])). 132.99/17.83 thf(zip_derived_cl70, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 (~ ('#form9' @ X0) 132.99/17.83 | ~ (exists_in_world @ X0 @ '#sk7') 132.99/17.83 | ~ (member @ X0 @ '#sk4' @ ('#sk8' @ X0)))), 132.99/17.83 inference('renaming', [status(thm)], [zip_derived_cl66, zip_derived_cl67])). 132.99/17.83 thf(zip_derived_cl67, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 ( ('#form9' @ X0) 132.99/17.83 | ~ (((!!) @ (^[Y0 : $i]: 132.99/17.83 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 132.99/17.83 '#sk6' @ Y0)))))))), 132.99/17.83 define([status(thm)])). 132.99/17.83 thf(zip_derived_cl68, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 (~ (((((~) @ (rel_s4 @ '#sk7' @ ('#sk10' @ X0)))) | (member @ X0 @ 132.99/17.83 '#sk6' @ ('#sk10' @ X0)))) 132.99/17.83 | ('#form9' @ X0))), 132.99/17.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl67])). 132.99/17.83 thf(zip_derived_cl71, plain, 132.99/17.83 (![X0 : mu]: ( (rel_s4 @ '#sk7' @ ('#sk10' @ X0)) | ('#form9' @ X0))), 132.99/17.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl68])). 132.99/17.83 thf(zip_derived_cl163, plain, 132.99/17.83 (![X0 : $i, X1 : mu, X2 : mu]: 132.99/17.83 ( ('#form12' @ X0 @ X1 @ X2) 132.99/17.83 | ~ (((!!) @ (^[Y0 : mu]: 132.99/17.83 (((exists_in_world @ Y0 @ X0) => (mnot @ 132.99/17.83 (mand @ (mbox_s4 @ (member @ Y0 @ X2)) @ 132.99/17.83 (mbox_s4 @ (member @ Y0 @ X1))) @ 132.99/17.83 X0)))))))), 132.99/17.83 define([status(thm)])). 132.99/17.83 thf(zip_derived_cl164, plain, 132.99/17.83 (![X0 : $i, X1 : mu, X2 : mu]: 132.99/17.83 (~ (((exists_in_world @ ('#sk13' @ X0 @ X1 @ X2) @ X0) => (mnot @ 132.99/17.83 (mand @ (mbox_s4 @ (member @ ('#sk13' @ X0 @ X1 @ X2) @ X2)) @ 132.99/17.83 (mbox_s4 @ (member @ ('#sk13' @ X0 @ X1 @ X2) @ X1))) @ 132.99/17.83 X0))) 132.99/17.83 | ('#form12' @ X0 @ X1 @ X2))), 132.99/17.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl163])). 132.99/17.83 thf(zip_derived_cl169, plain, 132.99/17.83 (![X0 : $i, X1 : mu, X2 : mu]: 132.99/17.83 ( (exists_in_world @ ('#sk13' @ X0 @ X1 @ X2) @ X0) 132.99/17.83 | ('#form12' @ X0 @ X1 @ X2))), 132.99/17.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 132.99/17.83 thf(zip_derived_cl170, plain, 132.99/17.83 (![X0 : $i, X1 : mu, X2 : mu]: 132.99/17.83 (~ (mnot @ 132.99/17.83 (mand @ (mbox_s4 @ (member @ ('#sk13' @ X0 @ X1 @ X2) @ X2)) @ 132.99/17.83 (mbox_s4 @ (member @ ('#sk13' @ X0 @ X1 @ X2) @ X1))) @ 132.99/17.83 X0) 132.99/17.83 | ('#form12' @ X0 @ X1 @ X2))), 132.99/17.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 132.99/17.83 thf(zip_derived_cl172, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i]: 132.99/17.83 ( (mand @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0)) @ 132.99/17.83 (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1)) @ X2) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('rw_clause', [status(thm)], [zip_derived_cl170, '8'])). 132.99/17.83 thf(zip_derived_cl174, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i]: 132.99/17.83 ( (mnot @ 132.99/17.83 (mor @ 132.99/17.83 (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0))) @ 132.99/17.83 (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1)))) @ 132.99/17.83 X2) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('rw', [status(thm)], [zip_derived_cl172, '12'])). 132.99/17.83 thf(zip_derived_cl175, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i]: 132.99/17.83 (~ (mor @ 132.99/17.83 (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0))) @ 132.99/17.83 (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1))) @ X2) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('rw_clause', [status(thm)], [zip_derived_cl174, '13'])). 132.99/17.83 thf(zip_derived_cl177, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i]: 132.99/17.83 (~ (((mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1)) @ 132.99/17.83 X2) | (mnot @ 132.99/17.83 (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0)) @ X2))) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('rw_clause', [status(thm)], [zip_derived_cl175, '6'])). 132.99/17.83 thf(zip_derived_cl179, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i]: 132.99/17.83 (~ (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1)) @ X2) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl177])). 132.99/17.83 thf(zip_derived_cl182, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i]: 132.99/17.83 ( (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1) @ X2) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('rw_clause', [status(thm)], [zip_derived_cl179, '8'])). 132.99/17.83 thf(zip_derived_cl185, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i]: 132.99/17.83 ( (((!!) @ (^[Y0 : $i]: 132.99/17.83 (((((~) @ (rel_s4 @ X2 @ Y0))) | (member @ 132.99/17.83 ('#sk13' @ X2 @ X1 @ X0) @ X1 @ Y0)))))) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('rw_clause', [status(thm)], [zip_derived_cl182, '9'])). 132.99/17.83 thf(zip_derived_cl188, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i, X4 : $i]: 132.99/17.83 ( (((((~) @ (rel_s4 @ X2 @ X4))) | (member @ 132.99/17.83 ('#sk13' @ X2 @ X1 @ X0) @ X1 @ X4))) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl185])). 132.99/17.83 thf(zip_derived_cl192, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i, X4 : $i]: 132.99/17.83 (~ (rel_s4 @ X2 @ X4) 132.99/17.83 | (member @ ('#sk13' @ X2 @ X1 @ X0) @ X1 @ X4) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl188])). 132.99/17.83 thf(zip_derived_cl72, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 (~ (member @ X0 @ '#sk6' @ ('#sk10' @ X0)) | ('#form9' @ X0))), 132.99/17.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl68])). 132.99/17.83 thf(zip_derived_cl1753, plain, 132.99/17.83 (![X0 : mu, X1 : $i]: 132.99/17.83 ( ('#form12' @ X1 @ '#sk6' @ X0) 132.99/17.83 | ~ (rel_s4 @ X1 @ ('#sk10' @ ('#sk13' @ X1 @ '#sk6' @ X0))) 132.99/17.83 | ('#form9' @ ('#sk13' @ X1 @ '#sk6' @ X0)))), 132.99/17.83 inference('sup-', [status(thm)], [zip_derived_cl192, zip_derived_cl72])). 132.99/17.83 thf(zip_derived_cl65, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 ( (rel_s4 @ '#sk7' @ ('#sk8' @ X0)) 132.99/17.83 | ~ (((!!) @ (^[Y0 : $i]: 132.99/17.83 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 132.99/17.83 '#sk6' @ Y0)))))) 132.99/17.83 | ~ (exists_in_world @ X0 @ '#sk7'))), 132.99/17.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl64])). 132.99/17.83 thf(zip_derived_cl67, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 ( ('#form9' @ X0) 132.99/17.83 | ~ (((!!) @ (^[Y0 : $i]: 132.99/17.83 (((((~) @ (rel_s4 @ '#sk7' @ Y0))) | (member @ X0 @ 132.99/17.83 '#sk6' @ Y0)))))))), 132.99/17.83 define([status(thm)])). 132.99/17.83 thf(zip_derived_cl69, plain, 132.99/17.83 (![X0 : mu]: 132.99/17.83 (~ ('#form9' @ X0) 132.99/17.83 | ~ (exists_in_world @ X0 @ '#sk7') 132.99/17.83 | (rel_s4 @ '#sk7' @ ('#sk8' @ X0)))), 132.99/17.83 inference('renaming', [status(thm)], [zip_derived_cl65, zip_derived_cl67])). 132.99/17.83 thf(zip_derived_cl180, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i]: 132.99/17.83 (~ (mnot @ (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0)) @ X2) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl177])). 132.99/17.83 thf(zip_derived_cl183, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i]: 132.99/17.83 ( (mbox_s4 @ (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0) @ X2) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('rw_clause', [status(thm)], [zip_derived_cl180, '8'])). 132.99/17.83 thf(zip_derived_cl186, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i]: 132.99/17.83 ( (((!!) @ (^[Y0 : $i]: 132.99/17.83 (((((~) @ (rel_s4 @ X2 @ Y0))) | (member @ 132.99/17.83 ('#sk13' @ X2 @ X1 @ X0) @ X0 @ Y0)))))) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('rw_clause', [status(thm)], [zip_derived_cl183, '9'])). 132.99/17.83 thf(zip_derived_cl189, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i, X4 : $i]: 132.99/17.83 ( (((((~) @ (rel_s4 @ X2 @ X4))) | (member @ 132.99/17.83 ('#sk13' @ X2 @ X1 @ X0) @ X0 @ X4))) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl186])). 132.99/17.83 thf(zip_derived_cl193, plain, 132.99/17.83 (![X0 : mu, X1 : mu, X2 : $i, X4 : $i]: 132.99/17.83 (~ (rel_s4 @ X2 @ X4) 132.99/17.83 | (member @ ('#sk13' @ X2 @ X1 @ X0) @ X0 @ X4) 132.99/17.83 | ('#form12' @ X2 @ X1 @ X0))), 132.99/17.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl189])). 132.99/17.83 thf(zip_derived_cl24337, plain, ($false), 132.99/17.83 inference('eprover', [status(thm)], 132.99/17.83 [zip_derived_cl40, zip_derived_cl26, zip_derived_cl35, 132.99/17.83 zip_derived_cl14, zip_derived_cl206, zip_derived_cl109, 132.99/17.83 zip_derived_cl54, zip_derived_cl166, zip_derived_cl1424, 132.99/17.83 zip_derived_cl1099, zip_derived_cl1095, zip_derived_cl70, 132.99/17.83 zip_derived_cl71, zip_derived_cl169, zip_derived_cl1753, 132.99/17.83 zip_derived_cl69, zip_derived_cl193])). 132.99/17.83 132.99/17.83 % SZS output end Refutation 132.99/17.83 132.99/17.83 132.99/17.83 % Terminating... 132.99/17.96 % Runner terminated. 132.99/17.98 % Zipperpin 1.5 exiting 132.99/17.99 EOF