0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.DdVImNHmt5 true 0.14/0.34 % Computer : n023.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 960 0.14/0.34 % WCLimit : 120 0.14/0.34 % DateTime : Tue Aug 9 07:12:28 EDT 2022 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 960 s 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.35 % Python version: Python 3.6.8 0.14/0.35 % Running in HO mode 0.54/0.64 % Total configuration time : 828 0.54/0.64 % Estimated wc time : 1656 0.54/0.64 % Estimated cpu time (8 cpus) : 207.0 0.54/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.54/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.54/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.54/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.54/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.54/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.54/0.76 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.54/0.76 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.56/0.89 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 6.34/1.39 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s 119.59/15.74 % Solved by lams/30_b.l.sh. 119.59/15.74 % running E: timeout 14 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.DdVImNHmt5/e_inputae14b8 --cpu-limit=12 --auto -s -p 119.59/15.74 % done 4457 iterations in 14.757s 119.59/15.74 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 119.59/15.74 % SZS output start Refutation 119.59/15.74 thf(mu_type, type, mu: $tType). 119.59/15.74 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 119.59/15.74 thf(mreflexive_type, type, mreflexive: ($i > $i > $o) > $o). 119.59/15.74 thf('#sk20_type', type, '#sk20': $i > mu). 119.59/15.74 thf('#sk7_type', type, '#sk7': mu). 119.59/15.74 thf('#sk13_type', type, '#sk13': $i > $i). 119.59/15.74 thf('#sk6_type', type, '#sk6': $i). 119.59/15.74 thf('#sk17_type', type, '#sk17': mu). 119.59/15.74 thf('#sk3_type', type, '#sk3': $i). 119.59/15.74 thf('#sk5_type', type, '#sk5': $i). 119.59/15.74 thf('#form9_type', type, '#form9': $o). 119.59/15.74 thf('#form4_type', type, '#form4': $o). 119.59/15.74 thf('#sk1_type', type, '#sk1': $i > mu). 119.59/15.74 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 119.59/15.74 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 119.59/15.74 thf('#sk14_type', type, '#sk14': mu). 119.59/15.74 thf('#sk10_type', type, '#sk10': $i). 119.59/15.74 thf('#sk2_type', type, '#sk2': $i). 119.59/15.74 thf('#sk21_type', type, '#sk21': $i > mu > $i). 119.59/15.74 thf(mtransitive_type, type, mtransitive: ($i > $i > $o) > $o). 119.59/15.74 thf('#form15_type', type, '#form15': $o). 119.59/15.74 thf('#sk16_type', type, '#sk16': $i). 119.59/15.74 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o). 119.59/15.74 thf(rel_s4_type, type, rel_s4: $i > $i > $o). 119.59/15.74 thf('#sk8_type', type, '#sk8': $i). 119.59/15.74 thf(mexists_ind_type, type, mexists_ind: (mu > $i > $o) > $i > $o). 119.59/15.74 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 119.59/15.74 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 119.59/15.74 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o). 119.59/15.74 thf(exists_in_world_type, type, exists_in_world: mu > $i > $o). 119.59/15.74 thf('#sk11_type', type, '#sk11': $i). 119.59/15.74 thf('#sk12_type', type, '#sk12': $i). 119.59/15.74 thf(big_p_type, type, big_p: mu > $i > $o). 119.59/15.74 thf(x2128, conjecture, 119.59/15.74 (mvalid @ 119.59/15.74 ( mand @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ 119.59/15.74 ( ^[X:mu]: 119.59/15.74 ( mand @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ ( big_p @ X ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ 119.59/15.74 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ 119.59/15.74 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) @ 119.59/15.74 ( mand @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 119.59/15.74 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mand @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 119.59/15.74 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ 119.59/15.74 ( ^[X:mu]: 119.59/15.74 ( mand @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ ( big_p @ X ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ 119.59/15.74 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ 119.59/15.74 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) ) ) ))). 119.59/15.74 thf(zf_stmt_0, negated_conjecture, 119.59/15.74 (~( mvalid @ 119.59/15.74 ( mand @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ 119.59/15.74 ( ^[X:mu]: 119.59/15.74 ( mand @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ ( big_p @ X ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ 119.59/15.74 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ 119.59/15.74 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) @ 119.59/15.74 ( mand @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 119.59/15.74 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mand @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 119.59/15.74 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ 119.59/15.74 ( ^[X:mu]: 119.59/15.74 ( mand @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ ( big_p @ X ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ 119.59/15.74 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mimplies @ 119.59/15.74 ( mbox_s4 @ 119.59/15.74 ( mforall_ind @ 119.59/15.74 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 119.59/15.74 ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) ) ) ) )), 119.59/15.74 inference('cnf.neg', [status(esa)], [x2128])). 119.59/15.74 thf(zip_derived_cl4, plain, 119.59/15.74 (~ (mvalid @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y0 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.74 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y0 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.74 (mbox_s4 @ (big_p @ Y0))))))))))))), 119.59/15.74 inference('cnf', [status(esa)], [zf_stmt_0])). 119.59/15.74 thf(mvalid, axiom, ~ (mvalid @ X0) => 119.59/15.74 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0)))) != ($true))). 119.59/15.74 thf('0', plain, 119.59/15.74 (![X0:( $i > $o )]: 119.59/15.74 ( ( ~( mvalid @ X0 ) ) <=> ( ~( ![X5:$i]: ( X0 @ X5 ) ) ) )), 119.59/15.74 inference('rw.lit', [status(esa)], [mvalid])). 119.59/15.74 thf(zip_derived_cl20, plain, 119.59/15.74 (~ (((!!) @ (^[Y0 : $i]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y1 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.74 (mbox_s4 @ (big_p @ Y1)))))))) @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mexists_ind @ 119.59/15.74 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.74 (mexists_ind @ 119.59/15.74 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mexists_ind @ 119.59/15.74 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.74 (mexists_ind @ 119.59/15.74 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y1 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.74 (mbox_s4 @ (big_p @ Y1)))))))))) @ 119.59/15.74 Y0))))), 119.59/15.74 inference('rw_clause', [status(thm)], [zip_derived_cl4, '0'])). 119.59/15.74 thf(zip_derived_cl21, plain, 119.59/15.74 (~ (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y0 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.74 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y0 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.74 (mbox_s4 @ (big_p @ Y0)))))))))) @ 119.59/15.74 '#sk2')), 119.59/15.74 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl20])). 119.59/15.74 thf(mand, axiom,(( mand @ (X0)@ (X1)@ (X2)) = 119.59/15.74 ((mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)) @ X2)))). 119.59/15.74 thf('1', plain, 119.59/15.74 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]: 119.59/15.74 ( ( mand @ X0 @ X1 @ X2 ) = 119.59/15.74 ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) @ X2 ) )), 119.59/15.74 define([status(thm)])). 119.59/15.74 thf(zip_derived_cl22, plain, 119.59/15.74 (~ (mnot @ 119.59/15.74 (mor @ 119.59/15.74 (mnot @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y0 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.74 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))))) @ 119.59/15.74 (mnot @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y0 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.74 (mbox_s4 @ (big_p @ Y0)))))))))))) @ 119.59/15.74 '#sk2')), 119.59/15.74 inference('rw', [status(thm)], [zip_derived_cl21, '1'])). 119.59/15.74 thf(mnot, axiom, ~ (mnot @ X0 @ X1) => ((X0 @ X1) = ($true))). 119.59/15.74 thf('2', plain, 119.59/15.74 (![X0:( $i > $o ),X1:$i]: ( ( ~( mnot @ X0 @ X1 ) ) <=> ( X0 @ X1 ) )), 119.59/15.74 inference('rw.lit', [status(esa)], [mnot])). 119.59/15.74 thf(zip_derived_cl23, plain, 119.59/15.74 ( (mor @ 119.59/15.74 (mnot @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y0 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.74 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))))) @ 119.59/15.74 (mnot @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y0 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.74 (mbox_s4 @ (big_p @ Y0))))))))))) @ 119.59/15.74 '#sk2')), 119.59/15.74 inference('rw_clause', [status(thm)], [zip_derived_cl22, '2'])). 119.59/15.74 thf(mor, axiom, (mor @ X0 @ X1 @ X2) => 119.59/15.74 ((((X1 @ X2) | (X0 @ X2))) = ($true))). 119.59/15.74 thf('3', plain, 119.59/15.74 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]: 119.59/15.74 ( ( mor @ X0 @ X1 @ X2 ) <=> ( ( X0 @ X2 ) | ( X1 @ X2 ) ) )), 119.59/15.74 inference('rw.lit', [status(esa)], [mor])). 119.59/15.74 thf(zip_derived_cl24, plain, 119.59/15.74 ( (((mnot @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y0 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.74 (mbox_s4 @ (big_p @ Y0)))))))))) @ 119.59/15.74 '#sk2') | (mnot @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y0 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.74 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))))) @ 119.59/15.74 '#sk2')))), 119.59/15.74 inference('rw_clause', [status(thm)], [zip_derived_cl23, '3'])). 119.59/15.74 thf(zip_derived_cl25, plain, 119.59/15.74 (( (mnot @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.74 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y0 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.74 (mbox_s4 @ (big_p @ Y0)))))))))) @ 119.59/15.74 '#sk2') 119.59/15.74 | (mnot @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ 119.59/15.74 (^[Y0 : mu]: 119.59/15.74 (mand @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.74 (mbox_s4 @ 119.59/15.74 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))))) @ 119.59/15.75 '#sk2'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl24])). 119.59/15.75 thf(mnot, axiom, (mnot @ X0 @ X1) => ((X0 @ X1) != ($true))). 119.59/15.75 thf('4', plain, 119.59/15.75 (![X0:( $i > $o ),X1:$i]: ( ( mnot @ X0 @ X1 ) <=> ( ~( X0 @ X1 ) ) )), 119.59/15.75 inference('rw.lit', [status(esa)], [mnot])). 119.59/15.75 thf(zip_derived_cl26, plain, 119.59/15.75 ((~ (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0))))))))) @ 119.59/15.75 '#sk2') 119.59/15.75 | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))))) @ 119.59/15.75 '#sk2'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl25, '4'])). 119.59/15.75 thf(mbox_s4, axiom, ~ (mbox_s4 @ X0 @ X1) => 119.59/15.75 ((((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X1 @ Y0))) | (X0 @ Y0)))))) != 119.59/15.75 ($true))). 119.59/15.75 thf('5', plain, 119.59/15.75 (![X0:( $i > $o ),X1:$i]: 119.59/15.75 ( ( ~( mbox_s4 @ X0 @ X1 ) ) <=> 119.59/15.75 ( ~( ![X6:$i]: ( ( ~( rel_s4 @ X1 @ X6 ) ) | ( X0 @ X6 ) ) ) ) )), 119.59/15.75 inference('rw.lit', [status(esa)], [mbox_s4])). 119.59/15.75 thf(zip_derived_cl27, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | (mimplies @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))))) @ 119.59/15.75 Y0)))))) 119.59/15.75 | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))))) @ 119.59/15.75 '#sk2'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl26, '5'])). 119.59/15.75 thf(zip_derived_cl28, plain, 119.59/15.75 ((~ (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 '#sk2') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | (mimplies @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl27, '4'])). 119.59/15.75 thf(zip_derived_cl29, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))))) @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 Y0)))))) 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | (mimplies @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl28, '5'])). 119.59/15.75 thf(zip_derived_cl30, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk2' @ '#sk3'))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk3'))) 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | (mimplies @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl29])). 119.59/15.75 thf(mimplies, axiom,(( mimplies @ (X0)@ (X1)@ (X2)) = 119.59/15.75 ((mor @ (mnot @ X0) @ X1 @ X2)))). 119.59/15.75 thf('6', plain, 119.59/15.75 (![X2:$i,X1:( $i > $o ),X0:( $i > $o )]: 119.59/15.75 ( ( mimplies @ X0 @ X1 @ X2 ) = ( mor @ ( mnot @ X0 ) @ X1 @ X2 ) )), 119.59/15.75 define([status(thm)])). 119.59/15.75 thf(zip_derived_cl31, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk2' @ '#sk3'))) | (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0))))))))) @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk3'))) 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | (mimplies @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl30, '6'])). 119.59/15.75 thf(zip_derived_cl33, plain, 119.59/15.75 ((~ (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0))))))))) @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk3') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | (mimplies @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 119.59/15.75 thf(zip_derived_cl32, plain, 119.59/15.75 (( (rel_s4 @ '#sk2' @ '#sk3') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | (mimplies @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 119.59/15.75 thf(zip_derived_cl34, plain, 119.59/15.75 (( ('#form4') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | (mimplies @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 define([status(thm)])). 119.59/15.75 thf(zip_derived_cl37, plain, 119.59/15.75 ((~ ('#form4') 119.59/15.75 | ~ (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0))))))))) @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk3'))), 119.59/15.75 inference('renaming', [status(thm)], [zip_derived_cl33, zip_derived_cl34])). 119.59/15.75 thf(mor, axiom, ~ (mor @ X0 @ X1 @ X2) => 119.59/15.75 ((((X1 @ X2) | (X0 @ X2))) != ($true))). 119.59/15.75 thf('7', plain, 119.59/15.75 (![X0:( $i > $o ),X1:( $i > $o ),X2:$i]: 119.59/15.75 ( ( ~( mor @ X0 @ X1 @ X2 ) ) <=> ( ~( ( X1 @ X2 ) | ( X0 @ X2 ) ) ) )), 119.59/15.75 inference('rw.lit', [status(esa)], [mor])). 119.59/15.75 thf(zip_derived_cl41, plain, 119.59/15.75 ((~ (((mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 '#sk3') | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 '#sk3'))) 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl37, '7'])). 119.59/15.75 thf(zip_derived_cl43, plain, 119.59/15.75 ((~ (((mnot @ 119.59/15.75 (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 '#sk3') | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 '#sk3'))) 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl41, '1'])). 119.59/15.75 thf(zip_derived_cl45, plain, 119.59/15.75 ((~ (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 '#sk3') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 119.59/15.75 thf(zip_derived_cl49, plain, 119.59/15.75 (( (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk3') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl45, '2'])). 119.59/15.75 thf(mbox_s4, axiom, (mbox_s4 @ X0 @ X1) => 119.59/15.75 ((((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X1 @ Y0))) | (X0 @ Y0)))))) = 119.59/15.75 ($true))). 119.59/15.75 thf('8', plain, 119.59/15.75 (![X0:( $i > $o ),X1:$i]: 119.59/15.75 ( ( mbox_s4 @ X0 @ X1 ) <=> 119.59/15.75 ( ![X6:$i]: ( ( ~( rel_s4 @ X1 @ X6 ) ) | ( X0 @ X6 ) ) ) )), 119.59/15.75 inference('rw.lit', [status(esa)], [mbox_s4])). 119.59/15.75 thf(zip_derived_cl53, plain, 119.59/15.75 (( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))) @ 119.59/15.75 Y0)))))) 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl49, '8'])). 119.59/15.75 thf(zip_derived_cl58, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ '#sk3' @ X2))) | (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 X2))) 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl53])). 119.59/15.75 thf(zip_derived_cl63, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 (~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 X2) 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl58])). 119.59/15.75 thf(mforall_ind, axiom, (mforall_ind @ X0 @ X1) => 119.59/15.75 ((((!!) @ (^[Y0 : mu]: (((exists_in_world @ Y0 @ X1) => (X0 @ Y0 @ X1)))))) 119.59/15.75 = ($true))). 119.59/15.75 thf('9', plain, 119.59/15.75 (![X0:( mu > $i > $o ),X1:$i]: 119.59/15.75 ( ( mforall_ind @ X0 @ X1 ) <=> 119.59/15.75 ( ![X6:mu]: ( ( exists_in_world @ X6 @ X1 ) => ( X0 @ X6 @ X1 ) ) ) )), 119.59/15.75 inference('rw.lit', [status(esa)], [mforall_ind])). 119.59/15.75 thf(zip_derived_cl68, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X0) => 119.59/15.75 ((^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))) @ 119.59/15.75 Y0 @ X0)))))) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl63, '9'])). 119.59/15.75 thf(zip_derived_cl74, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X0) => (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 X0)))))) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl68])). 119.59/15.75 thf(zip_derived_cl75, plain, 119.59/15.75 (![X0 : $i, X2 : mu]: 119.59/15.75 ( (((exists_in_world @ X2 @ X0) => (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ X2)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ X2)))) @ 119.59/15.75 X0))) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl74])). 119.59/15.75 thf(zip_derived_cl82, plain, 119.59/15.75 (![X0 : $i, X2 : mu]: 119.59/15.75 ( (((exists_in_world @ X2 @ X0) => (mnot @ 119.59/15.75 (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ X2)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ X2)))))) @ 119.59/15.75 X0))) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl75, '1'])). 119.59/15.75 thf(zip_derived_cl83, plain, 119.59/15.75 (![X0 : $i, X2 : mu]: 119.59/15.75 (~ (exists_in_world @ X2 @ X0) 119.59/15.75 | (mnot @ 119.59/15.75 (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ X2)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ X2)))))) @ 119.59/15.75 X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 119.59/15.75 thf(zip_derived_cl88, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 (~ (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ X1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ X1))))) @ 119.59/15.75 X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl83, '4'])). 119.59/15.75 thf(zip_derived_cl97, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 (~ (((mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ X1)))) @ 119.59/15.75 X0) | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ X1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 X0))) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl88, '7'])). 119.59/15.75 thf(zip_derived_cl106, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 (~ (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ X1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl97])). 119.59/15.75 thf(zip_derived_cl116, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 ( (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ X1)) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 X0) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl106, '2'])). 119.59/15.75 thf(zip_derived_cl124, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 ( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ (big_p @ X1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 Y0)))))) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl116, '8'])). 119.59/15.75 thf(zip_derived_cl134, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X3))) | (mimplies @ 119.59/15.75 (mbox_s4 @ (big_p @ X1)) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 X3))) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl124])). 119.59/15.75 thf(zip_derived_cl147, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X3))) | (mor @ 119.59/15.75 (mnot @ (mbox_s4 @ (big_p @ X1))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 X3))) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl134, '6'])). 119.59/15.75 thf(zip_derived_cl148, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ X3) 119.59/15.75 | (mor @ (mnot @ (mbox_s4 @ (big_p @ X1))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 X3) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl147])). 119.59/15.75 thf(zip_derived_cl158, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i]: 119.59/15.75 ( (((mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ X2) | 119.59/15.75 (mnot @ (mbox_s4 @ (big_p @ X1)) @ X2))) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl148, '3'])). 119.59/15.75 thf(zip_derived_cl172, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i]: 119.59/15.75 ( (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 X2) 119.59/15.75 | (mnot @ (mbox_s4 @ (big_p @ X1)) @ X2) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl158])). 119.59/15.75 thf(zip_derived_cl187, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X2 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2) 119.59/15.75 | (mnot @ (mbox_s4 @ (big_p @ X1)) @ X2))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl172, '8'])). 119.59/15.75 thf(zip_derived_cl203, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu]: 119.59/15.75 (~ (mbox_s4 @ (big_p @ X2) @ X0) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl187, '4'])). 119.59/15.75 thf(zip_derived_cl217, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu]: 119.59/15.75 (~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X2 @ Y0)))))) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl203, '5'])). 119.59/15.75 thf(zip_derived_cl231, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu]: 119.59/15.75 (~ (((((~) @ (rel_s4 @ X0 @ ('#sk21' @ X0 @ X2)))) | (big_p @ X2 @ 119.59/15.75 ('#sk21' @ X0 @ X2)))) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl217])). 119.59/15.75 thf(zip_derived_cl250, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu]: 119.59/15.75 (~ (big_p @ X2 @ ('#sk21' @ X0 @ X2)) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl231])). 119.59/15.75 thf(zip_derived_cl264, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X4))) | (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ X4))) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ (big_p @ X2 @ ('#sk21' @ X0 @ X2)))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl250])). 119.59/15.75 thf(zip_derived_cl279, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ X4) 119.59/15.75 | (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ X4) 119.59/15.75 | ~ (big_p @ X2 @ ('#sk21' @ X0 @ X2)) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl264])). 119.59/15.75 thf(zip_derived_cl290, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X3) => 119.59/15.75 ((^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0 @ X3)))))) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ (big_p @ X2 @ ('#sk21' @ X0 @ X2)) 119.59/15.75 | ~ (rel_s4 @ X0 @ X3))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl279, '9'])). 119.59/15.75 thf(zip_derived_cl302, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X3) => (mbox_s4 @ 119.59/15.75 (big_p @ Y0) @ X3)))))) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ (big_p @ X2 @ ('#sk21' @ X0 @ X2)) 119.59/15.75 | ~ (rel_s4 @ X0 @ X3))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl290])). 119.59/15.75 thf(zip_derived_cl303, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i, X5 : mu]: 119.59/15.75 ( (((exists_in_world @ X5 @ X3) => (mbox_s4 @ (big_p @ X5) @ X3))) 119.59/15.75 | ~ (rel_s4 @ X0 @ X3) 119.59/15.75 | ~ (big_p @ X2 @ ('#sk21' @ X0 @ X2)) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl302])). 119.59/15.75 thf(zip_derived_cl312, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i, X5 : mu]: 119.59/15.75 (~ (exists_in_world @ X5 @ X3) 119.59/15.75 | (mbox_s4 @ (big_p @ X5) @ X3) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ (big_p @ X2 @ ('#sk21' @ X0 @ X2)) 119.59/15.75 | ~ (rel_s4 @ X0 @ X3))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl303])). 119.59/15.75 thf(zip_derived_cl320, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i, X4 : mu]: 119.59/15.75 ( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X4 @ Y0)))))) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (big_p @ X2 @ ('#sk21' @ X1 @ X2)) 119.59/15.75 | ~ (exists_in_world @ X2 @ X3) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X3) 119.59/15.75 | ~ (rel_s4 @ X3 @ X1) 119.59/15.75 | ~ (exists_in_world @ X4 @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl312, '8'])). 119.59/15.75 thf(zip_derived_cl329, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i, X4 : mu, X6 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X6))) | (big_p @ X4 @ X6))) 119.59/15.75 | ~ (exists_in_world @ X4 @ X0) 119.59/15.75 | ~ (rel_s4 @ X3 @ X1) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X3) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X3) 119.59/15.75 | ~ (big_p @ X2 @ ('#sk21' @ X1 @ X2)) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl320])). 119.59/15.75 thf(zip_derived_cl336, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i, X4 : mu, X6 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ X6) 119.59/15.75 | (big_p @ X4 @ X6) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (big_p @ X2 @ ('#sk21' @ X1 @ X2)) 119.59/15.75 | ~ (exists_in_world @ X2 @ X3) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X3) 119.59/15.75 | ~ (rel_s4 @ X3 @ X1) 119.59/15.75 | ~ (exists_in_world @ X4 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl329])). 119.59/15.75 thf(zip_derived_cl44, plain, 119.59/15.75 ((~ (mnot @ 119.59/15.75 (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 '#sk3') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 119.59/15.75 thf(zip_derived_cl48, plain, 119.59/15.75 (( (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk3') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl44, '2'])). 119.59/15.75 thf(zip_derived_cl52, plain, 119.59/15.75 (( (((mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 '#sk3') | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk3'))) 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl48, '3'])). 119.59/15.75 thf(zip_derived_cl57, plain, 119.59/15.75 (( (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 '#sk3') 119.59/15.75 | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk3') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 119.59/15.75 thf(zip_derived_cl62, plain, 119.59/15.75 ((~ (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk3') 119.59/15.75 | ~ ('#form4') 119.59/15.75 | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk3'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl57, '4'])). 119.59/15.75 thf(zip_derived_cl67, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 Y0)))))) 119.59/15.75 | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk3') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl62, '5'])). 119.59/15.75 thf(zip_derived_cl73, plain, 119.59/15.75 ((~ (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 '#sk3') 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl67, '4'])). 119.59/15.75 thf(zip_derived_cl81, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 Y0)))))) 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 Y0)))))) 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl73, '5'])). 119.59/15.75 thf(zip_derived_cl87, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk3' @ '#sk8'))) | (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk8'))) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl81])). 119.59/15.75 thf(zip_derived_cl94, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk3' @ '#sk8'))) | (mor @ 119.59/15.75 (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk8'))) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl87, '6'])). 119.59/15.75 thf(zip_derived_cl96, plain, 119.59/15.75 ((~ (mor @ 119.59/15.75 (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk8') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 Y0)))))) 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl94])). 119.59/15.75 thf(zip_derived_cl95, plain, 119.59/15.75 (( (rel_s4 @ '#sk3' @ '#sk8') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 Y0)))))) 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl94])). 119.59/15.75 thf(zip_derived_cl101, plain, 119.59/15.75 (( ('#form9') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 define([status(thm)])). 119.59/15.75 thf(zip_derived_cl104, plain, 119.59/15.75 ((~ ('#form9') 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (mor @ 119.59/15.75 (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk8'))), 119.59/15.75 inference('renaming', [status(thm)], 119.59/15.75 [zip_derived_cl96, zip_derived_cl101])). 119.59/15.75 thf(zip_derived_cl114, plain, 119.59/15.75 ((~ (((mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ '#sk8') | 119.59/15.75 (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 '#sk8'))) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl104, '7'])). 119.59/15.75 thf(zip_derived_cl122, plain, 119.59/15.75 ((~ (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 '#sk8') 119.59/15.75 | ~ ('#form9') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl114])). 119.59/15.75 thf(zip_derived_cl132, plain, 119.59/15.75 (( (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ '#sk8') 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl122, '2'])). 119.59/15.75 thf(mexists_ind, axiom,(( mexists_ind @ (X0)@ (X1)) = 119.59/15.75 ((mnot @ (mforall_ind @ (^[Y0 : mu]: (mnot @ (X0 @ Y0)))) @ X1)))). 119.59/15.75 thf('10', plain, 119.59/15.75 (![X1:$i,X0:( mu > $i > $o )]: 119.59/15.75 ( ( mexists_ind @ X0 @ X1 ) = 119.59/15.75 ( mnot @ ( mforall_ind @ ( ^[V_1:mu]: ( mnot @ ( X0 @ V_1 ) ) ) ) @ X1 ) )), 119.59/15.75 define([status(thm)])). 119.59/15.75 thf(zip_derived_cl143, plain, 119.59/15.75 (( (mnot @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mnot @ (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk8') 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl132, '10'])). 119.59/15.75 thf(zip_derived_cl144, plain, 119.59/15.75 ((~ (mforall_ind @ (^[Y0 : mu]: (mnot @ (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 '#sk8') 119.59/15.75 | ~ ('#form9') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl143, '4'])). 119.59/15.75 thf(mforall_ind, axiom, ~ (mforall_ind @ X0 @ X1) => 119.59/15.75 ((((!!) @ (^[Y0 : mu]: (((exists_in_world @ Y0 @ X1) => (X0 @ Y0 @ X1)))))) 119.59/15.75 != ($true))). 119.59/15.75 thf('11', plain, 119.59/15.75 (![X0:( mu > $i > $o ),X1:$i]: 119.59/15.75 ( ( ~( mforall_ind @ X0 @ X1 ) ) <=> 119.59/15.75 ( ~( ![X6:mu]: ( ( exists_in_world @ X6 @ X1 ) => ( X0 @ X6 @ X1 ) ) ) ) )), 119.59/15.75 inference('rw.lit', [status(esa)], [mforall_ind])). 119.59/15.75 thf(zip_derived_cl156, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ '#sk8') => 119.59/15.75 ((^[Y1 : mu]: (mnot @ (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 Y0 @ '#sk8')))))) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl144, '11'])). 119.59/15.75 thf(zip_derived_cl169, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ '#sk8') => (mnot @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)) @ '#sk8')))))) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl156])). 119.59/15.75 thf(zip_derived_cl170, plain, 119.59/15.75 ((~ (((exists_in_world @ '#sk14' @ '#sk8') => (mnot @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk14')) @ '#sk8'))) 119.59/15.75 | ~ ('#form9') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl169])). 119.59/15.75 thf(zip_derived_cl185, plain, 119.59/15.75 ((~ (mnot @ (mbox_s4 @ (big_p @ '#sk14')) @ '#sk8') 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl170])). 119.59/15.75 thf(zip_derived_cl201, plain, 119.59/15.75 (( (mbox_s4 @ (big_p @ '#sk14') @ '#sk8') | ~ ('#form9') | ~ ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl185, '2'])). 119.59/15.75 thf(zip_derived_cl215, plain, 119.59/15.75 (( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk8' @ Y0))) | (big_p @ '#sk14' @ 119.59/15.75 Y0)))))) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl201, '8'])). 119.59/15.75 thf(zip_derived_cl229, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ '#sk8' @ X2))) | (big_p @ '#sk14' @ X2))) 119.59/15.75 | ~ ('#form9') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl215])). 119.59/15.75 thf(zip_derived_cl246, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 (~ (rel_s4 @ '#sk8' @ X2) 119.59/15.75 | (big_p @ '#sk14' @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl229])). 119.59/15.75 thf(zip_derived_cl105, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 (~ (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ X1)))) @ 119.59/15.75 X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl97])). 119.59/15.75 thf(zip_derived_cl115, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 ( (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ X1))) @ 119.59/15.75 X0) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl105, '2'])). 119.59/15.75 thf(zip_derived_cl123, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 ( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ X1)) @ Y0)))))) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl115, '8'])). 119.59/15.75 thf(zip_derived_cl133, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X3))) | (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ X1)) @ X3))) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl123])). 119.59/15.75 thf(zip_derived_cl145, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X3))) | (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ X1)) @ X3))) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl133, '6'])). 119.59/15.75 thf(zip_derived_cl146, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ X3) 119.59/15.75 | (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ X1)) @ X3) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl145])). 119.59/15.75 thf(zip_derived_cl157, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i]: 119.59/15.75 ( (((mbox_s4 @ (big_p @ X1) @ X2) | (mnot @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 X2))) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl146, '3'])). 119.59/15.75 thf(zip_derived_cl171, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i]: 119.59/15.75 ( (mbox_s4 @ (big_p @ X1) @ X2) 119.59/15.75 | (mnot @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 X2) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl157])). 119.59/15.75 thf(zip_derived_cl186, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X2 @ Y0))) | (big_p @ X1 @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X0) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2) 119.59/15.75 | (mnot @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 X2))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl171, '8'])). 119.59/15.75 thf(zip_derived_cl202, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu]: 119.59/15.75 (~ (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ X0) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X2 @ Y0)))))))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl186, '4'])). 119.59/15.75 thf(zip_derived_cl216, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i]: 119.59/15.75 (~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X1 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X1 @ Y0))) | (big_p @ X0 @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl202, '5'])). 119.59/15.75 thf(zip_derived_cl230, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i]: 119.59/15.75 (~ (((((~) @ (rel_s4 @ X1 @ ('#sk13' @ X1)))) | (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ ('#sk13' @ X1)))) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X1 @ Y0))) | (big_p @ X0 @ Y0)))))))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl216])). 119.59/15.75 thf(zip_derived_cl248, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i]: 119.59/15.75 (~ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ 119.59/15.75 ('#sk13' @ X1)) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X1 @ Y0))) | (big_p @ X0 @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl230])). 119.59/15.75 thf(zip_derived_cl262, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu]: 119.59/15.75 (~ (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ ('#sk13' @ X0)) => 119.59/15.75 ((^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0 @ 119.59/15.75 ('#sk13' @ X0))))))) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X2 @ Y0)))))))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl248, '11'])). 119.59/15.75 thf(zip_derived_cl276, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu]: 119.59/15.75 (~ (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ ('#sk13' @ X0)) => 119.59/15.75 (mbox_s4 @ (big_p @ Y0) @ ('#sk13' @ X0))))))) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X2 @ Y0)))))))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl262])). 119.59/15.75 thf(zip_derived_cl277, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu]: 119.59/15.75 (~ (((exists_in_world @ ('#sk20' @ X0) @ ('#sk13' @ X0)) => 119.59/15.75 (mbox_s4 @ (big_p @ ('#sk20' @ X0)) @ ('#sk13' @ X0)))) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X2 @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl276])). 119.59/15.75 thf(zip_derived_cl288, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu]: 119.59/15.75 (~ (mbox_s4 @ (big_p @ ('#sk20' @ X0)) @ ('#sk13' @ X0)) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X2 @ Y0)))))))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl277])). 119.59/15.75 thf(zip_derived_cl299, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i]: 119.59/15.75 (~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ ('#sk13' @ X1) @ Y0))) | (big_p @ 119.59/15.75 ('#sk20' @ X1) @ Y0)))))) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X1 @ Y0))) | (big_p @ X0 @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl288, '5'])). 119.59/15.75 thf(zip_derived_cl310, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i]: 119.59/15.75 (~ (((((~) @ (rel_s4 @ ('#sk13' @ X1) @ 119.59/15.75 ('#sk21' @ ('#sk13' @ X1) @ ('#sk20' @ X1))))) | 119.59/15.75 (big_p @ ('#sk20' @ X1) @ 119.59/15.75 ('#sk21' @ ('#sk13' @ X1) @ ('#sk20' @ X1))))) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X1 @ Y0))) | (big_p @ X0 @ Y0)))))))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl299])). 119.59/15.75 thf(zip_derived_cl318, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i]: 119.59/15.75 (~ (big_p @ ('#sk20' @ X1) @ 119.59/15.75 ('#sk21' @ ('#sk13' @ X1) @ ('#sk20' @ X1))) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X1 @ Y0))) | (big_p @ X0 @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl310])). 119.59/15.75 thf(zip_derived_cl327, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i, X4 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X1 @ X4))) | (big_p @ X0 @ X4))) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | ~ (big_p @ ('#sk20' @ X1) @ 119.59/15.75 ('#sk21' @ ('#sk13' @ X1) @ ('#sk20' @ X1))))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl318])). 119.59/15.75 thf(zip_derived_cl334, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i, X4 : $i]: 119.59/15.75 (~ (rel_s4 @ X1 @ X4) 119.59/15.75 | (big_p @ X0 @ X4) 119.59/15.75 | ~ (big_p @ ('#sk20' @ X1) @ 119.59/15.75 ('#sk21' @ ('#sk13' @ X1) @ ('#sk20' @ X1))) 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl327])). 119.59/15.75 thf(zip_derived_cl121, plain, 119.59/15.75 ((~ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 '#sk8') 119.59/15.75 | ~ ('#form9') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl114])). 119.59/15.75 thf(zip_derived_cl131, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk8' @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl121, '5'])). 119.59/15.75 thf(zip_derived_cl142, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk8' @ '#sk11'))) | (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ '#sk11'))) 119.59/15.75 | ~ ('#form9') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl131])). 119.59/15.75 thf(zip_derived_cl155, plain, 119.59/15.75 ((~ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ '#sk11') 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl142])). 119.59/15.75 thf(zip_derived_cl168, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ '#sk11') => 119.59/15.75 ((^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0 @ '#sk11')))))) 119.59/15.75 | ~ ('#form9') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl155, '11'])). 119.59/15.75 thf(zip_derived_cl182, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ '#sk11') => (mbox_s4 @ 119.59/15.75 (big_p @ Y0) @ '#sk11')))))) 119.59/15.75 | ~ ('#form9') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl168])). 119.59/15.75 thf(zip_derived_cl183, plain, 119.59/15.75 ((~ (((exists_in_world @ '#sk17' @ '#sk11') => (mbox_s4 @ 119.59/15.75 (big_p @ '#sk17') @ '#sk11'))) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl182])). 119.59/15.75 thf(zip_derived_cl200, plain, 119.59/15.75 ((~ (mbox_s4 @ (big_p @ '#sk17') @ '#sk11') | ~ ('#form9') | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl183])). 119.59/15.75 thf(zip_derived_cl214, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk11' @ Y0))) | (big_p @ '#sk17' @ 119.59/15.75 Y0)))))) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl200, '5'])). 119.59/15.75 thf(zip_derived_cl228, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk11' @ ('#sk21' @ '#sk11' @ '#sk17')))) | 119.59/15.75 (big_p @ '#sk17' @ ('#sk21' @ '#sk11' @ '#sk17')))) 119.59/15.75 | ~ ('#form9') 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl214])). 119.59/15.75 thf(zip_derived_cl245, plain, 119.59/15.75 ((~ (big_p @ '#sk17' @ ('#sk21' @ '#sk11' @ '#sk17')) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl228])). 119.59/15.75 thf(zip_derived_cl244, plain, 119.59/15.75 (( (rel_s4 @ '#sk11' @ ('#sk21' @ '#sk11' @ '#sk17')) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ ('#form9'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl228])). 119.59/15.75 thf(zip_derived_cl287, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu]: 119.59/15.75 ( (exists_in_world @ ('#sk20' @ X0) @ ('#sk13' @ X0)) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X2 @ Y0)))))))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl277])). 119.59/15.75 thf(zip_derived_cl298, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X4))) | (big_p @ X2 @ X4))) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | (exists_in_world @ ('#sk20' @ X0) @ ('#sk13' @ X0)))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl287])). 119.59/15.75 thf(zip_derived_cl309, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ X4) 119.59/15.75 | (big_p @ X2 @ X4) 119.59/15.75 | (exists_in_world @ ('#sk20' @ X0) @ ('#sk13' @ X0)) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl298])). 119.59/15.75 thf(zip_derived_cl199, plain, 119.59/15.75 (( (exists_in_world @ '#sk17' @ '#sk11') | ~ ('#form9') | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl183])). 119.59/15.75 thf(zip_derived_cl184, plain, 119.59/15.75 (( (exists_in_world @ '#sk14' @ '#sk8') | ~ ('#form4') | ~ ('#form9'))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl170])). 119.59/15.75 thf(zip_derived_cl317, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i]: 119.59/15.75 ( (rel_s4 @ ('#sk13' @ X1) @ 119.59/15.75 ('#sk21' @ ('#sk13' @ X1) @ ('#sk20' @ X1))) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X1 @ Y0))) | (big_p @ X0 @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl310])). 119.59/15.75 thf(zip_derived_cl326, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i, X4 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X1 @ X4))) | (big_p @ X0 @ X4))) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | (rel_s4 @ ('#sk13' @ X1) @ 119.59/15.75 ('#sk21' @ ('#sk13' @ X1) @ ('#sk20' @ X1))))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl317])). 119.59/15.75 thf(zip_derived_cl333, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i, X4 : $i]: 119.59/15.75 (~ (rel_s4 @ X1 @ X4) 119.59/15.75 | (big_p @ X0 @ X4) 119.59/15.75 | (rel_s4 @ ('#sk13' @ X1) @ 119.59/15.75 ('#sk21' @ ('#sk13' @ X1) @ ('#sk20' @ X1))) 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl326])). 119.59/15.75 thf(zip_derived_cl249, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu]: 119.59/15.75 ( (rel_s4 @ X0 @ ('#sk21' @ X0 @ X2)) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl231])). 119.59/15.75 thf(zip_derived_cl263, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X4))) | (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ X4))) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | (rel_s4 @ X0 @ ('#sk21' @ X0 @ X2)))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl249])). 119.59/15.75 thf(zip_derived_cl278, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X4 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ X4) 119.59/15.75 | (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ X4) 119.59/15.75 | (rel_s4 @ X0 @ ('#sk21' @ X0 @ X2)) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl263])). 119.59/15.75 thf(zip_derived_cl289, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X3) => 119.59/15.75 ((^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0 @ X3)))))) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | (rel_s4 @ X0 @ ('#sk21' @ X0 @ X2)) 119.59/15.75 | ~ (rel_s4 @ X0 @ X3))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl278, '9'])). 119.59/15.75 thf(zip_derived_cl300, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X3) => (mbox_s4 @ 119.59/15.75 (big_p @ Y0) @ X3)))))) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | (rel_s4 @ X0 @ ('#sk21' @ X0 @ X2)) 119.59/15.75 | ~ (rel_s4 @ X0 @ X3))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl289])). 119.59/15.75 thf(zip_derived_cl301, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i, X5 : mu]: 119.59/15.75 ( (((exists_in_world @ X5 @ X3) => (mbox_s4 @ (big_p @ X5) @ X3))) 119.59/15.75 | ~ (rel_s4 @ X0 @ X3) 119.59/15.75 | (rel_s4 @ X0 @ ('#sk21' @ X0 @ X2)) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl300])). 119.59/15.75 thf(zip_derived_cl311, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i, X5 : mu]: 119.59/15.75 (~ (exists_in_world @ X5 @ X3) 119.59/15.75 | (mbox_s4 @ (big_p @ X5) @ X3) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X1) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | (rel_s4 @ X0 @ ('#sk21' @ X0 @ X2)) 119.59/15.75 | ~ (rel_s4 @ X0 @ X3))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl301])). 119.59/15.75 thf(zip_derived_cl319, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i, X4 : mu]: 119.59/15.75 ( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X4 @ Y0)))))) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | (rel_s4 @ X1 @ ('#sk21' @ X1 @ X2)) 119.59/15.75 | ~ (exists_in_world @ X2 @ X3) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X3) 119.59/15.75 | ~ (rel_s4 @ X3 @ X1) 119.59/15.75 | ~ (exists_in_world @ X4 @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl311, '8'])). 119.59/15.75 thf(zip_derived_cl328, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i, X4 : mu, X6 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X6))) | (big_p @ X4 @ X6))) 119.59/15.75 | ~ (exists_in_world @ X4 @ X0) 119.59/15.75 | ~ (rel_s4 @ X3 @ X1) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X3) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X2 @ X3) 119.59/15.75 | (rel_s4 @ X1 @ ('#sk21' @ X1 @ X2)) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl319])). 119.59/15.75 thf(zip_derived_cl335, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : $i, X4 : mu, X6 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ X6) 119.59/15.75 | (big_p @ X4 @ X6) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | (rel_s4 @ X1 @ ('#sk21' @ X1 @ X2)) 119.59/15.75 | ~ (exists_in_world @ X2 @ X3) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X3) 119.59/15.75 | ~ (rel_s4 @ X3 @ X1) 119.59/15.75 | ~ (exists_in_world @ X4 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl328])). 119.59/15.75 thf(zip_derived_cl247, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i]: 119.59/15.75 ( (rel_s4 @ X1 @ ('#sk13' @ X1)) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X1 @ Y0))) | (big_p @ X0 @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl230])). 119.59/15.75 thf(zip_derived_cl261, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i, X4 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X1 @ X4))) | (big_p @ X0 @ X4))) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1) 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | (rel_s4 @ X1 @ ('#sk13' @ X1)))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl247])). 119.59/15.75 thf(zip_derived_cl275, plain, 119.59/15.75 (![X0 : mu, X1 : $i, X2 : $i, X4 : $i]: 119.59/15.75 (~ (rel_s4 @ X1 @ X4) 119.59/15.75 | (big_p @ X0 @ X4) 119.59/15.75 | (rel_s4 @ X1 @ ('#sk13' @ X1)) 119.59/15.75 | ~ (exists_in_world @ X0 @ X2) 119.59/15.75 | ~ ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk3' @ X2) 119.59/15.75 | ~ (rel_s4 @ X2 @ X1))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl261])). 119.59/15.75 thf(zip_derived_cl154, plain, 119.59/15.75 (( (rel_s4 @ '#sk8' @ '#sk11') | ~ ('#form4') | ~ ('#form9'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl142])). 119.59/15.75 thf(zip_derived_cl101, plain, 119.59/15.75 (( ('#form9') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 define([status(thm)])). 119.59/15.75 thf(zip_derived_cl102, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk3' @ '#sk10'))) | (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ '#sk10'))) 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl101])). 119.59/15.75 thf(zip_derived_cl111, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk3' @ '#sk10'))) | (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ '#sk10'))) 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl102, '6'])). 119.59/15.75 thf(zip_derived_cl113, plain, 119.59/15.75 ((~ (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ '#sk10') 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl111])). 119.59/15.75 thf(zip_derived_cl120, plain, 119.59/15.75 ((~ (((mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ '#sk10') | 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk10'))) 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl113, '7'])). 119.59/15.75 thf(zip_derived_cl128, plain, 119.59/15.75 ((~ (((mnot @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mnot @ (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk10') | (mnot @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk10'))) 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl120, '10'])). 119.59/15.75 thf(zip_derived_cl129, plain, 119.59/15.75 ((~ (mnot @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mnot @ (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk10') 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl128])). 119.59/15.75 thf(zip_derived_cl140, plain, 119.59/15.75 (( (mforall_ind @ (^[Y0 : mu]: (mnot @ (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 '#sk10') 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl129, '2'])). 119.59/15.75 thf(zip_derived_cl152, plain, 119.59/15.75 (( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ '#sk10') => 119.59/15.75 ((^[Y1 : mu]: (mnot @ (mbox_s4 @ (big_p @ Y1)))) @ Y0 @ 119.59/15.75 '#sk10')))))) 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl140, '9'])). 119.59/15.75 thf(zip_derived_cl165, plain, 119.59/15.75 (( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ '#sk10') => (mnot @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)) @ '#sk10')))))) 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl152])). 119.59/15.75 thf(zip_derived_cl166, plain, 119.59/15.75 (![X2 : mu]: 119.59/15.75 ( (((exists_in_world @ X2 @ '#sk10') => (mnot @ 119.59/15.75 (mbox_s4 @ (big_p @ X2)) @ '#sk10'))) 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl165])). 119.59/15.75 thf(zip_derived_cl180, plain, 119.59/15.75 (![X2 : mu]: 119.59/15.75 (~ (exists_in_world @ X2 @ '#sk10') 119.59/15.75 | (mnot @ (mbox_s4 @ (big_p @ X2)) @ '#sk10') 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl166])). 119.59/15.75 thf(zip_derived_cl197, plain, 119.59/15.75 (![X0 : mu]: 119.59/15.75 (~ (mbox_s4 @ (big_p @ X0) @ '#sk10') 119.59/15.75 | ('#form9') 119.59/15.75 | ~ (exists_in_world @ X0 @ '#sk10'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl180, '4'])). 119.59/15.75 thf(zip_derived_cl211, plain, 119.59/15.75 (![X0 : mu]: 119.59/15.75 (~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk10' @ Y0))) | (big_p @ X0 @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X0 @ '#sk10') 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl197, '5'])). 119.59/15.75 thf(zip_derived_cl226, plain, 119.59/15.75 (![X0 : mu]: 119.59/15.75 (~ (((((~) @ (rel_s4 @ '#sk10' @ ('#sk21' @ '#sk10' @ X0)))) | 119.59/15.75 (big_p @ X0 @ ('#sk21' @ '#sk10' @ X0)))) 119.59/15.75 | ('#form9') 119.59/15.75 | ~ (exists_in_world @ X0 @ '#sk10'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl211])). 119.59/15.75 thf(zip_derived_cl242, plain, 119.59/15.75 (![X0 : mu]: 119.59/15.75 (~ (big_p @ X0 @ ('#sk21' @ '#sk10' @ X0)) 119.59/15.75 | ~ (exists_in_world @ X0 @ '#sk10') 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl226])). 119.59/15.75 thf(zip_derived_cl95, plain, 119.59/15.75 (( (rel_s4 @ '#sk3' @ '#sk8') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 Y0)))))) 119.59/15.75 | ~ ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl94])). 119.59/15.75 thf(zip_derived_cl101, plain, 119.59/15.75 (( ('#form9') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 define([status(thm)])). 119.59/15.75 thf(zip_derived_cl103, plain, 119.59/15.75 ((~ ('#form9') | ~ ('#form4') | (rel_s4 @ '#sk3' @ '#sk8'))), 119.59/15.75 inference('renaming', [status(thm)], 119.59/15.75 [zip_derived_cl95, zip_derived_cl101])). 119.59/15.75 thf(nonempty_ax, axiom, (![V:$i]: ( ?[X:mu]: ( exists_in_world @ X @ V ) ))). 119.59/15.75 thf(zip_derived_cl0, plain, 119.59/15.75 ( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((??) @ (^[Y1 : mu]: (exists_in_world @ Y1 @ Y0)))))))), 119.59/15.75 inference('cnf', [status(esa)], [nonempty_ax])). 119.59/15.75 thf(zip_derived_cl13, plain, 119.59/15.75 (![X2 : $i]: (((??) @ (^[Y0 : mu]: (exists_in_world @ Y0 @ X2))))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 119.59/15.75 thf(zip_derived_cl14, plain, 119.59/15.75 (![X2 : $i]: (exists_in_world @ ('#sk1' @ X2) @ X2)), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl13])). 119.59/15.75 thf(zip_derived_cl112, plain, (( (rel_s4 @ '#sk3' @ '#sk10') | ('#form9'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl111])). 119.59/15.75 thf(zip_derived_cl241, plain, 119.59/15.75 (![X0 : mu]: 119.59/15.75 ( (rel_s4 @ '#sk10' @ ('#sk21' @ '#sk10' @ X0)) 119.59/15.75 | ~ (exists_in_world @ X0 @ '#sk10') 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl226])). 119.59/15.75 thf(zip_derived_cl130, plain, 119.59/15.75 ((~ (mnot @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk10') 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl128])). 119.59/15.75 thf(zip_derived_cl141, plain, 119.59/15.75 (( (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 '#sk10') 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl130, '2'])). 119.59/15.75 thf(zip_derived_cl153, plain, 119.59/15.75 (( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk10' @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl141, '8'])). 119.59/15.75 thf(zip_derived_cl167, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ '#sk10' @ X2))) | (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ X2))) 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl153])). 119.59/15.75 thf(zip_derived_cl181, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 (~ (rel_s4 @ '#sk10' @ X2) 119.59/15.75 | (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ X2) 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl167])). 119.59/15.75 thf(zip_derived_cl198, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X0) => 119.59/15.75 ((^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0 @ X0)))))) 119.59/15.75 | ('#form9') 119.59/15.75 | ~ (rel_s4 @ '#sk10' @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl181, '9'])). 119.59/15.75 thf(zip_derived_cl212, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X0) => (mbox_s4 @ 119.59/15.75 (big_p @ Y0) @ X0)))))) 119.59/15.75 | ('#form9') 119.59/15.75 | ~ (rel_s4 @ '#sk10' @ X0))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl198])). 119.59/15.75 thf(zip_derived_cl213, plain, 119.59/15.75 (![X0 : $i, X2 : mu]: 119.59/15.75 ( (((exists_in_world @ X2 @ X0) => (mbox_s4 @ (big_p @ X2) @ X0))) 119.59/15.75 | ~ (rel_s4 @ '#sk10' @ X0) 119.59/15.75 | ('#form9'))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl212])). 119.59/15.75 thf(zip_derived_cl227, plain, 119.59/15.75 (![X0 : $i, X2 : mu]: 119.59/15.75 (~ (exists_in_world @ X2 @ X0) 119.59/15.75 | (mbox_s4 @ (big_p @ X2) @ X0) 119.59/15.75 | ('#form9') 119.59/15.75 | ~ (rel_s4 @ '#sk10' @ X0))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl213])). 119.59/15.75 thf(zip_derived_cl243, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 ( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X1 @ Y0)))))) 119.59/15.75 | ~ (rel_s4 @ '#sk10' @ X0) 119.59/15.75 | ('#form9') 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl227, '8'])). 119.59/15.75 thf(zip_derived_cl260, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X3))) | (big_p @ X1 @ X3))) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ('#form9') 119.59/15.75 | ~ (rel_s4 @ '#sk10' @ X0))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl243])). 119.59/15.75 thf(zip_derived_cl274, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ X3) 119.59/15.75 | (big_p @ X1 @ X3) 119.59/15.75 | ~ (rel_s4 @ '#sk10' @ X0) 119.59/15.75 | ('#form9') 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl260])). 119.59/15.75 thf(zip_derived_cl34, plain, 119.59/15.75 (( ('#form4') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | (mimplies @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mexists_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))))) @ 119.59/15.75 Y0)))))))), 119.59/15.75 define([status(thm)])). 119.59/15.75 thf(zip_derived_cl35, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk2' @ '#sk5'))) | (mimplies @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 '#sk5'))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl34])). 119.59/15.75 thf(zip_derived_cl38, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk2' @ '#sk5'))) | (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 '#sk5'))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl35, '6'])). 119.59/15.75 thf(zip_derived_cl40, plain, 119.59/15.75 ((~ (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 '#sk5') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl38])). 119.59/15.75 thf(zip_derived_cl42, plain, 119.59/15.75 ((~ (((mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk5') | (mnot @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk5'))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl40, '7'])). 119.59/15.75 thf(zip_derived_cl47, plain, 119.59/15.75 ((~ (mnot @ 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk5') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])). 119.59/15.75 thf(zip_derived_cl51, plain, 119.59/15.75 (( (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 '#sk5') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl47, '2'])). 119.59/15.75 thf(zip_derived_cl55, plain, 119.59/15.75 (( (mnot @ 119.59/15.75 (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 '#sk5') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl51, '1'])). 119.59/15.75 thf(zip_derived_cl56, plain, 119.59/15.75 ((~ (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk5') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl55, '4'])). 119.59/15.75 thf(zip_derived_cl61, plain, 119.59/15.75 ((~ (((mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 '#sk5') | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk5'))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl56, '7'])). 119.59/15.75 thf(zip_derived_cl66, plain, 119.59/15.75 ((~ (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk5') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl61])). 119.59/15.75 thf(zip_derived_cl72, plain, 119.59/15.75 (( (mbox_s4 @ 119.59/15.75 (mimplies @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 '#sk5') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl66, '2'])). 119.59/15.75 thf(zip_derived_cl80, plain, 119.59/15.75 (( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 Y0)))))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl72, '8'])). 119.59/15.75 thf(zip_derived_cl86, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ '#sk5' @ X2))) | (mimplies @ 119.59/15.75 (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 X2))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl80])). 119.59/15.75 thf(zip_derived_cl92, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ '#sk5' @ X2))) | (mor @ 119.59/15.75 (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 X2))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl86, '6'])). 119.59/15.75 thf(zip_derived_cl93, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 (~ (rel_s4 @ '#sk5' @ X2) 119.59/15.75 | (mor @ 119.59/15.75 (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 X2) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl92])). 119.59/15.75 thf(zip_derived_cl100, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( (((mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ X0) | 119.59/15.75 (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 X0))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl93, '3'])). 119.59/15.75 thf(zip_derived_cl110, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 X0) 119.59/15.75 | (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 X0) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl100])). 119.59/15.75 thf(zip_derived_cl119, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl110, '8'])). 119.59/15.75 thf(zip_derived_cl127, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 (~ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ('#form4') 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl119, '4'])). 119.59/15.75 thf(zip_derived_cl138, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 (~ (mnot @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mnot @ (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 X0) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ('#form4') 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl127, '10'])). 119.59/15.75 thf(zip_derived_cl139, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( (mforall_ind @ (^[Y0 : mu]: (mnot @ (mbox_s4 @ (big_p @ Y0)))) @ X0) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl138, '2'])). 119.59/15.75 thf(zip_derived_cl151, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X0) => 119.59/15.75 ((^[Y1 : mu]: (mnot @ (mbox_s4 @ (big_p @ Y1)))) @ 119.59/15.75 Y0 @ X0)))))) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ('#form4') 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl139, '9'])). 119.59/15.75 thf(zip_derived_cl163, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X0) => (mnot @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)) @ X0)))))) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ('#form4') 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl151])). 119.59/15.75 thf(zip_derived_cl164, plain, 119.59/15.75 (![X0 : $i, X2 : mu]: 119.59/15.75 ( (((exists_in_world @ X2 @ X0) => (mnot @ (mbox_s4 @ (big_p @ X2)) @ 119.59/15.75 X0))) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl163])). 119.59/15.75 thf(zip_derived_cl179, plain, 119.59/15.75 (![X0 : $i, X2 : mu]: 119.59/15.75 (~ (exists_in_world @ X2 @ X0) 119.59/15.75 | (mnot @ (mbox_s4 @ (big_p @ X2)) @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ('#form4') 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 119.59/15.75 thf(zip_derived_cl196, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 (~ (mbox_s4 @ (big_p @ X1) @ X0) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl179, '4'])). 119.59/15.75 thf(zip_derived_cl210, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 (~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X1 @ Y0)))))) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ('#form4') 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl196, '5'])). 119.59/15.75 thf(zip_derived_cl225, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 (~ (((((~) @ (rel_s4 @ X0 @ ('#sk21' @ X0 @ X1)))) | (big_p @ X1 @ 119.59/15.75 ('#sk21' @ X0 @ X1)))) 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl210])). 119.59/15.75 thf(zip_derived_cl240, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 (~ (big_p @ X1 @ ('#sk21' @ X0 @ X1)) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ('#form4') 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl225])). 119.59/15.75 thf(zip_derived_cl259, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X3))) | (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ X3))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ (big_p @ X1 @ ('#sk21' @ X0 @ X1)))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl240])). 119.59/15.75 thf(zip_derived_cl273, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ X3) 119.59/15.75 | (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ X3) 119.59/15.75 | ~ (big_p @ X1 @ ('#sk21' @ X0 @ X1)) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl259])). 119.59/15.75 thf(zip_derived_cl286, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X2) => 119.59/15.75 ((^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0 @ X2)))))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ (big_p @ X1 @ ('#sk21' @ X0 @ X1)) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl273, '9'])). 119.59/15.75 thf(zip_derived_cl296, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X2) => (mbox_s4 @ 119.59/15.75 (big_p @ Y0) @ X2)))))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ (big_p @ X1 @ ('#sk21' @ X0 @ X1)) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl286])). 119.59/15.75 thf(zip_derived_cl297, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i, X4 : mu]: 119.59/15.75 ( (((exists_in_world @ X4 @ X2) => (mbox_s4 @ (big_p @ X4) @ X2))) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2) 119.59/15.75 | ~ (big_p @ X1 @ ('#sk21' @ X0 @ X1)) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl296])). 119.59/15.75 thf(zip_derived_cl308, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i, X4 : mu]: 119.59/15.75 (~ (exists_in_world @ X4 @ X2) 119.59/15.75 | (mbox_s4 @ (big_p @ X4) @ X2) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ (big_p @ X1 @ ('#sk21' @ X0 @ X1)) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl297])). 119.59/15.75 thf(zip_derived_cl316, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu]: 119.59/15.75 ( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X3 @ Y0)))))) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (big_p @ X2 @ ('#sk21' @ X1 @ X2)) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X1) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (exists_in_world @ X3 @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl308, '8'])). 119.59/15.75 thf(zip_derived_cl325, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu, X5 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X5))) | (big_p @ X3 @ X5))) 119.59/15.75 | ~ (exists_in_world @ X3 @ X0) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X1) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ (big_p @ X2 @ ('#sk21' @ X1 @ X2)) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl316])). 119.59/15.75 thf(zip_derived_cl332, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu, X5 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ X5) 119.59/15.75 | (big_p @ X3 @ X5) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | ~ (big_p @ X2 @ ('#sk21' @ X1 @ X2)) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X1) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (exists_in_world @ X3 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl325])). 119.59/15.75 thf(zip_derived_cl46, plain, 119.59/15.75 ((~ (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk5') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])). 119.59/15.75 thf(zip_derived_cl50, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))) @ 119.59/15.75 Y0)))))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl46, '5'])). 119.59/15.75 thf(zip_derived_cl54, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk5' @ '#sk6'))) | (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 '#sk6'))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl50])). 119.59/15.75 thf(zip_derived_cl60, plain, 119.59/15.75 ((~ (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 '#sk6') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])). 119.59/15.75 thf(zip_derived_cl64, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ '#sk6') => 119.59/15.75 ((^[Y1 : mu]: 119.59/15.75 (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y1)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y2 : mu]: (mbox_s4 @ (big_p @ Y2))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y1)))))) @ 119.59/15.75 Y0 @ '#sk6')))))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl60, '11'])). 119.59/15.75 thf(zip_derived_cl69, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ '#sk6') => (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 '#sk6')))))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl64])). 119.59/15.75 thf(zip_derived_cl70, plain, 119.59/15.75 ((~ (((exists_in_world @ '#sk7' @ '#sk6') => (mand @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ '#sk7')) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')))) @ 119.59/15.75 '#sk6'))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl69])). 119.59/15.75 thf(zip_derived_cl76, plain, 119.59/15.75 ((~ (((exists_in_world @ '#sk7' @ '#sk6') => (mnot @ 119.59/15.75 (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ '#sk7')) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')))))) @ 119.59/15.75 '#sk6'))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl70, '1'])). 119.59/15.75 thf(zip_derived_cl78, plain, 119.59/15.75 ((~ (mnot @ 119.59/15.75 (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ '#sk7')) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')))))) @ 119.59/15.75 '#sk6') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl76])). 119.59/15.75 thf(zip_derived_cl84, plain, 119.59/15.75 (( (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ '#sk7')) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))))) @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7'))))) @ 119.59/15.75 '#sk6') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl78, '2'])). 119.59/15.75 thf(zip_derived_cl89, plain, 119.59/15.75 (( (((mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')))) @ 119.59/15.75 '#sk6') | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ '#sk7')) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk6'))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl84, '3'])). 119.59/15.75 thf(zip_derived_cl98, plain, 119.59/15.75 (( (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')))) @ 119.59/15.75 '#sk6') 119.59/15.75 | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ '#sk7')) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk6') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl89])). 119.59/15.75 thf(zip_derived_cl107, plain, 119.59/15.75 ((~ (mbox_s4 @ 119.59/15.75 (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7'))) @ 119.59/15.75 '#sk6') 119.59/15.75 | ('#form4') 119.59/15.75 | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ '#sk7')) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk6'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl98, '4'])). 119.59/15.75 thf(zip_derived_cl117, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ Y0)))))) 119.59/15.75 | (mnot @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ '#sk7')) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))))) @ 119.59/15.75 '#sk6') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl107, '5'])). 119.59/15.75 thf(zip_derived_cl125, plain, 119.59/15.75 ((~ (mbox_s4 @ 119.59/15.75 (mimplies @ (mbox_s4 @ (big_p @ '#sk7')) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 '#sk6') 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ Y0)))))))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl117, '4'])). 119.59/15.75 thf(zip_derived_cl135, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 Y0)))))) 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ Y0)))))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl125, '5'])). 119.59/15.75 thf(zip_derived_cl149, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk6' @ '#sk12'))) | (mimplies @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk12'))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ Y0)))))))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl135])). 119.59/15.75 thf(zip_derived_cl159, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk6' @ '#sk12'))) | (mor @ 119.59/15.75 (mnot @ (mbox_s4 @ (big_p @ '#sk7'))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk12'))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ Y0)))))))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl149, '6'])). 119.59/15.75 thf(zip_derived_cl161, plain, 119.59/15.75 ((~ (mor @ (mnot @ (mbox_s4 @ (big_p @ '#sk7'))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk12') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ Y0)))))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl159])). 119.59/15.75 thf(zip_derived_cl160, plain, 119.59/15.75 (( (rel_s4 @ '#sk6' @ '#sk12') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ Y0)))))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl159])). 119.59/15.75 thf(zip_derived_cl173, plain, 119.59/15.75 (( ('#form15') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ Y0)))))))), 119.59/15.75 define([status(thm)])). 119.59/15.75 thf(zip_derived_cl176, plain, 119.59/15.75 ((~ ('#form15') 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (mor @ (mnot @ (mbox_s4 @ (big_p @ '#sk7'))) @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk12'))), 119.59/15.75 inference('renaming', [status(thm)], 119.59/15.75 [zip_derived_cl161, zip_derived_cl173])). 119.59/15.75 thf(zip_derived_cl191, plain, 119.59/15.75 ((~ (((mbox_s4 @ 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ '#sk12') | 119.59/15.75 (mnot @ (mbox_s4 @ (big_p @ '#sk7')) @ '#sk12'))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ ('#form15'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl176, '7'])). 119.59/15.75 thf(zip_derived_cl205, plain, 119.59/15.75 ((~ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 '#sk12') 119.59/15.75 | ~ ('#form15') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl191])). 119.59/15.75 thf(zip_derived_cl220, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk12' @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ ('#form15'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl205, '5'])). 119.59/15.75 thf(zip_derived_cl234, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk12' @ ('#sk13' @ '#sk12')))) | 119.59/15.75 (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ 119.59/15.75 ('#sk13' @ '#sk12')))) 119.59/15.75 | ~ ('#form15') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl220])). 119.59/15.75 thf(zip_derived_cl254, plain, 119.59/15.75 ((~ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ 119.59/15.75 ('#sk13' @ '#sk12')) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ ('#form15'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl234])). 119.59/15.75 thf(zip_derived_cl268, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ ('#sk13' @ '#sk12')) => 119.59/15.75 ((^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0 @ 119.59/15.75 ('#sk13' @ '#sk12'))))))) 119.59/15.75 | ~ ('#form15') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl254, '11'])). 119.59/15.75 thf(zip_derived_cl281, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ ('#sk13' @ '#sk12')) => 119.59/15.75 (mbox_s4 @ (big_p @ Y0) @ ('#sk13' @ '#sk12'))))))) 119.59/15.75 | ~ ('#form15') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl268])). 119.59/15.75 thf(zip_derived_cl282, plain, 119.59/15.75 ((~ (((exists_in_world @ ('#sk20' @ '#sk12') @ ('#sk13' @ '#sk12')) => 119.59/15.75 (mbox_s4 @ (big_p @ ('#sk20' @ '#sk12')) @ ('#sk13' @ '#sk12')))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ ('#form15'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl281])). 119.59/15.75 thf(zip_derived_cl293, plain, 119.59/15.75 ((~ (mbox_s4 @ (big_p @ ('#sk20' @ '#sk12')) @ ('#sk13' @ '#sk12')) 119.59/15.75 | ~ ('#form15') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl282])). 119.59/15.75 thf(zip_derived_cl306, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ ('#sk13' @ '#sk12') @ Y0))) | 119.59/15.75 (big_p @ ('#sk20' @ '#sk12') @ Y0)))))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ ('#form15'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl293, '5'])). 119.59/15.75 thf(zip_derived_cl314, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ ('#sk13' @ '#sk12') @ 119.59/15.75 ('#sk21' @ ('#sk13' @ '#sk12') @ ('#sk20' @ '#sk12'))))) | 119.59/15.75 (big_p @ ('#sk20' @ '#sk12') @ 119.59/15.75 ('#sk21' @ ('#sk13' @ '#sk12') @ ('#sk20' @ '#sk12'))))) 119.59/15.75 | ~ ('#form15') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl306])). 119.59/15.75 thf(zip_derived_cl323, plain, 119.59/15.75 ((~ (big_p @ ('#sk20' @ '#sk12') @ 119.59/15.75 ('#sk21' @ ('#sk13' @ '#sk12') @ ('#sk20' @ '#sk12'))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ ('#form15'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl314])). 119.59/15.75 thf(zip_derived_cl206, plain, 119.59/15.75 ((~ (mnot @ (mbox_s4 @ (big_p @ '#sk7')) @ '#sk12') 119.59/15.75 | ~ ('#form15') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl191])). 119.59/15.75 thf(zip_derived_cl221, plain, 119.59/15.75 (( (mbox_s4 @ (big_p @ '#sk7') @ '#sk12') | ('#form4') | ~ ('#form15'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl206, '2'])). 119.59/15.75 thf(zip_derived_cl235, plain, 119.59/15.75 (( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk12' @ Y0))) | (big_p @ '#sk7' @ 119.59/15.75 Y0)))))) 119.59/15.75 | ~ ('#form15') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl221, '8'])). 119.59/15.75 thf(zip_derived_cl255, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ '#sk12' @ X2))) | (big_p @ '#sk7' @ X2))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ ('#form15'))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl235])). 119.59/15.75 thf(zip_derived_cl269, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 (~ (rel_s4 @ '#sk12' @ X2) 119.59/15.75 | (big_p @ '#sk7' @ X2) 119.59/15.75 | ~ ('#form15') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl255])). 119.59/15.75 thf(cumulative_ax, axiom, 119.59/15.75 (![X:mu,V:$i,W:$i]: 119.59/15.75 ( ( ( exists_in_world @ X @ V ) & ( rel_s4 @ V @ W ) ) => 119.59/15.75 ( exists_in_world @ X @ W ) ))). 119.59/15.75 thf(zip_derived_cl3, plain, 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((!!) @ (^[Y1 : $i]: 119.59/15.75 (((!!) @ (^[Y2 : $i]: 119.59/15.75 (((((exists_in_world @ Y0 @ Y1) & 119.59/15.75 (rel_s4 @ Y1 @ Y2))) => 119.59/15.75 (exists_in_world @ Y0 @ Y2))))))))))))), 119.59/15.75 inference('cnf', [status(esa)], [cumulative_ax])). 119.59/15.75 thf(zip_derived_cl15, plain, 119.59/15.75 (![X2 : mu]: 119.59/15.75 (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((!!) @ (^[Y1 : $i]: 119.59/15.75 (((((exists_in_world @ X2 @ Y0) & (rel_s4 @ 119.59/15.75 Y0 @ Y1))) => 119.59/15.75 (exists_in_world @ X2 @ Y1)))))))))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 119.59/15.75 thf(zip_derived_cl16, plain, 119.59/15.75 (![X2 : mu, X4 : $i]: 119.59/15.75 (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((exists_in_world @ X2 @ X4) & (rel_s4 @ X4 @ Y0))) => 119.59/15.75 (exists_in_world @ X2 @ Y0))))))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 119.59/15.75 thf(zip_derived_cl17, plain, 119.59/15.75 (![X2 : mu, X4 : $i, X6 : $i]: 119.59/15.75 (((((exists_in_world @ X2 @ X4) & (rel_s4 @ X4 @ X6))) => 119.59/15.75 (exists_in_world @ X2 @ X6)))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 119.59/15.75 thf(zip_derived_cl18, plain, 119.59/15.75 (![X2 : mu, X4 : $i, X6 : $i]: 119.59/15.75 (~ (((exists_in_world @ X2 @ X4) & (rel_s4 @ X4 @ X6))) 119.59/15.75 | (exists_in_world @ X2 @ X6))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 119.59/15.75 thf(zip_derived_cl19, plain, 119.59/15.75 (![X2 : mu, X4 : $i, X6 : $i]: 119.59/15.75 (~ (exists_in_world @ X2 @ X4) 119.59/15.75 | ~ (rel_s4 @ X4 @ X6) 119.59/15.75 | (exists_in_world @ X2 @ X6))), 119.59/15.75 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])). 119.59/15.75 thf(zip_derived_cl292, plain, 119.59/15.75 (( (exists_in_world @ ('#sk20' @ '#sk12') @ ('#sk13' @ '#sk12')) 119.59/15.75 | ~ ('#form15') 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl282])). 119.59/15.75 thf(zip_derived_cl322, plain, 119.59/15.75 (( (rel_s4 @ ('#sk13' @ '#sk12') @ 119.59/15.75 ('#sk21' @ ('#sk13' @ '#sk12') @ ('#sk20' @ '#sk12'))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ ('#form15'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl314])). 119.59/15.75 thf(zip_derived_cl19, plain, 119.59/15.75 (![X2 : mu, X4 : $i, X6 : $i]: 119.59/15.75 (~ (exists_in_world @ X2 @ X4) 119.59/15.75 | ~ (rel_s4 @ X4 @ X6) 119.59/15.75 | (exists_in_world @ X2 @ X6))), 119.59/15.75 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])). 119.59/15.75 thf(zip_derived_cl1641, plain, 119.59/15.75 (![X0 : mu]: 119.59/15.75 (~ ('#form15') 119.59/15.75 | ('#form4') 119.59/15.75 | (exists_in_world @ X0 @ 119.59/15.75 ('#sk21' @ ('#sk13' @ '#sk12') @ ('#sk20' @ '#sk12'))) 119.59/15.75 | ~ (exists_in_world @ X0 @ ('#sk13' @ '#sk12')))), 119.59/15.75 inference('sup-', [status(thm)], [zip_derived_cl322, zip_derived_cl19])). 119.59/15.75 thf(zip_derived_cl322, plain, 119.59/15.75 (( (rel_s4 @ ('#sk13' @ '#sk12') @ 119.59/15.75 ('#sk21' @ ('#sk13' @ '#sk12') @ ('#sk20' @ '#sk12'))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ ('#form15'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl314])). 119.59/15.75 thf(zip_derived_cl239, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 ( (rel_s4 @ X0 @ ('#sk21' @ X0 @ X1)) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ('#form4') 119.59/15.75 | (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl225])). 119.59/15.75 thf(zip_derived_cl258, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X3))) | (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ X3))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | (rel_s4 @ X0 @ ('#sk21' @ X0 @ X1)))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl239])). 119.59/15.75 thf(zip_derived_cl272, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ X3) 119.59/15.75 | (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ X3) 119.59/15.75 | (rel_s4 @ X0 @ ('#sk21' @ X0 @ X1)) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl258])). 119.59/15.75 thf(zip_derived_cl285, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X2) => 119.59/15.75 ((^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0 @ X2)))))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | (rel_s4 @ X0 @ ('#sk21' @ X0 @ X1)) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl272, '9'])). 119.59/15.75 thf(zip_derived_cl294, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X2) => (mbox_s4 @ 119.59/15.75 (big_p @ Y0) @ X2)))))) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | (rel_s4 @ X0 @ ('#sk21' @ X0 @ X1)) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl285])). 119.59/15.75 thf(zip_derived_cl295, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i, X4 : mu]: 119.59/15.75 ( (((exists_in_world @ X4 @ X2) => (mbox_s4 @ (big_p @ X4) @ X2))) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2) 119.59/15.75 | (rel_s4 @ X0 @ ('#sk21' @ X0 @ X1)) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl294])). 119.59/15.75 thf(zip_derived_cl307, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X2 : $i, X4 : mu]: 119.59/15.75 (~ (exists_in_world @ X4 @ X2) 119.59/15.75 | (mbox_s4 @ (big_p @ X4) @ X2) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X0) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | (rel_s4 @ X0 @ ('#sk21' @ X0 @ X1)) 119.59/15.75 | ~ (rel_s4 @ X0 @ X2))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl295])). 119.59/15.75 thf(zip_derived_cl315, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu]: 119.59/15.75 ( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X3 @ Y0)))))) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | (rel_s4 @ X1 @ ('#sk21' @ X1 @ X2)) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X1) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (exists_in_world @ X3 @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl307, '8'])). 119.59/15.75 thf(zip_derived_cl324, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu, X5 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X5))) | (big_p @ X3 @ X5))) 119.59/15.75 | ~ (exists_in_world @ X3 @ X0) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X1) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | (rel_s4 @ X1 @ ('#sk21' @ X1 @ X2)) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl315])). 119.59/15.75 thf(zip_derived_cl331, plain, 119.59/15.75 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu, X5 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ X5) 119.59/15.75 | (big_p @ X3 @ X5) 119.59/15.75 | ~ (rel_s4 @ X1 @ X0) 119.59/15.75 | (rel_s4 @ X1 @ ('#sk21' @ X1 @ X2)) 119.59/15.75 | ~ (exists_in_world @ X2 @ X1) 119.59/15.75 | ~ (rel_s4 @ '#sk5' @ X1) 119.59/15.75 | ('#form4') 119.59/15.75 | ~ (exists_in_world @ X3 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl324])). 119.59/15.75 thf(zip_derived_cl253, plain, 119.59/15.75 (( (rel_s4 @ '#sk12' @ ('#sk13' @ '#sk12')) | ('#form4') | ~ ('#form15'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl234])). 119.59/15.75 thf(a2, axiom, (mtransitive @ rel_s4)). 119.59/15.75 thf(zip_derived_cl1, plain, ( (mtransitive @ rel_s4)), 119.59/15.75 inference('cnf', [status(esa)], [a2])). 119.59/15.75 thf(mtransitive, axiom, (mtransitive @ X0) => 119.59/15.75 ((((!!) @ (^[Y0 : $i]: 119.59/15.75 (((!!) @ (^[Y1 : $i]: 119.59/15.75 (((!!) @ (^[Y2 : $i]: 119.59/15.75 (((((X0 @ Y1 @ Y2) & (X0 @ Y0 @ Y1))) => 119.59/15.75 (X0 @ Y0 @ Y2)))))))))))) 119.59/15.75 = ($true))). 119.59/15.75 thf('12', plain, 119.59/15.75 (![X0:( $i > $i > $o )]: 119.59/15.75 ( ( mtransitive @ X0 ) <=> 119.59/15.75 ( ![X5:$i,X7:$i,X9:$i]: 119.59/15.75 ( ( ( X0 @ X7 @ X9 ) & ( X0 @ X5 @ X7 ) ) => ( X0 @ X5 @ X9 ) ) ) )), 119.59/15.75 inference('rw.lit', [status(esa)], [mtransitive])). 119.59/15.75 thf(zip_derived_cl5, plain, 119.59/15.75 ( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((!!) @ (^[Y1 : $i]: 119.59/15.75 (((!!) @ (^[Y2 : $i]: 119.59/15.75 (((((rel_s4 @ Y1 @ Y2) & (rel_s4 @ 119.59/15.75 Y0 @ Y1))) => 119.59/15.75 (rel_s4 @ Y0 @ Y2))))))))))))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl1, '12'])). 119.59/15.75 thf(zip_derived_cl6, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((!!) @ (^[Y1 : $i]: 119.59/15.75 (((((rel_s4 @ Y0 @ Y1) & (rel_s4 @ X2 @ Y0))) => 119.59/15.75 (rel_s4 @ X2 @ Y1)))))))))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 119.59/15.75 thf(zip_derived_cl7, plain, 119.59/15.75 (![X2 : $i, X4 : $i]: 119.59/15.75 (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((rel_s4 @ X4 @ Y0) & (rel_s4 @ X2 @ X4))) => 119.59/15.75 (rel_s4 @ X2 @ Y0))))))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 119.59/15.75 thf(zip_derived_cl8, plain, 119.59/15.75 (![X2 : $i, X4 : $i, X6 : $i]: 119.59/15.75 (((((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) => (rel_s4 @ X2 @ X6)))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 119.59/15.75 thf(zip_derived_cl9, plain, 119.59/15.75 (![X2 : $i, X4 : $i, X6 : $i]: 119.59/15.75 (~ (((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) | (rel_s4 @ X2 @ X6))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 119.59/15.75 thf(zip_derived_cl10, plain, 119.59/15.75 (![X2 : $i, X4 : $i, X6 : $i]: 119.59/15.75 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))), 119.59/15.75 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 119.59/15.75 thf(zip_derived_cl77, plain, 119.59/15.75 (( (exists_in_world @ '#sk7' @ '#sk6') | ('#form4'))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl76])). 119.59/15.75 thf(zip_derived_cl160, plain, 119.59/15.75 (( (rel_s4 @ '#sk6' @ '#sk12') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ Y0)))))) 119.59/15.75 | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl159])). 119.59/15.75 thf(zip_derived_cl173, plain, 119.59/15.75 (( ('#form15') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ Y0)))))))), 119.59/15.75 define([status(thm)])). 119.59/15.75 thf(zip_derived_cl175, plain, 119.59/15.75 ((~ ('#form15') | ('#form4') | (rel_s4 @ '#sk6' @ '#sk12'))), 119.59/15.75 inference('renaming', [status(thm)], 119.59/15.75 [zip_derived_cl160, zip_derived_cl173])). 119.59/15.75 thf(zip_derived_cl59, plain, (( (rel_s4 @ '#sk5' @ '#sk6') | ('#form4'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])). 119.59/15.75 thf(zip_derived_cl10, plain, 119.59/15.75 (![X2 : $i, X4 : $i, X6 : $i]: 119.59/15.75 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))), 119.59/15.75 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 119.59/15.75 thf(zip_derived_cl397, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( ('#form4') | (rel_s4 @ '#sk5' @ X0) | ~ (rel_s4 @ '#sk6' @ X0))), 119.59/15.75 inference('sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl10])). 119.59/15.75 thf(zip_derived_cl173, plain, 119.59/15.75 (( ('#form15') 119.59/15.75 | ~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | (mimplies @ 119.59/15.75 (mbox_s4 @ 119.59/15.75 (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ Y0)))))))), 119.59/15.75 define([status(thm)])). 119.59/15.75 thf(zip_derived_cl174, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk6' @ '#sk16'))) | (mimplies @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ '#sk16'))) 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl173])). 119.59/15.75 thf(zip_derived_cl188, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk6' @ '#sk16'))) | (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ '#sk16'))) 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('rw', [status(thm)], [zip_derived_cl174, '6'])). 119.59/15.75 thf(zip_derived_cl190, plain, 119.59/15.75 ((~ (mor @ 119.59/15.75 (mnot @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))))) @ 119.59/15.75 (mbox_s4 @ (big_p @ '#sk7')) @ '#sk16') 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl188])). 119.59/15.75 thf(zip_derived_cl204, plain, 119.59/15.75 ((~ (((mbox_s4 @ (big_p @ '#sk7') @ '#sk16') | (mnot @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk16'))) 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl190, '7'])). 119.59/15.75 thf(zip_derived_cl218, plain, 119.59/15.75 ((~ (mbox_s4 @ (big_p @ '#sk7') @ '#sk16') | ('#form15'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl204])). 119.59/15.75 thf(zip_derived_cl232, plain, 119.59/15.75 ((~ (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk16' @ Y0))) | (big_p @ '#sk7' @ 119.59/15.75 Y0)))))) 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl218, '5'])). 119.59/15.75 thf(zip_derived_cl251, plain, 119.59/15.75 ((~ (((((~) @ (rel_s4 @ '#sk16' @ ('#sk21' @ '#sk16' @ '#sk7')))) | 119.59/15.75 (big_p @ '#sk7' @ ('#sk21' @ '#sk16' @ '#sk7')))) 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl232])). 119.59/15.75 thf(zip_derived_cl265, plain, 119.59/15.75 (( (rel_s4 @ '#sk16' @ ('#sk21' @ '#sk16' @ '#sk7')) | ('#form15'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl251])). 119.59/15.75 thf(a1, axiom, (mreflexive @ rel_s4)). 119.59/15.75 thf(zip_derived_cl2, plain, ( (mreflexive @ rel_s4)), 119.59/15.75 inference('cnf', [status(esa)], [a1])). 119.59/15.75 thf(mreflexive, axiom, (mreflexive @ X0) => 119.59/15.75 ((((!!) @ (^[Y0 : $i]: (X0 @ Y0 @ Y0)))) = ($true))). 119.59/15.75 thf('13', plain, 119.59/15.75 (![X0:( $i > $i > $o )]: 119.59/15.75 ( ( mreflexive @ X0 ) <=> ( ![X5:$i]: ( X0 @ X5 @ X5 ) ) )), 119.59/15.75 inference('rw.lit', [status(esa)], [mreflexive])). 119.59/15.75 thf(zip_derived_cl11, plain, ( (((!!) @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl2, '13'])). 119.59/15.75 thf(zip_derived_cl12, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])). 119.59/15.75 thf(zip_derived_cl19, plain, 119.59/15.75 (![X2 : mu, X4 : $i, X6 : $i]: 119.59/15.75 (~ (exists_in_world @ X2 @ X4) 119.59/15.75 | ~ (rel_s4 @ X4 @ X6) 119.59/15.75 | (exists_in_world @ X2 @ X6))), 119.59/15.75 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])). 119.59/15.75 thf(zip_derived_cl189, plain, 119.59/15.75 (( (rel_s4 @ '#sk6' @ '#sk16') | ('#form15'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl188])). 119.59/15.75 thf(zip_derived_cl445, plain, 119.59/15.75 (![X0 : mu]: 119.59/15.75 ( (exists_in_world @ X0 @ '#sk16') 119.59/15.75 | ~ (exists_in_world @ X0 @ '#sk6') 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl189])). 119.59/15.75 thf(zip_derived_cl266, plain, 119.59/15.75 ((~ (big_p @ '#sk7' @ ('#sk21' @ '#sk16' @ '#sk7')) | ('#form15'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl251])). 119.59/15.75 thf(zip_derived_cl219, plain, 119.59/15.75 ((~ (mnot @ 119.59/15.75 (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))))) @ 119.59/15.75 '#sk16') 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl204])). 119.59/15.75 thf(zip_derived_cl233, plain, 119.59/15.75 (( (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0)))) @ 119.59/15.75 '#sk16') 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl219, '2'])). 119.59/15.75 thf(zip_derived_cl252, plain, 119.59/15.75 (( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ '#sk16' @ Y0))) | (mforall_ind @ 119.59/15.75 (^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0)))))) 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl233, '8'])). 119.59/15.75 thf(zip_derived_cl267, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ '#sk16' @ X2))) | (mforall_ind @ 119.59/15.75 (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ X2))) 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl252])). 119.59/15.75 thf(zip_derived_cl280, plain, 119.59/15.75 (![X2 : $i]: 119.59/15.75 (~ (rel_s4 @ '#sk16' @ X2) 119.59/15.75 | (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_p @ Y0))) @ X2) 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl267])). 119.59/15.75 thf(zip_derived_cl291, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X0) => 119.59/15.75 ((^[Y1 : mu]: (mbox_s4 @ (big_p @ Y1))) @ Y0 @ X0)))))) 119.59/15.75 | ('#form15') 119.59/15.75 | ~ (rel_s4 @ '#sk16' @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl280, '9'])). 119.59/15.75 thf(zip_derived_cl304, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( (((!!) @ (^[Y0 : mu]: 119.59/15.75 (((exists_in_world @ Y0 @ X0) => (mbox_s4 @ 119.59/15.75 (big_p @ Y0) @ X0)))))) 119.59/15.75 | ('#form15') 119.59/15.75 | ~ (rel_s4 @ '#sk16' @ X0))), 119.59/15.75 inference('ho_norm', [status(thm)], [zip_derived_cl291])). 119.59/15.75 thf(zip_derived_cl305, plain, 119.59/15.75 (![X0 : $i, X2 : mu]: 119.59/15.75 ( (((exists_in_world @ X2 @ X0) => (mbox_s4 @ (big_p @ X2) @ X0))) 119.59/15.75 | ~ (rel_s4 @ '#sk16' @ X0) 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl304])). 119.59/15.75 thf(zip_derived_cl313, plain, 119.59/15.75 (![X0 : $i, X2 : mu]: 119.59/15.75 (~ (exists_in_world @ X2 @ X0) 119.59/15.75 | (mbox_s4 @ (big_p @ X2) @ X0) 119.59/15.75 | ('#form15') 119.59/15.75 | ~ (rel_s4 @ '#sk16' @ X0))), 119.59/15.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl305])). 119.59/15.75 thf(zip_derived_cl321, plain, 119.59/15.75 (![X0 : $i, X1 : mu]: 119.59/15.75 ( (((!!) @ (^[Y0 : $i]: 119.59/15.75 (((((~) @ (rel_s4 @ X0 @ Y0))) | (big_p @ X1 @ Y0)))))) 119.59/15.75 | ~ (rel_s4 @ '#sk16' @ X0) 119.59/15.75 | ('#form15') 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('rw_clause', [status(thm)], [zip_derived_cl313, '8'])). 119.59/15.75 thf(zip_derived_cl330, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 ( (((((~) @ (rel_s4 @ X0 @ X3))) | (big_p @ X1 @ X3))) 119.59/15.75 | ~ (exists_in_world @ X1 @ X0) 119.59/15.75 | ('#form15') 119.59/15.75 | ~ (rel_s4 @ '#sk16' @ X0))), 119.59/15.75 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl321])). 119.59/15.75 thf(zip_derived_cl337, plain, 119.59/15.75 (![X0 : $i, X1 : mu, X3 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ X3) 119.59/15.75 | (big_p @ X1 @ X3) 119.59/15.75 | ~ (rel_s4 @ '#sk16' @ X0) 119.59/15.75 | ('#form15') 119.59/15.75 | ~ (exists_in_world @ X1 @ X0))), 119.59/15.75 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl330])). 119.59/15.75 thf(zip_derived_cl3792, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 ( ('#form15') 119.59/15.75 | ~ (exists_in_world @ '#sk7' @ X0) 119.59/15.75 | ('#form15') 119.59/15.75 | ~ (rel_s4 @ '#sk16' @ X0) 119.59/15.75 | ~ (rel_s4 @ X0 @ ('#sk21' @ '#sk16' @ '#sk7')))), 119.59/15.75 inference('sup+', [status(thm)], [zip_derived_cl266, zip_derived_cl337])). 119.59/15.75 thf(zip_derived_cl3875, plain, 119.59/15.75 (![X0 : $i]: 119.59/15.75 (~ (rel_s4 @ X0 @ ('#sk21' @ '#sk16' @ '#sk7')) 119.59/15.75 | ~ (rel_s4 @ '#sk16' @ X0) 119.59/15.75 | ~ (exists_in_world @ '#sk7' @ X0) 119.59/15.75 | ('#form15'))), 119.59/15.75 inference('simplify', [status(thm)], [zip_derived_cl3792])). 119.59/15.75 thf(zip_derived_cl57364, plain, ($false), 119.59/15.75 inference('eprover', [status(thm)], 119.59/15.75 [zip_derived_cl336, zip_derived_cl246, zip_derived_cl334, 119.59/15.75 zip_derived_cl245, zip_derived_cl244, zip_derived_cl309, 119.59/15.75 zip_derived_cl199, zip_derived_cl184, zip_derived_cl333, 119.59/15.75 zip_derived_cl335, zip_derived_cl275, zip_derived_cl154, 119.59/15.75 zip_derived_cl242, zip_derived_cl103, zip_derived_cl14, 119.59/15.75 zip_derived_cl112, zip_derived_cl241, zip_derived_cl274, 119.59/15.75 zip_derived_cl332, zip_derived_cl323, zip_derived_cl269, 119.59/15.75 zip_derived_cl19, zip_derived_cl292, zip_derived_cl1641, 119.59/15.75 zip_derived_cl322, zip_derived_cl331, zip_derived_cl253, 119.59/15.75 zip_derived_cl10, zip_derived_cl77, zip_derived_cl175, 119.59/15.75 zip_derived_cl397, zip_derived_cl265, zip_derived_cl12, 119.59/15.75 zip_derived_cl445, zip_derived_cl3875])). 119.59/15.75 119.59/15.75 % SZS output end Refutation 119.59/15.75 119.59/15.75 119.59/15.75 % Terminating... 119.98/15.85 % Runner terminated. 120.00/15.86 % Zipperpin 1.5 exiting 120.00/15.87 EOF