0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WON1FntihM true 0.12/0.33 % Computer : n007.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1920 0.12/0.33 % WCLimit : 240 0.12/0.33 % DateTime : Wed Jul 30 07:07:04 EDT 2025 0.12/0.33 % CPUTime : 0.12/0.33 % Running portfolio for 1920 s 0.12/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.12/0.34 % Number of cores: 8 0.12/0.34 % Python version: Python 3.6.8 0.12/0.34 % Running in HO mode 0.55/0.64 % Total configuration time : 828 0.55/0.64 % Estimated wc time : 1656 0.55/0.64 % Estimated cpu time (8 cpus) : 207.0 0.70/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.70/0.71 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.70/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.70/0.72 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.70/0.72 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.70/0.72 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.70/0.73 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.70/0.73 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.74/0.93 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 76.00/10.19 % Solved by lams/30_sp5.sh. 76.00/10.19 % done 1700 iterations in 9.325s 76.00/10.19 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 76.00/10.19 % SZS output start Refutation 76.00/10.19 thf(mu_type, type, mu: $tType). 76.00/10.19 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 76.00/10.19 thf(mreflexive_type, type, mreflexive: ($i > $i > $o) > $o). 76.00/10.19 thf(mexists_ind_type, type, mexists_ind: (mu > $i > $o) > $i > $o). 76.00/10.19 thf(string_type, type, string: mu > $i > $o). 76.00/10.19 thf(number_type, type, number: mu > mu > $i > $o). 76.00/10.19 thf(rel_s4_type, type, rel_s4: $i > $i > $o). 76.00/10.19 thf(userid_type, type, userid: mu > mu > $i > $o). 76.00/10.19 thf('#sk8_type', type, '#sk8': $i > mu). 76.00/10.19 thf(u_type, type, u: mu). 76.00/10.19 thf('#sk3_type', type, '#sk3': $i). 76.00/10.19 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 76.00/10.19 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 76.00/10.19 thf('#sk7_type', type, '#sk7': mu > mu > mu > mu > mu). 76.00/10.19 thf(mtransitive_type, type, mtransitive: ($i > $i > $o) > $o). 76.00/10.19 thf(one_type, type, one: mu). 76.00/10.19 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 76.00/10.19 thf(do_type, type, do: mu > mu > mu > $i > $o). 76.00/10.19 thf('#sk9_type', type, '#sk9': $i > mu > mu > mu > mu). 76.00/10.19 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o). 76.00/10.19 thf(exists_in_world_type, type, exists_in_world: mu > $i > $o). 76.00/10.19 thf('#sk6_type', type, '#sk6': mu > mu > $i). 76.00/10.19 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o). 76.00/10.19 thf(entry_box_type, type, entry_box: mu > $i > $o). 76.00/10.19 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 76.00/10.19 thf('#sk4_type', type, '#sk4': $i). 76.00/10.19 thf(in_type, type, in: mu > mu > mu > $i > $o). 76.00/10.19 thf('#sk2_type', type, '#sk2': $i > mu). 76.00/10.19 thf('#sk5_type', type, '#sk5': mu > mu > mu > mu > $i). 76.00/10.19 thf(mreflexive, axiom,(( mreflexive ) = 76.00/10.19 (^[R:( $i > $i > $o )]: ( ![S:$i]: ( R @ S @ S ) )))). 76.00/10.19 thf('0', plain, 76.00/10.19 (( mreflexive ) = ( ^[R:( $i > $i > $o )]: ( ![S:$i]: ( R @ S @ S ) ) )), 76.00/10.19 inference('simplify_rw_rule', [status(thm)], [mreflexive])). 76.00/10.19 thf('1', plain, 76.00/10.19 (( mreflexive ) = 76.00/10.19 ( ^[V_1:( $i > $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 @ X4 ) ) )), 76.00/10.19 define([status(thm)])).thf(a1, axiom, (mreflexive @ rel_s4)). 76.00/10.19 thf(zf_stmt_0, axiom, (![X4:$i]: ( rel_s4 @ X4 @ X4 ))). 76.00/10.19 thf(zip_derived_cl2, plain, ( (((!!) @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))), 76.00/10.19 inference('cnf', [status(esa)], [zf_stmt_0])). 76.00/10.19 thf(zip_derived_cl10, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 76.00/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 76.00/10.19 thf(mbox_s4, axiom,(( mbox_s4 ) = 76.00/10.19 (^[Phi:( $i > $o ),W:$i]: 76.00/10.19 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s4 @ W @ V ) ) ) )))). 76.00/10.19 thf('2', plain, 76.00/10.19 (( mbox_s4 ) = 76.00/10.19 ( ^[Phi:( $i > $o ),W:$i]: 76.00/10.19 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s4 @ W @ V ) ) ) ) )), 76.00/10.19 inference('simplify_rw_rule', [status(thm)], [mbox_s4])). 76.00/10.19 thf('3', plain, 76.00/10.19 (( mbox_s4 ) = 76.00/10.19 ( ^[V_1:( $i > $o ),V_2:$i]: 76.00/10.19 ( ![X4:$i]: ( ( V_1 @ X4 ) | ( ~( rel_s4 @ V_2 @ X4 ) ) ) ) )), 76.00/10.19 define([status(thm)])). 76.00/10.19 thf(mvalid, axiom,(( mvalid ) = 76.00/10.19 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 76.00/10.19 thf('4', plain, 76.00/10.19 (( mvalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 76.00/10.19 inference('simplify_rw_rule', [status(thm)], [mvalid])). 76.00/10.19 thf('5', plain, 76.00/10.19 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 76.00/10.19 define([status(thm)])). 76.00/10.19 thf(mexists_ind, axiom,(( mexists_ind ) = 76.00/10.19 (^[Phi:( mu > $i > $o )]: 76.00/10.19 ( mnot @ ( mforall_ind @ ( ^[X:mu]: ( mnot @ ( Phi @ X ) ) ) ) )))). 76.00/10.19 thf(mforall_ind, axiom,(( mforall_ind ) = 76.00/10.19 (^[Phi:( mu > $i > $o ),W:$i]: 76.00/10.19 ( ![X:mu]: ( ( exists_in_world @ X @ W ) => ( Phi @ X @ W ) ) )))). 76.00/10.19 thf('6', plain, 76.00/10.19 (( mforall_ind ) = 76.00/10.19 ( ^[Phi:( mu > $i > $o ),W:$i]: 76.00/10.19 ( ![X:mu]: ( ( exists_in_world @ X @ W ) => ( Phi @ X @ W ) ) ) )), 76.00/10.19 inference('simplify_rw_rule', [status(thm)], [mforall_ind])). 76.00/10.19 thf('7', plain, 76.00/10.19 (( mforall_ind ) = 76.00/10.19 ( ^[V_1:( mu > $i > $o ),V_2:$i]: 76.00/10.19 ( ![X4:mu]: ( ( exists_in_world @ X4 @ V_2 ) => ( V_1 @ X4 @ V_2 ) ) ) )), 76.00/10.19 define([status(thm)])). 76.00/10.19 thf(mnot, axiom,(( mnot ) = (^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) )))). 76.00/10.19 thf('8', plain, (( mnot ) = ( ^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) ) )), 76.00/10.19 inference('simplify_rw_rule', [status(thm)], [mnot])). 76.00/10.19 thf('9', plain, 76.00/10.19 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 76.00/10.19 define([status(thm)])). 76.00/10.19 thf('10', plain, 76.00/10.19 (( mexists_ind ) = 76.00/10.19 ( ^[Phi:( mu > $i > $o )]: 76.00/10.19 ( mnot @ ( mforall_ind @ ( ^[X:mu]: ( mnot @ ( Phi @ X ) ) ) ) ) )), 76.00/10.19 inference('simplify_rw_rule', [status(thm)], [mexists_ind, '7', '9'])). 76.00/10.19 thf('11', plain, 76.00/10.19 (( mexists_ind ) = 76.00/10.19 ( ^[V_1:( mu > $i > $o )]: 76.00/10.19 ( mnot @ ( mforall_ind @ ( ^[V_2:mu]: ( mnot @ ( V_1 @ V_2 ) ) ) ) ) )), 76.00/10.19 define([status(thm)])). 76.00/10.19 thf(mand, axiom,(( mand ) = 76.00/10.19 (^[Phi:( $i > $o ),Psi:( $i > $o )]: 76.00/10.19 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) )))). 76.00/10.19 thf(mor, axiom,(( mor ) = 76.00/10.19 (^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) )))). 76.00/10.19 thf('12', plain, 76.00/10.19 (( mor ) = 76.00/10.19 ( ^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) ) )), 76.00/10.19 inference('simplify_rw_rule', [status(thm)], [mor])). 76.00/10.19 thf('13', plain, 76.00/10.19 (( mor ) = 76.00/10.19 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 76.00/10.19 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 76.00/10.19 define([status(thm)])). 76.00/10.19 thf('14', plain, 76.00/10.19 (( mand ) = 76.00/10.19 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: 76.00/10.19 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) )), 76.00/10.19 inference('simplify_rw_rule', [status(thm)], [mand, '13', '9'])). 76.00/10.19 thf('15', plain, 76.00/10.19 (( mand ) = 76.00/10.19 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 76.00/10.19 ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) )), 76.00/10.19 define([status(thm)])). 76.00/10.19 thf(ax1, axiom, 76.00/10.19 (mvalid @ 76.00/10.19 ( mbox_s4 @ 76.00/10.19 ( mexists_ind @ 76.00/10.19 ( ^[I:mu]: 76.00/10.19 ( mbox_s4 @ ( mand @ ( userid @ u @ I ) @ ( string @ I ) ) ) ) ) ))). 76.00/10.19 thf(zf_stmt_1, axiom, 76.00/10.19 (![X4:$i,X6:$i]: 76.00/10.19 ( ( ~( rel_s4 @ X4 @ X6 ) ) | 76.00/10.19 ( ~( ![X8:mu]: 76.00/10.19 ( ( exists_in_world @ X8 @ X6 ) => 76.00/10.19 ( ~( ![X10:$i]: 76.00/10.19 ( ( ~( rel_s4 @ X6 @ X10 ) ) | 76.00/10.19 ( ~( ( ~( string @ X8 @ X10 ) ) | 76.00/10.19 ( ~( userid @ u @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) ))). 76.00/10.19 thf(zip_derived_cl6, plain, 76.00/10.19 ( (((!!) @ (^[Y0 : $i]: 76.00/10.19 (((!!) @ (^[Y1 : $i]: 76.00/10.19 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 76.00/10.19 (((~) @ (((!!) @ (^[Y2 : mu]: 76.00/10.19 (((exists_in_world @ 76.00/10.19 Y2 @ Y1) => 76.00/10.19 (((~) @ (((!!) @ ( 76.00/10.19 ^[Y3 : $i]: 76.00/10.19 (((( 76.00/10.19 (~) @ ( 76.00/10.19 rel_s4 @ 76.00/10.19 Y1 @ Y3))) | 76.00/10.19 (( 76.00/10.19 (~) @ ( 76.00/10.19 ( 76.00/10.19 (( 76.00/10.19 (~) @ ( 76.00/10.19 string @ 76.00/10.19 Y2 @ Y3))) | 76.00/10.19 (( 76.00/10.19 (~) @ ( 76.00/10.19 userid @ 76.00/10.19 u @ Y2 @ 76.00/10.19 Y3)))))))))))))))))))))))))))))), 76.00/10.19 inference('cnf', [status(esa)], [zf_stmt_1])). 76.00/10.19 thf(zip_derived_cl70, plain, 76.00/10.19 (![X2 : $i]: 76.00/10.19 (((!!) @ (^[Y0 : $i]: 76.00/10.19 (((((~) @ (rel_s4 @ X2 @ Y0))) | 76.00/10.19 (((~) @ (((!!) @ (^[Y1 : mu]: 76.00/10.19 (((exists_in_world @ Y1 @ Y0) => 76.00/10.19 (((~) @ (((!!) @ (^[Y2 : $i]: 76.00/10.19 (((((~) @ ( 76.00/10.19 rel_s4 @ 76.00/10.19 Y0 @ Y2))) | 76.00/10.19 (((~) @ ( 76.00/10.19 ( 76.00/10.19 (( 76.00/10.19 (~) @ ( 76.00/10.19 string @ 76.00/10.19 Y1 @ Y2))) | 76.00/10.19 (( 76.00/10.19 (~) @ ( 76.00/10.19 userid @ 76.00/10.19 u @ Y1 @ 76.00/10.19 Y2))))))))))))))))))))))))))), 76.00/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 76.00/10.19 thf(zip_derived_cl71, plain, 76.00/10.19 (![X2 : $i, X4 : $i]: 76.00/10.19 (((((~) @ (rel_s4 @ X2 @ X4))) | 76.00/10.19 (((~) @ (((!!) @ (^[Y0 : mu]: 76.00/10.19 (((exists_in_world @ Y0 @ X4) => 76.00/10.19 (((~) @ (((!!) @ (^[Y1 : $i]: 76.00/10.19 (((((~) @ (rel_s4 @ X4 @ 76.00/10.19 Y1))) | 76.00/10.19 (((~) @ (((((~) @ ( 76.00/10.19 string @ 76.00/10.19 Y0 @ Y1))) | 76.00/10.19 (((~) @ ( 76.00/10.19 userid @ 76.00/10.19 u @ Y0 @ Y1)))))))))))))))))))))))), 76.00/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])). 76.00/10.19 thf(zip_derived_cl72, plain, 76.00/10.19 (![X2 : $i, X4 : $i]: 76.00/10.19 (~ (rel_s4 @ X2 @ X4) 76.00/10.19 | ~ (((!!) @ (^[Y0 : mu]: 76.00/10.19 (((exists_in_world @ Y0 @ X4) => 76.00/10.19 (((~) @ (((!!) @ (^[Y1 : $i]: 76.00/10.19 (((((~) @ (rel_s4 @ X4 @ Y1))) | 76.00/10.19 (((~) @ (((((~) @ (string @ 76.00/10.19 Y0 @ Y1))) | 76.00/10.19 (((~) @ (userid @ 76.00/10.19 u @ Y0 @ 76.00/10.19 Y1))))))))))))))))))))), 76.00/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl71])). 76.00/10.19 thf(zip_derived_cl73, plain, 76.00/10.19 (![X2 : $i, X4 : $i]: 76.00/10.19 (~ (((exists_in_world @ ('#sk8' @ X4) @ X4) => 76.00/10.19 (((~) @ (((!!) @ (^[Y0 : $i]: 76.00/10.19 (((((~) @ (rel_s4 @ X4 @ Y0))) | 76.47/10.19 (((~) @ (((((~) @ (string @ 76.47/10.19 ('#sk8' @ X4) @ Y0))) | 76.47/10.19 (((~) @ (userid @ u @ 76.47/10.19 ('#sk8' @ X4) @ Y0)))))))))))))))) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4))), 76.47/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl72])). 76.47/10.19 thf(zip_derived_cl75, plain, 76.47/10.19 (![X2 : $i, X4 : $i]: 76.47/10.19 ( (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ X4 @ Y0))) | 76.47/10.19 (((~) @ (((((~) @ (string @ ('#sk8' @ X4) @ Y0))) | 76.47/10.19 (((~) @ (userid @ u @ ('#sk8' @ X4) @ Y0)))))))))))) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4))), 76.47/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 76.47/10.19 thf(zip_derived_cl76, plain, 76.47/10.19 (![X2 : $i, X4 : $i, X6 : $i]: 76.47/10.19 ( (((((~) @ (rel_s4 @ X4 @ X6))) | 76.47/10.19 (((~) @ (((((~) @ (string @ ('#sk8' @ X4) @ X6))) | 76.47/10.19 (((~) @ (userid @ u @ ('#sk8' @ X4) @ X6))))))))) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4))), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl75])). 76.47/10.19 thf(zip_derived_cl77, plain, 76.47/10.19 (![X2 : $i, X4 : $i, X6 : $i]: 76.47/10.19 (~ (rel_s4 @ X4 @ X6) 76.47/10.19 | ~ (((((~) @ (string @ ('#sk8' @ X4) @ X6))) | 76.47/10.19 (((~) @ (userid @ u @ ('#sk8' @ X4) @ X6))))) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4))), 76.47/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl76])). 76.47/10.19 thf(zip_derived_cl78, plain, 76.47/10.19 (![X2 : $i, X4 : $i, X6 : $i]: 76.47/10.19 ( (string @ ('#sk8' @ X4) @ X6) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4) 76.47/10.19 | ~ (rel_s4 @ X4 @ X6))), 76.47/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl77])). 76.47/10.19 thf(zip_derived_cl129, plain, 76.47/10.19 (![X0 : $i, X1 : $i]: 76.47/10.19 (~ (rel_s4 @ X0 @ X1) | (string @ ('#sk8' @ X0) @ X1))), 76.47/10.19 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl78])). 76.47/10.19 thf(ax2, axiom, 76.47/10.19 (mvalid @ 76.47/10.19 ( mexists_ind @ 76.47/10.19 ( ^[B:mu]: 76.47/10.19 ( mbox_s4 @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) ))). 76.47/10.19 thf(zf_stmt_2, axiom, 76.47/10.19 (![X4:$i]: 76.47/10.19 ( ~( ![X6:mu]: 76.47/10.19 ( ( exists_in_world @ X6 @ X4 ) => 76.47/10.19 ( ~( ![X8:$i]: 76.47/10.19 ( ( ~( rel_s4 @ X4 @ X8 ) ) | 76.47/10.19 ( ~( ( ~( number @ X6 @ one @ X8 ) ) | 76.47/10.19 ( ~( entry_box @ X6 @ X8 ) ) ) ) ) ) ) ) ) ))). 76.47/10.19 thf(zip_derived_cl7, plain, 76.47/10.19 ( (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((~) @ (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ Y0) => 76.47/10.19 (((~) @ (((!!) @ (^[Y2 : $i]: 76.47/10.19 (((((~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 Y0 @ Y2))) | 76.47/10.19 (((~) @ ( 76.47/10.19 ((((~) @ ( 76.47/10.19 number @ 76.47/10.19 Y1 @ 76.47/10.19 one @ Y2))) | 76.47/10.19 (((~) @ ( 76.47/10.19 entry_box @ 76.47/10.19 Y1 @ Y2))))))))))))))))))))))))), 76.47/10.19 inference('cnf', [status(esa)], [zf_stmt_2])). 76.47/10.19 thf(zip_derived_cl25, plain, 76.47/10.19 (![X2 : $i]: 76.47/10.19 ~ (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ X2) => 76.47/10.19 (((~) @ (((!!) @ (^[Y1 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ X2 @ Y1))) | 76.47/10.19 (((~) @ (((((~) @ (number @ 76.47/10.19 Y0 @ one @ Y1))) | 76.47/10.19 (((~) @ (entry_box @ 76.47/10.19 Y0 @ Y1)))))))))))))))))))), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 76.47/10.19 thf(zip_derived_cl26, plain, 76.47/10.19 (![X2 : $i]: 76.47/10.19 ~ (((exists_in_world @ ('#sk2' @ X2) @ X2) => 76.47/10.19 (((~) @ (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ X2 @ Y0))) | 76.47/10.19 (((~) @ (((((~) @ (number @ ('#sk2' @ X2) @ 76.47/10.19 one @ Y0))) | 76.47/10.19 (((~) @ (entry_box @ 76.47/10.19 ('#sk2' @ X2) @ Y0))))))))))))))))), 76.47/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl25])). 76.47/10.19 thf(zip_derived_cl28, plain, 76.47/10.19 (![X2 : $i]: 76.47/10.19 (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ X2 @ Y0))) | 76.47/10.19 (((~) @ (((((~) @ (number @ ('#sk2' @ X2) @ one @ Y0))) | 76.47/10.19 (((~) @ (entry_box @ ('#sk2' @ X2) @ Y0))))))))))))), 76.47/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 76.47/10.19 thf(zip_derived_cl29, plain, 76.47/10.19 (![X2 : $i, X4 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ X2 @ X4))) | 76.47/10.19 (((~) @ (((((~) @ (number @ ('#sk2' @ X2) @ one @ X4))) | 76.47/10.19 (((~) @ (entry_box @ ('#sk2' @ X2) @ X4)))))))))), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 76.47/10.19 thf(zip_derived_cl30, plain, 76.47/10.19 (![X2 : $i, X4 : $i]: 76.47/10.19 (~ (rel_s4 @ X2 @ X4) 76.47/10.19 | ~ (((((~) @ (number @ ('#sk2' @ X2) @ one @ X4))) | 76.47/10.19 (((~) @ (entry_box @ ('#sk2' @ X2) @ X4))))))), 76.47/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 76.47/10.19 thf(zip_derived_cl32, plain, 76.47/10.19 (![X2 : $i, X4 : $i]: 76.47/10.19 ( (entry_box @ ('#sk2' @ X2) @ X4) | ~ (rel_s4 @ X2 @ X4))), 76.47/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 76.47/10.19 thf(zip_derived_cl32, plain, 76.47/10.19 (![X2 : $i, X4 : $i]: 76.47/10.19 ( (entry_box @ ('#sk2' @ X2) @ X4) | ~ (rel_s4 @ X2 @ X4))), 76.47/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 76.47/10.19 thf(zip_derived_cl10, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 76.47/10.19 thf(mimplies, axiom,(( mimplies ) = 76.47/10.19 (^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi )))). 76.47/10.19 thf('16', plain, 76.47/10.19 (( mimplies ) = 76.47/10.19 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi ) )), 76.47/10.19 inference('simplify_rw_rule', [status(thm)], [mimplies, '13', '9'])). 76.47/10.19 thf('17', plain, 76.47/10.19 (( mimplies ) = 76.47/10.19 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 76.47/10.19 define([status(thm)])). 76.47/10.19 thf(ax3, axiom, 76.47/10.19 (mvalid @ 76.47/10.19 ( mbox_s4 @ 76.47/10.19 ( mforall_ind @ 76.47/10.19 ( ^[S:mu]: 76.47/10.19 ( mforall_ind @ 76.47/10.19 ( ^[I:mu]: 76.47/10.19 ( mforall_ind @ 76.47/10.19 ( ^[B:mu]: 76.47/10.19 ( mimplies @ 76.47/10.19 ( mand @ ( string @ I ) @ ( entry_box @ B ) ) @ 76.47/10.19 ( mexists_ind @ 76.47/10.19 ( ^[A:mu]: 76.47/10.19 ( mbox_s4 @ 76.47/10.19 ( mforall_ind @ 76.47/10.19 ( ^[S2:mu]: 76.47/10.19 ( mimplies @ 76.47/10.19 ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 76.47/10.19 thf(zf_stmt_3, axiom, 76.47/10.19 (![X4:$i,X6:$i]: 76.47/10.19 ( ( ~( rel_s4 @ X4 @ X6 ) ) | 76.47/10.19 ( ![X8:mu]: 76.47/10.19 ( ( exists_in_world @ X8 @ X6 ) => 76.47/10.19 ( ![X10:mu]: 76.47/10.19 ( ( exists_in_world @ X10 @ X6 ) => 76.47/10.19 ( ![X12:mu]: 76.47/10.19 ( ( exists_in_world @ X12 @ X6 ) => 76.47/10.19 ( ( ~( ![X14:mu]: 76.47/10.19 ( ( exists_in_world @ X14 @ X6 ) => 76.47/10.19 ( ~( ![X16:$i]: 76.47/10.19 ( ( ~( rel_s4 @ X6 @ X16 ) ) | 76.47/10.19 ( ![X18:mu]: 76.47/10.19 ( ( exists_in_world @ X18 @ X16 ) => 76.47/10.19 ( ( in @ X10 @ X12 @ X18 @ X16 ) | 76.47/10.19 ( ~( do @ X8 @ X14 @ X18 @ X16 ) ) ) ) ) ) ) ) ) ) ) | 76.47/10.19 ( ~( string @ X10 @ X6 ) ) | ( ~( entry_box @ X12 @ X6 ) ) ) ) ) ) ) ) ) ))). 76.47/10.19 thf(zip_derived_cl9, plain, 76.47/10.19 ( (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((!!) @ (^[Y1 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ Y2 @ Y1) => 76.47/10.19 (((!!) @ (^[Y3 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y3 @ Y1) => 76.47/10.19 (((!!) @ ( 76.47/10.19 ^[Y4 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y4 @ Y1) => 76.47/10.19 ((( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y5 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y5 @ 76.47/10.19 Y1) => 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y6 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 Y1 @ Y6))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y7 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y7 @ 76.47/10.19 Y6) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 Y3 @ 76.47/10.19 Y4 @ 76.47/10.19 Y7 @ 76.47/10.19 Y6) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 Y2 @ 76.47/10.19 Y5 @ 76.47/10.19 Y7 @ Y6)))))))))))))))))))))))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 string @ 76.47/10.19 Y3 @ Y1))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 entry_box @ 76.47/10.19 Y4 @ Y1))))))))))))))))))))))))))))), 76.47/10.19 inference('cnf', [status(esa)], [zf_stmt_3])). 76.47/10.19 thf(zip_derived_cl80, plain, 76.47/10.19 (![X2 : $i]: 76.47/10.19 (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ X2 @ Y0))) | 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ Y0) => 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ Y2 @ 76.47/10.19 Y0) => 76.47/10.19 (((!!) @ (^[Y3 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y3 @ Y0) => 76.47/10.19 (((((~) @ ( 76.47/10.19 ( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y4 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y4 @ 76.47/10.19 Y0) => 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y5 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 Y0 @ Y5))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y6 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y6 @ 76.47/10.19 Y5) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 Y2 @ 76.47/10.19 Y3 @ 76.47/10.19 Y6 @ 76.47/10.19 Y5) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 Y1 @ 76.47/10.19 Y4 @ 76.47/10.19 Y6 @ Y5)))))))))))))))))))))))) | 76.47/10.19 (((~) @ ( 76.47/10.19 string @ 76.47/10.19 Y2 @ Y0))) | 76.47/10.19 (((~) @ ( 76.47/10.19 entry_box @ 76.47/10.19 Y3 @ Y0)))))))))))))))))))))))))), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])). 76.47/10.19 thf(zip_derived_cl81, plain, 76.47/10.19 (![X2 : $i, X4 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ X2 @ X4))) | 76.47/10.19 (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ X4) => 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ X4) => 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ Y2 @ 76.47/10.19 X4) => 76.47/10.19 (((((~) @ (((!!) @ ( 76.47/10.19 ^[Y3 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y3 @ 76.47/10.19 X4) => 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y4 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 X4 @ Y4))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y5 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y5 @ 76.47/10.19 Y4) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 Y1 @ 76.47/10.19 Y2 @ 76.47/10.19 Y5 @ 76.47/10.19 Y4) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 Y0 @ 76.47/10.19 Y3 @ 76.47/10.19 Y5 @ Y4)))))))))))))))))))))))) | 76.47/10.19 (((~) @ (string @ Y1 @ 76.47/10.19 X4))) | 76.47/10.19 (((~) @ (entry_box @ 76.47/10.19 Y2 @ X4))))))))))))))))))))))), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl80])). 76.47/10.19 thf(zip_derived_cl82, plain, 76.47/10.19 (![X2 : $i, X4 : $i]: 76.47/10.19 (~ (rel_s4 @ X2 @ X4) 76.47/10.19 | (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ X4) => 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ X4) => 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ Y2 @ 76.47/10.19 X4) => 76.47/10.19 (((((~) @ (((!!) @ ( 76.47/10.19 ^[Y3 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y3 @ 76.47/10.19 X4) => 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y4 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 X4 @ Y4))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y5 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y5 @ 76.47/10.19 Y4) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 Y1 @ 76.47/10.19 Y2 @ 76.47/10.19 Y5 @ 76.47/10.19 Y4) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 Y0 @ 76.47/10.19 Y3 @ 76.47/10.19 Y5 @ Y4)))))))))))))))))))))))) | 76.47/10.19 (((~) @ (string @ 76.47/10.19 Y1 @ X4))) | 76.47/10.19 (((~) @ (entry_box @ 76.47/10.19 Y2 @ X4)))))))))))))))))))))), 76.47/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl81])). 76.47/10.19 thf(zip_derived_cl83, plain, 76.47/10.19 (![X2 : $i, X4 : $i, X6 : mu]: 76.47/10.19 ( (((exists_in_world @ X6 @ X4) => 76.47/10.19 (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ X4) => 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ X4) => 76.47/10.19 (((((~) @ (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y2 @ X4) => 76.47/10.19 (((~) @ ( 76.47/10.19 ((!!) @ ( 76.47/10.19 ^[Y3 : $i]: 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 X4 @ Y3))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y4 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y4 @ 76.47/10.19 Y3) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 Y0 @ 76.47/10.19 Y1 @ 76.47/10.19 Y4 @ 76.47/10.19 Y3) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 X6 @ 76.47/10.19 Y2 @ 76.47/10.19 Y4 @ Y3)))))))))))))))))))))))) | 76.47/10.19 (((~) @ (string @ Y0 @ X4))) | 76.47/10.19 (((~) @ (entry_box @ Y1 @ X4))))))))))))))))) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4))), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl82])). 76.47/10.19 thf(zip_derived_cl84, plain, 76.47/10.19 (![X2 : $i, X4 : $i, X6 : mu]: 76.47/10.19 (~ (exists_in_world @ X6 @ X4) 76.47/10.19 | (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ X4) => 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ X4) => 76.47/10.19 (((((~) @ (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y2 @ X4) => 76.47/10.19 (((~) @ ( 76.47/10.19 ((!!) @ ( 76.47/10.19 ^[Y3 : $i]: 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 X4 @ Y3))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y4 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y4 @ 76.47/10.19 Y3) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 Y0 @ 76.47/10.19 Y1 @ 76.47/10.19 Y4 @ 76.47/10.19 Y3) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 X6 @ 76.47/10.19 Y2 @ 76.47/10.19 Y4 @ Y3)))))))))))))))))))))))) | 76.47/10.19 (((~) @ (string @ Y0 @ X4))) | 76.47/10.19 (((~) @ (entry_box @ Y1 @ X4))))))))))))))) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4))), 76.47/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl83])). 76.47/10.19 thf(zip_derived_cl85, plain, 76.47/10.19 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu]: 76.47/10.19 ( (((exists_in_world @ X8 @ X4) => 76.47/10.19 (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ X4) => 76.47/10.19 (((((~) @ (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ 76.47/10.19 X4) => 76.47/10.19 (((~) @ (((!!) @ (^[Y2 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 X4 @ Y2))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y3 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y3 @ 76.47/10.19 Y2) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 X8 @ 76.47/10.19 Y0 @ 76.47/10.19 Y3 @ 76.47/10.19 Y2) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 X6 @ 76.47/10.19 Y1 @ 76.47/10.19 Y3 @ Y2)))))))))))))))))))))))) | 76.47/10.19 (((~) @ (string @ X8 @ X4))) | 76.47/10.19 (((~) @ (entry_box @ Y0 @ X4)))))))))))) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4) 76.47/10.19 | ~ (exists_in_world @ X6 @ X4))), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl84])). 76.47/10.19 thf(zip_derived_cl86, plain, 76.47/10.19 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu]: 76.47/10.19 (~ (exists_in_world @ X8 @ X4) 76.47/10.19 | (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ X4) => 76.47/10.19 (((((~) @ (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ 76.47/10.19 X4) => 76.47/10.19 (((~) @ (((!!) @ (^[Y2 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 X4 @ Y2))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y3 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y3 @ 76.47/10.19 Y2) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 X8 @ 76.47/10.19 Y0 @ 76.47/10.19 Y3 @ 76.47/10.19 Y2) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 X6 @ 76.47/10.19 Y1 @ 76.47/10.19 Y3 @ Y2)))))))))))))))))))))))) | 76.47/10.19 (((~) @ (string @ X8 @ X4))) | 76.47/10.19 (((~) @ (entry_box @ Y0 @ X4)))))))))) 76.47/10.19 | ~ (exists_in_world @ X6 @ X4) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4))), 76.47/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])). 76.47/10.19 thf(zip_derived_cl87, plain, 76.47/10.19 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu, X10 : mu]: 76.47/10.19 ( (((exists_in_world @ X10 @ X4) => 76.47/10.19 (((((~) @ (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ X4) => 76.47/10.19 (((~) @ (((!!) @ (^[Y1 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ 76.47/10.19 X4 @ Y1))) | 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y2 @ 76.47/10.19 Y1) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 X8 @ 76.47/10.19 X10 @ 76.47/10.19 Y2 @ 76.47/10.19 Y1) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 X6 @ 76.47/10.19 Y0 @ 76.47/10.19 Y2 @ Y1)))))))))))))))))))))))) | 76.47/10.19 (((~) @ (string @ X8 @ X4))) | (((~) @ (entry_box @ X10 @ X4))))))) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4) 76.47/10.19 | ~ (exists_in_world @ X6 @ X4) 76.47/10.19 | ~ (exists_in_world @ X8 @ X4))), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])). 76.47/10.19 thf(zip_derived_cl88, plain, 76.47/10.19 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu, X10 : mu]: 76.47/10.19 (~ (exists_in_world @ X10 @ X4) 76.47/10.19 | (((((~) @ (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ X4) => 76.47/10.19 (((~) @ (((!!) @ (^[Y1 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ 76.47/10.19 X4 @ Y1))) | 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y2 @ 76.47/10.19 Y1) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 X8 @ 76.47/10.19 X10 @ 76.47/10.19 Y2 @ 76.47/10.19 Y1) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 X6 @ 76.47/10.19 Y0 @ 76.47/10.19 Y2 @ Y1)))))))))))))))))))))))) | 76.47/10.19 (((~) @ (string @ X8 @ X4))) | (((~) @ (entry_box @ X10 @ X4))))) 76.47/10.19 | ~ (exists_in_world @ X8 @ X4) 76.47/10.19 | ~ (exists_in_world @ X6 @ X4) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4))), 76.47/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 76.47/10.19 thf(zip_derived_cl89, plain, 76.47/10.19 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu, X10 : mu]: 76.47/10.19 (~ (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ X4) => 76.47/10.19 (((~) @ (((!!) @ (^[Y1 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ X4 @ Y1))) | 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y2 @ Y1) => 76.47/10.19 (((in @ X8 @ 76.47/10.19 X10 @ Y2 @ 76.47/10.19 Y1) | 76.47/10.19 (((~) @ ( 76.47/10.19 do @ X6 @ 76.47/10.19 Y0 @ Y2 @ Y1)))))))))))))))))))))) 76.47/10.19 | ~ (string @ X8 @ X4) 76.47/10.19 | ~ (entry_box @ X10 @ X4) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4) 76.47/10.19 | ~ (exists_in_world @ X6 @ X4) 76.47/10.19 | ~ (exists_in_world @ X8 @ X4) 76.47/10.19 | ~ (exists_in_world @ X10 @ X4))), 76.47/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl88])). 76.47/10.19 thf(zip_derived_cl90, plain, 76.47/10.19 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu, X10 : mu]: 76.47/10.19 (~ (((exists_in_world @ ('#sk9' @ X4 @ X6 @ X8 @ X10) @ X4) => 76.47/10.19 (((~) @ (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ X4 @ Y0))) | 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ 76.47/10.19 Y0) => 76.47/10.19 (((in @ X8 @ X10 @ Y1 @ Y0) | 76.47/10.19 (((~) @ (do @ X6 @ 76.47/10.19 ('#sk9' @ X4 @ 76.47/10.19 X6 @ X8 @ X10) @ 76.47/10.19 Y1 @ Y0))))))))))))))))))) 76.47/10.19 | ~ (exists_in_world @ X10 @ X4) 76.47/10.19 | ~ (exists_in_world @ X8 @ X4) 76.47/10.19 | ~ (exists_in_world @ X6 @ X4) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4) 76.47/10.19 | ~ (entry_box @ X10 @ X4) 76.47/10.19 | ~ (string @ X8 @ X4))), 76.47/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl89])). 76.47/10.19 thf(zip_derived_cl91, plain, 76.47/10.19 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu, X10 : mu]: 76.47/10.19 ( (exists_in_world @ ('#sk9' @ X4 @ X6 @ X8 @ X10) @ X4) 76.47/10.19 | ~ (string @ X8 @ X4) 76.47/10.19 | ~ (entry_box @ X10 @ X4) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4) 76.47/10.19 | ~ (exists_in_world @ X6 @ X4) 76.47/10.19 | ~ (exists_in_world @ X8 @ X4) 76.47/10.19 | ~ (exists_in_world @ X10 @ X4))), 76.47/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl90])). 76.47/10.19 thf(zip_derived_cl137, plain, 76.47/10.19 (![X0 : $i, X1 : mu, X2 : mu, X3 : mu]: 76.47/10.19 (~ (exists_in_world @ X1 @ X0) 76.47/10.19 | ~ (exists_in_world @ X2 @ X0) 76.47/10.19 | ~ (exists_in_world @ X3 @ X0) 76.47/10.19 | ~ (entry_box @ X1 @ X0) 76.47/10.19 | ~ (string @ X2 @ X0) 76.47/10.19 | (exists_in_world @ ('#sk9' @ X0 @ X3 @ X2 @ X1) @ X0))), 76.47/10.19 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl91])). 76.47/10.19 thf(zip_derived_cl31, plain, 76.47/10.19 (![X2 : $i, X4 : $i]: 76.47/10.19 ( (number @ ('#sk2' @ X2) @ one @ X4) | ~ (rel_s4 @ X2 @ X4))), 76.47/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 76.47/10.19 thf(zip_derived_cl10, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 76.47/10.19 thf(zip_derived_cl79, plain, 76.47/10.19 (![X2 : $i, X4 : $i, X6 : $i]: 76.47/10.19 ( (userid @ u @ ('#sk8' @ X4) @ X6) 76.47/10.19 | ~ (rel_s4 @ X2 @ X4) 76.47/10.19 | ~ (rel_s4 @ X4 @ X6))), 76.47/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl77])). 76.47/10.19 thf(zip_derived_cl133, plain, 76.47/10.19 (![X0 : $i, X1 : $i]: 76.47/10.19 (~ (rel_s4 @ X0 @ X1) | (userid @ u @ ('#sk8' @ X0) @ X1))), 76.47/10.19 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl79])). 76.47/10.19 thf(con, conjecture, 76.47/10.19 (mvalid @ 76.47/10.19 ( mbox_s4 @ 76.47/10.19 ( mexists_ind @ 76.47/10.19 ( ^[I:mu]: 76.47/10.19 ( mexists_ind @ 76.47/10.19 ( ^[B:mu]: 76.47/10.19 ( mexists_ind @ 76.47/10.19 ( ^[A:mu]: 76.47/10.19 ( mexists_ind @ 76.47/10.19 ( ^[S:mu]: 76.47/10.19 ( mand @ 76.47/10.19 ( mbox_s4 @ 76.47/10.19 ( mand @ 76.47/10.19 ( userid @ u @ I ) @ 76.47/10.19 ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) @ 76.47/10.19 ( mbox_s4 @ 76.47/10.19 ( mforall_ind @ 76.47/10.19 ( ^[S2:mu]: 76.47/10.19 ( mimplies @ 76.47/10.19 ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 76.47/10.19 thf(zf_stmt_4, conjecture, 76.47/10.19 (![X4:$i,X6:$i]: 76.47/10.19 ( ( ~( rel_s4 @ X4 @ X6 ) ) | 76.47/10.19 ( ~( ![X8:mu]: 76.47/10.19 ( ( exists_in_world @ X8 @ X6 ) => 76.47/10.19 ( ![X10:mu]: 76.47/10.19 ( ( exists_in_world @ X10 @ X6 ) => 76.47/10.19 ( ![X12:mu]: 76.47/10.19 ( ( exists_in_world @ X12 @ X6 ) => 76.47/10.19 ( ![X14:mu]: 76.47/10.19 ( ( exists_in_world @ X14 @ X6 ) => 76.47/10.19 ( ( ~( ![X18:$i]: 76.47/10.19 ( ( ~( rel_s4 @ X6 @ X18 ) ) | 76.47/10.19 ( ![X20:mu]: 76.47/10.19 ( ( exists_in_world @ X20 @ X18 ) => 76.47/10.19 ( ( in @ X8 @ X10 @ X20 @ X18 ) | 76.47/10.19 ( ~( do @ X14 @ X12 @ X20 @ X18 ) ) ) ) ) ) ) ) | 76.47/10.19 ( ~( ![X16:$i]: 76.47/10.19 ( ( ~( rel_s4 @ X6 @ X16 ) ) | 76.47/10.19 ( ~( ( ~( entry_box @ X10 @ X16 ) ) | 76.47/10.19 ( ~( number @ X10 @ one @ X16 ) ) | 76.47/10.19 ( ~( userid @ u @ X8 @ X16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 76.47/10.19 thf(zf_stmt_5, negated_conjecture, 76.47/10.19 (~( ![X4:$i,X6:$i]: 76.47/10.19 ( ( ~( rel_s4 @ X4 @ X6 ) ) | 76.47/10.19 ( ~( ![X8:mu]: 76.47/10.19 ( ( exists_in_world @ X8 @ X6 ) => 76.47/10.19 ( ![X10:mu]: 76.47/10.19 ( ( exists_in_world @ X10 @ X6 ) => 76.47/10.19 ( ![X12:mu]: 76.47/10.19 ( ( exists_in_world @ X12 @ X6 ) => 76.47/10.19 ( ![X14:mu]: 76.47/10.19 ( ( exists_in_world @ X14 @ X6 ) => 76.47/10.19 ( ( ~( ![X18:$i]: 76.47/10.19 ( ( ~( rel_s4 @ X6 @ X18 ) ) | 76.47/10.19 ( ![X20:mu]: 76.47/10.19 ( ( exists_in_world @ X20 @ X18 ) => 76.47/10.19 ( ( in @ X8 @ X10 @ X20 @ X18 ) | 76.47/10.19 ( ~( do @ X14 @ X12 @ X20 @ X18 ) ) ) ) ) ) ) ) | 76.47/10.19 ( ~( ![X16:$i]: 76.47/10.19 ( ( ~( rel_s4 @ X6 @ X16 ) ) | 76.47/10.19 ( ~( ( ~( entry_box @ X10 @ X16 ) ) | 76.47/10.19 ( ~( number @ X10 @ one @ X16 ) ) | 76.47/10.19 ( ~( userid @ u @ X8 @ X16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 76.47/10.19 inference('cnf.neg', [status(esa)], [zf_stmt_4])). 76.47/10.19 thf(zip_derived_cl5, plain, 76.47/10.19 (~ (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((!!) @ (^[Y1 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 76.47/10.19 (((~) @ (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y2 @ Y1) => 76.47/10.19 (((!!) @ (^[Y3 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y3 @ 76.47/10.19 Y1) => 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y4 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y4 @ 76.47/10.19 Y1) => 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y5 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y5 @ 76.47/10.19 Y1) => 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y6 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 Y1 @ Y6))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y7 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y7 @ 76.47/10.19 Y6) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 Y2 @ 76.47/10.19 Y3 @ 76.47/10.19 Y7 @ 76.47/10.19 Y6) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 Y5 @ 76.47/10.19 Y4 @ 76.47/10.19 Y7 @ Y6))))))))))))))))) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y6 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 Y1 @ Y6))) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 entry_box @ 76.47/10.19 Y3 @ Y6))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 number @ 76.47/10.19 Y3 @ 76.47/10.19 one @ Y6))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 userid @ 76.47/10.19 u @ Y2 @ 76.47/10.19 Y6))))))))))))))))))))))))))))))))))))))))))))))), 76.47/10.19 inference('cnf', [status(esa)], [zf_stmt_5])). 76.47/10.19 thf(zip_derived_cl33, plain, 76.47/10.19 (~ (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ '#sk3' @ Y0))) | 76.47/10.19 (((~) @ (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ Y0) => 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y2 @ Y0) => 76.47/10.19 (((!!) @ (^[Y3 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y3 @ 76.47/10.19 Y0) => 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y4 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y4 @ 76.47/10.19 Y0) => 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y5 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 Y0 @ Y5))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y6 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y6 @ 76.47/10.19 Y5) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 Y1 @ 76.47/10.19 Y2 @ 76.47/10.19 Y6 @ 76.47/10.19 Y5) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 Y4 @ 76.47/10.19 Y3 @ 76.47/10.19 Y6 @ Y5))))))))))))))))) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y5 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 Y0 @ Y5))) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 entry_box @ 76.47/10.19 Y2 @ Y5))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 number @ 76.47/10.19 Y2 @ 76.47/10.19 one @ Y5))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 userid @ 76.47/10.19 u @ Y1 @ 76.47/10.19 Y5)))))))))))))))))))))))))))))))))))))))))))), 76.47/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5])). 76.47/10.19 thf(zip_derived_cl34, plain, 76.47/10.19 (~ (((((~) @ (rel_s4 @ '#sk3' @ '#sk4'))) | 76.47/10.19 (((~) @ (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ '#sk4') => 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ 76.47/10.19 '#sk4') => 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y2 @ '#sk4') => 76.47/10.19 (((!!) @ ( 76.47/10.19 ^[Y3 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y3 @ 76.47/10.19 '#sk4') => 76.47/10.19 (((( 76.47/10.19 (~) @ ( 76.47/10.19 ((!!) @ ( 76.47/10.19 ^[Y4 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 '#sk4' @ 76.47/10.19 Y4))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y5 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y5 @ 76.47/10.19 Y4) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 Y0 @ 76.47/10.19 Y1 @ 76.47/10.19 Y5 @ 76.47/10.19 Y4) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 Y3 @ 76.47/10.19 Y2 @ 76.47/10.19 Y5 @ Y4))))))))))))))))) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ((!!) @ ( 76.47/10.19 ^[Y4 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 '#sk4' @ 76.47/10.19 Y4))) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 entry_box @ 76.47/10.19 Y1 @ Y4))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 number @ 76.47/10.19 Y1 @ 76.47/10.19 one @ Y4))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 userid @ 76.47/10.19 u @ Y0 @ 76.47/10.19 Y4))))))))))))))))))))))))))))))))))))))))), 76.47/10.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl33])). 76.47/10.19 thf(zip_derived_cl36, plain, 76.47/10.19 ( (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ '#sk4') => 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ '#sk4') => 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ Y2 @ 76.47/10.19 '#sk4') => 76.47/10.19 (((!!) @ (^[Y3 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y3 @ '#sk4') => 76.47/10.19 (((((~) @ ( 76.47/10.19 ((!!) @ ( 76.47/10.19 ^[Y4 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 '#sk4' @ 76.47/10.19 Y4))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y5 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y5 @ 76.47/10.19 Y4) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 Y0 @ 76.47/10.19 Y1 @ 76.47/10.19 Y5 @ 76.47/10.19 Y4) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 Y3 @ 76.47/10.19 Y2 @ 76.47/10.19 Y5 @ Y4))))))))))))))))) | 76.47/10.19 (((~) @ ( 76.47/10.19 ((!!) @ ( 76.47/10.19 ^[Y4 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 '#sk4' @ 76.47/10.19 Y4))) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 entry_box @ 76.47/10.19 Y1 @ Y4))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 number @ 76.47/10.19 Y1 @ 76.47/10.19 one @ Y4))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 userid @ 76.47/10.19 u @ Y0 @ 76.47/10.19 Y4))))))))))))))))))))))))))))))))))))), 76.47/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 76.47/10.19 thf(zip_derived_cl37, plain, 76.47/10.19 (![X2 : mu]: 76.47/10.19 (((exists_in_world @ X2 @ '#sk4') => 76.47/10.19 (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ '#sk4') => 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ '#sk4') => 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ Y2 @ 76.47/10.19 '#sk4') => 76.47/10.19 (((((~) @ (((!!) @ ( 76.47/10.19 ^[Y3 : $i]: 76.47/10.19 (((( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 '#sk4' @ 76.47/10.19 Y3))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y4 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y4 @ 76.47/10.19 Y3) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 X2 @ 76.47/10.19 Y0 @ 76.47/10.19 Y4 @ 76.47/10.19 Y3) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 Y2 @ 76.47/10.19 Y1 @ 76.47/10.19 Y4 @ Y3))))))))))))))))) | 76.47/10.19 (((~) @ (((!!) @ ( 76.47/10.19 ^[Y3 : $i]: 76.47/10.19 (((( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 '#sk4' @ 76.47/10.19 Y3))) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 entry_box @ 76.47/10.19 Y0 @ Y3))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 number @ 76.47/10.19 Y0 @ 76.47/10.19 one @ Y3))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 userid @ 76.47/10.19 u @ X2 @ 76.47/10.19 Y3)))))))))))))))))))))))))))))))))), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl36])). 76.47/10.19 thf(zip_derived_cl38, plain, 76.47/10.19 (![X2 : mu]: 76.47/10.19 (~ (exists_in_world @ X2 @ '#sk4') 76.47/10.19 | (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ '#sk4') => 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ '#sk4') => 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ Y2 @ 76.47/10.19 '#sk4') => 76.47/10.19 (((((~) @ (((!!) @ ( 76.47/10.19 ^[Y3 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 '#sk4' @ 76.47/10.19 Y3))) | 76.47/10.19 (( 76.47/10.19 (!!) @ ( 76.47/10.19 ^[Y4 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y4 @ 76.47/10.19 Y3) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 X2 @ 76.47/10.19 Y0 @ 76.47/10.19 Y4 @ 76.47/10.19 Y3) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 Y2 @ 76.47/10.19 Y1 @ 76.47/10.19 Y4 @ Y3))))))))))))))))) | 76.47/10.19 (((~) @ (((!!) @ ( 76.47/10.19 ^[Y3 : $i]: 76.47/10.19 (( 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 '#sk4' @ 76.47/10.19 Y3))) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 entry_box @ 76.47/10.19 Y0 @ Y3))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 number @ 76.47/10.19 Y0 @ 76.47/10.19 one @ Y3))) | 76.47/10.19 ( 76.47/10.19 ( 76.47/10.19 (~) @ ( 76.47/10.19 userid @ 76.47/10.19 u @ X2 @ 76.47/10.19 Y3))))))))))))))))))))))))))))))))), 76.47/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 76.47/10.19 thf(zip_derived_cl39, plain, 76.47/10.19 (![X2 : mu, X4 : mu]: 76.47/10.19 ( (((exists_in_world @ X4 @ '#sk4') => 76.47/10.19 (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ '#sk4') => 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ '#sk4') => 76.47/10.19 (((((~) @ (((!!) @ (^[Y2 : $i]: 76.47/10.19 (((((~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 '#sk4' @ Y2))) | 76.47/10.19 (((!!) @ ( 76.47/10.19 ^[Y3 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y3 @ 76.47/10.19 Y2) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 X2 @ 76.47/10.19 X4 @ 76.47/10.19 Y3 @ 76.47/10.19 Y2) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 Y1 @ 76.47/10.19 Y0 @ 76.47/10.19 Y3 @ Y2))))))))))))))))) | 76.47/10.19 (((~) @ (((!!) @ (^[Y2 : $i]: 76.47/10.19 (((((~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 '#sk4' @ Y2))) | 76.47/10.19 (((~) @ ( 76.47/10.19 ((((~) @ ( 76.47/10.19 entry_box @ 76.47/10.19 X4 @ Y2))) | 76.47/10.19 (((~) @ ( 76.47/10.19 number @ 76.47/10.19 X4 @ 76.47/10.19 one @ Y2))) | 76.47/10.19 (((~) @ ( 76.47/10.19 userid @ 76.47/10.19 u @ X2 @ 76.47/10.19 Y2)))))))))))))))))))))))))))) 76.47/10.19 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 76.47/10.19 thf(zip_derived_cl40, plain, 76.47/10.19 (![X2 : mu, X4 : mu]: 76.47/10.19 (~ (exists_in_world @ X4 @ '#sk4') 76.47/10.19 | (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ '#sk4') => 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ '#sk4') => 76.47/10.19 (((((~) @ (((!!) @ (^[Y2 : $i]: 76.47/10.19 (((((~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 '#sk4' @ Y2))) | 76.47/10.19 (((!!) @ ( 76.47/10.19 ^[Y3 : mu]: 76.47/10.19 (( 76.47/10.19 (exists_in_world @ 76.47/10.19 Y3 @ 76.47/10.19 Y2) => 76.47/10.19 (( 76.47/10.19 (in @ 76.47/10.19 X2 @ 76.47/10.19 X4 @ 76.47/10.19 Y3 @ 76.47/10.19 Y2) | 76.47/10.19 (( 76.47/10.19 (~) @ ( 76.47/10.19 do @ 76.47/10.19 Y1 @ 76.47/10.19 Y0 @ 76.47/10.19 Y3 @ Y2))))))))))))))))) | 76.47/10.19 (((~) @ (((!!) @ (^[Y2 : $i]: 76.47/10.19 (((((~) @ ( 76.47/10.19 rel_s4 @ 76.47/10.19 '#sk4' @ Y2))) | 76.47/10.19 (((~) @ ( 76.47/10.19 ((((~) @ ( 76.47/10.19 entry_box @ 76.47/10.19 X4 @ Y2))) | 76.47/10.19 (((~) @ ( 76.47/10.19 number @ 76.47/10.19 X4 @ 76.47/10.19 one @ Y2))) | 76.47/10.19 (((~) @ ( 76.47/10.19 userid @ 76.47/10.19 u @ X2 @ 76.47/10.19 Y2)))))))))))))))))))))))))) 76.47/10.19 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 76.47/10.19 thf(zip_derived_cl41, plain, 76.47/10.19 (![X2 : mu, X4 : mu, X6 : mu]: 76.47/10.19 ( (((exists_in_world @ X6 @ '#sk4') => 76.47/10.19 (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ '#sk4') => 76.47/10.19 (((((~) @ (((!!) @ (^[Y1 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ '#sk4' @ 76.47/10.19 Y1))) | 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y2 @ Y1) => 76.47/10.19 (((in @ X2 @ 76.47/10.19 X4 @ Y2 @ 76.47/10.19 Y1) | 76.47/10.19 (((~) @ ( 76.47/10.19 do @ Y0 @ 76.47/10.19 X6 @ Y2 @ 76.47/10.19 Y1))))))))))))))))) | 76.47/10.19 (((~) @ (((!!) @ (^[Y1 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ '#sk4' @ 76.47/10.19 Y1))) | 76.47/10.19 (((~) @ (((((~) @ (entry_box @ 76.47/10.19 X4 @ Y1))) | 76.47/10.19 (((~) @ (number @ 76.47/10.19 X4 @ 76.47/10.19 one @ Y1))) | 76.47/10.19 (((~) @ (userid @ 76.47/10.19 u @ X2 @ 76.47/10.19 Y1))))))))))))))))))))))) 76.47/10.19 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.19 | ~ (exists_in_world @ X4 @ '#sk4'))), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl40])). 76.47/10.19 thf(zip_derived_cl42, plain, 76.47/10.19 (![X2 : mu, X4 : mu, X6 : mu]: 76.47/10.19 (~ (exists_in_world @ X6 @ '#sk4') 76.47/10.19 | (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ '#sk4') => 76.47/10.19 (((((~) @ (((!!) @ (^[Y1 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ '#sk4' @ 76.47/10.19 Y1))) | 76.47/10.19 (((!!) @ (^[Y2 : mu]: 76.47/10.19 (((exists_in_world @ 76.47/10.19 Y2 @ Y1) => 76.47/10.19 (((in @ X2 @ 76.47/10.19 X4 @ Y2 @ 76.47/10.19 Y1) | 76.47/10.19 (((~) @ ( 76.47/10.19 do @ Y0 @ 76.47/10.19 X6 @ Y2 @ 76.47/10.19 Y1))))))))))))))))) | 76.47/10.19 (((~) @ (((!!) @ (^[Y1 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ '#sk4' @ 76.47/10.19 Y1))) | 76.47/10.19 (((~) @ (((((~) @ (entry_box @ 76.47/10.19 X4 @ Y1))) | 76.47/10.19 (((~) @ (number @ 76.47/10.19 X4 @ 76.47/10.19 one @ Y1))) | 76.47/10.19 (((~) @ (userid @ 76.47/10.19 u @ X2 @ 76.47/10.19 Y1))))))))))))))))))))) 76.47/10.19 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.19 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 76.47/10.19 thf(zip_derived_cl43, plain, 76.47/10.19 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.19 ( (((exists_in_world @ X8 @ '#sk4') => 76.47/10.19 (((((~) @ (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ 76.47/10.19 Y0) => 76.47/10.19 (((in @ X2 @ X4 @ Y1 @ Y0) | 76.47/10.19 (((~) @ (do @ X8 @ X6 @ 76.47/10.19 Y1 @ Y0))))))))))))))))) | 76.47/10.19 (((~) @ (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.19 (((~) @ (((((~) @ (entry_box @ X4 @ Y0))) | 76.47/10.19 (((~) @ (number @ X4 @ one @ Y0))) | 76.47/10.19 (((~) @ (userid @ u @ X2 @ Y0)))))))))))))))))) 76.47/10.19 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.19 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.19 | ~ (exists_in_world @ X6 @ '#sk4'))), 76.47/10.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl42])). 76.47/10.19 thf(zip_derived_cl44, plain, 76.47/10.19 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.19 (~ (exists_in_world @ X8 @ '#sk4') 76.47/10.19 | (((((~) @ (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ 76.47/10.19 Y0) => 76.47/10.19 (((in @ X2 @ X4 @ Y1 @ Y0) | 76.47/10.19 (((~) @ (do @ X8 @ X6 @ 76.47/10.19 Y1 @ Y0))))))))))))))))) | 76.47/10.19 (((~) @ (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.19 (((~) @ (((((~) @ (entry_box @ X4 @ Y0))) | 76.47/10.19 (((~) @ (number @ X4 @ one @ Y0))) | 76.47/10.19 (((~) @ (userid @ u @ X2 @ Y0)))))))))))))))) 76.47/10.19 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.19 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.19 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl43])). 76.47/10.19 thf(zip_derived_cl45, plain, 76.47/10.19 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.19 (~ (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.19 (((!!) @ (^[Y1 : mu]: 76.47/10.19 (((exists_in_world @ Y1 @ Y0) => 76.47/10.19 (((in @ X2 @ X4 @ Y1 @ Y0) | 76.47/10.19 (((~) @ (do @ X8 @ X6 @ Y1 @ Y0))))))))))))))) 76.47/10.19 | ~ (((!!) @ (^[Y0 : $i]: 76.47/10.19 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.19 (((~) @ (((((~) @ (entry_box @ X4 @ Y0))) | 76.47/10.19 (((~) @ (number @ X4 @ one @ Y0))) | 76.47/10.19 (((~) @ (userid @ u @ X2 @ Y0)))))))))))) 76.47/10.19 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.19 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.19 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.19 | ~ (exists_in_world @ X8 @ '#sk4'))), 76.47/10.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 76.47/10.19 thf(zip_derived_cl46, plain, 76.47/10.19 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.19 (~ (((((~) @ (rel_s4 @ '#sk4' @ ('#sk5' @ X2 @ X4 @ X6 @ X8)))) | 76.47/10.19 (((!!) @ (^[Y0 : mu]: 76.47/10.19 (((exists_in_world @ Y0 @ 76.47/10.19 ('#sk5' @ X2 @ X4 @ X6 @ X8)) => 76.47/10.19 (((in @ X2 @ X4 @ Y0 @ 76.47/10.19 ('#sk5' @ X2 @ X4 @ X6 @ X8)) | 76.47/10.19 (((~) @ (do @ X8 @ X6 @ Y0 @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8))))))))))))) 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.20 (((~) @ (((((~) @ (entry_box @ X4 @ Y0))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ Y0))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ Y0)))))))))))))), 76.47/10.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl45])). 76.47/10.20 thf(zip_derived_cl48, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 (~ (((!!) @ (^[Y0 : mu]: 76.47/10.20 (((exists_in_world @ Y0 @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) => 76.47/10.20 (((in @ X2 @ X4 @ Y0 @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) | 76.47/10.20 (((~) @ (do @ X8 @ X6 @ Y0 @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8))))))))))) 76.47/10.20 | ~ (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.20 (((~) @ (((((~) @ (entry_box @ X4 @ Y0))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ Y0))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ Y0)))))))))))) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])). 76.47/10.20 thf(zip_derived_cl50, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 (~ (((exists_in_world @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) => 76.47/10.20 (((in @ X2 @ X4 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) | 76.47/10.20 (((~) @ (do @ X8 @ X6 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)))))))) 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.20 (((~) @ (((((~) @ (entry_box @ X4 @ Y0))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ Y0))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ Y0)))))))))))))), 76.47/10.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl48])). 76.47/10.20 thf(zip_derived_cl53, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 ( (exists_in_world @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.20 (((~) @ (((((~) @ (entry_box @ X4 @ Y0))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ Y0))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ Y0)))))))))))) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])). 76.47/10.20 thf(zip_derived_cl56, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 (~ (((((~) @ (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (((((~) @ (entry_box @ X4 @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ ('#sk6' @ X2 @ X4)))))))))) 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | (exists_in_world @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)))), 76.47/10.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl53])). 76.47/10.20 thf(zip_derived_cl59, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 ( (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | (exists_in_world @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl56])). 76.47/10.20 thf(zip_derived_cl54, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 (~ (((in @ X2 @ X4 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) | 76.47/10.20 (((~) @ (do @ X8 @ X6 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)))))) 76.47/10.20 | ~ (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.20 (((~) @ (((((~) @ (entry_box @ X4 @ Y0))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ Y0))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ Y0)))))))))))) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])). 76.47/10.20 thf(zip_derived_cl57, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 (~ (in @ X2 @ X4 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.20 (((~) @ (((((~) @ (entry_box @ X4 @ Y0))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ Y0))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ Y0)))))))))))))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])). 76.47/10.20 thf(zip_derived_cl61, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 (~ (((((~) @ (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (((((~) @ (entry_box @ X4 @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ ('#sk6' @ X2 @ X4)))))))))) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (in @ X2 @ X4 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)))), 76.47/10.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl57])). 76.47/10.20 thf(zip_derived_cl64, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 ( (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (in @ X2 @ X4 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl61])). 76.47/10.20 thf(zip_derived_cl35, plain, ( (rel_s4 @ '#sk3' @ '#sk4')), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 76.47/10.20 thf(zip_derived_cl58, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 ( (do @ X8 @ X6 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.20 (((~) @ (((((~) @ (entry_box @ X4 @ Y0))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ Y0))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ Y0)))))))))))))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])). 76.47/10.20 thf(zip_derived_cl62, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 (~ (((((~) @ (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (((((~) @ (entry_box @ X4 @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ ('#sk6' @ X2 @ X4)))))))))) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | (do @ X8 @ X6 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)))), 76.47/10.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 76.47/10.20 thf(zip_derived_cl66, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 ( (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | (do @ X8 @ X6 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 76.47/10.20 thf(zip_derived_cl92, plain, 76.47/10.20 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu, X10 : mu]: 76.47/10.20 ( (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((((~) @ (rel_s4 @ X4 @ Y0))) | 76.47/10.20 (((!!) @ (^[Y1 : mu]: 76.47/10.20 (((exists_in_world @ Y1 @ Y0) => 76.47/10.20 (((in @ X8 @ X10 @ Y1 @ Y0) | 76.47/10.20 (((~) @ (do @ X6 @ 76.47/10.20 ('#sk9' @ X4 @ X6 @ X8 @ X10) @ 76.47/10.20 Y1 @ Y0))))))))))))))) 76.47/10.20 | ~ (string @ X8 @ X4) 76.47/10.20 | ~ (entry_box @ X10 @ X4) 76.47/10.20 | ~ (rel_s4 @ X2 @ X4) 76.47/10.20 | ~ (exists_in_world @ X6 @ X4) 76.47/10.20 | ~ (exists_in_world @ X8 @ X4) 76.47/10.20 | ~ (exists_in_world @ X10 @ X4))), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl90])). 76.47/10.20 thf(zip_derived_cl93, plain, 76.47/10.20 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu, X10 : mu, X12 : $i]: 76.47/10.20 ( (((((~) @ (rel_s4 @ X4 @ X12))) | 76.47/10.20 (((!!) @ (^[Y0 : mu]: 76.47/10.20 (((exists_in_world @ Y0 @ X12) => 76.47/10.20 (((in @ X8 @ X10 @ Y0 @ X12) | 76.47/10.20 (((~) @ (do @ X6 @ 76.47/10.20 ('#sk9' @ X4 @ X6 @ X8 @ X10) @ Y0 @ X12)))))))))))) 76.47/10.20 | ~ (exists_in_world @ X10 @ X4) 76.47/10.20 | ~ (exists_in_world @ X8 @ X4) 76.47/10.20 | ~ (exists_in_world @ X6 @ X4) 76.47/10.20 | ~ (rel_s4 @ X2 @ X4) 76.47/10.20 | ~ (entry_box @ X10 @ X4) 76.47/10.20 | ~ (string @ X8 @ X4))), 76.47/10.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl92])). 76.47/10.20 thf(zip_derived_cl94, plain, 76.47/10.20 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu, X10 : mu, X12 : $i]: 76.47/10.20 (~ (rel_s4 @ X4 @ X12) 76.47/10.20 | (((!!) @ (^[Y0 : mu]: 76.47/10.20 (((exists_in_world @ Y0 @ X12) => 76.47/10.20 (((in @ X8 @ X10 @ Y0 @ X12) | 76.47/10.20 (((~) @ (do @ X6 @ 76.47/10.20 ('#sk9' @ X4 @ X6 @ X8 @ X10) @ Y0 @ X12)))))))))) 76.47/10.20 | ~ (string @ X8 @ X4) 76.47/10.20 | ~ (entry_box @ X10 @ X4) 76.47/10.20 | ~ (rel_s4 @ X2 @ X4) 76.47/10.20 | ~ (exists_in_world @ X6 @ X4) 76.47/10.20 | ~ (exists_in_world @ X8 @ X4) 76.47/10.20 | ~ (exists_in_world @ X10 @ X4))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl93])). 76.47/10.20 thf(zip_derived_cl95, plain, 76.47/10.20 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu, X10 : mu, X12 : $i, X14 : mu]: 76.47/10.20 ( (((exists_in_world @ X14 @ X12) => 76.47/10.20 (((in @ X8 @ X10 @ X14 @ X12) | 76.47/10.20 (((~) @ (do @ X6 @ ('#sk9' @ X4 @ X6 @ X8 @ X10) @ X14 @ X12))))))) 76.47/10.20 | ~ (exists_in_world @ X10 @ X4) 76.47/10.20 | ~ (exists_in_world @ X8 @ X4) 76.47/10.20 | ~ (exists_in_world @ X6 @ X4) 76.47/10.20 | ~ (rel_s4 @ X2 @ X4) 76.47/10.20 | ~ (entry_box @ X10 @ X4) 76.47/10.20 | ~ (string @ X8 @ X4) 76.47/10.20 | ~ (rel_s4 @ X4 @ X12))), 76.47/10.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 76.47/10.20 thf(zip_derived_cl96, plain, 76.47/10.20 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu, X10 : mu, X12 : $i, X14 : mu]: 76.47/10.20 (~ (exists_in_world @ X14 @ X12) 76.47/10.20 | (((in @ X8 @ X10 @ X14 @ X12) | 76.47/10.20 (((~) @ (do @ X6 @ ('#sk9' @ X4 @ X6 @ X8 @ X10) @ X14 @ X12))))) 76.47/10.20 | ~ (rel_s4 @ X4 @ X12) 76.47/10.20 | ~ (string @ X8 @ X4) 76.47/10.20 | ~ (entry_box @ X10 @ X4) 76.47/10.20 | ~ (rel_s4 @ X2 @ X4) 76.47/10.20 | ~ (exists_in_world @ X6 @ X4) 76.47/10.20 | ~ (exists_in_world @ X8 @ X4) 76.47/10.20 | ~ (exists_in_world @ X10 @ X4))), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 76.47/10.20 thf(zip_derived_cl97, plain, 76.47/10.20 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu, X10 : mu, X12 : $i, X14 : mu]: 76.47/10.20 ( (in @ X8 @ X10 @ X14 @ X12) 76.47/10.20 | ~ (do @ X6 @ ('#sk9' @ X4 @ X6 @ X8 @ X10) @ X14 @ X12) 76.47/10.20 | ~ (exists_in_world @ X10 @ X4) 76.47/10.20 | ~ (exists_in_world @ X8 @ X4) 76.47/10.20 | ~ (exists_in_world @ X6 @ X4) 76.47/10.20 | ~ (rel_s4 @ X2 @ X4) 76.47/10.20 | ~ (entry_box @ X10 @ X4) 76.47/10.20 | ~ (string @ X8 @ X4) 76.47/10.20 | ~ (rel_s4 @ X4 @ X12) 76.47/10.20 | ~ (exists_in_world @ X14 @ X12))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl96])). 76.47/10.20 thf(zip_derived_cl164, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu, X3 : $i, X4 : mu, X5 : mu, X6 : $i]: 76.47/10.20 (~ (exists_in_world @ X5 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X5 @ X4)) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (rel_s4 @ X3 @ 76.47/10.20 ('#sk5' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (string @ X2 @ X3) 76.47/10.20 | ~ (entry_box @ X1 @ X3) 76.47/10.20 | ~ (rel_s4 @ X6 @ X3) 76.47/10.20 | ~ (exists_in_world @ X0 @ X3) 76.47/10.20 | ~ (exists_in_world @ X2 @ X3) 76.47/10.20 | ~ (exists_in_world @ X1 @ X3) 76.47/10.20 | (in @ X2 @ X1 @ 76.47/10.20 ('#sk7' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl66, zip_derived_cl97])). 76.47/10.20 thf(zip_derived_cl179, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu, X3 : mu, X4 : mu]: 76.47/10.20 ( (in @ X2 @ X1 @ 76.47/10.20 ('#sk7' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | ~ (string @ X2 @ '#sk4') 76.47/10.20 | ~ (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X4 @ X3)) 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X3 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl164])). 76.47/10.20 thf(zip_derived_cl188, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu, X3 : mu, X4 : mu]: 76.47/10.20 (~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X3 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X4 @ X3)) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (string @ X2 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | (in @ X2 @ X1 @ 76.47/10.20 ('#sk7' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl179])). 76.47/10.20 thf(zip_derived_cl193, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu]: 76.47/10.20 (~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | ~ (string @ X2 @ '#sk4') 76.47/10.20 | ~ (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.20 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl188])). 76.47/10.20 thf(zip_derived_cl199, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu]: 76.47/10.20 (~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (string @ X2 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl193])). 76.47/10.20 thf(zip_derived_cl211, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu]: 76.47/10.20 (~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | ~ (string @ X2 @ '#sk4') 76.47/10.20 | ~ (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl199])). 76.47/10.20 thf(zip_derived_cl223, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu]: 76.47/10.20 (~ (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (string @ X2 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl211])). 76.47/10.20 thf(zip_derived_cl47, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 ( (rel_s4 @ '#sk4' @ ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 76.47/10.20 (((~) @ (((((~) @ (entry_box @ X4 @ Y0))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ Y0))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ Y0)))))))))))) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])). 76.47/10.20 thf(zip_derived_cl49, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 (~ (((((~) @ (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (((((~) @ (entry_box @ X4 @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ ('#sk6' @ X2 @ X4)))))))))) 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk5' @ X2 @ X4 @ X6 @ X8)))), 76.47/10.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 76.47/10.20 thf(zip_derived_cl51, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 ( (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl49])). 76.47/10.20 thf(zip_derived_cl238, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu]: 76.47/10.20 (~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | ~ (string @ X2 @ '#sk4'))), 76.47/10.20 inference('clc', [status(thm)], [zip_derived_cl223, zip_derived_cl51])). 76.47/10.20 thf(zip_derived_cl137, plain, 76.47/10.20 (![X0 : $i, X1 : mu, X2 : mu, X3 : mu]: 76.47/10.20 (~ (exists_in_world @ X1 @ X0) 76.47/10.20 | ~ (exists_in_world @ X2 @ X0) 76.47/10.20 | ~ (exists_in_world @ X3 @ X0) 76.47/10.20 | ~ (entry_box @ X1 @ X0) 76.47/10.20 | ~ (string @ X2 @ X0) 76.47/10.20 | (exists_in_world @ ('#sk9' @ X0 @ X3 @ X2 @ X1) @ X0))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl91])). 76.47/10.20 thf(zip_derived_cl239, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu]: 76.47/10.20 (~ (string @ X2 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('clc', [status(thm)], [zip_derived_cl238, zip_derived_cl137])). 76.47/10.20 thf(zip_derived_cl240, plain, 76.47/10.20 (![X0 : mu, X1 : mu]: 76.47/10.20 (~ (string @ X0 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X0 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4'))), 76.47/10.20 inference('condensation', [status(thm)], [zip_derived_cl239])). 76.47/10.20 thf(mtransitive, axiom,(( mtransitive ) = 76.47/10.20 (^[R:( $i > $i > $o )]: 76.47/10.20 ( ![S:$i,T:$i,U:$i]: 76.47/10.20 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) )))). 76.47/10.20 thf('18', plain, 76.47/10.20 (( mtransitive ) = 76.47/10.20 ( ^[R:( $i > $i > $o )]: 76.47/10.20 ( ![S:$i,T:$i,U:$i]: 76.47/10.20 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) ) )), 76.47/10.20 inference('simplify_rw_rule', [status(thm)], [mtransitive])). 76.47/10.20 thf('19', plain, 76.47/10.20 (( mtransitive ) = 76.47/10.20 ( ^[V_1:( $i > $i > $o )]: 76.47/10.20 ( ![X4:$i,X6:$i,X8:$i]: 76.47/10.20 ( ( ( V_1 @ X4 @ X6 ) & ( V_1 @ X6 @ X8 ) ) => ( V_1 @ X4 @ X8 ) ) ) )), 76.47/10.20 define([status(thm)])).thf(a2, axiom, (mtransitive @ rel_s4)). 76.47/10.20 thf(zf_stmt_6, axiom, 76.47/10.20 (![X4:$i,X6:$i,X8:$i]: 76.47/10.20 ( ( ( rel_s4 @ X6 @ X8 ) & ( rel_s4 @ X4 @ X6 ) ) => ( rel_s4 @ X4 @ X8 ) ))). 76.47/10.20 thf(zip_derived_cl1, plain, 76.47/10.20 ( (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((!!) @ (^[Y1 : $i]: 76.47/10.20 (((!!) @ (^[Y2 : $i]: 76.47/10.20 (((((rel_s4 @ Y1 @ Y2) & (rel_s4 @ 76.47/10.20 Y0 @ Y1))) => 76.47/10.20 (rel_s4 @ Y0 @ Y2))))))))))))), 76.47/10.20 inference('cnf', [status(esa)], [zf_stmt_6])). 76.47/10.20 thf(zip_derived_cl20, plain, 76.47/10.20 (![X2 : $i]: 76.47/10.20 (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((!!) @ (^[Y1 : $i]: 76.47/10.20 (((((rel_s4 @ Y0 @ Y1) & (rel_s4 @ X2 @ Y0))) => 76.47/10.20 (rel_s4 @ X2 @ Y1)))))))))), 76.47/10.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 76.47/10.20 thf(zip_derived_cl21, plain, 76.47/10.20 (![X2 : $i, X4 : $i]: 76.47/10.20 (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((((rel_s4 @ X4 @ Y0) & (rel_s4 @ X2 @ X4))) => 76.47/10.20 (rel_s4 @ X2 @ Y0))))))), 76.47/10.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 76.47/10.20 thf(zip_derived_cl22, plain, 76.47/10.20 (![X2 : $i, X4 : $i, X6 : $i]: 76.47/10.20 (((((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) => (rel_s4 @ X2 @ X6)))), 76.47/10.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])). 76.47/10.20 thf(zip_derived_cl23, plain, 76.47/10.20 (![X2 : $i, X4 : $i, X6 : $i]: 76.47/10.20 (~ (((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) | (rel_s4 @ X2 @ X6))), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 76.47/10.20 thf(zip_derived_cl24, plain, 76.47/10.20 (![X2 : $i, X4 : $i, X6 : $i]: 76.47/10.20 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))), 76.47/10.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 76.47/10.20 thf(zip_derived_cl244, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : $i]: 76.47/10.20 (~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X0 @ '#sk4') 76.47/10.20 | ~ (string @ X1 @ '#sk4') 76.47/10.20 | (rel_s4 @ X2 @ ('#sk6' @ X1 @ X0)) 76.47/10.20 | ~ (rel_s4 @ X2 @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl240, zip_derived_cl24])). 76.47/10.20 thf(zip_derived_cl133, plain, 76.47/10.20 (![X0 : $i, X1 : $i]: 76.47/10.20 (~ (rel_s4 @ X0 @ X1) | (userid @ u @ ('#sk8' @ X0) @ X1))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl79])). 76.47/10.20 thf(zip_derived_cl31, plain, 76.47/10.20 (![X2 : $i, X4 : $i]: 76.47/10.20 ( (number @ ('#sk2' @ X2) @ one @ X4) | ~ (rel_s4 @ X2 @ X4))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 76.47/10.20 thf(zip_derived_cl52, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 ( (((((~) @ (entry_box @ X4 @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ ('#sk6' @ X2 @ X4)))))) 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl49])). 76.47/10.20 thf(zip_derived_cl55, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 (~ (entry_box @ X4 @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (number @ X4 @ one @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (userid @ u @ X2 @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk5' @ X2 @ X4 @ X6 @ X8)))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])). 76.47/10.20 thf(zip_derived_cl158, plain, 76.47/10.20 (![X0 : $i, X1 : mu, X2 : mu, X3 : mu]: 76.47/10.20 (~ (rel_s4 @ X0 @ ('#sk6' @ X1 @ ('#sk2' @ X0))) 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk5' @ X1 @ ('#sk2' @ X0) @ X3 @ X2)) 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X3 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (userid @ u @ X1 @ ('#sk6' @ X1 @ ('#sk2' @ X0))) 76.47/10.20 | ~ (entry_box @ ('#sk2' @ X0) @ ('#sk6' @ X1 @ ('#sk2' @ X0))))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl55])). 76.47/10.20 thf(zip_derived_cl32, plain, 76.47/10.20 (![X2 : $i, X4 : $i]: 76.47/10.20 ( (entry_box @ ('#sk2' @ X2) @ X4) | ~ (rel_s4 @ X2 @ X4))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 76.47/10.20 thf(zip_derived_cl170, plain, 76.47/10.20 (![X0 : $i, X1 : mu, X2 : mu, X3 : mu]: 76.47/10.20 (~ (userid @ u @ X1 @ ('#sk6' @ X1 @ ('#sk2' @ X0))) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X3 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk5' @ X1 @ ('#sk2' @ X0) @ X3 @ X2)) 76.47/10.20 | ~ (rel_s4 @ X0 @ ('#sk6' @ X1 @ ('#sk2' @ X0))))), 76.47/10.20 inference('clc', [status(thm)], [zip_derived_cl158, zip_derived_cl32])). 76.47/10.20 thf(zip_derived_cl171, plain, 76.47/10.20 (![X0 : $i, X1 : $i, X2 : mu, X3 : mu]: 76.47/10.20 (~ (rel_s4 @ X1 @ ('#sk6' @ ('#sk8' @ X1) @ ('#sk2' @ X0))) 76.47/10.20 | ~ (rel_s4 @ X0 @ ('#sk6' @ ('#sk8' @ X1) @ ('#sk2' @ X0))) 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ ('#sk8' @ X1) @ ('#sk2' @ X0) @ X3 @ X2)) 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X3 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl170])). 76.47/10.20 thf(zip_derived_cl173, plain, 76.47/10.20 (![X0 : $i, X1 : mu, X2 : mu]: 76.47/10.20 (~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ ('#sk8' @ X0) @ ('#sk2' @ X0) @ X2 @ X1)) 76.47/10.20 | ~ (rel_s4 @ X0 @ ('#sk6' @ ('#sk8' @ X0) @ ('#sk2' @ X0))))), 76.47/10.20 inference('eq_fact', [status(thm)], [zip_derived_cl171])). 76.47/10.20 thf(zip_derived_cl257, plain, 76.47/10.20 (![X0 : $i, X1 : mu, X2 : mu]: 76.47/10.20 (~ (rel_s4 @ X0 @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ ('#sk8' @ X0) @ ('#sk2' @ X0) @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl244, zip_derived_cl173])). 76.47/10.20 thf(zip_derived_cl267, plain, 76.47/10.20 (![X0 : $i, X1 : mu, X2 : mu]: 76.47/10.20 (~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ ('#sk8' @ X0) @ ('#sk2' @ X0) @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | ~ (rel_s4 @ X0 @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl257])). 76.47/10.20 thf(zip_derived_cl32, plain, 76.47/10.20 (![X2 : $i, X4 : $i]: 76.47/10.20 ( (entry_box @ ('#sk2' @ X2) @ X4) | ~ (rel_s4 @ X2 @ X4))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 76.47/10.20 thf(zip_derived_cl472, plain, 76.47/10.20 (![X0 : $i, X1 : mu, X2 : mu]: 76.47/10.20 (~ (rel_s4 @ X0 @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ ('#sk8' @ X0) @ ('#sk2' @ X0) @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4'))), 76.47/10.20 inference('clc', [status(thm)], [zip_derived_cl267, zip_derived_cl32])). 76.47/10.20 thf(zip_derived_cl129, plain, 76.47/10.20 (![X0 : $i, X1 : $i]: 76.47/10.20 (~ (rel_s4 @ X0 @ X1) | (string @ ('#sk8' @ X0) @ X1))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl78])). 76.47/10.20 thf(zip_derived_cl473, plain, 76.47/10.20 (![X0 : $i, X1 : mu, X2 : mu]: 76.47/10.20 (~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ ('#sk8' @ X0) @ ('#sk2' @ X0) @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | ~ (rel_s4 @ X0 @ '#sk4'))), 76.47/10.20 inference('clc', [status(thm)], [zip_derived_cl472, zip_derived_cl129])). 76.47/10.20 thf(zip_derived_cl59, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 ( (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | (exists_in_world @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl56])). 76.47/10.20 thf(zip_derived_cl64, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 ( (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (in @ X2 @ X4 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl61])). 76.47/10.20 thf(zip_derived_cl10, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 76.47/10.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 76.47/10.20 thf(zip_derived_cl164, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu, X3 : $i, X4 : mu, X5 : mu, X6 : $i]: 76.47/10.20 (~ (exists_in_world @ X5 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X5 @ X4)) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (rel_s4 @ X3 @ 76.47/10.20 ('#sk5' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (string @ X2 @ X3) 76.47/10.20 | ~ (entry_box @ X1 @ X3) 76.47/10.20 | ~ (rel_s4 @ X6 @ X3) 76.47/10.20 | ~ (exists_in_world @ X0 @ X3) 76.47/10.20 | ~ (exists_in_world @ X2 @ X3) 76.47/10.20 | ~ (exists_in_world @ X1 @ X3) 76.47/10.20 | (in @ X2 @ X1 @ 76.47/10.20 ('#sk7' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl66, zip_derived_cl97])). 76.47/10.20 thf(zip_derived_cl182, plain, 76.47/10.20 (![X0 : $i, X1 : mu, X2 : mu, X3 : mu, X4 : mu, X5 : mu]: 76.47/10.20 ( (in @ X3 @ X2 @ 76.47/10.20 ('#sk7' @ X5 @ X4 @ ('#sk9' @ X0 @ X1 @ X3 @ X2) @ X1) @ 76.47/10.20 ('#sk5' @ X5 @ X4 @ ('#sk9' @ X0 @ X1 @ X3 @ X2) @ X1)) 76.47/10.20 | ~ (exists_in_world @ X2 @ X0) 76.47/10.20 | ~ (exists_in_world @ X3 @ X0) 76.47/10.20 | ~ (exists_in_world @ X1 @ X0) 76.47/10.20 | ~ (entry_box @ X2 @ X0) 76.47/10.20 | ~ (string @ X3 @ X0) 76.47/10.20 | ~ (rel_s4 @ X0 @ 76.47/10.20 ('#sk5' @ X5 @ X4 @ ('#sk9' @ X0 @ X1 @ X3 @ X2) @ X1)) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X5 @ X4 @ ('#sk9' @ X0 @ X1 @ X3 @ X2) @ X1) @ 76.47/10.20 ('#sk5' @ X5 @ X4 @ ('#sk9' @ X0 @ X1 @ X3 @ X2) @ X1)) 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X5 @ X4)) 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ X0 @ X1 @ X3 @ X2) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X5 @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl164])). 76.47/10.20 thf(zip_derived_cl431, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu, X3 : $i]: 76.47/10.20 (~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X2 @ X1 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (rel_s4 @ X3 @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (string @ X2 @ X3) 76.47/10.20 | ~ (entry_box @ X1 @ X3) 76.47/10.20 | ~ (exists_in_world @ X0 @ X3) 76.47/10.20 | ~ (exists_in_world @ X2 @ X3) 76.47/10.20 | ~ (exists_in_world @ X1 @ X3))), 76.47/10.20 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl182])). 76.47/10.20 thf(zip_derived_cl437, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu, X3 : $i]: 76.47/10.20 (~ (exists_in_world @ X1 @ X3) 76.47/10.20 | ~ (exists_in_world @ X2 @ X3) 76.47/10.20 | ~ (exists_in_world @ X0 @ X3) 76.47/10.20 | ~ (entry_box @ X1 @ X3) 76.47/10.20 | ~ (string @ X2 @ X3) 76.47/10.20 | ~ (rel_s4 @ X3 @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X2 @ X1 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl431])). 76.47/10.20 thf(zip_derived_cl797, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu, X3 : $i]: 76.47/10.20 (~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (rel_s4 @ X3 @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (string @ X2 @ X3) 76.47/10.20 | ~ (entry_box @ X1 @ X3) 76.47/10.20 | ~ (exists_in_world @ X0 @ X3) 76.47/10.20 | ~ (exists_in_world @ X2 @ X3) 76.47/10.20 | ~ (exists_in_world @ X1 @ X3))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl437])). 76.47/10.20 thf(zip_derived_cl875, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu, X3 : $i]: 76.47/10.20 (~ (exists_in_world @ X1 @ X3) 76.47/10.20 | ~ (exists_in_world @ X2 @ X3) 76.47/10.20 | ~ (exists_in_world @ X0 @ X3) 76.47/10.20 | ~ (entry_box @ X1 @ X3) 76.47/10.20 | ~ (string @ X2 @ X3) 76.47/10.20 | ~ (rel_s4 @ X3 @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl797])). 76.47/10.20 thf(zip_derived_cl1059, plain, 76.47/10.20 (![X0 : mu, X1 : $i]: 76.47/10.20 (~ (rel_s4 @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ X1) @ ('#sk2' @ X1)) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ X1) @ ('#sk2' @ X1)) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X1) @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ X1) @ ('#sk2' @ X1))) 76.47/10.20 | ~ (string @ ('#sk8' @ X1) @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X1) @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl473, zip_derived_cl875])). 76.47/10.20 thf(zip_derived_cl1172, plain, 76.47/10.20 (![X0 : mu, X1 : $i]: 76.47/10.20 (~ (entry_box @ ('#sk2' @ X1) @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ X1) @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ X1) @ ('#sk2' @ X1))) 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ X1) @ ('#sk2' @ X1)) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X1) @ '#sk4') 76.47/10.20 | ~ (rel_s4 @ X1 @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl1059])). 76.47/10.20 thf(zip_derived_cl32, plain, 76.47/10.20 (![X2 : $i, X4 : $i]: 76.47/10.20 ( (entry_box @ ('#sk2' @ X2) @ X4) | ~ (rel_s4 @ X2 @ X4))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 76.47/10.20 thf(zip_derived_cl2805, plain, 76.47/10.20 (![X0 : mu, X1 : $i]: 76.47/10.20 (~ (rel_s4 @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ X1) @ ('#sk2' @ X1)) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ X1) @ ('#sk2' @ X1))) 76.47/10.20 | ~ (string @ ('#sk8' @ X1) @ '#sk4'))), 76.47/10.20 inference('clc', [status(thm)], [zip_derived_cl1172, zip_derived_cl32])). 76.47/10.20 thf(zip_derived_cl129, plain, 76.47/10.20 (![X0 : $i, X1 : $i]: 76.47/10.20 (~ (rel_s4 @ X0 @ X1) | (string @ ('#sk8' @ X0) @ X1))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl78])). 76.47/10.20 thf(zip_derived_cl2806, plain, 76.47/10.20 (![X0 : mu, X1 : $i]: 76.47/10.20 ( (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ X1) @ ('#sk2' @ X1))) 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ X1) @ ('#sk2' @ X1)) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X1) @ '#sk4') 76.47/10.20 | ~ (rel_s4 @ X1 @ '#sk4'))), 76.47/10.20 inference('clc', [status(thm)], [zip_derived_cl2805, zip_derived_cl129])). 76.47/10.20 thf(zip_derived_cl137, plain, 76.47/10.20 (![X0 : $i, X1 : mu, X2 : mu, X3 : mu]: 76.47/10.20 (~ (exists_in_world @ X1 @ X0) 76.47/10.20 | ~ (exists_in_world @ X2 @ X0) 76.47/10.20 | ~ (exists_in_world @ X3 @ X0) 76.47/10.20 | ~ (entry_box @ X1 @ X0) 76.47/10.20 | ~ (string @ X2 @ X0) 76.47/10.20 | (exists_in_world @ ('#sk9' @ X0 @ X3 @ X2 @ X1) @ X0))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl91])). 76.47/10.20 thf(zip_derived_cl2807, plain, 76.47/10.20 (![X0 : $i, X1 : mu]: 76.47/10.20 (~ (rel_s4 @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ X0) @ ('#sk2' @ X0))) 76.47/10.20 | ~ (string @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4'))), 76.47/10.20 inference('sup+', [status(thm)], [zip_derived_cl2806, zip_derived_cl137])). 76.47/10.20 thf(zip_derived_cl2812, plain, 76.47/10.20 (![X0 : $i, X1 : mu]: 76.47/10.20 (~ (entry_box @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ X0) @ ('#sk2' @ X0))) 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | ~ (rel_s4 @ X0 @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl2807])). 76.47/10.20 thf(zip_derived_cl2817, plain, 76.47/10.20 (![X0 : $i]: 76.47/10.20 (~ (entry_box @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ X0) @ ('#sk2' @ X0))) 76.47/10.20 | ~ (rel_s4 @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4'))), 76.47/10.20 inference('condensation', [status(thm)], [zip_derived_cl2812])). 76.47/10.20 thf(zip_derived_cl32, plain, 76.47/10.20 (![X2 : $i, X4 : $i]: 76.47/10.20 ( (entry_box @ ('#sk2' @ X2) @ X4) | ~ (rel_s4 @ X2 @ X4))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 76.47/10.20 thf(zip_derived_cl2818, plain, 76.47/10.20 (![X0 : $i]: 76.47/10.20 (~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (rel_s4 @ X0 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ X0) @ ('#sk2' @ X0))) 76.47/10.20 | ~ (string @ ('#sk8' @ X0) @ '#sk4'))), 76.47/10.20 inference('clc', [status(thm)], [zip_derived_cl2817, zip_derived_cl32])). 76.47/10.20 thf(zip_derived_cl129, plain, 76.47/10.20 (![X0 : $i, X1 : $i]: 76.47/10.20 (~ (rel_s4 @ X0 @ X1) | (string @ ('#sk8' @ X0) @ X1))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl78])). 76.47/10.20 thf(zip_derived_cl2819, plain, 76.47/10.20 (![X0 : $i]: 76.47/10.20 ( (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ X0) @ ('#sk2' @ X0))) 76.47/10.20 | ~ (rel_s4 @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4'))), 76.47/10.20 inference('clc', [status(thm)], [zip_derived_cl2818, zip_derived_cl129])). 76.47/10.20 thf(zip_derived_cl173, plain, 76.47/10.20 (![X0 : $i, X1 : mu, X2 : mu]: 76.47/10.20 (~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ ('#sk8' @ X0) @ ('#sk2' @ X0) @ X2 @ X1)) 76.47/10.20 | ~ (rel_s4 @ X0 @ ('#sk6' @ ('#sk8' @ X0) @ ('#sk2' @ X0))))), 76.47/10.20 inference('eq_fact', [status(thm)], [zip_derived_cl171])). 76.47/10.20 thf(zip_derived_cl2821, plain, 76.47/10.20 (![X0 : mu, X1 : mu]: 76.47/10.20 (~ (exists_in_world @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (rel_s4 @ '#sk4' @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4') @ X1 @ X0)) 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl2819, zip_derived_cl173])). 76.47/10.20 thf(zip_derived_cl10, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 76.47/10.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 76.47/10.20 thf(zip_derived_cl74, plain, 76.47/10.20 (![X2 : $i, X4 : $i]: 76.47/10.20 ( (exists_in_world @ ('#sk8' @ X4) @ X4) | ~ (rel_s4 @ X2 @ X4))), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 76.47/10.20 thf(zip_derived_cl99, plain, 76.47/10.20 (![X0 : $i]: (exists_in_world @ ('#sk8' @ X0) @ X0)), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl74])). 76.47/10.20 thf(zip_derived_cl27, plain, 76.47/10.20 (![X2 : $i]: (exists_in_world @ ('#sk2' @ X2) @ X2)), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 76.47/10.20 thf(zip_derived_cl10, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 76.47/10.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 76.47/10.20 thf(zip_derived_cl99, plain, 76.47/10.20 (![X0 : $i]: (exists_in_world @ ('#sk8' @ X0) @ X0)), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl74])). 76.47/10.20 thf(zip_derived_cl27, plain, 76.47/10.20 (![X2 : $i]: (exists_in_world @ ('#sk2' @ X2) @ X2)), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 76.47/10.20 thf(zip_derived_cl2835, plain, 76.47/10.20 (![X0 : mu, X1 : mu]: 76.47/10.20 ( (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4') @ X1 @ X0)) 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('demod', [status(thm)], 76.47/10.20 [zip_derived_cl2821, zip_derived_cl99, zip_derived_cl27, 76.47/10.20 zip_derived_cl10, zip_derived_cl99, zip_derived_cl27])). 76.47/10.20 thf(zip_derived_cl60, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 ( (((((~) @ (entry_box @ X4 @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ ('#sk6' @ X2 @ X4)))))) 76.47/10.20 | (exists_in_world @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl56])). 76.47/10.20 thf(zip_derived_cl63, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 (~ (entry_box @ X4 @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (number @ X4 @ one @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (userid @ u @ X2 @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | (exists_in_world @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl60])). 76.47/10.20 thf(zip_derived_cl65, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 ( (((((~) @ (entry_box @ X4 @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ ('#sk6' @ X2 @ X4)))))) 76.47/10.20 | ~ (in @ X2 @ X4 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl61])). 76.47/10.20 thf(zip_derived_cl68, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 (~ (entry_box @ X4 @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (number @ X4 @ one @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (userid @ u @ X2 @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (in @ X2 @ X4 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl65])). 76.47/10.20 thf(zip_derived_cl35, plain, ( (rel_s4 @ '#sk3' @ '#sk4')), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 76.47/10.20 thf(zip_derived_cl67, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 ( (((((~) @ (entry_box @ X4 @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (number @ X4 @ one @ ('#sk6' @ X2 @ X4)))) | 76.47/10.20 (((~) @ (userid @ u @ X2 @ ('#sk6' @ X2 @ X4)))))) 76.47/10.20 | (do @ X8 @ X6 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)) 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 76.47/10.20 thf(zip_derived_cl69, plain, 76.47/10.20 (![X2 : mu, X4 : mu, X6 : mu, X8 : mu]: 76.47/10.20 (~ (entry_box @ X4 @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (number @ X4 @ one @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (userid @ u @ X2 @ ('#sk6' @ X2 @ X4)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X6 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X8 @ '#sk4') 76.47/10.20 | (do @ X8 @ X6 @ ('#sk7' @ X2 @ X4 @ X6 @ X8) @ 76.47/10.20 ('#sk5' @ X2 @ X4 @ X6 @ X8)))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl67])). 76.47/10.20 thf(zip_derived_cl97, plain, 76.47/10.20 (![X2 : $i, X4 : $i, X6 : mu, X8 : mu, X10 : mu, X12 : $i, X14 : mu]: 76.47/10.20 ( (in @ X8 @ X10 @ X14 @ X12) 76.47/10.20 | ~ (do @ X6 @ ('#sk9' @ X4 @ X6 @ X8 @ X10) @ X14 @ X12) 76.47/10.20 | ~ (exists_in_world @ X10 @ X4) 76.47/10.20 | ~ (exists_in_world @ X8 @ X4) 76.47/10.20 | ~ (exists_in_world @ X6 @ X4) 76.47/10.20 | ~ (rel_s4 @ X2 @ X4) 76.47/10.20 | ~ (entry_box @ X10 @ X4) 76.47/10.20 | ~ (string @ X8 @ X4) 76.47/10.20 | ~ (rel_s4 @ X4 @ X12) 76.47/10.20 | ~ (exists_in_world @ X14 @ X12))), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl96])). 76.47/10.20 thf(zip_derived_cl175, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu, X3 : $i, X4 : mu, X5 : mu, X6 : $i]: 76.47/10.20 (~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X5 @ '#sk4') 76.47/10.20 | ~ (userid @ u @ X5 @ ('#sk6' @ X5 @ X4)) 76.47/10.20 | ~ (number @ X4 @ one @ ('#sk6' @ X5 @ X4)) 76.47/10.20 | ~ (entry_box @ X4 @ ('#sk6' @ X5 @ X4)) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (rel_s4 @ X3 @ 76.47/10.20 ('#sk5' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (string @ X2 @ X3) 76.47/10.20 | ~ (entry_box @ X1 @ X3) 76.47/10.20 | ~ (rel_s4 @ X6 @ X3) 76.47/10.20 | ~ (exists_in_world @ X0 @ X3) 76.47/10.20 | ~ (exists_in_world @ X2 @ X3) 76.47/10.20 | ~ (exists_in_world @ X1 @ X3) 76.47/10.20 | (in @ X2 @ X1 @ 76.47/10.20 ('#sk7' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X5 @ X4 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl69, zip_derived_cl97])). 76.47/10.20 thf(zip_derived_cl291, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu, X3 : mu, X4 : mu]: 76.47/10.20 ( (in @ X2 @ X1 @ 76.47/10.20 ('#sk7' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | ~ (string @ X2 @ '#sk4') 76.47/10.20 | ~ (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (entry_box @ X3 @ ('#sk6' @ X4 @ X3)) 76.47/10.20 | ~ (number @ X3 @ one @ ('#sk6' @ X4 @ X3)) 76.47/10.20 | ~ (userid @ u @ X4 @ ('#sk6' @ X4 @ X3)) 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X3 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl175])). 76.47/10.20 thf(zip_derived_cl305, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu, X3 : mu, X4 : mu]: 76.47/10.20 (~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X3 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X4 @ '#sk4') 76.47/10.20 | ~ (userid @ u @ X4 @ ('#sk6' @ X4 @ X3)) 76.47/10.20 | ~ (number @ X3 @ one @ ('#sk6' @ X4 @ X3)) 76.47/10.20 | ~ (entry_box @ X3 @ ('#sk6' @ X4 @ X3)) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (string @ X2 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | (in @ X2 @ X1 @ 76.47/10.20 ('#sk7' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X4 @ X3 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl291])). 76.47/10.20 thf(zip_derived_cl1689, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu]: 76.47/10.20 (~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (userid @ u @ X2 @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (number @ X1 @ one @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (entry_box @ X1 @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | ~ (string @ X2 @ '#sk4') 76.47/10.20 | ~ (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (entry_box @ X1 @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (number @ X1 @ one @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (userid @ u @ X2 @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4'))), 76.47/10.20 inference('sup+', [status(thm)], [zip_derived_cl68, zip_derived_cl305])). 76.47/10.20 thf(zip_derived_cl1695, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu]: 76.47/10.20 (~ (exists_in_world @ 76.47/10.20 ('#sk7' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0) @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (string @ X2 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (number @ X1 @ one @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (userid @ u @ X2 @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl1689])). 76.47/10.20 thf(zip_derived_cl4643, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu]: 76.47/10.20 (~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (userid @ u @ X2 @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (number @ X1 @ one @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (entry_box @ X1 @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (userid @ u @ X2 @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (number @ X1 @ one @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (entry_box @ X1 @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | ~ (string @ X2 @ '#sk4') 76.47/10.20 | ~ (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl1695])). 76.47/10.20 thf(zip_derived_cl4757, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu]: 76.47/10.20 (~ (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | ~ (string @ X2 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (number @ X1 @ one @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (userid @ u @ X2 @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ '#sk4' @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl4643])). 76.47/10.20 thf(zip_derived_cl5053, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (userid @ u @ ('#sk8' @ '#sk4') @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (number @ ('#sk2' @ '#sk4') @ one @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl2835, zip_derived_cl4757])). 76.47/10.20 thf(zip_derived_cl99, plain, 76.47/10.20 (![X0 : $i]: (exists_in_world @ ('#sk8' @ X0) @ X0)), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl74])). 76.47/10.20 thf(zip_derived_cl27, plain, 76.47/10.20 (![X2 : $i]: (exists_in_world @ ('#sk2' @ X2) @ X2)), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 76.47/10.20 thf(zip_derived_cl5223, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (userid @ u @ ('#sk8' @ '#sk4') @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (number @ ('#sk2' @ '#sk4') @ one @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4'))), 76.47/10.20 inference('demod', [status(thm)], 76.47/10.20 [zip_derived_cl5053, zip_derived_cl99, zip_derived_cl27])). 76.47/10.20 thf(zip_derived_cl5224, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (number @ ('#sk2' @ '#sk4') @ one @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (userid @ u @ ('#sk8' @ '#sk4') @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl5223])). 76.47/10.20 thf(zip_derived_cl5575, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | ~ (number @ ('#sk2' @ '#sk4') @ one @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl133, zip_derived_cl5224])). 76.47/10.20 thf(zip_derived_cl99, plain, 76.47/10.20 (![X0 : $i]: (exists_in_world @ ('#sk8' @ X0) @ X0)), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl74])). 76.47/10.20 thf(zip_derived_cl35, plain, ( (rel_s4 @ '#sk3' @ '#sk4')), 76.47/10.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl34])). 76.47/10.20 thf(cumulative_ax, axiom, 76.47/10.20 (![X:mu,V:$i,W:$i]: 76.47/10.20 ( ( ( rel_s4 @ V @ W ) & ( exists_in_world @ X @ V ) ) => 76.47/10.20 ( exists_in_world @ X @ W ) ))). 76.47/10.20 thf(zip_derived_cl3, plain, 76.47/10.20 ( (((!!) @ (^[Y0 : mu]: 76.47/10.20 (((!!) @ (^[Y1 : $i]: 76.47/10.20 (((!!) @ (^[Y2 : $i]: 76.47/10.20 (((((rel_s4 @ Y1 @ Y2) & 76.47/10.20 (exists_in_world @ Y0 @ Y1))) => 76.47/10.20 (exists_in_world @ Y0 @ Y2))))))))))))), 76.47/10.20 inference('cnf', [status(esa)], [cumulative_ax])). 76.47/10.20 thf(zip_derived_cl15, plain, 76.47/10.20 (![X2 : mu]: 76.47/10.20 (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((!!) @ (^[Y1 : $i]: 76.47/10.20 (((((rel_s4 @ Y0 @ Y1) & (exists_in_world @ 76.47/10.20 X2 @ Y0))) => 76.47/10.20 (exists_in_world @ X2 @ Y1)))))))))), 76.47/10.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 76.47/10.20 thf(zip_derived_cl16, plain, 76.47/10.20 (![X2 : mu, X4 : $i]: 76.47/10.20 (((!!) @ (^[Y0 : $i]: 76.47/10.20 (((((rel_s4 @ X4 @ Y0) & (exists_in_world @ X2 @ X4))) => 76.47/10.20 (exists_in_world @ X2 @ Y0))))))), 76.47/10.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 76.47/10.20 thf(zip_derived_cl17, plain, 76.47/10.20 (![X2 : mu, X4 : $i, X6 : $i]: 76.47/10.20 (((((rel_s4 @ X4 @ X6) & (exists_in_world @ X2 @ X4))) => 76.47/10.20 (exists_in_world @ X2 @ X6)))), 76.47/10.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 76.47/10.20 thf(zip_derived_cl18, plain, 76.47/10.20 (![X2 : mu, X4 : $i, X6 : $i]: 76.47/10.20 (~ (((rel_s4 @ X4 @ X6) & (exists_in_world @ X2 @ X4))) 76.47/10.20 | (exists_in_world @ X2 @ X6))), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 76.47/10.20 thf(zip_derived_cl19, plain, 76.47/10.20 (![X2 : mu, X4 : $i, X6 : $i]: 76.47/10.20 (~ (rel_s4 @ X4 @ X6) 76.47/10.20 | ~ (exists_in_world @ X2 @ X4) 76.47/10.20 | (exists_in_world @ X2 @ X6))), 76.47/10.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl18])). 76.47/10.20 thf(zip_derived_cl102, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 ( (exists_in_world @ X0 @ '#sk4') | ~ (exists_in_world @ X0 @ '#sk3'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl35, zip_derived_cl19])). 76.47/10.20 thf(zip_derived_cl106, plain, 76.47/10.20 ( (exists_in_world @ ('#sk8' @ '#sk3') @ '#sk4')), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl99, zip_derived_cl102])). 76.47/10.20 thf(zip_derived_cl137, plain, 76.47/10.20 (![X0 : $i, X1 : mu, X2 : mu, X3 : mu]: 76.47/10.20 (~ (exists_in_world @ X1 @ X0) 76.47/10.20 | ~ (exists_in_world @ X2 @ X0) 76.47/10.20 | ~ (exists_in_world @ X3 @ X0) 76.47/10.20 | ~ (entry_box @ X1 @ X0) 76.47/10.20 | ~ (string @ X2 @ X0) 76.47/10.20 | (exists_in_world @ ('#sk9' @ X0 @ X3 @ X2 @ X1) @ X0))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl91])). 76.47/10.20 thf(zip_derived_cl240, plain, 76.47/10.20 (![X0 : mu, X1 : mu]: 76.47/10.20 (~ (string @ X0 @ '#sk4') 76.47/10.20 | ~ (entry_box @ X1 @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X0 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4'))), 76.47/10.20 inference('condensation', [status(thm)], [zip_derived_cl239])). 76.47/10.20 thf(zip_derived_cl173, plain, 76.47/10.20 (![X0 : $i, X1 : mu, X2 : mu]: 76.47/10.20 (~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ X0) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ X0) @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ ('#sk8' @ X0) @ ('#sk2' @ X0) @ X2 @ X1)) 76.47/10.20 | ~ (rel_s4 @ X0 @ ('#sk6' @ ('#sk8' @ X0) @ ('#sk2' @ X0))))), 76.47/10.20 inference('eq_fact', [status(thm)], [zip_derived_cl171])). 76.47/10.20 thf(zip_derived_cl241, plain, 76.47/10.20 (![X0 : mu, X1 : mu]: 76.47/10.20 (~ (exists_in_world @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4') @ X1 @ X0)) 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl240, zip_derived_cl173])). 76.47/10.20 thf(zip_derived_cl27, plain, 76.47/10.20 (![X2 : $i]: (exists_in_world @ ('#sk2' @ X2) @ X2)), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 76.47/10.20 thf(zip_derived_cl99, plain, 76.47/10.20 (![X0 : $i]: (exists_in_world @ ('#sk8' @ X0) @ X0)), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl74])). 76.47/10.20 thf(zip_derived_cl99, plain, 76.47/10.20 (![X0 : $i]: (exists_in_world @ ('#sk8' @ X0) @ X0)), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl74])). 76.47/10.20 thf(zip_derived_cl27, plain, 76.47/10.20 (![X2 : $i]: (exists_in_world @ ('#sk2' @ X2) @ X2)), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 76.47/10.20 thf(zip_derived_cl251, plain, 76.47/10.20 (![X0 : mu, X1 : mu]: 76.47/10.20 (~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk5' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4') @ X1 @ X0)) 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('demod', [status(thm)], 76.47/10.20 [zip_derived_cl241, zip_derived_cl27, zip_derived_cl99, 76.47/10.20 zip_derived_cl99, zip_derived_cl27])). 76.47/10.20 thf(zip_derived_cl875, plain, 76.47/10.20 (![X0 : mu, X1 : mu, X2 : mu, X3 : $i]: 76.47/10.20 (~ (exists_in_world @ X1 @ X3) 76.47/10.20 | ~ (exists_in_world @ X2 @ X3) 76.47/10.20 | ~ (exists_in_world @ X0 @ X3) 76.47/10.20 | ~ (entry_box @ X1 @ X3) 76.47/10.20 | ~ (string @ X2 @ X3) 76.47/10.20 | ~ (rel_s4 @ X3 @ 76.47/10.20 ('#sk5' @ X2 @ X1 @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ X0)) 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ X2 @ X1)) 76.47/10.20 | ~ (exists_in_world @ X2 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X1 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk9' @ X3 @ X0 @ X2 @ X1) @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl797])). 76.47/10.20 thf(zip_derived_cl1058, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ '#sk4') @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl251, zip_derived_cl875])). 76.47/10.20 thf(zip_derived_cl27, plain, 76.47/10.20 (![X2 : $i]: (exists_in_world @ ('#sk2' @ X2) @ X2)), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 76.47/10.20 thf(zip_derived_cl99, plain, 76.47/10.20 (![X0 : $i]: (exists_in_world @ ('#sk8' @ X0) @ X0)), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl74])). 76.47/10.20 thf(zip_derived_cl99, plain, 76.47/10.20 (![X0 : $i]: (exists_in_world @ ('#sk8' @ X0) @ X0)), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl74])). 76.47/10.20 thf(zip_derived_cl27, plain, 76.47/10.20 (![X2 : $i]: (exists_in_world @ ('#sk2' @ X2) @ X2)), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 76.47/10.20 thf(zip_derived_cl1170, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('demod', [status(thm)], 76.47/10.20 [zip_derived_cl1058, zip_derived_cl27, zip_derived_cl99, 76.47/10.20 zip_derived_cl99, zip_derived_cl27])). 76.47/10.20 thf(zip_derived_cl1171, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 ( (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl1170])). 76.47/10.20 thf(zip_derived_cl1375, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl1171])). 76.47/10.20 thf(zip_derived_cl99, plain, 76.47/10.20 (![X0 : $i]: (exists_in_world @ ('#sk8' @ X0) @ X0)), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl74])). 76.47/10.20 thf(zip_derived_cl27, plain, 76.47/10.20 (![X2 : $i]: (exists_in_world @ ('#sk2' @ X2) @ X2)), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 76.47/10.20 thf(zip_derived_cl1378, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))))), 76.47/10.20 inference('demod', [status(thm)], 76.47/10.20 [zip_derived_cl1375, zip_derived_cl99, zip_derived_cl27])). 76.47/10.20 thf(zip_derived_cl1379, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 ( (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl1378])). 76.47/10.20 thf(zip_derived_cl1388, plain, 76.47/10.20 ((~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl1379])). 76.47/10.20 thf(zip_derived_cl5577, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (number @ ('#sk2' @ '#sk4') @ one @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('clc', [status(thm)], [zip_derived_cl5575, zip_derived_cl1388])). 76.47/10.20 thf(zip_derived_cl5578, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl5577])). 76.47/10.20 thf(zip_derived_cl1388, plain, 76.47/10.20 ((~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl1379])). 76.47/10.20 thf(zip_derived_cl5580, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (exists_in_world @ 76.47/10.20 ('#sk9' @ '#sk4' @ X0 @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4')) @ 76.47/10.20 '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('clc', [status(thm)], [zip_derived_cl5578, zip_derived_cl1388])). 76.47/10.20 thf(zip_derived_cl5582, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl5580])). 76.47/10.20 thf(zip_derived_cl99, plain, 76.47/10.20 (![X0 : $i]: (exists_in_world @ ('#sk8' @ X0) @ X0)), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl74])). 76.47/10.20 thf(zip_derived_cl27, plain, 76.47/10.20 (![X2 : $i]: (exists_in_world @ ('#sk2' @ X2) @ X2)), 76.47/10.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 76.47/10.20 thf(zip_derived_cl5585, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4'))), 76.47/10.20 inference('demod', [status(thm)], 76.47/10.20 [zip_derived_cl5582, zip_derived_cl99, zip_derived_cl27])). 76.47/10.20 thf(zip_derived_cl5586, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (entry_box @ ('#sk2' @ '#sk4') @ 76.47/10.20 ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4'))), 76.47/10.20 inference('simplify', [status(thm)], [zip_derived_cl5585])). 76.47/10.20 thf(zip_derived_cl5593, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))) 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl5586])). 76.47/10.20 thf(zip_derived_cl1388, plain, 76.47/10.20 ((~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | (rel_s4 @ '#sk4' @ ('#sk6' @ ('#sk8' @ '#sk4') @ ('#sk2' @ '#sk4'))))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl106, zip_derived_cl1379])). 76.47/10.20 thf(zip_derived_cl5595, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (exists_in_world @ X0 @ '#sk4') 76.47/10.20 | ~ (entry_box @ ('#sk2' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4'))), 76.47/10.20 inference('clc', [status(thm)], [zip_derived_cl5593, zip_derived_cl1388])). 76.47/10.20 thf(zip_derived_cl5596, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (rel_s4 @ '#sk4' @ '#sk4') 76.47/10.20 | ~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl32, zip_derived_cl5595])). 76.47/10.20 thf(zip_derived_cl10, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 76.47/10.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 76.47/10.20 thf(zip_derived_cl5598, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (string @ ('#sk8' @ '#sk4') @ '#sk4') 76.47/10.20 | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('demod', [status(thm)], [zip_derived_cl5596, zip_derived_cl10])). 76.47/10.20 thf(zip_derived_cl5600, plain, 76.47/10.20 (![X0 : mu]: 76.47/10.20 (~ (rel_s4 @ '#sk4' @ '#sk4') | ~ (exists_in_world @ X0 @ '#sk4'))), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl129, zip_derived_cl5598])). 76.47/10.20 thf(zip_derived_cl10, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 76.47/10.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 76.47/10.20 thf(zip_derived_cl5602, plain, 76.47/10.20 (![X0 : mu]: ~ (exists_in_world @ X0 @ '#sk4')), 76.47/10.20 inference('demod', [status(thm)], [zip_derived_cl5600, zip_derived_cl10])). 76.47/10.20 thf(zip_derived_cl106, plain, 76.47/10.20 ( (exists_in_world @ ('#sk8' @ '#sk3') @ '#sk4')), 76.47/10.20 inference('sup-', [status(thm)], [zip_derived_cl99, zip_derived_cl102])). 76.47/10.20 thf(zip_derived_cl5606, plain, ($false), 76.47/10.20 inference('sup+', [status(thm)], [zip_derived_cl5602, zip_derived_cl106])). 76.47/10.20 76.47/10.20 % SZS output end Refutation 76.47/10.20 76.47/10.20 76.47/10.20 % Terminating... 76.50/10.28 % Runner terminated. 76.50/10.30 % Zipperpin 1.5 exiting 76.50/10.31 EOF