0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.mBH6UJzwIl true 0.13/0.34 % Computer : n014.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 06:52:16 EDT 2022 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 960 s 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.55/0.64 % Total configuration time : 828 0.55/0.64 % Estimated wc time : 1656 0.55/0.64 % Estimated cpu time (8 cpus) : 207.0 0.55/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.55/0.71 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.55/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.56/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.56/0.77 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.56/0.89 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 5.75/1.36 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s 237.29/30.58 % /export/starexec/sandbox/solver/bin/lams/15_old_s4.sh running for 30s 448.60/57.19 % /export/starexec/sandbox/solver/bin/lams/15_lifting3.sh running for 30s 474.25/60.42 % /export/starexec/sandbox/solver/bin/lams/33_shallow_sine.sh running for 66s 478.55/61.03 % /export/starexec/sandbox/solver/bin/lams/40_e_lift.sh running for 80s 558.07/71.16 % Solved by lams/15_lifting3.sh. 558.07/71.16 % done 4156 iterations in 13.767s 558.07/71.16 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 558.07/71.16 % SZS output start Refutation 558.07/71.16 thf(mu_type, type, mu: $tType). 558.07/71.16 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 558.07/71.16 thf('#form17_type', type, '#form17': $o). 558.07/71.16 thf(mreflexive_type, type, mreflexive: ($i > $i > $o) > $o). 558.07/71.16 thf('#sk5_type', type, '#sk5': $i). 558.07/71.16 thf('#form8_type', type, '#form8': $i > $o). 558.07/71.16 thf(mexists_ind_type, type, mexists_ind: (mu > $i > $o) > $i > $o). 558.07/71.16 thf('#sk9_type', type, '#sk9': $i > mu). 558.07/71.16 thf(big_p_type, type, big_p: mu > $i > $o). 558.07/71.16 thf('#form19_type', type, '#form19': mu > $i > $o). 558.07/71.16 thf('#sk2_type', type, '#sk2': $i). 558.07/71.16 thf('#sk20_type', type, '#sk20': $i > mu). 558.07/71.16 thf(rel_s4_type, type, rel_s4: $i > $i > $o). 558.07/71.16 thf('#form3_type', type, '#form3': $o). 558.07/71.16 thf('#form10_type', type, '#form10': $i > $o). 558.07/71.16 thf('#sk13_type', type, '#sk13': $i). 558.07/71.16 thf('#sk6_type', type, '#sk6': $i). 558.07/71.16 thf('#sk7_type', type, '#sk7': mu). 558.07/71.16 thf('#sk11_type', type, '#sk11': $i > $i). 558.07/71.16 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 558.07/71.16 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 558.07/71.16 thf('#form12_type', type, '#form12': $o). 558.07/71.16 thf(mtransitive_type, type, mtransitive: ($i > $i > $o) > $o). 558.07/71.16 thf('#sk15_type', type, '#sk15': $i). 558.07/71.16 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 558.07/71.16 thf('#sk16_type', type, '#sk16': $i > mu). 558.07/71.16 thf('#sk18_type', type, '#sk18': $i). 558.07/71.16 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o). 558.07/71.16 thf(exists_in_world_type, type, exists_in_world: mu > $i > $o). 558.07/71.16 thf('#sk1_type', type, '#sk1': $i). 558.07/71.16 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o). 558.07/71.16 thf('#sk14_type', type, '#sk14': $i > mu > $i). 558.07/71.16 thf('#sk4_type', type, '#sk4': $i). 558.07/71.16 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 558.07/71.16 thf(mbox_s4, axiom,(( mbox_s4 ) = 558.07/71.16 (^[Phi:( $i > $o ),W:$i]: 558.07/71.16 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s4 @ W @ V ) ) ) )))). 558.07/71.16 thf('0', plain, 558.07/71.16 (( mbox_s4 ) = 558.07/71.16 ( ^[Phi:( $i > $o ),W:$i]: 558.07/71.16 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s4 @ W @ V ) ) ) ) )), 558.07/71.16 inference('simplify_rw_rule', [status(thm)], [mbox_s4])). 558.07/71.16 thf('1', plain, 558.07/71.16 (( mbox_s4 ) = 558.07/71.16 ( ^[V_1:( $i > $o ),V_2:$i]: 558.07/71.16 ( ![X4:$i]: ( ( V_1 @ X4 ) | ( ~( rel_s4 @ V_2 @ X4 ) ) ) ) )), 558.07/71.16 define([status(thm)])). 558.07/71.16 thf(mvalid, axiom,(( mvalid ) = 558.07/71.16 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 558.07/71.16 thf('2', plain, 558.07/71.16 (( mvalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 558.07/71.16 inference('simplify_rw_rule', [status(thm)], [mvalid])). 558.07/71.16 thf('3', plain, 558.07/71.16 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 558.07/71.16 define([status(thm)])). 558.07/71.16 thf(mexists_ind, axiom,(( mexists_ind ) = 558.07/71.16 (^[Phi:( mu > $i > $o )]: 558.07/71.16 ( mnot @ ( mforall_ind @ ( ^[X:mu]: ( mnot @ ( Phi @ X ) ) ) ) )))). 558.07/71.16 thf(mforall_ind, axiom,(( mforall_ind ) = 558.07/71.16 (^[Phi:( mu > $i > $o ),W:$i]: 558.07/71.16 ( ![X:mu]: ( ( exists_in_world @ X @ W ) => ( Phi @ X @ W ) ) )))). 558.07/71.16 thf('4', plain, 558.07/71.16 (( mforall_ind ) = 558.07/71.16 ( ^[Phi:( mu > $i > $o ),W:$i]: 558.07/71.16 ( ![X:mu]: ( ( exists_in_world @ X @ W ) => ( Phi @ X @ W ) ) ) )), 558.07/71.16 inference('simplify_rw_rule', [status(thm)], [mforall_ind])). 558.07/71.16 thf('5', plain, 558.07/71.16 (( mforall_ind ) = 558.07/71.16 ( ^[V_1:( mu > $i > $o ),V_2:$i]: 558.07/71.16 ( ![X4:mu]: ( ( exists_in_world @ X4 @ V_2 ) => ( V_1 @ X4 @ V_2 ) ) ) )), 558.07/71.16 define([status(thm)])). 558.07/71.16 thf(mnot, axiom,(( mnot ) = (^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) )))). 558.07/71.16 thf('6', plain, (( mnot ) = ( ^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) ) )), 558.07/71.16 inference('simplify_rw_rule', [status(thm)], [mnot])). 558.07/71.16 thf('7', plain, 558.07/71.16 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 558.07/71.16 define([status(thm)])). 558.07/71.16 thf('8', plain, 558.07/71.16 (( mexists_ind ) = 558.07/71.16 ( ^[Phi:( mu > $i > $o )]: 558.07/71.16 ( mnot @ ( mforall_ind @ ( ^[X:mu]: ( mnot @ ( Phi @ X ) ) ) ) ) )), 558.07/71.16 inference('simplify_rw_rule', [status(thm)], [mexists_ind, '5', '7'])). 558.07/71.16 thf('9', plain, 558.07/71.16 (( mexists_ind ) = 558.07/71.16 ( ^[V_1:( mu > $i > $o )]: 558.07/71.16 ( mnot @ ( mforall_ind @ ( ^[V_2:mu]: ( mnot @ ( V_1 @ V_2 ) ) ) ) ) )), 558.07/71.16 define([status(thm)])). 558.07/71.16 thf(mimplies, axiom,(( mimplies ) = 558.07/71.16 (^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi )))). 558.07/71.16 thf(mor, axiom,(( mor ) = 558.07/71.16 (^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) )))). 558.07/71.16 thf('10', plain, 558.07/71.16 (( mor ) = 558.07/71.16 ( ^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) ) )), 558.07/71.16 inference('simplify_rw_rule', [status(thm)], [mor])). 558.07/71.16 thf('11', plain, 558.07/71.16 (( mor ) = 558.07/71.16 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 558.07/71.16 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 558.07/71.16 define([status(thm)])). 558.07/71.16 thf('12', plain, 558.07/71.16 (( mimplies ) = 558.07/71.16 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi ) )), 558.07/71.16 inference('simplify_rw_rule', [status(thm)], [mimplies, '11', '7'])). 558.07/71.16 thf('13', plain, 558.07/71.16 (( mimplies ) = 558.07/71.16 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 558.07/71.16 define([status(thm)])). 558.07/71.16 thf(mand, axiom,(( mand ) = 558.07/71.16 (^[Phi:( $i > $o ),Psi:( $i > $o )]: 558.07/71.16 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) )))). 558.07/71.16 thf('14', plain, 558.07/71.16 (( mand ) = 558.07/71.16 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: 558.07/71.16 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) )), 558.07/71.16 inference('simplify_rw_rule', [status(thm)], [mand, '11', '7'])). 558.07/71.16 thf('15', plain, 558.07/71.16 (( mand ) = 558.07/71.16 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 558.07/71.16 ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) )), 558.07/71.16 define([status(thm)])). 558.07/71.16 thf(x2128, conjecture, 558.07/71.16 (mvalid @ 558.07/71.16 ( mand @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mimplies @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mforall_ind @ 558.07/71.16 ( ^[X:mu]: 558.07/71.16 ( mand @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mimplies @ 558.07/71.16 ( mbox_s4 @ ( big_p @ X ) ) @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mforall_ind @ 558.07/71.16 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mimplies @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mforall_ind @ 558.07/71.16 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 558.07/71.16 ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) @ 558.07/71.16 ( mand @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mimplies @ 558.07/71.16 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mimplies @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 558.07/71.16 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) ) @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mimplies @ 558.07/71.16 ( mand @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mimplies @ 558.07/71.16 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mimplies @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 558.07/71.16 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mforall_ind @ 558.07/71.16 ( ^[X:mu]: 558.07/71.16 ( mand @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mimplies @ 558.07/71.16 ( mbox_s4 @ ( big_p @ X ) ) @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mforall_ind @ 558.07/71.16 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mimplies @ 558.07/71.16 ( mbox_s4 @ 558.07/71.16 ( mforall_ind @ 558.07/71.16 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 558.07/71.16 ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) ) ) ))). 558.07/71.16 thf(zf_stmt_0, conjecture, 558.07/71.16 (![X4:$i]: 558.07/71.16 ( ~( ( ~( ![X56:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X4 @ X56 ) ) | 558.07/71.16 ( ![X82:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X56 @ X82 ) ) | 558.07/71.16 ( ![X84:mu]: 558.07/71.16 ( ( exists_in_world @ X84 @ X82 ) => 558.07/71.16 ( ~( ( ~( ![X96:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X82 @ X96 ) ) | 558.07/71.16 ( ![X104:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X96 @ X104 ) ) | 558.07/71.16 ( big_p @ X84 @ X104 ) ) ) | 558.07/71.16 ( ~( ![X98:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X96 @ X98 ) ) | 558.07/71.16 ( ![X100:mu]: 558.07/71.16 ( ( exists_in_world @ X100 @ X98 ) => 558.07/71.16 ( ![X102:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X98 @ X102 ) ) | 558.07/71.16 ( big_p @ X100 @ X102 ) ) ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X86:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X82 @ X86 ) ) | 558.07/71.16 ( ![X90:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X86 @ X90 ) ) | 558.07/71.16 ( ![X92:mu]: 558.07/71.16 ( ( exists_in_world @ X92 @ X90 ) => 558.07/71.16 ( ![X94:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X90 @ X94 ) ) | 558.07/71.16 ( big_p @ X92 @ X94 ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X88:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X86 @ X88 ) ) | 558.07/71.16 ( big_p @ X84 @ X88 ) ) ) ) ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X58:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X56 @ X58 ) ) | 558.07/71.16 ( ![X64:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X58 @ X64 ) ) | 558.07/71.16 ( ![X66:mu]: 558.07/71.16 ( ( exists_in_world @ X66 @ X64 ) => 558.07/71.16 ( ![X68:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X64 @ X68 ) ) | 558.07/71.16 ( big_p @ X66 @ X68 ) ) ) ) ) ) ) | 558.07/71.16 ( ![X60:mu]: 558.07/71.16 ( ( exists_in_world @ X60 @ X58 ) => 558.07/71.16 ( ~( ![X62:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X58 @ X62 ) ) | 558.07/71.16 ( big_p @ X60 @ X62 ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X70:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X56 @ X70 ) ) | 558.07/71.16 ( ~( ![X78:mu]: 558.07/71.16 ( ( exists_in_world @ X78 @ X70 ) => 558.07/71.16 ( ~( ![X80:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X70 @ X80 ) ) | 558.07/71.16 ( big_p @ X78 @ X80 ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X72:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X70 @ X72 ) ) | 558.07/71.16 ( ![X74:mu]: 558.07/71.16 ( ( exists_in_world @ X74 @ X72 ) => 558.07/71.16 ( ![X76:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X72 @ X76 ) ) | 558.07/71.16 ( big_p @ X74 @ X76 ) ) ) ) ) ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X6:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X4 @ X6 ) ) | 558.07/71.16 ( ~( ( ~( ![X44:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X6 @ X44 ) ) | 558.07/71.16 ( ~( ![X52:mu]: 558.07/71.16 ( ( exists_in_world @ X52 @ X44 ) => 558.07/71.16 ( ~( ![X54:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X44 @ X54 ) ) | 558.07/71.16 ( big_p @ X52 @ X54 ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X46:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X44 @ X46 ) ) | 558.07/71.16 ( ![X48:mu]: 558.07/71.16 ( ( exists_in_world @ X48 @ X46 ) => 558.07/71.16 ( ![X50:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X46 @ X50 ) ) | 558.07/71.16 ( big_p @ X48 @ X50 ) ) ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X32:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X6 @ X32 ) ) | 558.07/71.16 ( ![X38:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X32 @ X38 ) ) | 558.07/71.16 ( ![X40:mu]: 558.07/71.16 ( ( exists_in_world @ X40 @ X38 ) => 558.07/71.16 ( ![X42:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X38 @ X42 ) ) | 558.07/71.16 ( big_p @ X40 @ X42 ) ) ) ) ) ) ) | 558.07/71.16 ( ![X34:mu]: 558.07/71.16 ( ( exists_in_world @ X34 @ X32 ) => 558.07/71.16 ( ~( ![X36:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X32 @ X36 ) ) | 558.07/71.16 ( big_p @ X34 @ X36 ) ) ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X8:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X6 @ X8 ) ) | 558.07/71.16 ( ![X10:mu]: 558.07/71.16 ( ( exists_in_world @ X10 @ X8 ) => 558.07/71.16 ( ~( ( ~( ![X22:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X8 @ X22 ) ) | 558.07/71.16 ( ![X30:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X22 @ X30 ) ) | 558.07/71.16 ( big_p @ X10 @ X30 ) ) ) | 558.07/71.16 ( ~( ![X24:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X22 @ X24 ) ) | 558.07/71.16 ( ![X26:mu]: 558.07/71.16 ( ( exists_in_world @ 558.07/71.16 X26 @ X24 ) => 558.07/71.16 ( ![X28:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X24 @ X28 ) ) | 558.07/71.16 ( big_p @ X26 @ X28 ) ) ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X12:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X8 @ X12 ) ) | 558.07/71.16 ( ![X16:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X12 @ X16 ) ) | 558.07/71.16 ( ![X18:mu]: 558.07/71.16 ( ( exists_in_world @ X18 @ X16 ) => 558.07/71.16 ( ![X20:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X16 @ X20 ) ) | 558.07/71.16 ( big_p @ X18 @ X20 ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X14:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X12 @ X14 ) ) | 558.07/71.16 ( big_p @ X10 @ X14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 558.07/71.16 thf(zf_stmt_1, negated_conjecture, 558.07/71.16 (~( ![X4:$i]: 558.07/71.16 ( ~( ( ~( ![X56:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X4 @ X56 ) ) | 558.07/71.16 ( ![X82:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X56 @ X82 ) ) | 558.07/71.16 ( ![X84:mu]: 558.07/71.16 ( ( exists_in_world @ X84 @ X82 ) => 558.07/71.16 ( ~( ( ~( ![X96:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X82 @ X96 ) ) | 558.07/71.16 ( ![X104:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X96 @ X104 ) ) | 558.07/71.16 ( big_p @ X84 @ X104 ) ) ) | 558.07/71.16 ( ~( ![X98:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X96 @ X98 ) ) | 558.07/71.16 ( ![X100:mu]: 558.07/71.16 ( ( exists_in_world @ 558.07/71.16 X100 @ X98 ) => 558.07/71.16 ( ![X102:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X98 @ X102 ) ) | 558.07/71.16 ( big_p @ X100 @ X102 ) ) ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X86:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X82 @ X86 ) ) | 558.07/71.16 ( ![X90:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X86 @ X90 ) ) | 558.07/71.16 ( ![X92:mu]: 558.07/71.16 ( ( exists_in_world @ X92 @ X90 ) => 558.07/71.16 ( ![X94:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X90 @ X94 ) ) | 558.07/71.16 ( big_p @ X92 @ X94 ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X88:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X86 @ X88 ) ) | 558.07/71.16 ( big_p @ X84 @ X88 ) ) ) ) ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X58:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X56 @ X58 ) ) | 558.07/71.16 ( ![X64:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X58 @ X64 ) ) | 558.07/71.16 ( ![X66:mu]: 558.07/71.16 ( ( exists_in_world @ X66 @ X64 ) => 558.07/71.16 ( ![X68:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X64 @ X68 ) ) | 558.07/71.16 ( big_p @ X66 @ X68 ) ) ) ) ) ) ) | 558.07/71.16 ( ![X60:mu]: 558.07/71.16 ( ( exists_in_world @ X60 @ X58 ) => 558.07/71.16 ( ~( ![X62:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X58 @ X62 ) ) | 558.07/71.16 ( big_p @ X60 @ X62 ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X70:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X56 @ X70 ) ) | 558.07/71.16 ( ~( ![X78:mu]: 558.07/71.16 ( ( exists_in_world @ X78 @ X70 ) => 558.07/71.16 ( ~( ![X80:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X70 @ X80 ) ) | 558.07/71.16 ( big_p @ X78 @ X80 ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X72:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X70 @ X72 ) ) | 558.07/71.16 ( ![X74:mu]: 558.07/71.16 ( ( exists_in_world @ X74 @ X72 ) => 558.07/71.16 ( ![X76:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X72 @ X76 ) ) | 558.07/71.16 ( big_p @ X74 @ X76 ) ) ) ) ) ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X6:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X4 @ X6 ) ) | 558.07/71.16 ( ~( ( ~( ![X44:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X6 @ X44 ) ) | 558.07/71.16 ( ~( ![X52:mu]: 558.07/71.16 ( ( exists_in_world @ X52 @ X44 ) => 558.07/71.16 ( ~( ![X54:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X44 @ X54 ) ) | 558.07/71.16 ( big_p @ X52 @ X54 ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X46:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X44 @ X46 ) ) | 558.07/71.16 ( ![X48:mu]: 558.07/71.16 ( ( exists_in_world @ X48 @ X46 ) => 558.07/71.16 ( ![X50:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X46 @ X50 ) ) | 558.07/71.16 ( big_p @ X48 @ X50 ) ) ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X32:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X6 @ X32 ) ) | 558.07/71.16 ( ![X38:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X32 @ X38 ) ) | 558.07/71.16 ( ![X40:mu]: 558.07/71.16 ( ( exists_in_world @ X40 @ X38 ) => 558.07/71.16 ( ![X42:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X38 @ X42 ) ) | 558.07/71.16 ( big_p @ X40 @ X42 ) ) ) ) ) ) ) | 558.07/71.16 ( ![X34:mu]: 558.07/71.16 ( ( exists_in_world @ X34 @ X32 ) => 558.07/71.16 ( ~( ![X36:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X32 @ X36 ) ) | 558.07/71.16 ( big_p @ X34 @ X36 ) ) ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X8:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X6 @ X8 ) ) | 558.07/71.16 ( ![X10:mu]: 558.07/71.16 ( ( exists_in_world @ X10 @ X8 ) => 558.07/71.16 ( ~( ( ~( ![X22:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X8 @ X22 ) ) | 558.07/71.16 ( ![X30:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X22 @ X30 ) ) | 558.07/71.16 ( big_p @ X10 @ X30 ) ) ) | 558.07/71.16 ( ~( ![X24:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X22 @ X24 ) ) | 558.07/71.16 ( ![X26:mu]: 558.07/71.16 ( ( exists_in_world @ 558.07/71.16 X26 @ X24 ) => 558.07/71.16 ( ![X28:$i]: 558.07/71.16 ( ( ~( rel_s4 @ 558.07/71.16 X24 @ X28 ) ) | 558.07/71.16 ( big_p @ X26 @ X28 ) ) ) ) ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X12:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X8 @ X12 ) ) | 558.07/71.16 ( ![X16:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X12 @ X16 ) ) | 558.07/71.16 ( ![X18:mu]: 558.07/71.16 ( ( exists_in_world @ 558.07/71.16 X18 @ X16 ) => 558.07/71.16 ( ![X20:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X16 @ X20 ) ) | 558.07/71.16 ( big_p @ X18 @ X20 ) ) ) ) ) ) ) | 558.07/71.16 ( ~( ![X14:$i]: 558.07/71.16 ( ( ~( rel_s4 @ X12 @ X14 ) ) | 558.07/71.16 ( big_p @ X10 @ X14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 558.07/71.16 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 558.07/71.16 thf(zip_derived_cl4, plain, 558.07/71.16 (~ (((!!) @ (^[Y0 : $i]: 558.07/71.16 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.16 (((!!) @ (^[Y2 : $i]: 558.07/71.16 (((((~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y2))) | 558.07/71.16 (((!!) @ ( 558.07/71.16 ^[Y3 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y3 @ 558.07/71.16 Y2) => 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y4))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y4 @ Y5))) | 558.07/71.16 (big_p @ 558.07/71.16 Y3 @ Y5)))))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y4 @ Y5))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y6 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y6 @ 558.07/71.16 Y5) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y7 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y5 @ Y7))) | 558.07/71.16 (big_p @ 558.07/71.16 Y6 @ Y7))))))))))))))))))))))))) | 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y4))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y4 @ Y5))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y6 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y6 @ 558.07/71.16 Y5) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y7 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y5 @ Y7))) | 558.07/71.16 (big_p @ 558.07/71.16 Y6 @ Y7)))))))))))))))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y4 @ Y5))) | 558.07/71.16 (big_p @ 558.07/71.16 Y3 @ Y5))))))))))))))))))))))))))))) | 558.07/71.16 (((~) @ (((!!) @ ( 558.07/71.16 ^[Y2 : $i]: 558.07/71.16 (((((~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y2))) | 558.07/71.16 (((!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y3))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y4 @ 558.07/71.16 Y3) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y5))) | 558.07/71.16 (big_p @ 558.07/71.16 Y4 @ Y5)))))))))))))))) | 558.07/71.16 (((!!) @ ( 558.07/71.16 ^[Y3 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y3 @ 558.07/71.16 Y2) => 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y4))) | 558.07/71.16 (big_p @ 558.07/71.16 Y3 @ Y4)))))))))))))))))))) | 558.07/71.16 (((~) @ (((!!) @ ( 558.07/71.16 ^[Y2 : $i]: 558.07/71.16 (((((~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y2))) | 558.07/71.16 (((~) @ ( 558.07/71.16 ((!!) @ ( 558.07/71.16 ^[Y3 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y3 @ 558.07/71.16 Y2) => 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y4))) | 558.07/71.16 (big_p @ 558.07/71.16 Y3 @ Y4))))))))))))))) | 558.07/71.16 (((~) @ ( 558.07/71.16 ((!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y3))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y4 @ 558.07/71.16 Y3) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y5))) | 558.07/71.16 (big_p @ 558.07/71.16 Y4 @ Y5)))))))))))))))))))))))))))))))) | 558.07/71.16 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.16 (((~) @ (((((~) @ ( 558.07/71.16 ((!!) @ ( 558.07/71.16 ^[Y2 : $i]: 558.07/71.16 ((( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y2))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y3 @ 558.07/71.16 Y2) => 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y4))) | 558.07/71.16 (big_p @ 558.07/71.16 Y3 @ Y4))))))))))))))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y3))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y4 @ 558.07/71.16 Y3) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y5))) | 558.07/71.16 (big_p @ 558.07/71.16 Y4 @ Y5))))))))))))))))))))))))) | 558.07/71.16 (((~) @ ( 558.07/71.16 ((!!) @ ( 558.07/71.16 ^[Y2 : $i]: 558.07/71.16 ((( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y2))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y3))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 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Y4))))))))))))))))))))))))))))))))))))))))), 558.07/71.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])). 558.07/71.16 thf(zip_derived_cl6, plain, 558.07/71.16 ((~ (((!!) @ (^[Y0 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 558.07/71.16 (((!!) @ (^[Y1 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.16 (((!!) @ (^[Y2 : mu]: 558.07/71.16 (((exists_in_world @ Y2 @ 558.07/71.16 Y1) => 558.07/71.16 (((~) @ (((((~) @ ( 558.07/71.16 ((!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (((( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y3))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y4))) | 558.07/71.16 (big_p @ 558.07/71.16 Y2 @ Y4)))))) | 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y4))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y5 @ 558.07/71.16 Y4) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y6 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y4 @ Y6))) | 558.07/71.16 (big_p @ 558.07/71.16 Y5 @ Y6))))))))))))))))))))))))) | 558.07/71.16 (((~) @ ( 558.07/71.16 ((!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (((( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y3))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y4))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y5 @ 558.07/71.16 Y4) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y6 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y4 @ Y6))) | 558.07/71.16 (big_p @ 558.07/71.16 Y5 @ Y6)))))))))))))))) | 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y4))) | 558.07/71.16 (big_p @ 558.07/71.16 Y2 @ Y4))))))))))))))))))))))))))))) | 558.07/71.16 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.16 (((!!) @ (^[Y2 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ 558.07/71.16 Y1 @ Y2))) | 558.07/71.16 (((!!) @ (^[Y3 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y3 @ 558.07/71.16 Y2) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y4))) | 558.07/71.16 (big_p @ 558.07/71.16 Y3 @ Y4)))))))))))))))) | 558.07/71.16 (((!!) @ (^[Y2 : mu]: 558.07/71.16 (((exists_in_world @ 558.07/71.16 Y2 @ Y1) => 558.07/71.16 (((~) @ (((!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y3))) | 558.07/71.16 (big_p @ 558.07/71.16 Y2 @ Y3)))))))))))))))))))) | 558.07/71.16 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.16 (((~) @ (((!!) @ (^[Y2 : mu]: 558.07/71.16 (((exists_in_world @ 558.07/71.16 Y2 @ Y1) => 558.07/71.16 (((~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y3))) | 558.07/71.16 (big_p @ 558.07/71.16 Y2 @ Y3))))))))))))))) | 558.07/71.16 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.16 (((((~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y2))) | 558.07/71.16 (((!!) @ ( 558.07/71.16 ^[Y3 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y3 @ 558.07/71.16 Y2) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y4))) | 558.07/71.16 (big_p @ 558.07/71.16 Y3 @ Y4)))))))))))))))))))))))))))))) 558.07/71.16 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 558.07/71.16 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ 558.07/71.16 Y0 @ Y1))) | 558.07/71.16 (((~) @ (((!!) @ ( 558.07/71.16 ^[Y2 : mu]: 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y2 @ 558.07/71.16 Y1) => 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y3))) | 558.07/71.16 (big_p @ 558.07/71.16 Y2 @ Y3))))))))))))))) | 558.07/71.16 (((~) @ (((!!) @ ( 558.07/71.16 ^[Y2 : $i]: 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y2))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y3 @ 558.07/71.16 Y2) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y4))) | 558.07/71.16 (big_p @ 558.07/71.16 Y3 @ Y4))))))))))))))))))))))))) | 558.07/71.16 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ 558.07/71.16 Y0 @ Y1))) | 558.07/71.16 (((!!) @ (^[Y2 : $i]: 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y2))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y3 @ 558.07/71.16 Y2) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y4))) | 558.07/71.16 (big_p @ 558.07/71.16 Y3 @ Y4)))))))))))))))) | 558.07/71.16 (((!!) @ (^[Y2 : mu]: 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y2 @ 558.07/71.16 Y1) => 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y3))) | 558.07/71.16 (big_p @ 558.07/71.16 Y2 @ Y3)))))))))))))))))))))))) | 558.07/71.16 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.16 (((!!) @ (^[Y2 : mu]: 558.07/71.16 (((exists_in_world @ 558.07/71.16 Y2 @ Y1) => 558.07/71.16 (((~) @ ( 558.07/71.16 ((((~) @ ( 558.07/71.16 ((!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y3))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y4))) | 558.07/71.16 (big_p @ 558.07/71.16 Y2 @ Y4)))))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y4))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y5 @ 558.07/71.16 Y4) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y6 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y4 @ Y6))) | 558.07/71.16 (big_p @ 558.07/71.16 Y5 @ Y6))))))))))))))))))))))))) | 558.07/71.16 (((~) @ ( 558.07/71.16 ((!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y3))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y4))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y5 @ 558.07/71.16 Y4) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y6 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y4 @ Y6))) | 558.07/71.16 (big_p @ 558.07/71.16 Y5 @ Y6)))))))))))))))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y4))) | 558.07/71.16 (big_p @ 558.07/71.16 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 558.07/71.16 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl5])). 558.07/71.16 thf(zip_derived_cl7, plain, 558.07/71.16 ((~ (((((~) @ (rel_s4 @ '#sk1' @ '#sk2'))) | 558.07/71.16 (((!!) @ (^[Y0 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 558.07/71.16 (((!!) @ (^[Y1 : mu]: 558.07/71.16 (((exists_in_world @ Y1 @ Y0) => 558.07/71.16 (((~) @ (((((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y0 @ Y2))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y3))) | 558.07/71.16 (big_p @ 558.07/71.16 Y1 @ Y3)))))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y3))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y4 @ 558.07/71.16 Y3) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y5))) | 558.07/71.16 (big_p @ 558.07/71.16 Y4 @ Y5))))))))))))))))))))))))) | 558.07/71.16 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y0 @ Y2))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y3))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y4 @ 558.07/71.16 Y3) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y5))) | 558.07/71.16 (big_p @ 558.07/71.16 Y4 @ Y5)))))))))))))))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y3))) | 558.07/71.16 (big_p @ 558.07/71.16 Y1 @ Y3))))))))))))))))))))))))))))) | 558.07/71.16 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 558.07/71.16 (((!!) @ (^[Y1 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.16 (((!!) @ (^[Y2 : mu]: 558.07/71.16 (((exists_in_world @ 558.07/71.16 Y2 @ Y1) => 558.07/71.16 (((!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (((((~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y3))) | 558.07/71.16 (big_p @ 558.07/71.16 Y2 @ Y3)))))))))))))))) | 558.07/71.16 (((!!) @ (^[Y1 : mu]: 558.07/71.16 (((exists_in_world @ Y1 @ Y0) => 558.07/71.16 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.16 (((( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y0 @ Y2))) | 558.07/71.16 (big_p @ 558.07/71.16 Y1 @ Y2)))))))))))))))))))) | 558.07/71.16 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 558.07/71.16 (((~) @ (((!!) @ (^[Y1 : mu]: 558.07/71.16 (((exists_in_world @ 558.07/71.16 Y1 @ Y0) => 558.07/71.16 (((~) @ 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Y2 @ Y1) => 558.07/71.16 (((~) @ ( 558.07/71.16 ((((~) @ ( 558.07/71.16 ((!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y3))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y4))) | 558.07/71.16 (big_p @ 558.07/71.16 Y2 @ Y4)))))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y4))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y5 @ 558.07/71.16 Y4) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y6 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y4 @ Y6))) | 558.07/71.16 (big_p @ 558.07/71.16 Y5 @ Y6))))))))))))))))))))))))) | 558.07/71.16 (((~) @ ( 558.07/71.16 ((!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y1 @ Y3))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y4))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y5 @ 558.07/71.16 Y4) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y6 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y4 @ Y6))) | 558.07/71.16 (big_p @ 558.07/71.16 Y5 @ Y6)))))))))))))))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y4))) | 558.07/71.16 (big_p @ 558.07/71.16 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 558.07/71.16 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 558.07/71.16 thf(zip_derived_cl9, plain, 558.07/71.16 ((~ (((!!) @ (^[Y0 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 558.07/71.16 (((!!) @ (^[Y1 : mu]: 558.07/71.16 (((exists_in_world @ Y1 @ Y0) => 558.07/71.16 (((~) @ (((((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.16 ((( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y0 @ Y2))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y3))) | 558.07/71.16 (big_p @ 558.07/71.16 Y1 @ Y3)))))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y3))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y4 @ 558.07/71.16 Y3) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y5))) | 558.07/71.16 (big_p @ 558.07/71.16 Y4 @ Y5))))))))))))))))))))))))) | 558.07/71.16 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.16 ((( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y0 @ Y2))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y3))) | 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y4 : mu]: 558.07/71.16 (( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y4 @ 558.07/71.16 Y3) => 558.07/71.16 (( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y5 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y3 @ Y5))) | 558.07/71.16 (big_p @ 558.07/71.16 Y4 @ Y5)))))))))))))))) | 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 rel_s4 @ 558.07/71.16 Y2 @ Y3))) | 558.07/71.16 (big_p @ 558.07/71.16 Y1 @ Y3))))))))))))))))))))))))))))) 558.07/71.16 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 558.07/71.16 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.16 (((((~) @ (rel_s4 @ 558.07/71.16 Y0 @ Y1))) | 558.07/71.16 (((~) @ (((!!) @ ( 558.07/71.16 ^[Y2 : mu]: 558.07/71.16 ( 558.07/71.16 ( 558.07/71.16 (exists_in_world @ 558.07/71.16 Y2 @ 558.07/71.16 Y1) => 558.07/71.16 (( 558.07/71.16 (~) @ ( 558.07/71.16 ( 558.07/71.16 (!!) @ ( 558.07/71.16 ^[Y3 : $i]: 558.07/71.16 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y3 @ 558.07/71.17 Y2) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y3 @ Y4))))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y3 @ 558.07/71.17 Y2) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y3 @ Y4)))))))))))))))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y2 @ Y1) => 558.07/71.17 (((~) @ ( 558.07/71.17 ((((~) @ ( 558.07/71.17 ((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y4)))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y5 @ 558.07/71.17 Y4) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y6 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y4 @ Y6))) | 558.07/71.17 (big_p @ 558.07/71.17 Y5 @ Y6))))))))))))))))))))))))) | 558.07/71.17 (((~) @ ( 558.07/71.17 ((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y5 @ 558.07/71.17 Y4) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y6 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y4 @ Y6))) | 558.07/71.17 (big_p @ 558.07/71.17 Y5 @ Y6)))))))))))))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])). 558.07/71.17 thf(zip_derived_cl8, plain, 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558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y2 @ Y1) => 558.07/71.17 (((~) @ ( 558.07/71.17 ((((~) @ ( 558.07/71.17 ((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y4)))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y5 @ 558.07/71.17 Y4) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y6 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y4 @ Y6))) | 558.07/71.17 (big_p @ 558.07/71.17 Y5 @ Y6))))))))))))))))))))))))) | 558.07/71.17 (((~) @ ( 558.07/71.17 ((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y5 @ 558.07/71.17 Y4) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y6 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y4 @ Y6))) | 558.07/71.17 (big_p @ 558.07/71.17 Y5 @ Y6)))))))))))))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])). 558.07/71.17 thf(zip_derived_cl12, plain, 558.07/71.17 (( ('#form3') 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 558.07/71.17 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : mu]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 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558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y2 @ Y1) => 558.07/71.17 (((~) @ ( 558.07/71.17 ((((~) @ ( 558.07/71.17 ((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y4)))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y5 @ 558.07/71.17 Y4) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y6 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y4 @ Y6))) | 558.07/71.17 (big_p @ 558.07/71.17 Y5 @ Y6))))))))))))))))))))))))) | 558.07/71.17 (((~) @ ( 558.07/71.17 ((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y5 @ 558.07/71.17 Y4) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y6 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y4 @ Y6))) | 558.07/71.17 (big_p @ 558.07/71.17 Y5 @ Y6)))))))))))))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 558.07/71.17 define([status(thm)])). 558.07/71.17 thf(zip_derived_cl15, plain, 558.07/71.17 ((~ ('#form3') 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((~) @ (((((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y0 @ Y2))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y1 @ Y3)))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y3))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y4 @ 558.07/71.17 Y3) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y5))) | 558.07/71.17 (big_p @ 558.07/71.17 Y4 @ Y5))))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y0 @ Y2))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y3))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y4 @ 558.07/71.17 Y3) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y5))) | 558.07/71.17 (big_p @ 558.07/71.17 Y4 @ Y5)))))))))))))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y1 @ Y3))))))))))))))))))))))))))))))), 558.07/71.17 inference('renaming', [status(thm)], [zip_derived_cl9, zip_derived_cl12])). 558.07/71.17 thf(zip_derived_cl21, plain, 558.07/71.17 ((~ (((((~) @ (rel_s4 @ '#sk2' @ '#sk5'))) | 558.07/71.17 (((!!) @ (^[Y0 : mu]: 558.07/71.17 (((exists_in_world @ Y0 @ '#sk5') => 558.07/71.17 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 '#sk5' @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (big_p @ 558.07/71.17 Y0 @ Y2)))))) | 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y3 @ 558.07/71.17 Y2) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y3 @ Y4))))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 '#sk5' @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y3 @ 558.07/71.17 Y2) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y3 @ Y4)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (big_p @ 558.07/71.17 Y0 @ Y2)))))))))))))))))))))))))) 558.07/71.17 | ~ ('#form3'))), 558.07/71.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 558.07/71.17 thf(zip_derived_cl27, plain, 558.07/71.17 ((~ (((!!) @ (^[Y0 : mu]: 558.07/71.17 (((exists_in_world @ Y0 @ '#sk5') => 558.07/71.17 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 '#sk5' @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (big_p @ 558.07/71.17 Y0 @ Y2)))))) | 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : $i]: 558.07/71.17 (((( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y3 @ 558.07/71.17 Y2) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y3 @ Y4))))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 '#sk5' @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y3 @ 558.07/71.17 Y2) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y3 @ Y4)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : $i]: 558.07/71.17 (((( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (big_p @ 558.07/71.17 Y0 @ Y2)))))))))))))))))))))))) 558.07/71.17 | ~ ('#form3'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl21])). 558.07/71.17 thf(zip_derived_cl32, plain, 558.07/71.17 ((~ (((exists_in_world @ '#sk7' @ '#sk5') => 558.07/71.17 (((~) @ (((((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (big_p @ '#sk7' @ Y1)))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (((!!) @ ( 558.07/71.17 ^[Y2 : mu]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3))))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (big_p @ 558.07/71.17 '#sk7' @ Y1))))))))))))))))))))) 558.07/71.17 | ~ ('#form3'))), 558.07/71.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl27])). 558.07/71.17 thf(zip_derived_cl44, plain, 558.07/71.17 (( (((((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (big_p @ '#sk7' @ Y1)))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.17 Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3))))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y2 @ Y1) => 558.07/71.17 (((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.17 Y1))) | 558.07/71.17 (big_p @ '#sk7' @ Y1))))))))))))))))) 558.07/71.17 | ~ ('#form3'))), 558.07/71.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl32])). 558.07/71.17 thf(zip_derived_cl60, plain, 558.07/71.17 ((~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | (big_p @ 558.07/71.17 '#sk7' @ Y1)))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y2 @ Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3))))))))))))))))))))))) 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (big_p @ '#sk7' @ Y1))))))))))))) 558.07/71.17 | ~ ('#form3'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 558.07/71.17 thf(zip_derived_cl74, plain, 558.07/71.17 ((~ (((((~) @ (rel_s4 @ '#sk5' @ '#sk15'))) | 558.07/71.17 (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk15' @ Y0))) | (big_p @ 558.07/71.17 '#sk7' @ Y0)))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk15' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ Y0 @ 558.07/71.17 Y2))) | 558.07/71.17 (big_p @ Y1 @ Y2)))))))))))))))))))) 558.07/71.17 | ~ ('#form3') 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (big_p @ '#sk7' @ Y1))))))))))))))), 558.07/71.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])). 558.07/71.17 thf(zip_derived_cl85, plain, 558.07/71.17 (( (rel_s4 @ '#sk5' @ '#sk15') 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (big_p @ '#sk7' @ Y1))))))))))))) 558.07/71.17 | ~ ('#form3'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 558.07/71.17 thf(zip_derived_cl98, plain, 558.07/71.17 (( ('#form17') 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (big_p @ '#sk7' @ Y1))))))))))))))), 558.07/71.17 define([status(thm)])). 558.07/71.17 thf(zip_derived_cl99, plain, 558.07/71.17 ((~ (((((~) @ (rel_s4 @ '#sk5' @ '#sk18'))) | 558.07/71.17 (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk18' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 558.07/71.17 (big_p @ Y1 @ Y2)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk18' @ Y0))) | (big_p @ 558.07/71.17 '#sk7' @ Y0)))))))))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl98])). 558.07/71.17 thf(zip_derived_cl111, plain, 558.07/71.17 ((~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk18' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 558.07/71.17 (big_p @ Y1 @ Y2)))))))))))))))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl99])). 558.07/71.17 thf(zip_derived_cl126, plain, 558.07/71.17 ((~ (((((~) @ (rel_s4 @ '#sk18' @ ('#sk11' @ '#sk18')))) | 558.07/71.17 (((!!) @ (^[Y0 : mu]: 558.07/71.17 (((exists_in_world @ Y0 @ ('#sk11' @ '#sk18')) => 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 ('#sk11' @ '#sk18') @ Y1))) | 558.07/71.17 (big_p @ Y0 @ Y1))))))))))))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl111])). 558.07/71.17 thf(zip_derived_cl135, plain, 558.07/71.17 ((~ (((!!) @ (^[Y0 : mu]: 558.07/71.17 (((exists_in_world @ Y0 @ ('#sk11' @ '#sk18')) => 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ ('#sk11' @ '#sk18') @ 558.07/71.17 Y1))) | 558.07/71.17 (big_p @ Y0 @ Y1))))))))))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl126])). 558.07/71.17 thf(zip_derived_cl139, plain, 558.07/71.17 ((~ (((exists_in_world @ ('#sk16' @ '#sk18') @ ('#sk11' @ '#sk18')) => 558.07/71.17 (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ ('#sk11' @ '#sk18') @ Y0))) | 558.07/71.17 (big_p @ ('#sk16' @ '#sk18') @ Y0)))))))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl135])). 558.07/71.17 thf(zip_derived_cl141, plain, 558.07/71.17 ((~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ ('#sk11' @ '#sk18') @ Y0))) | 558.07/71.17 (big_p @ ('#sk16' @ '#sk18') @ Y0)))))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 558.07/71.17 thf(zip_derived_cl142, plain, 558.07/71.17 ((~ (((((~) @ (rel_s4 @ ('#sk11' @ '#sk18') @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))))) | 558.07/71.17 (big_p @ ('#sk16' @ '#sk18') @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl141])). 558.07/71.17 thf(zip_derived_cl143, plain, 558.07/71.17 (( (rel_s4 @ ('#sk11' @ '#sk18') @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl142])). 558.07/71.17 thf(zip_derived_cl140, plain, 558.07/71.17 (( (exists_in_world @ ('#sk16' @ '#sk18') @ ('#sk11' @ '#sk18')) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 558.07/71.17 thf(cumulative_ax, axiom, 558.07/71.17 (![X:mu,V:$i,W:$i]: 558.07/71.17 ( ( ( exists_in_world @ X @ V ) & ( rel_s4 @ V @ W ) ) => 558.07/71.17 ( exists_in_world @ X @ W ) ))). 558.07/71.17 thf(zip_derived_cl3, plain, 558.07/71.17 ( (((!!) @ (^[Y0 : mu]: 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((exists_in_world @ Y0 @ Y1) & 558.07/71.17 (rel_s4 @ Y1 @ Y2))) => 558.07/71.17 (exists_in_world @ Y0 @ Y2))))))))))))), 558.07/71.17 inference('cnf', [status(esa)], [cumulative_ax])). 558.07/71.17 thf(zip_derived_cl191, plain, 558.07/71.17 (![X2 : mu]: 558.07/71.17 (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((exists_in_world @ X2 @ Y0) & (rel_s4 @ 558.07/71.17 Y0 @ Y1))) => 558.07/71.17 (exists_in_world @ X2 @ Y1)))))))))), 558.07/71.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 558.07/71.17 thf(zip_derived_cl192, plain, 558.07/71.17 (![X2 : mu, X4 : $i]: 558.07/71.17 (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((exists_in_world @ X2 @ X4) & (rel_s4 @ X4 @ Y0))) => 558.07/71.17 (exists_in_world @ X2 @ Y0))))))), 558.07/71.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl191])). 558.07/71.17 thf(zip_derived_cl193, plain, 558.07/71.17 (![X2 : mu, X4 : $i, X6 : $i]: 558.07/71.17 (((((exists_in_world @ X2 @ X4) & (rel_s4 @ X4 @ X6))) => 558.07/71.17 (exists_in_world @ X2 @ X6)))), 558.07/71.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl192])). 558.07/71.17 thf(zip_derived_cl194, plain, 558.07/71.17 (![X2 : mu, X4 : $i, X6 : $i]: 558.07/71.17 (~ (((exists_in_world @ X2 @ X4) & (rel_s4 @ X4 @ X6))) 558.07/71.17 | (exists_in_world @ X2 @ X6))), 558.07/71.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl193])). 558.07/71.17 thf(zip_derived_cl195, plain, 558.07/71.17 (![X2 : mu, X4 : $i, X6 : $i]: 558.07/71.17 (~ (exists_in_world @ X2 @ X4) 558.07/71.17 | ~ (rel_s4 @ X4 @ X6) 558.07/71.17 | (exists_in_world @ X2 @ X6))), 558.07/71.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl194])). 558.07/71.17 thf(zip_derived_cl744, plain, 558.07/71.17 (![X0 : $i]: 558.07/71.17 ( ('#form17') 558.07/71.17 | (exists_in_world @ ('#sk16' @ '#sk18') @ X0) 558.07/71.17 | ~ (rel_s4 @ ('#sk11' @ '#sk18') @ X0))), 558.07/71.17 inference('sup-', [status(thm)], [zip_derived_cl140, zip_derived_cl195])). 558.07/71.17 thf(zip_derived_cl2414, plain, 558.07/71.17 (( ('#form17') 558.07/71.17 | (exists_in_world @ ('#sk16' @ '#sk18') @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl744])). 558.07/71.17 thf(zip_derived_cl2415, plain, 558.07/71.17 (( (exists_in_world @ ('#sk16' @ '#sk18') @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('simplify', [status(thm)], [zip_derived_cl2414])). 558.07/71.17 thf(zip_derived_cl134, plain, 558.07/71.17 (( (rel_s4 @ '#sk18' @ ('#sk11' @ '#sk18')) | ('#form17'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl126])). 558.07/71.17 thf(zip_derived_cl143, plain, 558.07/71.17 (( (rel_s4 @ ('#sk11' @ '#sk18') @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl142])). 558.07/71.17 thf(mtransitive, axiom,(( mtransitive ) = 558.07/71.17 (^[R:( $i > $i > $o )]: 558.07/71.17 ( ![S:$i,T:$i,U:$i]: 558.07/71.17 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) )))). 558.07/71.17 thf('16', plain, 558.07/71.17 (( mtransitive ) = 558.07/71.17 ( ^[R:( $i > $i > $o )]: 558.07/71.17 ( ![S:$i,T:$i,U:$i]: 558.07/71.17 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) ) )), 558.07/71.17 inference('simplify_rw_rule', [status(thm)], [mtransitive])). 558.07/71.17 thf('17', plain, 558.07/71.17 (( mtransitive ) = 558.07/71.17 ( ^[V_1:( $i > $i > $o )]: 558.07/71.17 ( ![X4:$i,X6:$i,X8:$i]: 558.07/71.17 ( ( ( V_1 @ X4 @ X6 ) & ( V_1 @ X6 @ X8 ) ) => ( V_1 @ X4 @ X8 ) ) ) )), 558.07/71.17 define([status(thm)])).thf(a2, axiom, (mtransitive @ rel_s4)). 558.07/71.17 thf(zf_stmt_2, axiom, 558.07/71.17 (![X4:$i,X6:$i,X8:$i]: 558.07/71.17 ( ( ( rel_s4 @ X6 @ X8 ) & ( rel_s4 @ X4 @ X6 ) ) => ( rel_s4 @ X4 @ X8 ) ))). 558.07/71.17 thf(zip_derived_cl1, plain, 558.07/71.17 ( (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((rel_s4 @ Y1 @ Y2) & (rel_s4 @ 558.07/71.17 Y0 @ Y1))) => 558.07/71.17 (rel_s4 @ Y0 @ Y2))))))))))))), 558.07/71.17 inference('cnf', [status(esa)], [zf_stmt_2])). 558.07/71.17 thf(zip_derived_cl157, plain, 558.07/71.17 (![X2 : $i]: 558.07/71.17 (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((rel_s4 @ Y0 @ Y1) & (rel_s4 @ X2 @ Y0))) => 558.07/71.17 (rel_s4 @ X2 @ Y1)))))))))), 558.07/71.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 558.07/71.17 thf(zip_derived_cl158, plain, 558.07/71.17 (![X2 : $i, X4 : $i]: 558.07/71.17 (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((rel_s4 @ X4 @ Y0) & (rel_s4 @ X2 @ X4))) => 558.07/71.17 (rel_s4 @ X2 @ Y0))))))), 558.07/71.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl157])). 558.07/71.17 thf(zip_derived_cl159, plain, 558.07/71.17 (![X2 : $i, X4 : $i, X6 : $i]: 558.07/71.17 (((((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) => (rel_s4 @ X2 @ X6)))), 558.07/71.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl158])). 558.07/71.17 thf(zip_derived_cl160, plain, 558.07/71.17 (![X2 : $i, X4 : $i, X6 : $i]: 558.07/71.17 (~ (((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) | (rel_s4 @ X2 @ X6))), 558.07/71.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 558.07/71.17 thf(zip_derived_cl161, plain, 558.07/71.17 (![X2 : $i, X4 : $i, X6 : $i]: 558.07/71.17 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))), 558.07/71.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl160])). 558.07/71.17 thf(zip_derived_cl776, plain, 558.07/71.17 (![X0 : $i]: 558.07/71.17 ( ('#form17') 558.07/71.17 | (rel_s4 @ X0 @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.17 | ~ (rel_s4 @ X0 @ ('#sk11' @ '#sk18')))), 558.07/71.17 inference('sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl161])). 558.07/71.17 thf(zip_derived_cl7635, plain, 558.07/71.17 (( ('#form17') 558.07/71.17 | (rel_s4 @ '#sk18' @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl776])). 558.07/71.17 thf(zip_derived_cl7639, plain, 558.07/71.17 (( (rel_s4 @ '#sk18' @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('simplify', [status(thm)], [zip_derived_cl7635])). 558.07/71.17 thf(mreflexive, axiom,(( mreflexive ) = 558.07/71.17 (^[R:( $i > $i > $o )]: ( ![S:$i]: ( R @ S @ S ) )))). 558.07/71.17 thf('18', plain, 558.07/71.17 (( mreflexive ) = ( ^[R:( $i > $i > $o )]: ( ![S:$i]: ( R @ S @ S ) ) )), 558.07/71.17 inference('simplify_rw_rule', [status(thm)], [mreflexive])). 558.07/71.17 thf('19', plain, 558.07/71.17 (( mreflexive ) = 558.07/71.17 ( ^[V_1:( $i > $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 @ X4 ) ) )), 558.07/71.17 define([status(thm)])).thf(a1, axiom, (mreflexive @ rel_s4)). 558.07/71.17 thf(zf_stmt_3, axiom, (![X4:$i]: ( rel_s4 @ X4 @ X4 ))). 558.07/71.17 thf(zip_derived_cl2, plain, ( (((!!) @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))), 558.07/71.17 inference('cnf', [status(esa)], [zf_stmt_3])). 558.07/71.17 thf(zip_derived_cl145, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 558.07/71.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 558.07/71.17 thf(zip_derived_cl12, plain, 558.07/71.17 (( ('#form3') 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 558.07/71.17 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : mu]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y3 @ 558.07/71.17 Y2) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y3 @ Y4))))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y3 @ 558.07/71.17 Y2) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y3 @ Y4)))))))))))))))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y2 @ Y1) => 558.07/71.17 (((~) @ ( 558.07/71.17 ((((~) @ ( 558.07/71.17 ((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y4)))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y5 @ 558.07/71.17 Y4) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y6 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y4 @ Y6))) | 558.07/71.17 (big_p @ 558.07/71.17 Y5 @ Y6))))))))))))))))))))))))) | 558.07/71.17 (((~) @ ( 558.07/71.17 ((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y5 @ 558.07/71.17 Y4) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y6 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y4 @ Y6))) | 558.07/71.17 (big_p @ 558.07/71.17 Y5 @ Y6)))))))))))))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 558.07/71.17 define([status(thm)])). 558.07/71.17 thf(zip_derived_cl13, plain, 558.07/71.17 ((~ (((((~) @ (rel_s4 @ '#sk1' @ '#sk4'))) | 558.07/71.17 (((~) @ (((((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y1 @ Y0) => 558.07/71.17 (((~) @ ( 558.07/71.17 ((!!) @ ( 558.07/71.17 ^[Y2 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y0 @ Y2))) | 558.07/71.17 (big_p @ 558.07/71.17 Y1 @ Y2))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (((!!) @ ( 558.07/71.17 ^[Y2 : mu]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3))))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y1 @ Y0) => 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y0 @ Y2))) | 558.07/71.17 (big_p @ 558.07/71.17 Y1 @ Y2)))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((~) @ (((((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y0 @ Y2))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y1 @ Y3)))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y3))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y4 @ 558.07/71.17 Y3) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y5))) | 558.07/71.17 (big_p @ 558.07/71.17 Y4 @ Y5))))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y0 @ Y2))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y3))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y4 @ 558.07/71.17 Y3) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y5))) | 558.07/71.17 (big_p @ 558.07/71.17 Y4 @ Y5)))))))))))))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y1 @ Y3))))))))))))))))))))))))))))))))) 558.07/71.17 | ('#form3'))), 558.07/71.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 558.07/71.17 thf(zip_derived_cl19, plain, 558.07/71.17 (( (((((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ 558.07/71.17 Y0) => 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : $i]: 558.07/71.17 (((( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y0 @ Y2))) | 558.07/71.17 (big_p @ 558.07/71.17 Y1 @ Y2))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.17 Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3))))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y2 @ Y1) => 558.07/71.17 (((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y0 @ Y2))) | 558.07/71.17 (big_p @ 558.07/71.17 Y1 @ Y2)))))))))))))))))))))) 558.07/71.17 | ('#form3'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl13])). 558.07/71.17 thf(zip_derived_cl24, plain, 558.07/71.17 ((~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y0 @ Y2))) | 558.07/71.17 (big_p @ 558.07/71.17 Y1 @ Y2))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y2 @ Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3))))))))))))))))))))))) 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ Y0 @ 558.07/71.17 Y2))) | 558.07/71.17 (big_p @ Y1 @ Y2)))))))))))))))))) 558.07/71.17 | ('#form3'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 558.07/71.17 thf(zip_derived_cl30, plain, 558.07/71.17 ((~ (((((~) @ (rel_s4 @ '#sk4' @ '#sk6'))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y0 : mu]: 558.07/71.17 (((exists_in_world @ Y0 @ '#sk6') => 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 '#sk6' @ Y1))) | 558.07/71.17 (big_p @ Y0 @ Y1))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ Y0 @ 558.07/71.17 Y2))) | 558.07/71.17 (big_p @ Y1 @ Y2)))))))))))))))))))) 558.07/71.17 | ('#form3') 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ Y0 @ 558.07/71.17 Y2))) | 558.07/71.17 (big_p @ Y1 @ Y2)))))))))))))))))))), 558.07/71.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl24])). 558.07/71.17 thf(zip_derived_cl41, plain, 558.07/71.17 (( (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 558.07/71.17 (big_p @ Y1 @ Y2)))))))))))))))) 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ Y0 @ 558.07/71.17 Y2))) | 558.07/71.17 (big_p @ Y1 @ Y2)))))))))))))))))) 558.07/71.17 | ('#form3'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 558.07/71.17 thf(zip_derived_cl56, plain, 558.07/71.17 (![X2 : $i]: 558.07/71.17 (~ ('#form10' @ X2) 558.07/71.17 | (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.17 Y2))) | 558.07/71.17 (big_p @ Y1 @ Y2)))))))))))))))))), 558.07/71.17 define([status(thm)])). 558.07/71.17 thf(zip_derived_cl57, plain, 558.07/71.17 (![X2 : $i, X4 : $i]: 558.07/71.17 ( (((((~) @ (rel_s4 @ X2 @ X4))) | 558.07/71.17 (((!!) @ (^[Y0 : mu]: 558.07/71.17 (((exists_in_world @ Y0 @ X4) => 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ X4 @ Y1))) | 558.07/71.17 (big_p @ Y0 @ Y1))))))))))))) 558.07/71.17 | ~ ('#form10' @ X2))), 558.07/71.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl56])). 558.07/71.17 thf(zip_derived_cl71, plain, 558.07/71.17 (![X2 : $i, X4 : $i]: 558.07/71.17 (~ (rel_s4 @ X2 @ X4) 558.07/71.17 | (((!!) @ (^[Y0 : mu]: 558.07/71.17 (((exists_in_world @ Y0 @ X4) => 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ X4 @ Y1))) | 558.07/71.17 (big_p @ Y0 @ Y1))))))))))) 558.07/71.17 | ~ ('#form10' @ X2))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl57])). 558.07/71.17 thf(zip_derived_cl82, plain, 558.07/71.17 (![X2 : $i, X4 : $i, X6 : mu]: 558.07/71.17 ( (((exists_in_world @ X6 @ X4) => 558.07/71.17 (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ X4 @ Y0))) | (big_p @ X6 @ Y0)))))))) 558.07/71.17 | ~ ('#form10' @ X2) 558.07/71.17 | ~ (rel_s4 @ X2 @ X4))), 558.07/71.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 558.07/71.17 thf(zip_derived_cl95, plain, 558.07/71.17 (![X2 : $i, X4 : $i, X6 : mu]: 558.07/71.17 (~ (exists_in_world @ X6 @ X4) 558.07/71.17 | (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ X4 @ Y0))) | (big_p @ X6 @ Y0)))))) 558.07/71.17 | ~ (rel_s4 @ X2 @ X4) 558.07/71.17 | ~ ('#form10' @ X2))), 558.07/71.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 558.07/71.17 thf(zip_derived_cl107, plain, 558.07/71.17 (![X2 : $i, X4 : $i, X6 : mu, X8 : $i]: 558.07/71.17 ( (((((~) @ (rel_s4 @ X4 @ X8))) | (big_p @ X6 @ X8))) 558.07/71.17 | ~ ('#form10' @ X2) 558.07/71.17 | ~ (rel_s4 @ X2 @ X4) 558.07/71.17 | ~ (exists_in_world @ X6 @ X4))), 558.07/71.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 558.07/71.17 thf(zip_derived_cl121, plain, 558.07/71.17 (![X2 : $i, X4 : $i, X6 : mu, X8 : $i]: 558.07/71.17 (~ (rel_s4 @ X4 @ X8) 558.07/71.17 | (big_p @ X6 @ X8) 558.07/71.17 | ~ (exists_in_world @ X6 @ X4) 558.07/71.17 | ~ (rel_s4 @ X2 @ X4) 558.07/71.17 | ~ ('#form10' @ X2))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl107])). 558.07/71.17 thf(zip_derived_cl146, plain, 558.07/71.17 (![X0 : $i, X1 : $i, X2 : mu]: 558.07/71.17 (~ ('#form10' @ X1) 558.07/71.17 | ~ (rel_s4 @ X1 @ X0) 558.07/71.17 | ~ (exists_in_world @ X2 @ X0) 558.07/71.17 | (big_p @ X2 @ X0))), 558.07/71.17 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl121])). 558.07/71.17 thf(zip_derived_cl7690, plain, 558.07/71.17 (![X0 : mu]: 558.07/71.17 ( ('#form17') 558.07/71.17 | (big_p @ X0 @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.17 | ~ (exists_in_world @ X0 @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.17 | ~ ('#form10' @ '#sk18'))), 558.07/71.17 inference('sup-', [status(thm)], [zip_derived_cl7639, zip_derived_cl146])). 558.07/71.17 thf(zip_derived_cl29455, plain, 558.07/71.17 (( ('#form17') 558.07/71.17 | ~ ('#form10' @ '#sk18') 558.07/71.17 | (big_p @ ('#sk16' @ '#sk18') @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('sup-', [status(thm)], [zip_derived_cl2415, zip_derived_cl7690])). 558.07/71.17 thf(zip_derived_cl29463, plain, 558.07/71.17 (( (big_p @ ('#sk16' @ '#sk18') @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.17 | ~ ('#form10' @ '#sk18') 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('simplify', [status(thm)], [zip_derived_cl29455])). 558.07/71.17 thf(zip_derived_cl144, plain, 558.07/71.17 ((~ (big_p @ ('#sk16' @ '#sk18') @ 558.07/71.17 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.17 | ('#form17'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl142])). 558.07/71.17 thf(zip_derived_cl29467, plain, (( ('#form17') | ~ ('#form10' @ '#sk18'))), 558.07/71.17 inference('clc', [status(thm)], [zip_derived_cl29463, zip_derived_cl144])). 558.07/71.17 thf(zip_derived_cl85, plain, 558.07/71.17 (( (rel_s4 @ '#sk5' @ '#sk15') 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (big_p @ '#sk7' @ Y1))))))))))))) 558.07/71.17 | ~ ('#form3'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 558.07/71.17 thf(zip_derived_cl98, plain, 558.07/71.17 (( ('#form17') 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (big_p @ '#sk7' @ Y1))))))))))))))), 558.07/71.17 define([status(thm)])). 558.07/71.17 thf(zip_derived_cl100, plain, 558.07/71.17 ((~ ('#form17') | ~ ('#form3') | (rel_s4 @ '#sk5' @ '#sk15'))), 558.07/71.17 inference('renaming', [status(thm)], [zip_derived_cl85, zip_derived_cl98])). 558.07/71.17 thf(zip_derived_cl43, plain, 558.07/71.17 (( (exists_in_world @ '#sk7' @ '#sk5') | ~ ('#form3'))), 558.07/71.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl32])). 558.07/71.17 thf(zip_derived_cl195, plain, 558.07/71.17 (![X2 : mu, X4 : $i, X6 : $i]: 558.07/71.17 (~ (exists_in_world @ X2 @ X4) 558.07/71.17 | ~ (rel_s4 @ X4 @ X6) 558.07/71.17 | (exists_in_world @ X2 @ X6))), 558.07/71.17 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl194])). 558.07/71.17 thf(zip_derived_cl207, plain, 558.07/71.17 (![X0 : $i]: 558.07/71.17 (~ ('#form3') 558.07/71.17 | (exists_in_world @ '#sk7' @ X0) 558.07/71.17 | ~ (rel_s4 @ '#sk5' @ X0))), 558.07/71.17 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl195])). 558.07/71.17 thf(zip_derived_cl385, plain, 558.07/71.17 ((~ ('#form3') 558.07/71.17 | ~ ('#form17') 558.07/71.17 | (exists_in_world @ '#sk7' @ '#sk15') 558.07/71.17 | ~ ('#form3'))), 558.07/71.17 inference('sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl207])). 558.07/71.17 thf(zip_derived_cl387, plain, 558.07/71.17 (( (exists_in_world @ '#sk7' @ '#sk15') | ~ ('#form17') | ~ ('#form3'))), 558.07/71.17 inference('simplify', [status(thm)], [zip_derived_cl385])). 558.07/71.17 thf(zip_derived_cl145, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 558.07/71.17 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 558.07/71.17 thf(zip_derived_cl86, plain, 558.07/71.17 ((~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk15' @ Y0))) | (big_p @ '#sk7' @ 558.07/71.17 Y0)))))) 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (big_p @ '#sk7' @ Y1))))))))))))) 558.07/71.17 | ~ ('#form3'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 558.07/71.17 thf(zip_derived_cl98, plain, 558.07/71.17 (( ('#form17') 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (big_p @ '#sk7' @ Y1))))))))))))))), 558.07/71.17 define([status(thm)])). 558.07/71.17 thf(zip_derived_cl101, plain, 558.07/71.17 ((~ ('#form17') 558.07/71.17 | ~ ('#form3') 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk15' @ Y0))) | (big_p @ 558.07/71.17 '#sk7' @ Y0)))))))), 558.07/71.17 inference('renaming', [status(thm)], [zip_derived_cl86, zip_derived_cl98])). 558.07/71.17 thf(zip_derived_cl113, plain, 558.07/71.17 ((~ (((((~) @ (rel_s4 @ '#sk15' @ ('#sk14' @ '#sk15' @ '#sk7')))) | 558.07/71.17 (big_p @ '#sk7' @ ('#sk14' @ '#sk15' @ '#sk7')))) 558.07/71.17 | ~ ('#form3') 558.07/71.17 | ~ ('#form17'))), 558.07/71.17 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl101])). 558.07/71.17 thf(zip_derived_cl128, plain, 558.07/71.17 (( (rel_s4 @ '#sk15' @ ('#sk14' @ '#sk15' @ '#sk7')) 558.07/71.17 | ~ ('#form17') 558.07/71.17 | ~ ('#form3'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl113])). 558.07/71.17 thf(zip_derived_cl121, plain, 558.07/71.17 (![X2 : $i, X4 : $i, X6 : mu, X8 : $i]: 558.07/71.17 (~ (rel_s4 @ X4 @ X8) 558.07/71.17 | (big_p @ X6 @ X8) 558.07/71.17 | ~ (exists_in_world @ X6 @ X4) 558.07/71.17 | ~ (rel_s4 @ X2 @ X4) 558.07/71.17 | ~ ('#form10' @ X2))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl107])). 558.07/71.17 thf(zip_derived_cl585, plain, 558.07/71.17 (![X0 : $i, X1 : mu]: 558.07/71.17 (~ ('#form3') 558.07/71.17 | ~ ('#form17') 558.07/71.17 | ~ ('#form10' @ X0) 558.07/71.17 | ~ (rel_s4 @ X0 @ '#sk15') 558.07/71.17 | ~ (exists_in_world @ X1 @ '#sk15') 558.07/71.17 | (big_p @ X1 @ ('#sk14' @ '#sk15' @ '#sk7')))), 558.07/71.17 inference('sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl121])). 558.07/71.17 thf(zip_derived_cl3508, plain, 558.07/71.17 (![X0 : mu]: 558.07/71.17 ( (big_p @ X0 @ ('#sk14' @ '#sk15' @ '#sk7')) 558.07/71.17 | ~ (exists_in_world @ X0 @ '#sk15') 558.07/71.17 | ~ ('#form10' @ '#sk15') 558.07/71.17 | ~ ('#form17') 558.07/71.17 | ~ ('#form3'))), 558.07/71.17 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl585])). 558.07/71.17 thf(zip_derived_cl87, plain, 558.07/71.17 (( (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk15' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 558.07/71.17 (big_p @ Y1 @ Y2)))))))))))))))) 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (big_p @ '#sk7' @ Y1))))))))))))) 558.07/71.17 | ~ ('#form3'))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 558.07/71.17 thf(zip_derived_cl56, plain, 558.07/71.17 (![X2 : $i]: 558.07/71.17 (~ ('#form10' @ X2) 558.07/71.17 | (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.17 (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.17 Y2))) | 558.07/71.17 (big_p @ Y1 @ Y2)))))))))))))))))), 558.07/71.17 define([status(thm)])). 558.07/71.17 thf(zip_derived_cl11, plain, 558.07/71.17 (( (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : mu]: 558.07/71.17 (((exists_in_world @ Y1 @ Y0) => 558.07/71.17 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.17 (((((~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y0 @ Y2))) | 558.07/71.17 (big_p @ 558.07/71.17 Y1 @ Y2))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y2 @ Y1) => 558.07/71.17 (((!!) @ (^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3))))))))))))))))))))))) 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 558.07/71.17 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : mu]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y3 @ 558.07/71.17 Y2) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y3 @ Y4))))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y3 @ 558.07/71.17 Y2) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y3 @ Y4)))))))))))))))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y2 @ Y1) => 558.07/71.17 (((~) @ ( 558.07/71.17 ((((~) @ ( 558.07/71.17 ((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y4)))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y5 @ 558.07/71.17 Y4) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y6 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y4 @ Y6))) | 558.07/71.17 (big_p @ 558.07/71.17 Y5 @ Y6))))))))))))))))))))))))) | 558.07/71.17 (((~) @ ( 558.07/71.17 ((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y5 @ 558.07/71.17 Y4) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y6 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y4 @ Y6))) | 558.07/71.17 (big_p @ 558.07/71.17 Y5 @ Y6)))))))))))))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 558.07/71.17 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])). 558.07/71.17 thf(zip_derived_cl12, plain, 558.07/71.17 (( ('#form3') 558.07/71.17 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 558.07/71.17 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : mu]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ ( 558.07/71.17 ^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y3 @ 558.07/71.17 Y2) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y3 @ Y4))))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ 558.07/71.17 Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y2))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y3 @ 558.07/71.17 Y2) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y2 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y3 @ Y4)))))))))))))))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y2 @ 558.07/71.17 Y1) => 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y3)))))))))))))))))))))))) | 558.07/71.17 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.17 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.17 (((!!) @ (^[Y2 : mu]: 558.07/71.17 (((exists_in_world @ 558.07/71.17 Y2 @ Y1) => 558.07/71.17 (((~) @ ( 558.07/71.17 ((((~) @ ( 558.07/71.17 ((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (big_p @ 558.07/71.17 Y2 @ Y4)))))) | 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 ( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y4 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y3 @ Y4))) | 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y5 : mu]: 558.07/71.17 (( 558.07/71.17 (exists_in_world @ 558.07/71.17 Y5 @ 558.07/71.17 Y4) => 558.07/71.17 (( 558.07/71.17 (!!) @ ( 558.07/71.17 ^[Y6 : $i]: 558.07/71.17 (( 558.07/71.17 (( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y4 @ Y6))) | 558.07/71.17 (big_p @ 558.07/71.17 Y5 @ Y6))))))))))))))))))))))))) | 558.07/71.17 (((~) @ ( 558.07/71.17 ((!!) @ ( 558.07/71.17 ^[Y3 : $i]: 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 ( 558.07/71.17 (~) @ ( 558.07/71.17 rel_s4 @ 558.07/71.17 Y1 @ Y3))) | 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y3 @ Y4))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y5 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y5 @ 558.07/71.18 Y4) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y6 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y4 @ Y6))) | 558.07/71.18 (big_p @ 558.07/71.18 Y5 @ Y6)))))))))))))))) | 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (~) @ ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y3 @ Y4))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 558.07/71.18 define([status(thm)])). 558.07/71.18 thf(zip_derived_cl17, plain, 558.07/71.18 ((~ ('#form3') 558.07/71.18 | (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y0 @ Y2))) | 558.07/71.18 (big_p @ 558.07/71.18 Y1 @ Y2))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 (((exists_in_world @ 558.07/71.18 Y2 @ Y1) => 558.07/71.18 (((!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 (((((~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3))))))))))))))))))))))))), 558.07/71.18 inference('renaming', [status(thm)], [zip_derived_cl11, zip_derived_cl12])). 558.07/71.18 thf(zip_derived_cl23, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 ( (((((~) @ (rel_s4 @ '#sk2' @ X2))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y0 : mu]: 558.07/71.18 (((exists_in_world @ Y0 @ X2) => 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 X2 @ Y1))) | 558.07/71.18 (big_p @ Y0 @ Y1))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ ( 558.07/71.18 rel_s4 @ Y0 @ 558.07/71.18 Y2))) | 558.07/71.18 (big_p @ Y1 @ 558.07/71.18 Y2)))))))))))))))))))) 558.07/71.18 | ~ ('#form3'))), 558.07/71.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 558.07/71.18 thf(zip_derived_cl29, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 (~ (rel_s4 @ '#sk2' @ X2) 558.07/71.18 | ~ (((!!) @ (^[Y0 : mu]: 558.07/71.18 (((exists_in_world @ Y0 @ X2) => 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y1))) | 558.07/71.18 (big_p @ Y0 @ Y1))))))))))))) 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.18 Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))) 558.07/71.18 | ~ ('#form3'))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl23])). 558.07/71.18 thf(zip_derived_cl29, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 (~ (rel_s4 @ '#sk2' @ X2) 558.07/71.18 | ~ (((!!) @ (^[Y0 : mu]: 558.07/71.18 (((exists_in_world @ Y0 @ X2) => 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y1))) | 558.07/71.18 (big_p @ Y0 @ Y1))))))))))))) 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.18 Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))) 558.07/71.18 | ~ ('#form3'))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl23])). 558.07/71.18 thf(zip_derived_cl36, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 ( ('#form8' @ X2) 558.07/71.18 | ~ (((!!) @ (^[Y0 : mu]: 558.07/71.18 (((exists_in_world @ Y0 @ X2) => 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y1))) | 558.07/71.18 (big_p @ Y0 @ Y1))))))))))))))), 558.07/71.18 define([status(thm)])). 558.07/71.18 thf(zip_derived_cl10, plain, 558.07/71.18 (( (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 (((exists_in_world @ Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (((!!) @ (^[Y3 : $i]: 558.07/71.18 (((((~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ Y2 @ 558.07/71.18 Y3)))))))))))))))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 Y0 @ Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))))) 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 558.07/71.18 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 Y0 @ Y1))) | 558.07/71.18 (((~) @ (((!!) @ ( 558.07/71.18 ^[Y2 : mu]: 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ ( 558.07/71.18 ^[Y2 : $i]: 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y2))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y3 @ 558.07/71.18 Y2) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y2 @ Y4))) | 558.07/71.18 (big_p @ 558.07/71.18 Y3 @ Y4))))))))))))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y2))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y3 @ 558.07/71.18 Y2) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y2 @ Y4))) | 558.07/71.18 (big_p @ 558.07/71.18 Y3 @ Y4)))))))))))))))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3)))))))))))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 (((exists_in_world @ 558.07/71.18 Y2 @ Y1) => 558.07/71.18 (((~) @ ( 558.07/71.18 ((((~) @ ( 558.07/71.18 ((!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y3 @ Y4))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y4)))))) | 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (~) @ ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y3 @ Y4))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y5 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y5 @ 558.07/71.18 Y4) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y6 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y4 @ Y6))) | 558.07/71.18 (big_p @ 558.07/71.18 Y5 @ Y6))))))))))))))))))))))))) | 558.07/71.18 (((~) @ ( 558.07/71.18 ((!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y3 @ Y4))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y5 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y5 @ 558.07/71.18 Y4) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y6 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y4 @ Y6))) | 558.07/71.18 (big_p @ 558.07/71.18 Y5 @ Y6)))))))))))))))) | 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (~) @ ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y3 @ Y4))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])). 558.07/71.18 thf(zip_derived_cl12, plain, 558.07/71.18 (( ('#form3') 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 558.07/71.18 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 Y0 @ Y1))) | 558.07/71.18 (((~) @ (((!!) @ ( 558.07/71.18 ^[Y2 : mu]: 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ ( 558.07/71.18 ^[Y2 : $i]: 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y2))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y3 @ 558.07/71.18 Y2) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y2 @ Y4))) | 558.07/71.18 (big_p @ 558.07/71.18 Y3 @ Y4))))))))))))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y2))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y3 @ 558.07/71.18 Y2) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y2 @ Y4))) | 558.07/71.18 (big_p @ 558.07/71.18 Y3 @ Y4)))))))))))))))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3)))))))))))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 (((exists_in_world @ 558.07/71.18 Y2 @ Y1) => 558.07/71.18 (((~) @ ( 558.07/71.18 ((((~) @ ( 558.07/71.18 ((!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y3 @ Y4))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y4)))))) | 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (~) @ ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y3 @ Y4))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y5 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y5 @ 558.07/71.18 Y4) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y6 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y4 @ Y6))) | 558.07/71.18 (big_p @ 558.07/71.18 Y5 @ Y6))))))))))))))))))))))))) | 558.07/71.18 (((~) @ ( 558.07/71.18 ((!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y3 @ Y4))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y5 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y5 @ 558.07/71.18 Y4) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y6 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y4 @ Y6))) | 558.07/71.18 (big_p @ 558.07/71.18 Y5 @ Y6)))))))))))))))) | 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (~) @ ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y3 @ Y4))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 558.07/71.18 define([status(thm)])). 558.07/71.18 thf(zip_derived_cl16, plain, 558.07/71.18 ((~ ('#form3') 558.07/71.18 | (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 (((exists_in_world @ Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (((!!) @ (^[Y3 : $i]: 558.07/71.18 (((((~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3)))))))))))))))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 Y0 @ Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))))))), 558.07/71.18 inference('renaming', [status(thm)], [zip_derived_cl10, zip_derived_cl12])). 558.07/71.18 thf(zip_derived_cl22, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 ( (((((~) @ (rel_s4 @ '#sk2' @ X2))) | 558.07/71.18 (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.18 Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))) | 558.07/71.18 (((!!) @ (^[Y0 : mu]: 558.07/71.18 (((exists_in_world @ Y0 @ X2) => 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y1))) | 558.07/71.18 (big_p @ Y0 @ Y1))))))))))))))) 558.07/71.18 | ~ ('#form3'))), 558.07/71.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 558.07/71.18 thf(zip_derived_cl28, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 (~ (rel_s4 @ '#sk2' @ X2) 558.07/71.18 | (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.18 Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))) 558.07/71.18 | (((!!) @ (^[Y0 : mu]: 558.07/71.18 (((exists_in_world @ Y0 @ X2) => 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y1))) | 558.07/71.18 (big_p @ Y0 @ Y1))))))))))))) 558.07/71.18 | ~ ('#form3'))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl22])). 558.07/71.18 thf(zip_derived_cl33, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 (~ ('#form8' @ X2) 558.07/71.18 | (((!!) @ (^[Y0 : mu]: 558.07/71.18 (((exists_in_world @ Y0 @ X2) => 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y1))) | 558.07/71.18 (big_p @ Y0 @ Y1))))))))))))))), 558.07/71.18 define([status(thm)])). 558.07/71.18 thf(zip_derived_cl38, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 (~ ('#form8' @ X2) 558.07/71.18 | ~ ('#form3') 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.18 Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))) 558.07/71.18 | ~ (rel_s4 @ '#sk2' @ X2))), 558.07/71.18 inference('renaming', [status(thm)], 558.07/71.18 [zip_derived_cl29, zip_derived_cl36, zip_derived_cl33])). 558.07/71.18 thf(zip_derived_cl47, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 ( ('#form10' @ X2) 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.18 Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))))), 558.07/71.18 define([status(thm)])). 558.07/71.18 thf(zip_derived_cl102, plain, 558.07/71.18 (( ('#form10' @ '#sk15') 558.07/71.18 | ~ ('#form3') 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 (((exists_in_world @ Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (((!!) @ (^[Y3 : $i]: 558.07/71.18 (((((~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3)))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (big_p @ '#sk7' @ Y1))))))))))))))), 558.07/71.18 inference('renaming', [status(thm)], 558.07/71.18 [zip_derived_cl87, zip_derived_cl56, zip_derived_cl47])). 558.07/71.18 thf(zip_derived_cl98, plain, 558.07/71.18 (( ('#form17') 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 (((exists_in_world @ Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (((!!) @ (^[Y3 : $i]: 558.07/71.18 (((((~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3)))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (big_p @ '#sk7' @ Y1))))))))))))))), 558.07/71.18 define([status(thm)])). 558.07/71.18 thf(zip_derived_cl114, plain, 558.07/71.18 ((~ ('#form17') | ~ ('#form3') | ('#form10' @ '#sk15'))), 558.07/71.18 inference('renaming', [status(thm)], 558.07/71.18 [zip_derived_cl102, zip_derived_cl98])). 558.07/71.18 thf(zip_derived_cl3515, plain, 558.07/71.18 (![X0 : mu]: 558.07/71.18 (~ ('#form3') 558.07/71.18 | ~ ('#form17') 558.07/71.18 | ~ (exists_in_world @ X0 @ '#sk15') 558.07/71.18 | (big_p @ X0 @ ('#sk14' @ '#sk15' @ '#sk7')))), 558.07/71.18 inference('clc', [status(thm)], [zip_derived_cl3508, zip_derived_cl114])). 558.07/71.18 thf(zip_derived_cl3516, plain, 558.07/71.18 ((~ ('#form3') 558.07/71.18 | ~ ('#form17') 558.07/71.18 | (big_p @ '#sk7' @ ('#sk14' @ '#sk15' @ '#sk7')) 558.07/71.18 | ~ ('#form17') 558.07/71.18 | ~ ('#form3'))), 558.07/71.18 inference('sup-', [status(thm)], [zip_derived_cl387, zip_derived_cl3515])). 558.07/71.18 thf(zip_derived_cl3522, plain, 558.07/71.18 (( (big_p @ '#sk7' @ ('#sk14' @ '#sk15' @ '#sk7')) 558.07/71.18 | ~ ('#form17') 558.07/71.18 | ~ ('#form3'))), 558.07/71.18 inference('simplify', [status(thm)], [zip_derived_cl3516])). 558.07/71.18 thf(zip_derived_cl129, plain, 558.07/71.18 ((~ (big_p @ '#sk7' @ ('#sk14' @ '#sk15' @ '#sk7')) 558.07/71.18 | ~ ('#form17') 558.07/71.18 | ~ ('#form3'))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl113])). 558.07/71.18 thf(zip_derived_cl4225, plain, ((~ ('#form3') | ~ ('#form17'))), 558.07/71.18 inference('clc', [status(thm)], [zip_derived_cl3522, zip_derived_cl129])). 558.07/71.18 thf(zip_derived_cl20, plain, 558.07/71.18 (( (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((~) @ (((((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y0 @ Y2))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y2 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y1 @ Y3)))))) | 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y2 @ Y3))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y4 @ 558.07/71.18 Y3) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y5 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y3 @ Y5))) | 558.07/71.18 (big_p @ 558.07/71.18 Y4 @ Y5))))))))))))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y0 @ Y2))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y2 @ Y3))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y4 @ 558.07/71.18 Y3) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y5 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y3 @ Y5))) | 558.07/71.18 (big_p @ 558.07/71.18 Y4 @ Y5)))))))))))))))) | 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 ( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y2 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y1 @ Y3))))))))))))))))))))))))))))) 558.07/71.18 | ('#form3'))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl13])). 558.07/71.18 thf(zip_derived_cl25, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 ( (((((~) @ (rel_s4 @ '#sk4' @ X2))) | 558.07/71.18 (((!!) @ (^[Y0 : mu]: 558.07/71.18 (((exists_in_world @ Y0 @ X2) => 558.07/71.18 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 X2 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y2))) | 558.07/71.18 (big_p @ 558.07/71.18 Y0 @ Y2)))))) | 558.07/71.18 (((~) @ (((!!) @ ( 558.07/71.18 ^[Y2 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y2))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y3 @ 558.07/71.18 Y2) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y2 @ Y4))) | 558.07/71.18 (big_p @ 558.07/71.18 Y3 @ Y4))))))))))))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 X2 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y2))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y3 @ 558.07/71.18 Y2) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y2 @ Y4))) | 558.07/71.18 (big_p @ 558.07/71.18 Y3 @ Y4)))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ ( 558.07/71.18 ^[Y2 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y2))) | 558.07/71.18 (big_p @ 558.07/71.18 Y0 @ Y2)))))))))))))))))))))))))) 558.07/71.18 | ('#form3'))), 558.07/71.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 558.07/71.18 thf(zip_derived_cl31, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 (~ (rel_s4 @ '#sk4' @ X2) 558.07/71.18 | (((!!) @ (^[Y0 : mu]: 558.07/71.18 (((exists_in_world @ Y0 @ X2) => 558.07/71.18 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 X2 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y2))) | 558.07/71.18 (big_p @ 558.07/71.18 Y0 @ Y2)))))) | 558.07/71.18 (((~) @ (((!!) @ ( 558.07/71.18 ^[Y2 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y2))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y3 @ 558.07/71.18 Y2) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y2 @ Y4))) | 558.07/71.18 (big_p @ 558.07/71.18 Y3 @ Y4))))))))))))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 X2 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y2))) | 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y3 @ 558.07/71.18 Y2) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y4 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y2 @ Y4))) | 558.07/71.18 (big_p @ 558.07/71.18 Y3 @ Y4)))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ ( 558.07/71.18 ^[Y2 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y2))) | 558.07/71.18 (big_p @ 558.07/71.18 Y0 @ Y2)))))))))))))))))))))))) 558.07/71.18 | ('#form3'))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl25])). 558.07/71.18 thf(zip_derived_cl42, plain, 558.07/71.18 (![X2 : $i, X4 : mu]: 558.07/71.18 ( (((exists_in_world @ X4 @ X2) => 558.07/71.18 (((~) @ (((((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 Y0 @ Y1))) | 558.07/71.18 (big_p @ X4 @ Y1)))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y0 @ Y1))) | 558.07/71.18 (((!!) @ ( 558.07/71.18 ^[Y2 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3))))))))))))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3)))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y0 @ Y1))) | 558.07/71.18 (big_p @ 558.07/71.18 X4 @ Y1))))))))))))))))))))) 558.07/71.18 | ('#form3') 558.07/71.18 | ~ (rel_s4 @ '#sk4' @ X2))), 558.07/71.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl31])). 558.07/71.18 thf(zip_derived_cl59, plain, 558.07/71.18 (![X2 : $i, X4 : mu]: 558.07/71.18 (~ (exists_in_world @ X4 @ X2) 558.07/71.18 | ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (big_p @ X4 @ Y1)))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 (( 558.07/71.18 (exists_in_world @ 558.07/71.18 Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (( 558.07/71.18 (!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 (( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3))))))))))))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 (((exists_in_world @ 558.07/71.18 Y2 @ Y1) => 558.07/71.18 (((!!) @ ( 558.07/71.18 ^[Y3 : $i]: 558.07/71.18 ( 558.07/71.18 ( 558.07/71.18 (( 558.07/71.18 (~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3)))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ 558.07/71.18 Y0 @ Y1))) | 558.07/71.18 (big_p @ X4 @ Y1))))))))))))))))) 558.07/71.18 | ~ (rel_s4 @ '#sk4' @ X2) 558.07/71.18 | ('#form3'))), 558.07/71.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 558.07/71.18 thf(zip_derived_cl73, plain, 558.07/71.18 (![X2 : $i, X4 : mu]: 558.07/71.18 ( (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 (((exists_in_world @ Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (((!!) @ (^[Y3 : $i]: 558.07/71.18 (((((~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3)))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (big_p @ X4 @ Y1))))))))))))) 558.07/71.18 | ('#form3') 558.07/71.18 | ~ (rel_s4 @ '#sk4' @ X2) 558.07/71.18 | ~ (exists_in_world @ X4 @ X2))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl59])). 558.07/71.18 thf(zip_derived_cl84, plain, 558.07/71.18 (![X2 : $i, X4 : mu, X6 : $i]: 558.07/71.18 ( (((((~) @ (rel_s4 @ X2 @ X6))) | 558.07/71.18 (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X6 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.18 Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))) | 558.07/71.18 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X6 @ Y0))) | (big_p @ 558.07/71.18 X4 @ Y0)))))))))) 558.07/71.18 | ~ (exists_in_world @ X4 @ X2) 558.07/71.18 | ~ (rel_s4 @ '#sk4' @ X2) 558.07/71.18 | ('#form3'))), 558.07/71.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl73])). 558.07/71.18 thf(zip_derived_cl97, plain, 558.07/71.18 (![X2 : $i, X4 : mu, X6 : $i]: 558.07/71.18 (~ (rel_s4 @ X2 @ X6) 558.07/71.18 | (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X6 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.18 Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))) 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X6 @ Y0))) | (big_p @ X4 @ Y0)))))) 558.07/71.18 | ('#form3') 558.07/71.18 | ~ (rel_s4 @ '#sk4' @ X2) 558.07/71.18 | ~ (exists_in_world @ X4 @ X2))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl84])). 558.07/71.18 thf(zip_derived_cl56, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 (~ ('#form10' @ X2) 558.07/71.18 | (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.18 Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))))), 558.07/71.18 define([status(thm)])). 558.07/71.18 thf(zip_derived_cl47, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 ( ('#form10' @ X2) 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.18 Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))))), 558.07/71.18 define([status(thm)])). 558.07/71.18 thf(zip_derived_cl109, plain, 558.07/71.18 (![X2 : $i, X4 : mu, X6 : $i]: 558.07/71.18 ( ('#form10' @ X6) 558.07/71.18 | ~ (exists_in_world @ X4 @ X2) 558.07/71.18 | ~ (rel_s4 @ '#sk4' @ X2) 558.07/71.18 | ('#form3') 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X6 @ Y0))) | (big_p @ X4 @ Y0)))))) 558.07/71.18 | ~ (rel_s4 @ X2 @ X6))), 558.07/71.18 inference('renaming', [status(thm)], 558.07/71.18 [zip_derived_cl97, zip_derived_cl56, zip_derived_cl47])). 558.07/71.18 thf(zip_derived_cl123, plain, 558.07/71.18 (![X4 : mu, X6 : $i]: 558.07/71.18 ( ('#form19' @ X4 @ X6) 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X6 @ Y0))) | (big_p @ X4 @ Y0)))))))), 558.07/71.18 define([status(thm)])). 558.07/71.18 thf(zip_derived_cl124, plain, 558.07/71.18 (![X4 : mu, X6 : $i]: 558.07/71.18 (~ (((((~) @ (rel_s4 @ X6 @ ('#sk14' @ X6 @ X4)))) | (big_p @ X4 @ 558.07/71.18 ('#sk14' @ X6 @ X4)))) 558.07/71.18 | ('#form19' @ X4 @ X6))), 558.07/71.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl123])). 558.07/71.18 thf(zip_derived_cl132, plain, 558.07/71.18 (![X4 : mu, X6 : $i]: 558.07/71.18 ( (rel_s4 @ X6 @ ('#sk14' @ X6 @ X4)) | ('#form19' @ X4 @ X6))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl124])). 558.07/71.18 thf(zip_derived_cl36, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 ( ('#form8' @ X2) 558.07/71.18 | ~ (((!!) @ (^[Y0 : mu]: 558.07/71.18 (((exists_in_world @ Y0 @ X2) => 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y1))) | 558.07/71.18 (big_p @ Y0 @ Y1))))))))))))))), 558.07/71.18 define([status(thm)])). 558.07/71.18 thf(zip_derived_cl37, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 (~ (((exists_in_world @ ('#sk9' @ X2) @ X2) => 558.07/71.18 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | (big_p @ 558.07/71.18 ('#sk9' @ X2) @ Y0)))))))))) 558.07/71.18 | ('#form8' @ X2))), 558.07/71.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl36])). 558.07/71.18 thf(zip_derived_cl51, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 ( (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y0))) | (big_p @ 558.07/71.18 ('#sk9' @ X2) @ Y0)))))) 558.07/71.18 | ('#form8' @ X2))), 558.07/71.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 558.07/71.18 thf(zip_derived_cl65, plain, 558.07/71.18 (![X2 : $i, X4 : $i]: 558.07/71.18 ( (((((~) @ (rel_s4 @ X2 @ X4))) | (big_p @ ('#sk9' @ X2) @ X4))) 558.07/71.18 | ('#form8' @ X2))), 558.07/71.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl51])). 558.07/71.18 thf(zip_derived_cl79, plain, 558.07/71.18 (![X2 : $i, X4 : $i]: 558.07/71.18 (~ (rel_s4 @ X2 @ X4) 558.07/71.18 | (big_p @ ('#sk9' @ X2) @ X4) 558.07/71.18 | ('#form8' @ X2))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl65])). 558.07/71.18 thf(zip_derived_cl638, plain, 558.07/71.18 (![X0 : mu, X1 : $i]: 558.07/71.18 ( ('#form19' @ X0 @ X1) 558.07/71.18 | ('#form8' @ X1) 558.07/71.18 | (big_p @ ('#sk9' @ X1) @ ('#sk14' @ X1 @ X0)))), 558.07/71.18 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl79])). 558.07/71.18 thf(zip_derived_cl133, plain, 558.07/71.18 (![X4 : mu, X6 : $i]: 558.07/71.18 (~ (big_p @ X4 @ ('#sk14' @ X6 @ X4)) | ('#form19' @ X4 @ X6))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl124])). 558.07/71.18 thf(zip_derived_cl39017, plain, 558.07/71.18 (![X0 : $i]: 558.07/71.18 ( ('#form8' @ X0) 558.07/71.18 | ('#form19' @ ('#sk9' @ X0) @ X0) 558.07/71.18 | ('#form19' @ ('#sk9' @ X0) @ X0))), 558.07/71.18 inference('sup-', [status(thm)], [zip_derived_cl638, zip_derived_cl133])). 558.07/71.18 thf(zip_derived_cl39018, plain, 558.07/71.18 (![X0 : $i]: ( ('#form19' @ ('#sk9' @ X0) @ X0) | ('#form8' @ X0))), 558.07/71.18 inference('simplify', [status(thm)], [zip_derived_cl39017])). 558.07/71.18 thf(zip_derived_cl39, plain, 558.07/71.18 (( (rel_s4 @ '#sk4' @ '#sk6') 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 (((exists_in_world @ Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (((!!) @ (^[Y3 : $i]: 558.07/71.18 (((((~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3)))))))))))))))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ ( 558.07/71.18 rel_s4 @ Y0 @ 558.07/71.18 Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))))) 558.07/71.18 | ('#form3'))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 558.07/71.18 thf(zip_derived_cl52, plain, 558.07/71.18 (( ('#form12') 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.18 (((!!) @ (^[Y2 : mu]: 558.07/71.18 (((exists_in_world @ Y2 @ 558.07/71.18 Y1) => 558.07/71.18 (((!!) @ (^[Y3 : $i]: 558.07/71.18 (((((~) @ ( 558.07/71.18 rel_s4 @ 558.07/71.18 Y1 @ Y3))) | 558.07/71.18 (big_p @ 558.07/71.18 Y2 @ Y3)))))))))))))))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ ( 558.07/71.18 rel_s4 @ Y0 @ 558.07/71.18 Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))))))), 558.07/71.18 define([status(thm)])). 558.07/71.18 thf(zip_derived_cl53, plain, 558.07/71.18 ((~ (((((~) @ (rel_s4 @ '#sk4' @ '#sk13'))) | 558.07/71.18 (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk13' @ Y0))) | 558.07/71.18 (((!!) @ (^[Y1 : mu]: 558.07/71.18 (((exists_in_world @ Y1 @ Y0) => 558.07/71.18 (((!!) @ (^[Y2 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 558.07/71.18 (big_p @ Y1 @ Y2)))))))))))))))) | 558.07/71.18 (((!!) @ (^[Y0 : mu]: 558.07/71.18 (((exists_in_world @ Y0 @ '#sk13') => 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk13' @ Y1))) | 558.07/71.18 (big_p @ Y0 @ Y1))))))))))))))) 558.07/71.18 | ('#form12'))), 558.07/71.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl52])). 558.07/71.18 thf(zip_derived_cl66, plain, (( (rel_s4 @ '#sk4' @ '#sk13') | ('#form12'))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl53])). 558.07/71.18 thf(zip_derived_cl68, plain, 558.07/71.18 ((~ (((!!) @ (^[Y0 : mu]: 558.07/71.18 (((exists_in_world @ Y0 @ '#sk13') => 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk13' @ Y1))) | 558.07/71.18 (big_p @ Y0 @ Y1))))))))))))) 558.07/71.18 | ('#form12'))), 558.07/71.18 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl53])). 558.07/71.18 thf(zip_derived_cl81, plain, 558.07/71.18 ((~ (((exists_in_world @ ('#sk9' @ '#sk13') @ '#sk13') => 558.07/71.18 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ '#sk13' @ Y0))) | (big_p @ 558.07/71.18 ('#sk9' @ '#sk13') @ Y0)))))))))) 558.07/71.18 | ('#form12'))), 558.07/71.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl68])). 558.07/71.18 thf(zip_derived_cl93, plain, 558.07/71.18 (( (exists_in_world @ ('#sk9' @ '#sk13') @ '#sk13') | ('#form12'))), 558.07/71.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 558.07/71.18 thf(zip_derived_cl145, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 558.07/71.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 558.07/71.18 thf(zip_derived_cl109, plain, 558.07/71.18 (![X2 : $i, X4 : mu, X6 : $i]: 558.07/71.18 ( ('#form10' @ X6) 558.07/71.18 | ~ (exists_in_world @ X4 @ X2) 558.07/71.18 | ~ (rel_s4 @ '#sk4' @ X2) 558.07/71.18 | ('#form3') 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X6 @ Y0))) | (big_p @ X4 @ Y0)))))) 558.07/71.18 | ~ (rel_s4 @ X2 @ X6))), 558.07/71.18 inference('renaming', [status(thm)], 558.07/71.18 [zip_derived_cl97, zip_derived_cl56, zip_derived_cl47])). 558.07/71.18 thf(zip_derived_cl123, plain, 558.07/71.18 (![X4 : mu, X6 : $i]: 558.07/71.18 ( ('#form19' @ X4 @ X6) 558.07/71.18 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X6 @ Y0))) | (big_p @ X4 @ Y0)))))))), 558.07/71.18 define([status(thm)])). 558.07/71.18 thf(zip_derived_cl125, plain, 558.07/71.18 (![X2 : $i, X4 : mu, X6 : $i]: 558.07/71.18 (~ ('#form19' @ X4 @ X6) 558.07/71.18 | ~ (rel_s4 @ X2 @ X6) 558.07/71.18 | ('#form3') 558.07/71.18 | ~ (rel_s4 @ '#sk4' @ X2) 558.07/71.18 | ~ (exists_in_world @ X4 @ X2) 558.07/71.18 | ('#form10' @ X6))), 558.07/71.18 inference('renaming', [status(thm)], 558.07/71.18 [zip_derived_cl109, zip_derived_cl123])). 558.07/71.18 thf(zip_derived_cl264, plain, 558.07/71.18 (![X0 : $i, X1 : mu]: 558.07/71.18 ( ('#form10' @ X0) 558.07/71.18 | ~ (exists_in_world @ X1 @ X0) 558.07/71.18 | ~ (rel_s4 @ '#sk4' @ X0) 558.07/71.18 | ('#form3') 558.07/71.18 | ~ ('#form19' @ X1 @ X0))), 558.07/71.18 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl125])). 558.07/71.18 thf(zip_derived_cl419, plain, 558.07/71.18 (( ('#form12') 558.07/71.18 | ~ ('#form19' @ ('#sk9' @ '#sk13') @ '#sk13') 558.07/71.18 | ('#form3') 558.07/71.18 | ~ (rel_s4 @ '#sk4' @ '#sk13') 558.07/71.18 | ('#form10' @ '#sk13'))), 558.07/71.18 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl264])). 558.07/71.18 thf(nonempty_ax, axiom, (![V:$i]: ( ?[X:mu]: ( exists_in_world @ X @ V ) ))). 558.07/71.18 thf(zip_derived_cl0, plain, 558.07/71.18 ( (((!!) @ (^[Y0 : $i]: 558.07/71.18 (((??) @ (^[Y1 : mu]: (exists_in_world @ Y1 @ Y0)))))))), 558.07/71.18 inference('cnf', [status(esa)], [nonempty_ax])). 558.07/71.18 thf(zip_derived_cl150, plain, 558.07/71.18 (![X2 : $i]: (((??) @ (^[Y0 : mu]: (exists_in_world @ Y0 @ X2))))), 558.07/71.18 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 558.07/71.18 thf(zip_derived_cl151, plain, 558.07/71.18 (![X2 : $i]: (exists_in_world @ ('#sk20' @ X2) @ X2)), 558.07/71.18 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl150])). 558.07/71.18 thf(zip_derived_cl33, plain, 558.07/71.18 (![X2 : $i]: 558.07/71.18 (~ ('#form8' @ X2) 558.07/71.18 | (((!!) @ (^[Y0 : mu]: 558.07/71.18 (((exists_in_world @ Y0 @ X2) => 558.07/71.18 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.18 (((((~) @ (rel_s4 @ X2 @ Y1))) | 558.07/71.19 (big_p @ Y0 @ Y1))))))))))))))), 558.07/71.19 define([status(thm)])). 558.07/71.19 thf(zip_derived_cl34, plain, 558.07/71.19 (![X2 : $i, X4 : mu]: 558.07/71.19 ( (((exists_in_world @ X4 @ X2) => 558.07/71.19 (((~) @ (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X2 @ Y0))) | (big_p @ 558.07/71.19 X4 @ Y0)))))))))) 558.07/71.19 | ~ ('#form8' @ X2))), 558.07/71.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])). 558.07/71.19 thf(zip_derived_cl46, plain, 558.07/71.19 (![X2 : $i, X4 : mu]: 558.07/71.19 (~ (exists_in_world @ X4 @ X2) 558.07/71.19 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X2 @ Y0))) | (big_p @ X4 @ Y0)))))) 558.07/71.19 | ~ ('#form8' @ X2))), 558.07/71.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 558.07/71.19 thf(zip_derived_cl62, plain, 558.07/71.19 (![X2 : $i, X4 : mu]: 558.07/71.19 (~ (((((~) @ (rel_s4 @ X2 @ ('#sk14' @ X2 @ X4)))) | (big_p @ X4 @ 558.07/71.19 ('#sk14' @ X2 @ X4)))) 558.07/71.19 | ~ ('#form8' @ X2) 558.07/71.19 | ~ (exists_in_world @ X4 @ X2))), 558.07/71.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl46])). 558.07/71.19 thf(zip_derived_cl76, plain, 558.07/71.19 (![X2 : $i, X4 : mu]: 558.07/71.19 ( (rel_s4 @ X2 @ ('#sk14' @ X2 @ X4)) 558.07/71.19 | ~ (exists_in_world @ X4 @ X2) 558.07/71.19 | ~ ('#form8' @ X2))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 558.07/71.19 thf(zip_derived_cl226, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 (~ ('#form8' @ X0) | (rel_s4 @ X0 @ ('#sk14' @ X0 @ ('#sk20' @ X0))))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl76])). 558.07/71.19 thf(zip_derived_cl151, plain, 558.07/71.19 (![X2 : $i]: (exists_in_world @ ('#sk20' @ X2) @ X2)), 558.07/71.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl150])). 558.07/71.19 thf(zip_derived_cl195, plain, 558.07/71.19 (![X2 : mu, X4 : $i, X6 : $i]: 558.07/71.19 (~ (exists_in_world @ X2 @ X4) 558.07/71.19 | ~ (rel_s4 @ X4 @ X6) 558.07/71.19 | (exists_in_world @ X2 @ X6))), 558.07/71.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl194])). 558.07/71.19 thf(zip_derived_cl196, plain, 558.07/71.19 (![X0 : $i, X1 : $i]: 558.07/71.19 ( (exists_in_world @ ('#sk20' @ X0) @ X1) | ~ (rel_s4 @ X0 @ X1))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl195])). 558.07/71.19 thf(zip_derived_cl243, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 (~ ('#form8' @ X0) 558.07/71.19 | (exists_in_world @ ('#sk20' @ X0) @ 558.07/71.19 ('#sk14' @ X0 @ ('#sk20' @ X0))))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl226, zip_derived_cl196])). 558.07/71.19 thf(zip_derived_cl226, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 (~ ('#form8' @ X0) | (rel_s4 @ X0 @ ('#sk14' @ X0 @ ('#sk20' @ X0))))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl76])). 558.07/71.19 thf(zip_derived_cl146, plain, 558.07/71.19 (![X0 : $i, X1 : $i, X2 : mu]: 558.07/71.19 (~ ('#form10' @ X1) 558.07/71.19 | ~ (rel_s4 @ X1 @ X0) 558.07/71.19 | ~ (exists_in_world @ X2 @ X0) 558.07/71.19 | (big_p @ X2 @ X0))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl121])). 558.07/71.19 thf(zip_derived_cl240, plain, 558.07/71.19 (![X0 : $i, X1 : mu]: 558.07/71.19 (~ ('#form8' @ X0) 558.07/71.19 | (big_p @ X1 @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 558.07/71.19 | ~ (exists_in_world @ X1 @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 558.07/71.19 | ~ ('#form10' @ X0))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl226, zip_derived_cl146])). 558.07/71.19 thf(zip_derived_cl406, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 (~ ('#form8' @ X0) 558.07/71.19 | ~ ('#form10' @ X0) 558.07/71.19 | (big_p @ ('#sk20' @ X0) @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 558.07/71.19 | ~ ('#form8' @ X0))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl243, zip_derived_cl240])). 558.07/71.19 thf(zip_derived_cl407, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 ( (big_p @ ('#sk20' @ X0) @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 558.07/71.19 | ~ ('#form10' @ X0) 558.07/71.19 | ~ ('#form8' @ X0))), 558.07/71.19 inference('simplify', [status(thm)], [zip_derived_cl406])). 558.07/71.19 thf(zip_derived_cl151, plain, 558.07/71.19 (![X2 : $i]: (exists_in_world @ ('#sk20' @ X2) @ X2)), 558.07/71.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl150])). 558.07/71.19 thf(zip_derived_cl77, plain, 558.07/71.19 (![X2 : $i, X4 : mu]: 558.07/71.19 (~ (big_p @ X4 @ ('#sk14' @ X2 @ X4)) 558.07/71.19 | ~ (exists_in_world @ X4 @ X2) 558.07/71.19 | ~ ('#form8' @ X2))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 558.07/71.19 thf(zip_derived_cl152, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 (~ ('#form8' @ X0) 558.07/71.19 | ~ (big_p @ ('#sk20' @ X0) @ ('#sk14' @ X0 @ ('#sk20' @ X0))))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl77])). 558.07/71.19 thf(zip_derived_cl408, plain, 558.07/71.19 (![X0 : $i]: (~ ('#form8' @ X0) | ~ ('#form10' @ X0))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl407, zip_derived_cl152])). 558.07/71.19 thf(zip_derived_cl40, plain, 558.07/71.19 (( (((!!) @ (^[Y0 : mu]: 558.07/71.19 (((exists_in_world @ Y0 @ '#sk6') => 558.07/71.19 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ '#sk6' @ Y1))) | 558.07/71.19 (big_p @ Y0 @ Y1))))))))))))) 558.07/71.19 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.19 (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.19 (((!!) @ (^[Y2 : mu]: 558.07/71.19 (((exists_in_world @ Y2 @ 558.07/71.19 Y1) => 558.07/71.19 (((!!) @ (^[Y3 : $i]: 558.07/71.19 (((((~) @ ( 558.07/71.19 rel_s4 @ 558.07/71.19 Y1 @ Y3))) | 558.07/71.19 (big_p @ 558.07/71.19 Y2 @ Y3)))))))))))))))) | 558.07/71.19 (((!!) @ (^[Y1 : mu]: 558.07/71.19 (((exists_in_world @ Y1 @ Y0) => 558.07/71.19 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.19 (((((~) @ ( 558.07/71.19 rel_s4 @ Y0 @ 558.07/71.19 Y2))) | 558.07/71.19 (big_p @ Y1 @ Y2)))))))))))))))))) 558.07/71.19 | ('#form3'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 558.07/71.19 thf(zip_derived_cl36, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 ( ('#form8' @ X2) 558.07/71.19 | ~ (((!!) @ (^[Y0 : mu]: 558.07/71.19 (((exists_in_world @ Y0 @ X2) => 558.07/71.19 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X2 @ Y1))) | 558.07/71.19 (big_p @ Y0 @ Y1))))))))))))))), 558.07/71.19 define([status(thm)])). 558.07/71.19 thf(zip_derived_cl33, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 (~ ('#form8' @ X2) 558.07/71.19 | (((!!) @ (^[Y0 : mu]: 558.07/71.19 (((exists_in_world @ Y0 @ X2) => 558.07/71.19 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X2 @ Y1))) | 558.07/71.19 (big_p @ Y0 @ Y1))))))))))))))), 558.07/71.19 define([status(thm)])). 558.07/71.19 thf(zip_derived_cl55, plain, 558.07/71.19 (( ('#form8' @ '#sk6') 558.07/71.19 | ('#form3') 558.07/71.19 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.19 (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.19 (((!!) @ (^[Y2 : mu]: 558.07/71.19 (((exists_in_world @ Y2 @ 558.07/71.19 Y1) => 558.07/71.19 (((!!) @ (^[Y3 : $i]: 558.07/71.19 (((((~) @ ( 558.07/71.19 rel_s4 @ 558.07/71.19 Y1 @ Y3))) | 558.07/71.19 (big_p @ 558.07/71.19 Y2 @ Y3)))))))))))))))) | 558.07/71.19 (((!!) @ (^[Y1 : mu]: 558.07/71.19 (((exists_in_world @ Y1 @ Y0) => 558.07/71.19 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.19 (((((~) @ ( 558.07/71.19 rel_s4 @ Y0 @ 558.07/71.19 Y2))) | 558.07/71.19 (big_p @ Y1 @ Y2)))))))))))))))))))), 558.07/71.19 inference('renaming', [status(thm)], 558.07/71.19 [zip_derived_cl40, zip_derived_cl36, zip_derived_cl33])). 558.07/71.19 thf(zip_derived_cl52, plain, 558.07/71.19 (( ('#form12') 558.07/71.19 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.19 (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.19 (((!!) @ (^[Y2 : mu]: 558.07/71.19 (((exists_in_world @ Y2 @ 558.07/71.19 Y1) => 558.07/71.19 (((!!) @ (^[Y3 : $i]: 558.07/71.19 (((((~) @ ( 558.07/71.19 rel_s4 @ 558.07/71.19 Y1 @ Y3))) | 558.07/71.19 (big_p @ 558.07/71.19 Y2 @ Y3)))))))))))))))) | 558.07/71.19 (((!!) @ (^[Y1 : mu]: 558.07/71.19 (((exists_in_world @ Y1 @ Y0) => 558.07/71.19 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.19 (((((~) @ ( 558.07/71.19 rel_s4 @ Y0 @ 558.07/71.19 Y2))) | 558.07/71.19 (big_p @ Y1 @ Y2)))))))))))))))))))), 558.07/71.19 define([status(thm)])). 558.07/71.19 thf(zip_derived_cl69, plain, 558.07/71.19 ((~ ('#form12') | ('#form3') | ('#form8' @ '#sk6'))), 558.07/71.19 inference('renaming', [status(thm)], [zip_derived_cl55, zip_derived_cl52])). 558.07/71.19 thf(zip_derived_cl409, plain, 558.07/71.19 ((~ ('#form10' @ '#sk6') | ('#form3') | ~ ('#form12'))), 558.07/71.19 inference('sup+', [status(thm)], [zip_derived_cl408, zip_derived_cl69])). 558.07/71.19 thf(zip_derived_cl41, plain, 558.07/71.19 (( (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | 558.07/71.19 (((!!) @ (^[Y1 : mu]: 558.07/71.19 (((exists_in_world @ Y1 @ Y0) => 558.07/71.19 (((!!) @ (^[Y2 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 558.07/71.19 (big_p @ Y1 @ Y2)))))))))))))))) 558.07/71.19 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.19 (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.19 (((!!) @ (^[Y2 : mu]: 558.07/71.19 (((exists_in_world @ Y2 @ 558.07/71.19 Y1) => 558.07/71.19 (((!!) @ (^[Y3 : $i]: 558.07/71.19 (((((~) @ ( 558.07/71.19 rel_s4 @ 558.07/71.19 Y1 @ Y3))) | 558.07/71.19 (big_p @ 558.07/71.19 Y2 @ Y3)))))))))))))))) | 558.07/71.19 (((!!) @ (^[Y1 : mu]: 558.07/71.19 (((exists_in_world @ Y1 @ Y0) => 558.07/71.19 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.19 (((((~) @ ( 558.07/71.19 rel_s4 @ Y0 @ 558.07/71.19 Y2))) | 558.07/71.19 (big_p @ Y1 @ Y2)))))))))))))))))) 558.07/71.19 | ('#form3'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 558.07/71.19 thf(zip_derived_cl56, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 (~ ('#form10' @ X2) 558.07/71.19 | (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.19 (((!!) @ (^[Y1 : mu]: 558.07/71.19 (((exists_in_world @ Y1 @ Y0) => 558.07/71.19 (((!!) @ (^[Y2 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.19 Y2))) | 558.07/71.19 (big_p @ Y1 @ Y2)))))))))))))))))), 558.07/71.19 define([status(thm)])). 558.07/71.19 thf(zip_derived_cl47, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 ( ('#form10' @ X2) 558.07/71.19 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.19 (((!!) @ (^[Y1 : mu]: 558.07/71.19 (((exists_in_world @ Y1 @ Y0) => 558.07/71.19 (((!!) @ (^[Y2 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.19 Y2))) | 558.07/71.19 (big_p @ Y1 @ Y2)))))))))))))))))), 558.07/71.19 define([status(thm)])). 558.07/71.19 thf(zip_derived_cl58, plain, 558.07/71.19 (( ('#form10' @ '#sk6') 558.07/71.19 | ('#form3') 558.07/71.19 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.19 (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.19 (((!!) @ (^[Y2 : mu]: 558.07/71.19 (((exists_in_world @ Y2 @ 558.07/71.19 Y1) => 558.07/71.19 (((!!) @ (^[Y3 : $i]: 558.07/71.19 (((((~) @ ( 558.07/71.19 rel_s4 @ 558.07/71.19 Y1 @ Y3))) | 558.07/71.19 (big_p @ 558.07/71.19 Y2 @ Y3)))))))))))))))) | 558.07/71.19 (((!!) @ (^[Y1 : mu]: 558.07/71.19 (((exists_in_world @ Y1 @ Y0) => 558.07/71.19 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.19 (((((~) @ ( 558.07/71.19 rel_s4 @ Y0 @ 558.07/71.19 Y2))) | 558.07/71.19 (big_p @ Y1 @ Y2)))))))))))))))))))), 558.07/71.19 inference('renaming', [status(thm)], 558.07/71.19 [zip_derived_cl41, zip_derived_cl56, zip_derived_cl47])). 558.07/71.19 thf(zip_derived_cl52, plain, 558.07/71.19 (( ('#form12') 558.07/71.19 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 558.07/71.19 (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 558.07/71.19 (((!!) @ (^[Y2 : mu]: 558.07/71.19 (((exists_in_world @ Y2 @ 558.07/71.19 Y1) => 558.07/71.19 (((!!) @ (^[Y3 : $i]: 558.07/71.19 (((((~) @ ( 558.07/71.19 rel_s4 @ 558.07/71.19 Y1 @ Y3))) | 558.07/71.19 (big_p @ 558.07/71.19 Y2 @ Y3)))))))))))))))) | 558.07/71.19 (((!!) @ (^[Y1 : mu]: 558.07/71.19 (((exists_in_world @ Y1 @ Y0) => 558.07/71.19 (((~) @ (((!!) @ (^[Y2 : $i]: 558.07/71.19 (((((~) @ ( 558.07/71.19 rel_s4 @ Y0 @ 558.07/71.19 Y2))) | 558.07/71.19 (big_p @ Y1 @ Y2)))))))))))))))))))), 558.07/71.19 define([status(thm)])). 558.07/71.19 thf(zip_derived_cl70, plain, 558.07/71.19 ((~ ('#form12') | ('#form3') | ('#form10' @ '#sk6'))), 558.07/71.19 inference('renaming', [status(thm)], [zip_derived_cl58, zip_derived_cl52])). 558.07/71.19 thf(zip_derived_cl415, plain, ((~ ('#form12') | ('#form3'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl409, zip_derived_cl70])). 558.07/71.19 thf(zip_derived_cl6347, plain, 558.07/71.19 (( ('#form10' @ '#sk13') 558.07/71.19 | ~ (rel_s4 @ '#sk4' @ '#sk13') 558.07/71.19 | ('#form3') 558.07/71.19 | ~ ('#form19' @ ('#sk9' @ '#sk13') @ '#sk13'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl419, zip_derived_cl415])). 558.07/71.19 thf(zip_derived_cl6348, plain, 558.07/71.19 (( ('#form12') 558.07/71.19 | ~ ('#form19' @ ('#sk9' @ '#sk13') @ '#sk13') 558.07/71.19 | ('#form3') 558.07/71.19 | ('#form10' @ '#sk13'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl66, zip_derived_cl6347])). 558.07/71.19 thf(zip_derived_cl415, plain, ((~ ('#form12') | ('#form3'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl409, zip_derived_cl70])). 558.07/71.19 thf(zip_derived_cl6383, plain, 558.07/71.19 (( ('#form10' @ '#sk13') 558.07/71.19 | ('#form3') 558.07/71.19 | ~ ('#form19' @ ('#sk9' @ '#sk13') @ '#sk13'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl6348, zip_derived_cl415])). 558.07/71.19 thf(zip_derived_cl39020, plain, 558.07/71.19 (( ('#form8' @ '#sk13') | ('#form3') | ('#form10' @ '#sk13'))), 558.07/71.19 inference('sup-', [status(thm)], 558.07/71.19 [zip_derived_cl39018, zip_derived_cl6383])). 558.07/71.19 thf(zip_derived_cl93, plain, 558.07/71.19 (( (exists_in_world @ ('#sk9' @ '#sk13') @ '#sk13') | ('#form12'))), 558.07/71.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 558.07/71.19 thf(zip_derived_cl76, plain, 558.07/71.19 (![X2 : $i, X4 : mu]: 558.07/71.19 ( (rel_s4 @ X2 @ ('#sk14' @ X2 @ X4)) 558.07/71.19 | ~ (exists_in_world @ X4 @ X2) 558.07/71.19 | ~ ('#form8' @ X2))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 558.07/71.19 thf(zip_derived_cl416, plain, 558.07/71.19 (( ('#form12') 558.07/71.19 | ~ ('#form8' @ '#sk13') 558.07/71.19 | (rel_s4 @ '#sk13' @ ('#sk14' @ '#sk13' @ ('#sk9' @ '#sk13'))))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl76])). 558.07/71.19 thf(zip_derived_cl94, plain, 558.07/71.19 (( (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ '#sk13' @ Y0))) | (big_p @ 558.07/71.19 ('#sk9' @ '#sk13') @ Y0)))))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 558.07/71.19 thf(zip_derived_cl106, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 ( (((((~) @ (rel_s4 @ '#sk13' @ X2))) | (big_p @ ('#sk9' @ '#sk13') @ 558.07/71.19 X2))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 558.07/71.19 thf(zip_derived_cl120, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 (~ (rel_s4 @ '#sk13' @ X2) 558.07/71.19 | (big_p @ ('#sk9' @ '#sk13') @ X2) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl106])). 558.07/71.19 thf(zip_derived_cl6602, plain, 558.07/71.19 ((~ ('#form8' @ '#sk13') 558.07/71.19 | ('#form12') 558.07/71.19 | ('#form12') 558.07/71.19 | (big_p @ ('#sk9' @ '#sk13') @ 558.07/71.19 ('#sk14' @ '#sk13' @ ('#sk9' @ '#sk13'))))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl416, zip_derived_cl120])). 558.07/71.19 thf(zip_derived_cl6608, plain, 558.07/71.19 (( (big_p @ ('#sk9' @ '#sk13') @ ('#sk14' @ '#sk13' @ ('#sk9' @ '#sk13'))) 558.07/71.19 | ('#form12') 558.07/71.19 | ~ ('#form8' @ '#sk13'))), 558.07/71.19 inference('simplify', [status(thm)], [zip_derived_cl6602])). 558.07/71.19 thf(zip_derived_cl93, plain, 558.07/71.19 (( (exists_in_world @ ('#sk9' @ '#sk13') @ '#sk13') | ('#form12'))), 558.07/71.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 558.07/71.19 thf(zip_derived_cl77, plain, 558.07/71.19 (![X2 : $i, X4 : mu]: 558.07/71.19 (~ (big_p @ X4 @ ('#sk14' @ X2 @ X4)) 558.07/71.19 | ~ (exists_in_world @ X4 @ X2) 558.07/71.19 | ~ ('#form8' @ X2))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 558.07/71.19 thf(zip_derived_cl417, plain, 558.07/71.19 (( ('#form12') 558.07/71.19 | ~ ('#form8' @ '#sk13') 558.07/71.19 | ~ (big_p @ ('#sk9' @ '#sk13') @ 558.07/71.19 ('#sk14' @ '#sk13' @ ('#sk9' @ '#sk13'))))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl77])). 558.07/71.19 thf(zip_derived_cl9163, plain, ((~ ('#form8' @ '#sk13') | ('#form12'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl6608, zip_derived_cl417])). 558.07/71.19 thf(zip_derived_cl39026, plain, 558.07/71.19 (( ('#form10' @ '#sk13') | ('#form3') | ('#form12'))), 558.07/71.19 inference('sup-', [status(thm)], 558.07/71.19 [zip_derived_cl39020, zip_derived_cl9163])). 558.07/71.19 thf(zip_derived_cl67, plain, 558.07/71.19 ((~ (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ '#sk13' @ Y0))) | 558.07/71.19 (((!!) @ (^[Y1 : mu]: 558.07/71.19 (((exists_in_world @ Y1 @ Y0) => 558.07/71.19 (((!!) @ (^[Y2 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 558.07/71.19 (big_p @ Y1 @ Y2)))))))))))))))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl53])). 558.07/71.19 thf(zip_derived_cl80, plain, 558.07/71.19 ((~ (((((~) @ (rel_s4 @ '#sk13' @ ('#sk11' @ '#sk13')))) | 558.07/71.19 (((!!) @ (^[Y0 : mu]: 558.07/71.19 (((exists_in_world @ Y0 @ ('#sk11' @ '#sk13')) => 558.07/71.19 (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ 558.07/71.19 ('#sk11' @ '#sk13') @ Y1))) | 558.07/71.19 (big_p @ Y0 @ Y1))))))))))))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl67])). 558.07/71.19 thf(zip_derived_cl92, plain, 558.07/71.19 ((~ (((!!) @ (^[Y0 : mu]: 558.07/71.19 (((exists_in_world @ Y0 @ ('#sk11' @ '#sk13')) => 558.07/71.19 (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ ('#sk11' @ '#sk13') @ 558.07/71.19 Y1))) | 558.07/71.19 (big_p @ Y0 @ Y1))))))))))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl80])). 558.07/71.19 thf(zip_derived_cl105, plain, 558.07/71.19 ((~ (((exists_in_world @ ('#sk16' @ '#sk13') @ ('#sk11' @ '#sk13')) => 558.07/71.19 (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ ('#sk11' @ '#sk13') @ Y0))) | 558.07/71.19 (big_p @ ('#sk16' @ '#sk13') @ Y0)))))))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl92])). 558.07/71.19 thf(zip_derived_cl119, plain, 558.07/71.19 ((~ (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ ('#sk11' @ '#sk13') @ Y0))) | 558.07/71.19 (big_p @ ('#sk16' @ '#sk13') @ Y0)))))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 558.07/71.19 thf(zip_derived_cl130, plain, 558.07/71.19 ((~ (((((~) @ (rel_s4 @ ('#sk11' @ '#sk13') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))))) | 558.07/71.19 (big_p @ ('#sk16' @ '#sk13') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 558.07/71.19 thf(zip_derived_cl137, plain, 558.07/71.19 (( (rel_s4 @ ('#sk11' @ '#sk13') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl130])). 558.07/71.19 thf(zip_derived_cl118, plain, 558.07/71.19 (( (exists_in_world @ ('#sk16' @ '#sk13') @ ('#sk11' @ '#sk13')) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 558.07/71.19 thf(zip_derived_cl195, plain, 558.07/71.19 (![X2 : mu, X4 : $i, X6 : $i]: 558.07/71.19 (~ (exists_in_world @ X2 @ X4) 558.07/71.19 | ~ (rel_s4 @ X4 @ X6) 558.07/71.19 | (exists_in_world @ X2 @ X6))), 558.07/71.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl194])). 558.07/71.19 thf(zip_derived_cl543, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 ( ('#form12') 558.07/71.19 | (exists_in_world @ ('#sk16' @ '#sk13') @ X0) 558.07/71.19 | ~ (rel_s4 @ ('#sk11' @ '#sk13') @ X0))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl195])). 558.07/71.19 thf(zip_derived_cl1878, plain, 558.07/71.19 (( ('#form12') 558.07/71.19 | (exists_in_world @ ('#sk16' @ '#sk13') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl543])). 558.07/71.19 thf(zip_derived_cl1879, plain, 558.07/71.19 (( (exists_in_world @ ('#sk16' @ '#sk13') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('simplify', [status(thm)], [zip_derived_cl1878])). 558.07/71.19 thf(zip_derived_cl91, plain, 558.07/71.19 (( (rel_s4 @ '#sk13' @ ('#sk11' @ '#sk13')) | ('#form12'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl80])). 558.07/71.19 thf(zip_derived_cl137, plain, 558.07/71.19 (( (rel_s4 @ ('#sk11' @ '#sk13') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl130])). 558.07/71.19 thf(zip_derived_cl161, plain, 558.07/71.19 (![X2 : $i, X4 : $i, X6 : $i]: 558.07/71.19 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))), 558.07/71.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl160])). 558.07/71.19 thf(zip_derived_cl697, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 ( ('#form12') 558.07/71.19 | (rel_s4 @ X0 @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 558.07/71.19 | ~ (rel_s4 @ X0 @ ('#sk11' @ '#sk13')))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl161])). 558.07/71.19 thf(zip_derived_cl7058, plain, 558.07/71.19 (( ('#form12') 558.07/71.19 | (rel_s4 @ '#sk13' @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl91, zip_derived_cl697])). 558.07/71.19 thf(zip_derived_cl7060, plain, 558.07/71.19 (( (rel_s4 @ '#sk13' @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('simplify', [status(thm)], [zip_derived_cl7058])). 558.07/71.19 thf(zip_derived_cl146, plain, 558.07/71.19 (![X0 : $i, X1 : $i, X2 : mu]: 558.07/71.19 (~ ('#form10' @ X1) 558.07/71.19 | ~ (rel_s4 @ X1 @ X0) 558.07/71.19 | ~ (exists_in_world @ X2 @ X0) 558.07/71.19 | (big_p @ X2 @ X0))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl121])). 558.07/71.19 thf(zip_derived_cl7118, plain, 558.07/71.19 (![X0 : mu]: 558.07/71.19 ( ('#form12') 558.07/71.19 | (big_p @ X0 @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 558.07/71.19 | ~ (exists_in_world @ X0 @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 558.07/71.19 | ~ ('#form10' @ '#sk13'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl7060, zip_derived_cl146])). 558.07/71.19 thf(zip_derived_cl28857, plain, 558.07/71.19 (( ('#form12') 558.07/71.19 | ~ ('#form10' @ '#sk13') 558.07/71.19 | (big_p @ ('#sk16' @ '#sk13') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl1879, zip_derived_cl7118])). 558.07/71.19 thf(zip_derived_cl28866, plain, 558.07/71.19 (( (big_p @ ('#sk16' @ '#sk13') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 558.07/71.19 | ~ ('#form10' @ '#sk13') 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('simplify', [status(thm)], [zip_derived_cl28857])). 558.07/71.19 thf(zip_derived_cl138, plain, 558.07/71.19 ((~ (big_p @ ('#sk16' @ '#sk13') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 558.07/71.19 | ('#form12'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl130])). 558.07/71.19 thf(zip_derived_cl29010, plain, (( ('#form12') | ~ ('#form10' @ '#sk13'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl28866, zip_derived_cl138])). 558.07/71.19 thf(zip_derived_cl39037, plain, (( ('#form12') | ('#form3'))), 558.07/71.19 inference('clc', [status(thm)], 558.07/71.19 [zip_derived_cl39026, zip_derived_cl29010])). 558.07/71.19 thf(zip_derived_cl415, plain, ((~ ('#form12') | ('#form3'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl409, zip_derived_cl70])). 558.07/71.19 thf(zip_derived_cl39038, plain, ( ('#form3')), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl39037, zip_derived_cl415])). 558.07/71.19 thf(zip_derived_cl39377, plain, (~ ('#form17')), 558.07/71.19 inference('demod', [status(thm)], 558.07/71.19 [zip_derived_cl4225, zip_derived_cl39038])). 558.07/71.19 thf(zip_derived_cl40032, plain, (~ ('#form10' @ '#sk18')), 558.07/71.19 inference('demod', [status(thm)], 558.07/71.19 [zip_derived_cl29467, zip_derived_cl39377])). 558.07/71.19 thf(zip_derived_cl47, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 ( ('#form10' @ X2) 558.07/71.19 | ~ (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.19 (((!!) @ (^[Y1 : mu]: 558.07/71.19 (((exists_in_world @ Y1 @ Y0) => 558.07/71.19 (((!!) @ (^[Y2 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.19 Y2))) | 558.07/71.19 (big_p @ Y1 @ Y2)))))))))))))))))), 558.07/71.19 define([status(thm)])). 558.07/71.19 thf(zip_derived_cl48, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 (~ (((((~) @ (rel_s4 @ X2 @ ('#sk11' @ X2)))) | 558.07/71.19 (((!!) @ (^[Y0 : mu]: 558.07/71.19 (((exists_in_world @ Y0 @ ('#sk11' @ X2)) => 558.07/71.19 (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ ('#sk11' @ X2) @ Y1))) | 558.07/71.19 (big_p @ Y0 @ Y1))))))))))))) 558.07/71.19 | ('#form10' @ X2))), 558.07/71.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 558.07/71.19 thf(zip_derived_cl64, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 (~ (((!!) @ (^[Y0 : mu]: 558.07/71.19 (((exists_in_world @ Y0 @ ('#sk11' @ X2)) => 558.07/71.19 (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ ('#sk11' @ X2) @ Y1))) | 558.07/71.19 (big_p @ Y0 @ Y1))))))))))) 558.07/71.19 | ('#form10' @ X2))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl48])). 558.07/71.19 thf(zip_derived_cl78, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 (~ (((exists_in_world @ ('#sk16' @ X2) @ ('#sk11' @ X2)) => 558.07/71.19 (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ ('#sk11' @ X2) @ Y0))) | 558.07/71.19 (big_p @ ('#sk16' @ X2) @ Y0)))))))) 558.07/71.19 | ('#form10' @ X2))), 558.07/71.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl64])). 558.07/71.19 thf(zip_derived_cl90, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 (~ (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ ('#sk11' @ X2) @ Y0))) | (big_p @ 558.07/71.19 ('#sk16' @ X2) @ Y0)))))) 558.07/71.19 | ('#form10' @ X2))), 558.07/71.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 558.07/71.19 thf(zip_derived_cl104, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 (~ (((((~) @ (rel_s4 @ ('#sk11' @ X2) @ 558.07/71.19 ('#sk14' @ ('#sk11' @ X2) @ ('#sk16' @ X2))))) | 558.07/71.19 (big_p @ ('#sk16' @ X2) @ 558.07/71.19 ('#sk14' @ ('#sk11' @ X2) @ ('#sk16' @ X2))))) 558.07/71.19 | ('#form10' @ X2))), 558.07/71.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl90])). 558.07/71.19 thf(zip_derived_cl116, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 ( (rel_s4 @ ('#sk11' @ X2) @ 558.07/71.19 ('#sk14' @ ('#sk11' @ X2) @ ('#sk16' @ X2))) 558.07/71.19 | ('#form10' @ X2))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl104])). 558.07/71.19 thf(zip_derived_cl2415, plain, 558.07/71.19 (( (exists_in_world @ ('#sk16' @ '#sk18') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.19 | ('#form17'))), 558.07/71.19 inference('simplify', [status(thm)], [zip_derived_cl2414])). 558.07/71.19 thf(zip_derived_cl26, plain, (( (rel_s4 @ '#sk2' @ '#sk5') | ~ ('#form3'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl21])). 558.07/71.19 thf(zip_derived_cl110, plain, 558.07/71.19 (( (rel_s4 @ '#sk5' @ '#sk18') | ('#form17'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl99])). 558.07/71.19 thf(zip_derived_cl161, plain, 558.07/71.19 (![X2 : $i, X4 : $i, X6 : $i]: 558.07/71.19 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))), 558.07/71.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl160])). 558.07/71.19 thf(zip_derived_cl175, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 ( ('#form17') | (rel_s4 @ X0 @ '#sk18') | ~ (rel_s4 @ X0 @ '#sk5'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl161])). 558.07/71.19 thf(zip_derived_cl332, plain, 558.07/71.19 ((~ ('#form3') | (rel_s4 @ '#sk2' @ '#sk18') | ('#form17'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl175])). 558.07/71.19 thf(zip_derived_cl134, plain, 558.07/71.19 (( (rel_s4 @ '#sk18' @ ('#sk11' @ '#sk18')) | ('#form17'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl126])). 558.07/71.19 thf(zip_derived_cl161, plain, 558.07/71.19 (![X2 : $i, X4 : $i, X6 : $i]: 558.07/71.19 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))), 558.07/71.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl160])). 558.07/71.19 thf(zip_derived_cl455, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 ( ('#form17') 558.07/71.19 | (rel_s4 @ X0 @ ('#sk11' @ '#sk18')) 558.07/71.19 | ~ (rel_s4 @ X0 @ '#sk18'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl161])). 558.07/71.19 thf(zip_derived_cl1365, plain, 558.07/71.19 (( ('#form17') 558.07/71.19 | ~ ('#form3') 558.07/71.19 | (rel_s4 @ '#sk2' @ ('#sk11' @ '#sk18')) 558.07/71.19 | ('#form17'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl332, zip_derived_cl455])). 558.07/71.19 thf(zip_derived_cl1368, plain, 558.07/71.19 (( (rel_s4 @ '#sk2' @ ('#sk11' @ '#sk18')) | ~ ('#form3') | ('#form17'))), 558.07/71.19 inference('simplify', [status(thm)], [zip_derived_cl1365])). 558.07/71.19 thf(zip_derived_cl145, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 558.07/71.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 558.07/71.19 thf(zip_derived_cl28, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 (~ (rel_s4 @ '#sk2' @ X2) 558.07/71.19 | (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.19 (((!!) @ (^[Y1 : mu]: 558.07/71.19 (((exists_in_world @ Y1 @ Y0) => 558.07/71.19 (((!!) @ (^[Y2 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.19 Y2))) | 558.07/71.19 (big_p @ Y1 @ Y2)))))))))))))))) 558.07/71.19 | (((!!) @ (^[Y0 : mu]: 558.07/71.19 (((exists_in_world @ Y0 @ X2) => 558.07/71.19 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X2 @ Y1))) | 558.07/71.19 (big_p @ Y0 @ Y1))))))))))))) 558.07/71.19 | ~ ('#form3'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl22])). 558.07/71.19 thf(zip_derived_cl33, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 (~ ('#form8' @ X2) 558.07/71.19 | (((!!) @ (^[Y0 : mu]: 558.07/71.19 (((exists_in_world @ Y0 @ X2) => 558.07/71.19 (((~) @ (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X2 @ Y1))) | 558.07/71.19 (big_p @ Y0 @ Y1))))))))))))))), 558.07/71.19 define([status(thm)])). 558.07/71.19 thf(zip_derived_cl35, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 ( ('#form8' @ X2) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X2 @ Y0))) | 558.07/71.19 (((!!) @ (^[Y1 : mu]: 558.07/71.19 (((exists_in_world @ Y1 @ Y0) => 558.07/71.19 (((!!) @ (^[Y2 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ Y0 @ 558.07/71.19 Y2))) | 558.07/71.19 (big_p @ Y1 @ Y2)))))))))))))))) 558.07/71.19 | ~ (rel_s4 @ '#sk2' @ X2))), 558.07/71.19 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl33])). 558.07/71.19 thf(zip_derived_cl45, plain, 558.07/71.19 (![X2 : $i, X4 : $i]: 558.07/71.19 ( (((((~) @ (rel_s4 @ X2 @ X4))) | 558.07/71.19 (((!!) @ (^[Y0 : mu]: 558.07/71.19 (((exists_in_world @ Y0 @ X4) => 558.07/71.19 (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X4 @ Y1))) | 558.07/71.19 (big_p @ Y0 @ Y1))))))))))))) 558.07/71.19 | ~ (rel_s4 @ '#sk2' @ X2) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ('#form8' @ X2))), 558.07/71.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl35])). 558.07/71.19 thf(zip_derived_cl61, plain, 558.07/71.19 (![X2 : $i, X4 : $i]: 558.07/71.19 (~ (rel_s4 @ X2 @ X4) 558.07/71.19 | (((!!) @ (^[Y0 : mu]: 558.07/71.19 (((exists_in_world @ Y0 @ X4) => 558.07/71.19 (((!!) @ (^[Y1 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X4 @ Y1))) | 558.07/71.19 (big_p @ Y0 @ Y1))))))))))) 558.07/71.19 | ('#form8' @ X2) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ~ (rel_s4 @ '#sk2' @ X2))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl45])). 558.07/71.19 thf(zip_derived_cl75, plain, 558.07/71.19 (![X2 : $i, X4 : $i, X6 : mu]: 558.07/71.19 ( (((exists_in_world @ X6 @ X4) => 558.07/71.19 (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X4 @ Y0))) | (big_p @ X6 @ Y0)))))))) 558.07/71.19 | ~ (rel_s4 @ '#sk2' @ X2) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ('#form8' @ X2) 558.07/71.19 | ~ (rel_s4 @ X2 @ X4))), 558.07/71.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 558.07/71.19 thf(zip_derived_cl88, plain, 558.07/71.19 (![X2 : $i, X4 : $i, X6 : mu]: 558.07/71.19 (~ (exists_in_world @ X6 @ X4) 558.07/71.19 | (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ X4 @ Y0))) | (big_p @ X6 @ Y0)))))) 558.07/71.19 | ~ (rel_s4 @ X2 @ X4) 558.07/71.19 | ('#form8' @ X2) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ~ (rel_s4 @ '#sk2' @ X2))), 558.07/71.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 558.07/71.19 thf(zip_derived_cl103, plain, 558.07/71.19 (![X2 : $i, X4 : $i, X6 : mu, X8 : $i]: 558.07/71.19 ( (((((~) @ (rel_s4 @ X4 @ X8))) | (big_p @ X6 @ X8))) 558.07/71.19 | ~ (rel_s4 @ '#sk2' @ X2) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ('#form8' @ X2) 558.07/71.19 | ~ (rel_s4 @ X2 @ X4) 558.07/71.19 | ~ (exists_in_world @ X6 @ X4))), 558.07/71.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl88])). 558.07/71.19 thf(zip_derived_cl115, plain, 558.07/71.19 (![X2 : $i, X4 : $i, X6 : mu, X8 : $i]: 558.07/71.19 (~ (rel_s4 @ X4 @ X8) 558.07/71.19 | (big_p @ X6 @ X8) 558.07/71.19 | ~ (exists_in_world @ X6 @ X4) 558.07/71.19 | ~ (rel_s4 @ X2 @ X4) 558.07/71.19 | ('#form8' @ X2) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ~ (rel_s4 @ '#sk2' @ X2))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl103])). 558.07/71.19 thf(zip_derived_cl250, plain, 558.07/71.19 (![X0 : $i, X1 : $i, X2 : mu]: 558.07/71.19 (~ (rel_s4 @ '#sk2' @ X1) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ('#form8' @ X1) 558.07/71.19 | ~ (rel_s4 @ X1 @ X0) 558.07/71.19 | ~ (exists_in_world @ X2 @ X0) 558.07/71.19 | (big_p @ X2 @ X0))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl115])). 558.07/71.19 thf(zip_derived_cl1647, plain, 558.07/71.19 (![X0 : $i, X1 : mu]: 558.07/71.19 ( ('#form17') 558.07/71.19 | ~ ('#form3') 558.07/71.19 | (big_p @ X1 @ X0) 558.07/71.19 | ~ (exists_in_world @ X1 @ X0) 558.07/71.19 | ~ (rel_s4 @ ('#sk11' @ '#sk18') @ X0) 558.07/71.19 | ('#form8' @ ('#sk11' @ '#sk18')) 558.07/71.19 | ~ ('#form3'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl1368, zip_derived_cl250])). 558.07/71.19 thf(zip_derived_cl1655, plain, 558.07/71.19 (![X0 : $i, X1 : mu]: 558.07/71.19 ( ('#form8' @ ('#sk11' @ '#sk18')) 558.07/71.19 | ~ (rel_s4 @ ('#sk11' @ '#sk18') @ X0) 558.07/71.19 | ~ (exists_in_world @ X1 @ X0) 558.07/71.19 | (big_p @ X1 @ X0) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ('#form17'))), 558.07/71.19 inference('simplify', [status(thm)], [zip_derived_cl1647])). 558.07/71.19 thf(zip_derived_cl3819, plain, 558.07/71.19 (( ('#form17') 558.07/71.19 | ('#form17') 558.07/71.19 | ~ ('#form3') 558.07/71.19 | (big_p @ ('#sk16' @ '#sk18') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.19 | ~ (rel_s4 @ ('#sk11' @ '#sk18') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.19 | ('#form8' @ ('#sk11' @ '#sk18')))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl2415, zip_derived_cl1655])). 558.07/71.19 thf(zip_derived_cl3865, plain, 558.07/71.19 (( ('#form8' @ ('#sk11' @ '#sk18')) 558.07/71.19 | ~ (rel_s4 @ ('#sk11' @ '#sk18') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.19 | (big_p @ ('#sk16' @ '#sk18') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ('#form17'))), 558.07/71.19 inference('simplify', [status(thm)], [zip_derived_cl3819])). 558.07/71.19 thf(zip_derived_cl134, plain, 558.07/71.19 (( (rel_s4 @ '#sk18' @ ('#sk11' @ '#sk18')) | ('#form17'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl126])). 558.07/71.19 thf(zip_derived_cl151, plain, 558.07/71.19 (![X2 : $i]: (exists_in_world @ ('#sk20' @ X2) @ X2)), 558.07/71.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl150])). 558.07/71.19 thf(zip_derived_cl332, plain, 558.07/71.19 ((~ ('#form3') | (rel_s4 @ '#sk2' @ '#sk18') | ('#form17'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl175])). 558.07/71.19 thf(zip_derived_cl226, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 (~ ('#form8' @ X0) | (rel_s4 @ X0 @ ('#sk14' @ X0 @ ('#sk20' @ X0))))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl76])). 558.07/71.19 thf(zip_derived_cl115, plain, 558.07/71.19 (![X2 : $i, X4 : $i, X6 : mu, X8 : $i]: 558.07/71.19 (~ (rel_s4 @ X4 @ X8) 558.07/71.19 | (big_p @ X6 @ X8) 558.07/71.19 | ~ (exists_in_world @ X6 @ X4) 558.07/71.19 | ~ (rel_s4 @ X2 @ X4) 558.07/71.19 | ('#form8' @ X2) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ~ (rel_s4 @ '#sk2' @ X2))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl103])). 558.07/71.19 thf(zip_derived_cl251, plain, 558.07/71.19 (![X0 : $i, X1 : $i, X2 : mu]: 558.07/71.19 (~ ('#form8' @ X0) 558.07/71.19 | ~ (rel_s4 @ '#sk2' @ X1) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ('#form8' @ X1) 558.07/71.19 | ~ (rel_s4 @ X1 @ X0) 558.07/71.19 | ~ (exists_in_world @ X2 @ X0) 558.07/71.19 | (big_p @ X2 @ ('#sk14' @ X0 @ ('#sk20' @ X0))))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl226, zip_derived_cl115])). 558.07/71.19 thf(zip_derived_cl894, plain, 558.07/71.19 (![X0 : $i, X1 : mu]: 558.07/71.19 ( ('#form17') 558.07/71.19 | ~ ('#form3') 558.07/71.19 | (big_p @ X1 @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 558.07/71.19 | ~ (exists_in_world @ X1 @ X0) 558.07/71.19 | ~ (rel_s4 @ '#sk18' @ X0) 558.07/71.19 | ('#form8' @ '#sk18') 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ~ ('#form8' @ X0))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl332, zip_derived_cl251])). 558.07/71.19 thf(zip_derived_cl897, plain, 558.07/71.19 (![X0 : $i, X1 : mu]: 558.07/71.19 (~ ('#form8' @ X0) 558.07/71.19 | ('#form8' @ '#sk18') 558.07/71.19 | ~ (rel_s4 @ '#sk18' @ X0) 558.07/71.19 | ~ (exists_in_world @ X1 @ X0) 558.07/71.19 | (big_p @ X1 @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ('#form17'))), 558.07/71.19 inference('simplify', [status(thm)], [zip_derived_cl894])). 558.07/71.19 thf(zip_derived_cl4225, plain, ((~ ('#form3') | ~ ('#form17'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl3522, zip_derived_cl129])). 558.07/71.19 thf(zip_derived_cl6492, plain, 558.07/71.19 (![X0 : $i, X1 : mu]: 558.07/71.19 (~ ('#form3') 558.07/71.19 | (big_p @ X1 @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 558.07/71.19 | ~ (exists_in_world @ X1 @ X0) 558.07/71.19 | ~ (rel_s4 @ '#sk18' @ X0) 558.07/71.19 | ('#form8' @ '#sk18') 558.07/71.19 | ~ ('#form8' @ X0))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl897, zip_derived_cl4225])). 558.07/71.19 thf(zip_derived_cl6520, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 (~ ('#form8' @ X0) 558.07/71.19 | ('#form8' @ '#sk18') 558.07/71.19 | ~ (rel_s4 @ '#sk18' @ X0) 558.07/71.19 | (big_p @ ('#sk20' @ X0) @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 558.07/71.19 | ~ ('#form3'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl6492])). 558.07/71.19 thf(zip_derived_cl110, plain, 558.07/71.19 (( (rel_s4 @ '#sk5' @ '#sk18') | ('#form17'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl99])). 558.07/71.19 thf(zip_derived_cl207, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 (~ ('#form3') 558.07/71.19 | (exists_in_world @ '#sk7' @ X0) 558.07/71.19 | ~ (rel_s4 @ '#sk5' @ X0))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl195])). 558.07/71.19 thf(zip_derived_cl386, plain, 558.07/71.19 (( ('#form17') | (exists_in_world @ '#sk7' @ '#sk18') | ~ ('#form3'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl207])). 558.07/71.19 thf(zip_derived_cl76, plain, 558.07/71.19 (![X2 : $i, X4 : mu]: 558.07/71.19 ( (rel_s4 @ X2 @ ('#sk14' @ X2 @ X4)) 558.07/71.19 | ~ (exists_in_world @ X4 @ X2) 558.07/71.19 | ~ ('#form8' @ X2))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 558.07/71.19 thf(zip_derived_cl399, plain, 558.07/71.19 ((~ ('#form3') 558.07/71.19 | ('#form17') 558.07/71.19 | ~ ('#form8' @ '#sk18') 558.07/71.19 | (rel_s4 @ '#sk18' @ ('#sk14' @ '#sk18' @ '#sk7')))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl386, zip_derived_cl76])). 558.07/71.19 thf(zip_derived_cl112, plain, 558.07/71.19 (( (((!!) @ (^[Y0 : $i]: 558.07/71.19 (((((~) @ (rel_s4 @ '#sk18' @ Y0))) | (big_p @ '#sk7' @ 558.07/71.19 Y0)))))) 558.07/71.19 | ('#form17'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl99])). 558.07/71.19 thf(zip_derived_cl127, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 ( (((((~) @ (rel_s4 @ '#sk18' @ X2))) | (big_p @ '#sk7' @ X2))) 558.07/71.19 | ('#form17'))), 558.07/71.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl112])). 558.07/71.19 thf(zip_derived_cl136, plain, 558.07/71.19 (![X2 : $i]: 558.07/71.19 (~ (rel_s4 @ '#sk18' @ X2) | (big_p @ '#sk7' @ X2) | ('#form17'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl127])). 558.07/71.19 thf(zip_derived_cl2576, plain, 558.07/71.19 ((~ ('#form8' @ '#sk18') 558.07/71.19 | ('#form17') 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ('#form17') 558.07/71.19 | (big_p @ '#sk7' @ ('#sk14' @ '#sk18' @ '#sk7')))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl399, zip_derived_cl136])). 558.07/71.19 thf(zip_derived_cl2582, plain, 558.07/71.19 (( (big_p @ '#sk7' @ ('#sk14' @ '#sk18' @ '#sk7')) 558.07/71.19 | ~ ('#form3') 558.07/71.19 | ('#form17') 558.07/71.19 | ~ ('#form8' @ '#sk18'))), 558.07/71.19 inference('simplify', [status(thm)], [zip_derived_cl2576])). 558.07/71.19 thf(zip_derived_cl386, plain, 558.07/71.19 (( ('#form17') | (exists_in_world @ '#sk7' @ '#sk18') | ~ ('#form3'))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl207])). 558.07/71.19 thf(zip_derived_cl77, plain, 558.07/71.19 (![X2 : $i, X4 : mu]: 558.07/71.19 (~ (big_p @ X4 @ ('#sk14' @ X2 @ X4)) 558.07/71.19 | ~ (exists_in_world @ X4 @ X2) 558.07/71.19 | ~ ('#form8' @ X2))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 558.07/71.19 thf(zip_derived_cl400, plain, 558.07/71.19 ((~ ('#form3') 558.07/71.19 | ('#form17') 558.07/71.19 | ~ ('#form8' @ '#sk18') 558.07/71.19 | ~ (big_p @ '#sk7' @ ('#sk14' @ '#sk18' @ '#sk7')))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl386, zip_derived_cl77])). 558.07/71.19 thf(zip_derived_cl10907, plain, 558.07/71.19 ((~ ('#form8' @ '#sk18') | ('#form17') | ~ ('#form3'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl2582, zip_derived_cl400])). 558.07/71.19 thf(zip_derived_cl4225, plain, ((~ ('#form3') | ~ ('#form17'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl3522, zip_derived_cl129])). 558.07/71.19 thf(zip_derived_cl10908, plain, ((~ ('#form3') | ~ ('#form8' @ '#sk18'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl10907, zip_derived_cl4225])). 558.07/71.19 thf(zip_derived_cl21666, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 (~ ('#form3') 558.07/71.19 | (big_p @ ('#sk20' @ X0) @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 558.07/71.19 | ~ (rel_s4 @ '#sk18' @ X0) 558.07/71.19 | ~ ('#form8' @ X0))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl6520, zip_derived_cl10908])). 558.07/71.19 thf(zip_derived_cl152, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 (~ ('#form8' @ X0) 558.07/71.19 | ~ (big_p @ ('#sk20' @ X0) @ ('#sk14' @ X0 @ ('#sk20' @ X0))))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl77])). 558.07/71.19 thf(zip_derived_cl21667, plain, 558.07/71.19 (![X0 : $i]: 558.07/71.19 (~ ('#form8' @ X0) | ~ (rel_s4 @ '#sk18' @ X0) | ~ ('#form3'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl21666, zip_derived_cl152])). 558.07/71.19 thf(zip_derived_cl21677, plain, 558.07/71.19 (( ('#form17') | ~ ('#form3') | ~ ('#form8' @ ('#sk11' @ '#sk18')))), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl21667])). 558.07/71.19 thf(zip_derived_cl4225, plain, ((~ ('#form3') | ~ ('#form17'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl3522, zip_derived_cl129])). 558.07/71.19 thf(zip_derived_cl21736, plain, 558.07/71.19 ((~ ('#form8' @ ('#sk11' @ '#sk18')) | ~ ('#form3'))), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl21677, zip_derived_cl4225])). 558.07/71.19 thf(zip_derived_cl39038, plain, ( ('#form3')), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl39037, zip_derived_cl415])). 558.07/71.19 thf(zip_derived_cl39720, plain, (~ ('#form8' @ ('#sk11' @ '#sk18'))), 558.07/71.19 inference('demod', [status(thm)], 558.07/71.19 [zip_derived_cl21736, zip_derived_cl39038])). 558.07/71.19 thf(zip_derived_cl39038, plain, ( ('#form3')), 558.07/71.19 inference('clc', [status(thm)], [zip_derived_cl39037, zip_derived_cl415])). 558.07/71.19 thf(zip_derived_cl39377, plain, (~ ('#form17')), 558.07/71.19 inference('demod', [status(thm)], 558.07/71.19 [zip_derived_cl4225, zip_derived_cl39038])). 558.07/71.19 thf(zip_derived_cl43945, plain, 558.07/71.19 ((~ (rel_s4 @ ('#sk11' @ '#sk18') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.19 | (big_p @ ('#sk16' @ '#sk18') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))))), 558.07/71.19 inference('demod', [status(thm)], 558.07/71.19 [zip_derived_cl3865, zip_derived_cl39720, zip_derived_cl39038, 558.07/71.19 zip_derived_cl39377])). 558.07/71.19 thf(zip_derived_cl144, plain, 558.07/71.19 ((~ (big_p @ ('#sk16' @ '#sk18') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 558.07/71.19 | ('#form17'))), 558.07/71.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl142])). 558.07/71.19 thf(zip_derived_cl39377, plain, (~ ('#form17')), 558.07/71.19 inference('demod', [status(thm)], 558.07/71.19 [zip_derived_cl4225, zip_derived_cl39038])). 558.07/71.19 thf(zip_derived_cl39894, plain, 558.07/71.19 (~ (big_p @ ('#sk16' @ '#sk18') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18')))), 558.07/71.19 inference('demod', [status(thm)], 558.07/71.19 [zip_derived_cl144, zip_derived_cl39377])). 558.07/71.19 thf(zip_derived_cl43946, plain, 558.07/71.19 (~ (rel_s4 @ ('#sk11' @ '#sk18') @ 558.07/71.19 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18')))), 558.07/71.19 inference('clc', [status(thm)], 558.07/71.19 [zip_derived_cl43945, zip_derived_cl39894])). 558.07/71.19 thf(zip_derived_cl43948, plain, ( ('#form10' @ '#sk18')), 558.07/71.19 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl43946])). 558.07/71.19 thf(zip_derived_cl43949, plain, ($false), 558.07/71.19 inference('demod', [status(thm)], 558.07/71.19 [zip_derived_cl40032, zip_derived_cl43948])). 558.07/71.19 558.07/71.19 % SZS output end Refutation 558.07/71.19 558.07/71.19 558.07/71.19 % Terminating... 558.07/71.19 % /export/starexec/sandbox/solver/bin/lams/15_lifting1.sh running for 30s 558.60/71.33 % Runner terminated. 558.60/71.34 % Zipperpin 1.5 exiting 558.60/71.35 EOF