0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.08 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.d59dPieZMu true 0.16/0.42 % Computer : n002.cluster.edu 0.16/0.42 % Model : x86_64 x86_64 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.42 % Memory : 8046.5625MB 0.16/0.42 % OS : Linux 6.8.0-71-generic 0.16/0.43 % CPULimit : 1440 0.16/0.43 % WCLimit : 180 0.16/0.43 % DateTime : Mon Jul 27 13:09:59 UTC 2026 0.16/0.43 % CPUTime : 0.16/0.43 % Running portfolio for 1440 s 0.16/0.43 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.16/0.43 % Number of cores: 8 0.16/0.44 % Python version: Python 3.12.3 0.16/0.44 % Running in HO mode 0.37/0.74 % Total configuration time : 828 0.37/0.74 % Estimated wc time : 1656 0.37/0.74 % Estimated cpu time (8 cpus) : 207.0 0.40/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.40/0.92 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.40/0.93 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.40/0.93 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.40/0.93 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.40/0.93 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.40/0.93 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.40/0.94 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.40/1.04 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 3.92/1.24 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 5.73/1.60 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 222.48/30.98 % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s 228.04/31.66 % /export/starexec/sandbox2/solver/bin/lams/33_shallow_sine.sh running for 66s 198.88/31.89 % /export/starexec/sandbox2/solver/bin/lams/40_e_lift.sh running for 80s 269.34/37.93 % Solved by lams/15_lifting3.sh. 269.34/37.93 % done 416 iterations in 6.835s 269.34/37.93 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 269.34/37.93 % SZS output start Refutation 269.34/37.93 thf(mu_type, type, mu: $tType). 269.34/37.93 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 269.34/37.93 thf(and_1_type, type, and_1: $i > $o). 269.34/37.93 thf(mreflexive_type, type, mreflexive: ($i > $i > $o) > $o). 269.34/37.93 thf(and_type, type, and: mu > mu > mu). 269.34/37.93 thf('#sk98_type', type, '#sk98': $i > $i). 269.34/37.93 thf('#sk2_type', type, '#sk2': $i). 269.34/37.93 thf(kn2_type, type, kn2: $i > $o). 269.34/37.93 thf(is_a_theorem_type, type, is_a_theorem: mu > $i > $o). 269.34/37.93 thf(rel_s4_type, type, rel_s4: $i > $i > $o). 269.34/37.93 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 269.34/37.93 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 269.34/37.93 thf('#form95_type', type, '#form95': $i > $o). 269.34/37.93 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 269.34/37.93 thf(implies_type, type, implies: mu > mu > mu). 269.34/37.93 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o). 269.34/37.93 thf('#form97_type', type, '#form97': $i > $o). 269.34/37.93 thf(exists_in_world_type, type, exists_in_world: mu > $i > $o). 269.34/37.93 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o). 269.34/37.93 thf('#sk1_type', type, '#sk1': $i). 269.34/37.93 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 269.34/37.93 thf(mreflexive, axiom,(( mreflexive ) = 269.34/37.93 (^[R:( $i > $i > $o )]: ( ![S:$i]: ( R @ S @ S ) )))). 269.34/37.93 thf('0', plain, 269.34/37.93 (( mreflexive ) = ( ^[R:( $i > $i > $o )]: ( ![S:$i]: ( R @ S @ S ) ) )), 269.34/37.93 inference('simplify_rw_rule', [status(thm)], [mreflexive])). 269.34/37.93 thf('1', plain, 269.34/37.93 (( mreflexive ) = 269.34/37.93 ( ^[V_1:( $i > $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 @ X4 ) ) )), 269.34/37.93 define([status(thm)])).thf(a1, axiom, (mreflexive @ rel_s4)). 269.34/37.93 thf(zf_stmt_0, axiom, (![X4:$i]: ( rel_s4 @ X4 @ X4 ))). 269.34/37.93 thf(zip_derived_cl1, plain, ( (((!!) @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))), 269.34/37.93 inference('cnf', [status(esa)], [zf_stmt_0])). 269.34/37.93 thf(zip_derived_cl79, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 269.34/37.93 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 269.34/37.93 thf(mbox_s4, axiom,(( mbox_s4 ) = 269.34/37.93 (^[Phi:( $i > $o ),W:$i]: 269.34/37.93 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s4 @ W @ V ) ) ) )))). 269.34/37.93 thf('2', plain, 269.34/37.93 (( mbox_s4 ) = 269.34/37.93 ( ^[Phi:( $i > $o ),W:$i]: 269.34/37.93 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s4 @ W @ V ) ) ) ) )), 269.34/37.93 inference('simplify_rw_rule', [status(thm)], [mbox_s4])). 269.34/37.93 thf('3', plain, 269.34/37.93 (( mbox_s4 ) = 269.34/37.93 ( ^[V_1:( $i > $o ),V_2:$i]: 269.34/37.93 ( ![X4:$i]: ( ( V_1 @ X4 ) | ( ~( rel_s4 @ V_2 @ X4 ) ) ) ) )), 269.34/37.93 define([status(thm)])). 269.34/37.93 thf(mvalid, axiom,(( mvalid ) = 269.34/37.93 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 269.34/37.93 thf('4', plain, 269.34/37.93 (( mvalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 269.34/37.93 inference('simplify_rw_rule', [status(thm)], [mvalid])). 269.34/37.93 thf('5', plain, 269.34/37.93 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 269.34/37.93 define([status(thm)])). 269.34/37.93 thf(rosser_kn2, conjecture, (mvalid @ ( mbox_s4 @ kn2 ))). 269.34/37.93 thf(zf_stmt_1, conjecture, 269.34/37.93 (![X4:$i,X6:$i]: ( ( ~( rel_s4 @ X4 @ X6 ) ) | ( kn2 @ X6 ) ))). 269.34/37.93 thf(zf_stmt_2, negated_conjecture, 269.34/37.93 (~( ![X4:$i,X6:$i]: ( ( ~( rel_s4 @ X4 @ X6 ) ) | ( kn2 @ X6 ) ) )), 269.34/37.93 inference('cnf.neg', [status(esa)], [zf_stmt_1])). 269.34/37.93 thf(zip_derived_cl71, plain, 269.34/37.93 (~ (((!!) @ (^[Y0 : $i]: 269.34/37.93 (((!!) @ (^[Y1 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ Y0 @ Y1))) | (kn2 @ Y1)))))))))), 269.34/37.93 inference('cnf', [status(esa)], [zf_stmt_2])). 269.34/37.93 thf(zip_derived_cl75, plain, 269.34/37.93 (~ (((!!) @ (^[Y0 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | (kn2 @ Y0))))))), 269.34/37.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl71])). 269.34/37.93 thf(zip_derived_cl76, plain, 269.34/37.93 (~ (((((~) @ (rel_s4 @ '#sk1' @ '#sk2'))) | (kn2 @ '#sk2')))), 269.34/37.93 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl75])). 269.34/37.93 thf(zip_derived_cl77, plain, ( (rel_s4 @ '#sk1' @ '#sk2')), 269.34/37.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl76])). 269.34/37.93 thf(mforall_ind, axiom,(( mforall_ind ) = 269.34/37.93 (^[Phi:( mu > $i > $o ),W:$i]: 269.34/37.93 ( ![X:mu]: ( ( exists_in_world @ X @ W ) => ( Phi @ X @ W ) ) )))). 269.34/37.93 thf('6', plain, 269.34/37.93 (( mforall_ind ) = 269.34/37.93 ( ^[Phi:( mu > $i > $o ),W:$i]: 269.34/37.93 ( ![X:mu]: ( ( exists_in_world @ X @ W ) => ( Phi @ X @ W ) ) ) )), 269.34/37.93 inference('simplify_rw_rule', [status(thm)], [mforall_ind])). 269.34/37.93 thf('7', plain, 269.34/37.93 (( mforall_ind ) = 269.34/37.93 ( ^[V_1:( mu > $i > $o ),V_2:$i]: 269.34/37.93 ( ![X4:mu]: ( ( exists_in_world @ X4 @ V_2 ) => ( V_1 @ X4 @ V_2 ) ) ) )), 269.34/37.93 define([status(thm)])). 269.34/37.93 thf(mimplies, axiom,(( mimplies ) = 269.34/37.93 (^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi )))). 269.34/37.93 thf(mor, axiom,(( mor ) = 269.34/37.93 (^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) )))). 269.34/37.93 thf('8', plain, 269.34/37.93 (( mor ) = 269.34/37.93 ( ^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) ) )), 269.34/37.93 inference('simplify_rw_rule', [status(thm)], [mor])). 269.34/37.93 thf('9', plain, 269.34/37.93 (( mor ) = 269.34/37.93 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 269.34/37.93 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 269.34/37.93 define([status(thm)])). 269.34/37.93 thf(mnot, axiom,(( mnot ) = (^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) )))). 269.34/37.93 thf('10', plain, (( mnot ) = ( ^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) ) )), 269.34/37.93 inference('simplify_rw_rule', [status(thm)], [mnot])). 269.34/37.93 thf('11', plain, 269.34/37.93 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 269.34/37.93 define([status(thm)])). 269.34/37.93 thf('12', plain, 269.34/37.93 (( mimplies ) = 269.34/37.93 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi ) )), 269.34/37.93 inference('simplify_rw_rule', [status(thm)], [mimplies, '9', '11'])). 269.34/37.93 thf('13', plain, 269.34/37.93 (( mimplies ) = 269.34/37.93 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 269.34/37.93 define([status(thm)])). 269.34/37.93 thf(mand, axiom,(( mand ) = 269.34/37.93 (^[Phi:( $i > $o ),Psi:( $i > $o )]: 269.34/37.93 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) )))). 269.34/37.93 thf('14', plain, 269.34/37.93 (( mand ) = 269.34/37.93 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: 269.34/37.93 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) )), 269.34/37.93 inference('simplify_rw_rule', [status(thm)], [mand, '9', '11'])). 269.34/37.93 thf('15', plain, 269.34/37.93 (( mand ) = 269.34/37.93 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 269.34/37.93 ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) )), 269.34/37.93 define([status(thm)])). 269.34/37.93 thf(kn2, axiom, 269.34/37.93 (mvalid @ 269.34/37.93 ( mand @ 269.34/37.93 ( mbox_s4 @ 269.34/37.93 ( mimplies @ 269.34/37.93 ( mbox_s4 @ kn2 ) @ 269.34/37.93 ( mbox_s4 @ 269.34/37.93 ( mforall_ind @ 269.34/37.93 ( ^[P:mu]: 269.34/37.93 ( mbox_s4 @ 269.34/37.93 ( mforall_ind @ 269.34/37.93 ( ^[Q:mu]: 269.34/37.93 ( mbox_s4 @ 269.34/37.93 ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) ) ) ) ) ) ) ) ) @ 269.34/37.93 ( mbox_s4 @ 269.34/37.93 ( mimplies @ 269.34/37.93 ( mbox_s4 @ 269.34/37.93 ( mforall_ind @ 269.34/37.93 ( ^[P:mu]: 269.34/37.93 ( mbox_s4 @ 269.34/37.93 ( mforall_ind @ 269.34/37.93 ( ^[Q:mu]: 269.34/37.93 ( mbox_s4 @ 269.34/37.93 ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) ) ) ) ) ) ) @ 269.34/37.93 ( mbox_s4 @ kn2 ) ) ) ))). 269.34/37.93 thf(zf_stmt_3, axiom, 269.34/37.93 (![X4:$i]: 269.34/37.93 ( ~( ( ~( ![X20:$i]: 269.34/37.93 ( ( ~( rel_s4 @ X4 @ X20 ) ) | 269.34/37.93 ( ![X32:$i]: ( ( ~( rel_s4 @ X20 @ X32 ) ) | ( kn2 @ X32 ) ) ) | 269.34/37.93 ( ~( ![X22:$i]: 269.34/37.93 ( ( ~( rel_s4 @ X20 @ X22 ) ) | 269.34/37.93 ( ![X24:mu]: 269.34/37.93 ( ( exists_in_world @ X24 @ X22 ) => 269.34/37.93 ( ![X26:$i]: 269.34/37.93 ( ( ~( rel_s4 @ X22 @ X26 ) ) | 269.34/37.93 ( ![X28:mu]: 269.34/37.93 ( ( exists_in_world @ X28 @ X26 ) => 269.34/37.93 ( ![X30:$i]: 269.34/37.93 ( ( ~( rel_s4 @ X26 @ X30 ) ) | 269.34/37.93 ( is_a_theorem @ 269.34/37.93 ( implies @ ( and @ X24 @ X28 ) @ X24 ) @ 269.34/37.93 X30 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) | 269.34/37.93 ( ~( ![X6:$i]: 269.34/37.93 ( ( ~( rel_s4 @ X4 @ X6 ) ) | 269.34/37.93 ( ![X10:$i]: 269.34/37.93 ( ( ~( rel_s4 @ X6 @ X10 ) ) | 269.34/37.93 ( ![X12:mu]: 269.34/37.93 ( ( exists_in_world @ X12 @ X10 ) => 269.34/37.93 ( ![X14:$i]: 269.34/37.93 ( ( ~( rel_s4 @ X10 @ X14 ) ) | 269.34/37.93 ( ![X16:mu]: 269.34/37.93 ( ( exists_in_world @ X16 @ X14 ) => 269.34/37.93 ( ![X18:$i]: 269.34/37.93 ( ( ~( rel_s4 @ X14 @ X18 ) ) | 269.34/37.93 ( is_a_theorem @ 269.34/37.93 ( implies @ ( and @ X12 @ X16 ) @ X12 ) @ 269.34/37.93 X18 ) ) ) ) ) ) ) ) ) ) ) | 269.34/37.93 ( ~( ![X8:$i]: ( ( ~( rel_s4 @ X6 @ X8 ) ) | ( kn2 @ X8 ) ) ) ) ) ) ) ) ))). 269.34/37.93 thf(zip_derived_cl51, plain, 269.34/37.93 ( (((!!) @ (^[Y0 : $i]: 269.34/37.93 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 269.34/37.93 (((!!) @ (^[Y2 : $i]: 269.34/37.93 (((((~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y1 @ Y2))) | 269.34/37.93 (kn2 @ Y2)))))) | 269.34/37.93 (((~) @ (((!!) @ (^[Y2 : $i]: 269.34/37.93 (( 269.34/37.93 (( 269.34/37.93 (~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y1 @ Y2))) | 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y3 : mu]: 269.34/37.93 (( 269.34/37.93 (exists_in_world @ 269.34/37.93 Y3 @ 269.34/37.93 Y2) => 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y4 : $i]: 269.34/37.93 (( 269.34/37.93 (( 269.34/37.93 (~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y2 @ Y4))) | 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y5 : mu]: 269.34/37.93 (( 269.34/37.93 (exists_in_world @ 269.34/37.93 Y5 @ 269.34/37.93 Y4) => 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y6 : $i]: 269.34/37.93 (( 269.34/37.93 (( 269.34/37.93 (~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y4 @ Y6))) | 269.34/37.93 (is_a_theorem @ 269.34/37.93 ( 269.34/37.93 implies @ 269.34/37.93 ( 269.34/37.93 and @ 269.34/37.93 Y3 @ Y5) @ 269.34/37.93 Y3) @ Y6))))))))))))))))))))))))))))))))))) | 269.34/37.93 (((~) @ (((!!) @ (^[Y1 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 269.34/37.93 (((!!) @ (^[Y2 : $i]: 269.34/37.93 (((((~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y1 @ Y2))) | 269.34/37.93 (((!!) @ ( 269.34/37.93 ^[Y3 : mu]: 269.34/37.93 ( 269.34/37.93 ( 269.34/37.93 (exists_in_world @ 269.34/37.93 Y3 @ 269.34/37.93 Y2) => 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y4 : $i]: 269.34/37.93 (( 269.34/37.93 (( 269.34/37.93 (~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y2 @ Y4))) | 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y5 : mu]: 269.34/37.93 (( 269.34/37.93 (exists_in_world @ 269.34/37.93 Y5 @ 269.34/37.93 Y4) => 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y6 : $i]: 269.34/37.93 (( 269.34/37.93 (( 269.34/37.93 (~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y4 @ Y6))) | 269.34/37.93 (is_a_theorem @ 269.34/37.93 ( 269.34/37.93 implies @ 269.34/37.93 ( 269.34/37.93 and @ 269.34/37.93 Y3 @ Y5) @ 269.34/37.93 Y3) @ Y6)))))))))))))))))))))))))) | 269.34/37.93 (((~) @ (((!!) @ (^[Y2 : $i]: 269.34/37.93 (( 269.34/37.93 (( 269.34/37.93 (~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y1 @ Y2))) | 269.34/37.93 (kn2 @ 269.34/37.93 Y2))))))))))))))))))))))), 269.34/37.93 inference('cnf', [status(esa)], [zf_stmt_3])). 269.34/37.93 thf(zip_derived_cl5294, plain, 269.34/37.93 (![X2 : $i]: 269.34/37.93 ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | 269.34/37.93 (((!!) @ (^[Y1 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 269.34/37.93 (kn2 @ Y1)))))) | 269.34/37.93 (((~) @ (((!!) @ (^[Y1 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ 269.34/37.93 Y0 @ Y1))) | 269.34/37.93 (((!!) @ (^[Y2 : mu]: 269.34/37.93 (( 269.34/37.93 (exists_in_world @ 269.34/37.93 Y2 @ 269.34/37.93 Y1) => 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y3 : $i]: 269.34/37.93 (( 269.34/37.93 (( 269.34/37.93 (~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y1 @ Y3))) | 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y4 : mu]: 269.34/37.93 (( 269.34/37.93 (exists_in_world @ 269.34/37.93 Y4 @ 269.34/37.93 Y3) => 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y5 : $i]: 269.34/37.93 (( 269.34/37.93 (( 269.34/37.93 (~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y3 @ Y5))) | 269.34/37.93 (is_a_theorem @ 269.34/37.93 ( 269.34/37.93 implies @ 269.34/37.93 ( 269.34/37.93 and @ 269.34/37.93 Y2 @ Y4) @ 269.34/37.93 Y2) @ Y5))))))))))))))))))))))))))))))))))) | 269.34/37.93 (((~) @ (((!!) @ (^[Y0 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | 269.34/37.93 (((!!) @ (^[Y1 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 269.34/37.93 (((!!) @ (^[Y2 : mu]: 269.34/37.93 (((exists_in_world @ 269.34/37.93 Y2 @ Y1) => 269.34/37.93 (((!!) @ ( 269.34/37.93 ^[Y3 : $i]: 269.34/37.93 (((( 269.34/37.93 (~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y1 @ Y3))) | 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y4 : mu]: 269.34/37.93 (( 269.34/37.93 (exists_in_world @ 269.34/37.93 Y4 @ 269.34/37.93 Y3) => 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y5 : $i]: 269.34/37.93 (( 269.34/37.93 (( 269.34/37.93 (~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y3 @ Y5))) | 269.34/37.93 (is_a_theorem @ 269.34/37.93 ( 269.34/37.93 implies @ 269.34/37.93 ( 269.34/37.93 and @ 269.34/37.93 Y2 @ Y4) @ 269.34/37.93 Y2) @ Y5)))))))))))))))))))))))))) | 269.34/37.93 (((~) @ (((!!) @ (^[Y1 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ 269.34/37.93 Y0 @ Y1))) | 269.34/37.93 (kn2 @ Y1)))))))))))))))))), 269.34/37.93 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl51])). 269.34/37.93 thf(zip_derived_cl5295, plain, 269.34/37.93 (![X2 : $i]: 269.34/37.93 (((!!) @ (^[Y0 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ X2 @ Y0))) | 269.34/37.93 (((!!) @ (^[Y1 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ Y0 @ Y1))) | (kn2 @ Y1)))))) | 269.34/37.93 (((~) @ (((!!) @ (^[Y1 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 269.34/37.93 (((!!) @ (^[Y2 : mu]: 269.34/37.93 (((exists_in_world @ 269.34/37.93 Y2 @ Y1) => 269.34/37.93 (((!!) @ (^[Y3 : $i]: 269.34/37.93 (( 269.34/37.93 (( 269.34/37.93 (~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y1 @ Y3))) | 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y4 : mu]: 269.34/37.93 (( 269.34/37.93 (exists_in_world @ 269.34/37.93 Y4 @ 269.34/37.93 Y3) => 269.34/37.93 (( 269.34/37.93 (!!) @ ( 269.34/37.93 ^[Y5 : $i]: 269.34/37.93 (( 269.34/37.93 (( 269.34/37.93 (~) @ ( 269.34/37.93 rel_s4 @ 269.34/37.93 Y3 @ Y5))) | 269.34/37.93 (is_a_theorem @ 269.34/37.93 ( 269.34/37.93 implies @ 269.34/37.93 ( 269.34/37.93 and @ 269.34/37.93 Y2 @ Y4) @ 269.34/37.93 Y2) @ Y5)))))))))))))))))))))))))))))))))), 269.34/37.93 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl5294])). 269.34/37.93 thf(zip_derived_cl5297, plain, 269.34/37.93 (![X2 : $i, X4 : $i]: 269.34/37.93 (((((~) @ (rel_s4 @ X2 @ X4))) | 269.34/37.94 (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X4 @ Y0))) | (kn2 @ Y0)))))) | 269.34/37.94 (((~) @ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : mu]: 269.34/37.94 (((exists_in_world @ Y1 @ Y0) => 269.34/37.94 (((!!) @ (^[Y2 : $i]: 269.34/37.94 (((((~) @ ( 269.34/37.94 rel_s4 @ Y0 @ 269.34/37.94 Y2))) | 269.34/37.94 (((!!) @ ( 269.34/37.94 ^[Y3 : mu]: 269.34/37.94 (((exists_in_world @ 269.34/37.94 Y3 @ Y2) => 269.34/37.94 (((!!) @ ( 269.34/37.94 ^[Y4 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y2 @ Y4))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y1 @ Y3) @ 269.34/37.94 Y1) @ Y4))))))))))))))))))))))))))))))), 269.34/37.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5295])). 269.34/37.94 thf(zip_derived_cl5299, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: 269.34/37.94 (~ (rel_s4 @ X2 @ X4) 269.34/37.94 | (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | (kn2 @ Y0)))))) 269.34/37.94 | ~ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : mu]: 269.34/37.94 (((exists_in_world @ Y1 @ Y0) => 269.34/37.94 (((!!) @ (^[Y2 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ 269.34/37.94 Y2))) | 269.34/37.94 (((!!) @ (^[Y3 : mu]: 269.34/37.94 (((exists_in_world @ 269.34/37.94 Y3 @ 269.34/37.94 Y2) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y4 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y2 @ Y4))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y1 @ Y3) @ 269.34/37.94 Y1) @ Y4)))))))))))))))))))))))))))), 269.34/37.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl5297])). 269.34/37.94 thf(and_1, axiom, 269.34/37.94 (mvalid @ 269.34/37.94 ( mand @ 269.34/37.94 ( mbox_s4 @ 269.34/37.94 ( mimplies @ 269.34/37.94 ( mbox_s4 @ and_1 ) @ 269.34/37.94 ( mbox_s4 @ 269.34/37.94 ( mforall_ind @ 269.34/37.94 ( ^[X:mu]: 269.34/37.94 ( mbox_s4 @ 269.34/37.94 ( mforall_ind @ 269.34/37.94 ( ^[Y:mu]: 269.34/37.94 ( mbox_s4 @ 269.34/37.94 ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) ) ) ) ) ) ) ) ) @ 269.34/37.94 ( mbox_s4 @ 269.34/37.94 ( mimplies @ 269.34/37.94 ( mbox_s4 @ 269.34/37.94 ( mforall_ind @ 269.34/37.94 ( ^[X:mu]: 269.34/37.94 ( mbox_s4 @ 269.34/37.94 ( mforall_ind @ 269.34/37.94 ( ^[Y:mu]: 269.34/37.94 ( mbox_s4 @ 269.34/37.94 ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) ) ) ) ) ) ) @ 269.34/37.94 ( mbox_s4 @ and_1 ) ) ) ))). 269.34/37.94 thf(zf_stmt_4, axiom, 269.34/37.94 (![X4:$i]: 269.34/37.94 ( ~( ( ~( ![X20:$i]: 269.34/37.94 ( ( ~( rel_s4 @ X4 @ X20 ) ) | 269.34/37.94 ( ![X32:$i]: ( ( ~( rel_s4 @ X20 @ X32 ) ) | ( and_1 @ X32 ) ) ) | 269.34/37.94 ( ~( ![X22:$i]: 269.34/37.94 ( ( ~( rel_s4 @ X20 @ X22 ) ) | 269.34/37.94 ( ![X24:mu]: 269.34/37.94 ( ( exists_in_world @ X24 @ X22 ) => 269.34/37.94 ( ![X26:$i]: 269.34/37.94 ( ( ~( rel_s4 @ X22 @ X26 ) ) | 269.34/37.94 ( ![X28:mu]: 269.34/37.94 ( ( exists_in_world @ X28 @ X26 ) => 269.34/37.94 ( ![X30:$i]: 269.34/37.94 ( ( ~( rel_s4 @ X26 @ X30 ) ) | 269.34/37.94 ( is_a_theorem @ 269.34/37.94 ( implies @ ( and @ X24 @ X28 ) @ X24 ) @ 269.34/37.94 X30 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) | 269.34/37.94 ( ~( ![X6:$i]: 269.34/37.94 ( ( ~( rel_s4 @ X4 @ X6 ) ) | 269.34/37.94 ( ![X10:$i]: 269.34/37.94 ( ( ~( rel_s4 @ X6 @ X10 ) ) | 269.34/37.94 ( ![X12:mu]: 269.34/37.94 ( ( exists_in_world @ X12 @ X10 ) => 269.34/37.94 ( ![X14:$i]: 269.34/37.94 ( ( ~( rel_s4 @ X10 @ X14 ) ) | 269.34/37.94 ( ![X16:mu]: 269.34/37.94 ( ( exists_in_world @ X16 @ X14 ) => 269.34/37.94 ( ![X18:$i]: 269.34/37.94 ( ( ~( rel_s4 @ X14 @ X18 ) ) | 269.34/37.94 ( is_a_theorem @ 269.34/37.94 ( implies @ ( and @ X12 @ X16 ) @ X12 ) @ 269.34/37.94 X18 ) ) ) ) ) ) ) ) ) ) ) | 269.34/37.94 ( ~( ![X8:$i]: ( ( ~( rel_s4 @ X6 @ X8 ) ) | ( and_1 @ X8 ) ) ) ) ) ) ) ) ))). 269.34/37.94 thf(zip_derived_cl33, plain, 269.34/37.94 ( (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 269.34/37.94 (((!!) @ (^[Y2 : $i]: 269.34/37.94 (((((~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y1 @ Y2))) | 269.34/37.94 (and_1 @ Y2)))))) | 269.34/37.94 (((~) @ (((!!) @ (^[Y2 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y1 @ Y2))) | 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y3 : mu]: 269.34/37.94 (( 269.34/37.94 (exists_in_world @ 269.34/37.94 Y3 @ 269.34/37.94 Y2) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y4 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y2 @ Y4))) | 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y5 : mu]: 269.34/37.94 (( 269.34/37.94 (exists_in_world @ 269.34/37.94 Y5 @ 269.34/37.94 Y4) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y6 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y4 @ Y6))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y3 @ Y5) @ 269.34/37.94 Y3) @ Y6))))))))))))))))))))))))))))))))))) | 269.34/37.94 (((~) @ (((!!) @ (^[Y1 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 269.34/37.94 (((!!) @ (^[Y2 : $i]: 269.34/37.94 (((((~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y1 @ Y2))) | 269.34/37.94 (((!!) @ ( 269.34/37.94 ^[Y3 : mu]: 269.34/37.94 ( 269.34/37.94 ( 269.34/37.94 (exists_in_world @ 269.34/37.94 Y3 @ 269.34/37.94 Y2) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y4 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y2 @ Y4))) | 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y5 : mu]: 269.34/37.94 (( 269.34/37.94 (exists_in_world @ 269.34/37.94 Y5 @ 269.34/37.94 Y4) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y6 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y4 @ Y6))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y3 @ Y5) @ 269.34/37.94 Y3) @ Y6)))))))))))))))))))))))))) | 269.34/37.94 (((~) @ (((!!) @ (^[Y2 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y1 @ Y2))) | 269.34/37.94 (and_1 @ 269.34/37.94 Y2))))))))))))))))))))))), 269.34/37.94 inference('cnf', [status(esa)], [zf_stmt_4])). 269.34/37.94 thf(zip_derived_cl2517, plain, 269.34/37.94 (![X2 : $i]: 269.34/37.94 ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 269.34/37.94 (and_1 @ Y1)))))) | 269.34/37.94 (((~) @ (((!!) @ (^[Y1 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ 269.34/37.94 Y0 @ Y1))) | 269.34/37.94 (((!!) @ (^[Y2 : mu]: 269.34/37.94 (( 269.34/37.94 (exists_in_world @ 269.34/37.94 Y2 @ 269.34/37.94 Y1) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y3 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y1 @ Y3))) | 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y4 : mu]: 269.34/37.94 (( 269.34/37.94 (exists_in_world @ 269.34/37.94 Y4 @ 269.34/37.94 Y3) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y5 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y3 @ Y5))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y2 @ Y4) @ 269.34/37.94 Y2) @ Y5))))))))))))))))))))))))))))))))))) | 269.34/37.94 (((~) @ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 269.34/37.94 (((!!) @ (^[Y2 : mu]: 269.34/37.94 (((exists_in_world @ 269.34/37.94 Y2 @ Y1) => 269.34/37.94 (((!!) @ ( 269.34/37.94 ^[Y3 : $i]: 269.34/37.94 (((( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y1 @ Y3))) | 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y4 : mu]: 269.34/37.94 (( 269.34/37.94 (exists_in_world @ 269.34/37.94 Y4 @ 269.34/37.94 Y3) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y5 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y3 @ Y5))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y2 @ Y4) @ 269.34/37.94 Y2) @ Y5)))))))))))))))))))))))))) | 269.34/37.94 (((~) @ (((!!) @ (^[Y1 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ 269.34/37.94 Y0 @ Y1))) | 269.34/37.94 (and_1 @ Y1)))))))))))))))))), 269.34/37.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])). 269.34/37.94 thf(zip_derived_cl2519, plain, 269.34/37.94 (![X2 : $i]: 269.34/37.94 (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 269.34/37.94 (((!!) @ (^[Y2 : mu]: 269.34/37.94 (((exists_in_world @ Y2 @ 269.34/37.94 Y1) => 269.34/37.94 (((!!) @ (^[Y3 : $i]: 269.34/37.94 (((((~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y1 @ Y3))) | 269.34/37.94 (((!!) @ ( 269.34/37.94 ^[Y4 : mu]: 269.34/37.94 ( 269.34/37.94 ( 269.34/37.94 (exists_in_world @ 269.34/37.94 Y4 @ 269.34/37.94 Y3) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y5 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y3 @ Y5))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y2 @ Y4) @ 269.34/37.94 Y2) @ Y5)))))))))))))))))))))))))) | 269.34/37.94 (((~) @ (((!!) @ (^[Y1 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 269.34/37.94 (and_1 @ Y1)))))))))))))), 269.34/37.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2517])). 269.34/37.94 thf(zip_derived_cl2521, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X2 @ X4))) | 269.34/37.94 (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : mu]: 269.34/37.94 (((exists_in_world @ Y1 @ Y0) => 269.34/37.94 (((!!) @ (^[Y2 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 269.34/37.94 (((!!) @ (^[Y3 : mu]: 269.34/37.94 (((exists_in_world @ 269.34/37.94 Y3 @ Y2) => 269.34/37.94 (((!!) @ ( 269.34/37.94 ^[Y4 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y2 @ Y4))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y1 @ Y3) @ 269.34/37.94 Y1) @ Y4)))))))))))))))))))))))))) | 269.34/37.94 (((~) @ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | (and_1 @ Y0))))))))))), 269.34/37.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2519])). 269.34/37.94 thf(zip_derived_cl2523, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: 269.34/37.94 (~ (rel_s4 @ X2 @ X4) 269.34/37.94 | (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : mu]: 269.34/37.94 (((exists_in_world @ Y1 @ Y0) => 269.34/37.94 (((!!) @ (^[Y2 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ 269.34/37.94 Y2))) | 269.34/37.94 (((!!) @ (^[Y3 : mu]: 269.34/37.94 (((exists_in_world @ 269.34/37.94 Y3 @ 269.34/37.94 Y2) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y4 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y2 @ Y4))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y1 @ Y3) @ 269.34/37.94 Y1) @ Y4)))))))))))))))))))))))))) 269.34/37.94 | ~ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | (and_1 @ Y0)))))))), 269.34/37.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2521])). 269.34/37.94 thf(zip_derived_cl2527, plain, 269.34/37.94 (![X4 : $i]: 269.34/37.94 (~ ('#form95' @ X4) 269.34/37.94 | (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : mu]: 269.34/37.94 (((exists_in_world @ Y1 @ Y0) => 269.34/37.94 (((!!) @ (^[Y2 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ 269.34/37.94 Y2))) | 269.34/37.94 (((!!) @ (^[Y3 : mu]: 269.34/37.94 (((exists_in_world @ 269.34/37.94 Y3 @ 269.34/37.94 Y2) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y4 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y2 @ Y4))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y1 @ Y3) @ 269.34/37.94 Y1) @ Y4)))))))))))))))))))))))))))), 269.34/37.94 define([status(thm)])). 269.34/37.94 thf(zip_derived_cl2518, plain, 269.34/37.94 (![X2 : $i]: 269.34/37.94 (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X2 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ Y1))) | (and_1 @ 269.34/37.94 Y1)))))) | 269.34/37.94 (((~) @ (((!!) @ (^[Y1 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 269.34/37.94 (((!!) @ (^[Y2 : mu]: 269.34/37.94 (((exists_in_world @ 269.34/37.94 Y2 @ Y1) => 269.34/37.94 (((!!) @ (^[Y3 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y1 @ Y3))) | 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y4 : mu]: 269.34/37.94 (( 269.34/37.94 (exists_in_world @ 269.34/37.94 Y4 @ 269.34/37.94 Y3) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y5 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y3 @ Y5))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y2 @ Y4) @ 269.34/37.94 Y2) @ Y5)))))))))))))))))))))))))))))))))), 269.34/37.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2517])). 269.34/37.94 thf(zip_derived_cl2520, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X2 @ X4))) | 269.34/37.94 (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | (and_1 @ Y0)))))) | 269.34/37.94 (((~) @ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : mu]: 269.34/37.94 (((exists_in_world @ Y1 @ Y0) => 269.34/37.94 (((!!) @ (^[Y2 : $i]: 269.34/37.94 (((((~) @ ( 269.34/37.94 rel_s4 @ Y0 @ 269.34/37.94 Y2))) | 269.34/37.94 (((!!) @ ( 269.34/37.94 ^[Y3 : mu]: 269.34/37.94 (((exists_in_world @ 269.34/37.94 Y3 @ Y2) => 269.34/37.94 (((!!) @ ( 269.34/37.94 ^[Y4 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y2 @ Y4))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y1 @ Y3) @ 269.34/37.94 Y1) @ Y4))))))))))))))))))))))))))))))), 269.34/37.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2518])). 269.34/37.94 thf(zip_derived_cl2522, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: 269.34/37.94 (~ (rel_s4 @ X2 @ X4) 269.34/37.94 | (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | (and_1 @ Y0)))))) 269.34/37.94 | ~ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : mu]: 269.34/37.94 (((exists_in_world @ Y1 @ Y0) => 269.34/37.94 (((!!) @ (^[Y2 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ 269.34/37.94 Y2))) | 269.34/37.94 (((!!) @ (^[Y3 : mu]: 269.34/37.94 (((exists_in_world @ 269.34/37.94 Y3 @ 269.34/37.94 Y2) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y4 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y2 @ Y4))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y1 @ Y3) @ 269.34/37.94 Y1) @ Y4)))))))))))))))))))))))))))), 269.34/37.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2520])). 269.34/37.94 thf(zip_derived_cl2524, plain, 269.34/37.94 (![X4 : $i]: 269.34/37.94 ( ('#form95' @ X4) 269.34/37.94 | ~ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : mu]: 269.34/37.94 (((exists_in_world @ Y1 @ Y0) => 269.34/37.94 (((!!) @ (^[Y2 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ 269.34/37.94 Y2))) | 269.34/37.94 (((!!) @ (^[Y3 : mu]: 269.34/37.94 (((exists_in_world @ 269.34/37.94 Y3 @ 269.34/37.94 Y2) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y4 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y2 @ Y4))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y1 @ Y3) @ 269.34/37.94 Y1) @ Y4)))))))))))))))))))))))))))), 269.34/37.94 define([status(thm)])). 269.34/37.94 thf(zip_derived_cl5301, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: 269.34/37.94 (~ ('#form95' @ X4) 269.34/37.94 | (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | (kn2 @ Y0)))))) 269.34/37.94 | ~ (rel_s4 @ X2 @ X4))), 269.34/37.94 inference('renaming', [status(thm)], 269.34/37.94 [zip_derived_cl5299, zip_derived_cl2527, zip_derived_cl2524])). 269.34/37.94 thf(zip_derived_cl79, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 269.34/37.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 269.34/37.94 thf(zip_derived_cl2523, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: 269.34/37.94 (~ (rel_s4 @ X2 @ X4) 269.34/37.94 | (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : mu]: 269.34/37.94 (((exists_in_world @ Y1 @ Y0) => 269.34/37.94 (((!!) @ (^[Y2 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ 269.34/37.94 Y2))) | 269.34/37.94 (((!!) @ (^[Y3 : mu]: 269.34/37.94 (((exists_in_world @ 269.34/37.94 Y3 @ 269.34/37.94 Y2) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y4 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y2 @ Y4))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y1 @ Y3) @ 269.34/37.94 Y1) @ Y4)))))))))))))))))))))))))) 269.34/37.94 | ~ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | (and_1 @ Y0)))))))), 269.34/37.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl2521])). 269.34/37.94 thf(zip_derived_cl2527, plain, 269.34/37.94 (![X4 : $i]: 269.34/37.94 (~ ('#form95' @ X4) 269.34/37.94 | (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : mu]: 269.34/37.94 (((exists_in_world @ Y1 @ Y0) => 269.34/37.94 (((!!) @ (^[Y2 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ 269.34/37.94 Y2))) | 269.34/37.94 (((!!) @ (^[Y3 : mu]: 269.34/37.94 (((exists_in_world @ 269.34/37.94 Y3 @ 269.34/37.94 Y2) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y4 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y2 @ Y4))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y1 @ Y3) @ 269.34/37.94 Y1) @ Y4)))))))))))))))))))))))))))), 269.34/37.94 define([status(thm)])). 269.34/37.94 thf(zip_derived_cl2524, plain, 269.34/37.94 (![X4 : $i]: 269.34/37.94 ( ('#form95' @ X4) 269.34/37.94 | ~ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | 269.34/37.94 (((!!) @ (^[Y1 : mu]: 269.34/37.94 (((exists_in_world @ Y1 @ Y0) => 269.34/37.94 (((!!) @ (^[Y2 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ 269.34/37.94 Y2))) | 269.34/37.94 (((!!) @ (^[Y3 : mu]: 269.34/37.94 (((exists_in_world @ 269.34/37.94 Y3 @ 269.34/37.94 Y2) => 269.34/37.94 (( 269.34/37.94 (!!) @ ( 269.34/37.94 ^[Y4 : $i]: 269.34/37.94 (( 269.34/37.94 (( 269.34/37.94 (~) @ ( 269.34/37.94 rel_s4 @ 269.34/37.94 Y2 @ Y4))) | 269.34/37.94 (is_a_theorem @ 269.34/37.94 ( 269.34/37.94 implies @ 269.34/37.94 ( 269.34/37.94 and @ 269.34/37.94 Y1 @ Y3) @ 269.34/37.94 Y1) @ Y4)))))))))))))))))))))))))))), 269.34/37.94 define([status(thm)])). 269.34/37.94 thf(zip_derived_cl2529, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: 269.34/37.94 ( ('#form95' @ X4) 269.34/37.94 | ~ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | (and_1 @ Y0)))))) 269.34/37.94 | ~ (rel_s4 @ X2 @ X4))), 269.34/37.94 inference('renaming', [status(thm)], 269.34/37.94 [zip_derived_cl2523, zip_derived_cl2527, zip_derived_cl2524])). 269.34/37.94 thf(zip_derived_cl2529, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: 269.34/37.94 ( ('#form95' @ X4) 269.34/37.94 | ~ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | (and_1 @ Y0)))))) 269.34/37.94 | ~ (rel_s4 @ X2 @ X4))), 269.34/37.94 inference('renaming', [status(thm)], 269.34/37.94 [zip_derived_cl2523, zip_derived_cl2527, zip_derived_cl2524])). 269.34/37.94 thf(zip_derived_cl2533, plain, 269.34/37.94 (![X4 : $i]: 269.34/37.94 ( ('#form97' @ X4) 269.34/37.94 | ~ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | (and_1 @ Y0)))))))), 269.34/37.94 define([status(thm)])). 269.34/37.94 thf(zip_derived_cl2535, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: 269.34/37.94 (~ ('#form97' @ X4) | ~ (rel_s4 @ X2 @ X4) | ('#form95' @ X4))), 269.34/37.94 inference('renaming', [status(thm)], 269.34/37.94 [zip_derived_cl2529, zip_derived_cl2533])). 269.34/37.94 thf(zip_derived_cl2533, plain, 269.34/37.94 (![X4 : $i]: 269.34/37.94 ( ('#form97' @ X4) 269.34/37.94 | ~ (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ X4 @ Y0))) | (and_1 @ Y0)))))))), 269.34/37.94 define([status(thm)])). 269.34/37.94 thf(zip_derived_cl2534, plain, 269.34/37.94 (![X4 : $i]: 269.34/37.94 (~ (((((~) @ (rel_s4 @ X4 @ ('#sk98' @ X4)))) | (and_1 @ 269.34/37.94 ('#sk98' @ X4)))) 269.34/37.94 | ('#form97' @ X4))), 269.34/37.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2533])). 269.34/37.94 thf(zip_derived_cl79, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 269.34/37.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 269.34/37.94 thf(hilbert_and_1, axiom, (mvalid @ ( mbox_s4 @ and_1 ))). 269.34/37.94 thf(zf_stmt_5, axiom, 269.34/37.94 (![X4:$i,X6:$i]: ( ( ~( rel_s4 @ X4 @ X6 ) ) | ( and_1 @ X6 ) ))). 269.34/37.94 thf(zip_derived_cl6, plain, 269.34/37.94 ( (((!!) @ (^[Y0 : $i]: 269.34/37.94 (((!!) @ (^[Y1 : $i]: 269.34/37.94 (((((~) @ (rel_s4 @ Y0 @ Y1))) | (and_1 @ Y1)))))))))), 269.34/37.94 inference('cnf', [status(esa)], [zf_stmt_5])). 269.34/37.94 thf(zip_derived_cl100, plain, 269.34/37.94 (![X2 : $i]: 269.34/37.94 (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X2 @ Y0))) | (and_1 @ Y0))))))), 269.34/37.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 269.34/37.94 thf(zip_derived_cl101, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: (((((~) @ (rel_s4 @ X2 @ X4))) | (and_1 @ X4)))), 269.34/37.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl100])). 269.34/37.94 thf(zip_derived_cl102, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: (~ (rel_s4 @ X2 @ X4) | (and_1 @ X4))), 269.34/37.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl101])). 269.34/37.94 thf(zip_derived_cl103, plain, (![X0 : $i]: (and_1 @ X0)), 269.34/37.94 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl102])). 269.34/37.94 thf(zip_derived_cl2540, plain, 269.34/37.94 (![X4 : $i]: 269.34/37.94 (~ (((((~) @ (rel_s4 @ X4 @ ('#sk98' @ X4)))) | ($true))) 269.34/37.94 | ('#form97' @ X4))), 269.34/37.94 inference('demod', [status(thm)], [zip_derived_cl2534, zip_derived_cl103])). 269.34/37.94 thf(zip_derived_cl2541, plain, (![X4 : $i]: ('#form97' @ X4)), 269.34/37.94 inference('simplify boolean subterms', [status(thm)], 269.34/37.94 [zip_derived_cl2540])). 269.34/37.94 thf(zip_derived_cl2608, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: (~ (rel_s4 @ X2 @ X4) | ('#form95' @ X4))), 269.34/37.94 inference('demod', [status(thm)], 269.34/37.94 [zip_derived_cl2535, zip_derived_cl2541])). 269.34/37.94 thf(zip_derived_cl2609, plain, (![X0 : $i]: ('#form95' @ X0)), 269.34/37.94 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl2608])). 269.34/37.94 thf(zip_derived_cl5303, plain, 269.34/37.94 (![X2 : $i, X4 : $i]: 269.34/37.94 ( (((!!) @ (^[Y0 : $i]: (((((~) @ (rel_s4 @ X4 @ Y0))) | (kn2 @ Y0)))))) 269.34/37.94 | ~ (rel_s4 @ X2 @ X4))), 269.34/37.94 inference('demod', [status(thm)], 269.34/37.94 [zip_derived_cl5301, zip_derived_cl2609])). 269.34/37.94 thf(zip_derived_cl5304, plain, 269.34/37.94 (![X2 : $i, X4 : $i, X6 : $i]: 269.34/37.94 ( (((((~) @ (rel_s4 @ X4 @ X6))) | (kn2 @ X6))) | ~ (rel_s4 @ X2 @ X4))), 269.34/37.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5303])). 269.34/37.94 thf(zip_derived_cl5309, plain, 269.34/37.94 (![X2 : $i, X4 : $i, X6 : $i]: 269.34/37.94 (~ (rel_s4 @ X4 @ X6) | (kn2 @ X6) | ~ (rel_s4 @ X2 @ X4))), 269.34/37.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl5304])). 269.34/37.94 thf(zip_derived_cl5322, plain, 269.34/37.94 (![X0 : $i]: (~ (rel_s4 @ X0 @ '#sk1') | (kn2 @ '#sk2'))), 269.34/37.94 inference('sup-', [status(thm)], [zip_derived_cl77, zip_derived_cl5309])). 269.34/37.94 thf(zip_derived_cl78, plain, (~ (kn2 @ '#sk2')), 269.34/37.94 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl76])). 269.34/37.94 thf(zip_derived_cl5339, plain, (![X0 : $i]: ~ (rel_s4 @ X0 @ '#sk1')), 269.34/37.94 inference('clc', [status(thm)], [zip_derived_cl5322, zip_derived_cl78])). 269.34/37.94 thf(zip_derived_cl5340, plain, ($false), 269.34/37.94 inference('sup-', [status(thm)], [zip_derived_cl79, zip_derived_cl5339])). 269.34/37.94 269.34/37.94 % SZS output end Refutation 269.34/37.94 269.34/37.94 269.34/37.94 % Terminating... 269.34/37.98 % Runner terminated. 269.34/38.00 % Zipperpin 1.5 exiting 269.34/38.01 EOF