0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.IAKvy3SbLM true 0.13/0.34 % Computer : n027.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 03:57:51 EDT 2022 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 960 s 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.34 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.54/0.65 % Total configuration time : 828 0.54/0.65 % Estimated wc time : 1656 0.54/0.65 % Estimated cpu time (8 cpus) : 207.0 0.55/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.55/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.55/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.55/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.55/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 0.56/0.90 % Solved by lams/35_full_unif4.sh. 0.56/0.90 % done 39 iterations in 0.121s 0.56/0.90 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 0.56/0.90 % SZS output start Refutation 0.56/0.90 thf(mu_type, type, mu: $tType). 0.56/0.90 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 0.56/0.90 thf(in_type, type, in: mu > mu > $i > $o). 0.56/0.90 thf('#sk5_type', type, '#sk5': mu). 0.56/0.90 thf(singleton_type, type, singleton: mu > mu). 0.56/0.90 thf('#sk6_type', type, '#sk6': mu). 0.56/0.90 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 0.56/0.90 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 0.56/0.90 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 0.56/0.90 thf(empty_set_type, type, empty_set: mu). 0.56/0.90 thf('#sk4_type', type, '#sk4': $i). 0.56/0.90 thf(exists_in_world_type, type, exists_in_world: mu > $i > $o). 0.56/0.90 thf(qmltpeq_type, type, qmltpeq: mu > mu > $i > $o). 0.56/0.90 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o). 0.56/0.90 thf(mequiv_type, type, mequiv: ($i > $o) > ($i > $o) > $i > $o). 0.56/0.90 thf(set_difference_type, type, set_difference: mu > mu > mu). 0.56/0.90 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 0.56/0.90 thf(mvalid, axiom,(( mvalid ) = 0.56/0.90 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 0.56/0.90 thf('0', plain, 0.56/0.90 (( mvalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 0.56/0.90 inference('simplify_rw_rule', [status(thm)], [mvalid])). 0.56/0.90 thf('1', plain, 0.56/0.90 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 0.56/0.90 define([status(thm)])). 0.56/0.90 thf(mforall_ind, axiom,(( mforall_ind ) = 0.56/0.90 (^[Phi:( mu > $i > $o ),W:$i]: 0.56/0.90 ( ![X:mu]: ( ( exists_in_world @ X @ W ) => ( Phi @ X @ W ) ) )))). 0.56/0.90 thf('2', plain, 0.56/0.90 (( mforall_ind ) = 0.56/0.90 ( ^[Phi:( mu > $i > $o ),W:$i]: 0.56/0.90 ( ![X:mu]: ( ( exists_in_world @ X @ W ) => ( Phi @ X @ W ) ) ) )), 0.56/0.90 inference('simplify_rw_rule', [status(thm)], [mforall_ind])). 0.56/0.90 thf('3', plain, 0.56/0.90 (( mforall_ind ) = 0.56/0.90 ( ^[V_1:( mu > $i > $o ),V_2:$i]: 0.56/0.90 ( ![X4:mu]: ( ( exists_in_world @ X4 @ V_2 ) => ( V_1 @ X4 @ V_2 ) ) ) )), 0.56/0.90 define([status(thm)])). 0.56/0.90 thf(mor, axiom,(( mor ) = 0.56/0.90 (^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) )))). 0.56/0.90 thf('4', plain, 0.56/0.90 (( mor ) = 0.56/0.90 ( ^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) ) )), 0.56/0.90 inference('simplify_rw_rule', [status(thm)], [mor])). 0.56/0.90 thf('5', plain, 0.56/0.90 (( mor ) = 0.56/0.90 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 0.56/0.90 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 0.56/0.90 define([status(thm)])). 0.56/0.90 thf(t69_zfmisc_1, conjecture, 0.56/0.90 (mvalid @ 0.56/0.90 ( mforall_ind @ 0.56/0.90 ( ^[A:mu]: 0.56/0.90 ( mforall_ind @ 0.56/0.90 ( ^[B:mu]: 0.56/0.90 ( mor @ 0.56/0.90 ( qmltpeq @ 0.56/0.90 ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ 0.56/0.90 ( qmltpeq @ 0.56/0.90 ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ) ))). 0.56/0.90 thf(zf_stmt_0, conjecture, 0.56/0.90 (![X4:$i,X6:mu]: 0.56/0.90 ( ( exists_in_world @ X6 @ X4 ) => 0.56/0.90 ( ![X8:mu]: 0.56/0.90 ( ( exists_in_world @ X8 @ X4 ) => 0.56/0.90 ( ( qmltpeq @ 0.56/0.90 ( set_difference @ ( singleton @ X6 ) @ X8 ) @ 0.56/0.90 ( singleton @ X6 ) @ X4 ) | 0.56/0.90 ( qmltpeq @ 0.56/0.90 ( set_difference @ ( singleton @ X6 ) @ X8 ) @ empty_set @ X4 ) ) ) ) ))). 0.56/0.90 thf(zf_stmt_1, negated_conjecture, 0.56/0.90 (~( ![X4:$i,X6:mu]: 0.56/0.90 ( ( exists_in_world @ X6 @ X4 ) => 0.56/0.90 ( ![X8:mu]: 0.56/0.90 ( ( exists_in_world @ X8 @ X4 ) => 0.56/0.90 ( ( qmltpeq @ 0.56/0.90 ( set_difference @ ( singleton @ X6 ) @ X8 ) @ 0.56/0.90 ( singleton @ X6 ) @ X4 ) | 0.56/0.90 ( qmltpeq @ 0.56/0.90 ( set_difference @ ( singleton @ X6 ) @ X8 ) @ empty_set @ X4 ) ) ) ) ) )), 0.56/0.90 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 0.56/0.90 thf(zip_derived_cl11, plain, 0.56/0.90 (~ (((!!) @ (^[Y0 : $i]: 0.56/0.90 (((!!) @ (^[Y1 : mu]: 0.56/0.90 (((exists_in_world @ Y1 @ Y0) => 0.56/0.90 (((!!) @ (^[Y2 : mu]: 0.56/0.90 (((exists_in_world @ Y2 @ Y0) => 0.56/0.90 (((qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ Y1) @ Y2) @ 0.56/0.90 (singleton @ Y1) @ Y0) | 0.56/0.90 (qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ Y1) @ Y2) @ 0.56/0.90 empty_set @ Y0))))))))))))))))), 0.56/0.90 inference('cnf', [status(esa)], [zf_stmt_1])). 0.56/0.90 thf(zip_derived_cl64, plain, 0.56/0.90 (~ (((!!) @ (^[Y0 : mu]: 0.56/0.90 (((exists_in_world @ Y0 @ '#sk4') => 0.56/0.90 (((!!) @ (^[Y1 : mu]: 0.56/0.90 (((exists_in_world @ Y1 @ '#sk4') => 0.56/0.90 (((qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ Y0) @ Y1) @ 0.56/0.90 (singleton @ Y0) @ '#sk4') | (qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ Y0) @ Y1) @ 0.56/0.90 empty_set @ '#sk4')))))))))))))), 0.56/0.90 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl11])). 0.56/0.90 thf(zip_derived_cl65, plain, 0.56/0.90 (~ (((exists_in_world @ '#sk5' @ '#sk4') => 0.56/0.90 (((!!) @ (^[Y0 : mu]: 0.56/0.90 (((exists_in_world @ Y0 @ '#sk4') => 0.56/0.90 (((qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ '#sk5') @ Y0) @ 0.56/0.90 (singleton @ '#sk5') @ '#sk4') | (qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ '#sk5') @ Y0) @ 0.56/0.90 empty_set @ '#sk4'))))))))))), 0.56/0.90 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl64])). 0.56/0.90 thf(zip_derived_cl67, plain, 0.56/0.90 (~ (((!!) @ (^[Y0 : mu]: 0.56/0.90 (((exists_in_world @ Y0 @ '#sk4') => 0.56/0.90 (((qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ '#sk5') @ Y0) @ 0.56/0.90 (singleton @ '#sk5') @ '#sk4') | (qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ '#sk5') @ Y0) @ 0.56/0.90 empty_set @ '#sk4'))))))))), 0.56/0.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])). 0.56/0.90 thf(zip_derived_cl68, plain, 0.56/0.90 (~ (((exists_in_world @ '#sk6' @ '#sk4') => 0.56/0.90 (((qmltpeq @ (set_difference @ (singleton @ '#sk5') @ '#sk6') @ 0.56/0.90 (singleton @ '#sk5') @ '#sk4') | (qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ '#sk5') @ '#sk6') @ empty_set @ 0.56/0.90 '#sk4')))))), 0.56/0.90 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl67])). 0.56/0.90 thf(zip_derived_cl70, plain, 0.56/0.90 (~ (((qmltpeq @ (set_difference @ (singleton @ '#sk5') @ '#sk6') @ 0.56/0.90 (singleton @ '#sk5') @ '#sk4') | (qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ '#sk5') @ '#sk6') @ empty_set @ 0.56/0.90 '#sk4')))), 0.56/0.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 0.56/0.90 thf(zip_derived_cl72, plain, 0.56/0.90 (~ (qmltpeq @ (set_difference @ (singleton @ '#sk5') @ '#sk6') @ 0.56/0.90 empty_set @ '#sk4')), 0.56/0.90 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl70])). 0.56/0.90 thf(mequiv, axiom,(( mequiv ) = 0.56/0.90 (^[Phi:( $i > $o ),Psi:( $i > $o )]: 0.56/0.90 ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) )))). 0.56/0.90 thf(mimplies, axiom,(( mimplies ) = 0.56/0.90 (^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi )))). 0.56/0.90 thf(mnot, axiom,(( mnot ) = (^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) )))). 0.56/0.90 thf('6', plain, (( mnot ) = ( ^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) ) )), 0.56/0.90 inference('simplify_rw_rule', [status(thm)], [mnot])). 0.56/0.90 thf('7', plain, 0.56/0.90 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 0.56/0.90 define([status(thm)])). 0.56/0.90 thf('8', plain, 0.56/0.90 (( mimplies ) = 0.56/0.90 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi ) )), 0.56/0.90 inference('simplify_rw_rule', [status(thm)], [mimplies, '5', '7'])). 0.56/0.90 thf('9', plain, 0.56/0.90 (( mimplies ) = 0.56/0.90 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 0.56/0.90 define([status(thm)])). 0.56/0.90 thf(mand, axiom,(( mand ) = 0.56/0.90 (^[Phi:( $i > $o ),Psi:( $i > $o )]: 0.56/0.90 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) )))). 0.56/0.90 thf('10', plain, 0.56/0.90 (( mand ) = 0.56/0.90 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: 0.56/0.90 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) )), 0.56/0.90 inference('simplify_rw_rule', [status(thm)], [mand, '5', '7'])). 0.56/0.90 thf('11', plain, 0.56/0.90 (( mand ) = 0.56/0.90 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 0.56/0.90 ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) )), 0.56/0.90 define([status(thm)])). 0.56/0.90 thf('12', plain, 0.56/0.90 (( mequiv ) = 0.56/0.90 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: 0.56/0.90 ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) )), 0.56/0.90 inference('simplify_rw_rule', [status(thm)], 0.56/0.90 [mequiv, '9', '11', '5', '7'])). 0.56/0.90 thf('13', plain, 0.56/0.90 (( mequiv ) = 0.56/0.90 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 0.56/0.90 ( mand @ ( mimplies @ V_1 @ V_2 ) @ ( mimplies @ V_2 @ V_1 ) ) )), 0.56/0.90 define([status(thm)])). 0.56/0.90 thf(l36_zfmisc_1, axiom, 0.56/0.90 (mvalid @ 0.56/0.90 ( mforall_ind @ 0.56/0.90 ( ^[A:mu]: 0.56/0.90 ( mforall_ind @ 0.56/0.90 ( ^[B:mu]: 0.56/0.90 ( mequiv @ 0.56/0.90 ( qmltpeq @ 0.56/0.90 ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ 0.56/0.90 ( in @ A @ B ) ) ) ) ) ))). 0.56/0.90 thf(zf_stmt_2, axiom, 0.56/0.90 (![X4:$i,X6:mu]: 0.56/0.90 ( ( exists_in_world @ X6 @ X4 ) => 0.56/0.90 ( ![X8:mu]: 0.56/0.90 ( ( exists_in_world @ X8 @ X4 ) => 0.56/0.90 ( ~( ( ~( ( qmltpeq @ 0.56/0.90 ( set_difference @ ( singleton @ X6 ) @ X8 ) @ 0.56/0.90 empty_set @ X4 ) | 0.56/0.90 ( ~( in @ X6 @ X8 @ X4 ) ) ) ) | 0.56/0.90 ( ~( ( in @ X6 @ X8 @ X4 ) | 0.56/0.90 ( ~( qmltpeq @ 0.56/0.90 ( set_difference @ ( singleton @ X6 ) @ X8 ) @ 0.56/0.90 empty_set @ X4 ) ) ) ) ) ) ) ) ))). 0.56/0.90 thf(zip_derived_cl22, plain, 0.56/0.90 ( (((!!) @ (^[Y0 : $i]: 0.56/0.90 (((!!) @ (^[Y1 : mu]: 0.56/0.90 (((exists_in_world @ Y1 @ Y0) => 0.56/0.90 (((!!) @ (^[Y2 : mu]: 0.56/0.90 (((exists_in_world @ Y2 @ Y0) => 0.56/0.90 (((~) @ (((((~) @ (((qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ 0.56/0.90 Y1) @ 0.56/0.90 Y2) @ 0.56/0.90 empty_set @ 0.56/0.90 Y0) | 0.56/0.90 (((~) @ ( 0.56/0.90 in @ 0.56/0.90 Y1 @ 0.56/0.90 Y2 @ Y0))))))) | 0.56/0.90 (((~) @ (((in @ Y1 @ 0.56/0.90 Y2 @ Y0) | 0.56/0.90 (((~) @ ( 0.56/0.90 qmltpeq @ 0.56/0.90 ( 0.56/0.90 set_difference @ 0.56/0.90 ( 0.56/0.90 singleton @ 0.56/0.90 Y1) @ Y2) @ 0.56/0.90 empty_set @ 0.56/0.90 Y0))))))))))))))))))))))))), 0.56/0.90 inference('cnf', [status(esa)], [zf_stmt_2])). 0.56/0.90 thf(zip_derived_cl253, plain, 0.56/0.90 (![X2 : $i]: 0.56/0.90 (((!!) @ (^[Y0 : mu]: 0.56/0.90 (((exists_in_world @ Y0 @ X2) => 0.56/0.90 (((!!) @ (^[Y1 : mu]: 0.56/0.90 (((exists_in_world @ Y1 @ X2) => 0.56/0.90 (((~) @ (((((~) @ (((qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ Y0) @ 0.56/0.90 Y1) @ 0.56/0.90 empty_set @ X2) | 0.56/0.90 (((~) @ (in @ Y0 @ 0.56/0.90 Y1 @ X2))))))) | 0.56/0.90 (((~) @ (((in @ Y0 @ Y1 @ X2) | 0.56/0.90 (((~) @ (qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ 0.56/0.90 Y0) @ 0.56/0.90 Y1) @ 0.56/0.90 empty_set @ 0.56/0.90 X2)))))))))))))))))))))), 0.56/0.90 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 0.56/0.90 thf(zip_derived_cl254, plain, 0.56/0.90 (![X2 : $i, X4 : mu]: 0.56/0.90 (((exists_in_world @ X4 @ X2) => 0.56/0.90 (((!!) @ (^[Y0 : mu]: 0.56/0.90 (((exists_in_world @ Y0 @ X2) => 0.56/0.90 (((~) @ (((((~) @ (((qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ X4) @ Y0) @ 0.56/0.90 empty_set @ X2) | 0.56/0.90 (((~) @ (in @ X4 @ Y0 @ X2))))))) | 0.56/0.90 (((~) @ (((in @ X4 @ Y0 @ X2) | 0.56/0.90 (((~) @ (qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ X4) @ Y0) @ 0.56/0.90 empty_set @ X2))))))))))))))))))), 0.56/0.90 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl253])). 0.56/0.90 thf(zip_derived_cl255, plain, 0.56/0.90 (![X2 : $i, X4 : mu]: 0.56/0.90 (~ (exists_in_world @ X4 @ X2) 0.56/0.90 | (((!!) @ (^[Y0 : mu]: 0.56/0.90 (((exists_in_world @ Y0 @ X2) => 0.56/0.90 (((~) @ (((((~) @ (((qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ X4) @ Y0) @ 0.56/0.90 empty_set @ X2) | 0.56/0.90 (((~) @ (in @ X4 @ Y0 @ X2))))))) | 0.56/0.90 (((~) @ (((in @ X4 @ Y0 @ X2) | 0.56/0.90 (((~) @ (qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ X4) @ Y0) @ 0.56/0.90 empty_set @ X2)))))))))))))))))), 0.56/0.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl254])). 0.56/0.90 thf(zip_derived_cl256, plain, 0.56/0.90 (![X2 : $i, X4 : mu, X6 : mu]: 0.56/0.90 ( (((exists_in_world @ X6 @ X2) => 0.56/0.90 (((~) @ (((((~) @ (((qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ X4) @ X6) @ 0.56/0.90 empty_set @ X2) | 0.56/0.90 (((~) @ (in @ X4 @ X6 @ X2))))))) | 0.56/0.90 (((~) @ (((in @ X4 @ X6 @ X2) | 0.56/0.90 (((~) @ (qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ X4) @ 0.56/0.90 X6) @ 0.56/0.90 empty_set @ X2))))))))))))) 0.56/0.90 | ~ (exists_in_world @ X4 @ X2))), 0.56/0.90 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl255])). 0.56/0.90 thf(zip_derived_cl257, plain, 0.56/0.90 (![X2 : $i, X4 : mu, X6 : mu]: 0.56/0.90 (~ (exists_in_world @ X6 @ X2) 0.56/0.90 | ~ (((((~) @ (((qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ X4) @ X6) @ 0.56/0.90 empty_set @ X2) | (((~) @ (in @ X4 @ X6 @ X2))))))) | 0.56/0.90 (((~) @ (((in @ X4 @ X6 @ X2) | 0.56/0.90 (((~) @ (qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ X4) @ X6) @ 0.56/0.90 empty_set @ X2))))))))) 0.56/0.90 | ~ (exists_in_world @ X4 @ X2))), 0.56/0.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl256])). 0.56/0.90 thf(zip_derived_cl258, plain, 0.56/0.90 (![X2 : $i, X4 : mu, X6 : mu]: 0.56/0.90 ( (((qmltpeq @ (set_difference @ (singleton @ X4) @ X6) @ empty_set @ 0.56/0.90 X2) | (((~) @ (in @ X4 @ X6 @ X2))))) 0.56/0.90 | ~ (exists_in_world @ X4 @ X2) 0.56/0.90 | ~ (exists_in_world @ X6 @ X2))), 0.56/0.90 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl257])). 0.56/0.90 thf(zip_derived_cl260, plain, 0.56/0.90 (![X2 : $i, X4 : mu, X6 : mu]: 0.56/0.90 ( (qmltpeq @ (set_difference @ (singleton @ X4) @ X6) @ empty_set @ X2) 0.56/0.90 | ~ (in @ X4 @ X6 @ X2) 0.56/0.90 | ~ (exists_in_world @ X6 @ X2) 0.56/0.90 | ~ (exists_in_world @ X4 @ X2))), 0.56/0.90 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl258])). 0.56/0.90 thf(zip_derived_cl268, plain, 0.56/0.90 ((~ (exists_in_world @ '#sk5' @ '#sk4') 0.56/0.90 | ~ (exists_in_world @ '#sk6' @ '#sk4') 0.56/0.90 | ~ (in @ '#sk5' @ '#sk6' @ '#sk4'))), 0.56/0.90 inference('sup+', [status(thm)], [zip_derived_cl72, zip_derived_cl260])). 0.56/0.90 thf(zip_derived_cl66, plain, ( (exists_in_world @ '#sk5' @ '#sk4')), 0.56/0.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])). 0.56/0.90 thf(zip_derived_cl69, plain, ( (exists_in_world @ '#sk6' @ '#sk4')), 0.56/0.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 0.56/0.90 thf(zip_derived_cl276, plain, (~ (in @ '#sk5' @ '#sk6' @ '#sk4')), 0.56/0.90 inference('demod', [status(thm)], 0.56/0.90 [zip_derived_cl268, zip_derived_cl66, zip_derived_cl69])). 0.56/0.90 thf(zip_derived_cl71, plain, 0.56/0.90 (~ (qmltpeq @ (set_difference @ (singleton @ '#sk5') @ '#sk6') @ 0.56/0.90 (singleton @ '#sk5') @ '#sk4')), 0.56/0.90 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl70])). 0.56/0.90 thf(l34_zfmisc_1, axiom, 0.56/0.90 (mvalid @ 0.56/0.90 ( mforall_ind @ 0.56/0.90 ( ^[A:mu]: 0.56/0.90 ( mforall_ind @ 0.56/0.90 ( ^[B:mu]: 0.56/0.90 ( mequiv @ 0.56/0.90 ( qmltpeq @ 0.56/0.90 ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ 0.56/0.90 ( mnot @ ( in @ A @ B ) ) ) ) ) ) ))). 0.56/0.90 thf(zf_stmt_3, axiom, 0.56/0.90 (![X4:$i,X6:mu]: 0.56/0.90 ( ( exists_in_world @ X6 @ X4 ) => 0.56/0.90 ( ![X8:mu]: 0.56/0.90 ( ( exists_in_world @ X8 @ X4 ) => 0.56/0.90 ( ~( ( ~( ( qmltpeq @ 0.56/0.90 ( set_difference @ ( singleton @ X6 ) @ X8 ) @ 0.56/0.90 ( singleton @ X6 ) @ X4 ) | 0.56/0.90 ( in @ X6 @ X8 @ X4 ) ) ) | 0.56/0.90 ( ~( ( ~( in @ X6 @ X8 @ X4 ) ) | 0.56/0.90 ( ~( qmltpeq @ 0.56/0.90 ( set_difference @ ( singleton @ X6 ) @ X8 ) @ 0.56/0.90 ( singleton @ X6 ) @ X4 ) ) ) ) ) ) ) ) ))). 0.56/0.90 thf(zip_derived_cl16, plain, 0.56/0.90 ( (((!!) @ (^[Y0 : $i]: 0.56/0.90 (((!!) @ (^[Y1 : mu]: 0.56/0.90 (((exists_in_world @ Y1 @ Y0) => 0.56/0.90 (((!!) @ (^[Y2 : mu]: 0.56/0.90 (((exists_in_world @ Y2 @ Y0) => 0.56/0.90 (((~) @ (((((~) @ (((qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ 0.56/0.90 Y1) @ 0.56/0.90 Y2) @ 0.56/0.90 (singleton @ 0.56/0.90 Y1) @ 0.56/0.90 Y0) | 0.56/0.90 (in @ Y1 @ 0.56/0.90 Y2 @ Y0))))) | 0.56/0.90 (((~) @ (((((~) @ ( 0.56/0.90 in @ 0.56/0.90 Y1 @ 0.56/0.90 Y2 @ Y0))) | 0.56/0.90 (((~) @ ( 0.56/0.90 qmltpeq @ 0.56/0.90 ( 0.56/0.90 set_difference @ 0.56/0.90 ( 0.56/0.90 singleton @ 0.56/0.90 Y1) @ Y2) @ 0.56/0.90 ( 0.56/0.90 singleton @ 0.56/0.90 Y1) @ Y0))))))))))))))))))))))))), 0.56/0.90 inference('cnf', [status(esa)], [zf_stmt_3])). 0.56/0.90 thf(zip_derived_cl290, plain, 0.56/0.90 (![X2 : $i]: 0.56/0.90 (((!!) @ (^[Y0 : mu]: 0.56/0.90 (((exists_in_world @ Y0 @ X2) => 0.56/0.90 (((!!) @ (^[Y1 : mu]: 0.56/0.90 (((exists_in_world @ Y1 @ X2) => 0.56/0.90 (((~) @ (((((~) @ (((qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ Y0) @ 0.56/0.90 Y1) @ 0.56/0.90 (singleton @ Y0) @ 0.56/0.90 X2) | (in @ Y0 @ 0.56/0.90 Y1 @ X2))))) | 0.56/0.90 (((~) @ (((((~) @ (in @ Y0 @ 0.56/0.90 Y1 @ X2))) | 0.56/0.90 (((~) @ (qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ 0.56/0.90 Y0) @ 0.56/0.90 Y1) @ 0.56/0.90 (singleton @ 0.56/0.90 Y0) @ 0.56/0.90 X2)))))))))))))))))))))), 0.56/0.90 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 0.56/0.90 thf(zip_derived_cl291, plain, 0.56/0.90 (![X2 : $i, X4 : mu]: 0.56/0.90 (((exists_in_world @ X4 @ X2) => 0.56/0.90 (((!!) @ (^[Y0 : mu]: 0.56/0.90 (((exists_in_world @ Y0 @ X2) => 0.56/0.90 (((~) @ (((((~) @ (((qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ X4) @ Y0) @ 0.56/0.90 (singleton @ X4) @ X2) | (in @ 0.56/0.90 X4 @ Y0 @ X2))))) | 0.56/0.90 (((~) @ (((((~) @ (in @ X4 @ Y0 @ X2))) | 0.56/0.90 (((~) @ (qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ X4) @ Y0) @ 0.56/0.90 (singleton @ X4) @ X2))))))))))))))))))), 0.56/0.90 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl290])). 0.56/0.90 thf(zip_derived_cl292, plain, 0.56/0.90 (![X2 : $i, X4 : mu]: 0.56/0.90 (~ (exists_in_world @ X4 @ X2) 0.56/0.90 | (((!!) @ (^[Y0 : mu]: 0.56/0.90 (((exists_in_world @ Y0 @ X2) => 0.56/0.90 (((~) @ (((((~) @ (((qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ X4) @ Y0) @ 0.56/0.90 (singleton @ X4) @ X2) | (in @ 0.56/0.90 X4 @ Y0 @ X2))))) | 0.56/0.90 (((~) @ (((((~) @ (in @ X4 @ Y0 @ X2))) | 0.56/0.90 (((~) @ (qmltpeq @ 0.56/0.90 (set_difference @ 0.56/0.90 (singleton @ X4) @ Y0) @ 0.56/0.90 (singleton @ X4) @ X2)))))))))))))))))), 0.56/0.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl291])). 0.56/0.90 thf(zip_derived_cl293, plain, 0.56/0.90 (![X2 : $i, X4 : mu, X6 : mu]: 0.56/0.90 ( (((exists_in_world @ X6 @ X2) => 0.56/0.90 (((~) @ (((((~) @ (((qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ X4) @ X6) @ 0.56/0.90 (singleton @ X4) @ X2) | (in @ X4 @ X6 @ X2))))) | 0.56/0.90 (((~) @ (((((~) @ (in @ X4 @ X6 @ X2))) | 0.56/0.90 (((~) @ (qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ X4) @ 0.56/0.90 X6) @ 0.56/0.90 (singleton @ X4) @ X2))))))))))))) 0.56/0.90 | ~ (exists_in_world @ X4 @ X2))), 0.56/0.90 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl292])). 0.56/0.90 thf(zip_derived_cl294, plain, 0.56/0.90 (![X2 : $i, X4 : mu, X6 : mu]: 0.56/0.90 (~ (exists_in_world @ X6 @ X2) 0.56/0.90 | ~ (((((~) @ (((qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ X4) @ X6) @ 0.56/0.90 (singleton @ X4) @ X2) | (in @ X4 @ X6 @ X2))))) | 0.56/0.90 (((~) @ (((((~) @ (in @ X4 @ X6 @ X2))) | 0.56/0.90 (((~) @ (qmltpeq @ 0.56/0.90 (set_difference @ (singleton @ X4) @ X6) @ 0.56/0.90 (singleton @ X4) @ X2))))))))) 0.56/0.90 | ~ (exists_in_world @ X4 @ X2))), 0.56/0.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])). 0.56/0.90 thf(zip_derived_cl295, plain, 0.56/0.90 (![X2 : $i, X4 : mu, X6 : mu]: 0.56/0.90 ( (((qmltpeq @ (set_difference @ (singleton @ X4) @ X6) @ 0.56/0.90 (singleton @ X4) @ X2) | (in @ X4 @ X6 @ X2))) 0.56/0.90 | ~ (exists_in_world @ X4 @ X2) 0.56/0.90 | ~ (exists_in_world @ X6 @ X2))), 0.56/0.90 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl294])). 0.56/0.90 thf(zip_derived_cl297, plain, 0.56/0.90 (![X2 : $i, X4 : mu, X6 : mu]: 0.56/0.90 ( (qmltpeq @ (set_difference @ (singleton @ X4) @ X6) @ 0.56/0.90 (singleton @ X4) @ X2) 0.56/0.90 | (in @ X4 @ X6 @ X2) 0.56/0.90 | ~ (exists_in_world @ X6 @ X2) 0.56/0.90 | ~ (exists_in_world @ X4 @ X2))), 0.56/0.90 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl295])). 0.56/0.90 thf(zip_derived_cl305, plain, 0.56/0.90 ((~ (exists_in_world @ '#sk5' @ '#sk4') 0.56/0.90 | ~ (exists_in_world @ '#sk6' @ '#sk4') 0.56/0.90 | (in @ '#sk5' @ '#sk6' @ '#sk4'))), 0.56/0.90 inference('sup+', [status(thm)], [zip_derived_cl71, zip_derived_cl297])). 0.56/0.90 thf(zip_derived_cl66, plain, ( (exists_in_world @ '#sk5' @ '#sk4')), 0.56/0.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])). 0.56/0.90 thf(zip_derived_cl69, plain, ( (exists_in_world @ '#sk6' @ '#sk4')), 0.56/0.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 0.56/0.90 thf(zip_derived_cl313, plain, ( (in @ '#sk5' @ '#sk6' @ '#sk4')), 0.56/0.90 inference('demod', [status(thm)], 0.56/0.90 [zip_derived_cl305, zip_derived_cl66, zip_derived_cl69])). 0.56/0.90 thf(zip_derived_cl327, plain, ($false), 0.56/0.90 inference('demod', [status(thm)], [zip_derived_cl276, zip_derived_cl313])). 0.56/0.90 0.56/0.90 % SZS output end Refutation 0.56/0.90 0.56/0.90 0.56/0.90 % Terminating... 0.57/0.95 % Runner terminated. 0.57/0.96 % Zipperpin 1.5 exiting 0.57/0.96 EOF