0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.2vZuJO5KkO true 0.12/0.33 % Computer : n031.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1200 0.12/0.33 % WCLimit : 120 0.12/0.33 % DateTime : Tue Jul 13 14:43:44 EDT 2021 0.12/0.33 % CPUTime : 0.12/0.33 % Running portfolio for 120 s 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.33 % Number of cores: 8 0.12/0.33 % Python version: Python 3.6.8 0.12/0.33 % Running in HO mode 0.48/0.62 % Total configuration time : 828 0.48/0.62 % Estimated wc time : 983 0.48/0.62 % Estimated cpu time (8 cpus) : 122.875 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.49/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.49/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.49/0.71 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.49/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.49/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 46.15/6.38 % Solved by lams/30_sp5.sh. 46.15/6.38 % done 193 iterations in 5.310s 46.15/6.38 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 46.15/6.38 % SZS output start Refutation 46.15/6.38 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 46.15/6.38 thf(setunion_type, type, setunion: $i > $i). 46.15/6.38 thf(omega0Ax_type, type, omega0Ax: $o). 46.15/6.38 thf('#sk159_type', type, '#sk159': $i > $i > $i). 46.15/6.38 thf(omegaIndAx_type, type, omegaIndAx: $o). 46.15/6.38 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 46.15/6.38 thf(emptysetAx_type, type, emptysetAx: $o). 46.15/6.38 thf(descrp_type, type, descrp: $o). 46.15/6.38 thf(setunionAx_type, type, setunionAx: $o). 46.15/6.38 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 46.15/6.38 thf(powerset_type, type, powerset: $i > $i). 46.15/6.38 thf(prop2setE_type, type, prop2setE: $o). 46.15/6.38 thf(nonemptyI_type, type, nonemptyI: $o). 46.15/6.38 thf(exu_type, type, exu: ($i > $o) > $o). 46.15/6.38 thf(notinemptyset_type, type, notinemptyset: $o). 46.15/6.38 thf('#sk22_type', type, '#sk22': $i > $i). 46.15/6.38 thf(setextAx_type, type, setextAx: $o). 46.15/6.38 thf(exuE3e_type, type, exuE3e: $o). 46.15/6.38 thf(powersetAx_type, type, powersetAx: $o). 46.15/6.38 thf(replAx_type, type, replAx: $o). 46.15/6.39 thf(setbeta_type, type, setbeta: $o). 46.15/6.39 thf(omegaSAx_type, type, omegaSAx: $o). 46.15/6.39 thf(setadjoinIL_type, type, setadjoinIL: $o). 46.15/6.39 thf(setadjoinIR_type, type, setadjoinIR: $o). 46.15/6.39 thf(nonemptyI1_type, type, nonemptyI1: $o). 46.15/6.39 thf(setadjoinE_type, type, setadjoinE: $o). 46.15/6.39 thf(emptysetE_type, type, emptysetE: $o). 46.15/6.39 thf(omega_type, type, omega: $i). 46.15/6.39 thf(dsetconstrER_type, type, dsetconstrER: $o). 46.15/6.39 thf(nonempty_type, type, nonempty: $i > $o). 46.15/6.39 thf('#form193_type', type, '#form193': $i > $i > $o). 46.15/6.39 thf(emptyI_type, type, emptyI: $o). 46.15/6.39 thf(wellorderingAx_type, type, wellorderingAx: $o). 46.15/6.39 thf(descr_type, type, descr: ($i > $o) > $i). 46.15/6.39 thf(emptyset_type, type, emptyset: $i). 46.15/6.39 thf(exuE1_type, type, exuE1: $o). 46.15/6.39 thf(setext_type, type, setext: $o). 46.15/6.39 thf(in_type, type, in: $i > $i > $o). 46.15/6.39 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 46.15/6.39 thf(foundationAx_type, type, foundationAx: $o). 46.15/6.39 thf('#sk231_type', type, '#sk231': $i). 46.15/6.39 thf(prop2set_type, type, prop2set: $o > $i). 46.15/6.39 thf(nonemptyE1_type, type, nonemptyE1: $o). 46.15/6.39 thf(setadjoinOr_type, type, setadjoinOr: $o). 46.15/6.39 thf(dsetconstrI_type, type, dsetconstrI: $o). 46.15/6.39 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 46.15/6.39 thf(setadjoinAx_type, type, setadjoinAx: $o). 46.15/6.39 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 46.15/6.39 thf('#sk130_type', type, '#sk130': $i > $i > $i). 46.15/6.39 thf(setadjoinOr, axiom, setadjoinOr = 46.15/6.39 (![Xx:$i,A:$i,Xy:$i]: 46.15/6.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) => 46.15/6.39 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))). 46.15/6.39 thf('0', plain, 46.15/6.39 (( setadjoinOr ) = 46.15/6.39 ( ![X4:$i,X6:$i,X8:$i]: 46.15/6.39 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) => 46.15/6.39 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(setadjoinE, axiom, setadjoinE = 46.15/6.39 (![Xx:$i,A:$i,Xy:$i]: 46.15/6.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) => 46.15/6.39 ( ![Xphi:$o]: 46.15/6.39 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) => 46.15/6.39 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))). 46.15/6.39 thf('1', plain, 46.15/6.39 (( setadjoinE ) = 46.15/6.39 ( ![X4:$i,X6:$i,X8:$i]: 46.15/6.39 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) => 46.15/6.39 ( ![X10:$o]: 46.15/6.39 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) => 46.15/6.39 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(setadjoinIR, axiom, setadjoinIR = 46.15/6.39 (![Xx:$i,A:$i,Xy:$i]: 46.15/6.39 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))). 46.15/6.39 thf('2', plain, 46.15/6.39 (( setadjoinIR ) = 46.15/6.39 ( ![X4:$i,X6:$i,X8:$i]: 46.15/6.39 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(emptyinunitempty, axiom,(( emptyinunitempty ) = 46.15/6.39 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))). 46.15/6.39 thf('3', plain, 46.15/6.39 (( emptyinunitempty ) = 46.15/6.39 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )), 46.15/6.39 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])). 46.15/6.39 thf('4', plain, 46.15/6.39 (( emptyinunitempty ) = 46.15/6.39 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(setadjoinIL, axiom, setadjoinIL = 46.15/6.39 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))). 46.15/6.39 thf('5', plain, 46.15/6.39 (( setadjoinIL ) = 46.15/6.39 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(nonemptyI1, axiom, nonemptyI1 = 46.15/6.39 (![A:$i]: ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) => ( nonempty @ A ) ))). 46.15/6.39 thf('6', plain, 46.15/6.39 (( nonemptyI1 ) = 46.15/6.39 ( ![X4:$i]: ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) => ( nonempty @ X4 ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(nonemptyI, axiom, nonemptyI = 46.15/6.39 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 46.15/6.39 ( ( in @ Xx @ A ) => 46.15/6.39 ( ( Xphi @ Xx ) => 46.15/6.39 ( nonempty @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))). 46.15/6.39 thf('7', plain, 46.15/6.39 (( nonemptyI ) = 46.15/6.39 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 46.15/6.39 ( ( in @ X8 @ X4 ) => 46.15/6.39 ( ( X6 @ X8 ) => 46.15/6.39 ( nonempty @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(nonemptyE1, axiom, nonemptyE1 = 46.15/6.39 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))). 46.15/6.39 thf('8', plain, 46.15/6.39 (( nonemptyE1 ) = 46.15/6.39 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(nonempty, axiom,(( nonempty ) = (^[Xx:$i]: ( ( Xx ) != ( emptyset ) )))). 46.15/6.39 thf('9', plain, (( nonempty ) = ( ^[Xx:$i]: ( ( Xx ) != ( emptyset ) ) )), 46.15/6.39 inference('simplify_rw_rule', [status(thm)], [nonempty])). 46.15/6.39 thf('10', plain, (( nonempty ) = ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(setbeta, axiom, setbeta = 46.15/6.39 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 46.15/6.39 ( ( in @ Xx @ A ) => 46.15/6.39 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) <=> 46.15/6.39 ( Xphi @ Xx ) ) ))). 46.15/6.39 thf('11', plain, 46.15/6.39 (( setbeta ) = 46.15/6.39 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 46.15/6.39 ( ( in @ X8 @ X4 ) => 46.15/6.39 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=> 46.15/6.39 ( X6 @ X8 ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(noeltsimpempty, axiom, noeltsimpempty = 46.15/6.39 (![A:$i]: 46.15/6.39 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))). 46.15/6.39 thf('12', plain, 46.15/6.39 (( noeltsimpempty ) = 46.15/6.39 ( ![X4:$i]: 46.15/6.39 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(emptyI, axiom, emptyI = 46.15/6.39 (![A:$i]: 46.15/6.39 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))). 46.15/6.39 thf('13', plain, 46.15/6.39 (( emptyI ) = 46.15/6.39 ( ![X4:$i]: 46.15/6.39 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(setext, axiom, setext = 46.15/6.39 (![A:$i,B:$i]: 46.15/6.39 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) => 46.15/6.39 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) => 46.15/6.39 ( ( A ) = ( B ) ) ) ))). 46.15/6.39 thf('14', plain, 46.15/6.39 (( setext ) = 46.15/6.39 ( ![X4:$i,X6:$i]: 46.15/6.39 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) => 46.15/6.39 ( ( ![X10:$i]: ( ( in @ X10 @ X6 ) => ( in @ X10 @ X4 ) ) ) => 46.15/6.39 ( ( X4 ) = ( X6 ) ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(exuE3e, axiom, exuE3e = 46.15/6.39 (![Xphi:( $i > $o )]: 46.15/6.39 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) => ( ?[Xx:$i]: ( Xphi @ Xx ) ) ))). 46.15/6.39 thf('15', plain, 46.15/6.39 (( exuE3e ) = 46.15/6.39 ( ![X4:( $i > $o )]: 46.15/6.39 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) => ( ?[X6:$i]: ( X4 @ X6 ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(notinemptyset, axiom, notinemptyset = 46.15/6.39 (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))). 46.15/6.39 thf('16', plain, 46.15/6.39 (( notinemptyset ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(emptysetimpfalse, axiom, emptysetimpfalse = 46.15/6.39 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( $false ) ))). 46.15/6.39 thf('17', plain, 46.15/6.39 (( emptysetimpfalse ) = 46.15/6.39 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( $false ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(emptysetE, axiom, emptysetE = 46.15/6.39 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( ![Xphi:$o]: ( Xphi ) ) ))). 46.15/6.39 thf('18', plain, 46.15/6.39 (( emptysetE ) = 46.15/6.39 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( ![X6:$o]: ( X6 ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(prop2setE, axiom, prop2setE = 46.15/6.39 (![Xphi:$o,Xx:$i]: ( ( in @ Xx @ ( prop2set @ Xphi ) ) => ( Xphi ) ))). 46.15/6.39 thf('19', plain, 46.15/6.39 (( prop2setE ) = 46.15/6.39 ( ![X4:$o,X6:$i]: ( ( in @ X6 @ ( prop2set @ X4 ) ) => ( X4 ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(prop2set, axiom,(( prop2set ) = 46.15/6.39 (^[Xphi:$o]: 46.15/6.39 ( dsetconstr @ ( powerset @ emptyset ) @ ( ^[Xx:$i]: ( Xphi ) ) )))). 46.15/6.39 thf('20', plain, 46.15/6.39 (( prop2set ) = 46.15/6.39 ( ^[Xphi:$o]: 46.15/6.39 ( dsetconstr @ ( powerset @ emptyset ) @ ( ^[Xx:$i]: ( Xphi ) ) ) )), 46.15/6.39 inference('simplify_rw_rule', [status(thm)], [prop2set])). 46.15/6.39 thf('21', plain, 46.15/6.39 (( prop2set ) = 46.15/6.39 ( ^[V_1:$o]: 46.15/6.39 ( dsetconstr @ ( powerset @ emptyset ) @ ( ^[V_2:$i]: ( V_1 ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(exuE1, axiom, exuE1 = 46.15/6.39 (![Xphi:( $i > $o )]: 46.15/6.39 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) => 46.15/6.39 ( ?[Xx:$i]: 46.15/6.39 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & 46.15/6.39 ( Xphi @ Xx ) ) ) ))). 46.15/6.39 thf('22', plain, 46.15/6.39 (( exuE1 ) = 46.15/6.39 ( ![X4:( $i > $o )]: 46.15/6.39 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) => 46.15/6.39 ( ?[X6:$i]: 46.15/6.39 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) & 46.15/6.39 ( X4 @ X6 ) ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(dsetconstrER, axiom, dsetconstrER = 46.15/6.39 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 46.15/6.39 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) => 46.15/6.39 ( Xphi @ Xx ) ))). 46.15/6.39 thf('23', plain, 46.15/6.39 (( dsetconstrER ) = 46.15/6.39 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 46.15/6.39 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 46.15/6.39 ( X6 @ X8 ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(dsetconstrEL, axiom, dsetconstrEL = 46.15/6.39 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 46.15/6.39 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) => 46.15/6.39 ( in @ Xx @ A ) ))). 46.15/6.39 thf('24', plain, 46.15/6.39 (( dsetconstrEL ) = 46.15/6.39 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 46.15/6.39 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 46.15/6.39 ( in @ X8 @ X4 ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(dsetconstrI, axiom, dsetconstrI = 46.15/6.39 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 46.15/6.39 ( ( in @ Xx @ A ) => 46.15/6.39 ( ( Xphi @ Xx ) => 46.15/6.39 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))). 46.15/6.39 thf('25', plain, 46.15/6.39 (( dsetconstrI ) = 46.15/6.39 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 46.15/6.39 ( ( in @ X8 @ X4 ) => 46.15/6.39 ( ( X6 @ X8 ) => 46.15/6.39 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(descrp, axiom, descrp = 46.15/6.39 (![Xphi:( $i > $o )]: 46.15/6.39 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) => 46.15/6.39 ( Xphi @ ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))). 46.15/6.39 thf('26', plain, 46.15/6.39 (( descrp ) = 46.15/6.39 ( ![X4:( $i > $o )]: 46.15/6.39 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) => 46.15/6.39 ( X4 @ ( descr @ ( ^[V_2:$i]: ( X4 @ V_2 ) ) ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(wellorderingAx, axiom, wellorderingAx = 46.15/6.39 (![A:$i]: 46.15/6.39 ( ?[B:$i]: 46.15/6.39 ( ( ![C:$i]: 46.15/6.39 ( ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) & 46.15/6.39 ( ?[Xx:$i]: ( in @ Xx @ C ) ) ) => 46.15/6.39 ( ?[D:$i,Xx:$i]: 46.15/6.39 ( ( ![E:$i]: 46.15/6.39 ( ( in @ E @ B ) => 46.15/6.39 ( ( ![Xy:$i]: ( ( in @ Xy @ E ) => ( in @ Xy @ D ) ) ) | 46.15/6.39 ( in @ Xx @ E ) ) ) ) & 46.15/6.39 ( ~( ?[Xy:$i]: ( ( in @ Xy @ C ) & ( in @ Xy @ D ) ) ) ) & 46.15/6.39 ( in @ Xx @ C ) & ( in @ D @ B ) ) ) ) ) & 46.15/6.39 ( ![C:$i,D:$i]: 46.15/6.39 ( ( ( in @ C @ B ) & ( in @ D @ B ) ) => 46.15/6.39 ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ D ) ) ) | 46.15/6.39 ( ![Xx:$i]: ( ( in @ Xx @ D ) => ( in @ Xx @ C ) ) ) ) ) ) & 46.15/6.39 ( ![Xx:$i,Xy:$i]: 46.15/6.39 ( ( ( in @ Xx @ A ) & ( in @ Xy @ A ) ) => 46.15/6.39 ( ( ![C:$i]: 46.15/6.39 ( ( in @ C @ B ) => ( ( in @ Xx @ C ) <=> ( in @ Xy @ C ) ) ) ) => 46.15/6.39 ( ( Xx ) = ( Xy ) ) ) ) ) & 46.15/6.39 ( ![C:$i]: 46.15/6.39 ( ( in @ C @ B ) => 46.15/6.39 ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) ) ) ) ))). 46.15/6.39 thf('27', plain, 46.15/6.39 (( wellorderingAx ) = 46.15/6.39 ( ![X4:$i]: 46.15/6.39 ( ?[X6:$i]: 46.15/6.39 ( ( ![X8:$i]: 46.15/6.39 ( ( ( ![X10:$i]: ( ( in @ X10 @ X8 ) => ( in @ X10 @ X4 ) ) ) & 46.15/6.39 ( ?[X12:$i]: ( in @ X12 @ X8 ) ) ) => 46.15/6.39 ( ?[X14:$i,X16:$i]: 46.15/6.39 ( ( ![X18:$i]: 46.15/6.39 ( ( in @ X18 @ X6 ) => 46.15/6.39 ( ( ![X20:$i]: 46.15/6.39 ( ( in @ X20 @ X18 ) => ( in @ X20 @ X14 ) ) ) | 46.15/6.39 ( in @ X16 @ X18 ) ) ) ) & 46.15/6.39 ( ~( ?[X22:$i]: ( ( in @ X22 @ X8 ) & ( in @ X22 @ X14 ) ) ) ) & 46.15/6.39 ( in @ X16 @ X8 ) & ( in @ X14 @ X6 ) ) ) ) ) & 46.15/6.39 ( ![X24:$i,X26:$i]: 46.15/6.39 ( ( ( in @ X24 @ X6 ) & ( in @ X26 @ X6 ) ) => 46.15/6.39 ( ( ![X28:$i]: ( ( in @ X28 @ X24 ) => ( in @ X28 @ X26 ) ) ) | 46.15/6.39 ( ![X30:$i]: ( ( in @ X30 @ X26 ) => ( in @ X30 @ X24 ) ) ) ) ) ) & 46.15/6.39 ( ![X32:$i,X34:$i]: 46.15/6.39 ( ( ( in @ X32 @ X4 ) & ( in @ X34 @ X4 ) ) => 46.15/6.39 ( ( ![X36:$i]: 46.15/6.39 ( ( in @ X36 @ X6 ) => 46.15/6.39 ( ( in @ X32 @ X36 ) <=> ( in @ X34 @ X36 ) ) ) ) => 46.15/6.39 ( ( X32 ) = ( X34 ) ) ) ) ) & 46.15/6.39 ( ![X38:$i]: 46.15/6.39 ( ( in @ X38 @ X6 ) => 46.15/6.39 ( ![X40:$i]: ( ( in @ X40 @ X38 ) => ( in @ X40 @ X4 ) ) ) ) ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(foundationAx, axiom, foundationAx = 46.15/6.39 (![A:$i]: 46.15/6.39 ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) => 46.15/6.39 ( ?[B:$i]: 46.15/6.39 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ A ) & ( in @ Xx @ B ) ) ) ) & 46.15/6.39 ( in @ B @ A ) ) ) ))). 46.15/6.39 thf('28', plain, 46.15/6.39 (( foundationAx ) = 46.15/6.39 ( ![X4:$i]: 46.15/6.39 ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) => 46.15/6.39 ( ?[X8:$i]: 46.15/6.39 ( ( ~( ?[X10:$i]: ( ( in @ X10 @ X4 ) & ( in @ X10 @ X8 ) ) ) ) & 46.15/6.39 ( in @ X8 @ X4 ) ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(replAx, axiom, replAx = 46.15/6.39 (![Xphi:( $i > $i > $o ),A:$i]: 46.15/6.39 ( ( ![Xx:$i]: 46.15/6.39 ( ( in @ Xx @ A ) => ( exu @ ( ^[Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ) ) => 46.15/6.39 ( ?[B:$i]: 46.15/6.39 ( ![Xx:$i]: 46.15/6.39 ( ( in @ Xx @ B ) <=> 46.15/6.39 ( ?[Xy:$i]: ( ( Xphi @ Xy @ Xx ) & ( in @ Xy @ A ) ) ) ) ) ) ))). 46.15/6.39 thf('29', plain, 46.15/6.39 (( replAx ) = 46.15/6.39 ( ![X4:( $i > $i > $o ),X6:$i]: 46.15/6.39 ( ( ![X8:$i]: 46.15/6.39 ( ( in @ X8 @ X6 ) => ( exu @ ( ^[V_1:$i]: ( X4 @ X8 @ V_1 ) ) ) ) ) => 46.15/6.39 ( ?[X10:$i]: 46.15/6.39 ( ![X12:$i]: 46.15/6.39 ( ( in @ X12 @ X10 ) <=> 46.15/6.39 ( ?[X14:$i]: ( ( X4 @ X14 @ X12 ) & ( in @ X14 @ X6 ) ) ) ) ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(omegaIndAx, axiom, omegaIndAx = 46.15/6.39 (![A:$i]: 46.15/6.39 ( ( ( in @ emptyset @ A ) & 46.15/6.39 ( ![Xx:$i]: 46.15/6.39 ( ( ( in @ Xx @ omega ) & ( in @ Xx @ A ) ) => 46.15/6.39 ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) ) => 46.15/6.39 ( ![Xx:$i]: ( ( in @ Xx @ omega ) => ( in @ Xx @ A ) ) ) ))). 46.15/6.39 thf('30', plain, 46.15/6.39 (( omegaIndAx ) = 46.15/6.39 ( ![X4:$i]: 46.15/6.39 ( ( ( in @ emptyset @ X4 ) & 46.15/6.39 ( ![X6:$i]: 46.15/6.39 ( ( ( in @ X6 @ omega ) & ( in @ X6 @ X4 ) ) => 46.15/6.39 ( in @ ( setadjoin @ X6 @ X6 ) @ X4 ) ) ) ) => 46.15/6.39 ( ![X8:$i]: ( ( in @ X8 @ omega ) => ( in @ X8 @ X4 ) ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(omegaSAx, axiom, omegaSAx = 46.15/6.39 (![Xx:$i]: 46.15/6.39 ( ( in @ Xx @ omega ) => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ))). 46.15/6.39 thf('31', plain, 46.15/6.39 (( omegaSAx ) = 46.15/6.39 ( ![X4:$i]: 46.15/6.39 ( ( in @ X4 @ omega ) => ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(omega0Ax, axiom,(( omega0Ax ) = (in @ emptyset @ omega))). 46.15/6.39 thf('32', plain, (( omega0Ax ) = ( in @ emptyset @ omega )), 46.15/6.39 inference('simplify_rw_rule', [status(thm)], [omega0Ax])). 46.15/6.39 thf('33', plain, (( omega0Ax ) = ( in @ emptyset @ omega )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(setunionAx, axiom, setunionAx = 46.15/6.39 (![A:$i,Xx:$i]: 46.15/6.39 ( ( in @ Xx @ ( setunion @ A ) ) <=> 46.15/6.39 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))). 46.15/6.39 thf('34', plain, 46.15/6.39 (( setunionAx ) = 46.15/6.39 ( ![X4:$i,X6:$i]: 46.15/6.39 ( ( in @ X6 @ ( setunion @ X4 ) ) <=> 46.15/6.39 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(powersetAx, axiom, powersetAx = 46.15/6.39 (![A:$i,B:$i]: 46.15/6.39 ( ( in @ B @ ( powerset @ A ) ) <=> 46.15/6.39 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))). 46.15/6.39 thf('35', plain, 46.15/6.39 (( powersetAx ) = 46.15/6.39 ( ![X4:$i,X6:$i]: 46.15/6.39 ( ( in @ X6 @ ( powerset @ X4 ) ) <=> 46.15/6.39 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(setadjoinAx, axiom, setadjoinAx = 46.15/6.39 (![Xx:$i,A:$i,Xy:$i]: 46.15/6.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=> 46.15/6.39 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))). 46.15/6.39 thf('36', plain, 46.15/6.39 (( setadjoinAx ) = 46.15/6.39 ( ![X4:$i,X6:$i,X8:$i]: 46.15/6.39 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 46.15/6.39 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))). 46.15/6.39 thf('37', plain, 46.15/6.39 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(setextAx, axiom, setextAx = 46.15/6.39 (![A:$i,B:$i]: 46.15/6.39 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) <=> ( in @ Xx @ B ) ) ) => 46.15/6.39 ( ( A ) = ( B ) ) ))). 46.15/6.39 thf('38', plain, 46.15/6.39 (( setextAx ) = 46.15/6.39 ( ![X4:$i,X6:$i]: 46.15/6.39 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) => 46.15/6.39 ( ( X4 ) = ( X6 ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(exu, axiom,(( exu ) = 46.15/6.39 (^[Xphi:( $i > $o )]: 46.15/6.39 ( ?[Xx:$i]: 46.15/6.39 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & ( Xphi @ Xx ) ) )))). 46.15/6.39 thf('39', plain, 46.15/6.39 (( exu ) = 46.15/6.39 ( ^[Xphi:( $i > $o )]: 46.15/6.39 ( ?[Xx:$i]: 46.15/6.39 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & 46.15/6.39 ( Xphi @ Xx ) ) ) )), 46.15/6.39 inference('simplify_rw_rule', [status(thm)], [exu])). 46.15/6.39 thf('40', plain, 46.15/6.39 (( exu ) = 46.15/6.39 ( ^[V_1:( $i > $o )]: 46.15/6.39 ( ?[X4:$i]: 46.15/6.39 ( ( ![X6:$i]: ( ( V_1 @ X6 ) => ( ( X4 ) = ( X6 ) ) ) ) & 46.15/6.39 ( V_1 @ X4 ) ) ) )), 46.15/6.39 define([status(thm)])). 46.15/6.39 thf(setoftrueEq, conjecture, 46.15/6.39 (( setextAx ) => 46.15/6.39 ( ( emptysetAx ) => 46.15/6.39 ( ( setadjoinAx ) => 46.15/6.39 ( ( powersetAx ) => 46.15/6.39 ( ( setunionAx ) => 46.15/6.39 ( ( omega0Ax ) => 46.15/6.39 ( ( omegaSAx ) => 46.15/6.39 ( ( omegaIndAx ) => 46.15/6.39 ( ( replAx ) => 46.15/6.39 ( ( foundationAx ) => 46.15/6.39 ( ( wellorderingAx ) => 46.15/6.39 ( ( descrp ) => 46.15/6.39 ( ( dsetconstrI ) => 46.15/6.39 ( ( dsetconstrEL ) => 46.15/6.39 ( ( dsetconstrER ) => 46.15/6.39 ( ( exuE1 ) => 46.15/6.39 ( ( prop2setE ) => 46.15/6.39 ( ( emptysetE ) => 46.15/6.39 ( ( emptysetimpfalse ) => 46.15/6.39 ( ( notinemptyset ) => 46.15/6.39 ( ( exuE3e ) => 46.15/6.39 ( ( setext ) => 46.15/6.39 ( ( emptyI ) => 46.15/6.39 ( ( noeltsimpempty ) => 46.15/6.39 ( ( setbeta ) => 46.15/6.39 ( ( nonemptyE1 ) => 46.15/6.39 ( ( nonemptyI ) => 46.15/6.39 ( ( nonemptyI1 ) => 46.15/6.39 ( ( setadjoinIL ) => 46.15/6.39 ( ( emptyinunitempty ) => 46.15/6.39 ( ( setadjoinIR ) => 46.15/6.39 ( ( setadjoinE ) => 46.15/6.39 ( ( 46.15/6.39 setadjoinOr ) => 46.15/6.39 ( 46.15/6.39 ![ 46.15/6.39 A:$i]: 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 dsetconstr 46.15/6.39 @ 46.15/6.39 A @ 46.15/6.39 ( 46.15/6.39 ^[ 46.15/6.39 Xx:$i]: 46.15/6.39 ( 46.15/6.39 $true ) ) ) = 46.15/6.39 ( 46.15/6.39 A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 46.15/6.39 thf(zf_stmt_0, conjecture, 46.15/6.39 (( ![X4:$i,X6:$i]: 46.15/6.39 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) => 46.15/6.39 ( ( X4 ) = ( X6 ) ) ) ) => 46.15/6.39 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) => 46.15/6.39 ( ( ![X12:$i,X14:$i,X16:$i]: 46.15/6.39 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=> 46.15/6.39 ( ( in @ X16 @ X14 ) | ( ( X16 ) = ( X12 ) ) ) ) ) => 46.15/6.39 ( ( ![X18:$i,X20:$i]: 46.15/6.39 ( ( in @ X20 @ ( powerset @ X18 ) ) <=> 46.15/6.39 ( ![X22:$i]: ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ) ) ) => 46.15/6.39 ( ( ![X24:$i,X26:$i]: 46.15/6.39 ( ( in @ X26 @ ( setunion @ X24 ) ) <=> 46.15/6.39 ( ?[X28:$i]: ( ( in @ X26 @ X28 ) & ( in @ X28 @ X24 ) ) ) ) ) => 46.15/6.39 ( ( in @ emptyset @ omega ) => 46.15/6.39 ( ( ![X30:$i]: 46.15/6.39 ( ( in @ X30 @ omega ) => 46.15/6.39 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) => 46.15/6.39 ( ( ![X32:$i]: 46.15/6.39 ( ( ( ![X34:$i]: 46.15/6.39 ( ( ( in @ X34 @ X32 ) & ( in @ X34 @ omega ) ) => 46.15/6.39 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) & 46.15/6.39 ( in @ emptyset @ X32 ) ) => 46.15/6.39 ( ![X36:$i]: 46.15/6.39 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) => 46.15/6.39 ( ( ![X38:( $i > $i > $o ),X40:$i]: 46.15/6.39 ( ( ![X42:$i]: 46.15/6.39 ( ( in @ X42 @ X40 ) => 46.15/6.39 ( ?[X44:$i]: 46.15/6.39 ( ( X38 @ X42 @ X44 ) & 46.15/6.39 ( ![X46:$i]: 46.15/6.39 ( ( X38 @ X42 @ X46 ) => 46.15/6.39 ( ( X44 ) = ( X46 ) ) ) ) ) ) ) ) => 46.15/6.39 ( ?[X48:$i]: 46.15/6.39 ( ![X50:$i]: 46.15/6.39 ( ( in @ X50 @ X48 ) <=> 46.15/6.39 ( ?[X52:$i]: 46.15/6.39 ( ( in @ X52 @ X40 ) & ( X38 @ X52 @ X50 ) ) ) ) ) ) ) ) => 46.15/6.39 ( ( ![X54:$i]: 46.15/6.39 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) => 46.15/6.39 ( ?[X58:$i]: 46.15/6.39 ( ( in @ X58 @ X54 ) & 46.15/6.39 ( ~( ?[X60:$i]: 46.15/6.39 ( ( in @ X60 @ X58 ) & ( in @ X60 @ X54 ) ) ) ) ) ) ) ) => 46.15/6.39 ( ( ![X62:$i]: 46.15/6.39 ( ?[X64:$i]: 46.15/6.39 ( ( ![X96:$i]: 46.15/6.39 ( ( in @ X96 @ X64 ) => 46.15/6.39 ( ![X98:$i]: 46.15/6.39 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) & 46.15/6.39 ( ![X90:$i,X92:$i]: 46.15/6.39 ( ( ( in @ X92 @ X62 ) & ( in @ X90 @ X62 ) ) => 46.15/6.39 ( ( ![X94:$i]: 46.15/6.39 ( ( in @ X94 @ X64 ) => 46.15/6.39 ( ( in @ X90 @ X94 ) <=> 46.15/6.39 ( in @ X92 @ X94 ) ) ) ) => 46.15/6.39 ( ( X90 ) = ( X92 ) ) ) ) ) & 46.15/6.39 ( ![X82:$i,X84:$i]: 46.15/6.39 ( ( ( in @ X84 @ X64 ) & ( in @ X82 @ X64 ) ) => 46.15/6.39 ( ( ![X88:$i]: 46.15/6.39 ( ( in @ X88 @ X84 ) => 46.15/6.39 ( in @ X88 @ X82 ) ) ) | 46.15/6.39 ( ![X86:$i]: 46.15/6.39 ( ( in @ X86 @ X82 ) => 46.15/6.39 ( in @ X86 @ X84 ) ) ) ) ) ) & 46.15/6.39 ( ![X66:$i]: 46.15/6.39 ( ( ( ?[X70:$i]: ( in @ X70 @ X66 ) ) & 46.15/6.39 ( ![X68:$i]: 46.15/6.39 ( ( in @ X68 @ X66 ) => 46.15/6.39 ( in @ X68 @ X62 ) ) ) ) => 46.15/6.39 ( ?[X72:$i,X74:$i]: 46.15/6.39 ( ( in @ X72 @ X64 ) & 46.15/6.39 ( in @ X74 @ X66 ) & 46.15/6.39 ( ~( ?[X80:$i]: 46.15/6.39 ( ( in @ X80 @ X72 ) & 46.15/6.39 ( in @ X80 @ X66 ) ) ) ) & 46.15/6.39 ( ![X76:$i]: 46.15/6.39 ( ( in @ X76 @ X64 ) => 46.15/6.39 ( ( in @ X74 @ X76 ) | 46.15/6.39 ( ![X78:$i]: 46.15/6.39 ( ( in @ X78 @ X76 ) => 46.15/6.39 ( in @ X78 @ X72 ) ) ) ) ) ) ) ) ) ) ) ) ) => 46.15/6.39 ( ( ![X100:( $i > $o )]: 46.15/6.39 ( ( ?[X102:$i]: 46.15/6.39 ( ( X100 @ X102 ) & 46.15/6.39 ( ![X104:$i]: 46.15/6.39 ( ( X100 @ X104 ) => 46.15/6.39 ( ( X102 ) = ( X104 ) ) ) ) ) ) => 46.15/6.39 ( X100 @ 46.15/6.39 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) => 46.15/6.39 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]: 46.15/6.39 ( ( in @ X110 @ X106 ) => 46.15/6.39 ( ( X108 @ X110 ) => 46.15/6.39 ( in @ 46.15/6.39 X110 @ 46.15/6.39 ( dsetconstr @ 46.15/6.39 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) => 46.15/6.39 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]: 46.15/6.39 ( ( in @ 46.15/6.39 X116 @ 46.15/6.39 ( dsetconstr @ 46.15/6.39 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) => 46.15/6.39 ( in @ X116 @ X112 ) ) ) => 46.15/6.39 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]: 46.15/6.39 ( ( in @ 46.15/6.39 X122 @ 46.15/6.39 ( dsetconstr @ 46.15/6.39 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) => 46.15/6.39 ( X120 @ X122 ) ) ) => 46.15/6.39 ( ( ![X124:( $i > $o )]: 46.15/6.39 ( ( ?[X126:$i]: 46.15/6.39 ( ( X124 @ X126 ) & 46.15/6.39 ( ![X128:$i]: 46.15/6.39 ( ( X124 @ X128 ) => 46.15/6.39 ( ( X126 ) = ( X128 ) ) ) ) ) ) => 46.15/6.39 ( ?[X130:$i]: 46.15/6.39 ( ( X124 @ X130 ) & 46.15/6.39 ( ![X132:$i]: 46.15/6.39 ( ( X124 @ X132 ) => 46.15/6.39 ( ( X130 ) = ( X132 ) ) ) ) ) ) ) ) => 46.15/6.39 ( ( ![X134:$o,X136:$i]: 46.15/6.39 ( ( in @ 46.15/6.39 X136 @ 46.15/6.39 ( dsetconstr @ 46.15/6.39 ( powerset @ emptyset ) @ 46.15/6.39 ( ^[V_5:$i]: ( X134 ) ) ) ) => 46.15/6.39 ( X134 ) ) ) => 46.15/6.39 ( ( ![X138:$i]: 46.15/6.39 ( ( in @ X138 @ emptyset ) => 46.15/6.39 ( ![X140:$o]: ( X140 ) ) ) ) => 46.15/6.39 ( ( ![X142:$i]: 46.15/6.39 ( ~( in @ X142 @ emptyset ) ) ) => 46.15/6.39 ( ( ![X144:$i]: 46.15/6.39 ( ~( in @ X144 @ emptyset ) ) ) => 46.15/6.39 ( ( ![X146:( $i > $o )]: 46.15/6.39 ( ( ?[X148:$i]: 46.15/6.39 ( ( X146 @ X148 ) & 46.15/6.39 ( ![X150:$i]: 46.15/6.39 ( ( X146 @ X150 ) => 46.15/6.39 ( ( X148 ) = ( X150 ) ) ) ) ) ) => 46.15/6.39 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) => 46.15/6.39 ( ( ![X154:$i,X156:$i]: 46.15/6.39 ( ( ![X158:$i]: 46.15/6.39 ( ( in @ X158 @ X154 ) => 46.15/6.39 ( in @ X158 @ X156 ) ) ) => 46.15/6.39 ( ( ![X160:$i]: 46.15/6.39 ( ( in @ X160 @ X156 ) => 46.15/6.39 ( in @ X160 @ X154 ) ) ) => 46.15/6.39 ( ( X154 ) = ( X156 ) ) ) ) ) => 46.15/6.39 ( ( ![X162:$i]: 46.15/6.39 ( ( ![X164:$i]: 46.15/6.39 ( ~( in @ X164 @ X162 ) ) ) => 46.15/6.39 ( ( X162 ) = ( emptyset ) ) ) ) => 46.15/6.39 ( ( ![X166:$i]: 46.15/6.39 ( ( ![X168:$i]: 46.15/6.39 ( ~( in @ X168 @ X166 ) ) ) => 46.15/6.39 ( ( X166 ) = 46.15/6.39 ( emptyset ) ) ) ) => 46.15/6.39 ( ( ![X170:$i, 46.15/6.39 X172:( $i > $o ), 46.15/6.39 X174:$i]: 46.15/6.39 ( ( in @ X174 @ X170 ) => 46.15/6.39 ( ( in @ 46.15/6.39 X174 @ 46.15/6.39 ( dsetconstr @ 46.15/6.39 X170 @ 46.15/6.39 ( ^[V_6:$i]: 46.15/6.39 ( X172 @ V_6 ) ) ) ) <=> 46.15/6.39 ( X172 @ X174 ) ) ) ) => 46.15/6.39 ( ( ![X176:$i]: 46.15/6.39 ( ( ( X176 ) != 46.15/6.39 ( emptyset ) ) => 46.15/6.39 ( ?[X178:$i]: 46.15/6.39 ( in @ X178 @ X176 ) ) ) ) => 46.15/6.39 ( ( ![X180:$i, 46.15/6.39 X182:( $i > $o ), 46.15/6.39 X184:$i]: 46.15/6.39 ( ( in @ X184 @ X180 ) => 46.15/6.39 ( ( X182 @ X184 ) => 46.15/6.39 ( ( dsetconstr @ 46.15/6.39 X180 @ 46.15/6.39 ( ^[ 46.15/6.39 V_7:$i]: 46.15/6.39 ( 46.15/6.39 X182 @ V_7 ) ) ) != 46.15/6.39 ( emptyset ) ) ) ) ) => 46.15/6.39 ( ( ![X186:$i]: 46.15/6.39 ( ( ?[X188:$i]: 46.15/6.39 ( in @ 46.15/6.39 X188 @ X186 ) ) => 46.15/6.39 ( ( X186 ) != 46.15/6.39 ( emptyset ) ) ) ) => 46.15/6.39 ( ( ![X190:$i, 46.15/6.39 X192:$i]: 46.15/6.39 ( in @ 46.15/6.39 X190 @ 46.15/6.39 ( setadjoin @ 46.15/6.39 X190 @ X192 ) ) ) => 46.15/6.39 ( ( in @ 46.15/6.39 emptyset @ 46.15/6.39 ( setadjoin @ 46.15/6.39 emptyset @ 46.15/6.39 emptyset ) ) => 46.15/6.39 ( ( ![X194:$i, 46.15/6.39 X196:$i, 46.15/6.39 X198:$i]: 46.15/6.39 ( ( 46.15/6.39 in @ 46.15/6.39 X198 @ 46.15/6.39 X196 ) => 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 X198 @ 46.15/6.39 ( 46.15/6.39 setadjoin 46.15/6.39 @ 46.15/6.39 X194 @ 46.15/6.39 X196 ) ) ) ) => 46.15/6.39 ( ( ![ 46.15/6.39 X200:$i, 46.15/6.39 X202:$i, 46.15/6.39 X204:$i]: 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 X204 @ 46.15/6.39 ( 46.15/6.39 setadjoin 46.15/6.39 @ 46.15/6.39 X200 @ 46.15/6.39 X202 ) ) => 46.15/6.39 ( 46.15/6.39 ![ 46.15/6.39 X206:$o]: 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 X204 ) = 46.15/6.39 ( 46.15/6.39 X200 ) ) => 46.15/6.39 ( 46.15/6.39 X206 ) ) => 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 X204 @ 46.15/6.39 X202 ) => 46.15/6.39 ( 46.15/6.39 X206 ) ) => 46.15/6.39 ( 46.15/6.39 X206 ) ) ) ) ) ) => 46.15/6.39 ( ( 46.15/6.39 ![ 46.15/6.39 X208:$i, 46.15/6.39 X210:$i, 46.15/6.39 X212:$i]: 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 X212 @ 46.15/6.39 ( 46.15/6.39 setadjoin 46.15/6.39 @ 46.15/6.39 X208 @ 46.15/6.39 X210 ) ) => 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 X212 @ 46.15/6.39 X210 ) | 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 X212 ) = 46.15/6.39 ( 46.15/6.39 X208 ) ) ) ) ) => 46.15/6.39 ( 46.15/6.39 ![ 46.15/6.39 X214:$i]: 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 dsetconstr 46.15/6.39 @ 46.15/6.39 X214 @ 46.15/6.39 ( 46.15/6.39 ^[ 46.15/6.39 V_8:$i]: 46.15/6.39 ( 46.15/6.39 $true ) ) ) = 46.15/6.39 ( 46.15/6.39 X214 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 46.15/6.39 thf(zf_stmt_1, negated_conjecture, 46.15/6.39 (~( ( ![X4:$i,X6:$i]: 46.15/6.39 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) => 46.15/6.39 ( ( X4 ) = ( X6 ) ) ) ) => 46.15/6.39 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) => 46.15/6.39 ( ( ![X12:$i,X14:$i,X16:$i]: 46.15/6.39 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=> 46.15/6.39 ( ( in @ X16 @ X14 ) | ( ( X16 ) = ( X12 ) ) ) ) ) => 46.15/6.39 ( ( ![X18:$i,X20:$i]: 46.15/6.39 ( ( in @ X20 @ ( powerset @ X18 ) ) <=> 46.15/6.39 ( ![X22:$i]: ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ) ) ) => 46.15/6.39 ( ( ![X24:$i,X26:$i]: 46.15/6.39 ( ( in @ X26 @ ( setunion @ X24 ) ) <=> 46.15/6.39 ( ?[X28:$i]: ( ( in @ X26 @ X28 ) & ( in @ X28 @ X24 ) ) ) ) ) => 46.15/6.39 ( ( in @ emptyset @ omega ) => 46.15/6.39 ( ( ![X30:$i]: 46.15/6.39 ( ( in @ X30 @ omega ) => 46.15/6.39 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) => 46.15/6.39 ( ( ![X32:$i]: 46.15/6.39 ( ( ( ![X34:$i]: 46.15/6.39 ( ( ( in @ X34 @ X32 ) & ( in @ X34 @ omega ) ) => 46.15/6.39 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) & 46.15/6.39 ( in @ emptyset @ X32 ) ) => 46.15/6.39 ( ![X36:$i]: 46.15/6.39 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) => 46.15/6.39 ( ( ![X38:( $i > $i > $o ),X40:$i]: 46.15/6.39 ( ( ![X42:$i]: 46.15/6.39 ( ( in @ X42 @ X40 ) => 46.15/6.39 ( ?[X44:$i]: 46.15/6.39 ( ( X38 @ X42 @ X44 ) & 46.15/6.39 ( ![X46:$i]: 46.15/6.39 ( ( X38 @ X42 @ X46 ) => 46.15/6.39 ( ( X44 ) = ( X46 ) ) ) ) ) ) ) ) => 46.15/6.39 ( ?[X48:$i]: 46.15/6.39 ( ![X50:$i]: 46.15/6.39 ( ( in @ X50 @ X48 ) <=> 46.15/6.39 ( ?[X52:$i]: 46.15/6.39 ( ( in @ X52 @ X40 ) & ( X38 @ X52 @ X50 ) ) ) ) ) ) ) ) => 46.15/6.39 ( ( ![X54:$i]: 46.15/6.39 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) => 46.15/6.39 ( ?[X58:$i]: 46.15/6.39 ( ( in @ X58 @ X54 ) & 46.15/6.39 ( ~( ?[X60:$i]: 46.15/6.39 ( ( in @ X60 @ X58 ) & 46.15/6.39 ( in @ X60 @ X54 ) ) ) ) ) ) ) ) => 46.15/6.39 ( ( ![X62:$i]: 46.15/6.39 ( ?[X64:$i]: 46.15/6.39 ( ( ![X96:$i]: 46.15/6.39 ( ( in @ X96 @ X64 ) => 46.15/6.39 ( ![X98:$i]: 46.15/6.39 ( ( in @ X98 @ X96 ) => 46.15/6.39 ( in @ X98 @ X62 ) ) ) ) ) & 46.15/6.39 ( ![X90:$i,X92:$i]: 46.15/6.39 ( ( ( in @ X92 @ X62 ) & ( in @ X90 @ X62 ) ) => 46.15/6.39 ( ( ![X94:$i]: 46.15/6.39 ( ( in @ X94 @ X64 ) => 46.15/6.39 ( ( in @ X90 @ X94 ) <=> 46.15/6.39 ( in @ X92 @ X94 ) ) ) ) => 46.15/6.39 ( ( X90 ) = ( X92 ) ) ) ) ) & 46.15/6.39 ( ![X82:$i,X84:$i]: 46.15/6.39 ( ( ( in @ X84 @ X64 ) & ( in @ X82 @ X64 ) ) => 46.15/6.39 ( ( ![X88:$i]: 46.15/6.39 ( ( in @ X88 @ X84 ) => 46.15/6.39 ( in @ X88 @ X82 ) ) ) | 46.15/6.39 ( ![X86:$i]: 46.15/6.39 ( ( in @ X86 @ X82 ) => 46.15/6.39 ( in @ X86 @ X84 ) ) ) ) ) ) & 46.15/6.39 ( ![X66:$i]: 46.15/6.39 ( ( ( ?[X70:$i]: ( in @ X70 @ X66 ) ) & 46.15/6.39 ( ![X68:$i]: 46.15/6.39 ( ( in @ X68 @ X66 ) => 46.15/6.39 ( in @ X68 @ X62 ) ) ) ) => 46.15/6.39 ( ?[X72:$i,X74:$i]: 46.15/6.39 ( ( in @ X72 @ X64 ) & 46.15/6.39 ( in @ X74 @ X66 ) & 46.15/6.39 ( ~( ?[X80:$i]: 46.15/6.39 ( ( in @ X80 @ X72 ) & 46.15/6.39 ( in @ X80 @ X66 ) ) ) ) & 46.15/6.39 ( ![X76:$i]: 46.15/6.39 ( ( in @ X76 @ X64 ) => 46.15/6.39 ( ( in @ X74 @ X76 ) | 46.15/6.39 ( ![X78:$i]: 46.15/6.39 ( ( in @ X78 @ X76 ) => 46.15/6.39 ( in @ X78 @ X72 ) ) ) ) ) ) ) ) ) ) ) ) ) => 46.15/6.39 ( ( ![X100:( $i > $o )]: 46.15/6.39 ( ( ?[X102:$i]: 46.15/6.39 ( ( X100 @ X102 ) & 46.15/6.39 ( ![X104:$i]: 46.15/6.39 ( ( X100 @ X104 ) => 46.15/6.39 ( ( X102 ) = ( X104 ) ) ) ) ) ) => 46.15/6.39 ( X100 @ 46.15/6.39 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) => 46.15/6.39 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]: 46.15/6.39 ( ( in @ X110 @ X106 ) => 46.15/6.39 ( ( X108 @ X110 ) => 46.15/6.39 ( in @ 46.15/6.39 X110 @ 46.15/6.39 ( dsetconstr @ 46.15/6.39 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) => 46.15/6.39 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]: 46.15/6.39 ( ( in @ 46.15/6.39 X116 @ 46.15/6.39 ( dsetconstr @ 46.15/6.39 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) => 46.15/6.39 ( in @ X116 @ X112 ) ) ) => 46.15/6.39 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]: 46.15/6.39 ( ( in @ 46.15/6.39 X122 @ 46.15/6.39 ( dsetconstr @ 46.15/6.39 X118 @ 46.15/6.39 ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) => 46.15/6.39 ( X120 @ X122 ) ) ) => 46.15/6.39 ( ( ![X124:( $i > $o )]: 46.15/6.39 ( ( ?[X126:$i]: 46.15/6.39 ( ( X124 @ X126 ) & 46.15/6.39 ( ![X128:$i]: 46.15/6.39 ( ( X124 @ X128 ) => 46.15/6.39 ( ( X126 ) = ( X128 ) ) ) ) ) ) => 46.15/6.39 ( ?[X130:$i]: 46.15/6.39 ( ( X124 @ X130 ) & 46.15/6.39 ( ![X132:$i]: 46.15/6.39 ( ( X124 @ X132 ) => 46.15/6.39 ( ( X130 ) = ( X132 ) ) ) ) ) ) ) ) => 46.15/6.39 ( ( ![X134:$o,X136:$i]: 46.15/6.39 ( ( in @ 46.15/6.39 X136 @ 46.15/6.39 ( dsetconstr @ 46.15/6.39 ( powerset @ emptyset ) @ 46.15/6.39 ( ^[V_5:$i]: ( X134 ) ) ) ) => 46.15/6.39 ( X134 ) ) ) => 46.15/6.39 ( ( ![X138:$i]: 46.15/6.39 ( ( in @ X138 @ emptyset ) => 46.15/6.39 ( ![X140:$o]: ( X140 ) ) ) ) => 46.15/6.39 ( ( ![X142:$i]: 46.15/6.39 ( ~( in @ X142 @ emptyset ) ) ) => 46.15/6.39 ( ( ![X144:$i]: 46.15/6.39 ( ~( in @ X144 @ emptyset ) ) ) => 46.15/6.39 ( ( ![X146:( $i > $o )]: 46.15/6.39 ( ( ?[X148:$i]: 46.15/6.39 ( ( X146 @ X148 ) & 46.15/6.39 ( ![X150:$i]: 46.15/6.39 ( ( X146 @ X150 ) => 46.15/6.39 ( ( X148 ) = 46.15/6.39 ( X150 ) ) ) ) ) ) => 46.15/6.39 ( ?[X152:$i]: 46.15/6.39 ( X146 @ X152 ) ) ) ) => 46.15/6.39 ( ( ![X154:$i,X156:$i]: 46.15/6.39 ( ( ![X158:$i]: 46.15/6.39 ( ( in @ X158 @ X154 ) => 46.15/6.39 ( in @ X158 @ X156 ) ) ) => 46.15/6.39 ( ( ![X160:$i]: 46.15/6.39 ( ( in @ X160 @ X156 ) => 46.15/6.39 ( in @ X160 @ X154 ) ) ) => 46.15/6.39 ( ( X154 ) = ( X156 ) ) ) ) ) => 46.15/6.39 ( ( ![X162:$i]: 46.15/6.39 ( ( ![X164:$i]: 46.15/6.39 ( ~( in @ X164 @ X162 ) ) ) => 46.15/6.39 ( ( X162 ) = 46.15/6.39 ( emptyset ) ) ) ) => 46.15/6.39 ( ( ![X166:$i]: 46.15/6.39 ( ( ![X168:$i]: 46.15/6.39 ( ~( in @ 46.15/6.39 X168 @ X166 ) ) ) => 46.15/6.39 ( ( X166 ) = 46.15/6.39 ( emptyset ) ) ) ) => 46.15/6.39 ( ( ![X170:$i, 46.15/6.39 X172:( $i > $o ), 46.15/6.39 X174:$i]: 46.15/6.39 ( ( in @ X174 @ X170 ) => 46.15/6.39 ( ( in @ 46.15/6.39 X174 @ 46.15/6.39 ( dsetconstr @ 46.15/6.39 X170 @ 46.15/6.39 ( ^[V_6:$i]: 46.15/6.39 ( X172 @ 46.15/6.39 V_6 ) ) ) ) <=> 46.15/6.39 ( X172 @ X174 ) ) ) ) => 46.15/6.39 ( ( ![X176:$i]: 46.15/6.39 ( ( ( X176 ) != 46.15/6.39 ( emptyset ) ) => 46.15/6.39 ( ?[X178:$i]: 46.15/6.39 ( in @ 46.15/6.39 X178 @ X176 ) ) ) ) => 46.15/6.39 ( ( ![X180:$i, 46.15/6.39 X182:( 46.15/6.39 $i > $o ), 46.15/6.39 X184:$i]: 46.15/6.39 ( ( in @ 46.15/6.39 X184 @ X180 ) => 46.15/6.39 ( ( X182 @ X184 ) => 46.15/6.39 ( ( dsetconstr 46.15/6.39 @ 46.15/6.39 X180 @ 46.15/6.39 ( 46.15/6.39 ^[ 46.15/6.39 V_7:$i]: 46.15/6.39 ( 46.15/6.39 X182 @ 46.15/6.39 V_7 ) ) ) != 46.15/6.39 ( emptyset ) ) ) ) ) => 46.15/6.39 ( ( ![X186:$i]: 46.15/6.39 ( ( ?[X188:$i]: 46.15/6.39 ( in @ 46.15/6.39 X188 @ 46.15/6.39 X186 ) ) => 46.15/6.39 ( ( X186 ) != 46.15/6.39 ( emptyset ) ) ) ) => 46.15/6.39 ( ( ![X190:$i, 46.15/6.39 X192:$i]: 46.15/6.39 ( in @ 46.15/6.39 X190 @ 46.15/6.39 ( setadjoin 46.15/6.39 @ 46.15/6.39 X190 @ 46.15/6.39 X192 ) ) ) => 46.15/6.39 ( ( in @ 46.15/6.39 emptyset @ 46.15/6.39 ( setadjoin 46.15/6.39 @ 46.15/6.39 emptyset @ 46.15/6.39 emptyset ) ) => 46.15/6.39 ( ( ![ 46.15/6.39 X194:$i, 46.15/6.39 X196:$i, 46.15/6.39 X198:$i]: 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 X198 @ 46.15/6.39 X196 ) => 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 X198 @ 46.15/6.39 ( 46.15/6.39 setadjoin 46.15/6.39 @ 46.15/6.39 X194 @ 46.15/6.39 X196 ) ) ) ) => 46.15/6.39 ( ( 46.15/6.39 ![ 46.15/6.39 X200:$i, 46.15/6.39 X202:$i, 46.15/6.39 X204:$i]: 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 X204 @ 46.15/6.39 ( 46.15/6.39 setadjoin 46.15/6.39 @ 46.15/6.39 X200 @ 46.15/6.39 X202 ) ) => 46.15/6.39 ( 46.15/6.39 ![ 46.15/6.39 X206:$o]: 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 X204 ) = 46.15/6.39 ( 46.15/6.39 X200 ) ) => 46.15/6.39 ( 46.15/6.39 X206 ) ) => 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 X204 @ 46.15/6.39 X202 ) => 46.15/6.39 ( 46.15/6.39 X206 ) ) => 46.15/6.39 ( 46.15/6.39 X206 ) ) ) ) ) ) => 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 ![ 46.15/6.39 X208:$i, 46.15/6.39 X210:$i, 46.15/6.39 X212:$i]: 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 X212 @ 46.15/6.39 ( 46.15/6.39 setadjoin 46.15/6.39 @ 46.15/6.39 X208 @ 46.15/6.39 X210 ) ) => 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 X212 @ 46.15/6.39 X210 ) | 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 X212 ) = 46.15/6.39 ( 46.15/6.39 X208 ) ) ) ) ) => 46.15/6.39 ( 46.15/6.39 ![ 46.15/6.39 X214:$i]: 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 dsetconstr 46.15/6.39 @ 46.15/6.39 X214 @ 46.15/6.39 ( 46.15/6.39 ^[ 46.15/6.39 V_8:$i]: 46.15/6.39 ( 46.15/6.39 $true ) ) ) = 46.15/6.39 ( 46.15/6.39 X214 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 46.15/6.39 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 46.15/6.39 thf(zip_derived_cl0, plain, 46.15/6.39 (~ (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ Y0) <=> (in @ 46.15/6.39 Y2 @ Y1)))))) => 46.15/6.39 (((Y0) = (Y1))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 (setadjoin @ Y0 @ Y1)) <=> 46.15/6.39 (((in @ Y2 @ Y1) | 46.15/6.39 (((Y2) = (Y0)))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ (powerset @ Y0)) <=> 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ Y1) => 46.15/6.39 (in @ Y2 @ Y0)))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ (setunion @ Y0)) <=> 46.15/6.39 (((??) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y1 @ Y2) & 46.15/6.39 (in @ Y2 @ Y0)))))))))))))) => 46.15/6.39 (((in @ emptyset @ omega) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((in @ Y0 @ omega) => (in @ 46.15/6.39 (setadjoin @ Y0 @ Y0) @ omega)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((in @ Y1 @ Y0) & 46.15/6.39 (in @ Y1 @ omega))) => 46.15/6.39 (in @ 46.15/6.39 (setadjoin @ Y1 @ Y1) @ 46.15/6.39 Y0)))))) & 46.15/6.39 (in @ emptyset @ Y0))) => 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ omega) => 46.15/6.39 (in @ Y1 @ Y0))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $i > $o]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2 @ 46.15/6.39 Y3) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2 @ 46.15/6.39 Y4) => 46.15/6.39 (( 46.15/6.39 (Y3) = 46.15/6.39 (Y4)))))))))))))))))) => 46.15/6.39 (((??) @ (^[Y2 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) <=> 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y1) & 46.15/6.39 (Y0 @ 46.15/6.39 Y4 @ Y3)))))))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ Y0) & 46.15/6.39 (((~) @ (((??) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0)))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y0))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y0) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y4) <=> 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y4)))))))) => 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y3))))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y1) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y1))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y3) => 46.15/6.39 (in @ 46.15/6.39 Y4 @ Y2)))))) | 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y4 @ Y3)))))))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y2)))) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y0)))))))) => 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 Y3 @ Y1) & 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 Y4 @ Y2) & 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 (~) @ ( 46.15/6.39 ( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y5 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y5 @ 46.15/6.39 Y3) & 46.15/6.39 (in @ 46.15/6.39 Y5 @ Y2)))))))) & 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y5 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y5 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y5) | 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y6 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y6 @ 46.15/6.39 Y5) => 46.15/6.39 (in @ 46.15/6.39 Y6 @ Y3)))))))))))))))))))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: 46.15/6.39 (((Y0 @ Y1) & 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (((Y0 @ Y2) => 46.15/6.39 (((Y1) = 46.15/6.39 (Y2))))))))))))) => 46.15/6.39 (Y0 @ 46.15/6.39 (descr @ (^[Y1 : $i]: (Y0 @ Y1))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (Y1 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (Y1 @ Y3))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 (^[Y3 : $i]: 46.15/6.39 (Y1 @ Y3)))) => 46.15/6.39 (in @ Y2 @ 46.15/6.39 Y0)))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (((in @ 46.15/6.39 Y2 @ 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (Y1 @ Y3)))) => 46.15/6.39 (Y1 @ Y2)))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: 46.15/6.39 (((Y0 @ 46.15/6.39 Y1) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (Y1) = 46.15/6.39 (Y2))))))))))))) => 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((Y0 @ 46.15/6.39 Y1) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (Y1) = 46.15/6.39 (Y2)))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $o]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ 46.15/6.39 Y1 @ 46.15/6.39 (dsetconstr @ 46.15/6.39 ( 46.15/6.39 powerset @ 46.15/6.39 emptyset) @ 46.15/6.39 ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (Y0)))) => 46.15/6.39 (Y0))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((in @ Y0 @ 46.15/6.39 emptyset) => 46.15/6.39 (((!!) @ (^[Y1 : $o]: 46.15/6.39 (Y1))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((~) @ (in @ Y0 @ 46.15/6.39 emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((~) @ (in @ 46.15/6.39 Y0 @ 46.15/6.39 emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.39 (((((??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y1) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (Y1) = 46.15/6.39 (Y2))))))))))))) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (Y0 @ Y1))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y1)))))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0)))))) => 46.15/6.39 (( 46.15/6.39 (Y0) = 46.15/6.39 (Y1))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (~) @ ( 46.15/6.39 in @ 46.15/6.39 Y1 @ Y0)))))) => 46.15/6.39 (( 46.15/6.39 (Y0) = 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (~) @ ( 46.15/6.39 in @ 46.15/6.39 Y1 @ Y0)))))) => 46.15/6.39 (( 46.15/6.39 (Y0) = 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i > $o]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (Y1 @ Y3)))) <=> 46.15/6.39 (Y1 @ Y2)))))))))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (((((Y0) != 46.15/6.39 (emptyset))) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y1 @ Y0))))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y1 : $i > $o]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (Y1 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (Y1 @ Y3))) != 46.15/6.39 (emptyset)))))))))))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y1 @ Y0)))) => 46.15/6.39 (( 46.15/6.39 (Y0) != 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y0 @ 46.15/6.39 (setadjoin @ 46.15/6.39 Y0 @ Y1)))))))) => 46.15/6.39 (((in @ 46.15/6.39 emptyset @ 46.15/6.39 (setadjoin @ 46.15/6.39 emptyset @ 46.15/6.39 emptyset)) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1))))))))))))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $o]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y0))) => 46.15/6.39 (Y3))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (Y3))) => 46.15/6.39 (Y3))))))))))))))))))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) | 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y0)))))))))))))))) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 ($true))) = 46.15/6.39 (Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 46.15/6.39 inference('cnf', [status(esa)], [zf_stmt_1])). 46.15/6.39 thf(zip_derived_cl1, plain, 46.15/6.39 (~ (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ Y0) <=> (in @ 46.15/6.39 Y2 @ Y1)))))) => 46.15/6.39 (((Y0) = (Y1))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 (setadjoin @ Y0 @ Y1)) <=> 46.15/6.39 (((in @ Y2 @ Y1) | 46.15/6.39 (((Y2) = (Y0)))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ (powerset @ Y0)) <=> 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ Y1) => 46.15/6.39 (in @ Y2 @ Y0)))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ (setunion @ Y0)) <=> 46.15/6.39 (((??) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y1 @ Y2) & 46.15/6.39 (in @ Y2 @ Y0)))))))))))))) => 46.15/6.39 (((in @ emptyset @ omega) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((in @ Y0 @ omega) => (in @ 46.15/6.39 (setadjoin @ Y0 @ Y0) @ omega)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((in @ Y1 @ Y0) & 46.15/6.39 (in @ Y1 @ omega))) => 46.15/6.39 (in @ 46.15/6.39 (setadjoin @ Y1 @ Y1) @ 46.15/6.39 Y0)))))) & 46.15/6.39 (in @ emptyset @ Y0))) => 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ omega) => 46.15/6.39 (in @ Y1 @ Y0))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $i > $o]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2 @ 46.15/6.39 Y3) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2 @ 46.15/6.39 Y4) => 46.15/6.39 (( 46.15/6.39 (Y3) = 46.15/6.39 (Y4)))))))))))))))))) => 46.15/6.39 (((??) @ (^[Y2 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) <=> 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y1) & 46.15/6.39 (Y0 @ 46.15/6.39 Y4 @ Y3)))))))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ Y0) & 46.15/6.39 (((~) @ (((??) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0)))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y0))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y0) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y4) <=> 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y4)))))))) => 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y3))))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y1) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y1))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y3) => 46.15/6.39 (in @ 46.15/6.39 Y4 @ Y2)))))) | 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y4 @ Y3)))))))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y2)))) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y0)))))))) => 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 Y3 @ Y1) & 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 Y4 @ Y2) & 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 (~) @ ( 46.15/6.39 ( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y5 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y5 @ 46.15/6.39 Y3) & 46.15/6.39 (in @ 46.15/6.39 Y5 @ Y2)))))))) & 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y5 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y5 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y5) | 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y6 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y6 @ 46.15/6.39 Y5) => 46.15/6.39 (in @ 46.15/6.39 Y6 @ Y3)))))))))))))))))))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: 46.15/6.39 (((Y0 @ Y1) & 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (((Y0 @ Y2) => 46.15/6.39 (((Y1) = 46.15/6.39 (Y2))))))))))))) => 46.15/6.39 (Y0 @ (descr @ Y0))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (Y1 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 dsetconstr @ 46.15/6.39 Y0 @ Y1))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (in @ Y2 @ 46.15/6.39 Y0)))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (((in @ 46.15/6.39 Y2 @ 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (Y1 @ Y2)))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: 46.15/6.39 (((Y0 @ 46.15/6.39 Y1) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (Y1) = 46.15/6.39 (Y2))))))))))))) => 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((Y0 @ 46.15/6.39 Y1) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (Y1) = 46.15/6.39 (Y2)))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $o]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ 46.15/6.39 Y1 @ 46.15/6.39 (dsetconstr @ 46.15/6.39 ( 46.15/6.39 powerset @ 46.15/6.39 emptyset) @ 46.15/6.39 ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (Y0)))) => 46.15/6.39 (Y0))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((in @ Y0 @ 46.15/6.39 emptyset) => 46.15/6.39 (((!!) @ (^[Y1 : $o]: 46.15/6.39 (Y1))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((~) @ (in @ Y0 @ 46.15/6.39 emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((~) @ (in @ 46.15/6.39 Y0 @ 46.15/6.39 emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.39 (((((??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y1) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (Y1) = 46.15/6.39 (Y2))))))))))))) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (Y0 @ Y1))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y1)))))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0)))))) => 46.15/6.39 (( 46.15/6.39 (Y0) = 46.15/6.39 (Y1))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (~) @ ( 46.15/6.39 in @ 46.15/6.39 Y1 @ Y0)))))) => 46.15/6.39 (( 46.15/6.39 (Y0) = 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (~) @ ( 46.15/6.39 in @ 46.15/6.39 Y1 @ Y0)))))) => 46.15/6.39 (( 46.15/6.39 (Y0) = 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i > $o]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 dsetconstr @ 46.15/6.39 Y0 @ Y1)) <=> 46.15/6.39 (Y1 @ Y2)))))))))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (((((Y0) != 46.15/6.39 (emptyset))) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y1 @ Y0))))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y1 : $i > $o]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (Y1 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 Y1) != 46.15/6.39 (emptyset)))))))))))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y1 @ Y0)))) => 46.15/6.39 (( 46.15/6.39 (Y0) != 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y0 @ 46.15/6.39 (setadjoin @ 46.15/6.39 Y0 @ Y1)))))))) => 46.15/6.39 (((in @ 46.15/6.39 emptyset @ 46.15/6.39 (setadjoin @ 46.15/6.39 emptyset @ 46.15/6.39 emptyset)) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1))))))))))))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $o]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y0))) => 46.15/6.39 (Y3))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (Y3))) => 46.15/6.39 (Y3))))))))))))))))))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) | 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y0)))))))))))))))) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 ($true))) = 46.15/6.39 (Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 46.15/6.39 inference('ho_norm', [status(thm)], [zip_derived_cl0])). 46.15/6.39 thf(zip_derived_cl2, plain, 46.15/6.39 (~ (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ Y0) <=> (in @ 46.15/6.39 Y2 @ Y1)))))) => 46.15/6.39 (((Y0) = (Y1))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 (setadjoin @ Y0 @ Y1)) <=> 46.15/6.39 (((in @ Y2 @ Y1) | 46.15/6.39 (((Y2) = (Y0)))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ (powerset @ Y0)) <=> 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ Y1) => 46.15/6.39 (in @ Y2 @ Y0)))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ (setunion @ Y0)) <=> 46.15/6.39 (((??) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y1 @ Y2) & 46.15/6.39 (in @ Y2 @ Y0)))))))))))))) => 46.15/6.39 (((in @ emptyset @ omega) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((in @ Y0 @ omega) => (in @ 46.15/6.39 (setadjoin @ Y0 @ Y0) @ omega)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((in @ Y1 @ Y0) & 46.15/6.39 (in @ Y1 @ omega))) => 46.15/6.39 (in @ 46.15/6.39 (setadjoin @ Y1 @ Y1) @ 46.15/6.39 Y0)))))) & 46.15/6.39 (in @ emptyset @ Y0))) => 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ omega) => 46.15/6.39 (in @ Y1 @ Y0))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $i > $o]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2 @ 46.15/6.39 Y3) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2 @ 46.15/6.39 Y4) => 46.15/6.39 (( 46.15/6.39 (Y3) = 46.15/6.39 (Y4)))))))))))))))))) => 46.15/6.39 (((??) @ (^[Y2 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) <=> 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y1) & 46.15/6.39 (Y0 @ 46.15/6.39 Y4 @ Y3)))))))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ Y0) & 46.15/6.39 (((~) @ (((??) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0)))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y0))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y0) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y4) <=> 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y4)))))))) => 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y3))))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y1) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y1))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y3) => 46.15/6.39 (in @ 46.15/6.39 Y4 @ Y2)))))) | 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y4 @ Y3)))))))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y2)))) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y0)))))))) => 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 Y3 @ Y1) & 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 Y4 @ Y2) & 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 (~) @ ( 46.15/6.39 ( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y5 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y5 @ 46.15/6.39 Y3) & 46.15/6.39 (in @ 46.15/6.39 Y5 @ Y2)))))))) & 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y5 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y5 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y5) | 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y6 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y6 @ 46.15/6.39 Y5) => 46.15/6.39 (in @ 46.15/6.39 Y6 @ Y3)))))))))))))))))))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: 46.15/6.39 (((Y0 @ Y1) & 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (((Y0 @ Y2) => 46.15/6.39 (((Y1) = 46.15/6.39 (Y2))))))))))))) => 46.15/6.39 (Y0 @ (descr @ Y0))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (Y1 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 dsetconstr @ 46.15/6.39 Y0 @ Y1))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (in @ Y2 @ 46.15/6.39 Y0)))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (((in @ 46.15/6.39 Y2 @ 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (Y1 @ Y2)))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $o]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ 46.15/6.39 (dsetconstr @ 46.15/6.39 (powerset @ 46.15/6.39 emptyset) @ 46.15/6.39 (^[Y2 : $i]: 46.15/6.39 (Y0)))) => 46.15/6.39 (Y0))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((in @ Y0 @ 46.15/6.39 emptyset) => 46.15/6.39 (((!!) @ (^[Y1 : $o]: 46.15/6.39 (Y1))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((~) @ (in @ Y0 @ 46.15/6.39 emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((~) @ (in @ Y0 @ 46.15/6.39 emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.39 (((((??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (((Y0 @ 46.15/6.39 Y1) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (Y1) = 46.15/6.39 (Y2))))))))))))) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (Y0 @ Y1))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (((( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y1)))))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0)))))) => 46.15/6.39 (( 46.15/6.39 (Y0) = 46.15/6.39 (Y1))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (~) @ ( 46.15/6.39 in @ 46.15/6.39 Y1 @ Y0)))))) => 46.15/6.39 (((Y0) = 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (~) @ ( 46.15/6.39 in @ 46.15/6.39 Y1 @ Y0)))))) => 46.15/6.39 (( 46.15/6.39 (Y0) = 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i > $o]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 dsetconstr @ 46.15/6.39 Y0 @ Y1)) <=> 46.15/6.39 (Y1 @ Y2)))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (Y0) != 46.15/6.39 (emptyset))) => 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y1 @ Y0))))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y1 : $i > $o]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (Y1 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 Y1) != 46.15/6.39 (emptyset)))))))))))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (((( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y1 @ Y0)))) => 46.15/6.39 (( 46.15/6.39 (Y0) != 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y0 @ 46.15/6.39 (setadjoin @ 46.15/6.39 Y0 @ Y1)))))))) => 46.15/6.39 (((in @ 46.15/6.39 emptyset @ 46.15/6.39 (setadjoin @ 46.15/6.39 emptyset @ 46.15/6.39 emptyset)) => 46.15/6.39 (((( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1))))))))))))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $o]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y0))) => 46.15/6.39 (Y3))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (Y3))) => 46.15/6.39 (Y3))))))))))))))))))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) | 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y0)))))))))))))))) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 ($true))) = 46.15/6.39 (Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 46.15/6.39 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl1])). 46.15/6.39 thf(zip_derived_cl4, plain, 46.15/6.39 (~ (((((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 (setadjoin @ Y0 @ Y1)) <=> 46.15/6.39 (((in @ Y2 @ Y1) | 46.15/6.39 (((Y2) = (Y0)))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ (powerset @ Y0)) <=> 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ Y1) => (in @ 46.15/6.39 Y2 @ Y0)))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ (setunion @ Y0)) <=> 46.15/6.39 (((??) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y1 @ Y2) & 46.15/6.39 (in @ Y2 @ Y0)))))))))))))) => 46.15/6.39 (((in @ emptyset @ omega) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((in @ Y0 @ omega) => (in @ 46.15/6.39 (setadjoin @ Y0 @ Y0) @ omega)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((in @ Y1 @ Y0) & (in @ 46.15/6.39 Y1 @ omega))) => 46.15/6.39 (in @ 46.15/6.39 (setadjoin @ Y1 @ Y1) @ 46.15/6.39 Y0)))))) & 46.15/6.39 (in @ emptyset @ Y0))) => 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ omega) => (in @ 46.15/6.39 Y1 @ Y0))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $i > $o]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2 @ 46.15/6.39 Y3) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2 @ 46.15/6.39 Y4) => 46.15/6.39 (( 46.15/6.39 (Y3) = 46.15/6.39 (Y4)))))))))))))))))) => 46.15/6.39 (((??) @ (^[Y2 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (((in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) <=> 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y1) & 46.15/6.39 (Y0 @ 46.15/6.39 Y4 @ Y3)))))))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ Y0) & 46.15/6.39 (((~) @ (((??) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (((in @ 46.15/6.39 Y2 @ Y1) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0)))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y0))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y0) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y4) <=> 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y4)))))))) => 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y3))))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y1) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y1))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y3) => 46.15/6.39 (in @ 46.15/6.39 Y4 @ Y2)))))) | 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y4 @ Y3)))))))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((( 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y2)))) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y0)))))))) => 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 Y3 @ Y1) & 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 Y4 @ Y2) & 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 (~) @ ( 46.15/6.39 ( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y5 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y5 @ 46.15/6.39 Y3) & 46.15/6.39 (in @ 46.15/6.39 Y5 @ Y2)))))))) & 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y5 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y5 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y5) | 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y6 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y6 @ 46.15/6.39 Y5) => 46.15/6.39 (in @ 46.15/6.39 Y6 @ Y3)))))))))))))))))))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: 46.15/6.39 (((Y0 @ Y1) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (Y1) = 46.15/6.39 (Y2))))))))))))) => 46.15/6.39 (Y0 @ (descr @ Y0))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (Y1 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 dsetconstr @ 46.15/6.39 Y0 @ Y1))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 dsetconstr @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0)))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (Y1 @ Y2)))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $o]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ 46.15/6.39 (dsetconstr @ 46.15/6.39 (powerset @ 46.15/6.39 emptyset) @ 46.15/6.39 (^[Y2 : $i]: 46.15/6.39 (Y0)))) => 46.15/6.39 (Y0))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((in @ Y0 @ emptyset) => 46.15/6.39 (((!!) @ (^[Y1 : $o]: 46.15/6.39 (Y1))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((~) @ (in @ Y0 @ 46.15/6.39 emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((~) @ (in @ Y0 @ 46.15/6.39 emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.39 (((((??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (((Y0 @ Y1) & 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (Y1) = 46.15/6.39 (Y2))))))))))))) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (Y0 @ Y1))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y1)))))) => 46.15/6.39 (((( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0)))))) => 46.15/6.39 (( 46.15/6.39 (Y0) = 46.15/6.39 (Y1))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (~) @ ( 46.15/6.39 in @ 46.15/6.39 Y1 @ Y0)))))) => 46.15/6.39 (((Y0) = 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (~) @ ( 46.15/6.39 in @ 46.15/6.39 Y1 @ Y0)))))) => 46.15/6.39 (((Y0) = 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y1 : $i > $o]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 dsetconstr @ 46.15/6.39 Y0 @ Y1)) <=> 46.15/6.39 (Y1 @ Y2)))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (Y0) != 46.15/6.39 (emptyset))) => 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y1 @ Y0))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i > $o]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (Y1 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 Y1) != 46.15/6.39 (emptyset)))))))))))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (((((??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y1 @ Y0)))) => 46.15/6.39 (((Y0) != 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y0 @ 46.15/6.39 (setadjoin @ 46.15/6.39 Y0 @ Y1)))))))) => 46.15/6.39 (((in @ 46.15/6.39 emptyset @ 46.15/6.39 (setadjoin @ 46.15/6.39 emptyset @ 46.15/6.39 emptyset)) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1))))))))))))) => 46.15/6.39 (((( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $o]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y0))) => 46.15/6.39 (Y3))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (Y3))) => 46.15/6.39 (Y3))))))))))))))))))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) | 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y0)))))))))))))))) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 ($true))) = 46.15/6.39 (Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 46.15/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 46.15/6.39 thf(zip_derived_cl7, plain, 46.15/6.39 (~ (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 (setadjoin @ Y0 @ Y1)) <=> 46.15/6.39 (((in @ Y2 @ Y1) | 46.15/6.39 (((Y2) = (Y0)))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ (powerset @ Y0)) <=> 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ Y1) => (in @ 46.15/6.39 Y2 @ Y0)))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ (setunion @ Y0)) <=> 46.15/6.39 (((??) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y1 @ Y2) & (in @ 46.15/6.39 Y2 @ Y0)))))))))))))) => 46.15/6.39 (((in @ emptyset @ omega) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((in @ Y0 @ omega) => (in @ 46.15/6.39 (setadjoin @ Y0 @ Y0) @ omega)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((in @ Y1 @ Y0) & (in @ 46.15/6.39 Y1 @ omega))) => 46.15/6.39 (in @ 46.15/6.39 (setadjoin @ Y1 @ Y1) @ Y0)))))) & 46.15/6.39 (in @ emptyset @ Y0))) => 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ omega) => (in @ 46.15/6.39 Y1 @ Y0))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $i > $o]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (((Y0 @ 46.15/6.39 Y2 @ Y3) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2 @ 46.15/6.39 Y4) => 46.15/6.39 (( 46.15/6.39 (Y3) = 46.15/6.39 (Y4)))))))))))))))))) => 46.15/6.39 (((??) @ (^[Y2 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (((in @ Y3 @ 46.15/6.39 Y2) <=> 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y1) & 46.15/6.39 (Y0 @ 46.15/6.39 Y4 @ Y3)))))))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ Y0) & 46.15/6.39 (((~) @ (((??) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 Y1) & (in @ 46.15/6.39 Y2 @ Y0)))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y0))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y0) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y4) <=> 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y4)))))))) => 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y3))))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y1) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y1))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y3) => 46.15/6.39 (in @ 46.15/6.39 Y4 @ Y2)))))) | 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y4 @ Y3)))))))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((((( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y2)))) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y0)))))))) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 Y3 @ Y1) & 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 Y4 @ Y2) & 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 (~) @ ( 46.15/6.39 ( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y5 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y5 @ 46.15/6.39 Y3) & 46.15/6.39 (in @ 46.15/6.39 Y5 @ Y2)))))))) & 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y5 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y5 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y5) | 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y6 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y6 @ 46.15/6.39 Y5) => 46.15/6.39 (in @ 46.15/6.39 Y6 @ Y3)))))))))))))))))))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: 46.15/6.39 (((Y0 @ Y1) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (Y1) = 46.15/6.39 (Y2))))))))))))) => 46.15/6.39 (Y0 @ (descr @ Y0))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (Y1 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ Y1))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 dsetconstr @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0)))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 dsetconstr @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (Y1 @ Y2)))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $o]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ 46.15/6.39 (dsetconstr @ 46.15/6.39 (powerset @ 46.15/6.39 emptyset) @ 46.15/6.39 (^[Y2 : $i]: 46.15/6.39 (Y0)))) => 46.15/6.39 (Y0))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((in @ Y0 @ emptyset) => 46.15/6.39 (((!!) @ (^[Y1 : $o]: (Y1))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((~) @ (in @ Y0 @ 46.15/6.39 emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((~) @ (in @ Y0 @ 46.15/6.39 emptyset)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y1) & 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (Y1) = 46.15/6.39 (Y2))))))))))))) => 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (Y0 @ Y1))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y1)))))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0)))))) => 46.15/6.39 (( 46.15/6.39 (Y0) = 46.15/6.39 (Y1))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (((~) @ ( 46.15/6.39 in @ Y1 @ 46.15/6.39 Y0)))))) => 46.15/6.39 (((Y0) = 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (~) @ ( 46.15/6.39 in @ 46.15/6.39 Y1 @ Y0)))))) => 46.15/6.39 (((Y0) = 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y1 : $i > $o]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 dsetconstr @ 46.15/6.39 Y0 @ Y1)) <=> 46.15/6.39 (Y1 @ Y2)))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((( 46.15/6.39 (Y0) != 46.15/6.39 (emptyset))) => 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y1 @ Y0))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i > $o]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y0) => 46.15/6.39 (( 46.15/6.39 (Y1 @ 46.15/6.39 Y2) => 46.15/6.39 (( 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 Y1) != 46.15/6.39 (emptyset)))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y1 @ Y0)))) => 46.15/6.39 (( 46.15/6.39 (Y0) != 46.15/6.39 (emptyset)))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y0 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1)))))))) => 46.15/6.39 (((in @ 46.15/6.39 emptyset @ 46.15/6.39 (setadjoin @ 46.15/6.39 emptyset @ 46.15/6.39 emptyset)) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1))))))))))))) => 46.15/6.39 (((((!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y3 : $o]: 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y0))) => 46.15/6.39 (Y3))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (Y3))) => 46.15/6.39 (Y3))))))))))))))))))) => 46.15/6.39 (((( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 ( 46.15/6.39 setadjoin @ 46.15/6.39 Y0 @ Y1)) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) | 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y0)))))))))))))))) => 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y0 : $i]: 46.15/6.39 (( 46.15/6.39 (dsetconstr @ 46.15/6.39 Y0 @ 46.15/6.39 ( 46.15/6.39 ^[Y1 : $i]: 46.15/6.39 ($true))) = 46.15/6.39 (Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 46.15/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 46.15/6.39 thf(zip_derived_cl11, plain, 46.15/6.39 (~ (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ (powerset @ Y0)) <=> 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ Y1) => (in @ 46.15/6.39 Y2 @ Y0)))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ (setunion @ Y0)) <=> 46.15/6.39 (((??) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y1 @ Y2) & (in @ 46.15/6.39 Y2 @ Y0)))))))))))))) => 46.15/6.39 (((in @ emptyset @ omega) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((in @ Y0 @ omega) => (in @ 46.15/6.39 (setadjoin @ Y0 @ Y0) @ omega)))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((in @ Y1 @ Y0) & (in @ Y1 @ 46.15/6.39 omega))) => 46.15/6.39 (in @ (setadjoin @ Y1 @ Y1) @ 46.15/6.39 Y0)))))) & 46.15/6.39 (in @ emptyset @ Y0))) => 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ omega) => (in @ Y1 @ 46.15/6.39 Y0))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i > $i > $o]: 46.15/6.39 (((!!) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ Y1) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (((Y0 @ Y2 @ 46.15/6.39 Y3) & 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (Y0 @ 46.15/6.39 Y2 @ 46.15/6.39 Y4) => 46.15/6.39 (( 46.15/6.39 (Y3) = 46.15/6.39 (Y4)))))))))))))))))) => 46.15/6.39 (((??) @ (^[Y2 : $i]: 46.15/6.39 (((!!) @ (^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) <=> 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y1) & 46.15/6.39 (Y0 @ 46.15/6.39 Y4 @ Y3)))))))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((in @ Y1 @ Y0) & 46.15/6.39 (((~) @ (((??) @ (^[Y2 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y1) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0)))))))))))))))))) => 46.15/6.39 (((((!!) @ (^[Y0 : $i]: 46.15/6.39 (((??) @ (^[Y1 : $i]: 46.15/6.39 (((((!!) @ (^[Y2 : $i]: 46.15/6.39 (((in @ Y2 @ 46.15/6.39 Y1) => 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y0))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (((( 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y0) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y0))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y1) => 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y2 @ 46.15/6.39 Y4) <=> 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y4)))))))) => 46.15/6.39 (( 46.15/6.39 (Y2) = 46.15/6.39 (Y3))))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (((( 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y1) & 46.15/6.39 (in @ 46.15/6.39 Y2 @ Y1))) => 46.15/6.39 (( 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y3) => 46.15/6.39 (in @ 46.15/6.39 Y4 @ Y2)))))) | 46.15/6.39 (( 46.15/6.39 (!!) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y4 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y4 @ Y3)))))))))))))))) & 46.15/6.39 (((!!) @ (^[Y2 : $i]: 46.15/6.39 (((((((??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y2)))) & 46.15/6.39 (((!!) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y3 @ 46.15/6.39 Y2) => 46.15/6.39 (in @ 46.15/6.39 Y3 @ Y0)))))))) => 46.15/6.39 (((??) @ ( 46.15/6.39 ^[Y3 : $i]: 46.15/6.39 (( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y4 : $i]: 46.15/6.39 (( 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 Y3 @ Y1) & 46.15/6.39 ( 46.15/6.39 in @ 46.15/6.39 Y4 @ Y2) & 46.15/6.39 ( 46.15/6.39 ( 46.15/6.39 (~) @ ( 46.15/6.39 ( 46.15/6.39 (??) @ ( 46.15/6.39 ^[Y5 : $i]: 46.15/6.39 (( 46.15/6.39 (in @ 46.15/6.39 Y5 @ 46.15/6.39 Y3) & 46.15/6.39 (in @ 46.15/6.40 Y5 @ Y2)))))))) & 46.15/6.40 ( 46.15/6.40 ( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y5 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y5 @ 46.15/6.40 Y1) => 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y4 @ 46.15/6.40 Y5) | 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y6 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y6 @ 46.15/6.40 Y5) => 46.15/6.40 (in @ 46.15/6.40 Y6 @ Y3)))))))))))))))))))))))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.40 (((((??) @ (^[Y1 : $i]: 46.15/6.40 (((Y0 @ Y1) & 46.15/6.40 (((!!) @ (^[Y2 : $i]: 46.15/6.40 (((Y0 @ 46.15/6.40 Y2) => 46.15/6.40 (( 46.15/6.40 (Y1) = 46.15/6.40 (Y2))))))))))))) => 46.15/6.40 (Y0 @ (descr @ Y0))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.40 (((!!) @ (^[Y2 : $i]: 46.15/6.40 (((in @ Y2 @ 46.15/6.40 Y0) => 46.15/6.40 (((Y1 @ 46.15/6.40 Y2) => 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 (dsetconstr @ 46.15/6.40 Y0 @ Y1))))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.40 (((!!) @ (^[Y2 : $i]: 46.15/6.40 (((in @ 46.15/6.40 Y2 @ 46.15/6.40 (dsetconstr @ 46.15/6.40 Y0 @ Y1)) => 46.15/6.40 (in @ 46.15/6.40 Y2 @ Y0)))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.40 (((!!) @ (^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 ( 46.15/6.40 dsetconstr @ 46.15/6.40 Y0 @ Y1)) => 46.15/6.40 (Y1 @ Y2)))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $o]: 46.15/6.40 (((!!) @ (^[Y1 : $i]: 46.15/6.40 (((in @ Y1 @ 46.15/6.40 (dsetconstr @ 46.15/6.40 (powerset @ 46.15/6.40 emptyset) @ 46.15/6.40 (^[Y2 : $i]: (Y0)))) => 46.15/6.40 (Y0))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((in @ Y0 @ emptyset) => 46.15/6.40 (((!!) @ (^[Y1 : $o]: (Y1))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((~) @ (in @ Y0 @ emptyset)))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((~) @ (in @ Y0 @ 46.15/6.40 emptyset)))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.40 (((((??) @ (^[Y1 : $i]: 46.15/6.40 (( 46.15/6.40 (Y0 @ 46.15/6.40 Y1) & 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (Y0 @ 46.15/6.40 Y2) => 46.15/6.40 (( 46.15/6.40 (Y1) = 46.15/6.40 (Y2))))))))))))) => 46.15/6.40 (((??) @ (^[Y1 : $i]: 46.15/6.40 (Y0 @ Y1))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((!!) @ (^[Y1 : $i]: 46.15/6.40 (( 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y0) => 46.15/6.40 (in @ 46.15/6.40 Y2 @ Y1)))))) => 46.15/6.40 (( 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y1) => 46.15/6.40 (in @ 46.15/6.40 Y2 @ Y0)))))) => 46.15/6.40 (( 46.15/6.40 (Y0) = 46.15/6.40 (Y1))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((((!!) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (((~) @ ( 46.15/6.40 in @ Y1 @ Y0)))))) => 46.15/6.40 (((Y0) = 46.15/6.40 (emptyset)))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((((!!) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (((~) @ ( 46.15/6.40 in @ Y1 @ 46.15/6.40 Y0)))))) => 46.15/6.40 (((Y0) = 46.15/6.40 (emptyset)))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y1 : $i > $o]: 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y0) => 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 ( 46.15/6.40 dsetconstr @ 46.15/6.40 Y0 @ Y1)) <=> 46.15/6.40 (Y1 @ Y2)))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((((Y0) != 46.15/6.40 (emptyset))) => 46.15/6.40 (((??) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (in @ 46.15/6.40 Y1 @ Y0))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y1 : $i > $o]: 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y0) => 46.15/6.40 (( 46.15/6.40 (Y1 @ 46.15/6.40 Y2) => 46.15/6.40 (( 46.15/6.40 (dsetconstr @ 46.15/6.40 Y0 @ 46.15/6.40 Y1) != 46.15/6.40 (emptyset)))))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (( 46.15/6.40 (( 46.15/6.40 (??) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (in @ 46.15/6.40 Y1 @ Y0)))) => 46.15/6.40 (( 46.15/6.40 (Y0) != 46.15/6.40 (emptyset)))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (in @ 46.15/6.40 Y0 @ 46.15/6.40 (setadjoin @ 46.15/6.40 Y0 @ Y1)))))))) => 46.15/6.40 (((in @ emptyset @ 46.15/6.40 (setadjoin @ 46.15/6.40 emptyset @ 46.15/6.40 emptyset)) => 46.15/6.40 (((((!!) @ ( 46.15/6.40 ^[Y0 : $i]: 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y1) => 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 ( 46.15/6.40 setadjoin @ 46.15/6.40 Y0 @ Y1))))))))))))) => 46.15/6.40 (((((!!) @ ( 46.15/6.40 ^[Y0 : $i]: 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 ( 46.15/6.40 setadjoin @ 46.15/6.40 Y0 @ Y1)) => 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y3 : $o]: 46.15/6.40 (( 46.15/6.40 (( 46.15/6.40 (( 46.15/6.40 (Y2) = 46.15/6.40 (Y0))) => 46.15/6.40 (Y3))) => 46.15/6.40 (( 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y1) => 46.15/6.40 (Y3))) => 46.15/6.40 (Y3))))))))))))))))))) => 46.15/6.40 (((((!!) @ ( 46.15/6.40 ^[Y0 : $i]: 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 ( 46.15/6.40 setadjoin @ 46.15/6.40 Y0 @ Y1)) => 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y1) | 46.15/6.40 (( 46.15/6.40 (Y2) = 46.15/6.40 (Y0)))))))))))))))) => 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y0 : $i]: 46.15/6.40 (( 46.15/6.40 (dsetconstr @ 46.15/6.40 Y0 @ 46.15/6.40 ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 ($true))) = 46.15/6.40 (Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 46.15/6.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 46.15/6.40 thf(zip_derived_cl15, plain, 46.15/6.40 (~ (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((!!) @ (^[Y1 : $i]: 46.15/6.40 (((in @ Y1 @ (setunion @ Y0)) <=> 46.15/6.40 (((??) @ (^[Y2 : $i]: 46.15/6.40 (((in @ Y1 @ Y2) & (in @ Y2 @ 46.15/6.40 Y0)))))))))))))) => 46.15/6.40 (((in @ emptyset @ omega) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((in @ Y0 @ omega) => (in @ 46.15/6.40 (setadjoin @ Y0 @ Y0) @ omega)))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((((((!!) @ (^[Y1 : $i]: 46.15/6.40 (((((in @ Y1 @ Y0) & (in @ Y1 @ 46.15/6.40 omega))) => 46.15/6.40 (in @ (setadjoin @ Y1 @ Y1) @ 46.15/6.40 Y0)))))) & 46.15/6.40 (in @ emptyset @ Y0))) => 46.15/6.40 (((!!) @ (^[Y1 : $i]: 46.15/6.40 (((in @ Y1 @ omega) => (in @ Y1 @ 46.15/6.40 Y0))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i > $i > $o]: 46.15/6.40 (((!!) @ (^[Y1 : $i]: 46.15/6.40 (((((!!) @ (^[Y2 : $i]: 46.15/6.40 (((in @ Y2 @ Y1) => 46.15/6.40 (((??) @ (^[Y3 : $i]: 46.15/6.40 (( 46.15/6.40 (Y0 @ 46.15/6.40 Y2 @ 46.15/6.40 Y3) & 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y4 : $i]: 46.15/6.40 (( 46.15/6.40 (Y0 @ 46.15/6.40 Y2 @ 46.15/6.40 Y4) => 46.15/6.40 (( 46.15/6.40 (Y3) = 46.15/6.40 (Y4)))))))))))))))))) => 46.15/6.40 (((??) @ (^[Y2 : $i]: 46.15/6.40 (((!!) @ (^[Y3 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y3 @ 46.15/6.40 Y2) <=> 46.15/6.40 (( 46.15/6.40 (??) @ ( 46.15/6.40 ^[Y4 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y4 @ 46.15/6.40 Y1) & 46.15/6.40 (Y0 @ 46.15/6.40 Y4 @ Y3)))))))))))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.15/6.40 (((??) @ (^[Y1 : $i]: 46.15/6.40 (((in @ Y1 @ Y0) & 46.15/6.40 (((~) @ (((??) @ (^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y1) & 46.15/6.40 (in @ 46.15/6.40 Y2 @ Y0)))))))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((??) @ (^[Y1 : $i]: 46.15/6.40 (((((!!) @ (^[Y2 : $i]: 46.15/6.40 (((in @ Y2 @ 46.15/6.40 Y1) => 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y3 : $i]: 46.15/6.40 (((in @ 46.15/6.40 Y3 @ 46.15/6.40 Y2) => 46.15/6.40 (in @ 46.15/6.40 Y3 @ Y0))))))))))) & 46.15/6.40 (((!!) @ (^[Y2 : $i]: 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y3 : $i]: 46.15/6.40 (((((in @ 46.15/6.40 Y3 @ Y0) & 46.15/6.40 (in @ 46.15/6.40 Y2 @ Y0))) => 46.15/6.40 (((( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y4 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y4 @ 46.15/6.40 Y1) => 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y4) <=> 46.15/6.40 (in @ 46.15/6.40 Y3 @ Y4)))))))) => 46.15/6.40 (( 46.15/6.40 (Y2) = 46.15/6.40 (Y3))))))))))))) & 46.15/6.40 (((!!) @ (^[Y2 : $i]: 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y3 : $i]: 46.15/6.40 (((((in @ 46.15/6.40 Y3 @ Y1) & 46.15/6.40 (in @ 46.15/6.40 Y2 @ Y1))) => 46.15/6.40 (((( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y4 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y4 @ 46.15/6.40 Y3) => 46.15/6.40 (in @ 46.15/6.40 Y4 @ Y2)))))) | 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y4 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y4 @ 46.15/6.40 Y2) => 46.15/6.40 (in @ 46.15/6.40 Y4 @ Y3)))))))))))))))) & 46.15/6.40 (((!!) @ (^[Y2 : $i]: 46.15/6.40 (((((((??) @ ( 46.15/6.40 ^[Y3 : $i]: 46.15/6.40 (in @ 46.15/6.40 Y3 @ Y2)))) & 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y3 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y3 @ 46.15/6.40 Y2) => 46.15/6.40 (in @ 46.15/6.40 Y3 @ Y0)))))))) => 46.15/6.40 (((??) @ ( 46.15/6.40 ^[Y3 : $i]: 46.15/6.40 (((??) @ ( 46.15/6.40 ^[Y4 : $i]: 46.15/6.40 (( 46.15/6.40 ( 46.15/6.40 in @ 46.15/6.40 Y3 @ Y1) & 46.15/6.40 ( 46.15/6.40 in @ 46.15/6.40 Y4 @ Y2) & 46.15/6.40 ( 46.15/6.40 ( 46.15/6.40 (~) @ ( 46.15/6.40 ( 46.15/6.40 (??) @ ( 46.15/6.40 ^[Y5 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y5 @ 46.15/6.40 Y3) & 46.15/6.40 (in @ 46.15/6.40 Y5 @ Y2)))))))) & 46.15/6.40 ( 46.15/6.40 ( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y5 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y5 @ 46.15/6.40 Y1) => 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y4 @ 46.15/6.40 Y5) | 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y6 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y6 @ 46.15/6.40 Y5) => 46.15/6.40 (in @ 46.15/6.40 Y6 @ Y3)))))))))))))))))))))))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.40 (((((??) @ (^[Y1 : $i]: 46.15/6.40 (((Y0 @ Y1) & 46.15/6.40 (((!!) @ (^[Y2 : $i]: 46.15/6.40 (((Y0 @ Y2) => 46.15/6.40 (((Y1) = 46.15/6.40 (Y2))))))))))))) => 46.15/6.40 (Y0 @ (descr @ Y0))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.40 (((!!) @ (^[Y2 : $i]: 46.15/6.40 (((in @ Y2 @ 46.15/6.40 Y0) => 46.15/6.40 (((Y1 @ Y2) => 46.15/6.40 (in @ Y2 @ 46.15/6.40 (dsetconstr @ 46.15/6.40 Y0 @ Y1))))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.40 (((!!) @ (^[Y2 : $i]: 46.15/6.40 (((in @ Y2 @ 46.15/6.40 (dsetconstr @ 46.15/6.40 Y0 @ Y1)) => 46.15/6.40 (in @ Y2 @ 46.15/6.40 Y0)))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((!!) @ (^[Y1 : $i > $o]: 46.15/6.40 (((!!) @ (^[Y2 : $i]: 46.15/6.40 (((in @ 46.15/6.40 Y2 @ 46.15/6.40 (dsetconstr @ 46.15/6.40 Y0 @ Y1)) => 46.15/6.40 (Y1 @ Y2)))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $o]: 46.15/6.40 (((!!) @ (^[Y1 : $i]: 46.15/6.40 (((in @ Y1 @ 46.15/6.40 (dsetconstr @ 46.15/6.40 (powerset @ 46.15/6.40 emptyset) @ 46.15/6.40 (^[Y2 : $i]: (Y0)))) => 46.15/6.40 (Y0))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((in @ Y0 @ emptyset) => 46.15/6.40 (((!!) @ (^[Y1 : $o]: (Y1))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((~) @ (in @ Y0 @ emptyset)))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((~) @ (in @ Y0 @ emptyset)))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i > $o]: 46.15/6.40 (((((??) @ (^[Y1 : $i]: 46.15/6.40 (((Y0 @ 46.15/6.40 Y1) & 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (Y0 @ 46.15/6.40 Y2) => 46.15/6.40 (( 46.15/6.40 (Y1) = 46.15/6.40 (Y2))))))))))))) => 46.15/6.40 (((??) @ (^[Y1 : $i]: 46.15/6.40 (Y0 @ Y1))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((!!) @ (^[Y1 : $i]: 46.15/6.40 (((( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y0) => 46.15/6.40 (in @ 46.15/6.40 Y2 @ Y1)))))) => 46.15/6.40 (( 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y1) => 46.15/6.40 (in @ 46.15/6.40 Y2 @ Y0)))))) => 46.15/6.40 (( 46.15/6.40 (Y0) = 46.15/6.40 (Y1))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((((!!) @ (^[Y1 : $i]: 46.15/6.40 (( 46.15/6.40 (~) @ ( 46.15/6.40 in @ 46.15/6.40 Y1 @ Y0)))))) => 46.15/6.40 (((Y0) = (emptyset)))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((((!!) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (((~) @ ( 46.15/6.40 in @ Y1 @ Y0)))))) => 46.15/6.40 (((Y0) = 46.15/6.40 (emptyset)))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y1 : $i > $o]: 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y0) => 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 ( 46.15/6.40 dsetconstr @ 46.15/6.40 Y0 @ Y1)) <=> 46.15/6.40 (Y1 @ Y2)))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((((Y0) != 46.15/6.40 (emptyset))) => 46.15/6.40 (((??) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (in @ 46.15/6.40 Y1 @ Y0))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y1 : $i > $o]: 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y0) => 46.15/6.40 (( 46.15/6.40 (Y1 @ 46.15/6.40 Y2) => 46.15/6.40 (( 46.15/6.40 (dsetconstr @ 46.15/6.40 Y0 @ 46.15/6.40 Y1) != 46.15/6.40 (emptyset)))))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((( 46.15/6.40 (??) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (in @ 46.15/6.40 Y1 @ Y0)))) => 46.15/6.40 (( 46.15/6.40 (Y0) != 46.15/6.40 (emptyset)))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (in @ 46.15/6.40 Y0 @ 46.15/6.40 (setadjoin @ 46.15/6.40 Y0 @ Y1)))))))) => 46.15/6.40 (((in @ emptyset @ 46.15/6.40 (setadjoin @ 46.15/6.40 emptyset @ emptyset)) => 46.15/6.40 (((((!!) @ ( 46.15/6.40 ^[Y0 : $i]: 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y1) => 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 ( 46.15/6.40 setadjoin @ 46.15/6.40 Y0 @ Y1))))))))))))) => 46.15/6.40 (((((!!) @ ( 46.15/6.40 ^[Y0 : $i]: 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 ( 46.15/6.40 setadjoin @ 46.15/6.40 Y0 @ Y1)) => 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y3 : $o]: 46.15/6.40 (( 46.15/6.40 (( 46.15/6.40 (( 46.15/6.40 (Y2) = 46.15/6.40 (Y0))) => 46.15/6.40 (Y3))) => 46.15/6.40 (( 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y1) => 46.15/6.40 (Y3))) => 46.15/6.40 (Y3))))))))))))))))))) => 46.15/6.40 (((((!!) @ ( 46.15/6.40 ^[Y0 : $i]: 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y2 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 ( 46.15/6.40 setadjoin @ 46.15/6.40 Y0 @ Y1)) => 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y2 @ 46.15/6.40 Y1) | 46.15/6.40 (( 46.15/6.40 (Y2) = 46.15/6.40 (Y0)))))))))))))))) => 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y0 : $i]: 46.15/6.40 (( 46.15/6.40 (dsetconstr @ 46.15/6.40 Y0 @ 46.15/6.40 ( 46.15/6.40 ^[Y1 : $i]: 46.15/6.40 ($true))) = 46.15/6.40 (Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 46.15/6.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 46.15/6.40 thf(zip_derived_cl21, plain, 46.15/6.40 (~ (((in @ emptyset @ omega) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ 46.15/6.40 omega)))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((((((!!) @ (^[Y1 : $i]: 46.15/6.40 (((((in @ Y1 @ Y0) & (in @ Y1 @ 46.15/6.40 omega))) => 46.15/6.40 (in @ (setadjoin @ Y1 @ Y1) @ Y0)))))) & 46.15/6.40 (in @ emptyset @ Y0))) => 46.15/6.40 (((!!) @ (^[Y1 : $i]: 46.15/6.40 (((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i > $i > $o]: 46.15/6.40 (((!!) @ (^[Y1 : $i]: 46.15/6.40 (((((!!) @ (^[Y2 : $i]: 46.15/6.40 (((in @ Y2 @ Y1) => 46.15/6.40 (((??) @ (^[Y3 : $i]: 46.15/6.40 (( 46.15/6.40 (Y0 @ 46.15/6.40 Y2 @ 46.15/6.40 Y3) & 46.15/6.40 (( 46.15/6.40 (!!) @ ( 46.15/6.40 ^[Y4 : $i]: 46.15/6.40 (( 46.15/6.40 (Y0 @ 46.15/6.40 Y2 @ 46.15/6.40 Y4) => 46.15/6.40 (( 46.15/6.40 (Y3) = 46.15/6.40 (Y4)))))))))))))))))) => 46.15/6.40 (((??) @ (^[Y2 : $i]: 46.15/6.40 (((!!) @ (^[Y3 : $i]: 46.15/6.40 (((in @ 46.15/6.40 Y3 @ 46.15/6.40 Y2) <=> 46.15/6.40 (( 46.15/6.40 (??) @ ( 46.15/6.40 ^[Y4 : $i]: 46.15/6.40 (( 46.15/6.40 (in @ 46.15/6.40 Y4 @ 46.15/6.40 Y1) & 46.15/6.40 (Y0 @ 46.15/6.40 Y4 @ Y3)))))))))))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.15/6.40 (((??) @ (^[Y1 : $i]: 46.15/6.40 (((in @ Y1 @ Y0) & 46.15/6.40 (((~) @ (((??) @ (^[Y2 : $i]: 46.15/6.40 (((in @ 46.15/6.40 Y2 @ Y1) & 46.15/6.40 (in @ 46.15/6.40 Y2 @ Y0)))))))))))))))))) => 46.15/6.40 (((((!!) @ (^[Y0 : $i]: 46.15/6.40 (((??) @ (^[Y1 : $i]: 46.15/6.40 (((((!!) @ (^[Y2 : $i]: 46.15/6.40 (((in @ Y2 @ Y1) => 46.15/6.40 (((!!) @ ( 46.15/6.40 ^[Y3 : $i]: 46.15/6.40 (((in @ Y3 @ 46.15/6.40 Y2) => 46.15/6.40 (in @ Y3 @ 46.15/6.40 Y0))))))))))) & 46.15/6.40 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y3 @ 46.36/6.41 Y0) & 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y0))) => 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y1) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y4) <=> 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y4)))))))) => 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y3))))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y3 @ 46.36/6.41 Y1) & 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y1))) => 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y3) => 46.36/6.41 (in @ 46.36/6.41 Y4 @ Y2)))))) | 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ 46.36/6.41 Y4 @ Y3)))))))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((((((??) @ ( 46.36/6.41 ^[Y3 : $i]: 46.36/6.41 (in @ Y3 @ 46.36/6.41 Y2)))) & 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y3 : $i]: 46.36/6.41 (((in @ 46.36/6.41 Y3 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y0)))))))) => 46.36/6.41 (((??) @ ( 46.36/6.41 ^[Y3 : $i]: 46.36/6.41 (((??) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 ( 46.36/6.41 in @ 46.36/6.41 Y3 @ Y1) & 46.36/6.41 ( 46.36/6.41 in @ 46.36/6.41 Y4 @ Y2) & 46.36/6.41 ( 46.36/6.41 ( 46.36/6.41 (~) @ ( 46.36/6.41 ( 46.36/6.41 (??) @ ( 46.36/6.41 ^[Y5 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y5 @ 46.36/6.41 Y3) & 46.36/6.41 (in @ 46.36/6.41 Y5 @ Y2)))))))) & 46.36/6.41 ( 46.36/6.41 ( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y5 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y5 @ 46.36/6.41 Y1) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y5) | 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y6 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y6 @ 46.36/6.41 Y5) => 46.36/6.41 (in @ 46.36/6.41 Y6 @ Y3)))))))))))))))))))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (((Y0 @ Y1) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((Y0 @ Y2) => 46.36/6.41 (((Y1) = (Y2))))))))))))) => 46.36/6.41 (Y0 @ (descr @ Y0))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (((Y1 @ Y2) => 46.36/6.41 (in @ Y2 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ Y1))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (in @ Y2 @ Y0)))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (Y1 @ Y2)))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $o]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((in @ Y1 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 (powerset @ emptyset) @ 46.36/6.41 (^[Y2 : $i]: (Y0)))) => 46.36/6.41 (Y0))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((in @ Y0 @ emptyset) => 46.36/6.41 (((!!) @ (^[Y1 : $o]: (Y1))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (((Y0 @ Y1) & 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (Y0 @ 46.36/6.41 Y2) => 46.36/6.41 (( 46.36/6.41 (Y1) = 46.36/6.41 (Y2))))))))))))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (Y0 @ Y1))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y1)))))) => 46.36/6.41 (((( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y0)))))) => 46.36/6.41 (( 46.36/6.41 (Y0) = 46.36/6.41 (Y1))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((!!) @ (^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (~) @ ( 46.36/6.41 in @ 46.36/6.41 Y1 @ Y0)))))) => 46.36/6.41 (((Y0) = (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((!!) @ (^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (~) @ ( 46.36/6.41 in @ 46.36/6.41 Y1 @ Y0)))))) => 46.36/6.41 (((Y0) = (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 dsetconstr @ 46.36/6.41 Y0 @ Y1)) <=> 46.36/6.41 (Y1 @ Y2)))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((Y0) != 46.36/6.41 (emptyset))) => 46.36/6.41 (((??) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (in @ Y1 @ 46.36/6.41 Y0))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (( 46.36/6.41 (Y1 @ 46.36/6.41 Y2) => 46.36/6.41 (( 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ 46.36/6.41 Y1) != 46.36/6.41 (emptyset)))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((??) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (in @ 46.36/6.41 Y1 @ Y0)))) => 46.36/6.41 (((Y0) != 46.36/6.41 (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (in @ 46.36/6.41 Y0 @ 46.36/6.41 (setadjoin @ 46.36/6.41 Y0 @ Y1)))))))) => 46.36/6.41 (((in @ emptyset @ 46.36/6.41 (setadjoin @ 46.36/6.41 emptyset @ emptyset)) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1))))))))))))) => 46.36/6.41 (((((!!) @ ( 46.36/6.41 ^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y3 : $o]: 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0))) => 46.36/6.41 (Y3))) => 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (Y3))) => 46.36/6.41 (Y3))))))))))))))))))) => 46.36/6.41 (((((!!) @ ( 46.36/6.41 ^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) | 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0)))))))))))))))) => 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y0 : $i]: 46.36/6.41 (((dsetconstr @ 46.36/6.41 Y0 @ 46.36/6.41 (^[Y1 : $i]: 46.36/6.41 ($true))) = 46.36/6.41 (Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 46.36/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl15])). 46.36/6.41 thf(zip_derived_cl27, plain, 46.36/6.41 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ 46.36/6.41 omega)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((((!!) @ (^[Y1 : $i]: 46.36/6.41 (((((in @ Y1 @ Y0) & (in @ Y1 @ omega))) => 46.36/6.41 (in @ (setadjoin @ Y1 @ Y1) @ Y0)))))) & 46.36/6.41 (in @ emptyset @ Y0))) => 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $i > $o]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y1) => 46.36/6.41 (((??) @ (^[Y3 : $i]: 46.36/6.41 (((Y0 @ 46.36/6.41 Y2 @ Y3) & 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (Y0 @ 46.36/6.41 Y2 @ 46.36/6.41 Y4) => 46.36/6.41 (( 46.36/6.41 (Y3) = 46.36/6.41 (Y4)))))))))))))))))) => 46.36/6.41 (((??) @ (^[Y2 : $i]: 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (((in @ Y3 @ 46.36/6.41 Y2) <=> 46.36/6.41 (((??) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y1) & 46.36/6.41 (Y0 @ 46.36/6.41 Y4 @ Y3)))))))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (((in @ Y1 @ Y0) & 46.36/6.41 (((~) @ (((??) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 Y1) & (in @ 46.36/6.41 Y2 @ Y0)))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (((((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y1) => 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y3 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y0))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y3 @ 46.36/6.41 Y0) & 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y0))) => 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y1) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y4) <=> 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y4)))))))) => 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y3))))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y3 @ 46.36/6.41 Y1) & 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y1))) => 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y3) => 46.36/6.41 (in @ 46.36/6.41 Y4 @ Y2)))))) | 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ 46.36/6.41 Y4 @ Y3)))))))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((((((??) @ ( 46.36/6.41 ^[Y3 : $i]: 46.36/6.41 (in @ Y3 @ Y2)))) & 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y3 : $i]: 46.36/6.41 (((in @ Y3 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ Y3 @ 46.36/6.41 Y0)))))))) => 46.36/6.41 (((??) @ (^[Y3 : $i]: 46.36/6.41 (( 46.36/6.41 (??) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 ( 46.36/6.41 in @ 46.36/6.41 Y3 @ Y1) & 46.36/6.41 ( 46.36/6.41 in @ 46.36/6.41 Y4 @ Y2) & 46.36/6.41 ( 46.36/6.41 ( 46.36/6.41 (~) @ ( 46.36/6.41 ( 46.36/6.41 (??) @ ( 46.36/6.41 ^[Y5 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y5 @ 46.36/6.41 Y3) & 46.36/6.41 (in @ 46.36/6.41 Y5 @ Y2)))))))) & 46.36/6.41 ( 46.36/6.41 ( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y5 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y5 @ 46.36/6.41 Y1) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y5) | 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y6 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y6 @ 46.36/6.41 Y5) => 46.36/6.41 (in @ 46.36/6.41 Y6 @ Y3)))))))))))))))))))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (((Y0 @ Y1) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((Y0 @ Y2) => 46.36/6.41 (((Y1) = (Y2))))))))))))) => 46.36/6.41 (Y0 @ (descr @ Y0))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y0) => 46.36/6.41 (((Y1 @ Y2) => 46.36/6.41 (in @ Y2 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ Y1))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (in @ Y2 @ Y0)))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (Y1 @ Y2)))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $o]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((in @ Y1 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 (powerset @ emptyset) @ 46.36/6.41 (^[Y2 : $i]: (Y0)))) => 46.36/6.41 (Y0))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((in @ Y0 @ emptyset) => 46.36/6.41 (((!!) @ (^[Y1 : $o]: (Y1))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (((Y0 @ Y1) & 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (Y0 @ 46.36/6.41 Y2) => 46.36/6.41 (( 46.36/6.41 (Y1) = 46.36/6.41 (Y2))))))))))))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (Y0 @ Y1))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y1)))))) => 46.36/6.41 (((((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y0)))))) => 46.36/6.41 (((Y0) = 46.36/6.41 (Y1))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((!!) @ (^[Y1 : $i]: 46.36/6.41 (((~) @ ( 46.36/6.41 in @ Y1 @ 46.36/6.41 Y0)))))) => 46.36/6.41 (((Y0) = (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((!!) @ (^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (~) @ ( 46.36/6.41 in @ 46.36/6.41 Y1 @ Y0)))))) => 46.36/6.41 (((Y0) = (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 dsetconstr @ 46.36/6.41 Y0 @ Y1)) <=> 46.36/6.41 (Y1 @ Y2)))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((Y0) != 46.36/6.41 (emptyset))) => 46.36/6.41 (((??) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (in @ Y1 @ Y0))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (( 46.36/6.41 (Y1 @ 46.36/6.41 Y2) => 46.36/6.41 (( 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ 46.36/6.41 Y1) != 46.36/6.41 (emptyset)))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((??) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (in @ 46.36/6.41 Y1 @ Y0)))) => 46.36/6.41 (((Y0) != 46.36/6.41 (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (in @ 46.36/6.41 Y0 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)))))))) => 46.36/6.41 (((in @ emptyset @ 46.36/6.41 (setadjoin @ emptyset @ 46.36/6.41 emptyset)) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y3 : $o]: 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0))) => 46.36/6.41 (Y3))) => 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (Y3))) => 46.36/6.41 (Y3))))))))))))))))))) => 46.36/6.41 (((((!!) @ ( 46.36/6.41 ^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) | 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0)))))))))))))))) => 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y0 : $i]: 46.36/6.41 (((dsetconstr @ 46.36/6.41 Y0 @ 46.36/6.41 (^[Y1 : $i]: 46.36/6.41 ( 46.36/6.41 $true))) = 46.36/6.41 (Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 46.36/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 46.36/6.41 thf(zip_derived_cl32, plain, 46.36/6.41 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((((!!) @ (^[Y1 : $i]: 46.36/6.41 (((((in @ Y1 @ Y0) & (in @ Y1 @ omega))) => 46.36/6.41 (in @ (setadjoin @ Y1 @ Y1) @ Y0)))))) & 46.36/6.41 (in @ emptyset @ Y0))) => 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $i > $o]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y1) => 46.36/6.41 (((??) @ (^[Y3 : $i]: 46.36/6.41 (((Y0 @ Y2 @ 46.36/6.41 Y3) & 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (Y0 @ 46.36/6.41 Y2 @ 46.36/6.41 Y4) => 46.36/6.41 (( 46.36/6.41 (Y3) = 46.36/6.41 (Y4)))))))))))))))))) => 46.36/6.41 (((??) @ (^[Y2 : $i]: 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (((in @ Y3 @ 46.36/6.41 Y2) <=> 46.36/6.41 (((??) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y1) & 46.36/6.41 (Y0 @ 46.36/6.41 Y4 @ Y3)))))))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (((in @ Y1 @ Y0) & 46.36/6.41 (((~) @ (((??) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 Y1) & (in @ 46.36/6.41 Y2 @ Y0)))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (((((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y1) => 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y3 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y0))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (((( 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y0) & 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y0))) => 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y1) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y4) <=> 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y4)))))))) => 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y3))))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (((( 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y1) & 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y1))) => 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y3) => 46.36/6.41 (in @ 46.36/6.41 Y4 @ Y2)))))) | 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ 46.36/6.41 Y4 @ Y3)))))))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((((((??) @ (^[Y3 : $i]: 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y2)))) & 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y3 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y0)))))))) => 46.36/6.41 (((??) @ (^[Y3 : $i]: 46.36/6.41 (( 46.36/6.41 (??) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 ( 46.36/6.41 in @ 46.36/6.41 Y3 @ Y1) & 46.36/6.41 ( 46.36/6.41 in @ 46.36/6.41 Y4 @ Y2) & 46.36/6.41 ( 46.36/6.41 ( 46.36/6.41 (~) @ ( 46.36/6.41 ( 46.36/6.41 (??) @ ( 46.36/6.41 ^[Y5 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y5 @ 46.36/6.41 Y3) & 46.36/6.41 (in @ 46.36/6.41 Y5 @ Y2)))))))) & 46.36/6.41 ( 46.36/6.41 ( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y5 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y5 @ 46.36/6.41 Y1) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y5) | 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y6 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y6 @ 46.36/6.41 Y5) => 46.36/6.41 (in @ 46.36/6.41 Y6 @ Y3)))))))))))))))))))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (((Y0 @ Y1) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((Y0 @ Y2) => 46.36/6.41 (((Y1) = (Y2))))))))))))) => 46.36/6.41 (Y0 @ (descr @ Y0))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y0) => 46.36/6.41 (((Y1 @ Y2) => 46.36/6.41 (in @ Y2 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ Y1))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (in @ Y2 @ Y0)))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (Y1 @ Y2)))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $o]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((in @ Y1 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 (powerset @ emptyset) @ 46.36/6.41 (^[Y2 : $i]: (Y0)))) => 46.36/6.41 (Y0))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((in @ Y0 @ emptyset) => 46.36/6.41 (((!!) @ (^[Y1 : $o]: (Y1))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (((Y0 @ Y1) & 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (((Y0 @ 46.36/6.41 Y2) => 46.36/6.41 (( 46.36/6.41 (Y1) = 46.36/6.41 (Y2))))))))))))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (Y0 @ Y1))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (((in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y1)))))) => 46.36/6.41 (((((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y0)))))) => 46.36/6.41 (((Y0) = (Y1))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((!!) @ (^[Y1 : $i]: 46.36/6.41 (((~) @ ( 46.36/6.41 in @ Y1 @ Y0)))))) => 46.36/6.41 (((Y0) = (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((!!) @ (^[Y1 : $i]: 46.36/6.41 (((~) @ ( 46.36/6.41 in @ Y1 @ 46.36/6.41 Y0)))))) => 46.36/6.41 (((Y0) = (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 dsetconstr @ 46.36/6.41 Y0 @ Y1)) <=> 46.36/6.41 (Y1 @ Y2)))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((Y0) != (emptyset))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (in @ 46.36/6.41 Y1 @ Y0))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (( 46.36/6.41 (Y1 @ 46.36/6.41 Y2) => 46.36/6.41 (( 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ 46.36/6.41 Y1) != 46.36/6.41 (emptyset)))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((??) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (in @ Y1 @ 46.36/6.41 Y0)))) => 46.36/6.41 (((Y0) != 46.36/6.41 (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (in @ Y0 @ 46.36/6.41 (setadjoin @ 46.36/6.41 Y0 @ Y1)))))))) => 46.36/6.41 (((in @ emptyset @ 46.36/6.41 (setadjoin @ emptyset @ 46.36/6.41 emptyset)) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y3 : $o]: 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0))) => 46.36/6.41 (Y3))) => 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (Y3))) => 46.36/6.41 (Y3))))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) | 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0)))))))))))))))) => 46.36/6.41 (((!!) @ (^[Y0 : $i]: 46.36/6.41 (( 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ 46.36/6.41 ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 ($true))) = 46.36/6.41 (Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 46.36/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 46.36/6.41 thf(zip_derived_cl36, plain, 46.36/6.41 (~ (((((!!) @ (^[Y0 : $i > $i > $o]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y1) => 46.36/6.41 (((??) @ (^[Y3 : $i]: 46.36/6.41 (((Y0 @ Y2 @ 46.36/6.41 Y3) & 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (Y0 @ 46.36/6.41 Y2 @ 46.36/6.41 Y4) => 46.36/6.41 (( 46.36/6.41 (Y3) = 46.36/6.41 (Y4)))))))))))))))))) => 46.36/6.41 (((??) @ (^[Y2 : $i]: 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (((in @ Y3 @ 46.36/6.41 Y2) <=> 46.36/6.41 (((??) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (((in @ 46.36/6.41 Y4 @ Y1) & 46.36/6.41 (Y0 @ 46.36/6.41 Y4 @ Y3)))))))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (((in @ Y1 @ Y0) & 46.36/6.41 (((~) @ (((??) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y1) & 46.36/6.41 (in @ Y2 @ Y0)))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (((((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y1) => 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (((in @ 46.36/6.41 Y3 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y0))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (((((in @ 46.36/6.41 Y3 @ Y0) & 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y0))) => 46.36/6.41 (((( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y1) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y4) <=> 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y4)))))))) => 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y3))))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (((((in @ 46.36/6.41 Y3 @ Y1) & 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y1))) => 46.36/6.41 (((( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y3) => 46.36/6.41 (in @ 46.36/6.41 Y4 @ Y2)))))) | 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ 46.36/6.41 Y4 @ Y3)))))))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((((((??) @ (^[Y3 : $i]: 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y2)))) & 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y3 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y0)))))))) => 46.36/6.41 (((??) @ (^[Y3 : $i]: 46.36/6.41 (((??) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 ( 46.36/6.41 in @ 46.36/6.41 Y3 @ Y1) & 46.36/6.41 ( 46.36/6.41 in @ 46.36/6.41 Y4 @ Y2) & 46.36/6.41 ( 46.36/6.41 ( 46.36/6.41 (~) @ ( 46.36/6.41 ( 46.36/6.41 (??) @ ( 46.36/6.41 ^[Y5 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y5 @ 46.36/6.41 Y3) & 46.36/6.41 (in @ 46.36/6.41 Y5 @ Y2)))))))) & 46.36/6.41 ( 46.36/6.41 ( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y5 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y5 @ 46.36/6.41 Y1) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y5) | 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y6 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y6 @ 46.36/6.41 Y5) => 46.36/6.41 (in @ 46.36/6.41 Y6 @ Y3)))))))))))))))))))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (((Y0 @ Y1) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((Y0 @ Y2) => 46.36/6.41 (((Y1) = (Y2))))))))))))) => 46.36/6.41 (Y0 @ (descr @ Y0))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y0) => 46.36/6.41 (((Y1 @ Y2) => (in @ 46.36/6.41 Y2 @ 46.36/6.41 (dsetconstr @ Y0 @ 46.36/6.41 Y1))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ Y0 @ 46.36/6.41 Y1)) => 46.36/6.41 (in @ Y2 @ Y0)))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (Y1 @ Y2)))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $o]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((in @ Y1 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 (powerset @ emptyset) @ 46.36/6.41 (^[Y2 : $i]: (Y0)))) => 46.36/6.41 (Y0))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((in @ Y0 @ emptyset) => 46.36/6.41 (((!!) @ (^[Y1 : $o]: (Y1))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (((Y0 @ Y1) & 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (((Y0 @ Y2) => 46.36/6.41 (((Y1) = 46.36/6.41 (Y2))))))))))))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: (Y0 @ Y1))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (in @ Y2 @ 46.36/6.41 Y1)))))) => 46.36/6.41 (((((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (((in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y0)))))) => 46.36/6.41 (((Y0) = (Y1))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((!!) @ (^[Y1 : $i]: 46.36/6.41 (((~) @ ( 46.36/6.41 in @ Y1 @ Y0)))))) => 46.36/6.41 (((Y0) = (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((!!) @ (^[Y1 : $i]: 46.36/6.41 (((~) @ ( 46.36/6.41 in @ Y1 @ Y0)))))) => 46.36/6.41 (((Y0) = (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 dsetconstr @ 46.36/6.41 Y0 @ Y1)) <=> 46.36/6.41 (Y1 @ Y2)))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((Y0) != (emptyset))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (in @ 46.36/6.41 Y1 @ Y0))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (( 46.36/6.41 (Y1 @ 46.36/6.41 Y2) => 46.36/6.41 (( 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ 46.36/6.41 Y1) != 46.36/6.41 (emptyset)))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((??) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (in @ Y1 @ Y0)))) => 46.36/6.41 (((Y0) != 46.36/6.41 (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (in @ Y0 @ 46.36/6.41 (setadjoin @ 46.36/6.41 Y0 @ Y1)))))))) => 46.36/6.41 (((in @ emptyset @ 46.36/6.41 (setadjoin @ emptyset @ 46.36/6.41 emptyset)) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y3 : $o]: 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0))) => 46.36/6.41 (Y3))) => 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (Y3))) => 46.36/6.41 (Y3))))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) | 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0)))))))))))))))) => 46.36/6.41 (((!!) @ (^[Y0 : $i]: 46.36/6.41 (( 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ 46.36/6.41 ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 ($true))) = 46.36/6.41 (Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 46.36/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl32])). 46.36/6.41 thf(zip_derived_cl40, plain, 46.36/6.41 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (((in @ Y1 @ Y0) & 46.36/6.41 (((~) @ (((??) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y1) & 46.36/6.41 (in @ Y2 @ Y0)))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (((((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y1) => 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (((in @ Y3 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ Y3 @ 46.36/6.41 Y0))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (((((in @ Y3 @ 46.36/6.41 Y0) & (in @ 46.36/6.41 Y2 @ Y0))) => 46.36/6.41 (((((!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y1) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y4) <=> 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y4)))))))) => 46.36/6.41 (((Y2) = 46.36/6.41 (Y3))))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (((((in @ Y3 @ 46.36/6.41 Y1) & (in @ 46.36/6.41 Y2 @ Y1))) => 46.36/6.41 (((((!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y3) => 46.36/6.41 (in @ 46.36/6.41 Y4 @ Y2)))))) | 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ 46.36/6.41 Y4 @ Y3)))))))))))))))) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((((((??) @ (^[Y3 : $i]: 46.36/6.41 (in @ Y3 @ 46.36/6.41 Y2)))) & 46.36/6.41 (((!!) @ (^[Y3 : $i]: 46.36/6.41 (((in @ 46.36/6.41 Y3 @ 46.36/6.41 Y2) => 46.36/6.41 (in @ 46.36/6.41 Y3 @ Y0)))))))) => 46.36/6.41 (((??) @ (^[Y3 : $i]: 46.36/6.41 (((??) @ ( 46.36/6.41 ^[Y4 : $i]: 46.36/6.41 (( 46.36/6.41 ( 46.36/6.41 in @ 46.36/6.41 Y3 @ Y1) & 46.36/6.41 ( 46.36/6.41 in @ 46.36/6.41 Y4 @ Y2) & 46.36/6.41 ( 46.36/6.41 ( 46.36/6.41 (~) @ ( 46.36/6.41 ( 46.36/6.41 (??) @ ( 46.36/6.41 ^[Y5 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y5 @ 46.36/6.41 Y3) & 46.36/6.41 (in @ 46.36/6.41 Y5 @ Y2)))))))) & 46.36/6.41 ( 46.36/6.41 ( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y5 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y5 @ 46.36/6.41 Y1) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y4 @ 46.36/6.41 Y5) | 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y6 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y6 @ 46.36/6.41 Y5) => 46.36/6.41 (in @ 46.36/6.41 Y6 @ Y3)))))))))))))))))))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (((Y0 @ Y1) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((Y0 @ Y2) => 46.36/6.41 (((Y1) = (Y2))))))))))))) => 46.36/6.41 (Y0 @ (descr @ Y0))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y0) => 46.36/6.41 (((Y1 @ Y2) => (in @ 46.36/6.41 Y2 @ 46.36/6.41 (dsetconstr @ Y0 @ Y1))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ Y0 @ Y1)) => 46.36/6.41 (in @ Y2 @ Y0)))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ Y0 @ 46.36/6.41 Y1)) => 46.36/6.41 (Y1 @ Y2)))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $o]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((in @ Y1 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 (powerset @ emptyset) @ 46.36/6.41 (^[Y2 : $i]: (Y0)))) => 46.36/6.41 (Y0))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((in @ Y0 @ emptyset) => 46.36/6.41 (((!!) @ (^[Y1 : $o]: (Y1))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (((Y0 @ Y1) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (Y0 @ 46.36/6.41 Y2) => 46.36/6.41 (( 46.36/6.41 (Y1) = 46.36/6.41 (Y2))))))))))))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: (Y0 @ Y1))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((((!!) @ (^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y1)))))) => 46.36/6.41 (((((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (in @ Y2 @ 46.36/6.41 Y0)))))) => 46.36/6.41 (((Y0) = (Y1))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((!!) @ (^[Y1 : $i]: 46.36/6.41 (((~) @ (in @ 46.36/6.41 Y1 @ Y0)))))) => 46.36/6.41 (((Y0) = (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((!!) @ (^[Y1 : $i]: 46.36/6.41 (((~) @ ( 46.36/6.41 in @ Y1 @ Y0)))))) => 46.36/6.41 (((Y0) = (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (((in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ Y1)) <=> 46.36/6.41 (Y1 @ Y2)))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((Y0) != (emptyset))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (in @ Y1 @ 46.36/6.41 Y0))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (( 46.36/6.41 (Y1 @ 46.36/6.41 Y2) => 46.36/6.41 (( 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ 46.36/6.41 Y1) != 46.36/6.41 (emptyset)))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (in @ 46.36/6.41 Y1 @ Y0)))) => 46.36/6.41 (((Y0) != (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (in @ 46.36/6.41 Y0 @ 46.36/6.41 (setadjoin @ 46.36/6.41 Y0 @ Y1)))))))) => 46.36/6.41 (((in @ emptyset @ 46.36/6.41 (setadjoin @ emptyset @ 46.36/6.41 emptyset)) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y3 : $o]: 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0))) => 46.36/6.41 (Y3))) => 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (Y3))) => 46.36/6.41 (Y3))))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) | 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0)))))))))))))))) => 46.36/6.41 (((!!) @ (^[Y0 : $i]: 46.36/6.41 (((dsetconstr @ 46.36/6.41 Y0 @ 46.36/6.41 (^[Y1 : $i]: 46.36/6.41 ($true))) = 46.36/6.41 (Y0))))))))))))))))))))))))))))))))))))))))))))))))))))), 46.36/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl36])). 46.36/6.41 thf(zip_derived_cl49, plain, 46.36/6.41 (~ (((((!!) 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46.36/6.41 (((in @ Y1 @ 46.36/6.41 (dsetconstr @ 46.36/6.41 (powerset @ emptyset) @ 46.36/6.41 (^[Y2 : $i]: (Y0)))) => 46.36/6.41 (Y0))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((in @ Y0 @ emptyset) => 46.36/6.41 (((!!) @ (^[Y1 : $o]: (Y1))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (((Y0 @ Y1) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (Y0 @ 46.36/6.41 Y2) => 46.36/6.41 (( 46.36/6.41 (Y1) = 46.36/6.41 (Y2))))))))))))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: (Y0 @ Y1))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((((!!) @ (^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y1)))))) => 46.36/6.41 (((((!!) @ (^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 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46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (( 46.36/6.41 (Y1 @ 46.36/6.41 Y2) => 46.36/6.41 (( 46.36/6.41 (dsetconstr @ 46.36/6.41 Y0 @ 46.36/6.41 Y1) != 46.36/6.41 (emptyset)))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (in @ 46.36/6.41 Y1 @ Y0)))) => 46.36/6.41 (((Y0) != (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (in @ 46.36/6.41 Y0 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)))))))) => 46.36/6.41 (((in @ emptyset @ 46.36/6.41 (setadjoin @ emptyset @ emptyset)) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y3 : $o]: 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0))) => 46.36/6.41 (Y3))) => 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (Y3))) => 46.36/6.41 (Y3))))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) | 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0)))))))))))))))) => 46.36/6.41 (((!!) @ (^[Y0 : $i]: 46.36/6.41 (((dsetconstr @ 46.36/6.41 Y0 @ 46.36/6.41 (^[Y1 : $i]: 46.36/6.41 ( 46.36/6.41 $true))) = 46.36/6.41 (Y0))))))))))))))))))))))))))))))))))))))))))))))))))), 46.36/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 46.36/6.41 thf(zip_derived_cl54, plain, 46.36/6.41 (~ (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (((Y0 @ Y1) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((Y0 @ Y2) => 46.36/6.41 (((Y1) = (Y2))))))))))))) => 46.36/6.41 (Y0 @ (descr @ Y0))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ Y0) => 46.36/6.41 (((Y1 @ Y2) => (in @ Y2 @ 46.36/6.41 (dsetconstr @ Y0 @ Y1))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ Y0 @ Y1)) => 46.36/6.41 (in @ Y2 @ Y0)))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ 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@ Y1)))))) => 46.36/6.41 (((((!!) @ (^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ Y0)))))) => 46.36/6.41 (((Y0) = (Y1))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((!!) @ (^[Y1 : $i]: 46.36/6.41 (((~) @ (in @ Y1 @ Y0)))))) => 46.36/6.41 (((Y0) = (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((!!) @ (^[Y1 : $i]: 46.36/6.41 (((~) @ (in @ Y1 @ 46.36/6.41 Y0)))))) => 46.36/6.41 (((Y0) = (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y0) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 dsetconstr @ 46.36/6.41 Y0 @ Y1)) <=> 46.36/6.41 (Y1 @ Y2)))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((Y0) != (emptyset))) => 46.36/6.41 (((??) @ (^[Y1 : $i]: 46.36/6.41 (in @ Y1 @ Y0))))))))) => 46.36/6.41 (((((!!) @ 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(((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y3 : $o]: 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0))) => 46.36/6.41 (Y3))) => 46.36/6.41 (( 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (Y3))) => 46.36/6.41 (Y3))))))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y1 : $i]: 46.36/6.41 (((!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) | 46.36/6.41 (( 46.36/6.41 (Y2) = 46.36/6.41 (Y0)))))))))))))))) => 46.36/6.41 (((!!) @ (^[Y0 : $i]: 46.36/6.41 (((dsetconstr @ 46.36/6.41 Y0 @ 46.36/6.41 (^[Y1 : $i]: 46.36/6.41 ($true))) 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(emptyset)))))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (in @ Y1 @ Y0)))) => 46.36/6.41 (((Y0) != (emptyset)))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (in @ Y0 @ 46.36/6.41 (setadjoin @ 46.36/6.41 Y0 @ Y1)))))))) => 46.36/6.41 (((in @ emptyset @ 46.36/6.41 (setadjoin @ emptyset @ emptyset)) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 Y1) => 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1))))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y2 : $i]: 46.36/6.41 (( 46.36/6.41 (in @ 46.36/6.41 Y2 @ 46.36/6.41 ( 46.36/6.41 setadjoin @ 46.36/6.41 Y0 @ Y1)) => 46.36/6.41 (( 46.36/6.41 (!!) @ ( 46.36/6.41 ^[Y3 : $o]: 46.36/6.41 (( 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46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ Y0 @ Y1)) => 46.36/6.41 (in @ Y2 @ Y0)))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((in @ Y2 @ 46.36/6.41 (dsetconstr @ Y0 @ Y1)) => 46.36/6.41 (Y1 @ Y2)))))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $o]: 46.36/6.41 (((!!) @ (^[Y1 : $i]: 46.36/6.41 (((in @ Y1 @ 46.36/6.41 (dsetconstr @ (powerset @ emptyset) @ 46.36/6.41 (^[Y2 : $i]: (Y0)))) => 46.36/6.41 (Y0))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: 46.36/6.41 (((in @ Y0 @ emptyset) => 46.36/6.41 (((!!) @ (^[Y1 : $o]: (Y1))))))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.41 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.41 (((((??) @ (^[Y1 : $i]: 46.36/6.41 (((Y0 @ Y1) & 46.36/6.41 (((!!) @ (^[Y2 : $i]: 46.36/6.41 (((Y0 @ Y2) => 46.36/6.41 (((Y1) = (Y2))))))))))))) => 46.36/6.41 (((??) @ (^[Y1 : 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Y2)))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((Y0) != (emptyset))) => 46.36/6.42 (((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ 46.36/6.42 Y2 @ 46.36/6.42 Y0) => 46.36/6.42 (( 46.36/6.42 (Y1 @ 46.36/6.42 Y2) => 46.36/6.42 (( 46.36/6.42 (dsetconstr @ 46.36/6.42 Y0 @ 46.36/6.42 Y1) != 46.36/6.42 (emptyset)))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((??) @ (^[Y1 : $i]: 46.36/6.42 (in @ Y1 @ Y0)))) => 46.36/6.42 (((Y0) != (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (in @ Y0 @ 46.36/6.42 (setadjoin @ Y0 @ 46.36/6.42 Y1)))))))) => 46.36/6.42 (((in @ emptyset @ 46.36/6.42 (setadjoin @ emptyset @ emptyset)) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ ( 46.36/6.42 ^[Y2 : $i]: 46.36/6.42 (((in @ 46.36/6.42 Y2 @ 46.36/6.42 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(Y3))) => 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ ( 46.36/6.42 ^[Y2 : $i]: 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 ( 46.36/6.42 setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) | 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ 46.36/6.42 (^[Y1 : $i]: ($true))) = 46.36/6.42 (Y0))))))))))))))))))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl104])). 46.36/6.42 thf(zip_derived_cl142, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.42 (((((??) @ (^[Y1 : $i]: 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46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl122])). 46.36/6.42 thf(zip_derived_cl158, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset)))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.42 (((((??) @ (^[Y1 : $i]: 46.36/6.42 (((Y0 @ Y1) & 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((Y0 @ Y2) => 46.36/6.42 (((Y1) = (Y2))))))))))))) => 46.36/6.42 (((??) @ (^[Y1 : $i]: (Y0 @ Y1))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => (in @ 46.36/6.42 Y2 @ Y1)))))) => 46.36/6.42 (((((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => 46.36/6.42 (in @ Y2 @ Y0)))))) => 46.36/6.42 (((Y0) = (Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((!!) @ (^[Y1 : $i]: (((~) @ (in @ Y1 @ Y0)))))) => 46.36/6.42 (((Y0) = (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((!!) @ (^[Y1 : $i]: (((~) @ (in @ Y1 @ Y0)))))) => 46.36/6.42 (((Y0) = (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (dsetconstr @ 46.36/6.42 Y0 @ Y1)) <=> 46.36/6.42 (Y1 @ Y2)))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((Y0) != (emptyset))) => 46.36/6.42 (((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 Y0) => 46.36/6.42 (((Y1 @ Y2) => 46.36/6.42 (((dsetconstr @ 46.36/6.42 Y0 @ Y1) != 46.36/6.42 (emptyset)))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.36/6.42 (((Y0) != (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (in @ Y0 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)))))))) => 46.36/6.42 (((in @ emptyset @ 46.36/6.42 (setadjoin @ emptyset @ emptyset)) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 ( 46.36/6.42 setadjoin @ 46.36/6.42 Y0 @ Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 ( 46.36/6.42 setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (( 46.36/6.42 (!!) @ ( 46.36/6.42 ^[Y3 : $o]: 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0))) => 46.36/6.42 (Y3))) => 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ ( 46.36/6.42 ^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (((in @ 46.36/6.42 Y2 @ Y1) | 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ 46.36/6.42 (^[Y1 : $i]: ($true))) = 46.36/6.42 (Y0))))))))))))))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])). 46.36/6.42 thf(zip_derived_cl171, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i > $o]: 46.36/6.42 (((((??) @ (^[Y1 : $i]: 46.36/6.42 (((Y0 @ Y1) & 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((Y0 @ Y2) => 46.36/6.42 (((Y1) = (Y2))))))))))))) => 46.36/6.42 (((??) @ (^[Y1 : $i]: (Y0 @ Y1))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => (in @ 46.36/6.42 Y2 @ Y1)))))) => 46.36/6.42 (((((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => (in @ 46.36/6.42 Y2 @ Y0)))))) => 46.36/6.42 (((Y0) = (Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((!!) @ (^[Y1 : $i]: (((~) @ (in @ Y1 @ Y0)))))) => 46.36/6.42 (((Y0) = (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((!!) @ (^[Y1 : $i]: (((~) @ (in @ Y1 @ Y0)))))) => 46.36/6.42 (((Y0) = (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (dsetconstr @ Y0 @ 46.36/6.42 Y1)) <=> 46.36/6.42 (Y1 @ Y2)))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((Y0) != (emptyset))) => 46.36/6.42 (((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((Y1 @ Y2) => 46.36/6.42 (((dsetconstr @ 46.36/6.42 Y0 @ Y1) != 46.36/6.42 (emptyset)))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.36/6.42 (((Y0) != (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (in @ Y0 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)))))))) => 46.36/6.42 (((in @ emptyset @ 46.36/6.42 (setadjoin @ emptyset @ emptyset)) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 (setadjoin @ 46.36/6.42 Y0 @ Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 ( 46.36/6.42 setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (( 46.36/6.42 (!!) @ ( 46.36/6.42 ^[Y3 : $o]: 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0))) => 46.36/6.42 (Y3))) => 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 ( 46.36/6.42 setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) | 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ 46.36/6.42 (^[Y1 : $i]: ($true))) = (Y0))))))))))))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])). 46.36/6.42 thf(zip_derived_cl184, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => (in @ 46.36/6.42 Y2 @ Y1)))))) => 46.36/6.42 (((((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => (in @ 46.36/6.42 Y2 @ Y0)))))) => 46.36/6.42 (((Y0) = (Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((!!) @ (^[Y1 : $i]: (((~) @ (in @ Y1 @ Y0)))))) => 46.36/6.42 (((Y0) = (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((!!) @ (^[Y1 : $i]: (((~) @ (in @ Y1 @ Y0)))))) => 46.36/6.42 (((Y0) = (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (dsetconstr @ Y0 @ Y1)) <=> 46.36/6.42 (Y1 @ Y2)))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((Y0) != (emptyset))) => 46.36/6.42 (((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((Y1 @ Y2) => 46.36/6.42 (((dsetconstr @ 46.36/6.42 Y0 @ Y1) != 46.36/6.42 (emptyset)))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.36/6.42 (((Y0) != (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (in @ Y0 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)))))))) => 46.36/6.42 (((in @ emptyset @ 46.36/6.42 (setadjoin @ emptyset @ emptyset)) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (in @ Y2 @ 46.36/6.42 (setadjoin @ 46.36/6.42 Y0 @ Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ 46.36/6.42 Y2 @ 46.36/6.42 (setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (( 46.36/6.42 (!!) @ ( 46.36/6.42 ^[Y3 : $o]: 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0))) => 46.36/6.42 (Y3))) => 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 ( 46.36/6.42 setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) | 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ 46.36/6.42 (^[Y1 : $i]: ($true))) = (Y0))))))))))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl171])). 46.36/6.42 thf(zip_derived_cl199, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((!!) @ (^[Y1 : $i]: (((~) @ (in @ Y1 @ Y0)))))) => 46.36/6.42 (((Y0) = (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((!!) @ (^[Y1 : $i]: (((~) @ (in @ Y1 @ Y0)))))) => 46.36/6.42 (((Y0) = (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (dsetconstr @ Y0 @ Y1)) <=> 46.36/6.42 (Y1 @ Y2)))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((Y0) != (emptyset))) => 46.36/6.42 (((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((Y1 @ Y2) => 46.36/6.42 (((dsetconstr @ 46.36/6.42 Y0 @ Y1) != 46.36/6.42 (emptyset)))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.36/6.42 (((Y0) != (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))) => 46.36/6.42 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 Y1) => (in @ 46.36/6.42 Y2 @ 46.36/6.42 (setadjoin @ 46.36/6.42 Y0 @ Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (((!!) @ ( 46.36/6.42 ^[Y3 : $o]: 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0))) => 46.36/6.42 (Y3))) => 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ 46.36/6.42 Y2 @ 46.36/6.42 (setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ Y1) | 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ 46.36/6.42 (^[Y1 : $i]: ($true))) = (Y0))))))))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl184])). 46.36/6.42 thf(zip_derived_cl211, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((!!) @ (^[Y1 : $i]: (((~) @ (in @ Y1 @ Y0)))))) => 46.36/6.42 (((Y0) = (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (dsetconstr @ Y0 @ Y1)) <=> 46.36/6.42 (Y1 @ Y2)))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((Y0) != (emptyset))) => 46.36/6.42 (((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((Y1 @ Y2) => 46.36/6.42 (((dsetconstr @ Y0 @ 46.36/6.42 Y1) != (emptyset)))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.36/6.42 (((Y0) != (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))) => 46.36/6.42 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 Y1) => (in @ 46.36/6.42 Y2 @ 46.36/6.42 (setadjoin @ 46.36/6.42 Y0 @ Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (((!!) @ ( 46.36/6.42 ^[Y3 : $o]: 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0))) => 46.36/6.42 (Y3))) => 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (((in @ 46.36/6.42 Y2 @ Y1) | 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ 46.36/6.42 (^[Y1 : $i]: ($true))) = (Y0))))))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl199])). 46.36/6.42 thf(zip_derived_cl221, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (dsetconstr @ Y0 @ Y1)) <=> 46.36/6.42 (Y1 @ Y2)))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((Y0) != (emptyset))) => 46.36/6.42 (((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((Y1 @ Y2) => 46.36/6.42 (((dsetconstr @ Y0 @ 46.36/6.42 Y1) != (emptyset)))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.36/6.42 (((Y0) != (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))) => 46.36/6.42 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => 46.36/6.42 (in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ 46.36/6.42 Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (((!!) @ ( 46.36/6.42 ^[Y3 : $o]: 46.36/6.42 (((( 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0))) => 46.36/6.42 (Y3))) => 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (((in @ Y2 @ 46.36/6.42 Y1) | 46.36/6.42 (((Y2) = 46.36/6.42 (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ 46.36/6.42 (^[Y1 : $i]: ($true))) = (Y0))))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl211])). 46.36/6.42 thf(zip_derived_cl229, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((Y0) != (emptyset))) => 46.36/6.42 (((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((Y1 @ Y2) => 46.36/6.42 (((dsetconstr @ Y0 @ 46.36/6.42 Y1) != (emptyset)))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.36/6.42 (((Y0) != (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))) => 46.36/6.42 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => 46.36/6.42 (in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ 46.36/6.42 Y1)) => 46.36/6.42 (((!!) @ ( 46.36/6.42 ^[Y3 : $o]: 46.36/6.42 (((((( 46.36/6.42 (Y2) = 46.36/6.42 (Y0))) => 46.36/6.42 (Y3))) => 46.36/6.42 (((( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ 46.36/6.42 Y0 @ Y1)) => 46.36/6.42 (((in @ Y2 @ 46.36/6.42 Y1) | 46.36/6.42 (((Y2) = (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ 46.36/6.42 (^[Y1 : $i]: ($true))) = (Y0))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl221])). 46.36/6.42 thf(zip_derived_cl239, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((Y1 @ Y2) => 46.36/6.42 (((dsetconstr @ Y0 @ Y1) != 46.36/6.42 (emptyset)))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.36/6.42 (((Y0) != (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))) => 46.36/6.42 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => 46.36/6.42 (in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)) => 46.36/6.42 (((!!) @ (^[Y3 : $o]: 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0))) => 46.36/6.42 (Y3))) => 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ 46.36/6.42 Y1)) => 46.36/6.42 (((in @ Y2 @ Y1) | 46.36/6.42 (((Y2) = (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ 46.36/6.42 (^[Y1 : $i]: ($true))) = (Y0))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl229])). 46.36/6.42 thf(zip_derived_cl254, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) => 46.36/6.42 (((Y0) != (emptyset)))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))) => 46.36/6.42 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => (in @ 46.36/6.42 Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)) => 46.36/6.42 (((!!) @ (^[Y3 : $o]: 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0))) => 46.36/6.42 (Y3))) => 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)) => 46.36/6.42 (((in @ Y2 @ Y1) | 46.36/6.42 (((Y2) = (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = 46.36/6.42 (Y0))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl239])). 46.36/6.42 thf(zip_derived_cl265, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))) => 46.36/6.42 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => (in @ 46.36/6.42 Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)) => 46.36/6.42 (((!!) @ (^[Y3 : $o]: 46.36/6.42 (((( 46.36/6.42 (( 46.36/6.42 (Y2) = 46.36/6.42 (Y0))) => 46.36/6.42 (Y3))) => 46.36/6.42 (( 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)) => 46.36/6.42 (((in @ Y2 @ Y1) | 46.36/6.42 (((Y2) = (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = 46.36/6.42 (Y0))))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl254])). 46.36/6.42 thf(zip_derived_cl275, plain, 46.36/6.42 (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => (in @ 46.36/6.42 Y2 @ (setadjoin @ Y0 @ Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)) => 46.36/6.42 (((!!) @ (^[Y3 : $o]: 46.36/6.42 (((((( 46.36/6.42 (Y2) = 46.36/6.42 (Y0))) => 46.36/6.42 (Y3))) => 46.36/6.42 (((( 46.36/6.42 (in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)) => 46.36/6.42 (((in @ Y2 @ Y1) | 46.36/6.42 (((Y2) = (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = (Y0))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl265])). 46.36/6.42 thf(zip_derived_cl281, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => (in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)) => 46.36/6.42 (((!!) @ (^[Y3 : $o]: 46.36/6.42 (((((((Y2) = 46.36/6.42 (Y0))) => 46.36/6.42 (Y3))) => 46.36/6.42 (((((in @ 46.36/6.42 Y2 @ 46.36/6.42 Y1) => 46.36/6.42 (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)) => 46.36/6.42 (((in @ Y2 @ Y1) | 46.36/6.42 (((Y2) = (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = (Y0))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl275])). 46.36/6.42 thf(zip_derived_cl288, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)) => 46.36/6.42 (((!!) @ (^[Y3 : $o]: 46.36/6.42 (((((((Y2) = (Y0))) => 46.36/6.42 (Y3))) => 46.36/6.42 (((((in @ Y2 @ 46.36/6.42 Y1) => (Y3))) => 46.36/6.42 (Y3))))))))))))))))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)) => 46.36/6.42 (((in @ Y2 @ Y1) | 46.36/6.42 (((Y2) = (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = (Y0))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl281])). 46.36/6.42 thf(zip_derived_cl292, plain, 46.36/6.42 (~ (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (setadjoin @ Y0 @ Y1)) => 46.36/6.42 (((in @ Y2 @ Y1) | 46.36/6.42 (((Y2) = (Y0)))))))))))))))) => 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = (Y0))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl288])). 46.36/6.42 thf(zip_derived_cl297, plain, 46.36/6.42 (~ (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = (Y0))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl292])). 46.36/6.42 thf(zip_derived_cl301, plain, 46.36/6.42 (~ (((dsetconstr @ '#sk231' @ (^[Y0 : $i]: ($true))) = ('#sk231')))), 46.36/6.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl297])). 46.36/6.42 thf(zip_derived_cl304, plain, 46.36/6.42 (((dsetconstr @ '#sk231' @ (^[Y0 : $i]: ($true))) != ('#sk231'))), 46.36/6.42 inference('simplify nested equalities', [status(thm)], 46.36/6.42 [zip_derived_cl301])). 46.36/6.42 thf(zip_derived_cl70, plain, 46.36/6.42 ( (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => 46.36/6.42 (((Y1 @ Y2) => (in @ Y2 @ 46.36/6.42 (dsetconstr @ Y0 @ Y1)))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl60])). 46.36/6.42 thf(zip_derived_cl83, plain, 46.36/6.42 (![X2 : $i]: 46.36/6.42 (((!!) @ (^[Y0 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y1 @ X2) => 46.36/6.42 (((Y0 @ Y1) => (in @ Y1 @ 46.36/6.42 (dsetconstr @ X2 @ Y0))))))))))))), 46.36/6.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl70])). 46.36/6.42 thf(zip_derived_cl98, plain, 46.36/6.42 (![X2 : $i, X4 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((in @ Y0 @ X2) => 46.36/6.42 (((X4 @ Y0) => (in @ Y0 @ (dsetconstr @ X2 @ X4)))))))))), 46.36/6.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl83])). 46.36/6.42 thf(zip_derived_cl101, plain, 46.36/6.42 (![X0 : $i]: 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((in @ Y0 @ X0) => 46.36/6.42 ((($true) => (in @ Y0 @ 46.36/6.42 (dsetconstr @ X0 @ (^[Y1 : $i]: ($true)))))))))))), 46.36/6.42 inference('ho.refine.early.bird', [status(thm)], [zip_derived_cl98])). 46.36/6.42 thf(zip_derived_cl363, plain, 46.36/6.42 (![X0 : $i]: 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((in @ Y0 @ X0) => (in @ Y0 @ 46.36/6.42 (dsetconstr @ X0 @ (^[Y1 : $i]: ($true)))))))))), 46.36/6.42 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl101])). 46.36/6.42 thf(zip_derived_cl53, plain, 46.36/6.42 ( (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((??) @ (^[Y1 : $i]: 46.36/6.42 (((((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => 46.36/6.42 (((!!) @ (^[Y3 : $i]: 46.36/6.42 (((in @ Y3 @ Y2) => 46.36/6.42 (in @ Y3 @ Y0))))))))))) & 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((!!) @ (^[Y3 : $i]: 46.36/6.42 (((((in @ Y3 @ Y0) & 46.36/6.42 (in @ Y2 @ Y0))) => 46.36/6.42 (((((!!) @ ( 46.36/6.42 ^[Y4 : $i]: 46.36/6.42 (((in @ Y4 @ 46.36/6.42 Y1) => 46.36/6.42 (((in @ 46.36/6.42 Y2 @ 46.36/6.42 Y4) <=> 46.36/6.42 (in @ 46.36/6.42 Y3 @ Y4)))))))) => 46.36/6.42 (((Y2) = (Y3))))))))))))) & 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((!!) @ (^[Y3 : $i]: 46.36/6.42 (((((in @ Y3 @ Y1) & 46.36/6.42 (in @ Y2 @ Y1))) => 46.36/6.42 (((((!!) @ ( 46.36/6.42 ^[Y4 : $i]: 46.36/6.42 (((in @ Y4 @ 46.36/6.42 Y3) => 46.36/6.42 (in @ Y4 @ 46.36/6.42 Y2)))))) | 46.36/6.42 (((!!) @ ( 46.36/6.42 ^[Y4 : $i]: 46.36/6.42 (((in @ Y4 @ 46.36/6.42 Y2) => 46.36/6.42 (in @ Y4 @ 46.36/6.42 Y3)))))))))))))))) & 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((((((??) @ (^[Y3 : $i]: 46.36/6.42 (in @ Y3 @ Y2)))) & 46.36/6.42 (((!!) @ (^[Y3 : $i]: 46.36/6.42 (((in @ Y3 @ 46.36/6.42 Y2) => (in @ 46.36/6.42 Y3 @ Y0)))))))) => 46.36/6.42 (((??) @ (^[Y3 : $i]: 46.36/6.42 (((??) @ (^[Y4 : $i]: 46.36/6.42 (( 46.36/6.42 ( 46.36/6.42 in @ 46.36/6.42 Y3 @ Y1) & 46.36/6.42 ( 46.36/6.42 in @ 46.36/6.42 Y4 @ Y2) & 46.36/6.42 ( 46.36/6.42 ( 46.36/6.42 (~) @ ( 46.36/6.42 ( 46.36/6.42 (??) @ ( 46.36/6.42 ^[Y5 : $i]: 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y5 @ 46.36/6.42 Y3) & 46.36/6.42 (in @ 46.36/6.42 Y5 @ Y2)))))))) & 46.36/6.42 ( 46.36/6.42 ( 46.36/6.42 (!!) @ ( 46.36/6.42 ^[Y5 : $i]: 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y5 @ 46.36/6.42 Y1) => 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y4 @ 46.36/6.42 Y5) | 46.36/6.42 (( 46.36/6.42 (!!) @ ( 46.36/6.42 ^[Y6 : $i]: 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y6 @ 46.36/6.42 Y5) => 46.36/6.42 (in @ 46.36/6.42 Y6 @ Y3))))))))))))))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 46.36/6.42 thf(zip_derived_cl58, plain, 46.36/6.42 (![X2 : $i]: 46.36/6.42 (((??) @ (^[Y0 : $i]: 46.36/6.42 (((((!!) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y1 @ Y0) => 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => (in @ 46.36/6.42 Y2 @ X2))))))))))) & 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((((in @ Y2 @ X2) & (in @ 46.36/6.42 Y1 @ X2))) => 46.36/6.42 (((((!!) @ (^[Y3 : $i]: 46.36/6.42 (((in @ Y3 @ 46.36/6.42 Y0) => 46.36/6.42 (((in @ Y1 @ 46.36/6.42 Y3) <=> 46.36/6.42 (in @ Y2 @ 46.36/6.42 Y3)))))))) => 46.36/6.42 (((Y1) = (Y2))))))))))))) & 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((((in @ Y2 @ Y0) & (in @ 46.36/6.42 Y1 @ Y0))) => 46.36/6.42 (((((!!) @ (^[Y3 : $i]: 46.36/6.42 (((in @ Y3 @ 46.36/6.42 Y2) => (in @ 46.36/6.42 Y3 @ Y1)))))) | 46.36/6.42 (((!!) @ (^[Y3 : $i]: 46.36/6.42 (((in @ Y3 @ 46.36/6.42 Y1) => (in @ 46.36/6.42 Y3 @ Y2)))))))))))))))) & 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((((((??) @ (^[Y2 : $i]: (in @ Y2 @ Y1)))) & 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => (in @ 46.36/6.42 Y2 @ X2)))))))) => 46.36/6.42 (((??) @ (^[Y2 : $i]: 46.36/6.42 (((??) @ (^[Y3 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) & 46.36/6.42 (in @ Y3 @ Y1) & 46.36/6.42 (((~) @ ( 46.36/6.42 ((??) @ ( 46.36/6.42 ^[Y4 : $i]: 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y4 @ 46.36/6.42 Y2) & 46.36/6.42 (in @ 46.36/6.42 Y4 @ Y1)))))))) & 46.36/6.42 (((!!) @ ( 46.36/6.42 ^[Y4 : $i]: 46.36/6.42 (((in @ 46.36/6.42 Y4 @ 46.36/6.42 Y0) => 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y3 @ 46.36/6.42 Y4) | 46.36/6.42 (( 46.36/6.42 (!!) @ ( 46.36/6.42 ^[Y5 : $i]: 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y5 @ 46.36/6.42 Y4) => 46.36/6.42 (in @ 46.36/6.42 Y5 @ Y2)))))))))))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl53])). 46.36/6.42 thf(zip_derived_cl65, plain, 46.36/6.42 (![X2 : $i]: 46.36/6.42 (((((!!) @ (^[Y0 : $i]: 46.36/6.42 (((in @ Y0 @ ('#sk22' @ X2)) => 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y1 @ Y0) => (in @ Y1 @ X2))))))))))) & 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((((in @ Y1 @ X2) & (in @ Y0 @ X2))) => 46.36/6.42 (((((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 ('#sk22' @ X2)) => 46.36/6.42 (((in @ Y0 @ Y2) <=> 46.36/6.42 (in @ Y1 @ Y2)))))))) => 46.36/6.42 (((Y0) = (Y1))))))))))))) & 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((((in @ Y1 @ ('#sk22' @ X2)) & (in @ 46.36/6.42 Y0 @ ('#sk22' @ X2)))) => 46.36/6.42 (((((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => (in @ 46.36/6.42 Y2 @ Y0)))))) | 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => (in @ 46.36/6.42 Y2 @ Y1)))))))))))))))) & 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) & 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y1 @ Y0) => (in @ Y1 @ X2)))))))) => 46.36/6.42 (((??) @ (^[Y1 : $i]: 46.36/6.42 (((??) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y1 @ ('#sk22' @ X2)) & 46.36/6.42 (in @ Y2 @ Y0) & 46.36/6.42 (((~) @ (((??) @ (^[Y3 : $i]: 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y3 @ 46.36/6.42 Y1) & 46.36/6.42 (in @ 46.36/6.42 Y3 @ Y0)))))))) & 46.36/6.42 (((!!) @ (^[Y3 : $i]: 46.36/6.42 (((in @ Y3 @ 46.36/6.42 ('#sk22' @ X2)) => 46.36/6.42 (((in @ Y2 @ 46.36/6.42 Y3) | 46.36/6.42 (((!!) @ ( 46.36/6.42 ^[Y4 : $i]: 46.36/6.42 (( 46.36/6.42 (in @ 46.36/6.42 Y4 @ 46.36/6.42 Y3) => 46.36/6.42 (in @ 46.36/6.42 Y4 @ Y1))))))))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 46.36/6.42 thf(zip_derived_cl81, plain, 46.36/6.42 (![X2 : $i]: 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) & 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y1 @ Y0) => (in @ Y1 @ X2)))))))) => 46.36/6.42 (((??) @ (^[Y1 : $i]: 46.36/6.42 (((??) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y1 @ ('#sk22' @ X2)) & 46.36/6.42 (in @ Y2 @ Y0) & 46.36/6.42 (((~) @ (((??) @ (^[Y3 : $i]: 46.36/6.42 ( 46.36/6.42 ( 46.36/6.42 (in @ 46.36/6.42 Y3 @ 46.36/6.42 Y1) & 46.36/6.42 (in @ 46.36/6.42 Y3 @ Y0)))))))) & 46.36/6.42 (((!!) @ (^[Y3 : $i]: 46.36/6.42 (((in @ Y3 @ 46.36/6.42 ('#sk22' @ X2)) => 46.36/6.42 (((in @ Y2 @ 46.36/6.42 Y3) | 46.36/6.42 (((!!) @ ( 46.36/6.42 ^[Y4 : $i]: 46.36/6.42 ( 46.36/6.42 ( 46.36/6.42 (in @ 46.36/6.42 Y4 @ 46.36/6.42 Y3) => 46.36/6.42 (in @ 46.36/6.42 Y4 @ Y1))))))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])). 46.36/6.42 thf(zip_derived_cl96, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 (((((((??) @ (^[Y0 : $i]: (in @ Y0 @ X4)))) & 46.36/6.42 (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))) => 46.36/6.42 (((??) @ (^[Y0 : $i]: 46.36/6.42 (((??) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y0 @ ('#sk22' @ X2)) & 46.36/6.42 (in @ Y1 @ X4) & 46.36/6.42 (((~) @ (((??) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) & 46.36/6.42 (in @ Y2 @ X4)))))))) & 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 ('#sk22' @ X2)) => 46.36/6.42 (((in @ Y1 @ Y2) | 46.36/6.42 (((!!) @ (^[Y3 : $i]: 46.36/6.42 (((in @ Y3 @ 46.36/6.42 Y2) => 46.36/6.42 (in @ Y3 @ 46.36/6.42 Y0)))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl81])). 46.36/6.42 thf(zip_derived_cl113, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 (~ (((((??) @ (^[Y0 : $i]: (in @ Y0 @ X4)))) & 46.36/6.42 (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))) 46.36/6.42 | (((??) @ (^[Y0 : $i]: 46.36/6.42 (((??) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y0 @ ('#sk22' @ X2)) & 46.36/6.42 (in @ Y1 @ X4) & 46.36/6.42 (((~) @ (((??) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) & 46.36/6.42 (in @ Y2 @ X4)))))))) & 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 ('#sk22' @ X2)) => 46.36/6.42 (((in @ Y1 @ Y2) | 46.36/6.42 (((!!) @ (^[Y3 : $i]: 46.36/6.42 (((in @ 46.36/6.42 Y3 @ 46.36/6.42 Y2) => 46.36/6.42 (in @ 46.36/6.42 Y3 @ Y0))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl96])). 46.36/6.42 thf(zip_derived_cl129, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 (~ (((??) @ (^[Y0 : $i]: (in @ Y0 @ X4)))) 46.36/6.42 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))) 46.36/6.42 | (((??) @ (^[Y0 : $i]: 46.36/6.42 (((??) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y0 @ ('#sk22' @ X2)) & 46.36/6.42 (in @ Y1 @ X4) & 46.36/6.42 (((~) @ (((??) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) & 46.36/6.42 (in @ Y2 @ X4)))))))) & 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 ('#sk22' @ X2)) => 46.36/6.42 (((in @ Y1 @ Y2) | 46.36/6.42 (((!!) @ (^[Y3 : $i]: 46.36/6.42 (((in @ 46.36/6.42 Y3 @ 46.36/6.42 Y2) => 46.36/6.42 (in @ 46.36/6.42 Y3 @ Y0))))))))))))))))))))))), 46.36/6.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl113])). 46.36/6.42 thf(zip_derived_cl149, plain, 46.36/6.42 (![X2 : $i, X4 : $i, X6 : $i]: 46.36/6.42 (~ (in @ X6 @ X4) 46.36/6.42 | (((??) @ (^[Y0 : $i]: 46.36/6.42 (((??) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y0 @ ('#sk22' @ X2)) & 46.36/6.42 (in @ Y1 @ X4) & 46.36/6.42 (((~) @ (((??) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) & 46.36/6.42 (in @ Y2 @ X4)))))))) & 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 ('#sk22' @ X2)) => 46.36/6.42 (((in @ Y1 @ Y2) | 46.36/6.42 (((!!) @ (^[Y3 : $i]: 46.36/6.42 (((in @ 46.36/6.42 Y3 @ 46.36/6.42 Y2) => 46.36/6.42 (in @ 46.36/6.42 Y3 @ Y0))))))))))))))))))))) 46.36/6.42 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))), 46.36/6.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl129])). 46.36/6.42 thf(zip_derived_cl164, plain, 46.36/6.42 (![X2 : $i, X4 : $i, X6 : $i]: 46.36/6.42 ( (((??) @ (^[Y0 : $i]: 46.36/6.42 (((in @ ('#sk130' @ X2 @ X4) @ ('#sk22' @ X2)) & 46.36/6.42 (in @ Y0 @ X4) & 46.36/6.42 (((~) @ (((??) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y1 @ 46.36/6.42 ('#sk130' @ X2 @ X4)) & (in @ 46.36/6.42 Y1 @ X4)))))))) & 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y1 @ ('#sk22' @ X2)) => 46.36/6.42 (((in @ Y0 @ Y1) | 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => (in @ 46.36/6.42 Y2 @ 46.36/6.42 ('#sk130' @ X2 @ X4))))))))))))))))))) 46.36/6.42 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))) 46.36/6.42 | ~ (in @ X6 @ X4))), 46.36/6.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl149])). 46.36/6.42 thf(zip_derived_cl177, plain, 46.36/6.42 (![X2 : $i, X4 : $i, X6 : $i]: 46.36/6.42 ( (((in @ ('#sk130' @ X2 @ X4) @ ('#sk22' @ X2)) & 46.36/6.42 (in @ ('#sk159' @ X2 @ X4) @ X4) & 46.36/6.42 (((~) @ (((??) @ (^[Y0 : $i]: 46.36/6.42 (((in @ Y0 @ ('#sk130' @ X2 @ X4)) & (in @ 46.36/6.42 Y0 @ X4)))))))) & 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((in @ Y0 @ ('#sk22' @ X2)) => 46.36/6.42 (((in @ ('#sk159' @ X2 @ X4) @ Y0) | 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y1 @ Y0) => (in @ Y1 @ 46.36/6.42 ('#sk130' @ X2 @ X4)))))))))))))))) 46.36/6.42 | ~ (in @ X6 @ X4) 46.36/6.42 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))), 46.36/6.42 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl164])). 46.36/6.42 thf(zip_derived_cl193, plain, 46.36/6.42 (![X2 : $i, X4 : $i, X6 : $i]: 46.36/6.42 ( (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((in @ Y0 @ ('#sk22' @ X2)) => 46.36/6.42 (((in @ ('#sk159' @ X2 @ X4) @ Y0) | 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y1 @ Y0) => (in @ Y1 @ 46.36/6.42 ('#sk130' @ X2 @ X4)))))))))))))) 46.36/6.42 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))) 46.36/6.42 | ~ (in @ X6 @ X4))), 46.36/6.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl177])). 46.36/6.42 thf(zip_derived_cl190, plain, 46.36/6.42 (![X2 : $i, X4 : $i, X6 : $i]: 46.36/6.42 ( (in @ ('#sk130' @ X2 @ X4) @ ('#sk22' @ X2)) 46.36/6.42 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))) 46.36/6.42 | ~ (in @ X6 @ X4))), 46.36/6.42 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl177])). 46.36/6.42 thf(zip_derived_cl202, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 ( ('#form193' @ X2 @ X4) 46.36/6.42 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))), 46.36/6.42 define([status(thm)])). 46.36/6.42 thf(zip_derived_cl207, plain, 46.36/6.42 (![X2 : $i, X4 : $i, X6 : $i]: 46.36/6.42 (~ ('#form193' @ X2 @ X4) 46.36/6.42 | ~ (in @ X6 @ X4) 46.36/6.42 | (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((in @ Y0 @ ('#sk22' @ X2)) => 46.36/6.42 (((in @ ('#sk159' @ X2 @ X4) @ Y0) | 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y1 @ Y0) => (in @ Y1 @ 46.36/6.42 ('#sk130' @ X2 @ X4)))))))))))))))), 46.36/6.42 inference('renaming', [status(thm)], 46.36/6.42 [zip_derived_cl193, zip_derived_cl202])). 46.36/6.42 thf(zip_derived_cl216, plain, 46.36/6.42 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 46.36/6.42 ( (((in @ X8 @ ('#sk22' @ X2)) => 46.36/6.42 (((in @ ('#sk159' @ X2 @ X4) @ X8) | 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((in @ Y0 @ X8) => (in @ Y0 @ ('#sk130' @ X2 @ X4))))))))))) 46.36/6.42 | ~ (in @ X6 @ X4) 46.36/6.42 | ~ ('#form193' @ X2 @ X4))), 46.36/6.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl207])). 46.36/6.42 thf(zip_derived_cl223, plain, 46.36/6.42 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 46.36/6.42 (~ (in @ X8 @ ('#sk22' @ X2)) 46.36/6.42 | (((in @ ('#sk159' @ X2 @ X4) @ X8) | 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((in @ Y0 @ X8) => (in @ Y0 @ ('#sk130' @ X2 @ X4))))))))) 46.36/6.42 | ~ ('#form193' @ X2 @ X4) 46.36/6.42 | ~ (in @ X6 @ X4))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl216])). 46.36/6.42 thf(zip_derived_cl231, plain, 46.36/6.42 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 46.36/6.42 ( (in @ ('#sk159' @ X2 @ X4) @ X8) 46.36/6.42 | (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((in @ Y0 @ X8) => (in @ Y0 @ ('#sk130' @ X2 @ X4))))))) 46.36/6.42 | ~ (in @ X6 @ X4) 46.36/6.42 | ~ ('#form193' @ X2 @ X4) 46.36/6.42 | ~ (in @ X8 @ ('#sk22' @ X2)))), 46.36/6.42 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl223])). 46.36/6.42 thf(zip_derived_cl240, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 (~ ('#form193' @ X2 @ X4) 46.36/6.42 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))), 46.36/6.42 define([status(thm)])). 46.36/6.42 thf(zip_derived_cl202, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 ( ('#form193' @ X2 @ X4) 46.36/6.42 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))), 46.36/6.42 define([status(thm)])). 46.36/6.42 thf(zip_derived_cl364, plain, 46.36/6.42 (![X0 : $i]: 46.36/6.42 ('#form193' @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true))) @ X0)), 46.36/6.42 inference('renaming', [status(thm)], 46.36/6.42 [zip_derived_cl363, zip_derived_cl240, zip_derived_cl202])). 46.36/6.42 thf(zip_derived_cl198, plain, 46.36/6.42 ( (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y0) => (in @ Y2 @ 46.36/6.42 Y1)))))) => 46.36/6.42 (((((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ Y1) => (in @ Y2 @ 46.36/6.42 Y0)))))) => 46.36/6.42 (((Y0) = (Y1)))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl184])). 46.36/6.42 thf(zip_derived_cl209, plain, 46.36/6.42 (![X2 : $i]: 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((((!!) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y1 @ X2) => (in @ Y1 @ Y0)))))) => 46.36/6.42 (((((!!) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y1 @ Y0) => (in @ Y1 @ X2)))))) => 46.36/6.42 (((X2) = (Y0))))))))))), 46.36/6.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl198])). 46.36/6.42 thf(zip_derived_cl218, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 (((((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (in @ Y0 @ X4)))))) => 46.36/6.42 (((((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))) => 46.36/6.42 (((X2) = (X4)))))))), 46.36/6.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl209])). 46.36/6.42 thf(zip_derived_cl225, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 (~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (in @ Y0 @ X4)))))) 46.36/6.42 | (((((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))) => 46.36/6.42 (((X2) = (X4))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl218])). 46.36/6.42 thf(zip_derived_cl202, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 ( ('#form193' @ X2 @ X4) 46.36/6.42 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))), 46.36/6.42 define([status(thm)])). 46.36/6.42 thf(zip_derived_cl233, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 (~ ('#form193' @ X4 @ X2) 46.36/6.42 | (((((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))) => 46.36/6.42 (((X2) = (X4))))))), 46.36/6.42 inference('renaming', [status(thm)], 46.36/6.42 [zip_derived_cl225, zip_derived_cl202])). 46.36/6.42 thf(zip_derived_cl245, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 (~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))) 46.36/6.42 | (((X2) = (X4))) 46.36/6.42 | ~ ('#form193' @ X4 @ X2))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl233])). 46.36/6.42 thf(zip_derived_cl259, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 (~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))) 46.36/6.42 | ((X2) = (X4)) 46.36/6.42 | ~ ('#form193' @ X4 @ X2))), 46.36/6.42 inference('simplify nested equalities', [status(thm)], 46.36/6.42 [zip_derived_cl245])). 46.36/6.42 thf(zip_derived_cl240, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 (~ ('#form193' @ X2 @ X4) 46.36/6.42 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))), 46.36/6.42 define([status(thm)])). 46.36/6.42 thf(zip_derived_cl202, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 ( ('#form193' @ X2 @ X4) 46.36/6.42 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))), 46.36/6.42 define([status(thm)])). 46.36/6.42 thf(zip_derived_cl260, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 (~ ('#form193' @ X2 @ X4) | ~ ('#form193' @ X4 @ X2) | ((X2) = (X4)))), 46.36/6.42 inference('renaming', [status(thm)], 46.36/6.42 [zip_derived_cl259, zip_derived_cl240, zip_derived_cl202])). 46.36/6.42 thf(zip_derived_cl3665, plain, 46.36/6.42 (![X0 : $i]: 46.36/6.42 (((X0) = (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) 46.36/6.42 | ~ ('#form193' @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))))), 46.36/6.42 inference('sup-', [status(thm)], [zip_derived_cl364, zip_derived_cl260])). 46.36/6.42 thf(zip_derived_cl84, plain, 46.36/6.42 ( (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((!!) @ (^[Y1 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y2 : $i]: 46.36/6.42 (((in @ Y2 @ 46.36/6.42 (dsetconstr @ Y0 @ Y1)) => (in @ 46.36/6.42 Y2 @ Y0))))))))))))), 46.36/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 46.36/6.42 thf(zip_derived_cl102, plain, 46.36/6.42 (![X2 : $i]: 46.36/6.42 (((!!) @ (^[Y0 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y1 : $i]: 46.36/6.42 (((in @ Y1 @ (dsetconstr @ X2 @ Y0)) => 46.36/6.42 (in @ Y1 @ X2)))))))))), 46.36/6.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl84])). 46.36/6.42 thf(zip_derived_cl116, plain, 46.36/6.42 (![X2 : $i, X4 : $i > $o]: 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) => (in @ Y0 @ X2))))))), 46.36/6.42 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl102])). 46.36/6.42 thf(zip_derived_cl119, plain, 46.36/6.42 (![X0 : $i]: 46.36/6.42 (((!!) @ (^[Y0 : $i]: 46.36/6.42 (((in @ Y0 @ 46.36/6.42 (dsetconstr @ X0 @ (^[Y1 : $i]: ($true)))) => (in @ 46.36/6.42 Y0 @ X0))))))), 46.36/6.42 inference('ho.refine.early.bird', [status(thm)], [zip_derived_cl116])). 46.36/6.42 thf(zip_derived_cl240, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 (~ ('#form193' @ X2 @ X4) 46.36/6.42 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))), 46.36/6.42 define([status(thm)])). 46.36/6.42 thf(zip_derived_cl202, plain, 46.36/6.42 (![X2 : $i, X4 : $i]: 46.36/6.42 ( ('#form193' @ X2 @ X4) 46.36/6.42 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))), 46.36/6.42 define([status(thm)])). 46.36/6.42 thf(zip_derived_cl359, plain, 46.36/6.42 (![X0 : $i]: 46.36/6.42 ('#form193' @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true))))), 46.36/6.42 inference('renaming', [status(thm)], 46.36/6.42 [zip_derived_cl119, zip_derived_cl240, zip_derived_cl202])). 46.36/6.42 thf(zip_derived_cl3691, plain, 46.36/6.42 (![X0 : $i]: ((X0) = (dsetconstr @ X0 @ (^[Y0 : $i]: ($true))))), 46.36/6.42 inference('demod', [status(thm)], [zip_derived_cl3665, zip_derived_cl359])). 46.36/6.42 thf(zip_derived_cl3699, plain, ((('#sk231') != ('#sk231'))), 46.36/6.42 inference('demod', [status(thm)], [zip_derived_cl304, zip_derived_cl3691])). 46.36/6.42 thf(zip_derived_cl3700, plain, ($false), 46.36/6.42 inference('simplify', [status(thm)], [zip_derived_cl3699])). 46.36/6.42 46.36/6.42 % SZS output end Refutation 46.36/6.42 46.36/6.42 46.36/6.42 % Terminating... 46.63/6.50 % Runner terminated. 46.63/6.51 % Zipperpin 1.5 exiting 46.63/6.52 EOF