%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU534^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.37C1VhC1QT true
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:54:57 PM UTC 2025
% Result : Theorem 3.27s 1.65s
% Output : Refutation 3.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.27 % Problem : SEU534^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.28 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.37C1VhC1QT true
% 0.09/0.47 % Computer : n004.cluster.edu
% 0.09/0.47 % Model : x86_64 x86_64
% 0.09/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.47 % Memory : 8042.1875MB
% 0.09/0.47 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.47 % CPULimit : 300
% 0.09/0.47 % WCLimit : 300
% 0.09/0.47 % DateTime : Wed Oct 1 16:14:38 EDT 2025
% 0.09/0.47 % CPUTime :
% 0.09/0.47 % Running portfolio for 300 s
% 0.09/0.47 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.48 % Number of cores: 8
% 0.13/0.48 % Python version: Python 3.6.8
% 0.13/0.48 % Running in HO mode
% 0.27/0.79 % Total configuration time : 828
% 0.27/0.79 % Estimated wc time : 1656
% 0.27/0.79 % Estimated cpu time (8 cpus) : 207.0
% 0.27/0.85 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.27/0.95 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.27/1.01 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.41/1.10 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.41/1.15 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.54/1.16 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.54/1.18 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.61/1.19 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 3.27/1.65 % Solved by lams/40_noforms.sh.
% 3.27/1.65 % done 61 iterations in 0.343s
% 3.27/1.65 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.27/1.65 % SZS output start Refutation
% 3.27/1.65 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 3.27/1.65 thf(setunionAx_type, type, setunionAx: $o).
% 3.27/1.65 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 3.27/1.65 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 3.27/1.65 thf(omegaSAx_type, type, omegaSAx: $o).
% 3.27/1.65 thf(eqinunit_type, type, eqinunit: $o).
% 3.27/1.65 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 3.27/1.65 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 3.27/1.65 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 3.27/1.65 thf(emptysetE_type, type, emptysetE: $o).
% 3.27/1.65 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 3.27/1.65 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 3.27/1.65 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 3.27/1.65 thf(in_type, type, in: $i > $i > $o).
% 3.27/1.65 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 3.27/1.65 thf(emptyI_type, type, emptyI: $o).
% 3.27/1.65 thf(upairsetE_type, type, upairsetE: $o).
% 3.27/1.65 thf(sk__153_type, type, sk__153: $i).
% 3.27/1.65 thf(exuE2_type, type, exuE2: $o).
% 3.27/1.65 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 3.27/1.65 thf(notinsingleton_type, type, notinsingleton: $o).
% 3.27/1.65 thf(powersetAx_type, type, powersetAx: $o).
% 3.27/1.65 thf(subPowSU_type, type, subPowSU: $o).
% 3.27/1.65 thf(sk__154_type, type, sk__154: $i > $o).
% 3.27/1.65 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 3.27/1.65 thf(notinemptyset_type, type, notinemptyset: $o).
% 3.27/1.65 thf(emptyset_type, type, emptyset: $i).
% 3.27/1.65 thf(setext_type, type, setext: $o).
% 3.27/1.65 thf(setbeta_type, type, setbeta: $o).
% 3.27/1.65 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 3.27/1.65 thf(uniqinunit_type, type, uniqinunit: $o).
% 3.27/1.65 thf(upairsetIR_type, type, upairsetIR: $o).
% 3.27/1.65 thf(zip_tseitin_3_type, type, zip_tseitin_3: $i > $i > $i > ($i > $i > $o) > $o).
% 3.27/1.65 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 3.27/1.65 thf(descr_type, type, descr: ($i > $o) > $i).
% 3.27/1.65 thf(exuE1_type, type, exuE1: $o).
% 3.27/1.65 thf(prop2set_type, type, prop2set: $o > $i).
% 3.27/1.65 thf(sk__155_type, type, sk__155: $i).
% 3.27/1.65 thf(nonemptyI_type, type, nonemptyI: $o).
% 3.27/1.65 thf(omega0Ax_type, type, omega0Ax: $o).
% 3.27/1.65 thf(powersetI_type, type, powersetI: $o).
% 3.27/1.65 thf(upairsetIL_type, type, upairsetIL: $o).
% 3.27/1.65 thf(prop2setE_type, type, prop2setE: $o).
% 3.27/1.65 thf(setextAx_type, type, setextAx: $o).
% 3.27/1.65 thf(setunion_type, type, setunion: $i > $i).
% 3.27/1.65 thf(zip_tseitin_2_type, type, zip_tseitin_2: $i > $i > $i > $o).
% 3.27/1.65 thf(descrp_type, type, descrp: $o).
% 3.27/1.65 thf(foundationAx_type, type, foundationAx: $o).
% 3.27/1.65 thf(emptysetAx_type, type, emptysetAx: $o).
% 3.27/1.65 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 3.27/1.65 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 3.27/1.65 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 3.27/1.65 thf(exu_type, type, exu: ($i > $o) > $o).
% 3.27/1.65 thf(powersetE_type, type, powersetE: $o).
% 3.27/1.65 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 3.27/1.65 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 3.27/1.65 thf(omega_type, type, omega: $i).
% 3.27/1.65 thf(setunionI_type, type, setunionI: $o).
% 3.27/1.65 thf(exuE3e_type, type, exuE3e: $o).
% 3.27/1.65 thf(powerset_type, type, powerset: $i > $i).
% 3.27/1.65 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 3.27/1.65 thf(setadjoinE_type, type, setadjoinE: $o).
% 3.27/1.65 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 3.27/1.65 thf(replAx_type, type, replAx: $o).
% 3.27/1.65 thf(nonempty_type, type, nonempty: $i > $o).
% 3.27/1.65 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 3.27/1.65 thf(setunionE_type, type, setunionE: $o).
% 3.27/1.65 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 3.27/1.65 thf(upairsetIR, axiom, upairsetIR =
% 3.27/1.65 (![Xx:$i,Xy:$i]:
% 3.27/1.65 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 3.27/1.65 thf('0', plain,
% 3.27/1.65 (( upairsetIR ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(upairsetIL, axiom, upairsetIL =
% 3.27/1.65 (![Xx:$i,Xy:$i]:
% 3.27/1.65 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 3.27/1.65 thf('1', plain,
% 3.27/1.65 (( upairsetIL ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(upairsetE, axiom, upairsetE =
% 3.27/1.65 (![Xx:$i,Xy:$i,Xz:$i]:
% 3.27/1.65 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 3.27/1.65 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 3.27/1.65 thf('2', plain,
% 3.27/1.65 (( upairsetE ) =
% 3.27/1.65 ( ![X4:$i,X6:$i,X8:$i]:
% 3.27/1.65 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 3.27/1.65 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(singletonsswitch, axiom, singletonsswitch =
% 3.27/1.65 (![Xx:$i,Xy:$i]:
% 3.27/1.65 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 3.27/1.65 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 3.27/1.65 thf('3', plain,
% 3.27/1.65 (( singletonsswitch ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 3.27/1.65 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(eqinunit, axiom, eqinunit =
% 3.27/1.65 (![Xx:$i,Xy:$i]:
% 3.27/1.65 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 3.27/1.65 thf('4', plain,
% 3.27/1.65 (( eqinunit ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(notinsingleton, axiom, notinsingleton =
% 3.27/1.65 (![Xx:$i,Xy:$i]:
% 3.27/1.65 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 3.27/1.65 thf('5', plain,
% 3.27/1.65 (( notinsingleton ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( ( X4 ) != ( X6 ) ) =>
% 3.27/1.65 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(uniqinunit, axiom, uniqinunit =
% 3.27/1.65 (![Xx:$i,Xy:$i]:
% 3.27/1.65 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 3.27/1.65 thf('6', plain,
% 3.27/1.65 (( uniqinunit ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(nonemptyImpWitness, axiom, nonemptyImpWitness =
% 3.27/1.65 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 3.27/1.65 thf('7', plain,
% 3.27/1.65 (( nonemptyImpWitness ) =
% 3.27/1.65 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(exuE2, axiom, exuE2 =
% 3.27/1.65 (![Xphi:( $i > $o )]:
% 3.27/1.65 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 3.27/1.65 ( ?[Xx:$i]: ( ![Xy:$i]: ( ( Xphi @ Xy ) <=> ( ( Xy ) = ( Xx ) ) ) ) ) ))).
% 3.27/1.65 thf('8', plain,
% 3.27/1.65 (( exuE2 ) =
% 3.27/1.65 ( ![X4:( $i > $o )]:
% 3.27/1.65 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 3.27/1.65 ( ?[X6:$i]: ( ![X8:$i]: ( ( X4 @ X8 ) <=> ( ( X8 ) = ( X6 ) ) ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(subPowSU, axiom, subPowSU =
% 3.27/1.65 (![A:$i,Xx:$i]:
% 3.27/1.65 ( ( in @ Xx @ A ) => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ))).
% 3.27/1.65 thf('9', plain,
% 3.27/1.65 (( subPowSU ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( in @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ ( setunion @ X4 ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(setunionE, axiom, setunionE =
% 3.27/1.65 (![A:$i,Xx:$i]:
% 3.27/1.65 ( ( in @ Xx @ ( setunion @ A ) ) =>
% 3.27/1.65 ( ![Xphi:$o]:
% 3.27/1.65 ( ( ![B:$i]: ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( Xphi ) ) ) ) =>
% 3.27/1.65 ( Xphi ) ) ) ))).
% 3.27/1.65 thf('10', plain,
% 3.27/1.65 (( setunionE ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( in @ X6 @ ( setunion @ X4 ) ) =>
% 3.27/1.65 ( ![X8:$o]:
% 3.27/1.65 ( ( ![X10:$i]:
% 3.27/1.65 ( ( in @ X6 @ X10 ) => ( ( in @ X10 @ X4 ) => ( X8 ) ) ) ) =>
% 3.27/1.65 ( X8 ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(setunionI, axiom, setunionI =
% 3.27/1.65 (![A:$i,Xx:$i,B:$i]:
% 3.27/1.65 ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( in @ Xx @ ( setunion @ A ) ) ) ))).
% 3.27/1.65 thf('11', plain,
% 3.27/1.65 (( setunionI ) =
% 3.27/1.65 ( ![X4:$i,X6:$i,X8:$i]:
% 3.27/1.65 ( ( in @ X6 @ X8 ) =>
% 3.27/1.65 ( ( in @ X8 @ X4 ) => ( in @ X6 @ ( setunion @ X4 ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(powersetE, axiom, powersetE =
% 3.27/1.65 (![A:$i,B:$i,Xx:$i]:
% 3.27/1.65 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 3.27/1.65 thf('12', plain,
% 3.27/1.65 (( powersetE ) =
% 3.27/1.65 ( ![X4:$i,X6:$i,X8:$i]:
% 3.27/1.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.27/1.65 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(emptyInPowerset, axiom, emptyInPowerset =
% 3.27/1.65 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 3.27/1.65 thf('13', plain,
% 3.27/1.65 (( emptyInPowerset ) =
% 3.27/1.65 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(emptyinPowerset, axiom, emptyinPowerset =
% 3.27/1.65 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 3.27/1.65 thf('14', plain,
% 3.27/1.65 (( emptyinPowerset ) =
% 3.27/1.65 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(powersetI, axiom, powersetI =
% 3.27/1.65 (![A:$i,B:$i]:
% 3.27/1.65 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 3.27/1.65 ( in @ B @ ( powerset @ A ) ) ))).
% 3.27/1.65 thf('15', plain,
% 3.27/1.65 (( powersetI ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 3.27/1.65 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(setoftrueEq, axiom, setoftrueEq =
% 3.27/1.65 (![A:$i]: ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( $true ) ) ) = ( A ) ))).
% 3.27/1.65 thf('16', plain,
% 3.27/1.65 (( setoftrueEq ) =
% 3.27/1.65 ( ![X4:$i]: ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( $true ) ) ) = ( X4 ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(setadjoinOr, axiom, setadjoinOr =
% 3.27/1.65 (![Xx:$i,A:$i,Xy:$i]:
% 3.27/1.65 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 3.27/1.65 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 3.27/1.65 thf('17', plain,
% 3.27/1.65 (( setadjoinOr ) =
% 3.27/1.65 ( ![X4:$i,X6:$i,X8:$i]:
% 3.27/1.65 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 3.27/1.65 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(setadjoinE, axiom, setadjoinE =
% 3.27/1.65 (![Xx:$i,A:$i,Xy:$i]:
% 3.27/1.65 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 3.27/1.65 ( ![Xphi:$o]:
% 3.27/1.65 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 3.27/1.65 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 3.27/1.65 thf('18', plain,
% 3.27/1.65 (( setadjoinE ) =
% 3.27/1.65 ( ![X4:$i,X6:$i,X8:$i]:
% 3.27/1.65 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 3.27/1.65 ( ![X10:$o]:
% 3.27/1.65 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 3.27/1.65 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(setadjoinIR, axiom, setadjoinIR =
% 3.27/1.65 (![Xx:$i,A:$i,Xy:$i]:
% 3.27/1.65 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 3.27/1.65 thf('19', plain,
% 3.27/1.65 (( setadjoinIR ) =
% 3.27/1.65 ( ![X4:$i,X6:$i,X8:$i]:
% 3.27/1.65 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 3.27/1.65 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 3.27/1.65 thf('20', plain,
% 3.27/1.65 (( emptyinunitempty ) =
% 3.27/1.65 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 3.27/1.65 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 3.27/1.65 thf('21', plain,
% 3.27/1.65 (( emptyinunitempty ) =
% 3.27/1.65 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(setadjoinIL, axiom, setadjoinIL =
% 3.27/1.65 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 3.27/1.65 thf('22', plain,
% 3.27/1.65 (( setadjoinIL ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(nonemptyI1, axiom, nonemptyI1 =
% 3.27/1.65 (![A:$i]: ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) => ( nonempty @ A ) ))).
% 3.27/1.65 thf('23', plain,
% 3.27/1.65 (( nonemptyI1 ) =
% 3.27/1.65 ( ![X4:$i]: ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) => ( nonempty @ X4 ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(nonemptyI, axiom, nonemptyI =
% 3.27/1.65 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 3.27/1.65 ( ( in @ Xx @ A ) =>
% 3.27/1.65 ( ( Xphi @ Xx ) =>
% 3.27/1.65 ( nonempty @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 3.27/1.65 thf('24', plain,
% 3.27/1.65 (( nonemptyI ) =
% 3.27/1.65 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 3.27/1.65 ( ( in @ X8 @ X4 ) =>
% 3.27/1.65 ( ( X6 @ X8 ) =>
% 3.27/1.65 ( nonempty @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(nonemptyE1, axiom, nonemptyE1 =
% 3.27/1.65 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 3.27/1.65 thf('25', plain,
% 3.27/1.65 (( nonemptyE1 ) =
% 3.27/1.65 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(nonempty, axiom,(( nonempty ) = (^[Xx:$i]: ( ( Xx ) != ( emptyset ) )))).
% 3.27/1.65 thf('26', plain, (( nonempty ) = ( ^[Xx:$i]: ( ( Xx ) != ( emptyset ) ) )),
% 3.27/1.65 inference('simplify_rw_rule', [status(thm)], [nonempty])).
% 3.27/1.65 thf('27', plain, (( nonempty ) = ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(setbeta, axiom, setbeta =
% 3.27/1.65 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 3.27/1.65 ( ( in @ Xx @ A ) =>
% 3.27/1.65 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) <=>
% 3.27/1.65 ( Xphi @ Xx ) ) ))).
% 3.27/1.65 thf('28', plain,
% 3.27/1.65 (( setbeta ) =
% 3.27/1.65 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 3.27/1.65 ( ( in @ X8 @ X4 ) =>
% 3.27/1.65 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=>
% 3.27/1.65 ( X6 @ X8 ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(noeltsimpempty, axiom, noeltsimpempty =
% 3.27/1.65 (![A:$i]:
% 3.27/1.65 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 3.27/1.65 thf('29', plain,
% 3.27/1.65 (( noeltsimpempty ) =
% 3.27/1.65 ( ![X4:$i]:
% 3.27/1.65 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(emptyI, axiom, emptyI =
% 3.27/1.65 (![A:$i]:
% 3.27/1.65 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 3.27/1.65 thf('30', plain,
% 3.27/1.65 (( emptyI ) =
% 3.27/1.65 ( ![X4:$i]:
% 3.27/1.65 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(setext, axiom, setext =
% 3.27/1.65 (![A:$i,B:$i]:
% 3.27/1.65 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 3.27/1.65 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 3.27/1.65 ( ( A ) = ( B ) ) ) ))).
% 3.27/1.65 thf('31', plain,
% 3.27/1.65 (( setext ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 3.27/1.65 ( ( ![X10:$i]: ( ( in @ X10 @ X6 ) => ( in @ X10 @ X4 ) ) ) =>
% 3.27/1.65 ( ( X4 ) = ( X6 ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(exuE3e, axiom, exuE3e =
% 3.27/1.65 (![Xphi:( $i > $o )]:
% 3.27/1.65 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) => ( ?[Xx:$i]: ( Xphi @ Xx ) ) ))).
% 3.27/1.65 thf('32', plain,
% 3.27/1.65 (( exuE3e ) =
% 3.27/1.65 ( ![X4:( $i > $o )]:
% 3.27/1.65 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) => ( ?[X6:$i]: ( X4 @ X6 ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(notinemptyset, axiom, notinemptyset =
% 3.27/1.65 (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 3.27/1.65 thf('33', plain,
% 3.27/1.65 (( notinemptyset ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(emptysetimpfalse, axiom, emptysetimpfalse =
% 3.27/1.65 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( $false ) ))).
% 3.27/1.65 thf('34', plain,
% 3.27/1.65 (( emptysetimpfalse ) =
% 3.27/1.65 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( $false ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(emptysetE, axiom, emptysetE =
% 3.27/1.65 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( ![Xphi:$o]: ( Xphi ) ) ))).
% 3.27/1.65 thf('35', plain,
% 3.27/1.65 (( emptysetE ) =
% 3.27/1.65 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( ![X6:$o]: ( X6 ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(prop2setE, axiom, prop2setE =
% 3.27/1.65 (![Xphi:$o,Xx:$i]: ( ( in @ Xx @ ( prop2set @ Xphi ) ) => ( Xphi ) ))).
% 3.27/1.65 thf('36', plain,
% 3.27/1.65 (( prop2setE ) =
% 3.27/1.65 ( ![X4:$o,X6:$i]: ( ( in @ X6 @ ( prop2set @ X4 ) ) => ( X4 ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(exuE1, axiom, exuE1 =
% 3.27/1.65 (![Xphi:( $i > $o )]:
% 3.27/1.65 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 3.27/1.65 ( ?[Xx:$i]:
% 3.27/1.65 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 3.27/1.65 ( Xphi @ Xx ) ) ) ))).
% 3.27/1.65 thf('37', plain,
% 3.27/1.65 (( exuE1 ) =
% 3.27/1.65 ( ![X4:( $i > $o )]:
% 3.27/1.65 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 3.27/1.65 ( ?[X6:$i]:
% 3.27/1.65 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 3.27/1.65 ( X4 @ X6 ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(dsetconstrER, axiom, dsetconstrER =
% 3.27/1.65 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 3.27/1.65 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 3.27/1.65 ( Xphi @ Xx ) ))).
% 3.27/1.65 thf('38', plain,
% 3.27/1.65 (( dsetconstrER ) =
% 3.27/1.65 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 3.27/1.65 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 3.27/1.65 ( X6 @ X8 ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(dsetconstrEL, axiom, dsetconstrEL =
% 3.27/1.65 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 3.27/1.65 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 3.27/1.65 ( in @ Xx @ A ) ))).
% 3.27/1.65 thf('39', plain,
% 3.27/1.65 (( dsetconstrEL ) =
% 3.27/1.65 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 3.27/1.65 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 3.27/1.65 ( in @ X8 @ X4 ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(dsetconstrI, axiom, dsetconstrI =
% 3.27/1.65 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 3.27/1.65 ( ( in @ Xx @ A ) =>
% 3.27/1.65 ( ( Xphi @ Xx ) =>
% 3.27/1.65 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 3.27/1.65 thf('40', plain,
% 3.27/1.65 (( dsetconstrI ) =
% 3.27/1.65 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 3.27/1.65 ( ( in @ X8 @ X4 ) =>
% 3.27/1.65 ( ( X6 @ X8 ) =>
% 3.27/1.65 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(descrp, axiom, descrp =
% 3.27/1.65 (![Xphi:( $i > $o )]:
% 3.27/1.65 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 3.27/1.65 ( Xphi @ ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 3.27/1.65 thf('41', plain,
% 3.27/1.65 (( descrp ) =
% 3.27/1.65 ( ![X4:( $i > $o )]:
% 3.27/1.65 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 3.27/1.65 ( X4 @ ( descr @ ( ^[V_2:$i]: ( X4 @ V_2 ) ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(wellorderingAx, axiom, wellorderingAx =
% 3.27/1.65 (![A:$i]:
% 3.27/1.65 ( ?[B:$i]:
% 3.27/1.65 ( ( ![C:$i]:
% 3.27/1.65 ( ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) &
% 3.27/1.65 ( ?[Xx:$i]: ( in @ Xx @ C ) ) ) =>
% 3.27/1.65 ( ?[D:$i,Xx:$i]:
% 3.27/1.65 ( ( ![E:$i]:
% 3.27/1.65 ( ( in @ E @ B ) =>
% 3.27/1.65 ( ( ![Xy:$i]: ( ( in @ Xy @ E ) => ( in @ Xy @ D ) ) ) |
% 3.27/1.65 ( in @ Xx @ E ) ) ) ) &
% 3.27/1.65 ( ~( ?[Xy:$i]: ( ( in @ Xy @ C ) & ( in @ Xy @ D ) ) ) ) &
% 3.27/1.65 ( in @ Xx @ C ) & ( in @ D @ B ) ) ) ) ) &
% 3.27/1.65 ( ![C:$i,D:$i]:
% 3.27/1.65 ( ( ( in @ C @ B ) & ( in @ D @ B ) ) =>
% 3.27/1.65 ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ D ) ) ) |
% 3.27/1.65 ( ![Xx:$i]: ( ( in @ Xx @ D ) => ( in @ Xx @ C ) ) ) ) ) ) &
% 3.27/1.65 ( ![Xx:$i,Xy:$i]:
% 3.27/1.65 ( ( ( in @ Xx @ A ) & ( in @ Xy @ A ) ) =>
% 3.27/1.65 ( ( ![C:$i]:
% 3.27/1.65 ( ( in @ C @ B ) => ( ( in @ Xx @ C ) <=> ( in @ Xy @ C ) ) ) ) =>
% 3.27/1.65 ( ( Xx ) = ( Xy ) ) ) ) ) &
% 3.27/1.65 ( ![C:$i]:
% 3.27/1.65 ( ( in @ C @ B ) =>
% 3.27/1.65 ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) ) ) ) ))).
% 3.27/1.65 thf('42', plain,
% 3.27/1.65 (( wellorderingAx ) =
% 3.27/1.65 ( ![X4:$i]:
% 3.27/1.65 ( ?[X6:$i]:
% 3.27/1.65 ( ( ![X8:$i]:
% 3.27/1.65 ( ( ( ![X10:$i]: ( ( in @ X10 @ X8 ) => ( in @ X10 @ X4 ) ) ) &
% 3.27/1.65 ( ?[X12:$i]: ( in @ X12 @ X8 ) ) ) =>
% 3.27/1.65 ( ?[X14:$i,X16:$i]:
% 3.27/1.65 ( ( ![X18:$i]:
% 3.27/1.65 ( ( in @ X18 @ X6 ) =>
% 3.27/1.65 ( ( ![X20:$i]:
% 3.27/1.65 ( ( in @ X20 @ X18 ) => ( in @ X20 @ X14 ) ) ) |
% 3.27/1.65 ( in @ X16 @ X18 ) ) ) ) &
% 3.27/1.65 ( ~( ?[X22:$i]: ( ( in @ X22 @ X8 ) & ( in @ X22 @ X14 ) ) ) ) &
% 3.27/1.65 ( in @ X16 @ X8 ) & ( in @ X14 @ X6 ) ) ) ) ) &
% 3.27/1.65 ( ![X24:$i,X26:$i]:
% 3.27/1.65 ( ( ( in @ X24 @ X6 ) & ( in @ X26 @ X6 ) ) =>
% 3.27/1.65 ( ( ![X28:$i]: ( ( in @ X28 @ X24 ) => ( in @ X28 @ X26 ) ) ) |
% 3.27/1.65 ( ![X30:$i]: ( ( in @ X30 @ X26 ) => ( in @ X30 @ X24 ) ) ) ) ) ) &
% 3.27/1.65 ( ![X32:$i,X34:$i]:
% 3.27/1.65 ( ( ( in @ X32 @ X4 ) & ( in @ X34 @ X4 ) ) =>
% 3.27/1.65 ( ( ![X36:$i]:
% 3.27/1.65 ( ( in @ X36 @ X6 ) =>
% 3.27/1.65 ( ( in @ X32 @ X36 ) <=> ( in @ X34 @ X36 ) ) ) ) =>
% 3.27/1.65 ( ( X32 ) = ( X34 ) ) ) ) ) &
% 3.27/1.65 ( ![X38:$i]:
% 3.27/1.65 ( ( in @ X38 @ X6 ) =>
% 3.27/1.65 ( ![X40:$i]: ( ( in @ X40 @ X38 ) => ( in @ X40 @ X4 ) ) ) ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(foundationAx, axiom, foundationAx =
% 3.27/1.65 (![A:$i]:
% 3.27/1.65 ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) =>
% 3.27/1.65 ( ?[B:$i]:
% 3.27/1.65 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ A ) & ( in @ Xx @ B ) ) ) ) &
% 3.27/1.65 ( in @ B @ A ) ) ) ))).
% 3.27/1.65 thf('43', plain,
% 3.27/1.65 (( foundationAx ) =
% 3.27/1.65 ( ![X4:$i]:
% 3.27/1.65 ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) =>
% 3.27/1.65 ( ?[X8:$i]:
% 3.27/1.65 ( ( ~( ?[X10:$i]: ( ( in @ X10 @ X4 ) & ( in @ X10 @ X8 ) ) ) ) &
% 3.27/1.65 ( in @ X8 @ X4 ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(replAx, axiom, replAx =
% 3.27/1.65 (![Xphi:( $i > $i > $o ),A:$i]:
% 3.27/1.65 ( ( ![Xx:$i]:
% 3.27/1.65 ( ( in @ Xx @ A ) => ( exu @ ( ^[Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ) ) =>
% 3.27/1.65 ( ?[B:$i]:
% 3.27/1.65 ( ![Xx:$i]:
% 3.27/1.65 ( ( in @ Xx @ B ) <=>
% 3.27/1.65 ( ?[Xy:$i]: ( ( Xphi @ Xy @ Xx ) & ( in @ Xy @ A ) ) ) ) ) ) ))).
% 3.27/1.65 thf('44', plain,
% 3.27/1.65 (( replAx ) =
% 3.27/1.65 ( ![X4:( $i > $i > $o ),X6:$i]:
% 3.27/1.65 ( ( ![X8:$i]:
% 3.27/1.65 ( ( in @ X8 @ X6 ) => ( exu @ ( ^[V_1:$i]: ( X4 @ X8 @ V_1 ) ) ) ) ) =>
% 3.27/1.65 ( ?[X10:$i]:
% 3.27/1.65 ( ![X12:$i]:
% 3.27/1.65 ( ( in @ X12 @ X10 ) <=>
% 3.27/1.65 ( ?[X14:$i]: ( ( X4 @ X14 @ X12 ) & ( in @ X14 @ X6 ) ) ) ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(omegaIndAx, axiom, omegaIndAx =
% 3.27/1.65 (![A:$i]:
% 3.27/1.65 ( ( ( in @ emptyset @ A ) &
% 3.27/1.65 ( ![Xx:$i]:
% 3.27/1.65 ( ( ( in @ Xx @ omega ) & ( in @ Xx @ A ) ) =>
% 3.27/1.65 ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) ) =>
% 3.27/1.65 ( ![Xx:$i]: ( ( in @ Xx @ omega ) => ( in @ Xx @ A ) ) ) ))).
% 3.27/1.65 thf('45', plain,
% 3.27/1.65 (( omegaIndAx ) =
% 3.27/1.65 ( ![X4:$i]:
% 3.27/1.65 ( ( ( in @ emptyset @ X4 ) &
% 3.27/1.65 ( ![X6:$i]:
% 3.27/1.65 ( ( ( in @ X6 @ omega ) & ( in @ X6 @ X4 ) ) =>
% 3.27/1.65 ( in @ ( setadjoin @ X6 @ X6 ) @ X4 ) ) ) ) =>
% 3.27/1.65 ( ![X8:$i]: ( ( in @ X8 @ omega ) => ( in @ X8 @ X4 ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(omegaSAx, axiom, omegaSAx =
% 3.27/1.65 (![Xx:$i]:
% 3.27/1.65 ( ( in @ Xx @ omega ) => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ))).
% 3.27/1.65 thf('46', plain,
% 3.27/1.65 (( omegaSAx ) =
% 3.27/1.65 ( ![X4:$i]:
% 3.27/1.65 ( ( in @ X4 @ omega ) => ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(omega0Ax, axiom,(( omega0Ax ) = (in @ emptyset @ omega))).
% 3.27/1.65 thf('47', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 3.27/1.65 inference('simplify_rw_rule', [status(thm)], [omega0Ax])).
% 3.27/1.65 thf('48', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(setunionAx, axiom, setunionAx =
% 3.27/1.65 (![A:$i,Xx:$i]:
% 3.27/1.65 ( ( in @ Xx @ ( setunion @ A ) ) <=>
% 3.27/1.65 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))).
% 3.27/1.65 thf('49', plain,
% 3.27/1.65 (( setunionAx ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( in @ X6 @ ( setunion @ X4 ) ) <=>
% 3.27/1.65 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(powersetAx, axiom, powersetAx =
% 3.27/1.65 (![A:$i,B:$i]:
% 3.27/1.65 ( ( in @ B @ ( powerset @ A ) ) <=>
% 3.27/1.65 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 3.27/1.65 thf('50', plain,
% 3.27/1.65 (( powersetAx ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.27/1.65 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(setadjoinAx, axiom, setadjoinAx =
% 3.27/1.65 (![Xx:$i,A:$i,Xy:$i]:
% 3.27/1.65 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 3.27/1.65 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 3.27/1.65 thf('51', plain,
% 3.27/1.65 (( setadjoinAx ) =
% 3.27/1.65 ( ![X4:$i,X6:$i,X8:$i]:
% 3.27/1.65 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 3.27/1.65 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 3.27/1.65 thf('52', plain,
% 3.27/1.65 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(setextAx, axiom, setextAx =
% 3.27/1.65 (![A:$i,B:$i]:
% 3.27/1.65 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) <=> ( in @ Xx @ B ) ) ) =>
% 3.27/1.65 ( ( A ) = ( B ) ) ))).
% 3.27/1.65 thf('53', plain,
% 3.27/1.65 (( setextAx ) =
% 3.27/1.65 ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 3.27/1.65 ( ( X4 ) = ( X6 ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(exu, axiom,(( exu ) =
% 3.27/1.65 (^[Xphi:( $i > $o )]:
% 3.27/1.65 ( ?[Xx:$i]:
% 3.27/1.65 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & ( Xphi @ Xx ) ) )))).
% 3.27/1.65 thf('54', plain,
% 3.27/1.65 (( exu ) =
% 3.27/1.65 ( ^[Xphi:( $i > $o )]:
% 3.27/1.65 ( ?[Xx:$i]:
% 3.27/1.65 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 3.27/1.65 ( Xphi @ Xx ) ) ) )),
% 3.27/1.65 inference('simplify_rw_rule', [status(thm)], [exu])).
% 3.27/1.65 thf('55', plain,
% 3.27/1.65 (( exu ) =
% 3.27/1.65 ( ^[V_1:( $i > $o )]:
% 3.27/1.65 ( ?[X4:$i]:
% 3.27/1.65 ( ( ![X6:$i]: ( ( V_1 @ X6 ) => ( ( X4 ) = ( X6 ) ) ) ) &
% 3.27/1.65 ( V_1 @ X4 ) ) ) )),
% 3.27/1.65 define([status(thm)])).
% 3.27/1.65 thf(emptyE1, conjecture,
% 3.27/1.65 (( setextAx ) =>
% 3.27/1.65 ( ( emptysetAx ) =>
% 3.27/1.65 ( ( setadjoinAx ) =>
% 3.27/1.65 ( ( powersetAx ) =>
% 3.27/1.65 ( ( setunionAx ) =>
% 3.27/1.65 ( ( omega0Ax ) =>
% 3.27/1.65 ( ( omegaSAx ) =>
% 3.27/1.65 ( ( omegaIndAx ) =>
% 3.27/1.65 ( ( replAx ) =>
% 3.27/1.65 ( ( foundationAx ) =>
% 3.27/1.65 ( ( wellorderingAx ) =>
% 3.27/1.65 ( ( descrp ) =>
% 3.27/1.65 ( ( dsetconstrI ) =>
% 3.27/1.65 ( ( dsetconstrEL ) =>
% 3.27/1.65 ( ( dsetconstrER ) =>
% 3.27/1.65 ( ( exuE1 ) =>
% 3.27/1.65 ( ( prop2setE ) =>
% 3.27/1.65 ( ( emptysetE ) =>
% 3.27/1.65 ( ( emptysetimpfalse ) =>
% 3.27/1.65 ( ( notinemptyset ) =>
% 3.27/1.65 ( ( exuE3e ) =>
% 3.27/1.65 ( ( setext ) =>
% 3.27/1.65 ( ( emptyI ) =>
% 3.27/1.65 ( ( noeltsimpempty ) =>
% 3.27/1.65 ( ( setbeta ) =>
% 3.27/1.65 ( ( nonemptyE1 ) =>
% 3.27/1.65 ( ( nonemptyI ) =>
% 3.27/1.65 ( ( nonemptyI1 ) =>
% 3.27/1.65 ( ( setadjoinIL ) =>
% 3.27/1.65 ( ( emptyinunitempty ) =>
% 3.27/1.65 ( ( setadjoinIR ) =>
% 3.27/1.65 ( ( setadjoinE ) =>
% 3.27/1.65 ( (
% 3.27/1.65 setadjoinOr ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 setoftrueEq ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 powersetI ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 emptyinPowerset ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 emptyInPowerset ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 powersetE ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 setunionI ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 setunionE ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 subPowSU ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 exuE2 ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 nonemptyImpWitness ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 uniqinunit ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 notinsingleton ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 eqinunit ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 singletonsswitch ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 upairsetE ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 upairsetIL ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 upairsetIR ) =>
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 A:$i,
% 3.27/1.65 Xphi:(
% 3.27/1.65 $i > $o )]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ?[
% 3.27/1.65 Xx:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 Xphi @ Xx ) &
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 Xx @ A ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 dsetconstr
% 3.27/1.65 @
% 3.27/1.65 A @
% 3.27/1.65 (
% 3.27/1.65 ^[
% 3.27/1.65 Xx:$i]:
% 3.27/1.65 (
% 3.27/1.65 Xphi @ Xx ) ) ) =
% 3.27/1.65 (
% 3.27/1.65 emptyset ) ) =>
% 3.27/1.65 (
% 3.27/1.65 $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.27/1.65 thf(zf_stmt_0, conjecture,
% 3.27/1.65 (( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 3.27/1.65 ( ( X4 ) = ( X6 ) ) ) ) =>
% 3.27/1.65 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 3.27/1.65 ( ( ![X12:$i,X14:$i,X16:$i]:
% 3.27/1.65 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 3.27/1.65 ( ( in @ X16 @ X14 ) | ( ( X16 ) = ( X12 ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X18:$i,X20:$i]:
% 3.27/1.65 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 3.27/1.65 ( ![X22:$i]: ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X24:$i,X26:$i]:
% 3.27/1.65 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 3.27/1.65 ( ?[X28:$i]: ( ( in @ X26 @ X28 ) & ( in @ X28 @ X24 ) ) ) ) ) =>
% 3.27/1.65 ( ( in @ emptyset @ omega ) =>
% 3.27/1.65 ( ( ![X30:$i]:
% 3.27/1.65 ( ( in @ X30 @ omega ) =>
% 3.27/1.65 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 3.27/1.65 ( ( ![X32:$i]:
% 3.27/1.65 ( ( ( ![X34:$i]:
% 3.27/1.65 ( ( ( in @ X34 @ X32 ) & ( in @ X34 @ omega ) ) =>
% 3.27/1.65 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) &
% 3.27/1.65 ( in @ emptyset @ X32 ) ) =>
% 3.27/1.65 ( ![X36:$i]:
% 3.27/1.65 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 3.27/1.65 ( ( ![X42:$i]:
% 3.27/1.65 ( ( in @ X42 @ X40 ) =>
% 3.27/1.65 ( ?[X44:$i]:
% 3.27/1.65 ( ( X38 @ X42 @ X44 ) &
% 3.27/1.65 ( ![X46:$i]:
% 3.27/1.65 ( ( X38 @ X42 @ X46 ) =>
% 3.27/1.65 ( ( X44 ) = ( X46 ) ) ) ) ) ) ) ) =>
% 3.27/1.65 ( ?[X48:$i]:
% 3.27/1.65 ( ![X50:$i]:
% 3.27/1.65 ( ( in @ X50 @ X48 ) <=>
% 3.27/1.65 ( ?[X52:$i]:
% 3.27/1.65 ( ( in @ X52 @ X40 ) & ( X38 @ X52 @ X50 ) ) ) ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X54:$i]:
% 3.27/1.65 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 3.27/1.65 ( ?[X58:$i]:
% 3.27/1.65 ( ( in @ X58 @ X54 ) &
% 3.27/1.65 ( ~( ?[X60:$i]:
% 3.27/1.65 ( ( in @ X60 @ X58 ) & ( in @ X60 @ X54 ) ) ) ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X62:$i]:
% 3.27/1.65 ( ?[X64:$i]:
% 3.27/1.65 ( ( ![X96:$i]:
% 3.27/1.65 ( ( in @ X96 @ X64 ) =>
% 3.27/1.65 ( ![X98:$i]:
% 3.27/1.65 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) &
% 3.27/1.65 ( ![X90:$i,X92:$i]:
% 3.27/1.65 ( ( ( in @ X92 @ X62 ) & ( in @ X90 @ X62 ) ) =>
% 3.27/1.65 ( ( ![X94:$i]:
% 3.27/1.65 ( ( in @ X94 @ X64 ) =>
% 3.27/1.65 ( ( in @ X90 @ X94 ) <=>
% 3.27/1.65 ( in @ X92 @ X94 ) ) ) ) =>
% 3.27/1.65 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 3.27/1.65 ( ![X82:$i,X84:$i]:
% 3.27/1.65 ( ( ( in @ X84 @ X64 ) & ( in @ X82 @ X64 ) ) =>
% 3.27/1.65 ( ( ![X88:$i]:
% 3.27/1.65 ( ( in @ X88 @ X84 ) =>
% 3.27/1.65 ( in @ X88 @ X82 ) ) ) |
% 3.27/1.65 ( ![X86:$i]:
% 3.27/1.65 ( ( in @ X86 @ X82 ) =>
% 3.27/1.65 ( in @ X86 @ X84 ) ) ) ) ) ) &
% 3.27/1.65 ( ![X66:$i]:
% 3.27/1.65 ( ( ( ?[X70:$i]: ( in @ X70 @ X66 ) ) &
% 3.27/1.65 ( ![X68:$i]:
% 3.27/1.65 ( ( in @ X68 @ X66 ) =>
% 3.27/1.65 ( in @ X68 @ X62 ) ) ) ) =>
% 3.27/1.65 ( ?[X72:$i,X74:$i]:
% 3.27/1.65 ( ( in @ X72 @ X64 ) &
% 3.27/1.65 ( in @ X74 @ X66 ) &
% 3.27/1.65 ( ~( ?[X80:$i]:
% 3.27/1.65 ( ( in @ X80 @ X72 ) &
% 3.27/1.65 ( in @ X80 @ X66 ) ) ) ) &
% 3.27/1.65 ( ![X76:$i]:
% 3.27/1.65 ( ( in @ X76 @ X64 ) =>
% 3.27/1.65 ( ( in @ X74 @ X76 ) |
% 3.27/1.65 ( ![X78:$i]:
% 3.27/1.65 ( ( in @ X78 @ X76 ) =>
% 3.27/1.65 ( in @ X78 @ X72 ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X100:( $i > $o )]:
% 3.27/1.65 ( ( ?[X102:$i]:
% 3.27/1.65 ( ( X100 @ X102 ) &
% 3.27/1.65 ( ![X104:$i]:
% 3.27/1.65 ( ( X100 @ X104 ) =>
% 3.27/1.65 ( ( X102 ) = ( X104 ) ) ) ) ) ) =>
% 3.27/1.65 ( X100 @
% 3.27/1.65 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 3.27/1.65 ( ( in @ X110 @ X106 ) =>
% 3.27/1.65 ( ( X108 @ X110 ) =>
% 3.27/1.65 ( in @
% 3.27/1.65 X110 @
% 3.27/1.65 ( dsetconstr @
% 3.27/1.65 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 3.27/1.65 ( ( in @
% 3.27/1.65 X116 @
% 3.27/1.65 ( dsetconstr @
% 3.27/1.65 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 3.27/1.65 ( in @ X116 @ X112 ) ) ) =>
% 3.27/1.65 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 3.27/1.65 ( ( in @
% 3.27/1.65 X122 @
% 3.27/1.65 ( dsetconstr @
% 3.27/1.65 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 3.27/1.65 ( X120 @ X122 ) ) ) =>
% 3.27/1.65 ( ( ![X124:( $i > $o )]:
% 3.27/1.65 ( ( ?[X126:$i]:
% 3.27/1.65 ( ( X124 @ X126 ) &
% 3.27/1.65 ( ![X128:$i]:
% 3.27/1.65 ( ( X124 @ X128 ) =>
% 3.27/1.65 ( ( X126 ) = ( X128 ) ) ) ) ) ) =>
% 3.27/1.65 ( ?[X130:$i]:
% 3.27/1.65 ( ( X124 @ X130 ) &
% 3.27/1.65 ( ![X132:$i]:
% 3.27/1.65 ( ( X124 @ X132 ) =>
% 3.27/1.65 ( ( X130 ) = ( X132 ) ) ) ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X134:$o,X136:$i]:
% 3.27/1.65 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 3.27/1.65 ( X134 ) ) ) =>
% 3.27/1.65 ( ( ![X138:$i]:
% 3.27/1.65 ( ( in @ X138 @ emptyset ) =>
% 3.27/1.65 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 3.27/1.65 ( ( ![X142:$i]:
% 3.27/1.65 ( ( in @ X142 @ emptyset ) =>
% 3.27/1.65 ( $false ) ) ) =>
% 3.27/1.65 ( ( ![X144:$i]:
% 3.27/1.65 ( ~( in @ X144 @ emptyset ) ) ) =>
% 3.27/1.65 ( ( ![X146:( $i > $o )]:
% 3.27/1.65 ( ( ?[X148:$i]:
% 3.27/1.65 ( ( X146 @ X148 ) &
% 3.27/1.65 ( ![X150:$i]:
% 3.27/1.65 ( ( X146 @ X150 ) =>
% 3.27/1.65 ( ( X148 ) = ( X150 ) ) ) ) ) ) =>
% 3.27/1.65 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 3.27/1.65 ( ( ![X154:$i,X156:$i]:
% 3.27/1.65 ( ( ![X158:$i]:
% 3.27/1.65 ( ( in @ X158 @ X154 ) =>
% 3.27/1.65 ( in @ X158 @ X156 ) ) ) =>
% 3.27/1.65 ( ( ![X160:$i]:
% 3.27/1.65 ( ( in @ X160 @ X156 ) =>
% 3.27/1.65 ( in @ X160 @ X154 ) ) ) =>
% 3.27/1.65 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X162:$i]:
% 3.27/1.65 ( ( ![X164:$i]:
% 3.27/1.65 ( ~( in @ X164 @ X162 ) ) ) =>
% 3.27/1.65 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 3.27/1.65 ( ( ![X166:$i]:
% 3.27/1.65 ( ( ![X168:$i]:
% 3.27/1.65 ( ~( in @ X168 @ X166 ) ) ) =>
% 3.27/1.65 ( ( X166 ) =
% 3.27/1.65 ( emptyset ) ) ) ) =>
% 3.27/1.65 ( ( ![X170:$i,
% 3.27/1.65 X172:( $i > $o ),
% 3.27/1.65 X174:$i]:
% 3.27/1.65 ( ( in @ X174 @ X170 ) =>
% 3.27/1.65 ( ( in @
% 3.27/1.65 X174 @
% 3.27/1.65 ( dsetconstr @
% 3.27/1.65 X170 @
% 3.27/1.65 ( ^[V_5:$i]:
% 3.27/1.65 ( X172 @ V_5 ) ) ) ) <=>
% 3.27/1.65 ( X172 @ X174 ) ) ) ) =>
% 3.27/1.65 ( ( ![X176:$i]:
% 3.27/1.65 ( ( ( X176 ) !=
% 3.27/1.65 ( emptyset ) ) =>
% 3.27/1.65 ( ?[X178:$i]:
% 3.27/1.65 ( in @ X178 @ X176 ) ) ) ) =>
% 3.27/1.65 ( ( ![X180:$i,
% 3.27/1.65 X182:( $i > $o ),
% 3.27/1.65 X184:$i]:
% 3.27/1.65 ( ( in @ X184 @ X180 ) =>
% 3.27/1.65 ( ( X182 @ X184 ) =>
% 3.27/1.65 ( ( dsetconstr @
% 3.27/1.65 X180 @
% 3.27/1.65 ( ^[
% 3.27/1.65 V_6:$i]:
% 3.27/1.65 (
% 3.27/1.65 X182 @ V_6 ) ) ) !=
% 3.27/1.65 ( emptyset ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X186:$i]:
% 3.27/1.65 ( ( ?[X188:$i]:
% 3.27/1.65 ( in @
% 3.27/1.65 X188 @ X186 ) ) =>
% 3.27/1.65 ( ( X186 ) !=
% 3.27/1.65 ( emptyset ) ) ) ) =>
% 3.27/1.65 ( ( ![X190:$i,
% 3.27/1.65 X192:$i]:
% 3.27/1.65 ( in @
% 3.27/1.65 X190 @
% 3.27/1.65 ( setadjoin @
% 3.27/1.65 X190 @ X192 ) ) ) =>
% 3.27/1.65 ( ( in @
% 3.27/1.65 emptyset @
% 3.27/1.65 ( setadjoin @
% 3.27/1.65 emptyset @
% 3.27/1.65 emptyset ) ) =>
% 3.27/1.65 ( ( ![X194:$i,
% 3.27/1.65 X196:$i,
% 3.27/1.65 X198:$i]:
% 3.27/1.65 ( (
% 3.27/1.65 in @
% 3.27/1.65 X198 @
% 3.27/1.65 X196 ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X198 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X194 @
% 3.27/1.65 X196 ) ) ) ) =>
% 3.27/1.65 ( ( ![
% 3.27/1.65 X200:$i,
% 3.27/1.65 X202:$i,
% 3.27/1.65 X204:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X204 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X200 @
% 3.27/1.65 X202 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X206:$o]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X204 ) =
% 3.27/1.65 (
% 3.27/1.65 X200 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 X206 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X204 @
% 3.27/1.65 X202 ) =>
% 3.27/1.65 (
% 3.27/1.65 X206 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 X206 ) ) ) ) ) ) =>
% 3.27/1.65 ( (
% 3.27/1.65 ![
% 3.27/1.65 X208:$i,
% 3.27/1.65 X210:$i,
% 3.27/1.65 X212:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X212 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X208 @
% 3.27/1.65 X210 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X212 @
% 3.27/1.65 X210 ) |
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X212 ) =
% 3.27/1.65 (
% 3.27/1.65 X208 ) ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X214:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 dsetconstr
% 3.27/1.65 @
% 3.27/1.65 X214 @
% 3.27/1.65 (
% 3.27/1.65 ^[
% 3.27/1.65 V_7:$i]:
% 3.27/1.65 (
% 3.27/1.65 $true ) ) ) =
% 3.27/1.65 (
% 3.27/1.65 X214 ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X216:$i,
% 3.27/1.65 X218:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X220:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X220 @
% 3.27/1.65 X218 ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X220 @
% 3.27/1.65 X216 ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X218 @
% 3.27/1.65 (
% 3.27/1.65 powerset @
% 3.27/1.65 X216 ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X222:$i]:
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 emptyset @
% 3.27/1.65 (
% 3.27/1.65 powerset @
% 3.27/1.65 X222 ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X224:$i]:
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 emptyset @
% 3.27/1.65 (
% 3.27/1.65 powerset @
% 3.27/1.65 X224 ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X226:$i,
% 3.27/1.65 X228:$i,
% 3.27/1.65 X230:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X228 @
% 3.27/1.65 (
% 3.27/1.65 powerset @
% 3.27/1.65 X226 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X230 @
% 3.27/1.65 X228 ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X230 @
% 3.27/1.65 X226 ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X232:$i,
% 3.27/1.65 X234:$i,
% 3.27/1.65 X236:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X234 @
% 3.27/1.65 X236 ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X236 @
% 3.27/1.65 X232 ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X234 @
% 3.27/1.65 (
% 3.27/1.65 setunion @
% 3.27/1.65 X232 ) ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X238:$i,
% 3.27/1.65 X240:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X240 @
% 3.27/1.65 (
% 3.27/1.65 setunion @
% 3.27/1.65 X238 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X242:$o]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X244:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X240 @
% 3.27/1.65 X244 ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X244 @
% 3.27/1.65 X238 ) =>
% 3.27/1.65 (
% 3.27/1.65 X242 ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 X242 ) ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X246:$i,
% 3.27/1.65 X248:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X248 @
% 3.27/1.65 X246 ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X248 @
% 3.27/1.65 (
% 3.27/1.65 powerset @
% 3.27/1.65 (
% 3.27/1.65 setunion @
% 3.27/1.65 X246 ) ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X250:(
% 3.27/1.65 $i > $o )]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ?[
% 3.27/1.65 X252:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X250 @
% 3.27/1.65 X252 ) &
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X254:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X250 @
% 3.27/1.65 X254 ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X252 ) =
% 3.27/1.65 (
% 3.27/1.65 X254 ) ) ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 ?[
% 3.27/1.65 X256:$i]:
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X258:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X250 @
% 3.27/1.65 X258 ) <=>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X258 ) =
% 3.27/1.65 (
% 3.27/1.65 X256 ) ) ) ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X260:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X260 ) !=
% 3.27/1.65 (
% 3.27/1.65 emptyset ) ) =>
% 3.27/1.65 (
% 3.27/1.65 ?[
% 3.27/1.65 X262:$i]:
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X262 @
% 3.27/1.65 X260 ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X264:$i,
% 3.27/1.65 X266:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X264 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X266 @
% 3.27/1.65 emptyset ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X264 ) =
% 3.27/1.65 (
% 3.27/1.65 X266 ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X268:$i,
% 3.27/1.65 X270:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X268 ) !=
% 3.27/1.65 (
% 3.27/1.65 X270 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 ~(
% 3.27/1.65 in @
% 3.27/1.65 X270 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X268 @
% 3.27/1.65 emptyset ) ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X272:$i,
% 3.27/1.65 X274:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X272 ) =
% 3.27/1.65 (
% 3.27/1.65 X274 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X272 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X274 @
% 3.27/1.65 emptyset ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X276:$i,
% 3.27/1.65 X278:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X276 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X278 @
% 3.27/1.65 emptyset ) ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X278 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X276 @
% 3.27/1.65 emptyset ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X280:$i,
% 3.27/1.65 X282:$i,
% 3.27/1.65 X284:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X284 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X280 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X282 @
% 3.27/1.65 emptyset ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X284 ) =
% 3.27/1.65 (
% 3.27/1.65 X282 ) ) |
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X284 ) =
% 3.27/1.65 (
% 3.27/1.65 X280 ) ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X286:$i,
% 3.27/1.65 X288:$i]:
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X286 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X286 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X288 @
% 3.27/1.65 emptyset ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X290:$i,
% 3.27/1.65 X292:$i]:
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X292 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X290 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X292 @
% 3.27/1.65 emptyset ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X294:$i,
% 3.27/1.65 X296:(
% 3.27/1.65 $i > $o )]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ?[
% 3.27/1.65 X298:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X298 @
% 3.27/1.65 X294 ) &
% 3.27/1.65 (
% 3.27/1.65 X296 @
% 3.27/1.65 X298 ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 dsetconstr
% 3.27/1.65 @
% 3.27/1.65 X294 @
% 3.27/1.65 (
% 3.27/1.65 ^[
% 3.27/1.65 V_8:$i]:
% 3.27/1.65 (
% 3.27/1.65 X296 @ V_8 ) ) ) =
% 3.27/1.65 (
% 3.27/1.65 emptyset ) ) =>
% 3.27/1.65 (
% 3.27/1.65 $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.27/1.65 thf(zf_stmt_1, type, zip_tseitin_3 : $i > $i > $i > ( $i > $i > $o ) > $o).
% 3.27/1.65 thf(zf_stmt_2, axiom,
% 3.27/1.65 (![X52:$i,X50:$i,X40:$i,X38:( $i > $i > $o )]:
% 3.27/1.65 ( ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) <=>
% 3.27/1.65 ( ( X38 @ X52 @ X50 ) & ( in @ X52 @ X40 ) ) ))).
% 3.27/1.65 thf(zf_stmt_3, type, zip_tseitin_2 : $i > $i > $i > $o).
% 3.27/1.65 thf(zf_stmt_4, axiom,
% 3.27/1.65 (![X28:$i,X26:$i,X24:$i]:
% 3.27/1.65 ( ( zip_tseitin_2 @ X28 @ X26 @ X24 ) <=>
% 3.27/1.65 ( ( in @ X28 @ X24 ) & ( in @ X26 @ X28 ) ) ))).
% 3.27/1.65 thf(zf_stmt_5, type, zip_tseitin_1 : $i > $i > $i > $o).
% 3.27/1.65 thf(zf_stmt_6, axiom,
% 3.27/1.65 (![X22:$i,X20:$i,X18:$i]:
% 3.27/1.65 ( ( zip_tseitin_1 @ X22 @ X20 @ X18 ) <=>
% 3.27/1.65 ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ))).
% 3.27/1.65 thf(zf_stmt_7, type, zip_tseitin_0 : $i > $i > $i > $o).
% 3.27/1.65 thf(zf_stmt_8, axiom,
% 3.27/1.65 (![X16:$i,X14:$i,X12:$i]:
% 3.27/1.65 ( ( zip_tseitin_0 @ X16 @ X14 @ X12 ) <=>
% 3.27/1.65 ( ( ( X16 ) = ( X12 ) ) | ( in @ X16 @ X14 ) ) ))).
% 3.27/1.65 thf(zf_stmt_9, conjecture,
% 3.27/1.65 (( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 3.27/1.65 ( ( X4 ) = ( X6 ) ) ) ) =>
% 3.27/1.65 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 3.27/1.65 ( ( ![X12:$i,X14:$i,X16:$i]:
% 3.27/1.65 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 3.27/1.65 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 3.27/1.65 ( ( ![X18:$i,X20:$i]:
% 3.27/1.65 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 3.27/1.65 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 3.27/1.65 ( ( ![X24:$i,X26:$i]:
% 3.27/1.65 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 3.27/1.65 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 3.27/1.65 ( ( in @ emptyset @ omega ) =>
% 3.27/1.65 ( ( ![X30:$i]:
% 3.27/1.65 ( ( in @ X30 @ omega ) =>
% 3.27/1.65 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 3.27/1.65 ( ( ![X32:$i]:
% 3.27/1.65 ( ( ( in @ emptyset @ X32 ) &
% 3.27/1.65 ( ![X34:$i]:
% 3.27/1.65 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 3.27/1.65 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 3.27/1.65 ( ![X36:$i]:
% 3.27/1.65 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 3.27/1.65 ( ( ![X42:$i]:
% 3.27/1.65 ( ( in @ X42 @ X40 ) =>
% 3.27/1.65 ( ?[X44:$i]:
% 3.27/1.65 ( ( ![X46:$i]:
% 3.27/1.65 ( ( X38 @ X42 @ X46 ) =>
% 3.27/1.65 ( ( X44 ) = ( X46 ) ) ) ) &
% 3.27/1.65 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 3.27/1.65 ( ?[X48:$i]:
% 3.27/1.65 ( ![X50:$i]:
% 3.27/1.65 ( ( in @ X50 @ X48 ) <=>
% 3.27/1.65 ( ?[X52:$i]:
% 3.27/1.65 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X54:$i]:
% 3.27/1.65 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 3.27/1.65 ( ?[X58:$i]:
% 3.27/1.65 ( ( ~( ?[X60:$i]:
% 3.27/1.65 ( ( in @ X60 @ X54 ) & ( in @ X60 @ X58 ) ) ) ) &
% 3.27/1.65 ( in @ X58 @ X54 ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X62:$i]:
% 3.27/1.65 ( ?[X64:$i]:
% 3.27/1.65 ( ( ![X66:$i]:
% 3.27/1.65 ( ( ( ![X68:$i]:
% 3.27/1.65 ( ( in @ X68 @ X66 ) =>
% 3.27/1.65 ( in @ X68 @ X62 ) ) ) &
% 3.27/1.65 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 3.27/1.65 ( ?[X72:$i,X74:$i]:
% 3.27/1.65 ( ( ![X76:$i]:
% 3.27/1.65 ( ( in @ X76 @ X64 ) =>
% 3.27/1.65 ( ( ![X78:$i]:
% 3.27/1.65 ( ( in @ X78 @ X76 ) =>
% 3.27/1.65 ( in @ X78 @ X72 ) ) ) |
% 3.27/1.65 ( in @ X74 @ X76 ) ) ) ) &
% 3.27/1.65 ( ~( ?[X80:$i]:
% 3.27/1.65 ( ( in @ X80 @ X66 ) &
% 3.27/1.65 ( in @ X80 @ X72 ) ) ) ) &
% 3.27/1.65 ( in @ X74 @ X66 ) & ( in @ X72 @ X64 ) ) ) ) ) &
% 3.27/1.65 ( ![X82:$i,X84:$i]:
% 3.27/1.65 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 3.27/1.65 ( ( ![X86:$i]:
% 3.27/1.65 ( ( in @ X86 @ X82 ) =>
% 3.27/1.65 ( in @ X86 @ X84 ) ) ) |
% 3.27/1.65 ( ![X88:$i]:
% 3.27/1.65 ( ( in @ X88 @ X84 ) =>
% 3.27/1.65 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 3.27/1.65 ( ![X90:$i,X92:$i]:
% 3.27/1.65 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 3.27/1.65 ( ( ![X94:$i]:
% 3.27/1.65 ( ( in @ X94 @ X64 ) =>
% 3.27/1.65 ( ( in @ X90 @ X94 ) <=>
% 3.27/1.65 ( in @ X92 @ X94 ) ) ) ) =>
% 3.27/1.65 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 3.27/1.65 ( ![X96:$i]:
% 3.27/1.65 ( ( in @ X96 @ X64 ) =>
% 3.27/1.65 ( ![X98:$i]:
% 3.27/1.65 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X100:( $i > $o )]:
% 3.27/1.65 ( ( ?[X102:$i]:
% 3.27/1.65 ( ( ![X104:$i]:
% 3.27/1.65 ( ( X100 @ X104 ) =>
% 3.27/1.65 ( ( X102 ) = ( X104 ) ) ) ) &
% 3.27/1.65 ( X100 @ X102 ) ) ) =>
% 3.27/1.65 ( X100 @
% 3.27/1.65 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 3.27/1.65 ( ( in @ X110 @ X106 ) =>
% 3.27/1.65 ( ( X108 @ X110 ) =>
% 3.27/1.65 ( in @
% 3.27/1.65 X110 @
% 3.27/1.65 ( dsetconstr @
% 3.27/1.65 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 3.27/1.65 ( ( in @
% 3.27/1.65 X116 @
% 3.27/1.65 ( dsetconstr @
% 3.27/1.65 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 3.27/1.65 ( in @ X116 @ X112 ) ) ) =>
% 3.27/1.65 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 3.27/1.65 ( ( in @
% 3.27/1.65 X122 @
% 3.27/1.65 ( dsetconstr @
% 3.27/1.65 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 3.27/1.65 ( X120 @ X122 ) ) ) =>
% 3.27/1.65 ( ( ![X124:( $i > $o )]:
% 3.27/1.65 ( ( ?[X126:$i]:
% 3.27/1.65 ( ( ![X128:$i]:
% 3.27/1.65 ( ( X124 @ X128 ) =>
% 3.27/1.65 ( ( X126 ) = ( X128 ) ) ) ) &
% 3.27/1.65 ( X124 @ X126 ) ) ) =>
% 3.27/1.65 ( ?[X130:$i]:
% 3.27/1.65 ( ( ![X132:$i]:
% 3.27/1.65 ( ( X124 @ X132 ) =>
% 3.27/1.65 ( ( X130 ) = ( X132 ) ) ) ) &
% 3.27/1.65 ( X124 @ X130 ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X134:$o,X136:$i]:
% 3.27/1.65 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 3.27/1.65 ( X134 ) ) ) =>
% 3.27/1.65 ( ( ![X138:$i]:
% 3.27/1.65 ( ( in @ X138 @ emptyset ) =>
% 3.27/1.65 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 3.27/1.65 ( ( ![X142:$i]:
% 3.27/1.65 ( ~( in @ X142 @ emptyset ) ) ) =>
% 3.27/1.65 ( ( ![X144:$i]:
% 3.27/1.65 ( ~( in @ X144 @ emptyset ) ) ) =>
% 3.27/1.65 ( ( ![X146:( $i > $o )]:
% 3.27/1.65 ( ( ?[X148:$i]:
% 3.27/1.65 ( ( ![X150:$i]:
% 3.27/1.65 ( ( X146 @ X150 ) =>
% 3.27/1.65 ( ( X148 ) = ( X150 ) ) ) ) &
% 3.27/1.65 ( X146 @ X148 ) ) ) =>
% 3.27/1.65 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 3.27/1.65 ( ( ![X154:$i,X156:$i]:
% 3.27/1.65 ( ( ![X158:$i]:
% 3.27/1.65 ( ( in @ X158 @ X154 ) =>
% 3.27/1.65 ( in @ X158 @ X156 ) ) ) =>
% 3.27/1.65 ( ( ![X160:$i]:
% 3.27/1.65 ( ( in @ X160 @ X156 ) =>
% 3.27/1.65 ( in @ X160 @ X154 ) ) ) =>
% 3.27/1.65 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X162:$i]:
% 3.27/1.65 ( ( ![X164:$i]:
% 3.27/1.65 ( ~( in @ X164 @ X162 ) ) ) =>
% 3.27/1.65 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 3.27/1.65 ( ( ![X166:$i]:
% 3.27/1.65 ( ( ![X168:$i]:
% 3.27/1.65 ( ~( in @ X168 @ X166 ) ) ) =>
% 3.27/1.65 ( ( X166 ) =
% 3.27/1.65 ( emptyset ) ) ) ) =>
% 3.27/1.65 ( ( ![X170:$i,
% 3.27/1.65 X172:( $i > $o ),
% 3.27/1.65 X174:$i]:
% 3.27/1.65 ( ( in @ X174 @ X170 ) =>
% 3.27/1.65 ( ( in @
% 3.27/1.65 X174 @
% 3.27/1.65 ( dsetconstr @
% 3.27/1.65 X170 @
% 3.27/1.65 ( ^[V_5:$i]:
% 3.27/1.65 ( X172 @ V_5 ) ) ) ) <=>
% 3.27/1.65 ( X172 @ X174 ) ) ) ) =>
% 3.27/1.65 ( ( ![X176:$i]:
% 3.27/1.65 ( ( ( X176 ) !=
% 3.27/1.65 ( emptyset ) ) =>
% 3.27/1.65 ( ?[X178:$i]:
% 3.27/1.65 ( in @ X178 @ X176 ) ) ) ) =>
% 3.27/1.65 ( ( ![X180:$i,
% 3.27/1.65 X182:( $i > $o ),
% 3.27/1.65 X184:$i]:
% 3.27/1.65 ( ( in @ X184 @ X180 ) =>
% 3.27/1.65 ( ( X182 @ X184 ) =>
% 3.27/1.65 ( ( dsetconstr @
% 3.27/1.65 X180 @
% 3.27/1.65 ( ^[
% 3.27/1.65 V_6:$i]:
% 3.27/1.65 (
% 3.27/1.65 X182 @ V_6 ) ) ) !=
% 3.27/1.65 ( emptyset ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X186:$i]:
% 3.27/1.65 ( ( ?[X188:$i]:
% 3.27/1.65 ( in @
% 3.27/1.65 X188 @ X186 ) ) =>
% 3.27/1.65 ( ( X186 ) !=
% 3.27/1.65 ( emptyset ) ) ) ) =>
% 3.27/1.65 ( ( ![X190:$i,
% 3.27/1.65 X192:$i]:
% 3.27/1.65 ( in @
% 3.27/1.65 X190 @
% 3.27/1.65 ( setadjoin @
% 3.27/1.65 X190 @ X192 ) ) ) =>
% 3.27/1.65 ( ( in @
% 3.27/1.65 emptyset @
% 3.27/1.65 ( setadjoin @
% 3.27/1.65 emptyset @
% 3.27/1.65 emptyset ) ) =>
% 3.27/1.65 ( ( ![X194:$i,
% 3.27/1.65 X196:$i,
% 3.27/1.65 X198:$i]:
% 3.27/1.65 ( (
% 3.27/1.65 in @
% 3.27/1.65 X198 @
% 3.27/1.65 X196 ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X198 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X194 @
% 3.27/1.65 X196 ) ) ) ) =>
% 3.27/1.65 ( ( ![
% 3.27/1.65 X200:$i,
% 3.27/1.65 X202:$i,
% 3.27/1.65 X204:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X204 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X200 @
% 3.27/1.65 X202 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X206:$o]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X204 ) =
% 3.27/1.65 (
% 3.27/1.65 X200 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 X206 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X204 @
% 3.27/1.65 X202 ) =>
% 3.27/1.65 (
% 3.27/1.65 X206 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 X206 ) ) ) ) ) ) =>
% 3.27/1.65 ( (
% 3.27/1.65 ![
% 3.27/1.65 X208:$i,
% 3.27/1.65 X210:$i,
% 3.27/1.65 X212:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X212 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X208 @
% 3.27/1.65 X210 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X212 ) =
% 3.27/1.65 (
% 3.27/1.65 X208 ) ) |
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X212 @
% 3.27/1.65 X210 ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X214:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 dsetconstr
% 3.27/1.65 @
% 3.27/1.65 X214 @
% 3.27/1.65 (
% 3.27/1.65 ^[
% 3.27/1.65 V_7:$i]:
% 3.27/1.65 (
% 3.27/1.65 $true ) ) ) =
% 3.27/1.65 (
% 3.27/1.65 X214 ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X216:$i,
% 3.27/1.65 X218:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X220:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X220 @
% 3.27/1.65 X218 ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X220 @
% 3.27/1.65 X216 ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X218 @
% 3.27/1.65 (
% 3.27/1.65 powerset @
% 3.27/1.65 X216 ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X222:$i]:
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 emptyset @
% 3.27/1.65 (
% 3.27/1.65 powerset @
% 3.27/1.65 X222 ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X224:$i]:
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 emptyset @
% 3.27/1.65 (
% 3.27/1.65 powerset @
% 3.27/1.65 X224 ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X226:$i,
% 3.27/1.65 X228:$i,
% 3.27/1.65 X230:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X228 @
% 3.27/1.65 (
% 3.27/1.65 powerset @
% 3.27/1.65 X226 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X230 @
% 3.27/1.65 X228 ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X230 @
% 3.27/1.65 X226 ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X232:$i,
% 3.27/1.65 X234:$i,
% 3.27/1.65 X236:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X234 @
% 3.27/1.65 X236 ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X236 @
% 3.27/1.65 X232 ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X234 @
% 3.27/1.65 (
% 3.27/1.65 setunion @
% 3.27/1.65 X232 ) ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X238:$i,
% 3.27/1.65 X240:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X240 @
% 3.27/1.65 (
% 3.27/1.65 setunion @
% 3.27/1.65 X238 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X242:$o]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X244:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X240 @
% 3.27/1.65 X244 ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X244 @
% 3.27/1.65 X238 ) =>
% 3.27/1.65 (
% 3.27/1.65 X242 ) ) ) ) =>
% 3.27/1.65 (
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% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X246:$i,
% 3.27/1.65 X248:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X248 @
% 3.27/1.65 X246 ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X248 @
% 3.27/1.65 (
% 3.27/1.65 powerset @
% 3.27/1.65 (
% 3.27/1.65 setunion @
% 3.27/1.65 X246 ) ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X250:(
% 3.27/1.65 $i > $o )]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ?[
% 3.27/1.65 X252:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X254:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X250 @
% 3.27/1.65 X254 ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X252 ) =
% 3.27/1.65 (
% 3.27/1.65 X254 ) ) ) ) &
% 3.27/1.65 (
% 3.27/1.65 X250 @
% 3.27/1.65 X252 ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 ?[
% 3.27/1.65 X256:$i]:
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X258:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X250 @
% 3.27/1.65 X258 ) <=>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X258 ) =
% 3.27/1.65 (
% 3.27/1.65 X256 ) ) ) ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X260:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X260 ) !=
% 3.27/1.65 (
% 3.27/1.65 emptyset ) ) =>
% 3.27/1.65 (
% 3.27/1.65 ?[
% 3.27/1.65 X262:$i]:
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X262 @
% 3.27/1.65 X260 ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X264:$i,
% 3.27/1.65 X266:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X264 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X266 @
% 3.27/1.65 emptyset ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X264 ) =
% 3.27/1.65 (
% 3.27/1.65 X266 ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X268:$i,
% 3.27/1.65 X270:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X268 ) !=
% 3.27/1.65 (
% 3.27/1.65 X270 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 ~(
% 3.27/1.65 in @
% 3.27/1.65 X270 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X268 @
% 3.27/1.65 emptyset ) ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X272:$i,
% 3.27/1.65 X274:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X272 ) =
% 3.27/1.65 (
% 3.27/1.65 X274 ) ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X272 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X274 @
% 3.27/1.65 emptyset ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X276:$i,
% 3.27/1.65 X278:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X276 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X278 @
% 3.27/1.65 emptyset ) ) =>
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X278 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X276 @
% 3.27/1.65 emptyset ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X280:$i,
% 3.27/1.65 X282:$i,
% 3.27/1.65 X284:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X284 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X280 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X282 @
% 3.27/1.65 emptyset ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X284 ) =
% 3.27/1.65 (
% 3.27/1.65 X280 ) ) |
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X284 ) =
% 3.27/1.65 (
% 3.27/1.65 X282 ) ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X286:$i,
% 3.27/1.65 X288:$i]:
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X286 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X286 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X288 @
% 3.27/1.65 emptyset ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X290:$i,
% 3.27/1.65 X292:$i]:
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X292 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X290 @
% 3.27/1.65 (
% 3.27/1.65 setadjoin
% 3.27/1.65 @
% 3.27/1.65 X292 @
% 3.27/1.65 emptyset ) ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 ![
% 3.27/1.65 X294:$i,
% 3.27/1.65 X296:(
% 3.27/1.65 $i > $o )]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 ?[
% 3.27/1.65 X298:$i]:
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 X296 @
% 3.27/1.65 X298 ) &
% 3.27/1.65 (
% 3.27/1.65 in @
% 3.27/1.65 X298 @
% 3.27/1.65 X294 ) ) ) =>
% 3.27/1.65 (
% 3.27/1.65 (
% 3.27/1.65 dsetconstr
% 3.27/1.65 @
% 3.27/1.65 X294 @
% 3.27/1.65 (
% 3.27/1.65 ^[
% 3.27/1.65 V_8:$i]:
% 3.27/1.65 (
% 3.27/1.65 X296 @ V_8 ) ) ) !=
% 3.27/1.65 (
% 3.27/1.65 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.27/1.65 thf(zf_stmt_10, negated_conjecture,
% 3.27/1.65 (~( ( ![X4:$i,X6:$i]:
% 3.27/1.65 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 3.27/1.65 ( ( X4 ) = ( X6 ) ) ) ) =>
% 3.27/1.65 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 3.27/1.65 ( ( ![X12:$i,X14:$i,X16:$i]:
% 3.27/1.65 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 3.27/1.65 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 3.27/1.65 ( ( ![X18:$i,X20:$i]:
% 3.27/1.65 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 3.27/1.65 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 3.27/1.65 ( ( ![X24:$i,X26:$i]:
% 3.27/1.65 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 3.27/1.65 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 3.27/1.65 ( ( in @ emptyset @ omega ) =>
% 3.27/1.65 ( ( ![X30:$i]:
% 3.27/1.65 ( ( in @ X30 @ omega ) =>
% 3.27/1.65 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 3.27/1.65 ( ( ![X32:$i]:
% 3.27/1.65 ( ( ( in @ emptyset @ X32 ) &
% 3.27/1.65 ( ![X34:$i]:
% 3.27/1.65 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 3.27/1.65 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 3.27/1.65 ( ![X36:$i]:
% 3.27/1.65 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 3.27/1.65 ( ( ![X42:$i]:
% 3.27/1.65 ( ( in @ X42 @ X40 ) =>
% 3.27/1.65 ( ?[X44:$i]:
% 3.27/1.65 ( ( ![X46:$i]:
% 3.27/1.65 ( ( X38 @ X42 @ X46 ) =>
% 3.27/1.65 ( ( X44 ) = ( X46 ) ) ) ) &
% 3.27/1.65 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 3.27/1.65 ( ?[X48:$i]:
% 3.27/1.65 ( ![X50:$i]:
% 3.27/1.65 ( ( in @ X50 @ X48 ) <=>
% 3.27/1.65 ( ?[X52:$i]:
% 3.27/1.65 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X54:$i]:
% 3.27/1.65 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 3.27/1.65 ( ?[X58:$i]:
% 3.27/1.65 ( ( ~( ?[X60:$i]:
% 3.27/1.65 ( ( in @ X60 @ X54 ) &
% 3.27/1.65 ( in @ X60 @ X58 ) ) ) ) &
% 3.27/1.65 ( in @ X58 @ X54 ) ) ) ) ) =>
% 3.27/1.65 ( ( ![X62:$i]:
% 3.27/1.65 ( ?[X64:$i]:
% 3.27/1.65 ( ( ![X66:$i]:
% 3.27/1.65 ( ( ( ![X68:$i]:
% 3.27/1.65 ( ( in @ X68 @ X66 ) =>
% 3.27/1.65 ( in @ X68 @ X62 ) ) ) &
% 3.27/1.65 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 3.27/1.65 ( ?[X72:$i,X74:$i]:
% 3.27/1.65 ( ( ![X76:$i]:
% 3.27/1.65 ( ( in @ X76 @ X64 ) =>
% 3.27/1.65 ( ( ![X78:$i]:
% 3.27/1.65 ( ( in @ X78 @ X76 ) =>
% 3.27/1.65 ( in @ X78 @ X72 ) ) ) |
% 3.27/1.65 ( in @ X74 @ X76 ) ) ) ) &
% 3.27/1.65 ( ~( ?[X80:$i]:
% 3.27/1.65 ( ( in @ X80 @ X66 ) &
% 3.27/1.65 ( in @ X80 @ X72 ) ) ) ) &
% 3.27/1.65 ( in @ X74 @ X66 ) &
% 3.27/1.65 ( in @ X72 @ X64 ) ) ) ) ) &
% 3.27/1.65 ( ![X82:$i,X84:$i]:
% 3.27/1.65 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 3.27/1.65 ( ( ![X86:$i]:
% 3.27/1.66 ( ( in @ X86 @ X82 ) =>
% 3.27/1.66 ( in @ X86 @ X84 ) ) ) |
% 3.27/1.66 ( ![X88:$i]:
% 3.27/1.66 ( ( in @ X88 @ X84 ) =>
% 3.27/1.66 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 3.27/1.66 ( ![X90:$i,X92:$i]:
% 3.27/1.66 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 3.27/1.66 ( ( ![X94:$i]:
% 3.27/1.66 ( ( in @ X94 @ X64 ) =>
% 3.27/1.66 ( ( in @ X90 @ X94 ) <=>
% 3.27/1.66 ( in @ X92 @ X94 ) ) ) ) =>
% 3.27/1.66 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 3.27/1.66 ( ![X96:$i]:
% 3.27/1.66 ( ( in @ X96 @ X64 ) =>
% 3.27/1.66 ( ![X98:$i]:
% 3.27/1.66 ( ( in @ X98 @ X96 ) =>
% 3.27/1.66 ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 3.27/1.66 ( ( ![X100:( $i > $o )]:
% 3.27/1.66 ( ( ?[X102:$i]:
% 3.27/1.66 ( ( ![X104:$i]:
% 3.27/1.66 ( ( X100 @ X104 ) =>
% 3.27/1.66 ( ( X102 ) = ( X104 ) ) ) ) &
% 3.27/1.66 ( X100 @ X102 ) ) ) =>
% 3.27/1.66 ( X100 @
% 3.27/1.66 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 3.27/1.66 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 3.27/1.66 ( ( in @ X110 @ X106 ) =>
% 3.27/1.66 ( ( X108 @ X110 ) =>
% 3.27/1.66 ( in @
% 3.27/1.66 X110 @
% 3.27/1.66 ( dsetconstr @
% 3.27/1.66 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 3.27/1.66 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 3.27/1.66 ( ( in @
% 3.27/1.66 X116 @
% 3.27/1.66 ( dsetconstr @
% 3.27/1.66 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 3.27/1.66 ( in @ X116 @ X112 ) ) ) =>
% 3.27/1.66 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 3.27/1.66 ( ( in @
% 3.27/1.66 X122 @
% 3.27/1.66 ( dsetconstr @
% 3.27/1.66 X118 @
% 3.27/1.66 ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 3.27/1.66 ( X120 @ X122 ) ) ) =>
% 3.27/1.66 ( ( ![X124:( $i > $o )]:
% 3.27/1.66 ( ( ?[X126:$i]:
% 3.27/1.66 ( ( ![X128:$i]:
% 3.27/1.66 ( ( X124 @ X128 ) =>
% 3.27/1.66 ( ( X126 ) = ( X128 ) ) ) ) &
% 3.27/1.66 ( X124 @ X126 ) ) ) =>
% 3.27/1.66 ( ?[X130:$i]:
% 3.27/1.66 ( ( ![X132:$i]:
% 3.27/1.66 ( ( X124 @ X132 ) =>
% 3.27/1.66 ( ( X130 ) = ( X132 ) ) ) ) &
% 3.27/1.66 ( X124 @ X130 ) ) ) ) ) =>
% 3.27/1.66 ( ( ![X134:$o,X136:$i]:
% 3.27/1.66 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 3.27/1.66 ( X134 ) ) ) =>
% 3.27/1.66 ( ( ![X138:$i]:
% 3.27/1.66 ( ( in @ X138 @ emptyset ) =>
% 3.27/1.66 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 3.27/1.66 ( ( ![X142:$i]:
% 3.27/1.66 ( ~( in @ X142 @ emptyset ) ) ) =>
% 3.27/1.66 ( ( ![X144:$i]:
% 3.27/1.66 ( ~( in @ X144 @ emptyset ) ) ) =>
% 3.27/1.66 ( ( ![X146:( $i > $o )]:
% 3.27/1.66 ( ( ?[X148:$i]:
% 3.27/1.66 ( ( ![X150:$i]:
% 3.27/1.66 ( ( X146 @ X150 ) =>
% 3.27/1.66 ( ( X148 ) =
% 3.27/1.66 ( X150 ) ) ) ) &
% 3.27/1.66 ( X146 @ X148 ) ) ) =>
% 3.27/1.66 ( ?[X152:$i]:
% 3.27/1.66 ( X146 @ X152 ) ) ) ) =>
% 3.27/1.66 ( ( ![X154:$i,X156:$i]:
% 3.27/1.66 ( ( ![X158:$i]:
% 3.27/1.66 ( ( in @ X158 @ X154 ) =>
% 3.27/1.66 ( in @ X158 @ X156 ) ) ) =>
% 3.27/1.66 ( ( ![X160:$i]:
% 3.27/1.66 ( ( in @ X160 @ X156 ) =>
% 3.27/1.66 ( in @ X160 @ X154 ) ) ) =>
% 3.27/1.66 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 3.27/1.66 ( ( ![X162:$i]:
% 3.27/1.66 ( ( ![X164:$i]:
% 3.27/1.66 ( ~( in @ X164 @ X162 ) ) ) =>
% 3.27/1.66 ( ( X162 ) =
% 3.27/1.66 ( emptyset ) ) ) ) =>
% 3.27/1.66 ( ( ![X166:$i]:
% 3.27/1.66 ( ( ![X168:$i]:
% 3.27/1.66 ( ~( in @
% 3.27/1.66 X168 @ X166 ) ) ) =>
% 3.27/1.66 ( ( X166 ) =
% 3.27/1.66 ( emptyset ) ) ) ) =>
% 3.27/1.66 ( ( ![X170:$i,
% 3.27/1.66 X172:( $i > $o ),
% 3.27/1.66 X174:$i]:
% 3.27/1.66 ( ( in @ X174 @ X170 ) =>
% 3.27/1.66 ( ( in @
% 3.27/1.66 X174 @
% 3.27/1.66 ( dsetconstr @
% 3.27/1.66 X170 @
% 3.27/1.66 ( ^[V_5:$i]:
% 3.27/1.66 ( X172 @
% 3.27/1.66 V_5 ) ) ) ) <=>
% 3.27/1.66 ( X172 @ X174 ) ) ) ) =>
% 3.27/1.66 ( ( ![X176:$i]:
% 3.27/1.66 ( ( ( X176 ) !=
% 3.27/1.66 ( emptyset ) ) =>
% 3.27/1.66 ( ?[X178:$i]:
% 3.27/1.66 ( in @
% 3.27/1.66 X178 @ X176 ) ) ) ) =>
% 3.27/1.66 ( ( ![X180:$i,
% 3.27/1.66 X182:(
% 3.27/1.66 $i > $o ),
% 3.27/1.66 X184:$i]:
% 3.27/1.66 ( ( in @
% 3.27/1.66 X184 @ X180 ) =>
% 3.27/1.66 ( ( X182 @ X184 ) =>
% 3.27/1.66 ( ( dsetconstr
% 3.27/1.66 @
% 3.27/1.66 X180 @
% 3.27/1.66 (
% 3.27/1.66 ^[
% 3.27/1.66 V_6:$i]:
% 3.27/1.66 (
% 3.27/1.66 X182 @
% 3.27/1.66 V_6 ) ) ) !=
% 3.27/1.66 ( emptyset ) ) ) ) ) =>
% 3.27/1.66 ( ( ![X186:$i]:
% 3.27/1.66 ( ( ?[X188:$i]:
% 3.27/1.66 ( in @
% 3.27/1.66 X188 @
% 3.27/1.66 X186 ) ) =>
% 3.27/1.66 ( ( X186 ) !=
% 3.27/1.66 ( emptyset ) ) ) ) =>
% 3.27/1.66 ( ( ![X190:$i,
% 3.27/1.66 X192:$i]:
% 3.27/1.66 ( in @
% 3.27/1.66 X190 @
% 3.27/1.66 ( setadjoin
% 3.27/1.66 @
% 3.27/1.66 X190 @
% 3.27/1.66 X192 ) ) ) =>
% 3.27/1.66 ( ( in @
% 3.27/1.66 emptyset @
% 3.27/1.66 ( setadjoin
% 3.27/1.66 @
% 3.27/1.66 emptyset @
% 3.27/1.66 emptyset ) ) =>
% 3.27/1.66 ( ( ![
% 3.27/1.66 X194:$i,
% 3.27/1.66 X196:$i,
% 3.27/1.66 X198:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X198 @
% 3.27/1.66 X196 ) =>
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X198 @
% 3.27/1.66 (
% 3.27/1.66 setadjoin
% 3.27/1.66 @
% 3.27/1.66 X194 @
% 3.27/1.66 X196 ) ) ) ) =>
% 3.27/1.66 ( (
% 3.27/1.66 ![
% 3.27/1.66 X200:$i,
% 3.27/1.66 X202:$i,
% 3.27/1.66 X204:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X204 @
% 3.27/1.66 (
% 3.27/1.66 setadjoin
% 3.27/1.66 @
% 3.27/1.66 X200 @
% 3.27/1.66 X202 ) ) =>
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X206:$o]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 X204 ) =
% 3.27/1.66 (
% 3.27/1.66 X200 ) ) =>
% 3.27/1.66 (
% 3.27/1.66 X206 ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X204 @
% 3.27/1.66 X202 ) =>
% 3.27/1.66 (
% 3.27/1.66 X206 ) ) =>
% 3.27/1.66 (
% 3.27/1.66 X206 ) ) ) ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X208:$i,
% 3.27/1.66 X210:$i,
% 3.27/1.66 X212:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X212 @
% 3.27/1.66 (
% 3.27/1.66 setadjoin
% 3.27/1.66 @
% 3.27/1.66 X208 @
% 3.27/1.66 X210 ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 X212 ) =
% 3.27/1.66 (
% 3.27/1.66 X208 ) ) |
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X212 @
% 3.27/1.66 X210 ) ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X214:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 dsetconstr
% 3.27/1.66 @
% 3.27/1.66 X214 @
% 3.27/1.66 (
% 3.27/1.66 ^[
% 3.27/1.66 V_7:$i]:
% 3.27/1.66 (
% 3.27/1.66 $true ) ) ) =
% 3.27/1.66 (
% 3.27/1.66 X214 ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X216:$i,
% 3.27/1.66 X218:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X220:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X220 @
% 3.27/1.66 X218 ) =>
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X220 @
% 3.27/1.66 X216 ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X218 @
% 3.27/1.66 (
% 3.27/1.66 powerset
% 3.27/1.66 @
% 3.27/1.66 X216 ) ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X222:$i]:
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 emptyset @
% 3.27/1.66 (
% 3.27/1.66 powerset
% 3.27/1.66 @
% 3.27/1.66 X222 ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X224:$i]:
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 emptyset @
% 3.27/1.66 (
% 3.27/1.66 powerset
% 3.27/1.66 @
% 3.27/1.66 X224 ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X226:$i,
% 3.27/1.66 X228:$i,
% 3.27/1.66 X230:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X228 @
% 3.27/1.66 (
% 3.27/1.66 powerset
% 3.27/1.66 @
% 3.27/1.66 X226 ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X230 @
% 3.27/1.66 X228 ) =>
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X230 @
% 3.27/1.66 X226 ) ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X232:$i,
% 3.27/1.66 X234:$i,
% 3.27/1.66 X236:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X234 @
% 3.27/1.66 X236 ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X236 @
% 3.27/1.66 X232 ) =>
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X234 @
% 3.27/1.66 (
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% 3.27/1.66 @
% 3.27/1.66 X232 ) ) ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X238:$i,
% 3.27/1.66 X240:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X240 @
% 3.27/1.66 (
% 3.27/1.66 setunion
% 3.27/1.66 @
% 3.27/1.66 X238 ) ) =>
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X242:$o]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X244:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X240 @
% 3.27/1.66 X244 ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X244 @
% 3.27/1.66 X238 ) =>
% 3.27/1.66 (
% 3.27/1.66 X242 ) ) ) ) =>
% 3.27/1.66 (
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% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X246:$i,
% 3.27/1.66 X248:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X248 @
% 3.27/1.66 X246 ) =>
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X248 @
% 3.27/1.66 (
% 3.27/1.66 powerset
% 3.27/1.66 @
% 3.27/1.66 (
% 3.27/1.66 setunion
% 3.27/1.66 @
% 3.27/1.66 X246 ) ) ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X250:(
% 3.27/1.66 $i > $o )]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ?[
% 3.27/1.66 X252:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X254:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 X250 @
% 3.27/1.66 X254 ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 X252 ) =
% 3.27/1.66 (
% 3.27/1.66 X254 ) ) ) ) &
% 3.27/1.66 (
% 3.27/1.66 X250 @
% 3.27/1.66 X252 ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 ?[
% 3.27/1.66 X256:$i]:
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X258:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 X250 @
% 3.27/1.66 X258 ) <=>
% 3.27/1.66 (
% 3.27/1.66 (
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% 3.27/1.66 (
% 3.27/1.66 X256 ) ) ) ) ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X260:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 X260 ) !=
% 3.27/1.66 (
% 3.27/1.66 emptyset ) ) =>
% 3.27/1.66 (
% 3.27/1.66 ?[
% 3.27/1.66 X262:$i]:
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X262 @
% 3.27/1.66 X260 ) ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X264:$i,
% 3.27/1.66 X266:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X264 @
% 3.27/1.66 (
% 3.27/1.66 setadjoin
% 3.27/1.66 @
% 3.27/1.66 X266 @
% 3.27/1.66 emptyset ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 X264 ) =
% 3.27/1.66 (
% 3.27/1.66 X266 ) ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X268:$i,
% 3.27/1.66 X270:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 X268 ) !=
% 3.27/1.66 (
% 3.27/1.66 X270 ) ) =>
% 3.27/1.66 (
% 3.27/1.66 ~
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X270 @
% 3.27/1.66 (
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% 3.27/1.66 X268 @
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% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X272:$i,
% 3.27/1.66 X274:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 X272 ) =
% 3.27/1.66 (
% 3.27/1.66 X274 ) ) =>
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X272 @
% 3.27/1.66 (
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% 3.27/1.66 X274 @
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% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X276:$i,
% 3.27/1.66 X278:$i]:
% 3.27/1.66 (
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% 3.27/1.66 (
% 3.27/1.66 setadjoin
% 3.27/1.66 @
% 3.27/1.66 X278 @
% 3.27/1.66 emptyset ) ) =>
% 3.27/1.66 (
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% 3.27/1.66 X278 @
% 3.27/1.66 (
% 3.27/1.66 setadjoin
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% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X280:$i,
% 3.27/1.66 X282:$i,
% 3.27/1.66 X284:$i]:
% 3.27/1.66 (
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% 3.27/1.66 X284 @
% 3.27/1.66 (
% 3.27/1.66 setadjoin
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% 3.27/1.66 (
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% 3.27/1.66 @
% 3.27/1.66 X282 @
% 3.27/1.66 emptyset ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 X284 ) =
% 3.27/1.66 (
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% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 X284 ) =
% 3.27/1.66 (
% 3.27/1.66 X282 ) ) ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X286:$i,
% 3.27/1.66 X288:$i]:
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X286 @
% 3.27/1.66 (
% 3.27/1.66 setadjoin
% 3.27/1.66 @
% 3.27/1.66 X286 @
% 3.27/1.66 (
% 3.27/1.66 setadjoin
% 3.27/1.66 @
% 3.27/1.66 X288 @
% 3.27/1.66 emptyset ) ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X290:$i,
% 3.27/1.66 X292:$i]:
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X292 @
% 3.27/1.66 (
% 3.27/1.66 setadjoin
% 3.27/1.66 @
% 3.27/1.66 X290 @
% 3.27/1.66 (
% 3.27/1.66 setadjoin
% 3.27/1.66 @
% 3.27/1.66 X292 @
% 3.27/1.66 emptyset ) ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 ![
% 3.27/1.66 X294:$i,
% 3.27/1.66 X296:(
% 3.27/1.66 $i > $o )]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 ?[
% 3.27/1.66 X298:$i]:
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 X296 @
% 3.27/1.66 X298 ) &
% 3.27/1.66 (
% 3.27/1.66 in @
% 3.27/1.66 X298 @
% 3.27/1.66 X294 ) ) ) =>
% 3.27/1.66 (
% 3.27/1.66 (
% 3.27/1.66 dsetconstr
% 3.27/1.66 @
% 3.27/1.66 X294 @
% 3.27/1.66 (
% 3.27/1.66 ^[
% 3.27/1.66 V_8:$i]:
% 3.27/1.66 (
% 3.27/1.66 X296 @
% 3.27/1.66 V_8 ) ) ) !=
% 3.27/1.66 (
% 3.27/1.66 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 3.27/1.66 inference('cnf.neg', [status(esa)], [zf_stmt_9])).
% 3.27/1.66 thf(zip_derived_cl61, plain,
% 3.27/1.66 (((dsetconstr @ sk__153 @ (^[Y0 : $i]: (sk__154 @ Y0))) = (emptyset))),
% 3.27/1.66 inference('cnf', [status(esa)], [zf_stmt_10])).
% 3.27/1.66 thf(zip_derived_cl264, plain,
% 3.27/1.66 (((dsetconstr @ sk__153 @ sk__154) = (emptyset))),
% 3.27/1.66 inference('ho_norm', [status(thm)], [zip_derived_cl61])).
% 3.27/1.66 thf(zip_derived_cl63, plain, ( (sk__154 @ sk__155)),
% 3.27/1.66 inference('cnf', [status(esa)], [zf_stmt_10])).
% 3.27/1.66 thf(zip_derived_cl62, plain, ( (in @ sk__155 @ sk__153)),
% 3.27/1.66 inference('cnf', [status(esa)], [zf_stmt_10])).
% 3.27/1.66 thf(zip_derived_cl48, plain,
% 3.27/1.66 (![X46 : $i, X47 : $i > $o, X48 : $i]:
% 3.27/1.66 (((dsetconstr @ X46 @ (^[Y0 : $i]: (X47 @ Y0))) != (emptyset))
% 3.27/1.66 | ~ (in @ X48 @ X46)
% 3.27/1.66 | ~ (X47 @ X48))),
% 3.27/1.66 inference('cnf', [status(esa)], [zf_stmt_10])).
% 3.27/1.66 thf(zip_derived_cl118, plain,
% 3.27/1.66 (![X46 : $i, X47 : $i > $o, X48 : $i]:
% 3.27/1.66 (((dsetconstr @ X46 @ X47) != (emptyset))
% 3.27/1.66 | ~ (in @ X48 @ X46)
% 3.27/1.66 | ~ (X47 @ X48))),
% 3.27/1.66 inference('ho_norm', [status(thm)], [zip_derived_cl48])).
% 3.27/1.66 thf(zip_derived_cl119, plain,
% 3.27/1.66 (![X0 : $i > $o]:
% 3.27/1.66 (~ (X0 @ sk__155) | ((dsetconstr @ sk__153 @ X0) != (emptyset)))),
% 3.27/1.66 inference('sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl118])).
% 3.27/1.66 thf(zip_derived_cl134, plain,
% 3.27/1.66 (((dsetconstr @ sk__153 @
% 3.27/1.66 (^[Y0 : $i]: (sk__154 @ ((^[Y1 : $i]: (Y1)) @ Y0)))) != (emptyset))),
% 3.27/1.66 inference('sup-', [status(thm)], [zip_derived_cl63, zip_derived_cl119])).
% 3.27/1.66 thf(zip_derived_cl140, plain,
% 3.27/1.66 (((dsetconstr @ sk__153 @ sk__154) != (emptyset))),
% 3.27/1.66 inference('ho_norm', [status(thm)], [zip_derived_cl134])).
% 3.27/1.66 thf(zip_derived_cl265, plain, ($false),
% 3.27/1.66 inference('simplify_reflect-', [status(thm)],
% 3.27/1.66 [zip_derived_cl264, zip_derived_cl140])).
% 3.27/1.66
% 3.27/1.66 % SZS output end Refutation
% 3.27/1.66
% 3.27/1.66
% 3.27/1.66 % Terminating...
% 3.55/1.84 % Runner terminated.
% 3.55/1.88 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------