%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU580^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.s9LufEjS1p true
% Computer : n014.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 04:55:10 PM UTC 2025
% Result : Theorem 5.29s 1.21s
% Output : Refutation 5.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU580^1 : TPTP v9.2.0. Released v3.7.0.
% 0.00/0.09 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.s9LufEjS1p true
% 0.07/0.28 % Computer : n014.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 300
% 0.07/0.28 % DateTime : Wed Oct 1 16:10:38 EDT 2025
% 0.07/0.28 % CPUTime :
% 0.07/0.28 % Running portfolio for 300 s
% 0.07/0.28 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.28 % Number of cores: 8
% 0.07/0.28 % Python version: Python 3.6.8
% 0.07/0.28 % Running in HO mode
% 0.12/0.52 % Total configuration time : 828
% 0.12/0.52 % Estimated wc time : 1656
% 0.12/0.52 % Estimated cpu time (8 cpus) : 207.0
% 0.68/0.61 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.68/0.61 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.68/0.62 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.68/0.62 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.68/0.62 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.68/0.62 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.68/0.62 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.68/0.62 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 5.29/1.21 % Solved by lams/40_c_ic.sh.
% 5.29/1.21 % done 164 iterations in 0.551s
% 5.29/1.21 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 5.29/1.21 % SZS output start Refutation
% 5.29/1.21 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 5.29/1.21 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 5.29/1.21 thf(notdexE_type, type, notdexE: $o).
% 5.29/1.21 thf(setunionAx_type, type, setunionAx: $o).
% 5.29/1.21 thf(powersetE_type, type, powersetE: $o).
% 5.29/1.21 thf(omegaSAx_type, type, omegaSAx: $o).
% 5.29/1.21 thf(exuI1_type, type, exuI1: $o).
% 5.29/1.21 thf(exuI2_type, type, exuI2: $o).
% 5.29/1.21 thf(notequalI2_type, type, notequalI2: $o).
% 5.29/1.21 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 5.29/1.21 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 5.29/1.21 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 5.29/1.21 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 5.29/1.21 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 5.29/1.21 thf(setext_type, type, setext: $o).
% 5.29/1.21 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 5.29/1.21 thf(descr__Cong_type, type, descr__Cong: $o).
% 5.29/1.21 thf(in_type, type, in: $i > $i > $o).
% 5.29/1.21 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 5.29/1.21 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 5.29/1.21 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 5.29/1.21 thf(subsetE_type, type, subsetE: $o).
% 5.29/1.21 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 5.29/1.21 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 5.29/1.21 thf(setbeta_type, type, setbeta: $o).
% 5.29/1.21 thf(sk__46_type, type, sk__46: $i).
% 5.29/1.21 thf(eqinunit_type, type, eqinunit: $o).
% 5.29/1.21 thf(upairsetIL_type, type, upairsetIL: $o).
% 5.29/1.21 thf(powersetI1_type, type, powersetI1: $o).
% 5.29/1.21 thf(powersetAx_type, type, powersetAx: $o).
% 5.29/1.21 thf(powersetI_type, type, powersetI: $o).
% 5.29/1.21 thf(upairsetIR_type, type, upairsetIR: $o).
% 5.29/1.21 thf(inCongP_type, type, inCongP: $o).
% 5.29/1.21 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 5.29/1.21 thf(exuE3e_type, type, exuE3e: $o).
% 5.29/1.21 thf(emptysetE_type, type, emptysetE: $o).
% 5.29/1.21 thf(setunionI_type, type, setunionI: $o).
% 5.29/1.21 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 5.29/1.21 thf(prop2setI_type, type, prop2setI: $o).
% 5.29/1.21 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 5.29/1.21 thf(exuE2_type, type, exuE2: $o).
% 5.29/1.21 thf(emptyset_type, type, emptyset: $i).
% 5.29/1.21 thf(powersetsubset_type, type, powersetsubset: $o).
% 5.29/1.21 thf(subPowSU_type, type, subPowSU: $o).
% 5.29/1.21 thf(notequalI1_type, type, notequalI1: $o).
% 5.29/1.21 thf(notinemptyset_type, type, notinemptyset: $o).
% 5.29/1.21 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 5.29/1.21 thf(subsetTrans_type, type, subsetTrans: $o).
% 5.29/1.21 thf(subsetE2_type, type, subsetE2: $o).
% 5.29/1.21 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 5.29/1.21 thf(setextsub_type, type, setextsub: $o).
% 5.29/1.21 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 5.29/1.21 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 5.29/1.21 thf(setunionE_type, type, setunionE: $o).
% 5.29/1.21 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 5.29/1.21 thf(setadjoinE_type, type, setadjoinE: $o).
% 5.29/1.21 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 5.29/1.21 thf(exuE1_type, type, exuE1: $o).
% 5.29/1.21 thf(notinsingleton_type, type, notinsingleton: $o).
% 5.29/1.21 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 5.29/1.21 thf(exuEu_type, type, exuEu: $o).
% 5.29/1.21 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 5.29/1.21 thf(upairsetE_type, type, upairsetE: $o).
% 5.29/1.21 thf(omega0Ax_type, type, omega0Ax: $o).
% 5.29/1.21 thf(notsubsetI_type, type, notsubsetI: $o).
% 5.29/1.21 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 5.29/1.21 thf(setextAx_type, type, setextAx: $o).
% 5.29/1.21 thf(powersetE1_type, type, powersetE1: $o).
% 5.29/1.21 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 5.29/1.21 thf(subsetI1_type, type, subsetI1: $o).
% 5.29/1.21 thf(descrp_type, type, descrp: $o).
% 5.29/1.21 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 5.29/1.21 thf(foundationAx_type, type, foundationAx: $o).
% 5.29/1.21 thf(emptysetAx_type, type, emptysetAx: $o).
% 5.29/1.21 thf(emptyI_type, type, emptyI: $o).
% 5.29/1.21 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 5.29/1.21 thf(emptyE1_type, type, emptyE1: $o).
% 5.29/1.21 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 5.29/1.21 thf(vacuousDall_type, type, vacuousDall: $o).
% 5.29/1.21 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 5.29/1.21 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 5.29/1.21 thf(sk__47_type, type, sk__47: $i > $o).
% 5.29/1.21 thf(subsetI2_type, type, subsetI2: $o).
% 5.29/1.21 thf(omega__Cong_type, type, omega__Cong: $o).
% 5.29/1.21 thf(subsetRefl_type, type, subsetRefl: $o).
% 5.29/1.21 thf(uniqinunit_type, type, uniqinunit: $o).
% 5.29/1.21 thf(prop2setE_type, type, prop2setE: $o).
% 5.29/1.21 thf(nonemptyI_type, type, nonemptyI: $o).
% 5.29/1.21 thf(exuE3u_type, type, exuE3u: $o).
% 5.29/1.21 thf(sk__50_type, type, sk__50: $i > $i > $i).
% 5.29/1.21 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 5.29/1.21 thf(exuI3_type, type, exuI3: $o).
% 5.29/1.21 thf(notdallE_type, type, notdallE: $o).
% 5.29/1.21 thf(powerset_type, type, powerset: $i > $i).
% 5.29/1.21 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 5.29/1.21 thf(exu__Cong_type, type, exu__Cong: $o).
% 5.29/1.21 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 5.29/1.21 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 5.29/1.21 thf(replAx_type, type, replAx: $o).
% 5.29/1.21 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 5.29/1.21 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 5.29/1.21 thf(inPowerset_type, type, inPowerset: $o).
% 5.29/1.21 thf(subset_type, type, subset: $i > $i > $o).
% 5.29/1.21 thf(in__Cong_type, type, in__Cong: $o).
% 5.29/1.21 thf(subset2powerset_type, type, subset2powerset: $o).
% 5.29/1.21 thf(powersetsubset, axiom, powersetsubset =
% 5.29/1.21 (![A:$i,B:$i]:
% 5.29/1.21 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 5.29/1.21 thf('0', plain,
% 5.29/1.21 (( powersetsubset ) =
% 5.29/1.21 ( ![X4:$i,X6:$i]:
% 5.29/1.21 ( ( subset @ X4 @ X6 ) =>
% 5.29/1.21 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 5.29/1.21 thf('1', plain,
% 5.29/1.21 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(powersetE1, axiom, powersetE1 =
% 5.29/1.21 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 5.29/1.21 thf('2', plain,
% 5.29/1.21 (( powersetE1 ) =
% 5.29/1.21 ( ![X4:$i,X6:$i]:
% 5.29/1.21 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(powersetI1, axiom, powersetI1 =
% 5.29/1.21 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 5.29/1.21 thf('3', plain,
% 5.29/1.21 (( powersetI1 ) =
% 5.29/1.21 ( ![X4:$i,X6:$i]:
% 5.29/1.21 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(subset2powerset, axiom, subset2powerset =
% 5.29/1.21 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 5.29/1.21 thf('4', plain,
% 5.29/1.21 (( subset2powerset ) =
% 5.29/1.21 ( ![X4:$i,X6:$i]:
% 5.29/1.21 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(dsetconstr__Cong, axiom, dsetconstr__Cong =
% 5.29/1.21 (![A:$i,B:$i]:
% 5.29/1.21 ( ( ( A ) = ( B ) ) =>
% 5.29/1.21 ( ![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 5.29/1.21 ( ( ![Xx:$i]:
% 5.29/1.21 ( ( in @ Xx @ A ) =>
% 5.29/1.21 ( ![Xy:$i]:
% 5.29/1.21 ( ( in @ Xy @ B ) =>
% 5.29/1.21 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) ) ) ) =>
% 5.29/1.21 ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =
% 5.29/1.21 ( dsetconstr @ B @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ) ) ))).
% 5.29/1.21 thf('5', plain,
% 5.29/1.21 (( dsetconstr__Cong ) =
% 5.29/1.21 ( ![X4:$i,X6:$i]:
% 5.29/1.21 ( ( ( X4 ) = ( X6 ) ) =>
% 5.29/1.21 ( ![X8:( $i > $o ),X10:( $i > $o )]:
% 5.29/1.21 ( ( ![X12:$i]:
% 5.29/1.21 ( ( in @ X12 @ X4 ) =>
% 5.29/1.21 ( ![X14:$i]:
% 5.29/1.21 ( ( in @ X14 @ X6 ) =>
% 5.29/1.21 ( ( ( X12 ) = ( X14 ) ) =>
% 5.29/1.21 ( ( X8 @ X12 ) <=> ( X10 @ X14 ) ) ) ) ) ) ) =>
% 5.29/1.21 ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) =
% 5.29/1.21 ( dsetconstr @ X6 @ ( ^[V_2:$i]: ( X10 @ V_2 ) ) ) ) ) ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(powerset__Cong, axiom, powerset__Cong =
% 5.29/1.21 (![A:$i,B:$i]:
% 5.29/1.21 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 5.29/1.21 thf('6', plain,
% 5.29/1.21 (( powerset__Cong ) =
% 5.29/1.21 ( ![X4:$i,X6:$i]:
% 5.29/1.21 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(emptyE1, axiom, emptyE1 =
% 5.29/1.21 (![A:$i,Xphi:( $i > $o )]:
% 5.29/1.21 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) =>
% 5.29/1.21 ( ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) = ( emptyset ) ) =>
% 5.29/1.21 ( $false ) ) ))).
% 5.29/1.21 thf('7', plain,
% 5.29/1.21 (( emptyE1 ) =
% 5.29/1.21 ( ![X4:$i,X6:( $i > $o )]:
% 5.29/1.21 ( ( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) =>
% 5.29/1.21 ( ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = ( emptyset ) ) =>
% 5.29/1.21 ( $false ) ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(powersetE, axiom, powersetE =
% 5.29/1.21 (![A:$i,B:$i,Xx:$i]:
% 5.29/1.21 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 5.29/1.21 thf('8', plain,
% 5.29/1.21 (( powersetE ) =
% 5.29/1.21 ( ![X4:$i,X6:$i,X8:$i]:
% 5.29/1.21 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 5.29/1.21 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(emptyInPowerset, axiom, emptyInPowerset =
% 5.29/1.21 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 5.29/1.21 thf('9', plain,
% 5.29/1.21 (( emptyInPowerset ) =
% 5.29/1.21 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(emptyinPowerset, axiom, emptyinPowerset =
% 5.29/1.21 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 5.29/1.21 thf('10', plain,
% 5.29/1.21 (( emptyinPowerset ) =
% 5.29/1.21 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(powersetI, axiom, powersetI =
% 5.29/1.21 (![A:$i,B:$i]:
% 5.29/1.21 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 5.29/1.21 ( in @ B @ ( powerset @ A ) ) ))).
% 5.29/1.21 thf('11', plain,
% 5.29/1.21 (( powersetI ) =
% 5.29/1.21 ( ![X4:$i,X6:$i]:
% 5.29/1.21 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 5.29/1.21 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(setoftrueEq, axiom, setoftrueEq =
% 5.29/1.21 (![A:$i]: ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( $true ) ) ) = ( A ) ))).
% 5.29/1.21 thf('12', plain,
% 5.29/1.21 (( setoftrueEq ) =
% 5.29/1.21 ( ![X4:$i]: ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( $true ) ) ) = ( X4 ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(setbeta, axiom, setbeta =
% 5.29/1.21 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 5.29/1.21 ( ( in @ Xx @ A ) =>
% 5.29/1.21 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) <=>
% 5.29/1.21 ( Xphi @ Xx ) ) ))).
% 5.29/1.21 thf('13', plain,
% 5.29/1.21 (( setbeta ) =
% 5.29/1.21 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 5.29/1.21 ( ( in @ X8 @ X4 ) =>
% 5.29/1.21 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=>
% 5.29/1.21 ( X6 @ X8 ) ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(dsetconstrER, axiom, dsetconstrER =
% 5.29/1.21 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 5.29/1.21 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 5.29/1.21 ( Xphi @ Xx ) ))).
% 5.29/1.21 thf('14', plain,
% 5.29/1.21 (( dsetconstrER ) =
% 5.29/1.21 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 5.29/1.21 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 5.29/1.21 ( X6 @ X8 ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(dsetconstrEL, axiom, dsetconstrEL =
% 5.29/1.21 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 5.29/1.21 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 5.29/1.21 ( in @ Xx @ A ) ))).
% 5.29/1.21 thf('15', plain,
% 5.29/1.21 (( dsetconstrEL ) =
% 5.29/1.21 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 5.29/1.21 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 5.29/1.21 ( in @ X8 @ X4 ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(dsetconstrI, axiom, dsetconstrI =
% 5.29/1.21 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 5.29/1.21 ( ( in @ Xx @ A ) =>
% 5.29/1.21 ( ( Xphi @ Xx ) =>
% 5.29/1.21 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 5.29/1.21 thf('16', plain,
% 5.29/1.21 (( dsetconstrI ) =
% 5.29/1.21 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 5.29/1.21 ( ( in @ X8 @ X4 ) =>
% 5.29/1.21 ( ( X6 @ X8 ) =>
% 5.29/1.21 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(powersetAx, axiom, powersetAx =
% 5.29/1.21 (![A:$i,B:$i]:
% 5.29/1.21 ( ( in @ B @ ( powerset @ A ) ) <=>
% 5.29/1.21 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 5.29/1.21 thf('17', plain,
% 5.29/1.21 (( powersetAx ) =
% 5.29/1.21 ( ![X4:$i,X6:$i]:
% 5.29/1.21 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 5.29/1.21 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 5.29/1.21 define([status(thm)])).
% 5.29/1.21 thf(sepInPowerset, conjecture,
% 5.29/1.21 (( setextAx ) =>
% 5.29/1.21 ( ( emptysetAx ) =>
% 5.29/1.21 ( ( setadjoinAx ) =>
% 5.29/1.21 ( ( powersetAx ) =>
% 5.29/1.21 ( ( setunionAx ) =>
% 5.29/1.21 ( ( omega0Ax ) =>
% 5.29/1.21 ( ( omegaSAx ) =>
% 5.29/1.21 ( ( omegaIndAx ) =>
% 5.29/1.21 ( ( replAx ) =>
% 5.29/1.21 ( ( foundationAx ) =>
% 5.29/1.21 ( ( wellorderingAx ) =>
% 5.29/1.21 ( ( descrp ) =>
% 5.29/1.21 ( ( dsetconstrI ) =>
% 5.29/1.21 ( ( dsetconstrEL ) =>
% 5.29/1.21 ( ( dsetconstrER ) =>
% 5.29/1.21 ( ( exuE1 ) =>
% 5.29/1.21 ( ( prop2setE ) =>
% 5.29/1.21 ( ( emptysetE ) =>
% 5.29/1.21 ( ( emptysetimpfalse ) =>
% 5.29/1.21 ( ( notinemptyset ) =>
% 5.29/1.21 ( ( exuE3e ) =>
% 5.29/1.21 ( ( setext ) =>
% 5.29/1.21 ( ( emptyI ) =>
% 5.29/1.21 ( ( noeltsimpempty ) =>
% 5.29/1.21 ( ( setbeta ) =>
% 5.29/1.21 ( ( nonemptyE1 ) =>
% 5.29/1.21 ( ( nonemptyI ) =>
% 5.29/1.21 ( ( nonemptyI1 ) =>
% 5.29/1.21 ( ( setadjoinIL ) =>
% 5.29/1.21 ( ( emptyinunitempty ) =>
% 5.29/1.21 ( ( setadjoinIR ) =>
% 5.29/1.21 ( ( setadjoinE ) =>
% 5.29/1.21 ( (
% 5.29/1.21 setadjoinOr ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setoftrueEq ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 powersetI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 emptyinPowerset ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 emptyInPowerset ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 powersetE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setunionI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setunionE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subPowSU ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuE2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 nonemptyImpWitness ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 uniqinunit ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notinsingleton ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 eqinunit ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 singletonsswitch ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 upairsetE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 upairsetIL ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 upairsetIR ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 emptyE1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 vacuousDall ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan3 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan4 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 prop2setI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 prop2set2propI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notdexE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notdallE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuI1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuI3 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuI2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 inCongP ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuE3u ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exu__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 emptyset__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setadjoin__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 powerset__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setunion__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 omega__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuEu ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 descr__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 dsetconstr__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetI1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 eqimpsubset2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 eqimpsubset1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetI2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 emptysetsubset ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetE2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notsubsetI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notequalI1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notequalI2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetRefl ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetTrans ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setadjoinSub ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setadjoinSub2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subset2powerset ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setextsub ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetemptysetimpeq ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 powersetI1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 powersetE1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 inPowerset ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 powersetsubset ) =>
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 A:$i,
% 5.29/1.21 Xphi:(
% 5.29/1.21 $i > $o )]:
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 A @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 Xx:$i]:
% 5.29/1.21 (
% 5.29/1.21 Xphi @ Xx ) ) ) @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 5.29/1.21 thf(zf_stmt_0, conjecture,
% 5.29/1.21 (( setextAx ) =>
% 5.29/1.21 ( ( emptysetAx ) =>
% 5.29/1.21 ( ( setadjoinAx ) =>
% 5.29/1.21 ( ( ![X4:$i,X6:$i]:
% 5.29/1.21 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 5.29/1.21 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 5.29/1.21 ( ( setunionAx ) =>
% 5.29/1.21 ( ( omega0Ax ) =>
% 5.29/1.21 ( ( omegaSAx ) =>
% 5.29/1.21 ( ( omegaIndAx ) =>
% 5.29/1.21 ( ( replAx ) =>
% 5.29/1.21 ( ( foundationAx ) =>
% 5.29/1.21 ( ( wellorderingAx ) =>
% 5.29/1.21 ( ( descrp ) =>
% 5.29/1.21 ( ( ![X10:$i,X12:( $i > $o ),X14:$i]:
% 5.29/1.21 ( ( in @ X14 @ X10 ) =>
% 5.29/1.21 ( ( X12 @ X14 ) =>
% 5.29/1.21 ( in @
% 5.29/1.21 X14 @
% 5.29/1.21 ( dsetconstr @
% 5.29/1.21 X10 @ ( ^[V_1:$i]: ( X12 @ V_1 ) ) ) ) ) ) ) =>
% 5.29/1.21 ( ( ![X16:$i,X18:( $i > $o ),X20:$i]:
% 5.29/1.21 ( ( in @
% 5.29/1.21 X20 @
% 5.29/1.21 ( dsetconstr @
% 5.29/1.21 X16 @ ( ^[V_2:$i]: ( X18 @ V_2 ) ) ) ) =>
% 5.29/1.21 ( in @ X20 @ X16 ) ) ) =>
% 5.29/1.21 ( ( ![X22:$i,X24:( $i > $o ),X26:$i]:
% 5.29/1.21 ( ( in @
% 5.29/1.21 X26 @
% 5.29/1.21 ( dsetconstr @
% 5.29/1.21 X22 @ ( ^[V_3:$i]: ( X24 @ V_3 ) ) ) ) =>
% 5.29/1.21 ( X24 @ X26 ) ) ) =>
% 5.29/1.21 ( ( exuE1 ) =>
% 5.29/1.21 ( ( prop2setE ) =>
% 5.29/1.21 ( ( emptysetE ) =>
% 5.29/1.21 ( ( emptysetimpfalse ) =>
% 5.29/1.21 ( ( notinemptyset ) =>
% 5.29/1.21 ( ( exuE3e ) =>
% 5.29/1.21 ( ( setext ) =>
% 5.29/1.21 ( ( emptyI ) =>
% 5.29/1.21 ( ( noeltsimpempty ) =>
% 5.29/1.21 ( ( ![X28:$i,
% 5.29/1.21 X30:( $i > $o ),X32:$i]:
% 5.29/1.21 ( ( in @ X32 @ X28 ) =>
% 5.29/1.21 ( ( in @
% 5.29/1.21 X32 @
% 5.29/1.21 ( dsetconstr @
% 5.29/1.21 X28 @
% 5.29/1.21 ( ^[V_4:$i]:
% 5.29/1.21 ( X30 @ V_4 ) ) ) ) <=>
% 5.29/1.21 ( X30 @ X32 ) ) ) ) =>
% 5.29/1.21 ( ( nonemptyE1 ) =>
% 5.29/1.21 ( ( nonemptyI ) =>
% 5.29/1.21 ( ( nonemptyI1 ) =>
% 5.29/1.21 ( ( setadjoinIL ) =>
% 5.29/1.21 ( ( emptyinunitempty ) =>
% 5.29/1.21 ( ( setadjoinIR ) =>
% 5.29/1.21 ( ( setadjoinE ) =>
% 5.29/1.21 ( (
% 5.29/1.21 setadjoinOr ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X34:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X34 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_5:$i]:
% 5.29/1.21 (
% 5.29/1.21 $true ) ) ) =
% 5.29/1.21 (
% 5.29/1.21 X34 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X36:$i,
% 5.29/1.21 X38:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X40:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X40 @ X38 ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X40 @ X36 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X38 @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X36 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X42:$i]:
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 emptyset @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X42 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X44:$i]:
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 emptyset @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X44 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X46:$i,
% 5.29/1.21 X48:$i,
% 5.29/1.21 X50:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X48 @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X46 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X50 @ X48 ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X50 @ X46 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setunionI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setunionE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subPowSU ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuE2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 nonemptyImpWitness ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 uniqinunit ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notinsingleton ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 eqinunit ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 singletonsswitch ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 upairsetE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 upairsetIL ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 upairsetIR ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X52:$i,
% 5.29/1.21 X54:(
% 5.29/1.21 $i > $o )]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ?[
% 5.29/1.21 X56:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X56 @ X52 ) &
% 5.29/1.21 (
% 5.29/1.21 X54 @ X56 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X52 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_6:$i]:
% 5.29/1.21 (
% 5.29/1.21 X54 @ V_6 ) ) ) =
% 5.29/1.21 (
% 5.29/1.21 emptyset ) ) =>
% 5.29/1.21 (
% 5.29/1.21 $false ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 vacuousDall ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan3 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan4 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 prop2setI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 prop2set2propI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notdexE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notdallE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuI1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuI3 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuI2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 inCongP ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuE3u ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exu__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 emptyset__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setadjoin__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X58:$i,
% 5.29/1.21 X60:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X58 ) =
% 5.29/1.21 (
% 5.29/1.21 X60 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X58 ) =
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X60 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setunion__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 omega__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuEu ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 descr__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X62:$i,
% 5.29/1.21 X64:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X62 ) =
% 5.29/1.21 (
% 5.29/1.21 X64 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X66:(
% 5.29/1.21 $i > $o ),
% 5.29/1.21 X68:(
% 5.29/1.21 $i > $o )]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X70:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X70 @ X62 ) =>
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X72:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X72 @ X64 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X70 ) =
% 5.29/1.21 (
% 5.29/1.21 X72 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X66 @ X70 ) <=>
% 5.29/1.21 (
% 5.29/1.21 X68 @ X72 ) ) ) ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X62 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_7:$i]:
% 5.29/1.21 (
% 5.29/1.21 X66 @ V_7 ) ) ) =
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X64 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_8:$i]:
% 5.29/1.21 (
% 5.29/1.21 X68 @ V_8 ) ) ) ) ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetI1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 eqimpsubset2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 eqimpsubset1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetI2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 emptysetsubset ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetE2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notsubsetI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notequalI1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notequalI2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetRefl ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetTrans ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setadjoinSub ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setadjoinSub2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X74:$i,
% 5.29/1.21 X76:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 X74 @ X76 ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X74 @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X76 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setextsub ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetemptysetimpeq ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X78:$i,
% 5.29/1.21 X80:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 X80 @ X78 ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X80 @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X78 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X82:$i,
% 5.29/1.21 X84:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X84 @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X82 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 X84 @ X82 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X86:$i]:
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X86 @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X86 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X88:$i,
% 5.29/1.21 X90:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 X88 @ X90 ) =>
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X88 ) @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X90 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X92:$i,
% 5.29/1.21 X94:(
% 5.29/1.21 $i > $o )]:
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X92 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_9:$i]:
% 5.29/1.21 (
% 5.29/1.21 X94 @ V_9 ) ) ) @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X92 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 5.29/1.21 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 5.29/1.21 thf(zf_stmt_2, axiom,
% 5.29/1.21 (![X8:$i,X6:$i,X4:$i]:
% 5.29/1.21 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 5.29/1.21 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 5.29/1.21 thf(zf_stmt_3, conjecture,
% 5.29/1.21 (( setextAx ) =>
% 5.29/1.21 ( ( emptysetAx ) =>
% 5.29/1.21 ( ( setadjoinAx ) =>
% 5.29/1.21 ( ( ![X4:$i,X6:$i]:
% 5.29/1.21 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 5.29/1.21 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 5.29/1.21 ( ( setunionAx ) =>
% 5.29/1.21 ( ( omega0Ax ) =>
% 5.29/1.21 ( ( omegaSAx ) =>
% 5.29/1.21 ( ( omegaIndAx ) =>
% 5.29/1.21 ( ( replAx ) =>
% 5.29/1.21 ( ( foundationAx ) =>
% 5.29/1.21 ( ( wellorderingAx ) =>
% 5.29/1.21 ( ( descrp ) =>
% 5.29/1.21 ( ( ![X10:$i,X12:( $i > $o ),X14:$i]:
% 5.29/1.21 ( ( in @ X14 @ X10 ) =>
% 5.29/1.21 ( ( X12 @ X14 ) =>
% 5.29/1.21 ( in @
% 5.29/1.21 X14 @
% 5.29/1.21 ( dsetconstr @
% 5.29/1.21 X10 @ ( ^[V_1:$i]: ( X12 @ V_1 ) ) ) ) ) ) ) =>
% 5.29/1.21 ( ( ![X16:$i,X18:( $i > $o ),X20:$i]:
% 5.29/1.21 ( ( in @
% 5.29/1.21 X20 @
% 5.29/1.21 ( dsetconstr @
% 5.29/1.21 X16 @ ( ^[V_2:$i]: ( X18 @ V_2 ) ) ) ) =>
% 5.29/1.21 ( in @ X20 @ X16 ) ) ) =>
% 5.29/1.21 ( ( ![X22:$i,X24:( $i > $o ),X26:$i]:
% 5.29/1.21 ( ( in @
% 5.29/1.21 X26 @
% 5.29/1.21 ( dsetconstr @
% 5.29/1.21 X22 @ ( ^[V_3:$i]: ( X24 @ V_3 ) ) ) ) =>
% 5.29/1.21 ( X24 @ X26 ) ) ) =>
% 5.29/1.21 ( ( exuE1 ) =>
% 5.29/1.21 ( ( prop2setE ) =>
% 5.29/1.21 ( ( emptysetE ) =>
% 5.29/1.21 ( ( emptysetimpfalse ) =>
% 5.29/1.21 ( ( notinemptyset ) =>
% 5.29/1.21 ( ( exuE3e ) =>
% 5.29/1.21 ( ( setext ) =>
% 5.29/1.21 ( ( emptyI ) =>
% 5.29/1.21 ( ( noeltsimpempty ) =>
% 5.29/1.21 ( ( ![X28:$i,
% 5.29/1.21 X30:( $i > $o ),X32:$i]:
% 5.29/1.21 ( ( in @ X32 @ X28 ) =>
% 5.29/1.21 ( ( in @
% 5.29/1.21 X32 @
% 5.29/1.21 ( dsetconstr @
% 5.29/1.21 X28 @
% 5.29/1.21 ( ^[V_4:$i]:
% 5.29/1.21 ( X30 @ V_4 ) ) ) ) <=>
% 5.29/1.21 ( X30 @ X32 ) ) ) ) =>
% 5.29/1.21 ( ( nonemptyE1 ) =>
% 5.29/1.21 ( ( nonemptyI ) =>
% 5.29/1.21 ( ( nonemptyI1 ) =>
% 5.29/1.21 ( ( setadjoinIL ) =>
% 5.29/1.21 ( ( emptyinunitempty ) =>
% 5.29/1.21 ( ( setadjoinIR ) =>
% 5.29/1.21 ( ( setadjoinE ) =>
% 5.29/1.21 ( (
% 5.29/1.21 setadjoinOr ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X34:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X34 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_5:$i]:
% 5.29/1.21 (
% 5.29/1.21 $true ) ) ) =
% 5.29/1.21 (
% 5.29/1.21 X34 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X36:$i,
% 5.29/1.21 X38:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X40:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X40 @ X38 ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X40 @ X36 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X38 @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X36 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X42:$i]:
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 emptyset @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X42 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X44:$i]:
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 emptyset @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X44 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X46:$i,
% 5.29/1.21 X48:$i,
% 5.29/1.21 X50:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X48 @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X46 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X50 @ X48 ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X50 @ X46 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setunionI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setunionE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subPowSU ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuE2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 nonemptyImpWitness ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 uniqinunit ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notinsingleton ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 eqinunit ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 singletonsswitch ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 upairsetE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 upairsetIL ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 upairsetIR ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X52:$i,
% 5.29/1.21 X54:(
% 5.29/1.21 $i > $o )]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ?[
% 5.29/1.21 X56:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X54 @ X56 ) &
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X56 @ X52 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X52 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_6:$i]:
% 5.29/1.21 (
% 5.29/1.21 X54 @ V_6 ) ) ) !=
% 5.29/1.21 (
% 5.29/1.21 emptyset ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 vacuousDall ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan3 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan4 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 prop2setI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 prop2set2propI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notdexE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notdallE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuI1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuI3 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuI2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 inCongP ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuE3u ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exu__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 emptyset__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setadjoin__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X58:$i,
% 5.29/1.21 X60:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X58 ) =
% 5.29/1.21 (
% 5.29/1.21 X60 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X58 ) =
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X60 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setunion__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 omega__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuEu ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 descr__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X62:$i,
% 5.29/1.21 X64:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X62 ) =
% 5.29/1.21 (
% 5.29/1.21 X64 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X66:(
% 5.29/1.21 $i > $o ),
% 5.29/1.21 X68:(
% 5.29/1.21 $i > $o )]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X70:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X70 @ X62 ) =>
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X72:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X72 @ X64 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X70 ) =
% 5.29/1.21 (
% 5.29/1.21 X72 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X66 @ X70 ) <=>
% 5.29/1.21 (
% 5.29/1.21 X68 @ X72 ) ) ) ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X62 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_7:$i]:
% 5.29/1.21 (
% 5.29/1.21 X66 @ V_7 ) ) ) =
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X64 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_8:$i]:
% 5.29/1.21 (
% 5.29/1.21 X68 @ V_8 ) ) ) ) ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetI1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 eqimpsubset2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 eqimpsubset1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetI2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 emptysetsubset ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetE2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notsubsetI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notequalI1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notequalI2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetRefl ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetTrans ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setadjoinSub ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setadjoinSub2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X74:$i,
% 5.29/1.21 X76:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 X74 @ X76 ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X74 @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X76 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setextsub ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetemptysetimpeq ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X78:$i,
% 5.29/1.21 X80:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 X80 @ X78 ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X80 @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X78 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X82:$i,
% 5.29/1.21 X84:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X84 @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X82 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 X84 @ X82 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X86:$i]:
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X86 @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X86 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X88:$i,
% 5.29/1.21 X90:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 X88 @ X90 ) =>
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X88 ) @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X90 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X92:$i,
% 5.29/1.21 X94:(
% 5.29/1.21 $i > $o )]:
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X92 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_9:$i]:
% 5.29/1.21 (
% 5.29/1.21 X94 @ V_9 ) ) ) @
% 5.29/1.21 (
% 5.29/1.21 powerset @
% 5.29/1.21 X92 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 5.29/1.21 thf(zf_stmt_4, negated_conjecture,
% 5.29/1.21 (~( ( setextAx ) =>
% 5.29/1.21 ( ( emptysetAx ) =>
% 5.29/1.21 ( ( setadjoinAx ) =>
% 5.29/1.21 ( ( ![X4:$i,X6:$i]:
% 5.29/1.21 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 5.29/1.21 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 5.29/1.21 ( ( setunionAx ) =>
% 5.29/1.21 ( ( omega0Ax ) =>
% 5.29/1.21 ( ( omegaSAx ) =>
% 5.29/1.21 ( ( omegaIndAx ) =>
% 5.29/1.21 ( ( replAx ) =>
% 5.29/1.21 ( ( foundationAx ) =>
% 5.29/1.21 ( ( wellorderingAx ) =>
% 5.29/1.21 ( ( descrp ) =>
% 5.29/1.21 ( ( ![X10:$i,X12:( $i > $o ),X14:$i]:
% 5.29/1.21 ( ( in @ X14 @ X10 ) =>
% 5.29/1.21 ( ( X12 @ X14 ) =>
% 5.29/1.21 ( in @
% 5.29/1.21 X14 @
% 5.29/1.21 ( dsetconstr @
% 5.29/1.21 X10 @ ( ^[V_1:$i]: ( X12 @ V_1 ) ) ) ) ) ) ) =>
% 5.29/1.21 ( ( ![X16:$i,X18:( $i > $o ),X20:$i]:
% 5.29/1.21 ( ( in @
% 5.29/1.21 X20 @
% 5.29/1.21 ( dsetconstr @
% 5.29/1.21 X16 @ ( ^[V_2:$i]: ( X18 @ V_2 ) ) ) ) =>
% 5.29/1.21 ( in @ X20 @ X16 ) ) ) =>
% 5.29/1.21 ( ( ![X22:$i,X24:( $i > $o ),X26:$i]:
% 5.29/1.21 ( ( in @
% 5.29/1.21 X26 @
% 5.29/1.21 ( dsetconstr @
% 5.29/1.21 X22 @ ( ^[V_3:$i]: ( X24 @ V_3 ) ) ) ) =>
% 5.29/1.21 ( X24 @ X26 ) ) ) =>
% 5.29/1.21 ( ( exuE1 ) =>
% 5.29/1.21 ( ( prop2setE ) =>
% 5.29/1.21 ( ( emptysetE ) =>
% 5.29/1.21 ( ( emptysetimpfalse ) =>
% 5.29/1.21 ( ( notinemptyset ) =>
% 5.29/1.21 ( ( exuE3e ) =>
% 5.29/1.21 ( ( setext ) =>
% 5.29/1.21 ( ( emptyI ) =>
% 5.29/1.21 ( ( noeltsimpempty ) =>
% 5.29/1.21 ( ( ![X28:$i,
% 5.29/1.21 X30:( $i > $o ),
% 5.29/1.21 X32:$i]:
% 5.29/1.21 ( ( in @ X32 @ X28 ) =>
% 5.29/1.21 ( ( in @
% 5.29/1.21 X32 @
% 5.29/1.21 ( dsetconstr @
% 5.29/1.21 X28 @
% 5.29/1.21 ( ^[V_4:$i]:
% 5.29/1.21 ( X30 @ V_4 ) ) ) ) <=>
% 5.29/1.21 ( X30 @ X32 ) ) ) ) =>
% 5.29/1.21 ( ( nonemptyE1 ) =>
% 5.29/1.21 ( ( nonemptyI ) =>
% 5.29/1.21 ( ( nonemptyI1 ) =>
% 5.29/1.21 ( ( setadjoinIL ) =>
% 5.29/1.21 ( ( emptyinunitempty ) =>
% 5.29/1.21 ( ( setadjoinIR ) =>
% 5.29/1.21 ( (
% 5.29/1.21 setadjoinE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setadjoinOr ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X34:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X34 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_5:$i]:
% 5.29/1.21 (
% 5.29/1.21 $true ) ) ) =
% 5.29/1.21 (
% 5.29/1.21 X34 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X36:$i,
% 5.29/1.21 X38:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X40:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X40 @ X38 ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X40 @ X36 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X38 @
% 5.29/1.21 (
% 5.29/1.21 powerset
% 5.29/1.21 @
% 5.29/1.21 X36 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X42:$i]:
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 emptyset @
% 5.29/1.21 (
% 5.29/1.21 powerset
% 5.29/1.21 @
% 5.29/1.21 X42 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X44:$i]:
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 emptyset @
% 5.29/1.21 (
% 5.29/1.21 powerset
% 5.29/1.21 @
% 5.29/1.21 X44 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X46:$i,
% 5.29/1.21 X48:$i,
% 5.29/1.21 X50:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X48 @
% 5.29/1.21 (
% 5.29/1.21 powerset
% 5.29/1.21 @
% 5.29/1.21 X46 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X50 @ X48 ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X50 @ X46 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setunionI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setunionE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subPowSU ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuE2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 nonemptyImpWitness ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 uniqinunit ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notinsingleton ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 eqinunit ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 singletonsswitch ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 upairsetE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 upairsetIL ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 upairsetIR ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X52:$i,
% 5.29/1.21 X54:(
% 5.29/1.21 $i > $o )]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ?[
% 5.29/1.21 X56:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X54 @ X56 ) &
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X56 @ X52 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X52 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_6:$i]:
% 5.29/1.21 (
% 5.29/1.21 X54 @ V_6 ) ) ) !=
% 5.29/1.21 (
% 5.29/1.21 emptyset ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 vacuousDall ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan3 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 quantDeMorgan4 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 prop2setI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 prop2set2propI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notdexE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notdallE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuI1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuI3 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuI2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 inCongP ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuE3u ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exu__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 emptyset__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setadjoin__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X58:$i,
% 5.29/1.21 X60:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X58 ) =
% 5.29/1.21 (
% 5.29/1.21 X60 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 powerset
% 5.29/1.21 @
% 5.29/1.21 X58 ) =
% 5.29/1.21 (
% 5.29/1.21 powerset
% 5.29/1.21 @
% 5.29/1.21 X60 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setunion__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 omega__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 exuEu ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 descr__Cong ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X62:$i,
% 5.29/1.21 X64:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X62 ) =
% 5.29/1.21 (
% 5.29/1.21 X64 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X66:(
% 5.29/1.21 $i > $o ),
% 5.29/1.21 X68:(
% 5.29/1.21 $i > $o )]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X70:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X70 @ X62 ) =>
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X72:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X72 @ X64 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X70 ) =
% 5.29/1.21 (
% 5.29/1.21 X72 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 X66 @ X70 ) <=>
% 5.29/1.21 (
% 5.29/1.21 X68 @ X72 ) ) ) ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X62 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_7:$i]:
% 5.29/1.21 (
% 5.29/1.21 X66 @ V_7 ) ) ) =
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X64 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_8:$i]:
% 5.29/1.21 (
% 5.29/1.21 X68 @ V_8 ) ) ) ) ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetI1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 eqimpsubset2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 eqimpsubset1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetI2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 emptysetsubset ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetE ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetE2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notsubsetI ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notequalI1 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 notequalI2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetRefl ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetTrans ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setadjoinSub ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setadjoinSub2 ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X74:$i,
% 5.29/1.21 X76:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 X74 @ X76 ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X74 @
% 5.29/1.21 (
% 5.29/1.21 powerset
% 5.29/1.21 @
% 5.29/1.21 X76 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 setextsub ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subsetemptysetimpeq ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X78:$i,
% 5.29/1.21 X80:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 X80 @ X78 ) =>
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X80 @
% 5.29/1.21 (
% 5.29/1.21 powerset
% 5.29/1.21 @
% 5.29/1.21 X78 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X82:$i,
% 5.29/1.21 X84:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X84 @
% 5.29/1.21 (
% 5.29/1.21 powerset
% 5.29/1.21 @
% 5.29/1.21 X82 ) ) =>
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 X84 @ X82 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X86:$i]:
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 X86 @
% 5.29/1.21 (
% 5.29/1.21 powerset
% 5.29/1.21 @
% 5.29/1.21 X86 ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X88:$i,
% 5.29/1.21 X90:$i]:
% 5.29/1.21 (
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 X88 @ X90 ) =>
% 5.29/1.21 (
% 5.29/1.21 subset @
% 5.29/1.21 (
% 5.29/1.21 powerset
% 5.29/1.21 @
% 5.29/1.21 X88 ) @
% 5.29/1.21 (
% 5.29/1.21 powerset
% 5.29/1.21 @
% 5.29/1.21 X90 ) ) ) ) =>
% 5.29/1.21 (
% 5.29/1.21 ![
% 5.29/1.21 X92:$i,
% 5.29/1.21 X94:(
% 5.29/1.21 $i > $o )]:
% 5.29/1.21 (
% 5.29/1.21 in @
% 5.29/1.21 (
% 5.29/1.21 dsetconstr
% 5.29/1.21 @
% 5.29/1.21 X92 @
% 5.29/1.21 (
% 5.29/1.21 ^[
% 5.29/1.21 V_9:$i]:
% 5.29/1.21 (
% 5.29/1.21 X94 @ V_9 ) ) ) @
% 5.29/1.21 (
% 5.29/1.21 powerset
% 5.29/1.21 @
% 5.29/1.21 X92 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 5.29/1.21 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 5.29/1.21 thf(zip_derived_cl57, plain,
% 5.29/1.21 (~ (in @ (dsetconstr @ sk__46 @ (^[Y0 : $i]: (sk__47 @ Y0))) @
% 5.29/1.21 (powerset @ sk__46))),
% 5.29/1.21 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.29/1.21 thf(zip_derived_cl107, plain,
% 5.29/1.21 (~ (in @ (dsetconstr @ sk__46 @ sk__47) @ (powerset @ sk__46))),
% 5.29/1.21 inference('ho_norm', [status(thm)], [zip_derived_cl57])).
% 5.29/1.21 thf(zip_derived_cl21, plain,
% 5.29/1.21 (![X9 : $i, X10 : $i]:
% 5.29/1.21 ( (in @ X9 @ (powerset @ X10)) | ~ (in @ (sk__50 @ X9 @ X10) @ X10))),
% 5.29/1.21 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.29/1.21 thf(zip_derived_cl22, plain,
% 5.29/1.21 (![X9 : $i, X10 : $i]:
% 5.29/1.21 ( (in @ X9 @ (powerset @ X10)) | (in @ (sk__50 @ X9 @ X10) @ X9))),
% 5.29/1.21 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.29/1.21 thf(zip_derived_cl99, plain,
% 5.29/1.21 (![X35 : $i, X36 : $i, X37 : $i > $o]:
% 5.29/1.21 ( (in @ X35 @ X36)
% 5.29/1.21 | ~ (in @ X35 @ (dsetconstr @ X36 @ (^[Y0 : $i]: (X37 @ Y0)))))),
% 5.29/1.21 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.29/1.21 thf(zip_derived_cl111, plain,
% 5.29/1.21 (![X35 : $i, X36 : $i, X37 : $i > $o]:
% 5.29/1.21 ( (in @ X35 @ X36) | ~ (in @ X35 @ (dsetconstr @ X36 @ X37)))),
% 5.29/1.21 inference('ho_norm', [status(thm)], [zip_derived_cl99])).
% 5.29/1.21 thf(zip_derived_cl430, plain,
% 5.29/1.21 (![X0 : $i > $o, X1 : $i, X2 : $i]:
% 5.29/1.21 ( (in @ (dsetconstr @ X1 @ X0) @ (powerset @ X2))
% 5.29/1.21 | (in @ (sk__50 @ (dsetconstr @ X1 @ X0) @ X2) @ X1))),
% 5.29/1.21 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl111])).
% 5.29/1.21 thf(zip_derived_cl788, plain,
% 5.29/1.21 (![X0 : $i, X1 : $i > $o]:
% 5.29/1.21 ( (in @ (dsetconstr @ X0 @ X1) @ (powerset @ X0))
% 5.29/1.21 | (in @ (dsetconstr @ X0 @ X1) @ (powerset @ X0)))),
% 5.29/1.21 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl430])).
% 5.29/1.21 thf(zip_derived_cl805, plain,
% 5.29/1.21 (![X0 : $i, X1 : $i > $o]:
% 5.29/1.21 (in @ (dsetconstr @ X0 @ X1) @ (powerset @ X0))),
% 5.29/1.21 inference('simplify', [status(thm)], [zip_derived_cl788])).
% 5.29/1.21 thf(zip_derived_cl812, plain, ($false),
% 5.29/1.21 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl805])).
% 5.29/1.21
% 5.29/1.21 % SZS output end Refutation
% 5.29/1.21
% 5.29/1.21
% 5.29/1.21 % Terminating...
% 6.73/1.41 % Runner terminated.
% 6.77/1.42 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------