%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU592^1 : 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.dUtBtCSE4m true
% Computer : n006.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 04:55:14 PM UTC 2025
% Result : Theorem 4.07s 3.66s
% Output : Refutation 4.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/1.15 % Problem : SEU592^1 : TPTP v9.2.0. Released v3.7.0.
% 0.13/1.24 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.dUtBtCSE4m true
% 0.16/1.64 % Computer : n006.cluster.edu
% 0.16/1.64 % Model : x86_64 x86_64
% 0.16/1.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/1.64 % Memory : 8042.1875MB
% 0.16/1.64 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/1.64 % CPULimit : 300
% 0.16/1.64 % WCLimit : 300
% 0.16/1.64 % DateTime : Wed Oct 1 16:04:54 EDT 2025
% 0.19/1.65 % CPUTime :
% 0.19/1.65 % Running portfolio for 300 s
% 0.19/1.65 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/1.67 % Number of cores: 8
% 0.19/1.68 % Python version: Python 3.6.8
% 0.19/1.69 % Running in HO mode
% 0.54/2.37 % Total configuration time : 828
% 0.54/2.37 % Estimated wc time : 1656
% 0.54/2.37 % Estimated cpu time (8 cpus) : 207.0
% 0.55/2.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.55/2.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.47/2.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.48/2.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.48/2.80 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.48/2.83 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.53/2.92 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.53/2.95 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 4.07/3.66 % Solved by lams/40_c.s.sh.
% 4.07/3.66 % done 32 iterations in 0.602s
% 4.07/3.66 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.07/3.66 % SZS output start Refutation
% 4.07/3.66 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 4.07/3.66 thf(notdexE_type, type, notdexE: $o).
% 4.07/3.66 thf(setunionAx_type, type, setunionAx: $o).
% 4.07/3.66 thf(sk__321_type, type, sk__321: $i).
% 4.07/3.66 thf(powersetE_type, type, powersetE: $o).
% 4.07/3.66 thf(omegaSAx_type, type, omegaSAx: $o).
% 4.07/3.66 thf(exuI1_type, type, exuI1: $o).
% 4.07/3.66 thf(exuI2_type, type, exuI2: $o).
% 4.07/3.66 thf(notequalI2_type, type, notequalI2: $o).
% 4.07/3.66 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 4.07/3.66 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 4.07/3.66 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 4.07/3.66 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 4.07/3.66 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 4.07/3.66 thf(zip_tseitin_3_type, type, zip_tseitin_3: $i > $i > $i > ($i > $i > $o) > $o).
% 4.07/3.66 thf(zip_tseitin_5_type, type, zip_tseitin_5: $i > ($i > $o) > $o).
% 4.07/3.66 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 4.07/3.66 thf(binunionE_type, type, binunionE: $o).
% 4.07/3.66 thf(setext_type, type, setext: $o).
% 4.07/3.66 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 4.07/3.66 thf(descr__Cong_type, type, descr__Cong: $o).
% 4.07/3.66 thf(in_type, type, in: $i > $i > $o).
% 4.07/3.66 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 4.07/3.66 thf(binunion_type, type, binunion: $i > $i > $i).
% 4.07/3.66 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 4.07/3.66 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 4.07/3.66 thf(upairset2IR_type, type, upairset2IR: $o).
% 4.07/3.66 thf(subsetE_type, type, subsetE: $o).
% 4.07/3.66 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 4.07/3.66 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 4.07/3.66 thf(setbeta_type, type, setbeta: $o).
% 4.07/3.66 thf(eqinunit_type, type, eqinunit: $o).
% 4.07/3.66 thf(upairsetIL_type, type, upairsetIL: $o).
% 4.07/3.66 thf(powersetI1_type, type, powersetI1: $o).
% 4.07/3.66 thf(powersetAx_type, type, powersetAx: $o).
% 4.07/3.66 thf(powersetI_type, type, powersetI: $o).
% 4.07/3.66 thf(upairsetIR_type, type, upairsetIR: $o).
% 4.07/3.66 thf(inCongP_type, type, inCongP: $o).
% 4.07/3.66 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 4.07/3.66 thf(exuE3e_type, type, exuE3e: $o).
% 4.07/3.66 thf(emptysetE_type, type, emptysetE: $o).
% 4.07/3.66 thf(setunionI_type, type, setunionI: $o).
% 4.07/3.66 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 4.07/3.66 thf(prop2setI_type, type, prop2setI: $o).
% 4.07/3.66 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 4.07/3.66 thf(exuE2_type, type, exuE2: $o).
% 4.07/3.66 thf(emptyset_type, type, emptyset: $i).
% 4.07/3.66 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 4.07/3.66 thf(powersetsubset_type, type, powersetsubset: $o).
% 4.07/3.66 thf(subPowSU_type, type, subPowSU: $o).
% 4.07/3.66 thf(notequalI1_type, type, notequalI1: $o).
% 4.07/3.66 thf(notinemptyset_type, type, notinemptyset: $o).
% 4.07/3.66 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 4.07/3.66 thf(subsetTrans_type, type, subsetTrans: $o).
% 4.07/3.66 thf(binunionIL_type, type, binunionIL: $o).
% 4.07/3.66 thf(subsetE2_type, type, subsetE2: $o).
% 4.07/3.66 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 4.07/3.66 thf(setextsub_type, type, setextsub: $o).
% 4.07/3.66 thf(binunionLsub_type, type, binunionLsub: $o).
% 4.07/3.66 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 4.07/3.66 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 4.07/3.66 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 4.07/3.66 thf(setunionE_type, type, setunionE: $o).
% 4.07/3.66 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 4.07/3.66 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 4.07/3.66 thf(binunionIR_type, type, binunionIR: $o).
% 4.07/3.66 thf(setadjoinE_type, type, setadjoinE: $o).
% 4.07/3.66 thf(descr_type, type, descr: ($i > $o) > $i).
% 4.07/3.66 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 4.07/3.66 thf(exuE1_type, type, exuE1: $o).
% 4.07/3.66 thf(prop2set_type, type, prop2set: $o > $i).
% 4.07/3.66 thf(notinsingleton_type, type, notinsingleton: $o).
% 4.07/3.66 thf(sk__322_type, type, sk__322: $i).
% 4.07/3.66 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 4.07/3.66 thf(exuEu_type, type, exuEu: $o).
% 4.07/3.66 thf(binintersectI_type, type, binintersectI: $o).
% 4.07/3.66 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 4.07/3.66 thf(upairsetE_type, type, upairsetE: $o).
% 4.07/3.66 thf(omega0Ax_type, type, omega0Ax: $o).
% 4.07/3.66 thf(notsubsetI_type, type, notsubsetI: $o).
% 4.07/3.66 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 4.07/3.66 thf(setextAx_type, type, setextAx: $o).
% 4.07/3.66 thf(powersetE1_type, type, powersetE1: $o).
% 4.07/3.66 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 4.07/3.66 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 4.07/3.66 thf(setunion_type, type, setunion: $i > $i).
% 4.07/3.66 thf(subsetI1_type, type, subsetI1: $o).
% 4.07/3.66 thf(descrp_type, type, descrp: $o).
% 4.07/3.66 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 4.07/3.66 thf(foundationAx_type, type, foundationAx: $o).
% 4.07/3.66 thf(emptysetAx_type, type, emptysetAx: $o).
% 4.07/3.66 thf(emptyI_type, type, emptyI: $o).
% 4.07/3.66 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 4.07/3.66 thf(emptyE1_type, type, emptyE1: $o).
% 4.07/3.66 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 4.07/3.66 thf(vacuousDall_type, type, vacuousDall: $o).
% 4.07/3.66 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 4.07/3.66 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 4.07/3.66 thf(exu_type, type, exu: ($i > $o) > $o).
% 4.07/3.66 thf(subsetI2_type, type, subsetI2: $o).
% 4.07/3.66 thf(binintersectEL_type, type, binintersectEL: $o).
% 4.07/3.66 thf(omega__Cong_type, type, omega__Cong: $o).
% 4.07/3.66 thf(subsetRefl_type, type, subsetRefl: $o).
% 4.07/3.66 thf(uniqinunit_type, type, uniqinunit: $o).
% 4.07/3.66 thf(prop2setE_type, type, prop2setE: $o).
% 4.07/3.66 thf(binunionEcases_type, type, binunionEcases: $o).
% 4.07/3.66 thf(omega_type, type, omega: $i).
% 4.07/3.66 thf(nonemptyI_type, type, nonemptyI: $o).
% 4.07/3.66 thf(exuE3u_type, type, exuE3u: $o).
% 4.07/3.66 thf(sepSubset_type, type, sepSubset: $o).
% 4.07/3.66 thf(zip_tseitin_4_type, type, zip_tseitin_4: $i > $i > ($i > $o) > $o).
% 4.07/3.66 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 4.07/3.66 thf(exuI3_type, type, exuI3: $o).
% 4.07/3.66 thf(notdallE_type, type, notdallE: $o).
% 4.07/3.66 thf(powerset_type, type, powerset: $i > $i).
% 4.07/3.66 thf(zip_tseitin_2_type, type, zip_tseitin_2: $i > $i > $i > $o).
% 4.07/3.66 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 4.07/3.66 thf(nonempty_type, type, nonempty: $i > $o).
% 4.07/3.66 thf(set2prop_type, type, set2prop: $i > $o).
% 4.07/3.66 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 4.07/3.66 thf(exu__Cong_type, type, exu__Cong: $o).
% 4.07/3.66 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 4.07/3.66 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 4.07/3.66 thf(replAx_type, type, replAx: $o).
% 4.07/3.66 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 4.07/3.66 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 4.07/3.66 thf(inPowerset_type, type, inPowerset: $o).
% 4.07/3.66 thf(subset_type, type, subset: $i > $i > $o).
% 4.07/3.66 thf(in__Cong_type, type, in__Cong: $o).
% 4.07/3.66 thf(binunionRsub_type, type, binunionRsub: $o).
% 4.07/3.66 thf(subset2powerset_type, type, subset2powerset: $o).
% 4.07/3.66 thf(binintersectEL, axiom, binintersectEL =
% 4.07/3.66 (![A:$i,B:$i,Xx:$i]:
% 4.07/3.66 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 4.07/3.66 thf('0', plain,
% 4.07/3.66 (( binintersectEL ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.66 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(binintersectSubset5, axiom, binintersectSubset5 =
% 4.07/3.66 (![A:$i,B:$i,C:$i]:
% 4.07/3.66 ( ( subset @ C @ A ) =>
% 4.07/3.66 ( ( subset @ C @ B ) => ( subset @ C @ ( binintersect @ A @ B ) ) ) ))).
% 4.07/3.66 thf('1', plain,
% 4.07/3.66 (( binintersectSubset5 ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.66 ( ( subset @ X8 @ X4 ) =>
% 4.07/3.66 ( ( subset @ X8 @ X6 ) =>
% 4.07/3.66 ( subset @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(binintersectI, axiom, binintersectI =
% 4.07/3.66 (![A:$i,B:$i,Xx:$i]:
% 4.07/3.66 ( ( in @ Xx @ A ) =>
% 4.07/3.66 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ))).
% 4.07/3.66 thf('2', plain,
% 4.07/3.66 (( binintersectI ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.66 ( ( in @ X8 @ X4 ) =>
% 4.07/3.66 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(binintersect, axiom,(( binintersect ) =
% 4.07/3.66 (^[A:$i,B:$i]: ( dsetconstr @ A @ ( ^[Xx:$i]: ( in @ Xx @ B ) ) )))).
% 4.07/3.66 thf('3', plain,
% 4.07/3.66 (( binintersect ) =
% 4.07/3.66 ( ^[A:$i,B:$i]: ( dsetconstr @ A @ ( ^[Xx:$i]: ( in @ Xx @ B ) ) ) )),
% 4.07/3.66 inference('simplify_rw_rule', [status(thm)], [binintersect])).
% 4.07/3.66 thf('4', plain,
% 4.07/3.66 (( binintersect ) =
% 4.07/3.66 ( ^[V_1:$i,V_2:$i]:
% 4.07/3.66 ( dsetconstr @ V_1 @ ( ^[V_3:$i]: ( in @ V_3 @ V_2 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(binunionRsub, axiom, binunionRsub =
% 4.07/3.66 (![A:$i,B:$i]: ( subset @ B @ ( binunion @ A @ B ) ))).
% 4.07/3.66 thf('5', plain,
% 4.07/3.66 (( binunionRsub ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(binunionLsub, axiom, binunionLsub =
% 4.07/3.66 (![A:$i,B:$i]: ( subset @ A @ ( binunion @ A @ B ) ))).
% 4.07/3.66 thf('6', plain,
% 4.07/3.66 (( binunionLsub ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]: ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(binunionE, axiom, binunionE =
% 4.07/3.66 (![A:$i,B:$i,Xx:$i]:
% 4.07/3.66 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 4.07/3.66 ( ( in @ Xx @ A ) | ( in @ Xx @ B ) ) ))).
% 4.07/3.66 thf('7', plain,
% 4.07/3.66 (( binunionE ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.66 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 4.07/3.66 ( ( in @ X8 @ X4 ) | ( in @ X8 @ X6 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(binunionEcases, axiom, binunionEcases =
% 4.07/3.66 (![A:$i,B:$i,Xx:$i,Xphi:$o]:
% 4.07/3.66 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 4.07/3.66 ( ( ( in @ Xx @ A ) => ( Xphi ) ) =>
% 4.07/3.66 ( ( ( in @ Xx @ B ) => ( Xphi ) ) => ( Xphi ) ) ) ))).
% 4.07/3.66 thf('8', plain,
% 4.07/3.66 (( binunionEcases ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i,X10:$o]:
% 4.07/3.66 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 4.07/3.66 ( ( ( in @ X8 @ X4 ) => ( X10 ) ) =>
% 4.07/3.66 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(binunionIR, axiom, binunionIR =
% 4.07/3.66 (![A:$i,B:$i,Xx:$i]:
% 4.07/3.66 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 4.07/3.66 thf('9', plain,
% 4.07/3.66 (( binunionIR ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.66 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(upairset2IR, axiom, upairset2IR =
% 4.07/3.66 (![Xx:$i,Xy:$i]:
% 4.07/3.66 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 4.07/3.66 thf('10', plain,
% 4.07/3.66 (( upairset2IR ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(binunionIL, axiom, binunionIL =
% 4.07/3.66 (![A:$i,B:$i,Xx:$i]:
% 4.07/3.66 ( ( in @ Xx @ A ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 4.07/3.66 thf('11', plain,
% 4.07/3.66 (( binunionIL ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.66 ( ( in @ X8 @ X4 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(sepSubset, axiom, sepSubset =
% 4.07/3.66 (![A:$i,Xphi:( $i > $o )]:
% 4.07/3.66 ( subset @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ A ))).
% 4.07/3.66 thf('12', plain,
% 4.07/3.66 (( sepSubset ) =
% 4.07/3.66 ( ![X4:$i,X6:( $i > $o )]:
% 4.07/3.66 ( subset @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @ X4 ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(sepInPowerset, axiom, sepInPowerset =
% 4.07/3.66 (![A:$i,Xphi:( $i > $o )]:
% 4.07/3.66 ( in @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ ( powerset @ A ) ))).
% 4.07/3.66 thf('13', plain,
% 4.07/3.66 (( sepInPowerset ) =
% 4.07/3.66 ( ![X4:$i,X6:( $i > $o )]:
% 4.07/3.66 ( in @
% 4.07/3.66 ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @
% 4.07/3.66 ( powerset @ X4 ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(powersetsubset, axiom, powersetsubset =
% 4.07/3.66 (![A:$i,B:$i]:
% 4.07/3.66 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 4.07/3.66 thf('14', plain,
% 4.07/3.66 (( powersetsubset ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( ( subset @ X4 @ X6 ) =>
% 4.07/3.66 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 4.07/3.66 thf('15', plain,
% 4.07/3.66 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(powersetE1, axiom, powersetE1 =
% 4.07/3.66 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 4.07/3.66 thf('16', plain,
% 4.07/3.66 (( powersetE1 ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(powersetI1, axiom, powersetI1 =
% 4.07/3.66 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 4.07/3.66 thf('17', plain,
% 4.07/3.66 (( powersetI1 ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 4.07/3.66 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 4.07/3.66 thf('18', plain,
% 4.07/3.66 (( subsetemptysetimpeq ) =
% 4.07/3.66 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(setextsub, axiom, setextsub =
% 4.07/3.66 (![A:$i,B:$i]:
% 4.07/3.66 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 4.07/3.66 thf('19', plain,
% 4.07/3.66 (( setextsub ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( ( subset @ X4 @ X6 ) =>
% 4.07/3.66 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(subset2powerset, axiom, subset2powerset =
% 4.07/3.66 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 4.07/3.66 thf('20', plain,
% 4.07/3.66 (( subset2powerset ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 4.07/3.66 (![A:$i,Xx:$i,B:$i]:
% 4.07/3.66 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 4.07/3.66 thf('21', plain,
% 4.07/3.66 (( setadjoinSub2 ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.66 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(setadjoinSub, axiom, setadjoinSub =
% 4.07/3.66 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 4.07/3.66 thf('22', plain,
% 4.07/3.66 (( setadjoinSub ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(subsetTrans, axiom, subsetTrans =
% 4.07/3.66 (![A:$i,B:$i,C:$i]:
% 4.07/3.66 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 4.07/3.66 thf('23', plain,
% 4.07/3.66 (( subsetTrans ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.66 ( ( subset @ X4 @ X6 ) =>
% 4.07/3.66 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 4.07/3.66 thf('24', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(notequalI2, axiom, notequalI2 =
% 4.07/3.66 (![A:$i,B:$i,Xx:$i]:
% 4.07/3.66 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ( A ) != ( B ) ) ) ))).
% 4.07/3.66 thf('25', plain,
% 4.07/3.66 (( notequalI2 ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.66 ( ( in @ X8 @ X4 ) =>
% 4.07/3.66 ( ( ~( in @ X8 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(notequalI1, axiom, notequalI1 =
% 4.07/3.66 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 4.07/3.66 thf('26', plain,
% 4.07/3.66 (( notequalI1 ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(notsubsetI, axiom, notsubsetI =
% 4.07/3.66 (![A:$i,B:$i,Xx:$i]:
% 4.07/3.66 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 4.07/3.66 thf('27', plain,
% 4.07/3.66 (( notsubsetI ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.66 ( ( in @ X8 @ X4 ) =>
% 4.07/3.66 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(subsetE2, axiom, subsetE2 =
% 4.07/3.66 (![A:$i,B:$i,Xx:$i]:
% 4.07/3.66 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 4.07/3.66 thf('28', plain,
% 4.07/3.66 (( subsetE2 ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.66 ( ( subset @ X4 @ X6 ) =>
% 4.07/3.66 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(subsetE, axiom, subsetE =
% 4.07/3.66 (![A:$i,B:$i,Xx:$i]:
% 4.07/3.66 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 4.07/3.66 thf('29', plain,
% 4.07/3.66 (( subsetE ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.66 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(emptysetsubset, axiom, emptysetsubset =
% 4.07/3.66 (![A:$i]: ( subset @ emptyset @ A ))).
% 4.07/3.66 thf('30', plain,
% 4.07/3.66 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(subsetI2, axiom, subsetI2 =
% 4.07/3.66 (![A:$i,B:$i]:
% 4.07/3.66 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 4.07/3.66 ( subset @ A @ B ) ))).
% 4.07/3.66 thf('31', plain,
% 4.07/3.66 (( subsetI2 ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 4.07/3.66 ( subset @ X4 @ X6 ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 4.07/3.66 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 4.07/3.66 thf('32', plain,
% 4.07/3.66 (( eqimpsubset1 ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 4.07/3.66 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 4.07/3.66 thf('33', plain,
% 4.07/3.66 (( eqimpsubset2 ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(subsetI1, axiom, subsetI1 =
% 4.07/3.66 (![A:$i,B:$i]:
% 4.07/3.66 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 4.07/3.66 ( subset @ A @ B ) ))).
% 4.07/3.66 thf('34', plain,
% 4.07/3.66 (( subsetI1 ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 4.07/3.66 ( subset @ X4 @ X6 ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(dsetconstr__Cong, axiom, dsetconstr__Cong =
% 4.07/3.66 (![A:$i,B:$i]:
% 4.07/3.66 ( ( ( A ) = ( B ) ) =>
% 4.07/3.66 ( ![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 4.07/3.66 ( ( ![Xx:$i]:
% 4.07/3.66 ( ( in @ Xx @ A ) =>
% 4.07/3.66 ( ![Xy:$i]:
% 4.07/3.66 ( ( in @ Xy @ B ) =>
% 4.07/3.66 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) ) ) ) =>
% 4.07/3.66 ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =
% 4.07/3.66 ( dsetconstr @ B @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ) ) ))).
% 4.07/3.66 thf('35', plain,
% 4.07/3.66 (( dsetconstr__Cong ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( ( ( X4 ) = ( X6 ) ) =>
% 4.07/3.66 ( ![X8:( $i > $o ),X10:( $i > $o )]:
% 4.07/3.66 ( ( ![X12:$i]:
% 4.07/3.66 ( ( in @ X12 @ X4 ) =>
% 4.07/3.66 ( ![X14:$i]:
% 4.07/3.66 ( ( in @ X14 @ X6 ) =>
% 4.07/3.66 ( ( ( X12 ) = ( X14 ) ) =>
% 4.07/3.66 ( ( X8 @ X12 ) <=> ( X10 @ X14 ) ) ) ) ) ) ) =>
% 4.07/3.66 ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) =
% 4.07/3.66 ( dsetconstr @ X6 @ ( ^[V_2:$i]: ( X10 @ V_2 ) ) ) ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(descr__Cong, axiom, descr__Cong =
% 4.07/3.66 (![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 4.07/3.66 ( ( ![Xx:$i,Xy:$i]:
% 4.07/3.66 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) =>
% 4.07/3.66 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 4.07/3.66 ( ( exu @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) =>
% 4.07/3.66 ( ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =
% 4.07/3.66 ( descr @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ) ) ))).
% 4.07/3.66 thf('36', plain,
% 4.07/3.66 (( descr__Cong ) =
% 4.07/3.66 ( ![X4:( $i > $o ),X6:( $i > $o )]:
% 4.07/3.66 ( ( ![X8:$i,X10:$i]:
% 4.07/3.66 ( ( ( X8 ) = ( X10 ) ) => ( ( X4 @ X8 ) <=> ( X6 @ X10 ) ) ) ) =>
% 4.07/3.66 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 4.07/3.66 ( ( exu @ ( ^[V_2:$i]: ( X6 @ V_2 ) ) ) =>
% 4.07/3.66 ( ( descr @ ( ^[V_3:$i]: ( X4 @ V_3 ) ) ) =
% 4.07/3.66 ( descr @ ( ^[V_4:$i]: ( X6 @ V_4 ) ) ) ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(exuEu, axiom, exuEu =
% 4.07/3.66 (![Xphi:( $i > $o )]:
% 4.07/3.66 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 4.07/3.66 ( ![Xx:$i,Xy:$i]:
% 4.07/3.66 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ))).
% 4.07/3.66 thf('37', plain,
% 4.07/3.66 (( exuEu ) =
% 4.07/3.66 ( ![X4:( $i > $o )]:
% 4.07/3.66 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 4.07/3.66 ( ![X6:$i,X8:$i]:
% 4.07/3.66 ( ( X4 @ X6 ) => ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(omega__Cong, axiom, omega__Cong = (( omega ) = ( omega ))).
% 4.07/3.66 thf('38', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(setunion__Cong, axiom, setunion__Cong =
% 4.07/3.66 (![A:$i,B:$i]:
% 4.07/3.66 ( ( ( A ) = ( B ) ) => ( ( setunion @ A ) = ( setunion @ B ) ) ))).
% 4.07/3.66 thf('39', plain,
% 4.07/3.66 (( setunion__Cong ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( ( ( X4 ) = ( X6 ) ) => ( ( setunion @ X4 ) = ( setunion @ X6 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(powerset__Cong, axiom, powerset__Cong =
% 4.07/3.66 (![A:$i,B:$i]:
% 4.07/3.66 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 4.07/3.66 thf('40', plain,
% 4.07/3.66 (( powerset__Cong ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 4.07/3.66 (![Xx:$i,Xy:$i]:
% 4.07/3.66 ( ( ( Xx ) = ( Xy ) ) =>
% 4.07/3.66 ( ![Xz:$i,Xu:$i]:
% 4.07/3.66 ( ( ( Xz ) = ( Xu ) ) =>
% 4.07/3.66 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 4.07/3.66 thf('41', plain,
% 4.07/3.66 (( setadjoin__Cong ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( ( ( X4 ) = ( X6 ) ) =>
% 4.07/3.66 ( ![X8:$i,X10:$i]:
% 4.07/3.66 ( ( ( X8 ) = ( X10 ) ) =>
% 4.07/3.66 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(emptyset__Cong, axiom, emptyset__Cong = (( emptyset ) = ( emptyset ))).
% 4.07/3.66 thf('42', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(exu__Cong, axiom, exu__Cong =
% 4.07/3.66 (![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 4.07/3.66 ( ( ![Xx:$i,Xy:$i]:
% 4.07/3.66 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) =>
% 4.07/3.66 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) <=>
% 4.07/3.66 ( exu @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ))).
% 4.07/3.66 thf('43', plain,
% 4.07/3.66 (( exu__Cong ) =
% 4.07/3.66 ( ![X4:( $i > $o ),X6:( $i > $o )]:
% 4.07/3.66 ( ( ![X8:$i,X10:$i]:
% 4.07/3.66 ( ( ( X8 ) = ( X10 ) ) => ( ( X4 @ X8 ) <=> ( X6 @ X10 ) ) ) ) =>
% 4.07/3.66 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) <=>
% 4.07/3.66 ( exu @ ( ^[V_2:$i]: ( X6 @ V_2 ) ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(exuE3u, axiom, exuE3u =
% 4.07/3.66 (![Xphi:( $i > $o )]:
% 4.07/3.66 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 4.07/3.66 ( ![Xx:$i,Xy:$i]:
% 4.07/3.66 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ))).
% 4.07/3.66 thf('44', plain,
% 4.07/3.66 (( exuE3u ) =
% 4.07/3.66 ( ![X4:( $i > $o )]:
% 4.07/3.66 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 4.07/3.66 ( ![X6:$i,X8:$i]:
% 4.07/3.66 ( ( X4 @ X6 ) => ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(in__Cong, axiom, in__Cong =
% 4.07/3.66 (![A:$i,B:$i]:
% 4.07/3.66 ( ( ( A ) = ( B ) ) =>
% 4.07/3.66 ( ![Xx:$i,Xy:$i]:
% 4.07/3.66 ( ( ( Xx ) = ( Xy ) ) => ( ( in @ Xx @ A ) <=> ( in @ Xy @ B ) ) ) ) ))).
% 4.07/3.66 thf('45', plain,
% 4.07/3.66 (( in__Cong ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( ( ( X4 ) = ( X6 ) ) =>
% 4.07/3.66 ( ![X8:$i,X10:$i]:
% 4.07/3.66 ( ( ( X8 ) = ( X10 ) ) =>
% 4.07/3.66 ( ( in @ X8 @ X4 ) <=> ( in @ X10 @ X6 ) ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(inCongP, axiom, inCongP =
% 4.07/3.66 (![A:$i,B:$i]:
% 4.07/3.66 ( ( ( A ) = ( B ) ) =>
% 4.07/3.66 ( ![Xx:$i,Xy:$i]:
% 4.07/3.66 ( ( ( Xx ) = ( Xy ) ) => ( ( in @ Xx @ A ) => ( in @ Xy @ B ) ) ) ) ))).
% 4.07/3.66 thf('46', plain,
% 4.07/3.66 (( inCongP ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( ( ( X4 ) = ( X6 ) ) =>
% 4.07/3.66 ( ![X8:$i,X10:$i]:
% 4.07/3.66 ( ( ( X8 ) = ( X10 ) ) =>
% 4.07/3.66 ( ( in @ X8 @ X4 ) => ( in @ X10 @ X6 ) ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(exuI2, axiom, exuI2 =
% 4.07/3.66 (![Xphi:( $i > $o )]:
% 4.07/3.66 ( ( ?[Xx:$i]: ( ![Xy:$i]: ( ( Xphi @ Xy ) <=> ( ( Xy ) = ( Xx ) ) ) ) ) =>
% 4.07/3.66 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ))).
% 4.07/3.66 thf('47', plain,
% 4.07/3.66 (( exuI2 ) =
% 4.07/3.66 ( ![X4:( $i > $o )]:
% 4.07/3.66 ( ( ?[X6:$i]: ( ![X8:$i]: ( ( X4 @ X8 ) <=> ( ( X8 ) = ( X6 ) ) ) ) ) =>
% 4.07/3.66 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(exuI3, axiom, exuI3 =
% 4.07/3.66 (![Xphi:( $i > $o )]:
% 4.07/3.66 ( ( ?[Xx:$i]: ( Xphi @ Xx ) ) =>
% 4.07/3.66 ( ( ![Xx:$i,Xy:$i]:
% 4.07/3.66 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) =>
% 4.07/3.66 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 4.07/3.66 thf('48', plain,
% 4.07/3.66 (( exuI3 ) =
% 4.07/3.66 ( ![X4:( $i > $o )]:
% 4.07/3.66 ( ( ?[X6:$i]: ( X4 @ X6 ) ) =>
% 4.07/3.66 ( ( ![X8:$i,X10:$i]:
% 4.07/3.66 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( ( X8 ) = ( X10 ) ) ) ) ) =>
% 4.07/3.66 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(exuI1, axiom, exuI1 =
% 4.07/3.66 (![Xphi:( $i > $o )]:
% 4.07/3.66 ( ( ?[Xx:$i]:
% 4.07/3.66 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 4.07/3.66 ( Xphi @ Xx ) ) ) =>
% 4.07/3.66 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ))).
% 4.07/3.66 thf('49', plain,
% 4.07/3.66 (( exuI1 ) =
% 4.07/3.66 ( ![X4:( $i > $o )]:
% 4.07/3.66 ( ( ?[X6:$i]:
% 4.07/3.66 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 4.07/3.66 ( X4 @ X6 ) ) ) =>
% 4.07/3.66 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(notdallE, axiom, notdallE =
% 4.07/3.66 (![A:$i,Xphi:( $i > $o )]:
% 4.07/3.66 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) =>
% 4.07/3.66 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))).
% 4.07/3.66 thf('50', plain,
% 4.07/3.66 (( notdallE ) =
% 4.07/3.66 ( ![X4:$i,X6:( $i > $o )]:
% 4.07/3.66 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) =>
% 4.07/3.66 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(notdexE, axiom, notdexE =
% 4.07/3.66 (![A:$i,Xphi:( $i > $o )]:
% 4.07/3.66 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) =>
% 4.07/3.66 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))).
% 4.07/3.66 thf('51', plain,
% 4.07/3.66 (( notdexE ) =
% 4.07/3.66 ( ![X4:$i,X6:( $i > $o )]:
% 4.07/3.66 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 4.07/3.66 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(prop2set2propI, axiom, prop2set2propI =
% 4.07/3.66 (![Xphi:$o]: ( ( Xphi ) => ( set2prop @ ( prop2set @ Xphi ) ) ))).
% 4.07/3.66 thf('52', plain,
% 4.07/3.66 (( prop2set2propI ) =
% 4.07/3.66 ( ![X4:$o]: ( ( X4 ) => ( set2prop @ ( prop2set @ X4 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(prop2setI, axiom, prop2setI =
% 4.07/3.66 (![Xphi:$o]: ( ( Xphi ) => ( in @ emptyset @ ( prop2set @ Xphi ) ) ))).
% 4.07/3.66 thf('53', plain,
% 4.07/3.66 (( prop2setI ) =
% 4.07/3.66 ( ![X4:$o]: ( ( X4 ) => ( in @ emptyset @ ( prop2set @ X4 ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(quantDeMorgan4, axiom, quantDeMorgan4 =
% 4.07/3.66 (![A:$i,Xphi:( $i > $o )]:
% 4.07/3.66 ( ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) =>
% 4.07/3.66 ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) ))).
% 4.07/3.66 thf('54', plain,
% 4.07/3.66 (( quantDeMorgan4 ) =
% 4.07/3.66 ( ![X4:$i,X6:( $i > $o )]:
% 4.07/3.66 ( ( ?[X8:$i]: ( ( ~( X6 @ X8 ) ) & ( in @ X8 @ X4 ) ) ) =>
% 4.07/3.66 ( ~( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( X6 @ X10 ) ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(quantDeMorgan3, axiom, quantDeMorgan3 =
% 4.07/3.66 (![A:$i,Xphi:( $i > $o )]:
% 4.07/3.66 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) =>
% 4.07/3.66 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))).
% 4.07/3.66 thf('55', plain,
% 4.07/3.66 (( quantDeMorgan3 ) =
% 4.07/3.66 ( ![X4:$i,X6:( $i > $o )]:
% 4.07/3.66 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 4.07/3.66 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(quantDeMorgan2, axiom, quantDeMorgan2 =
% 4.07/3.66 (![A:$i,Xphi:( $i > $o )]:
% 4.07/3.66 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) =>
% 4.07/3.66 ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) ))).
% 4.07/3.66 thf('56', plain,
% 4.07/3.66 (( quantDeMorgan2 ) =
% 4.07/3.66 ( ![X4:$i,X6:( $i > $o )]:
% 4.07/3.66 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( ~( X6 @ X8 ) ) ) ) =>
% 4.07/3.66 ( ~( ?[X10:$i]: ( ( X6 @ X10 ) & ( in @ X10 @ X4 ) ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(quantDeMorgan1, axiom, quantDeMorgan1 =
% 4.07/3.66 (![A:$i,Xphi:( $i > $o )]:
% 4.07/3.66 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) =>
% 4.07/3.66 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))).
% 4.07/3.66 thf('57', plain,
% 4.07/3.66 (( quantDeMorgan1 ) =
% 4.07/3.66 ( ![X4:$i,X6:( $i > $o )]:
% 4.07/3.66 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) =>
% 4.07/3.66 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(vacuousDall, axiom, vacuousDall =
% 4.07/3.66 (![Xphi:( $i > $o ),Xx:$i]: ( ( in @ Xx @ emptyset ) => ( Xphi @ Xx ) ))).
% 4.07/3.66 thf('58', plain,
% 4.07/3.66 (( vacuousDall ) =
% 4.07/3.66 ( ![X4:( $i > $o ),X6:$i]: ( ( in @ X6 @ emptyset ) => ( X4 @ X6 ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(emptyE1, axiom, emptyE1 =
% 4.07/3.66 (![A:$i,Xphi:( $i > $o )]:
% 4.07/3.66 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) =>
% 4.07/3.66 ( ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) = ( emptyset ) ) =>
% 4.07/3.66 ( $false ) ) ))).
% 4.07/3.66 thf('59', plain,
% 4.07/3.66 (( emptyE1 ) =
% 4.07/3.66 ( ![X4:$i,X6:( $i > $o )]:
% 4.07/3.66 ( ( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) =>
% 4.07/3.66 ( ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = ( emptyset ) ) =>
% 4.07/3.66 ( $false ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(upairsetIR, axiom, upairsetIR =
% 4.07/3.66 (![Xx:$i,Xy:$i]:
% 4.07/3.66 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 4.07/3.66 thf('60', plain,
% 4.07/3.66 (( upairsetIR ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(upairsetIL, axiom, upairsetIL =
% 4.07/3.66 (![Xx:$i,Xy:$i]:
% 4.07/3.66 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 4.07/3.66 thf('61', plain,
% 4.07/3.66 (( upairsetIL ) =
% 4.07/3.66 ( ![X4:$i,X6:$i]:
% 4.07/3.66 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(upairsetE, axiom, upairsetE =
% 4.07/3.66 (![Xx:$i,Xy:$i,Xz:$i]:
% 4.07/3.66 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 4.07/3.66 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 4.07/3.66 thf('62', plain,
% 4.07/3.66 (( upairsetE ) =
% 4.07/3.66 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.66 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 4.07/3.66 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 4.07/3.66 define([status(thm)])).
% 4.07/3.66 thf(singletonsswitch, axiom, singletonsswitch =
% 4.07/3.66 (![Xx:$i,Xy:$i]:
% 4.07/3.66 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 4.07/3.66 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 4.07/3.66 thf('63', plain,
% 4.07/3.67 (( singletonsswitch ) =
% 4.07/3.67 ( ![X4:$i,X6:$i]:
% 4.07/3.67 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 4.07/3.67 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(eqinunit, axiom, eqinunit =
% 4.07/3.67 (![Xx:$i,Xy:$i]:
% 4.07/3.67 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 4.07/3.67 thf('64', plain,
% 4.07/3.67 (( eqinunit ) =
% 4.07/3.67 ( ![X4:$i,X6:$i]:
% 4.07/3.67 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(notinsingleton, axiom, notinsingleton =
% 4.07/3.67 (![Xx:$i,Xy:$i]:
% 4.07/3.67 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 4.07/3.67 thf('65', plain,
% 4.07/3.67 (( notinsingleton ) =
% 4.07/3.67 ( ![X4:$i,X6:$i]:
% 4.07/3.67 ( ( ( X4 ) != ( X6 ) ) =>
% 4.07/3.67 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(uniqinunit, axiom, uniqinunit =
% 4.07/3.67 (![Xx:$i,Xy:$i]:
% 4.07/3.67 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 4.07/3.67 thf('66', plain,
% 4.07/3.67 (( uniqinunit ) =
% 4.07/3.67 ( ![X4:$i,X6:$i]:
% 4.07/3.67 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(nonemptyImpWitness, axiom, nonemptyImpWitness =
% 4.07/3.67 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 4.07/3.67 thf('67', plain,
% 4.07/3.67 (( nonemptyImpWitness ) =
% 4.07/3.67 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(exuE2, axiom, exuE2 =
% 4.07/3.67 (![Xphi:( $i > $o )]:
% 4.07/3.67 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 4.07/3.67 ( ?[Xx:$i]: ( ![Xy:$i]: ( ( Xphi @ Xy ) <=> ( ( Xy ) = ( Xx ) ) ) ) ) ))).
% 4.07/3.67 thf('68', plain,
% 4.07/3.67 (( exuE2 ) =
% 4.07/3.67 ( ![X4:( $i > $o )]:
% 4.07/3.67 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 4.07/3.67 ( ?[X6:$i]: ( ![X8:$i]: ( ( X4 @ X8 ) <=> ( ( X8 ) = ( X6 ) ) ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(subPowSU, axiom, subPowSU =
% 4.07/3.67 (![A:$i,Xx:$i]:
% 4.07/3.67 ( ( in @ Xx @ A ) => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ))).
% 4.07/3.67 thf('69', plain,
% 4.07/3.67 (( subPowSU ) =
% 4.07/3.67 ( ![X4:$i,X6:$i]:
% 4.07/3.67 ( ( in @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ ( setunion @ X4 ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(setunionE, axiom, setunionE =
% 4.07/3.67 (![A:$i,Xx:$i]:
% 4.07/3.67 ( ( in @ Xx @ ( setunion @ A ) ) =>
% 4.07/3.67 ( ![Xphi:$o]:
% 4.07/3.67 ( ( ![B:$i]: ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( Xphi ) ) ) ) =>
% 4.07/3.67 ( Xphi ) ) ) ))).
% 4.07/3.67 thf('70', plain,
% 4.07/3.67 (( setunionE ) =
% 4.07/3.67 ( ![X4:$i,X6:$i]:
% 4.07/3.67 ( ( in @ X6 @ ( setunion @ X4 ) ) =>
% 4.07/3.67 ( ![X8:$o]:
% 4.07/3.67 ( ( ![X10:$i]:
% 4.07/3.67 ( ( in @ X6 @ X10 ) => ( ( in @ X10 @ X4 ) => ( X8 ) ) ) ) =>
% 4.07/3.67 ( X8 ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(setunionI, axiom, setunionI =
% 4.07/3.67 (![A:$i,Xx:$i,B:$i]:
% 4.07/3.67 ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( in @ Xx @ ( setunion @ A ) ) ) ))).
% 4.07/3.67 thf('71', plain,
% 4.07/3.67 (( setunionI ) =
% 4.07/3.67 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.67 ( ( in @ X6 @ X8 ) =>
% 4.07/3.67 ( ( in @ X8 @ X4 ) => ( in @ X6 @ ( setunion @ X4 ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(powersetE, axiom, powersetE =
% 4.07/3.67 (![A:$i,B:$i,Xx:$i]:
% 4.07/3.67 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 4.07/3.67 thf('72', plain,
% 4.07/3.67 (( powersetE ) =
% 4.07/3.67 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.67 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.07/3.67 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(emptyInPowerset, axiom, emptyInPowerset =
% 4.07/3.67 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 4.07/3.67 thf('73', plain,
% 4.07/3.67 (( emptyInPowerset ) =
% 4.07/3.67 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(emptyinPowerset, axiom, emptyinPowerset =
% 4.07/3.67 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 4.07/3.67 thf('74', plain,
% 4.07/3.67 (( emptyinPowerset ) =
% 4.07/3.67 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(powersetI, axiom, powersetI =
% 4.07/3.67 (![A:$i,B:$i]:
% 4.07/3.67 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 4.07/3.67 ( in @ B @ ( powerset @ A ) ) ))).
% 4.07/3.67 thf('75', plain,
% 4.07/3.67 (( powersetI ) =
% 4.07/3.67 ( ![X4:$i,X6:$i]:
% 4.07/3.67 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 4.07/3.67 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(setoftrueEq, axiom, setoftrueEq =
% 4.07/3.67 (![A:$i]: ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( $true ) ) ) = ( A ) ))).
% 4.07/3.67 thf('76', plain,
% 4.07/3.67 (( setoftrueEq ) =
% 4.07/3.67 ( ![X4:$i]: ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( $true ) ) ) = ( X4 ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(setadjoinOr, axiom, setadjoinOr =
% 4.07/3.67 (![Xx:$i,A:$i,Xy:$i]:
% 4.07/3.67 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 4.07/3.67 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 4.07/3.67 thf('77', plain,
% 4.07/3.67 (( setadjoinOr ) =
% 4.07/3.67 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.67 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 4.07/3.67 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(setadjoinE, axiom, setadjoinE =
% 4.07/3.67 (![Xx:$i,A:$i,Xy:$i]:
% 4.07/3.67 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 4.07/3.67 ( ![Xphi:$o]:
% 4.07/3.67 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 4.07/3.67 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 4.07/3.67 thf('78', plain,
% 4.07/3.67 (( setadjoinE ) =
% 4.07/3.67 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.67 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 4.07/3.67 ( ![X10:$o]:
% 4.07/3.67 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 4.07/3.67 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(setadjoinIR, axiom, setadjoinIR =
% 4.07/3.67 (![Xx:$i,A:$i,Xy:$i]:
% 4.07/3.67 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 4.07/3.67 thf('79', plain,
% 4.07/3.67 (( setadjoinIR ) =
% 4.07/3.67 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.67 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 4.07/3.67 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 4.07/3.67 thf('80', plain,
% 4.07/3.67 (( emptyinunitempty ) =
% 4.07/3.67 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 4.07/3.67 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 4.07/3.67 thf('81', plain,
% 4.07/3.67 (( emptyinunitempty ) =
% 4.07/3.67 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(setadjoinIL, axiom, setadjoinIL =
% 4.07/3.67 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 4.07/3.67 thf('82', plain,
% 4.07/3.67 (( setadjoinIL ) =
% 4.07/3.67 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(nonemptyI1, axiom, nonemptyI1 =
% 4.07/3.67 (![A:$i]: ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) => ( nonempty @ A ) ))).
% 4.07/3.67 thf('83', plain,
% 4.07/3.67 (( nonemptyI1 ) =
% 4.07/3.67 ( ![X4:$i]: ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) => ( nonempty @ X4 ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(nonemptyI, axiom, nonemptyI =
% 4.07/3.67 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 4.07/3.67 ( ( in @ Xx @ A ) =>
% 4.07/3.67 ( ( Xphi @ Xx ) =>
% 4.07/3.67 ( nonempty @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 4.07/3.67 thf('84', plain,
% 4.07/3.67 (( nonemptyI ) =
% 4.07/3.67 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 4.07/3.67 ( ( in @ X8 @ X4 ) =>
% 4.07/3.67 ( ( X6 @ X8 ) =>
% 4.07/3.67 ( nonempty @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(nonemptyE1, axiom, nonemptyE1 =
% 4.07/3.67 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 4.07/3.67 thf('85', plain,
% 4.07/3.67 (( nonemptyE1 ) =
% 4.07/3.67 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(nonempty, axiom,(( nonempty ) = (^[Xx:$i]: ( ( Xx ) != ( emptyset ) )))).
% 4.07/3.67 thf('86', plain, (( nonempty ) = ( ^[Xx:$i]: ( ( Xx ) != ( emptyset ) ) )),
% 4.07/3.67 inference('simplify_rw_rule', [status(thm)], [nonempty])).
% 4.07/3.67 thf('87', plain, (( nonempty ) = ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(setbeta, axiom, setbeta =
% 4.07/3.67 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 4.07/3.67 ( ( in @ Xx @ A ) =>
% 4.07/3.67 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) <=>
% 4.07/3.67 ( Xphi @ Xx ) ) ))).
% 4.07/3.67 thf('88', plain,
% 4.07/3.67 (( setbeta ) =
% 4.07/3.67 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 4.07/3.67 ( ( in @ X8 @ X4 ) =>
% 4.07/3.67 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=>
% 4.07/3.67 ( X6 @ X8 ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(noeltsimpempty, axiom, noeltsimpempty =
% 4.07/3.67 (![A:$i]:
% 4.07/3.67 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 4.07/3.67 thf('89', plain,
% 4.07/3.67 (( noeltsimpempty ) =
% 4.07/3.67 ( ![X4:$i]:
% 4.07/3.67 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(emptyI, axiom, emptyI =
% 4.07/3.67 (![A:$i]:
% 4.07/3.67 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 4.07/3.67 thf('90', plain,
% 4.07/3.67 (( emptyI ) =
% 4.07/3.67 ( ![X4:$i]:
% 4.07/3.67 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(setext, axiom, setext =
% 4.07/3.67 (![A:$i,B:$i]:
% 4.07/3.67 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 4.07/3.67 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 4.07/3.67 ( ( A ) = ( B ) ) ) ))).
% 4.07/3.67 thf('91', plain,
% 4.07/3.67 (( setext ) =
% 4.07/3.67 ( ![X4:$i,X6:$i]:
% 4.07/3.67 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 4.07/3.67 ( ( ![X10:$i]: ( ( in @ X10 @ X6 ) => ( in @ X10 @ X4 ) ) ) =>
% 4.07/3.67 ( ( X4 ) = ( X6 ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(exuE3e, axiom, exuE3e =
% 4.07/3.67 (![Xphi:( $i > $o )]:
% 4.07/3.67 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) => ( ?[Xx:$i]: ( Xphi @ Xx ) ) ))).
% 4.07/3.67 thf('92', plain,
% 4.07/3.67 (( exuE3e ) =
% 4.07/3.67 ( ![X4:( $i > $o )]:
% 4.07/3.67 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) => ( ?[X6:$i]: ( X4 @ X6 ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(notinemptyset, axiom, notinemptyset =
% 4.07/3.67 (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 4.07/3.67 thf('93', plain,
% 4.07/3.67 (( notinemptyset ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(emptysetimpfalse, axiom, emptysetimpfalse =
% 4.07/3.67 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( $false ) ))).
% 4.07/3.67 thf('94', plain,
% 4.07/3.67 (( emptysetimpfalse ) =
% 4.07/3.67 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( $false ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(emptysetE, axiom, emptysetE =
% 4.07/3.67 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( ![Xphi:$o]: ( Xphi ) ) ))).
% 4.07/3.67 thf('95', plain,
% 4.07/3.67 (( emptysetE ) =
% 4.07/3.67 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( ![X6:$o]: ( X6 ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(prop2setE, axiom, prop2setE =
% 4.07/3.67 (![Xphi:$o,Xx:$i]: ( ( in @ Xx @ ( prop2set @ Xphi ) ) => ( Xphi ) ))).
% 4.07/3.67 thf('96', plain,
% 4.07/3.67 (( prop2setE ) =
% 4.07/3.67 ( ![X4:$o,X6:$i]: ( ( in @ X6 @ ( prop2set @ X4 ) ) => ( X4 ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(exuE1, axiom, exuE1 =
% 4.07/3.67 (![Xphi:( $i > $o )]:
% 4.07/3.67 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 4.07/3.67 ( ?[Xx:$i]:
% 4.07/3.67 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 4.07/3.67 ( Xphi @ Xx ) ) ) ))).
% 4.07/3.67 thf('97', plain,
% 4.07/3.67 (( exuE1 ) =
% 4.07/3.67 ( ![X4:( $i > $o )]:
% 4.07/3.67 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 4.07/3.67 ( ?[X6:$i]:
% 4.07/3.67 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 4.07/3.67 ( X4 @ X6 ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(dsetconstrER, axiom, dsetconstrER =
% 4.07/3.67 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 4.07/3.67 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 4.07/3.67 ( Xphi @ Xx ) ))).
% 4.07/3.67 thf('98', plain,
% 4.07/3.67 (( dsetconstrER ) =
% 4.07/3.67 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 4.07/3.67 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 4.07/3.67 ( X6 @ X8 ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(dsetconstrEL, axiom, dsetconstrEL =
% 4.07/3.67 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 4.07/3.67 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 4.07/3.67 ( in @ Xx @ A ) ))).
% 4.07/3.67 thf('99', plain,
% 4.07/3.67 (( dsetconstrEL ) =
% 4.07/3.67 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 4.07/3.67 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 4.07/3.67 ( in @ X8 @ X4 ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(dsetconstrI, axiom, dsetconstrI =
% 4.07/3.67 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 4.07/3.67 ( ( in @ Xx @ A ) =>
% 4.07/3.67 ( ( Xphi @ Xx ) =>
% 4.07/3.67 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 4.07/3.67 thf('100', plain,
% 4.07/3.67 (( dsetconstrI ) =
% 4.07/3.67 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 4.07/3.67 ( ( in @ X8 @ X4 ) =>
% 4.07/3.67 ( ( X6 @ X8 ) =>
% 4.07/3.67 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(descrp, axiom, descrp =
% 4.07/3.67 (![Xphi:( $i > $o )]:
% 4.07/3.67 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 4.07/3.67 ( Xphi @ ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 4.07/3.67 thf('101', plain,
% 4.07/3.67 (( descrp ) =
% 4.07/3.67 ( ![X4:( $i > $o )]:
% 4.07/3.67 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 4.07/3.67 ( X4 @ ( descr @ ( ^[V_2:$i]: ( X4 @ V_2 ) ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(wellorderingAx, axiom, wellorderingAx =
% 4.07/3.67 (![A:$i]:
% 4.07/3.67 ( ?[B:$i]:
% 4.07/3.67 ( ( ![C:$i]:
% 4.07/3.67 ( ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) &
% 4.07/3.67 ( ?[Xx:$i]: ( in @ Xx @ C ) ) ) =>
% 4.07/3.67 ( ?[D:$i,Xx:$i]:
% 4.07/3.67 ( ( ![E:$i]:
% 4.07/3.67 ( ( in @ E @ B ) =>
% 4.07/3.67 ( ( ![Xy:$i]: ( ( in @ Xy @ E ) => ( in @ Xy @ D ) ) ) |
% 4.07/3.67 ( in @ Xx @ E ) ) ) ) &
% 4.07/3.67 ( ~( ?[Xy:$i]: ( ( in @ Xy @ C ) & ( in @ Xy @ D ) ) ) ) &
% 4.07/3.67 ( in @ Xx @ C ) & ( in @ D @ B ) ) ) ) ) &
% 4.07/3.67 ( ![C:$i,D:$i]:
% 4.07/3.67 ( ( ( in @ C @ B ) & ( in @ D @ B ) ) =>
% 4.07/3.67 ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ D ) ) ) |
% 4.07/3.67 ( ![Xx:$i]: ( ( in @ Xx @ D ) => ( in @ Xx @ C ) ) ) ) ) ) &
% 4.07/3.67 ( ![Xx:$i,Xy:$i]:
% 4.07/3.67 ( ( ( in @ Xx @ A ) & ( in @ Xy @ A ) ) =>
% 4.07/3.67 ( ( ![C:$i]:
% 4.07/3.67 ( ( in @ C @ B ) => ( ( in @ Xx @ C ) <=> ( in @ Xy @ C ) ) ) ) =>
% 4.07/3.67 ( ( Xx ) = ( Xy ) ) ) ) ) &
% 4.07/3.67 ( ![C:$i]:
% 4.07/3.67 ( ( in @ C @ B ) =>
% 4.07/3.67 ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) ) ) ) ))).
% 4.07/3.67 thf('102', plain,
% 4.07/3.67 (( wellorderingAx ) =
% 4.07/3.67 ( ![X4:$i]:
% 4.07/3.67 ( ?[X6:$i]:
% 4.07/3.67 ( ( ![X8:$i]:
% 4.07/3.67 ( ( ( ![X10:$i]: ( ( in @ X10 @ X8 ) => ( in @ X10 @ X4 ) ) ) &
% 4.07/3.67 ( ?[X12:$i]: ( in @ X12 @ X8 ) ) ) =>
% 4.07/3.67 ( ?[X14:$i,X16:$i]:
% 4.07/3.67 ( ( ![X18:$i]:
% 4.07/3.67 ( ( in @ X18 @ X6 ) =>
% 4.07/3.67 ( ( ![X20:$i]:
% 4.07/3.67 ( ( in @ X20 @ X18 ) => ( in @ X20 @ X14 ) ) ) |
% 4.07/3.67 ( in @ X16 @ X18 ) ) ) ) &
% 4.07/3.67 ( ~( ?[X22:$i]: ( ( in @ X22 @ X8 ) & ( in @ X22 @ X14 ) ) ) ) &
% 4.07/3.67 ( in @ X16 @ X8 ) & ( in @ X14 @ X6 ) ) ) ) ) &
% 4.07/3.67 ( ![X24:$i,X26:$i]:
% 4.07/3.67 ( ( ( in @ X24 @ X6 ) & ( in @ X26 @ X6 ) ) =>
% 4.07/3.67 ( ( ![X28:$i]: ( ( in @ X28 @ X24 ) => ( in @ X28 @ X26 ) ) ) |
% 4.07/3.67 ( ![X30:$i]: ( ( in @ X30 @ X26 ) => ( in @ X30 @ X24 ) ) ) ) ) ) &
% 4.07/3.67 ( ![X32:$i,X34:$i]:
% 4.07/3.67 ( ( ( in @ X32 @ X4 ) & ( in @ X34 @ X4 ) ) =>
% 4.07/3.67 ( ( ![X36:$i]:
% 4.07/3.67 ( ( in @ X36 @ X6 ) =>
% 4.07/3.67 ( ( in @ X32 @ X36 ) <=> ( in @ X34 @ X36 ) ) ) ) =>
% 4.07/3.67 ( ( X32 ) = ( X34 ) ) ) ) ) &
% 4.07/3.67 ( ![X38:$i]:
% 4.07/3.67 ( ( in @ X38 @ X6 ) =>
% 4.07/3.67 ( ![X40:$i]: ( ( in @ X40 @ X38 ) => ( in @ X40 @ X4 ) ) ) ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(foundationAx, axiom, foundationAx =
% 4.07/3.67 (![A:$i]:
% 4.07/3.67 ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) =>
% 4.07/3.67 ( ?[B:$i]:
% 4.07/3.67 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ A ) & ( in @ Xx @ B ) ) ) ) &
% 4.07/3.67 ( in @ B @ A ) ) ) ))).
% 4.07/3.67 thf('103', plain,
% 4.07/3.67 (( foundationAx ) =
% 4.07/3.67 ( ![X4:$i]:
% 4.07/3.67 ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) =>
% 4.07/3.67 ( ?[X8:$i]:
% 4.07/3.67 ( ( ~( ?[X10:$i]: ( ( in @ X10 @ X4 ) & ( in @ X10 @ X8 ) ) ) ) &
% 4.07/3.67 ( in @ X8 @ X4 ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(replAx, axiom, replAx =
% 4.07/3.67 (![Xphi:( $i > $i > $o ),A:$i]:
% 4.07/3.67 ( ( ![Xx:$i]:
% 4.07/3.67 ( ( in @ Xx @ A ) => ( exu @ ( ^[Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ) ) =>
% 4.07/3.67 ( ?[B:$i]:
% 4.07/3.67 ( ![Xx:$i]:
% 4.07/3.67 ( ( in @ Xx @ B ) <=>
% 4.07/3.67 ( ?[Xy:$i]: ( ( Xphi @ Xy @ Xx ) & ( in @ Xy @ A ) ) ) ) ) ) ))).
% 4.07/3.67 thf('104', plain,
% 4.07/3.67 (( replAx ) =
% 4.07/3.67 ( ![X4:( $i > $i > $o ),X6:$i]:
% 4.07/3.67 ( ( ![X8:$i]:
% 4.07/3.67 ( ( in @ X8 @ X6 ) => ( exu @ ( ^[V_1:$i]: ( X4 @ X8 @ V_1 ) ) ) ) ) =>
% 4.07/3.67 ( ?[X10:$i]:
% 4.07/3.67 ( ![X12:$i]:
% 4.07/3.67 ( ( in @ X12 @ X10 ) <=>
% 4.07/3.67 ( ?[X14:$i]: ( ( X4 @ X14 @ X12 ) & ( in @ X14 @ X6 ) ) ) ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(omegaIndAx, axiom, omegaIndAx =
% 4.07/3.67 (![A:$i]:
% 4.07/3.67 ( ( ( in @ emptyset @ A ) &
% 4.07/3.67 ( ![Xx:$i]:
% 4.07/3.67 ( ( ( in @ Xx @ omega ) & ( in @ Xx @ A ) ) =>
% 4.07/3.67 ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) ) =>
% 4.07/3.67 ( ![Xx:$i]: ( ( in @ Xx @ omega ) => ( in @ Xx @ A ) ) ) ))).
% 4.07/3.67 thf('105', plain,
% 4.07/3.67 (( omegaIndAx ) =
% 4.07/3.67 ( ![X4:$i]:
% 4.07/3.67 ( ( ( in @ emptyset @ X4 ) &
% 4.07/3.67 ( ![X6:$i]:
% 4.07/3.67 ( ( ( in @ X6 @ omega ) & ( in @ X6 @ X4 ) ) =>
% 4.07/3.67 ( in @ ( setadjoin @ X6 @ X6 ) @ X4 ) ) ) ) =>
% 4.07/3.67 ( ![X8:$i]: ( ( in @ X8 @ omega ) => ( in @ X8 @ X4 ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(omegaSAx, axiom, omegaSAx =
% 4.07/3.67 (![Xx:$i]:
% 4.07/3.67 ( ( in @ Xx @ omega ) => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ))).
% 4.07/3.67 thf('106', plain,
% 4.07/3.67 (( omegaSAx ) =
% 4.07/3.67 ( ![X4:$i]:
% 4.07/3.67 ( ( in @ X4 @ omega ) => ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(omega0Ax, axiom,(( omega0Ax ) = (in @ emptyset @ omega))).
% 4.07/3.67 thf('107', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 4.07/3.67 inference('simplify_rw_rule', [status(thm)], [omega0Ax])).
% 4.07/3.67 thf('108', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(setunionAx, axiom, setunionAx =
% 4.07/3.67 (![A:$i,Xx:$i]:
% 4.07/3.67 ( ( in @ Xx @ ( setunion @ A ) ) <=>
% 4.07/3.67 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))).
% 4.07/3.67 thf('109', plain,
% 4.07/3.67 (( setunionAx ) =
% 4.07/3.67 ( ![X4:$i,X6:$i]:
% 4.07/3.67 ( ( in @ X6 @ ( setunion @ X4 ) ) <=>
% 4.07/3.67 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(powersetAx, axiom, powersetAx =
% 4.07/3.67 (![A:$i,B:$i]:
% 4.07/3.67 ( ( in @ B @ ( powerset @ A ) ) <=>
% 4.07/3.67 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 4.07/3.67 thf('110', plain,
% 4.07/3.67 (( powersetAx ) =
% 4.07/3.67 ( ![X4:$i,X6:$i]:
% 4.07/3.67 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 4.07/3.67 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(setadjoinAx, axiom, setadjoinAx =
% 4.07/3.67 (![Xx:$i,A:$i,Xy:$i]:
% 4.07/3.67 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 4.07/3.67 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 4.07/3.67 thf('111', plain,
% 4.07/3.67 (( setadjoinAx ) =
% 4.07/3.67 ( ![X4:$i,X6:$i,X8:$i]:
% 4.07/3.67 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 4.07/3.67 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 4.07/3.67 thf('112', plain,
% 4.07/3.67 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(setextAx, axiom, setextAx =
% 4.07/3.67 (![A:$i,B:$i]:
% 4.07/3.67 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) <=> ( in @ Xx @ B ) ) ) =>
% 4.07/3.67 ( ( A ) = ( B ) ) ))).
% 4.07/3.67 thf('113', plain,
% 4.07/3.67 (( setextAx ) =
% 4.07/3.67 ( ![X4:$i,X6:$i]:
% 4.07/3.67 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 4.07/3.67 ( ( X4 ) = ( X6 ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(exu, axiom,(( exu ) =
% 4.07/3.67 (^[Xphi:( $i > $o )]:
% 4.07/3.67 ( ?[Xx:$i]:
% 4.07/3.67 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & ( Xphi @ Xx ) ) )))).
% 4.07/3.67 thf('114', plain,
% 4.07/3.67 (( exu ) =
% 4.07/3.67 ( ^[Xphi:( $i > $o )]:
% 4.07/3.67 ( ?[Xx:$i]:
% 4.07/3.67 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 4.07/3.67 ( Xphi @ Xx ) ) ) )),
% 4.07/3.67 inference('simplify_rw_rule', [status(thm)], [exu])).
% 4.07/3.67 thf('115', plain,
% 4.07/3.67 (( exu ) =
% 4.07/3.67 ( ^[V_1:( $i > $o )]:
% 4.07/3.67 ( ?[X4:$i]:
% 4.07/3.67 ( ( ![X6:$i]: ( ( V_1 @ X6 ) => ( ( X4 ) = ( X6 ) ) ) ) &
% 4.07/3.67 ( V_1 @ X4 ) ) ) )),
% 4.07/3.67 define([status(thm)])).
% 4.07/3.67 thf(binintersectLsub, conjecture,
% 4.07/3.67 (( setextAx ) =>
% 4.07/3.67 ( ( emptysetAx ) =>
% 4.07/3.67 ( ( setadjoinAx ) =>
% 4.07/3.67 ( ( powersetAx ) =>
% 4.07/3.67 ( ( setunionAx ) =>
% 4.07/3.67 ( ( omega0Ax ) =>
% 4.07/3.67 ( ( omegaSAx ) =>
% 4.07/3.67 ( ( omegaIndAx ) =>
% 4.07/3.67 ( ( replAx ) =>
% 4.07/3.67 ( ( foundationAx ) =>
% 4.07/3.67 ( ( wellorderingAx ) =>
% 4.07/3.67 ( ( descrp ) =>
% 4.07/3.67 ( ( dsetconstrI ) =>
% 4.07/3.67 ( ( dsetconstrEL ) =>
% 4.07/3.67 ( ( dsetconstrER ) =>
% 4.07/3.67 ( ( exuE1 ) =>
% 4.07/3.67 ( ( prop2setE ) =>
% 4.07/3.67 ( ( emptysetE ) =>
% 4.07/3.67 ( ( emptysetimpfalse ) =>
% 4.07/3.67 ( ( notinemptyset ) =>
% 4.07/3.67 ( ( exuE3e ) =>
% 4.07/3.67 ( ( setext ) =>
% 4.07/3.67 ( ( emptyI ) =>
% 4.07/3.67 ( ( noeltsimpempty ) =>
% 4.07/3.67 ( ( setbeta ) =>
% 4.07/3.67 ( ( nonemptyE1 ) =>
% 4.07/3.67 ( ( nonemptyI ) =>
% 4.07/3.67 ( ( nonemptyI1 ) =>
% 4.07/3.67 ( ( setadjoinIL ) =>
% 4.07/3.67 ( ( emptyinunitempty ) =>
% 4.07/3.67 ( ( setadjoinIR ) =>
% 4.07/3.67 ( ( setadjoinE ) =>
% 4.07/3.67 ( (
% 4.07/3.67 setadjoinOr ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 setoftrueEq ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 powersetI ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 emptyinPowerset ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 emptyInPowerset ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 powersetE ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 setunionI ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 setunionE ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 subPowSU ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 exuE2 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 nonemptyImpWitness ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 uniqinunit ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 notinsingleton ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 eqinunit ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 singletonsswitch ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 upairsetE ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 upairsetIL ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 upairsetIR ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 emptyE1 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 vacuousDall ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 quantDeMorgan1 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 quantDeMorgan2 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 quantDeMorgan3 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 quantDeMorgan4 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 prop2setI ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 prop2set2propI ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 notdexE ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 notdallE ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 exuI1 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 exuI3 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 exuI2 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 inCongP ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in__Cong ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 exuE3u ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 exu__Cong ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 emptyset__Cong ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 setadjoin__Cong ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 powerset__Cong ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 setunion__Cong ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 omega__Cong ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 exuEu ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 descr__Cong ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 dsetconstr__Cong ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 subsetI1 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 eqimpsubset2 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 eqimpsubset1 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 subsetI2 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 emptysetsubset ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 subsetE ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 subsetE2 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 notsubsetI ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 notequalI1 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 notequalI2 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 subsetRefl ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 subsetTrans ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 setadjoinSub ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 setadjoinSub2 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 subset2powerset ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 setextsub ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 subsetemptysetimpeq ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 powersetI1 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 powersetE1 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 inPowerset ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 powersetsubset ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 sepInPowerset ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 sepSubset ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 binunionIL ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 upairset2IR ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 binunionIR ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 binunionEcases ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 binunionE ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 binunionLsub ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 binunionRsub ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 binintersectI ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 binintersectSubset5 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 binintersectEL ) =>
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 A:$i,B:$i]:
% 4.07/3.67 (
% 4.07/3.67 subset @
% 4.07/3.67 (
% 4.07/3.67 binintersect
% 4.07/3.67 @
% 4.07/3.67 A @ B ) @
% 4.07/3.67 A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 4.07/3.67 thf(zf_stmt_0, conjecture,
% 4.07/3.67 (( ![X4:$i,X6:$i]:
% 4.07/3.67 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 4.07/3.67 ( ( X4 ) = ( X6 ) ) ) ) =>
% 4.07/3.67 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 4.07/3.67 ( ( ![X12:$i,X14:$i,X16:$i]:
% 4.07/3.67 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 4.07/3.67 ( ( in @ X16 @ X14 ) | ( ( X16 ) = ( X12 ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X18:$i,X20:$i]:
% 4.07/3.67 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 4.07/3.67 ( ![X22:$i]: ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X24:$i,X26:$i]:
% 4.07/3.67 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 4.07/3.67 ( ?[X28:$i]: ( ( in @ X26 @ X28 ) & ( in @ X28 @ X24 ) ) ) ) ) =>
% 4.07/3.67 ( ( in @ emptyset @ omega ) =>
% 4.07/3.67 ( ( ![X30:$i]:
% 4.07/3.67 ( ( in @ X30 @ omega ) =>
% 4.07/3.67 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 4.07/3.67 ( ( ![X32:$i]:
% 4.07/3.67 ( ( ( ![X34:$i]:
% 4.07/3.67 ( ( ( in @ X34 @ X32 ) & ( in @ X34 @ omega ) ) =>
% 4.07/3.67 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) &
% 4.07/3.67 ( in @ emptyset @ X32 ) ) =>
% 4.07/3.67 ( ![X36:$i]:
% 4.07/3.67 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 4.07/3.67 ( ( ![X42:$i]:
% 4.07/3.67 ( ( in @ X42 @ X40 ) =>
% 4.07/3.67 ( ?[X44:$i]:
% 4.07/3.67 ( ( X38 @ X42 @ X44 ) &
% 4.07/3.67 ( ![X46:$i]:
% 4.07/3.67 ( ( X38 @ X42 @ X46 ) =>
% 4.07/3.67 ( ( X44 ) = ( X46 ) ) ) ) ) ) ) ) =>
% 4.07/3.67 ( ?[X48:$i]:
% 4.07/3.67 ( ![X50:$i]:
% 4.07/3.67 ( ( in @ X50 @ X48 ) <=>
% 4.07/3.67 ( ?[X52:$i]:
% 4.07/3.67 ( ( in @ X52 @ X40 ) & ( X38 @ X52 @ X50 ) ) ) ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X54:$i]:
% 4.07/3.67 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 4.07/3.67 ( ?[X58:$i]:
% 4.07/3.67 ( ( in @ X58 @ X54 ) &
% 4.07/3.67 ( ~( ?[X60:$i]:
% 4.07/3.67 ( ( in @ X60 @ X58 ) & ( in @ X60 @ X54 ) ) ) ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X62:$i]:
% 4.07/3.67 ( ?[X64:$i]:
% 4.07/3.67 ( ( ![X96:$i]:
% 4.07/3.67 ( ( in @ X96 @ X64 ) =>
% 4.07/3.67 ( ![X98:$i]:
% 4.07/3.67 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) &
% 4.07/3.67 ( ![X90:$i,X92:$i]:
% 4.07/3.67 ( ( ( in @ X92 @ X62 ) & ( in @ X90 @ X62 ) ) =>
% 4.07/3.67 ( ( ![X94:$i]:
% 4.07/3.67 ( ( in @ X94 @ X64 ) =>
% 4.07/3.67 ( ( in @ X90 @ X94 ) <=>
% 4.07/3.67 ( in @ X92 @ X94 ) ) ) ) =>
% 4.07/3.67 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 4.07/3.67 ( ![X82:$i,X84:$i]:
% 4.07/3.67 ( ( ( in @ X84 @ X64 ) & ( in @ X82 @ X64 ) ) =>
% 4.07/3.67 ( ( ![X88:$i]:
% 4.07/3.67 ( ( in @ X88 @ X84 ) =>
% 4.07/3.67 ( in @ X88 @ X82 ) ) ) |
% 4.07/3.67 ( ![X86:$i]:
% 4.07/3.67 ( ( in @ X86 @ X82 ) =>
% 4.07/3.67 ( in @ X86 @ X84 ) ) ) ) ) ) &
% 4.07/3.67 ( ![X66:$i]:
% 4.07/3.67 ( ( ( ?[X70:$i]: ( in @ X70 @ X66 ) ) &
% 4.07/3.67 ( ![X68:$i]:
% 4.07/3.67 ( ( in @ X68 @ X66 ) =>
% 4.07/3.67 ( in @ X68 @ X62 ) ) ) ) =>
% 4.07/3.67 ( ?[X72:$i,X74:$i]:
% 4.07/3.67 ( ( in @ X72 @ X64 ) &
% 4.07/3.67 ( in @ X74 @ X66 ) &
% 4.07/3.67 ( ~( ?[X80:$i]:
% 4.07/3.67 ( ( in @ X80 @ X72 ) &
% 4.07/3.67 ( in @ X80 @ X66 ) ) ) ) &
% 4.07/3.67 ( ![X76:$i]:
% 4.07/3.67 ( ( in @ X76 @ X64 ) =>
% 4.07/3.67 ( ( in @ X74 @ X76 ) |
% 4.07/3.67 ( ![X78:$i]:
% 4.07/3.67 ( ( in @ X78 @ X76 ) =>
% 4.07/3.67 ( in @ X78 @ X72 ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X100:( $i > $o )]:
% 4.07/3.67 ( ( ?[X102:$i]:
% 4.07/3.67 ( ( X100 @ X102 ) &
% 4.07/3.67 ( ![X104:$i]:
% 4.07/3.67 ( ( X100 @ X104 ) =>
% 4.07/3.67 ( ( X102 ) = ( X104 ) ) ) ) ) ) =>
% 4.07/3.67 ( X100 @
% 4.07/3.67 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 4.07/3.67 ( ( in @ X110 @ X106 ) =>
% 4.07/3.67 ( ( X108 @ X110 ) =>
% 4.07/3.67 ( in @
% 4.07/3.67 X110 @
% 4.07/3.67 ( dsetconstr @
% 4.07/3.67 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 4.07/3.67 ( ( in @
% 4.07/3.67 X116 @
% 4.07/3.67 ( dsetconstr @
% 4.07/3.67 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 4.07/3.67 ( in @ X116 @ X112 ) ) ) =>
% 4.07/3.67 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 4.07/3.67 ( ( in @
% 4.07/3.67 X122 @
% 4.07/3.67 ( dsetconstr @
% 4.07/3.67 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 4.07/3.67 ( X120 @ X122 ) ) ) =>
% 4.07/3.67 ( ( ![X124:( $i > $o )]:
% 4.07/3.67 ( ( ?[X126:$i]:
% 4.07/3.67 ( ( X124 @ X126 ) &
% 4.07/3.67 ( ![X128:$i]:
% 4.07/3.67 ( ( X124 @ X128 ) =>
% 4.07/3.67 ( ( X126 ) = ( X128 ) ) ) ) ) ) =>
% 4.07/3.67 ( ?[X130:$i]:
% 4.07/3.67 ( ( X124 @ X130 ) &
% 4.07/3.67 ( ![X132:$i]:
% 4.07/3.67 ( ( X124 @ X132 ) =>
% 4.07/3.67 ( ( X130 ) = ( X132 ) ) ) ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X134:$o,X136:$i]:
% 4.07/3.67 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 4.07/3.67 ( X134 ) ) ) =>
% 4.07/3.67 ( ( ![X138:$i]:
% 4.07/3.67 ( ( in @ X138 @ emptyset ) =>
% 4.07/3.67 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 4.07/3.67 ( ( ![X142:$i]:
% 4.07/3.67 ( ( in @ X142 @ emptyset ) =>
% 4.07/3.67 ( $false ) ) ) =>
% 4.07/3.67 ( ( ![X144:$i]:
% 4.07/3.67 ( ~( in @ X144 @ emptyset ) ) ) =>
% 4.07/3.67 ( ( ![X146:( $i > $o )]:
% 4.07/3.67 ( ( ?[X148:$i]:
% 4.07/3.67 ( ( X146 @ X148 ) &
% 4.07/3.67 ( ![X150:$i]:
% 4.07/3.67 ( ( X146 @ X150 ) =>
% 4.07/3.67 ( ( X148 ) = ( X150 ) ) ) ) ) ) =>
% 4.07/3.67 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 4.07/3.67 ( ( ![X154:$i,X156:$i]:
% 4.07/3.67 ( ( ![X158:$i]:
% 4.07/3.67 ( ( in @ X158 @ X154 ) =>
% 4.07/3.67 ( in @ X158 @ X156 ) ) ) =>
% 4.07/3.67 ( ( ![X160:$i]:
% 4.07/3.67 ( ( in @ X160 @ X156 ) =>
% 4.07/3.67 ( in @ X160 @ X154 ) ) ) =>
% 4.07/3.67 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X162:$i]:
% 4.07/3.67 ( ( ![X164:$i]:
% 4.07/3.67 ( ~( in @ X164 @ X162 ) ) ) =>
% 4.07/3.67 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 4.07/3.67 ( ( ![X166:$i]:
% 4.07/3.67 ( ( ![X168:$i]:
% 4.07/3.67 ( ~( in @ X168 @ X166 ) ) ) =>
% 4.07/3.67 ( ( X166 ) =
% 4.07/3.67 ( emptyset ) ) ) ) =>
% 4.07/3.67 ( ( ![X170:$i,
% 4.07/3.67 X172:( $i > $o ),
% 4.07/3.67 X174:$i]:
% 4.07/3.67 ( ( in @ X174 @ X170 ) =>
% 4.07/3.67 ( ( in @
% 4.07/3.67 X174 @
% 4.07/3.67 ( dsetconstr @
% 4.07/3.67 X170 @
% 4.07/3.67 ( ^[V_5:$i]:
% 4.07/3.67 ( X172 @ V_5 ) ) ) ) <=>
% 4.07/3.67 ( X172 @ X174 ) ) ) ) =>
% 4.07/3.67 ( ( ![X176:$i]:
% 4.07/3.67 ( ( ( X176 ) !=
% 4.07/3.67 ( emptyset ) ) =>
% 4.07/3.67 ( ?[X178:$i]:
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% 4.07/3.67 X340:$i,
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% 4.07/3.67 X400:$i,
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% 4.07/3.67 X408 ) =>
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% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X410:$i,
% 4.07/3.67 X412:$i]:
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% 4.07/3.67 (
% 4.07/3.67 X404 @
% 4.07/3.67 X410 ) =>
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% 4.07/3.67 (
% 4.07/3.67 X404 @
% 4.07/3.67 X412 ) =>
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% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X414:(
% 4.07/3.67 $i > $o ),
% 4.07/3.67 X416:(
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% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X418:$i,
% 4.07/3.67 X420:$i]:
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% 4.07/3.67 (
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% 4.07/3.67 ?[
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% 4.07/3.67 ![
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% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 (
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% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
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% 4.07/3.67 X432:$i]:
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% 4.07/3.67 (
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% 4.07/3.67 (
% 4.07/3.67 X432 ) ) =>
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X434:$i,
% 4.07/3.67 X436:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 X434 ) =
% 4.07/3.67 (
% 4.07/3.67 X436 ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 setadjoin
% 4.07/3.67 @
% 4.07/3.67 X430 @
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% 4.07/3.67 (
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% 4.07/3.67 X440:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 X438 ) =
% 4.07/3.67 (
% 4.07/3.67 X440 ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 powerset @
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% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X442:$i,
% 4.07/3.67 X444:$i]:
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% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 X442 ) =
% 4.07/3.67 (
% 4.07/3.67 X444 ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 setunion @
% 4.07/3.67 X442 ) =
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% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 omega ) =
% 4.07/3.67 (
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% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X446:(
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% 4.07/3.67 (
% 4.07/3.67 (
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% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X452:$i,
% 4.07/3.67 X454:$i]:
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% 4.07/3.67 X446 @
% 4.07/3.67 X452 ) =>
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% 4.07/3.67 (
% 4.07/3.67 X446 @
% 4.07/3.67 X454 ) =>
% 4.07/3.67 (
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% 4.07/3.67 (
% 4.07/3.67 ![
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% 4.07/3.67 X458:(
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% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X460:$i,
% 4.07/3.67 X462:$i]:
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% 4.07/3.67 (
% 4.07/3.67 X462 ) ) =>
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% 4.07/3.67 ?[
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% 4.07/3.67 (
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% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ?[
% 4.07/3.67 X468:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
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% 4.07/3.67 X470 ) =>
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% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 descr @
% 4.07/3.67 (
% 4.07/3.67 ^[
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% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X472:$i,
% 4.07/3.67 X474:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 (
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% 4.07/3.67 (
% 4.07/3.67 X474 ) ) =>
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X476:(
% 4.07/3.67 $i > $o ),
% 4.07/3.67 X478:(
% 4.07/3.67 $i > $o )]:
% 4.07/3.67 (
% 4.07/3.67 (
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% 4.07/3.67 in @
% 4.07/3.67 X480 @
% 4.07/3.67 X472 ) =>
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% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X482 @
% 4.07/3.67 X474 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 (
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% 4.07/3.67 dsetconstr
% 4.07/3.67 @
% 4.07/3.67 X472 @
% 4.07/3.67 (
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% 4.07/3.67 X642 ) ) ) @
% 4.07/3.67 X640 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 4.07/3.67 thf(zf_stmt_1, type, zip_tseitin_5 : $i > ( $i > $o ) > $o).
% 4.07/3.67 thf(zf_stmt_2, axiom,
% 4.07/3.67 (![X422:$i,X414:( $i > $o )]:
% 4.07/3.67 ( ( zip_tseitin_5 @ X422 @ X414 ) <=>
% 4.07/3.67 ( ( ![X424:$i]: ( zip_tseitin_4 @ X424 @ X422 @ X414 ) ) &
% 4.07/3.67 ( X414 @ X422 ) ) ))).
% 4.07/3.67 thf(zf_stmt_3, type, zip_tseitin_4 : $i > $i > ( $i > $o ) > $o).
% 4.07/3.67 thf(zf_stmt_4, axiom,
% 4.07/3.67 (![X424:$i,X422:$i,X414:( $i > $o )]:
% 4.07/3.67 ( ( zip_tseitin_4 @ X424 @ X422 @ X414 ) <=>
% 4.07/3.67 ( ( X414 @ X424 ) => ( ( X422 ) = ( X424 ) ) ) ))).
% 4.07/3.67 thf(zf_stmt_5, type, zip_tseitin_3 : $i > $i > $i > ( $i > $i > $o ) > $o).
% 4.07/3.67 thf(zf_stmt_6, axiom,
% 4.07/3.67 (![X52:$i,X50:$i,X40:$i,X38:( $i > $i > $o )]:
% 4.07/3.67 ( ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) <=>
% 4.07/3.67 ( ( X38 @ X52 @ X50 ) & ( in @ X52 @ X40 ) ) ))).
% 4.07/3.67 thf(zf_stmt_7, type, zip_tseitin_2 : $i > $i > $i > $o).
% 4.07/3.67 thf(zf_stmt_8, axiom,
% 4.07/3.67 (![X28:$i,X26:$i,X24:$i]:
% 4.07/3.67 ( ( zip_tseitin_2 @ X28 @ X26 @ X24 ) <=>
% 4.07/3.67 ( ( in @ X28 @ X24 ) & ( in @ X26 @ X28 ) ) ))).
% 4.07/3.67 thf(zf_stmt_9, type, zip_tseitin_1 : $i > $i > $i > $o).
% 4.07/3.67 thf(zf_stmt_10, axiom,
% 4.07/3.67 (![X22:$i,X20:$i,X18:$i]:
% 4.07/3.67 ( ( zip_tseitin_1 @ X22 @ X20 @ X18 ) <=>
% 4.07/3.67 ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ))).
% 4.07/3.67 thf(zf_stmt_11, type, zip_tseitin_0 : $i > $i > $i > $o).
% 4.07/3.67 thf(zf_stmt_12, axiom,
% 4.07/3.67 (![X16:$i,X14:$i,X12:$i]:
% 4.07/3.67 ( ( zip_tseitin_0 @ X16 @ X14 @ X12 ) <=>
% 4.07/3.67 ( ( ( X16 ) = ( X12 ) ) | ( in @ X16 @ X14 ) ) ))).
% 4.07/3.67 thf(zf_stmt_13, conjecture,
% 4.07/3.67 (( ![X4:$i,X6:$i]:
% 4.07/3.67 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 4.07/3.67 ( ( X4 ) = ( X6 ) ) ) ) =>
% 4.07/3.67 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 4.07/3.67 ( ( ![X12:$i,X14:$i,X16:$i]:
% 4.07/3.67 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 4.07/3.67 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 4.07/3.67 ( ( ![X18:$i,X20:$i]:
% 4.07/3.67 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 4.07/3.67 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 4.07/3.67 ( ( ![X24:$i,X26:$i]:
% 4.07/3.67 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 4.07/3.67 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 4.07/3.67 ( ( in @ emptyset @ omega ) =>
% 4.07/3.67 ( ( ![X30:$i]:
% 4.07/3.67 ( ( in @ X30 @ omega ) =>
% 4.07/3.67 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 4.07/3.67 ( ( ![X32:$i]:
% 4.07/3.67 ( ( ( in @ emptyset @ X32 ) &
% 4.07/3.67 ( ![X34:$i]:
% 4.07/3.67 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 4.07/3.67 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 4.07/3.67 ( ![X36:$i]:
% 4.07/3.67 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 4.07/3.67 ( ( ![X42:$i]:
% 4.07/3.67 ( ( in @ X42 @ X40 ) =>
% 4.07/3.67 ( ?[X44:$i]:
% 4.07/3.67 ( ( ![X46:$i]:
% 4.07/3.67 ( ( X38 @ X42 @ X46 ) =>
% 4.07/3.67 ( ( X44 ) = ( X46 ) ) ) ) &
% 4.07/3.67 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 4.07/3.67 ( ?[X48:$i]:
% 4.07/3.67 ( ![X50:$i]:
% 4.07/3.67 ( ( in @ X50 @ X48 ) <=>
% 4.07/3.67 ( ?[X52:$i]:
% 4.07/3.67 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X54:$i]:
% 4.07/3.67 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 4.07/3.67 ( ?[X58:$i]:
% 4.07/3.67 ( ( ~( ?[X60:$i]:
% 4.07/3.67 ( ( in @ X60 @ X54 ) & ( in @ X60 @ X58 ) ) ) ) &
% 4.07/3.67 ( in @ X58 @ X54 ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X62:$i]:
% 4.07/3.67 ( ?[X64:$i]:
% 4.07/3.67 ( ( ![X66:$i]:
% 4.07/3.67 ( ( ( ![X68:$i]:
% 4.07/3.67 ( ( in @ X68 @ X66 ) =>
% 4.07/3.67 ( in @ X68 @ X62 ) ) ) &
% 4.07/3.67 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 4.07/3.67 ( ?[X72:$i,X74:$i]:
% 4.07/3.67 ( ( ![X76:$i]:
% 4.07/3.67 ( ( in @ X76 @ X64 ) =>
% 4.07/3.67 ( ( ![X78:$i]:
% 4.07/3.67 ( ( in @ X78 @ X76 ) =>
% 4.07/3.67 ( in @ X78 @ X72 ) ) ) |
% 4.07/3.67 ( in @ X74 @ X76 ) ) ) ) &
% 4.07/3.67 ( ~( ?[X80:$i]:
% 4.07/3.67 ( ( in @ X80 @ X66 ) &
% 4.07/3.67 ( in @ X80 @ X72 ) ) ) ) &
% 4.07/3.67 ( in @ X74 @ X66 ) & ( in @ X72 @ X64 ) ) ) ) ) &
% 4.07/3.67 ( ![X82:$i,X84:$i]:
% 4.07/3.67 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 4.07/3.67 ( ( ![X86:$i]:
% 4.07/3.67 ( ( in @ X86 @ X82 ) =>
% 4.07/3.67 ( in @ X86 @ X84 ) ) ) |
% 4.07/3.67 ( ![X88:$i]:
% 4.07/3.67 ( ( in @ X88 @ X84 ) =>
% 4.07/3.67 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 4.07/3.67 ( ![X90:$i,X92:$i]:
% 4.07/3.67 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 4.07/3.67 ( ( ![X94:$i]:
% 4.07/3.67 ( ( in @ X94 @ X64 ) =>
% 4.07/3.67 ( ( in @ X90 @ X94 ) <=>
% 4.07/3.67 ( in @ X92 @ X94 ) ) ) ) =>
% 4.07/3.67 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 4.07/3.67 ( ![X96:$i]:
% 4.07/3.67 ( ( in @ X96 @ X64 ) =>
% 4.07/3.67 ( ![X98:$i]:
% 4.07/3.67 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X100:( $i > $o )]:
% 4.07/3.67 ( ( ?[X102:$i]:
% 4.07/3.67 ( ( ![X104:$i]:
% 4.07/3.67 ( ( X100 @ X104 ) =>
% 4.07/3.67 ( ( X102 ) = ( X104 ) ) ) ) &
% 4.07/3.67 ( X100 @ X102 ) ) ) =>
% 4.07/3.67 ( X100 @
% 4.07/3.67 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 4.07/3.67 ( ( in @ X110 @ X106 ) =>
% 4.07/3.67 ( ( X108 @ X110 ) =>
% 4.07/3.67 ( in @
% 4.07/3.67 X110 @
% 4.07/3.67 ( dsetconstr @
% 4.07/3.67 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 4.07/3.67 ( ( in @
% 4.07/3.67 X116 @
% 4.07/3.67 ( dsetconstr @
% 4.07/3.67 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 4.07/3.67 ( in @ X116 @ X112 ) ) ) =>
% 4.07/3.67 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 4.07/3.67 ( ( in @
% 4.07/3.67 X122 @
% 4.07/3.67 ( dsetconstr @
% 4.07/3.67 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 4.07/3.67 ( X120 @ X122 ) ) ) =>
% 4.07/3.67 ( ( ![X124:( $i > $o )]:
% 4.07/3.67 ( ( ?[X126:$i]:
% 4.07/3.67 ( ( ![X128:$i]:
% 4.07/3.67 ( ( X124 @ X128 ) =>
% 4.07/3.67 ( ( X126 ) = ( X128 ) ) ) ) &
% 4.07/3.67 ( X124 @ X126 ) ) ) =>
% 4.07/3.67 ( ?[X130:$i]:
% 4.07/3.67 ( ( ![X132:$i]:
% 4.07/3.67 ( ( X124 @ X132 ) =>
% 4.07/3.67 ( ( X130 ) = ( X132 ) ) ) ) &
% 4.07/3.67 ( X124 @ X130 ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X134:$o,X136:$i]:
% 4.07/3.67 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 4.07/3.67 ( X134 ) ) ) =>
% 4.07/3.67 ( ( ![X138:$i]:
% 4.07/3.67 ( ( in @ X138 @ emptyset ) =>
% 4.07/3.67 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 4.07/3.67 ( ( ![X142:$i]:
% 4.07/3.67 ( ~( in @ X142 @ emptyset ) ) ) =>
% 4.07/3.67 ( ( ![X144:$i]:
% 4.07/3.67 ( ~( in @ X144 @ emptyset ) ) ) =>
% 4.07/3.67 ( ( ![X146:( $i > $o )]:
% 4.07/3.67 ( ( ?[X148:$i]:
% 4.07/3.67 ( ( ![X150:$i]:
% 4.07/3.67 ( ( X146 @ X150 ) =>
% 4.07/3.67 ( ( X148 ) = ( X150 ) ) ) ) &
% 4.07/3.67 ( X146 @ X148 ) ) ) =>
% 4.07/3.67 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 4.07/3.67 ( ( ![X154:$i,X156:$i]:
% 4.07/3.67 ( ( ![X158:$i]:
% 4.07/3.67 ( ( in @ X158 @ X154 ) =>
% 4.07/3.67 ( in @ X158 @ X156 ) ) ) =>
% 4.07/3.67 ( ( ![X160:$i]:
% 4.07/3.67 ( ( in @ X160 @ X156 ) =>
% 4.07/3.67 ( in @ X160 @ X154 ) ) ) =>
% 4.07/3.67 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X162:$i]:
% 4.07/3.67 ( ( ![X164:$i]:
% 4.07/3.67 ( ~( in @ X164 @ X162 ) ) ) =>
% 4.07/3.67 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 4.07/3.67 ( ( ![X166:$i]:
% 4.07/3.67 ( ( ![X168:$i]:
% 4.07/3.67 ( ~( in @ X168 @ X166 ) ) ) =>
% 4.07/3.67 ( ( X166 ) =
% 4.07/3.67 ( emptyset ) ) ) ) =>
% 4.07/3.67 ( ( ![X170:$i,
% 4.07/3.67 X172:( $i > $o ),
% 4.07/3.67 X174:$i]:
% 4.07/3.67 ( ( in @ X174 @ X170 ) =>
% 4.07/3.67 ( ( in @
% 4.07/3.67 X174 @
% 4.07/3.67 ( dsetconstr @
% 4.07/3.67 X170 @
% 4.07/3.67 ( ^[V_5:$i]:
% 4.07/3.67 ( X172 @ V_5 ) ) ) ) <=>
% 4.07/3.67 ( X172 @ X174 ) ) ) ) =>
% 4.07/3.67 ( ( ![X176:$i]:
% 4.07/3.67 ( ( ( X176 ) !=
% 4.07/3.67 ( emptyset ) ) =>
% 4.07/3.67 ( ?[X178:$i]:
% 4.07/3.67 ( in @ X178 @ X176 ) ) ) ) =>
% 4.07/3.67 ( ( ![X180:$i,
% 4.07/3.67 X182:( $i > $o ),
% 4.07/3.67 X184:$i]:
% 4.07/3.67 ( ( in @ X184 @ X180 ) =>
% 4.07/3.67 ( ( X182 @ X184 ) =>
% 4.07/3.67 ( ( dsetconstr @
% 4.07/3.67 X180 @
% 4.07/3.67 ( ^[
% 4.07/3.67 V_6:$i]:
% 4.07/3.67 (
% 4.07/3.67 X182 @ V_6 ) ) ) !=
% 4.07/3.67 ( emptyset ) ) ) ) ) =>
% 4.07/3.67 ( ( ![X186:$i]:
% 4.07/3.67 ( ( ?[X188:$i]:
% 4.07/3.67 ( in @
% 4.07/3.67 X188 @ X186 ) ) =>
% 4.07/3.67 ( ( X186 ) !=
% 4.07/3.67 ( emptyset ) ) ) ) =>
% 4.07/3.67 ( ( ![X190:$i,
% 4.07/3.67 X192:$i]:
% 4.07/3.67 ( in @
% 4.07/3.67 X190 @
% 4.07/3.67 ( setadjoin @
% 4.07/3.67 X190 @ X192 ) ) ) =>
% 4.07/3.67 ( ( in @
% 4.07/3.67 emptyset @
% 4.07/3.67 ( setadjoin @
% 4.07/3.67 emptyset @
% 4.07/3.67 emptyset ) ) =>
% 4.07/3.67 ( ( ![X194:$i,
% 4.07/3.67 X196:$i,
% 4.07/3.67 X198:$i]:
% 4.07/3.67 ( (
% 4.07/3.67 in @
% 4.07/3.67 X198 @
% 4.07/3.67 X196 ) =>
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X198 @
% 4.07/3.67 (
% 4.07/3.67 setadjoin
% 4.07/3.67 @
% 4.07/3.67 X194 @
% 4.07/3.67 X196 ) ) ) ) =>
% 4.07/3.67 ( ( ![
% 4.07/3.67 X200:$i,
% 4.07/3.67 X202:$i,
% 4.07/3.67 X204:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X204 @
% 4.07/3.67 (
% 4.07/3.67 setadjoin
% 4.07/3.67 @
% 4.07/3.67 X200 @
% 4.07/3.67 X202 ) ) =>
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X206:$o]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 X204 ) =
% 4.07/3.67 (
% 4.07/3.67 X200 ) ) =>
% 4.07/3.67 (
% 4.07/3.67 X206 ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X204 @
% 4.07/3.67 X202 ) =>
% 4.07/3.67 (
% 4.07/3.67 X206 ) ) =>
% 4.07/3.67 (
% 4.07/3.67 X206 ) ) ) ) ) ) =>
% 4.07/3.67 ( (
% 4.07/3.67 ![
% 4.07/3.67 X208:$i,
% 4.07/3.67 X210:$i,
% 4.07/3.67 X212:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X212 @
% 4.07/3.67 (
% 4.07/3.67 setadjoin
% 4.07/3.67 @
% 4.07/3.67 X208 @
% 4.07/3.67 X210 ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 X212 ) =
% 4.07/3.67 (
% 4.07/3.67 X208 ) ) |
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X212 @
% 4.07/3.67 X210 ) ) ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X214:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 dsetconstr
% 4.07/3.67 @
% 4.07/3.67 X214 @
% 4.07/3.67 (
% 4.07/3.67 ^[
% 4.07/3.67 V_7:$i]:
% 4.07/3.67 (
% 4.07/3.67 $true ) ) ) =
% 4.07/3.67 (
% 4.07/3.67 X214 ) ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X216:$i,
% 4.07/3.67 X218:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X220:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X220 @
% 4.07/3.67 X218 ) =>
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X220 @
% 4.07/3.67 X216 ) ) ) =>
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X218 @
% 4.07/3.67 (
% 4.07/3.67 powerset @
% 4.07/3.67 X216 ) ) ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X222:$i]:
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 emptyset @
% 4.07/3.67 (
% 4.07/3.67 powerset @
% 4.07/3.67 X222 ) ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X224:$i]:
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 emptyset @
% 4.07/3.67 (
% 4.07/3.67 powerset @
% 4.07/3.67 X224 ) ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X226:$i,
% 4.07/3.67 X228:$i,
% 4.07/3.67 X230:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X228 @
% 4.07/3.67 (
% 4.07/3.67 powerset @
% 4.07/3.67 X226 ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X230 @
% 4.07/3.67 X228 ) =>
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X230 @
% 4.07/3.67 X226 ) ) ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X232:$i,
% 4.07/3.67 X234:$i,
% 4.07/3.67 X236:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X234 @
% 4.07/3.67 X236 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X236 @
% 4.07/3.67 X232 ) =>
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X234 @
% 4.07/3.67 (
% 4.07/3.67 setunion @
% 4.07/3.67 X232 ) ) ) ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X238:$i,
% 4.07/3.67 X240:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X240 @
% 4.07/3.67 (
% 4.07/3.67 setunion @
% 4.07/3.67 X238 ) ) =>
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X242:$o]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X244:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X240 @
% 4.07/3.67 X244 ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X244 @
% 4.07/3.67 X238 ) =>
% 4.07/3.67 (
% 4.07/3.67 X242 ) ) ) ) =>
% 4.07/3.67 (
% 4.07/3.67 X242 ) ) ) ) ) =>
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 ![
% 4.07/3.67 X246:$i,
% 4.07/3.67 X248:$i]:
% 4.07/3.67 (
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X248 @
% 4.07/3.67 X246 ) =>
% 4.07/3.67 (
% 4.07/3.67 in @
% 4.07/3.67 X248 @
% 4.07/3.67 (
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% 4.07/3.68 X408:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 X404 @
% 4.07/3.68 X408 ) =>
% 4.07/3.68 (
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% 4.07/3.68 X406 ) ) ) =>
% 4.07/3.68 (
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% 4.07/3.68 X410:$i,
% 4.07/3.68 X412:$i]:
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% 4.07/3.68 X404 @
% 4.07/3.68 X410 ) =>
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% 4.07/3.68 (
% 4.07/3.68 X404 @
% 4.07/3.68 X412 ) =>
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% 4.07/3.68 (
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% 4.07/3.68 X434:$i,
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% 4.07/3.68 (
% 4.07/3.68 X434 ) =
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% 4.07/3.68 X436 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 setadjoin
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% 4.07/3.68 (
% 4.07/3.68 X438 ) =
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% 4.07/3.68 X440 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
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% 4.07/3.68 (
% 4.07/3.68 (
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% 4.07/3.68 X442:$i,
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% 4.07/3.68 (
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% 4.07/3.68 X444 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 setunion @
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 (
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% 4.07/3.68 (
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% 4.07/3.68 X450 ) =>
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% 4.07/3.68 X450 ) ) ) ) &
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% 4.07/3.68 (
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% 4.07/3.68 X452:$i,
% 4.07/3.68 X454:$i]:
% 4.07/3.68 (
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% 4.07/3.68 X446 @
% 4.07/3.68 X452 ) =>
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% 4.07/3.68 (
% 4.07/3.68 X446 @
% 4.07/3.68 X454 ) =>
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% 4.07/3.68 (
% 4.07/3.68 ![
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% 4.07/3.68 X458:(
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% 4.07/3.68 (
% 4.07/3.68 (
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% 4.07/3.68 X460:$i,
% 4.07/3.68 X462:$i]:
% 4.07/3.68 (
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% 4.07/3.68 (
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% 4.07/3.68 ?[
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% 4.07/3.68 (
% 4.07/3.68 (
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% 4.07/3.68 X466:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 X456 @
% 4.07/3.68 X466 ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 X464 ) =
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% 4.07/3.68 X466 ) ) ) ) &
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ?[
% 4.07/3.68 X468:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X470:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 X458 @
% 4.07/3.68 X470 ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 X468 ) =
% 4.07/3.68 (
% 4.07/3.68 X470 ) ) ) ) &
% 4.07/3.68 (
% 4.07/3.68 X458 @
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 descr @
% 4.07/3.68 (
% 4.07/3.68 ^[
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% 4.07/3.68 (
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% 4.07/3.68 (
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% 4.07/3.68 ^[
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X472:$i,
% 4.07/3.68 X474:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 X472 ) =
% 4.07/3.68 (
% 4.07/3.68 X474 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X476:(
% 4.07/3.68 $i > $o ),
% 4.07/3.68 X478:(
% 4.07/3.68 $i > $o )]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X480:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X480 @
% 4.07/3.68 X472 ) =>
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X482:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X482 @
% 4.07/3.68 X474 ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 X480 ) =
% 4.07/3.68 (
% 4.07/3.68 X482 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 dsetconstr
% 4.07/3.68 @
% 4.07/3.68 X472 @
% 4.07/3.68 (
% 4.07/3.68 ^[
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% 4.07/3.68 (
% 4.07/3.68 X476 @
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% 4.07/3.68 (
% 4.07/3.68 dsetconstr
% 4.07/3.68 @
% 4.07/3.68 X474 @
% 4.07/3.68 (
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X484:$i,
% 4.07/3.68 X486:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X488:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X488 @
% 4.07/3.68 X484 ) =>
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X488 @
% 4.07/3.68 X486 ) ) ) =>
% 4.07/3.68 (
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% 4.07/3.68 X484 @
% 4.07/3.68 X486 ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X490:$i,
% 4.07/3.68 X492:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 X490 ) =
% 4.07/3.68 (
% 4.07/3.68 X492 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 subset @
% 4.07/3.68 X492 @
% 4.07/3.68 X490 ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X494:$i,
% 4.07/3.68 X496:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 (
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% 4.07/3.68 (
% 4.07/3.68 X496 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 subset @
% 4.07/3.68 X494 @
% 4.07/3.68 X496 ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X498:$i,
% 4.07/3.68 X500:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X502:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X502 @
% 4.07/3.68 X498 ) =>
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X502 @
% 4.07/3.68 X500 ) ) ) =>
% 4.07/3.68 (
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% 4.07/3.68 X498 @
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X504:$i]:
% 4.07/3.68 (
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% 4.07/3.68 emptyset @
% 4.07/3.68 X504 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X506:$i,
% 4.07/3.68 X508:$i,
% 4.07/3.68 X510:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 subset @
% 4.07/3.68 X506 @
% 4.07/3.68 X508 ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X510 @
% 4.07/3.68 X506 ) =>
% 4.07/3.68 (
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X512:$i,
% 4.07/3.68 X514:$i,
% 4.07/3.68 X516:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 subset @
% 4.07/3.68 X512 @
% 4.07/3.68 X514 ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ~(
% 4.07/3.68 in @
% 4.07/3.68 X516 @
% 4.07/3.68 X514 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 ~(
% 4.07/3.68 in @
% 4.07/3.68 X516 @
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X518:$i,
% 4.07/3.68 X520:$i,
% 4.07/3.68 X522:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X522 @
% 4.07/3.68 X518 ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ~(
% 4.07/3.68 in @
% 4.07/3.68 X522 @
% 4.07/3.68 X520 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 ~(
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% 4.07/3.68 X520 ) ) ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X524:$i,
% 4.07/3.68 X526:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ~(
% 4.07/3.68 subset @
% 4.07/3.68 X524 @
% 4.07/3.68 X526 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
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% 4.07/3.68 (
% 4.07/3.68 X526 ) ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X528:$i,
% 4.07/3.68 X530:$i,
% 4.07/3.68 X532:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X532 @
% 4.07/3.68 X528 ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ~(
% 4.07/3.68 in @
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% 4.07/3.68 (
% 4.07/3.68 (
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X536:$i,
% 4.07/3.68 X538:$i,
% 4.07/3.68 X540:$i]:
% 4.07/3.68 (
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% 4.07/3.68 subset @
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% 4.07/3.68 X538 ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 subset @
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X542:$i,
% 4.07/3.68 X544:$i]:
% 4.07/3.68 (
% 4.07/3.68 subset @
% 4.07/3.68 X544 @
% 4.07/3.68 (
% 4.07/3.68 setadjoin
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% 4.07/3.68 X544 ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X546:$i,
% 4.07/3.68 X548:$i,
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 subset @
% 4.07/3.68 X546 @
% 4.07/3.68 X550 ) =>
% 4.07/3.68 (
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X552:$i,
% 4.07/3.68 X554:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 subset @
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% 4.07/3.68 X554 ) =>
% 4.07/3.68 (
% 4.07/3.68 in @
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% 4.07/3.68 X554 ) ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X556:$i,
% 4.07/3.68 X558:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
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% 4.07/3.68 X558 ) =>
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% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X560:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 subset @
% 4.07/3.68 X560 @
% 4.07/3.68 emptyset ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 X560 ) =
% 4.07/3.68 (
% 4.07/3.68 emptyset ) ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X562:$i,
% 4.07/3.68 X564:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 subset @
% 4.07/3.68 X564 @
% 4.07/3.68 X562 ) =>
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X564 @
% 4.07/3.68 (
% 4.07/3.68 powerset @
% 4.07/3.68 X562 ) ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X566:$i,
% 4.07/3.68 X568:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X568 @
% 4.07/3.68 (
% 4.07/3.68 powerset @
% 4.07/3.68 X566 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 subset @
% 4.07/3.68 X568 @
% 4.07/3.68 X566 ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X570:$i]:
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X570 @
% 4.07/3.68 (
% 4.07/3.68 powerset @
% 4.07/3.68 X570 ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X572:$i,
% 4.07/3.68 X574:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 subset @
% 4.07/3.68 X572 @
% 4.07/3.68 X574 ) =>
% 4.07/3.68 (
% 4.07/3.68 subset @
% 4.07/3.68 (
% 4.07/3.68 powerset @
% 4.07/3.68 X572 ) @
% 4.07/3.68 (
% 4.07/3.68 powerset @
% 4.07/3.68 X574 ) ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X576:$i,
% 4.07/3.68 X578:(
% 4.07/3.68 $i > $o )]:
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 (
% 4.07/3.68 dsetconstr
% 4.07/3.68 @
% 4.07/3.68 X576 @
% 4.07/3.68 (
% 4.07/3.68 ^[
% 4.07/3.68 V_13:$i]:
% 4.07/3.68 (
% 4.07/3.68 X578 @
% 4.07/3.68 V_13 ) ) ) @
% 4.07/3.68 (
% 4.07/3.68 powerset @
% 4.07/3.68 X576 ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X580:$i,
% 4.07/3.68 X582:(
% 4.07/3.68 $i > $o )]:
% 4.07/3.68 (
% 4.07/3.68 subset @
% 4.07/3.68 (
% 4.07/3.68 dsetconstr
% 4.07/3.68 @
% 4.07/3.68 X580 @
% 4.07/3.68 (
% 4.07/3.68 ^[
% 4.07/3.68 V_14:$i]:
% 4.07/3.68 (
% 4.07/3.68 X582 @
% 4.07/3.68 V_14 ) ) ) @
% 4.07/3.68 X580 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X584:$i,
% 4.07/3.68 X586:$i,
% 4.07/3.68 X588:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X588 @
% 4.07/3.68 X584 ) =>
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X588 @
% 4.07/3.68 (
% 4.07/3.68 binunion @
% 4.07/3.68 X584 @
% 4.07/3.68 X586 ) ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X590:$i,
% 4.07/3.68 X592:$i]:
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X592 @
% 4.07/3.68 (
% 4.07/3.68 setadjoin
% 4.07/3.68 @
% 4.07/3.68 X590 @
% 4.07/3.68 (
% 4.07/3.68 setadjoin
% 4.07/3.68 @
% 4.07/3.68 X592 @
% 4.07/3.68 emptyset ) ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X594:$i,
% 4.07/3.68 X596:$i,
% 4.07/3.68 X598:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X598 @
% 4.07/3.68 X596 ) =>
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X598 @
% 4.07/3.68 (
% 4.07/3.68 binunion @
% 4.07/3.68 X594 @
% 4.07/3.68 X596 ) ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X600:$i,
% 4.07/3.68 X602:$i,
% 4.07/3.68 X604:$i,
% 4.07/3.68 X606:$o]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X604 @
% 4.07/3.68 (
% 4.07/3.68 binunion @
% 4.07/3.68 X600 @
% 4.07/3.68 X602 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X604 @
% 4.07/3.68 X600 ) =>
% 4.07/3.68 (
% 4.07/3.68 X606 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X604 @
% 4.07/3.68 X602 ) =>
% 4.07/3.68 (
% 4.07/3.68 X606 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 X606 ) ) ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X608:$i,
% 4.07/3.68 X610:$i,
% 4.07/3.68 X612:$i]:
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X612 @
% 4.07/3.68 (
% 4.07/3.68 binunion @
% 4.07/3.68 X608 @
% 4.07/3.68 X610 ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X612 @
% 4.07/3.68 X608 ) |
% 4.07/3.68 (
% 4.07/3.68 in @
% 4.07/3.68 X612 @
% 4.07/3.68 X610 ) ) ) ) =>
% 4.07/3.68 (
% 4.07/3.68 (
% 4.07/3.68 ![
% 4.07/3.68 X614:$i,
% 4.07/3.69 X616:$i]:
% 4.07/3.69 (
% 4.07/3.69 subset @
% 4.07/3.69 X614 @
% 4.07/3.69 (
% 4.07/3.69 binunion @
% 4.07/3.69 X614 @
% 4.07/3.69 X616 ) ) ) =>
% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 ![
% 4.07/3.69 X618:$i,
% 4.07/3.69 X620:$i]:
% 4.07/3.69 (
% 4.07/3.69 subset @
% 4.07/3.69 X620 @
% 4.07/3.69 (
% 4.07/3.69 binunion @
% 4.07/3.69 X618 @
% 4.07/3.69 X620 ) ) ) =>
% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 ![
% 4.07/3.69 X622:$i,
% 4.07/3.69 X624:$i,
% 4.07/3.69 X626:$i]:
% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 in @
% 4.07/3.69 X626 @
% 4.07/3.69 X622 ) =>
% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 in @
% 4.07/3.69 X626 @
% 4.07/3.69 X624 ) =>
% 4.07/3.69 (
% 4.07/3.69 in @
% 4.07/3.69 X626 @
% 4.07/3.69 (
% 4.07/3.69 dsetconstr
% 4.07/3.69 @
% 4.07/3.69 X622 @
% 4.07/3.69 (
% 4.07/3.69 ^[
% 4.07/3.69 V_15:$i]:
% 4.07/3.69 (
% 4.07/3.69 in @
% 4.07/3.69 V_15 @
% 4.07/3.69 X624 ) ) ) ) ) ) ) =>
% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 ![
% 4.07/3.69 X628:$i,
% 4.07/3.69 X630:$i,
% 4.07/3.69 X632:$i]:
% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 subset @
% 4.07/3.69 X632 @
% 4.07/3.69 X628 ) =>
% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 subset @
% 4.07/3.69 X632 @
% 4.07/3.69 X630 ) =>
% 4.07/3.69 (
% 4.07/3.69 subset @
% 4.07/3.69 X632 @
% 4.07/3.69 (
% 4.07/3.69 dsetconstr
% 4.07/3.69 @
% 4.07/3.69 X628 @
% 4.07/3.69 (
% 4.07/3.69 ^[
% 4.07/3.69 V_16:$i]:
% 4.07/3.69 (
% 4.07/3.69 in @
% 4.07/3.69 V_16 @
% 4.07/3.69 X630 ) ) ) ) ) ) ) =>
% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 ![
% 4.07/3.69 X634:$i,
% 4.07/3.69 X636:$i,
% 4.07/3.69 X638:$i]:
% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 in @
% 4.07/3.69 X638 @
% 4.07/3.69 (
% 4.07/3.69 dsetconstr
% 4.07/3.69 @
% 4.07/3.69 X634 @
% 4.07/3.69 (
% 4.07/3.69 ^[
% 4.07/3.69 V_17:$i]:
% 4.07/3.69 (
% 4.07/3.69 in @
% 4.07/3.69 V_17 @
% 4.07/3.69 X636 ) ) ) ) =>
% 4.07/3.69 (
% 4.07/3.69 in @
% 4.07/3.69 X638 @
% 4.07/3.69 X634 ) ) ) =>
% 4.07/3.69 (
% 4.07/3.69 ![
% 4.07/3.69 X640:$i,
% 4.07/3.69 X642:$i]:
% 4.07/3.69 (
% 4.07/3.69 subset @
% 4.07/3.69 (
% 4.07/3.69 dsetconstr
% 4.07/3.69 @
% 4.07/3.69 X640 @
% 4.07/3.69 (
% 4.07/3.69 ^[
% 4.07/3.69 V_18:$i]:
% 4.07/3.69 (
% 4.07/3.69 in @
% 4.07/3.69 V_18 @
% 4.07/3.69 X642 ) ) ) @
% 4.07/3.69 X640 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 4.07/3.69 thf(zf_stmt_14, negated_conjecture,
% 4.07/3.69 (~( ( ![X4:$i,X6:$i]:
% 4.07/3.69 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 4.07/3.69 ( ( X4 ) = ( X6 ) ) ) ) =>
% 4.07/3.69 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 4.07/3.69 ( ( ![X12:$i,X14:$i,X16:$i]:
% 4.07/3.69 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 4.07/3.69 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 4.07/3.69 ( ( ![X18:$i,X20:$i]:
% 4.07/3.69 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 4.07/3.69 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 4.07/3.69 ( ( ![X24:$i,X26:$i]:
% 4.07/3.69 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 4.07/3.69 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 4.07/3.69 ( ( in @ emptyset @ omega ) =>
% 4.07/3.69 ( ( ![X30:$i]:
% 4.07/3.69 ( ( in @ X30 @ omega ) =>
% 4.07/3.69 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 4.07/3.69 ( ( ![X32:$i]:
% 4.07/3.69 ( ( ( in @ emptyset @ X32 ) &
% 4.07/3.69 ( ![X34:$i]:
% 4.07/3.69 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 4.07/3.69 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 4.07/3.69 ( ![X36:$i]:
% 4.07/3.69 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 4.07/3.69 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 4.07/3.69 ( ( ![X42:$i]:
% 4.07/3.69 ( ( in @ X42 @ X40 ) =>
% 4.07/3.69 ( ?[X44:$i]:
% 4.07/3.69 ( ( ![X46:$i]:
% 4.07/3.69 ( ( X38 @ X42 @ X46 ) =>
% 4.07/3.69 ( ( X44 ) = ( X46 ) ) ) ) &
% 4.07/3.69 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 4.07/3.69 ( ?[X48:$i]:
% 4.07/3.69 ( ![X50:$i]:
% 4.07/3.69 ( ( in @ X50 @ X48 ) <=>
% 4.07/3.69 ( ?[X52:$i]:
% 4.07/3.69 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 4.07/3.69 ( ( ![X54:$i]:
% 4.07/3.69 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 4.07/3.69 ( ?[X58:$i]:
% 4.07/3.69 ( ( ~( ?[X60:$i]:
% 4.07/3.69 ( ( in @ X60 @ X54 ) &
% 4.07/3.69 ( in @ X60 @ X58 ) ) ) ) &
% 4.07/3.69 ( in @ X58 @ X54 ) ) ) ) ) =>
% 4.07/3.69 ( ( ![X62:$i]:
% 4.07/3.69 ( ?[X64:$i]:
% 4.07/3.69 ( ( ![X66:$i]:
% 4.07/3.69 ( ( ( ![X68:$i]:
% 4.07/3.69 ( ( in @ X68 @ X66 ) =>
% 4.07/3.69 ( in @ X68 @ X62 ) ) ) &
% 4.07/3.69 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 4.07/3.69 ( ?[X72:$i,X74:$i]:
% 4.07/3.69 ( ( ![X76:$i]:
% 4.07/3.69 ( ( in @ X76 @ X64 ) =>
% 4.07/3.69 ( ( ![X78:$i]:
% 4.07/3.69 ( ( in @ X78 @ X76 ) =>
% 4.07/3.69 ( in @ X78 @ X72 ) ) ) |
% 4.07/3.69 ( in @ X74 @ X76 ) ) ) ) &
% 4.07/3.69 ( ~( ?[X80:$i]:
% 4.07/3.69 ( ( in @ X80 @ X66 ) &
% 4.07/3.69 ( in @ X80 @ X72 ) ) ) ) &
% 4.07/3.69 ( in @ X74 @ X66 ) &
% 4.07/3.69 ( in @ X72 @ X64 ) ) ) ) ) &
% 4.07/3.69 ( ![X82:$i,X84:$i]:
% 4.07/3.69 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 4.07/3.69 ( ( ![X86:$i]:
% 4.07/3.69 ( ( in @ X86 @ X82 ) =>
% 4.07/3.69 ( in @ X86 @ X84 ) ) ) |
% 4.07/3.69 ( ![X88:$i]:
% 4.07/3.69 ( ( in @ X88 @ X84 ) =>
% 4.07/3.69 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 4.07/3.69 ( ![X90:$i,X92:$i]:
% 4.07/3.69 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 4.07/3.69 ( ( ![X94:$i]:
% 4.07/3.69 ( ( in @ X94 @ X64 ) =>
% 4.07/3.69 ( ( in @ X90 @ X94 ) <=>
% 4.07/3.69 ( in @ X92 @ X94 ) ) ) ) =>
% 4.07/3.69 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 4.07/3.69 ( ![X96:$i]:
% 4.07/3.69 ( ( in @ X96 @ X64 ) =>
% 4.07/3.69 ( ![X98:$i]:
% 4.07/3.69 ( ( in @ X98 @ X96 ) =>
% 4.07/3.69 ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 4.07/3.69 ( ( ![X100:( $i > $o )]:
% 4.07/3.69 ( ( ?[X102:$i]:
% 4.07/3.69 ( ( ![X104:$i]:
% 4.07/3.69 ( ( X100 @ X104 ) =>
% 4.07/3.69 ( ( X102 ) = ( X104 ) ) ) ) &
% 4.07/3.69 ( X100 @ X102 ) ) ) =>
% 4.07/3.69 ( X100 @
% 4.07/3.69 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 4.07/3.69 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 4.07/3.69 ( ( in @ X110 @ X106 ) =>
% 4.07/3.69 ( ( X108 @ X110 ) =>
% 4.07/3.69 ( in @
% 4.07/3.69 X110 @
% 4.07/3.69 ( dsetconstr @
% 4.07/3.69 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 4.07/3.69 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 4.07/3.69 ( ( in @
% 4.07/3.69 X116 @
% 4.07/3.69 ( dsetconstr @
% 4.07/3.69 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 4.07/3.69 ( in @ X116 @ X112 ) ) ) =>
% 4.07/3.69 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 4.07/3.69 ( ( in @
% 4.07/3.69 X122 @
% 4.07/3.69 ( dsetconstr @
% 4.07/3.69 X118 @
% 4.07/3.69 ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 4.07/3.69 ( X120 @ X122 ) ) ) =>
% 4.07/3.69 ( ( ![X124:( $i > $o )]:
% 4.07/3.69 ( ( ?[X126:$i]:
% 4.07/3.69 ( ( ![X128:$i]:
% 4.07/3.69 ( ( X124 @ X128 ) =>
% 4.07/3.69 ( ( X126 ) = ( X128 ) ) ) ) &
% 4.07/3.69 ( X124 @ X126 ) ) ) =>
% 4.07/3.69 ( ?[X130:$i]:
% 4.07/3.69 ( ( ![X132:$i]:
% 4.07/3.69 ( ( X124 @ X132 ) =>
% 4.07/3.69 ( ( X130 ) = ( X132 ) ) ) ) &
% 4.07/3.69 ( X124 @ X130 ) ) ) ) ) =>
% 4.07/3.69 ( ( ![X134:$o,X136:$i]:
% 4.07/3.69 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 4.07/3.69 ( X134 ) ) ) =>
% 4.07/3.69 ( ( ![X138:$i]:
% 4.07/3.69 ( ( in @ X138 @ emptyset ) =>
% 4.07/3.69 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 4.07/3.69 ( ( ![X142:$i]:
% 4.07/3.69 ( ~( in @ X142 @ emptyset ) ) ) =>
% 4.07/3.69 ( ( ![X144:$i]:
% 4.07/3.69 ( ~( in @ X144 @ emptyset ) ) ) =>
% 4.07/3.69 ( ( ![X146:( $i > $o )]:
% 4.07/3.69 ( ( ?[X148:$i]:
% 4.07/3.69 ( ( ![X150:$i]:
% 4.07/3.69 ( ( X146 @ X150 ) =>
% 4.07/3.69 ( ( X148 ) =
% 4.07/3.69 ( X150 ) ) ) ) &
% 4.07/3.69 ( X146 @ X148 ) ) ) =>
% 4.07/3.69 ( ?[X152:$i]:
% 4.07/3.69 ( X146 @ X152 ) ) ) ) =>
% 4.07/3.69 ( ( ![X154:$i,X156:$i]:
% 4.07/3.69 ( ( ![X158:$i]:
% 4.07/3.69 ( ( in @ X158 @ X154 ) =>
% 4.07/3.69 ( in @ X158 @ X156 ) ) ) =>
% 4.07/3.69 ( ( ![X160:$i]:
% 4.07/3.69 ( ( in @ X160 @ X156 ) =>
% 4.07/3.69 ( in @ X160 @ X154 ) ) ) =>
% 4.07/3.69 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 4.07/3.69 ( ( ![X162:$i]:
% 4.07/3.69 ( ( ![X164:$i]:
% 4.07/3.69 ( ~( in @ X164 @ X162 ) ) ) =>
% 4.07/3.69 ( ( X162 ) =
% 4.07/3.69 ( emptyset ) ) ) ) =>
% 4.07/3.69 ( ( ![X166:$i]:
% 4.07/3.69 ( ( ![X168:$i]:
% 4.07/3.69 ( ~( in @
% 4.07/3.69 X168 @ X166 ) ) ) =>
% 4.07/3.69 ( ( X166 ) =
% 4.07/3.69 ( emptyset ) ) ) ) =>
% 4.07/3.69 ( ( ![X170:$i,
% 4.07/3.69 X172:( $i > $o ),
% 4.07/3.69 X174:$i]:
% 4.07/3.69 ( ( in @ X174 @ X170 ) =>
% 4.07/3.69 ( ( in @
% 4.07/3.69 X174 @
% 4.07/3.69 ( dsetconstr @
% 4.07/3.69 X170 @
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% 4.07/3.69 X394:$i]:
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% 4.07/3.69 X394 ) ) =>
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% 4.07/3.69 (
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% 4.07/3.69 X400:$i,
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% 4.07/3.69 (
% 4.07/3.69 X400 ) =
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% 4.07/3.69 X402 ) ) =>
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% 4.07/3.69 X404 @
% 4.07/3.69 X408 ) =>
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% 4.07/3.69 (
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% 4.07/3.69 X412:$i]:
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% 4.07/3.69 X404 @
% 4.07/3.69 X410 ) =>
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% 4.07/3.69 X404 @
% 4.07/3.69 X412 ) =>
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% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 ![
% 4.07/3.69 X414:(
% 4.07/3.69 $i > $o ),
% 4.07/3.69 X416:(
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% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 ![
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% 4.07/3.69 X420:$i]:
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% 4.07/3.69 (
% 4.07/3.69 (
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% 4.07/3.69 (
% 4.07/3.69 (
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% 4.07/3.69 X432:$i]:
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% 4.07/3.69 X432 ) ) =>
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% 4.07/3.69 ![
% 4.07/3.69 X434:$i,
% 4.07/3.69 X436:$i]:
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% 4.07/3.69 (
% 4.07/3.69 X434 ) =
% 4.07/3.69 (
% 4.07/3.69 X436 ) ) =>
% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 setadjoin
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% 4.07/3.69 X440:$i]:
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% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 X438 ) =
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% 4.07/3.69 X440 ) ) =>
% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 powerset
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% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 ![
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% 4.07/3.69 X444:$i]:
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% 4.07/3.69 (
% 4.07/3.69 X442 ) =
% 4.07/3.69 (
% 4.07/3.69 X444 ) ) =>
% 4.07/3.69 (
% 4.07/3.69 (
% 4.07/3.69 setunion
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% 4.07/3.69 (
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% 4.07/3.69 (
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% 4.07/3.69 (
% 4.07/3.69 (
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% 4.07/3.69 (
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% 4.07/3.69 (
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% 4.07/3.69 X446 @
% 4.07/3.69 X450 ) =>
% 4.07/3.69 (
% 4.07/3.69 (
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% 4.07/3.69 (
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% 4.07/3.69 X452:$i,
% 4.07/3.69 X454:$i]:
% 4.07/3.69 (
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% 4.07/3.69 X452 ) =>
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% 4.07/3.69 X454 ) =>
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% 4.07/3.69 (
% 4.07/3.69 ![
% 4.07/3.69 X456:(
% 4.07/3.69 $i > $o ),
% 4.07/3.69 X458:(
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% 4.07/3.69 (
% 4.07/3.69 (
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% 4.07/3.69 X462 ) ) =>
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% 4.07/3.69 (
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% 4.07/3.69 (
% 4.07/3.69 (
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% 4.07/3.69 (
% 4.07/3.69 (
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% 4.07/3.69 X474:$i]:
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% 4.07/3.69 (
% 4.07/3.69 (
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% 4.07/3.69 (
% 4.07/3.69 X474 ) ) =>
% 4.07/3.69 (
% 4.07/3.69 ![
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% 4.07/3.69 X478:(
% 4.07/3.69 $i > $o )]:
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% 4.07/3.69 (
% 4.07/3.69 in @
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% 4.07/3.69 X472 ) =>
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% 4.07/3.69 X482:$i]:
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% 4.07/3.69 (
% 4.07/3.69 dsetconstr
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% 4.07/3.71 V_17:$i]:
% 4.07/3.71 (
% 4.07/3.71 in @
% 4.07/3.71 V_17 @
% 4.07/3.71 X636 ) ) ) ) =>
% 4.07/3.71 (
% 4.07/3.71 in @
% 4.07/3.71 X638 @
% 4.07/3.71 X634 ) ) ) =>
% 4.07/3.71 (
% 4.07/3.71 ![
% 4.07/3.71 X640:$i,
% 4.07/3.71 X642:$i]:
% 4.07/3.71 (
% 4.07/3.71 subset @
% 4.07/3.71 (
% 4.07/3.71 dsetconstr
% 4.07/3.71 @
% 4.07/3.71 X640 @
% 4.07/3.71 (
% 4.07/3.71 ^[
% 4.07/3.71 V_18:$i]:
% 4.07/3.71 (
% 4.07/3.71 in @
% 4.07/3.71 V_18 @
% 4.07/3.71 X642 ) ) ) @
% 4.07/3.71 X640 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 4.07/3.71 inference('cnf.neg', [status(esa)], [zf_stmt_13])).
% 4.07/3.71 thf(zip_derived_cl116, plain,
% 4.07/3.71 (~ (subset @
% 4.07/3.71 (dsetconstr @ sk__321 @ (^[Y0 : $i]: (in @ Y0 @ sk__322))) @ sk__321)),
% 4.07/3.71 inference('cnf', [status(esa)], [zf_stmt_14])).
% 4.07/3.71 thf(zip_derived_cl125, plain,
% 4.07/3.71 (![X167 : $i, X168 : $i > $o]:
% 4.07/3.71 (subset @ (dsetconstr @ X167 @ (^[Y0 : $i]: (X168 @ Y0))) @ X167)),
% 4.07/3.71 inference('cnf', [status(esa)], [zf_stmt_14])).
% 4.07/3.71 thf(zip_derived_cl290, plain,
% 4.07/3.71 (![X167 : $i, X168 : $i > $o]:
% 4.07/3.71 (subset @ (dsetconstr @ X167 @ X168) @ X167)),
% 4.07/3.71 inference('ho_norm', [status(thm)], [zip_derived_cl125])).
% 4.07/3.71 thf(zip_derived_cl291, plain, ($false),
% 4.07/3.71 inference('demod', [status(thm)], [zip_derived_cl116, zip_derived_cl290])).
% 4.07/3.71
% 4.07/3.71 % SZS output end Refutation
% 4.07/3.71
% 4.07/3.71
% 4.07/3.71 % Terminating...
% 4.46/3.91 % Runner terminated.
% 4.51/3.94 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------