%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU602^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.oiZBjv0rP6 true
% Computer : n022.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 04:55:18 PM UTC 2025
% Result : Theorem 3.99s 1.18s
% Output : Refutation 4.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU602^1 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.oiZBjv0rP6 true
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 16:07:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.54/0.64 % Total configuration time : 828
% 0.54/0.64 % Estimated wc time : 1656
% 0.54/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.55/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.80 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.56/0.82 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.85 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 3.99/1.18 % Solved by lams/40_c.s.sh.
% 3.99/1.18 % done 36 iterations in 0.282s
% 3.99/1.18 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.99/1.18 % SZS output start Refutation
% 3.99/1.18 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 3.99/1.18 thf(notdexE_type, type, notdexE: $o).
% 3.99/1.18 thf(setunionAx_type, type, setunionAx: $o).
% 3.99/1.18 thf(powersetE_type, type, powersetE: $o).
% 3.99/1.18 thf(omegaSAx_type, type, omegaSAx: $o).
% 3.99/1.18 thf(exuI1_type, type, exuI1: $o).
% 3.99/1.18 thf(exuI2_type, type, exuI2: $o).
% 3.99/1.18 thf(notequalI2_type, type, notequalI2: $o).
% 3.99/1.18 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 3.99/1.18 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 3.99/1.18 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 3.99/1.18 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 3.99/1.18 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 3.99/1.18 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 3.99/1.18 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 3.99/1.18 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 3.99/1.18 thf(binunionE_type, type, binunionE: $o).
% 3.99/1.18 thf(setext_type, type, setext: $o).
% 3.99/1.18 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 3.99/1.18 thf(descr__Cong_type, type, descr__Cong: $o).
% 3.99/1.18 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 3.99/1.18 thf(in_type, type, in: $i > $i > $o).
% 3.99/1.18 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 3.99/1.18 thf(binunion_type, type, binunion: $i > $i > $i).
% 3.99/1.18 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 3.99/1.18 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 3.99/1.18 thf(zip_tseitin_2_type, type, zip_tseitin_2: $i > $i > $i > $o).
% 3.99/1.18 thf(upairset2IR_type, type, upairset2IR: $o).
% 3.99/1.18 thf(subsetE_type, type, subsetE: $o).
% 3.99/1.18 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 3.99/1.18 thf(sk__346_type, type, sk__346: $i).
% 3.99/1.18 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 3.99/1.18 thf(setbeta_type, type, setbeta: $o).
% 3.99/1.18 thf(eqinunit_type, type, eqinunit: $o).
% 3.99/1.18 thf(upairsetIL_type, type, upairsetIL: $o).
% 3.99/1.18 thf(powersetI1_type, type, powersetI1: $o).
% 3.99/1.18 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 3.99/1.18 thf(powersetAx_type, type, powersetAx: $o).
% 3.99/1.18 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 3.99/1.18 thf(powersetI_type, type, powersetI: $o).
% 3.99/1.18 thf(zip_tseitin_3_type, type, zip_tseitin_3: $i > $i > $i > ($i > $i > $o) > $o).
% 3.99/1.18 thf(upairsetIR_type, type, upairsetIR: $o).
% 3.99/1.18 thf(inCongP_type, type, inCongP: $o).
% 3.99/1.18 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 3.99/1.18 thf(exuE3e_type, type, exuE3e: $o).
% 3.99/1.18 thf(emptysetE_type, type, emptysetE: $o).
% 3.99/1.18 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 3.99/1.18 thf(setunionI_type, type, setunionI: $o).
% 3.99/1.18 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 3.99/1.18 thf(prop2setI_type, type, prop2setI: $o).
% 3.99/1.18 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 3.99/1.18 thf(exuE2_type, type, exuE2: $o).
% 3.99/1.18 thf(emptyset_type, type, emptyset: $i).
% 3.99/1.18 thf(setminus_type, type, setminus: $i > $i > $i).
% 3.99/1.18 thf(powersetsubset_type, type, powersetsubset: $o).
% 3.99/1.18 thf(subPowSU_type, type, subPowSU: $o).
% 3.99/1.18 thf(notequalI1_type, type, notequalI1: $o).
% 3.99/1.18 thf(notinemptyset_type, type, notinemptyset: $o).
% 3.99/1.18 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 3.99/1.18 thf(subsetTrans_type, type, subsetTrans: $o).
% 3.99/1.18 thf(binunionIL_type, type, binunionIL: $o).
% 3.99/1.18 thf(subsetE2_type, type, subsetE2: $o).
% 3.99/1.18 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 3.99/1.18 thf(setextsub_type, type, setextsub: $o).
% 3.99/1.18 thf(binunionLsub_type, type, binunionLsub: $o).
% 3.99/1.18 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 3.99/1.18 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 3.99/1.18 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 3.99/1.18 thf(setunionE_type, type, setunionE: $o).
% 3.99/1.18 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 3.99/1.18 thf(binunionIR_type, type, binunionIR: $o).
% 3.99/1.18 thf(setadjoinE_type, type, setadjoinE: $o).
% 3.99/1.18 thf(descr_type, type, descr: ($i > $o) > $i).
% 3.99/1.18 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 3.99/1.18 thf(exuE1_type, type, exuE1: $o).
% 3.99/1.18 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 3.99/1.18 thf(prop2set_type, type, prop2set: $o > $i).
% 3.99/1.18 thf(notinsingleton_type, type, notinsingleton: $o).
% 3.99/1.18 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 3.99/1.18 thf(exuEu_type, type, exuEu: $o).
% 3.99/1.18 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 3.99/1.18 thf(upairsetE_type, type, upairsetE: $o).
% 3.99/1.18 thf(omega0Ax_type, type, omega0Ax: $o).
% 3.99/1.18 thf(notsubsetI_type, type, notsubsetI: $o).
% 3.99/1.18 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 3.99/1.18 thf(setextAx_type, type, setextAx: $o).
% 3.99/1.18 thf(powersetE1_type, type, powersetE1: $o).
% 3.99/1.18 thf(bs114d_type, type, bs114d: $o).
% 3.99/1.18 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 3.99/1.18 thf(setunion_type, type, setunion: $i > $i).
% 3.99/1.18 thf(sk__347_type, type, sk__347: $i).
% 3.99/1.18 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 3.99/1.18 thf(subsetI1_type, type, subsetI1: $o).
% 3.99/1.18 thf(descrp_type, type, descrp: $o).
% 3.99/1.18 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 3.99/1.18 thf(foundationAx_type, type, foundationAx: $o).
% 3.99/1.18 thf(emptysetAx_type, type, emptysetAx: $o).
% 3.99/1.18 thf(emptyI_type, type, emptyI: $o).
% 3.99/1.18 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 3.99/1.18 thf(binintersectEL_type, type, binintersectEL: $o).
% 3.99/1.18 thf(emptyE1_type, type, emptyE1: $o).
% 3.99/1.18 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 3.99/1.18 thf(vacuousDall_type, type, vacuousDall: $o).
% 3.99/1.18 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 3.99/1.18 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 3.99/1.18 thf(exu_type, type, exu: ($i > $o) > $o).
% 3.99/1.18 thf(zip_tseitin_5_type, type, zip_tseitin_5: $i > ($i > $o) > $o).
% 3.99/1.18 thf(binintersectI_type, type, binintersectI: $o).
% 3.99/1.18 thf(subsetI2_type, type, subsetI2: $o).
% 3.99/1.18 thf(setminusI_type, type, setminusI: $o).
% 3.99/1.18 thf(omega__Cong_type, type, omega__Cong: $o).
% 3.99/1.18 thf(subsetRefl_type, type, subsetRefl: $o).
% 3.99/1.18 thf(uniqinunit_type, type, uniqinunit: $o).
% 3.99/1.18 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 3.99/1.18 thf(prop2setE_type, type, prop2setE: $o).
% 3.99/1.18 thf(binunionEcases_type, type, binunionEcases: $o).
% 3.99/1.18 thf(omega_type, type, omega: $i).
% 3.99/1.18 thf(nonemptyI_type, type, nonemptyI: $o).
% 3.99/1.18 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 3.99/1.18 thf(exuE3u_type, type, exuE3u: $o).
% 3.99/1.18 thf(sk__345_type, type, sk__345: $i).
% 3.99/1.18 thf(sepSubset_type, type, sepSubset: $o).
% 3.99/1.18 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 3.99/1.18 thf(exuI3_type, type, exuI3: $o).
% 3.99/1.18 thf(notdallE_type, type, notdallE: $o).
% 3.99/1.18 thf(binintersectER_type, type, binintersectER: $o).
% 3.99/1.18 thf(zip_tseitin_4_type, type, zip_tseitin_4: $i > $i > ($i > $o) > $o).
% 3.99/1.18 thf(powerset_type, type, powerset: $i > $i).
% 3.99/1.18 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 3.99/1.18 thf(nonempty_type, type, nonempty: $i > $o).
% 3.99/1.18 thf(set2prop_type, type, set2prop: $i > $o).
% 3.99/1.18 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 3.99/1.18 thf(exu__Cong_type, type, exu__Cong: $o).
% 3.99/1.18 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 3.99/1.18 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 3.99/1.18 thf(replAx_type, type, replAx: $o).
% 3.99/1.18 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 3.99/1.18 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 3.99/1.18 thf(inPowerset_type, type, inPowerset: $o).
% 3.99/1.18 thf(subset_type, type, subset: $i > $i > $o).
% 3.99/1.18 thf(in__Cong_type, type, in__Cong: $o).
% 3.99/1.18 thf(binunionRsub_type, type, binunionRsub: $o).
% 3.99/1.18 thf(subset2powerset_type, type, subset2powerset: $o).
% 3.99/1.18 thf(setminusI, axiom, setminusI =
% 3.99/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ A ) =>
% 3.99/1.18 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 3.99/1.18 thf('0', plain,
% 3.99/1.18 (( setminusI ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ X4 ) =>
% 3.99/1.18 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setminus, axiom,(( setminus ) =
% 3.99/1.18 (^[A:$i,B:$i]: ( dsetconstr @ A @ ( ^[Xx:$i]: ( ~( in @ Xx @ B ) ) ) )))).
% 3.99/1.18 thf('1', plain,
% 3.99/1.18 (( setminus ) =
% 3.99/1.18 ( ^[A:$i,B:$i]: ( dsetconstr @ A @ ( ^[Xx:$i]: ( ~( in @ Xx @ B ) ) ) ) )),
% 3.99/1.18 inference('simplify_rw_rule', [status(thm)], [setminus])).
% 3.99/1.18 thf('2', plain,
% 3.99/1.18 (( setminus ) =
% 3.99/1.18 ( ^[V_1:$i,V_2:$i]:
% 3.99/1.18 ( dsetconstr @ V_1 @ ( ^[V_3:$i]: ( ~( in @ V_3 @ V_2 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(bs114d, axiom, bs114d =
% 3.99/1.18 (![A:$i,B:$i,C:$i]:
% 3.99/1.18 ( ( binintersect @ A @ ( binunion @ B @ C ) ) =
% 3.99/1.18 ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ))).
% 3.99/1.18 thf('3', plain,
% 3.99/1.18 (( bs114d ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) ) =
% 3.99/1.18 ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binintersectSubset1, axiom, binintersectSubset1 =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( ( binintersect @ A @ B ) = ( A ) ) => ( subset @ A @ B ) ))).
% 3.99/1.18 thf('4', plain,
% 3.99/1.18 (( binintersectSubset1 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) => ( subset @ X4 @ X6 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binintersectSubset4, axiom, binintersectSubset4 =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( subset @ B @ A ) => ( ( binintersect @ A @ B ) = ( B ) ) ))).
% 3.99/1.18 thf('5', plain,
% 3.99/1.18 (( binintersectSubset4 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( subset @ X6 @ X4 ) => ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binintersectRsub, axiom, binintersectRsub =
% 3.99/1.18 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ B ))).
% 3.99/1.18 thf('6', plain,
% 3.99/1.18 (( binintersectRsub ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X6 ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(disjointsetsI1, axiom, disjointsetsI1 =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ B ) & ( in @ Xx @ A ) ) ) ) =>
% 3.99/1.18 ( ( binintersect @ A @ B ) = ( emptyset ) ) ))).
% 3.99/1.18 thf('7', plain,
% 3.99/1.18 (( disjointsetsI1 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ~( ?[X8:$i]: ( ( in @ X8 @ X6 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 3.99/1.18 ( ( binintersect @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binintersectER, axiom, binintersectER =
% 3.99/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ B ) ))).
% 3.99/1.18 thf('8', plain,
% 3.99/1.18 (( binintersectER ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X6 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binintersectSubset3, axiom, binintersectSubset3 =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( ( binintersect @ A @ B ) = ( B ) ) => ( subset @ B @ A ) ))).
% 3.99/1.18 thf('9', plain,
% 3.99/1.18 (( binintersectSubset3 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binintersectSubset2, axiom, binintersectSubset2 =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( subset @ A @ B ) => ( ( binintersect @ A @ B ) = ( A ) ) ))).
% 3.99/1.18 thf('10', plain,
% 3.99/1.18 (( binintersectSubset2 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( subset @ X4 @ X6 ) => ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binintersectLsub, axiom, binintersectLsub =
% 3.99/1.18 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ A ))).
% 3.99/1.18 thf('11', plain,
% 3.99/1.18 (( binintersectLsub ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X4 ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binintersectEL, axiom, binintersectEL =
% 3.99/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 3.99/1.18 thf('12', plain,
% 3.99/1.18 (( binintersectEL ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binintersectSubset5, axiom, binintersectSubset5 =
% 3.99/1.18 (![A:$i,B:$i,C:$i]:
% 3.99/1.18 ( ( subset @ C @ A ) =>
% 3.99/1.18 ( ( subset @ C @ B ) => ( subset @ C @ ( binintersect @ A @ B ) ) ) ))).
% 3.99/1.18 thf('13', plain,
% 3.99/1.18 (( binintersectSubset5 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( subset @ X8 @ X4 ) =>
% 3.99/1.18 ( ( subset @ X8 @ X6 ) =>
% 3.99/1.18 ( subset @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binintersectI, axiom, binintersectI =
% 3.99/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ A ) =>
% 3.99/1.18 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ))).
% 3.99/1.18 thf('14', plain,
% 3.99/1.18 (( binintersectI ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ X4 ) =>
% 3.99/1.18 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binunionRsub, axiom, binunionRsub =
% 3.99/1.18 (![A:$i,B:$i]: ( subset @ B @ ( binunion @ A @ B ) ))).
% 3.99/1.18 thf('15', plain,
% 3.99/1.18 (( binunionRsub ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binunionLsub, axiom, binunionLsub =
% 3.99/1.18 (![A:$i,B:$i]: ( subset @ A @ ( binunion @ A @ B ) ))).
% 3.99/1.18 thf('16', plain,
% 3.99/1.18 (( binunionLsub ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]: ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binunionE, axiom, binunionE =
% 3.99/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 3.99/1.18 ( ( in @ Xx @ A ) | ( in @ Xx @ B ) ) ))).
% 3.99/1.18 thf('17', plain,
% 3.99/1.18 (( binunionE ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 3.99/1.18 ( ( in @ X8 @ X4 ) | ( in @ X8 @ X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binunionEcases, axiom, binunionEcases =
% 3.99/1.18 (![A:$i,B:$i,Xx:$i,Xphi:$o]:
% 3.99/1.18 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 3.99/1.18 ( ( ( in @ Xx @ A ) => ( Xphi ) ) =>
% 3.99/1.18 ( ( ( in @ Xx @ B ) => ( Xphi ) ) => ( Xphi ) ) ) ))).
% 3.99/1.18 thf('18', plain,
% 3.99/1.18 (( binunionEcases ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i,X10:$o]:
% 3.99/1.18 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 3.99/1.18 ( ( ( in @ X8 @ X4 ) => ( X10 ) ) =>
% 3.99/1.18 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binunionIR, axiom, binunionIR =
% 3.99/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 3.99/1.18 thf('19', plain,
% 3.99/1.18 (( binunionIR ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(upairset2IR, axiom, upairset2IR =
% 3.99/1.18 (![Xx:$i,Xy:$i]:
% 3.99/1.18 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 3.99/1.18 thf('20', plain,
% 3.99/1.18 (( upairset2IR ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(binunionIL, axiom, binunionIL =
% 3.99/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ A ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 3.99/1.18 thf('21', plain,
% 3.99/1.18 (( binunionIL ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ X4 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(sepSubset, axiom, sepSubset =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o )]:
% 3.99/1.18 ( subset @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ A ))).
% 3.99/1.18 thf('22', plain,
% 3.99/1.18 (( sepSubset ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o )]:
% 3.99/1.18 ( subset @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @ X4 ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(sepInPowerset, axiom, sepInPowerset =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o )]:
% 3.99/1.18 ( in @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ ( powerset @ A ) ))).
% 3.99/1.18 thf('23', plain,
% 3.99/1.18 (( sepInPowerset ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o )]:
% 3.99/1.18 ( in @
% 3.99/1.18 ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @
% 3.99/1.18 ( powerset @ X4 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(powersetsubset, axiom, powersetsubset =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 3.99/1.18 thf('24', plain,
% 3.99/1.18 (( powersetsubset ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( subset @ X4 @ X6 ) =>
% 3.99/1.18 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 3.99/1.18 thf('25', plain,
% 3.99/1.18 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(powersetE1, axiom, powersetE1 =
% 3.99/1.18 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 3.99/1.18 thf('26', plain,
% 3.99/1.18 (( powersetE1 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(powersetI1, axiom, powersetI1 =
% 3.99/1.18 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 3.99/1.18 thf('27', plain,
% 3.99/1.18 (( powersetI1 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 3.99/1.18 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 3.99/1.18 thf('28', plain,
% 3.99/1.18 (( subsetemptysetimpeq ) =
% 3.99/1.18 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setextsub, axiom, setextsub =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 3.99/1.18 thf('29', plain,
% 3.99/1.18 (( setextsub ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( subset @ X4 @ X6 ) =>
% 3.99/1.18 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(subset2powerset, axiom, subset2powerset =
% 3.99/1.18 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 3.99/1.18 thf('30', plain,
% 3.99/1.18 (( subset2powerset ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 3.99/1.18 (![A:$i,Xx:$i,B:$i]:
% 3.99/1.18 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 3.99/1.18 thf('31', plain,
% 3.99/1.18 (( setadjoinSub2 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setadjoinSub, axiom, setadjoinSub =
% 3.99/1.18 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 3.99/1.18 thf('32', plain,
% 3.99/1.18 (( setadjoinSub ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(subsetTrans, axiom, subsetTrans =
% 3.99/1.18 (![A:$i,B:$i,C:$i]:
% 3.99/1.18 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 3.99/1.18 thf('33', plain,
% 3.99/1.18 (( subsetTrans ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( subset @ X4 @ X6 ) =>
% 3.99/1.18 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 3.99/1.18 thf('34', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(notequalI2, axiom, notequalI2 =
% 3.99/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ( A ) != ( B ) ) ) ))).
% 3.99/1.18 thf('35', plain,
% 3.99/1.18 (( notequalI2 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ X4 ) =>
% 3.99/1.18 ( ( ~( in @ X8 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(notequalI1, axiom, notequalI1 =
% 3.99/1.18 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 3.99/1.18 thf('36', plain,
% 3.99/1.18 (( notequalI1 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(notsubsetI, axiom, notsubsetI =
% 3.99/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 3.99/1.18 thf('37', plain,
% 3.99/1.18 (( notsubsetI ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ X4 ) =>
% 3.99/1.18 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(subsetE2, axiom, subsetE2 =
% 3.99/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.99/1.18 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 3.99/1.18 thf('38', plain,
% 3.99/1.18 (( subsetE2 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( subset @ X4 @ X6 ) =>
% 3.99/1.18 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(subsetE, axiom, subsetE =
% 3.99/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.99/1.18 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 3.99/1.18 thf('39', plain,
% 3.99/1.18 (( subsetE ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(emptysetsubset, axiom, emptysetsubset =
% 3.99/1.18 (![A:$i]: ( subset @ emptyset @ A ))).
% 3.99/1.18 thf('40', plain,
% 3.99/1.18 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(subsetI2, axiom, subsetI2 =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 3.99/1.18 ( subset @ A @ B ) ))).
% 3.99/1.18 thf('41', plain,
% 3.99/1.18 (( subsetI2 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 3.99/1.18 ( subset @ X4 @ X6 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 3.99/1.18 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 3.99/1.18 thf('42', plain,
% 3.99/1.18 (( eqimpsubset1 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 3.99/1.18 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 3.99/1.18 thf('43', plain,
% 3.99/1.18 (( eqimpsubset2 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(subsetI1, axiom, subsetI1 =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 3.99/1.18 ( subset @ A @ B ) ))).
% 3.99/1.18 thf('44', plain,
% 3.99/1.18 (( subsetI1 ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 3.99/1.18 ( subset @ X4 @ X6 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(dsetconstr__Cong, axiom, dsetconstr__Cong =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( ( A ) = ( B ) ) =>
% 3.99/1.18 ( ![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 3.99/1.18 ( ( ![Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ A ) =>
% 3.99/1.18 ( ![Xy:$i]:
% 3.99/1.18 ( ( in @ Xy @ B ) =>
% 3.99/1.18 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) ) ) ) =>
% 3.99/1.18 ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =
% 3.99/1.18 ( dsetconstr @ B @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ) ) ))).
% 3.99/1.18 thf('45', plain,
% 3.99/1.18 (( dsetconstr__Cong ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ( X4 ) = ( X6 ) ) =>
% 3.99/1.18 ( ![X8:( $i > $o ),X10:( $i > $o )]:
% 3.99/1.18 ( ( ![X12:$i]:
% 3.99/1.18 ( ( in @ X12 @ X4 ) =>
% 3.99/1.18 ( ![X14:$i]:
% 3.99/1.18 ( ( in @ X14 @ X6 ) =>
% 3.99/1.18 ( ( ( X12 ) = ( X14 ) ) =>
% 3.99/1.18 ( ( X8 @ X12 ) <=> ( X10 @ X14 ) ) ) ) ) ) ) =>
% 3.99/1.18 ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) =
% 3.99/1.18 ( dsetconstr @ X6 @ ( ^[V_2:$i]: ( X10 @ V_2 ) ) ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(descr__Cong, axiom, descr__Cong =
% 3.99/1.18 (![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 3.99/1.18 ( ( ![Xx:$i,Xy:$i]:
% 3.99/1.18 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) =>
% 3.99/1.18 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 3.99/1.18 ( ( exu @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) =>
% 3.99/1.18 ( ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =
% 3.99/1.18 ( descr @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ) ) ))).
% 3.99/1.18 thf('46', plain,
% 3.99/1.18 (( descr__Cong ) =
% 3.99/1.18 ( ![X4:( $i > $o ),X6:( $i > $o )]:
% 3.99/1.18 ( ( ![X8:$i,X10:$i]:
% 3.99/1.18 ( ( ( X8 ) = ( X10 ) ) => ( ( X4 @ X8 ) <=> ( X6 @ X10 ) ) ) ) =>
% 3.99/1.18 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 3.99/1.18 ( ( exu @ ( ^[V_2:$i]: ( X6 @ V_2 ) ) ) =>
% 3.99/1.18 ( ( descr @ ( ^[V_3:$i]: ( X4 @ V_3 ) ) ) =
% 3.99/1.18 ( descr @ ( ^[V_4:$i]: ( X6 @ V_4 ) ) ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(exuEu, axiom, exuEu =
% 3.99/1.18 (![Xphi:( $i > $o )]:
% 3.99/1.18 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 3.99/1.18 ( ![Xx:$i,Xy:$i]:
% 3.99/1.18 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ))).
% 3.99/1.18 thf('47', plain,
% 3.99/1.18 (( exuEu ) =
% 3.99/1.18 ( ![X4:( $i > $o )]:
% 3.99/1.18 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 3.99/1.18 ( ![X6:$i,X8:$i]:
% 3.99/1.18 ( ( X4 @ X6 ) => ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(omega__Cong, axiom, omega__Cong = (( omega ) = ( omega ))).
% 3.99/1.18 thf('48', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setunion__Cong, axiom, setunion__Cong =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( ( A ) = ( B ) ) => ( ( setunion @ A ) = ( setunion @ B ) ) ))).
% 3.99/1.18 thf('49', plain,
% 3.99/1.18 (( setunion__Cong ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ( X4 ) = ( X6 ) ) => ( ( setunion @ X4 ) = ( setunion @ X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(powerset__Cong, axiom, powerset__Cong =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 3.99/1.18 thf('50', plain,
% 3.99/1.18 (( powerset__Cong ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 3.99/1.18 (![Xx:$i,Xy:$i]:
% 3.99/1.18 ( ( ( Xx ) = ( Xy ) ) =>
% 3.99/1.18 ( ![Xz:$i,Xu:$i]:
% 3.99/1.18 ( ( ( Xz ) = ( Xu ) ) =>
% 3.99/1.18 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 3.99/1.18 thf('51', plain,
% 3.99/1.18 (( setadjoin__Cong ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ( X4 ) = ( X6 ) ) =>
% 3.99/1.18 ( ![X8:$i,X10:$i]:
% 3.99/1.18 ( ( ( X8 ) = ( X10 ) ) =>
% 3.99/1.18 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(emptyset__Cong, axiom, emptyset__Cong = (( emptyset ) = ( emptyset ))).
% 3.99/1.18 thf('52', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(exu__Cong, axiom, exu__Cong =
% 3.99/1.18 (![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 3.99/1.18 ( ( ![Xx:$i,Xy:$i]:
% 3.99/1.18 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) =>
% 3.99/1.18 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) <=>
% 3.99/1.18 ( exu @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ))).
% 3.99/1.18 thf('53', plain,
% 3.99/1.18 (( exu__Cong ) =
% 3.99/1.18 ( ![X4:( $i > $o ),X6:( $i > $o )]:
% 3.99/1.18 ( ( ![X8:$i,X10:$i]:
% 3.99/1.18 ( ( ( X8 ) = ( X10 ) ) => ( ( X4 @ X8 ) <=> ( X6 @ X10 ) ) ) ) =>
% 3.99/1.18 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) <=>
% 3.99/1.18 ( exu @ ( ^[V_2:$i]: ( X6 @ V_2 ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(exuE3u, axiom, exuE3u =
% 3.99/1.18 (![Xphi:( $i > $o )]:
% 3.99/1.18 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 3.99/1.18 ( ![Xx:$i,Xy:$i]:
% 3.99/1.18 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ))).
% 3.99/1.18 thf('54', plain,
% 3.99/1.18 (( exuE3u ) =
% 3.99/1.18 ( ![X4:( $i > $o )]:
% 3.99/1.18 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 3.99/1.18 ( ![X6:$i,X8:$i]:
% 3.99/1.18 ( ( X4 @ X6 ) => ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(in__Cong, axiom, in__Cong =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( ( A ) = ( B ) ) =>
% 3.99/1.18 ( ![Xx:$i,Xy:$i]:
% 3.99/1.18 ( ( ( Xx ) = ( Xy ) ) => ( ( in @ Xx @ A ) <=> ( in @ Xy @ B ) ) ) ) ))).
% 3.99/1.18 thf('55', plain,
% 3.99/1.18 (( in__Cong ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ( X4 ) = ( X6 ) ) =>
% 3.99/1.18 ( ![X8:$i,X10:$i]:
% 3.99/1.18 ( ( ( X8 ) = ( X10 ) ) =>
% 3.99/1.18 ( ( in @ X8 @ X4 ) <=> ( in @ X10 @ X6 ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(inCongP, axiom, inCongP =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( ( A ) = ( B ) ) =>
% 3.99/1.18 ( ![Xx:$i,Xy:$i]:
% 3.99/1.18 ( ( ( Xx ) = ( Xy ) ) => ( ( in @ Xx @ A ) => ( in @ Xy @ B ) ) ) ) ))).
% 3.99/1.18 thf('56', plain,
% 3.99/1.18 (( inCongP ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ( X4 ) = ( X6 ) ) =>
% 3.99/1.18 ( ![X8:$i,X10:$i]:
% 3.99/1.18 ( ( ( X8 ) = ( X10 ) ) =>
% 3.99/1.18 ( ( in @ X8 @ X4 ) => ( in @ X10 @ X6 ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(exuI2, axiom, exuI2 =
% 3.99/1.18 (![Xphi:( $i > $o )]:
% 3.99/1.18 ( ( ?[Xx:$i]: ( ![Xy:$i]: ( ( Xphi @ Xy ) <=> ( ( Xy ) = ( Xx ) ) ) ) ) =>
% 3.99/1.18 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ))).
% 3.99/1.18 thf('57', plain,
% 3.99/1.18 (( exuI2 ) =
% 3.99/1.18 ( ![X4:( $i > $o )]:
% 3.99/1.18 ( ( ?[X6:$i]: ( ![X8:$i]: ( ( X4 @ X8 ) <=> ( ( X8 ) = ( X6 ) ) ) ) ) =>
% 3.99/1.18 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(exuI3, axiom, exuI3 =
% 3.99/1.18 (![Xphi:( $i > $o )]:
% 3.99/1.18 ( ( ?[Xx:$i]: ( Xphi @ Xx ) ) =>
% 3.99/1.18 ( ( ![Xx:$i,Xy:$i]:
% 3.99/1.18 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) =>
% 3.99/1.18 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 3.99/1.18 thf('58', plain,
% 3.99/1.18 (( exuI3 ) =
% 3.99/1.18 ( ![X4:( $i > $o )]:
% 3.99/1.18 ( ( ?[X6:$i]: ( X4 @ X6 ) ) =>
% 3.99/1.18 ( ( ![X8:$i,X10:$i]:
% 3.99/1.18 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( ( X8 ) = ( X10 ) ) ) ) ) =>
% 3.99/1.18 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(exuI1, axiom, exuI1 =
% 3.99/1.18 (![Xphi:( $i > $o )]:
% 3.99/1.18 ( ( ?[Xx:$i]:
% 3.99/1.18 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 3.99/1.18 ( Xphi @ Xx ) ) ) =>
% 3.99/1.18 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ))).
% 3.99/1.18 thf('59', plain,
% 3.99/1.18 (( exuI1 ) =
% 3.99/1.18 ( ![X4:( $i > $o )]:
% 3.99/1.18 ( ( ?[X6:$i]:
% 3.99/1.18 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 3.99/1.18 ( X4 @ X6 ) ) ) =>
% 3.99/1.18 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(notdallE, axiom, notdallE =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o )]:
% 3.99/1.18 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) =>
% 3.99/1.18 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))).
% 3.99/1.18 thf('60', plain,
% 3.99/1.18 (( notdallE ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o )]:
% 3.99/1.18 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) =>
% 3.99/1.18 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(notdexE, axiom, notdexE =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o )]:
% 3.99/1.18 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) =>
% 3.99/1.18 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))).
% 3.99/1.18 thf('61', plain,
% 3.99/1.18 (( notdexE ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o )]:
% 3.99/1.18 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 3.99/1.18 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(prop2set2propI, axiom, prop2set2propI =
% 3.99/1.18 (![Xphi:$o]: ( ( Xphi ) => ( set2prop @ ( prop2set @ Xphi ) ) ))).
% 3.99/1.18 thf('62', plain,
% 3.99/1.18 (( prop2set2propI ) =
% 3.99/1.18 ( ![X4:$o]: ( ( X4 ) => ( set2prop @ ( prop2set @ X4 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(prop2setI, axiom, prop2setI =
% 3.99/1.18 (![Xphi:$o]: ( ( Xphi ) => ( in @ emptyset @ ( prop2set @ Xphi ) ) ))).
% 3.99/1.18 thf('63', plain,
% 3.99/1.18 (( prop2setI ) =
% 3.99/1.18 ( ![X4:$o]: ( ( X4 ) => ( in @ emptyset @ ( prop2set @ X4 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(quantDeMorgan4, axiom, quantDeMorgan4 =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o )]:
% 3.99/1.18 ( ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) =>
% 3.99/1.18 ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) ))).
% 3.99/1.18 thf('64', plain,
% 3.99/1.18 (( quantDeMorgan4 ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o )]:
% 3.99/1.18 ( ( ?[X8:$i]: ( ( ~( X6 @ X8 ) ) & ( in @ X8 @ X4 ) ) ) =>
% 3.99/1.18 ( ~( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( X6 @ X10 ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(quantDeMorgan3, axiom, quantDeMorgan3 =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o )]:
% 3.99/1.18 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) =>
% 3.99/1.18 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))).
% 3.99/1.18 thf('65', plain,
% 3.99/1.18 (( quantDeMorgan3 ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o )]:
% 3.99/1.18 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 3.99/1.18 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(quantDeMorgan2, axiom, quantDeMorgan2 =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o )]:
% 3.99/1.18 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) =>
% 3.99/1.18 ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) ))).
% 3.99/1.18 thf('66', plain,
% 3.99/1.18 (( quantDeMorgan2 ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o )]:
% 3.99/1.18 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( ~( X6 @ X8 ) ) ) ) =>
% 3.99/1.18 ( ~( ?[X10:$i]: ( ( X6 @ X10 ) & ( in @ X10 @ X4 ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(quantDeMorgan1, axiom, quantDeMorgan1 =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o )]:
% 3.99/1.18 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) =>
% 3.99/1.18 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))).
% 3.99/1.18 thf('67', plain,
% 3.99/1.18 (( quantDeMorgan1 ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o )]:
% 3.99/1.18 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) =>
% 3.99/1.18 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(vacuousDall, axiom, vacuousDall =
% 3.99/1.18 (![Xphi:( $i > $o ),Xx:$i]: ( ( in @ Xx @ emptyset ) => ( Xphi @ Xx ) ))).
% 3.99/1.18 thf('68', plain,
% 3.99/1.18 (( vacuousDall ) =
% 3.99/1.18 ( ![X4:( $i > $o ),X6:$i]: ( ( in @ X6 @ emptyset ) => ( X4 @ X6 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(emptyE1, axiom, emptyE1 =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o )]:
% 3.99/1.18 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) =>
% 3.99/1.18 ( ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) = ( emptyset ) ) =>
% 3.99/1.18 ( $false ) ) ))).
% 3.99/1.18 thf('69', plain,
% 3.99/1.18 (( emptyE1 ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o )]:
% 3.99/1.18 ( ( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) =>
% 3.99/1.18 ( ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = ( emptyset ) ) =>
% 3.99/1.18 ( $false ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(upairsetIR, axiom, upairsetIR =
% 3.99/1.18 (![Xx:$i,Xy:$i]:
% 3.99/1.18 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 3.99/1.18 thf('70', plain,
% 3.99/1.18 (( upairsetIR ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(upairsetIL, axiom, upairsetIL =
% 3.99/1.18 (![Xx:$i,Xy:$i]:
% 3.99/1.18 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 3.99/1.18 thf('71', plain,
% 3.99/1.18 (( upairsetIL ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(upairsetE, axiom, upairsetE =
% 3.99/1.18 (![Xx:$i,Xy:$i,Xz:$i]:
% 3.99/1.18 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 3.99/1.18 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 3.99/1.18 thf('72', plain,
% 3.99/1.18 (( upairsetE ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 3.99/1.18 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(singletonsswitch, axiom, singletonsswitch =
% 3.99/1.18 (![Xx:$i,Xy:$i]:
% 3.99/1.18 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 3.99/1.18 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 3.99/1.18 thf('73', plain,
% 3.99/1.18 (( singletonsswitch ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 3.99/1.18 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(eqinunit, axiom, eqinunit =
% 3.99/1.18 (![Xx:$i,Xy:$i]:
% 3.99/1.18 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 3.99/1.18 thf('74', plain,
% 3.99/1.18 (( eqinunit ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(notinsingleton, axiom, notinsingleton =
% 3.99/1.18 (![Xx:$i,Xy:$i]:
% 3.99/1.18 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 3.99/1.18 thf('75', plain,
% 3.99/1.18 (( notinsingleton ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ( X4 ) != ( X6 ) ) =>
% 3.99/1.18 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(uniqinunit, axiom, uniqinunit =
% 3.99/1.18 (![Xx:$i,Xy:$i]:
% 3.99/1.18 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 3.99/1.18 thf('76', plain,
% 3.99/1.18 (( uniqinunit ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(nonemptyImpWitness, axiom, nonemptyImpWitness =
% 3.99/1.18 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 3.99/1.18 thf('77', plain,
% 3.99/1.18 (( nonemptyImpWitness ) =
% 3.99/1.18 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(exuE2, axiom, exuE2 =
% 3.99/1.18 (![Xphi:( $i > $o )]:
% 3.99/1.18 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 3.99/1.18 ( ?[Xx:$i]: ( ![Xy:$i]: ( ( Xphi @ Xy ) <=> ( ( Xy ) = ( Xx ) ) ) ) ) ))).
% 3.99/1.18 thf('78', plain,
% 3.99/1.18 (( exuE2 ) =
% 3.99/1.18 ( ![X4:( $i > $o )]:
% 3.99/1.18 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 3.99/1.18 ( ?[X6:$i]: ( ![X8:$i]: ( ( X4 @ X8 ) <=> ( ( X8 ) = ( X6 ) ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(subPowSU, axiom, subPowSU =
% 3.99/1.18 (![A:$i,Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ A ) => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ))).
% 3.99/1.18 thf('79', plain,
% 3.99/1.18 (( subPowSU ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( in @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ ( setunion @ X4 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setunionE, axiom, setunionE =
% 3.99/1.18 (![A:$i,Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ ( setunion @ A ) ) =>
% 3.99/1.18 ( ![Xphi:$o]:
% 3.99/1.18 ( ( ![B:$i]: ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( Xphi ) ) ) ) =>
% 3.99/1.18 ( Xphi ) ) ) ))).
% 3.99/1.18 thf('80', plain,
% 3.99/1.18 (( setunionE ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( in @ X6 @ ( setunion @ X4 ) ) =>
% 3.99/1.18 ( ![X8:$o]:
% 3.99/1.18 ( ( ![X10:$i]:
% 3.99/1.18 ( ( in @ X6 @ X10 ) => ( ( in @ X10 @ X4 ) => ( X8 ) ) ) ) =>
% 3.99/1.18 ( X8 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setunionI, axiom, setunionI =
% 3.99/1.18 (![A:$i,Xx:$i,B:$i]:
% 3.99/1.18 ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( in @ Xx @ ( setunion @ A ) ) ) ))).
% 3.99/1.18 thf('81', plain,
% 3.99/1.18 (( setunionI ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X6 @ X8 ) =>
% 3.99/1.18 ( ( in @ X8 @ X4 ) => ( in @ X6 @ ( setunion @ X4 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(powersetE, axiom, powersetE =
% 3.99/1.18 (![A:$i,B:$i,Xx:$i]:
% 3.99/1.18 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 3.99/1.18 thf('82', plain,
% 3.99/1.18 (( powersetE ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.99/1.18 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(emptyInPowerset, axiom, emptyInPowerset =
% 3.99/1.18 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 3.99/1.18 thf('83', plain,
% 3.99/1.18 (( emptyInPowerset ) =
% 3.99/1.18 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(emptyinPowerset, axiom, emptyinPowerset =
% 3.99/1.18 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 3.99/1.18 thf('84', plain,
% 3.99/1.18 (( emptyinPowerset ) =
% 3.99/1.18 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(powersetI, axiom, powersetI =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 3.99/1.18 ( in @ B @ ( powerset @ A ) ) ))).
% 3.99/1.18 thf('85', plain,
% 3.99/1.18 (( powersetI ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 3.99/1.18 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setoftrueEq, axiom, setoftrueEq =
% 3.99/1.18 (![A:$i]: ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( $true ) ) ) = ( A ) ))).
% 3.99/1.18 thf('86', plain,
% 3.99/1.18 (( setoftrueEq ) =
% 3.99/1.18 ( ![X4:$i]: ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( $true ) ) ) = ( X4 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setadjoinOr, axiom, setadjoinOr =
% 3.99/1.18 (![Xx:$i,A:$i,Xy:$i]:
% 3.99/1.18 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 3.99/1.18 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 3.99/1.18 thf('87', plain,
% 3.99/1.18 (( setadjoinOr ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 3.99/1.18 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setadjoinE, axiom, setadjoinE =
% 3.99/1.18 (![Xx:$i,A:$i,Xy:$i]:
% 3.99/1.18 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 3.99/1.18 ( ![Xphi:$o]:
% 3.99/1.18 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 3.99/1.18 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 3.99/1.18 thf('88', plain,
% 3.99/1.18 (( setadjoinE ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 3.99/1.18 ( ![X10:$o]:
% 3.99/1.18 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 3.99/1.18 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setadjoinIR, axiom, setadjoinIR =
% 3.99/1.18 (![Xx:$i,A:$i,Xy:$i]:
% 3.99/1.18 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 3.99/1.18 thf('89', plain,
% 3.99/1.18 (( setadjoinIR ) =
% 3.99/1.18 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 3.99/1.18 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 3.99/1.18 thf('90', plain,
% 3.99/1.18 (( emptyinunitempty ) =
% 3.99/1.18 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 3.99/1.18 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 3.99/1.18 thf('91', plain,
% 3.99/1.18 (( emptyinunitempty ) =
% 3.99/1.18 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setadjoinIL, axiom, setadjoinIL =
% 3.99/1.18 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 3.99/1.18 thf('92', plain,
% 3.99/1.18 (( setadjoinIL ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(nonemptyI1, axiom, nonemptyI1 =
% 3.99/1.18 (![A:$i]: ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) => ( nonempty @ A ) ))).
% 3.99/1.18 thf('93', plain,
% 3.99/1.18 (( nonemptyI1 ) =
% 3.99/1.18 ( ![X4:$i]: ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) => ( nonempty @ X4 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(nonemptyI, axiom, nonemptyI =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ A ) =>
% 3.99/1.18 ( ( Xphi @ Xx ) =>
% 3.99/1.18 ( nonempty @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 3.99/1.18 thf('94', plain,
% 3.99/1.18 (( nonemptyI ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ X4 ) =>
% 3.99/1.18 ( ( X6 @ X8 ) =>
% 3.99/1.18 ( nonempty @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(nonemptyE1, axiom, nonemptyE1 =
% 3.99/1.18 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 3.99/1.18 thf('95', plain,
% 3.99/1.18 (( nonemptyE1 ) =
% 3.99/1.18 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(nonempty, axiom,(( nonempty ) = (^[Xx:$i]: ( ( Xx ) != ( emptyset ) )))).
% 3.99/1.18 thf('96', plain, (( nonempty ) = ( ^[Xx:$i]: ( ( Xx ) != ( emptyset ) ) )),
% 3.99/1.18 inference('simplify_rw_rule', [status(thm)], [nonempty])).
% 3.99/1.18 thf('97', plain, (( nonempty ) = ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setbeta, axiom, setbeta =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ A ) =>
% 3.99/1.18 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) <=>
% 3.99/1.18 ( Xphi @ Xx ) ) ))).
% 3.99/1.18 thf('98', plain,
% 3.99/1.18 (( setbeta ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ X4 ) =>
% 3.99/1.18 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=>
% 3.99/1.18 ( X6 @ X8 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(noeltsimpempty, axiom, noeltsimpempty =
% 3.99/1.18 (![A:$i]:
% 3.99/1.18 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 3.99/1.18 thf('99', plain,
% 3.99/1.18 (( noeltsimpempty ) =
% 3.99/1.18 ( ![X4:$i]:
% 3.99/1.18 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(emptyI, axiom, emptyI =
% 3.99/1.18 (![A:$i]:
% 3.99/1.18 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 3.99/1.18 thf('100', plain,
% 3.99/1.18 (( emptyI ) =
% 3.99/1.18 ( ![X4:$i]:
% 3.99/1.18 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(setext, axiom, setext =
% 3.99/1.18 (![A:$i,B:$i]:
% 3.99/1.18 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 3.99/1.18 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 3.99/1.18 ( ( A ) = ( B ) ) ) ))).
% 3.99/1.18 thf('101', plain,
% 3.99/1.18 (( setext ) =
% 3.99/1.18 ( ![X4:$i,X6:$i]:
% 3.99/1.18 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 3.99/1.18 ( ( ![X10:$i]: ( ( in @ X10 @ X6 ) => ( in @ X10 @ X4 ) ) ) =>
% 3.99/1.18 ( ( X4 ) = ( X6 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(exuE3e, axiom, exuE3e =
% 3.99/1.18 (![Xphi:( $i > $o )]:
% 3.99/1.18 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) => ( ?[Xx:$i]: ( Xphi @ Xx ) ) ))).
% 3.99/1.18 thf('102', plain,
% 3.99/1.18 (( exuE3e ) =
% 3.99/1.18 ( ![X4:( $i > $o )]:
% 3.99/1.18 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) => ( ?[X6:$i]: ( X4 @ X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(notinemptyset, axiom, notinemptyset =
% 3.99/1.18 (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 3.99/1.18 thf('103', plain,
% 3.99/1.18 (( notinemptyset ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(emptysetimpfalse, axiom, emptysetimpfalse =
% 3.99/1.18 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( $false ) ))).
% 3.99/1.18 thf('104', plain,
% 3.99/1.18 (( emptysetimpfalse ) =
% 3.99/1.18 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( $false ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(emptysetE, axiom, emptysetE =
% 3.99/1.18 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( ![Xphi:$o]: ( Xphi ) ) ))).
% 3.99/1.18 thf('105', plain,
% 3.99/1.18 (( emptysetE ) =
% 3.99/1.18 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( ![X6:$o]: ( X6 ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(prop2setE, axiom, prop2setE =
% 3.99/1.18 (![Xphi:$o,Xx:$i]: ( ( in @ Xx @ ( prop2set @ Xphi ) ) => ( Xphi ) ))).
% 3.99/1.18 thf('106', plain,
% 3.99/1.18 (( prop2setE ) =
% 3.99/1.18 ( ![X4:$o,X6:$i]: ( ( in @ X6 @ ( prop2set @ X4 ) ) => ( X4 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(exuE1, axiom, exuE1 =
% 3.99/1.18 (![Xphi:( $i > $o )]:
% 3.99/1.18 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 3.99/1.18 ( ?[Xx:$i]:
% 3.99/1.18 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 3.99/1.18 ( Xphi @ Xx ) ) ) ))).
% 3.99/1.18 thf('107', plain,
% 3.99/1.18 (( exuE1 ) =
% 3.99/1.18 ( ![X4:( $i > $o )]:
% 3.99/1.18 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 3.99/1.18 ( ?[X6:$i]:
% 3.99/1.18 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 3.99/1.18 ( X4 @ X6 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(dsetconstrER, axiom, dsetconstrER =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 3.99/1.18 ( Xphi @ Xx ) ))).
% 3.99/1.18 thf('108', plain,
% 3.99/1.18 (( dsetconstrER ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 3.99/1.18 ( X6 @ X8 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(dsetconstrEL, axiom, dsetconstrEL =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 3.99/1.18 ( in @ Xx @ A ) ))).
% 3.99/1.18 thf('109', plain,
% 3.99/1.18 (( dsetconstrEL ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 3.99/1.18 ( in @ X8 @ X4 ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(dsetconstrI, axiom, dsetconstrI =
% 3.99/1.18 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ A ) =>
% 3.99/1.18 ( ( Xphi @ Xx ) =>
% 3.99/1.18 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 3.99/1.18 thf('110', plain,
% 3.99/1.18 (( dsetconstrI ) =
% 3.99/1.18 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ X4 ) =>
% 3.99/1.18 ( ( X6 @ X8 ) =>
% 3.99/1.18 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(descrp, axiom, descrp =
% 3.99/1.18 (![Xphi:( $i > $o )]:
% 3.99/1.18 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 3.99/1.18 ( Xphi @ ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 3.99/1.18 thf('111', plain,
% 3.99/1.18 (( descrp ) =
% 3.99/1.18 ( ![X4:( $i > $o )]:
% 3.99/1.18 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 3.99/1.18 ( X4 @ ( descr @ ( ^[V_2:$i]: ( X4 @ V_2 ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(wellorderingAx, axiom, wellorderingAx =
% 3.99/1.18 (![A:$i]:
% 3.99/1.18 ( ?[B:$i]:
% 3.99/1.18 ( ( ![C:$i]:
% 3.99/1.18 ( ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) &
% 3.99/1.18 ( ?[Xx:$i]: ( in @ Xx @ C ) ) ) =>
% 3.99/1.18 ( ?[D:$i,Xx:$i]:
% 3.99/1.18 ( ( ![E:$i]:
% 3.99/1.18 ( ( in @ E @ B ) =>
% 3.99/1.18 ( ( ![Xy:$i]: ( ( in @ Xy @ E ) => ( in @ Xy @ D ) ) ) |
% 3.99/1.18 ( in @ Xx @ E ) ) ) ) &
% 3.99/1.18 ( ~( ?[Xy:$i]: ( ( in @ Xy @ C ) & ( in @ Xy @ D ) ) ) ) &
% 3.99/1.18 ( in @ Xx @ C ) & ( in @ D @ B ) ) ) ) ) &
% 3.99/1.18 ( ![C:$i,D:$i]:
% 3.99/1.18 ( ( ( in @ C @ B ) & ( in @ D @ B ) ) =>
% 3.99/1.18 ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ D ) ) ) |
% 3.99/1.18 ( ![Xx:$i]: ( ( in @ Xx @ D ) => ( in @ Xx @ C ) ) ) ) ) ) &
% 3.99/1.18 ( ![Xx:$i,Xy:$i]:
% 3.99/1.18 ( ( ( in @ Xx @ A ) & ( in @ Xy @ A ) ) =>
% 3.99/1.18 ( ( ![C:$i]:
% 3.99/1.18 ( ( in @ C @ B ) => ( ( in @ Xx @ C ) <=> ( in @ Xy @ C ) ) ) ) =>
% 3.99/1.18 ( ( Xx ) = ( Xy ) ) ) ) ) &
% 3.99/1.18 ( ![C:$i]:
% 3.99/1.18 ( ( in @ C @ B ) =>
% 3.99/1.18 ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) ) ) ) ))).
% 3.99/1.18 thf('112', plain,
% 3.99/1.18 (( wellorderingAx ) =
% 3.99/1.18 ( ![X4:$i]:
% 3.99/1.18 ( ?[X6:$i]:
% 3.99/1.18 ( ( ![X8:$i]:
% 3.99/1.18 ( ( ( ![X10:$i]: ( ( in @ X10 @ X8 ) => ( in @ X10 @ X4 ) ) ) &
% 3.99/1.18 ( ?[X12:$i]: ( in @ X12 @ X8 ) ) ) =>
% 3.99/1.18 ( ?[X14:$i,X16:$i]:
% 3.99/1.18 ( ( ![X18:$i]:
% 3.99/1.18 ( ( in @ X18 @ X6 ) =>
% 3.99/1.18 ( ( ![X20:$i]:
% 3.99/1.18 ( ( in @ X20 @ X18 ) => ( in @ X20 @ X14 ) ) ) |
% 3.99/1.18 ( in @ X16 @ X18 ) ) ) ) &
% 3.99/1.18 ( ~( ?[X22:$i]: ( ( in @ X22 @ X8 ) & ( in @ X22 @ X14 ) ) ) ) &
% 3.99/1.18 ( in @ X16 @ X8 ) & ( in @ X14 @ X6 ) ) ) ) ) &
% 3.99/1.18 ( ![X24:$i,X26:$i]:
% 3.99/1.18 ( ( ( in @ X24 @ X6 ) & ( in @ X26 @ X6 ) ) =>
% 3.99/1.18 ( ( ![X28:$i]: ( ( in @ X28 @ X24 ) => ( in @ X28 @ X26 ) ) ) |
% 3.99/1.18 ( ![X30:$i]: ( ( in @ X30 @ X26 ) => ( in @ X30 @ X24 ) ) ) ) ) ) &
% 3.99/1.18 ( ![X32:$i,X34:$i]:
% 3.99/1.18 ( ( ( in @ X32 @ X4 ) & ( in @ X34 @ X4 ) ) =>
% 3.99/1.18 ( ( ![X36:$i]:
% 3.99/1.18 ( ( in @ X36 @ X6 ) =>
% 3.99/1.18 ( ( in @ X32 @ X36 ) <=> ( in @ X34 @ X36 ) ) ) ) =>
% 3.99/1.18 ( ( X32 ) = ( X34 ) ) ) ) ) &
% 3.99/1.18 ( ![X38:$i]:
% 3.99/1.18 ( ( in @ X38 @ X6 ) =>
% 3.99/1.18 ( ![X40:$i]: ( ( in @ X40 @ X38 ) => ( in @ X40 @ X4 ) ) ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(foundationAx, axiom, foundationAx =
% 3.99/1.18 (![A:$i]:
% 3.99/1.18 ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) =>
% 3.99/1.18 ( ?[B:$i]:
% 3.99/1.18 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ A ) & ( in @ Xx @ B ) ) ) ) &
% 3.99/1.18 ( in @ B @ A ) ) ) ))).
% 3.99/1.18 thf('113', plain,
% 3.99/1.18 (( foundationAx ) =
% 3.99/1.18 ( ![X4:$i]:
% 3.99/1.18 ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) =>
% 3.99/1.18 ( ?[X8:$i]:
% 3.99/1.18 ( ( ~( ?[X10:$i]: ( ( in @ X10 @ X4 ) & ( in @ X10 @ X8 ) ) ) ) &
% 3.99/1.18 ( in @ X8 @ X4 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(replAx, axiom, replAx =
% 3.99/1.18 (![Xphi:( $i > $i > $o ),A:$i]:
% 3.99/1.18 ( ( ![Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ A ) => ( exu @ ( ^[Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ) ) =>
% 3.99/1.18 ( ?[B:$i]:
% 3.99/1.18 ( ![Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ B ) <=>
% 3.99/1.18 ( ?[Xy:$i]: ( ( Xphi @ Xy @ Xx ) & ( in @ Xy @ A ) ) ) ) ) ) ))).
% 3.99/1.18 thf('114', plain,
% 3.99/1.18 (( replAx ) =
% 3.99/1.18 ( ![X4:( $i > $i > $o ),X6:$i]:
% 3.99/1.18 ( ( ![X8:$i]:
% 3.99/1.18 ( ( in @ X8 @ X6 ) => ( exu @ ( ^[V_1:$i]: ( X4 @ X8 @ V_1 ) ) ) ) ) =>
% 3.99/1.18 ( ?[X10:$i]:
% 3.99/1.18 ( ![X12:$i]:
% 3.99/1.18 ( ( in @ X12 @ X10 ) <=>
% 3.99/1.18 ( ?[X14:$i]: ( ( X4 @ X14 @ X12 ) & ( in @ X14 @ X6 ) ) ) ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(omegaIndAx, axiom, omegaIndAx =
% 3.99/1.18 (![A:$i]:
% 3.99/1.18 ( ( ( in @ emptyset @ A ) &
% 3.99/1.18 ( ![Xx:$i]:
% 3.99/1.18 ( ( ( in @ Xx @ omega ) & ( in @ Xx @ A ) ) =>
% 3.99/1.18 ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) ) =>
% 3.99/1.18 ( ![Xx:$i]: ( ( in @ Xx @ omega ) => ( in @ Xx @ A ) ) ) ))).
% 3.99/1.18 thf('115', plain,
% 3.99/1.18 (( omegaIndAx ) =
% 3.99/1.18 ( ![X4:$i]:
% 3.99/1.18 ( ( ( in @ emptyset @ X4 ) &
% 3.99/1.18 ( ![X6:$i]:
% 3.99/1.18 ( ( ( in @ X6 @ omega ) & ( in @ X6 @ X4 ) ) =>
% 3.99/1.18 ( in @ ( setadjoin @ X6 @ X6 ) @ X4 ) ) ) ) =>
% 3.99/1.18 ( ![X8:$i]: ( ( in @ X8 @ omega ) => ( in @ X8 @ X4 ) ) ) ) )),
% 3.99/1.18 define([status(thm)])).
% 3.99/1.18 thf(omegaSAx, axiom, omegaSAx =
% 3.99/1.18 (![Xx:$i]:
% 3.99/1.18 ( ( in @ Xx @ omega ) => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ))).
% 3.99/1.19 thf('116', plain,
% 3.99/1.19 (( omegaSAx ) =
% 3.99/1.19 ( ![X4:$i]:
% 3.99/1.19 ( ( in @ X4 @ omega ) => ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) )),
% 3.99/1.19 define([status(thm)])).
% 3.99/1.19 thf(omega0Ax, axiom,(( omega0Ax ) = (in @ emptyset @ omega))).
% 3.99/1.19 thf('117', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 3.99/1.19 inference('simplify_rw_rule', [status(thm)], [omega0Ax])).
% 3.99/1.19 thf('118', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 3.99/1.19 define([status(thm)])).
% 3.99/1.19 thf(setunionAx, axiom, setunionAx =
% 3.99/1.19 (![A:$i,Xx:$i]:
% 3.99/1.19 ( ( in @ Xx @ ( setunion @ A ) ) <=>
% 3.99/1.19 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))).
% 3.99/1.19 thf('119', plain,
% 3.99/1.19 (( setunionAx ) =
% 3.99/1.19 ( ![X4:$i,X6:$i]:
% 3.99/1.19 ( ( in @ X6 @ ( setunion @ X4 ) ) <=>
% 3.99/1.19 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )),
% 3.99/1.19 define([status(thm)])).
% 3.99/1.19 thf(powersetAx, axiom, powersetAx =
% 3.99/1.19 (![A:$i,B:$i]:
% 3.99/1.19 ( ( in @ B @ ( powerset @ A ) ) <=>
% 3.99/1.19 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 3.99/1.19 thf('120', plain,
% 3.99/1.19 (( powersetAx ) =
% 3.99/1.19 ( ![X4:$i,X6:$i]:
% 3.99/1.19 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.99/1.19 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 3.99/1.19 define([status(thm)])).
% 3.99/1.19 thf(setadjoinAx, axiom, setadjoinAx =
% 3.99/1.19 (![Xx:$i,A:$i,Xy:$i]:
% 3.99/1.19 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 3.99/1.19 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 3.99/1.19 thf('121', plain,
% 3.99/1.19 (( setadjoinAx ) =
% 3.99/1.19 ( ![X4:$i,X6:$i,X8:$i]:
% 3.99/1.19 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 3.99/1.19 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 3.99/1.19 define([status(thm)])).
% 3.99/1.19 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 3.99/1.19 thf('122', plain,
% 3.99/1.19 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 3.99/1.19 define([status(thm)])).
% 3.99/1.19 thf(setextAx, axiom, setextAx =
% 3.99/1.19 (![A:$i,B:$i]:
% 3.99/1.19 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) <=> ( in @ Xx @ B ) ) ) =>
% 3.99/1.19 ( ( A ) = ( B ) ) ))).
% 3.99/1.19 thf('123', plain,
% 3.99/1.19 (( setextAx ) =
% 3.99/1.19 ( ![X4:$i,X6:$i]:
% 3.99/1.19 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 3.99/1.19 ( ( X4 ) = ( X6 ) ) ) )),
% 3.99/1.19 define([status(thm)])).
% 3.99/1.19 thf(exu, axiom,(( exu ) =
% 3.99/1.19 (^[Xphi:( $i > $o )]:
% 3.99/1.19 ( ?[Xx:$i]:
% 3.99/1.19 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & ( Xphi @ Xx ) ) )))).
% 3.99/1.19 thf('124', plain,
% 3.99/1.19 (( exu ) =
% 3.99/1.19 ( ^[Xphi:( $i > $o )]:
% 3.99/1.19 ( ?[Xx:$i]:
% 3.99/1.19 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 3.99/1.19 ( Xphi @ Xx ) ) ) )),
% 3.99/1.19 inference('simplify_rw_rule', [status(thm)], [exu])).
% 3.99/1.19 thf('125', plain,
% 3.99/1.19 (( exu ) =
% 3.99/1.19 ( ^[V_1:( $i > $o )]:
% 3.99/1.19 ( ?[X4:$i]:
% 3.99/1.19 ( ( ![X6:$i]: ( ( V_1 @ X6 ) => ( ( X4 ) = ( X6 ) ) ) ) &
% 3.99/1.19 ( V_1 @ X4 ) ) ) )),
% 3.99/1.19 define([status(thm)])).
% 3.99/1.19 thf(setminusEL, conjecture,
% 3.99/1.19 (( setextAx ) =>
% 3.99/1.19 ( ( emptysetAx ) =>
% 3.99/1.19 ( ( setadjoinAx ) =>
% 3.99/1.19 ( ( powersetAx ) =>
% 3.99/1.19 ( ( setunionAx ) =>
% 3.99/1.19 ( ( omega0Ax ) =>
% 3.99/1.19 ( ( omegaSAx ) =>
% 3.99/1.19 ( ( omegaIndAx ) =>
% 3.99/1.19 ( ( replAx ) =>
% 3.99/1.19 ( ( foundationAx ) =>
% 3.99/1.19 ( ( wellorderingAx ) =>
% 3.99/1.19 ( ( descrp ) =>
% 3.99/1.19 ( ( dsetconstrI ) =>
% 3.99/1.19 ( ( dsetconstrEL ) =>
% 3.99/1.19 ( ( dsetconstrER ) =>
% 3.99/1.19 ( ( exuE1 ) =>
% 3.99/1.19 ( ( prop2setE ) =>
% 3.99/1.19 ( ( emptysetE ) =>
% 3.99/1.19 ( ( emptysetimpfalse ) =>
% 3.99/1.19 ( ( notinemptyset ) =>
% 3.99/1.19 ( ( exuE3e ) =>
% 3.99/1.19 ( ( setext ) =>
% 3.99/1.19 ( ( emptyI ) =>
% 3.99/1.19 ( ( noeltsimpempty ) =>
% 3.99/1.19 ( ( setbeta ) =>
% 3.99/1.19 ( ( nonemptyE1 ) =>
% 3.99/1.19 ( ( nonemptyI ) =>
% 3.99/1.19 ( ( nonemptyI1 ) =>
% 3.99/1.19 ( ( setadjoinIL ) =>
% 3.99/1.19 ( ( emptyinunitempty ) =>
% 3.99/1.19 ( ( setadjoinIR ) =>
% 3.99/1.19 ( ( setadjoinE ) =>
% 3.99/1.19 ( (
% 3.99/1.19 setadjoinOr ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 setoftrueEq ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 powersetI ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 emptyinPowerset ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 emptyInPowerset ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 powersetE ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 setunionI ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 setunionE ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 subPowSU ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 exuE2 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 nonemptyImpWitness ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 uniqinunit ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 notinsingleton ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 eqinunit ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 singletonsswitch ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 upairsetE ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 upairsetIL ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 upairsetIR ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 emptyE1 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 vacuousDall ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 quantDeMorgan1 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 quantDeMorgan2 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 quantDeMorgan3 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 quantDeMorgan4 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 prop2setI ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 prop2set2propI ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 notdexE ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 notdallE ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 exuI1 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 exuI3 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 exuI2 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 inCongP ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in__Cong ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 exuE3u ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 exu__Cong ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 emptyset__Cong ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 setadjoin__Cong ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 powerset__Cong ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 setunion__Cong ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 omega__Cong ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 exuEu ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 descr__Cong ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 dsetconstr__Cong ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 subsetI1 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 eqimpsubset2 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 eqimpsubset1 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 subsetI2 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 emptysetsubset ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 subsetE ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 subsetE2 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 notsubsetI ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 notequalI1 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 notequalI2 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 subsetRefl ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 subsetTrans ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 setadjoinSub ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 setadjoinSub2 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 subset2powerset ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 setextsub ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 subsetemptysetimpeq ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 powersetI1 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 powersetE1 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 inPowerset ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 powersetsubset ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 sepInPowerset ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 sepSubset ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binunionIL ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 upairset2IR ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binunionIR ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binunionEcases ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binunionE ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binunionLsub ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binunionRsub ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersectI ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersectSubset5 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersectEL ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersectLsub ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersectSubset2 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersectSubset3 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersectER ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 disjointsetsI1 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersectRsub ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersectSubset4 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersectSubset1 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 bs114d ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 setminusI ) =>
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 A:$i,B:$i,
% 3.99/1.19 Xx:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 Xx @
% 3.99/1.19 (
% 3.99/1.19 setminus @
% 3.99/1.19 A @ B ) ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.99/1.19 thf(zf_stmt_0, conjecture,
% 3.99/1.19 (( ![X4:$i,X6:$i]:
% 3.99/1.19 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 3.99/1.19 ( ( X4 ) = ( X6 ) ) ) ) =>
% 3.99/1.19 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 3.99/1.19 ( ( ![X12:$i,X14:$i,X16:$i]:
% 3.99/1.19 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 3.99/1.19 ( ( in @ X16 @ X14 ) | ( ( X16 ) = ( X12 ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X18:$i,X20:$i]:
% 3.99/1.19 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 3.99/1.19 ( ![X22:$i]: ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X24:$i,X26:$i]:
% 3.99/1.19 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 3.99/1.19 ( ?[X28:$i]: ( ( in @ X26 @ X28 ) & ( in @ X28 @ X24 ) ) ) ) ) =>
% 3.99/1.19 ( ( in @ emptyset @ omega ) =>
% 3.99/1.19 ( ( ![X30:$i]:
% 3.99/1.19 ( ( in @ X30 @ omega ) =>
% 3.99/1.19 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 3.99/1.19 ( ( ![X32:$i]:
% 3.99/1.19 ( ( ( ![X34:$i]:
% 3.99/1.19 ( ( ( in @ X34 @ X32 ) & ( in @ X34 @ omega ) ) =>
% 3.99/1.19 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) &
% 3.99/1.19 ( in @ emptyset @ X32 ) ) =>
% 3.99/1.19 ( ![X36:$i]:
% 3.99/1.19 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 3.99/1.19 ( ( ![X42:$i]:
% 3.99/1.19 ( ( in @ X42 @ X40 ) =>
% 3.99/1.19 ( ?[X44:$i]:
% 3.99/1.19 ( ( X38 @ X42 @ X44 ) &
% 3.99/1.19 ( ![X46:$i]:
% 3.99/1.19 ( ( X38 @ X42 @ X46 ) =>
% 3.99/1.19 ( ( X44 ) = ( X46 ) ) ) ) ) ) ) ) =>
% 3.99/1.19 ( ?[X48:$i]:
% 3.99/1.19 ( ![X50:$i]:
% 3.99/1.19 ( ( in @ X50 @ X48 ) <=>
% 3.99/1.19 ( ?[X52:$i]:
% 3.99/1.19 ( ( in @ X52 @ X40 ) & ( X38 @ X52 @ X50 ) ) ) ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X54:$i]:
% 3.99/1.19 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 3.99/1.19 ( ?[X58:$i]:
% 3.99/1.19 ( ( in @ X58 @ X54 ) &
% 3.99/1.19 ( ~( ?[X60:$i]:
% 3.99/1.19 ( ( in @ X60 @ X58 ) & ( in @ X60 @ X54 ) ) ) ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X62:$i]:
% 3.99/1.19 ( ?[X64:$i]:
% 3.99/1.19 ( ( ![X96:$i]:
% 3.99/1.19 ( ( in @ X96 @ X64 ) =>
% 3.99/1.19 ( ![X98:$i]:
% 3.99/1.19 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) &
% 3.99/1.19 ( ![X90:$i,X92:$i]:
% 3.99/1.19 ( ( ( in @ X92 @ X62 ) & ( in @ X90 @ X62 ) ) =>
% 3.99/1.19 ( ( ![X94:$i]:
% 3.99/1.19 ( ( in @ X94 @ X64 ) =>
% 3.99/1.19 ( ( in @ X90 @ X94 ) <=>
% 3.99/1.19 ( in @ X92 @ X94 ) ) ) ) =>
% 3.99/1.19 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 3.99/1.19 ( ![X82:$i,X84:$i]:
% 3.99/1.19 ( ( ( in @ X84 @ X64 ) & ( in @ X82 @ X64 ) ) =>
% 3.99/1.19 ( ( ![X88:$i]:
% 3.99/1.19 ( ( in @ X88 @ X84 ) =>
% 3.99/1.19 ( in @ X88 @ X82 ) ) ) |
% 3.99/1.19 ( ![X86:$i]:
% 3.99/1.19 ( ( in @ X86 @ X82 ) =>
% 3.99/1.19 ( in @ X86 @ X84 ) ) ) ) ) ) &
% 3.99/1.19 ( ![X66:$i]:
% 3.99/1.19 ( ( ( ?[X70:$i]: ( in @ X70 @ X66 ) ) &
% 3.99/1.19 ( ![X68:$i]:
% 3.99/1.19 ( ( in @ X68 @ X66 ) =>
% 3.99/1.19 ( in @ X68 @ X62 ) ) ) ) =>
% 3.99/1.19 ( ?[X72:$i,X74:$i]:
% 3.99/1.19 ( ( in @ X72 @ X64 ) &
% 3.99/1.19 ( in @ X74 @ X66 ) &
% 3.99/1.19 ( ~( ?[X80:$i]:
% 3.99/1.19 ( ( in @ X80 @ X72 ) &
% 3.99/1.19 ( in @ X80 @ X66 ) ) ) ) &
% 3.99/1.19 ( ![X76:$i]:
% 3.99/1.19 ( ( in @ X76 @ X64 ) =>
% 3.99/1.19 ( ( in @ X74 @ X76 ) |
% 3.99/1.19 ( ![X78:$i]:
% 3.99/1.19 ( ( in @ X78 @ X76 ) =>
% 3.99/1.19 ( in @ X78 @ X72 ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X100:( $i > $o )]:
% 3.99/1.19 ( ( ?[X102:$i]:
% 3.99/1.19 ( ( X100 @ X102 ) &
% 3.99/1.19 ( ![X104:$i]:
% 3.99/1.19 ( ( X100 @ X104 ) =>
% 3.99/1.19 ( ( X102 ) = ( X104 ) ) ) ) ) ) =>
% 3.99/1.19 ( X100 @
% 3.99/1.19 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 3.99/1.19 ( ( in @ X110 @ X106 ) =>
% 3.99/1.19 ( ( X108 @ X110 ) =>
% 3.99/1.19 ( in @
% 3.99/1.19 X110 @
% 3.99/1.19 ( dsetconstr @
% 3.99/1.19 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 3.99/1.19 ( ( in @
% 3.99/1.19 X116 @
% 3.99/1.19 ( dsetconstr @
% 3.99/1.19 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 3.99/1.19 ( in @ X116 @ X112 ) ) ) =>
% 3.99/1.19 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 3.99/1.19 ( ( in @
% 3.99/1.19 X122 @
% 3.99/1.19 ( dsetconstr @
% 3.99/1.19 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 3.99/1.19 ( X120 @ X122 ) ) ) =>
% 3.99/1.19 ( ( ![X124:( $i > $o )]:
% 3.99/1.19 ( ( ?[X126:$i]:
% 3.99/1.19 ( ( X124 @ X126 ) &
% 3.99/1.19 ( ![X128:$i]:
% 3.99/1.19 ( ( X124 @ X128 ) =>
% 3.99/1.19 ( ( X126 ) = ( X128 ) ) ) ) ) ) =>
% 3.99/1.19 ( ?[X130:$i]:
% 3.99/1.19 ( ( X124 @ X130 ) &
% 3.99/1.19 ( ![X132:$i]:
% 3.99/1.19 ( ( X124 @ X132 ) =>
% 3.99/1.19 ( ( X130 ) = ( X132 ) ) ) ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X134:$o,X136:$i]:
% 3.99/1.19 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 3.99/1.19 ( X134 ) ) ) =>
% 3.99/1.19 ( ( ![X138:$i]:
% 3.99/1.19 ( ( in @ X138 @ emptyset ) =>
% 3.99/1.19 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 3.99/1.19 ( ( ![X142:$i]:
% 3.99/1.19 ( ( in @ X142 @ emptyset ) =>
% 3.99/1.19 ( $false ) ) ) =>
% 3.99/1.19 ( ( ![X144:$i]:
% 3.99/1.19 ( ~( in @ X144 @ emptyset ) ) ) =>
% 3.99/1.19 ( ( ![X146:( $i > $o )]:
% 3.99/1.19 ( ( ?[X148:$i]:
% 3.99/1.19 ( ( X146 @ X148 ) &
% 3.99/1.19 ( ![X150:$i]:
% 3.99/1.19 ( ( X146 @ X150 ) =>
% 3.99/1.19 ( ( X148 ) = ( X150 ) ) ) ) ) ) =>
% 3.99/1.19 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 3.99/1.19 ( ( ![X154:$i,X156:$i]:
% 3.99/1.19 ( ( ![X158:$i]:
% 3.99/1.19 ( ( in @ X158 @ X154 ) =>
% 3.99/1.19 ( in @ X158 @ X156 ) ) ) =>
% 3.99/1.19 ( ( ![X160:$i]:
% 3.99/1.19 ( ( in @ X160 @ X156 ) =>
% 3.99/1.19 ( in @ X160 @ X154 ) ) ) =>
% 3.99/1.19 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X162:$i]:
% 3.99/1.19 ( ( ![X164:$i]:
% 3.99/1.19 ( ~( in @ X164 @ X162 ) ) ) =>
% 3.99/1.19 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 3.99/1.19 ( ( ![X166:$i]:
% 3.99/1.19 ( ( ![X168:$i]:
% 3.99/1.19 ( ~( in @ X168 @ X166 ) ) ) =>
% 3.99/1.19 ( ( X166 ) =
% 3.99/1.19 ( emptyset ) ) ) ) =>
% 3.99/1.19 ( ( ![X170:$i,
% 3.99/1.19 X172:( $i > $o ),
% 3.99/1.19 X174:$i]:
% 3.99/1.19 ( ( in @ X174 @ X170 ) =>
% 3.99/1.19 ( ( in @
% 3.99/1.19 X174 @
% 3.99/1.19 ( dsetconstr @
% 3.99/1.19 X170 @
% 3.99/1.19 ( ^[V_5:$i]:
% 3.99/1.19 ( X172 @ V_5 ) ) ) ) <=>
% 3.99/1.19 ( X172 @ X174 ) ) ) ) =>
% 3.99/1.19 ( ( ![X176:$i]:
% 3.99/1.19 ( ( ( X176 ) !=
% 3.99/1.19 ( emptyset ) ) =>
% 3.99/1.19 ( ?[X178:$i]:
% 3.99/1.19 ( in @ X178 @ X176 ) ) ) ) =>
% 3.99/1.19 ( ( ![X180:$i,
% 3.99/1.19 X182:( $i > $o ),
% 3.99/1.19 X184:$i]:
% 3.99/1.19 ( ( in @ X184 @ X180 ) =>
% 3.99/1.19 ( ( X182 @ X184 ) =>
% 3.99/1.19 ( ( dsetconstr @
% 3.99/1.19 X180 @
% 3.99/1.19 ( ^[
% 3.99/1.19 V_6:$i]:
% 3.99/1.19 (
% 3.99/1.19 X182 @ V_6 ) ) ) !=
% 3.99/1.19 ( emptyset ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X186:$i]:
% 3.99/1.19 ( ( ?[X188:$i]:
% 3.99/1.19 ( in @
% 3.99/1.19 X188 @ X186 ) ) =>
% 3.99/1.19 ( ( X186 ) !=
% 3.99/1.19 ( emptyset ) ) ) ) =>
% 3.99/1.19 ( ( ![X190:$i,
% 3.99/1.19 X192:$i]:
% 3.99/1.19 ( in @
% 3.99/1.19 X190 @
% 3.99/1.19 ( setadjoin @
% 3.99/1.19 X190 @ X192 ) ) ) =>
% 3.99/1.19 ( ( in @
% 3.99/1.19 emptyset @
% 3.99/1.19 ( setadjoin @
% 3.99/1.19 emptyset @
% 3.99/1.19 emptyset ) ) =>
% 3.99/1.19 ( ( ![X194:$i,
% 3.99/1.19 X196:$i,
% 3.99/1.19 X198:$i]:
% 3.99/1.19 ( (
% 3.99/1.19 in @
% 3.99/1.19 X198 @
% 3.99/1.19 X196 ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X198 @
% 3.99/1.19 (
% 3.99/1.19 setadjoin
% 3.99/1.19 @
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% 3.99/1.19 X196 ) ) ) ) =>
% 3.99/1.19 ( ( ![
% 3.99/1.19 X200:$i,
% 3.99/1.19 X202:$i,
% 3.99/1.19 X204:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X204 @
% 3.99/1.19 (
% 3.99/1.19 setadjoin
% 3.99/1.19 @
% 3.99/1.19 X200 @
% 3.99/1.19 X202 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X206:$o]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 X204 ) =
% 3.99/1.19 (
% 3.99/1.19 X200 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 X206 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X204 @
% 3.99/1.19 X202 ) =>
% 3.99/1.19 (
% 3.99/1.19 X206 ) ) =>
% 3.99/1.19 (
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% 3.99/1.19 ( (
% 3.99/1.19 ![
% 3.99/1.19 X208:$i,
% 3.99/1.19 X210:$i,
% 3.99/1.19 X212:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X212 @
% 3.99/1.19 (
% 3.99/1.19 setadjoin
% 3.99/1.19 @
% 3.99/1.19 X208 @
% 3.99/1.19 X210 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X212 @
% 3.99/1.19 X210 ) |
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 X212 ) =
% 3.99/1.19 (
% 3.99/1.19 X208 ) ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X214:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 dsetconstr
% 3.99/1.19 @
% 3.99/1.19 X214 @
% 3.99/1.19 (
% 3.99/1.19 ^[
% 3.99/1.19 V_7:$i]:
% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 X214 ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X216:$i,
% 3.99/1.19 X218:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X220:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X220 @
% 3.99/1.19 X218 ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
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% 3.99/1.19 X216 ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X218 @
% 3.99/1.19 (
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% 3.99/1.19 X216 ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X222:$i]:
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 emptyset @
% 3.99/1.19 (
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% 3.99/1.19 X222 ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 in @
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X226:$i,
% 3.99/1.19 X228:$i,
% 3.99/1.19 X230:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
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% 3.99/1.19 (
% 3.99/1.19 powerset @
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% 3.99/1.19 (
% 3.99/1.19 (
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% 3.99/1.19 X228 ) =>
% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X232:$i,
% 3.99/1.19 X234:$i,
% 3.99/1.19 X236:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
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% 3.99/1.19 X236 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
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% 3.99/1.19 X232 ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X238:$i,
% 3.99/1.19 X240:$i]:
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
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% 3.99/1.19 X244:$i]:
% 3.99/1.19 (
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% 3.99/1.19 X244 ) =>
% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 ![
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% 3.99/1.19 X248:$i]:
% 3.99/1.19 (
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% 3.99/1.19 X246 ) =>
% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X250:(
% 3.99/1.19 $i > $o )]:
% 3.99/1.19 (
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% 3.99/1.19 X252:$i]:
% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
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% 3.99/1.19 X254 ) =>
% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 in @
% 3.99/1.19 X588 @
% 3.99/1.19 (
% 3.99/1.19 binunion @
% 3.99/1.19 X584 @
% 3.99/1.19 X586 ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X590:$i,
% 3.99/1.19 X592:$i]:
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X592 @
% 3.99/1.19 (
% 3.99/1.19 setadjoin
% 3.99/1.19 @
% 3.99/1.19 X590 @
% 3.99/1.19 (
% 3.99/1.19 setadjoin
% 3.99/1.19 @
% 3.99/1.19 X592 @
% 3.99/1.19 emptyset ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X594:$i,
% 3.99/1.19 X596:$i,
% 3.99/1.19 X598:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X598 @
% 3.99/1.19 X596 ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X598 @
% 3.99/1.19 (
% 3.99/1.19 binunion @
% 3.99/1.19 X594 @
% 3.99/1.19 X596 ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X600:$i,
% 3.99/1.19 X602:$i,
% 3.99/1.19 X604:$i,
% 3.99/1.19 X606:$o]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X604 @
% 3.99/1.19 (
% 3.99/1.19 binunion @
% 3.99/1.19 X600 @
% 3.99/1.19 X602 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X604 @
% 3.99/1.19 X600 ) =>
% 3.99/1.19 (
% 3.99/1.19 X606 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X604 @
% 3.99/1.19 X602 ) =>
% 3.99/1.19 (
% 3.99/1.19 X606 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 X606 ) ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X608:$i,
% 3.99/1.19 X610:$i,
% 3.99/1.19 X612:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X612 @
% 3.99/1.19 (
% 3.99/1.19 binunion @
% 3.99/1.19 X608 @
% 3.99/1.19 X610 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X612 @
% 3.99/1.19 X610 ) |
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X612 @
% 3.99/1.19 X608 ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X614:$i,
% 3.99/1.19 X616:$i]:
% 3.99/1.19 (
% 3.99/1.19 subset @
% 3.99/1.19 X614 @
% 3.99/1.19 (
% 3.99/1.19 binunion @
% 3.99/1.19 X614 @
% 3.99/1.19 X616 ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X618:$i,
% 3.99/1.19 X620:$i]:
% 3.99/1.19 (
% 3.99/1.19 subset @
% 3.99/1.19 X620 @
% 3.99/1.19 (
% 3.99/1.19 binunion @
% 3.99/1.19 X618 @
% 3.99/1.19 X620 ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X622:$i,
% 3.99/1.19 X624:$i,
% 3.99/1.19 X626:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X626 @
% 3.99/1.19 X622 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X626 @
% 3.99/1.19 X624 ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X626 @
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X622 @
% 3.99/1.19 X624 ) ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X628:$i,
% 3.99/1.19 X630:$i,
% 3.99/1.19 X632:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 subset @
% 3.99/1.19 X632 @
% 3.99/1.19 X628 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 subset @
% 3.99/1.19 X632 @
% 3.99/1.19 X630 ) =>
% 3.99/1.19 (
% 3.99/1.19 subset @
% 3.99/1.19 X632 @
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X628 @
% 3.99/1.19 X630 ) ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X634:$i,
% 3.99/1.19 X636:$i,
% 3.99/1.19 X638:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X638 @
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X634 @
% 3.99/1.19 X636 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X638 @
% 3.99/1.19 X634 ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X640:$i,
% 3.99/1.19 X642:$i]:
% 3.99/1.19 (
% 3.99/1.19 subset @
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X640 @
% 3.99/1.19 X642 ) @
% 3.99/1.19 X640 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X644:$i,
% 3.99/1.19 X646:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 subset @
% 3.99/1.19 X644 @
% 3.99/1.19 X646 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X644 @
% 3.99/1.19 X646 ) =
% 3.99/1.19 (
% 3.99/1.19 X644 ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X648:$i,
% 3.99/1.19 X650:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X648 @
% 3.99/1.19 X650 ) =
% 3.99/1.19 (
% 3.99/1.19 X650 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 subset @
% 3.99/1.19 X650 @
% 3.99/1.19 X648 ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X652:$i,
% 3.99/1.19 X654:$i,
% 3.99/1.19 X656:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X656 @
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X652 @
% 3.99/1.19 X654 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X656 @
% 3.99/1.19 X654 ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X658:$i,
% 3.99/1.19 X660:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ~(
% 3.99/1.19 ?[
% 3.99/1.19 X662:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X662 @
% 3.99/1.19 X658 ) &
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X662 @
% 3.99/1.19 X660 ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X658 @
% 3.99/1.19 X660 ) =
% 3.99/1.19 (
% 3.99/1.19 emptyset ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X664:$i,
% 3.99/1.19 X666:$i]:
% 3.99/1.19 (
% 3.99/1.19 subset @
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X664 @
% 3.99/1.19 X666 ) @
% 3.99/1.19 X666 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X668:$i,
% 3.99/1.19 X670:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 subset @
% 3.99/1.19 X670 @
% 3.99/1.19 X668 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X668 @
% 3.99/1.19 X670 ) =
% 3.99/1.19 (
% 3.99/1.19 X670 ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X672:$i,
% 3.99/1.19 X674:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X672 @
% 3.99/1.19 X674 ) =
% 3.99/1.19 (
% 3.99/1.19 X672 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 subset @
% 3.99/1.19 X672 @
% 3.99/1.19 X674 ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X676:$i,
% 3.99/1.19 X678:$i,
% 3.99/1.19 X680:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X676 @
% 3.99/1.19 (
% 3.99/1.19 binunion @
% 3.99/1.19 X678 @
% 3.99/1.19 X680 ) ) =
% 3.99/1.19 (
% 3.99/1.19 binunion @
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X676 @
% 3.99/1.19 X678 ) @
% 3.99/1.19 (
% 3.99/1.19 binintersect
% 3.99/1.19 @
% 3.99/1.19 X676 @
% 3.99/1.19 X680 ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X682:$i,
% 3.99/1.19 X684:$i,
% 3.99/1.19 X686:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X686 @
% 3.99/1.19 X682 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ~(
% 3.99/1.19 in @
% 3.99/1.19 X686 @
% 3.99/1.19 X684 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X686 @
% 3.99/1.19 (
% 3.99/1.19 dsetconstr
% 3.99/1.19 @
% 3.99/1.19 X682 @
% 3.99/1.19 (
% 3.99/1.19 ^[
% 3.99/1.19 V_15:$i]:
% 3.99/1.19 (
% 3.99/1.19 ~(
% 3.99/1.19 in @
% 3.99/1.19 V_15 @
% 3.99/1.19 X684 ) ) ) ) ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X688:$i,
% 3.99/1.19 X690:$i,
% 3.99/1.19 X692:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X692 @
% 3.99/1.19 (
% 3.99/1.19 dsetconstr
% 3.99/1.19 @
% 3.99/1.19 X688 @
% 3.99/1.19 (
% 3.99/1.19 ^[
% 3.99/1.19 V_16:$i]:
% 3.99/1.19 (
% 3.99/1.19 ~(
% 3.99/1.19 in @
% 3.99/1.19 V_16 @
% 3.99/1.19 X690 ) ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X692 @
% 3.99/1.19 X688 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.99/1.19 thf(zf_stmt_1, type, zip_tseitin_5 : $i > ( $i > $o ) > $o).
% 3.99/1.19 thf(zf_stmt_2, axiom,
% 3.99/1.19 (![X422:$i,X414:( $i > $o )]:
% 3.99/1.19 ( ( zip_tseitin_5 @ X422 @ X414 ) <=>
% 3.99/1.19 ( ( ![X424:$i]: ( zip_tseitin_4 @ X424 @ X422 @ X414 ) ) &
% 3.99/1.19 ( X414 @ X422 ) ) ))).
% 3.99/1.19 thf(zf_stmt_3, type, zip_tseitin_4 : $i > $i > ( $i > $o ) > $o).
% 3.99/1.19 thf(zf_stmt_4, axiom,
% 3.99/1.19 (![X424:$i,X422:$i,X414:( $i > $o )]:
% 3.99/1.19 ( ( zip_tseitin_4 @ X424 @ X422 @ X414 ) <=>
% 3.99/1.19 ( ( X414 @ X424 ) => ( ( X422 ) = ( X424 ) ) ) ))).
% 3.99/1.19 thf(zf_stmt_5, type, zip_tseitin_3 : $i > $i > $i > ( $i > $i > $o ) > $o).
% 3.99/1.19 thf(zf_stmt_6, axiom,
% 3.99/1.19 (![X52:$i,X50:$i,X40:$i,X38:( $i > $i > $o )]:
% 3.99/1.19 ( ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) <=>
% 3.99/1.19 ( ( X38 @ X52 @ X50 ) & ( in @ X52 @ X40 ) ) ))).
% 3.99/1.19 thf(zf_stmt_7, type, zip_tseitin_2 : $i > $i > $i > $o).
% 3.99/1.19 thf(zf_stmt_8, axiom,
% 3.99/1.19 (![X28:$i,X26:$i,X24:$i]:
% 3.99/1.19 ( ( zip_tseitin_2 @ X28 @ X26 @ X24 ) <=>
% 3.99/1.19 ( ( in @ X28 @ X24 ) & ( in @ X26 @ X28 ) ) ))).
% 3.99/1.19 thf(zf_stmt_9, type, zip_tseitin_1 : $i > $i > $i > $o).
% 3.99/1.19 thf(zf_stmt_10, axiom,
% 3.99/1.19 (![X22:$i,X20:$i,X18:$i]:
% 3.99/1.19 ( ( zip_tseitin_1 @ X22 @ X20 @ X18 ) <=>
% 3.99/1.19 ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ))).
% 3.99/1.19 thf(zf_stmt_11, type, zip_tseitin_0 : $i > $i > $i > $o).
% 3.99/1.19 thf(zf_stmt_12, axiom,
% 3.99/1.19 (![X16:$i,X14:$i,X12:$i]:
% 3.99/1.19 ( ( zip_tseitin_0 @ X16 @ X14 @ X12 ) <=>
% 3.99/1.19 ( ( ( X16 ) = ( X12 ) ) | ( in @ X16 @ X14 ) ) ))).
% 3.99/1.19 thf(zf_stmt_13, conjecture,
% 3.99/1.19 (( ![X4:$i,X6:$i]:
% 3.99/1.19 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 3.99/1.19 ( ( X4 ) = ( X6 ) ) ) ) =>
% 3.99/1.19 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 3.99/1.19 ( ( ![X12:$i,X14:$i,X16:$i]:
% 3.99/1.19 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 3.99/1.19 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 3.99/1.19 ( ( ![X18:$i,X20:$i]:
% 3.99/1.19 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 3.99/1.19 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 3.99/1.19 ( ( ![X24:$i,X26:$i]:
% 3.99/1.19 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 3.99/1.19 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 3.99/1.19 ( ( in @ emptyset @ omega ) =>
% 3.99/1.19 ( ( ![X30:$i]:
% 3.99/1.19 ( ( in @ X30 @ omega ) =>
% 3.99/1.19 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 3.99/1.19 ( ( ![X32:$i]:
% 3.99/1.19 ( ( ( in @ emptyset @ X32 ) &
% 3.99/1.19 ( ![X34:$i]:
% 3.99/1.19 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 3.99/1.19 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 3.99/1.19 ( ![X36:$i]:
% 3.99/1.19 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 3.99/1.19 ( ( ![X42:$i]:
% 3.99/1.19 ( ( in @ X42 @ X40 ) =>
% 3.99/1.19 ( ?[X44:$i]:
% 3.99/1.19 ( ( ![X46:$i]:
% 3.99/1.19 ( ( X38 @ X42 @ X46 ) =>
% 3.99/1.19 ( ( X44 ) = ( X46 ) ) ) ) &
% 3.99/1.19 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 3.99/1.19 ( ?[X48:$i]:
% 3.99/1.19 ( ![X50:$i]:
% 3.99/1.19 ( ( in @ X50 @ X48 ) <=>
% 3.99/1.19 ( ?[X52:$i]:
% 3.99/1.19 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X54:$i]:
% 3.99/1.19 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 3.99/1.19 ( ?[X58:$i]:
% 3.99/1.19 ( ( ~( ?[X60:$i]:
% 3.99/1.19 ( ( in @ X60 @ X54 ) & ( in @ X60 @ X58 ) ) ) ) &
% 3.99/1.19 ( in @ X58 @ X54 ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X62:$i]:
% 3.99/1.19 ( ?[X64:$i]:
% 3.99/1.19 ( ( ![X66:$i]:
% 3.99/1.19 ( ( ( ![X68:$i]:
% 3.99/1.19 ( ( in @ X68 @ X66 ) =>
% 3.99/1.19 ( in @ X68 @ X62 ) ) ) &
% 3.99/1.19 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 3.99/1.19 ( ?[X72:$i,X74:$i]:
% 3.99/1.19 ( ( ![X76:$i]:
% 3.99/1.19 ( ( in @ X76 @ X64 ) =>
% 3.99/1.19 ( ( ![X78:$i]:
% 3.99/1.19 ( ( in @ X78 @ X76 ) =>
% 3.99/1.19 ( in @ X78 @ X72 ) ) ) |
% 3.99/1.19 ( in @ X74 @ X76 ) ) ) ) &
% 3.99/1.19 ( ~( ?[X80:$i]:
% 3.99/1.19 ( ( in @ X80 @ X66 ) &
% 3.99/1.19 ( in @ X80 @ X72 ) ) ) ) &
% 3.99/1.19 ( in @ X74 @ X66 ) & ( in @ X72 @ X64 ) ) ) ) ) &
% 3.99/1.19 ( ![X82:$i,X84:$i]:
% 3.99/1.19 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 3.99/1.19 ( ( ![X86:$i]:
% 3.99/1.19 ( ( in @ X86 @ X82 ) =>
% 3.99/1.19 ( in @ X86 @ X84 ) ) ) |
% 3.99/1.19 ( ![X88:$i]:
% 3.99/1.19 ( ( in @ X88 @ X84 ) =>
% 3.99/1.19 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 3.99/1.19 ( ![X90:$i,X92:$i]:
% 3.99/1.19 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 3.99/1.19 ( ( ![X94:$i]:
% 3.99/1.19 ( ( in @ X94 @ X64 ) =>
% 3.99/1.19 ( ( in @ X90 @ X94 ) <=>
% 3.99/1.19 ( in @ X92 @ X94 ) ) ) ) =>
% 3.99/1.19 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 3.99/1.19 ( ![X96:$i]:
% 3.99/1.19 ( ( in @ X96 @ X64 ) =>
% 3.99/1.19 ( ![X98:$i]:
% 3.99/1.19 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X100:( $i > $o )]:
% 3.99/1.19 ( ( ?[X102:$i]:
% 3.99/1.19 ( ( ![X104:$i]:
% 3.99/1.19 ( ( X100 @ X104 ) =>
% 3.99/1.19 ( ( X102 ) = ( X104 ) ) ) ) &
% 3.99/1.19 ( X100 @ X102 ) ) ) =>
% 3.99/1.19 ( X100 @
% 3.99/1.19 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 3.99/1.19 ( ( in @ X110 @ X106 ) =>
% 3.99/1.19 ( ( X108 @ X110 ) =>
% 3.99/1.19 ( in @
% 3.99/1.19 X110 @
% 3.99/1.19 ( dsetconstr @
% 3.99/1.19 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 3.99/1.19 ( ( in @
% 3.99/1.19 X116 @
% 3.99/1.19 ( dsetconstr @
% 3.99/1.19 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 3.99/1.19 ( in @ X116 @ X112 ) ) ) =>
% 3.99/1.19 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 3.99/1.19 ( ( in @
% 3.99/1.19 X122 @
% 3.99/1.19 ( dsetconstr @
% 3.99/1.19 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 3.99/1.19 ( X120 @ X122 ) ) ) =>
% 3.99/1.19 ( ( ![X124:( $i > $o )]:
% 3.99/1.19 ( ( ?[X126:$i]:
% 3.99/1.19 ( ( ![X128:$i]:
% 3.99/1.19 ( ( X124 @ X128 ) =>
% 3.99/1.19 ( ( X126 ) = ( X128 ) ) ) ) &
% 3.99/1.19 ( X124 @ X126 ) ) ) =>
% 3.99/1.19 ( ?[X130:$i]:
% 3.99/1.19 ( ( ![X132:$i]:
% 3.99/1.19 ( ( X124 @ X132 ) =>
% 3.99/1.19 ( ( X130 ) = ( X132 ) ) ) ) &
% 3.99/1.19 ( X124 @ X130 ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X134:$o,X136:$i]:
% 3.99/1.19 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 3.99/1.19 ( X134 ) ) ) =>
% 3.99/1.19 ( ( ![X138:$i]:
% 3.99/1.19 ( ( in @ X138 @ emptyset ) =>
% 3.99/1.19 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 3.99/1.19 ( ( ![X142:$i]:
% 3.99/1.19 ( ~( in @ X142 @ emptyset ) ) ) =>
% 3.99/1.19 ( ( ![X144:$i]:
% 3.99/1.19 ( ~( in @ X144 @ emptyset ) ) ) =>
% 3.99/1.19 ( ( ![X146:( $i > $o )]:
% 3.99/1.19 ( ( ?[X148:$i]:
% 3.99/1.19 ( ( ![X150:$i]:
% 3.99/1.19 ( ( X146 @ X150 ) =>
% 3.99/1.19 ( ( X148 ) = ( X150 ) ) ) ) &
% 3.99/1.19 ( X146 @ X148 ) ) ) =>
% 3.99/1.19 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 3.99/1.19 ( ( ![X154:$i,X156:$i]:
% 3.99/1.19 ( ( ![X158:$i]:
% 3.99/1.19 ( ( in @ X158 @ X154 ) =>
% 3.99/1.19 ( in @ X158 @ X156 ) ) ) =>
% 3.99/1.19 ( ( ![X160:$i]:
% 3.99/1.19 ( ( in @ X160 @ X156 ) =>
% 3.99/1.19 ( in @ X160 @ X154 ) ) ) =>
% 3.99/1.19 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X162:$i]:
% 3.99/1.19 ( ( ![X164:$i]:
% 3.99/1.19 ( ~( in @ X164 @ X162 ) ) ) =>
% 3.99/1.19 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 3.99/1.19 ( ( ![X166:$i]:
% 3.99/1.19 ( ( ![X168:$i]:
% 3.99/1.19 ( ~( in @ X168 @ X166 ) ) ) =>
% 3.99/1.19 ( ( X166 ) =
% 3.99/1.19 ( emptyset ) ) ) ) =>
% 3.99/1.19 ( ( ![X170:$i,
% 3.99/1.19 X172:( $i > $o ),
% 3.99/1.19 X174:$i]:
% 3.99/1.19 ( ( in @ X174 @ X170 ) =>
% 3.99/1.19 ( ( in @
% 3.99/1.19 X174 @
% 3.99/1.19 ( dsetconstr @
% 3.99/1.19 X170 @
% 3.99/1.19 ( ^[V_5:$i]:
% 3.99/1.19 ( X172 @ V_5 ) ) ) ) <=>
% 3.99/1.19 ( X172 @ X174 ) ) ) ) =>
% 3.99/1.19 ( ( ![X176:$i]:
% 3.99/1.19 ( ( ( X176 ) !=
% 3.99/1.19 ( emptyset ) ) =>
% 3.99/1.19 ( ?[X178:$i]:
% 3.99/1.19 ( in @ X178 @ X176 ) ) ) ) =>
% 3.99/1.19 ( ( ![X180:$i,
% 3.99/1.19 X182:( $i > $o ),
% 3.99/1.19 X184:$i]:
% 3.99/1.19 ( ( in @ X184 @ X180 ) =>
% 3.99/1.19 ( ( X182 @ X184 ) =>
% 3.99/1.19 ( ( dsetconstr @
% 3.99/1.19 X180 @
% 3.99/1.19 ( ^[
% 3.99/1.19 V_6:$i]:
% 3.99/1.19 (
% 3.99/1.19 X182 @ V_6 ) ) ) !=
% 3.99/1.19 ( emptyset ) ) ) ) ) =>
% 3.99/1.19 ( ( ![X186:$i]:
% 3.99/1.19 ( ( ?[X188:$i]:
% 3.99/1.19 ( in @
% 3.99/1.19 X188 @ X186 ) ) =>
% 3.99/1.19 ( ( X186 ) !=
% 3.99/1.19 ( emptyset ) ) ) ) =>
% 3.99/1.19 ( ( ![X190:$i,
% 3.99/1.19 X192:$i]:
% 3.99/1.19 ( in @
% 3.99/1.19 X190 @
% 3.99/1.19 ( setadjoin @
% 3.99/1.19 X190 @ X192 ) ) ) =>
% 3.99/1.19 ( ( in @
% 3.99/1.19 emptyset @
% 3.99/1.19 ( setadjoin @
% 3.99/1.19 emptyset @
% 3.99/1.19 emptyset ) ) =>
% 3.99/1.19 ( ( ![X194:$i,
% 3.99/1.19 X196:$i,
% 3.99/1.19 X198:$i]:
% 3.99/1.19 ( (
% 3.99/1.19 in @
% 3.99/1.19 X198 @
% 3.99/1.19 X196 ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X198 @
% 3.99/1.19 (
% 3.99/1.19 setadjoin
% 3.99/1.19 @
% 3.99/1.19 X194 @
% 3.99/1.19 X196 ) ) ) ) =>
% 3.99/1.19 ( ( ![
% 3.99/1.19 X200:$i,
% 3.99/1.19 X202:$i,
% 3.99/1.19 X204:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X204 @
% 3.99/1.19 (
% 3.99/1.19 setadjoin
% 3.99/1.19 @
% 3.99/1.19 X200 @
% 3.99/1.19 X202 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X206:$o]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 X204 ) =
% 3.99/1.19 (
% 3.99/1.19 X200 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 X206 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X204 @
% 3.99/1.19 X202 ) =>
% 3.99/1.19 (
% 3.99/1.19 X206 ) ) =>
% 3.99/1.19 (
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% 3.99/1.19 ( (
% 3.99/1.19 ![
% 3.99/1.19 X208:$i,
% 3.99/1.19 X210:$i,
% 3.99/1.19 X212:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X212 @
% 3.99/1.19 (
% 3.99/1.19 setadjoin
% 3.99/1.19 @
% 3.99/1.19 X208 @
% 3.99/1.19 X210 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 X212 ) =
% 3.99/1.19 (
% 3.99/1.19 X208 ) ) |
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X212 @
% 3.99/1.19 X210 ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X214:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 dsetconstr
% 3.99/1.19 @
% 3.99/1.19 X214 @
% 3.99/1.19 (
% 3.99/1.19 ^[
% 3.99/1.19 V_7:$i]:
% 3.99/1.19 (
% 3.99/1.19 $true ) ) ) =
% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X216:$i,
% 3.99/1.19 X218:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X220:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X220 @
% 3.99/1.19 X218 ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X220 @
% 3.99/1.19 X216 ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X218 @
% 3.99/1.19 (
% 3.99/1.19 powerset @
% 3.99/1.19 X216 ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X222:$i]:
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 emptyset @
% 3.99/1.19 (
% 3.99/1.19 powerset @
% 3.99/1.19 X222 ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X224:$i]:
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 emptyset @
% 3.99/1.19 (
% 3.99/1.19 powerset @
% 3.99/1.19 X224 ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X226:$i,
% 3.99/1.19 X228:$i,
% 3.99/1.19 X230:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X228 @
% 3.99/1.19 (
% 3.99/1.19 powerset @
% 3.99/1.19 X226 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X230 @
% 3.99/1.19 X228 ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
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% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X232:$i,
% 3.99/1.19 X234:$i,
% 3.99/1.19 X236:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X234 @
% 3.99/1.19 X236 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X236 @
% 3.99/1.19 X232 ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X234 @
% 3.99/1.19 (
% 3.99/1.19 setunion @
% 3.99/1.19 X232 ) ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X238:$i,
% 3.99/1.19 X240:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X240 @
% 3.99/1.19 (
% 3.99/1.19 setunion @
% 3.99/1.19 X238 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X242:$o]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X244:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X240 @
% 3.99/1.19 X244 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X244 @
% 3.99/1.19 X238 ) =>
% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X246:$i,
% 3.99/1.19 X248:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X248 @
% 3.99/1.19 X246 ) =>
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X248 @
% 3.99/1.19 (
% 3.99/1.19 powerset @
% 3.99/1.19 (
% 3.99/1.19 setunion @
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% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X250:(
% 3.99/1.19 $i > $o )]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ?[
% 3.99/1.19 X252:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X254:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 X250 @
% 3.99/1.19 X254 ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 X252 ) =
% 3.99/1.19 (
% 3.99/1.19 X254 ) ) ) ) &
% 3.99/1.19 (
% 3.99/1.19 X250 @
% 3.99/1.19 X252 ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 ?[
% 3.99/1.19 X256:$i]:
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X258:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 X250 @
% 3.99/1.19 X258 ) <=>
% 3.99/1.19 (
% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X260:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 X260 ) !=
% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 ?[
% 3.99/1.19 X262:$i]:
% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X264:$i,
% 3.99/1.19 X266:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
% 3.99/1.19 X264 @
% 3.99/1.19 (
% 3.99/1.19 setadjoin
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% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 X264 ) =
% 3.99/1.19 (
% 3.99/1.19 X266 ) ) ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X268:$i,
% 3.99/1.19 X270:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 X268 ) !=
% 3.99/1.19 (
% 3.99/1.19 X270 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 ~(
% 3.99/1.19 in @
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X272:$i,
% 3.99/1.19 X274:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 X272 ) =
% 3.99/1.19 (
% 3.99/1.19 X274 ) ) =>
% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 X278:$i]:
% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X280:$i,
% 3.99/1.19 X282:$i,
% 3.99/1.19 X284:$i]:
% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 ![
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X294:$i,
% 3.99/1.19 X296:(
% 3.99/1.19 $i > $o )]:
% 3.99/1.19 (
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% 3.99/1.19 ?[
% 3.99/1.19 X298:$i]:
% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
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% 3.99/1.19 X300:(
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% 3.99/1.19 X302:$i]:
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% 3.99/1.19 (
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% 3.99/1.19 ![
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% 3.99/1.19 X306:(
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% 3.99/1.19 ![
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 X312:$i,
% 3.99/1.19 X314:(
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% 3.99/1.19 (
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
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% 3.99/1.19 X386:$i]:
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% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 (
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% 3.99/1.19 X390:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
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% 3.99/1.19 (
% 3.99/1.19 ![
% 3.99/1.19 X392:$i,
% 3.99/1.19 X394:$i]:
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 X392 ) =
% 3.99/1.19 (
% 3.99/1.19 X394 ) ) =>
% 3.99/1.19 (
% 3.99/1.19 (
% 3.99/1.19 in @
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% 3.99/1.19 (
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% 3.99/1.20 (
% 3.99/1.20 (
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% 3.99/1.20 X398:$i]:
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X396 ) =
% 3.99/1.20 (
% 3.99/1.20 X398 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X400:$i,
% 3.99/1.20 X402:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X400 ) =
% 3.99/1.20 (
% 3.99/1.20 X402 ) ) =>
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% 3.99/1.20 (
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
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% 3.99/1.20 X406:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X408:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X404 @
% 3.99/1.20 X408 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X406 ) =
% 3.99/1.20 (
% 3.99/1.20 X408 ) ) ) ) &
% 3.99/1.20 (
% 3.99/1.20 X404 @
% 3.99/1.20 X406 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X410:$i,
% 3.99/1.20 X412:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X404 @
% 3.99/1.20 X410 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X404 @
% 3.99/1.20 X412 ) =>
% 3.99/1.20 (
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X414:(
% 3.99/1.20 $i > $o ),
% 3.99/1.20 X416:(
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X418:$i,
% 3.99/1.20 X420:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X418 ) =
% 3.99/1.20 (
% 3.99/1.20 X420 ) ) =>
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% 3.99/1.20 (
% 3.99/1.20 X414 @
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X422:$i]:
% 3.99/1.20 (
% 3.99/1.20 zip_tseitin_5
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 emptyset ) =
% 3.99/1.20 (
% 3.99/1.20 emptyset ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X430:$i,
% 3.99/1.20 X432:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X430 ) =
% 3.99/1.20 (
% 3.99/1.20 X432 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X434:$i,
% 3.99/1.20 X436:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X434 ) =
% 3.99/1.20 (
% 3.99/1.20 X436 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 setadjoin
% 3.99/1.20 @
% 3.99/1.20 X430 @
% 3.99/1.20 X434 ) =
% 3.99/1.20 (
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X438:$i,
% 3.99/1.20 X440:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X438 ) =
% 3.99/1.20 (
% 3.99/1.20 X440 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 powerset @
% 3.99/1.20 X438 ) =
% 3.99/1.20 (
% 3.99/1.20 powerset @
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X442:$i,
% 3.99/1.20 X444:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X442 ) =
% 3.99/1.20 (
% 3.99/1.20 X444 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 setunion @
% 3.99/1.20 X442 ) =
% 3.99/1.20 (
% 3.99/1.20 setunion @
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
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% 3.99/1.20 (
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% 3.99/1.20 (
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% 3.99/1.20 (
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% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X450:$i]:
% 3.99/1.20 (
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% 3.99/1.20 (
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% 3.99/1.20 (
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% 3.99/1.20 (
% 3.99/1.20 X446 @
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% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X452:$i,
% 3.99/1.20 X454:$i]:
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% 3.99/1.20 (
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% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X456:(
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% 3.99/1.20 X458:(
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X460:$i,
% 3.99/1.20 X462:$i]:
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% 3.99/1.20 X460 ) =
% 3.99/1.20 (
% 3.99/1.20 X462 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X456 @
% 3.99/1.20 X460 ) <=>
% 3.99/1.20 (
% 3.99/1.20 X458 @
% 3.99/1.20 X462 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X464:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X466:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X456 @
% 3.99/1.20 X466 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X464 ) =
% 3.99/1.20 (
% 3.99/1.20 X466 ) ) ) ) &
% 3.99/1.20 (
% 3.99/1.20 X456 @
% 3.99/1.20 X464 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X468:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X470:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X458 @
% 3.99/1.20 X470 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X468 ) =
% 3.99/1.20 (
% 3.99/1.20 X470 ) ) ) ) &
% 3.99/1.20 (
% 3.99/1.20 X458 @
% 3.99/1.20 X468 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 descr @
% 3.99/1.20 (
% 3.99/1.20 ^[
% 3.99/1.20 V_9:$i]:
% 3.99/1.20 (
% 3.99/1.20 X456 @ V_9 ) ) ) =
% 3.99/1.20 (
% 3.99/1.20 descr @
% 3.99/1.20 (
% 3.99/1.20 ^[
% 3.99/1.20 V_10:$i]:
% 3.99/1.20 (
% 3.99/1.20 X458 @
% 3.99/1.20 V_10 ) ) ) ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X472:$i,
% 3.99/1.20 X474:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X472 ) =
% 3.99/1.20 (
% 3.99/1.20 X474 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X476:(
% 3.99/1.20 $i > $o ),
% 3.99/1.20 X478:(
% 3.99/1.20 $i > $o )]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X480:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X480 @
% 3.99/1.20 X472 ) =>
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X482:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X482 @
% 3.99/1.20 X474 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X480 ) =
% 3.99/1.20 (
% 3.99/1.20 X482 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X476 @
% 3.99/1.20 X480 ) <=>
% 3.99/1.20 (
% 3.99/1.20 X478 @
% 3.99/1.20 X482 ) ) ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 dsetconstr
% 3.99/1.20 @
% 3.99/1.20 X472 @
% 3.99/1.20 (
% 3.99/1.20 ^[
% 3.99/1.20 V_11:$i]:
% 3.99/1.20 (
% 3.99/1.20 X476 @
% 3.99/1.20 V_11 ) ) ) =
% 3.99/1.20 (
% 3.99/1.20 dsetconstr
% 3.99/1.20 @
% 3.99/1.20 X474 @
% 3.99/1.20 (
% 3.99/1.20 ^[
% 3.99/1.20 V_12:$i]:
% 3.99/1.20 (
% 3.99/1.20 X478 @
% 3.99/1.20 V_12 ) ) ) ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X484:$i,
% 3.99/1.20 X486:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X488:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X488 @
% 3.99/1.20 X484 ) =>
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X488 @
% 3.99/1.20 X486 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X484 @
% 3.99/1.20 X486 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X490:$i,
% 3.99/1.20 X492:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X490 ) =
% 3.99/1.20 (
% 3.99/1.20 X492 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X492 @
% 3.99/1.20 X490 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X494:$i,
% 3.99/1.20 X496:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X494 ) =
% 3.99/1.20 (
% 3.99/1.20 X496 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X494 @
% 3.99/1.20 X496 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X498:$i,
% 3.99/1.20 X500:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X502:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X502 @
% 3.99/1.20 X498 ) =>
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X502 @
% 3.99/1.20 X500 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X498 @
% 3.99/1.20 X500 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X504:$i]:
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 emptyset @
% 3.99/1.20 X504 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X506:$i,
% 3.99/1.20 X508:$i,
% 3.99/1.20 X510:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X506 @
% 3.99/1.20 X508 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X510 @
% 3.99/1.20 X506 ) =>
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X510 @
% 3.99/1.20 X508 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X512:$i,
% 3.99/1.20 X514:$i,
% 3.99/1.20 X516:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X512 @
% 3.99/1.20 X514 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ~(
% 3.99/1.20 in @
% 3.99/1.20 X516 @
% 3.99/1.20 X514 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ~(
% 3.99/1.20 in @
% 3.99/1.20 X516 @
% 3.99/1.20 X512 ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X518:$i,
% 3.99/1.20 X520:$i,
% 3.99/1.20 X522:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X522 @
% 3.99/1.20 X518 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ~(
% 3.99/1.20 in @
% 3.99/1.20 X522 @
% 3.99/1.20 X520 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ~(
% 3.99/1.20 subset @
% 3.99/1.20 X518 @
% 3.99/1.20 X520 ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X524:$i,
% 3.99/1.20 X526:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ~(
% 3.99/1.20 subset @
% 3.99/1.20 X524 @
% 3.99/1.20 X526 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X524 ) !=
% 3.99/1.20 (
% 3.99/1.20 X526 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X528:$i,
% 3.99/1.20 X530:$i,
% 3.99/1.20 X532:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X532 @
% 3.99/1.20 X528 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ~(
% 3.99/1.20 in @
% 3.99/1.20 X532 @
% 3.99/1.20 X530 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X528 ) !=
% 3.99/1.20 (
% 3.99/1.20 X530 ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X534:$i]:
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X534 @
% 3.99/1.20 X534 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X536:$i,
% 3.99/1.20 X538:$i,
% 3.99/1.20 X540:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X536 @
% 3.99/1.20 X538 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X538 @
% 3.99/1.20 X540 ) =>
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X536 @
% 3.99/1.20 X540 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X542:$i,
% 3.99/1.20 X544:$i]:
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X544 @
% 3.99/1.20 (
% 3.99/1.20 setadjoin
% 3.99/1.20 @
% 3.99/1.20 X542 @
% 3.99/1.20 X544 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X546:$i,
% 3.99/1.20 X548:$i,
% 3.99/1.20 X550:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X546 @
% 3.99/1.20 X550 ) =>
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X546 @
% 3.99/1.20 (
% 3.99/1.20 setadjoin
% 3.99/1.20 @
% 3.99/1.20 X548 @
% 3.99/1.20 X550 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X552:$i,
% 3.99/1.20 X554:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X552 @
% 3.99/1.20 X554 ) =>
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X552 @
% 3.99/1.20 (
% 3.99/1.20 powerset @
% 3.99/1.20 X554 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X556:$i,
% 3.99/1.20 X558:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X556 @
% 3.99/1.20 X558 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X558 @
% 3.99/1.20 X556 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X556 ) =
% 3.99/1.20 (
% 3.99/1.20 X558 ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X560:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X560 @
% 3.99/1.20 emptyset ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X560 ) =
% 3.99/1.20 (
% 3.99/1.20 emptyset ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X562:$i,
% 3.99/1.20 X564:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X564 @
% 3.99/1.20 X562 ) =>
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X564 @
% 3.99/1.20 (
% 3.99/1.20 powerset @
% 3.99/1.20 X562 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X566:$i,
% 3.99/1.20 X568:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X568 @
% 3.99/1.20 (
% 3.99/1.20 powerset @
% 3.99/1.20 X566 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X568 @
% 3.99/1.20 X566 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X570:$i]:
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X570 @
% 3.99/1.20 (
% 3.99/1.20 powerset @
% 3.99/1.20 X570 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X572:$i,
% 3.99/1.20 X574:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X572 @
% 3.99/1.20 X574 ) =>
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 (
% 3.99/1.20 powerset @
% 3.99/1.20 X572 ) @
% 3.99/1.20 (
% 3.99/1.20 powerset @
% 3.99/1.20 X574 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X576:$i,
% 3.99/1.20 X578:(
% 3.99/1.20 $i > $o )]:
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 (
% 3.99/1.20 dsetconstr
% 3.99/1.20 @
% 3.99/1.20 X576 @
% 3.99/1.20 (
% 3.99/1.20 ^[
% 3.99/1.20 V_13:$i]:
% 3.99/1.20 (
% 3.99/1.20 X578 @
% 3.99/1.20 V_13 ) ) ) @
% 3.99/1.20 (
% 3.99/1.20 powerset @
% 3.99/1.20 X576 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X580:$i,
% 3.99/1.20 X582:(
% 3.99/1.20 $i > $o )]:
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 (
% 3.99/1.20 dsetconstr
% 3.99/1.20 @
% 3.99/1.20 X580 @
% 3.99/1.20 (
% 3.99/1.20 ^[
% 3.99/1.20 V_14:$i]:
% 3.99/1.20 (
% 3.99/1.20 X582 @
% 3.99/1.20 V_14 ) ) ) @
% 3.99/1.20 X580 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X584:$i,
% 3.99/1.20 X586:$i,
% 3.99/1.20 X588:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X588 @
% 3.99/1.20 X584 ) =>
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X588 @
% 3.99/1.20 (
% 3.99/1.20 binunion @
% 3.99/1.20 X584 @
% 3.99/1.20 X586 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X590:$i,
% 3.99/1.20 X592:$i]:
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X592 @
% 3.99/1.20 (
% 3.99/1.20 setadjoin
% 3.99/1.20 @
% 3.99/1.20 X590 @
% 3.99/1.20 (
% 3.99/1.20 setadjoin
% 3.99/1.20 @
% 3.99/1.20 X592 @
% 3.99/1.20 emptyset ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X594:$i,
% 3.99/1.20 X596:$i,
% 3.99/1.20 X598:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X598 @
% 3.99/1.20 X596 ) =>
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X598 @
% 3.99/1.20 (
% 3.99/1.20 binunion @
% 3.99/1.20 X594 @
% 3.99/1.20 X596 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X600:$i,
% 3.99/1.20 X602:$i,
% 3.99/1.20 X604:$i,
% 3.99/1.20 X606:$o]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X604 @
% 3.99/1.20 (
% 3.99/1.20 binunion @
% 3.99/1.20 X600 @
% 3.99/1.20 X602 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X604 @
% 3.99/1.20 X600 ) =>
% 3.99/1.20 (
% 3.99/1.20 X606 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X604 @
% 3.99/1.20 X602 ) =>
% 3.99/1.20 (
% 3.99/1.20 X606 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 X606 ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X608:$i,
% 3.99/1.20 X610:$i,
% 3.99/1.20 X612:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X612 @
% 3.99/1.20 (
% 3.99/1.20 binunion @
% 3.99/1.20 X608 @
% 3.99/1.20 X610 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X612 @
% 3.99/1.20 X608 ) |
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X612 @
% 3.99/1.20 X610 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X614:$i,
% 3.99/1.20 X616:$i]:
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X614 @
% 3.99/1.20 (
% 3.99/1.20 binunion @
% 3.99/1.20 X614 @
% 3.99/1.20 X616 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X618:$i,
% 3.99/1.20 X620:$i]:
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X620 @
% 3.99/1.20 (
% 3.99/1.20 binunion @
% 3.99/1.20 X618 @
% 3.99/1.20 X620 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X622:$i,
% 3.99/1.20 X624:$i,
% 3.99/1.20 X626:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X626 @
% 3.99/1.20 X622 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X626 @
% 3.99/1.20 X624 ) =>
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X626 @
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X622 @
% 3.99/1.20 X624 ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X628:$i,
% 3.99/1.20 X630:$i,
% 3.99/1.20 X632:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X632 @
% 3.99/1.20 X628 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X632 @
% 3.99/1.20 X630 ) =>
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X632 @
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X628 @
% 3.99/1.20 X630 ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X634:$i,
% 3.99/1.20 X636:$i,
% 3.99/1.20 X638:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X638 @
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X634 @
% 3.99/1.20 X636 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X638 @
% 3.99/1.20 X634 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X640:$i,
% 3.99/1.20 X642:$i]:
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X640 @
% 3.99/1.20 X642 ) @
% 3.99/1.20 X640 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X644:$i,
% 3.99/1.20 X646:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X644 @
% 3.99/1.20 X646 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X644 @
% 3.99/1.20 X646 ) =
% 3.99/1.20 (
% 3.99/1.20 X644 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X648:$i,
% 3.99/1.20 X650:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X648 @
% 3.99/1.20 X650 ) =
% 3.99/1.20 (
% 3.99/1.20 X650 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X650 @
% 3.99/1.20 X648 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X652:$i,
% 3.99/1.20 X654:$i,
% 3.99/1.20 X656:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X656 @
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X652 @
% 3.99/1.20 X654 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X656 @
% 3.99/1.20 X654 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X658:$i,
% 3.99/1.20 X660:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ~(
% 3.99/1.20 ?[
% 3.99/1.20 X662:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X662 @
% 3.99/1.20 X660 ) &
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X662 @
% 3.99/1.20 X658 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X658 @
% 3.99/1.20 X660 ) =
% 3.99/1.20 (
% 3.99/1.20 emptyset ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X664:$i,
% 3.99/1.20 X666:$i]:
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X664 @
% 3.99/1.20 X666 ) @
% 3.99/1.20 X666 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X668:$i,
% 3.99/1.20 X670:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X670 @
% 3.99/1.20 X668 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X668 @
% 3.99/1.20 X670 ) =
% 3.99/1.20 (
% 3.99/1.20 X670 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X672:$i,
% 3.99/1.20 X674:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X672 @
% 3.99/1.20 X674 ) =
% 3.99/1.20 (
% 3.99/1.20 X672 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 subset @
% 3.99/1.20 X672 @
% 3.99/1.20 X674 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X676:$i,
% 3.99/1.20 X678:$i,
% 3.99/1.20 X680:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X676 @
% 3.99/1.20 (
% 3.99/1.20 binunion @
% 3.99/1.20 X678 @
% 3.99/1.20 X680 ) ) =
% 3.99/1.20 (
% 3.99/1.20 binunion @
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X676 @
% 3.99/1.20 X678 ) @
% 3.99/1.20 (
% 3.99/1.20 binintersect
% 3.99/1.20 @
% 3.99/1.20 X676 @
% 3.99/1.20 X680 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X682:$i,
% 3.99/1.20 X684:$i,
% 3.99/1.20 X686:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X686 @
% 3.99/1.20 X682 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ~(
% 3.99/1.20 in @
% 3.99/1.20 X686 @
% 3.99/1.20 X684 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X686 @
% 3.99/1.20 (
% 3.99/1.20 dsetconstr
% 3.99/1.20 @
% 3.99/1.20 X682 @
% 3.99/1.20 (
% 3.99/1.20 ^[
% 3.99/1.20 V_15:$i]:
% 3.99/1.20 (
% 3.99/1.20 ~(
% 3.99/1.20 in @
% 3.99/1.20 V_15 @
% 3.99/1.20 X684 ) ) ) ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X688:$i,
% 3.99/1.20 X690:$i,
% 3.99/1.20 X692:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X692 @
% 3.99/1.20 (
% 3.99/1.20 dsetconstr
% 3.99/1.20 @
% 3.99/1.20 X688 @
% 3.99/1.20 (
% 3.99/1.20 ^[
% 3.99/1.20 V_16:$i]:
% 3.99/1.20 (
% 3.99/1.20 ~(
% 3.99/1.20 in @
% 3.99/1.20 V_16 @
% 3.99/1.20 X690 ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X692 @
% 3.99/1.20 X688 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.99/1.20 thf(zf_stmt_14, negated_conjecture,
% 3.99/1.20 (~( ( ![X4:$i,X6:$i]:
% 3.99/1.20 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 3.99/1.20 ( ( X4 ) = ( X6 ) ) ) ) =>
% 3.99/1.20 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 3.99/1.20 ( ( ![X12:$i,X14:$i,X16:$i]:
% 3.99/1.20 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 3.99/1.20 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 3.99/1.20 ( ( ![X18:$i,X20:$i]:
% 3.99/1.20 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 3.99/1.20 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 3.99/1.20 ( ( ![X24:$i,X26:$i]:
% 3.99/1.20 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 3.99/1.20 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 3.99/1.20 ( ( in @ emptyset @ omega ) =>
% 3.99/1.20 ( ( ![X30:$i]:
% 3.99/1.20 ( ( in @ X30 @ omega ) =>
% 3.99/1.20 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 3.99/1.20 ( ( ![X32:$i]:
% 3.99/1.20 ( ( ( in @ emptyset @ X32 ) &
% 3.99/1.20 ( ![X34:$i]:
% 3.99/1.20 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 3.99/1.20 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 3.99/1.20 ( ![X36:$i]:
% 3.99/1.20 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 3.99/1.20 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 3.99/1.20 ( ( ![X42:$i]:
% 3.99/1.20 ( ( in @ X42 @ X40 ) =>
% 3.99/1.20 ( ?[X44:$i]:
% 3.99/1.20 ( ( ![X46:$i]:
% 3.99/1.20 ( ( X38 @ X42 @ X46 ) =>
% 3.99/1.20 ( ( X44 ) = ( X46 ) ) ) ) &
% 3.99/1.20 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 3.99/1.20 ( ?[X48:$i]:
% 3.99/1.20 ( ![X50:$i]:
% 3.99/1.20 ( ( in @ X50 @ X48 ) <=>
% 3.99/1.20 ( ?[X52:$i]:
% 3.99/1.20 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 3.99/1.20 ( ( ![X54:$i]:
% 3.99/1.20 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 3.99/1.20 ( ?[X58:$i]:
% 3.99/1.20 ( ( ~( ?[X60:$i]:
% 3.99/1.20 ( ( in @ X60 @ X54 ) &
% 3.99/1.20 ( in @ X60 @ X58 ) ) ) ) &
% 3.99/1.20 ( in @ X58 @ X54 ) ) ) ) ) =>
% 3.99/1.20 ( ( ![X62:$i]:
% 3.99/1.20 ( ?[X64:$i]:
% 3.99/1.20 ( ( ![X66:$i]:
% 3.99/1.20 ( ( ( ![X68:$i]:
% 3.99/1.20 ( ( in @ X68 @ X66 ) =>
% 3.99/1.20 ( in @ X68 @ X62 ) ) ) &
% 3.99/1.20 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 3.99/1.20 ( ?[X72:$i,X74:$i]:
% 3.99/1.20 ( ( ![X76:$i]:
% 3.99/1.20 ( ( in @ X76 @ X64 ) =>
% 3.99/1.20 ( ( ![X78:$i]:
% 3.99/1.20 ( ( in @ X78 @ X76 ) =>
% 3.99/1.20 ( in @ X78 @ X72 ) ) ) |
% 3.99/1.20 ( in @ X74 @ X76 ) ) ) ) &
% 3.99/1.20 ( ~( ?[X80:$i]:
% 3.99/1.20 ( ( in @ X80 @ X66 ) &
% 3.99/1.20 ( in @ X80 @ X72 ) ) ) ) &
% 3.99/1.20 ( in @ X74 @ X66 ) &
% 3.99/1.20 ( in @ X72 @ X64 ) ) ) ) ) &
% 3.99/1.20 ( ![X82:$i,X84:$i]:
% 3.99/1.20 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 3.99/1.20 ( ( ![X86:$i]:
% 3.99/1.20 ( ( in @ X86 @ X82 ) =>
% 3.99/1.20 ( in @ X86 @ X84 ) ) ) |
% 3.99/1.20 ( ![X88:$i]:
% 3.99/1.20 ( ( in @ X88 @ X84 ) =>
% 3.99/1.20 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 3.99/1.20 ( ![X90:$i,X92:$i]:
% 3.99/1.20 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 3.99/1.20 ( ( ![X94:$i]:
% 3.99/1.20 ( ( in @ X94 @ X64 ) =>
% 3.99/1.20 ( ( in @ X90 @ X94 ) <=>
% 3.99/1.20 ( in @ X92 @ X94 ) ) ) ) =>
% 3.99/1.20 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 3.99/1.20 ( ![X96:$i]:
% 3.99/1.20 ( ( in @ X96 @ X64 ) =>
% 3.99/1.20 ( ![X98:$i]:
% 3.99/1.20 ( ( in @ X98 @ X96 ) =>
% 3.99/1.20 ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 3.99/1.20 ( ( ![X100:( $i > $o )]:
% 3.99/1.20 ( ( ?[X102:$i]:
% 3.99/1.20 ( ( ![X104:$i]:
% 3.99/1.20 ( ( X100 @ X104 ) =>
% 3.99/1.20 ( ( X102 ) = ( X104 ) ) ) ) &
% 3.99/1.20 ( X100 @ X102 ) ) ) =>
% 3.99/1.20 ( X100 @
% 3.99/1.20 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 3.99/1.20 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 3.99/1.20 ( ( in @ X110 @ X106 ) =>
% 3.99/1.20 ( ( X108 @ X110 ) =>
% 3.99/1.20 ( in @
% 3.99/1.20 X110 @
% 3.99/1.20 ( dsetconstr @
% 3.99/1.20 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 3.99/1.20 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 3.99/1.20 ( ( in @
% 3.99/1.20 X116 @
% 3.99/1.20 ( dsetconstr @
% 3.99/1.20 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 3.99/1.20 ( in @ X116 @ X112 ) ) ) =>
% 3.99/1.20 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 3.99/1.20 ( ( in @
% 3.99/1.20 X122 @
% 3.99/1.20 ( dsetconstr @
% 3.99/1.20 X118 @
% 3.99/1.20 ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 3.99/1.20 ( X120 @ X122 ) ) ) =>
% 3.99/1.20 ( ( ![X124:( $i > $o )]:
% 3.99/1.20 ( ( ?[X126:$i]:
% 3.99/1.20 ( ( ![X128:$i]:
% 3.99/1.20 ( ( X124 @ X128 ) =>
% 3.99/1.20 ( ( X126 ) = ( X128 ) ) ) ) &
% 3.99/1.20 ( X124 @ X126 ) ) ) =>
% 3.99/1.20 ( ?[X130:$i]:
% 3.99/1.20 ( ( ![X132:$i]:
% 3.99/1.20 ( ( X124 @ X132 ) =>
% 3.99/1.20 ( ( X130 ) = ( X132 ) ) ) ) &
% 3.99/1.20 ( X124 @ X130 ) ) ) ) ) =>
% 3.99/1.20 ( ( ![X134:$o,X136:$i]:
% 3.99/1.20 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 3.99/1.20 ( X134 ) ) ) =>
% 3.99/1.20 ( ( ![X138:$i]:
% 3.99/1.20 ( ( in @ X138 @ emptyset ) =>
% 3.99/1.20 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 3.99/1.20 ( ( ![X142:$i]:
% 3.99/1.20 ( ~( in @ X142 @ emptyset ) ) ) =>
% 3.99/1.20 ( ( ![X144:$i]:
% 3.99/1.20 ( ~( in @ X144 @ emptyset ) ) ) =>
% 3.99/1.20 ( ( ![X146:( $i > $o )]:
% 3.99/1.20 ( ( ?[X148:$i]:
% 3.99/1.20 ( ( ![X150:$i]:
% 3.99/1.20 ( ( X146 @ X150 ) =>
% 3.99/1.20 ( ( X148 ) =
% 3.99/1.20 ( X150 ) ) ) ) &
% 3.99/1.20 ( X146 @ X148 ) ) ) =>
% 3.99/1.20 ( ?[X152:$i]:
% 3.99/1.20 ( X146 @ X152 ) ) ) ) =>
% 3.99/1.20 ( ( ![X154:$i,X156:$i]:
% 3.99/1.20 ( ( ![X158:$i]:
% 3.99/1.20 ( ( in @ X158 @ X154 ) =>
% 3.99/1.20 ( in @ X158 @ X156 ) ) ) =>
% 3.99/1.20 ( ( ![X160:$i]:
% 3.99/1.20 ( ( in @ X160 @ X156 ) =>
% 3.99/1.20 ( in @ X160 @ X154 ) ) ) =>
% 3.99/1.20 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 3.99/1.20 ( ( ![X162:$i]:
% 3.99/1.20 ( ( ![X164:$i]:
% 3.99/1.20 ( ~( in @ X164 @ X162 ) ) ) =>
% 3.99/1.20 ( ( X162 ) =
% 3.99/1.20 ( emptyset ) ) ) ) =>
% 3.99/1.20 ( ( ![X166:$i]:
% 3.99/1.20 ( ( ![X168:$i]:
% 3.99/1.20 ( ~( in @
% 3.99/1.20 X168 @ X166 ) ) ) =>
% 3.99/1.20 ( ( X166 ) =
% 3.99/1.20 ( emptyset ) ) ) ) =>
% 3.99/1.20 ( ( ![X170:$i,
% 3.99/1.20 X172:( $i > $o ),
% 3.99/1.20 X174:$i]:
% 3.99/1.20 ( ( in @ X174 @ X170 ) =>
% 3.99/1.20 ( ( in @
% 3.99/1.20 X174 @
% 3.99/1.20 ( dsetconstr @
% 3.99/1.20 X170 @
% 3.99/1.20 ( ^[V_5:$i]:
% 3.99/1.20 ( X172 @
% 3.99/1.20 V_5 ) ) ) ) <=>
% 3.99/1.20 ( X172 @ X174 ) ) ) ) =>
% 3.99/1.20 ( ( ![X176:$i]:
% 3.99/1.20 ( ( ( X176 ) !=
% 3.99/1.20 ( emptyset ) ) =>
% 3.99/1.20 ( ?[X178:$i]:
% 3.99/1.20 ( in @
% 3.99/1.20 X178 @ X176 ) ) ) ) =>
% 3.99/1.20 ( ( ![X180:$i,
% 3.99/1.20 X182:(
% 3.99/1.20 $i > $o ),
% 3.99/1.20 X184:$i]:
% 3.99/1.20 ( ( in @
% 3.99/1.20 X184 @ X180 ) =>
% 3.99/1.20 ( ( X182 @ X184 ) =>
% 3.99/1.20 ( ( dsetconstr
% 3.99/1.20 @
% 3.99/1.20 X180 @
% 3.99/1.20 (
% 3.99/1.20 ^[
% 3.99/1.20 V_6:$i]:
% 3.99/1.20 (
% 3.99/1.20 X182 @
% 3.99/1.20 V_6 ) ) ) !=
% 3.99/1.20 ( emptyset ) ) ) ) ) =>
% 3.99/1.20 ( ( ![X186:$i]:
% 3.99/1.20 ( ( ?[X188:$i]:
% 3.99/1.20 ( in @
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% 3.99/1.20 @
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X338 ) =>
% 3.99/1.20 (
% 3.99/1.20 set2prop
% 3.99/1.20 @
% 3.99/1.20 (
% 3.99/1.20 prop2set
% 3.99/1.20 @
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X340:$i,
% 3.99/1.20 X342:(
% 3.99/1.20 $i > $o )]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ~
% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X344:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X342 @
% 3.99/1.20 X344 ) &
% 3.99/1.20 (
% 3.99/1.20 in @
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% 3.99/1.20 (
% 3.99/1.20 ![
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
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% 3.99/1.20 X340 ) =>
% 3.99/1.20 (
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% 3.99/1.20 (
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% 3.99/1.20 ![
% 3.99/1.20 X348:$i,
% 3.99/1.20 X350:(
% 3.99/1.20 $i > $o )]:
% 3.99/1.20 (
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% 3.99/1.20 (
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
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% 3.99/1.20 X348 ) =>
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% 3.99/1.20 (
% 3.99/1.20 ?[
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% 3.99/1.20 (
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% 3.99/1.20 X354 ) ) &
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% 3.99/1.20 (
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% 3.99/1.20 X356:(
% 3.99/1.20 $i > $o )]:
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% 3.99/1.20 ?[
% 3.99/1.20 X358:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
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% 3.99/1.20 X360:$i]:
% 3.99/1.20 (
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% 3.99/1.20 X356 @
% 3.99/1.20 X360 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X358 ) =
% 3.99/1.20 (
% 3.99/1.20 X360 ) ) ) ) &
% 3.99/1.20 (
% 3.99/1.20 X356 @
% 3.99/1.20 X358 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X362:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X364:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X356 @
% 3.99/1.20 X364 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X362 ) =
% 3.99/1.20 (
% 3.99/1.20 X364 ) ) ) ) &
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X366:(
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% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X368:$i]:
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% 3.99/1.20 X366 @
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
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% 3.99/1.20 X372:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X366 @
% 3.99/1.20 X370 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X366 @
% 3.99/1.20 X372 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
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% 3.99/1.20 (
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% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X374:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X376:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X366 @
% 3.99/1.20 X376 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X374 ) =
% 3.99/1.20 (
% 3.99/1.20 X376 ) ) ) ) &
% 3.99/1.20 (
% 3.99/1.20 X366 @
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X378:(
% 3.99/1.20 $i > $o )]:
% 3.99/1.20 (
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% 3.99/1.20 ?[
% 3.99/1.20 X380:$i]:
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X382:$i]:
% 3.99/1.20 (
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% 3.99/1.20 X378 @
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% 3.99/1.20 (
% 3.99/1.20 (
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% 3.99/1.20 (
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% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X384:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X386:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X378 @
% 3.99/1.20 X386 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X384 ) =
% 3.99/1.20 (
% 3.99/1.20 X386 ) ) ) ) &
% 3.99/1.20 (
% 3.99/1.20 X378 @
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X388:$i,
% 3.99/1.20 X390:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X388 ) =
% 3.99/1.20 (
% 3.99/1.20 X390 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X392:$i,
% 3.99/1.20 X394:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X392 ) =
% 3.99/1.20 (
% 3.99/1.20 X394 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X392 @
% 3.99/1.20 X388 ) =>
% 3.99/1.20 (
% 3.99/1.20 in @
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X396:$i,
% 3.99/1.20 X398:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X396 ) =
% 3.99/1.20 (
% 3.99/1.20 X398 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X400:$i,
% 3.99/1.20 X402:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X400 ) =
% 3.99/1.20 (
% 3.99/1.20 X402 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X400 @
% 3.99/1.20 X396 ) <=>
% 3.99/1.20 (
% 3.99/1.20 in @
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X404:(
% 3.99/1.20 $i > $o )]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X406:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X408:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X404 @
% 3.99/1.20 X408 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X406 ) =
% 3.99/1.20 (
% 3.99/1.20 X408 ) ) ) ) &
% 3.99/1.20 (
% 3.99/1.20 X404 @
% 3.99/1.20 X406 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X410:$i,
% 3.99/1.20 X412:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X404 @
% 3.99/1.20 X410 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X404 @
% 3.99/1.20 X412 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X410 ) =
% 3.99/1.20 (
% 3.99/1.20 X412 ) ) ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X414:(
% 3.99/1.20 $i > $o ),
% 3.99/1.20 X416:(
% 3.99/1.20 $i > $o )]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X418:$i,
% 3.99/1.20 X420:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X418 ) =
% 3.99/1.20 (
% 3.99/1.20 X420 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X414 @
% 3.99/1.20 X418 ) <=>
% 3.99/1.20 (
% 3.99/1.20 X416 @
% 3.99/1.20 X420 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X422:$i]:
% 3.99/1.20 (
% 3.99/1.20 zip_tseitin_5
% 3.99/1.20 @
% 3.99/1.20 X422 @
% 3.99/1.20 X414 ) ) <=>
% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X426:$i]:
% 3.99/1.20 (
% 3.99/1.20 zip_tseitin_5
% 3.99/1.20 @
% 3.99/1.20 X426 @
% 3.99/1.20 X416 ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 emptyset ) =
% 3.99/1.20 (
% 3.99/1.20 emptyset ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X430:$i,
% 3.99/1.20 X432:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X430 ) =
% 3.99/1.20 (
% 3.99/1.20 X432 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X434:$i,
% 3.99/1.20 X436:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X434 ) =
% 3.99/1.20 (
% 3.99/1.20 X436 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 setadjoin
% 3.99/1.20 @
% 3.99/1.20 X430 @
% 3.99/1.20 X434 ) =
% 3.99/1.20 (
% 3.99/1.20 setadjoin
% 3.99/1.20 @
% 3.99/1.20 X432 @
% 3.99/1.20 X436 ) ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X438:$i,
% 3.99/1.20 X440:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X438 ) =
% 3.99/1.20 (
% 3.99/1.20 X440 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 powerset
% 3.99/1.20 @
% 3.99/1.20 X438 ) =
% 3.99/1.20 (
% 3.99/1.20 powerset
% 3.99/1.20 @
% 3.99/1.20 X440 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X442:$i,
% 3.99/1.20 X444:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X442 ) =
% 3.99/1.20 (
% 3.99/1.20 X444 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 setunion
% 3.99/1.20 @
% 3.99/1.20 X442 ) =
% 3.99/1.20 (
% 3.99/1.20 setunion
% 3.99/1.20 @
% 3.99/1.20 X444 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 omega ) =
% 3.99/1.20 (
% 3.99/1.20 omega ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X446:(
% 3.99/1.20 $i > $o )]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X448:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X450:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X446 @
% 3.99/1.20 X450 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X448 ) =
% 3.99/1.20 (
% 3.99/1.20 X450 ) ) ) ) &
% 3.99/1.20 (
% 3.99/1.20 X446 @
% 3.99/1.20 X448 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X452:$i,
% 3.99/1.20 X454:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X446 @
% 3.99/1.20 X452 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X446 @
% 3.99/1.20 X454 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X452 ) =
% 3.99/1.20 (
% 3.99/1.20 X454 ) ) ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X456:(
% 3.99/1.20 $i > $o ),
% 3.99/1.20 X458:(
% 3.99/1.20 $i > $o )]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X460:$i,
% 3.99/1.20 X462:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X460 ) =
% 3.99/1.20 (
% 3.99/1.20 X462 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X456 @
% 3.99/1.20 X460 ) <=>
% 3.99/1.20 (
% 3.99/1.20 X458 @
% 3.99/1.20 X462 ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X464:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X466:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X456 @
% 3.99/1.20 X466 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X464 ) =
% 3.99/1.20 (
% 3.99/1.20 X466 ) ) ) ) &
% 3.99/1.20 (
% 3.99/1.20 X456 @
% 3.99/1.20 X464 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ?[
% 3.99/1.20 X468:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X470:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X458 @
% 3.99/1.20 X470 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X468 ) =
% 3.99/1.20 (
% 3.99/1.20 X470 ) ) ) ) &
% 3.99/1.20 (
% 3.99/1.20 X458 @
% 3.99/1.20 X468 ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 descr @
% 3.99/1.20 (
% 3.99/1.20 ^[
% 3.99/1.20 V_9:$i]:
% 3.99/1.20 (
% 3.99/1.20 X456 @
% 3.99/1.20 V_9 ) ) ) =
% 3.99/1.20 (
% 3.99/1.20 descr @
% 3.99/1.20 (
% 3.99/1.20 ^[
% 3.99/1.20 V_10:$i]:
% 3.99/1.20 (
% 3.99/1.20 X458 @
% 3.99/1.20 V_10 ) ) ) ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X472:$i,
% 3.99/1.20 X474:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X472 ) =
% 3.99/1.20 (
% 3.99/1.20 X474 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X476:(
% 3.99/1.20 $i > $o ),
% 3.99/1.20 X478:(
% 3.99/1.20 $i > $o )]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X480:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X480 @
% 3.99/1.20 X472 ) =>
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X482:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 in @
% 3.99/1.20 X482 @
% 3.99/1.20 X474 ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X480 ) =
% 3.99/1.20 (
% 3.99/1.20 X482 ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 X476 @
% 3.99/1.20 X480 ) <=>
% 3.99/1.20 (
% 3.99/1.20 X478 @
% 3.99/1.20 X482 ) ) ) ) ) ) ) =>
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 dsetconstr
% 3.99/1.20 @
% 3.99/1.20 X472 @
% 3.99/1.20 (
% 3.99/1.20 ^[
% 3.99/1.20 V_11:$i]:
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% 3.99/1.20 (
% 3.99/1.20 dsetconstr
% 3.99/1.20 @
% 3.99/1.20 X474 @
% 3.99/1.20 (
% 3.99/1.20 ^[
% 3.99/1.20 V_12:$i]:
% 3.99/1.20 (
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% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X484:$i,
% 3.99/1.20 X486:$i]:
% 3.99/1.20 (
% 3.99/1.20 (
% 3.99/1.20 ![
% 3.99/1.20 X488:$i]:
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% 4.22/1.21 X650 @
% 4.22/1.21 X648 ) ) ) =>
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 ![
% 4.22/1.21 X652:$i,
% 4.22/1.21 X654:$i,
% 4.22/1.21 X656:$i]:
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 in @
% 4.22/1.21 X656 @
% 4.22/1.21 (
% 4.22/1.21 binintersect
% 4.22/1.21 @
% 4.22/1.21 X652 @
% 4.22/1.21 X654 ) ) =>
% 4.22/1.21 (
% 4.22/1.21 in @
% 4.22/1.21 X656 @
% 4.22/1.21 X654 ) ) ) =>
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 ![
% 4.22/1.21 X658:$i,
% 4.22/1.21 X660:$i]:
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 ~
% 4.22/1.21 (
% 4.22/1.21 ?[
% 4.22/1.21 X662:$i]:
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 in @
% 4.22/1.21 X662 @
% 4.22/1.21 X660 ) &
% 4.22/1.21 (
% 4.22/1.21 in @
% 4.22/1.21 X662 @
% 4.22/1.21 X658 ) ) ) ) =>
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 binintersect
% 4.22/1.21 @
% 4.22/1.21 X658 @
% 4.22/1.21 X660 ) =
% 4.22/1.21 (
% 4.22/1.21 emptyset ) ) ) ) =>
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 ![
% 4.22/1.21 X664:$i,
% 4.22/1.21 X666:$i]:
% 4.22/1.21 (
% 4.22/1.21 subset @
% 4.22/1.21 (
% 4.22/1.21 binintersect
% 4.22/1.21 @
% 4.22/1.21 X664 @
% 4.22/1.21 X666 ) @
% 4.22/1.21 X666 ) ) =>
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 ![
% 4.22/1.21 X668:$i,
% 4.22/1.21 X670:$i]:
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 subset @
% 4.22/1.21 X670 @
% 4.22/1.21 X668 ) =>
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 binintersect
% 4.22/1.21 @
% 4.22/1.21 X668 @
% 4.22/1.21 X670 ) =
% 4.22/1.21 (
% 4.22/1.21 X670 ) ) ) ) =>
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 ![
% 4.22/1.21 X672:$i,
% 4.22/1.21 X674:$i]:
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 binintersect
% 4.22/1.21 @
% 4.22/1.21 X672 @
% 4.22/1.21 X674 ) =
% 4.22/1.21 (
% 4.22/1.21 X672 ) ) =>
% 4.22/1.21 (
% 4.22/1.21 subset @
% 4.22/1.21 X672 @
% 4.22/1.21 X674 ) ) ) =>
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 ![
% 4.22/1.21 X676:$i,
% 4.22/1.21 X678:$i,
% 4.22/1.21 X680:$i]:
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 binintersect
% 4.22/1.21 @
% 4.22/1.21 X676 @
% 4.22/1.21 (
% 4.22/1.21 binunion
% 4.22/1.21 @
% 4.22/1.21 X678 @
% 4.22/1.21 X680 ) ) =
% 4.22/1.21 (
% 4.22/1.21 binunion
% 4.22/1.21 @
% 4.22/1.21 (
% 4.22/1.21 binintersect
% 4.22/1.21 @
% 4.22/1.21 X676 @
% 4.22/1.21 X678 ) @
% 4.22/1.21 (
% 4.22/1.21 binintersect
% 4.22/1.21 @
% 4.22/1.21 X676 @
% 4.22/1.21 X680 ) ) ) ) =>
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 ![
% 4.22/1.21 X682:$i,
% 4.22/1.21 X684:$i,
% 4.22/1.21 X686:$i]:
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 in @
% 4.22/1.21 X686 @
% 4.22/1.21 X682 ) =>
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 ~
% 4.22/1.21 (
% 4.22/1.21 in @
% 4.22/1.21 X686 @
% 4.22/1.21 X684 ) ) =>
% 4.22/1.21 (
% 4.22/1.21 in @
% 4.22/1.21 X686 @
% 4.22/1.21 (
% 4.22/1.21 dsetconstr
% 4.22/1.21 @
% 4.22/1.21 X682 @
% 4.22/1.21 (
% 4.22/1.21 ^[
% 4.22/1.21 V_15:$i]:
% 4.22/1.21 (
% 4.22/1.21 ~
% 4.22/1.21 (
% 4.22/1.21 in @
% 4.22/1.21 V_15 @
% 4.22/1.21 X684 ) ) ) ) ) ) ) ) =>
% 4.22/1.21 (
% 4.22/1.21 ![
% 4.22/1.21 X688:$i,
% 4.22/1.21 X690:$i,
% 4.22/1.21 X692:$i]:
% 4.22/1.21 (
% 4.22/1.21 (
% 4.22/1.21 in @
% 4.22/1.21 X692 @
% 4.22/1.21 (
% 4.22/1.21 dsetconstr
% 4.22/1.21 @
% 4.22/1.21 X688 @
% 4.22/1.21 (
% 4.22/1.21 ^[
% 4.22/1.21 V_16:$i]:
% 4.22/1.21 (
% 4.22/1.21 ~
% 4.22/1.21 (
% 4.22/1.21 in @
% 4.22/1.21 V_16 @
% 4.22/1.21 X690 ) ) ) ) ) =>
% 4.22/1.21 (
% 4.22/1.21 in @
% 4.22/1.21 X692 @
% 4.22/1.21 X688 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 4.22/1.21 inference('cnf.neg', [status(esa)], [zf_stmt_13])).
% 4.22/1.21 thf(zip_derived_cl122, plain, (~ (in @ sk__347 @ sk__345)),
% 4.22/1.21 inference('cnf', [status(esa)], [zf_stmt_14])).
% 4.22/1.21 thf(zip_derived_cl123, plain,
% 4.22/1.21 ( (in @ sk__347 @
% 4.22/1.21 (dsetconstr @ sk__345 @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ sk__346))))))),
% 4.22/1.21 inference('cnf', [status(esa)], [zf_stmt_14])).
% 4.22/1.21 thf(zip_derived_cl212, plain,
% 4.22/1.21 (![X278 : $i, X279 : $i, X280 : $i > $o]:
% 4.22/1.21 ( (in @ X278 @ X279)
% 4.22/1.21 | ~ (in @ X278 @ (dsetconstr @ X279 @ (^[Y0 : $i]: (X280 @ Y0)))))),
% 4.22/1.21 inference('cnf', [status(esa)], [zf_stmt_14])).
% 4.22/1.21 thf(zip_derived_cl245, plain,
% 4.22/1.21 (![X278 : $i, X279 : $i, X280 : $i > $o]:
% 4.22/1.21 ( (in @ X278 @ X279) | ~ (in @ X278 @ (dsetconstr @ X279 @ X280)))),
% 4.22/1.21 inference('ho_norm', [status(thm)], [zip_derived_cl212])).
% 4.22/1.21 thf(zip_derived_cl292, plain, ( (in @ sk__347 @ sk__345)),
% 4.22/1.21 inference('sup-', [status(thm)], [zip_derived_cl123, zip_derived_cl245])).
% 4.22/1.21 thf(zip_derived_cl310, plain, ($false),
% 4.22/1.21 inference('demod', [status(thm)], [zip_derived_cl122, zip_derived_cl292])).
% 4.22/1.21
% 4.22/1.21 % SZS output end Refutation
% 4.22/1.21
% 4.22/1.21
% 4.22/1.21 % Terminating...
% 4.22/1.28 % Runner terminated.
% 4.22/1.30 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------