%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU618^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.TnGJDWkcPf true
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:55:23 PM UTC 2025
% Result : Theorem 4.64s 1.75s
% Output : Refutation 4.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.16 % Problem : SEU618^1 : TPTP v9.2.0. Released v3.7.0.
% 0.02/0.17 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.TnGJDWkcPf true
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8042.1875MB
% 0.09/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Oct 1 16:05:38 EDT 2025
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Running portfolio for 300 s
% 0.09/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Number of cores: 8
% 0.09/0.38 % Python version: Python 3.6.8
% 0.09/0.38 % Running in HO mode
% 0.43/0.69 % Total configuration time : 828
% 0.43/0.69 % Estimated wc time : 1656
% 0.43/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.46/0.82 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.46/0.86 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.47/0.89 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.47/0.89 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.47/0.89 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.48/0.94 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.48/0.96 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.48/0.98 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 4.64/1.75 % Solved by lams/40_c_ic.sh.
% 4.64/1.75 % done 282 iterations in 0.739s
% 4.64/1.75 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.64/1.75 % SZS output start Refutation
% 4.64/1.75 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 4.64/1.75 thf(notdexE_type, type, notdexE: $o).
% 4.64/1.75 thf(setunionAx_type, type, setunionAx: $o).
% 4.64/1.75 thf(setminusELneg_type, type, setminusELneg: $o).
% 4.64/1.75 thf(powersetE_type, type, powersetE: $o).
% 4.64/1.75 thf(omegaSAx_type, type, omegaSAx: $o).
% 4.64/1.75 thf(exuI1_type, type, exuI1: $o).
% 4.64/1.75 thf(exuI2_type, type, exuI2: $o).
% 4.64/1.75 thf(notequalI2_type, type, notequalI2: $o).
% 4.64/1.75 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 4.64/1.75 thf(setminusILneg_type, type, setminusILneg: $o).
% 4.64/1.75 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 4.64/1.75 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 4.64/1.75 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 4.64/1.75 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 4.64/1.75 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 4.64/1.75 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 4.64/1.75 thf(setukpairIL_type, type, setukpairIL: $o).
% 4.64/1.75 thf(binunionE_type, type, binunionE: $o).
% 4.64/1.75 thf(setext_type, type, setext: $o).
% 4.64/1.75 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 4.64/1.75 thf(descr__Cong_type, type, descr__Cong: $o).
% 4.64/1.75 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 4.64/1.75 thf(in_type, type, in: $i > $i > $o).
% 4.64/1.75 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 4.64/1.75 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 4.64/1.75 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 4.64/1.75 thf(symdiffI2_type, type, symdiffI2: $o).
% 4.64/1.75 thf(upairset2IR_type, type, upairset2IR: $o).
% 4.64/1.75 thf(subsetE_type, type, subsetE: $o).
% 4.64/1.75 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 4.64/1.75 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 4.64/1.75 thf(setbeta_type, type, setbeta: $o).
% 4.64/1.75 thf(eqinunit_type, type, eqinunit: $o).
% 4.64/1.75 thf(upairsetIL_type, type, upairsetIL: $o).
% 4.64/1.75 thf(powersetI1_type, type, powersetI1: $o).
% 4.64/1.75 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 4.64/1.75 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 4.64/1.75 thf(powersetAx_type, type, powersetAx: $o).
% 4.64/1.75 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 4.64/1.75 thf(powersetI_type, type, powersetI: $o).
% 4.64/1.75 thf(upairsetIR_type, type, upairsetIR: $o).
% 4.64/1.75 thf(inCongP_type, type, inCongP: $o).
% 4.64/1.75 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 4.64/1.75 thf(exuE3e_type, type, exuE3e: $o).
% 4.64/1.75 thf(emptysetE_type, type, emptysetE: $o).
% 4.64/1.75 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 4.64/1.75 thf(setunionI_type, type, setunionI: $o).
% 4.64/1.75 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 4.64/1.75 thf(prop2setI_type, type, prop2setI: $o).
% 4.64/1.75 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 4.64/1.75 thf(setminusER_type, type, setminusER: $o).
% 4.64/1.75 thf(exuE2_type, type, exuE2: $o).
% 4.64/1.75 thf(emptyset_type, type, emptyset: $i).
% 4.64/1.75 thf(powersetsubset_type, type, powersetsubset: $o).
% 4.64/1.75 thf(subPowSU_type, type, subPowSU: $o).
% 4.64/1.75 thf(notequalI1_type, type, notequalI1: $o).
% 4.64/1.75 thf(notinemptyset_type, type, notinemptyset: $o).
% 4.64/1.75 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 4.64/1.75 thf(subsetTrans_type, type, subsetTrans: $o).
% 4.64/1.75 thf(sk__77_type, type, sk__77: $i).
% 4.64/1.75 thf(setminusI_type, type, setminusI: $o).
% 4.64/1.75 thf(binunionIL_type, type, binunionIL: $o).
% 4.64/1.75 thf(subsetE2_type, type, subsetE2: $o).
% 4.64/1.75 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 4.64/1.75 thf(setextsub_type, type, setextsub: $o).
% 4.64/1.75 thf(binunionLsub_type, type, binunionLsub: $o).
% 4.64/1.75 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 4.64/1.75 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 4.64/1.75 thf(setunionE_type, type, setunionE: $o).
% 4.64/1.75 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 4.64/1.75 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 4.64/1.75 thf(binunionIR_type, type, binunionIR: $o).
% 4.64/1.75 thf(setadjoinE_type, type, setadjoinE: $o).
% 4.64/1.75 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 4.64/1.75 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 4.64/1.75 thf(exuE1_type, type, exuE1: $o).
% 4.64/1.75 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 4.64/1.75 thf(setminusLsub_type, type, setminusLsub: $o).
% 4.64/1.75 thf(notinsingleton_type, type, notinsingleton: $o).
% 4.64/1.75 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 4.64/1.75 thf(exuEu_type, type, exuEu: $o).
% 4.64/1.75 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 4.64/1.75 thf(upairsetE_type, type, upairsetE: $o).
% 4.64/1.75 thf(omega0Ax_type, type, omega0Ax: $o).
% 4.64/1.75 thf(notsubsetI_type, type, notsubsetI: $o).
% 4.64/1.75 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 4.64/1.75 thf(setextAx_type, type, setextAx: $o).
% 4.64/1.75 thf(powersetE1_type, type, powersetE1: $o).
% 4.64/1.75 thf(bs114d_type, type, bs114d: $o).
% 4.64/1.75 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 4.64/1.75 thf(setunion_type, type, setunion: $i > $i).
% 4.64/1.75 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 4.64/1.75 thf(subsetI1_type, type, subsetI1: $o).
% 4.64/1.75 thf(symdiffE_type, type, symdiffE: $o).
% 4.64/1.75 thf(descrp_type, type, descrp: $o).
% 4.64/1.75 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 4.64/1.75 thf(foundationAx_type, type, foundationAx: $o).
% 4.64/1.75 thf(emptysetAx_type, type, emptysetAx: $o).
% 4.64/1.75 thf(emptyI_type, type, emptyI: $o).
% 4.64/1.75 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 4.64/1.75 thf(binintersectEL_type, type, binintersectEL: $o).
% 4.64/1.75 thf(emptyE1_type, type, emptyE1: $o).
% 4.64/1.75 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 4.64/1.75 thf(vacuousDall_type, type, vacuousDall: $o).
% 4.64/1.75 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 4.64/1.75 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 4.64/1.75 thf(binintersectI_type, type, binintersectI: $o).
% 4.64/1.75 thf(symdiffI1_type, type, symdiffI1: $o).
% 4.64/1.75 thf(subsetI2_type, type, subsetI2: $o).
% 4.64/1.75 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 4.64/1.75 thf(setminusERneg_type, type, setminusERneg: $o).
% 4.64/1.75 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 4.64/1.75 thf(omega__Cong_type, type, omega__Cong: $o).
% 4.64/1.75 thf(subsetRefl_type, type, subsetRefl: $o).
% 4.64/1.75 thf(uniqinunit_type, type, uniqinunit: $o).
% 4.64/1.75 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 4.64/1.75 thf(prop2setE_type, type, prop2setE: $o).
% 4.64/1.75 thf(binunionEcases_type, type, binunionEcases: $o).
% 4.64/1.75 thf(nonemptyI_type, type, nonemptyI: $o).
% 4.64/1.75 thf(sk__78_type, type, sk__78: $i).
% 4.64/1.75 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 4.64/1.75 thf(exuE3u_type, type, exuE3u: $o).
% 4.64/1.75 thf(setminusEL_type, type, setminusEL: $o).
% 4.64/1.75 thf(sepSubset_type, type, sepSubset: $o).
% 4.64/1.75 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 4.64/1.75 thf(exuI3_type, type, exuI3: $o).
% 4.64/1.75 thf(notdallE_type, type, notdallE: $o).
% 4.64/1.75 thf(binintersectER_type, type, binintersectER: $o).
% 4.64/1.75 thf(powerset_type, type, powerset: $i > $i).
% 4.64/1.75 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 4.64/1.75 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 4.64/1.75 thf(exu__Cong_type, type, exu__Cong: $o).
% 4.64/1.75 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 4.64/1.75 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 4.64/1.75 thf(replAx_type, type, replAx: $o).
% 4.64/1.75 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 4.64/1.75 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 4.64/1.75 thf(secondinupair_type, type, secondinupair: $o).
% 4.64/1.75 thf(inPowerset_type, type, inPowerset: $o).
% 4.64/1.75 thf(subset_type, type, subset: $i > $i > $o).
% 4.64/1.75 thf(in__Cong_type, type, in__Cong: $o).
% 4.64/1.75 thf(binunionRsub_type, type, binunionRsub: $o).
% 4.64/1.75 thf(subset2powerset_type, type, subset2powerset: $o).
% 4.64/1.75 thf(setukpairIL, axiom, setukpairIL =
% 4.64/1.75 (![Xx:$i,Xy:$i]:
% 4.64/1.75 ( in @
% 4.64/1.75 Xx @
% 4.64/1.75 ( setunion @
% 4.64/1.75 ( setadjoin @
% 4.64/1.75 ( setadjoin @ Xx @ emptyset ) @
% 4.64/1.75 ( setadjoin @
% 4.64/1.75 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ))).
% 4.64/1.75 thf('0', plain,
% 4.64/1.75 (( setukpairIL ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( in @
% 4.64/1.75 X4 @
% 4.64/1.75 ( setunion @
% 4.64/1.75 ( setadjoin @
% 4.64/1.75 ( setadjoin @ X4 @ emptyset ) @
% 4.64/1.75 ( setadjoin @
% 4.64/1.75 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(secondinupair, axiom, secondinupair =
% 4.64/1.75 (![Xx:$i,Xy:$i]:
% 4.64/1.75 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 4.64/1.75 thf('1', plain,
% 4.64/1.75 (( secondinupair ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(upairset2IR, axiom, upairset2IR =
% 4.64/1.75 (![Xx:$i,Xy:$i]:
% 4.64/1.75 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 4.64/1.75 thf('2', plain,
% 4.64/1.75 (( upairset2IR ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 4.64/1.75 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 4.64/1.75 thf('3', plain,
% 4.64/1.75 (( subsetemptysetimpeq ) =
% 4.64/1.75 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 4.64/1.75 (![A:$i,Xx:$i,B:$i]:
% 4.64/1.75 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 4.64/1.75 thf('4', plain,
% 4.64/1.75 (( setadjoinSub2 ) =
% 4.64/1.75 ( ![X4:$i,X6:$i,X8:$i]:
% 4.64/1.75 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(setadjoinSub, axiom, setadjoinSub =
% 4.64/1.75 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 4.64/1.75 thf('5', plain,
% 4.64/1.75 (( setadjoinSub ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(emptysetsubset, axiom, emptysetsubset =
% 4.64/1.75 (![A:$i]: ( subset @ emptyset @ A ))).
% 4.64/1.75 thf('6', plain,
% 4.64/1.75 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(setunion__Cong, axiom, setunion__Cong =
% 4.64/1.75 (![A:$i,B:$i]:
% 4.64/1.75 ( ( ( A ) = ( B ) ) => ( ( setunion @ A ) = ( setunion @ B ) ) ))).
% 4.64/1.75 thf('7', plain,
% 4.64/1.75 (( setunion__Cong ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( ( ( X4 ) = ( X6 ) ) => ( ( setunion @ X4 ) = ( setunion @ X6 ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 4.64/1.75 (![Xx:$i,Xy:$i]:
% 4.64/1.75 ( ( ( Xx ) = ( Xy ) ) =>
% 4.64/1.75 ( ![Xz:$i,Xu:$i]:
% 4.64/1.75 ( ( ( Xz ) = ( Xu ) ) =>
% 4.64/1.75 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 4.64/1.75 thf('8', plain,
% 4.64/1.75 (( setadjoin__Cong ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( ( ( X4 ) = ( X6 ) ) =>
% 4.64/1.75 ( ![X8:$i,X10:$i]:
% 4.64/1.75 ( ( ( X8 ) = ( X10 ) ) =>
% 4.64/1.75 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(emptyset__Cong, axiom, emptyset__Cong = (( emptyset ) = ( emptyset ))).
% 4.64/1.75 thf('9', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(vacuousDall, axiom, vacuousDall =
% 4.64/1.75 (![Xphi:( $i > $o ),Xx:$i]: ( ( in @ Xx @ emptyset ) => ( Xphi @ Xx ) ))).
% 4.64/1.75 thf('10', plain,
% 4.64/1.75 (( vacuousDall ) =
% 4.64/1.75 ( ![X4:( $i > $o ),X6:$i]: ( ( in @ X6 @ emptyset ) => ( X4 @ X6 ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(upairsetIR, axiom, upairsetIR =
% 4.64/1.75 (![Xx:$i,Xy:$i]:
% 4.64/1.75 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 4.64/1.75 thf('11', plain,
% 4.64/1.75 (( upairsetIR ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(upairsetIL, axiom, upairsetIL =
% 4.64/1.75 (![Xx:$i,Xy:$i]:
% 4.64/1.75 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 4.64/1.75 thf('12', plain,
% 4.64/1.75 (( upairsetIL ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(upairsetE, axiom, upairsetE =
% 4.64/1.75 (![Xx:$i,Xy:$i,Xz:$i]:
% 4.64/1.75 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 4.64/1.75 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 4.64/1.75 thf('13', plain,
% 4.64/1.75 (( upairsetE ) =
% 4.64/1.75 ( ![X4:$i,X6:$i,X8:$i]:
% 4.64/1.75 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 4.64/1.75 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(singletonsswitch, axiom, singletonsswitch =
% 4.64/1.75 (![Xx:$i,Xy:$i]:
% 4.64/1.75 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 4.64/1.75 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 4.64/1.75 thf('14', plain,
% 4.64/1.75 (( singletonsswitch ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 4.64/1.75 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(eqinunit, axiom, eqinunit =
% 4.64/1.75 (![Xx:$i,Xy:$i]:
% 4.64/1.75 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 4.64/1.75 thf('15', plain,
% 4.64/1.75 (( eqinunit ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(notinsingleton, axiom, notinsingleton =
% 4.64/1.75 (![Xx:$i,Xy:$i]:
% 4.64/1.75 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 4.64/1.75 thf('16', plain,
% 4.64/1.75 (( notinsingleton ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( ( ( X4 ) != ( X6 ) ) =>
% 4.64/1.75 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(uniqinunit, axiom, uniqinunit =
% 4.64/1.75 (![Xx:$i,Xy:$i]:
% 4.64/1.75 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 4.64/1.75 thf('17', plain,
% 4.64/1.75 (( uniqinunit ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(subPowSU, axiom, subPowSU =
% 4.64/1.75 (![A:$i,Xx:$i]:
% 4.64/1.75 ( ( in @ Xx @ A ) => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ))).
% 4.64/1.75 thf('18', plain,
% 4.64/1.75 (( subPowSU ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( ( in @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ ( setunion @ X4 ) ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(setunionE, axiom, setunionE =
% 4.64/1.75 (![A:$i,Xx:$i]:
% 4.64/1.75 ( ( in @ Xx @ ( setunion @ A ) ) =>
% 4.64/1.75 ( ![Xphi:$o]:
% 4.64/1.75 ( ( ![B:$i]: ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( Xphi ) ) ) ) =>
% 4.64/1.75 ( Xphi ) ) ) ))).
% 4.64/1.75 thf('19', plain,
% 4.64/1.75 (( setunionE ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( ( in @ X6 @ ( setunion @ X4 ) ) =>
% 4.64/1.75 ( ![X8:$o]:
% 4.64/1.75 ( ( ![X10:$i]:
% 4.64/1.75 ( ( in @ X6 @ X10 ) => ( ( in @ X10 @ X4 ) => ( X8 ) ) ) ) =>
% 4.64/1.75 ( X8 ) ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(setunionI, axiom, setunionI =
% 4.64/1.75 (![A:$i,Xx:$i,B:$i]:
% 4.64/1.75 ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( in @ Xx @ ( setunion @ A ) ) ) ))).
% 4.64/1.75 thf('20', plain,
% 4.64/1.75 (( setunionI ) =
% 4.64/1.75 ( ![X4:$i,X6:$i,X8:$i]:
% 4.64/1.75 ( ( in @ X6 @ X8 ) =>
% 4.64/1.75 ( ( in @ X8 @ X4 ) => ( in @ X6 @ ( setunion @ X4 ) ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(setadjoinOr, axiom, setadjoinOr =
% 4.64/1.75 (![Xx:$i,A:$i,Xy:$i]:
% 4.64/1.75 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 4.64/1.75 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 4.64/1.75 thf('21', plain,
% 4.64/1.75 (( setadjoinOr ) =
% 4.64/1.75 ( ![X4:$i,X6:$i,X8:$i]:
% 4.64/1.75 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 4.64/1.75 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(setadjoinE, axiom, setadjoinE =
% 4.64/1.75 (![Xx:$i,A:$i,Xy:$i]:
% 4.64/1.75 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 4.64/1.75 ( ![Xphi:$o]:
% 4.64/1.75 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 4.64/1.75 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 4.64/1.75 thf('22', plain,
% 4.64/1.75 (( setadjoinE ) =
% 4.64/1.75 ( ![X4:$i,X6:$i,X8:$i]:
% 4.64/1.75 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 4.64/1.75 ( ![X10:$o]:
% 4.64/1.75 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 4.64/1.75 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(setadjoinIR, axiom, setadjoinIR =
% 4.64/1.75 (![Xx:$i,A:$i,Xy:$i]:
% 4.64/1.75 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 4.64/1.75 thf('23', plain,
% 4.64/1.75 (( setadjoinIR ) =
% 4.64/1.75 ( ![X4:$i,X6:$i,X8:$i]:
% 4.64/1.75 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 4.64/1.75 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 4.64/1.75 thf('24', plain,
% 4.64/1.75 (( emptyinunitempty ) =
% 4.64/1.75 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 4.64/1.75 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 4.64/1.75 thf('25', plain,
% 4.64/1.75 (( emptyinunitempty ) =
% 4.64/1.75 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(setadjoinIL, axiom, setadjoinIL =
% 4.64/1.75 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 4.64/1.75 thf('26', plain,
% 4.64/1.75 (( setadjoinIL ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(noeltsimpempty, axiom, noeltsimpempty =
% 4.64/1.75 (![A:$i]:
% 4.64/1.75 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 4.64/1.75 thf('27', plain,
% 4.64/1.75 (( noeltsimpempty ) =
% 4.64/1.75 ( ![X4:$i]:
% 4.64/1.75 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(emptyI, axiom, emptyI =
% 4.64/1.75 (![A:$i]:
% 4.64/1.75 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 4.64/1.75 thf('28', plain,
% 4.64/1.75 (( emptyI ) =
% 4.64/1.75 ( ![X4:$i]:
% 4.64/1.75 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(notinemptyset, axiom, notinemptyset =
% 4.64/1.75 (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 4.64/1.75 thf('29', plain,
% 4.64/1.75 (( notinemptyset ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(emptysetimpfalse, axiom, emptysetimpfalse =
% 4.64/1.75 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( $false ) ))).
% 4.64/1.75 thf('30', plain,
% 4.64/1.75 (( emptysetimpfalse ) =
% 4.64/1.75 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( $false ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(emptysetE, axiom, emptysetE =
% 4.64/1.75 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( ![Xphi:$o]: ( Xphi ) ) ))).
% 4.64/1.75 thf('31', plain,
% 4.64/1.75 (( emptysetE ) =
% 4.64/1.75 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( ![X6:$o]: ( X6 ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(setunionAx, axiom, setunionAx =
% 4.64/1.75 (![A:$i,Xx:$i]:
% 4.64/1.75 ( ( in @ Xx @ ( setunion @ A ) ) <=>
% 4.64/1.75 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))).
% 4.64/1.75 thf('32', plain,
% 4.64/1.75 (( setunionAx ) =
% 4.64/1.75 ( ![X4:$i,X6:$i]:
% 4.64/1.75 ( ( in @ X6 @ ( setunion @ X4 ) ) <=>
% 4.64/1.75 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(setadjoinAx, axiom, setadjoinAx =
% 4.64/1.75 (![Xx:$i,A:$i,Xy:$i]:
% 4.64/1.75 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 4.64/1.75 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 4.64/1.75 thf('33', plain,
% 4.64/1.75 (( setadjoinAx ) =
% 4.64/1.75 ( ![X4:$i,X6:$i,X8:$i]:
% 4.64/1.75 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 4.64/1.75 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 4.64/1.75 thf('34', plain,
% 4.64/1.75 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 4.64/1.75 define([status(thm)])).
% 4.64/1.75 thf(setukpairIR, conjecture,
% 4.64/1.75 (( setextAx ) =>
% 4.64/1.75 ( ( emptysetAx ) =>
% 4.64/1.75 ( ( setadjoinAx ) =>
% 4.64/1.75 ( ( powersetAx ) =>
% 4.64/1.75 ( ( setunionAx ) =>
% 4.64/1.75 ( ( omega0Ax ) =>
% 4.64/1.75 ( ( omegaSAx ) =>
% 4.64/1.75 ( ( omegaIndAx ) =>
% 4.64/1.75 ( ( replAx ) =>
% 4.64/1.75 ( ( foundationAx ) =>
% 4.64/1.75 ( ( wellorderingAx ) =>
% 4.64/1.75 ( ( descrp ) =>
% 4.64/1.75 ( ( dsetconstrI ) =>
% 4.64/1.75 ( ( dsetconstrEL ) =>
% 4.64/1.75 ( ( dsetconstrER ) =>
% 4.64/1.75 ( ( exuE1 ) =>
% 4.64/1.75 ( ( prop2setE ) =>
% 4.64/1.75 ( ( emptysetE ) =>
% 4.64/1.75 ( ( emptysetimpfalse ) =>
% 4.64/1.75 ( ( notinemptyset ) =>
% 4.64/1.75 ( ( exuE3e ) =>
% 4.64/1.75 ( ( setext ) =>
% 4.64/1.75 ( ( emptyI ) =>
% 4.64/1.75 ( ( noeltsimpempty ) =>
% 4.64/1.75 ( ( setbeta ) =>
% 4.64/1.75 ( ( nonemptyE1 ) =>
% 4.64/1.75 ( ( nonemptyI ) =>
% 4.64/1.75 ( ( nonemptyI1 ) =>
% 4.64/1.75 ( ( setadjoinIL ) =>
% 4.64/1.75 ( ( emptyinunitempty ) =>
% 4.64/1.75 ( ( setadjoinIR ) =>
% 4.64/1.75 ( ( setadjoinE ) =>
% 4.64/1.75 ( (
% 4.64/1.75 setadjoinOr ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setoftrueEq ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 powersetI ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 emptyinPowerset ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 emptyInPowerset ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 powersetE ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setunionI ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setunionE ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 subPowSU ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 exuE2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 nonemptyImpWitness ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 uniqinunit ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 notinsingleton ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 eqinunit ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 singletonsswitch ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 upairsetE ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 upairsetIL ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 upairsetIR ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 emptyE1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 vacuousDall ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 quantDeMorgan1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 quantDeMorgan2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 quantDeMorgan3 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 quantDeMorgan4 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 prop2setI ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 prop2set2propI ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 notdexE ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 notdallE ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 exuI1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 exuI3 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 exuI2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 inCongP ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in__Cong ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 exuE3u ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 exu__Cong ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 emptyset__Cong ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setadjoin__Cong ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 powerset__Cong ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setunion__Cong ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 omega__Cong ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 exuEu ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 descr__Cong ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 dsetconstr__Cong ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 subsetI1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 eqimpsubset2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 eqimpsubset1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 subsetI2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 emptysetsubset ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 subsetE ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 subsetE2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 notsubsetI ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 notequalI1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 notequalI2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 subsetRefl ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 subsetTrans ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setadjoinSub ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setadjoinSub2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 subset2powerset ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setextsub ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 subsetemptysetimpeq ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 powersetI1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 powersetE1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 inPowerset ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 powersetsubset ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 sepInPowerset ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 sepSubset ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binunionIL ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 upairset2IR ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binunionIR ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binunionEcases ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binunionE ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binunionLsub ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binunionRsub ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binintersectI ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binintersectSubset5 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binintersectEL ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binintersectLsub ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binintersectSubset2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binintersectSubset3 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binintersectER ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 disjointsetsI1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binintersectRsub ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binintersectSubset4 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 binintersectSubset1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 bs114d ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setminusI ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setminusEL ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setminusER ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setminusSubset2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setminusERneg ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setminusELneg ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setminusILneg ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setminusIRneg ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setminusLsub ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setminusSubset1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 symdiffE ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 symdiffI1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 symdiffI2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 symdiffIneg1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 symdiffIneg2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 secondinupair ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setukpairIL ) =>
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 Xx:$i,
% 4.64/1.75 Xy:$i]:
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 Xy @
% 4.64/1.75 (
% 4.64/1.75 setunion @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 Xx @
% 4.64/1.75 emptyset ) @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 Xx @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 Xy @
% 4.64/1.75 emptyset ) ) @
% 4.64/1.75 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 4.64/1.75 thf(zf_stmt_0, conjecture,
% 4.64/1.75 (( setextAx ) =>
% 4.64/1.75 ( ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) ) =>
% 4.64/1.75 ( ( ![X6:$i,X8:$i,X10:$i]:
% 4.64/1.75 ( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) ) <=>
% 4.64/1.75 ( ( in @ X10 @ X8 ) | ( ( X10 ) = ( X6 ) ) ) ) ) =>
% 4.64/1.75 ( ( powersetAx ) =>
% 4.64/1.75 ( ( ![X12:$i,X14:$i]:
% 4.64/1.75 ( ( in @ X14 @ ( setunion @ X12 ) ) <=>
% 4.64/1.75 ( ?[X16:$i]: ( ( in @ X14 @ X16 ) & ( in @ X16 @ X12 ) ) ) ) ) =>
% 4.64/1.75 ( ( omega0Ax ) =>
% 4.64/1.75 ( ( omegaSAx ) =>
% 4.64/1.75 ( ( omegaIndAx ) =>
% 4.64/1.75 ( ( replAx ) =>
% 4.64/1.75 ( ( foundationAx ) =>
% 4.64/1.75 ( ( wellorderingAx ) =>
% 4.64/1.75 ( ( descrp ) =>
% 4.64/1.75 ( ( dsetconstrI ) =>
% 4.64/1.75 ( ( dsetconstrEL ) =>
% 4.64/1.75 ( ( dsetconstrER ) =>
% 4.64/1.75 ( ( exuE1 ) =>
% 4.64/1.75 ( ( prop2setE ) =>
% 4.64/1.75 ( ( ![X18:$i]:
% 4.64/1.75 ( ( in @ X18 @ emptyset ) =>
% 4.64/1.75 ( ![X20:$o]: ( X20 ) ) ) ) =>
% 4.64/1.75 ( ( ![X22:$i]:
% 4.64/1.75 ( ( in @ X22 @ emptyset ) =>
% 4.64/1.75 ( $false ) ) ) =>
% 4.64/1.75 ( ( ![X24:$i]:
% 4.64/1.75 ( ~( in @ X24 @ emptyset ) ) ) =>
% 4.64/1.75 ( ( exuE3e ) =>
% 4.64/1.75 ( ( setext ) =>
% 4.64/1.75 ( ( ![X26:$i]:
% 4.64/1.75 ( ( ![X28:$i]:
% 4.64/1.75 ( ~( in @ X28 @ X26 ) ) ) =>
% 4.64/1.75 ( ( X26 ) = ( emptyset ) ) ) ) =>
% 4.64/1.75 ( ( ![X30:$i]:
% 4.64/1.75 ( ( ![X32:$i]:
% 4.64/1.75 ( ~( in @ X32 @ X30 ) ) ) =>
% 4.64/1.75 ( ( X30 ) = ( emptyset ) ) ) ) =>
% 4.64/1.75 ( ( setbeta ) =>
% 4.64/1.75 ( ( nonemptyE1 ) =>
% 4.64/1.75 ( ( nonemptyI ) =>
% 4.64/1.75 ( ( nonemptyI1 ) =>
% 4.64/1.75 ( ( ![X34:$i,X36:$i]:
% 4.64/1.75 ( in @
% 4.64/1.75 X34 @
% 4.64/1.75 ( setadjoin @
% 4.64/1.75 X34 @ X36 ) ) ) =>
% 4.64/1.75 ( ( in @
% 4.64/1.75 emptyset @
% 4.64/1.75 ( setadjoin @
% 4.64/1.75 emptyset @
% 4.64/1.75 emptyset ) ) =>
% 4.64/1.75 ( ( ![X38:$i,
% 4.64/1.75 X40:$i,
% 4.64/1.75 X42:$i]:
% 4.64/1.75 ( (
% 4.64/1.75 in @
% 4.64/1.75 X42 @ X40 ) =>
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X42 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X38 @ X40 ) ) ) ) =>
% 4.64/1.75 ( ( ![
% 4.64/1.75 X44:$i,
% 4.64/1.75 X46:$i,
% 4.64/1.75 X48:$i]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X48 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X44 @ X46 ) ) =>
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X50:$o]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 X48 ) =
% 4.64/1.75 (
% 4.64/1.75 X44 ) ) =>
% 4.64/1.75 (
% 4.64/1.75 X50 ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X48 @ X46 ) =>
% 4.64/1.75 (
% 4.64/1.75 X50 ) ) =>
% 4.64/1.75 (
% 4.64/1.75 X50 ) ) ) ) ) ) =>
% 4.64/1.75 ( (
% 4.64/1.75 ![
% 4.64/1.75 X52:$i,
% 4.64/1.75 X54:$i,
% 4.64/1.75 X56:$i]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X56 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X52 @ X54 ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X56 @ X54 ) |
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 X56 ) =
% 4.64/1.75 (
% 4.64/1.75 X52 ) ) ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 setoftrueEq ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 powersetI ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 emptyinPowerset ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 emptyInPowerset ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 powersetE ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X58:$i,
% 4.64/1.75 X60:$i,
% 4.64/1.75 X62:$i]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X60 @ X62 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X62 @ X58 ) =>
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X60 @
% 4.64/1.75 (
% 4.64/1.75 setunion @
% 4.64/1.75 X58 ) ) ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X64:$i,
% 4.64/1.75 X66:$i]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X66 @
% 4.64/1.75 (
% 4.64/1.75 setunion @
% 4.64/1.75 X64 ) ) =>
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X68:$o]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X70:$i]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X66 @ X70 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X70 @ X64 ) =>
% 4.64/1.75 (
% 4.64/1.75 X68 ) ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 X68 ) ) ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X72:$i,
% 4.64/1.75 X74:$i]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X74 @ X72 ) =>
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X74 @
% 4.64/1.75 (
% 4.64/1.75 powerset @
% 4.64/1.75 (
% 4.64/1.75 setunion @
% 4.64/1.75 X72 ) ) ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 exuE2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 nonemptyImpWitness ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X76:$i,
% 4.64/1.75 X78:$i]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X76 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X78 @
% 4.64/1.75 emptyset ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 X76 ) =
% 4.64/1.75 (
% 4.64/1.75 X78 ) ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X80:$i,
% 4.64/1.75 X82:$i]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 X80 ) !=
% 4.64/1.75 (
% 4.64/1.75 X82 ) ) =>
% 4.64/1.75 (
% 4.64/1.75 ~(
% 4.64/1.75 in @
% 4.64/1.75 X82 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X80 @
% 4.64/1.75 emptyset ) ) ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X84:$i,
% 4.64/1.75 X86:$i]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 X84 ) =
% 4.64/1.75 (
% 4.64/1.75 X86 ) ) =>
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X84 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X86 @
% 4.64/1.75 emptyset ) ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X88:$i,
% 4.64/1.75 X90:$i]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X88 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X90 @
% 4.64/1.75 emptyset ) ) =>
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X90 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X88 @
% 4.64/1.75 emptyset ) ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X92:$i,
% 4.64/1.75 X94:$i,
% 4.64/1.75 X96:$i]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X96 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X92 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X94 @
% 4.64/1.75 emptyset ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 X96 ) =
% 4.64/1.75 (
% 4.64/1.75 X94 ) ) |
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 X96 ) =
% 4.64/1.75 (
% 4.64/1.75 X92 ) ) ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X98:$i,
% 4.64/1.75 X100:$i]:
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X98 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X98 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X100 @
% 4.64/1.75 emptyset ) ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X102:$i,
% 4.64/1.75 X104:$i]:
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X104 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X102 @
% 4.64/1.75 (
% 4.64/1.75 setadjoin
% 4.64/1.75 @
% 4.64/1.75 X104 @
% 4.64/1.75 emptyset ) ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 emptyE1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 ![
% 4.64/1.75 X106:(
% 4.64/1.75 $i > $o ),
% 4.64/1.75 X108:$i]:
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 in @
% 4.64/1.75 X108 @
% 4.64/1.75 emptyset ) =>
% 4.64/1.75 (
% 4.64/1.75 X106 @
% 4.64/1.75 X108 ) ) ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 quantDeMorgan1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 quantDeMorgan2 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 quantDeMorgan3 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 quantDeMorgan4 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 prop2setI ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 prop2set2propI ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 notdexE ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 notdallE ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 exuI1 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 exuI3 ) =>
% 4.64/1.75 (
% 4.64/1.75 (
% 4.64/1.75 exuI2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 inCongP ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 exuE3u ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 exu__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 emptyset ) =
% 4.64/1.76 (
% 4.64/1.76 emptyset ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X110:$i,
% 4.64/1.76 X112:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X110 ) =
% 4.64/1.76 (
% 4.64/1.76 X112 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X114:$i,
% 4.64/1.76 X116:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X114 ) =
% 4.64/1.76 (
% 4.64/1.76 X116 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X110 @
% 4.64/1.76 X114 ) =
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X112 @
% 4.64/1.76 X116 ) ) ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 powerset__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X118:$i,
% 4.64/1.76 X120:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X118 ) =
% 4.64/1.76 (
% 4.64/1.76 X120 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setunion @
% 4.64/1.76 X118 ) =
% 4.64/1.76 (
% 4.64/1.76 setunion @
% 4.64/1.76 X120 ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 omega__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 exuEu ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 descr__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 dsetconstr__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetI1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 eqimpsubset2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 eqimpsubset1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetI2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X122:$i]:
% 4.64/1.76 (
% 4.64/1.76 subset @
% 4.64/1.76 emptyset @
% 4.64/1.76 X122 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetE ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetE2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 notsubsetI ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 notequalI1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 notequalI2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetRefl ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetTrans ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X124:$i,
% 4.64/1.76 X126:$i]:
% 4.64/1.76 (
% 4.64/1.76 subset @
% 4.64/1.76 X126 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X124 @
% 4.64/1.76 X126 ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X128:$i,
% 4.64/1.76 X130:$i,
% 4.64/1.76 X132:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subset @
% 4.64/1.76 X128 @
% 4.64/1.76 X132 ) =>
% 4.64/1.76 (
% 4.64/1.76 subset @
% 4.64/1.76 X128 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X130 @
% 4.64/1.76 X132 ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subset2powerset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setextsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X134:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subset @
% 4.64/1.76 X134 @
% 4.64/1.76 emptyset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X134 ) =
% 4.64/1.76 (
% 4.64/1.76 emptyset ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 powersetI1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 powersetE1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 inPowerset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 powersetsubset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 sepInPowerset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 sepSubset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionIL ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X136:$i,
% 4.64/1.76 X138:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X138 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X136 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X138 @
% 4.64/1.76 emptyset ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionIR ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionEcases ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionE ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionLsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionRsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectI ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectSubset5 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectEL ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectLsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectSubset2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectSubset3 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectER ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 disjointsetsI1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectRsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectSubset4 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectSubset1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 bs114d ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusI ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusEL ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusER ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusSubset2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusERneg ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusELneg ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusILneg ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusIRneg ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusLsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusSubset1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 symdiffE ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 symdiffI1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 symdiffI2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 symdiffIneg1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 symdiffIneg2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X140:$i,
% 4.64/1.76 X142:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X142 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X140 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X142 @
% 4.64/1.76 emptyset ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X144:$i,
% 4.64/1.76 X146:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X144 @
% 4.64/1.76 (
% 4.64/1.76 setunion @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X144 @
% 4.64/1.76 emptyset ) @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X144 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X146 @
% 4.64/1.76 emptyset ) ) @
% 4.64/1.76 emptyset ) ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X148:$i,
% 4.64/1.76 X150:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X150 @
% 4.64/1.76 (
% 4.64/1.76 setunion @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X148 @
% 4.64/1.76 emptyset ) @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X148 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X150 @
% 4.64/1.76 emptyset ) ) @
% 4.64/1.76 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 4.64/1.76 thf(zf_stmt_1, type, zip_tseitin_1 : $i > $i > $i > $o).
% 4.64/1.76 thf(zf_stmt_2, axiom,
% 4.64/1.76 (![X16:$i,X14:$i,X12:$i]:
% 4.64/1.76 ( ( zip_tseitin_1 @ X16 @ X14 @ X12 ) <=>
% 4.64/1.76 ( ( in @ X16 @ X12 ) & ( in @ X14 @ X16 ) ) ))).
% 4.64/1.76 thf(zf_stmt_3, type, zip_tseitin_0 : $i > $i > $i > $o).
% 4.64/1.76 thf(zf_stmt_4, axiom,
% 4.64/1.76 (![X10:$i,X8:$i,X6:$i]:
% 4.64/1.76 ( ( zip_tseitin_0 @ X10 @ X8 @ X6 ) <=>
% 4.64/1.76 ( ( ( X10 ) = ( X6 ) ) | ( in @ X10 @ X8 ) ) ))).
% 4.64/1.76 thf(zf_stmt_5, conjecture,
% 4.64/1.76 (( setextAx ) =>
% 4.64/1.76 ( ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) ) =>
% 4.64/1.76 ( ( ![X6:$i,X8:$i,X10:$i]:
% 4.64/1.76 ( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) ) <=>
% 4.64/1.76 ( zip_tseitin_0 @ X10 @ X8 @ X6 ) ) ) =>
% 4.64/1.76 ( ( powersetAx ) =>
% 4.64/1.76 ( ( ![X12:$i,X14:$i]:
% 4.64/1.76 ( ( in @ X14 @ ( setunion @ X12 ) ) <=>
% 4.64/1.76 ( ?[X16:$i]: ( zip_tseitin_1 @ X16 @ X14 @ X12 ) ) ) ) =>
% 4.64/1.76 ( ( omega0Ax ) =>
% 4.64/1.76 ( ( omegaSAx ) =>
% 4.64/1.76 ( ( omegaIndAx ) =>
% 4.64/1.76 ( ( replAx ) =>
% 4.64/1.76 ( ( foundationAx ) =>
% 4.64/1.76 ( ( wellorderingAx ) =>
% 4.64/1.76 ( ( descrp ) =>
% 4.64/1.76 ( ( dsetconstrI ) =>
% 4.64/1.76 ( ( dsetconstrEL ) =>
% 4.64/1.76 ( ( dsetconstrER ) =>
% 4.64/1.76 ( ( exuE1 ) =>
% 4.64/1.76 ( ( prop2setE ) =>
% 4.64/1.76 ( ( ![X18:$i]:
% 4.64/1.76 ( ( in @ X18 @ emptyset ) =>
% 4.64/1.76 ( ![X20:$o]: ( X20 ) ) ) ) =>
% 4.64/1.76 ( ( ![X22:$i]:
% 4.64/1.76 ( ~( in @ X22 @ emptyset ) ) ) =>
% 4.64/1.76 ( ( ![X24:$i]:
% 4.64/1.76 ( ~( in @ X24 @ emptyset ) ) ) =>
% 4.64/1.76 ( ( exuE3e ) =>
% 4.64/1.76 ( ( setext ) =>
% 4.64/1.76 ( ( ![X26:$i]:
% 4.64/1.76 ( ( ![X28:$i]:
% 4.64/1.76 ( ~( in @ X28 @ X26 ) ) ) =>
% 4.64/1.76 ( ( X26 ) = ( emptyset ) ) ) ) =>
% 4.64/1.76 ( ( ![X30:$i]:
% 4.64/1.76 ( ( ![X32:$i]:
% 4.64/1.76 ( ~( in @ X32 @ X30 ) ) ) =>
% 4.64/1.76 ( ( X30 ) = ( emptyset ) ) ) ) =>
% 4.64/1.76 ( ( setbeta ) =>
% 4.64/1.76 ( ( nonemptyE1 ) =>
% 4.64/1.76 ( ( nonemptyI ) =>
% 4.64/1.76 ( ( nonemptyI1 ) =>
% 4.64/1.76 ( ( ![X34:$i,X36:$i]:
% 4.64/1.76 ( in @
% 4.64/1.76 X34 @
% 4.64/1.76 ( setadjoin @
% 4.64/1.76 X34 @ X36 ) ) ) =>
% 4.64/1.76 ( ( in @
% 4.64/1.76 emptyset @
% 4.64/1.76 ( setadjoin @
% 4.64/1.76 emptyset @
% 4.64/1.76 emptyset ) ) =>
% 4.64/1.76 ( ( ![X38:$i,
% 4.64/1.76 X40:$i,
% 4.64/1.76 X42:$i]:
% 4.64/1.76 ( (
% 4.64/1.76 in @
% 4.64/1.76 X42 @ X40 ) =>
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X42 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X38 @ X40 ) ) ) ) =>
% 4.64/1.76 ( ( ![
% 4.64/1.76 X44:$i,
% 4.64/1.76 X46:$i,
% 4.64/1.76 X48:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X48 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X44 @ X46 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X50:$o]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X48 ) =
% 4.64/1.76 (
% 4.64/1.76 X44 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 X50 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X48 @ X46 ) =>
% 4.64/1.76 (
% 4.64/1.76 X50 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 X50 ) ) ) ) ) ) =>
% 4.64/1.76 ( (
% 4.64/1.76 ![
% 4.64/1.76 X52:$i,
% 4.64/1.76 X54:$i,
% 4.64/1.76 X56:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X56 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X52 @ X54 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X56 ) =
% 4.64/1.76 (
% 4.64/1.76 X52 ) ) |
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X56 @ X54 ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setoftrueEq ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 powersetI ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 emptyinPowerset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 emptyInPowerset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 powersetE ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X58:$i,
% 4.64/1.76 X60:$i,
% 4.64/1.76 X62:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X60 @ X62 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X62 @ X58 ) =>
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X60 @
% 4.64/1.76 (
% 4.64/1.76 setunion @
% 4.64/1.76 X58 ) ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X64:$i,
% 4.64/1.76 X66:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X66 @
% 4.64/1.76 (
% 4.64/1.76 setunion @
% 4.64/1.76 X64 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X68:$o]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X70:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X66 @ X70 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X70 @ X64 ) =>
% 4.64/1.76 (
% 4.64/1.76 X68 ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 X68 ) ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X72:$i,
% 4.64/1.76 X74:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X74 @ X72 ) =>
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X74 @
% 4.64/1.76 (
% 4.64/1.76 powerset @
% 4.64/1.76 (
% 4.64/1.76 setunion @
% 4.64/1.76 X72 ) ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 exuE2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 nonemptyImpWitness ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X76:$i,
% 4.64/1.76 X78:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X78 @
% 4.64/1.76 emptyset ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X76 ) =
% 4.64/1.76 (
% 4.64/1.76 X78 ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X80:$i,
% 4.64/1.76 X82:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X80 ) !=
% 4.64/1.76 (
% 4.64/1.76 X82 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 ~(
% 4.64/1.76 in @
% 4.64/1.76 X82 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X80 @
% 4.64/1.76 emptyset ) ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X84:$i,
% 4.64/1.76 X86:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X84 ) =
% 4.64/1.76 (
% 4.64/1.76 X86 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X84 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X86 @
% 4.64/1.76 emptyset ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X88:$i,
% 4.64/1.76 X90:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X88 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X90 @
% 4.64/1.76 emptyset ) ) =>
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X90 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X88 @
% 4.64/1.76 emptyset ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X92:$i,
% 4.64/1.76 X94:$i,
% 4.64/1.76 X96:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X96 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X92 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X94 @
% 4.64/1.76 emptyset ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X96 ) =
% 4.64/1.76 (
% 4.64/1.76 X92 ) ) |
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X96 ) =
% 4.64/1.76 (
% 4.64/1.76 X94 ) ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X98:$i,
% 4.64/1.76 X100:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X98 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X98 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X100 @
% 4.64/1.76 emptyset ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X102:$i,
% 4.64/1.76 X104:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X104 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X102 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X104 @
% 4.64/1.76 emptyset ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 emptyE1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X106:(
% 4.64/1.76 $i > $o ),
% 4.64/1.76 X108:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X108 @
% 4.64/1.76 emptyset ) =>
% 4.64/1.76 (
% 4.64/1.76 X106 @
% 4.64/1.76 X108 ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 quantDeMorgan1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 quantDeMorgan2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 quantDeMorgan3 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 quantDeMorgan4 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 prop2setI ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 prop2set2propI ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 notdexE ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 notdallE ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 exuI1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 exuI3 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 exuI2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 inCongP ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 exuE3u ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 exu__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 emptyset ) =
% 4.64/1.76 (
% 4.64/1.76 emptyset ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X110:$i,
% 4.64/1.76 X112:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X110 ) =
% 4.64/1.76 (
% 4.64/1.76 X112 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X114:$i,
% 4.64/1.76 X116:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X114 ) =
% 4.64/1.76 (
% 4.64/1.76 X116 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X110 @
% 4.64/1.76 X114 ) =
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X112 @
% 4.64/1.76 X116 ) ) ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 powerset__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X118:$i,
% 4.64/1.76 X120:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X118 ) =
% 4.64/1.76 (
% 4.64/1.76 X120 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setunion @
% 4.64/1.76 X118 ) =
% 4.64/1.76 (
% 4.64/1.76 setunion @
% 4.64/1.76 X120 ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 omega__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 exuEu ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 descr__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 dsetconstr__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetI1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 eqimpsubset2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 eqimpsubset1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetI2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X122:$i]:
% 4.64/1.76 (
% 4.64/1.76 subset @
% 4.64/1.76 emptyset @
% 4.64/1.76 X122 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetE ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetE2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 notsubsetI ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 notequalI1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 notequalI2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetRefl ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetTrans ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X124:$i,
% 4.64/1.76 X126:$i]:
% 4.64/1.76 (
% 4.64/1.76 subset @
% 4.64/1.76 X126 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X124 @
% 4.64/1.76 X126 ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X128:$i,
% 4.64/1.76 X130:$i,
% 4.64/1.76 X132:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subset @
% 4.64/1.76 X128 @
% 4.64/1.76 X132 ) =>
% 4.64/1.76 (
% 4.64/1.76 subset @
% 4.64/1.76 X128 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X130 @
% 4.64/1.76 X132 ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subset2powerset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setextsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X134:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subset @
% 4.64/1.76 X134 @
% 4.64/1.76 emptyset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X134 ) =
% 4.64/1.76 (
% 4.64/1.76 emptyset ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 powersetI1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 powersetE1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 inPowerset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 powersetsubset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 sepInPowerset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 sepSubset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionIL ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X136:$i,
% 4.64/1.76 X138:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X138 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X136 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X138 @
% 4.64/1.76 emptyset ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionIR ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionEcases ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionE ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionLsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionRsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectI ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectSubset5 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectEL ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectLsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectSubset2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectSubset3 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectER ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 disjointsetsI1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectRsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectSubset4 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectSubset1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 bs114d ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusI ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusEL ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusER ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusSubset2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusERneg ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusELneg ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusILneg ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusIRneg ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusLsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 setminusSubset1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 symdiffE ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 symdiffI1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 symdiffI2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 symdiffIneg1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 symdiffIneg2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X140:$i,
% 4.64/1.76 X142:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X142 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X140 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X142 @
% 4.64/1.76 emptyset ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X144:$i,
% 4.64/1.76 X146:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X144 @
% 4.64/1.76 (
% 4.64/1.76 setunion @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X144 @
% 4.64/1.76 emptyset ) @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X144 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X146 @
% 4.64/1.76 emptyset ) ) @
% 4.64/1.76 emptyset ) ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X148:$i,
% 4.64/1.76 X150:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X150 @
% 4.64/1.76 (
% 4.64/1.76 setunion @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X148 @
% 4.64/1.76 emptyset ) @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X148 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X150 @
% 4.64/1.76 emptyset ) ) @
% 4.64/1.76 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 4.64/1.76 thf(zf_stmt_6, negated_conjecture,
% 4.64/1.76 (~( ( setextAx ) =>
% 4.64/1.76 ( ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) ) =>
% 4.64/1.76 ( ( ![X6:$i,X8:$i,X10:$i]:
% 4.64/1.76 ( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) ) <=>
% 4.64/1.76 ( zip_tseitin_0 @ X10 @ X8 @ X6 ) ) ) =>
% 4.64/1.76 ( ( powersetAx ) =>
% 4.64/1.76 ( ( ![X12:$i,X14:$i]:
% 4.64/1.76 ( ( in @ X14 @ ( setunion @ X12 ) ) <=>
% 4.64/1.76 ( ?[X16:$i]: ( zip_tseitin_1 @ X16 @ X14 @ X12 ) ) ) ) =>
% 4.64/1.76 ( ( omega0Ax ) =>
% 4.64/1.76 ( ( omegaSAx ) =>
% 4.64/1.76 ( ( omegaIndAx ) =>
% 4.64/1.76 ( ( replAx ) =>
% 4.64/1.76 ( ( foundationAx ) =>
% 4.64/1.76 ( ( wellorderingAx ) =>
% 4.64/1.76 ( ( descrp ) =>
% 4.64/1.76 ( ( dsetconstrI ) =>
% 4.64/1.76 ( ( dsetconstrEL ) =>
% 4.64/1.76 ( ( dsetconstrER ) =>
% 4.64/1.76 ( ( exuE1 ) =>
% 4.64/1.76 ( ( prop2setE ) =>
% 4.64/1.76 ( ( ![X18:$i]:
% 4.64/1.76 ( ( in @ X18 @ emptyset ) =>
% 4.64/1.76 ( ![X20:$o]: ( X20 ) ) ) ) =>
% 4.64/1.76 ( ( ![X22:$i]:
% 4.64/1.76 ( ~( in @ X22 @ emptyset ) ) ) =>
% 4.64/1.76 ( ( ![X24:$i]:
% 4.64/1.76 ( ~( in @ X24 @ emptyset ) ) ) =>
% 4.64/1.76 ( ( exuE3e ) =>
% 4.64/1.76 ( ( setext ) =>
% 4.64/1.76 ( ( ![X26:$i]:
% 4.64/1.76 ( ( ![X28:$i]:
% 4.64/1.76 ( ~( in @ X28 @ X26 ) ) ) =>
% 4.64/1.76 ( ( X26 ) =
% 4.64/1.76 ( emptyset ) ) ) ) =>
% 4.64/1.76 ( ( ![X30:$i]:
% 4.64/1.76 ( ( ![X32:$i]:
% 4.64/1.76 ( ~( in @ X32 @ X30 ) ) ) =>
% 4.64/1.76 ( ( X30 ) =
% 4.64/1.76 ( emptyset ) ) ) ) =>
% 4.64/1.76 ( ( setbeta ) =>
% 4.64/1.76 ( ( nonemptyE1 ) =>
% 4.64/1.76 ( ( nonemptyI ) =>
% 4.64/1.76 ( ( nonemptyI1 ) =>
% 4.64/1.76 ( ( ![X34:$i,
% 4.64/1.76 X36:$i]:
% 4.64/1.76 ( in @
% 4.64/1.76 X34 @
% 4.64/1.76 ( setadjoin
% 4.64/1.76 @
% 4.64/1.76 X34 @ X36 ) ) ) =>
% 4.64/1.76 ( ( in @
% 4.64/1.76 emptyset @
% 4.64/1.76 ( setadjoin
% 4.64/1.76 @
% 4.64/1.76 emptyset @
% 4.64/1.76 emptyset ) ) =>
% 4.64/1.76 ( ( ![
% 4.64/1.76 X38:$i,
% 4.64/1.76 X40:$i,
% 4.64/1.76 X42:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X42 @ X40 ) =>
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X42 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X38 @ X40 ) ) ) ) =>
% 4.64/1.76 ( (
% 4.64/1.76 ![
% 4.64/1.76 X44:$i,
% 4.64/1.76 X46:$i,
% 4.64/1.76 X48:$i]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X48 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X44 @ X46 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X50:$o]:
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 X48 ) =
% 4.64/1.76 (
% 4.64/1.76 X44 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 X50 ) ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 in @
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% 4.64/1.76 (
% 4.64/1.76 quantDeMorgan3 ) =>
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
% 4.64/1.76 (
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% 4.64/1.76 (
% 4.64/1.76 (
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% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X118:$i,
% 4.64/1.76 X120:$i]:
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% 4.64/1.76 (
% 4.64/1.76 (
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% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 omega__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 exuEu ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 descr__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 dsetconstr__Cong ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetI1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetE ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetE2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 notsubsetI ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 notequalI1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
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% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 subsetRefl ) =>
% 4.64/1.76 (
% 4.64/1.76 (
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% 4.64/1.76 X130:$i,
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
% 4.64/1.76 (
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% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 powersetE1 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 inPowerset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 powersetsubset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 sepInPowerset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 sepSubset ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionIL ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X136:$i,
% 4.64/1.76 X138:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
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% 4.64/1.76 (
% 4.64/1.76 setadjoin
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% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionIR ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionEcases ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionE ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionLsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binunionRsub ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectI ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectSubset5 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 binintersectEL ) =>
% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
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% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 symdiffI2 ) =>
% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 symdiffIneg1 ) =>
% 4.64/1.76 (
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% 4.64/1.76 (
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X140:$i,
% 4.64/1.76 X142:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X142 @
% 4.64/1.76 (
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% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X144:$i,
% 4.64/1.76 X146:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X144 @
% 4.64/1.76 (
% 4.64/1.76 setunion
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X144 @
% 4.64/1.76 emptyset ) @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X144 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X146 @
% 4.64/1.76 emptyset ) ) @
% 4.64/1.76 emptyset ) ) ) ) ) =>
% 4.64/1.76 (
% 4.64/1.76 ![
% 4.64/1.76 X148:$i,
% 4.64/1.76 X150:$i]:
% 4.64/1.76 (
% 4.64/1.76 in @
% 4.64/1.76 X150 @
% 4.64/1.76 (
% 4.64/1.76 setunion
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X148 @
% 4.64/1.76 emptyset ) @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X148 @
% 4.64/1.76 (
% 4.64/1.76 setadjoin
% 4.64/1.76 @
% 4.64/1.76 X150 @
% 4.64/1.76 emptyset ) ) @
% 4.64/1.76 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 4.64/1.76 inference('cnf.neg', [status(esa)], [zf_stmt_5])).
% 4.64/1.76 thf(zip_derived_cl75, plain,
% 4.64/1.76 (~ (in @ sk__78 @
% 4.64/1.76 (setunion @
% 4.64/1.76 (setadjoin @ (setadjoin @ sk__77 @ emptyset) @
% 4.64/1.76 (setadjoin @
% 4.64/1.76 (setadjoin @ sk__77 @ (setadjoin @ sk__78 @ emptyset)) @ emptyset))))),
% 4.64/1.76 inference('cnf', [status(esa)], [zf_stmt_6])).
% 4.64/1.76 thf(zip_derived_cl74, plain,
% 4.64/1.76 (![X38 : $i, X39 : $i]:
% 4.64/1.76 (in @ X38 @ (setadjoin @ X39 @ (setadjoin @ X38 @ emptyset)))),
% 4.64/1.76 inference('cnf', [status(esa)], [zf_stmt_6])).
% 4.64/1.76 thf(zip_derived_cl74, plain,
% 4.64/1.76 (![X38 : $i, X39 : $i]:
% 4.64/1.76 (in @ X38 @ (setadjoin @ X39 @ (setadjoin @ X38 @ emptyset)))),
% 4.64/1.76 inference('cnf', [status(esa)], [zf_stmt_6])).
% 4.64/1.76 thf(zip_derived_cl27, plain,
% 4.64/1.76 (![X18 : $i, X19 : $i, X20 : $i]:
% 4.64/1.76 ( (in @ X18 @ (setunion @ X19))
% 4.64/1.76 | ~ (in @ X18 @ X20)
% 4.64/1.76 | ~ (in @ X20 @ X19))),
% 4.64/1.76 inference('cnf', [status(esa)], [zf_stmt_6])).
% 4.64/1.76 thf(zip_derived_cl227, plain,
% 4.64/1.76 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.64/1.76 (~ (in @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ X2)
% 4.64/1.76 | (in @ X0 @ (setunion @ X2)))),
% 4.64/1.76 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl27])).
% 4.64/1.76 thf(zip_derived_cl245, plain,
% 4.64/1.76 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.64/1.76 (in @ X0 @
% 4.64/1.76 (setunion @
% 4.64/1.76 (setadjoin @ X2 @
% 4.64/1.76 (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @
% 4.64/1.76 emptyset))))),
% 4.64/1.76 inference('sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl227])).
% 4.64/1.76 thf(zip_derived_cl985, plain, ($false),
% 4.64/1.76 inference('demod', [status(thm)], [zip_derived_cl75, zip_derived_cl245])).
% 4.64/1.76
% 4.64/1.76 % SZS output end Refutation
% 4.64/1.76
% 4.64/1.76
% 4.64/1.76 % Terminating...
% 5.25/1.97 % Runner terminated.
% 5.25/2.01 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------