%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU624^1 : 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.Ee8SSQSfli true
% Computer : n016.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 04:55:25 PM UTC 2025
% Result : Theorem 1.17s 1.53s
% Output : Refutation 1.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.32 % Problem : SEU624^1 : TPTP v9.2.0. Released v3.7.0.
% 0.04/0.33 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Ee8SSQSfli true
% 0.11/0.59 % Computer : n016.cluster.edu
% 0.11/0.59 % Model : x86_64 x86_64
% 0.11/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.59 % Memory : 8042.1875MB
% 0.11/0.59 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.59 % CPULimit : 300
% 0.11/0.59 % WCLimit : 300
% 0.11/0.59 % DateTime : Wed Oct 1 16:01:08 EDT 2025
% 0.11/0.60 % CPUTime :
% 0.11/0.60 % Running portfolio for 300 s
% 0.11/0.60 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.60 % Number of cores: 8
% 0.11/0.61 % Python version: Python 3.6.8
% 0.14/0.62 % Running in HO mode
% 0.14/1.07 % Total configuration time : 828
% 0.14/1.07 % Estimated wc time : 1656
% 0.14/1.07 % Estimated cpu time (8 cpus) : 207.0
% 0.57/1.17 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.06/1.31 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.06/1.38 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.06/1.40 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.06/1.43 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.06/1.44 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.06/1.45 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.06/1.46 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.17/1.53 % Solved by lams/40_c_ic.sh.
% 1.17/1.53 % done 152 iterations in 0.068s
% 1.17/1.53 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.17/1.53 % SZS output start Refutation
% 1.17/1.53 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 1.17/1.53 thf(notdexE_type, type, notdexE: $o).
% 1.17/1.53 thf(setunionAx_type, type, setunionAx: $o).
% 1.17/1.53 thf(setminusELneg_type, type, setminusELneg: $o).
% 1.17/1.53 thf(powersetE_type, type, powersetE: $o).
% 1.17/1.53 thf(omegaSAx_type, type, omegaSAx: $o).
% 1.17/1.53 thf(exuI1_type, type, exuI1: $o).
% 1.17/1.53 thf(exuI2_type, type, exuI2: $o).
% 1.17/1.53 thf(notequalI2_type, type, notequalI2: $o).
% 1.17/1.53 thf(setukpairIR_type, type, setukpairIR: $o).
% 1.17/1.53 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 1.17/1.53 thf(setminusILneg_type, type, setminusILneg: $o).
% 1.17/1.53 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 1.17/1.53 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 1.17/1.53 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 1.17/1.53 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 1.17/1.53 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 1.17/1.53 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 1.17/1.53 thf(setukpairIL_type, type, setukpairIL: $o).
% 1.17/1.53 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 1.17/1.53 thf(binunionE_type, type, binunionE: $o).
% 1.17/1.53 thf(setext_type, type, setext: $o).
% 1.17/1.53 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 1.17/1.53 thf(descr__Cong_type, type, descr__Cong: $o).
% 1.17/1.53 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 1.17/1.53 thf(in_type, type, in: $i > $i > $o).
% 1.17/1.53 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 1.17/1.53 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 1.17/1.53 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 1.17/1.53 thf(symdiffI2_type, type, symdiffI2: $o).
% 1.17/1.53 thf(upairset2IR_type, type, upairset2IR: $o).
% 1.17/1.53 thf(subsetE_type, type, subsetE: $o).
% 1.17/1.53 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 1.17/1.53 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 1.17/1.53 thf(setbeta_type, type, setbeta: $o).
% 1.17/1.53 thf(eqinunit_type, type, eqinunit: $o).
% 1.17/1.53 thf(upairsetIL_type, type, upairsetIL: $o).
% 1.17/1.53 thf(powersetI1_type, type, powersetI1: $o).
% 1.17/1.53 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 1.17/1.53 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 1.17/1.53 thf(powersetAx_type, type, powersetAx: $o).
% 1.17/1.53 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 1.17/1.53 thf(powersetI_type, type, powersetI: $o).
% 1.17/1.53 thf(upairsetIR_type, type, upairsetIR: $o).
% 1.17/1.53 thf(sk__47_type, type, sk__47: $i).
% 1.17/1.53 thf(inCongP_type, type, inCongP: $o).
% 1.17/1.53 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 1.17/1.53 thf(exuE3e_type, type, exuE3e: $o).
% 1.17/1.53 thf(emptysetE_type, type, emptysetE: $o).
% 1.17/1.53 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 1.17/1.53 thf(setunionI_type, type, setunionI: $o).
% 1.17/1.53 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 1.17/1.53 thf(prop2setI_type, type, prop2setI: $o).
% 1.17/1.53 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 1.17/1.53 thf(setminusER_type, type, setminusER: $o).
% 1.17/1.53 thf(exuE2_type, type, exuE2: $o).
% 1.17/1.53 thf(emptyset_type, type, emptyset: $i).
% 1.17/1.53 thf(powersetsubset_type, type, powersetsubset: $o).
% 1.17/1.53 thf(subPowSU_type, type, subPowSU: $o).
% 1.17/1.53 thf(notequalI1_type, type, notequalI1: $o).
% 1.17/1.53 thf(notinemptyset_type, type, notinemptyset: $o).
% 1.17/1.53 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 1.17/1.53 thf(subsetTrans_type, type, subsetTrans: $o).
% 1.17/1.53 thf(setminusI_type, type, setminusI: $o).
% 1.17/1.53 thf(binunionIL_type, type, binunionIL: $o).
% 1.17/1.53 thf(subsetE2_type, type, subsetE2: $o).
% 1.17/1.53 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 1.17/1.53 thf(setextsub_type, type, setextsub: $o).
% 1.17/1.53 thf(binunionLsub_type, type, binunionLsub: $o).
% 1.17/1.53 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 1.17/1.53 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 1.17/1.53 thf(setunionE_type, type, setunionE: $o).
% 1.17/1.53 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 1.17/1.53 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 1.17/1.53 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 1.17/1.53 thf(binunionIR_type, type, binunionIR: $o).
% 1.17/1.53 thf(setadjoinE_type, type, setadjoinE: $o).
% 1.17/1.53 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 1.17/1.53 thf(sk__45_type, type, sk__45: $i).
% 1.17/1.53 thf(exuE1_type, type, exuE1: $o).
% 1.17/1.53 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 1.17/1.53 thf(setminusLsub_type, type, setminusLsub: $o).
% 1.17/1.53 thf(notinsingleton_type, type, notinsingleton: $o).
% 1.17/1.53 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 1.17/1.53 thf(exuEu_type, type, exuEu: $o).
% 1.17/1.53 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 1.17/1.53 thf(upairsetE_type, type, upairsetE: $o).
% 1.17/1.53 thf(omega0Ax_type, type, omega0Ax: $o).
% 1.17/1.53 thf(notsubsetI_type, type, notsubsetI: $o).
% 1.17/1.53 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 1.17/1.53 thf(setextAx_type, type, setextAx: $o).
% 1.17/1.53 thf(powersetE1_type, type, powersetE1: $o).
% 1.17/1.53 thf(bs114d_type, type, bs114d: $o).
% 1.17/1.53 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 1.17/1.53 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 1.17/1.53 thf(subsetI1_type, type, subsetI1: $o).
% 1.17/1.53 thf(symdiffE_type, type, symdiffE: $o).
% 1.17/1.53 thf(descrp_type, type, descrp: $o).
% 1.17/1.53 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 1.17/1.53 thf(foundationAx_type, type, foundationAx: $o).
% 1.17/1.53 thf(emptysetAx_type, type, emptysetAx: $o).
% 1.17/1.53 thf(emptyI_type, type, emptyI: $o).
% 1.17/1.53 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 1.17/1.53 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 1.17/1.53 thf(binintersectEL_type, type, binintersectEL: $o).
% 1.17/1.53 thf(emptyE1_type, type, emptyE1: $o).
% 1.17/1.53 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 1.17/1.53 thf(vacuousDall_type, type, vacuousDall: $o).
% 1.17/1.53 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 1.17/1.53 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 1.17/1.53 thf(binintersectI_type, type, binintersectI: $o).
% 1.17/1.53 thf(symdiffI1_type, type, symdiffI1: $o).
% 1.17/1.53 thf(subsetI2_type, type, subsetI2: $o).
% 1.17/1.53 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 1.17/1.53 thf(setminusERneg_type, type, setminusERneg: $o).
% 1.17/1.53 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 1.17/1.53 thf(omega__Cong_type, type, omega__Cong: $o).
% 1.17/1.53 thf(subsetRefl_type, type, subsetRefl: $o).
% 1.17/1.53 thf(uniqinunit_type, type, uniqinunit: $o).
% 1.17/1.53 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 1.17/1.53 thf(prop2setE_type, type, prop2setE: $o).
% 1.17/1.53 thf(binunionEcases_type, type, binunionEcases: $o).
% 1.17/1.53 thf(nonemptyI_type, type, nonemptyI: $o).
% 1.17/1.53 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 1.17/1.53 thf(exuE3u_type, type, exuE3u: $o).
% 1.17/1.53 thf(setminusEL_type, type, setminusEL: $o).
% 1.17/1.53 thf(sepSubset_type, type, sepSubset: $o).
% 1.17/1.53 thf(singletonsubset_type, type, singletonsubset: $o).
% 1.17/1.53 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 1.17/1.53 thf(exuI3_type, type, exuI3: $o).
% 1.17/1.53 thf(notdallE_type, type, notdallE: $o).
% 1.17/1.53 thf(binintersectER_type, type, binintersectER: $o).
% 1.17/1.53 thf(kpairp_type, type, kpairp: $o).
% 1.17/1.53 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 1.17/1.53 thf(sk__46_type, type, sk__46: $i).
% 1.17/1.53 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 1.17/1.53 thf(exu__Cong_type, type, exu__Cong: $o).
% 1.17/1.53 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 1.17/1.53 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 1.17/1.53 thf(replAx_type, type, replAx: $o).
% 1.17/1.53 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 1.17/1.53 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 1.17/1.53 thf(secondinupair_type, type, secondinupair: $o).
% 1.17/1.53 thf(inPowerset_type, type, inPowerset: $o).
% 1.17/1.53 thf(subset_type, type, subset: $i > $i > $o).
% 1.17/1.53 thf(in__Cong_type, type, in__Cong: $o).
% 1.17/1.53 thf(binunionRsub_type, type, binunionRsub: $o).
% 1.17/1.53 thf(subset2powerset_type, type, subset2powerset: $o).
% 1.17/1.53 thf(singletonsubset, axiom, singletonsubset =
% 1.17/1.53 (![A:$i,Xx:$i]:
% 1.17/1.53 ( ( in @ Xx @ A ) => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ))).
% 1.17/1.53 thf('0', plain,
% 1.17/1.53 (( singletonsubset ) =
% 1.17/1.53 ( ![X4:$i,X6:$i]:
% 1.17/1.53 ( ( in @ X6 @ X4 ) => ( subset @ ( setadjoin @ X6 @ emptyset ) @ X4 ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(secondinupair, axiom, secondinupair =
% 1.17/1.53 (![Xx:$i,Xy:$i]:
% 1.17/1.53 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 1.17/1.53 thf('1', plain,
% 1.17/1.53 (( secondinupair ) =
% 1.17/1.53 ( ![X4:$i,X6:$i]:
% 1.17/1.53 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(upairset2IR, axiom, upairset2IR =
% 1.17/1.53 (![Xx:$i,Xy:$i]:
% 1.17/1.53 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 1.17/1.53 thf('2', plain,
% 1.17/1.53 (( upairset2IR ) =
% 1.17/1.53 ( ![X4:$i,X6:$i]:
% 1.17/1.53 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 1.17/1.53 (![A:$i,Xx:$i,B:$i]:
% 1.17/1.53 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 1.17/1.53 thf('3', plain,
% 1.17/1.53 (( setadjoinSub2 ) =
% 1.17/1.53 ( ![X4:$i,X6:$i,X8:$i]:
% 1.17/1.53 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(setadjoinSub, axiom, setadjoinSub =
% 1.17/1.53 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 1.17/1.53 thf('4', plain,
% 1.17/1.53 (( setadjoinSub ) =
% 1.17/1.53 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 1.17/1.53 (![Xx:$i,Xy:$i]:
% 1.17/1.53 ( ( ( Xx ) = ( Xy ) ) =>
% 1.17/1.53 ( ![Xz:$i,Xu:$i]:
% 1.17/1.53 ( ( ( Xz ) = ( Xu ) ) =>
% 1.17/1.53 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 1.17/1.53 thf('5', plain,
% 1.17/1.53 (( setadjoin__Cong ) =
% 1.17/1.53 ( ![X4:$i,X6:$i]:
% 1.17/1.53 ( ( ( X4 ) = ( X6 ) ) =>
% 1.17/1.53 ( ![X8:$i,X10:$i]:
% 1.17/1.53 ( ( ( X8 ) = ( X10 ) ) =>
% 1.17/1.53 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(upairsetIR, axiom, upairsetIR =
% 1.17/1.53 (![Xx:$i,Xy:$i]:
% 1.17/1.53 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 1.17/1.53 thf('6', plain,
% 1.17/1.53 (( upairsetIR ) =
% 1.17/1.53 ( ![X4:$i,X6:$i]:
% 1.17/1.53 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(upairsetIL, axiom, upairsetIL =
% 1.17/1.53 (![Xx:$i,Xy:$i]:
% 1.17/1.53 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 1.17/1.53 thf('7', plain,
% 1.17/1.53 (( upairsetIL ) =
% 1.17/1.53 ( ![X4:$i,X6:$i]:
% 1.17/1.53 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(upairsetE, axiom, upairsetE =
% 1.17/1.53 (![Xx:$i,Xy:$i,Xz:$i]:
% 1.17/1.53 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 1.17/1.53 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 1.17/1.53 thf('8', plain,
% 1.17/1.53 (( upairsetE ) =
% 1.17/1.53 ( ![X4:$i,X6:$i,X8:$i]:
% 1.17/1.53 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 1.17/1.53 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(singletonsswitch, axiom, singletonsswitch =
% 1.17/1.53 (![Xx:$i,Xy:$i]:
% 1.17/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 1.17/1.53 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 1.17/1.53 thf('9', plain,
% 1.17/1.53 (( singletonsswitch ) =
% 1.17/1.53 ( ![X4:$i,X6:$i]:
% 1.17/1.53 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 1.17/1.53 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(eqinunit, axiom, eqinunit =
% 1.17/1.53 (![Xx:$i,Xy:$i]:
% 1.17/1.53 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 1.17/1.53 thf('10', plain,
% 1.17/1.53 (( eqinunit ) =
% 1.17/1.53 ( ![X4:$i,X6:$i]:
% 1.17/1.53 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(notinsingleton, axiom, notinsingleton =
% 1.17/1.53 (![Xx:$i,Xy:$i]:
% 1.17/1.53 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 1.17/1.53 thf('11', plain,
% 1.17/1.53 (( notinsingleton ) =
% 1.17/1.53 ( ![X4:$i,X6:$i]:
% 1.17/1.53 ( ( ( X4 ) != ( X6 ) ) =>
% 1.17/1.53 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(uniqinunit, axiom, uniqinunit =
% 1.17/1.53 (![Xx:$i,Xy:$i]:
% 1.17/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 1.17/1.53 thf('12', plain,
% 1.17/1.53 (( uniqinunit ) =
% 1.17/1.53 ( ![X4:$i,X6:$i]:
% 1.17/1.53 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(setadjoinOr, axiom, setadjoinOr =
% 1.17/1.53 (![Xx:$i,A:$i,Xy:$i]:
% 1.17/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 1.17/1.53 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 1.17/1.53 thf('13', plain,
% 1.17/1.53 (( setadjoinOr ) =
% 1.17/1.53 ( ![X4:$i,X6:$i,X8:$i]:
% 1.17/1.53 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 1.17/1.53 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(setadjoinE, axiom, setadjoinE =
% 1.17/1.53 (![Xx:$i,A:$i,Xy:$i]:
% 1.17/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 1.17/1.53 ( ![Xphi:$o]:
% 1.17/1.53 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 1.17/1.53 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 1.17/1.53 thf('14', plain,
% 1.17/1.53 (( setadjoinE ) =
% 1.17/1.53 ( ![X4:$i,X6:$i,X8:$i]:
% 1.17/1.53 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 1.17/1.53 ( ![X10:$o]:
% 1.17/1.53 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 1.17/1.53 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(setadjoinIR, axiom, setadjoinIR =
% 1.17/1.53 (![Xx:$i,A:$i,Xy:$i]:
% 1.17/1.53 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 1.17/1.53 thf('15', plain,
% 1.17/1.53 (( setadjoinIR ) =
% 1.17/1.53 ( ![X4:$i,X6:$i,X8:$i]:
% 1.17/1.53 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 1.17/1.53 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 1.17/1.53 thf('16', plain,
% 1.17/1.53 (( emptyinunitempty ) =
% 1.17/1.53 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 1.17/1.53 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 1.17/1.53 thf('17', plain,
% 1.17/1.53 (( emptyinunitempty ) =
% 1.17/1.53 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(setadjoinIL, axiom, setadjoinIL =
% 1.17/1.53 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 1.17/1.53 thf('18', plain,
% 1.17/1.53 (( setadjoinIL ) =
% 1.17/1.53 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(setadjoinAx, axiom, setadjoinAx =
% 1.17/1.53 (![Xx:$i,A:$i,Xy:$i]:
% 1.17/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 1.17/1.53 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 1.17/1.53 thf('19', plain,
% 1.17/1.53 (( setadjoinAx ) =
% 1.17/1.53 ( ![X4:$i,X6:$i,X8:$i]:
% 1.17/1.53 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 1.17/1.53 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 1.17/1.53 define([status(thm)])).
% 1.17/1.53 thf(upairset2E, conjecture,
% 1.17/1.53 (( setextAx ) =>
% 1.17/1.53 ( ( emptysetAx ) =>
% 1.17/1.53 ( ( setadjoinAx ) =>
% 1.17/1.53 ( ( powersetAx ) =>
% 1.17/1.53 ( ( setunionAx ) =>
% 1.17/1.53 ( ( omega0Ax ) =>
% 1.17/1.53 ( ( omegaSAx ) =>
% 1.17/1.53 ( ( omegaIndAx ) =>
% 1.17/1.53 ( ( replAx ) =>
% 1.17/1.53 ( ( foundationAx ) =>
% 1.17/1.53 ( ( wellorderingAx ) =>
% 1.17/1.53 ( ( descrp ) =>
% 1.17/1.53 ( ( dsetconstrI ) =>
% 1.17/1.53 ( ( dsetconstrEL ) =>
% 1.17/1.53 ( ( dsetconstrER ) =>
% 1.17/1.53 ( ( exuE1 ) =>
% 1.17/1.53 ( ( prop2setE ) =>
% 1.17/1.53 ( ( emptysetE ) =>
% 1.17/1.53 ( ( emptysetimpfalse ) =>
% 1.17/1.53 ( ( notinemptyset ) =>
% 1.17/1.53 ( ( exuE3e ) =>
% 1.17/1.53 ( ( setext ) =>
% 1.17/1.53 ( ( emptyI ) =>
% 1.17/1.53 ( ( noeltsimpempty ) =>
% 1.17/1.53 ( ( setbeta ) =>
% 1.17/1.53 ( ( nonemptyE1 ) =>
% 1.17/1.53 ( ( nonemptyI ) =>
% 1.17/1.53 ( ( nonemptyI1 ) =>
% 1.17/1.53 ( ( setadjoinIL ) =>
% 1.17/1.53 ( ( emptyinunitempty ) =>
% 1.17/1.53 ( ( setadjoinIR ) =>
% 1.17/1.53 ( ( setadjoinE ) =>
% 1.17/1.53 ( (
% 1.17/1.53 setadjoinOr ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setoftrueEq ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 powersetI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 emptyinPowerset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 emptyInPowerset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 powersetE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setunionI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setunionE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subPowSU ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exuE2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 nonemptyImpWitness ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 uniqinunit ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 notinsingleton ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 eqinunit ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 singletonsswitch ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 upairsetE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 upairsetIL ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 upairsetIR ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 emptyE1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 vacuousDall ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 quantDeMorgan1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 quantDeMorgan2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 quantDeMorgan3 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 quantDeMorgan4 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 prop2setI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 prop2set2propI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 notdexE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 notdallE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exuI1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exuI3 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exuI2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 inCongP ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exuE3u ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exu__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 emptyset__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setadjoin__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 powerset__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setunion__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 omega__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exuEu ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 descr__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 dsetconstr__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetI1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 eqimpsubset2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 eqimpsubset1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetI2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 emptysetsubset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetE2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 notsubsetI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 notequalI1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 notequalI2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetRefl ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetTrans ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setadjoinSub ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setadjoinSub2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subset2powerset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setextsub ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetemptysetimpeq ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 powersetI1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 powersetE1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 inPowerset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 powersetsubset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 sepInPowerset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 sepSubset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binunionIL ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 upairset2IR ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binunionIR ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binunionEcases ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binunionE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binunionLsub ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binunionRsub ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectSubset5 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectEL ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectLsub ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectSubset2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectSubset3 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectER ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 disjointsetsI1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectRsub ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectSubset4 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectSubset1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 bs114d ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusEL ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusER ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusSubset2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusERneg ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusELneg ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusILneg ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusIRneg ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusLsub ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusSubset1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 symdiffE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 symdiffI1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 symdiffI2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 symdiffIneg1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 symdiffIneg2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 secondinupair ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setukpairIL ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setukpairIR ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 kpairiskpair ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 kpairp ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 singletonsubset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 singletoninpowerset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 singletoninpowunion ) =>
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 Xx:$i,
% 1.17/1.53 Xy:$i,
% 1.17/1.53 Xz:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 Xz @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 Xx @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 Xy @
% 1.17/1.53 emptyset ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 Xz ) =
% 1.17/1.53 (
% 1.17/1.53 Xx ) ) |
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 Xz ) =
% 1.17/1.53 (
% 1.17/1.53 Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.17/1.53 thf(zf_stmt_0, conjecture,
% 1.17/1.53 (( setextAx ) =>
% 1.17/1.53 ( ( emptysetAx ) =>
% 1.17/1.53 ( ( ![X4:$i,X6:$i,X8:$i]:
% 1.17/1.53 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 1.17/1.53 ( ( in @ X8 @ X6 ) | ( ( X8 ) = ( X4 ) ) ) ) ) =>
% 1.17/1.53 ( ( powersetAx ) =>
% 1.17/1.53 ( ( setunionAx ) =>
% 1.17/1.53 ( ( omega0Ax ) =>
% 1.17/1.53 ( ( omegaSAx ) =>
% 1.17/1.53 ( ( omegaIndAx ) =>
% 1.17/1.53 ( ( replAx ) =>
% 1.17/1.53 ( ( foundationAx ) =>
% 1.17/1.53 ( ( wellorderingAx ) =>
% 1.17/1.53 ( ( descrp ) =>
% 1.17/1.53 ( ( dsetconstrI ) =>
% 1.17/1.53 ( ( dsetconstrEL ) =>
% 1.17/1.53 ( ( dsetconstrER ) =>
% 1.17/1.53 ( ( exuE1 ) =>
% 1.17/1.53 ( ( prop2setE ) =>
% 1.17/1.53 ( ( emptysetE ) =>
% 1.17/1.53 ( ( emptysetimpfalse ) =>
% 1.17/1.53 ( ( notinemptyset ) =>
% 1.17/1.53 ( ( exuE3e ) =>
% 1.17/1.53 ( ( setext ) =>
% 1.17/1.53 ( ( emptyI ) =>
% 1.17/1.53 ( ( noeltsimpempty ) =>
% 1.17/1.53 ( ( setbeta ) =>
% 1.17/1.53 ( ( nonemptyE1 ) =>
% 1.17/1.53 ( ( nonemptyI ) =>
% 1.17/1.53 ( ( nonemptyI1 ) =>
% 1.17/1.53 ( ( ![X10:$i,X12:$i]:
% 1.17/1.53 ( in @
% 1.17/1.53 X10 @
% 1.17/1.53 ( setadjoin @
% 1.17/1.53 X10 @ X12 ) ) ) =>
% 1.17/1.53 ( ( in @
% 1.17/1.53 emptyset @
% 1.17/1.53 ( setadjoin @
% 1.17/1.53 emptyset @
% 1.17/1.53 emptyset ) ) =>
% 1.17/1.53 ( ( ![X14:$i,
% 1.17/1.53 X16:$i,
% 1.17/1.53 X18:$i]:
% 1.17/1.53 ( (
% 1.17/1.53 in @
% 1.17/1.53 X18 @ X16 ) =>
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X18 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X14 @ X16 ) ) ) ) =>
% 1.17/1.53 ( ( ![
% 1.17/1.53 X20:$i,
% 1.17/1.53 X22:$i,
% 1.17/1.53 X24:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X24 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X20 @ X22 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X26:$o]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 X24 ) =
% 1.17/1.53 (
% 1.17/1.53 X20 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 X26 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X24 @ X22 ) =>
% 1.17/1.53 (
% 1.17/1.53 X26 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 X26 ) ) ) ) ) ) =>
% 1.17/1.53 ( (
% 1.17/1.53 ![
% 1.17/1.53 X28:$i,
% 1.17/1.53 X30:$i,
% 1.17/1.53 X32:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X32 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X28 @ X30 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X32 @ X30 ) |
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 X32 ) =
% 1.17/1.53 (
% 1.17/1.53 X28 ) ) ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setoftrueEq ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 powersetI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 emptyinPowerset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 emptyInPowerset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 powersetE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setunionI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setunionE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subPowSU ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exuE2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 nonemptyImpWitness ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X34:$i,
% 1.17/1.53 X36:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X34 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X36 @
% 1.17/1.53 emptyset ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 X34 ) =
% 1.17/1.53 (
% 1.17/1.53 X36 ) ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X38:$i,
% 1.17/1.53 X40:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 X38 ) !=
% 1.17/1.53 (
% 1.17/1.53 X40 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 ~(
% 1.17/1.53 in @
% 1.17/1.53 X40 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X38 @
% 1.17/1.53 emptyset ) ) ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X42:$i,
% 1.17/1.53 X44:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 X42 ) =
% 1.17/1.53 (
% 1.17/1.53 X44 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X42 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X44 @
% 1.17/1.53 emptyset ) ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X46:$i,
% 1.17/1.53 X48:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X46 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X48 @
% 1.17/1.53 emptyset ) ) =>
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X48 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X46 @
% 1.17/1.53 emptyset ) ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X50:$i,
% 1.17/1.53 X52:$i,
% 1.17/1.53 X54:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X54 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X50 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X52 @
% 1.17/1.53 emptyset ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 X54 ) =
% 1.17/1.53 (
% 1.17/1.53 X52 ) ) |
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 X54 ) =
% 1.17/1.53 (
% 1.17/1.53 X50 ) ) ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X56:$i,
% 1.17/1.53 X58:$i]:
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X56 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X56 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X58 @
% 1.17/1.53 emptyset ) ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X60:$i,
% 1.17/1.53 X62:$i]:
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X62 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X60 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X62 @
% 1.17/1.53 emptyset ) ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 emptyE1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 vacuousDall ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 quantDeMorgan1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 quantDeMorgan2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 quantDeMorgan3 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 quantDeMorgan4 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 prop2setI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 prop2set2propI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 notdexE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 notdallE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exuI1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exuI3 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exuI2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 inCongP ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exuE3u ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exu__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 emptyset__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X64:$i,
% 1.17/1.53 X66:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 X64 ) =
% 1.17/1.53 (
% 1.17/1.53 X66 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X68:$i,
% 1.17/1.53 X70:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 X68 ) =
% 1.17/1.53 (
% 1.17/1.53 X70 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X64 @ X68 ) =
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X66 @ X70 ) ) ) ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 powerset__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setunion__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 omega__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 exuEu ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 descr__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 dsetconstr__Cong ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetI1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 eqimpsubset2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 eqimpsubset1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetI2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 emptysetsubset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetE2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 notsubsetI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 notequalI1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 notequalI2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetRefl ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetTrans ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X72:$i,
% 1.17/1.53 X74:$i]:
% 1.17/1.53 (
% 1.17/1.53 subset @
% 1.17/1.53 X74 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X72 @ X74 ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X76:$i,
% 1.17/1.53 X78:$i,
% 1.17/1.53 X80:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subset @
% 1.17/1.53 X76 @ X80 ) =>
% 1.17/1.53 (
% 1.17/1.53 subset @
% 1.17/1.53 X76 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X78 @ X80 ) ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subset2powerset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setextsub ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 subsetemptysetimpeq ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 powersetI1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 powersetE1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 inPowerset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 powersetsubset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 sepInPowerset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 sepSubset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binunionIL ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X82:$i,
% 1.17/1.53 X84:$i]:
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X84 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X82 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X84 @
% 1.17/1.53 emptyset ) ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binunionIR ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binunionEcases ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binunionE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binunionLsub ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binunionRsub ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectSubset5 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectEL ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectLsub ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectSubset2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectSubset3 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectER ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 disjointsetsI1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectRsub ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectSubset4 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 binintersectSubset1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 bs114d ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusEL ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusER ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusSubset2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusERneg ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusELneg ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusILneg ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusIRneg ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusLsub ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setminusSubset1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 symdiffE ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 symdiffI1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 symdiffI2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 symdiffIneg1 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 symdiffIneg2 ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X86:$i,
% 1.17/1.53 X88:$i]:
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X88 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X86 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X88 @
% 1.17/1.53 emptyset ) ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setukpairIL ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setukpairIR ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 kpairiskpair ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 kpairp ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X90:$i,
% 1.17/1.53 X92:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X92 @ X90 ) =>
% 1.17/1.53 (
% 1.17/1.53 subset @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X92 @
% 1.17/1.53 emptyset ) @
% 1.17/1.53 X90 ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 singletoninpowerset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 singletoninpowunion ) =>
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X94:$i,
% 1.17/1.53 X96:$i,
% 1.17/1.53 X98:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X98 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X94 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X96 @
% 1.17/1.53 emptyset ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 X98 ) =
% 1.17/1.53 (
% 1.17/1.53 X96 ) ) |
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 X98 ) =
% 1.17/1.53 (
% 1.17/1.53 X94 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.17/1.53 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 1.17/1.53 thf(zf_stmt_2, axiom,
% 1.17/1.53 (![X8:$i,X6:$i,X4:$i]:
% 1.17/1.53 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 1.17/1.53 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ))).
% 1.17/1.53 thf(zf_stmt_3, conjecture,
% 1.17/1.53 (( setextAx ) =>
% 1.17/1.53 ( ( emptysetAx ) =>
% 1.17/1.53 ( ( ![X4:$i,X6:$i,X8:$i]:
% 1.17/1.53 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 1.17/1.53 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 1.17/1.53 ( ( powersetAx ) =>
% 1.17/1.53 ( ( setunionAx ) =>
% 1.17/1.53 ( ( omega0Ax ) =>
% 1.17/1.53 ( ( omegaSAx ) =>
% 1.17/1.53 ( ( omegaIndAx ) =>
% 1.17/1.53 ( ( replAx ) =>
% 1.17/1.53 ( ( foundationAx ) =>
% 1.17/1.53 ( ( wellorderingAx ) =>
% 1.17/1.53 ( ( descrp ) =>
% 1.17/1.53 ( ( dsetconstrI ) =>
% 1.17/1.53 ( ( dsetconstrEL ) =>
% 1.17/1.53 ( ( dsetconstrER ) =>
% 1.17/1.53 ( ( exuE1 ) =>
% 1.17/1.53 ( ( prop2setE ) =>
% 1.17/1.53 ( ( emptysetE ) =>
% 1.17/1.53 ( ( emptysetimpfalse ) =>
% 1.17/1.53 ( ( notinemptyset ) =>
% 1.17/1.53 ( ( exuE3e ) =>
% 1.17/1.53 ( ( setext ) =>
% 1.17/1.53 ( ( emptyI ) =>
% 1.17/1.53 ( ( noeltsimpempty ) =>
% 1.17/1.53 ( ( setbeta ) =>
% 1.17/1.53 ( ( nonemptyE1 ) =>
% 1.17/1.53 ( ( nonemptyI ) =>
% 1.17/1.53 ( ( nonemptyI1 ) =>
% 1.17/1.53 ( ( ![X10:$i,X12:$i]:
% 1.17/1.53 ( in @
% 1.17/1.53 X10 @
% 1.17/1.53 ( setadjoin @
% 1.17/1.53 X10 @ X12 ) ) ) =>
% 1.17/1.53 ( ( in @
% 1.17/1.53 emptyset @
% 1.17/1.53 ( setadjoin @
% 1.17/1.53 emptyset @
% 1.17/1.53 emptyset ) ) =>
% 1.17/1.53 ( ( ![X14:$i,
% 1.17/1.53 X16:$i,
% 1.17/1.53 X18:$i]:
% 1.17/1.53 ( (
% 1.17/1.53 in @
% 1.17/1.53 X18 @ X16 ) =>
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X18 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X14 @ X16 ) ) ) ) =>
% 1.17/1.53 ( ( ![
% 1.17/1.53 X20:$i,
% 1.17/1.53 X22:$i,
% 1.17/1.53 X24:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X24 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X20 @ X22 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 ![
% 1.17/1.53 X26:$o]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 X24 ) =
% 1.17/1.53 (
% 1.17/1.53 X20 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 X26 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X24 @ X22 ) =>
% 1.17/1.53 (
% 1.17/1.53 X26 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 X26 ) ) ) ) ) ) =>
% 1.17/1.53 ( (
% 1.17/1.53 ![
% 1.17/1.53 X28:$i,
% 1.17/1.53 X30:$i,
% 1.17/1.53 X32:$i]:
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X32 @
% 1.17/1.53 (
% 1.17/1.53 setadjoin
% 1.17/1.53 @
% 1.17/1.53 X28 @ X30 ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 X32 ) =
% 1.17/1.53 (
% 1.17/1.53 X28 ) ) |
% 1.17/1.53 (
% 1.17/1.53 in @
% 1.17/1.53 X32 @ X30 ) ) ) ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 setoftrueEq ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 powersetI ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.53 emptyinPowerset ) =>
% 1.17/1.53 (
% 1.17/1.53 (
% 1.17/1.54 emptyInPowerset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 powersetE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setunionI ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setunionE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subPowSU ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exuE2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 nonemptyImpWitness ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X34:$i,
% 1.17/1.54 X36:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X34 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X36 @
% 1.17/1.54 emptyset ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X34 ) =
% 1.17/1.54 (
% 1.17/1.54 X36 ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X38:$i,
% 1.17/1.54 X40:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X38 ) !=
% 1.17/1.54 (
% 1.17/1.54 X40 ) ) =>
% 1.17/1.54 (
% 1.17/1.54 ~(
% 1.17/1.54 in @
% 1.17/1.54 X40 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X38 @
% 1.17/1.54 emptyset ) ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X42:$i,
% 1.17/1.54 X44:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X42 ) =
% 1.17/1.54 (
% 1.17/1.54 X44 ) ) =>
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X42 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X44 @
% 1.17/1.54 emptyset ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X46:$i,
% 1.17/1.54 X48:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X46 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X48 @
% 1.17/1.54 emptyset ) ) =>
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X48 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X46 @
% 1.17/1.54 emptyset ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X50:$i,
% 1.17/1.54 X52:$i,
% 1.17/1.54 X54:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X54 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X50 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X52 @
% 1.17/1.54 emptyset ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X54 ) =
% 1.17/1.54 (
% 1.17/1.54 X50 ) ) |
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X54 ) =
% 1.17/1.54 (
% 1.17/1.54 X52 ) ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X56:$i,
% 1.17/1.54 X58:$i]:
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X56 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X56 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X58 @
% 1.17/1.54 emptyset ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X60:$i,
% 1.17/1.54 X62:$i]:
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X62 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X60 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X62 @
% 1.17/1.54 emptyset ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 emptyE1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 vacuousDall ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 quantDeMorgan1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 quantDeMorgan2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 quantDeMorgan3 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 quantDeMorgan4 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 prop2setI ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 prop2set2propI ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 notdexE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 notdallE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exuI1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exuI3 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exuI2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 inCongP ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exuE3u ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exu__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 emptyset__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X64:$i,
% 1.17/1.54 X66:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X64 ) =
% 1.17/1.54 (
% 1.17/1.54 X66 ) ) =>
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X68:$i,
% 1.17/1.54 X70:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X68 ) =
% 1.17/1.54 (
% 1.17/1.54 X70 ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X64 @ X68 ) =
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X66 @ X70 ) ) ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 powerset__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setunion__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 omega__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exuEu ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 descr__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 dsetconstr__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetI1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 eqimpsubset2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 eqimpsubset1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetI2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 emptysetsubset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetE2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 notsubsetI ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 notequalI1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 notequalI2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetRefl ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetTrans ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X72:$i,
% 1.17/1.54 X74:$i]:
% 1.17/1.54 (
% 1.17/1.54 subset @
% 1.17/1.54 X74 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X72 @ X74 ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X76:$i,
% 1.17/1.54 X78:$i,
% 1.17/1.54 X80:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subset @
% 1.17/1.54 X76 @ X80 ) =>
% 1.17/1.54 (
% 1.17/1.54 subset @
% 1.17/1.54 X76 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X78 @ X80 ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subset2powerset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setextsub ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetemptysetimpeq ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 powersetI1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 powersetE1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 inPowerset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 powersetsubset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 sepInPowerset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 sepSubset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binunionIL ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X82:$i,
% 1.17/1.54 X84:$i]:
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X84 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X82 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X84 @
% 1.17/1.54 emptyset ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binunionIR ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binunionEcases ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binunionE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binunionLsub ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binunionRsub ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectI ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectSubset5 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectEL ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectLsub ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectSubset2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectSubset3 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectER ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 disjointsetsI1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectRsub ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectSubset4 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectSubset1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 bs114d ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusI ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusEL ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusER ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusSubset2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusERneg ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusELneg ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusILneg ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusIRneg ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusLsub ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusSubset1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 symdiffE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 symdiffI1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 symdiffI2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 symdiffIneg1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 symdiffIneg2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X86:$i,
% 1.17/1.54 X88:$i]:
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X88 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X86 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X88 @
% 1.17/1.54 emptyset ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setukpairIL ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setukpairIR ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 kpairiskpair ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 kpairp ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X90:$i,
% 1.17/1.54 X92:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X92 @ X90 ) =>
% 1.17/1.54 (
% 1.17/1.54 subset @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X92 @
% 1.17/1.54 emptyset ) @
% 1.17/1.54 X90 ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 singletoninpowerset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 singletoninpowunion ) =>
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X94:$i,
% 1.17/1.54 X96:$i,
% 1.17/1.54 X98:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X98 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X94 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X96 @
% 1.17/1.54 emptyset ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X98 ) =
% 1.17/1.54 (
% 1.17/1.54 X94 ) ) |
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X98 ) =
% 1.17/1.54 (
% 1.17/1.54 X96 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.17/1.54 thf(zf_stmt_4, negated_conjecture,
% 1.17/1.54 (~( ( setextAx ) =>
% 1.17/1.54 ( ( emptysetAx ) =>
% 1.17/1.54 ( ( ![X4:$i,X6:$i,X8:$i]:
% 1.17/1.54 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 1.17/1.54 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 1.17/1.54 ( ( powersetAx ) =>
% 1.17/1.54 ( ( setunionAx ) =>
% 1.17/1.54 ( ( omega0Ax ) =>
% 1.17/1.54 ( ( omegaSAx ) =>
% 1.17/1.54 ( ( omegaIndAx ) =>
% 1.17/1.54 ( ( replAx ) =>
% 1.17/1.54 ( ( foundationAx ) =>
% 1.17/1.54 ( ( wellorderingAx ) =>
% 1.17/1.54 ( ( descrp ) =>
% 1.17/1.54 ( ( dsetconstrI ) =>
% 1.17/1.54 ( ( dsetconstrEL ) =>
% 1.17/1.54 ( ( dsetconstrER ) =>
% 1.17/1.54 ( ( exuE1 ) =>
% 1.17/1.54 ( ( prop2setE ) =>
% 1.17/1.54 ( ( emptysetE ) =>
% 1.17/1.54 ( ( emptysetimpfalse ) =>
% 1.17/1.54 ( ( notinemptyset ) =>
% 1.17/1.54 ( ( exuE3e ) =>
% 1.17/1.54 ( ( setext ) =>
% 1.17/1.54 ( ( emptyI ) =>
% 1.17/1.54 ( ( noeltsimpempty ) =>
% 1.17/1.54 ( ( setbeta ) =>
% 1.17/1.54 ( ( nonemptyE1 ) =>
% 1.17/1.54 ( ( nonemptyI ) =>
% 1.17/1.54 ( ( nonemptyI1 ) =>
% 1.17/1.54 ( ( ![X10:$i,
% 1.17/1.54 X12:$i]:
% 1.17/1.54 ( in @
% 1.17/1.54 X10 @
% 1.17/1.54 ( setadjoin
% 1.17/1.54 @
% 1.17/1.54 X10 @ X12 ) ) ) =>
% 1.17/1.54 ( ( in @
% 1.17/1.54 emptyset @
% 1.17/1.54 ( setadjoin
% 1.17/1.54 @
% 1.17/1.54 emptyset @
% 1.17/1.54 emptyset ) ) =>
% 1.17/1.54 ( ( ![
% 1.17/1.54 X14:$i,
% 1.17/1.54 X16:$i,
% 1.17/1.54 X18:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X18 @ X16 ) =>
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X18 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X14 @ X16 ) ) ) ) =>
% 1.17/1.54 ( (
% 1.17/1.54 ![
% 1.17/1.54 X20:$i,
% 1.17/1.54 X22:$i,
% 1.17/1.54 X24:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X24 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X20 @ X22 ) ) =>
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X26:$o]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X24 ) =
% 1.17/1.54 (
% 1.17/1.54 X20 ) ) =>
% 1.17/1.54 (
% 1.17/1.54 X26 ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X24 @ X22 ) =>
% 1.17/1.54 (
% 1.17/1.54 X26 ) ) =>
% 1.17/1.54 (
% 1.17/1.54 X26 ) ) ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X28:$i,
% 1.17/1.54 X30:$i,
% 1.17/1.54 X32:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X32 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X28 @ X30 ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X32 ) =
% 1.17/1.54 (
% 1.17/1.54 X28 ) ) |
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X32 @ X30 ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setoftrueEq ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 powersetI ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 emptyinPowerset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 emptyInPowerset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 powersetE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setunionI ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setunionE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subPowSU ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exuE2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 nonemptyImpWitness ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X34:$i,
% 1.17/1.54 X36:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X34 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X36 @
% 1.17/1.54 emptyset ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X34 ) =
% 1.17/1.54 (
% 1.17/1.54 X36 ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X38:$i,
% 1.17/1.54 X40:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X38 ) !=
% 1.17/1.54 (
% 1.17/1.54 X40 ) ) =>
% 1.17/1.54 (
% 1.17/1.54 ~
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X40 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X38 @
% 1.17/1.54 emptyset ) ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X42:$i,
% 1.17/1.54 X44:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X42 ) =
% 1.17/1.54 (
% 1.17/1.54 X44 ) ) =>
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X42 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X44 @
% 1.17/1.54 emptyset ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X46:$i,
% 1.17/1.54 X48:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X46 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X48 @
% 1.17/1.54 emptyset ) ) =>
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X48 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X46 @
% 1.17/1.54 emptyset ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X50:$i,
% 1.17/1.54 X52:$i,
% 1.17/1.54 X54:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X54 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X50 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X52 @
% 1.17/1.54 emptyset ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X54 ) =
% 1.17/1.54 (
% 1.17/1.54 X50 ) ) |
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X54 ) =
% 1.17/1.54 (
% 1.17/1.54 X52 ) ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X56:$i,
% 1.17/1.54 X58:$i]:
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X56 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X56 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X58 @
% 1.17/1.54 emptyset ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X60:$i,
% 1.17/1.54 X62:$i]:
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X62 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X60 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X62 @
% 1.17/1.54 emptyset ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 emptyE1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 vacuousDall ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 quantDeMorgan1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 quantDeMorgan2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 quantDeMorgan3 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 quantDeMorgan4 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 prop2setI ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 prop2set2propI ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 notdexE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 notdallE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exuI1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exuI3 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exuI2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 inCongP ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exuE3u ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exu__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 emptyset__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X64:$i,
% 1.17/1.54 X66:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X64 ) =
% 1.17/1.54 (
% 1.17/1.54 X66 ) ) =>
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X68:$i,
% 1.17/1.54 X70:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X68 ) =
% 1.17/1.54 (
% 1.17/1.54 X70 ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X64 @ X68 ) =
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X66 @ X70 ) ) ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 powerset__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setunion__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 omega__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 exuEu ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 descr__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 dsetconstr__Cong ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetI1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 eqimpsubset2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 eqimpsubset1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetI2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 emptysetsubset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetE2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 notsubsetI ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 notequalI1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 notequalI2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetRefl ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetTrans ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X72:$i,
% 1.17/1.54 X74:$i]:
% 1.17/1.54 (
% 1.17/1.54 subset @
% 1.17/1.54 X74 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X72 @ X74 ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X76:$i,
% 1.17/1.54 X78:$i,
% 1.17/1.54 X80:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subset @
% 1.17/1.54 X76 @ X80 ) =>
% 1.17/1.54 (
% 1.17/1.54 subset @
% 1.17/1.54 X76 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X78 @ X80 ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subset2powerset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setextsub ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 subsetemptysetimpeq ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 powersetI1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 powersetE1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 inPowerset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 powersetsubset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 sepInPowerset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 sepSubset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binunionIL ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X82:$i,
% 1.17/1.54 X84:$i]:
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X84 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X82 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X84 @
% 1.17/1.54 emptyset ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binunionIR ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binunionEcases ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binunionE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binunionLsub ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binunionRsub ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectI ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectSubset5 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectEL ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectLsub ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectSubset2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectSubset3 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectER ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 disjointsetsI1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectRsub ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectSubset4 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 binintersectSubset1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 bs114d ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusI ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusEL ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusER ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusSubset2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusERneg ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusELneg ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusILneg ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusIRneg ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusLsub ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setminusSubset1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 symdiffE ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 symdiffI1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 symdiffI2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 symdiffIneg1 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 symdiffIneg2 ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X86:$i,
% 1.17/1.54 X88:$i]:
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X88 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X86 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X88 @
% 1.17/1.54 emptyset ) ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setukpairIL ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 setukpairIR ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 kpairiskpair ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 kpairp ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X90:$i,
% 1.17/1.54 X92:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X92 @ X90 ) =>
% 1.17/1.54 (
% 1.17/1.54 subset @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X92 @
% 1.17/1.54 emptyset ) @
% 1.17/1.54 X90 ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 singletoninpowerset ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 singletoninpowunion ) =>
% 1.17/1.54 (
% 1.17/1.54 ![
% 1.17/1.54 X94:$i,
% 1.17/1.54 X96:$i,
% 1.17/1.54 X98:$i]:
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 in @
% 1.17/1.54 X98 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X94 @
% 1.17/1.54 (
% 1.17/1.54 setadjoin
% 1.17/1.54 @
% 1.17/1.54 X96 @
% 1.17/1.54 emptyset ) ) ) =>
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X98 ) =
% 1.17/1.54 (
% 1.17/1.54 X94 ) ) |
% 1.17/1.54 (
% 1.17/1.54 (
% 1.17/1.54 X98 ) =
% 1.17/1.54 (
% 1.17/1.54 X96 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 1.17/1.54 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 1.17/1.54 thf(zip_derived_cl26, plain,
% 1.17/1.54 (![X12 : $i, X13 : $i]:
% 1.17/1.54 (~ (in @ X12 @ (setadjoin @ X13 @ emptyset)) | ((X13) = (X12)))),
% 1.17/1.54 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.17/1.54 thf(zip_derived_cl76, plain,
% 1.17/1.54 ( (in @ sk__47 @ (setadjoin @ sk__45 @ (setadjoin @ sk__46 @ emptyset)))),
% 1.17/1.54 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.17/1.54 thf(zip_derived_cl20, plain,
% 1.17/1.54 (![X9 : $i, X10 : $i, X11 : $i]:
% 1.17/1.54 ( (in @ X9 @ X10)
% 1.17/1.54 | ((X9) = (X11))
% 1.17/1.54 | ~ (in @ X9 @ (setadjoin @ X11 @ X10)))),
% 1.17/1.54 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.17/1.54 thf(zip_derived_cl223, plain,
% 1.17/1.54 ((((sk__47) = (sk__45))
% 1.17/1.54 | (in @ sk__47 @ (setadjoin @ sk__46 @ emptyset)))),
% 1.17/1.54 inference('sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl20])).
% 1.17/1.54 thf(zip_derived_cl75, plain, (((sk__47) != (sk__45))),
% 1.17/1.54 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.17/1.54 thf(zip_derived_cl239, plain,
% 1.17/1.54 ( (in @ sk__47 @ (setadjoin @ sk__46 @ emptyset))),
% 1.17/1.54 inference('simplify_reflect-', [status(thm)],
% 1.17/1.54 [zip_derived_cl223, zip_derived_cl75])).
% 1.17/1.54 thf(zip_derived_cl250, plain, (((sk__46) = (sk__47))),
% 1.17/1.54 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl239])).
% 1.17/1.54 thf(zip_derived_cl74, plain, (((sk__47) != (sk__46))),
% 1.17/1.54 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.17/1.54 thf(zip_derived_cl256, plain, ($false),
% 1.17/1.54 inference('simplify_reflect-', [status(thm)],
% 1.17/1.54 [zip_derived_cl250, zip_derived_cl74])).
% 1.17/1.54
% 1.17/1.54 % SZS output end Refutation
% 1.17/1.54
% 1.17/1.54
% 1.17/1.54 % Terminating...
% 1.89/1.69 % Runner terminated.
% 1.89/1.69 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------