%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU622^1 : 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.tOKQiY8vfH true
% Computer : n009.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 0.54s 1.03s
% Output : Refutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SEU622^1 : TPTP v9.2.0. Released v3.7.0.
% 0.02/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.tOKQiY8vfH true
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Oct 1 16:12:23 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Running portfolio for 300 s
% 0.11/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.33 % Number of cores: 8
% 0.11/0.33 % Python version: Python 3.6.8
% 0.11/0.33 % Running in HO mode
% 0.51/0.63 % Total configuration time : 828
% 0.51/0.63 % Estimated wc time : 1656
% 0.51/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.52/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.52/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.52/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.52/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/0.79 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.52/0.80 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.52/0.81 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.52/0.81 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.54/1.03 % Solved by lams/40_c_ic.sh.
% 0.54/1.03 % done 171 iterations in 0.159s
% 0.54/1.03 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.54/1.03 % SZS output start Refutation
% 0.54/1.03 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 0.54/1.03 thf(notdexE_type, type, notdexE: $o).
% 0.54/1.03 thf(setunionAx_type, type, setunionAx: $o).
% 0.54/1.03 thf(setminusELneg_type, type, setminusELneg: $o).
% 0.54/1.03 thf(powersetE_type, type, powersetE: $o).
% 0.54/1.03 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 0.54/1.03 thf(omegaSAx_type, type, omegaSAx: $o).
% 0.54/1.03 thf(exuI1_type, type, exuI1: $o).
% 0.54/1.03 thf(exuI2_type, type, exuI2: $o).
% 0.54/1.03 thf(notequalI2_type, type, notequalI2: $o).
% 0.54/1.03 thf(setukpairIR_type, type, setukpairIR: $o).
% 0.54/1.03 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 0.54/1.03 thf(setminusILneg_type, type, setminusILneg: $o).
% 0.54/1.03 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 0.54/1.03 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 0.54/1.03 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 0.54/1.03 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 0.54/1.03 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 0.54/1.03 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 0.54/1.03 thf(setukpairIL_type, type, setukpairIL: $o).
% 0.54/1.03 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 0.54/1.03 thf(binunionE_type, type, binunionE: $o).
% 0.54/1.03 thf(setext_type, type, setext: $o).
% 0.54/1.03 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 0.54/1.03 thf(descr__Cong_type, type, descr__Cong: $o).
% 0.54/1.03 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 0.54/1.03 thf(sk__70_type, type, sk__70: $i).
% 0.54/1.03 thf(in_type, type, in: $i > $i > $o).
% 0.54/1.03 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 0.54/1.03 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 0.54/1.03 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 0.54/1.03 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 0.54/1.03 thf(symdiffI2_type, type, symdiffI2: $o).
% 0.54/1.03 thf(upairset2IR_type, type, upairset2IR: $o).
% 0.54/1.03 thf(subsetE_type, type, subsetE: $o).
% 0.54/1.03 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 0.54/1.03 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 0.54/1.03 thf(setbeta_type, type, setbeta: $o).
% 0.54/1.03 thf(eqinunit_type, type, eqinunit: $o).
% 0.54/1.03 thf(upairsetIL_type, type, upairsetIL: $o).
% 0.54/1.03 thf(powersetI1_type, type, powersetI1: $o).
% 0.54/1.03 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 0.54/1.03 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 0.54/1.03 thf(powersetAx_type, type, powersetAx: $o).
% 0.54/1.03 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 0.54/1.03 thf(powersetI_type, type, powersetI: $o).
% 0.54/1.03 thf(upairsetIR_type, type, upairsetIR: $o).
% 0.54/1.03 thf(inCongP_type, type, inCongP: $o).
% 0.54/1.03 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 0.54/1.03 thf(exuE3e_type, type, exuE3e: $o).
% 0.54/1.03 thf(emptysetE_type, type, emptysetE: $o).
% 0.54/1.03 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 0.54/1.03 thf(setunionI_type, type, setunionI: $o).
% 0.54/1.03 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 0.54/1.03 thf(prop2setI_type, type, prop2setI: $o).
% 0.54/1.03 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 0.54/1.03 thf(setminusER_type, type, setminusER: $o).
% 0.54/1.03 thf(exuE2_type, type, exuE2: $o).
% 0.54/1.03 thf(emptyset_type, type, emptyset: $i).
% 0.54/1.03 thf(powersetsubset_type, type, powersetsubset: $o).
% 0.54/1.03 thf(subPowSU_type, type, subPowSU: $o).
% 0.54/1.03 thf(notequalI1_type, type, notequalI1: $o).
% 0.54/1.03 thf(notinemptyset_type, type, notinemptyset: $o).
% 0.54/1.03 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 0.54/1.03 thf(subsetTrans_type, type, subsetTrans: $o).
% 0.54/1.03 thf(setminusI_type, type, setminusI: $o).
% 0.54/1.03 thf(binunionIL_type, type, binunionIL: $o).
% 0.54/1.03 thf(subsetE2_type, type, subsetE2: $o).
% 0.54/1.03 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 0.54/1.03 thf(setextsub_type, type, setextsub: $o).
% 0.54/1.03 thf(binunionLsub_type, type, binunionLsub: $o).
% 0.54/1.03 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 0.54/1.03 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 0.54/1.03 thf(setunionE_type, type, setunionE: $o).
% 0.54/1.03 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 0.54/1.03 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 0.54/1.03 thf(binunionIR_type, type, binunionIR: $o).
% 0.54/1.03 thf(setadjoinE_type, type, setadjoinE: $o).
% 0.54/1.03 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 0.54/1.03 thf(exuE1_type, type, exuE1: $o).
% 0.54/1.03 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 0.54/1.03 thf(setminusLsub_type, type, setminusLsub: $o).
% 0.54/1.03 thf(notinsingleton_type, type, notinsingleton: $o).
% 0.54/1.03 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 0.54/1.03 thf(exuEu_type, type, exuEu: $o).
% 0.54/1.03 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 0.54/1.03 thf(upairsetE_type, type, upairsetE: $o).
% 0.54/1.03 thf(omega0Ax_type, type, omega0Ax: $o).
% 0.54/1.03 thf(sk__69_type, type, sk__69: $i).
% 0.54/1.03 thf(notsubsetI_type, type, notsubsetI: $o).
% 0.54/1.03 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 0.54/1.03 thf(setextAx_type, type, setextAx: $o).
% 0.54/1.03 thf(powersetE1_type, type, powersetE1: $o).
% 0.54/1.03 thf(bs114d_type, type, bs114d: $o).
% 0.54/1.03 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 0.54/1.03 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 0.54/1.03 thf(subsetI1_type, type, subsetI1: $o).
% 0.54/1.03 thf(symdiffE_type, type, symdiffE: $o).
% 0.54/1.03 thf(descrp_type, type, descrp: $o).
% 0.54/1.03 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 0.54/1.03 thf(foundationAx_type, type, foundationAx: $o).
% 0.54/1.03 thf(emptysetAx_type, type, emptysetAx: $o).
% 0.54/1.03 thf(emptyI_type, type, emptyI: $o).
% 0.54/1.03 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 0.54/1.03 thf(binintersectEL_type, type, binintersectEL: $o).
% 0.54/1.03 thf(emptyE1_type, type, emptyE1: $o).
% 0.54/1.03 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 0.54/1.03 thf(vacuousDall_type, type, vacuousDall: $o).
% 0.54/1.03 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 0.54/1.03 thf(binintersectI_type, type, binintersectI: $o).
% 0.54/1.03 thf(symdiffI1_type, type, symdiffI1: $o).
% 0.54/1.03 thf(subsetI2_type, type, subsetI2: $o).
% 0.54/1.03 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 0.54/1.03 thf(setminusERneg_type, type, setminusERneg: $o).
% 0.54/1.03 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 0.54/1.03 thf(omega__Cong_type, type, omega__Cong: $o).
% 0.54/1.03 thf(subsetRefl_type, type, subsetRefl: $o).
% 0.54/1.03 thf(uniqinunit_type, type, uniqinunit: $o).
% 0.54/1.03 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 0.54/1.03 thf(prop2setE_type, type, prop2setE: $o).
% 0.54/1.03 thf(binunionEcases_type, type, binunionEcases: $o).
% 0.54/1.03 thf(nonemptyI_type, type, nonemptyI: $o).
% 0.54/1.03 thf(sk__71_type, type, sk__71: $i > $i > $i).
% 0.54/1.03 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 0.54/1.03 thf(exuE3u_type, type, exuE3u: $o).
% 0.54/1.03 thf(setminusEL_type, type, setminusEL: $o).
% 0.54/1.03 thf(sepSubset_type, type, sepSubset: $o).
% 0.54/1.03 thf(singletonsubset_type, type, singletonsubset: $o).
% 0.54/1.03 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 0.54/1.03 thf(exuI3_type, type, exuI3: $o).
% 0.54/1.03 thf(notdallE_type, type, notdallE: $o).
% 0.54/1.03 thf(binintersectER_type, type, binintersectER: $o).
% 0.54/1.03 thf(powerset_type, type, powerset: $i > $i).
% 0.54/1.03 thf(kpairp_type, type, kpairp: $o).
% 0.54/1.03 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 0.54/1.03 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 0.54/1.03 thf(exu__Cong_type, type, exu__Cong: $o).
% 0.54/1.03 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 0.54/1.03 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 0.54/1.03 thf(replAx_type, type, replAx: $o).
% 0.54/1.03 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 0.54/1.03 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 0.54/1.03 thf(secondinupair_type, type, secondinupair: $o).
% 0.54/1.03 thf(inPowerset_type, type, inPowerset: $o).
% 0.54/1.03 thf(subset_type, type, subset: $i > $i > $o).
% 0.54/1.03 thf(in__Cong_type, type, in__Cong: $o).
% 0.54/1.03 thf(binunionRsub_type, type, binunionRsub: $o).
% 0.54/1.03 thf(subset2powerset_type, type, subset2powerset: $o).
% 0.54/1.03 thf(singletonsubset, axiom, singletonsubset =
% 0.54/1.03 (![A:$i,Xx:$i]:
% 0.54/1.03 ( ( in @ Xx @ A ) => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ))).
% 0.54/1.03 thf('0', plain,
% 0.54/1.03 (( singletonsubset ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( ( in @ X6 @ X4 ) => ( subset @ ( setadjoin @ X6 @ emptyset ) @ X4 ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(secondinupair, axiom, secondinupair =
% 0.54/1.03 (![Xx:$i,Xy:$i]:
% 0.54/1.03 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.54/1.03 thf('1', plain,
% 0.54/1.03 (( secondinupair ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(upairset2IR, axiom, upairset2IR =
% 0.54/1.03 (![Xx:$i,Xy:$i]:
% 0.54/1.03 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.54/1.03 thf('2', plain,
% 0.54/1.03 (( upairset2IR ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(powersetsubset, axiom, powersetsubset =
% 0.54/1.03 (![A:$i,B:$i]:
% 0.54/1.03 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 0.54/1.03 thf('3', plain,
% 0.54/1.03 (( powersetsubset ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( ( subset @ X4 @ X6 ) =>
% 0.54/1.03 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 0.54/1.03 thf('4', plain,
% 0.54/1.03 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(powersetE1, axiom, powersetE1 =
% 0.54/1.03 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 0.54/1.03 thf('5', plain,
% 0.54/1.03 (( powersetE1 ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(powersetI1, axiom, powersetI1 =
% 0.54/1.03 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 0.54/1.03 thf('6', plain,
% 0.54/1.03 (( powersetI1 ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(subset2powerset, axiom, subset2powerset =
% 0.54/1.03 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 0.54/1.03 thf('7', plain,
% 0.54/1.03 (( subset2powerset ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 0.54/1.03 (![A:$i,Xx:$i,B:$i]:
% 0.54/1.03 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 0.54/1.03 thf('8', plain,
% 0.54/1.03 (( setadjoinSub2 ) =
% 0.54/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/1.03 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(setadjoinSub, axiom, setadjoinSub =
% 0.54/1.03 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 0.54/1.03 thf('9', plain,
% 0.54/1.03 (( setadjoinSub ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(powerset__Cong, axiom, powerset__Cong =
% 0.54/1.03 (![A:$i,B:$i]:
% 0.54/1.03 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 0.54/1.03 thf('10', plain,
% 0.54/1.03 (( powerset__Cong ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 0.54/1.03 (![Xx:$i,Xy:$i]:
% 0.54/1.03 ( ( ( Xx ) = ( Xy ) ) =>
% 0.54/1.03 ( ![Xz:$i,Xu:$i]:
% 0.54/1.03 ( ( ( Xz ) = ( Xu ) ) =>
% 0.54/1.03 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 0.54/1.03 thf('11', plain,
% 0.54/1.03 (( setadjoin__Cong ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( ( ( X4 ) = ( X6 ) ) =>
% 0.54/1.03 ( ![X8:$i,X10:$i]:
% 0.54/1.03 ( ( ( X8 ) = ( X10 ) ) =>
% 0.54/1.03 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(upairsetIR, axiom, upairsetIR =
% 0.54/1.03 (![Xx:$i,Xy:$i]:
% 0.54/1.03 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.54/1.03 thf('12', plain,
% 0.54/1.03 (( upairsetIR ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(upairsetIL, axiom, upairsetIL =
% 0.54/1.03 (![Xx:$i,Xy:$i]:
% 0.54/1.03 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.54/1.03 thf('13', plain,
% 0.54/1.03 (( upairsetIL ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(upairsetE, axiom, upairsetE =
% 0.54/1.03 (![Xx:$i,Xy:$i,Xz:$i]:
% 0.54/1.03 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 0.54/1.03 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 0.54/1.03 thf('14', plain,
% 0.54/1.03 (( upairsetE ) =
% 0.54/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/1.03 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 0.54/1.03 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(singletonsswitch, axiom, singletonsswitch =
% 0.54/1.03 (![Xx:$i,Xy:$i]:
% 0.54/1.03 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 0.54/1.03 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 0.54/1.03 thf('15', plain,
% 0.54/1.03 (( singletonsswitch ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 0.54/1.03 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(eqinunit, axiom, eqinunit =
% 0.54/1.03 (![Xx:$i,Xy:$i]:
% 0.54/1.03 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.54/1.03 thf('16', plain,
% 0.54/1.03 (( eqinunit ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(notinsingleton, axiom, notinsingleton =
% 0.54/1.03 (![Xx:$i,Xy:$i]:
% 0.54/1.03 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 0.54/1.03 thf('17', plain,
% 0.54/1.03 (( notinsingleton ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( ( ( X4 ) != ( X6 ) ) =>
% 0.54/1.03 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(uniqinunit, axiom, uniqinunit =
% 0.54/1.03 (![Xx:$i,Xy:$i]:
% 0.54/1.03 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 0.54/1.03 thf('18', plain,
% 0.54/1.03 (( uniqinunit ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(powersetE, axiom, powersetE =
% 0.54/1.03 (![A:$i,B:$i,Xx:$i]:
% 0.54/1.03 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 0.54/1.03 thf('19', plain,
% 0.54/1.03 (( powersetE ) =
% 0.54/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/1.03 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 0.54/1.03 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(emptyInPowerset, axiom, emptyInPowerset =
% 0.54/1.03 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 0.54/1.03 thf('20', plain,
% 0.54/1.03 (( emptyInPowerset ) =
% 0.54/1.03 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(emptyinPowerset, axiom, emptyinPowerset =
% 0.54/1.03 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 0.54/1.03 thf('21', plain,
% 0.54/1.03 (( emptyinPowerset ) =
% 0.54/1.03 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(powersetI, axiom, powersetI =
% 0.54/1.03 (![A:$i,B:$i]:
% 0.54/1.03 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 0.54/1.03 ( in @ B @ ( powerset @ A ) ) ))).
% 0.54/1.03 thf('22', plain,
% 0.54/1.03 (( powersetI ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 0.54/1.03 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(setadjoinOr, axiom, setadjoinOr =
% 0.54/1.03 (![Xx:$i,A:$i,Xy:$i]:
% 0.54/1.03 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 0.54/1.03 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 0.54/1.03 thf('23', plain,
% 0.54/1.03 (( setadjoinOr ) =
% 0.54/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/1.03 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 0.54/1.03 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(setadjoinE, axiom, setadjoinE =
% 0.54/1.03 (![Xx:$i,A:$i,Xy:$i]:
% 0.54/1.03 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 0.54/1.03 ( ![Xphi:$o]:
% 0.54/1.03 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 0.54/1.03 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 0.54/1.03 thf('24', plain,
% 0.54/1.03 (( setadjoinE ) =
% 0.54/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/1.03 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 0.54/1.03 ( ![X10:$o]:
% 0.54/1.03 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 0.54/1.03 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(setadjoinIR, axiom, setadjoinIR =
% 0.54/1.03 (![Xx:$i,A:$i,Xy:$i]:
% 0.54/1.03 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 0.54/1.03 thf('25', plain,
% 0.54/1.03 (( setadjoinIR ) =
% 0.54/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/1.03 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 0.54/1.03 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 0.54/1.03 thf('26', plain,
% 0.54/1.03 (( emptyinunitempty ) =
% 0.54/1.03 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 0.54/1.03 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 0.54/1.03 thf('27', plain,
% 0.54/1.03 (( emptyinunitempty ) =
% 0.54/1.03 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(setadjoinIL, axiom, setadjoinIL =
% 0.54/1.03 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 0.54/1.03 thf('28', plain,
% 0.54/1.03 (( setadjoinIL ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(powersetAx, axiom, powersetAx =
% 0.54/1.03 (![A:$i,B:$i]:
% 0.54/1.03 ( ( in @ B @ ( powerset @ A ) ) <=>
% 0.54/1.03 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 0.54/1.03 thf('29', plain,
% 0.54/1.03 (( powersetAx ) =
% 0.54/1.03 ( ![X4:$i,X6:$i]:
% 0.54/1.03 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 0.54/1.03 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(setadjoinAx, axiom, setadjoinAx =
% 0.54/1.03 (![Xx:$i,A:$i,Xy:$i]:
% 0.54/1.03 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 0.54/1.03 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 0.54/1.03 thf('30', plain,
% 0.54/1.03 (( setadjoinAx ) =
% 0.54/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/1.03 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.54/1.03 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 0.54/1.03 define([status(thm)])).
% 0.54/1.03 thf(singletoninpowerset, conjecture,
% 0.54/1.03 (( setextAx ) =>
% 0.54/1.03 ( ( emptysetAx ) =>
% 0.54/1.03 ( ( setadjoinAx ) =>
% 0.54/1.03 ( ( powersetAx ) =>
% 0.54/1.03 ( ( setunionAx ) =>
% 0.54/1.03 ( ( omega0Ax ) =>
% 0.54/1.03 ( ( omegaSAx ) =>
% 0.54/1.03 ( ( omegaIndAx ) =>
% 0.54/1.03 ( ( replAx ) =>
% 0.54/1.03 ( ( foundationAx ) =>
% 0.54/1.03 ( ( wellorderingAx ) =>
% 0.54/1.03 ( ( descrp ) =>
% 0.54/1.03 ( ( dsetconstrI ) =>
% 0.54/1.03 ( ( dsetconstrEL ) =>
% 0.54/1.03 ( ( dsetconstrER ) =>
% 0.54/1.03 ( ( exuE1 ) =>
% 0.54/1.03 ( ( prop2setE ) =>
% 0.54/1.03 ( ( emptysetE ) =>
% 0.54/1.03 ( ( emptysetimpfalse ) =>
% 0.54/1.03 ( ( notinemptyset ) =>
% 0.54/1.03 ( ( exuE3e ) =>
% 0.54/1.03 ( ( setext ) =>
% 0.54/1.03 ( ( emptyI ) =>
% 0.54/1.03 ( ( noeltsimpempty ) =>
% 0.54/1.03 ( ( setbeta ) =>
% 0.54/1.03 ( ( nonemptyE1 ) =>
% 0.54/1.03 ( ( nonemptyI ) =>
% 0.54/1.03 ( ( nonemptyI1 ) =>
% 0.54/1.03 ( ( setadjoinIL ) =>
% 0.54/1.03 ( ( emptyinunitempty ) =>
% 0.54/1.03 ( ( setadjoinIR ) =>
% 0.54/1.03 ( ( setadjoinE ) =>
% 0.54/1.03 ( (
% 0.54/1.03 setadjoinOr ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setoftrueEq ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 powersetI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 emptyinPowerset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 emptyInPowerset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 powersetE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setunionI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setunionE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subPowSU ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuE2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 nonemptyImpWitness ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 uniqinunit ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notinsingleton ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 eqinunit ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 singletonsswitch ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 upairsetE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 upairsetIL ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 upairsetIR ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 emptyE1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 vacuousDall ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 quantDeMorgan1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 quantDeMorgan2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 quantDeMorgan3 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 quantDeMorgan4 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 prop2setI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 prop2set2propI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notdexE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notdallE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuI3 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuI2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 inCongP ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuE3u ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exu__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 emptyset__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setadjoin__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 powerset__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setunion__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 omega__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuEu ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 descr__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 dsetconstr__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 eqimpsubset2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 eqimpsubset1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetI2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 emptysetsubset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetE2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notsubsetI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notequalI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notequalI2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetRefl ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetTrans ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setadjoinSub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setadjoinSub2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subset2powerset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setextsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetemptysetimpeq ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 powersetI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 powersetE1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 inPowerset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 powersetsubset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 sepInPowerset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 sepSubset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionIL ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 upairset2IR ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionIR ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionEcases ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionLsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionRsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset5 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectEL ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectLsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset3 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectER ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 disjointsetsI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectRsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset4 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 bs114d ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusEL ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusER ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusSubset2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusERneg ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusELneg ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusILneg ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusIRneg ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusLsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusSubset1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffI2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffIneg1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffIneg2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 secondinupair ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setukpairIL ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setukpairIR ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 kpairiskpair ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 kpairp ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 singletonsubset ) =>
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 A:$i,Xx:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 Xx @ A ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 Xx @
% 0.54/1.03 emptyset ) @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.54/1.03 thf(zf_stmt_0, conjecture,
% 0.54/1.03 (( setextAx ) =>
% 0.54/1.03 ( ( emptysetAx ) =>
% 0.54/1.03 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/1.03 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.54/1.03 ( ( in @ X8 @ X6 ) | ( ( X8 ) = ( X4 ) ) ) ) ) =>
% 0.54/1.03 ( ( ![X10:$i,X12:$i]:
% 0.54/1.03 ( ( in @ X12 @ ( powerset @ X10 ) ) <=>
% 0.54/1.03 ( ![X14:$i]: ( ( in @ X14 @ X12 ) => ( in @ X14 @ X10 ) ) ) ) ) =>
% 0.54/1.03 ( ( setunionAx ) =>
% 0.54/1.03 ( ( omega0Ax ) =>
% 0.54/1.03 ( ( omegaSAx ) =>
% 0.54/1.03 ( ( omegaIndAx ) =>
% 0.54/1.03 ( ( replAx ) =>
% 0.54/1.03 ( ( foundationAx ) =>
% 0.54/1.03 ( ( wellorderingAx ) =>
% 0.54/1.03 ( ( descrp ) =>
% 0.54/1.03 ( ( dsetconstrI ) =>
% 0.54/1.03 ( ( dsetconstrEL ) =>
% 0.54/1.03 ( ( dsetconstrER ) =>
% 0.54/1.03 ( ( exuE1 ) =>
% 0.54/1.03 ( ( prop2setE ) =>
% 0.54/1.03 ( ( emptysetE ) =>
% 0.54/1.03 ( ( emptysetimpfalse ) =>
% 0.54/1.03 ( ( notinemptyset ) =>
% 0.54/1.03 ( ( exuE3e ) =>
% 0.54/1.03 ( ( setext ) =>
% 0.54/1.03 ( ( emptyI ) =>
% 0.54/1.03 ( ( noeltsimpempty ) =>
% 0.54/1.03 ( ( setbeta ) =>
% 0.54/1.03 ( ( nonemptyE1 ) =>
% 0.54/1.03 ( ( nonemptyI ) =>
% 0.54/1.03 ( ( nonemptyI1 ) =>
% 0.54/1.03 ( ( ![X16:$i,X18:$i]:
% 0.54/1.03 ( in @
% 0.54/1.03 X16 @
% 0.54/1.03 ( setadjoin @
% 0.54/1.03 X16 @ X18 ) ) ) =>
% 0.54/1.03 ( ( in @
% 0.54/1.03 emptyset @
% 0.54/1.03 ( setadjoin @
% 0.54/1.03 emptyset @
% 0.54/1.03 emptyset ) ) =>
% 0.54/1.03 ( ( ![X20:$i,
% 0.54/1.03 X22:$i,
% 0.54/1.03 X24:$i]:
% 0.54/1.03 ( (
% 0.54/1.03 in @
% 0.54/1.03 X24 @ X22 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X24 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X20 @ X22 ) ) ) ) =>
% 0.54/1.03 ( ( ![
% 0.54/1.03 X26:$i,
% 0.54/1.03 X28:$i,
% 0.54/1.03 X30:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X30 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X26 @ X28 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X32:$o]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X30 ) =
% 0.54/1.03 (
% 0.54/1.03 X26 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 X32 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X30 @ X28 ) =>
% 0.54/1.03 (
% 0.54/1.03 X32 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 X32 ) ) ) ) ) ) =>
% 0.54/1.03 ( (
% 0.54/1.03 ![
% 0.54/1.03 X34:$i,
% 0.54/1.03 X36:$i,
% 0.54/1.03 X38:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X38 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X34 @ X36 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X38 @ X36 ) |
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X38 ) =
% 0.54/1.03 (
% 0.54/1.03 X34 ) ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setoftrueEq ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X40:$i,
% 0.54/1.03 X42:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X44:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X44 @ X42 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X44 @ X40 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X42 @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X40 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X46:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 emptyset @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X46 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X48:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 emptyset @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X48 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X50:$i,
% 0.54/1.03 X52:$i,
% 0.54/1.03 X54:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X52 @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X50 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X54 @ X52 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X54 @ X50 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setunionI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setunionE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subPowSU ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuE2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 nonemptyImpWitness ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X56:$i,
% 0.54/1.03 X58:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X56 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X58 @
% 0.54/1.03 emptyset ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X56 ) =
% 0.54/1.03 (
% 0.54/1.03 X58 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X60:$i,
% 0.54/1.03 X62:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X60 ) !=
% 0.54/1.03 (
% 0.54/1.03 X62 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 ~(
% 0.54/1.03 in @
% 0.54/1.03 X62 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X60 @
% 0.54/1.03 emptyset ) ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X64:$i,
% 0.54/1.03 X66:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X64 ) =
% 0.54/1.03 (
% 0.54/1.03 X66 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X64 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X66 @
% 0.54/1.03 emptyset ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X68:$i,
% 0.54/1.03 X70:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X68 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X70 @
% 0.54/1.03 emptyset ) ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X70 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X68 @
% 0.54/1.03 emptyset ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X72:$i,
% 0.54/1.03 X74:$i,
% 0.54/1.03 X76:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X76 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X72 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X74 @
% 0.54/1.03 emptyset ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X76 ) =
% 0.54/1.03 (
% 0.54/1.03 X74 ) ) |
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X76 ) =
% 0.54/1.03 (
% 0.54/1.03 X72 ) ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X78:$i,
% 0.54/1.03 X80:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X78 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X78 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X80 @
% 0.54/1.03 emptyset ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X82:$i,
% 0.54/1.03 X84:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X84 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X82 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X84 @
% 0.54/1.03 emptyset ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 emptyE1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 vacuousDall ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 quantDeMorgan1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 quantDeMorgan2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 quantDeMorgan3 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 quantDeMorgan4 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 prop2setI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 prop2set2propI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notdexE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notdallE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuI3 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuI2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 inCongP ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuE3u ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exu__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 emptyset__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X86:$i,
% 0.54/1.03 X88:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X86 ) =
% 0.54/1.03 (
% 0.54/1.03 X88 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X90:$i,
% 0.54/1.03 X92:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X90 ) =
% 0.54/1.03 (
% 0.54/1.03 X92 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X86 @ X90 ) =
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X88 @ X92 ) ) ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X94:$i,
% 0.54/1.03 X96:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X94 ) =
% 0.54/1.03 (
% 0.54/1.03 X96 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X94 ) =
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X96 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setunion__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 omega__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuEu ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 descr__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 dsetconstr__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 eqimpsubset2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 eqimpsubset1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetI2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 emptysetsubset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetE2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notsubsetI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notequalI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notequalI2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetRefl ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetTrans ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X98:$i,
% 0.54/1.03 X100:$i]:
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X100 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X98 @ X100 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X102:$i,
% 0.54/1.03 X104:$i,
% 0.54/1.03 X106:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X102 @
% 0.54/1.03 X106 ) =>
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X102 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X104 @
% 0.54/1.03 X106 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X108:$i,
% 0.54/1.03 X110:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X108 @
% 0.54/1.03 X110 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X108 @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X110 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setextsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetemptysetimpeq ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X112:$i,
% 0.54/1.03 X114:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X114 @
% 0.54/1.03 X112 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X114 @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X112 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X116:$i,
% 0.54/1.03 X118:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X118 @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X116 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X118 @
% 0.54/1.03 X116 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X120:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X120 @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X120 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X122:$i,
% 0.54/1.03 X124:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X122 @
% 0.54/1.03 X124 ) =>
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X122 ) @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X124 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 sepInPowerset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 sepSubset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionIL ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X126:$i,
% 0.54/1.03 X128:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X128 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X126 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X128 @
% 0.54/1.03 emptyset ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionIR ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionEcases ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionLsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionRsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset5 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectEL ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectLsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset3 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectER ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 disjointsetsI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectRsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset4 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 bs114d ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusEL ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusER ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusSubset2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusERneg ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusELneg ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusILneg ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusIRneg ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusLsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusSubset1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffI2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffIneg1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffIneg2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X130:$i,
% 0.54/1.03 X132:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X132 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X130 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X132 @
% 0.54/1.03 emptyset ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setukpairIL ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setukpairIR ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 kpairiskpair ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 kpairp ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X134:$i,
% 0.54/1.03 X136:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X136 @
% 0.54/1.03 X134 ) =>
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X136 @
% 0.54/1.03 emptyset ) @
% 0.54/1.03 X134 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X138:$i,
% 0.54/1.03 X140:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X140 @
% 0.54/1.03 X138 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X140 @
% 0.54/1.03 emptyset ) @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X138 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.54/1.03 thf(zf_stmt_1, type, zip_tseitin_1 : $i > $i > $i > $o).
% 0.54/1.03 thf(zf_stmt_2, axiom,
% 0.54/1.03 (![X14:$i,X12:$i,X10:$i]:
% 0.54/1.03 ( ( zip_tseitin_1 @ X14 @ X12 @ X10 ) <=>
% 0.54/1.03 ( ( in @ X14 @ X12 ) => ( in @ X14 @ X10 ) ) ))).
% 0.54/1.03 thf(zf_stmt_3, type, zip_tseitin_0 : $i > $i > $i > $o).
% 0.54/1.03 thf(zf_stmt_4, axiom,
% 0.54/1.03 (![X8:$i,X6:$i,X4:$i]:
% 0.54/1.03 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 0.54/1.03 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ))).
% 0.54/1.03 thf(zf_stmt_5, conjecture,
% 0.54/1.03 (( setextAx ) =>
% 0.54/1.03 ( ( emptysetAx ) =>
% 0.54/1.03 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/1.03 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.54/1.03 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 0.54/1.03 ( ( ![X10:$i,X12:$i]:
% 0.54/1.03 ( ( in @ X12 @ ( powerset @ X10 ) ) <=>
% 0.54/1.03 ( ![X14:$i]: ( zip_tseitin_1 @ X14 @ X12 @ X10 ) ) ) ) =>
% 0.54/1.03 ( ( setunionAx ) =>
% 0.54/1.03 ( ( omega0Ax ) =>
% 0.54/1.03 ( ( omegaSAx ) =>
% 0.54/1.03 ( ( omegaIndAx ) =>
% 0.54/1.03 ( ( replAx ) =>
% 0.54/1.03 ( ( foundationAx ) =>
% 0.54/1.03 ( ( wellorderingAx ) =>
% 0.54/1.03 ( ( descrp ) =>
% 0.54/1.03 ( ( dsetconstrI ) =>
% 0.54/1.03 ( ( dsetconstrEL ) =>
% 0.54/1.03 ( ( dsetconstrER ) =>
% 0.54/1.03 ( ( exuE1 ) =>
% 0.54/1.03 ( ( prop2setE ) =>
% 0.54/1.03 ( ( emptysetE ) =>
% 0.54/1.03 ( ( emptysetimpfalse ) =>
% 0.54/1.03 ( ( notinemptyset ) =>
% 0.54/1.03 ( ( exuE3e ) =>
% 0.54/1.03 ( ( setext ) =>
% 0.54/1.03 ( ( emptyI ) =>
% 0.54/1.03 ( ( noeltsimpempty ) =>
% 0.54/1.03 ( ( setbeta ) =>
% 0.54/1.03 ( ( nonemptyE1 ) =>
% 0.54/1.03 ( ( nonemptyI ) =>
% 0.54/1.03 ( ( nonemptyI1 ) =>
% 0.54/1.03 ( ( ![X16:$i,X18:$i]:
% 0.54/1.03 ( in @
% 0.54/1.03 X16 @
% 0.54/1.03 ( setadjoin @
% 0.54/1.03 X16 @ X18 ) ) ) =>
% 0.54/1.03 ( ( in @
% 0.54/1.03 emptyset @
% 0.54/1.03 ( setadjoin @
% 0.54/1.03 emptyset @
% 0.54/1.03 emptyset ) ) =>
% 0.54/1.03 ( ( ![X20:$i,
% 0.54/1.03 X22:$i,
% 0.54/1.03 X24:$i]:
% 0.54/1.03 ( (
% 0.54/1.03 in @
% 0.54/1.03 X24 @ X22 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X24 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X20 @ X22 ) ) ) ) =>
% 0.54/1.03 ( ( ![
% 0.54/1.03 X26:$i,
% 0.54/1.03 X28:$i,
% 0.54/1.03 X30:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X30 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X26 @ X28 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X32:$o]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X30 ) =
% 0.54/1.03 (
% 0.54/1.03 X26 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 X32 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X30 @ X28 ) =>
% 0.54/1.03 (
% 0.54/1.03 X32 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 X32 ) ) ) ) ) ) =>
% 0.54/1.03 ( (
% 0.54/1.03 ![
% 0.54/1.03 X34:$i,
% 0.54/1.03 X36:$i,
% 0.54/1.03 X38:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X38 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X34 @ X36 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X38 ) =
% 0.54/1.03 (
% 0.54/1.03 X34 ) ) |
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X38 @ X36 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setoftrueEq ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X40:$i,
% 0.54/1.03 X42:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X44:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X44 @ X42 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X44 @ X40 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X42 @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X40 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X46:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 emptyset @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X46 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X48:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 emptyset @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X48 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X50:$i,
% 0.54/1.03 X52:$i,
% 0.54/1.03 X54:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X52 @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X50 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X54 @ X52 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X54 @ X50 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setunionI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setunionE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subPowSU ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuE2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 nonemptyImpWitness ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X56:$i,
% 0.54/1.03 X58:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X56 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X58 @
% 0.54/1.03 emptyset ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X56 ) =
% 0.54/1.03 (
% 0.54/1.03 X58 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X60:$i,
% 0.54/1.03 X62:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X60 ) !=
% 0.54/1.03 (
% 0.54/1.03 X62 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 ~(
% 0.54/1.03 in @
% 0.54/1.03 X62 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X60 @
% 0.54/1.03 emptyset ) ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X64:$i,
% 0.54/1.03 X66:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X64 ) =
% 0.54/1.03 (
% 0.54/1.03 X66 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X64 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X66 @
% 0.54/1.03 emptyset ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X68:$i,
% 0.54/1.03 X70:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X68 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X70 @
% 0.54/1.03 emptyset ) ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X70 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X68 @
% 0.54/1.03 emptyset ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X72:$i,
% 0.54/1.03 X74:$i,
% 0.54/1.03 X76:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X76 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X72 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X74 @
% 0.54/1.03 emptyset ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X76 ) =
% 0.54/1.03 (
% 0.54/1.03 X72 ) ) |
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X76 ) =
% 0.54/1.03 (
% 0.54/1.03 X74 ) ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X78:$i,
% 0.54/1.03 X80:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X78 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X78 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X80 @
% 0.54/1.03 emptyset ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X82:$i,
% 0.54/1.03 X84:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X84 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X82 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X84 @
% 0.54/1.03 emptyset ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 emptyE1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 vacuousDall ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 quantDeMorgan1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 quantDeMorgan2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 quantDeMorgan3 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 quantDeMorgan4 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 prop2setI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 prop2set2propI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notdexE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notdallE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuI3 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuI2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 inCongP ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuE3u ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exu__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 emptyset__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X86:$i,
% 0.54/1.03 X88:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X86 ) =
% 0.54/1.03 (
% 0.54/1.03 X88 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X90:$i,
% 0.54/1.03 X92:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X90 ) =
% 0.54/1.03 (
% 0.54/1.03 X92 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X86 @ X90 ) =
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X88 @ X92 ) ) ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X94:$i,
% 0.54/1.03 X96:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X94 ) =
% 0.54/1.03 (
% 0.54/1.03 X96 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X94 ) =
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X96 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setunion__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 omega__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 exuEu ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 descr__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 dsetconstr__Cong ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 eqimpsubset2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 eqimpsubset1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetI2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 emptysetsubset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetE2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notsubsetI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notequalI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 notequalI2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetRefl ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetTrans ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X98:$i,
% 0.54/1.03 X100:$i]:
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X100 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X98 @ X100 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X102:$i,
% 0.54/1.03 X104:$i,
% 0.54/1.03 X106:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X102 @
% 0.54/1.03 X106 ) =>
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X102 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X104 @
% 0.54/1.03 X106 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X108:$i,
% 0.54/1.03 X110:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X108 @
% 0.54/1.03 X110 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X108 @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X110 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setextsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subsetemptysetimpeq ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X112:$i,
% 0.54/1.03 X114:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X114 @
% 0.54/1.03 X112 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X114 @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X112 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X116:$i,
% 0.54/1.03 X118:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X118 @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X116 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X118 @
% 0.54/1.03 X116 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X120:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X120 @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X120 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X122:$i,
% 0.54/1.03 X124:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 X122 @
% 0.54/1.03 X124 ) =>
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X122 ) @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X124 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 sepInPowerset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 sepSubset ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionIL ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X126:$i,
% 0.54/1.03 X128:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X128 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X126 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X128 @
% 0.54/1.03 emptyset ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionIR ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionEcases ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionLsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binunionRsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset5 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectEL ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectLsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset3 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectER ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 disjointsetsI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectRsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset4 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 binintersectSubset1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 bs114d ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusI ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusEL ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusER ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusSubset2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusERneg ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusELneg ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusILneg ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusIRneg ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusLsub ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setminusSubset1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffE ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffI1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffI2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffIneg1 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 symdiffIneg2 ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X130:$i,
% 0.54/1.03 X132:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X132 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X130 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X132 @
% 0.54/1.03 emptyset ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setukpairIL ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setukpairIR ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 kpairiskpair ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 kpairp ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X134:$i,
% 0.54/1.03 X136:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X136 @
% 0.54/1.03 X134 ) =>
% 0.54/1.03 (
% 0.54/1.03 subset @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X136 @
% 0.54/1.03 emptyset ) @
% 0.54/1.03 X134 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X138:$i,
% 0.54/1.03 X140:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X140 @
% 0.54/1.03 X138 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X140 @
% 0.54/1.03 emptyset ) @
% 0.54/1.03 (
% 0.54/1.03 powerset @
% 0.54/1.03 X138 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.54/1.03 thf(zf_stmt_6, negated_conjecture,
% 0.54/1.03 (~( ( setextAx ) =>
% 0.54/1.03 ( ( emptysetAx ) =>
% 0.54/1.03 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/1.03 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.54/1.03 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 0.54/1.03 ( ( ![X10:$i,X12:$i]:
% 0.54/1.03 ( ( in @ X12 @ ( powerset @ X10 ) ) <=>
% 0.54/1.03 ( ![X14:$i]: ( zip_tseitin_1 @ X14 @ X12 @ X10 ) ) ) ) =>
% 0.54/1.03 ( ( setunionAx ) =>
% 0.54/1.03 ( ( omega0Ax ) =>
% 0.54/1.03 ( ( omegaSAx ) =>
% 0.54/1.03 ( ( omegaIndAx ) =>
% 0.54/1.03 ( ( replAx ) =>
% 0.54/1.03 ( ( foundationAx ) =>
% 0.54/1.03 ( ( wellorderingAx ) =>
% 0.54/1.03 ( ( descrp ) =>
% 0.54/1.03 ( ( dsetconstrI ) =>
% 0.54/1.03 ( ( dsetconstrEL ) =>
% 0.54/1.03 ( ( dsetconstrER ) =>
% 0.54/1.03 ( ( exuE1 ) =>
% 0.54/1.03 ( ( prop2setE ) =>
% 0.54/1.03 ( ( emptysetE ) =>
% 0.54/1.03 ( ( emptysetimpfalse ) =>
% 0.54/1.03 ( ( notinemptyset ) =>
% 0.54/1.03 ( ( exuE3e ) =>
% 0.54/1.03 ( ( setext ) =>
% 0.54/1.03 ( ( emptyI ) =>
% 0.54/1.03 ( ( noeltsimpempty ) =>
% 0.54/1.03 ( ( setbeta ) =>
% 0.54/1.03 ( ( nonemptyE1 ) =>
% 0.54/1.03 ( ( nonemptyI ) =>
% 0.54/1.03 ( ( nonemptyI1 ) =>
% 0.54/1.03 ( ( ![X16:$i,
% 0.54/1.03 X18:$i]:
% 0.54/1.03 ( in @
% 0.54/1.03 X16 @
% 0.54/1.03 ( setadjoin
% 0.54/1.03 @
% 0.54/1.03 X16 @ X18 ) ) ) =>
% 0.54/1.03 ( ( in @
% 0.54/1.03 emptyset @
% 0.54/1.03 ( setadjoin
% 0.54/1.03 @
% 0.54/1.03 emptyset @
% 0.54/1.03 emptyset ) ) =>
% 0.54/1.03 ( ( ![
% 0.54/1.03 X20:$i,
% 0.54/1.03 X22:$i,
% 0.54/1.03 X24:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X24 @ X22 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X24 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X20 @ X22 ) ) ) ) =>
% 0.54/1.03 ( (
% 0.54/1.03 ![
% 0.54/1.03 X26:$i,
% 0.54/1.03 X28:$i,
% 0.54/1.03 X30:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X30 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X26 @ X28 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X32:$o]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X30 ) =
% 0.54/1.03 (
% 0.54/1.03 X26 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 X32 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X30 @ X28 ) =>
% 0.54/1.03 (
% 0.54/1.03 X32 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 X32 ) ) ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X34:$i,
% 0.54/1.03 X36:$i,
% 0.54/1.03 X38:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X38 @
% 0.54/1.03 (
% 0.54/1.03 setadjoin
% 0.54/1.03 @
% 0.54/1.03 X34 @ X36 ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 X38 ) =
% 0.54/1.03 (
% 0.54/1.03 X34 ) ) |
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X38 @ X36 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 setoftrueEq ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X40:$i,
% 0.54/1.03 X42:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X44:$i]:
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X44 @ X42 ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X44 @ X40 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 X42 @
% 0.54/1.03 (
% 0.54/1.03 powerset
% 0.54/1.03 @
% 0.54/1.03 X40 ) ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X46:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 emptyset @
% 0.54/1.03 (
% 0.54/1.03 powerset
% 0.54/1.03 @
% 0.54/1.03 X46 ) ) ) =>
% 0.54/1.03 (
% 0.54/1.03 (
% 0.54/1.03 ![
% 0.54/1.03 X48:$i]:
% 0.54/1.03 (
% 0.54/1.03 in @
% 0.54/1.03 emptyset @
% 0.54/1.03 (
% 0.54/1.03 powerset
% 0.54/1.03 @
% 0.54/1.04 X48 ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X50:$i,
% 0.54/1.04 X52:$i,
% 0.54/1.04 X54:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X52 @
% 0.54/1.04 (
% 0.54/1.04 powerset
% 0.54/1.04 @
% 0.54/1.04 X50 ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X54 @ X52 ) =>
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X54 @ X50 ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setunionI ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setunionE ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 subPowSU ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 exuE2 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 nonemptyImpWitness ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X56:$i,
% 0.54/1.04 X58:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X56 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X58 @
% 0.54/1.04 emptyset ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 X56 ) =
% 0.54/1.04 (
% 0.54/1.04 X58 ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X60:$i,
% 0.54/1.04 X62:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 X60 ) !=
% 0.54/1.04 (
% 0.54/1.04 X62 ) ) =>
% 0.54/1.04 (
% 0.54/1.04 ~
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X62 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X60 @
% 0.54/1.04 emptyset ) ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X64:$i,
% 0.54/1.04 X66:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 X64 ) =
% 0.54/1.04 (
% 0.54/1.04 X66 ) ) =>
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X64 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X66 @
% 0.54/1.04 emptyset ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X68:$i,
% 0.54/1.04 X70:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X68 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X70 @
% 0.54/1.04 emptyset ) ) =>
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X70 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X68 @
% 0.54/1.04 emptyset ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X72:$i,
% 0.54/1.04 X74:$i,
% 0.54/1.04 X76:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X76 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X72 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X74 @
% 0.54/1.04 emptyset ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 X76 ) =
% 0.54/1.04 (
% 0.54/1.04 X72 ) ) |
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 X76 ) =
% 0.54/1.04 (
% 0.54/1.04 X74 ) ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X78:$i,
% 0.54/1.04 X80:$i]:
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X78 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X78 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X80 @
% 0.54/1.04 emptyset ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X82:$i,
% 0.54/1.04 X84:$i]:
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X84 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X82 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X84 @
% 0.54/1.04 emptyset ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 emptyE1 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 vacuousDall ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 quantDeMorgan1 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 quantDeMorgan2 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 quantDeMorgan3 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 quantDeMorgan4 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 prop2setI ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 prop2set2propI ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 notdexE ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 notdallE ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 exuI1 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 exuI3 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 exuI2 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 inCongP ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 in__Cong ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 exuE3u ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 exu__Cong ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 emptyset__Cong ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X86:$i,
% 0.54/1.04 X88:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 X86 ) =
% 0.54/1.04 (
% 0.54/1.04 X88 ) ) =>
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X90:$i,
% 0.54/1.04 X92:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 X90 ) =
% 0.54/1.04 (
% 0.54/1.04 X92 ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X86 @ X90 ) =
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X88 @ X92 ) ) ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X94:$i,
% 0.54/1.04 X96:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 X94 ) =
% 0.54/1.04 (
% 0.54/1.04 X96 ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 powerset
% 0.54/1.04 @
% 0.54/1.04 X94 ) =
% 0.54/1.04 (
% 0.54/1.04 powerset
% 0.54/1.04 @
% 0.54/1.04 X96 ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setunion__Cong ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 omega__Cong ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 exuEu ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 descr__Cong ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 dsetconstr__Cong ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 subsetI1 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 eqimpsubset2 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 eqimpsubset1 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 subsetI2 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 emptysetsubset ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 subsetE ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 subsetE2 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 notsubsetI ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 notequalI1 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 notequalI2 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 subsetRefl ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 subsetTrans ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X98:$i,
% 0.54/1.04 X100:$i]:
% 0.54/1.04 (
% 0.54/1.04 subset @
% 0.54/1.04 X100 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X98 @
% 0.54/1.04 X100 ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X102:$i,
% 0.54/1.04 X104:$i,
% 0.54/1.04 X106:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 subset @
% 0.54/1.04 X102 @
% 0.54/1.04 X106 ) =>
% 0.54/1.04 (
% 0.54/1.04 subset @
% 0.54/1.04 X102 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X104 @
% 0.54/1.04 X106 ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X108:$i,
% 0.54/1.04 X110:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 subset @
% 0.54/1.04 X108 @
% 0.54/1.04 X110 ) =>
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X108 @
% 0.54/1.04 (
% 0.54/1.04 powerset
% 0.54/1.04 @
% 0.54/1.04 X110 ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setextsub ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 subsetemptysetimpeq ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X112:$i,
% 0.54/1.04 X114:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 subset @
% 0.54/1.04 X114 @
% 0.54/1.04 X112 ) =>
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X114 @
% 0.54/1.04 (
% 0.54/1.04 powerset
% 0.54/1.04 @
% 0.54/1.04 X112 ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X116:$i,
% 0.54/1.04 X118:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X118 @
% 0.54/1.04 (
% 0.54/1.04 powerset
% 0.54/1.04 @
% 0.54/1.04 X116 ) ) =>
% 0.54/1.04 (
% 0.54/1.04 subset @
% 0.54/1.04 X118 @
% 0.54/1.04 X116 ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X120:$i]:
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X120 @
% 0.54/1.04 (
% 0.54/1.04 powerset
% 0.54/1.04 @
% 0.54/1.04 X120 ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X122:$i,
% 0.54/1.04 X124:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 subset @
% 0.54/1.04 X122 @
% 0.54/1.04 X124 ) =>
% 0.54/1.04 (
% 0.54/1.04 subset @
% 0.54/1.04 (
% 0.54/1.04 powerset
% 0.54/1.04 @
% 0.54/1.04 X122 ) @
% 0.54/1.04 (
% 0.54/1.04 powerset
% 0.54/1.04 @
% 0.54/1.04 X124 ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 sepInPowerset ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 sepSubset ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binunionIL ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X126:$i,
% 0.54/1.04 X128:$i]:
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X128 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X126 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X128 @
% 0.54/1.04 emptyset ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binunionIR ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binunionEcases ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binunionE ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binunionLsub ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binunionRsub ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binintersectI ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binintersectSubset5 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binintersectEL ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binintersectLsub ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binintersectSubset2 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binintersectSubset3 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binintersectER ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 disjointsetsI1 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binintersectRsub ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binintersectSubset4 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 binintersectSubset1 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 bs114d ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setminusI ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setminusEL ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setminusER ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setminusSubset2 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setminusERneg ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setminusELneg ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setminusILneg ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setminusIRneg ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setminusLsub ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setminusSubset1 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 symdiffE ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 symdiffI1 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 symdiffI2 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 symdiffIneg1 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 symdiffIneg2 ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X130:$i,
% 0.54/1.04 X132:$i]:
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X132 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X130 @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X132 @
% 0.54/1.04 emptyset ) ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setukpairIL ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 setukpairIR ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 kpairiskpair ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 kpairp ) =>
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X134:$i,
% 0.54/1.04 X136:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X136 @
% 0.54/1.04 X134 ) =>
% 0.54/1.04 (
% 0.54/1.04 subset @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X136 @
% 0.54/1.04 emptyset ) @
% 0.54/1.04 X134 ) ) ) =>
% 0.54/1.04 (
% 0.54/1.04 ![
% 0.54/1.04 X138:$i,
% 0.54/1.04 X140:$i]:
% 0.54/1.04 (
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 X140 @
% 0.54/1.04 X138 ) =>
% 0.54/1.04 (
% 0.54/1.04 in @
% 0.54/1.04 (
% 0.54/1.04 setadjoin
% 0.54/1.04 @
% 0.54/1.04 X140 @
% 0.54/1.04 emptyset ) @
% 0.54/1.04 (
% 0.54/1.04 powerset
% 0.54/1.04 @
% 0.54/1.04 X138 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 0.54/1.04 inference('cnf.neg', [status(esa)], [zf_stmt_5])).
% 0.54/1.04 thf(zip_derived_cl25, plain,
% 0.54/1.04 (![X12 : $i, X13 : $i]:
% 0.54/1.04 ( (in @ X12 @ (powerset @ X13)) | (in @ (sk__71 @ X12 @ X13) @ X12))),
% 0.54/1.04 inference('cnf', [status(esa)], [zf_stmt_6])).
% 0.54/1.04 thf(zip_derived_cl30, plain,
% 0.54/1.04 (![X15 : $i, X16 : $i]:
% 0.54/1.04 (~ (in @ X15 @ (setadjoin @ X16 @ emptyset)) | ((X16) = (X15)))),
% 0.54/1.04 inference('cnf', [status(esa)], [zf_stmt_6])).
% 0.54/1.04 thf(zip_derived_cl213, plain,
% 0.54/1.04 (![X0 : $i, X1 : $i]:
% 0.54/1.04 ( (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1))
% 0.54/1.04 | ((X0) = (sk__71 @ (setadjoin @ X0 @ emptyset) @ X1)))),
% 0.54/1.04 inference('sup-', [status(thm)], [zip_derived_cl25, zip_derived_cl30])).
% 0.54/1.04 thf(zip_derived_cl24, plain,
% 0.54/1.04 (![X12 : $i, X13 : $i]:
% 0.54/1.04 ( (in @ X12 @ (powerset @ X13)) | ~ (in @ (sk__71 @ X12 @ X13) @ X13))),
% 0.54/1.04 inference('cnf', [status(esa)], [zf_stmt_6])).
% 0.54/1.04 thf(zip_derived_cl285, plain,
% 0.54/1.04 (![X0 : $i, X1 : $i]:
% 0.54/1.04 (~ (in @ X0 @ X1)
% 0.54/1.04 | (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1))
% 0.54/1.04 | (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1)))),
% 0.54/1.04 inference('sup-', [status(thm)], [zip_derived_cl213, zip_derived_cl24])).
% 0.54/1.04 thf(zip_derived_cl290, plain,
% 0.54/1.04 (![X0 : $i, X1 : $i]:
% 0.54/1.04 ( (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1))
% 0.54/1.04 | ~ (in @ X0 @ X1))),
% 0.54/1.04 inference('simplify', [status(thm)], [zip_derived_cl285])).
% 0.54/1.04 thf(zip_derived_cl77, plain,
% 0.54/1.04 (~ (in @ (setadjoin @ sk__70 @ emptyset) @ (powerset @ sk__69))),
% 0.54/1.04 inference('cnf', [status(esa)], [zf_stmt_6])).
% 0.54/1.04 thf(zip_derived_cl320, plain, (~ (in @ sk__70 @ sk__69)),
% 0.54/1.04 inference('sup-', [status(thm)], [zip_derived_cl290, zip_derived_cl77])).
% 0.54/1.04 thf(zip_derived_cl78, plain, ( (in @ sk__70 @ sk__69)),
% 0.54/1.04 inference('cnf', [status(esa)], [zf_stmt_6])).
% 0.54/1.04 thf(zip_derived_cl324, plain, ($false),
% 0.54/1.04 inference('demod', [status(thm)], [zip_derived_cl320, zip_derived_cl78])).
% 0.54/1.04
% 0.54/1.04 % SZS output end Refutation
% 0.54/1.04
% 0.54/1.04
% 0.54/1.04 % Terminating...
% 3.06/1.25 % Runner terminated.
% 3.06/1.28 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------