%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU641^1 : 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.95Ub60GDup 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 04:55:31 PM UTC 2025
% Result : Theorem 0.62s 1.11s
% Output : Refutation 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU641^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.95Ub60GDup true
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 16:08:08 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.49/0.61 % Total configuration time : 828
% 0.49/0.61 % Estimated wc time : 1656
% 0.49/0.61 % Estimated cpu time (8 cpus) : 207.0
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.55/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.61/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.61/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.61/0.78 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.61/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.61/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.62/1.11 % Solved by lams/40_c_ic.sh.
% 0.62/1.11 % done 156 iterations in 0.200s
% 0.62/1.11 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.62/1.11 % SZS output start Refutation
% 0.62/1.11 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 0.62/1.11 thf(notdexE_type, type, notdexE: $o).
% 0.62/1.11 thf(setunionAx_type, type, setunionAx: $o).
% 0.62/1.11 thf(setminusELneg_type, type, setminusELneg: $o).
% 0.62/1.11 thf(powersetE_type, type, powersetE: $o).
% 0.62/1.11 thf(omegaSAx_type, type, omegaSAx: $o).
% 0.62/1.11 thf(exuI1_type, type, exuI1: $o).
% 0.62/1.11 thf(exuI2_type, type, exuI2: $o).
% 0.62/1.11 thf(notequalI2_type, type, notequalI2: $o).
% 0.62/1.11 thf(setukpairIR_type, type, setukpairIR: $o).
% 0.62/1.11 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 0.62/1.11 thf(setminusILneg_type, type, setminusILneg: $o).
% 0.62/1.11 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 0.62/1.11 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 0.62/1.11 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 0.62/1.11 thf(upairsubunion_type, type, upairsubunion: $o).
% 0.62/1.11 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 0.62/1.11 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 0.62/1.11 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 0.62/1.11 thf(setukpairIL_type, type, setukpairIL: $o).
% 0.62/1.11 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 0.62/1.11 thf(binunionE_type, type, binunionE: $o).
% 0.62/1.11 thf(setext_type, type, setext: $o).
% 0.62/1.11 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 0.62/1.11 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 0.62/1.11 thf(descr__Cong_type, type, descr__Cong: $o).
% 0.62/1.11 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 0.62/1.11 thf(in_type, type, in: $i > $i > $o).
% 0.62/1.11 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 0.62/1.11 thf(upairset2E_type, type, upairset2E: $o).
% 0.62/1.11 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 0.62/1.11 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 0.62/1.11 thf(symdiffI2_type, type, symdiffI2: $o).
% 0.62/1.11 thf(upairset2IR_type, type, upairset2IR: $o).
% 0.62/1.11 thf(subsetE_type, type, subsetE: $o).
% 0.62/1.11 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 0.62/1.11 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 0.62/1.11 thf(setbeta_type, type, setbeta: $o).
% 0.62/1.11 thf(eqinunit_type, type, eqinunit: $o).
% 0.62/1.11 thf(upairsetIL_type, type, upairsetIL: $o).
% 0.62/1.11 thf(powersetI1_type, type, powersetI1: $o).
% 0.62/1.11 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 0.62/1.11 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 0.62/1.11 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 0.62/1.11 thf(powersetAx_type, type, powersetAx: $o).
% 0.62/1.11 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 0.62/1.11 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 0.62/1.11 thf(powersetI_type, type, powersetI: $o).
% 0.62/1.11 thf(upairsetIR_type, type, upairsetIR: $o).
% 0.62/1.11 thf(inCongP_type, type, inCongP: $o).
% 0.62/1.11 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 0.62/1.11 thf(exuE3e_type, type, exuE3e: $o).
% 0.62/1.11 thf(emptysetE_type, type, emptysetE: $o).
% 0.62/1.11 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 0.62/1.11 thf(setunionI_type, type, setunionI: $o).
% 0.62/1.11 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 0.62/1.11 thf(prop2setI_type, type, prop2setI: $o).
% 0.62/1.11 thf(ex1I2_type, type, ex1I2: $o).
% 0.62/1.11 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 0.62/1.11 thf(setminusER_type, type, setminusER: $o).
% 0.62/1.11 thf(exuE2_type, type, exuE2: $o).
% 0.62/1.11 thf(emptyset_type, type, emptyset: $i).
% 0.62/1.11 thf(powersetsubset_type, type, powersetsubset: $o).
% 0.62/1.11 thf(subPowSU_type, type, subPowSU: $o).
% 0.62/1.11 thf(notequalI1_type, type, notequalI1: $o).
% 0.62/1.11 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 0.62/1.11 thf(notinemptyset_type, type, notinemptyset: $o).
% 0.62/1.11 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 0.62/1.11 thf(subsetTrans_type, type, subsetTrans: $o).
% 0.62/1.11 thf(setminusI_type, type, setminusI: $o).
% 0.62/1.11 thf(binunionIL_type, type, binunionIL: $o).
% 0.62/1.11 thf(subsetE2_type, type, subsetE2: $o).
% 0.62/1.11 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 0.62/1.11 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 0.62/1.11 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 0.62/1.11 thf(setextsub_type, type, setextsub: $o).
% 0.62/1.11 thf(binunionLsub_type, type, binunionLsub: $o).
% 0.62/1.11 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 0.62/1.11 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 0.62/1.11 thf(setunionE_type, type, setunionE: $o).
% 0.62/1.11 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 0.62/1.11 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 0.62/1.11 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 0.62/1.11 thf(binunionIR_type, type, binunionIR: $o).
% 0.62/1.11 thf(setadjoinE_type, type, setadjoinE: $o).
% 0.62/1.11 thf(singletonprop_type, type, singletonprop: $o).
% 0.62/1.11 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 0.62/1.11 thf(exuE1_type, type, exuE1: $o).
% 0.62/1.11 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 0.62/1.11 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 0.62/1.11 thf(setminusLsub_type, type, setminusLsub: $o).
% 0.62/1.11 thf(notinsingleton_type, type, notinsingleton: $o).
% 0.62/1.11 thf(sk__48_type, type, sk__48: $i).
% 0.62/1.11 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 0.62/1.11 thf(exuEu_type, type, exuEu: $o).
% 0.62/1.11 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 0.62/1.11 thf(upairsetE_type, type, upairsetE: $o).
% 0.62/1.11 thf(omega0Ax_type, type, omega0Ax: $o).
% 0.62/1.11 thf(notsubsetI_type, type, notsubsetI: $o).
% 0.62/1.11 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 0.62/1.11 thf(setextAx_type, type, setextAx: $o).
% 0.62/1.11 thf(powersetE1_type, type, powersetE1: $o).
% 0.62/1.11 thf(bs114d_type, type, bs114d: $o).
% 0.62/1.11 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 0.62/1.11 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 0.62/1.11 thf(subsetI1_type, type, subsetI1: $o).
% 0.62/1.11 thf(symdiffE_type, type, symdiffE: $o).
% 0.62/1.11 thf(descrp_type, type, descrp: $o).
% 0.62/1.11 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 0.62/1.11 thf(foundationAx_type, type, foundationAx: $o).
% 0.62/1.11 thf(emptysetAx_type, type, emptysetAx: $o).
% 0.62/1.11 thf(emptyI_type, type, emptyI: $o).
% 0.62/1.11 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 0.62/1.11 thf(binintersectEL_type, type, binintersectEL: $o).
% 0.62/1.11 thf(emptyE1_type, type, emptyE1: $o).
% 0.62/1.11 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 0.62/1.11 thf(vacuousDall_type, type, vacuousDall: $o).
% 0.62/1.11 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 0.62/1.11 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 0.62/1.11 thf(binintersectI_type, type, binintersectI: $o).
% 0.62/1.11 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 0.62/1.11 thf(ex1E1_type, type, ex1E1: $o).
% 0.62/1.11 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 0.62/1.11 thf(symdiffI1_type, type, symdiffI1: $o).
% 0.62/1.11 thf(subsetI2_type, type, subsetI2: $o).
% 0.62/1.11 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 0.62/1.11 thf(setminusERneg_type, type, setminusERneg: $o).
% 0.62/1.11 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 0.62/1.11 thf(omega__Cong_type, type, omega__Cong: $o).
% 0.62/1.11 thf(subsetRefl_type, type, subsetRefl: $o).
% 0.62/1.11 thf(uniqinunit_type, type, uniqinunit: $o).
% 0.62/1.11 thf(sk__49_type, type, sk__49: $i).
% 0.62/1.11 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 0.62/1.11 thf(prop2setE_type, type, prop2setE: $o).
% 0.62/1.11 thf(binunionEcases_type, type, binunionEcases: $o).
% 0.62/1.11 thf(nonemptyI_type, type, nonemptyI: $o).
% 0.62/1.11 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 0.62/1.11 thf(exuE3u_type, type, exuE3u: $o).
% 0.62/1.11 thf(setminusEL_type, type, setminusEL: $o).
% 0.62/1.11 thf(singletonsubset_type, type, singletonsubset: $o).
% 0.62/1.11 thf(sepSubset_type, type, sepSubset: $o).
% 0.62/1.11 thf(setunionE2_type, type, setunionE2: $o).
% 0.62/1.11 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 0.62/1.11 thf(ex1I_type, type, ex1I: $o).
% 0.62/1.11 thf(exuI3_type, type, exuI3: $o).
% 0.62/1.11 thf(notdallE_type, type, notdallE: $o).
% 0.62/1.11 thf(binintersectER_type, type, binintersectER: $o).
% 0.62/1.11 thf(kpairp_type, type, kpairp: $o).
% 0.62/1.11 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 0.62/1.11 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 0.62/1.11 thf(exu__Cong_type, type, exu__Cong: $o).
% 0.62/1.11 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 0.62/1.11 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 0.62/1.11 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 0.62/1.11 thf(replAx_type, type, replAx: $o).
% 0.62/1.11 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 0.62/1.11 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 0.62/1.11 thf(secondinupair_type, type, secondinupair: $o).
% 0.62/1.11 thf(inPowerset_type, type, inPowerset: $o).
% 0.62/1.11 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 0.62/1.11 thf(subset_type, type, subset: $i > $i > $o).
% 0.62/1.11 thf(in__Cong_type, type, in__Cong: $o).
% 0.62/1.11 thf(binunionRsub_type, type, binunionRsub: $o).
% 0.62/1.11 thf(subset2powerset_type, type, subset2powerset: $o).
% 0.62/1.11 thf(upairset2E, axiom, upairset2E =
% 0.62/1.11 (![Xx:$i,Xy:$i,Xz:$i]:
% 0.62/1.11 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 0.62/1.11 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 0.62/1.11 thf('0', plain,
% 0.62/1.11 (( upairset2E ) =
% 0.62/1.11 ( ![X4:$i,X6:$i,X8:$i]:
% 0.62/1.11 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 0.62/1.11 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(singletonsubset, axiom, singletonsubset =
% 0.62/1.11 (![A:$i,Xx:$i]:
% 0.62/1.11 ( ( in @ Xx @ A ) => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ))).
% 0.62/1.11 thf('1', plain,
% 0.62/1.11 (( singletonsubset ) =
% 0.62/1.11 ( ![X4:$i,X6:$i]:
% 0.62/1.11 ( ( in @ X6 @ X4 ) => ( subset @ ( setadjoin @ X6 @ emptyset ) @ X4 ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(secondinupair, axiom, secondinupair =
% 0.62/1.11 (![Xx:$i,Xy:$i]:
% 0.62/1.11 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.62/1.11 thf('2', plain,
% 0.62/1.11 (( secondinupair ) =
% 0.62/1.11 ( ![X4:$i,X6:$i]:
% 0.62/1.11 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(upairset2IR, axiom, upairset2IR =
% 0.62/1.11 (![Xx:$i,Xy:$i]:
% 0.62/1.11 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.62/1.11 thf('3', plain,
% 0.62/1.11 (( upairset2IR ) =
% 0.62/1.11 ( ![X4:$i,X6:$i]:
% 0.62/1.11 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 0.62/1.11 (![A:$i,Xx:$i,B:$i]:
% 0.62/1.11 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 0.62/1.11 thf('4', plain,
% 0.62/1.11 (( setadjoinSub2 ) =
% 0.62/1.11 ( ![X4:$i,X6:$i,X8:$i]:
% 0.62/1.11 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(setadjoinSub, axiom, setadjoinSub =
% 0.62/1.11 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 0.62/1.11 thf('5', plain,
% 0.62/1.11 (( setadjoinSub ) =
% 0.62/1.11 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 0.62/1.11 (![Xx:$i,Xy:$i]:
% 0.62/1.11 ( ( ( Xx ) = ( Xy ) ) =>
% 0.62/1.11 ( ![Xz:$i,Xu:$i]:
% 0.62/1.11 ( ( ( Xz ) = ( Xu ) ) =>
% 0.62/1.11 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 0.62/1.11 thf('6', plain,
% 0.62/1.11 (( setadjoin__Cong ) =
% 0.62/1.11 ( ![X4:$i,X6:$i]:
% 0.62/1.11 ( ( ( X4 ) = ( X6 ) ) =>
% 0.62/1.11 ( ![X8:$i,X10:$i]:
% 0.62/1.11 ( ( ( X8 ) = ( X10 ) ) =>
% 0.62/1.11 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(upairsetIR, axiom, upairsetIR =
% 0.62/1.11 (![Xx:$i,Xy:$i]:
% 0.62/1.11 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.62/1.11 thf('7', plain,
% 0.62/1.11 (( upairsetIR ) =
% 0.62/1.11 ( ![X4:$i,X6:$i]:
% 0.62/1.11 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(upairsetIL, axiom, upairsetIL =
% 0.62/1.11 (![Xx:$i,Xy:$i]:
% 0.62/1.11 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.62/1.11 thf('8', plain,
% 0.62/1.11 (( upairsetIL ) =
% 0.62/1.11 ( ![X4:$i,X6:$i]:
% 0.62/1.11 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(upairsetE, axiom, upairsetE =
% 0.62/1.11 (![Xx:$i,Xy:$i,Xz:$i]:
% 0.62/1.11 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 0.62/1.11 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 0.62/1.11 thf('9', plain,
% 0.62/1.11 (( upairsetE ) =
% 0.62/1.11 ( ![X4:$i,X6:$i,X8:$i]:
% 0.62/1.11 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 0.62/1.11 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(singletonsswitch, axiom, singletonsswitch =
% 0.62/1.11 (![Xx:$i,Xy:$i]:
% 0.62/1.11 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 0.62/1.11 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 0.62/1.11 thf('10', plain,
% 0.62/1.11 (( singletonsswitch ) =
% 0.62/1.11 ( ![X4:$i,X6:$i]:
% 0.62/1.11 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 0.62/1.11 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(eqinunit, axiom, eqinunit =
% 0.62/1.11 (![Xx:$i,Xy:$i]:
% 0.62/1.11 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.62/1.11 thf('11', plain,
% 0.62/1.11 (( eqinunit ) =
% 0.62/1.11 ( ![X4:$i,X6:$i]:
% 0.62/1.11 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(notinsingleton, axiom, notinsingleton =
% 0.62/1.11 (![Xx:$i,Xy:$i]:
% 0.62/1.11 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 0.62/1.11 thf('12', plain,
% 0.62/1.11 (( notinsingleton ) =
% 0.62/1.11 ( ![X4:$i,X6:$i]:
% 0.62/1.11 ( ( ( X4 ) != ( X6 ) ) =>
% 0.62/1.11 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(uniqinunit, axiom, uniqinunit =
% 0.62/1.11 (![Xx:$i,Xy:$i]:
% 0.62/1.11 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 0.62/1.11 thf('13', plain,
% 0.62/1.11 (( uniqinunit ) =
% 0.62/1.11 ( ![X4:$i,X6:$i]:
% 0.62/1.11 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(setadjoinOr, axiom, setadjoinOr =
% 0.62/1.11 (![Xx:$i,A:$i,Xy:$i]:
% 0.62/1.11 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 0.62/1.11 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 0.62/1.11 thf('14', plain,
% 0.62/1.11 (( setadjoinOr ) =
% 0.62/1.11 ( ![X4:$i,X6:$i,X8:$i]:
% 0.62/1.11 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 0.62/1.11 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(setadjoinE, axiom, setadjoinE =
% 0.62/1.11 (![Xx:$i,A:$i,Xy:$i]:
% 0.62/1.11 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 0.62/1.11 ( ![Xphi:$o]:
% 0.62/1.11 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 0.62/1.11 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 0.62/1.11 thf('15', plain,
% 0.62/1.11 (( setadjoinE ) =
% 0.62/1.11 ( ![X4:$i,X6:$i,X8:$i]:
% 0.62/1.11 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 0.62/1.11 ( ![X10:$o]:
% 0.62/1.11 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 0.62/1.11 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(setadjoinIR, axiom, setadjoinIR =
% 0.62/1.11 (![Xx:$i,A:$i,Xy:$i]:
% 0.62/1.11 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 0.62/1.11 thf('16', plain,
% 0.62/1.11 (( setadjoinIR ) =
% 0.62/1.11 ( ![X4:$i,X6:$i,X8:$i]:
% 0.62/1.11 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 0.62/1.11 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 0.62/1.11 thf('17', plain,
% 0.62/1.11 (( emptyinunitempty ) =
% 0.62/1.11 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 0.62/1.11 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 0.62/1.11 thf('18', plain,
% 0.62/1.11 (( emptyinunitempty ) =
% 0.62/1.11 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(setadjoinIL, axiom, setadjoinIL =
% 0.62/1.11 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 0.62/1.11 thf('19', plain,
% 0.62/1.11 (( setadjoinIL ) =
% 0.62/1.11 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(setadjoinAx, axiom, setadjoinAx =
% 0.62/1.11 (![Xx:$i,A:$i,Xy:$i]:
% 0.62/1.11 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 0.62/1.11 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 0.62/1.11 thf('20', plain,
% 0.62/1.11 (( setadjoinAx ) =
% 0.62/1.11 ( ![X4:$i,X6:$i,X8:$i]:
% 0.62/1.11 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.62/1.11 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 0.62/1.11 define([status(thm)])).
% 0.62/1.11 thf(singletonsuniq, conjecture,
% 0.62/1.11 (( setextAx ) =>
% 0.62/1.11 ( ( emptysetAx ) =>
% 0.62/1.11 ( ( setadjoinAx ) =>
% 0.62/1.11 ( ( powersetAx ) =>
% 0.62/1.11 ( ( setunionAx ) =>
% 0.62/1.11 ( ( omega0Ax ) =>
% 0.62/1.11 ( ( omegaSAx ) =>
% 0.62/1.11 ( ( omegaIndAx ) =>
% 0.62/1.11 ( ( replAx ) =>
% 0.62/1.11 ( ( foundationAx ) =>
% 0.62/1.11 ( ( wellorderingAx ) =>
% 0.62/1.11 ( ( descrp ) =>
% 0.62/1.11 ( ( dsetconstrI ) =>
% 0.62/1.11 ( ( dsetconstrEL ) =>
% 0.62/1.11 ( ( dsetconstrER ) =>
% 0.62/1.11 ( ( exuE1 ) =>
% 0.62/1.11 ( ( prop2setE ) =>
% 0.62/1.11 ( ( emptysetE ) =>
% 0.62/1.11 ( ( emptysetimpfalse ) =>
% 0.62/1.11 ( ( notinemptyset ) =>
% 0.62/1.11 ( ( exuE3e ) =>
% 0.62/1.11 ( ( setext ) =>
% 0.62/1.11 ( ( emptyI ) =>
% 0.62/1.11 ( ( noeltsimpempty ) =>
% 0.62/1.11 ( ( setbeta ) =>
% 0.62/1.11 ( ( nonemptyE1 ) =>
% 0.62/1.11 ( ( nonemptyI ) =>
% 0.62/1.11 ( ( nonemptyI1 ) =>
% 0.62/1.11 ( ( setadjoinIL ) =>
% 0.62/1.11 ( ( emptyinunitempty ) =>
% 0.62/1.11 ( ( setadjoinIR ) =>
% 0.62/1.11 ( ( setadjoinE ) =>
% 0.62/1.11 ( (
% 0.62/1.11 setadjoinOr ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setoftrueEq ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powersetI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 emptyinPowerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 emptyInPowerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powersetE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subPowSU ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuE2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 nonemptyImpWitness ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 uniqinunit ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 notinsingleton ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 eqinunit ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 singletonsswitch ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 upairsetE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 upairsetIL ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 upairsetIR ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 emptyE1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 vacuousDall ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 quantDeMorgan1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 quantDeMorgan2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 quantDeMorgan3 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 quantDeMorgan4 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 prop2setI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 prop2set2propI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 notdexE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 notdallE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuI1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuI3 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuI2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 inCongP ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuE3u ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exu__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 emptyset__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setadjoin__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powerset__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunion__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 omega__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuEu ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 descr__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 dsetconstr__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetI1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 eqimpsubset2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 eqimpsubset1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetI2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 emptysetsubset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetE2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 notsubsetI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 notequalI1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 notequalI2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetRefl ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetTrans ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setadjoinSub ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setadjoinSub2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subset2powerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setextsub ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetemptysetimpeq ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powersetI1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powersetE1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 inPowerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powersetsubset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 sepInPowerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 sepSubset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binunionIL ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 upairset2IR ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binunionIR ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binunionEcases ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binunionE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binunionLsub ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binunionRsub ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectSubset5 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectEL ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectLsub ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectSubset2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectSubset3 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectER ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 disjointsetsI1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectRsub ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectSubset4 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectSubset1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 bs114d ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusEL ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusER ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusSubset2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusERneg ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusELneg ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusILneg ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusIRneg ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusLsub ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusSubset1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 symdiffE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 symdiffI1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 symdiffI2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 symdiffIneg1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 symdiffIneg2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 secondinupair ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setukpairIL ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setukpairIR ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 kpairiskpair ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 kpairp ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 singletonsubset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 singletoninpowerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 singletoninpowunion ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 upairset2E ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 upairsubunion ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 upairinpowunion ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ubforcartprodlem1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ubforcartprodlem2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ubforcartprodlem3 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 cartprodpairin ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 cartprodmempair1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 cartprodmempair ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionE2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionsingleton1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionsingleton2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionsingleton ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 singletonprop ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ex1E1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ex1I ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ex1I2 ) =>
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 Xx:$i,
% 0.62/1.11 Xy:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 Xx @
% 0.62/1.11 emptyset ) =
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 Xy @
% 0.62/1.11 emptyset ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 Xx ) =
% 0.62/1.11 (
% 0.62/1.11 Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.62/1.11 thf(zf_stmt_0, conjecture,
% 0.62/1.11 (( setextAx ) =>
% 0.62/1.11 ( ( emptysetAx ) =>
% 0.62/1.11 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.62/1.11 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.62/1.11 ( ( in @ X8 @ X6 ) | ( ( X8 ) = ( X4 ) ) ) ) ) =>
% 0.62/1.11 ( ( powersetAx ) =>
% 0.62/1.11 ( ( setunionAx ) =>
% 0.62/1.11 ( ( omega0Ax ) =>
% 0.62/1.11 ( ( omegaSAx ) =>
% 0.62/1.11 ( ( omegaIndAx ) =>
% 0.62/1.11 ( ( replAx ) =>
% 0.62/1.11 ( ( foundationAx ) =>
% 0.62/1.11 ( ( wellorderingAx ) =>
% 0.62/1.11 ( ( descrp ) =>
% 0.62/1.11 ( ( dsetconstrI ) =>
% 0.62/1.11 ( ( dsetconstrEL ) =>
% 0.62/1.11 ( ( dsetconstrER ) =>
% 0.62/1.11 ( ( exuE1 ) =>
% 0.62/1.11 ( ( prop2setE ) =>
% 0.62/1.11 ( ( emptysetE ) =>
% 0.62/1.11 ( ( emptysetimpfalse ) =>
% 0.62/1.11 ( ( notinemptyset ) =>
% 0.62/1.11 ( ( exuE3e ) =>
% 0.62/1.11 ( ( setext ) =>
% 0.62/1.11 ( ( emptyI ) =>
% 0.62/1.11 ( ( noeltsimpempty ) =>
% 0.62/1.11 ( ( setbeta ) =>
% 0.62/1.11 ( ( nonemptyE1 ) =>
% 0.62/1.11 ( ( nonemptyI ) =>
% 0.62/1.11 ( ( nonemptyI1 ) =>
% 0.62/1.11 ( ( ![X10:$i,X12:$i]:
% 0.62/1.11 ( in @
% 0.62/1.11 X10 @
% 0.62/1.11 ( setadjoin @
% 0.62/1.11 X10 @ X12 ) ) ) =>
% 0.62/1.11 ( ( in @
% 0.62/1.11 emptyset @
% 0.62/1.11 ( setadjoin @
% 0.62/1.11 emptyset @
% 0.62/1.11 emptyset ) ) =>
% 0.62/1.11 ( ( ![X14:$i,
% 0.62/1.11 X16:$i,
% 0.62/1.11 X18:$i]:
% 0.62/1.11 ( (
% 0.62/1.11 in @
% 0.62/1.11 X18 @ X16 ) =>
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X18 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X14 @ X16 ) ) ) ) =>
% 0.62/1.11 ( ( ![
% 0.62/1.11 X20:$i,
% 0.62/1.11 X22:$i,
% 0.62/1.11 X24:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X24 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X20 @ X22 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X26:$o]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X24 ) =
% 0.62/1.11 (
% 0.62/1.11 X20 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 X26 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X24 @ X22 ) =>
% 0.62/1.11 (
% 0.62/1.11 X26 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 X26 ) ) ) ) ) ) =>
% 0.62/1.11 ( (
% 0.62/1.11 ![
% 0.62/1.11 X28:$i,
% 0.62/1.11 X30:$i,
% 0.62/1.11 X32:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X32 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X28 @ X30 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X32 @ X30 ) |
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X32 ) =
% 0.62/1.11 (
% 0.62/1.11 X28 ) ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setoftrueEq ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powersetI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 emptyinPowerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 emptyInPowerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powersetE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subPowSU ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuE2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 nonemptyImpWitness ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X34:$i,
% 0.62/1.11 X36:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X34 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X36 @
% 0.62/1.11 emptyset ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X34 ) =
% 0.62/1.11 (
% 0.62/1.11 X36 ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X38:$i,
% 0.62/1.11 X40:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X38 ) !=
% 0.62/1.11 (
% 0.62/1.11 X40 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 ~(
% 0.62/1.11 in @
% 0.62/1.11 X40 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X38 @
% 0.62/1.11 emptyset ) ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X42:$i,
% 0.62/1.11 X44:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X42 ) =
% 0.62/1.11 (
% 0.62/1.11 X44 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X42 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X44 @
% 0.62/1.11 emptyset ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X46:$i,
% 0.62/1.11 X48:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X46 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X48 @
% 0.62/1.11 emptyset ) ) =>
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X48 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X46 @
% 0.62/1.11 emptyset ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X50:$i,
% 0.62/1.11 X52:$i,
% 0.62/1.11 X54:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X54 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X50 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X52 @
% 0.62/1.11 emptyset ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X54 ) =
% 0.62/1.11 (
% 0.62/1.11 X52 ) ) |
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X54 ) =
% 0.62/1.11 (
% 0.62/1.11 X50 ) ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X56:$i,
% 0.62/1.11 X58:$i]:
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X56 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X56 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X58 @
% 0.62/1.11 emptyset ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X60:$i,
% 0.62/1.11 X62:$i]:
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X62 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X60 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X62 @
% 0.62/1.11 emptyset ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 emptyE1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 vacuousDall ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 quantDeMorgan1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 quantDeMorgan2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 quantDeMorgan3 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 quantDeMorgan4 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 prop2setI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 prop2set2propI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 notdexE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 notdallE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuI1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuI3 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuI2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 inCongP ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuE3u ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exu__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 emptyset__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X64:$i,
% 0.62/1.11 X66:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X64 ) =
% 0.62/1.11 (
% 0.62/1.11 X66 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X68:$i,
% 0.62/1.11 X70:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X68 ) =
% 0.62/1.11 (
% 0.62/1.11 X70 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X64 @ X68 ) =
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X66 @ X70 ) ) ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powerset__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunion__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 omega__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuEu ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 descr__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 dsetconstr__Cong ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetI1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 eqimpsubset2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 eqimpsubset1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetI2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 emptysetsubset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetE2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 notsubsetI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 notequalI1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 notequalI2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetRefl ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetTrans ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X72:$i,
% 0.62/1.11 X74:$i]:
% 0.62/1.11 (
% 0.62/1.11 subset @
% 0.62/1.11 X74 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X72 @ X74 ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X76:$i,
% 0.62/1.11 X78:$i,
% 0.62/1.11 X80:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subset @
% 0.62/1.11 X76 @ X80 ) =>
% 0.62/1.11 (
% 0.62/1.11 subset @
% 0.62/1.11 X76 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X78 @ X80 ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subset2powerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setextsub ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subsetemptysetimpeq ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powersetI1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powersetE1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 inPowerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powersetsubset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 sepInPowerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 sepSubset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binunionIL ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X82:$i,
% 0.62/1.11 X84:$i]:
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X84 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X82 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X84 @
% 0.62/1.11 emptyset ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binunionIR ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binunionEcases ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binunionE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binunionLsub ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binunionRsub ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectSubset5 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectEL ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectLsub ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectSubset2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectSubset3 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectER ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 disjointsetsI1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectRsub ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectSubset4 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 binintersectSubset1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 bs114d ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusEL ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusER ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusSubset2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusERneg ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusELneg ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusILneg ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusIRneg ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusLsub ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setminusSubset1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 symdiffE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 symdiffI1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 symdiffI2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 symdiffIneg1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 symdiffIneg2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X86:$i,
% 0.62/1.11 X88:$i]:
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X88 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X86 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X88 @
% 0.62/1.11 emptyset ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setukpairIL ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setukpairIR ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 kpairiskpair ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 kpairp ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X90:$i,
% 0.62/1.11 X92:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X92 @ X90 ) =>
% 0.62/1.11 (
% 0.62/1.11 subset @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X92 @
% 0.62/1.11 emptyset ) @
% 0.62/1.11 X90 ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 singletoninpowerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 singletoninpowunion ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X94:$i,
% 0.62/1.11 X96:$i,
% 0.62/1.11 X98:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X98 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X94 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X96 @
% 0.62/1.11 emptyset ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X98 ) =
% 0.62/1.11 (
% 0.62/1.11 X96 ) ) |
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X98 ) =
% 0.62/1.11 (
% 0.62/1.11 X94 ) ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 upairsubunion ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 upairinpowunion ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ubforcartprodlem1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ubforcartprodlem2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ubforcartprodlem3 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 cartprodpairin ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 cartprodmempair1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 cartprodmempair ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionE2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionsingleton1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionsingleton2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionsingleton ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 singletonprop ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ex1E1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ex1I ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ex1I2 ) =>
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X100:$i,
% 0.62/1.11 X102:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X100 @
% 0.62/1.11 emptyset ) =
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X102 @
% 0.62/1.11 emptyset ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X100 ) =
% 0.62/1.11 (
% 0.62/1.11 X102 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.62/1.11 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 0.62/1.11 thf(zf_stmt_2, axiom,
% 0.62/1.11 (![X8:$i,X6:$i,X4:$i]:
% 0.62/1.11 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 0.62/1.11 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ))).
% 0.62/1.11 thf(zf_stmt_3, conjecture,
% 0.62/1.11 (( setextAx ) =>
% 0.62/1.11 ( ( emptysetAx ) =>
% 0.62/1.11 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.62/1.11 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.62/1.11 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 0.62/1.11 ( ( powersetAx ) =>
% 0.62/1.11 ( ( setunionAx ) =>
% 0.62/1.11 ( ( omega0Ax ) =>
% 0.62/1.11 ( ( omegaSAx ) =>
% 0.62/1.11 ( ( omegaIndAx ) =>
% 0.62/1.11 ( ( replAx ) =>
% 0.62/1.11 ( ( foundationAx ) =>
% 0.62/1.11 ( ( wellorderingAx ) =>
% 0.62/1.11 ( ( descrp ) =>
% 0.62/1.11 ( ( dsetconstrI ) =>
% 0.62/1.11 ( ( dsetconstrEL ) =>
% 0.62/1.11 ( ( dsetconstrER ) =>
% 0.62/1.11 ( ( exuE1 ) =>
% 0.62/1.11 ( ( prop2setE ) =>
% 0.62/1.11 ( ( emptysetE ) =>
% 0.62/1.11 ( ( emptysetimpfalse ) =>
% 0.62/1.11 ( ( notinemptyset ) =>
% 0.62/1.11 ( ( exuE3e ) =>
% 0.62/1.11 ( ( setext ) =>
% 0.62/1.11 ( ( emptyI ) =>
% 0.62/1.11 ( ( noeltsimpempty ) =>
% 0.62/1.11 ( ( setbeta ) =>
% 0.62/1.11 ( ( nonemptyE1 ) =>
% 0.62/1.11 ( ( nonemptyI ) =>
% 0.62/1.11 ( ( nonemptyI1 ) =>
% 0.62/1.11 ( ( ![X10:$i,X12:$i]:
% 0.62/1.11 ( in @
% 0.62/1.11 X10 @
% 0.62/1.11 ( setadjoin @
% 0.62/1.11 X10 @ X12 ) ) ) =>
% 0.62/1.11 ( ( in @
% 0.62/1.11 emptyset @
% 0.62/1.11 ( setadjoin @
% 0.62/1.11 emptyset @
% 0.62/1.11 emptyset ) ) =>
% 0.62/1.11 ( ( ![X14:$i,
% 0.62/1.11 X16:$i,
% 0.62/1.11 X18:$i]:
% 0.62/1.11 ( (
% 0.62/1.11 in @
% 0.62/1.11 X18 @ X16 ) =>
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X18 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X14 @ X16 ) ) ) ) =>
% 0.62/1.11 ( ( ![
% 0.62/1.11 X20:$i,
% 0.62/1.11 X22:$i,
% 0.62/1.11 X24:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X24 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X20 @ X22 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X26:$o]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X24 ) =
% 0.62/1.11 (
% 0.62/1.11 X20 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 X26 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X24 @ X22 ) =>
% 0.62/1.11 (
% 0.62/1.11 X26 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 X26 ) ) ) ) ) ) =>
% 0.62/1.11 ( (
% 0.62/1.11 ![
% 0.62/1.11 X28:$i,
% 0.62/1.11 X30:$i,
% 0.62/1.11 X32:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X32 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X28 @ X30 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X32 ) =
% 0.62/1.11 (
% 0.62/1.11 X28 ) ) |
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X32 @ X30 ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setoftrueEq ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powersetI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 emptyinPowerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 emptyInPowerset ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 powersetE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 setunionE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 subPowSU ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuE2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 nonemptyImpWitness ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X34:$i,
% 0.62/1.11 X36:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X34 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X36 @
% 0.62/1.11 emptyset ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X34 ) =
% 0.62/1.11 (
% 0.62/1.11 X36 ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X38:$i,
% 0.62/1.11 X40:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X38 ) !=
% 0.62/1.11 (
% 0.62/1.11 X40 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 ~(
% 0.62/1.11 in @
% 0.62/1.11 X40 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X38 @
% 0.62/1.11 emptyset ) ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X42:$i,
% 0.62/1.11 X44:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X42 ) =
% 0.62/1.11 (
% 0.62/1.11 X44 ) ) =>
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X42 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X44 @
% 0.62/1.11 emptyset ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X46:$i,
% 0.62/1.11 X48:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X46 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X48 @
% 0.62/1.11 emptyset ) ) =>
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X48 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X46 @
% 0.62/1.11 emptyset ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X50:$i,
% 0.62/1.11 X52:$i,
% 0.62/1.11 X54:$i]:
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X54 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X50 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X52 @
% 0.62/1.11 emptyset ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X54 ) =
% 0.62/1.11 (
% 0.62/1.11 X50 ) ) |
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 X54 ) =
% 0.62/1.11 (
% 0.62/1.11 X52 ) ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X56:$i,
% 0.62/1.11 X58:$i]:
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X56 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X56 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X58 @
% 0.62/1.11 emptyset ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 ![
% 0.62/1.11 X60:$i,
% 0.62/1.11 X62:$i]:
% 0.62/1.11 (
% 0.62/1.11 in @
% 0.62/1.11 X62 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X60 @
% 0.62/1.11 (
% 0.62/1.11 setadjoin
% 0.62/1.11 @
% 0.62/1.11 X62 @
% 0.62/1.11 emptyset ) ) ) ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 emptyE1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 vacuousDall ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 quantDeMorgan1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 quantDeMorgan2 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 quantDeMorgan3 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 quantDeMorgan4 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 prop2setI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 prop2set2propI ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 notdexE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 notdallE ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuI1 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.11 exuI3 ) =>
% 0.62/1.11 (
% 0.62/1.11 (
% 0.62/1.12 exuI2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 inCongP ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 in__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 exuE3u ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 exu__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 emptyset__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X64:$i,
% 0.62/1.12 X66:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X64 ) =
% 0.62/1.12 (
% 0.62/1.12 X66 ) ) =>
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X68:$i,
% 0.62/1.12 X70:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X68 ) =
% 0.62/1.12 (
% 0.62/1.12 X70 ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X64 @ X68 ) =
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X66 @ X70 ) ) ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 powerset__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setunion__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 omega__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 exuEu ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 descr__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 dsetconstr__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetI1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 eqimpsubset2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 eqimpsubset1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetI2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 emptysetsubset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetE ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetE2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 notsubsetI ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 notequalI1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 notequalI2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetRefl ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetTrans ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X72:$i,
% 0.62/1.12 X74:$i]:
% 0.62/1.12 (
% 0.62/1.12 subset @
% 0.62/1.12 X74 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X72 @ X74 ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X76:$i,
% 0.62/1.12 X78:$i,
% 0.62/1.12 X80:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subset @
% 0.62/1.12 X76 @ X80 ) =>
% 0.62/1.12 (
% 0.62/1.12 subset @
% 0.62/1.12 X76 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X78 @ X80 ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subset2powerset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setextsub ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetemptysetimpeq ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 powersetI1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 powersetE1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 inPowerset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 powersetsubset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 sepInPowerset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 sepSubset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binunionIL ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X82:$i,
% 0.62/1.12 X84:$i]:
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X84 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X82 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X84 @
% 0.62/1.12 emptyset ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binunionIR ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binunionEcases ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binunionE ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binunionLsub ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binunionRsub ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectI ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectSubset5 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectEL ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectLsub ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectSubset2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectSubset3 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectER ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 disjointsetsI1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectRsub ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectSubset4 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectSubset1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 bs114d ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusI ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusEL ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusER ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusSubset2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusERneg ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusELneg ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusILneg ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusIRneg ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusLsub ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusSubset1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 symdiffE ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 symdiffI1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 symdiffI2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 symdiffIneg1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 symdiffIneg2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X86:$i,
% 0.62/1.12 X88:$i]:
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X88 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X86 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X88 @
% 0.62/1.12 emptyset ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setukpairIL ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setukpairIR ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 kpairiskpair ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 kpairp ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X90:$i,
% 0.62/1.12 X92:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X92 @ X90 ) =>
% 0.62/1.12 (
% 0.62/1.12 subset @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X92 @
% 0.62/1.12 emptyset ) @
% 0.62/1.12 X90 ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 singletoninpowerset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 singletoninpowunion ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X94:$i,
% 0.62/1.12 X96:$i,
% 0.62/1.12 X98:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X98 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X94 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X96 @
% 0.62/1.12 emptyset ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X98 ) =
% 0.62/1.12 (
% 0.62/1.12 X94 ) ) |
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X98 ) =
% 0.62/1.12 (
% 0.62/1.12 X96 ) ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 upairsubunion ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 upairinpowunion ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ubforcartprodlem1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ubforcartprodlem2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ubforcartprodlem3 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 cartprodpairin ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 cartprodmempair1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 cartprodmempair ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setunionE2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setunionsingleton1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setunionsingleton2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setunionsingleton ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 singletonprop ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ex1E1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ex1I ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ex1I2 ) =>
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X100:$i,
% 0.62/1.12 X102:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X100 @
% 0.62/1.12 emptyset ) =
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X102 @
% 0.62/1.12 emptyset ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X100 ) =
% 0.62/1.12 (
% 0.62/1.12 X102 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.62/1.12 thf(zf_stmt_4, negated_conjecture,
% 0.62/1.12 (~( ( setextAx ) =>
% 0.62/1.12 ( ( emptysetAx ) =>
% 0.62/1.12 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.62/1.12 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.62/1.12 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 0.62/1.12 ( ( powersetAx ) =>
% 0.62/1.12 ( ( setunionAx ) =>
% 0.62/1.12 ( ( omega0Ax ) =>
% 0.62/1.12 ( ( omegaSAx ) =>
% 0.62/1.12 ( ( omegaIndAx ) =>
% 0.62/1.12 ( ( replAx ) =>
% 0.62/1.12 ( ( foundationAx ) =>
% 0.62/1.12 ( ( wellorderingAx ) =>
% 0.62/1.12 ( ( descrp ) =>
% 0.62/1.12 ( ( dsetconstrI ) =>
% 0.62/1.12 ( ( dsetconstrEL ) =>
% 0.62/1.12 ( ( dsetconstrER ) =>
% 0.62/1.12 ( ( exuE1 ) =>
% 0.62/1.12 ( ( prop2setE ) =>
% 0.62/1.12 ( ( emptysetE ) =>
% 0.62/1.12 ( ( emptysetimpfalse ) =>
% 0.62/1.12 ( ( notinemptyset ) =>
% 0.62/1.12 ( ( exuE3e ) =>
% 0.62/1.12 ( ( setext ) =>
% 0.62/1.12 ( ( emptyI ) =>
% 0.62/1.12 ( ( noeltsimpempty ) =>
% 0.62/1.12 ( ( setbeta ) =>
% 0.62/1.12 ( ( nonemptyE1 ) =>
% 0.62/1.12 ( ( nonemptyI ) =>
% 0.62/1.12 ( ( nonemptyI1 ) =>
% 0.62/1.12 ( ( ![X10:$i,
% 0.62/1.12 X12:$i]:
% 0.62/1.12 ( in @
% 0.62/1.12 X10 @
% 0.62/1.12 ( setadjoin
% 0.62/1.12 @
% 0.62/1.12 X10 @ X12 ) ) ) =>
% 0.62/1.12 ( ( in @
% 0.62/1.12 emptyset @
% 0.62/1.12 ( setadjoin
% 0.62/1.12 @
% 0.62/1.12 emptyset @
% 0.62/1.12 emptyset ) ) =>
% 0.62/1.12 ( ( ![
% 0.62/1.12 X14:$i,
% 0.62/1.12 X16:$i,
% 0.62/1.12 X18:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X18 @ X16 ) =>
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X18 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X14 @ X16 ) ) ) ) =>
% 0.62/1.12 ( (
% 0.62/1.12 ![
% 0.62/1.12 X20:$i,
% 0.62/1.12 X22:$i,
% 0.62/1.12 X24:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X24 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X20 @ X22 ) ) =>
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X26:$o]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X24 ) =
% 0.62/1.12 (
% 0.62/1.12 X20 ) ) =>
% 0.62/1.12 (
% 0.62/1.12 X26 ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X24 @ X22 ) =>
% 0.62/1.12 (
% 0.62/1.12 X26 ) ) =>
% 0.62/1.12 (
% 0.62/1.12 X26 ) ) ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X28:$i,
% 0.62/1.12 X30:$i,
% 0.62/1.12 X32:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X32 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X28 @ X30 ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X32 ) =
% 0.62/1.12 (
% 0.62/1.12 X28 ) ) |
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X32 @ X30 ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setoftrueEq ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 powersetI ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 emptyinPowerset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 emptyInPowerset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 powersetE ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setunionI ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setunionE ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subPowSU ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 exuE2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 nonemptyImpWitness ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X34:$i,
% 0.62/1.12 X36:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X34 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X36 @
% 0.62/1.12 emptyset ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X34 ) =
% 0.62/1.12 (
% 0.62/1.12 X36 ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X38:$i,
% 0.62/1.12 X40:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X38 ) !=
% 0.62/1.12 (
% 0.62/1.12 X40 ) ) =>
% 0.62/1.12 (
% 0.62/1.12 ~
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X40 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X38 @
% 0.62/1.12 emptyset ) ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X42:$i,
% 0.62/1.12 X44:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X42 ) =
% 0.62/1.12 (
% 0.62/1.12 X44 ) ) =>
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X42 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X44 @
% 0.62/1.12 emptyset ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X46:$i,
% 0.62/1.12 X48:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X46 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X48 @
% 0.62/1.12 emptyset ) ) =>
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X48 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X46 @
% 0.62/1.12 emptyset ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X50:$i,
% 0.62/1.12 X52:$i,
% 0.62/1.12 X54:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X54 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X50 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X52 @
% 0.62/1.12 emptyset ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X54 ) =
% 0.62/1.12 (
% 0.62/1.12 X50 ) ) |
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X54 ) =
% 0.62/1.12 (
% 0.62/1.12 X52 ) ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X56:$i,
% 0.62/1.12 X58:$i]:
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X56 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X56 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X58 @
% 0.62/1.12 emptyset ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X60:$i,
% 0.62/1.12 X62:$i]:
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X62 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X60 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X62 @
% 0.62/1.12 emptyset ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 emptyE1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 vacuousDall ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 quantDeMorgan1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 quantDeMorgan2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 quantDeMorgan3 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 quantDeMorgan4 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 prop2setI ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 prop2set2propI ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 notdexE ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 notdallE ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 exuI1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 exuI3 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 exuI2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 inCongP ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 in__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 exuE3u ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 exu__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 emptyset__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X64:$i,
% 0.62/1.12 X66:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X64 ) =
% 0.62/1.12 (
% 0.62/1.12 X66 ) ) =>
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X68:$i,
% 0.62/1.12 X70:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X68 ) =
% 0.62/1.12 (
% 0.62/1.12 X70 ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X64 @ X68 ) =
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X66 @ X70 ) ) ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 powerset__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setunion__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 omega__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 exuEu ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 descr__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 dsetconstr__Cong ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetI1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 eqimpsubset2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 eqimpsubset1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetI2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 emptysetsubset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetE ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetE2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 notsubsetI ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 notequalI1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 notequalI2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetRefl ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetTrans ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X72:$i,
% 0.62/1.12 X74:$i]:
% 0.62/1.12 (
% 0.62/1.12 subset @
% 0.62/1.12 X74 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X72 @ X74 ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X76:$i,
% 0.62/1.12 X78:$i,
% 0.62/1.12 X80:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subset @
% 0.62/1.12 X76 @ X80 ) =>
% 0.62/1.12 (
% 0.62/1.12 subset @
% 0.62/1.12 X76 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X78 @ X80 ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subset2powerset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setextsub ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 subsetemptysetimpeq ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 powersetI1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 powersetE1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 inPowerset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 powersetsubset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 sepInPowerset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 sepSubset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binunionIL ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X82:$i,
% 0.62/1.12 X84:$i]:
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X84 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X82 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X84 @
% 0.62/1.12 emptyset ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binunionIR ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binunionEcases ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binunionE ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binunionLsub ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binunionRsub ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectI ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectSubset5 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectEL ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectLsub ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectSubset2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectSubset3 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectER ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 disjointsetsI1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectRsub ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectSubset4 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 binintersectSubset1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 bs114d ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusI ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusEL ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusER ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusSubset2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusERneg ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusELneg ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusILneg ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusIRneg ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusLsub ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setminusSubset1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 symdiffE ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 symdiffI1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 symdiffI2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 symdiffIneg1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 symdiffIneg2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X86:$i,
% 0.62/1.12 X88:$i]:
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X88 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X86 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X88 @
% 0.62/1.12 emptyset ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setukpairIL ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setukpairIR ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 kpairiskpair ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 kpairp ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X90:$i,
% 0.62/1.12 X92:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X92 @ X90 ) =>
% 0.62/1.12 (
% 0.62/1.12 subset @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X92 @
% 0.62/1.12 emptyset ) @
% 0.62/1.12 X90 ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 singletoninpowerset ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 singletoninpowunion ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X94:$i,
% 0.62/1.12 X96:$i,
% 0.62/1.12 X98:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 in @
% 0.62/1.12 X98 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X94 @
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X96 @
% 0.62/1.12 emptyset ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X98 ) =
% 0.62/1.12 (
% 0.62/1.12 X94 ) ) |
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X98 ) =
% 0.62/1.12 (
% 0.62/1.12 X96 ) ) ) ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 upairsubunion ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 upairinpowunion ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ubforcartprodlem1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ubforcartprodlem2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ubforcartprodlem3 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 cartprodpairin ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 cartprodmempair1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 cartprodmempair ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setunionE2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setunionsingleton1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setunionsingleton2 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setunionsingleton ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 singletonprop ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ex1E1 ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ex1I ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 ex1I2 ) =>
% 0.62/1.12 (
% 0.62/1.12 ![
% 0.62/1.12 X100:$i,
% 0.62/1.12 X102:$i]:
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X100 @
% 0.62/1.12 emptyset ) =
% 0.62/1.12 (
% 0.62/1.12 setadjoin
% 0.62/1.12 @
% 0.62/1.12 X102 @
% 0.62/1.12 emptyset ) ) =>
% 0.62/1.12 (
% 0.62/1.12 (
% 0.62/1.12 X100 ) =
% 0.62/1.12 (
% 0.62/1.12 X102 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 0.62/1.12 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 0.62/1.12 thf(zip_derived_cl84, plain,
% 0.62/1.12 (((setadjoin @ sk__48 @ emptyset) = (setadjoin @ sk__49 @ emptyset))),
% 0.62/1.12 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.62/1.12 thf(zip_derived_cl18, plain,
% 0.62/1.12 (![X4 : $i, X5 : $i]: (in @ X4 @ (setadjoin @ X4 @ X5))),
% 0.62/1.12 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.62/1.12 thf(zip_derived_cl191, plain,
% 0.62/1.12 ( (in @ sk__49 @ (setadjoin @ sk__48 @ emptyset))),
% 0.62/1.12 inference('sup+', [status(thm)], [zip_derived_cl84, zip_derived_cl18])).
% 0.62/1.12 thf(zip_derived_cl26, plain,
% 0.62/1.12 (![X12 : $i, X13 : $i]:
% 0.62/1.12 (~ (in @ X12 @ (setadjoin @ X13 @ emptyset)) | ((X13) = (X12)))),
% 0.62/1.12 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.62/1.12 thf(zip_derived_cl205, plain, (((sk__48) = (sk__49))),
% 0.62/1.12 inference('sup-', [status(thm)], [zip_derived_cl191, zip_derived_cl26])).
% 0.62/1.12 thf(zip_derived_cl83, plain, (((sk__48) != (sk__49))),
% 0.62/1.12 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.62/1.12 thf(zip_derived_cl215, plain, ($false),
% 0.62/1.12 inference('simplify_reflect-', [status(thm)],
% 0.62/1.12 [zip_derived_cl205, zip_derived_cl83])).
% 0.62/1.12
% 0.62/1.12 % SZS output end Refutation
% 0.62/1.12
% 0.62/1.12
% 0.62/1.12 % Terminating...
% 4.61/1.34 % Runner terminated.
% 4.61/1.36 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------