%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU635^1 : 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.pJLYb2CY8Q true
% Computer : n023.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 04:55:28 PM UTC 2025
% Result : Theorem 10.43s 2.91s
% Output : Refutation 10.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU635^1 : TPTP v9.2.0. Released v3.7.0.
% 0.10/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.pJLYb2CY8Q true
% 0.11/0.33 % Computer : n023.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 16:04:08 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
% 0.11/0.34 % Running in HO mode
% 0.50/0.65 % Total configuration time : 828
% 0.50/0.65 % Estimated wc time : 1656
% 0.50/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.51/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.51/0.82 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.51/0.85 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.51/0.85 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/0.93 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.52/0.95 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.52/0.96 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.52/0.98 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 10.43/2.91 % Solved by lams/40_c_ic.sh.
% 10.43/2.91 % done 904 iterations in 1.967s
% 10.43/2.91 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 10.43/2.91 % SZS output start Refutation
% 10.43/2.91 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 10.43/2.91 thf(notdexE_type, type, notdexE: $o).
% 10.43/2.91 thf(setunionAx_type, type, setunionAx: $o).
% 10.43/2.91 thf(setminusELneg_type, type, setminusELneg: $o).
% 10.43/2.91 thf(powersetE_type, type, powersetE: $o).
% 10.43/2.91 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 10.43/2.91 thf(omegaSAx_type, type, omegaSAx: $o).
% 10.43/2.91 thf(exuI1_type, type, exuI1: $o).
% 10.43/2.91 thf(exuI2_type, type, exuI2: $o).
% 10.43/2.91 thf(notequalI2_type, type, notequalI2: $o).
% 10.43/2.91 thf(setukpairIR_type, type, setukpairIR: $o).
% 10.43/2.91 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 10.43/2.91 thf(setminusILneg_type, type, setminusILneg: $o).
% 10.43/2.91 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 10.43/2.91 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 10.43/2.91 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 10.43/2.91 thf(upairsubunion_type, type, upairsubunion: $o).
% 10.43/2.91 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 10.43/2.91 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 10.43/2.91 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 10.43/2.91 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 10.43/2.91 thf(setukpairIL_type, type, setukpairIL: $o).
% 10.43/2.91 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 10.43/2.91 thf(binunionE_type, type, binunionE: $o).
% 10.43/2.91 thf(setext_type, type, setext: $o).
% 10.43/2.91 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 10.43/2.91 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 10.43/2.91 thf(descr__Cong_type, type, descr__Cong: $o).
% 10.43/2.91 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 10.43/2.91 thf(in_type, type, in: $i > $i > $o).
% 10.43/2.91 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 10.43/2.91 thf(upairset2E_type, type, upairset2E: $o).
% 10.43/2.91 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 10.43/2.91 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 10.43/2.91 thf(symdiffI2_type, type, symdiffI2: $o).
% 10.43/2.91 thf(sk__104_type, type, sk__104: $i > $i > $i).
% 10.43/2.91 thf(upairset2IR_type, type, upairset2IR: $o).
% 10.43/2.91 thf(subsetE_type, type, subsetE: $o).
% 10.43/2.91 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 10.43/2.91 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 10.43/2.91 thf(setbeta_type, type, setbeta: $o).
% 10.43/2.91 thf(eqinunit_type, type, eqinunit: $o).
% 10.43/2.91 thf(upairsetIL_type, type, upairsetIL: $o).
% 10.43/2.91 thf(powersetI1_type, type, powersetI1: $o).
% 10.43/2.91 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 10.43/2.91 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 10.43/2.91 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 10.43/2.91 thf(powersetAx_type, type, powersetAx: $o).
% 10.43/2.91 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 10.43/2.91 thf(powersetI_type, type, powersetI: $o).
% 10.43/2.91 thf(upairsetIR_type, type, upairsetIR: $o).
% 10.43/2.91 thf(inCongP_type, type, inCongP: $o).
% 10.43/2.91 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 10.43/2.91 thf(exuE3e_type, type, exuE3e: $o).
% 10.43/2.91 thf(emptysetE_type, type, emptysetE: $o).
% 10.43/2.91 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 10.43/2.91 thf(setunionI_type, type, setunionI: $o).
% 10.43/2.91 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 10.43/2.91 thf(prop2setI_type, type, prop2setI: $o).
% 10.43/2.91 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 10.43/2.91 thf(setminusER_type, type, setminusER: $o).
% 10.43/2.91 thf(exuE2_type, type, exuE2: $o).
% 10.43/2.91 thf(emptyset_type, type, emptyset: $i).
% 10.43/2.91 thf(powersetsubset_type, type, powersetsubset: $o).
% 10.43/2.91 thf(subPowSU_type, type, subPowSU: $o).
% 10.43/2.91 thf(notequalI1_type, type, notequalI1: $o).
% 10.43/2.91 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 10.43/2.91 thf(notinemptyset_type, type, notinemptyset: $o).
% 10.43/2.91 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 10.43/2.91 thf(subsetTrans_type, type, subsetTrans: $o).
% 10.43/2.91 thf(setminusI_type, type, setminusI: $o).
% 10.43/2.91 thf(binunionIL_type, type, binunionIL: $o).
% 10.43/2.91 thf(subsetE2_type, type, subsetE2: $o).
% 10.43/2.91 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 10.43/2.91 thf(sk__103_type, type, sk__103: $i).
% 10.43/2.91 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 10.43/2.91 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 10.43/2.91 thf(setextsub_type, type, setextsub: $o).
% 10.43/2.91 thf(binunionLsub_type, type, binunionLsub: $o).
% 10.43/2.91 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 10.43/2.91 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 10.43/2.91 thf(setunionE_type, type, setunionE: $o).
% 10.43/2.91 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 10.43/2.91 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 10.43/2.91 thf(binunionIR_type, type, binunionIR: $o).
% 10.43/2.91 thf(setadjoinE_type, type, setadjoinE: $o).
% 10.43/2.91 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 10.43/2.91 thf(exuE1_type, type, exuE1: $o).
% 10.43/2.91 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 10.43/2.91 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 10.43/2.91 thf(setminusLsub_type, type, setminusLsub: $o).
% 10.43/2.91 thf(notinsingleton_type, type, notinsingleton: $o).
% 10.43/2.91 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 10.43/2.91 thf(exuEu_type, type, exuEu: $o).
% 10.43/2.91 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 10.43/2.91 thf(upairsetE_type, type, upairsetE: $o).
% 10.43/2.91 thf(omega0Ax_type, type, omega0Ax: $o).
% 10.43/2.91 thf(notsubsetI_type, type, notsubsetI: $o).
% 10.43/2.91 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 10.43/2.91 thf(setextAx_type, type, setextAx: $o).
% 10.43/2.91 thf(powersetE1_type, type, powersetE1: $o).
% 10.43/2.91 thf(bs114d_type, type, bs114d: $o).
% 10.43/2.91 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 10.43/2.91 thf(setunion_type, type, setunion: $i > $i).
% 10.43/2.91 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 10.43/2.91 thf(subsetI1_type, type, subsetI1: $o).
% 10.43/2.91 thf(symdiffE_type, type, symdiffE: $o).
% 10.43/2.91 thf(descrp_type, type, descrp: $o).
% 10.43/2.91 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 10.43/2.91 thf(foundationAx_type, type, foundationAx: $o).
% 10.43/2.91 thf(emptysetAx_type, type, emptysetAx: $o).
% 10.43/2.91 thf(emptyI_type, type, emptyI: $o).
% 10.43/2.91 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 10.43/2.91 thf(binintersectEL_type, type, binintersectEL: $o).
% 10.43/2.91 thf(emptyE1_type, type, emptyE1: $o).
% 10.43/2.91 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 10.43/2.91 thf(vacuousDall_type, type, vacuousDall: $o).
% 10.43/2.91 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 10.43/2.91 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 10.43/2.91 thf(binintersectI_type, type, binintersectI: $o).
% 10.43/2.91 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 10.43/2.91 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 10.43/2.91 thf(symdiffI1_type, type, symdiffI1: $o).
% 10.43/2.91 thf(subsetI2_type, type, subsetI2: $o).
% 10.43/2.91 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 10.43/2.91 thf(setminusERneg_type, type, setminusERneg: $o).
% 10.43/2.91 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 10.43/2.91 thf(omega__Cong_type, type, omega__Cong: $o).
% 10.43/2.91 thf(subsetRefl_type, type, subsetRefl: $o).
% 10.43/2.91 thf(uniqinunit_type, type, uniqinunit: $o).
% 10.43/2.91 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 10.43/2.91 thf(prop2setE_type, type, prop2setE: $o).
% 10.43/2.91 thf(binunionEcases_type, type, binunionEcases: $o).
% 10.43/2.91 thf(nonemptyI_type, type, nonemptyI: $o).
% 10.43/2.91 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 10.43/2.91 thf(exuE3u_type, type, exuE3u: $o).
% 10.43/2.91 thf(setminusEL_type, type, setminusEL: $o).
% 10.43/2.91 thf(singletonsubset_type, type, singletonsubset: $o).
% 10.43/2.91 thf(sepSubset_type, type, sepSubset: $o).
% 10.43/2.91 thf(setunionE2_type, type, setunionE2: $o).
% 10.43/2.91 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 10.43/2.91 thf(exuI3_type, type, exuI3: $o).
% 10.43/2.91 thf(notdallE_type, type, notdallE: $o).
% 10.43/2.91 thf(binintersectER_type, type, binintersectER: $o).
% 10.43/2.91 thf(powerset_type, type, powerset: $i > $i).
% 10.43/2.91 thf(kpairp_type, type, kpairp: $o).
% 10.43/2.91 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 10.43/2.91 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 10.43/2.91 thf(exu__Cong_type, type, exu__Cong: $o).
% 10.43/2.91 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 10.43/2.91 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 10.43/2.91 thf(replAx_type, type, replAx: $o).
% 10.43/2.91 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 10.43/2.91 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 10.43/2.91 thf(secondinupair_type, type, secondinupair: $o).
% 10.43/2.91 thf(inPowerset_type, type, inPowerset: $o).
% 10.43/2.91 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 10.43/2.91 thf(subset_type, type, subset: $i > $i > $o).
% 10.43/2.91 thf(in__Cong_type, type, in__Cong: $o).
% 10.43/2.91 thf(binunionRsub_type, type, binunionRsub: $o).
% 10.43/2.91 thf(subset2powerset_type, type, subset2powerset: $o).
% 10.43/2.91 thf(setunionsingleton1, axiom, setunionsingleton1 =
% 10.43/2.91 (![A:$i]: ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ))).
% 10.43/2.91 thf('0', plain,
% 10.43/2.91 (( setunionsingleton1 ) =
% 10.43/2.91 ( ![X4:$i]:
% 10.43/2.91 ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(setunionE2, axiom, setunionE2 =
% 10.43/2.91 (![A:$i,Xx:$i]:
% 10.43/2.91 ( ( in @ Xx @ ( setunion @ A ) ) =>
% 10.43/2.91 ( ?[X:$i]: ( ( in @ Xx @ X ) & ( in @ X @ A ) ) ) ))).
% 10.43/2.91 thf('1', plain,
% 10.43/2.91 (( setunionE2 ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( ( in @ X6 @ ( setunion @ X4 ) ) =>
% 10.43/2.91 ( ?[X8:$i]: ( ( in @ X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(upairset2E, axiom, upairset2E =
% 10.43/2.91 (![Xx:$i,Xy:$i,Xz:$i]:
% 10.43/2.91 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 10.43/2.91 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 10.43/2.91 thf('2', plain,
% 10.43/2.91 (( upairset2E ) =
% 10.43/2.91 ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.91 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 10.43/2.91 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(singletonsubset, axiom, singletonsubset =
% 10.43/2.91 (![A:$i,Xx:$i]:
% 10.43/2.91 ( ( in @ Xx @ A ) => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ))).
% 10.43/2.91 thf('3', plain,
% 10.43/2.91 (( singletonsubset ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( ( in @ X6 @ X4 ) => ( subset @ ( setadjoin @ X6 @ emptyset ) @ X4 ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(setukpairIR, axiom, setukpairIR =
% 10.43/2.91 (![Xx:$i,Xy:$i]:
% 10.43/2.91 ( in @
% 10.43/2.91 Xy @
% 10.43/2.91 ( setunion @
% 10.43/2.91 ( setadjoin @
% 10.43/2.91 ( setadjoin @ Xx @ emptyset ) @
% 10.43/2.91 ( setadjoin @
% 10.43/2.91 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ))).
% 10.43/2.91 thf('4', plain,
% 10.43/2.91 (( setukpairIR ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( in @
% 10.43/2.91 X6 @
% 10.43/2.91 ( setunion @
% 10.43/2.91 ( setadjoin @
% 10.43/2.91 ( setadjoin @ X4 @ emptyset ) @
% 10.43/2.91 ( setadjoin @
% 10.43/2.91 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(setukpairIL, axiom, setukpairIL =
% 10.43/2.91 (![Xx:$i,Xy:$i]:
% 10.43/2.91 ( in @
% 10.43/2.91 Xx @
% 10.43/2.91 ( setunion @
% 10.43/2.91 ( setadjoin @
% 10.43/2.91 ( setadjoin @ Xx @ emptyset ) @
% 10.43/2.91 ( setadjoin @
% 10.43/2.91 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ))).
% 10.43/2.91 thf('5', plain,
% 10.43/2.91 (( setukpairIL ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( in @
% 10.43/2.91 X4 @
% 10.43/2.91 ( setunion @
% 10.43/2.91 ( setadjoin @
% 10.43/2.91 ( setadjoin @ X4 @ emptyset ) @
% 10.43/2.91 ( setadjoin @
% 10.43/2.91 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(secondinupair, axiom, secondinupair =
% 10.43/2.91 (![Xx:$i,Xy:$i]:
% 10.43/2.91 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 10.43/2.91 thf('6', plain,
% 10.43/2.91 (( secondinupair ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(upairset2IR, axiom, upairset2IR =
% 10.43/2.91 (![Xx:$i,Xy:$i]:
% 10.43/2.91 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 10.43/2.91 thf('7', plain,
% 10.43/2.91 (( upairset2IR ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 10.43/2.91 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 10.43/2.91 thf('8', plain,
% 10.43/2.91 (( subsetemptysetimpeq ) =
% 10.43/2.91 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(setextsub, axiom, setextsub =
% 10.43/2.91 (![A:$i,B:$i]:
% 10.43/2.91 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 10.43/2.91 thf('9', plain,
% 10.43/2.91 (( setextsub ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( ( subset @ X4 @ X6 ) =>
% 10.43/2.91 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 10.43/2.91 (![A:$i,Xx:$i,B:$i]:
% 10.43/2.91 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 10.43/2.91 thf('10', plain,
% 10.43/2.91 (( setadjoinSub2 ) =
% 10.43/2.91 ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.91 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(setadjoinSub, axiom, setadjoinSub =
% 10.43/2.91 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 10.43/2.91 thf('11', plain,
% 10.43/2.91 (( setadjoinSub ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(subsetTrans, axiom, subsetTrans =
% 10.43/2.91 (![A:$i,B:$i,C:$i]:
% 10.43/2.91 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 10.43/2.91 thf('12', plain,
% 10.43/2.91 (( subsetTrans ) =
% 10.43/2.91 ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.91 ( ( subset @ X4 @ X6 ) =>
% 10.43/2.91 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 10.43/2.91 thf('13', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(notequalI1, axiom, notequalI1 =
% 10.43/2.91 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 10.43/2.91 thf('14', plain,
% 10.43/2.91 (( notequalI1 ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(notsubsetI, axiom, notsubsetI =
% 10.43/2.91 (![A:$i,B:$i,Xx:$i]:
% 10.43/2.91 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 10.43/2.91 thf('15', plain,
% 10.43/2.91 (( notsubsetI ) =
% 10.43/2.91 ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.91 ( ( in @ X8 @ X4 ) =>
% 10.43/2.91 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(subsetE2, axiom, subsetE2 =
% 10.43/2.91 (![A:$i,B:$i,Xx:$i]:
% 10.43/2.91 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 10.43/2.91 thf('16', plain,
% 10.43/2.91 (( subsetE2 ) =
% 10.43/2.91 ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.91 ( ( subset @ X4 @ X6 ) =>
% 10.43/2.91 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(subsetE, axiom, subsetE =
% 10.43/2.91 (![A:$i,B:$i,Xx:$i]:
% 10.43/2.91 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 10.43/2.91 thf('17', plain,
% 10.43/2.91 (( subsetE ) =
% 10.43/2.91 ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.91 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(emptysetsubset, axiom, emptysetsubset =
% 10.43/2.91 (![A:$i]: ( subset @ emptyset @ A ))).
% 10.43/2.91 thf('18', plain,
% 10.43/2.91 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(subsetI2, axiom, subsetI2 =
% 10.43/2.91 (![A:$i,B:$i]:
% 10.43/2.91 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 10.43/2.91 ( subset @ A @ B ) ))).
% 10.43/2.91 thf('19', plain,
% 10.43/2.91 (( subsetI2 ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 10.43/2.91 ( subset @ X4 @ X6 ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 10.43/2.91 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 10.43/2.91 thf('20', plain,
% 10.43/2.91 (( eqimpsubset1 ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 10.43/2.91 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 10.43/2.91 thf('21', plain,
% 10.43/2.91 (( eqimpsubset2 ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(subsetI1, axiom, subsetI1 =
% 10.43/2.91 (![A:$i,B:$i]:
% 10.43/2.91 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 10.43/2.91 ( subset @ A @ B ) ))).
% 10.43/2.91 thf('22', plain,
% 10.43/2.91 (( subsetI1 ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 10.43/2.91 ( subset @ X4 @ X6 ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(setunion__Cong, axiom, setunion__Cong =
% 10.43/2.91 (![A:$i,B:$i]:
% 10.43/2.91 ( ( ( A ) = ( B ) ) => ( ( setunion @ A ) = ( setunion @ B ) ) ))).
% 10.43/2.91 thf('23', plain,
% 10.43/2.91 (( setunion__Cong ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( ( ( X4 ) = ( X6 ) ) => ( ( setunion @ X4 ) = ( setunion @ X6 ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 10.43/2.91 (![Xx:$i,Xy:$i]:
% 10.43/2.91 ( ( ( Xx ) = ( Xy ) ) =>
% 10.43/2.91 ( ![Xz:$i,Xu:$i]:
% 10.43/2.91 ( ( ( Xz ) = ( Xu ) ) =>
% 10.43/2.91 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 10.43/2.91 thf('24', plain,
% 10.43/2.91 (( setadjoin__Cong ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( ( ( X4 ) = ( X6 ) ) =>
% 10.43/2.91 ( ![X8:$i,X10:$i]:
% 10.43/2.91 ( ( ( X8 ) = ( X10 ) ) =>
% 10.43/2.91 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(upairsetIR, axiom, upairsetIR =
% 10.43/2.91 (![Xx:$i,Xy:$i]:
% 10.43/2.91 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 10.43/2.91 thf('25', plain,
% 10.43/2.91 (( upairsetIR ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(upairsetIL, axiom, upairsetIL =
% 10.43/2.91 (![Xx:$i,Xy:$i]:
% 10.43/2.91 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 10.43/2.91 thf('26', plain,
% 10.43/2.91 (( upairsetIL ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(upairsetE, axiom, upairsetE =
% 10.43/2.91 (![Xx:$i,Xy:$i,Xz:$i]:
% 10.43/2.91 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 10.43/2.91 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 10.43/2.91 thf('27', plain,
% 10.43/2.91 (( upairsetE ) =
% 10.43/2.91 ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.91 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 10.43/2.91 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(singletonsswitch, axiom, singletonsswitch =
% 10.43/2.91 (![Xx:$i,Xy:$i]:
% 10.43/2.91 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 10.43/2.91 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 10.43/2.91 thf('28', plain,
% 10.43/2.91 (( singletonsswitch ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 10.43/2.91 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(eqinunit, axiom, eqinunit =
% 10.43/2.91 (![Xx:$i,Xy:$i]:
% 10.43/2.91 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 10.43/2.91 thf('29', plain,
% 10.43/2.91 (( eqinunit ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(notinsingleton, axiom, notinsingleton =
% 10.43/2.91 (![Xx:$i,Xy:$i]:
% 10.43/2.91 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 10.43/2.91 thf('30', plain,
% 10.43/2.91 (( notinsingleton ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( ( ( X4 ) != ( X6 ) ) =>
% 10.43/2.91 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(uniqinunit, axiom, uniqinunit =
% 10.43/2.91 (![Xx:$i,Xy:$i]:
% 10.43/2.91 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 10.43/2.91 thf('31', plain,
% 10.43/2.91 (( uniqinunit ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.91 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 10.43/2.91 define([status(thm)])).
% 10.43/2.91 thf(subPowSU, axiom, subPowSU =
% 10.43/2.91 (![A:$i,Xx:$i]:
% 10.43/2.91 ( ( in @ Xx @ A ) => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ))).
% 10.43/2.91 thf('32', plain,
% 10.43/2.91 (( subPowSU ) =
% 10.43/2.91 ( ![X4:$i,X6:$i]:
% 10.43/2.92 ( ( in @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ ( setunion @ X4 ) ) ) ) )),
% 10.43/2.92 define([status(thm)])).
% 10.43/2.92 thf(setunionE, axiom, setunionE =
% 10.43/2.92 (![A:$i,Xx:$i]:
% 10.43/2.92 ( ( in @ Xx @ ( setunion @ A ) ) =>
% 10.43/2.92 ( ![Xphi:$o]:
% 10.43/2.92 ( ( ![B:$i]: ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( Xphi ) ) ) ) =>
% 10.43/2.92 ( Xphi ) ) ) ))).
% 10.43/2.92 thf('33', plain,
% 10.43/2.92 (( setunionE ) =
% 10.43/2.92 ( ![X4:$i,X6:$i]:
% 10.43/2.92 ( ( in @ X6 @ ( setunion @ X4 ) ) =>
% 10.43/2.92 ( ![X8:$o]:
% 10.43/2.92 ( ( ![X10:$i]:
% 10.43/2.92 ( ( in @ X6 @ X10 ) => ( ( in @ X10 @ X4 ) => ( X8 ) ) ) ) =>
% 10.43/2.92 ( X8 ) ) ) ) )),
% 10.43/2.92 define([status(thm)])).
% 10.43/2.92 thf(setunionI, axiom, setunionI =
% 10.43/2.92 (![A:$i,Xx:$i,B:$i]:
% 10.43/2.92 ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( in @ Xx @ ( setunion @ A ) ) ) ))).
% 10.43/2.92 thf('34', plain,
% 10.43/2.92 (( setunionI ) =
% 10.43/2.92 ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.92 ( ( in @ X6 @ X8 ) =>
% 10.43/2.92 ( ( in @ X8 @ X4 ) => ( in @ X6 @ ( setunion @ X4 ) ) ) ) )),
% 10.43/2.92 define([status(thm)])).
% 10.43/2.92 thf(setadjoinOr, axiom, setadjoinOr =
% 10.43/2.92 (![Xx:$i,A:$i,Xy:$i]:
% 10.43/2.92 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 10.43/2.92 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 10.43/2.92 thf('35', plain,
% 10.43/2.92 (( setadjoinOr ) =
% 10.43/2.92 ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.92 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 10.43/2.92 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 10.43/2.92 define([status(thm)])).
% 10.43/2.92 thf(setadjoinE, axiom, setadjoinE =
% 10.43/2.92 (![Xx:$i,A:$i,Xy:$i]:
% 10.43/2.92 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 10.43/2.92 ( ![Xphi:$o]:
% 10.43/2.92 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 10.43/2.92 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 10.43/2.92 thf('36', plain,
% 10.43/2.92 (( setadjoinE ) =
% 10.43/2.92 ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.92 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 10.43/2.92 ( ![X10:$o]:
% 10.43/2.92 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 10.43/2.92 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 10.43/2.92 define([status(thm)])).
% 10.43/2.92 thf(setadjoinIR, axiom, setadjoinIR =
% 10.43/2.92 (![Xx:$i,A:$i,Xy:$i]:
% 10.43/2.92 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 10.43/2.92 thf('37', plain,
% 10.43/2.92 (( setadjoinIR ) =
% 10.43/2.92 ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.92 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 10.43/2.92 define([status(thm)])).
% 10.43/2.92 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 10.43/2.92 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 10.43/2.92 thf('38', plain,
% 10.43/2.92 (( emptyinunitempty ) =
% 10.43/2.92 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 10.43/2.92 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 10.43/2.92 thf('39', plain,
% 10.43/2.92 (( emptyinunitempty ) =
% 10.43/2.92 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 10.43/2.92 define([status(thm)])).
% 10.43/2.92 thf(setadjoinIL, axiom, setadjoinIL =
% 10.43/2.92 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 10.43/2.92 thf('40', plain,
% 10.43/2.92 (( setadjoinIL ) =
% 10.43/2.92 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 10.43/2.92 define([status(thm)])).
% 10.43/2.92 thf(setunionAx, axiom, setunionAx =
% 10.43/2.92 (![A:$i,Xx:$i]:
% 10.43/2.92 ( ( in @ Xx @ ( setunion @ A ) ) <=>
% 10.43/2.92 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))).
% 10.43/2.92 thf('41', plain,
% 10.43/2.92 (( setunionAx ) =
% 10.43/2.92 ( ![X4:$i,X6:$i]:
% 10.43/2.92 ( ( in @ X6 @ ( setunion @ X4 ) ) <=>
% 10.43/2.92 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )),
% 10.43/2.92 define([status(thm)])).
% 10.43/2.92 thf(setadjoinAx, axiom, setadjoinAx =
% 10.43/2.92 (![Xx:$i,A:$i,Xy:$i]:
% 10.43/2.92 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 10.43/2.92 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 10.43/2.92 thf('42', plain,
% 10.43/2.92 (( setadjoinAx ) =
% 10.43/2.92 ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.92 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 10.43/2.92 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 10.43/2.92 define([status(thm)])).
% 10.43/2.92 thf(setunionsingleton2, conjecture,
% 10.43/2.92 (( setextAx ) =>
% 10.43/2.92 ( ( emptysetAx ) =>
% 10.43/2.92 ( ( setadjoinAx ) =>
% 10.43/2.92 ( ( powersetAx ) =>
% 10.43/2.92 ( ( setunionAx ) =>
% 10.43/2.92 ( ( omega0Ax ) =>
% 10.43/2.92 ( ( omegaSAx ) =>
% 10.43/2.92 ( ( omegaIndAx ) =>
% 10.43/2.92 ( ( replAx ) =>
% 10.43/2.92 ( ( foundationAx ) =>
% 10.43/2.92 ( ( wellorderingAx ) =>
% 10.43/2.92 ( ( descrp ) =>
% 10.43/2.92 ( ( dsetconstrI ) =>
% 10.43/2.92 ( ( dsetconstrEL ) =>
% 10.43/2.92 ( ( dsetconstrER ) =>
% 10.43/2.92 ( ( exuE1 ) =>
% 10.43/2.92 ( ( prop2setE ) =>
% 10.43/2.92 ( ( emptysetE ) =>
% 10.43/2.92 ( ( emptysetimpfalse ) =>
% 10.43/2.92 ( ( notinemptyset ) =>
% 10.43/2.92 ( ( exuE3e ) =>
% 10.43/2.92 ( ( setext ) =>
% 10.43/2.92 ( ( emptyI ) =>
% 10.43/2.92 ( ( noeltsimpempty ) =>
% 10.43/2.92 ( ( setbeta ) =>
% 10.43/2.92 ( ( nonemptyE1 ) =>
% 10.43/2.92 ( ( nonemptyI ) =>
% 10.43/2.92 ( ( nonemptyI1 ) =>
% 10.43/2.92 ( ( setadjoinIL ) =>
% 10.43/2.92 ( ( emptyinunitempty ) =>
% 10.43/2.92 ( ( setadjoinIR ) =>
% 10.43/2.92 ( ( setadjoinE ) =>
% 10.43/2.92 ( (
% 10.43/2.92 setadjoinOr ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setoftrueEq ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyinPowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyInPowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setunionI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setunionE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subPowSU ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuE2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 nonemptyImpWitness ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 uniqinunit ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 notinsingleton ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 eqinunit ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 singletonsswitch ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 upairsetE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 upairsetIL ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 upairsetIR ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyE1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 vacuousDall ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 quantDeMorgan1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 quantDeMorgan2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 quantDeMorgan3 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 quantDeMorgan4 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 prop2setI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 prop2set2propI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 notdexE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 notdallE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuI1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuI3 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuI2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 inCongP ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuE3u ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exu__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyset__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setadjoin__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powerset__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setunion__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 omega__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuEu ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 descr__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 dsetconstr__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subsetI1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 eqimpsubset2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 eqimpsubset1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subsetI2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptysetsubset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subsetE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subsetE2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 notsubsetI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 notequalI1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 notequalI2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subsetRefl ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subsetTrans ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setadjoinSub ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setadjoinSub2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subset2powerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setextsub ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subsetemptysetimpeq ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetI1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetE1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 inPowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetsubset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 sepInPowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 sepSubset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binunionIL ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 upairset2IR ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binunionIR ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binunionEcases ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binunionE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binunionLsub ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binunionRsub ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectSubset5 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectEL ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectLsub ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectSubset2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectSubset3 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectER ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 disjointsetsI1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectRsub ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectSubset4 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectSubset1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 bs114d ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusEL ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusER ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusSubset2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusERneg ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusELneg ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusILneg ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusIRneg ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusLsub ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusSubset1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 symdiffE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 symdiffI1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 symdiffI2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 symdiffIneg1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 symdiffIneg2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 secondinupair ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setukpairIL ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setukpairIR ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 kpairiskpair ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 kpairp ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 singletonsubset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 singletoninpowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 singletoninpowunion ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 upairset2E ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 upairsubunion ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 upairinpowunion ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ubforcartprodlem1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ubforcartprodlem2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ubforcartprodlem3 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 cartprodpairin ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 cartprodmempair1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 cartprodmempair ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setunionE2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setunionsingleton1 ) =>
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 A:$i]:
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 A @
% 10.43/2.92 (
% 10.43/2.92 setunion @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 A @
% 10.43/2.92 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 10.43/2.92 thf(zf_stmt_0, conjecture,
% 10.43/2.92 (( setextAx ) =>
% 10.43/2.92 ( ( emptysetAx ) =>
% 10.43/2.92 ( ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.92 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 10.43/2.92 ( ( in @ X8 @ X6 ) | ( ( X8 ) = ( X4 ) ) ) ) ) =>
% 10.43/2.92 ( ( powersetAx ) =>
% 10.43/2.92 ( ( ![X10:$i,X12:$i]:
% 10.43/2.92 ( ( in @ X12 @ ( setunion @ X10 ) ) <=>
% 10.43/2.92 ( ?[X14:$i]: ( ( in @ X12 @ X14 ) & ( in @ X14 @ X10 ) ) ) ) ) =>
% 10.43/2.92 ( ( omega0Ax ) =>
% 10.43/2.92 ( ( omegaSAx ) =>
% 10.43/2.92 ( ( omegaIndAx ) =>
% 10.43/2.92 ( ( replAx ) =>
% 10.43/2.92 ( ( foundationAx ) =>
% 10.43/2.92 ( ( wellorderingAx ) =>
% 10.43/2.92 ( ( descrp ) =>
% 10.43/2.92 ( ( dsetconstrI ) =>
% 10.43/2.92 ( ( dsetconstrEL ) =>
% 10.43/2.92 ( ( dsetconstrER ) =>
% 10.43/2.92 ( ( exuE1 ) =>
% 10.43/2.92 ( ( prop2setE ) =>
% 10.43/2.92 ( ( emptysetE ) =>
% 10.43/2.92 ( ( emptysetimpfalse ) =>
% 10.43/2.92 ( ( notinemptyset ) =>
% 10.43/2.92 ( ( exuE3e ) =>
% 10.43/2.92 ( ( setext ) =>
% 10.43/2.92 ( ( emptyI ) =>
% 10.43/2.92 ( ( noeltsimpempty ) =>
% 10.43/2.92 ( ( setbeta ) =>
% 10.43/2.92 ( ( nonemptyE1 ) =>
% 10.43/2.92 ( ( nonemptyI ) =>
% 10.43/2.92 ( ( nonemptyI1 ) =>
% 10.43/2.92 ( ( ![X16:$i,X18:$i]:
% 10.43/2.92 ( in @
% 10.43/2.92 X16 @
% 10.43/2.92 ( setadjoin @
% 10.43/2.92 X16 @ X18 ) ) ) =>
% 10.43/2.92 ( ( in @
% 10.43/2.92 emptyset @
% 10.43/2.92 ( setadjoin @
% 10.43/2.92 emptyset @
% 10.43/2.92 emptyset ) ) =>
% 10.43/2.92 ( ( ![X20:$i,
% 10.43/2.92 X22:$i,
% 10.43/2.92 X24:$i]:
% 10.43/2.92 ( (
% 10.43/2.92 in @
% 10.43/2.92 X24 @ X22 ) =>
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X24 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X20 @ X22 ) ) ) ) =>
% 10.43/2.92 ( ( ![
% 10.43/2.92 X26:$i,
% 10.43/2.92 X28:$i,
% 10.43/2.92 X30:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X30 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X26 @ X28 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X32:$o]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X30 ) =
% 10.43/2.92 (
% 10.43/2.92 X26 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 X32 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X30 @ X28 ) =>
% 10.43/2.92 (
% 10.43/2.92 X32 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 X32 ) ) ) ) ) ) =>
% 10.43/2.92 ( (
% 10.43/2.92 ![
% 10.43/2.92 X34:$i,
% 10.43/2.92 X36:$i,
% 10.43/2.92 X38:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X38 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X34 @ X36 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X38 @ X36 ) |
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X38 ) =
% 10.43/2.92 (
% 10.43/2.92 X34 ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setoftrueEq ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyinPowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyInPowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X40:$i,
% 10.43/2.92 X42:$i,
% 10.43/2.92 X44:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X42 @ X44 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X44 @ X40 ) =>
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X42 @
% 10.43/2.92 (
% 10.43/2.92 setunion @
% 10.43/2.92 X40 ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X46:$i,
% 10.43/2.92 X48:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X48 @
% 10.43/2.92 (
% 10.43/2.92 setunion @
% 10.43/2.92 X46 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X50:$o]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X52:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X48 @ X52 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X52 @ X46 ) =>
% 10.43/2.92 (
% 10.43/2.92 X50 ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 X50 ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X54:$i,
% 10.43/2.92 X56:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X56 @ X54 ) =>
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X56 @
% 10.43/2.92 (
% 10.43/2.92 powerset @
% 10.43/2.92 (
% 10.43/2.92 setunion @
% 10.43/2.92 X54 ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuE2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 nonemptyImpWitness ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X58:$i,
% 10.43/2.92 X60:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X58 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X60 @
% 10.43/2.92 emptyset ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X58 ) =
% 10.43/2.92 (
% 10.43/2.92 X60 ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X62:$i,
% 10.43/2.92 X64:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X62 ) !=
% 10.43/2.92 (
% 10.43/2.92 X64 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 ~(
% 10.43/2.92 in @
% 10.43/2.92 X64 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X62 @
% 10.43/2.92 emptyset ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X66:$i,
% 10.43/2.92 X68:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X66 ) =
% 10.43/2.92 (
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% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X176 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X178 @
% 10.43/2.92 emptyset ) ) @
% 10.43/2.92 emptyset ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X180:$i,
% 10.43/2.92 X182:$i]:
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X182 @
% 10.43/2.92 (
% 10.43/2.92 setunion @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X180 @
% 10.43/2.92 emptyset ) @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X180 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X182 @
% 10.43/2.92 emptyset ) ) @
% 10.43/2.92 emptyset ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 kpairiskpair ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 kpairp ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X184:$i,
% 10.43/2.92 X186:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X186 @
% 10.43/2.92 X184 ) =>
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X186 @
% 10.43/2.92 emptyset ) @
% 10.43/2.92 X184 ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 singletoninpowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 singletoninpowunion ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X188:$i,
% 10.43/2.92 X190:$i,
% 10.43/2.92 X192:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X192 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X188 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X190 @
% 10.43/2.92 emptyset ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X192 ) =
% 10.43/2.92 (
% 10.43/2.92 X190 ) ) |
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X192 ) =
% 10.43/2.92 (
% 10.43/2.92 X188 ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 upairsubunion ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 upairinpowunion ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ubforcartprodlem1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ubforcartprodlem2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ubforcartprodlem3 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 cartprodpairin ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 cartprodmempair1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 cartprodmempair ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X194:$i,
% 10.43/2.92 X196:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X196 @
% 10.43/2.92 (
% 10.43/2.92 setunion @
% 10.43/2.92 X194 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 ?[
% 10.43/2.92 X198:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X198 @
% 10.43/2.92 X194 ) &
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X196 @
% 10.43/2.92 X198 ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X200:$i]:
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 (
% 10.43/2.92 setunion @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X200 @
% 10.43/2.92 emptyset ) ) @
% 10.43/2.92 X200 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X202:$i]:
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 X202 @
% 10.43/2.92 (
% 10.43/2.92 setunion @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X202 @
% 10.43/2.92 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 10.43/2.92 thf(zf_stmt_1, type, zip_tseitin_1 : $i > $i > $i > $o).
% 10.43/2.92 thf(zf_stmt_2, axiom,
% 10.43/2.92 (![X14:$i,X12:$i,X10:$i]:
% 10.43/2.92 ( ( zip_tseitin_1 @ X14 @ X12 @ X10 ) <=>
% 10.43/2.92 ( ( in @ X14 @ X10 ) & ( in @ X12 @ X14 ) ) ))).
% 10.43/2.92 thf(zf_stmt_3, type, zip_tseitin_0 : $i > $i > $i > $o).
% 10.43/2.92 thf(zf_stmt_4, axiom,
% 10.43/2.92 (![X8:$i,X6:$i,X4:$i]:
% 10.43/2.92 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 10.43/2.92 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ))).
% 10.43/2.92 thf(zf_stmt_5, conjecture,
% 10.43/2.92 (( setextAx ) =>
% 10.43/2.92 ( ( emptysetAx ) =>
% 10.43/2.92 ( ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.92 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 10.43/2.92 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 10.43/2.92 ( ( powersetAx ) =>
% 10.43/2.92 ( ( ![X10:$i,X12:$i]:
% 10.43/2.92 ( ( in @ X12 @ ( setunion @ X10 ) ) <=>
% 10.43/2.92 ( ?[X14:$i]: ( zip_tseitin_1 @ X14 @ X12 @ X10 ) ) ) ) =>
% 10.43/2.92 ( ( omega0Ax ) =>
% 10.43/2.92 ( ( omegaSAx ) =>
% 10.43/2.92 ( ( omegaIndAx ) =>
% 10.43/2.92 ( ( replAx ) =>
% 10.43/2.92 ( ( foundationAx ) =>
% 10.43/2.92 ( ( wellorderingAx ) =>
% 10.43/2.92 ( ( descrp ) =>
% 10.43/2.92 ( ( dsetconstrI ) =>
% 10.43/2.92 ( ( dsetconstrEL ) =>
% 10.43/2.92 ( ( dsetconstrER ) =>
% 10.43/2.92 ( ( exuE1 ) =>
% 10.43/2.92 ( ( prop2setE ) =>
% 10.43/2.92 ( ( emptysetE ) =>
% 10.43/2.92 ( ( emptysetimpfalse ) =>
% 10.43/2.92 ( ( notinemptyset ) =>
% 10.43/2.92 ( ( exuE3e ) =>
% 10.43/2.92 ( ( setext ) =>
% 10.43/2.92 ( ( emptyI ) =>
% 10.43/2.92 ( ( noeltsimpempty ) =>
% 10.43/2.92 ( ( setbeta ) =>
% 10.43/2.92 ( ( nonemptyE1 ) =>
% 10.43/2.92 ( ( nonemptyI ) =>
% 10.43/2.92 ( ( nonemptyI1 ) =>
% 10.43/2.92 ( ( ![X16:$i,X18:$i]:
% 10.43/2.92 ( in @
% 10.43/2.92 X16 @
% 10.43/2.92 ( setadjoin @
% 10.43/2.92 X16 @ X18 ) ) ) =>
% 10.43/2.92 ( ( in @
% 10.43/2.92 emptyset @
% 10.43/2.92 ( setadjoin @
% 10.43/2.92 emptyset @
% 10.43/2.92 emptyset ) ) =>
% 10.43/2.92 ( ( ![X20:$i,
% 10.43/2.92 X22:$i,
% 10.43/2.92 X24:$i]:
% 10.43/2.92 ( (
% 10.43/2.92 in @
% 10.43/2.92 X24 @ X22 ) =>
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X24 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X20 @ X22 ) ) ) ) =>
% 10.43/2.92 ( ( ![
% 10.43/2.92 X26:$i,
% 10.43/2.92 X28:$i,
% 10.43/2.92 X30:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X30 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X26 @ X28 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X32:$o]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X30 ) =
% 10.43/2.92 (
% 10.43/2.92 X26 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 X32 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X30 @ X28 ) =>
% 10.43/2.92 (
% 10.43/2.92 X32 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 X32 ) ) ) ) ) ) =>
% 10.43/2.92 ( (
% 10.43/2.92 ![
% 10.43/2.92 X34:$i,
% 10.43/2.92 X36:$i,
% 10.43/2.92 X38:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X38 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X34 @ X36 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X38 ) =
% 10.43/2.92 (
% 10.43/2.92 X34 ) ) |
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X38 @ X36 ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setoftrueEq ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyinPowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyInPowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X40:$i,
% 10.43/2.92 X42:$i,
% 10.43/2.92 X44:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X42 @ X44 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X44 @ X40 ) =>
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X42 @
% 10.43/2.92 (
% 10.43/2.92 setunion @
% 10.43/2.92 X40 ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X46:$i,
% 10.43/2.92 X48:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X48 @
% 10.43/2.92 (
% 10.43/2.92 setunion @
% 10.43/2.92 X46 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X50:$o]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X52:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X48 @ X52 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X52 @ X46 ) =>
% 10.43/2.92 (
% 10.43/2.92 X50 ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 X50 ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X54:$i,
% 10.43/2.92 X56:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X56 @ X54 ) =>
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X56 @
% 10.43/2.92 (
% 10.43/2.92 powerset @
% 10.43/2.92 (
% 10.43/2.92 setunion @
% 10.43/2.92 X54 ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuE2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 nonemptyImpWitness ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X58:$i,
% 10.43/2.92 X60:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X58 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X60 @
% 10.43/2.92 emptyset ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X58 ) =
% 10.43/2.92 (
% 10.43/2.92 X60 ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X62:$i,
% 10.43/2.92 X64:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X62 ) !=
% 10.43/2.92 (
% 10.43/2.92 X64 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 ~(
% 10.43/2.92 in @
% 10.43/2.92 X64 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X62 @
% 10.43/2.92 emptyset ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X66:$i,
% 10.43/2.92 X68:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X66 ) =
% 10.43/2.92 (
% 10.43/2.92 X68 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X66 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X68 @
% 10.43/2.92 emptyset ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X70:$i,
% 10.43/2.92 X72:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X70 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X72 @
% 10.43/2.92 emptyset ) ) =>
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X72 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X70 @
% 10.43/2.92 emptyset ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X74:$i,
% 10.43/2.92 X76:$i,
% 10.43/2.92 X78:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X78 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X74 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X76 @
% 10.43/2.92 emptyset ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X78 ) =
% 10.43/2.92 (
% 10.43/2.92 X74 ) ) |
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X78 ) =
% 10.43/2.92 (
% 10.43/2.92 X76 ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X80:$i,
% 10.43/2.92 X82:$i]:
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X80 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X80 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X82 @
% 10.43/2.92 emptyset ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X84:$i,
% 10.43/2.92 X86:$i]:
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X86 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X84 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X86 @
% 10.43/2.92 emptyset ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyE1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 vacuousDall ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 quantDeMorgan1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 quantDeMorgan2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 quantDeMorgan3 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 quantDeMorgan4 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 prop2setI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 prop2set2propI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 notdexE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 notdallE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuI1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuI3 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuI2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 inCongP ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuE3u ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exu__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyset__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X88:$i,
% 10.43/2.92 X90:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X88 ) =
% 10.43/2.92 (
% 10.43/2.92 X90 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X92:$i,
% 10.43/2.92 X94:$i]:
% 10.43/2.92 (
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% 10.43/2.92 subset @
% 10.43/2.92 X202 @
% 10.43/2.92 (
% 10.43/2.92 setunion @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X202 @
% 10.43/2.92 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 10.43/2.92 thf(zf_stmt_6, negated_conjecture,
% 10.43/2.92 (~( ( setextAx ) =>
% 10.43/2.92 ( ( emptysetAx ) =>
% 10.43/2.92 ( ( ![X4:$i,X6:$i,X8:$i]:
% 10.43/2.92 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 10.43/2.92 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 10.43/2.92 ( ( powersetAx ) =>
% 10.43/2.92 ( ( ![X10:$i,X12:$i]:
% 10.43/2.92 ( ( in @ X12 @ ( setunion @ X10 ) ) <=>
% 10.43/2.92 ( ?[X14:$i]: ( zip_tseitin_1 @ X14 @ X12 @ X10 ) ) ) ) =>
% 10.43/2.92 ( ( omega0Ax ) =>
% 10.43/2.92 ( ( omegaSAx ) =>
% 10.43/2.92 ( ( omegaIndAx ) =>
% 10.43/2.92 ( ( replAx ) =>
% 10.43/2.92 ( ( foundationAx ) =>
% 10.43/2.92 ( ( wellorderingAx ) =>
% 10.43/2.92 ( ( descrp ) =>
% 10.43/2.92 ( ( dsetconstrI ) =>
% 10.43/2.92 ( ( dsetconstrEL ) =>
% 10.43/2.92 ( ( dsetconstrER ) =>
% 10.43/2.92 ( ( exuE1 ) =>
% 10.43/2.92 ( ( prop2setE ) =>
% 10.43/2.92 ( ( emptysetE ) =>
% 10.43/2.92 ( ( emptysetimpfalse ) =>
% 10.43/2.92 ( ( notinemptyset ) =>
% 10.43/2.92 ( ( exuE3e ) =>
% 10.43/2.92 ( ( setext ) =>
% 10.43/2.92 ( ( emptyI ) =>
% 10.43/2.92 ( ( noeltsimpempty ) =>
% 10.43/2.92 ( ( setbeta ) =>
% 10.43/2.92 ( ( nonemptyE1 ) =>
% 10.43/2.92 ( ( nonemptyI ) =>
% 10.43/2.92 ( ( nonemptyI1 ) =>
% 10.43/2.92 ( ( ![X16:$i,
% 10.43/2.92 X18:$i]:
% 10.43/2.92 ( in @
% 10.43/2.92 X16 @
% 10.43/2.92 ( setadjoin
% 10.43/2.92 @
% 10.43/2.92 X16 @ X18 ) ) ) =>
% 10.43/2.92 ( ( in @
% 10.43/2.92 emptyset @
% 10.43/2.92 ( setadjoin
% 10.43/2.92 @
% 10.43/2.92 emptyset @
% 10.43/2.92 emptyset ) ) =>
% 10.43/2.92 ( ( ![
% 10.43/2.92 X20:$i,
% 10.43/2.92 X22:$i,
% 10.43/2.92 X24:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X24 @ X22 ) =>
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X24 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X20 @ X22 ) ) ) ) =>
% 10.43/2.92 ( (
% 10.43/2.92 ![
% 10.43/2.92 X26:$i,
% 10.43/2.92 X28:$i,
% 10.43/2.92 X30:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X30 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X26 @ X28 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X32:$o]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X30 ) =
% 10.43/2.92 (
% 10.43/2.92 X26 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 X32 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X30 @ X28 ) =>
% 10.43/2.92 (
% 10.43/2.92 X32 ) ) =>
% 10.43/2.92 (
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% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X34:$i,
% 10.43/2.92 X36:$i,
% 10.43/2.92 X38:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X38 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X34 @ X36 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X38 ) =
% 10.43/2.92 (
% 10.43/2.92 X34 ) ) |
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X38 @ X36 ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setoftrueEq ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyinPowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyInPowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X40:$i,
% 10.43/2.92 X42:$i,
% 10.43/2.92 X44:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X42 @ X44 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X44 @ X40 ) =>
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X42 @
% 10.43/2.92 (
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% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X46:$i,
% 10.43/2.92 X48:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X48 @
% 10.43/2.92 (
% 10.43/2.92 setunion
% 10.43/2.92 @
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% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X50:$o]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X52:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X48 @ X52 ) =>
% 10.43/2.92 (
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% 10.43/2.92 (
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% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X54:$i,
% 10.43/2.92 X56:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X56 @ X54 ) =>
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X56 @
% 10.43/2.92 (
% 10.43/2.92 powerset
% 10.43/2.92 @
% 10.43/2.92 (
% 10.43/2.92 setunion
% 10.43/2.92 @
% 10.43/2.92 X54 ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuE2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 nonemptyImpWitness ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X58:$i,
% 10.43/2.92 X60:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X58 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X60 @
% 10.43/2.92 emptyset ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X58 ) =
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% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X62:$i,
% 10.43/2.92 X64:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X62 ) !=
% 10.43/2.92 (
% 10.43/2.92 X64 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 ~
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X64 @
% 10.43/2.92 (
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% 10.43/2.92 @
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% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X66:$i,
% 10.43/2.92 X68:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X66 ) =
% 10.43/2.92 (
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% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X66 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
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% 10.43/2.92 emptyset ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X70:$i,
% 10.43/2.92 X72:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X70 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X72 @
% 10.43/2.92 emptyset ) ) =>
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X72 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X70 @
% 10.43/2.92 emptyset ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X74:$i,
% 10.43/2.92 X76:$i,
% 10.43/2.92 X78:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X78 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X74 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X76 @
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% 10.43/2.92 (
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% 10.43/2.92 (
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% 10.43/2.92 (
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% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
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% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X80 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
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% 10.43/2.92 (
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% 10.43/2.92 @
% 10.43/2.92 X82 @
% 10.43/2.92 emptyset ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X84:$i,
% 10.43/2.92 X86:$i]:
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X86 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X84 @
% 10.43/2.92 (
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% 10.43/2.92 @
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% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyE1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 vacuousDall ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 quantDeMorgan1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 quantDeMorgan2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 quantDeMorgan3 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 quantDeMorgan4 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 prop2setI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 prop2set2propI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 notdexE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 notdallE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuI1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuI3 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuI2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 inCongP ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuE3u ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exu__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 emptyset__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X88:$i,
% 10.43/2.92 X90:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X88 ) =
% 10.43/2.92 (
% 10.43/2.92 X90 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X92:$i,
% 10.43/2.92 X94:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X92 ) =
% 10.43/2.92 (
% 10.43/2.92 X94 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X88 @ X92 ) =
% 10.43/2.92 (
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% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powerset__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X96:$i,
% 10.43/2.92 X98:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X96 ) =
% 10.43/2.92 (
% 10.43/2.92 X98 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setunion
% 10.43/2.92 @
% 10.43/2.92 X96 ) =
% 10.43/2.92 (
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% 10.43/2.92 @
% 10.43/2.92 X98 ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 omega__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 exuEu ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 descr__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 dsetconstr__Cong ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X100:$i,
% 10.43/2.92 X102:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X104:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X104 @
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% 10.43/2.92 (
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% 10.43/2.92 X104 @
% 10.43/2.92 X102 ) ) ) =>
% 10.43/2.92 (
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% 10.43/2.92 X100 @
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% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X106:$i,
% 10.43/2.92 X108:$i]:
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% 10.43/2.92 (
% 10.43/2.92 X106 ) =
% 10.43/2.92 (
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% 10.43/2.92 (
% 10.43/2.92 subset @
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% 10.43/2.92 (
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% 10.43/2.92 ![
% 10.43/2.92 X110:$i,
% 10.43/2.92 X112:$i]:
% 10.43/2.92 (
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% 10.43/2.92 (
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% 10.43/2.92 (
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% 10.43/2.92 (
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% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X114:$i,
% 10.43/2.92 X116:$i]:
% 10.43/2.92 (
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% 10.43/2.92 X118:$i]:
% 10.43/2.92 (
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% 10.43/2.92 (
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% 10.43/2.92 ![
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% 10.43/2.92 (
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% 10.43/2.92 emptyset @
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% 10.43/2.92 (
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% 10.43/2.92 ![
% 10.43/2.92 X122:$i,
% 10.43/2.92 X124:$i,
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% 10.43/2.92 (
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% 10.43/2.92 (
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% 10.43/2.92 (
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% 10.43/2.92 X128:$i,
% 10.43/2.92 X130:$i,
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% 10.43/2.92 (
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% 10.43/2.92 (
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% 10.43/2.92 (
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% 10.43/2.92 X134:$i,
% 10.43/2.92 X136:$i,
% 10.43/2.92 X138:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X138 @
% 10.43/2.92 X134 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ~
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X138 @
% 10.43/2.92 X136 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 ~
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 X134 @
% 10.43/2.92 X136 ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X140:$i,
% 10.43/2.92 X142:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ~
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 X140 @
% 10.43/2.92 X142 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X140 ) !=
% 10.43/2.92 (
% 10.43/2.92 X142 ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 notequalI2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X144:$i]:
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 X144 @
% 10.43/2.92 X144 ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X146:$i,
% 10.43/2.92 X148:$i,
% 10.43/2.92 X150:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 X146 @
% 10.43/2.92 X148 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 X148 @
% 10.43/2.92 X150 ) =>
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 X146 @
% 10.43/2.92 X150 ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X152:$i,
% 10.43/2.92 X154:$i]:
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 X154 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X152 @
% 10.43/2.92 X154 ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X156:$i,
% 10.43/2.92 X158:$i,
% 10.43/2.92 X160:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 X156 @
% 10.43/2.92 X160 ) =>
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 X156 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X158 @
% 10.43/2.92 X160 ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subset2powerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X162:$i,
% 10.43/2.92 X164:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 X162 @
% 10.43/2.92 X164 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 X164 @
% 10.43/2.92 X162 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X162 ) =
% 10.43/2.92 (
% 10.43/2.92 X164 ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X166:$i]:
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 subset @
% 10.43/2.92 X166 @
% 10.43/2.92 emptyset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 X166 ) =
% 10.43/2.92 (
% 10.43/2.92 emptyset ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetI1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetE1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 inPowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 powersetsubset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 sepInPowerset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 sepSubset ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binunionIL ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X168:$i,
% 10.43/2.92 X170:$i]:
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X170 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X168 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X170 @
% 10.43/2.92 emptyset ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binunionIR ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binunionEcases ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binunionE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binunionLsub ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binunionRsub ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectSubset5 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectEL ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectLsub ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectSubset2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectSubset3 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectER ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 disjointsetsI1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectRsub ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectSubset4 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 binintersectSubset1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 bs114d ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusI ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusEL ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusER ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusSubset2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusERneg ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusELneg ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusILneg ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusIRneg ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusLsub ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 setminusSubset1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 symdiffE ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 symdiffI1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 symdiffI2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 symdiffIneg1 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 symdiffIneg2 ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X172:$i,
% 10.43/2.92 X174:$i]:
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X174 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X172 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X174 @
% 10.43/2.92 emptyset ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.92 (
% 10.43/2.92 ![
% 10.43/2.92 X176:$i,
% 10.43/2.92 X178:$i]:
% 10.43/2.92 (
% 10.43/2.92 in @
% 10.43/2.92 X176 @
% 10.43/2.92 (
% 10.43/2.92 setunion
% 10.43/2.92 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X176 @
% 10.43/2.92 emptyset ) @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X176 @
% 10.43/2.92 (
% 10.43/2.92 setadjoin
% 10.43/2.92 @
% 10.43/2.92 X178 @
% 10.43/2.92 emptyset ) ) @
% 10.43/2.92 emptyset ) ) ) ) ) =>
% 10.43/2.92 (
% 10.43/2.93 (
% 10.43/2.93 ![
% 10.43/2.93 X180:$i,
% 10.43/2.93 X182:$i]:
% 10.43/2.93 (
% 10.43/2.93 in @
% 10.43/2.93 X182 @
% 10.43/2.93 (
% 10.43/2.93 setunion
% 10.43/2.93 @
% 10.43/2.93 (
% 10.43/2.93 setadjoin
% 10.43/2.93 @
% 10.43/2.93 (
% 10.43/2.93 setadjoin
% 10.43/2.93 @
% 10.43/2.93 X180 @
% 10.43/2.93 emptyset ) @
% 10.43/2.93 (
% 10.43/2.93 setadjoin
% 10.43/2.93 @
% 10.43/2.93 (
% 10.43/2.93 setadjoin
% 10.43/2.93 @
% 10.43/2.93 X180 @
% 10.43/2.93 (
% 10.43/2.93 setadjoin
% 10.43/2.93 @
% 10.43/2.93 X182 @
% 10.43/2.93 emptyset ) ) @
% 10.43/2.93 emptyset ) ) ) ) ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 kpairiskpair ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 kpairp ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 ![
% 10.43/2.93 X184:$i,
% 10.43/2.93 X186:$i]:
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 in @
% 10.43/2.93 X186 @
% 10.43/2.93 X184 ) =>
% 10.43/2.93 (
% 10.43/2.93 subset @
% 10.43/2.93 (
% 10.43/2.93 setadjoin
% 10.43/2.93 @
% 10.43/2.93 X186 @
% 10.43/2.93 emptyset ) @
% 10.43/2.93 X184 ) ) ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 singletoninpowerset ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 singletoninpowunion ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 ![
% 10.43/2.93 X188:$i,
% 10.43/2.93 X190:$i,
% 10.43/2.93 X192:$i]:
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 in @
% 10.43/2.93 X192 @
% 10.43/2.93 (
% 10.43/2.93 setadjoin
% 10.43/2.93 @
% 10.43/2.93 X188 @
% 10.43/2.93 (
% 10.43/2.93 setadjoin
% 10.43/2.93 @
% 10.43/2.93 X190 @
% 10.43/2.93 emptyset ) ) ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 X192 ) =
% 10.43/2.93 (
% 10.43/2.93 X188 ) ) |
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 X192 ) =
% 10.43/2.93 (
% 10.43/2.93 X190 ) ) ) ) ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 upairsubunion ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 upairinpowunion ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 ubforcartprodlem1 ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 ubforcartprodlem2 ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 ubforcartprodlem3 ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 cartprodpairin ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 cartprodmempair1 ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 cartprodmempair ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 ![
% 10.43/2.93 X194:$i,
% 10.43/2.93 X196:$i]:
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 in @
% 10.43/2.93 X196 @
% 10.43/2.93 (
% 10.43/2.93 setunion
% 10.43/2.93 @
% 10.43/2.93 X194 ) ) =>
% 10.43/2.93 (
% 10.43/2.93 ?[
% 10.43/2.93 X198:$i]:
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 in @
% 10.43/2.93 X196 @
% 10.43/2.93 X198 ) &
% 10.43/2.93 (
% 10.43/2.93 in @
% 10.43/2.93 X198 @
% 10.43/2.93 X194 ) ) ) ) ) =>
% 10.43/2.93 (
% 10.43/2.93 (
% 10.43/2.93 ![
% 10.43/2.93 X200:$i]:
% 10.43/2.93 (
% 10.43/2.93 subset @
% 10.43/2.93 (
% 10.43/2.93 setunion
% 10.43/2.93 @
% 10.43/2.93 (
% 10.43/2.93 setadjoin
% 10.43/2.93 @
% 10.43/2.93 X200 @
% 10.43/2.93 emptyset ) ) @
% 10.43/2.93 X200 ) ) =>
% 10.43/2.93 (
% 10.43/2.93 ![
% 10.43/2.93 X202:$i]:
% 10.43/2.93 (
% 10.43/2.93 subset @
% 10.43/2.93 X202 @
% 10.43/2.93 (
% 10.43/2.93 setunion
% 10.43/2.93 @
% 10.43/2.93 (
% 10.43/2.93 setadjoin
% 10.43/2.93 @
% 10.43/2.93 X202 @
% 10.43/2.93 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 10.43/2.93 inference('cnf.neg', [status(esa)], [zf_stmt_5])).
% 10.43/2.93 thf(zip_derived_cl85, plain,
% 10.43/2.93 (~ (subset @ sk__103 @ (setunion @ (setadjoin @ sk__103 @ emptyset)))),
% 10.43/2.93 inference('cnf', [status(esa)], [zf_stmt_6])).
% 10.43/2.93 thf(zip_derived_cl47, plain,
% 10.43/2.93 (![X35 : $i, X36 : $i]:
% 10.43/2.93 ( (subset @ X35 @ X36) | ~ (in @ (sk__104 @ X36 @ X35) @ X36))),
% 10.43/2.93 inference('cnf', [status(esa)], [zf_stmt_6])).
% 10.43/2.93 thf(zip_derived_cl22, plain,
% 10.43/2.93 (![X8 : $i, X9 : $i]: (in @ X8 @ (setadjoin @ X8 @ X9))),
% 10.43/2.93 inference('cnf', [status(esa)], [zf_stmt_6])).
% 10.43/2.93 thf(zip_derived_cl48, plain,
% 10.43/2.93 (![X35 : $i, X36 : $i]:
% 10.43/2.93 ( (subset @ X35 @ X36) | (in @ (sk__104 @ X36 @ X35) @ X35))),
% 10.43/2.93 inference('cnf', [status(esa)], [zf_stmt_6])).
% 10.43/2.93 thf(zip_derived_cl27, plain,
% 10.43/2.93 (![X16 : $i, X17 : $i, X18 : $i]:
% 10.43/2.93 ( (in @ X16 @ (setunion @ X17))
% 10.43/2.93 | ~ (in @ X16 @ X18)
% 10.43/2.93 | ~ (in @ X18 @ X17))),
% 10.43/2.93 inference('cnf', [status(esa)], [zf_stmt_6])).
% 10.43/2.93 thf(zip_derived_cl528, plain,
% 10.43/2.93 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.43/2.93 ( (subset @ X0 @ X1)
% 10.43/2.93 | ~ (in @ X0 @ X2)
% 10.43/2.93 | (in @ (sk__104 @ X1 @ X0) @ (setunion @ X2)))),
% 10.43/2.93 inference('sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl27])).
% 10.43/2.93 thf(zip_derived_cl3504, plain,
% 10.43/2.93 (![X0 : $i, X1 : $i, X2 : $i]:
% 10.43/2.93 ( (in @ (sk__104 @ X2 @ X1) @ (setunion @ (setadjoin @ X1 @ X0)))
% 10.43/2.93 | (subset @ X1 @ X2))),
% 10.43/2.93 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl528])).
% 10.43/2.93 thf(zip_derived_cl3637, plain,
% 10.43/2.93 (![X0 : $i, X1 : $i]:
% 10.43/2.93 ( (subset @ X1 @ (setunion @ (setadjoin @ X1 @ X0)))
% 10.43/2.93 | (subset @ X1 @ (setunion @ (setadjoin @ X1 @ X0))))),
% 10.43/2.93 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl3504])).
% 10.43/2.93 thf(zip_derived_cl3662, plain,
% 10.43/2.93 (![X0 : $i, X1 : $i]: (subset @ X1 @ (setunion @ (setadjoin @ X1 @ X0)))),
% 10.43/2.93 inference('simplify', [status(thm)], [zip_derived_cl3637])).
% 10.43/2.93 thf(zip_derived_cl3670, plain, ($false),
% 10.43/2.93 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl3662])).
% 10.43/2.93
% 10.43/2.93 % SZS output end Refutation
% 10.43/2.93
% 10.43/2.93
% 10.43/2.93 % Terminating...
% 10.83/3.06 % Runner terminated.
% 10.83/3.09 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------