%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU629^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.iNKPUqEdWB true
% Computer : n029.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 04:55:26 PM UTC 2025
% Result : Theorem 3.85s 3.46s
% Output : Refutation 3.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/1.10 % Problem : SEU629^1 : TPTP v9.2.0. Released v3.7.0.
% 0.12/1.19 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.iNKPUqEdWB true
% 0.12/1.60 % Computer : n029.cluster.edu
% 0.12/1.60 % Model : x86_64 x86_64
% 0.12/1.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/1.60 % Memory : 8042.1875MB
% 0.12/1.60 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/1.60 % CPULimit : 300
% 0.12/1.60 % WCLimit : 300
% 0.12/1.60 % DateTime : Wed Oct 1 16:13:25 EDT 2025
% 0.12/1.62 % CPUTime :
% 0.12/1.62 % Running portfolio for 300 s
% 0.12/1.62 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/1.63 % Number of cores: 8
% 0.12/1.65 % Python version: Python 3.6.8
% 0.19/1.66 % Running in HO mode
% 0.55/2.31 % Total configuration time : 828
% 0.55/2.31 % Estimated wc time : 1656
% 0.55/2.31 % Estimated cpu time (8 cpus) : 207.0
% 0.67/2.70 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.67/2.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.67/2.77 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.67/2.79 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.67/2.81 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.67/2.81 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.67/2.82 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.67/2.84 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 3.85/3.46 % Solved by lams/40_c_ic.sh.
% 3.85/3.46 % done 246 iterations in 0.498s
% 3.85/3.46 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 3.85/3.46 % SZS output start Refutation
% 3.85/3.46 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 3.85/3.46 thf(notdexE_type, type, notdexE: $o).
% 3.85/3.46 thf(setunionAx_type, type, setunionAx: $o).
% 3.85/3.46 thf(setminusELneg_type, type, setminusELneg: $o).
% 3.85/3.46 thf(powersetE_type, type, powersetE: $o).
% 3.85/3.46 thf(omegaSAx_type, type, omegaSAx: $o).
% 3.85/3.46 thf(exuI1_type, type, exuI1: $o).
% 3.85/3.46 thf(exuI2_type, type, exuI2: $o).
% 3.85/3.46 thf(notequalI2_type, type, notequalI2: $o).
% 3.85/3.46 thf(setukpairIR_type, type, setukpairIR: $o).
% 3.85/3.46 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 3.85/3.46 thf(setminusILneg_type, type, setminusILneg: $o).
% 3.85/3.46 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 3.85/3.46 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 3.85/3.46 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 3.85/3.46 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 3.85/3.46 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 3.85/3.46 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 3.85/3.46 thf(setukpairIL_type, type, setukpairIL: $o).
% 3.85/3.46 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 3.85/3.46 thf(binunionE_type, type, binunionE: $o).
% 3.85/3.46 thf(setext_type, type, setext: $o).
% 3.85/3.46 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 3.85/3.46 thf(upairsubunion_type, type, upairsubunion: $o).
% 3.85/3.46 thf(descr__Cong_type, type, descr__Cong: $o).
% 3.85/3.46 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 3.85/3.46 thf(in_type, type, in: $i > $i > $o).
% 3.85/3.46 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 3.85/3.46 thf(binunion_type, type, binunion: $i > $i > $i).
% 3.85/3.46 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 3.85/3.46 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 3.85/3.46 thf(symdiffI2_type, type, symdiffI2: $o).
% 3.85/3.46 thf(upairset2IR_type, type, upairset2IR: $o).
% 3.85/3.46 thf(subsetE_type, type, subsetE: $o).
% 3.85/3.46 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 3.85/3.46 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 3.85/3.46 thf(setbeta_type, type, setbeta: $o).
% 3.85/3.46 thf(eqinunit_type, type, eqinunit: $o).
% 3.85/3.46 thf(upairsetIL_type, type, upairsetIL: $o).
% 3.85/3.46 thf(powersetI1_type, type, powersetI1: $o).
% 3.85/3.46 thf(sk__64_type, type, sk__64: $i).
% 3.85/3.46 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 3.85/3.46 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 3.85/3.46 thf(powersetAx_type, type, powersetAx: $o).
% 3.85/3.46 thf(sk__67_type, type, sk__67: $i).
% 3.85/3.46 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 3.85/3.46 thf(powersetI_type, type, powersetI: $o).
% 3.85/3.46 thf(upairsetIR_type, type, upairsetIR: $o).
% 3.85/3.46 thf(inCongP_type, type, inCongP: $o).
% 3.85/3.46 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 3.85/3.46 thf(exuE3e_type, type, exuE3e: $o).
% 3.85/3.46 thf(emptysetE_type, type, emptysetE: $o).
% 3.85/3.46 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 3.85/3.46 thf(setunionI_type, type, setunionI: $o).
% 3.85/3.46 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 3.85/3.46 thf(prop2setI_type, type, prop2setI: $o).
% 3.85/3.46 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 3.85/3.46 thf(setminusER_type, type, setminusER: $o).
% 3.85/3.46 thf(exuE2_type, type, exuE2: $o).
% 3.85/3.46 thf(emptyset_type, type, emptyset: $i).
% 3.85/3.46 thf(powersetsubset_type, type, powersetsubset: $o).
% 3.85/3.46 thf(upairset2E_type, type, upairset2E: $o).
% 3.85/3.46 thf(subPowSU_type, type, subPowSU: $o).
% 3.85/3.46 thf(notequalI1_type, type, notequalI1: $o).
% 3.85/3.46 thf(notinemptyset_type, type, notinemptyset: $o).
% 3.85/3.46 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 3.85/3.46 thf(subsetTrans_type, type, subsetTrans: $o).
% 3.85/3.46 thf(setminusI_type, type, setminusI: $o).
% 3.85/3.46 thf(binunionIL_type, type, binunionIL: $o).
% 3.85/3.46 thf(subsetE2_type, type, subsetE2: $o).
% 3.85/3.46 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 3.85/3.46 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 3.85/3.46 thf(setextsub_type, type, setextsub: $o).
% 3.85/3.46 thf(binunionLsub_type, type, binunionLsub: $o).
% 3.85/3.46 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 3.85/3.46 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 3.85/3.46 thf(setunionE_type, type, setunionE: $o).
% 3.85/3.46 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 3.85/3.46 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 3.85/3.46 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 3.85/3.46 thf(binunionIR_type, type, binunionIR: $o).
% 3.85/3.46 thf(setadjoinE_type, type, setadjoinE: $o).
% 3.85/3.46 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 3.85/3.46 thf(exuE1_type, type, exuE1: $o).
% 3.85/3.46 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 3.85/3.46 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 3.85/3.46 thf(setminusLsub_type, type, setminusLsub: $o).
% 3.85/3.46 thf(notinsingleton_type, type, notinsingleton: $o).
% 3.85/3.46 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 3.85/3.46 thf(exuEu_type, type, exuEu: $o).
% 3.85/3.46 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 3.85/3.46 thf(upairsetE_type, type, upairsetE: $o).
% 3.85/3.46 thf(omega0Ax_type, type, omega0Ax: $o).
% 3.85/3.46 thf(notsubsetI_type, type, notsubsetI: $o).
% 3.85/3.46 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 3.85/3.46 thf(setextAx_type, type, setextAx: $o).
% 3.85/3.46 thf(kpair_type, type, kpair: $i > $i > $i).
% 3.85/3.46 thf(powersetE1_type, type, powersetE1: $o).
% 3.85/3.46 thf(bs114d_type, type, bs114d: $o).
% 3.85/3.46 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 3.85/3.46 thf(iskpair_type, type, iskpair: $i > $o).
% 3.85/3.46 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 3.85/3.46 thf(subsetI1_type, type, subsetI1: $o).
% 3.85/3.46 thf(symdiffE_type, type, symdiffE: $o).
% 3.85/3.46 thf(descrp_type, type, descrp: $o).
% 3.85/3.46 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 3.85/3.46 thf(foundationAx_type, type, foundationAx: $o).
% 3.85/3.46 thf(emptysetAx_type, type, emptysetAx: $o).
% 3.85/3.46 thf(emptyI_type, type, emptyI: $o).
% 3.85/3.46 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 3.85/3.46 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 3.85/3.46 thf(binintersectEL_type, type, binintersectEL: $o).
% 3.85/3.46 thf(emptyE1_type, type, emptyE1: $o).
% 3.85/3.46 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 3.85/3.46 thf(vacuousDall_type, type, vacuousDall: $o).
% 3.85/3.46 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 3.85/3.46 thf(binintersectI_type, type, binintersectI: $o).
% 3.85/3.46 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 3.85/3.46 thf(symdiffI1_type, type, symdiffI1: $o).
% 3.85/3.46 thf(subsetI2_type, type, subsetI2: $o).
% 3.85/3.46 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 3.85/3.46 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 3.85/3.46 thf(setminusERneg_type, type, setminusERneg: $o).
% 3.85/3.46 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 3.85/3.46 thf(omega__Cong_type, type, omega__Cong: $o).
% 3.85/3.46 thf(subsetRefl_type, type, subsetRefl: $o).
% 3.85/3.46 thf(uniqinunit_type, type, uniqinunit: $o).
% 3.85/3.46 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 3.85/3.46 thf(prop2setE_type, type, prop2setE: $o).
% 3.85/3.46 thf(binunionEcases_type, type, binunionEcases: $o).
% 3.85/3.46 thf(nonemptyI_type, type, nonemptyI: $o).
% 3.85/3.46 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 3.85/3.46 thf(exuE3u_type, type, exuE3u: $o).
% 3.85/3.46 thf(setminusEL_type, type, setminusEL: $o).
% 3.85/3.46 thf(sepSubset_type, type, sepSubset: $o).
% 3.85/3.46 thf(singletonsubset_type, type, singletonsubset: $o).
% 3.85/3.46 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 3.85/3.46 thf(exuI3_type, type, exuI3: $o).
% 3.85/3.46 thf(notdallE_type, type, notdallE: $o).
% 3.85/3.46 thf(binintersectER_type, type, binintersectER: $o).
% 3.85/3.46 thf(powerset_type, type, powerset: $i > $i).
% 3.85/3.46 thf(kpairp_type, type, kpairp: $o).
% 3.85/3.46 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 3.85/3.46 thf(sk__66_type, type, sk__66: $i).
% 3.85/3.46 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 3.85/3.46 thf(exu__Cong_type, type, exu__Cong: $o).
% 3.85/3.46 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 3.85/3.46 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 3.85/3.46 thf(replAx_type, type, replAx: $o).
% 3.85/3.46 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 3.85/3.46 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 3.85/3.46 thf(secondinupair_type, type, secondinupair: $o).
% 3.85/3.46 thf(inPowerset_type, type, inPowerset: $o).
% 3.85/3.46 thf(sk__65_type, type, sk__65: $i).
% 3.85/3.46 thf(subset_type, type, subset: $i > $i > $o).
% 3.85/3.46 thf(in__Cong_type, type, in__Cong: $o).
% 3.85/3.46 thf(binunionRsub_type, type, binunionRsub: $o).
% 3.85/3.46 thf(subset2powerset_type, type, subset2powerset: $o).
% 3.85/3.46 thf(ubforcartprodlem2, axiom, ubforcartprodlem2 =
% 3.85/3.46 (![A:$i,B:$i,Xx:$i]:
% 3.85/3.46 ( ( in @ Xx @ A ) =>
% 3.85/3.46 ( ![Xy:$i]:
% 3.85/3.46 ( ( in @ Xy @ B ) =>
% 3.85/3.46 ( in @
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ Xx @ emptyset ) @
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 3.85/3.46 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 3.85/3.46 thf('0', plain,
% 3.85/3.46 (( ubforcartprodlem2 ) =
% 3.85/3.46 ( ![X4:$i,X6:$i,X8:$i]:
% 3.85/3.46 ( ( in @ X8 @ X4 ) =>
% 3.85/3.46 ( ![X10:$i]:
% 3.85/3.46 ( ( in @ X10 @ X6 ) =>
% 3.85/3.46 ( in @
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ X8 @ emptyset ) @
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 3.85/3.46 emptyset ) ) @
% 3.85/3.46 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(ubforcartprodlem1, axiom, ubforcartprodlem1 =
% 3.85/3.46 (![A:$i,B:$i,Xx:$i]:
% 3.85/3.46 ( ( in @ Xx @ A ) =>
% 3.85/3.46 ( ![Xy:$i]:
% 3.85/3.46 ( ( in @ Xy @ B ) =>
% 3.85/3.46 ( subset @
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ Xx @ emptyset ) @
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 3.85/3.46 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 3.85/3.46 thf('1', plain,
% 3.85/3.46 (( ubforcartprodlem1 ) =
% 3.85/3.46 ( ![X4:$i,X6:$i,X8:$i]:
% 3.85/3.46 ( ( in @ X8 @ X4 ) =>
% 3.85/3.46 ( ![X10:$i]:
% 3.85/3.46 ( ( in @ X10 @ X6 ) =>
% 3.85/3.46 ( subset @
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ X8 @ emptyset ) @
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 3.85/3.46 emptyset ) ) @
% 3.85/3.46 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(upairinpowunion, axiom, upairinpowunion =
% 3.85/3.46 (![A:$i,B:$i,Xx:$i]:
% 3.85/3.46 ( ( in @ Xx @ A ) =>
% 3.85/3.46 ( ![Xy:$i]:
% 3.85/3.46 ( ( in @ Xy @ B ) =>
% 3.85/3.46 ( in @
% 3.85/3.46 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 3.85/3.46 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 3.85/3.46 thf('2', plain,
% 3.85/3.46 (( upairinpowunion ) =
% 3.85/3.46 ( ![X4:$i,X6:$i,X8:$i]:
% 3.85/3.46 ( ( in @ X8 @ X4 ) =>
% 3.85/3.46 ( ![X10:$i]:
% 3.85/3.46 ( ( in @ X10 @ X6 ) =>
% 3.85/3.46 ( in @
% 3.85/3.46 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 3.85/3.46 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(upairsubunion, axiom, upairsubunion =
% 3.85/3.46 (![A:$i,B:$i,Xx:$i]:
% 3.85/3.46 ( ( in @ Xx @ A ) =>
% 3.85/3.46 ( ![Xy:$i]:
% 3.85/3.46 ( ( in @ Xy @ B ) =>
% 3.85/3.46 ( subset @
% 3.85/3.46 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 3.85/3.46 ( binunion @ A @ B ) ) ) ) ))).
% 3.85/3.46 thf('3', plain,
% 3.85/3.46 (( upairsubunion ) =
% 3.85/3.46 ( ![X4:$i,X6:$i,X8:$i]:
% 3.85/3.46 ( ( in @ X8 @ X4 ) =>
% 3.85/3.46 ( ![X10:$i]:
% 3.85/3.46 ( ( in @ X10 @ X6 ) =>
% 3.85/3.46 ( subset @
% 3.85/3.46 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 3.85/3.46 ( binunion @ X4 @ X6 ) ) ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(singletoninpowunion, axiom, singletoninpowunion =
% 3.85/3.46 (![A:$i,B:$i,Xx:$i]:
% 3.85/3.46 ( ( in @ Xx @ A ) =>
% 3.85/3.46 ( in @
% 3.85/3.46 ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ))).
% 3.85/3.46 thf('4', plain,
% 3.85/3.46 (( singletoninpowunion ) =
% 3.85/3.46 ( ![X4:$i,X6:$i,X8:$i]:
% 3.85/3.46 ( ( in @ X8 @ X4 ) =>
% 3.85/3.46 ( in @
% 3.85/3.46 ( setadjoin @ X8 @ emptyset ) @
% 3.85/3.46 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(singletoninpowerset, axiom, singletoninpowerset =
% 3.85/3.46 (![A:$i,Xx:$i]:
% 3.85/3.46 ( ( in @ Xx @ A ) =>
% 3.85/3.46 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 3.85/3.46 thf('5', plain,
% 3.85/3.46 (( singletoninpowerset ) =
% 3.85/3.46 ( ![X4:$i,X6:$i]:
% 3.85/3.46 ( ( in @ X6 @ X4 ) =>
% 3.85/3.46 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(kpairp, axiom, kpairp =
% 3.85/3.46 (![Xx:$i,Xy:$i]: ( iskpair @ ( kpair @ Xx @ Xy ) ))).
% 3.85/3.46 thf('6', plain,
% 3.85/3.46 (( kpairp ) = ( ![X4:$i,X6:$i]: ( iskpair @ ( kpair @ X4 @ X6 ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(kpair, axiom,(( kpair ) =
% 3.85/3.46 (^[Xx:$i,Xy:$i]:
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ Xx @ emptyset ) @
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )))).
% 3.85/3.46 thf('7', plain,
% 3.85/3.46 (( kpair ) =
% 3.85/3.46 ( ^[Xx:$i,Xy:$i]:
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ Xx @ emptyset ) @
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )),
% 3.85/3.46 inference('simplify_rw_rule', [status(thm)], [kpair])).
% 3.85/3.46 thf('8', plain,
% 3.85/3.46 (( kpair ) =
% 3.85/3.46 ( ^[V_1:$i,V_2:$i]:
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ V_1 @ emptyset ) @
% 3.85/3.46 ( setadjoin @
% 3.85/3.46 ( setadjoin @ V_1 @ ( setadjoin @ V_2 @ emptyset ) ) @ emptyset ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(binunionRsub, axiom, binunionRsub =
% 3.85/3.46 (![A:$i,B:$i]: ( subset @ B @ ( binunion @ A @ B ) ))).
% 3.85/3.46 thf('9', plain,
% 3.85/3.46 (( binunionRsub ) =
% 3.85/3.46 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(binunionLsub, axiom, binunionLsub =
% 3.85/3.46 (![A:$i,B:$i]: ( subset @ A @ ( binunion @ A @ B ) ))).
% 3.85/3.46 thf('10', plain,
% 3.85/3.46 (( binunionLsub ) =
% 3.85/3.46 ( ![X4:$i,X6:$i]: ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(binunionE, axiom, binunionE =
% 3.85/3.46 (![A:$i,B:$i,Xx:$i]:
% 3.85/3.46 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 3.85/3.46 ( ( in @ Xx @ A ) | ( in @ Xx @ B ) ) ))).
% 3.85/3.46 thf('11', plain,
% 3.85/3.46 (( binunionE ) =
% 3.85/3.46 ( ![X4:$i,X6:$i,X8:$i]:
% 3.85/3.46 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 3.85/3.46 ( ( in @ X8 @ X4 ) | ( in @ X8 @ X6 ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(binunionEcases, axiom, binunionEcases =
% 3.85/3.46 (![A:$i,B:$i,Xx:$i,Xphi:$o]:
% 3.85/3.46 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 3.85/3.46 ( ( ( in @ Xx @ A ) => ( Xphi ) ) =>
% 3.85/3.46 ( ( ( in @ Xx @ B ) => ( Xphi ) ) => ( Xphi ) ) ) ))).
% 3.85/3.46 thf('12', plain,
% 3.85/3.46 (( binunionEcases ) =
% 3.85/3.46 ( ![X4:$i,X6:$i,X8:$i,X10:$o]:
% 3.85/3.46 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 3.85/3.46 ( ( ( in @ X8 @ X4 ) => ( X10 ) ) =>
% 3.85/3.46 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(binunionIR, axiom, binunionIR =
% 3.85/3.46 (![A:$i,B:$i,Xx:$i]:
% 3.85/3.46 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 3.85/3.46 thf('13', plain,
% 3.85/3.46 (( binunionIR ) =
% 3.85/3.46 ( ![X4:$i,X6:$i,X8:$i]:
% 3.85/3.46 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(binunionIL, axiom, binunionIL =
% 3.85/3.46 (![A:$i,B:$i,Xx:$i]:
% 3.85/3.46 ( ( in @ Xx @ A ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 3.85/3.46 thf('14', plain,
% 3.85/3.46 (( binunionIL ) =
% 3.85/3.46 ( ![X4:$i,X6:$i,X8:$i]:
% 3.85/3.46 ( ( in @ X8 @ X4 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(powersetsubset, axiom, powersetsubset =
% 3.85/3.46 (![A:$i,B:$i]:
% 3.85/3.46 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 3.85/3.46 thf('15', plain,
% 3.85/3.46 (( powersetsubset ) =
% 3.85/3.46 ( ![X4:$i,X6:$i]:
% 3.85/3.46 ( ( subset @ X4 @ X6 ) =>
% 3.85/3.46 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 3.85/3.46 thf('16', plain,
% 3.85/3.46 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(powersetE1, axiom, powersetE1 =
% 3.85/3.46 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 3.85/3.46 thf('17', plain,
% 3.85/3.46 (( powersetE1 ) =
% 3.85/3.46 ( ![X4:$i,X6:$i]:
% 3.85/3.46 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(powersetI1, axiom, powersetI1 =
% 3.85/3.46 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 3.85/3.46 thf('18', plain,
% 3.85/3.46 (( powersetI1 ) =
% 3.85/3.46 ( ![X4:$i,X6:$i]:
% 3.85/3.46 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(subset2powerset, axiom, subset2powerset =
% 3.85/3.46 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 3.85/3.46 thf('19', plain,
% 3.85/3.46 (( subset2powerset ) =
% 3.85/3.46 ( ![X4:$i,X6:$i]:
% 3.85/3.46 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(powerset__Cong, axiom, powerset__Cong =
% 3.85/3.46 (![A:$i,B:$i]:
% 3.85/3.46 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 3.85/3.46 thf('20', plain,
% 3.85/3.46 (( powerset__Cong ) =
% 3.85/3.46 ( ![X4:$i,X6:$i]:
% 3.85/3.46 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(powersetE, axiom, powersetE =
% 3.85/3.46 (![A:$i,B:$i,Xx:$i]:
% 3.85/3.46 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 3.85/3.46 thf('21', plain,
% 3.85/3.46 (( powersetE ) =
% 3.85/3.46 ( ![X4:$i,X6:$i,X8:$i]:
% 3.85/3.46 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 3.85/3.46 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(emptyInPowerset, axiom, emptyInPowerset =
% 3.85/3.46 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 3.85/3.46 thf('22', plain,
% 3.85/3.46 (( emptyInPowerset ) =
% 3.85/3.46 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(emptyinPowerset, axiom, emptyinPowerset =
% 3.85/3.46 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 3.85/3.46 thf('23', plain,
% 3.85/3.46 (( emptyinPowerset ) =
% 3.85/3.46 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(powersetI, axiom, powersetI =
% 3.85/3.46 (![A:$i,B:$i]:
% 3.85/3.46 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 3.85/3.46 ( in @ B @ ( powerset @ A ) ) ))).
% 3.85/3.46 thf('24', plain,
% 3.85/3.46 (( powersetI ) =
% 3.85/3.46 ( ![X4:$i,X6:$i]:
% 3.85/3.46 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 3.85/3.46 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(powersetAx, axiom, powersetAx =
% 3.85/3.46 (![A:$i,B:$i]:
% 3.85/3.46 ( ( in @ B @ ( powerset @ A ) ) <=>
% 3.85/3.46 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 3.85/3.46 thf('25', plain,
% 3.85/3.46 (( powersetAx ) =
% 3.85/3.46 ( ![X4:$i,X6:$i]:
% 3.85/3.46 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.85/3.46 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 3.85/3.46 define([status(thm)])).
% 3.85/3.46 thf(ubforcartprodlem3, conjecture,
% 3.85/3.46 (( setextAx ) =>
% 3.85/3.46 ( ( emptysetAx ) =>
% 3.85/3.46 ( ( setadjoinAx ) =>
% 3.85/3.46 ( ( powersetAx ) =>
% 3.85/3.46 ( ( setunionAx ) =>
% 3.85/3.46 ( ( omega0Ax ) =>
% 3.85/3.46 ( ( omegaSAx ) =>
% 3.85/3.46 ( ( omegaIndAx ) =>
% 3.85/3.46 ( ( replAx ) =>
% 3.85/3.46 ( ( foundationAx ) =>
% 3.85/3.46 ( ( wellorderingAx ) =>
% 3.85/3.46 ( ( descrp ) =>
% 3.85/3.46 ( ( dsetconstrI ) =>
% 3.85/3.46 ( ( dsetconstrEL ) =>
% 3.85/3.46 ( ( dsetconstrER ) =>
% 3.85/3.46 ( ( exuE1 ) =>
% 3.85/3.46 ( ( prop2setE ) =>
% 3.85/3.46 ( ( emptysetE ) =>
% 3.85/3.46 ( ( emptysetimpfalse ) =>
% 3.85/3.46 ( ( notinemptyset ) =>
% 3.85/3.46 ( ( exuE3e ) =>
% 3.85/3.46 ( ( setext ) =>
% 3.85/3.46 ( ( emptyI ) =>
% 3.85/3.46 ( ( noeltsimpempty ) =>
% 3.85/3.46 ( ( setbeta ) =>
% 3.85/3.46 ( ( nonemptyE1 ) =>
% 3.85/3.46 ( ( nonemptyI ) =>
% 3.85/3.46 ( ( nonemptyI1 ) =>
% 3.85/3.46 ( ( setadjoinIL ) =>
% 3.85/3.46 ( ( emptyinunitempty ) =>
% 3.85/3.46 ( ( setadjoinIR ) =>
% 3.85/3.46 ( ( setadjoinE ) =>
% 3.85/3.46 ( (
% 3.85/3.46 setadjoinOr ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setoftrueEq ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 powersetI ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 emptyinPowerset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 emptyInPowerset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 powersetE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setunionI ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setunionE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subPowSU ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exuE2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 nonemptyImpWitness ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 uniqinunit ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 notinsingleton ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 eqinunit ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 singletonsswitch ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 upairsetE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 upairsetIL ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 upairsetIR ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 emptyE1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 vacuousDall ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 quantDeMorgan1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 quantDeMorgan2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 quantDeMorgan3 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 quantDeMorgan4 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 prop2setI ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 prop2set2propI ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 notdexE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 notdallE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exuI1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exuI3 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exuI2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 inCongP ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exuE3u ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exu__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 emptyset__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setadjoin__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 powerset__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setunion__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 omega__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exuEu ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 descr__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 dsetconstr__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetI1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 eqimpsubset2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 eqimpsubset1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetI2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 emptysetsubset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetE2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 notsubsetI ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 notequalI1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 notequalI2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetRefl ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetTrans ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setadjoinSub ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setadjoinSub2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subset2powerset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setextsub ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetemptysetimpeq ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 powersetI1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 powersetE1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 inPowerset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 powersetsubset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 sepInPowerset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 sepSubset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binunionIL ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 upairset2IR ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binunionIR ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binunionEcases ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binunionE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binunionLsub ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binunionRsub ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectI ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectSubset5 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectEL ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectLsub ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectSubset2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectSubset3 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectER ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 disjointsetsI1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectRsub ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectSubset4 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectSubset1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 bs114d ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusI ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusEL ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusER ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusSubset2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusERneg ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusELneg ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusILneg ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusIRneg ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusLsub ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusSubset1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 symdiffE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 symdiffI1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 symdiffI2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 symdiffIneg1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 symdiffIneg2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 secondinupair ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setukpairIL ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setukpairIR ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 kpairiskpair ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 kpairp ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 singletonsubset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 singletoninpowerset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 singletoninpowunion ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 upairset2E ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 upairsubunion ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 upairinpowunion ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ubforcartprodlem1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ubforcartprodlem2 ) =>
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 A:$i,B:$i,
% 3.85/3.46 Xx:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 Xx @ A ) =>
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 Xy:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 Xy @ B ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 (
% 3.85/3.46 kpair @
% 3.85/3.46 Xx @ Xy ) @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 (
% 3.85/3.46 binunion @
% 3.85/3.46 A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.85/3.46 thf(zf_stmt_0, conjecture,
% 3.85/3.46 (( setextAx ) =>
% 3.85/3.46 ( ( emptysetAx ) =>
% 3.85/3.46 ( ( setadjoinAx ) =>
% 3.85/3.46 ( ( ![X4:$i,X6:$i]:
% 3.85/3.46 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.85/3.46 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 3.85/3.46 ( ( setunionAx ) =>
% 3.85/3.46 ( ( omega0Ax ) =>
% 3.85/3.46 ( ( omegaSAx ) =>
% 3.85/3.46 ( ( omegaIndAx ) =>
% 3.85/3.46 ( ( replAx ) =>
% 3.85/3.46 ( ( foundationAx ) =>
% 3.85/3.46 ( ( wellorderingAx ) =>
% 3.85/3.46 ( ( descrp ) =>
% 3.85/3.46 ( ( dsetconstrI ) =>
% 3.85/3.46 ( ( dsetconstrEL ) =>
% 3.85/3.46 ( ( dsetconstrER ) =>
% 3.85/3.46 ( ( exuE1 ) =>
% 3.85/3.46 ( ( prop2setE ) =>
% 3.85/3.46 ( ( emptysetE ) =>
% 3.85/3.46 ( ( emptysetimpfalse ) =>
% 3.85/3.46 ( ( notinemptyset ) =>
% 3.85/3.46 ( ( exuE3e ) =>
% 3.85/3.46 ( ( setext ) =>
% 3.85/3.46 ( ( emptyI ) =>
% 3.85/3.46 ( ( noeltsimpempty ) =>
% 3.85/3.46 ( ( setbeta ) =>
% 3.85/3.46 ( ( nonemptyE1 ) =>
% 3.85/3.46 ( ( nonemptyI ) =>
% 3.85/3.46 ( ( nonemptyI1 ) =>
% 3.85/3.46 ( ( setadjoinIL ) =>
% 3.85/3.46 ( ( emptyinunitempty ) =>
% 3.85/3.46 ( ( setadjoinIR ) =>
% 3.85/3.46 ( ( setadjoinE ) =>
% 3.85/3.46 ( (
% 3.85/3.46 setadjoinOr ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setoftrueEq ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X10:$i,
% 3.85/3.46 X12:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X14:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X14 @ X12 ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X14 @ X10 ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X12 @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X10 ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X16:$i]:
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 emptyset @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X16 ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X18:$i]:
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 emptyset @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X18 ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X20:$i,
% 3.85/3.46 X22:$i,
% 3.85/3.46 X24:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X22 @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X20 ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X24 @ X22 ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X24 @ X20 ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setunionI ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setunionE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subPowSU ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exuE2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 nonemptyImpWitness ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 uniqinunit ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 notinsingleton ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 eqinunit ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 singletonsswitch ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 upairsetE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 upairsetIL ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 upairsetIR ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 emptyE1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 vacuousDall ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 quantDeMorgan1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 quantDeMorgan2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 quantDeMorgan3 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 quantDeMorgan4 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 prop2setI ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 prop2set2propI ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 notdexE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 notdallE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exuI1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exuI3 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exuI2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 inCongP ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exuE3u ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exu__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 emptyset__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setadjoin__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X26:$i,
% 3.85/3.46 X28:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 X26 ) =
% 3.85/3.46 (
% 3.85/3.46 X28 ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X26 ) =
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X28 ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setunion__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 omega__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 exuEu ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 descr__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 dsetconstr__Cong ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetI1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 eqimpsubset2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 eqimpsubset1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetI2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 emptysetsubset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetE2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 notsubsetI ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 notequalI1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 notequalI2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetRefl ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetTrans ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setadjoinSub ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setadjoinSub2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X30:$i,
% 3.85/3.46 X32:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subset @
% 3.85/3.46 X30 @ X32 ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X30 @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X32 ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setextsub ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subsetemptysetimpeq ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X34:$i,
% 3.85/3.46 X36:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subset @
% 3.85/3.46 X36 @ X34 ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X36 @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X34 ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X38:$i,
% 3.85/3.46 X40:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X40 @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X38 ) ) =>
% 3.85/3.46 (
% 3.85/3.46 subset @
% 3.85/3.46 X40 @ X38 ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X42:$i]:
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X42 @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X42 ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X44:$i,
% 3.85/3.46 X46:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 subset @
% 3.85/3.46 X44 @ X46 ) =>
% 3.85/3.46 (
% 3.85/3.46 subset @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X44 ) @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X46 ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 sepInPowerset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 sepSubset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X48:$i,
% 3.85/3.46 X50:$i,
% 3.85/3.46 X52:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X52 @ X48 ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X52 @
% 3.85/3.46 (
% 3.85/3.46 binunion @
% 3.85/3.46 X48 @ X50 ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 upairset2IR ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X54:$i,
% 3.85/3.46 X56:$i,
% 3.85/3.46 X58:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X58 @ X56 ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X58 @
% 3.85/3.46 (
% 3.85/3.46 binunion @
% 3.85/3.46 X54 @ X56 ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X60:$i,
% 3.85/3.46 X62:$i,
% 3.85/3.46 X64:$i,
% 3.85/3.46 X66:$o]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X64 @
% 3.85/3.46 (
% 3.85/3.46 binunion @
% 3.85/3.46 X60 @ X62 ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X64 @ X60 ) =>
% 3.85/3.46 (
% 3.85/3.46 X66 ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X64 @ X62 ) =>
% 3.85/3.46 (
% 3.85/3.46 X66 ) ) =>
% 3.85/3.46 (
% 3.85/3.46 X66 ) ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X68:$i,
% 3.85/3.46 X70:$i,
% 3.85/3.46 X72:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X72 @
% 3.85/3.46 (
% 3.85/3.46 binunion @
% 3.85/3.46 X68 @ X70 ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X72 @ X70 ) |
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X72 @ X68 ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X74:$i,
% 3.85/3.46 X76:$i]:
% 3.85/3.46 (
% 3.85/3.46 subset @
% 3.85/3.46 X74 @
% 3.85/3.46 (
% 3.85/3.46 binunion @
% 3.85/3.46 X74 @ X76 ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X78:$i,
% 3.85/3.46 X80:$i]:
% 3.85/3.46 (
% 3.85/3.46 subset @
% 3.85/3.46 X80 @
% 3.85/3.46 (
% 3.85/3.46 binunion @
% 3.85/3.46 X78 @ X80 ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectI ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectSubset5 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectEL ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectLsub ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectSubset2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectSubset3 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectER ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 disjointsetsI1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectRsub ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectSubset4 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 binintersectSubset1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 bs114d ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusI ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusEL ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusER ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusSubset2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusERneg ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusELneg ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusILneg ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusIRneg ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusLsub ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setminusSubset1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 symdiffE ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 symdiffI1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 symdiffI2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 symdiffIneg1 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 symdiffIneg2 ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 secondinupair ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setukpairIL ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setukpairIR ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 kpairiskpair ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X82:$i,
% 3.85/3.46 X84:$i]:
% 3.85/3.46 (
% 3.85/3.46 iskpair @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X82 @
% 3.85/3.46 emptyset ) @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X82 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X84 @
% 3.85/3.46 emptyset ) ) @
% 3.85/3.46 emptyset ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 singletonsubset ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X86:$i,
% 3.85/3.46 X88:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X88 @ X86 ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X88 @
% 3.85/3.46 emptyset ) @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X86 ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X90:$i,
% 3.85/3.46 X92:$i,
% 3.85/3.46 X94:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X94 @ X90 ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X94 @
% 3.85/3.46 emptyset ) @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 (
% 3.85/3.46 binunion @
% 3.85/3.46 X90 @ X92 ) ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 upairset2E ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X96:$i,
% 3.85/3.46 X98:$i,
% 3.85/3.46 X100:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X100 @ X96 ) =>
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X102:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X102 @ X98 ) =>
% 3.85/3.46 (
% 3.85/3.46 subset @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X100 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X102 @
% 3.85/3.46 emptyset ) ) @
% 3.85/3.46 (
% 3.85/3.46 binunion @
% 3.85/3.46 X96 @ X98 ) ) ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X104:$i,
% 3.85/3.46 X106:$i,
% 3.85/3.46 X108:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X108 @
% 3.85/3.46 X104 ) =>
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X110:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X110 @
% 3.85/3.46 X106 ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X108 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X110 @
% 3.85/3.46 emptyset ) ) @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 (
% 3.85/3.46 binunion @
% 3.85/3.46 X104 @
% 3.85/3.46 X106 ) ) ) ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X112:$i,
% 3.85/3.46 X114:$i,
% 3.85/3.46 X116:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X116 @
% 3.85/3.46 X112 ) =>
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X118:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X118 @
% 3.85/3.46 X114 ) =>
% 3.85/3.46 (
% 3.85/3.46 subset @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X116 @
% 3.85/3.46 emptyset ) @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X116 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X118 @
% 3.85/3.46 emptyset ) ) @
% 3.85/3.46 emptyset ) ) @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 (
% 3.85/3.46 binunion @
% 3.85/3.46 X112 @
% 3.85/3.46 X114 ) ) ) ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X120:$i,
% 3.85/3.46 X122:$i,
% 3.85/3.46 X124:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X124 @
% 3.85/3.46 X120 ) =>
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X126:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X126 @
% 3.85/3.46 X122 ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X124 @
% 3.85/3.46 emptyset ) @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X124 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X126 @
% 3.85/3.46 emptyset ) ) @
% 3.85/3.46 emptyset ) ) @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 (
% 3.85/3.46 binunion @
% 3.85/3.46 X120 @
% 3.85/3.46 X122 ) ) ) ) ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X128:$i,
% 3.85/3.46 X130:$i,
% 3.85/3.46 X132:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X132 @
% 3.85/3.46 X128 ) =>
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X134:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X134 @
% 3.85/3.46 X130 ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X132 @
% 3.85/3.46 emptyset ) @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X132 @
% 3.85/3.46 (
% 3.85/3.46 setadjoin
% 3.85/3.46 @
% 3.85/3.46 X134 @
% 3.85/3.46 emptyset ) ) @
% 3.85/3.46 emptyset ) ) @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 (
% 3.85/3.46 binunion @
% 3.85/3.46 X128 @
% 3.85/3.46 X130 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.85/3.46 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 3.85/3.46 thf(zf_stmt_2, axiom,
% 3.85/3.46 (![X8:$i,X6:$i,X4:$i]:
% 3.85/3.46 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 3.85/3.46 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 3.85/3.46 thf(zf_stmt_3, conjecture,
% 3.85/3.46 (( setextAx ) =>
% 3.85/3.46 ( ( emptysetAx ) =>
% 3.85/3.46 ( ( setadjoinAx ) =>
% 3.85/3.46 ( ( ![X4:$i,X6:$i]:
% 3.85/3.46 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.85/3.46 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 3.85/3.46 ( ( setunionAx ) =>
% 3.85/3.46 ( ( omega0Ax ) =>
% 3.85/3.46 ( ( omegaSAx ) =>
% 3.85/3.46 ( ( omegaIndAx ) =>
% 3.85/3.46 ( ( replAx ) =>
% 3.85/3.46 ( ( foundationAx ) =>
% 3.85/3.46 ( ( wellorderingAx ) =>
% 3.85/3.46 ( ( descrp ) =>
% 3.85/3.46 ( ( dsetconstrI ) =>
% 3.85/3.46 ( ( dsetconstrEL ) =>
% 3.85/3.46 ( ( dsetconstrER ) =>
% 3.85/3.46 ( ( exuE1 ) =>
% 3.85/3.46 ( ( prop2setE ) =>
% 3.85/3.46 ( ( emptysetE ) =>
% 3.85/3.46 ( ( emptysetimpfalse ) =>
% 3.85/3.46 ( ( notinemptyset ) =>
% 3.85/3.46 ( ( exuE3e ) =>
% 3.85/3.46 ( ( setext ) =>
% 3.85/3.46 ( ( emptyI ) =>
% 3.85/3.46 ( ( noeltsimpempty ) =>
% 3.85/3.46 ( ( setbeta ) =>
% 3.85/3.46 ( ( nonemptyE1 ) =>
% 3.85/3.46 ( ( nonemptyI ) =>
% 3.85/3.46 ( ( nonemptyI1 ) =>
% 3.85/3.46 ( ( setadjoinIL ) =>
% 3.85/3.46 ( ( emptyinunitempty ) =>
% 3.85/3.46 ( ( setadjoinIR ) =>
% 3.85/3.46 ( ( setadjoinE ) =>
% 3.85/3.46 ( (
% 3.85/3.46 setadjoinOr ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setoftrueEq ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X10:$i,
% 3.85/3.46 X12:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X14:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X14 @ X12 ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X14 @ X10 ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X12 @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X10 ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X16:$i]:
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 emptyset @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X16 ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X18:$i]:
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 emptyset @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X18 ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 ![
% 3.85/3.46 X20:$i,
% 3.85/3.46 X22:$i,
% 3.85/3.46 X24:$i]:
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X22 @
% 3.85/3.46 (
% 3.85/3.46 powerset @
% 3.85/3.46 X20 ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X24 @ X22 ) =>
% 3.85/3.46 (
% 3.85/3.46 in @
% 3.85/3.46 X24 @ X20 ) ) ) ) =>
% 3.85/3.46 (
% 3.85/3.46 (
% 3.85/3.46 setunionI ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 setunionE ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 subPowSU ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 exuE2 ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 nonemptyImpWitness ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 uniqinunit ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 notinsingleton ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 eqinunit ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 singletonsswitch ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 upairsetE ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 upairsetIL ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 upairsetIR ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 emptyE1 ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 vacuousDall ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 quantDeMorgan1 ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 quantDeMorgan2 ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 quantDeMorgan3 ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 quantDeMorgan4 ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 prop2setI ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 prop2set2propI ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 notdexE ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 notdallE ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 exuI1 ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 exuI3 ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 exuI2 ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 inCongP ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 in__Cong ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 exuE3u ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 exu__Cong ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 emptyset__Cong ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 setadjoin__Cong ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 ![
% 3.87/3.46 X26:$i,
% 3.87/3.46 X28:$i]:
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 X26 ) =
% 3.87/3.46 (
% 3.87/3.46 X28 ) ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.46 powerset @
% 3.87/3.46 X26 ) =
% 3.87/3.46 (
% 3.87/3.46 powerset @
% 3.87/3.46 X28 ) ) ) ) =>
% 3.87/3.46 (
% 3.87/3.46 (
% 3.87/3.47 setunion__Cong ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 omega__Cong ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 exuEu ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 descr__Cong ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 dsetconstr__Cong ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subsetI1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 eqimpsubset2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 eqimpsubset1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subsetI2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 emptysetsubset ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subsetE ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subsetE2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 notsubsetI ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 notequalI1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 notequalI2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subsetRefl ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subsetTrans ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setadjoinSub ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setadjoinSub2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X30:$i,
% 3.87/3.47 X32:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 X30 @ X32 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X30 @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 X32 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setextsub ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subsetemptysetimpeq ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X34:$i,
% 3.87/3.47 X36:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 X36 @ X34 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X36 @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 X34 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X38:$i,
% 3.87/3.47 X40:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X40 @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 X38 ) ) =>
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 X40 @ X38 ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X42:$i]:
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X42 @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 X42 ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X44:$i,
% 3.87/3.47 X46:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 X44 @ X46 ) =>
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 X44 ) @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 X46 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 sepInPowerset ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 sepSubset ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X48:$i,
% 3.87/3.47 X50:$i,
% 3.87/3.47 X52:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X52 @ X48 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X52 @
% 3.87/3.47 (
% 3.87/3.47 binunion @
% 3.87/3.47 X48 @ X50 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 upairset2IR ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X54:$i,
% 3.87/3.47 X56:$i,
% 3.87/3.47 X58:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X58 @ X56 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X58 @
% 3.87/3.47 (
% 3.87/3.47 binunion @
% 3.87/3.47 X54 @ X56 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X60:$i,
% 3.87/3.47 X62:$i,
% 3.87/3.47 X64:$i,
% 3.87/3.47 X66:$o]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X64 @
% 3.87/3.47 (
% 3.87/3.47 binunion @
% 3.87/3.47 X60 @ X62 ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X64 @ X60 ) =>
% 3.87/3.47 (
% 3.87/3.47 X66 ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X64 @ X62 ) =>
% 3.87/3.47 (
% 3.87/3.47 X66 ) ) =>
% 3.87/3.47 (
% 3.87/3.47 X66 ) ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X68:$i,
% 3.87/3.47 X70:$i,
% 3.87/3.47 X72:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X72 @
% 3.87/3.47 (
% 3.87/3.47 binunion @
% 3.87/3.47 X68 @ X70 ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X72 @ X68 ) |
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X72 @ X70 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X74:$i,
% 3.87/3.47 X76:$i]:
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 X74 @
% 3.87/3.47 (
% 3.87/3.47 binunion @
% 3.87/3.47 X74 @ X76 ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X78:$i,
% 3.87/3.47 X80:$i]:
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 X80 @
% 3.87/3.47 (
% 3.87/3.47 binunion @
% 3.87/3.47 X78 @ X80 ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectI ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectSubset5 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectEL ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectLsub ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectSubset2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectSubset3 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectER ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 disjointsetsI1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectRsub ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectSubset4 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectSubset1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 bs114d ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setminusI ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setminusEL ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setminusER ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setminusSubset2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setminusERneg ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setminusELneg ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setminusILneg ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setminusIRneg ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setminusLsub ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setminusSubset1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 symdiffE ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 symdiffI1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 symdiffI2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 symdiffIneg1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 symdiffIneg2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 secondinupair ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setukpairIL ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setukpairIR ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 kpairiskpair ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X82:$i,
% 3.87/3.47 X84:$i]:
% 3.87/3.47 (
% 3.87/3.47 iskpair @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X82 @
% 3.87/3.47 emptyset ) @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X82 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X84 @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 emptyset ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 singletonsubset ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X86:$i,
% 3.87/3.47 X88:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X88 @ X86 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X88 @
% 3.87/3.47 emptyset ) @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 X86 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X90:$i,
% 3.87/3.47 X92:$i,
% 3.87/3.47 X94:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X94 @ X90 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X94 @
% 3.87/3.47 emptyset ) @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 (
% 3.87/3.47 binunion @
% 3.87/3.47 X90 @ X92 ) ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 upairset2E ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X96:$i,
% 3.87/3.47 X98:$i,
% 3.87/3.47 X100:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X100 @ X96 ) =>
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X102:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X102 @ X98 ) =>
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X100 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X102 @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 (
% 3.87/3.47 binunion @
% 3.87/3.47 X96 @ X98 ) ) ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X104:$i,
% 3.87/3.47 X106:$i,
% 3.87/3.47 X108:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X108 @
% 3.87/3.47 X104 ) =>
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X110:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X110 @
% 3.87/3.47 X106 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X108 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X110 @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 (
% 3.87/3.47 binunion @
% 3.87/3.47 X104 @
% 3.87/3.47 X106 ) ) ) ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X112:$i,
% 3.87/3.47 X114:$i,
% 3.87/3.47 X116:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X116 @
% 3.87/3.47 X112 ) =>
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X118:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X118 @
% 3.87/3.47 X114 ) =>
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X116 @
% 3.87/3.47 emptyset ) @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X116 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X118 @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 (
% 3.87/3.47 binunion @
% 3.87/3.47 X112 @
% 3.87/3.47 X114 ) ) ) ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X120:$i,
% 3.87/3.47 X122:$i,
% 3.87/3.47 X124:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X124 @
% 3.87/3.47 X120 ) =>
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X126:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X126 @
% 3.87/3.47 X122 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X124 @
% 3.87/3.47 emptyset ) @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X124 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X126 @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 (
% 3.87/3.47 binunion @
% 3.87/3.47 X120 @
% 3.87/3.47 X122 ) ) ) ) ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X128:$i,
% 3.87/3.47 X130:$i,
% 3.87/3.47 X132:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X132 @
% 3.87/3.47 X128 ) =>
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X134:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X134 @
% 3.87/3.47 X130 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X132 @
% 3.87/3.47 emptyset ) @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X132 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X134 @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 (
% 3.87/3.47 powerset @
% 3.87/3.47 (
% 3.87/3.47 binunion @
% 3.87/3.47 X128 @
% 3.87/3.47 X130 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.87/3.47 thf(zf_stmt_4, negated_conjecture,
% 3.87/3.47 (~( ( setextAx ) =>
% 3.87/3.47 ( ( emptysetAx ) =>
% 3.87/3.47 ( ( setadjoinAx ) =>
% 3.87/3.47 ( ( ![X4:$i,X6:$i]:
% 3.87/3.47 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 3.87/3.47 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 3.87/3.47 ( ( setunionAx ) =>
% 3.87/3.47 ( ( omega0Ax ) =>
% 3.87/3.47 ( ( omegaSAx ) =>
% 3.87/3.47 ( ( omegaIndAx ) =>
% 3.87/3.47 ( ( replAx ) =>
% 3.87/3.47 ( ( foundationAx ) =>
% 3.87/3.47 ( ( wellorderingAx ) =>
% 3.87/3.47 ( ( descrp ) =>
% 3.87/3.47 ( ( dsetconstrI ) =>
% 3.87/3.47 ( ( dsetconstrEL ) =>
% 3.87/3.47 ( ( dsetconstrER ) =>
% 3.87/3.47 ( ( exuE1 ) =>
% 3.87/3.47 ( ( prop2setE ) =>
% 3.87/3.47 ( ( emptysetE ) =>
% 3.87/3.47 ( ( emptysetimpfalse ) =>
% 3.87/3.47 ( ( notinemptyset ) =>
% 3.87/3.47 ( ( exuE3e ) =>
% 3.87/3.47 ( ( setext ) =>
% 3.87/3.47 ( ( emptyI ) =>
% 3.87/3.47 ( ( noeltsimpempty ) =>
% 3.87/3.47 ( ( setbeta ) =>
% 3.87/3.47 ( ( nonemptyE1 ) =>
% 3.87/3.47 ( ( nonemptyI ) =>
% 3.87/3.47 ( ( nonemptyI1 ) =>
% 3.87/3.47 ( ( setadjoinIL ) =>
% 3.87/3.47 ( ( emptyinunitempty ) =>
% 3.87/3.47 ( ( setadjoinIR ) =>
% 3.87/3.47 ( (
% 3.87/3.47 setadjoinE ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setadjoinOr ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setoftrueEq ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X10:$i,
% 3.87/3.47 X12:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X14:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X14 @ X12 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X14 @ X10 ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X12 @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 X10 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X16:$i]:
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 emptyset @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 X16 ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X18:$i]:
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 emptyset @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 X18 ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X20:$i,
% 3.87/3.47 X22:$i,
% 3.87/3.47 X24:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X22 @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 X20 ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X24 @ X22 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X24 @ X20 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setunionI ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setunionE ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subPowSU ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 exuE2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 nonemptyImpWitness ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 uniqinunit ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 notinsingleton ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 eqinunit ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 singletonsswitch ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 upairsetE ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 upairsetIL ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 upairsetIR ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 emptyE1 ) =>
% 3.87/3.47 (
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% 3.87/3.47 vacuousDall ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 quantDeMorgan1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 quantDeMorgan2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 quantDeMorgan3 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 quantDeMorgan4 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 prop2setI ) =>
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% 3.87/3.47 (
% 3.87/3.47 prop2set2propI ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 notdexE ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 notdallE ) =>
% 3.87/3.47 (
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% 3.87/3.47 exuI1 ) =>
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% 3.87/3.47 (
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% 3.87/3.47 (
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% 3.87/3.47 (
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% 3.87/3.47 in__Cong ) =>
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% 3.87/3.47 (
% 3.87/3.47 exuE3u ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 exu__Cong ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 emptyset__Cong ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setadjoin__Cong ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X26:$i,
% 3.87/3.47 X28:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 X26 ) =
% 3.87/3.47 (
% 3.87/3.47 X28 ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 X26 ) =
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 X28 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setunion__Cong ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 omega__Cong ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 exuEu ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 descr__Cong ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 dsetconstr__Cong ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subsetI1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 eqimpsubset2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 eqimpsubset1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subsetI2 ) =>
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% 3.87/3.47 (
% 3.87/3.47 emptysetsubset ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subsetE ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subsetE2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 notsubsetI ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 notequalI1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 notequalI2 ) =>
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% 3.87/3.47 (
% 3.87/3.47 subsetRefl ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subsetTrans ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setadjoinSub ) =>
% 3.87/3.47 (
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% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X30:$i,
% 3.87/3.47 X32:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 X30 @ X32 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X30 @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 X32 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 setextsub ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subsetemptysetimpeq ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X34:$i,
% 3.87/3.47 X36:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 X36 @ X34 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X36 @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 X34 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X38:$i,
% 3.87/3.47 X40:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X40 @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 X38 ) ) =>
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 X40 @ X38 ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X42:$i]:
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X42 @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 X42 ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X44:$i,
% 3.87/3.47 X46:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 X44 @ X46 ) =>
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 X44 ) @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 X46 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 sepInPowerset ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 sepSubset ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X48:$i,
% 3.87/3.47 X50:$i,
% 3.87/3.47 X52:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X52 @ X48 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X52 @
% 3.87/3.47 (
% 3.87/3.47 binunion
% 3.87/3.47 @
% 3.87/3.47 X48 @ X50 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 upairset2IR ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X54:$i,
% 3.87/3.47 X56:$i,
% 3.87/3.47 X58:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X58 @ X56 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X58 @
% 3.87/3.47 (
% 3.87/3.47 binunion
% 3.87/3.47 @
% 3.87/3.47 X54 @ X56 ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X60:$i,
% 3.87/3.47 X62:$i,
% 3.87/3.47 X64:$i,
% 3.87/3.47 X66:$o]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X64 @
% 3.87/3.47 (
% 3.87/3.47 binunion
% 3.87/3.47 @
% 3.87/3.47 X60 @ X62 ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X64 @ X60 ) =>
% 3.87/3.47 (
% 3.87/3.47 X66 ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X64 @ X62 ) =>
% 3.87/3.47 (
% 3.87/3.47 X66 ) ) =>
% 3.87/3.47 (
% 3.87/3.47 X66 ) ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X68:$i,
% 3.87/3.47 X70:$i,
% 3.87/3.47 X72:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X72 @
% 3.87/3.47 (
% 3.87/3.47 binunion
% 3.87/3.47 @
% 3.87/3.47 X68 @ X70 ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X72 @ X68 ) |
% 3.87/3.47 (
% 3.87/3.47 in @
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% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X74:$i,
% 3.87/3.47 X76:$i]:
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 X74 @
% 3.87/3.47 (
% 3.87/3.47 binunion
% 3.87/3.47 @
% 3.87/3.47 X74 @ X76 ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X78:$i,
% 3.87/3.47 X80:$i]:
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 X80 @
% 3.87/3.47 (
% 3.87/3.47 binunion
% 3.87/3.47 @
% 3.87/3.47 X78 @ X80 ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectI ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectSubset5 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectEL ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectLsub ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectSubset2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectSubset3 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectER ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 disjointsetsI1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectRsub ) =>
% 3.87/3.47 (
% 3.87/3.47 (
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% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 binintersectSubset1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 bs114d ) =>
% 3.87/3.47 (
% 3.87/3.47 (
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% 3.87/3.47 (
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% 3.87/3.47 (
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% 3.87/3.47 (
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% 3.87/3.47 setminusLsub ) =>
% 3.87/3.47 (
% 3.87/3.47 (
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% 3.87/3.47 (
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% 3.87/3.47 symdiffE ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 symdiffI1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 symdiffI2 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 symdiffIneg1 ) =>
% 3.87/3.47 (
% 3.87/3.47 (
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% 3.87/3.47 (
% 3.87/3.47 (
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% 3.87/3.47 (
% 3.87/3.47 (
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% 3.87/3.47 (
% 3.87/3.47 setukpairIR ) =>
% 3.87/3.47 (
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% 3.87/3.47 kpairiskpair ) =>
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% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X82:$i,
% 3.87/3.47 X84:$i]:
% 3.87/3.47 (
% 3.87/3.47 iskpair @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X82 @
% 3.87/3.47 emptyset ) @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X82 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
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% 3.87/3.47 emptyset ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 singletonsubset ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X86:$i,
% 3.87/3.47 X88:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X88 @ X86 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X88 @
% 3.87/3.47 emptyset ) @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
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% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X90:$i,
% 3.87/3.47 X92:$i,
% 3.87/3.47 X94:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X94 @ X90 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X94 @
% 3.87/3.47 emptyset ) @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 binunion
% 3.87/3.47 @
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% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 upairset2E ) =>
% 3.87/3.47 (
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% 3.87/3.47 ![
% 3.87/3.47 X96:$i,
% 3.87/3.47 X98:$i,
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% 3.87/3.47 (
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% 3.87/3.47 ![
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% 3.87/3.47 (
% 3.87/3.47 (
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% 3.87/3.47 X98 ) =>
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% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X100 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
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% 3.87/3.47 X102 @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 (
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% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X104:$i,
% 3.87/3.47 X106:$i,
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% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X108 @
% 3.87/3.47 X104 ) =>
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X110:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X110 @
% 3.87/3.47 X106 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X108 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X110 @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 binunion
% 3.87/3.47 @
% 3.87/3.47 X104 @
% 3.87/3.47 X106 ) ) ) ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X112:$i,
% 3.87/3.47 X114:$i,
% 3.87/3.47 X116:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X116 @
% 3.87/3.47 X112 ) =>
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X118:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X118 @
% 3.87/3.47 X114 ) =>
% 3.87/3.47 (
% 3.87/3.47 subset @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X116 @
% 3.87/3.47 emptyset ) @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X116 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X118 @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 binunion
% 3.87/3.47 @
% 3.87/3.47 X112 @
% 3.87/3.47 X114 ) ) ) ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X120:$i,
% 3.87/3.47 X122:$i,
% 3.87/3.47 X124:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X124 @
% 3.87/3.47 X120 ) =>
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X126:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X126 @
% 3.87/3.47 X122 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X124 @
% 3.87/3.47 emptyset ) @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X124 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X126 @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 binunion
% 3.87/3.47 @
% 3.87/3.47 X120 @
% 3.87/3.47 X122 ) ) ) ) ) ) ) ) =>
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X128:$i,
% 3.87/3.47 X130:$i,
% 3.87/3.47 X132:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X132 @
% 3.87/3.47 X128 ) =>
% 3.87/3.47 (
% 3.87/3.47 ![
% 3.87/3.47 X134:$i]:
% 3.87/3.47 (
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 X134 @
% 3.87/3.47 X130 ) =>
% 3.87/3.47 (
% 3.87/3.47 in @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X132 @
% 3.87/3.47 emptyset ) @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X132 @
% 3.87/3.47 (
% 3.87/3.47 setadjoin
% 3.87/3.47 @
% 3.87/3.47 X134 @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 emptyset ) ) @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 powerset
% 3.87/3.47 @
% 3.87/3.47 (
% 3.87/3.47 binunion
% 3.87/3.47 @
% 3.87/3.47 X128 @
% 3.87/3.47 X130 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 3.87/3.47 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 3.87/3.47 thf(zip_derived_cl76, plain,
% 3.87/3.47 (![X25 : $i, X26 : $i, X27 : $i, X28 : $i]:
% 3.87/3.47 (~ (in @ X25 @ X26)
% 3.87/3.47 | (in @
% 3.87/3.47 (setadjoin @ (setadjoin @ X27 @ emptyset) @
% 3.87/3.47 (setadjoin @ (setadjoin @ X27 @ (setadjoin @ X25 @ emptyset)) @
% 3.87/3.47 emptyset)) @
% 3.87/3.47 (powerset @ (powerset @ (binunion @ X28 @ X26))))
% 3.87/3.47 | ~ (in @ X27 @ X28))),
% 3.87/3.47 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.87/3.47 thf(zip_derived_cl78, plain,
% 3.87/3.47 (~ (in @
% 3.87/3.47 (setadjoin @ (setadjoin @ sk__66 @ emptyset) @
% 3.87/3.47 (setadjoin @
% 3.87/3.47 (setadjoin @ sk__66 @ (setadjoin @ sk__67 @ emptyset)) @ emptyset)) @
% 3.87/3.47 (powerset @ (powerset @ (binunion @ sk__64 @ sk__65))))),
% 3.87/3.47 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.87/3.47 thf(zip_derived_cl416, plain,
% 3.87/3.47 ((~ (in @ sk__66 @ sk__64) | ~ (in @ sk__67 @ sk__65))),
% 3.87/3.47 inference('sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl78])).
% 3.87/3.47 thf(zip_derived_cl79, plain, ( (in @ sk__66 @ sk__64)),
% 3.87/3.47 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.87/3.47 thf(zip_derived_cl77, plain, ( (in @ sk__67 @ sk__65)),
% 3.87/3.47 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.87/3.47 thf(zip_derived_cl420, plain, ($false),
% 3.87/3.47 inference('demod', [status(thm)],
% 3.87/3.47 [zip_derived_cl416, zip_derived_cl79, zip_derived_cl77])).
% 3.87/3.47
% 3.87/3.47 % SZS output end Refutation
% 3.87/3.47
% 3.87/3.47
% 3.87/3.47 % Terminating...
% 4.26/3.66 % Runner terminated.
% 4.26/3.69 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------