%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU653^1 : 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.EkKK8s5q4U true
% Computer : n017.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 04:55:34 PM UTC 2025
% Result : Theorem 5.37s 1.29s
% Output : Refutation 5.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU653^1 : TPTP v9.2.0. Released v3.7.0.
% 0.11/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.EkKK8s5q4U true
% 0.11/0.33 % Computer : n017.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 16:04:23 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Running portfolio for 300 s
% 0.11/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.33 % Number of cores: 8
% 0.11/0.33 % Python version: Python 3.6.8
% 0.18/0.33 % Running in HO mode
% 0.50/0.62 % Total configuration time : 828
% 0.50/0.62 % Estimated wc time : 1656
% 0.50/0.62 % Estimated cpu time (8 cpus) : 207.0
% 0.50/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.50/0.71 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.50/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.50/0.72 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.50/0.72 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.50/0.72 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.50/0.73 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.50/0.74 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 5.37/1.29 % Solved by lams/40_c_ic.sh.
% 5.37/1.29 % done 277 iterations in 0.517s
% 5.37/1.29 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 5.37/1.29 % SZS output start Refutation
% 5.37/1.29 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 5.37/1.29 thf(notdexE_type, type, notdexE: $o).
% 5.37/1.29 thf(upairequniteq_type, type, upairequniteq: $o).
% 5.37/1.29 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 5.37/1.29 thf(setunionAx_type, type, setunionAx: $o).
% 5.37/1.29 thf(setminusELneg_type, type, setminusELneg: $o).
% 5.37/1.29 thf(sk__61_type, type, sk__61: $i).
% 5.37/1.29 thf(powersetE_type, type, powersetE: $o).
% 5.37/1.29 thf(omegaSAx_type, type, omegaSAx: $o).
% 5.37/1.29 thf(exuI1_type, type, exuI1: $o).
% 5.37/1.29 thf(exuI2_type, type, exuI2: $o).
% 5.37/1.29 thf(notequalI2_type, type, notequalI2: $o).
% 5.37/1.29 thf(setukpairIR_type, type, setukpairIR: $o).
% 5.37/1.29 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 5.37/1.29 thf(setminusILneg_type, type, setminusILneg: $o).
% 5.37/1.29 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 5.37/1.29 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 5.37/1.29 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 5.37/1.29 thf(upairsubunion_type, type, upairsubunion: $o).
% 5.37/1.29 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 5.37/1.29 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 5.37/1.29 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 5.37/1.29 thf(setukpairIL_type, type, setukpairIL: $o).
% 5.37/1.29 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 5.37/1.29 thf(binunionE_type, type, binunionE: $o).
% 5.37/1.29 thf(setext_type, type, setext: $o).
% 5.37/1.29 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 5.37/1.29 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 5.37/1.29 thf(descr__Cong_type, type, descr__Cong: $o).
% 5.37/1.29 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 5.37/1.29 thf(in_type, type, in: $i > $i > $o).
% 5.37/1.29 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 5.37/1.29 thf(theprop_type, type, theprop: $o).
% 5.37/1.29 thf(upairset2E_type, type, upairset2E: $o).
% 5.37/1.29 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 5.37/1.29 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 5.37/1.29 thf(symdiffI2_type, type, symdiffI2: $o).
% 5.37/1.29 thf(upairset2IR_type, type, upairset2IR: $o).
% 5.37/1.29 thf(subsetE_type, type, subsetE: $o).
% 5.37/1.29 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 5.37/1.29 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 5.37/1.29 thf(setbeta_type, type, setbeta: $o).
% 5.37/1.29 thf(eqinunit_type, type, eqinunit: $o).
% 5.37/1.29 thf(upairsetIL_type, type, upairsetIL: $o).
% 5.37/1.29 thf(powersetI1_type, type, powersetI1: $o).
% 5.37/1.29 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 5.37/1.29 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 5.37/1.29 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 5.37/1.29 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 5.37/1.29 thf(powersetAx_type, type, powersetAx: $o).
% 5.37/1.29 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 5.37/1.29 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 5.37/1.29 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 5.37/1.29 thf(powersetI_type, type, powersetI: $o).
% 5.37/1.29 thf(upairsetIR_type, type, upairsetIR: $o).
% 5.37/1.29 thf(sk__63_type, type, sk__63: $i).
% 5.37/1.29 thf(inCongP_type, type, inCongP: $o).
% 5.37/1.29 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 5.37/1.29 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 5.37/1.29 thf(exuE3e_type, type, exuE3e: $o).
% 5.37/1.29 thf(emptysetE_type, type, emptysetE: $o).
% 5.37/1.29 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 5.37/1.29 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 5.37/1.29 thf(setunionI_type, type, setunionI: $o).
% 5.37/1.29 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 5.37/1.29 thf(prop2setI_type, type, prop2setI: $o).
% 5.37/1.29 thf(ex1I2_type, type, ex1I2: $o).
% 5.37/1.29 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 5.37/1.29 thf(setminusER_type, type, setminusER: $o).
% 5.37/1.29 thf(exuE2_type, type, exuE2: $o).
% 5.37/1.29 thf(emptyset_type, type, emptyset: $i).
% 5.37/1.29 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 5.37/1.29 thf(powersetsubset_type, type, powersetsubset: $o).
% 5.37/1.29 thf(subPowSU_type, type, subPowSU: $o).
% 5.37/1.29 thf(notequalI1_type, type, notequalI1: $o).
% 5.37/1.29 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 5.37/1.29 thf(notinemptyset_type, type, notinemptyset: $o).
% 5.37/1.29 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 5.37/1.29 thf(subsetTrans_type, type, subsetTrans: $o).
% 5.37/1.29 thf(setminusI_type, type, setminusI: $o).
% 5.37/1.29 thf(binunionIL_type, type, binunionIL: $o).
% 5.37/1.29 thf(subsetE2_type, type, subsetE2: $o).
% 5.37/1.29 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 5.37/1.29 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 5.37/1.29 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 5.37/1.29 thf(setextsub_type, type, setextsub: $o).
% 5.37/1.29 thf(binunionLsub_type, type, binunionLsub: $o).
% 5.37/1.29 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 5.37/1.29 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 5.37/1.29 thf(setunionE_type, type, setunionE: $o).
% 5.37/1.29 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 5.37/1.29 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 5.37/1.29 thf(binunionIR_type, type, binunionIR: $o).
% 5.37/1.29 thf(setadjoinE_type, type, setadjoinE: $o).
% 5.37/1.29 thf(singletonprop_type, type, singletonprop: $o).
% 5.37/1.29 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 5.37/1.29 thf(exuE1_type, type, exuE1: $o).
% 5.37/1.29 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 5.37/1.29 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 5.37/1.29 thf(setminusLsub_type, type, setminusLsub: $o).
% 5.37/1.29 thf(notinsingleton_type, type, notinsingleton: $o).
% 5.37/1.29 thf(sk__62_type, type, sk__62: $i).
% 5.37/1.29 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 5.37/1.29 thf(exuEu_type, type, exuEu: $o).
% 5.37/1.29 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 5.37/1.29 thf(upairsetE_type, type, upairsetE: $o).
% 5.37/1.29 thf(omega0Ax_type, type, omega0Ax: $o).
% 5.37/1.29 thf(notsubsetI_type, type, notsubsetI: $o).
% 5.37/1.29 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 5.37/1.29 thf(setextAx_type, type, setextAx: $o).
% 5.37/1.29 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 5.37/1.29 thf(powersetE1_type, type, powersetE1: $o).
% 5.37/1.29 thf(bs114d_type, type, bs114d: $o).
% 5.37/1.29 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 5.37/1.29 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 5.37/1.29 thf(subsetI1_type, type, subsetI1: $o).
% 5.37/1.29 thf(symdiffE_type, type, symdiffE: $o).
% 5.37/1.29 thf(descrp_type, type, descrp: $o).
% 5.37/1.29 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 5.37/1.29 thf(foundationAx_type, type, foundationAx: $o).
% 5.37/1.29 thf(emptysetAx_type, type, emptysetAx: $o).
% 5.37/1.29 thf(emptyI_type, type, emptyI: $o).
% 5.37/1.29 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 5.37/1.29 thf(binintersectEL_type, type, binintersectEL: $o).
% 5.37/1.29 thf(emptyE1_type, type, emptyE1: $o).
% 5.37/1.29 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 5.37/1.29 thf(vacuousDall_type, type, vacuousDall: $o).
% 5.37/1.29 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 5.37/1.29 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 5.37/1.29 thf(binintersectI_type, type, binintersectI: $o).
% 5.37/1.29 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 5.37/1.29 thf(ex1E1_type, type, ex1E1: $o).
% 5.37/1.29 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 5.37/1.29 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 5.37/1.29 thf(symdiffI1_type, type, symdiffI1: $o).
% 5.37/1.29 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 5.37/1.29 thf(subsetI2_type, type, subsetI2: $o).
% 5.37/1.29 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 5.37/1.29 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 5.37/1.29 thf(setminusERneg_type, type, setminusERneg: $o).
% 5.37/1.29 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 5.37/1.29 thf(omega__Cong_type, type, omega__Cong: $o).
% 5.37/1.29 thf(subsetRefl_type, type, subsetRefl: $o).
% 5.37/1.29 thf(uniqinunit_type, type, uniqinunit: $o).
% 5.37/1.29 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 5.37/1.29 thf(sk__64_type, type, sk__64: $i).
% 5.37/1.29 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 5.37/1.29 thf(prop2setE_type, type, prop2setE: $o).
% 5.37/1.29 thf(binunionEcases_type, type, binunionEcases: $o).
% 5.37/1.29 thf(nonemptyI_type, type, nonemptyI: $o).
% 5.37/1.29 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 5.37/1.29 thf(exuE3u_type, type, exuE3u: $o).
% 5.37/1.29 thf(setminusEL_type, type, setminusEL: $o).
% 5.37/1.29 thf(singletonsubset_type, type, singletonsubset: $o).
% 5.37/1.29 thf(sepSubset_type, type, sepSubset: $o).
% 5.37/1.29 thf(setunionE2_type, type, setunionE2: $o).
% 5.37/1.29 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 5.37/1.29 thf(ex1I_type, type, ex1I: $o).
% 5.37/1.29 thf(exuI3_type, type, exuI3: $o).
% 5.37/1.29 thf(notdallE_type, type, notdallE: $o).
% 5.37/1.29 thf(binintersectER_type, type, binintersectER: $o).
% 5.37/1.29 thf(kpairp_type, type, kpairp: $o).
% 5.37/1.29 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 5.37/1.29 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 5.37/1.29 thf(exu__Cong_type, type, exu__Cong: $o).
% 5.37/1.29 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 5.37/1.29 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 5.37/1.29 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 5.37/1.29 thf(replAx_type, type, replAx: $o).
% 5.37/1.29 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 5.37/1.29 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 5.37/1.29 thf(secondinupair_type, type, secondinupair: $o).
% 5.37/1.29 thf(inPowerset_type, type, inPowerset: $o).
% 5.37/1.29 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 5.37/1.29 thf(in__Cong_type, type, in__Cong: $o).
% 5.37/1.29 thf(binunionRsub_type, type, binunionRsub: $o).
% 5.37/1.29 thf(subset2powerset_type, type, subset2powerset: $o).
% 5.37/1.29 thf(upairequniteq, axiom, upairequniteq =
% 5.37/1.29 (![Xx:$i,Xy:$i,Xz:$i]:
% 5.37/1.29 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =
% 5.37/1.29 ( setadjoin @ Xz @ emptyset ) ) =>
% 5.37/1.29 ( ( Xx ) = ( Xy ) ) ))).
% 5.37/1.29 thf('0', plain,
% 5.37/1.29 (( upairequniteq ) =
% 5.37/1.29 ( ![X4:$i,X6:$i,X8:$i]:
% 5.37/1.29 ( ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =
% 5.37/1.29 ( setadjoin @ X8 @ emptyset ) ) =>
% 5.37/1.29 ( ( X4 ) = ( X6 ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(setukpairinjR1, axiom, setukpairinjR1 =
% 5.37/1.29 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 5.37/1.29 ( ( ( setadjoin @
% 5.37/1.29 ( setadjoin @ Xx @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ Xz @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) =>
% 5.37/1.29 ( ( ( Xz ) = ( Xu ) ) => ( ( Xy ) = ( Xu ) ) ) ))).
% 5.37/1.29 thf('1', plain,
% 5.37/1.29 (( setukpairinjR1 ) =
% 5.37/1.29 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 5.37/1.29 ( ( ( setadjoin @
% 5.37/1.29 ( setadjoin @ X4 @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ X8 @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) =>
% 5.37/1.29 ( ( ( X8 ) = ( X10 ) ) => ( ( X6 ) = ( X10 ) ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(setukpairinjR12, axiom, setukpairinjR12 =
% 5.37/1.29 (![Xx:$i,Xy:$i]:
% 5.37/1.29 ( ( ( Xx ) = ( Xy ) ) =>
% 5.37/1.29 ( ( setadjoin @
% 5.37/1.29 ( setadjoin @ Xx @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 5.37/1.29 ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ))).
% 5.37/1.29 thf('2', plain,
% 5.37/1.29 (( setukpairinjR12 ) =
% 5.37/1.29 ( ![X4:$i,X6:$i]:
% 5.37/1.29 ( ( ( X4 ) = ( X6 ) ) =>
% 5.37/1.29 ( ( setadjoin @
% 5.37/1.29 ( setadjoin @ X4 @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 5.37/1.29 ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ emptyset ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(setukpairinjR11, axiom, setukpairinjR11 =
% 5.37/1.29 (![Xx:$i,Xy:$i]:
% 5.37/1.29 ( ( ( Xx ) = ( Xy ) ) =>
% 5.37/1.29 ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =
% 5.37/1.29 ( setadjoin @ Xx @ emptyset ) ) ))).
% 5.37/1.29 thf('3', plain,
% 5.37/1.29 (( setukpairinjR11 ) =
% 5.37/1.29 ( ![X4:$i,X6:$i]:
% 5.37/1.29 ( ( ( X4 ) = ( X6 ) ) =>
% 5.37/1.29 ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =
% 5.37/1.29 ( setadjoin @ X4 @ emptyset ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(setukpairinjL2, axiom, setukpairinjL2 =
% 5.37/1.29 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 5.37/1.29 ( ( ( setadjoin @
% 5.37/1.29 ( setadjoin @ Xx @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ Xz @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) =>
% 5.37/1.29 ( ( Xx ) = ( Xz ) ) ))).
% 5.37/1.29 thf('4', plain,
% 5.37/1.29 (( setukpairinjL2 ) =
% 5.37/1.29 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 5.37/1.29 ( ( ( setadjoin @
% 5.37/1.29 ( setadjoin @ X4 @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ X8 @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) =>
% 5.37/1.29 ( ( X4 ) = ( X8 ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(setukpairinjL1, axiom, setukpairinjL1 =
% 5.37/1.29 (![Xx:$i,Xy:$i,Xz:$i]:
% 5.37/1.29 ( ( in @
% 5.37/1.29 ( setadjoin @ Xz @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ Xx @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) =>
% 5.37/1.29 ( ( Xx ) = ( Xz ) ) ))).
% 5.37/1.29 thf('5', plain,
% 5.37/1.29 (( setukpairinjL1 ) =
% 5.37/1.29 ( ![X4:$i,X6:$i,X8:$i]:
% 5.37/1.29 ( ( in @
% 5.37/1.29 ( setadjoin @ X8 @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ X4 @ emptyset ) @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) =>
% 5.37/1.29 ( ( X4 ) = ( X8 ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(singletonsuniq, axiom, singletonsuniq =
% 5.37/1.29 (![Xx:$i,Xy:$i]:
% 5.37/1.29 ( ( ( setadjoin @ Xx @ emptyset ) = ( setadjoin @ Xy @ emptyset ) ) =>
% 5.37/1.29 ( ( Xx ) = ( Xy ) ) ))).
% 5.37/1.29 thf('6', plain,
% 5.37/1.29 (( singletonsuniq ) =
% 5.37/1.29 ( ![X4:$i,X6:$i]:
% 5.37/1.29 ( ( ( setadjoin @ X4 @ emptyset ) = ( setadjoin @ X6 @ emptyset ) ) =>
% 5.37/1.29 ( ( X4 ) = ( X6 ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(upairset2E, axiom, upairset2E =
% 5.37/1.29 (![Xx:$i,Xy:$i,Xz:$i]:
% 5.37/1.29 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 5.37/1.29 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 5.37/1.29 thf('7', plain,
% 5.37/1.29 (( upairset2E ) =
% 5.37/1.29 ( ![X4:$i,X6:$i,X8:$i]:
% 5.37/1.29 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 5.37/1.29 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(secondinupair, axiom, secondinupair =
% 5.37/1.29 (![Xx:$i,Xy:$i]:
% 5.37/1.29 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 5.37/1.29 thf('8', plain,
% 5.37/1.29 (( secondinupair ) =
% 5.37/1.29 ( ![X4:$i,X6:$i]:
% 5.37/1.29 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(upairset2IR, axiom, upairset2IR =
% 5.37/1.29 (![Xx:$i,Xy:$i]:
% 5.37/1.29 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 5.37/1.29 thf('9', plain,
% 5.37/1.29 (( upairset2IR ) =
% 5.37/1.29 ( ![X4:$i,X6:$i]:
% 5.37/1.29 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 5.37/1.29 (![Xx:$i,Xy:$i]:
% 5.37/1.29 ( ( ( Xx ) = ( Xy ) ) =>
% 5.37/1.29 ( ![Xz:$i,Xu:$i]:
% 5.37/1.29 ( ( ( Xz ) = ( Xu ) ) =>
% 5.37/1.29 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 5.37/1.29 thf('10', plain,
% 5.37/1.29 (( setadjoin__Cong ) =
% 5.37/1.29 ( ![X4:$i,X6:$i]:
% 5.37/1.29 ( ( ( X4 ) = ( X6 ) ) =>
% 5.37/1.29 ( ![X8:$i,X10:$i]:
% 5.37/1.29 ( ( ( X8 ) = ( X10 ) ) =>
% 5.37/1.29 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(upairsetIR, axiom, upairsetIR =
% 5.37/1.29 (![Xx:$i,Xy:$i]:
% 5.37/1.29 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 5.37/1.29 thf('11', plain,
% 5.37/1.29 (( upairsetIR ) =
% 5.37/1.29 ( ![X4:$i,X6:$i]:
% 5.37/1.29 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(upairsetIL, axiom, upairsetIL =
% 5.37/1.29 (![Xx:$i,Xy:$i]:
% 5.37/1.29 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 5.37/1.29 thf('12', plain,
% 5.37/1.29 (( upairsetIL ) =
% 5.37/1.29 ( ![X4:$i,X6:$i]:
% 5.37/1.29 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(upairsetE, axiom, upairsetE =
% 5.37/1.29 (![Xx:$i,Xy:$i,Xz:$i]:
% 5.37/1.29 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 5.37/1.29 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 5.37/1.29 thf('13', plain,
% 5.37/1.29 (( upairsetE ) =
% 5.37/1.29 ( ![X4:$i,X6:$i,X8:$i]:
% 5.37/1.29 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 5.37/1.29 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(singletonsswitch, axiom, singletonsswitch =
% 5.37/1.29 (![Xx:$i,Xy:$i]:
% 5.37/1.29 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 5.37/1.29 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 5.37/1.29 thf('14', plain,
% 5.37/1.29 (( singletonsswitch ) =
% 5.37/1.29 ( ![X4:$i,X6:$i]:
% 5.37/1.29 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 5.37/1.29 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(eqinunit, axiom, eqinunit =
% 5.37/1.29 (![Xx:$i,Xy:$i]:
% 5.37/1.29 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 5.37/1.29 thf('15', plain,
% 5.37/1.29 (( eqinunit ) =
% 5.37/1.29 ( ![X4:$i,X6:$i]:
% 5.37/1.29 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(notinsingleton, axiom, notinsingleton =
% 5.37/1.29 (![Xx:$i,Xy:$i]:
% 5.37/1.29 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 5.37/1.29 thf('16', plain,
% 5.37/1.29 (( notinsingleton ) =
% 5.37/1.29 ( ![X4:$i,X6:$i]:
% 5.37/1.29 ( ( ( X4 ) != ( X6 ) ) =>
% 5.37/1.29 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(uniqinunit, axiom, uniqinunit =
% 5.37/1.29 (![Xx:$i,Xy:$i]:
% 5.37/1.29 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 5.37/1.29 thf('17', plain,
% 5.37/1.29 (( uniqinunit ) =
% 5.37/1.29 ( ![X4:$i,X6:$i]:
% 5.37/1.29 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(setadjoinOr, axiom, setadjoinOr =
% 5.37/1.29 (![Xx:$i,A:$i,Xy:$i]:
% 5.37/1.29 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 5.37/1.29 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 5.37/1.29 thf('18', plain,
% 5.37/1.29 (( setadjoinOr ) =
% 5.37/1.29 ( ![X4:$i,X6:$i,X8:$i]:
% 5.37/1.29 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 5.37/1.29 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(setadjoinE, axiom, setadjoinE =
% 5.37/1.29 (![Xx:$i,A:$i,Xy:$i]:
% 5.37/1.29 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 5.37/1.29 ( ![Xphi:$o]:
% 5.37/1.29 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 5.37/1.29 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 5.37/1.29 thf('19', plain,
% 5.37/1.29 (( setadjoinE ) =
% 5.37/1.29 ( ![X4:$i,X6:$i,X8:$i]:
% 5.37/1.29 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 5.37/1.29 ( ![X10:$o]:
% 5.37/1.29 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 5.37/1.29 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(setadjoinIR, axiom, setadjoinIR =
% 5.37/1.29 (![Xx:$i,A:$i,Xy:$i]:
% 5.37/1.29 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 5.37/1.29 thf('20', plain,
% 5.37/1.29 (( setadjoinIR ) =
% 5.37/1.29 ( ![X4:$i,X6:$i,X8:$i]:
% 5.37/1.29 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 5.37/1.29 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 5.37/1.29 thf('21', plain,
% 5.37/1.29 (( emptyinunitempty ) =
% 5.37/1.29 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 5.37/1.29 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 5.37/1.29 thf('22', plain,
% 5.37/1.29 (( emptyinunitempty ) =
% 5.37/1.29 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(setadjoinIL, axiom, setadjoinIL =
% 5.37/1.29 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 5.37/1.29 thf('23', plain,
% 5.37/1.29 (( setadjoinIL ) =
% 5.37/1.29 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(setadjoinAx, axiom, setadjoinAx =
% 5.37/1.29 (![Xx:$i,A:$i,Xy:$i]:
% 5.37/1.29 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 5.37/1.29 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 5.37/1.29 thf('24', plain,
% 5.37/1.29 (( setadjoinAx ) =
% 5.37/1.29 ( ![X4:$i,X6:$i,X8:$i]:
% 5.37/1.29 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 5.37/1.29 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 5.37/1.29 define([status(thm)])).
% 5.37/1.29 thf(setukpairinjR2, conjecture,
% 5.37/1.29 (( setextAx ) =>
% 5.37/1.29 ( ( emptysetAx ) =>
% 5.37/1.29 ( ( setadjoinAx ) =>
% 5.37/1.29 ( ( powersetAx ) =>
% 5.37/1.29 ( ( setunionAx ) =>
% 5.37/1.29 ( ( omega0Ax ) =>
% 5.37/1.29 ( ( omegaSAx ) =>
% 5.37/1.29 ( ( omegaIndAx ) =>
% 5.37/1.29 ( ( replAx ) =>
% 5.37/1.29 ( ( foundationAx ) =>
% 5.37/1.29 ( ( wellorderingAx ) =>
% 5.37/1.29 ( ( descrp ) =>
% 5.37/1.29 ( ( dsetconstrI ) =>
% 5.37/1.29 ( ( dsetconstrEL ) =>
% 5.37/1.29 ( ( dsetconstrER ) =>
% 5.37/1.29 ( ( exuE1 ) =>
% 5.37/1.29 ( ( prop2setE ) =>
% 5.37/1.29 ( ( emptysetE ) =>
% 5.37/1.29 ( ( emptysetimpfalse ) =>
% 5.37/1.29 ( ( notinemptyset ) =>
% 5.37/1.29 ( ( exuE3e ) =>
% 5.37/1.29 ( ( setext ) =>
% 5.37/1.29 ( ( emptyI ) =>
% 5.37/1.29 ( ( noeltsimpempty ) =>
% 5.37/1.29 ( ( setbeta ) =>
% 5.37/1.29 ( ( nonemptyE1 ) =>
% 5.37/1.29 ( ( nonemptyI ) =>
% 5.37/1.29 ( ( nonemptyI1 ) =>
% 5.37/1.29 ( ( setadjoinIL ) =>
% 5.37/1.29 ( ( emptyinunitempty ) =>
% 5.37/1.29 ( ( setadjoinIR ) =>
% 5.37/1.29 ( ( setadjoinE ) =>
% 5.37/1.29 ( (
% 5.37/1.29 setadjoinOr ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setoftrueEq ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 powersetI ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 emptyinPowerset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 emptyInPowerset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 powersetE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setunionI ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setunionE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subPowSU ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exuE2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 nonemptyImpWitness ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 uniqinunit ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 notinsingleton ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 eqinunit ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 singletonsswitch ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 upairsetE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 upairsetIL ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 upairsetIR ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 emptyE1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 vacuousDall ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 quantDeMorgan1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 quantDeMorgan2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 quantDeMorgan3 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 quantDeMorgan4 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 prop2setI ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 prop2set2propI ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 notdexE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 notdallE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exuI1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exuI3 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exuI2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 inCongP ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 in__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exuE3u ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exu__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 emptyset__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setadjoin__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 powerset__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setunion__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 omega__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exuEu ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 descr__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 dsetconstr__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetI1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 eqimpsubset2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 eqimpsubset1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetI2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 emptysetsubset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetE2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 notsubsetI ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 notequalI1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 notequalI2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetRefl ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetTrans ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setadjoinSub ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setadjoinSub2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subset2powerset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setextsub ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetemptysetimpeq ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 powersetI1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 powersetE1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 inPowerset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 powersetsubset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 sepInPowerset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 sepSubset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binunionIL ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 upairset2IR ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binunionIR ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binunionEcases ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binunionE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binunionLsub ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binunionRsub ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectI ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectSubset5 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectEL ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectLsub ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectSubset2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectSubset3 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectER ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 disjointsetsI1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectRsub ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectSubset4 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectSubset1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 bs114d ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setminusI ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setminusEL ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setminusER ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setminusSubset2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setminusERneg ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setminusELneg ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setminusILneg ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setminusIRneg ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setminusLsub ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setminusSubset1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 symdiffE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 symdiffI1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 symdiffI2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 symdiffIneg1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 symdiffIneg2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 secondinupair ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setukpairIL ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setukpairIR ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 kpairiskpair ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 kpairp ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 singletonsubset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 singletoninpowerset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 singletoninpowunion ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 upairset2E ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 upairsubunion ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 upairinpowunion ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ubforcartprodlem1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ubforcartprodlem2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ubforcartprodlem3 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 cartprodpairin ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 cartprodmempair1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 cartprodmempair ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setunionE2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setunionsingleton1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setunionsingleton2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setunionsingleton ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 singletonprop ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ex1E1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ex1I ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ex1I2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 singletonsuniq ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setukpairinjL1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 kfstsingleton ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 theprop ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 kfstpairEq ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 cartprodfstin ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setukpairinjL2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setukpairinjL ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setukpairinjR11 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setukpairinjR12 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setukpairinjR1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 upairequniteq ) =>
% 5.37/1.29 (
% 5.37/1.29 ![
% 5.37/1.29 Xx:$i,
% 5.37/1.29 Xy:$i,
% 5.37/1.29 Xz:$i,
% 5.37/1.29 Xu:$i]:
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 Xx @
% 5.37/1.29 emptyset ) @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 Xx @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 Xy @
% 5.37/1.29 emptyset ) ) @
% 5.37/1.29 emptyset ) ) =
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 Xz @
% 5.37/1.29 emptyset ) @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 Xz @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 Xu @
% 5.37/1.29 emptyset ) ) @
% 5.37/1.29 emptyset ) ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 Xy ) =
% 5.37/1.29 (
% 5.37/1.29 Xu ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 5.37/1.29 thf(zf_stmt_0, conjecture,
% 5.37/1.29 (( setextAx ) =>
% 5.37/1.29 ( ( emptysetAx ) =>
% 5.37/1.29 ( ( ![X4:$i,X6:$i,X8:$i]:
% 5.37/1.29 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 5.37/1.29 ( ( in @ X8 @ X6 ) | ( ( X8 ) = ( X4 ) ) ) ) ) =>
% 5.37/1.29 ( ( powersetAx ) =>
% 5.37/1.29 ( ( setunionAx ) =>
% 5.37/1.29 ( ( omega0Ax ) =>
% 5.37/1.29 ( ( omegaSAx ) =>
% 5.37/1.29 ( ( omegaIndAx ) =>
% 5.37/1.29 ( ( replAx ) =>
% 5.37/1.29 ( ( foundationAx ) =>
% 5.37/1.29 ( ( wellorderingAx ) =>
% 5.37/1.29 ( ( descrp ) =>
% 5.37/1.29 ( ( dsetconstrI ) =>
% 5.37/1.29 ( ( dsetconstrEL ) =>
% 5.37/1.29 ( ( dsetconstrER ) =>
% 5.37/1.29 ( ( exuE1 ) =>
% 5.37/1.29 ( ( prop2setE ) =>
% 5.37/1.29 ( ( emptysetE ) =>
% 5.37/1.29 ( ( emptysetimpfalse ) =>
% 5.37/1.29 ( ( notinemptyset ) =>
% 5.37/1.29 ( ( exuE3e ) =>
% 5.37/1.29 ( ( setext ) =>
% 5.37/1.29 ( ( emptyI ) =>
% 5.37/1.29 ( ( noeltsimpempty ) =>
% 5.37/1.29 ( ( setbeta ) =>
% 5.37/1.29 ( ( nonemptyE1 ) =>
% 5.37/1.29 ( ( nonemptyI ) =>
% 5.37/1.29 ( ( nonemptyI1 ) =>
% 5.37/1.29 ( ( ![X10:$i,X12:$i]:
% 5.37/1.29 ( in @
% 5.37/1.29 X10 @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 X10 @ X12 ) ) ) =>
% 5.37/1.29 ( ( in @
% 5.37/1.29 emptyset @
% 5.37/1.29 ( setadjoin @
% 5.37/1.29 emptyset @
% 5.37/1.29 emptyset ) ) =>
% 5.37/1.29 ( ( ![X14:$i,
% 5.37/1.29 X16:$i,
% 5.37/1.29 X18:$i]:
% 5.37/1.29 ( (
% 5.37/1.29 in @
% 5.37/1.29 X18 @ X16 ) =>
% 5.37/1.29 (
% 5.37/1.29 in @
% 5.37/1.29 X18 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X14 @ X16 ) ) ) ) =>
% 5.37/1.29 ( ( ![
% 5.37/1.29 X20:$i,
% 5.37/1.29 X22:$i,
% 5.37/1.29 X24:$i]:
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 in @
% 5.37/1.29 X24 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X20 @ X22 ) ) =>
% 5.37/1.29 (
% 5.37/1.29 ![
% 5.37/1.29 X26:$o]:
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 X24 ) =
% 5.37/1.29 (
% 5.37/1.29 X20 ) ) =>
% 5.37/1.29 (
% 5.37/1.29 X26 ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 in @
% 5.37/1.29 X24 @ X22 ) =>
% 5.37/1.29 (
% 5.37/1.29 X26 ) ) =>
% 5.37/1.29 (
% 5.37/1.29 X26 ) ) ) ) ) ) =>
% 5.37/1.29 ( (
% 5.37/1.29 ![
% 5.37/1.29 X28:$i,
% 5.37/1.29 X30:$i,
% 5.37/1.29 X32:$i]:
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 in @
% 5.37/1.29 X32 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X28 @ X30 ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 in @
% 5.37/1.29 X32 @ X30 ) |
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 X32 ) =
% 5.37/1.29 (
% 5.37/1.29 X28 ) ) ) ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setoftrueEq ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 powersetI ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 emptyinPowerset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 emptyInPowerset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 powersetE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setunionI ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setunionE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subPowSU ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exuE2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 nonemptyImpWitness ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ![
% 5.37/1.29 X34:$i,
% 5.37/1.29 X36:$i]:
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 in @
% 5.37/1.29 X34 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X36 @
% 5.37/1.29 emptyset ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 X34 ) =
% 5.37/1.29 (
% 5.37/1.29 X36 ) ) ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ![
% 5.37/1.29 X38:$i,
% 5.37/1.29 X40:$i]:
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 X38 ) !=
% 5.37/1.29 (
% 5.37/1.29 X40 ) ) =>
% 5.37/1.29 (
% 5.37/1.29 ~(
% 5.37/1.29 in @
% 5.37/1.29 X40 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X38 @
% 5.37/1.29 emptyset ) ) ) ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ![
% 5.37/1.29 X42:$i,
% 5.37/1.29 X44:$i]:
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 X42 ) =
% 5.37/1.29 (
% 5.37/1.29 X44 ) ) =>
% 5.37/1.29 (
% 5.37/1.29 in @
% 5.37/1.29 X42 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X44 @
% 5.37/1.29 emptyset ) ) ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ![
% 5.37/1.29 X46:$i,
% 5.37/1.29 X48:$i]:
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 in @
% 5.37/1.29 X46 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X48 @
% 5.37/1.29 emptyset ) ) =>
% 5.37/1.29 (
% 5.37/1.29 in @
% 5.37/1.29 X48 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X46 @
% 5.37/1.29 emptyset ) ) ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ![
% 5.37/1.29 X50:$i,
% 5.37/1.29 X52:$i,
% 5.37/1.29 X54:$i]:
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 in @
% 5.37/1.29 X54 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X50 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X52 @
% 5.37/1.29 emptyset ) ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 X54 ) =
% 5.37/1.29 (
% 5.37/1.29 X52 ) ) |
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 X54 ) =
% 5.37/1.29 (
% 5.37/1.29 X50 ) ) ) ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ![
% 5.37/1.29 X56:$i,
% 5.37/1.29 X58:$i]:
% 5.37/1.29 (
% 5.37/1.29 in @
% 5.37/1.29 X56 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X56 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X58 @
% 5.37/1.29 emptyset ) ) ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ![
% 5.37/1.29 X60:$i,
% 5.37/1.29 X62:$i]:
% 5.37/1.29 (
% 5.37/1.29 in @
% 5.37/1.29 X62 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X60 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X62 @
% 5.37/1.29 emptyset ) ) ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 emptyE1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 vacuousDall ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 quantDeMorgan1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 quantDeMorgan2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 quantDeMorgan3 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 quantDeMorgan4 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 prop2setI ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 prop2set2propI ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 notdexE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 notdallE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exuI1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exuI3 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exuI2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 inCongP ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 in__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exuE3u ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exu__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 emptyset__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ![
% 5.37/1.29 X64:$i,
% 5.37/1.29 X66:$i]:
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 X64 ) =
% 5.37/1.29 (
% 5.37/1.29 X66 ) ) =>
% 5.37/1.29 (
% 5.37/1.29 ![
% 5.37/1.29 X68:$i,
% 5.37/1.29 X70:$i]:
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 X68 ) =
% 5.37/1.29 (
% 5.37/1.29 X70 ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X64 @ X68 ) =
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X66 @ X70 ) ) ) ) ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 powerset__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setunion__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 omega__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 exuEu ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 descr__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 dsetconstr__Cong ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetI1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 eqimpsubset2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 eqimpsubset1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetI2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 emptysetsubset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetE2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 notsubsetI ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 notequalI1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 notequalI2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetRefl ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetTrans ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setadjoinSub ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setadjoinSub2 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subset2powerset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 setextsub ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 subsetemptysetimpeq ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 powersetI1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 powersetE1 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 inPowerset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 powersetsubset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 sepInPowerset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 sepSubset ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binunionIL ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 ![
% 5.37/1.29 X72:$i,
% 5.37/1.29 X74:$i]:
% 5.37/1.29 (
% 5.37/1.29 in @
% 5.37/1.29 X74 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X72 @
% 5.37/1.29 (
% 5.37/1.29 setadjoin
% 5.37/1.29 @
% 5.37/1.29 X74 @
% 5.37/1.29 emptyset ) ) ) ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binunionIR ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binunionEcases ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binunionE ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binunionLsub ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binunionRsub ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectI ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectSubset5 ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectEL ) =>
% 5.37/1.29 (
% 5.37/1.29 (
% 5.37/1.29 binintersectLsub ) =>
% 5.37/1.29 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset3 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectER ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 disjointsetsI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectRsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset4 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 bs114d ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusEL ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusER ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusSubset2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusERneg ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusELneg ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusILneg ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusIRneg ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusLsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusSubset1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffI2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffIneg1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffIneg2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X76:$i,
% 5.37/1.30 X78:$i]:
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X78 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X76 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X78 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setukpairIL ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setukpairIR ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 kpairiskpair ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 kpairp ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 singletonsubset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 singletoninpowerset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 singletoninpowunion ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X80:$i,
% 5.37/1.30 X82:$i,
% 5.37/1.30 X84:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X84 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X80 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X82 @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X84 ) =
% 5.37/1.30 (
% 5.37/1.30 X82 ) ) |
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X84 ) =
% 5.37/1.30 (
% 5.37/1.30 X80 ) ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 upairsubunion ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 upairinpowunion ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ubforcartprodlem1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ubforcartprodlem2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ubforcartprodlem3 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 cartprodpairin ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 cartprodmempair1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 cartprodmempair ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionE2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionsingleton1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionsingleton2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionsingleton ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 singletonprop ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ex1E1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ex1I ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ex1I2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X86:$i,
% 5.37/1.30 X88:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X86 @
% 5.37/1.30 emptyset ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X88 @
% 5.37/1.30 emptyset ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X86 ) =
% 5.37/1.30 (
% 5.37/1.30 X88 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X90:$i,
% 5.37/1.30 X92:$i,
% 5.37/1.30 X94:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X94 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X90 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X90 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X92 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X90 ) =
% 5.37/1.30 (
% 5.37/1.30 X94 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 kfstsingleton ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 theprop ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 kfstpairEq ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 cartprodfstin ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X96:$i,
% 5.37/1.30 X98:$i,
% 5.37/1.30 X100:$i,
% 5.37/1.30 X102:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X96 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X96 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X98 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X100 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X100 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X102 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X96 ) =
% 5.37/1.30 (
% 5.37/1.30 X100 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setukpairinjL ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X104:$i,
% 5.37/1.30 X106:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X104 ) =
% 5.37/1.30 (
% 5.37/1.30 X106 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X104 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X106 @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X104 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X108:$i,
% 5.37/1.30 X110:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X108 ) =
% 5.37/1.30 (
% 5.37/1.30 X110 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X108 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X108 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X110 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X108 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X112:$i,
% 5.37/1.30 X114:$i,
% 5.37/1.30 X116:$i,
% 5.37/1.30 X118:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X112 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X112 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X114 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X116 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X116 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X118 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X116 ) =
% 5.37/1.30 (
% 5.37/1.30 X118 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X114 ) =
% 5.37/1.30 (
% 5.37/1.30 X118 ) ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X120:$i,
% 5.37/1.30 X122:$i,
% 5.37/1.30 X124:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X120 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X122 @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X124 @
% 5.37/1.30 emptyset ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X120 ) =
% 5.37/1.30 (
% 5.37/1.30 X122 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X126:$i,
% 5.37/1.30 X128:$i,
% 5.37/1.30 X130:$i,
% 5.37/1.30 X132:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X126 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X126 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X128 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X130 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X130 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X132 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X128 ) =
% 5.37/1.30 (
% 5.37/1.30 X132 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 5.37/1.30 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 5.37/1.30 thf(zf_stmt_2, axiom,
% 5.37/1.30 (![X8:$i,X6:$i,X4:$i]:
% 5.37/1.30 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 5.37/1.30 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ))).
% 5.37/1.30 thf(zf_stmt_3, conjecture,
% 5.37/1.30 (( setextAx ) =>
% 5.37/1.30 ( ( emptysetAx ) =>
% 5.37/1.30 ( ( ![X4:$i,X6:$i,X8:$i]:
% 5.37/1.30 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 5.37/1.30 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 5.37/1.30 ( ( powersetAx ) =>
% 5.37/1.30 ( ( setunionAx ) =>
% 5.37/1.30 ( ( omega0Ax ) =>
% 5.37/1.30 ( ( omegaSAx ) =>
% 5.37/1.30 ( ( omegaIndAx ) =>
% 5.37/1.30 ( ( replAx ) =>
% 5.37/1.30 ( ( foundationAx ) =>
% 5.37/1.30 ( ( wellorderingAx ) =>
% 5.37/1.30 ( ( descrp ) =>
% 5.37/1.30 ( ( dsetconstrI ) =>
% 5.37/1.30 ( ( dsetconstrEL ) =>
% 5.37/1.30 ( ( dsetconstrER ) =>
% 5.37/1.30 ( ( exuE1 ) =>
% 5.37/1.30 ( ( prop2setE ) =>
% 5.37/1.30 ( ( emptysetE ) =>
% 5.37/1.30 ( ( emptysetimpfalse ) =>
% 5.37/1.30 ( ( notinemptyset ) =>
% 5.37/1.30 ( ( exuE3e ) =>
% 5.37/1.30 ( ( setext ) =>
% 5.37/1.30 ( ( emptyI ) =>
% 5.37/1.30 ( ( noeltsimpempty ) =>
% 5.37/1.30 ( ( setbeta ) =>
% 5.37/1.30 ( ( nonemptyE1 ) =>
% 5.37/1.30 ( ( nonemptyI ) =>
% 5.37/1.30 ( ( nonemptyI1 ) =>
% 5.37/1.30 ( ( ![X10:$i,X12:$i]:
% 5.37/1.30 ( in @
% 5.37/1.30 X10 @
% 5.37/1.30 ( setadjoin @
% 5.37/1.30 X10 @ X12 ) ) ) =>
% 5.37/1.30 ( ( in @
% 5.37/1.30 emptyset @
% 5.37/1.30 ( setadjoin @
% 5.37/1.30 emptyset @
% 5.37/1.30 emptyset ) ) =>
% 5.37/1.30 ( ( ![X14:$i,
% 5.37/1.30 X16:$i,
% 5.37/1.30 X18:$i]:
% 5.37/1.30 ( (
% 5.37/1.30 in @
% 5.37/1.30 X18 @ X16 ) =>
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X18 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X14 @ X16 ) ) ) ) =>
% 5.37/1.30 ( ( ![
% 5.37/1.30 X20:$i,
% 5.37/1.30 X22:$i,
% 5.37/1.30 X24:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X24 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X20 @ X22 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X26:$o]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X24 ) =
% 5.37/1.30 (
% 5.37/1.30 X20 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 X26 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X24 @ X22 ) =>
% 5.37/1.30 (
% 5.37/1.30 X26 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 X26 ) ) ) ) ) ) =>
% 5.37/1.30 ( (
% 5.37/1.30 ![
% 5.37/1.30 X28:$i,
% 5.37/1.30 X30:$i,
% 5.37/1.30 X32:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X32 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X28 @ X30 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X32 ) =
% 5.37/1.30 (
% 5.37/1.30 X28 ) ) |
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X32 @ X30 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setoftrueEq ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 powersetI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 emptyinPowerset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 emptyInPowerset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 powersetE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subPowSU ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exuE2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 nonemptyImpWitness ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X34:$i,
% 5.37/1.30 X36:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X34 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X36 @
% 5.37/1.30 emptyset ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X34 ) =
% 5.37/1.30 (
% 5.37/1.30 X36 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X38:$i,
% 5.37/1.30 X40:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X38 ) !=
% 5.37/1.30 (
% 5.37/1.30 X40 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 ~(
% 5.37/1.30 in @
% 5.37/1.30 X40 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X38 @
% 5.37/1.30 emptyset ) ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X42:$i,
% 5.37/1.30 X44:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X42 ) =
% 5.37/1.30 (
% 5.37/1.30 X44 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X42 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X44 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X46:$i,
% 5.37/1.30 X48:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X46 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X48 @
% 5.37/1.30 emptyset ) ) =>
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X48 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X46 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X50:$i,
% 5.37/1.30 X52:$i,
% 5.37/1.30 X54:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X54 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X50 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X52 @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X54 ) =
% 5.37/1.30 (
% 5.37/1.30 X50 ) ) |
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X54 ) =
% 5.37/1.30 (
% 5.37/1.30 X52 ) ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X56:$i,
% 5.37/1.30 X58:$i]:
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X56 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X56 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X58 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X60:$i,
% 5.37/1.30 X62:$i]:
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X62 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X60 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X62 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 emptyE1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 vacuousDall ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 quantDeMorgan1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 quantDeMorgan2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 quantDeMorgan3 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 quantDeMorgan4 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 prop2setI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 prop2set2propI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 notdexE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 notdallE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exuI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exuI3 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exuI2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 inCongP ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exuE3u ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exu__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 emptyset__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X64:$i,
% 5.37/1.30 X66:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X64 ) =
% 5.37/1.30 (
% 5.37/1.30 X66 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X68:$i,
% 5.37/1.30 X70:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X68 ) =
% 5.37/1.30 (
% 5.37/1.30 X70 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X64 @ X68 ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X66 @ X70 ) ) ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 powerset__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunion__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 omega__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exuEu ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 descr__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 dsetconstr__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 eqimpsubset2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 eqimpsubset1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetI2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 emptysetsubset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetE2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 notsubsetI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 notequalI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 notequalI2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetRefl ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetTrans ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoinSub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoinSub2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subset2powerset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setextsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetemptysetimpeq ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 powersetI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 powersetE1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 inPowerset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 powersetsubset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 sepInPowerset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 sepSubset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binunionIL ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X72:$i,
% 5.37/1.30 X74:$i]:
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X74 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X72 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X74 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binunionIR ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binunionEcases ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binunionE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binunionLsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binunionRsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset5 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectEL ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectLsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset3 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectER ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 disjointsetsI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectRsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset4 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 bs114d ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusEL ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusER ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusSubset2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusERneg ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusELneg ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusILneg ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusIRneg ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusLsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusSubset1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffI2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffIneg1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffIneg2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X76:$i,
% 5.37/1.30 X78:$i]:
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X78 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X76 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X78 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setukpairIL ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setukpairIR ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 kpairiskpair ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 kpairp ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 singletonsubset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 singletoninpowerset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 singletoninpowunion ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X80:$i,
% 5.37/1.30 X82:$i,
% 5.37/1.30 X84:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X84 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X80 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X82 @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X84 ) =
% 5.37/1.30 (
% 5.37/1.30 X80 ) ) |
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X84 ) =
% 5.37/1.30 (
% 5.37/1.30 X82 ) ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 upairsubunion ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 upairinpowunion ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ubforcartprodlem1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ubforcartprodlem2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ubforcartprodlem3 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 cartprodpairin ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 cartprodmempair1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 cartprodmempair ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionE2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionsingleton1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionsingleton2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionsingleton ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 singletonprop ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ex1E1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ex1I ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ex1I2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X86:$i,
% 5.37/1.30 X88:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X86 @
% 5.37/1.30 emptyset ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X88 @
% 5.37/1.30 emptyset ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X86 ) =
% 5.37/1.30 (
% 5.37/1.30 X88 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X90:$i,
% 5.37/1.30 X92:$i,
% 5.37/1.30 X94:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X94 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X90 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X90 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X92 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X90 ) =
% 5.37/1.30 (
% 5.37/1.30 X94 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 kfstsingleton ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 theprop ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 kfstpairEq ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 cartprodfstin ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X96:$i,
% 5.37/1.30 X98:$i,
% 5.37/1.30 X100:$i,
% 5.37/1.30 X102:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X96 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X96 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X98 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X100 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X100 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X102 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X96 ) =
% 5.37/1.30 (
% 5.37/1.30 X100 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setukpairinjL ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X104:$i,
% 5.37/1.30 X106:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X104 ) =
% 5.37/1.30 (
% 5.37/1.30 X106 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X104 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X106 @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X104 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X108:$i,
% 5.37/1.30 X110:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X108 ) =
% 5.37/1.30 (
% 5.37/1.30 X110 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X108 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X108 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X110 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X108 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X112:$i,
% 5.37/1.30 X114:$i,
% 5.37/1.30 X116:$i,
% 5.37/1.30 X118:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X112 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X112 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X114 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X116 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X116 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X118 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X116 ) =
% 5.37/1.30 (
% 5.37/1.30 X118 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X114 ) =
% 5.37/1.30 (
% 5.37/1.30 X118 ) ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X120:$i,
% 5.37/1.30 X122:$i,
% 5.37/1.30 X124:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X120 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X122 @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X124 @
% 5.37/1.30 emptyset ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X120 ) =
% 5.37/1.30 (
% 5.37/1.30 X122 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X126:$i,
% 5.37/1.30 X128:$i,
% 5.37/1.30 X130:$i,
% 5.37/1.30 X132:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X126 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X126 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X128 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X130 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X130 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X132 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X128 ) =
% 5.37/1.30 (
% 5.37/1.30 X132 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 5.37/1.30 thf(zf_stmt_4, negated_conjecture,
% 5.37/1.30 (~( ( setextAx ) =>
% 5.37/1.30 ( ( emptysetAx ) =>
% 5.37/1.30 ( ( ![X4:$i,X6:$i,X8:$i]:
% 5.37/1.30 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 5.37/1.30 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 5.37/1.30 ( ( powersetAx ) =>
% 5.37/1.30 ( ( setunionAx ) =>
% 5.37/1.30 ( ( omega0Ax ) =>
% 5.37/1.30 ( ( omegaSAx ) =>
% 5.37/1.30 ( ( omegaIndAx ) =>
% 5.37/1.30 ( ( replAx ) =>
% 5.37/1.30 ( ( foundationAx ) =>
% 5.37/1.30 ( ( wellorderingAx ) =>
% 5.37/1.30 ( ( descrp ) =>
% 5.37/1.30 ( ( dsetconstrI ) =>
% 5.37/1.30 ( ( dsetconstrEL ) =>
% 5.37/1.30 ( ( dsetconstrER ) =>
% 5.37/1.30 ( ( exuE1 ) =>
% 5.37/1.30 ( ( prop2setE ) =>
% 5.37/1.30 ( ( emptysetE ) =>
% 5.37/1.30 ( ( emptysetimpfalse ) =>
% 5.37/1.30 ( ( notinemptyset ) =>
% 5.37/1.30 ( ( exuE3e ) =>
% 5.37/1.30 ( ( setext ) =>
% 5.37/1.30 ( ( emptyI ) =>
% 5.37/1.30 ( ( noeltsimpempty ) =>
% 5.37/1.30 ( ( setbeta ) =>
% 5.37/1.30 ( ( nonemptyE1 ) =>
% 5.37/1.30 ( ( nonemptyI ) =>
% 5.37/1.30 ( ( nonemptyI1 ) =>
% 5.37/1.30 ( ( ![X10:$i,
% 5.37/1.30 X12:$i]:
% 5.37/1.30 ( in @
% 5.37/1.30 X10 @
% 5.37/1.30 ( setadjoin
% 5.37/1.30 @
% 5.37/1.30 X10 @ X12 ) ) ) =>
% 5.37/1.30 ( ( in @
% 5.37/1.30 emptyset @
% 5.37/1.30 ( setadjoin
% 5.37/1.30 @
% 5.37/1.30 emptyset @
% 5.37/1.30 emptyset ) ) =>
% 5.37/1.30 ( ( ![
% 5.37/1.30 X14:$i,
% 5.37/1.30 X16:$i,
% 5.37/1.30 X18:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X18 @ X16 ) =>
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X18 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X14 @ X16 ) ) ) ) =>
% 5.37/1.30 ( (
% 5.37/1.30 ![
% 5.37/1.30 X20:$i,
% 5.37/1.30 X22:$i,
% 5.37/1.30 X24:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X24 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X20 @ X22 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X26:$o]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X24 ) =
% 5.37/1.30 (
% 5.37/1.30 X20 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 X26 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X24 @ X22 ) =>
% 5.37/1.30 (
% 5.37/1.30 X26 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 X26 ) ) ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X28:$i,
% 5.37/1.30 X30:$i,
% 5.37/1.30 X32:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X32 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X28 @ X30 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X32 ) =
% 5.37/1.30 (
% 5.37/1.30 X28 ) ) |
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X32 @ X30 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setoftrueEq ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 powersetI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 emptyinPowerset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 emptyInPowerset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 powersetE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subPowSU ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exuE2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 nonemptyImpWitness ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X34:$i,
% 5.37/1.30 X36:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X34 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X36 @
% 5.37/1.30 emptyset ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X34 ) =
% 5.37/1.30 (
% 5.37/1.30 X36 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X38:$i,
% 5.37/1.30 X40:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X38 ) !=
% 5.37/1.30 (
% 5.37/1.30 X40 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 ~
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X40 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X38 @
% 5.37/1.30 emptyset ) ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X42:$i,
% 5.37/1.30 X44:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X42 ) =
% 5.37/1.30 (
% 5.37/1.30 X44 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X42 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X44 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X46:$i,
% 5.37/1.30 X48:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X46 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X48 @
% 5.37/1.30 emptyset ) ) =>
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X48 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X46 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X50:$i,
% 5.37/1.30 X52:$i,
% 5.37/1.30 X54:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X54 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X50 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X52 @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X54 ) =
% 5.37/1.30 (
% 5.37/1.30 X50 ) ) |
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X54 ) =
% 5.37/1.30 (
% 5.37/1.30 X52 ) ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X56:$i,
% 5.37/1.30 X58:$i]:
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X56 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X56 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X58 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X60:$i,
% 5.37/1.30 X62:$i]:
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X62 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X60 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X62 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 emptyE1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 vacuousDall ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 quantDeMorgan1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 quantDeMorgan2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 quantDeMorgan3 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 quantDeMorgan4 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 prop2setI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 prop2set2propI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 notdexE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 notdallE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exuI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exuI3 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exuI2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 inCongP ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exuE3u ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exu__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 emptyset__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X64:$i,
% 5.37/1.30 X66:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X64 ) =
% 5.37/1.30 (
% 5.37/1.30 X66 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X68:$i,
% 5.37/1.30 X70:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X68 ) =
% 5.37/1.30 (
% 5.37/1.30 X70 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X64 @ X68 ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X66 @ X70 ) ) ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 powerset__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunion__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 omega__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 exuEu ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 descr__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 dsetconstr__Cong ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 eqimpsubset2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 eqimpsubset1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetI2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 emptysetsubset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetE2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 notsubsetI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 notequalI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 notequalI2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetRefl ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetTrans ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoinSub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoinSub2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subset2powerset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setextsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 subsetemptysetimpeq ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 powersetI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 powersetE1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 inPowerset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 powersetsubset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 sepInPowerset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 sepSubset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binunionIL ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X72:$i,
% 5.37/1.30 X74:$i]:
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X74 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X72 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X74 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binunionIR ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binunionEcases ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binunionE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binunionLsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binunionRsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset5 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectEL ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectLsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset3 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectER ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 disjointsetsI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectRsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset4 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 binintersectSubset1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 bs114d ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusI ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusEL ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusER ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusSubset2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusERneg ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusELneg ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusILneg ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusIRneg ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusLsub ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setminusSubset1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffE ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffI1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffI2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffIneg1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 symdiffIneg2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X76:$i,
% 5.37/1.30 X78:$i]:
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X78 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X76 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X78 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setukpairIL ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setukpairIR ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 kpairiskpair ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 kpairp ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 singletonsubset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 singletoninpowerset ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 singletoninpowunion ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X80:$i,
% 5.37/1.30 X82:$i,
% 5.37/1.30 X84:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 X84 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X80 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X82 @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X84 ) =
% 5.37/1.30 (
% 5.37/1.30 X80 ) ) |
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X84 ) =
% 5.37/1.30 (
% 5.37/1.30 X82 ) ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 upairsubunion ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 upairinpowunion ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ubforcartprodlem1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ubforcartprodlem2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ubforcartprodlem3 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 cartprodpairin ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 cartprodmempair1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 cartprodmempair ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionE2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionsingleton1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionsingleton2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setunionsingleton ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 singletonprop ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ex1E1 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ex1I ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ex1I2 ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X86:$i,
% 5.37/1.30 X88:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X86 @
% 5.37/1.30 emptyset ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X88 @
% 5.37/1.30 emptyset ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X86 ) =
% 5.37/1.30 (
% 5.37/1.30 X88 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X90:$i,
% 5.37/1.30 X92:$i,
% 5.37/1.30 X94:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 in @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X94 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X90 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X90 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X92 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X90 ) =
% 5.37/1.30 (
% 5.37/1.30 X94 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 kfstsingleton ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 theprop ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 kfstpairEq ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 cartprodfstin ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X96:$i,
% 5.37/1.30 X98:$i,
% 5.37/1.30 X100:$i,
% 5.37/1.30 X102:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X96 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X96 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X98 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X100 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X100 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X102 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X96 ) =
% 5.37/1.30 (
% 5.37/1.30 X100 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setukpairinjL ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X104:$i,
% 5.37/1.30 X106:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X104 ) =
% 5.37/1.30 (
% 5.37/1.30 X106 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X104 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X106 @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X104 @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X108:$i,
% 5.37/1.30 X110:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X108 ) =
% 5.37/1.30 (
% 5.37/1.30 X110 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X108 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X108 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X110 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X108 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 emptyset ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X112:$i,
% 5.37/1.30 X114:$i,
% 5.37/1.30 X116:$i,
% 5.37/1.30 X118:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X112 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X112 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X114 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X116 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X116 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X118 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X116 ) =
% 5.37/1.30 (
% 5.37/1.30 X118 ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X114 ) =
% 5.37/1.30 (
% 5.37/1.30 X118 ) ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X120:$i,
% 5.37/1.30 X122:$i,
% 5.37/1.30 X124:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X120 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X122 @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X124 @
% 5.37/1.30 emptyset ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X120 ) =
% 5.37/1.30 (
% 5.37/1.30 X122 ) ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 ![
% 5.37/1.30 X126:$i,
% 5.37/1.30 X128:$i,
% 5.37/1.30 X130:$i,
% 5.37/1.30 X132:$i]:
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X126 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X126 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X128 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) =
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X130 @
% 5.37/1.30 emptyset ) @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X130 @
% 5.37/1.30 (
% 5.37/1.30 setadjoin
% 5.37/1.30 @
% 5.37/1.30 X132 @
% 5.37/1.30 emptyset ) ) @
% 5.37/1.30 emptyset ) ) ) =>
% 5.37/1.30 (
% 5.37/1.30 (
% 5.37/1.30 X128 ) =
% 5.37/1.30 (
% 5.37/1.30 X132 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 5.37/1.30 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 5.37/1.30 thf(zip_derived_cl90, plain,
% 5.37/1.30 (((setadjoin @ (setadjoin @ sk__61 @ emptyset) @
% 5.37/1.30 (setadjoin @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @
% 5.37/1.30 emptyset))
% 5.37/1.30 = (setadjoin @ (setadjoin @ sk__63 @ emptyset) @
% 5.37/1.30 (setadjoin @
% 5.37/1.30 (setadjoin @ sk__63 @ (setadjoin @ sk__64 @ emptyset)) @ emptyset)))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl90, plain,
% 5.37/1.30 (((setadjoin @ (setadjoin @ sk__61 @ emptyset) @
% 5.37/1.30 (setadjoin @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @
% 5.37/1.30 emptyset))
% 5.37/1.30 = (setadjoin @ (setadjoin @ sk__63 @ emptyset) @
% 5.37/1.30 (setadjoin @
% 5.37/1.30 (setadjoin @ sk__63 @ (setadjoin @ sk__64 @ emptyset)) @ emptyset)))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl18, plain,
% 5.37/1.30 (![X4 : $i, X5 : $i]: (in @ X4 @ (setadjoin @ X4 @ X5))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl465, plain,
% 5.37/1.30 ( (in @ (setadjoin @ sk__63 @ emptyset) @
% 5.37/1.30 (setadjoin @ (setadjoin @ sk__61 @ emptyset) @
% 5.37/1.30 (setadjoin @
% 5.37/1.30 (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @ emptyset)))),
% 5.37/1.30 inference('sup+', [status(thm)], [zip_derived_cl90, zip_derived_cl18])).
% 5.37/1.30 thf(zip_derived_cl83, plain,
% 5.37/1.30 (![X27 : $i, X28 : $i, X29 : $i]:
% 5.37/1.30 (((X28) = (X27))
% 5.37/1.30 | ~ (in @ (setadjoin @ X27 @ emptyset) @
% 5.37/1.30 (setadjoin @ (setadjoin @ X28 @ emptyset) @
% 5.37/1.30 (setadjoin @
% 5.37/1.30 (setadjoin @ X28 @ (setadjoin @ X29 @ emptyset)) @ emptyset))))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl492, plain, (((sk__61) = (sk__63))),
% 5.37/1.30 inference('sup-', [status(thm)], [zip_derived_cl465, zip_derived_cl83])).
% 5.37/1.30 thf(zip_derived_cl492, plain, (((sk__61) = (sk__63))),
% 5.37/1.30 inference('sup-', [status(thm)], [zip_derived_cl465, zip_derived_cl83])).
% 5.37/1.30 thf(zip_derived_cl518, plain,
% 5.37/1.30 (((setadjoin @ (setadjoin @ sk__61 @ emptyset) @
% 5.37/1.30 (setadjoin @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @
% 5.37/1.30 emptyset))
% 5.37/1.30 = (setadjoin @ (setadjoin @ sk__61 @ emptyset) @
% 5.37/1.30 (setadjoin @
% 5.37/1.30 (setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset)) @ emptyset)))),
% 5.37/1.30 inference('demod', [status(thm)],
% 5.37/1.30 [zip_derived_cl90, zip_derived_cl492, zip_derived_cl492])).
% 5.37/1.30 thf(zip_derived_cl518, plain,
% 5.37/1.30 (((setadjoin @ (setadjoin @ sk__61 @ emptyset) @
% 5.37/1.30 (setadjoin @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @
% 5.37/1.30 emptyset))
% 5.37/1.30 = (setadjoin @ (setadjoin @ sk__61 @ emptyset) @
% 5.37/1.30 (setadjoin @
% 5.37/1.30 (setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset)) @ emptyset)))),
% 5.37/1.30 inference('demod', [status(thm)],
% 5.37/1.30 [zip_derived_cl90, zip_derived_cl492, zip_derived_cl492])).
% 5.37/1.30 thf(zip_derived_cl70, plain,
% 5.37/1.30 (![X22 : $i, X23 : $i]:
% 5.37/1.30 (in @ X22 @ (setadjoin @ X23 @ (setadjoin @ X22 @ emptyset)))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl524, plain,
% 5.37/1.30 ( (in @ (setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset)) @
% 5.37/1.30 (setadjoin @ (setadjoin @ sk__61 @ emptyset) @
% 5.37/1.30 (setadjoin @
% 5.37/1.30 (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @ emptyset)))),
% 5.37/1.30 inference('sup+', [status(thm)], [zip_derived_cl518, zip_derived_cl70])).
% 5.37/1.30 thf(zip_derived_cl74, plain,
% 5.37/1.30 (![X24 : $i, X25 : $i, X26 : $i]:
% 5.37/1.30 (((X25) = (X24))
% 5.37/1.30 | ((X25) = (X26))
% 5.37/1.30 | ~ (in @ X25 @ (setadjoin @ X26 @ (setadjoin @ X24 @ emptyset))))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl570, plain,
% 5.37/1.30 ((((setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset))
% 5.37/1.30 = (setadjoin @ sk__61 @ emptyset))
% 5.37/1.30 | ((setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset))
% 5.37/1.30 = (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset))))),
% 5.37/1.30 inference('sup-', [status(thm)], [zip_derived_cl524, zip_derived_cl74])).
% 5.37/1.30 thf(zip_derived_cl70, plain,
% 5.37/1.30 (![X22 : $i, X23 : $i]:
% 5.37/1.30 (in @ X22 @ (setadjoin @ X23 @ (setadjoin @ X22 @ emptyset)))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl604, plain,
% 5.37/1.30 (( (in @ sk__64 @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)))
% 5.37/1.30 | ((setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset))
% 5.37/1.30 = (setadjoin @ sk__61 @ emptyset)))),
% 5.37/1.30 inference('sup+', [status(thm)], [zip_derived_cl570, zip_derived_cl70])).
% 5.37/1.30 thf(zip_derived_cl74, plain,
% 5.37/1.30 (![X24 : $i, X25 : $i, X26 : $i]:
% 5.37/1.30 (((X25) = (X24))
% 5.37/1.30 | ((X25) = (X26))
% 5.37/1.30 | ~ (in @ X25 @ (setadjoin @ X26 @ (setadjoin @ X24 @ emptyset))))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl626, plain,
% 5.37/1.30 ((((setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset))
% 5.37/1.30 = (setadjoin @ sk__61 @ emptyset))
% 5.37/1.30 | ((sk__64) = (sk__61))
% 5.37/1.30 | ((sk__64) = (sk__62)))),
% 5.37/1.30 inference('sup-', [status(thm)], [zip_derived_cl604, zip_derived_cl74])).
% 5.37/1.30 thf(zip_derived_cl89, plain, (((sk__62) != (sk__64))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl640, plain,
% 5.37/1.30 ((((setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset))
% 5.37/1.30 = (setadjoin @ sk__61 @ emptyset))
% 5.37/1.30 | ((sk__64) = (sk__61)))),
% 5.37/1.30 inference('simplify_reflect-', [status(thm)],
% 5.37/1.30 [zip_derived_cl626, zip_derived_cl89])).
% 5.37/1.30 thf(zip_derived_cl88, plain,
% 5.37/1.30 (![X32 : $i, X33 : $i, X34 : $i]:
% 5.37/1.30 (((X33) = (X32))
% 5.37/1.30 | ((setadjoin @ X33 @ (setadjoin @ X32 @ emptyset))
% 5.37/1.30 != (setadjoin @ X34 @ emptyset)))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl642, plain, (((sk__64) = (sk__61))),
% 5.37/1.30 inference('clc', [status(thm)], [zip_derived_cl640, zip_derived_cl88])).
% 5.37/1.30 thf(zip_derived_cl92, plain,
% 5.37/1.30 (![X39 : $i, X40 : $i]:
% 5.37/1.30 (((setadjoin @ X39 @ (setadjoin @ X40 @ emptyset))
% 5.37/1.30 = (setadjoin @ X39 @ emptyset))
% 5.37/1.30 | ((X39) != (X40)))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl397, plain,
% 5.37/1.30 (![X40 : $i]:
% 5.37/1.30 ((setadjoin @ X40 @ (setadjoin @ X40 @ emptyset))
% 5.37/1.30 = (setadjoin @ X40 @ emptyset))),
% 5.37/1.30 inference('simplify', [status(thm)], [zip_derived_cl92])).
% 5.37/1.30 thf(zip_derived_cl397, plain,
% 5.37/1.30 (![X40 : $i]:
% 5.37/1.30 ((setadjoin @ X40 @ (setadjoin @ X40 @ emptyset))
% 5.37/1.30 = (setadjoin @ X40 @ emptyset))),
% 5.37/1.30 inference('simplify', [status(thm)], [zip_derived_cl92])).
% 5.37/1.30 thf(zip_derived_cl645, plain,
% 5.37/1.30 (((setadjoin @ (setadjoin @ sk__61 @ emptyset) @
% 5.37/1.30 (setadjoin @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @
% 5.37/1.30 emptyset))
% 5.37/1.30 = (setadjoin @ (setadjoin @ sk__61 @ emptyset) @ emptyset))),
% 5.37/1.30 inference('demod', [status(thm)],
% 5.37/1.30 [zip_derived_cl518, zip_derived_cl642, zip_derived_cl397,
% 5.37/1.30 zip_derived_cl397])).
% 5.37/1.30 thf(zip_derived_cl70, plain,
% 5.37/1.30 (![X22 : $i, X23 : $i]:
% 5.37/1.30 (in @ X22 @ (setadjoin @ X23 @ (setadjoin @ X22 @ emptyset)))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl994, plain,
% 5.37/1.30 ( (in @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @
% 5.37/1.30 (setadjoin @ (setadjoin @ sk__61 @ emptyset) @ emptyset))),
% 5.37/1.30 inference('sup+', [status(thm)], [zip_derived_cl645, zip_derived_cl70])).
% 5.37/1.30 thf(zip_derived_cl26, plain,
% 5.37/1.30 (![X12 : $i, X13 : $i]:
% 5.37/1.30 (~ (in @ X12 @ (setadjoin @ X13 @ emptyset)) | ((X13) = (X12)))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl1047, plain,
% 5.37/1.30 (((setadjoin @ sk__61 @ emptyset)
% 5.37/1.30 = (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)))),
% 5.37/1.30 inference('sup-', [status(thm)], [zip_derived_cl994, zip_derived_cl26])).
% 5.37/1.30 thf(zip_derived_cl88, plain,
% 5.37/1.30 (![X32 : $i, X33 : $i, X34 : $i]:
% 5.37/1.30 (((X33) = (X32))
% 5.37/1.30 | ((setadjoin @ X33 @ (setadjoin @ X32 @ emptyset))
% 5.37/1.30 != (setadjoin @ X34 @ emptyset)))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl1095, plain,
% 5.37/1.30 (![X0 : $i]:
% 5.37/1.30 (((setadjoin @ sk__61 @ emptyset) != (setadjoin @ X0 @ emptyset))
% 5.37/1.30 | ((sk__61) = (sk__62)))),
% 5.37/1.30 inference('sup-', [status(thm)], [zip_derived_cl1047, zip_derived_cl88])).
% 5.37/1.30 thf(zip_derived_cl89, plain, (((sk__62) != (sk__64))),
% 5.37/1.30 inference('cnf', [status(esa)], [zf_stmt_4])).
% 5.37/1.30 thf(zip_derived_cl642, plain, (((sk__64) = (sk__61))),
% 5.37/1.30 inference('clc', [status(thm)], [zip_derived_cl640, zip_derived_cl88])).
% 5.37/1.30 thf(zip_derived_cl643, plain, (((sk__62) != (sk__61))),
% 5.37/1.30 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl642])).
% 5.37/1.30 thf(zip_derived_cl1118, plain,
% 5.37/1.30 (![X0 : $i]:
% 5.37/1.30 ((setadjoin @ sk__61 @ emptyset) != (setadjoin @ X0 @ emptyset))),
% 5.37/1.30 inference('simplify_reflect-', [status(thm)],
% 5.37/1.30 [zip_derived_cl1095, zip_derived_cl643])).
% 5.37/1.30 thf(zip_derived_cl1136, plain, ($false),
% 5.37/1.30 inference('eq_res', [status(thm)], [zip_derived_cl1118])).
% 5.37/1.30
% 5.37/1.30 % SZS output end Refutation
% 5.37/1.30
% 5.37/1.30
% 5.37/1.30 % Terminating...
% 6.39/1.44 % Runner terminated.
% 6.39/1.46 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------