%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU651^1 : 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.O2yCGH3Jg8 true
% Computer : n028.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 04:55:33 PM UTC 2025
% Result : Theorem 3.79s 1.13s
% Output : Refutation 3.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU651^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.O2yCGH3Jg8 true
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 16:04:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.36 % Running in HO mode
% 0.55/0.65 % Total configuration time : 828
% 0.55/0.65 % Estimated wc time : 1656
% 0.55/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.57/0.79 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.58/0.82 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.58/0.85 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 3.79/1.13 % Solved by lams/40_c_ic.sh.
% 3.79/1.13 % done 257 iterations in 0.276s
% 3.79/1.13 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.79/1.13 % SZS output start Refutation
% 3.79/1.13 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 3.79/1.13 thf(notdexE_type, type, notdexE: $o).
% 3.79/1.13 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 3.79/1.13 thf(setunionAx_type, type, setunionAx: $o).
% 3.79/1.13 thf(setminusELneg_type, type, setminusELneg: $o).
% 3.79/1.13 thf(powersetE_type, type, powersetE: $o).
% 3.79/1.13 thf(omegaSAx_type, type, omegaSAx: $o).
% 3.79/1.13 thf(exuI1_type, type, exuI1: $o).
% 3.79/1.13 thf(exuI2_type, type, exuI2: $o).
% 3.79/1.13 thf(notequalI2_type, type, notequalI2: $o).
% 3.79/1.13 thf(setukpairIR_type, type, setukpairIR: $o).
% 3.79/1.13 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 3.79/1.13 thf(setminusILneg_type, type, setminusILneg: $o).
% 3.79/1.13 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 3.79/1.13 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 3.79/1.13 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 3.79/1.13 thf(upairsubunion_type, type, upairsubunion: $o).
% 3.79/1.13 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 3.79/1.13 thf(sk__54_type, type, sk__54: $i).
% 3.79/1.13 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 3.79/1.13 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 3.79/1.13 thf(setukpairIL_type, type, setukpairIL: $o).
% 3.79/1.13 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 3.79/1.13 thf(binunionE_type, type, binunionE: $o).
% 3.79/1.13 thf(setext_type, type, setext: $o).
% 3.79/1.13 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 3.79/1.13 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 3.79/1.13 thf(descr__Cong_type, type, descr__Cong: $o).
% 3.79/1.13 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 3.79/1.13 thf(in_type, type, in: $i > $i > $o).
% 3.79/1.13 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 3.79/1.13 thf(theprop_type, type, theprop: $o).
% 3.79/1.13 thf(upairset2E_type, type, upairset2E: $o).
% 3.79/1.13 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 3.79/1.13 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 3.79/1.13 thf(symdiffI2_type, type, symdiffI2: $o).
% 3.79/1.13 thf(upairset2IR_type, type, upairset2IR: $o).
% 3.79/1.13 thf(subsetE_type, type, subsetE: $o).
% 3.79/1.13 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 3.79/1.13 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 3.79/1.13 thf(setbeta_type, type, setbeta: $o).
% 3.79/1.13 thf(eqinunit_type, type, eqinunit: $o).
% 3.79/1.13 thf(upairsetIL_type, type, upairsetIL: $o).
% 3.79/1.13 thf(powersetI1_type, type, powersetI1: $o).
% 3.79/1.13 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 3.79/1.13 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 3.79/1.13 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 3.79/1.13 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 3.79/1.13 thf(powersetAx_type, type, powersetAx: $o).
% 3.79/1.13 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 3.79/1.13 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 3.79/1.13 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 3.79/1.13 thf(powersetI_type, type, powersetI: $o).
% 3.79/1.13 thf(upairsetIR_type, type, upairsetIR: $o).
% 3.79/1.13 thf(inCongP_type, type, inCongP: $o).
% 3.79/1.13 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 3.79/1.13 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 3.79/1.13 thf(exuE3e_type, type, exuE3e: $o).
% 3.79/1.13 thf(emptysetE_type, type, emptysetE: $o).
% 3.79/1.13 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 3.79/1.13 thf(setunionI_type, type, setunionI: $o).
% 3.79/1.13 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 3.79/1.13 thf(prop2setI_type, type, prop2setI: $o).
% 3.79/1.13 thf(ex1I2_type, type, ex1I2: $o).
% 3.79/1.13 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 3.79/1.13 thf(setminusER_type, type, setminusER: $o).
% 3.79/1.13 thf(exuE2_type, type, exuE2: $o).
% 3.79/1.13 thf(emptyset_type, type, emptyset: $i).
% 3.79/1.13 thf(sk__56_type, type, sk__56: $i).
% 3.79/1.13 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 3.79/1.13 thf(powersetsubset_type, type, powersetsubset: $o).
% 3.79/1.13 thf(subPowSU_type, type, subPowSU: $o).
% 3.79/1.13 thf(notequalI1_type, type, notequalI1: $o).
% 3.79/1.13 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 3.79/1.13 thf(notinemptyset_type, type, notinemptyset: $o).
% 3.79/1.13 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 3.79/1.13 thf(subsetTrans_type, type, subsetTrans: $o).
% 3.79/1.13 thf(setminusI_type, type, setminusI: $o).
% 3.79/1.13 thf(binunionIL_type, type, binunionIL: $o).
% 3.79/1.13 thf(sk__55_type, type, sk__55: $i).
% 3.79/1.13 thf(subsetE2_type, type, subsetE2: $o).
% 3.79/1.13 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 3.79/1.13 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 3.79/1.13 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 3.79/1.13 thf(setextsub_type, type, setextsub: $o).
% 3.79/1.13 thf(binunionLsub_type, type, binunionLsub: $o).
% 3.79/1.13 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 3.79/1.13 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 3.79/1.13 thf(setunionE_type, type, setunionE: $o).
% 3.79/1.13 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 3.79/1.13 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 3.79/1.13 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 3.79/1.13 thf(binunionIR_type, type, binunionIR: $o).
% 3.79/1.13 thf(setadjoinE_type, type, setadjoinE: $o).
% 3.79/1.13 thf(singletonprop_type, type, singletonprop: $o).
% 3.79/1.13 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 3.79/1.13 thf(exuE1_type, type, exuE1: $o).
% 3.79/1.13 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 3.79/1.13 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 3.79/1.13 thf(setminusLsub_type, type, setminusLsub: $o).
% 3.79/1.13 thf(sk__57_type, type, sk__57: $i).
% 3.79/1.13 thf(notinsingleton_type, type, notinsingleton: $o).
% 3.79/1.13 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 3.79/1.13 thf(exuEu_type, type, exuEu: $o).
% 3.79/1.13 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 3.79/1.13 thf(upairsetE_type, type, upairsetE: $o).
% 3.79/1.13 thf(omega0Ax_type, type, omega0Ax: $o).
% 3.79/1.13 thf(notsubsetI_type, type, notsubsetI: $o).
% 3.79/1.13 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 3.79/1.13 thf(setextAx_type, type, setextAx: $o).
% 3.79/1.13 thf(powersetE1_type, type, powersetE1: $o).
% 3.79/1.13 thf(bs114d_type, type, bs114d: $o).
% 3.79/1.13 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 3.79/1.13 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 3.79/1.13 thf(subsetI1_type, type, subsetI1: $o).
% 3.79/1.13 thf(symdiffE_type, type, symdiffE: $o).
% 3.79/1.13 thf(descrp_type, type, descrp: $o).
% 3.79/1.13 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 3.79/1.13 thf(foundationAx_type, type, foundationAx: $o).
% 3.79/1.13 thf(emptysetAx_type, type, emptysetAx: $o).
% 3.79/1.13 thf(emptyI_type, type, emptyI: $o).
% 3.79/1.13 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 3.79/1.13 thf(binintersectEL_type, type, binintersectEL: $o).
% 3.79/1.13 thf(emptyE1_type, type, emptyE1: $o).
% 3.79/1.13 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 3.79/1.13 thf(vacuousDall_type, type, vacuousDall: $o).
% 3.79/1.13 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 3.79/1.13 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 3.79/1.13 thf(binintersectI_type, type, binintersectI: $o).
% 3.79/1.13 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 3.79/1.13 thf(ex1E1_type, type, ex1E1: $o).
% 3.79/1.13 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 3.79/1.13 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 3.79/1.13 thf(symdiffI1_type, type, symdiffI1: $o).
% 3.79/1.13 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 3.79/1.13 thf(subsetI2_type, type, subsetI2: $o).
% 3.79/1.13 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 3.79/1.13 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 3.79/1.13 thf(setminusERneg_type, type, setminusERneg: $o).
% 3.79/1.13 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 3.79/1.13 thf(omega__Cong_type, type, omega__Cong: $o).
% 3.79/1.13 thf(subsetRefl_type, type, subsetRefl: $o).
% 3.79/1.13 thf(uniqinunit_type, type, uniqinunit: $o).
% 3.79/1.13 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 3.79/1.13 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 3.79/1.13 thf(prop2setE_type, type, prop2setE: $o).
% 3.79/1.13 thf(binunionEcases_type, type, binunionEcases: $o).
% 3.79/1.13 thf(nonemptyI_type, type, nonemptyI: $o).
% 3.79/1.13 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 3.79/1.13 thf(exuE3u_type, type, exuE3u: $o).
% 3.79/1.13 thf(setminusEL_type, type, setminusEL: $o).
% 3.79/1.13 thf(singletonsubset_type, type, singletonsubset: $o).
% 3.79/1.13 thf(sepSubset_type, type, sepSubset: $o).
% 3.79/1.13 thf(setunionE2_type, type, setunionE2: $o).
% 3.79/1.13 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 3.79/1.13 thf(ex1I_type, type, ex1I: $o).
% 3.79/1.13 thf(exuI3_type, type, exuI3: $o).
% 3.79/1.13 thf(notdallE_type, type, notdallE: $o).
% 3.79/1.13 thf(binintersectER_type, type, binintersectER: $o).
% 3.79/1.13 thf(kpairp_type, type, kpairp: $o).
% 3.79/1.13 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 3.79/1.13 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 3.79/1.13 thf(exu__Cong_type, type, exu__Cong: $o).
% 3.79/1.13 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 3.79/1.13 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 3.79/1.13 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 3.79/1.13 thf(replAx_type, type, replAx: $o).
% 3.79/1.13 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 3.79/1.13 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 3.79/1.13 thf(secondinupair_type, type, secondinupair: $o).
% 3.79/1.13 thf(inPowerset_type, type, inPowerset: $o).
% 3.79/1.13 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 3.79/1.13 thf(in__Cong_type, type, in__Cong: $o).
% 3.79/1.13 thf(binunionRsub_type, type, binunionRsub: $o).
% 3.79/1.13 thf(subset2powerset_type, type, subset2powerset: $o).
% 3.79/1.13 thf(setukpairinjR12, axiom, setukpairinjR12 =
% 3.79/1.13 (![Xx:$i,Xy:$i]:
% 3.79/1.13 ( ( ( Xx ) = ( Xy ) ) =>
% 3.79/1.13 ( ( setadjoin @
% 3.79/1.13 ( setadjoin @ Xx @ emptyset ) @
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 3.79/1.13 ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ))).
% 3.79/1.13 thf('0', plain,
% 3.79/1.13 (( setukpairinjR12 ) =
% 3.79/1.13 ( ![X4:$i,X6:$i]:
% 3.79/1.13 ( ( ( X4 ) = ( X6 ) ) =>
% 3.79/1.13 ( ( setadjoin @
% 3.79/1.13 ( setadjoin @ X4 @ emptyset ) @
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 3.79/1.13 ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ emptyset ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(setukpairinjR11, axiom, setukpairinjR11 =
% 3.79/1.13 (![Xx:$i,Xy:$i]:
% 3.79/1.13 ( ( ( Xx ) = ( Xy ) ) =>
% 3.79/1.13 ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =
% 3.79/1.13 ( setadjoin @ Xx @ emptyset ) ) ))).
% 3.79/1.13 thf('1', plain,
% 3.79/1.13 (( setukpairinjR11 ) =
% 3.79/1.13 ( ![X4:$i,X6:$i]:
% 3.79/1.13 ( ( ( X4 ) = ( X6 ) ) =>
% 3.79/1.13 ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =
% 3.79/1.13 ( setadjoin @ X4 @ emptyset ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(setukpairinjL2, axiom, setukpairinjL2 =
% 3.79/1.13 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 3.79/1.13 ( ( ( setadjoin @
% 3.79/1.13 ( setadjoin @ Xx @ emptyset ) @
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 ( setadjoin @ Xz @ emptyset ) @
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) =>
% 3.79/1.13 ( ( Xx ) = ( Xz ) ) ))).
% 3.79/1.13 thf('2', plain,
% 3.79/1.13 (( setukpairinjL2 ) =
% 3.79/1.13 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 3.79/1.13 ( ( ( setadjoin @
% 3.79/1.13 ( setadjoin @ X4 @ emptyset ) @
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 ( setadjoin @ X8 @ emptyset ) @
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) =>
% 3.79/1.13 ( ( X4 ) = ( X8 ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(setukpairinjL1, axiom, setukpairinjL1 =
% 3.79/1.13 (![Xx:$i,Xy:$i,Xz:$i]:
% 3.79/1.13 ( ( in @
% 3.79/1.13 ( setadjoin @ Xz @ emptyset ) @
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 ( setadjoin @ Xx @ emptyset ) @
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) =>
% 3.79/1.13 ( ( Xx ) = ( Xz ) ) ))).
% 3.79/1.13 thf('3', plain,
% 3.79/1.13 (( setukpairinjL1 ) =
% 3.79/1.13 ( ![X4:$i,X6:$i,X8:$i]:
% 3.79/1.13 ( ( in @
% 3.79/1.13 ( setadjoin @ X8 @ emptyset ) @
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 ( setadjoin @ X4 @ emptyset ) @
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) =>
% 3.79/1.13 ( ( X4 ) = ( X8 ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(singletonsuniq, axiom, singletonsuniq =
% 3.79/1.13 (![Xx:$i,Xy:$i]:
% 3.79/1.13 ( ( ( setadjoin @ Xx @ emptyset ) = ( setadjoin @ Xy @ emptyset ) ) =>
% 3.79/1.13 ( ( Xx ) = ( Xy ) ) ))).
% 3.79/1.13 thf('4', plain,
% 3.79/1.13 (( singletonsuniq ) =
% 3.79/1.13 ( ![X4:$i,X6:$i]:
% 3.79/1.13 ( ( ( setadjoin @ X4 @ emptyset ) = ( setadjoin @ X6 @ emptyset ) ) =>
% 3.79/1.13 ( ( X4 ) = ( X6 ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(upairset2E, axiom, upairset2E =
% 3.79/1.13 (![Xx:$i,Xy:$i,Xz:$i]:
% 3.79/1.13 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 3.79/1.13 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 3.79/1.13 thf('5', plain,
% 3.79/1.13 (( upairset2E ) =
% 3.79/1.13 ( ![X4:$i,X6:$i,X8:$i]:
% 3.79/1.13 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 3.79/1.13 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(secondinupair, axiom, secondinupair =
% 3.79/1.13 (![Xx:$i,Xy:$i]:
% 3.79/1.13 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 3.79/1.13 thf('6', plain,
% 3.79/1.13 (( secondinupair ) =
% 3.79/1.13 ( ![X4:$i,X6:$i]:
% 3.79/1.13 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(upairset2IR, axiom, upairset2IR =
% 3.79/1.13 (![Xx:$i,Xy:$i]:
% 3.79/1.13 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 3.79/1.13 thf('7', plain,
% 3.79/1.13 (( upairset2IR ) =
% 3.79/1.13 ( ![X4:$i,X6:$i]:
% 3.79/1.13 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 3.79/1.13 (![Xx:$i,Xy:$i]:
% 3.79/1.13 ( ( ( Xx ) = ( Xy ) ) =>
% 3.79/1.13 ( ![Xz:$i,Xu:$i]:
% 3.79/1.13 ( ( ( Xz ) = ( Xu ) ) =>
% 3.79/1.13 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 3.79/1.13 thf('8', plain,
% 3.79/1.13 (( setadjoin__Cong ) =
% 3.79/1.13 ( ![X4:$i,X6:$i]:
% 3.79/1.13 ( ( ( X4 ) = ( X6 ) ) =>
% 3.79/1.13 ( ![X8:$i,X10:$i]:
% 3.79/1.13 ( ( ( X8 ) = ( X10 ) ) =>
% 3.79/1.13 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(upairsetIR, axiom, upairsetIR =
% 3.79/1.13 (![Xx:$i,Xy:$i]:
% 3.79/1.13 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 3.79/1.13 thf('9', plain,
% 3.79/1.13 (( upairsetIR ) =
% 3.79/1.13 ( ![X4:$i,X6:$i]:
% 3.79/1.13 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(upairsetIL, axiom, upairsetIL =
% 3.79/1.13 (![Xx:$i,Xy:$i]:
% 3.79/1.13 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 3.79/1.13 thf('10', plain,
% 3.79/1.13 (( upairsetIL ) =
% 3.79/1.13 ( ![X4:$i,X6:$i]:
% 3.79/1.13 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(upairsetE, axiom, upairsetE =
% 3.79/1.13 (![Xx:$i,Xy:$i,Xz:$i]:
% 3.79/1.13 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 3.79/1.13 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 3.79/1.13 thf('11', plain,
% 3.79/1.13 (( upairsetE ) =
% 3.79/1.13 ( ![X4:$i,X6:$i,X8:$i]:
% 3.79/1.13 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 3.79/1.13 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(singletonsswitch, axiom, singletonsswitch =
% 3.79/1.13 (![Xx:$i,Xy:$i]:
% 3.79/1.13 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 3.79/1.13 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 3.79/1.13 thf('12', plain,
% 3.79/1.13 (( singletonsswitch ) =
% 3.79/1.13 ( ![X4:$i,X6:$i]:
% 3.79/1.13 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 3.79/1.13 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(eqinunit, axiom, eqinunit =
% 3.79/1.13 (![Xx:$i,Xy:$i]:
% 3.79/1.13 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 3.79/1.13 thf('13', plain,
% 3.79/1.13 (( eqinunit ) =
% 3.79/1.13 ( ![X4:$i,X6:$i]:
% 3.79/1.13 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(notinsingleton, axiom, notinsingleton =
% 3.79/1.13 (![Xx:$i,Xy:$i]:
% 3.79/1.13 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 3.79/1.13 thf('14', plain,
% 3.79/1.13 (( notinsingleton ) =
% 3.79/1.13 ( ![X4:$i,X6:$i]:
% 3.79/1.13 ( ( ( X4 ) != ( X6 ) ) =>
% 3.79/1.13 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(uniqinunit, axiom, uniqinunit =
% 3.79/1.13 (![Xx:$i,Xy:$i]:
% 3.79/1.13 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 3.79/1.13 thf('15', plain,
% 3.79/1.13 (( uniqinunit ) =
% 3.79/1.13 ( ![X4:$i,X6:$i]:
% 3.79/1.13 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(setadjoinOr, axiom, setadjoinOr =
% 3.79/1.13 (![Xx:$i,A:$i,Xy:$i]:
% 3.79/1.13 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 3.79/1.13 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 3.79/1.13 thf('16', plain,
% 3.79/1.13 (( setadjoinOr ) =
% 3.79/1.13 ( ![X4:$i,X6:$i,X8:$i]:
% 3.79/1.13 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 3.79/1.13 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(setadjoinE, axiom, setadjoinE =
% 3.79/1.13 (![Xx:$i,A:$i,Xy:$i]:
% 3.79/1.13 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 3.79/1.13 ( ![Xphi:$o]:
% 3.79/1.13 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 3.79/1.13 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 3.79/1.13 thf('17', plain,
% 3.79/1.13 (( setadjoinE ) =
% 3.79/1.13 ( ![X4:$i,X6:$i,X8:$i]:
% 3.79/1.13 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 3.79/1.13 ( ![X10:$o]:
% 3.79/1.13 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 3.79/1.13 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(setadjoinIR, axiom, setadjoinIR =
% 3.79/1.13 (![Xx:$i,A:$i,Xy:$i]:
% 3.79/1.13 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 3.79/1.13 thf('18', plain,
% 3.79/1.13 (( setadjoinIR ) =
% 3.79/1.13 ( ![X4:$i,X6:$i,X8:$i]:
% 3.79/1.13 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 3.79/1.13 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 3.79/1.13 thf('19', plain,
% 3.79/1.13 (( emptyinunitempty ) =
% 3.79/1.13 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 3.79/1.13 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 3.79/1.13 thf('20', plain,
% 3.79/1.13 (( emptyinunitempty ) =
% 3.79/1.13 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(setadjoinIL, axiom, setadjoinIL =
% 3.79/1.13 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 3.79/1.13 thf('21', plain,
% 3.79/1.13 (( setadjoinIL ) =
% 3.79/1.13 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(setadjoinAx, axiom, setadjoinAx =
% 3.79/1.13 (![Xx:$i,A:$i,Xy:$i]:
% 3.79/1.13 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 3.79/1.13 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 3.79/1.13 thf('22', plain,
% 3.79/1.13 (( setadjoinAx ) =
% 3.79/1.13 ( ![X4:$i,X6:$i,X8:$i]:
% 3.79/1.13 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 3.79/1.13 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 3.79/1.13 define([status(thm)])).
% 3.79/1.13 thf(setukpairinjR1, conjecture,
% 3.79/1.13 (( setextAx ) =>
% 3.79/1.13 ( ( emptysetAx ) =>
% 3.79/1.13 ( ( setadjoinAx ) =>
% 3.79/1.13 ( ( powersetAx ) =>
% 3.79/1.13 ( ( setunionAx ) =>
% 3.79/1.13 ( ( omega0Ax ) =>
% 3.79/1.13 ( ( omegaSAx ) =>
% 3.79/1.13 ( ( omegaIndAx ) =>
% 3.79/1.13 ( ( replAx ) =>
% 3.79/1.13 ( ( foundationAx ) =>
% 3.79/1.13 ( ( wellorderingAx ) =>
% 3.79/1.13 ( ( descrp ) =>
% 3.79/1.13 ( ( dsetconstrI ) =>
% 3.79/1.13 ( ( dsetconstrEL ) =>
% 3.79/1.13 ( ( dsetconstrER ) =>
% 3.79/1.13 ( ( exuE1 ) =>
% 3.79/1.13 ( ( prop2setE ) =>
% 3.79/1.13 ( ( emptysetE ) =>
% 3.79/1.13 ( ( emptysetimpfalse ) =>
% 3.79/1.13 ( ( notinemptyset ) =>
% 3.79/1.13 ( ( exuE3e ) =>
% 3.79/1.13 ( ( setext ) =>
% 3.79/1.13 ( ( emptyI ) =>
% 3.79/1.13 ( ( noeltsimpempty ) =>
% 3.79/1.13 ( ( setbeta ) =>
% 3.79/1.13 ( ( nonemptyE1 ) =>
% 3.79/1.13 ( ( nonemptyI ) =>
% 3.79/1.13 ( ( nonemptyI1 ) =>
% 3.79/1.13 ( ( setadjoinIL ) =>
% 3.79/1.13 ( ( emptyinunitempty ) =>
% 3.79/1.13 ( ( setadjoinIR ) =>
% 3.79/1.13 ( ( setadjoinE ) =>
% 3.79/1.13 ( (
% 3.79/1.13 setadjoinOr ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setoftrueEq ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 powersetI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 emptyinPowerset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 emptyInPowerset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 powersetE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunionI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunionE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subPowSU ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exuE2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 nonemptyImpWitness ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 uniqinunit ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 notinsingleton ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 eqinunit ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 singletonsswitch ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 upairsetE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 upairsetIL ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 upairsetIR ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 emptyE1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 vacuousDall ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 quantDeMorgan1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 quantDeMorgan2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 quantDeMorgan3 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 quantDeMorgan4 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 prop2setI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 prop2set2propI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 notdexE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 notdallE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exuI1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exuI3 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exuI2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 inCongP ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 in__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exuE3u ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exu__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 emptyset__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setadjoin__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 powerset__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunion__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 omega__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exuEu ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 descr__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 dsetconstr__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetI1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 eqimpsubset2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 eqimpsubset1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetI2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 emptysetsubset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetE2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 notsubsetI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 notequalI1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 notequalI2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetRefl ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetTrans ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setadjoinSub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setadjoinSub2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subset2powerset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setextsub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetemptysetimpeq ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 powersetI1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 powersetE1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 inPowerset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 powersetsubset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 sepInPowerset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 sepSubset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binunionIL ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 upairset2IR ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binunionIR ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binunionEcases ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binunionE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binunionLsub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binunionRsub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectSubset5 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectEL ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectLsub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectSubset2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectSubset3 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectER ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 disjointsetsI1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectRsub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectSubset4 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectSubset1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 bs114d ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusEL ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusER ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusSubset2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusERneg ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusELneg ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusILneg ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusIRneg ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusLsub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusSubset1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 symdiffE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 symdiffI1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 symdiffI2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 symdiffIneg1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 symdiffIneg2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 secondinupair ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setukpairIL ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setukpairIR ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 kpairiskpair ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 kpairp ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 singletonsubset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 singletoninpowerset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 singletoninpowunion ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 upairset2E ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 upairsubunion ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 upairinpowunion ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ubforcartprodlem1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ubforcartprodlem2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ubforcartprodlem3 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 cartprodpairin ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 cartprodmempair1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 cartprodmempair ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunionE2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunionsingleton1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunionsingleton2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunionsingleton ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 singletonprop ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ex1E1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ex1I ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ex1I2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 singletonsuniq ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setukpairinjL1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 kfstsingleton ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 theprop ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 kfstpairEq ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 cartprodfstin ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setukpairinjL2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setukpairinjL ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setukpairinjR11 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setukpairinjR12 ) =>
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 Xx:$i,
% 3.79/1.13 Xy:$i,
% 3.79/1.13 Xz:$i,
% 3.79/1.13 Xu:$i]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 Xx @
% 3.79/1.13 emptyset ) @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 Xx @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 Xy @
% 3.79/1.13 emptyset ) ) @
% 3.79/1.13 emptyset ) ) =
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 Xz @
% 3.79/1.13 emptyset ) @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 Xz @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 Xu @
% 3.79/1.13 emptyset ) ) @
% 3.79/1.13 emptyset ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 Xz ) =
% 3.79/1.13 (
% 3.79/1.13 Xu ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 Xy ) =
% 3.79/1.13 (
% 3.79/1.13 Xu ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.79/1.13 thf(zf_stmt_0, conjecture,
% 3.79/1.13 (( setextAx ) =>
% 3.79/1.13 ( ( emptysetAx ) =>
% 3.79/1.13 ( ( ![X4:$i,X6:$i,X8:$i]:
% 3.79/1.13 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 3.79/1.13 ( ( in @ X8 @ X6 ) | ( ( X8 ) = ( X4 ) ) ) ) ) =>
% 3.79/1.13 ( ( powersetAx ) =>
% 3.79/1.13 ( ( setunionAx ) =>
% 3.79/1.13 ( ( omega0Ax ) =>
% 3.79/1.13 ( ( omegaSAx ) =>
% 3.79/1.13 ( ( omegaIndAx ) =>
% 3.79/1.13 ( ( replAx ) =>
% 3.79/1.13 ( ( foundationAx ) =>
% 3.79/1.13 ( ( wellorderingAx ) =>
% 3.79/1.13 ( ( descrp ) =>
% 3.79/1.13 ( ( dsetconstrI ) =>
% 3.79/1.13 ( ( dsetconstrEL ) =>
% 3.79/1.13 ( ( dsetconstrER ) =>
% 3.79/1.13 ( ( exuE1 ) =>
% 3.79/1.13 ( ( prop2setE ) =>
% 3.79/1.13 ( ( emptysetE ) =>
% 3.79/1.13 ( ( emptysetimpfalse ) =>
% 3.79/1.13 ( ( notinemptyset ) =>
% 3.79/1.13 ( ( exuE3e ) =>
% 3.79/1.13 ( ( setext ) =>
% 3.79/1.13 ( ( emptyI ) =>
% 3.79/1.13 ( ( noeltsimpempty ) =>
% 3.79/1.13 ( ( setbeta ) =>
% 3.79/1.13 ( ( nonemptyE1 ) =>
% 3.79/1.13 ( ( nonemptyI ) =>
% 3.79/1.13 ( ( nonemptyI1 ) =>
% 3.79/1.13 ( ( ![X10:$i,X12:$i]:
% 3.79/1.13 ( in @
% 3.79/1.13 X10 @
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 X10 @ X12 ) ) ) =>
% 3.79/1.13 ( ( in @
% 3.79/1.13 emptyset @
% 3.79/1.13 ( setadjoin @
% 3.79/1.13 emptyset @
% 3.79/1.13 emptyset ) ) =>
% 3.79/1.13 ( ( ![X14:$i,
% 3.79/1.13 X16:$i,
% 3.79/1.13 X18:$i]:
% 3.79/1.13 ( (
% 3.79/1.13 in @
% 3.79/1.13 X18 @ X16 ) =>
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X18 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X14 @ X16 ) ) ) ) =>
% 3.79/1.13 ( ( ![
% 3.79/1.13 X20:$i,
% 3.79/1.13 X22:$i,
% 3.79/1.13 X24:$i]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X24 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X20 @ X22 ) ) =>
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X26:$o]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 X24 ) =
% 3.79/1.13 (
% 3.79/1.13 X20 ) ) =>
% 3.79/1.13 (
% 3.79/1.13 X26 ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X24 @ X22 ) =>
% 3.79/1.13 (
% 3.79/1.13 X26 ) ) =>
% 3.79/1.13 (
% 3.79/1.13 X26 ) ) ) ) ) ) =>
% 3.79/1.13 ( (
% 3.79/1.13 ![
% 3.79/1.13 X28:$i,
% 3.79/1.13 X30:$i,
% 3.79/1.13 X32:$i]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X32 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X28 @ X30 ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X32 @ X30 ) |
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 X32 ) =
% 3.79/1.13 (
% 3.79/1.13 X28 ) ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setoftrueEq ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 powersetI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 emptyinPowerset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 emptyInPowerset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 powersetE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunionI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunionE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subPowSU ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exuE2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 nonemptyImpWitness ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X34:$i,
% 3.79/1.13 X36:$i]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X34 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X36 @
% 3.79/1.13 emptyset ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 X34 ) =
% 3.79/1.13 (
% 3.79/1.13 X36 ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X38:$i,
% 3.79/1.13 X40:$i]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 X38 ) !=
% 3.79/1.13 (
% 3.79/1.13 X40 ) ) =>
% 3.79/1.13 (
% 3.79/1.13 ~(
% 3.79/1.13 in @
% 3.79/1.13 X40 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X38 @
% 3.79/1.13 emptyset ) ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X42:$i,
% 3.79/1.13 X44:$i]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 X42 ) =
% 3.79/1.13 (
% 3.79/1.13 X44 ) ) =>
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X42 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X44 @
% 3.79/1.13 emptyset ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X46:$i,
% 3.79/1.13 X48:$i]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X46 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X48 @
% 3.79/1.13 emptyset ) ) =>
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X48 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X46 @
% 3.79/1.13 emptyset ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X50:$i,
% 3.79/1.13 X52:$i,
% 3.79/1.13 X54:$i]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X54 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X50 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X52 @
% 3.79/1.13 emptyset ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 X54 ) =
% 3.79/1.13 (
% 3.79/1.13 X52 ) ) |
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 X54 ) =
% 3.79/1.13 (
% 3.79/1.13 X50 ) ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X56:$i,
% 3.79/1.13 X58:$i]:
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X56 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X56 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X58 @
% 3.79/1.13 emptyset ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X60:$i,
% 3.79/1.13 X62:$i]:
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X62 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X60 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X62 @
% 3.79/1.13 emptyset ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 emptyE1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 vacuousDall ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 quantDeMorgan1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 quantDeMorgan2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 quantDeMorgan3 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 quantDeMorgan4 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 prop2setI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 prop2set2propI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 notdexE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 notdallE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exuI1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exuI3 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exuI2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 inCongP ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 in__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exuE3u ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exu__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 emptyset__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X64:$i,
% 3.79/1.13 X66:$i]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 X64 ) =
% 3.79/1.13 (
% 3.79/1.13 X66 ) ) =>
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X68:$i,
% 3.79/1.13 X70:$i]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 X68 ) =
% 3.79/1.13 (
% 3.79/1.13 X70 ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X64 @ X68 ) =
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X66 @ X70 ) ) ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 powerset__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunion__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 omega__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 exuEu ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 descr__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 dsetconstr__Cong ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetI1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 eqimpsubset2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 eqimpsubset1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetI2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 emptysetsubset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetE2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 notsubsetI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 notequalI1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 notequalI2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetRefl ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetTrans ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setadjoinSub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setadjoinSub2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subset2powerset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setextsub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 subsetemptysetimpeq ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 powersetI1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 powersetE1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 inPowerset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 powersetsubset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 sepInPowerset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 sepSubset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binunionIL ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X72:$i,
% 3.79/1.13 X74:$i]:
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X74 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X72 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X74 @
% 3.79/1.13 emptyset ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binunionIR ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binunionEcases ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binunionE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binunionLsub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binunionRsub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectSubset5 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectEL ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectLsub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectSubset2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectSubset3 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectER ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 disjointsetsI1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectRsub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectSubset4 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 binintersectSubset1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 bs114d ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusI ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusEL ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusER ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusSubset2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusERneg ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusELneg ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusILneg ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusIRneg ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusLsub ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setminusSubset1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 symdiffE ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 symdiffI1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 symdiffI2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 symdiffIneg1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 symdiffIneg2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X76:$i,
% 3.79/1.13 X78:$i]:
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X78 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X76 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X78 @
% 3.79/1.13 emptyset ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setukpairIL ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setukpairIR ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 kpairiskpair ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 kpairp ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 singletonsubset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 singletoninpowerset ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 singletoninpowunion ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X80:$i,
% 3.79/1.13 X82:$i,
% 3.79/1.13 X84:$i]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 X84 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X80 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X82 @
% 3.79/1.13 emptyset ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 X84 ) =
% 3.79/1.13 (
% 3.79/1.13 X82 ) ) |
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 X84 ) =
% 3.79/1.13 (
% 3.79/1.13 X80 ) ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 upairsubunion ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 upairinpowunion ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ubforcartprodlem1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ubforcartprodlem2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ubforcartprodlem3 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 cartprodpairin ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 cartprodmempair1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 cartprodmempair ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunionE2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunionsingleton1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunionsingleton2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setunionsingleton ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 singletonprop ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ex1E1 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ex1I ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ex1I2 ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X86:$i,
% 3.79/1.13 X88:$i]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X86 @
% 3.79/1.13 emptyset ) =
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X88 @
% 3.79/1.13 emptyset ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 X86 ) =
% 3.79/1.13 (
% 3.79/1.13 X88 ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 ![
% 3.79/1.13 X90:$i,
% 3.79/1.13 X92:$i,
% 3.79/1.13 X94:$i]:
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 in @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X94 @
% 3.79/1.13 emptyset ) @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X90 @
% 3.79/1.13 emptyset ) @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X90 @
% 3.79/1.13 (
% 3.79/1.13 setadjoin
% 3.79/1.13 @
% 3.79/1.13 X92 @
% 3.79/1.13 emptyset ) ) @
% 3.79/1.13 emptyset ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 X90 ) =
% 3.79/1.13 (
% 3.79/1.13 X94 ) ) ) ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 kfstsingleton ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 theprop ) =>
% 3.79/1.13 (
% 3.79/1.13 (
% 3.79/1.13 kfstpairEq ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 cartprodfstin ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X96:$i,
% 3.79/1.14 X98:$i,
% 3.79/1.14 X100:$i,
% 3.79/1.14 X102:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X96 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X96 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X98 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X100 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X100 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X102 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X96 ) =
% 3.79/1.14 (
% 3.79/1.14 X100 ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setukpairinjL ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X104:$i,
% 3.79/1.14 X106:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X104 ) =
% 3.79/1.14 (
% 3.79/1.14 X106 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X104 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X106 @
% 3.79/1.14 emptyset ) ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X104 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X108:$i,
% 3.79/1.14 X110:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X108 ) =
% 3.79/1.14 (
% 3.79/1.14 X110 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X108 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X108 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X110 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X108 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X112:$i,
% 3.79/1.14 X114:$i,
% 3.79/1.14 X116:$i,
% 3.79/1.14 X118:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X112 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X112 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X114 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X116 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X116 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X118 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X116 ) =
% 3.79/1.14 (
% 3.79/1.14 X118 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X114 ) =
% 3.79/1.14 (
% 3.79/1.14 X118 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.79/1.14 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 3.79/1.14 thf(zf_stmt_2, axiom,
% 3.79/1.14 (![X8:$i,X6:$i,X4:$i]:
% 3.79/1.14 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 3.79/1.14 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ))).
% 3.79/1.14 thf(zf_stmt_3, conjecture,
% 3.79/1.14 (( setextAx ) =>
% 3.79/1.14 ( ( emptysetAx ) =>
% 3.79/1.14 ( ( ![X4:$i,X6:$i,X8:$i]:
% 3.79/1.14 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 3.79/1.14 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 3.79/1.14 ( ( powersetAx ) =>
% 3.79/1.14 ( ( setunionAx ) =>
% 3.79/1.14 ( ( omega0Ax ) =>
% 3.79/1.14 ( ( omegaSAx ) =>
% 3.79/1.14 ( ( omegaIndAx ) =>
% 3.79/1.14 ( ( replAx ) =>
% 3.79/1.14 ( ( foundationAx ) =>
% 3.79/1.14 ( ( wellorderingAx ) =>
% 3.79/1.14 ( ( descrp ) =>
% 3.79/1.14 ( ( dsetconstrI ) =>
% 3.79/1.14 ( ( dsetconstrEL ) =>
% 3.79/1.14 ( ( dsetconstrER ) =>
% 3.79/1.14 ( ( exuE1 ) =>
% 3.79/1.14 ( ( prop2setE ) =>
% 3.79/1.14 ( ( emptysetE ) =>
% 3.79/1.14 ( ( emptysetimpfalse ) =>
% 3.79/1.14 ( ( notinemptyset ) =>
% 3.79/1.14 ( ( exuE3e ) =>
% 3.79/1.14 ( ( setext ) =>
% 3.79/1.14 ( ( emptyI ) =>
% 3.79/1.14 ( ( noeltsimpempty ) =>
% 3.79/1.14 ( ( setbeta ) =>
% 3.79/1.14 ( ( nonemptyE1 ) =>
% 3.79/1.14 ( ( nonemptyI ) =>
% 3.79/1.14 ( ( nonemptyI1 ) =>
% 3.79/1.14 ( ( ![X10:$i,X12:$i]:
% 3.79/1.14 ( in @
% 3.79/1.14 X10 @
% 3.79/1.14 ( setadjoin @
% 3.79/1.14 X10 @ X12 ) ) ) =>
% 3.79/1.14 ( ( in @
% 3.79/1.14 emptyset @
% 3.79/1.14 ( setadjoin @
% 3.79/1.14 emptyset @
% 3.79/1.14 emptyset ) ) =>
% 3.79/1.14 ( ( ![X14:$i,
% 3.79/1.14 X16:$i,
% 3.79/1.14 X18:$i]:
% 3.79/1.14 ( (
% 3.79/1.14 in @
% 3.79/1.14 X18 @ X16 ) =>
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X18 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X14 @ X16 ) ) ) ) =>
% 3.79/1.14 ( ( ![
% 3.79/1.14 X20:$i,
% 3.79/1.14 X22:$i,
% 3.79/1.14 X24:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X24 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X20 @ X22 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X26:$o]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X24 ) =
% 3.79/1.14 (
% 3.79/1.14 X20 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 X26 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X24 @ X22 ) =>
% 3.79/1.14 (
% 3.79/1.14 X26 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 X26 ) ) ) ) ) ) =>
% 3.79/1.14 ( (
% 3.79/1.14 ![
% 3.79/1.14 X28:$i,
% 3.79/1.14 X30:$i,
% 3.79/1.14 X32:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X32 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X28 @ X30 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X32 ) =
% 3.79/1.14 (
% 3.79/1.14 X28 ) ) |
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X32 @ X30 ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setoftrueEq ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 powersetI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 emptyinPowerset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 emptyInPowerset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 powersetE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunionI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunionE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subPowSU ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exuE2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 nonemptyImpWitness ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X34:$i,
% 3.79/1.14 X36:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X34 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X36 @
% 3.79/1.14 emptyset ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X34 ) =
% 3.79/1.14 (
% 3.79/1.14 X36 ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X38:$i,
% 3.79/1.14 X40:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X38 ) !=
% 3.79/1.14 (
% 3.79/1.14 X40 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 ~(
% 3.79/1.14 in @
% 3.79/1.14 X40 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X38 @
% 3.79/1.14 emptyset ) ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X42:$i,
% 3.79/1.14 X44:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X42 ) =
% 3.79/1.14 (
% 3.79/1.14 X44 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X42 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X44 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X46:$i,
% 3.79/1.14 X48:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X46 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X48 @
% 3.79/1.14 emptyset ) ) =>
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X48 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X46 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X50:$i,
% 3.79/1.14 X52:$i,
% 3.79/1.14 X54:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X54 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X50 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X52 @
% 3.79/1.14 emptyset ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X54 ) =
% 3.79/1.14 (
% 3.79/1.14 X50 ) ) |
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X54 ) =
% 3.79/1.14 (
% 3.79/1.14 X52 ) ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X56:$i,
% 3.79/1.14 X58:$i]:
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X56 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X56 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X58 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X60:$i,
% 3.79/1.14 X62:$i]:
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X62 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X60 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X62 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 emptyE1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 vacuousDall ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 quantDeMorgan1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 quantDeMorgan2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 quantDeMorgan3 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 quantDeMorgan4 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 prop2setI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 prop2set2propI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 notdexE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 notdallE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exuI1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exuI3 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exuI2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 inCongP ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exuE3u ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exu__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 emptyset__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X64:$i,
% 3.79/1.14 X66:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X64 ) =
% 3.79/1.14 (
% 3.79/1.14 X66 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X68:$i,
% 3.79/1.14 X70:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X68 ) =
% 3.79/1.14 (
% 3.79/1.14 X70 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X64 @ X68 ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X66 @ X70 ) ) ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 powerset__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunion__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 omega__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exuEu ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 descr__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 dsetconstr__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetI1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 eqimpsubset2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 eqimpsubset1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetI2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 emptysetsubset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetE2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 notsubsetI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 notequalI1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 notequalI2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetRefl ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetTrans ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoinSub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoinSub2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subset2powerset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setextsub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetemptysetimpeq ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 powersetI1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 powersetE1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 inPowerset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 powersetsubset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 sepInPowerset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 sepSubset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binunionIL ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X72:$i,
% 3.79/1.14 X74:$i]:
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X74 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X72 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X74 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binunionIR ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binunionEcases ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binunionE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binunionLsub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binunionRsub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectSubset5 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectEL ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectLsub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectSubset2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectSubset3 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectER ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 disjointsetsI1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectRsub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectSubset4 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectSubset1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 bs114d ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusEL ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusER ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusSubset2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusERneg ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusELneg ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusILneg ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusIRneg ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusLsub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusSubset1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 symdiffE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 symdiffI1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 symdiffI2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 symdiffIneg1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 symdiffIneg2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X76:$i,
% 3.79/1.14 X78:$i]:
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X78 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X76 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X78 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setukpairIL ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setukpairIR ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 kpairiskpair ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 kpairp ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 singletonsubset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 singletoninpowerset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 singletoninpowunion ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X80:$i,
% 3.79/1.14 X82:$i,
% 3.79/1.14 X84:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X84 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X80 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X82 @
% 3.79/1.14 emptyset ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X84 ) =
% 3.79/1.14 (
% 3.79/1.14 X80 ) ) |
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X84 ) =
% 3.79/1.14 (
% 3.79/1.14 X82 ) ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 upairsubunion ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 upairinpowunion ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ubforcartprodlem1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ubforcartprodlem2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ubforcartprodlem3 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 cartprodpairin ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 cartprodmempair1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 cartprodmempair ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunionE2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunionsingleton1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunionsingleton2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunionsingleton ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 singletonprop ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ex1E1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ex1I ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ex1I2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X86:$i,
% 3.79/1.14 X88:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X86 @
% 3.79/1.14 emptyset ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X88 @
% 3.79/1.14 emptyset ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X86 ) =
% 3.79/1.14 (
% 3.79/1.14 X88 ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X90:$i,
% 3.79/1.14 X92:$i,
% 3.79/1.14 X94:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X94 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X90 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X90 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X92 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X90 ) =
% 3.79/1.14 (
% 3.79/1.14 X94 ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 kfstsingleton ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 theprop ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 kfstpairEq ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 cartprodfstin ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X96:$i,
% 3.79/1.14 X98:$i,
% 3.79/1.14 X100:$i,
% 3.79/1.14 X102:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X96 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X96 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X98 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X100 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X100 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X102 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X96 ) =
% 3.79/1.14 (
% 3.79/1.14 X100 ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setukpairinjL ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X104:$i,
% 3.79/1.14 X106:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X104 ) =
% 3.79/1.14 (
% 3.79/1.14 X106 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X104 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X106 @
% 3.79/1.14 emptyset ) ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X104 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X108:$i,
% 3.79/1.14 X110:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X108 ) =
% 3.79/1.14 (
% 3.79/1.14 X110 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X108 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X108 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X110 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X108 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X112:$i,
% 3.79/1.14 X114:$i,
% 3.79/1.14 X116:$i,
% 3.79/1.14 X118:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X112 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X112 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X114 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X116 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X116 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X118 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X116 ) =
% 3.79/1.14 (
% 3.79/1.14 X118 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X114 ) =
% 3.79/1.14 (
% 3.79/1.14 X118 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 3.79/1.14 thf(zf_stmt_4, negated_conjecture,
% 3.79/1.14 (~( ( setextAx ) =>
% 3.79/1.14 ( ( emptysetAx ) =>
% 3.79/1.14 ( ( ![X4:$i,X6:$i,X8:$i]:
% 3.79/1.14 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 3.79/1.14 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 3.79/1.14 ( ( powersetAx ) =>
% 3.79/1.14 ( ( setunionAx ) =>
% 3.79/1.14 ( ( omega0Ax ) =>
% 3.79/1.14 ( ( omegaSAx ) =>
% 3.79/1.14 ( ( omegaIndAx ) =>
% 3.79/1.14 ( ( replAx ) =>
% 3.79/1.14 ( ( foundationAx ) =>
% 3.79/1.14 ( ( wellorderingAx ) =>
% 3.79/1.14 ( ( descrp ) =>
% 3.79/1.14 ( ( dsetconstrI ) =>
% 3.79/1.14 ( ( dsetconstrEL ) =>
% 3.79/1.14 ( ( dsetconstrER ) =>
% 3.79/1.14 ( ( exuE1 ) =>
% 3.79/1.14 ( ( prop2setE ) =>
% 3.79/1.14 ( ( emptysetE ) =>
% 3.79/1.14 ( ( emptysetimpfalse ) =>
% 3.79/1.14 ( ( notinemptyset ) =>
% 3.79/1.14 ( ( exuE3e ) =>
% 3.79/1.14 ( ( setext ) =>
% 3.79/1.14 ( ( emptyI ) =>
% 3.79/1.14 ( ( noeltsimpempty ) =>
% 3.79/1.14 ( ( setbeta ) =>
% 3.79/1.14 ( ( nonemptyE1 ) =>
% 3.79/1.14 ( ( nonemptyI ) =>
% 3.79/1.14 ( ( nonemptyI1 ) =>
% 3.79/1.14 ( ( ![X10:$i,
% 3.79/1.14 X12:$i]:
% 3.79/1.14 ( in @
% 3.79/1.14 X10 @
% 3.79/1.14 ( setadjoin
% 3.79/1.14 @
% 3.79/1.14 X10 @ X12 ) ) ) =>
% 3.79/1.14 ( ( in @
% 3.79/1.14 emptyset @
% 3.79/1.14 ( setadjoin
% 3.79/1.14 @
% 3.79/1.14 emptyset @
% 3.79/1.14 emptyset ) ) =>
% 3.79/1.14 ( ( ![
% 3.79/1.14 X14:$i,
% 3.79/1.14 X16:$i,
% 3.79/1.14 X18:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X18 @ X16 ) =>
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X18 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X14 @ X16 ) ) ) ) =>
% 3.79/1.14 ( (
% 3.79/1.14 ![
% 3.79/1.14 X20:$i,
% 3.79/1.14 X22:$i,
% 3.79/1.14 X24:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X24 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X20 @ X22 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X26:$o]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X24 ) =
% 3.79/1.14 (
% 3.79/1.14 X20 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 X26 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X24 @ X22 ) =>
% 3.79/1.14 (
% 3.79/1.14 X26 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 X26 ) ) ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X28:$i,
% 3.79/1.14 X30:$i,
% 3.79/1.14 X32:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X32 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X28 @ X30 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X32 ) =
% 3.79/1.14 (
% 3.79/1.14 X28 ) ) |
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X32 @ X30 ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setoftrueEq ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 powersetI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 emptyinPowerset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 emptyInPowerset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 powersetE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunionI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunionE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subPowSU ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exuE2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 nonemptyImpWitness ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X34:$i,
% 3.79/1.14 X36:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X34 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X36 @
% 3.79/1.14 emptyset ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X34 ) =
% 3.79/1.14 (
% 3.79/1.14 X36 ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X38:$i,
% 3.79/1.14 X40:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X38 ) !=
% 3.79/1.14 (
% 3.79/1.14 X40 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 ~
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X40 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X38 @
% 3.79/1.14 emptyset ) ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X42:$i,
% 3.79/1.14 X44:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X42 ) =
% 3.79/1.14 (
% 3.79/1.14 X44 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X42 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X44 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X46:$i,
% 3.79/1.14 X48:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X46 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X48 @
% 3.79/1.14 emptyset ) ) =>
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X48 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X46 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X50:$i,
% 3.79/1.14 X52:$i,
% 3.79/1.14 X54:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X54 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X50 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X52 @
% 3.79/1.14 emptyset ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X54 ) =
% 3.79/1.14 (
% 3.79/1.14 X50 ) ) |
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X54 ) =
% 3.79/1.14 (
% 3.79/1.14 X52 ) ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X56:$i,
% 3.79/1.14 X58:$i]:
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X56 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X56 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X58 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X60:$i,
% 3.79/1.14 X62:$i]:
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X62 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X60 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X62 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 emptyE1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 vacuousDall ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 quantDeMorgan1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 quantDeMorgan2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 quantDeMorgan3 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 quantDeMorgan4 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 prop2setI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 prop2set2propI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 notdexE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 notdallE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exuI1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exuI3 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exuI2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 inCongP ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exuE3u ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exu__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 emptyset__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X64:$i,
% 3.79/1.14 X66:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X64 ) =
% 3.79/1.14 (
% 3.79/1.14 X66 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X68:$i,
% 3.79/1.14 X70:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X68 ) =
% 3.79/1.14 (
% 3.79/1.14 X70 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X64 @ X68 ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X66 @ X70 ) ) ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 powerset__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunion__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 omega__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 exuEu ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 descr__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 dsetconstr__Cong ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetI1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 eqimpsubset2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 eqimpsubset1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetI2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 emptysetsubset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetE2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 notsubsetI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 notequalI1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 notequalI2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetRefl ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetTrans ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoinSub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoinSub2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subset2powerset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setextsub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 subsetemptysetimpeq ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 powersetI1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 powersetE1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 inPowerset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 powersetsubset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 sepInPowerset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 sepSubset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binunionIL ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X72:$i,
% 3.79/1.14 X74:$i]:
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X74 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X72 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X74 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binunionIR ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binunionEcases ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binunionE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binunionLsub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binunionRsub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectSubset5 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectEL ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectLsub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectSubset2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectSubset3 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectER ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 disjointsetsI1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectRsub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectSubset4 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 binintersectSubset1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 bs114d ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusI ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusEL ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusER ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusSubset2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusERneg ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusELneg ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusILneg ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusIRneg ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusLsub ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setminusSubset1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 symdiffE ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 symdiffI1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 symdiffI2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 symdiffIneg1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 symdiffIneg2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X76:$i,
% 3.79/1.14 X78:$i]:
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X78 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X76 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X78 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setukpairIL ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setukpairIR ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 kpairiskpair ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 kpairp ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 singletonsubset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 singletoninpowerset ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 singletoninpowunion ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X80:$i,
% 3.79/1.14 X82:$i,
% 3.79/1.14 X84:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 X84 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X80 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X82 @
% 3.79/1.14 emptyset ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X84 ) =
% 3.79/1.14 (
% 3.79/1.14 X80 ) ) |
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X84 ) =
% 3.79/1.14 (
% 3.79/1.14 X82 ) ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 upairsubunion ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 upairinpowunion ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ubforcartprodlem1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ubforcartprodlem2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ubforcartprodlem3 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 cartprodpairin ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 cartprodmempair1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 cartprodmempair ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunionE2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunionsingleton1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunionsingleton2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setunionsingleton ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 singletonprop ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ex1E1 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ex1I ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ex1I2 ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X86:$i,
% 3.79/1.14 X88:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X86 @
% 3.79/1.14 emptyset ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X88 @
% 3.79/1.14 emptyset ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X86 ) =
% 3.79/1.14 (
% 3.79/1.14 X88 ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X90:$i,
% 3.79/1.14 X92:$i,
% 3.79/1.14 X94:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 in @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X94 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X90 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X90 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X92 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X90 ) =
% 3.79/1.14 (
% 3.79/1.14 X94 ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 kfstsingleton ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 theprop ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 kfstpairEq ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 cartprodfstin ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X96:$i,
% 3.79/1.14 X98:$i,
% 3.79/1.14 X100:$i,
% 3.79/1.14 X102:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X96 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X96 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X98 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X100 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X100 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X102 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X96 ) =
% 3.79/1.14 (
% 3.79/1.14 X100 ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setukpairinjL ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X104:$i,
% 3.79/1.14 X106:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X104 ) =
% 3.79/1.14 (
% 3.79/1.14 X106 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X104 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X106 @
% 3.79/1.14 emptyset ) ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X104 @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X108:$i,
% 3.79/1.14 X110:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X108 ) =
% 3.79/1.14 (
% 3.79/1.14 X110 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X108 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X108 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X110 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X108 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 emptyset ) ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 ![
% 3.79/1.14 X112:$i,
% 3.79/1.14 X114:$i,
% 3.79/1.14 X116:$i,
% 3.79/1.14 X118:$i]:
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X112 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X112 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X114 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) =
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X116 @
% 3.79/1.14 emptyset ) @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X116 @
% 3.79/1.14 (
% 3.79/1.14 setadjoin
% 3.79/1.14 @
% 3.79/1.14 X118 @
% 3.79/1.14 emptyset ) ) @
% 3.79/1.14 emptyset ) ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X116 ) =
% 3.79/1.14 (
% 3.79/1.14 X118 ) ) =>
% 3.79/1.14 (
% 3.79/1.14 (
% 3.79/1.14 X114 ) =
% 3.79/1.14 (
% 3.79/1.14 X118 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 3.79/1.14 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 3.79/1.14 thf(zip_derived_cl26, plain,
% 3.79/1.14 (![X12 : $i, X13 : $i]:
% 3.79/1.14 (~ (in @ X12 @ (setadjoin @ X13 @ emptyset)) | ((X13) = (X12)))),
% 3.79/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.79/1.14 thf(zip_derived_cl90, plain,
% 3.79/1.14 (((setadjoin @ (setadjoin @ sk__54 @ emptyset) @
% 3.79/1.14 (setadjoin @ (setadjoin @ sk__54 @ (setadjoin @ sk__55 @ emptyset)) @
% 3.79/1.14 emptyset))
% 3.79/1.14 = (setadjoin @ (setadjoin @ sk__56 @ emptyset) @
% 3.79/1.14 (setadjoin @
% 3.79/1.14 (setadjoin @ sk__56 @ (setadjoin @ sk__57 @ emptyset)) @ emptyset)))),
% 3.79/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.79/1.14 thf(zip_derived_cl88, plain, (((sk__56) = (sk__57))),
% 3.79/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.79/1.14 thf(zip_derived_cl91, plain,
% 3.79/1.14 (![X32 : $i, X33 : $i]:
% 3.79/1.14 (((setadjoin @ X32 @ (setadjoin @ X33 @ emptyset))
% 3.79/1.14 = (setadjoin @ X32 @ emptyset))
% 3.79/1.14 | ((X32) != (X33)))),
% 3.79/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.79/1.14 thf(zip_derived_cl381, plain,
% 3.79/1.14 (![X33 : $i]:
% 3.79/1.14 ((setadjoin @ X33 @ (setadjoin @ X33 @ emptyset))
% 3.79/1.14 = (setadjoin @ X33 @ emptyset))),
% 3.79/1.14 inference('simplify', [status(thm)], [zip_derived_cl91])).
% 3.79/1.14 thf(zip_derived_cl381, plain,
% 3.79/1.14 (![X33 : $i]:
% 3.79/1.14 ((setadjoin @ X33 @ (setadjoin @ X33 @ emptyset))
% 3.79/1.14 = (setadjoin @ X33 @ emptyset))),
% 3.79/1.14 inference('simplify', [status(thm)], [zip_derived_cl91])).
% 3.79/1.14 thf(zip_derived_cl440, plain,
% 3.79/1.14 (((setadjoin @ (setadjoin @ sk__54 @ emptyset) @
% 3.79/1.14 (setadjoin @ (setadjoin @ sk__54 @ (setadjoin @ sk__55 @ emptyset)) @
% 3.79/1.14 emptyset))
% 3.79/1.14 = (setadjoin @ (setadjoin @ sk__56 @ emptyset) @ emptyset))),
% 3.79/1.14 inference('demod', [status(thm)],
% 3.79/1.14 [zip_derived_cl90, zip_derived_cl88, zip_derived_cl381,
% 3.79/1.14 zip_derived_cl381])).
% 3.79/1.14 thf(zip_derived_cl440, plain,
% 3.79/1.14 (((setadjoin @ (setadjoin @ sk__54 @ emptyset) @
% 3.79/1.14 (setadjoin @ (setadjoin @ sk__54 @ (setadjoin @ sk__55 @ emptyset)) @
% 3.79/1.14 emptyset))
% 3.79/1.14 = (setadjoin @ (setadjoin @ sk__56 @ emptyset) @ emptyset))),
% 3.79/1.14 inference('demod', [status(thm)],
% 3.79/1.14 [zip_derived_cl90, zip_derived_cl88, zip_derived_cl381,
% 3.79/1.14 zip_derived_cl381])).
% 3.79/1.14 thf(zip_derived_cl18, plain,
% 3.79/1.14 (![X4 : $i, X5 : $i]: (in @ X4 @ (setadjoin @ X4 @ X5))),
% 3.79/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.79/1.14 thf(zip_derived_cl447, plain,
% 3.79/1.14 ( (in @ (setadjoin @ sk__54 @ emptyset) @
% 3.79/1.14 (setadjoin @ (setadjoin @ sk__56 @ emptyset) @ emptyset))),
% 3.79/1.14 inference('sup+', [status(thm)], [zip_derived_cl440, zip_derived_cl18])).
% 3.79/1.14 thf(zip_derived_cl381, plain,
% 3.79/1.14 (![X33 : $i]:
% 3.79/1.14 ((setadjoin @ X33 @ (setadjoin @ X33 @ emptyset))
% 3.79/1.14 = (setadjoin @ X33 @ emptyset))),
% 3.79/1.14 inference('simplify', [status(thm)], [zip_derived_cl91])).
% 3.79/1.14 thf(zip_derived_cl83, plain,
% 3.79/1.14 (![X27 : $i, X28 : $i, X29 : $i]:
% 3.79/1.14 (((X28) = (X27))
% 3.79/1.14 | ~ (in @ (setadjoin @ X27 @ emptyset) @
% 3.79/1.14 (setadjoin @ (setadjoin @ X28 @ emptyset) @
% 3.79/1.14 (setadjoin @
% 3.79/1.14 (setadjoin @ X28 @ (setadjoin @ X29 @ emptyset)) @ emptyset))))),
% 3.79/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.79/1.14 thf(zip_derived_cl404, plain,
% 3.79/1.14 (![X0 : $i, X1 : $i]:
% 3.79/1.14 (~ (in @ (setadjoin @ X1 @ emptyset) @
% 3.79/1.14 (setadjoin @ (setadjoin @ X0 @ emptyset) @
% 3.79/1.14 (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset)))
% 3.79/1.14 | ((X0) = (X1)))),
% 3.79/1.14 inference('sup-', [status(thm)], [zip_derived_cl381, zip_derived_cl83])).
% 3.79/1.14 thf(zip_derived_cl381, plain,
% 3.79/1.14 (![X33 : $i]:
% 3.79/1.14 ((setadjoin @ X33 @ (setadjoin @ X33 @ emptyset))
% 3.79/1.14 = (setadjoin @ X33 @ emptyset))),
% 3.79/1.14 inference('simplify', [status(thm)], [zip_derived_cl91])).
% 3.79/1.14 thf(zip_derived_cl416, plain,
% 3.79/1.14 (![X0 : $i, X1 : $i]:
% 3.79/1.14 (~ (in @ (setadjoin @ X1 @ emptyset) @
% 3.79/1.14 (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))
% 3.79/1.14 | ((X0) = (X1)))),
% 3.79/1.14 inference('demod', [status(thm)], [zip_derived_cl404, zip_derived_cl381])).
% 3.79/1.14 thf(zip_derived_cl469, plain, (((sk__56) = (sk__54))),
% 3.79/1.14 inference('sup-', [status(thm)], [zip_derived_cl447, zip_derived_cl416])).
% 3.79/1.14 thf(zip_derived_cl469, plain, (((sk__56) = (sk__54))),
% 3.79/1.14 inference('sup-', [status(thm)], [zip_derived_cl447, zip_derived_cl416])).
% 3.79/1.14 thf(zip_derived_cl493, plain,
% 3.79/1.14 (((setadjoin @ (setadjoin @ sk__56 @ emptyset) @
% 3.79/1.14 (setadjoin @ (setadjoin @ sk__56 @ (setadjoin @ sk__55 @ emptyset)) @
% 3.79/1.14 emptyset))
% 3.79/1.14 = (setadjoin @ (setadjoin @ sk__56 @ emptyset) @ emptyset))),
% 3.79/1.14 inference('demod', [status(thm)],
% 3.79/1.14 [zip_derived_cl440, zip_derived_cl469, zip_derived_cl469])).
% 3.79/1.14 thf(zip_derived_cl70, plain,
% 3.79/1.14 (![X22 : $i, X23 : $i]:
% 3.79/1.14 (in @ X22 @ (setadjoin @ X23 @ (setadjoin @ X22 @ emptyset)))),
% 3.79/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.79/1.14 thf(zip_derived_cl498, plain,
% 3.79/1.14 ( (in @ (setadjoin @ sk__56 @ (setadjoin @ sk__55 @ emptyset)) @
% 3.79/1.14 (setadjoin @ (setadjoin @ sk__56 @ emptyset) @ emptyset))),
% 3.79/1.14 inference('sup+', [status(thm)], [zip_derived_cl493, zip_derived_cl70])).
% 3.79/1.14 thf(zip_derived_cl26, plain,
% 3.79/1.14 (![X12 : $i, X13 : $i]:
% 3.79/1.14 (~ (in @ X12 @ (setadjoin @ X13 @ emptyset)) | ((X13) = (X12)))),
% 3.79/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.79/1.14 thf(zip_derived_cl546, plain,
% 3.79/1.14 (((setadjoin @ sk__56 @ emptyset)
% 3.79/1.14 = (setadjoin @ sk__56 @ (setadjoin @ sk__55 @ emptyset)))),
% 3.79/1.14 inference('sup-', [status(thm)], [zip_derived_cl498, zip_derived_cl26])).
% 3.79/1.14 thf(zip_derived_cl70, plain,
% 3.79/1.14 (![X22 : $i, X23 : $i]:
% 3.79/1.14 (in @ X22 @ (setadjoin @ X23 @ (setadjoin @ X22 @ emptyset)))),
% 3.79/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.79/1.14 thf(zip_derived_cl574, plain,
% 3.79/1.14 ( (in @ sk__55 @ (setadjoin @ sk__56 @ emptyset))),
% 3.79/1.14 inference('sup+', [status(thm)], [zip_derived_cl546, zip_derived_cl70])).
% 3.79/1.14 thf(zip_derived_cl603, plain, (((sk__56) = (sk__55))),
% 3.79/1.14 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl574])).
% 3.79/1.14 thf(zip_derived_cl89, plain, (((sk__55) != (sk__57))),
% 3.79/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.79/1.14 thf(zip_derived_cl88, plain, (((sk__56) = (sk__57))),
% 3.79/1.14 inference('cnf', [status(esa)], [zf_stmt_4])).
% 3.79/1.14 thf(zip_derived_cl200, plain, (((sk__55) != (sk__56))),
% 3.79/1.14 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl88])).
% 3.79/1.14 thf(zip_derived_cl609, plain, ($false),
% 3.79/1.14 inference('simplify_reflect-', [status(thm)],
% 3.79/1.14 [zip_derived_cl603, zip_derived_cl200])).
% 3.79/1.14
% 3.79/1.14 % SZS output end Refutation
% 3.79/1.14
% 3.79/1.14
% 3.79/1.14 % Terminating...
% 4.54/1.32 % Runner terminated.
% 4.57/1.35 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------