%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU652^1 : 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.bxfKXN4lo7 true
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:55:34 PM UTC 2025
% Result : Theorem 2.91s 1.41s
% Output : Refutation 2.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.14 % Problem : SEU652^1 : TPTP v9.2.0. Released v3.7.0.
% 0.10/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.bxfKXN4lo7 true
% 0.11/0.36 % Computer : n027.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8042.1875MB
% 0.11/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Oct 1 16:07:53 EDT 2025
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Running portfolio for 300 s
% 0.11/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Number of cores: 8
% 0.11/0.37 % Python version: Python 3.6.8
% 0.11/0.37 % Running in HO mode
% 0.50/0.66 % Total configuration time : 828
% 0.50/0.66 % Estimated wc time : 1656
% 0.50/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.51/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.51/0.84 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.51/0.86 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.51/0.87 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.52/0.98 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.52/1.00 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/1.01 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.52/1.02 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 2.91/1.41 % Solved by lams/40_c_ic.sh.
% 2.91/1.41 % done 199 iterations in 0.357s
% 2.91/1.41 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 2.91/1.41 % SZS output start Refutation
% 2.91/1.41 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 2.91/1.41 thf(notdexE_type, type, notdexE: $o).
% 2.91/1.41 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 2.91/1.41 thf(setunionAx_type, type, setunionAx: $o).
% 2.91/1.41 thf(setminusELneg_type, type, setminusELneg: $o).
% 2.91/1.41 thf(powersetE_type, type, powersetE: $o).
% 2.91/1.41 thf(omegaSAx_type, type, omegaSAx: $o).
% 2.91/1.41 thf(exuI1_type, type, exuI1: $o).
% 2.91/1.41 thf(exuI2_type, type, exuI2: $o).
% 2.91/1.41 thf(notequalI2_type, type, notequalI2: $o).
% 2.91/1.41 thf(setukpairIR_type, type, setukpairIR: $o).
% 2.91/1.41 thf(sk__59_type, type, sk__59: $i).
% 2.91/1.41 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 2.91/1.41 thf(setminusILneg_type, type, setminusILneg: $o).
% 2.91/1.41 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 2.91/1.41 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 2.91/1.41 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 2.91/1.41 thf(upairsubunion_type, type, upairsubunion: $o).
% 2.91/1.41 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 2.91/1.41 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 2.91/1.41 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 2.91/1.41 thf(setukpairIL_type, type, setukpairIL: $o).
% 2.91/1.41 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 2.91/1.41 thf(binunionE_type, type, binunionE: $o).
% 2.91/1.41 thf(setext_type, type, setext: $o).
% 2.91/1.41 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 2.91/1.41 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 2.91/1.41 thf(descr__Cong_type, type, descr__Cong: $o).
% 2.91/1.41 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 2.91/1.41 thf(in_type, type, in: $i > $i > $o).
% 2.91/1.41 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 2.91/1.41 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 2.91/1.41 thf(theprop_type, type, theprop: $o).
% 2.91/1.41 thf(upairset2E_type, type, upairset2E: $o).
% 2.91/1.41 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 2.91/1.41 thf(sk__60_type, type, sk__60: $i).
% 2.91/1.41 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 2.91/1.41 thf(symdiffI2_type, type, symdiffI2: $o).
% 2.91/1.41 thf(upairset2IR_type, type, upairset2IR: $o).
% 2.91/1.41 thf(subsetE_type, type, subsetE: $o).
% 2.91/1.41 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 2.91/1.41 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 2.91/1.41 thf(setbeta_type, type, setbeta: $o).
% 2.91/1.41 thf(eqinunit_type, type, eqinunit: $o).
% 2.91/1.41 thf(upairsetIL_type, type, upairsetIL: $o).
% 2.91/1.41 thf(powersetI1_type, type, powersetI1: $o).
% 2.91/1.41 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 2.91/1.41 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 2.91/1.41 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 2.91/1.41 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 2.91/1.41 thf(powersetAx_type, type, powersetAx: $o).
% 2.91/1.41 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 2.91/1.41 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 2.91/1.41 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 2.91/1.41 thf(powersetI_type, type, powersetI: $o).
% 2.91/1.41 thf(upairsetIR_type, type, upairsetIR: $o).
% 2.91/1.41 thf(inCongP_type, type, inCongP: $o).
% 2.91/1.41 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 2.91/1.41 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 2.91/1.41 thf(exuE3e_type, type, exuE3e: $o).
% 2.91/1.41 thf(emptysetE_type, type, emptysetE: $o).
% 2.91/1.41 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 2.91/1.41 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 2.91/1.41 thf(setunionI_type, type, setunionI: $o).
% 2.91/1.41 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 2.91/1.41 thf(prop2setI_type, type, prop2setI: $o).
% 2.91/1.41 thf(ex1I2_type, type, ex1I2: $o).
% 2.91/1.41 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 2.91/1.41 thf(setminusER_type, type, setminusER: $o).
% 2.91/1.41 thf(exuE2_type, type, exuE2: $o).
% 2.91/1.41 thf(emptyset_type, type, emptyset: $i).
% 2.91/1.41 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 2.91/1.41 thf(powersetsubset_type, type, powersetsubset: $o).
% 2.91/1.41 thf(subPowSU_type, type, subPowSU: $o).
% 2.91/1.41 thf(notequalI1_type, type, notequalI1: $o).
% 2.91/1.41 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 2.91/1.41 thf(notinemptyset_type, type, notinemptyset: $o).
% 2.91/1.41 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 2.91/1.41 thf(subsetTrans_type, type, subsetTrans: $o).
% 2.91/1.41 thf(setminusI_type, type, setminusI: $o).
% 2.91/1.41 thf(binunionIL_type, type, binunionIL: $o).
% 2.91/1.41 thf(subsetE2_type, type, subsetE2: $o).
% 2.91/1.41 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 2.91/1.41 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 2.91/1.41 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 2.91/1.41 thf(setextsub_type, type, setextsub: $o).
% 2.91/1.41 thf(binunionLsub_type, type, binunionLsub: $o).
% 2.91/1.41 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 2.91/1.41 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 2.91/1.41 thf(setunionE_type, type, setunionE: $o).
% 2.91/1.41 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 2.91/1.41 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 2.91/1.41 thf(binunionIR_type, type, binunionIR: $o).
% 2.91/1.41 thf(setadjoinE_type, type, setadjoinE: $o).
% 2.91/1.41 thf(singletonprop_type, type, singletonprop: $o).
% 2.91/1.41 thf(sk__58_type, type, sk__58: $i).
% 2.91/1.41 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 2.91/1.41 thf(exuE1_type, type, exuE1: $o).
% 2.91/1.41 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 2.91/1.41 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 2.91/1.41 thf(setminusLsub_type, type, setminusLsub: $o).
% 2.91/1.41 thf(notinsingleton_type, type, notinsingleton: $o).
% 2.91/1.41 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 2.91/1.41 thf(exuEu_type, type, exuEu: $o).
% 2.91/1.41 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 2.91/1.41 thf(upairsetE_type, type, upairsetE: $o).
% 2.91/1.41 thf(omega0Ax_type, type, omega0Ax: $o).
% 2.91/1.41 thf(notsubsetI_type, type, notsubsetI: $o).
% 2.91/1.41 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 2.91/1.41 thf(setextAx_type, type, setextAx: $o).
% 2.91/1.41 thf(powersetE1_type, type, powersetE1: $o).
% 2.91/1.41 thf(bs114d_type, type, bs114d: $o).
% 2.91/1.41 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 2.91/1.41 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 2.91/1.41 thf(subsetI1_type, type, subsetI1: $o).
% 2.91/1.41 thf(symdiffE_type, type, symdiffE: $o).
% 2.91/1.41 thf(descrp_type, type, descrp: $o).
% 2.91/1.41 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 2.91/1.41 thf(foundationAx_type, type, foundationAx: $o).
% 2.91/1.41 thf(emptysetAx_type, type, emptysetAx: $o).
% 2.91/1.41 thf(emptyI_type, type, emptyI: $o).
% 2.91/1.41 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 2.91/1.41 thf(binintersectEL_type, type, binintersectEL: $o).
% 2.91/1.41 thf(emptyE1_type, type, emptyE1: $o).
% 2.91/1.41 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 2.91/1.41 thf(vacuousDall_type, type, vacuousDall: $o).
% 2.91/1.41 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 2.91/1.41 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 2.91/1.41 thf(binintersectI_type, type, binintersectI: $o).
% 2.91/1.41 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 2.91/1.41 thf(ex1E1_type, type, ex1E1: $o).
% 2.91/1.41 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 2.91/1.41 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 2.91/1.41 thf(symdiffI1_type, type, symdiffI1: $o).
% 2.91/1.41 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 2.91/1.41 thf(subsetI2_type, type, subsetI2: $o).
% 2.91/1.41 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 2.91/1.41 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 2.91/1.41 thf(setminusERneg_type, type, setminusERneg: $o).
% 2.91/1.41 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 2.91/1.41 thf(omega__Cong_type, type, omega__Cong: $o).
% 2.91/1.41 thf(subsetRefl_type, type, subsetRefl: $o).
% 2.91/1.41 thf(uniqinunit_type, type, uniqinunit: $o).
% 2.91/1.41 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 2.91/1.41 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 2.91/1.41 thf(prop2setE_type, type, prop2setE: $o).
% 2.91/1.41 thf(binunionEcases_type, type, binunionEcases: $o).
% 2.91/1.41 thf(nonemptyI_type, type, nonemptyI: $o).
% 2.91/1.41 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 2.91/1.41 thf(exuE3u_type, type, exuE3u: $o).
% 2.91/1.41 thf(setminusEL_type, type, setminusEL: $o).
% 2.91/1.41 thf(singletonsubset_type, type, singletonsubset: $o).
% 2.91/1.41 thf(sepSubset_type, type, sepSubset: $o).
% 2.91/1.41 thf(setunionE2_type, type, setunionE2: $o).
% 2.91/1.41 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 2.91/1.41 thf(ex1I_type, type, ex1I: $o).
% 2.91/1.41 thf(exuI3_type, type, exuI3: $o).
% 2.91/1.41 thf(notdallE_type, type, notdallE: $o).
% 2.91/1.41 thf(binintersectER_type, type, binintersectER: $o).
% 2.91/1.41 thf(kpairp_type, type, kpairp: $o).
% 2.91/1.41 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 2.91/1.41 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 2.91/1.41 thf(exu__Cong_type, type, exu__Cong: $o).
% 2.91/1.41 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 2.91/1.41 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 2.91/1.41 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 2.91/1.41 thf(replAx_type, type, replAx: $o).
% 2.91/1.41 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 2.91/1.41 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 2.91/1.41 thf(secondinupair_type, type, secondinupair: $o).
% 2.91/1.41 thf(inPowerset_type, type, inPowerset: $o).
% 2.91/1.41 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 2.91/1.41 thf(in__Cong_type, type, in__Cong: $o).
% 2.91/1.41 thf(binunionRsub_type, type, binunionRsub: $o).
% 2.91/1.41 thf(subset2powerset_type, type, subset2powerset: $o).
% 2.91/1.41 thf(setukpairinjR1, axiom, setukpairinjR1 =
% 2.91/1.41 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 2.91/1.41 ( ( ( setadjoin @
% 2.91/1.41 ( setadjoin @ Xx @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ Xz @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) =>
% 2.91/1.41 ( ( ( Xz ) = ( Xu ) ) => ( ( Xy ) = ( Xu ) ) ) ))).
% 2.91/1.41 thf('0', plain,
% 2.91/1.41 (( setukpairinjR1 ) =
% 2.91/1.41 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 2.91/1.41 ( ( ( setadjoin @
% 2.91/1.41 ( setadjoin @ X4 @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ X8 @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) =>
% 2.91/1.41 ( ( ( X8 ) = ( X10 ) ) => ( ( X6 ) = ( X10 ) ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(setukpairinjR12, axiom, setukpairinjR12 =
% 2.91/1.41 (![Xx:$i,Xy:$i]:
% 2.91/1.41 ( ( ( Xx ) = ( Xy ) ) =>
% 2.91/1.41 ( ( setadjoin @
% 2.91/1.41 ( setadjoin @ Xx @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 2.91/1.41 ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ))).
% 2.91/1.41 thf('1', plain,
% 2.91/1.41 (( setukpairinjR12 ) =
% 2.91/1.41 ( ![X4:$i,X6:$i]:
% 2.91/1.41 ( ( ( X4 ) = ( X6 ) ) =>
% 2.91/1.41 ( ( setadjoin @
% 2.91/1.41 ( setadjoin @ X4 @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 2.91/1.41 ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ emptyset ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(setukpairinjR11, axiom, setukpairinjR11 =
% 2.91/1.41 (![Xx:$i,Xy:$i]:
% 2.91/1.41 ( ( ( Xx ) = ( Xy ) ) =>
% 2.91/1.41 ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =
% 2.91/1.41 ( setadjoin @ Xx @ emptyset ) ) ))).
% 2.91/1.41 thf('2', plain,
% 2.91/1.41 (( setukpairinjR11 ) =
% 2.91/1.41 ( ![X4:$i,X6:$i]:
% 2.91/1.41 ( ( ( X4 ) = ( X6 ) ) =>
% 2.91/1.41 ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =
% 2.91/1.41 ( setadjoin @ X4 @ emptyset ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(setukpairinjL2, axiom, setukpairinjL2 =
% 2.91/1.41 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 2.91/1.41 ( ( ( setadjoin @
% 2.91/1.41 ( setadjoin @ Xx @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ Xz @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) =>
% 2.91/1.41 ( ( Xx ) = ( Xz ) ) ))).
% 2.91/1.41 thf('3', plain,
% 2.91/1.41 (( setukpairinjL2 ) =
% 2.91/1.41 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 2.91/1.41 ( ( ( setadjoin @
% 2.91/1.41 ( setadjoin @ X4 @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ X8 @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) =>
% 2.91/1.41 ( ( X4 ) = ( X8 ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(setukpairinjL1, axiom, setukpairinjL1 =
% 2.91/1.41 (![Xx:$i,Xy:$i,Xz:$i]:
% 2.91/1.41 ( ( in @
% 2.91/1.41 ( setadjoin @ Xz @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ Xx @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) =>
% 2.91/1.41 ( ( Xx ) = ( Xz ) ) ))).
% 2.91/1.41 thf('4', plain,
% 2.91/1.41 (( setukpairinjL1 ) =
% 2.91/1.41 ( ![X4:$i,X6:$i,X8:$i]:
% 2.91/1.41 ( ( in @
% 2.91/1.41 ( setadjoin @ X8 @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ X4 @ emptyset ) @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) =>
% 2.91/1.41 ( ( X4 ) = ( X8 ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(singletonsuniq, axiom, singletonsuniq =
% 2.91/1.41 (![Xx:$i,Xy:$i]:
% 2.91/1.41 ( ( ( setadjoin @ Xx @ emptyset ) = ( setadjoin @ Xy @ emptyset ) ) =>
% 2.91/1.41 ( ( Xx ) = ( Xy ) ) ))).
% 2.91/1.41 thf('5', plain,
% 2.91/1.41 (( singletonsuniq ) =
% 2.91/1.41 ( ![X4:$i,X6:$i]:
% 2.91/1.41 ( ( ( setadjoin @ X4 @ emptyset ) = ( setadjoin @ X6 @ emptyset ) ) =>
% 2.91/1.41 ( ( X4 ) = ( X6 ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(upairset2E, axiom, upairset2E =
% 2.91/1.41 (![Xx:$i,Xy:$i,Xz:$i]:
% 2.91/1.41 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 2.91/1.41 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 2.91/1.41 thf('6', plain,
% 2.91/1.41 (( upairset2E ) =
% 2.91/1.41 ( ![X4:$i,X6:$i,X8:$i]:
% 2.91/1.41 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 2.91/1.41 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(secondinupair, axiom, secondinupair =
% 2.91/1.41 (![Xx:$i,Xy:$i]:
% 2.91/1.41 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 2.91/1.41 thf('7', plain,
% 2.91/1.41 (( secondinupair ) =
% 2.91/1.41 ( ![X4:$i,X6:$i]:
% 2.91/1.41 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(upairset2IR, axiom, upairset2IR =
% 2.91/1.41 (![Xx:$i,Xy:$i]:
% 2.91/1.41 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 2.91/1.41 thf('8', plain,
% 2.91/1.41 (( upairset2IR ) =
% 2.91/1.41 ( ![X4:$i,X6:$i]:
% 2.91/1.41 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 2.91/1.41 (![Xx:$i,Xy:$i]:
% 2.91/1.41 ( ( ( Xx ) = ( Xy ) ) =>
% 2.91/1.41 ( ![Xz:$i,Xu:$i]:
% 2.91/1.41 ( ( ( Xz ) = ( Xu ) ) =>
% 2.91/1.41 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 2.91/1.41 thf('9', plain,
% 2.91/1.41 (( setadjoin__Cong ) =
% 2.91/1.41 ( ![X4:$i,X6:$i]:
% 2.91/1.41 ( ( ( X4 ) = ( X6 ) ) =>
% 2.91/1.41 ( ![X8:$i,X10:$i]:
% 2.91/1.41 ( ( ( X8 ) = ( X10 ) ) =>
% 2.91/1.41 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(upairsetIR, axiom, upairsetIR =
% 2.91/1.41 (![Xx:$i,Xy:$i]:
% 2.91/1.41 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 2.91/1.41 thf('10', plain,
% 2.91/1.41 (( upairsetIR ) =
% 2.91/1.41 ( ![X4:$i,X6:$i]:
% 2.91/1.41 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(upairsetIL, axiom, upairsetIL =
% 2.91/1.41 (![Xx:$i,Xy:$i]:
% 2.91/1.41 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 2.91/1.41 thf('11', plain,
% 2.91/1.41 (( upairsetIL ) =
% 2.91/1.41 ( ![X4:$i,X6:$i]:
% 2.91/1.41 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(upairsetE, axiom, upairsetE =
% 2.91/1.41 (![Xx:$i,Xy:$i,Xz:$i]:
% 2.91/1.41 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 2.91/1.41 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 2.91/1.41 thf('12', plain,
% 2.91/1.41 (( upairsetE ) =
% 2.91/1.41 ( ![X4:$i,X6:$i,X8:$i]:
% 2.91/1.41 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 2.91/1.41 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(singletonsswitch, axiom, singletonsswitch =
% 2.91/1.41 (![Xx:$i,Xy:$i]:
% 2.91/1.41 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 2.91/1.41 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 2.91/1.41 thf('13', plain,
% 2.91/1.41 (( singletonsswitch ) =
% 2.91/1.41 ( ![X4:$i,X6:$i]:
% 2.91/1.41 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 2.91/1.41 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(eqinunit, axiom, eqinunit =
% 2.91/1.41 (![Xx:$i,Xy:$i]:
% 2.91/1.41 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 2.91/1.41 thf('14', plain,
% 2.91/1.41 (( eqinunit ) =
% 2.91/1.41 ( ![X4:$i,X6:$i]:
% 2.91/1.41 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(notinsingleton, axiom, notinsingleton =
% 2.91/1.41 (![Xx:$i,Xy:$i]:
% 2.91/1.41 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 2.91/1.41 thf('15', plain,
% 2.91/1.41 (( notinsingleton ) =
% 2.91/1.41 ( ![X4:$i,X6:$i]:
% 2.91/1.41 ( ( ( X4 ) != ( X6 ) ) =>
% 2.91/1.41 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(uniqinunit, axiom, uniqinunit =
% 2.91/1.41 (![Xx:$i,Xy:$i]:
% 2.91/1.41 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 2.91/1.41 thf('16', plain,
% 2.91/1.41 (( uniqinunit ) =
% 2.91/1.41 ( ![X4:$i,X6:$i]:
% 2.91/1.41 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(setadjoinOr, axiom, setadjoinOr =
% 2.91/1.41 (![Xx:$i,A:$i,Xy:$i]:
% 2.91/1.41 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 2.91/1.41 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 2.91/1.41 thf('17', plain,
% 2.91/1.41 (( setadjoinOr ) =
% 2.91/1.41 ( ![X4:$i,X6:$i,X8:$i]:
% 2.91/1.41 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 2.91/1.41 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(setadjoinE, axiom, setadjoinE =
% 2.91/1.41 (![Xx:$i,A:$i,Xy:$i]:
% 2.91/1.41 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 2.91/1.41 ( ![Xphi:$o]:
% 2.91/1.41 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 2.91/1.41 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 2.91/1.41 thf('18', plain,
% 2.91/1.41 (( setadjoinE ) =
% 2.91/1.41 ( ![X4:$i,X6:$i,X8:$i]:
% 2.91/1.41 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 2.91/1.41 ( ![X10:$o]:
% 2.91/1.41 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 2.91/1.41 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(setadjoinIR, axiom, setadjoinIR =
% 2.91/1.41 (![Xx:$i,A:$i,Xy:$i]:
% 2.91/1.41 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 2.91/1.41 thf('19', plain,
% 2.91/1.41 (( setadjoinIR ) =
% 2.91/1.41 ( ![X4:$i,X6:$i,X8:$i]:
% 2.91/1.41 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 2.91/1.41 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 2.91/1.41 thf('20', plain,
% 2.91/1.41 (( emptyinunitempty ) =
% 2.91/1.41 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 2.91/1.41 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 2.91/1.41 thf('21', plain,
% 2.91/1.41 (( emptyinunitempty ) =
% 2.91/1.41 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(setadjoinIL, axiom, setadjoinIL =
% 2.91/1.41 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 2.91/1.41 thf('22', plain,
% 2.91/1.41 (( setadjoinIL ) =
% 2.91/1.41 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(setadjoinAx, axiom, setadjoinAx =
% 2.91/1.41 (![Xx:$i,A:$i,Xy:$i]:
% 2.91/1.41 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 2.91/1.41 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 2.91/1.41 thf('23', plain,
% 2.91/1.41 (( setadjoinAx ) =
% 2.91/1.41 ( ![X4:$i,X6:$i,X8:$i]:
% 2.91/1.41 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 2.91/1.41 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 2.91/1.41 define([status(thm)])).
% 2.91/1.41 thf(upairequniteq, conjecture,
% 2.91/1.41 (( setextAx ) =>
% 2.91/1.41 ( ( emptysetAx ) =>
% 2.91/1.41 ( ( setadjoinAx ) =>
% 2.91/1.41 ( ( powersetAx ) =>
% 2.91/1.41 ( ( setunionAx ) =>
% 2.91/1.41 ( ( omega0Ax ) =>
% 2.91/1.41 ( ( omegaSAx ) =>
% 2.91/1.41 ( ( omegaIndAx ) =>
% 2.91/1.41 ( ( replAx ) =>
% 2.91/1.41 ( ( foundationAx ) =>
% 2.91/1.41 ( ( wellorderingAx ) =>
% 2.91/1.41 ( ( descrp ) =>
% 2.91/1.41 ( ( dsetconstrI ) =>
% 2.91/1.41 ( ( dsetconstrEL ) =>
% 2.91/1.41 ( ( dsetconstrER ) =>
% 2.91/1.41 ( ( exuE1 ) =>
% 2.91/1.41 ( ( prop2setE ) =>
% 2.91/1.41 ( ( emptysetE ) =>
% 2.91/1.41 ( ( emptysetimpfalse ) =>
% 2.91/1.41 ( ( notinemptyset ) =>
% 2.91/1.41 ( ( exuE3e ) =>
% 2.91/1.41 ( ( setext ) =>
% 2.91/1.41 ( ( emptyI ) =>
% 2.91/1.41 ( ( noeltsimpempty ) =>
% 2.91/1.41 ( ( setbeta ) =>
% 2.91/1.41 ( ( nonemptyE1 ) =>
% 2.91/1.41 ( ( nonemptyI ) =>
% 2.91/1.41 ( ( nonemptyI1 ) =>
% 2.91/1.41 ( ( setadjoinIL ) =>
% 2.91/1.41 ( ( emptyinunitempty ) =>
% 2.91/1.41 ( ( setadjoinIR ) =>
% 2.91/1.41 ( ( setadjoinE ) =>
% 2.91/1.41 ( (
% 2.91/1.41 setadjoinOr ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setoftrueEq ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 powersetI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 emptyinPowerset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 emptyInPowerset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 powersetE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunionI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunionE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subPowSU ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exuE2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 nonemptyImpWitness ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 uniqinunit ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 notinsingleton ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 eqinunit ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 singletonsswitch ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 upairsetE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 upairsetIL ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 upairsetIR ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 emptyE1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 vacuousDall ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 quantDeMorgan1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 quantDeMorgan2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 quantDeMorgan3 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 quantDeMorgan4 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 prop2setI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 prop2set2propI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 notdexE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 notdallE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exuI1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exuI3 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exuI2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 inCongP ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 in__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exuE3u ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exu__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 emptyset__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setadjoin__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 powerset__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunion__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 omega__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exuEu ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 descr__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 dsetconstr__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetI1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 eqimpsubset2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 eqimpsubset1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetI2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 emptysetsubset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetE2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 notsubsetI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 notequalI1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 notequalI2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetRefl ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetTrans ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setadjoinSub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setadjoinSub2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subset2powerset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setextsub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetemptysetimpeq ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 powersetI1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 powersetE1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 inPowerset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 powersetsubset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 sepInPowerset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 sepSubset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binunionIL ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 upairset2IR ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binunionIR ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binunionEcases ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binunionE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binunionLsub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binunionRsub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectSubset5 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectEL ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectLsub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectSubset2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectSubset3 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectER ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 disjointsetsI1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectRsub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectSubset4 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectSubset1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 bs114d ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusEL ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusER ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusSubset2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusERneg ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusELneg ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusILneg ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusIRneg ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusLsub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusSubset1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 symdiffE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 symdiffI1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 symdiffI2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 symdiffIneg1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 symdiffIneg2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 secondinupair ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setukpairIL ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setukpairIR ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 kpairiskpair ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 kpairp ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 singletonsubset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 singletoninpowerset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 singletoninpowunion ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 upairset2E ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 upairsubunion ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 upairinpowunion ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ubforcartprodlem1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ubforcartprodlem2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ubforcartprodlem3 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 cartprodpairin ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 cartprodmempair1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 cartprodmempair ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunionE2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunionsingleton1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunionsingleton2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunionsingleton ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 singletonprop ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ex1E1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ex1I ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ex1I2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 singletonsuniq ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setukpairinjL1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 kfstsingleton ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 theprop ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 kfstpairEq ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 cartprodfstin ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setukpairinjL2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setukpairinjL ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setukpairinjR11 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setukpairinjR12 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setukpairinjR1 ) =>
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 Xx:$i,
% 2.91/1.41 Xy:$i,
% 2.91/1.41 Xz:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 Xx @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 Xy @
% 2.91/1.41 emptyset ) ) =
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 Xz @
% 2.91/1.41 emptyset ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 Xx ) =
% 2.91/1.41 (
% 2.91/1.41 Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 2.91/1.41 thf(zf_stmt_0, conjecture,
% 2.91/1.41 (( setextAx ) =>
% 2.91/1.41 ( ( emptysetAx ) =>
% 2.91/1.41 ( ( ![X4:$i,X6:$i,X8:$i]:
% 2.91/1.41 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 2.91/1.41 ( ( in @ X8 @ X6 ) | ( ( X8 ) = ( X4 ) ) ) ) ) =>
% 2.91/1.41 ( ( powersetAx ) =>
% 2.91/1.41 ( ( setunionAx ) =>
% 2.91/1.41 ( ( omega0Ax ) =>
% 2.91/1.41 ( ( omegaSAx ) =>
% 2.91/1.41 ( ( omegaIndAx ) =>
% 2.91/1.41 ( ( replAx ) =>
% 2.91/1.41 ( ( foundationAx ) =>
% 2.91/1.41 ( ( wellorderingAx ) =>
% 2.91/1.41 ( ( descrp ) =>
% 2.91/1.41 ( ( dsetconstrI ) =>
% 2.91/1.41 ( ( dsetconstrEL ) =>
% 2.91/1.41 ( ( dsetconstrER ) =>
% 2.91/1.41 ( ( exuE1 ) =>
% 2.91/1.41 ( ( prop2setE ) =>
% 2.91/1.41 ( ( emptysetE ) =>
% 2.91/1.41 ( ( emptysetimpfalse ) =>
% 2.91/1.41 ( ( notinemptyset ) =>
% 2.91/1.41 ( ( exuE3e ) =>
% 2.91/1.41 ( ( setext ) =>
% 2.91/1.41 ( ( emptyI ) =>
% 2.91/1.41 ( ( noeltsimpempty ) =>
% 2.91/1.41 ( ( setbeta ) =>
% 2.91/1.41 ( ( nonemptyE1 ) =>
% 2.91/1.41 ( ( nonemptyI ) =>
% 2.91/1.41 ( ( nonemptyI1 ) =>
% 2.91/1.41 ( ( ![X10:$i,X12:$i]:
% 2.91/1.41 ( in @
% 2.91/1.41 X10 @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 X10 @ X12 ) ) ) =>
% 2.91/1.41 ( ( in @
% 2.91/1.41 emptyset @
% 2.91/1.41 ( setadjoin @
% 2.91/1.41 emptyset @
% 2.91/1.41 emptyset ) ) =>
% 2.91/1.41 ( ( ![X14:$i,
% 2.91/1.41 X16:$i,
% 2.91/1.41 X18:$i]:
% 2.91/1.41 ( (
% 2.91/1.41 in @
% 2.91/1.41 X18 @ X16 ) =>
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X18 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X14 @ X16 ) ) ) ) =>
% 2.91/1.41 ( ( ![
% 2.91/1.41 X20:$i,
% 2.91/1.41 X22:$i,
% 2.91/1.41 X24:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X24 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X20 @ X22 ) ) =>
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X26:$o]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X24 ) =
% 2.91/1.41 (
% 2.91/1.41 X20 ) ) =>
% 2.91/1.41 (
% 2.91/1.41 X26 ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X24 @ X22 ) =>
% 2.91/1.41 (
% 2.91/1.41 X26 ) ) =>
% 2.91/1.41 (
% 2.91/1.41 X26 ) ) ) ) ) ) =>
% 2.91/1.41 ( (
% 2.91/1.41 ![
% 2.91/1.41 X28:$i,
% 2.91/1.41 X30:$i,
% 2.91/1.41 X32:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X32 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X28 @ X30 ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X32 @ X30 ) |
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X32 ) =
% 2.91/1.41 (
% 2.91/1.41 X28 ) ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setoftrueEq ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 powersetI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 emptyinPowerset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 emptyInPowerset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 powersetE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunionI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunionE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subPowSU ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exuE2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 nonemptyImpWitness ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X34:$i,
% 2.91/1.41 X36:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X34 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X36 @
% 2.91/1.41 emptyset ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X34 ) =
% 2.91/1.41 (
% 2.91/1.41 X36 ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X38:$i,
% 2.91/1.41 X40:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X38 ) !=
% 2.91/1.41 (
% 2.91/1.41 X40 ) ) =>
% 2.91/1.41 (
% 2.91/1.41 ~(
% 2.91/1.41 in @
% 2.91/1.41 X40 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X38 @
% 2.91/1.41 emptyset ) ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X42:$i,
% 2.91/1.41 X44:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X42 ) =
% 2.91/1.41 (
% 2.91/1.41 X44 ) ) =>
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X42 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X44 @
% 2.91/1.41 emptyset ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X46:$i,
% 2.91/1.41 X48:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X46 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X48 @
% 2.91/1.41 emptyset ) ) =>
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X48 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X46 @
% 2.91/1.41 emptyset ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X50:$i,
% 2.91/1.41 X52:$i,
% 2.91/1.41 X54:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X54 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X50 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X52 @
% 2.91/1.41 emptyset ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X54 ) =
% 2.91/1.41 (
% 2.91/1.41 X52 ) ) |
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X54 ) =
% 2.91/1.41 (
% 2.91/1.41 X50 ) ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X56:$i,
% 2.91/1.41 X58:$i]:
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X56 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X56 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X58 @
% 2.91/1.41 emptyset ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X60:$i,
% 2.91/1.41 X62:$i]:
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X62 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X60 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X62 @
% 2.91/1.41 emptyset ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 emptyE1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 vacuousDall ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 quantDeMorgan1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 quantDeMorgan2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 quantDeMorgan3 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 quantDeMorgan4 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 prop2setI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 prop2set2propI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 notdexE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 notdallE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exuI1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exuI3 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exuI2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 inCongP ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 in__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exuE3u ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exu__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 emptyset__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X64:$i,
% 2.91/1.41 X66:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X64 ) =
% 2.91/1.41 (
% 2.91/1.41 X66 ) ) =>
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X68:$i,
% 2.91/1.41 X70:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X68 ) =
% 2.91/1.41 (
% 2.91/1.41 X70 ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X64 @ X68 ) =
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X66 @ X70 ) ) ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 powerset__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunion__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 omega__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 exuEu ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 descr__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 dsetconstr__Cong ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetI1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 eqimpsubset2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 eqimpsubset1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetI2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 emptysetsubset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetE2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 notsubsetI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 notequalI1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 notequalI2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetRefl ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetTrans ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setadjoinSub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setadjoinSub2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subset2powerset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setextsub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 subsetemptysetimpeq ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 powersetI1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 powersetE1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 inPowerset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 powersetsubset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 sepInPowerset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 sepSubset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binunionIL ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X72:$i,
% 2.91/1.41 X74:$i]:
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X74 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X72 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X74 @
% 2.91/1.41 emptyset ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binunionIR ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binunionEcases ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binunionE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binunionLsub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binunionRsub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectSubset5 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectEL ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectLsub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectSubset2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectSubset3 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectER ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 disjointsetsI1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectRsub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectSubset4 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 binintersectSubset1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 bs114d ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusI ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusEL ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusER ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusSubset2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusERneg ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusELneg ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusILneg ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusIRneg ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusLsub ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setminusSubset1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 symdiffE ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 symdiffI1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 symdiffI2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 symdiffIneg1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 symdiffIneg2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X76:$i,
% 2.91/1.41 X78:$i]:
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X78 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X76 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X78 @
% 2.91/1.41 emptyset ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setukpairIL ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setukpairIR ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 kpairiskpair ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 kpairp ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 singletonsubset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 singletoninpowerset ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 singletoninpowunion ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X80:$i,
% 2.91/1.41 X82:$i,
% 2.91/1.41 X84:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 X84 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X80 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X82 @
% 2.91/1.41 emptyset ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X84 ) =
% 2.91/1.41 (
% 2.91/1.41 X82 ) ) |
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X84 ) =
% 2.91/1.41 (
% 2.91/1.41 X80 ) ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 upairsubunion ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 upairinpowunion ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ubforcartprodlem1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ubforcartprodlem2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ubforcartprodlem3 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 cartprodpairin ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 cartprodmempair1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 cartprodmempair ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunionE2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunionsingleton1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunionsingleton2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setunionsingleton ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 singletonprop ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ex1E1 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ex1I ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ex1I2 ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X86:$i,
% 2.91/1.41 X88:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X86 @
% 2.91/1.41 emptyset ) =
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X88 @
% 2.91/1.41 emptyset ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X86 ) =
% 2.91/1.41 (
% 2.91/1.41 X88 ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X90:$i,
% 2.91/1.41 X92:$i,
% 2.91/1.41 X94:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 in @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X94 @
% 2.91/1.41 emptyset ) @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X90 @
% 2.91/1.41 emptyset ) @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X90 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X92 @
% 2.91/1.41 emptyset ) ) @
% 2.91/1.41 emptyset ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X90 ) =
% 2.91/1.41 (
% 2.91/1.41 X94 ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 kfstsingleton ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 theprop ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 kfstpairEq ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 cartprodfstin ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X96:$i,
% 2.91/1.41 X98:$i,
% 2.91/1.41 X100:$i,
% 2.91/1.41 X102:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X96 @
% 2.91/1.41 emptyset ) @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X96 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X98 @
% 2.91/1.41 emptyset ) ) @
% 2.91/1.41 emptyset ) ) =
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X100 @
% 2.91/1.41 emptyset ) @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X100 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X102 @
% 2.91/1.41 emptyset ) ) @
% 2.91/1.41 emptyset ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X96 ) =
% 2.91/1.41 (
% 2.91/1.41 X100 ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setukpairinjL ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X104:$i,
% 2.91/1.41 X106:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X104 ) =
% 2.91/1.41 (
% 2.91/1.41 X106 ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X104 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X106 @
% 2.91/1.41 emptyset ) ) =
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X104 @
% 2.91/1.41 emptyset ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X108:$i,
% 2.91/1.41 X110:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X108 ) =
% 2.91/1.41 (
% 2.91/1.41 X110 ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X108 @
% 2.91/1.41 emptyset ) @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X108 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X110 @
% 2.91/1.41 emptyset ) ) @
% 2.91/1.41 emptyset ) ) =
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X108 @
% 2.91/1.41 emptyset ) @
% 2.91/1.41 emptyset ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X112:$i,
% 2.91/1.41 X114:$i,
% 2.91/1.41 X116:$i,
% 2.91/1.41 X118:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X112 @
% 2.91/1.41 emptyset ) @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X112 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X114 @
% 2.91/1.41 emptyset ) ) @
% 2.91/1.41 emptyset ) ) =
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X116 @
% 2.91/1.41 emptyset ) @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X116 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X118 @
% 2.91/1.41 emptyset ) ) @
% 2.91/1.41 emptyset ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X116 ) =
% 2.91/1.41 (
% 2.91/1.41 X118 ) ) =>
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 X114 ) =
% 2.91/1.41 (
% 2.91/1.41 X118 ) ) ) ) ) =>
% 2.91/1.41 (
% 2.91/1.41 ![
% 2.91/1.41 X120:$i,
% 2.91/1.41 X122:$i,
% 2.91/1.41 X124:$i]:
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X120 @
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X122 @
% 2.91/1.41 emptyset ) ) =
% 2.91/1.41 (
% 2.91/1.41 setadjoin
% 2.91/1.41 @
% 2.91/1.41 X124 @
% 2.91/1.41 emptyset ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X120 ) =
% 2.91/1.42 (
% 2.91/1.42 X122 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 2.91/1.42 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 2.91/1.42 thf(zf_stmt_2, axiom,
% 2.91/1.42 (![X8:$i,X6:$i,X4:$i]:
% 2.91/1.42 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 2.91/1.42 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ))).
% 2.91/1.42 thf(zf_stmt_3, conjecture,
% 2.91/1.42 (( setextAx ) =>
% 2.91/1.42 ( ( emptysetAx ) =>
% 2.91/1.42 ( ( ![X4:$i,X6:$i,X8:$i]:
% 2.91/1.42 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 2.91/1.42 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 2.91/1.42 ( ( powersetAx ) =>
% 2.91/1.42 ( ( setunionAx ) =>
% 2.91/1.42 ( ( omega0Ax ) =>
% 2.91/1.42 ( ( omegaSAx ) =>
% 2.91/1.42 ( ( omegaIndAx ) =>
% 2.91/1.42 ( ( replAx ) =>
% 2.91/1.42 ( ( foundationAx ) =>
% 2.91/1.42 ( ( wellorderingAx ) =>
% 2.91/1.42 ( ( descrp ) =>
% 2.91/1.42 ( ( dsetconstrI ) =>
% 2.91/1.42 ( ( dsetconstrEL ) =>
% 2.91/1.42 ( ( dsetconstrER ) =>
% 2.91/1.42 ( ( exuE1 ) =>
% 2.91/1.42 ( ( prop2setE ) =>
% 2.91/1.42 ( ( emptysetE ) =>
% 2.91/1.42 ( ( emptysetimpfalse ) =>
% 2.91/1.42 ( ( notinemptyset ) =>
% 2.91/1.42 ( ( exuE3e ) =>
% 2.91/1.42 ( ( setext ) =>
% 2.91/1.42 ( ( emptyI ) =>
% 2.91/1.42 ( ( noeltsimpempty ) =>
% 2.91/1.42 ( ( setbeta ) =>
% 2.91/1.42 ( ( nonemptyE1 ) =>
% 2.91/1.42 ( ( nonemptyI ) =>
% 2.91/1.42 ( ( nonemptyI1 ) =>
% 2.91/1.42 ( ( ![X10:$i,X12:$i]:
% 2.91/1.42 ( in @
% 2.91/1.42 X10 @
% 2.91/1.42 ( setadjoin @
% 2.91/1.42 X10 @ X12 ) ) ) =>
% 2.91/1.42 ( ( in @
% 2.91/1.42 emptyset @
% 2.91/1.42 ( setadjoin @
% 2.91/1.42 emptyset @
% 2.91/1.42 emptyset ) ) =>
% 2.91/1.42 ( ( ![X14:$i,
% 2.91/1.42 X16:$i,
% 2.91/1.42 X18:$i]:
% 2.91/1.42 ( (
% 2.91/1.42 in @
% 2.91/1.42 X18 @ X16 ) =>
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X18 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X14 @ X16 ) ) ) ) =>
% 2.91/1.42 ( ( ![
% 2.91/1.42 X20:$i,
% 2.91/1.42 X22:$i,
% 2.91/1.42 X24:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X24 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X20 @ X22 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X26:$o]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X24 ) =
% 2.91/1.42 (
% 2.91/1.42 X20 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 X26 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X24 @ X22 ) =>
% 2.91/1.42 (
% 2.91/1.42 X26 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 X26 ) ) ) ) ) ) =>
% 2.91/1.42 ( (
% 2.91/1.42 ![
% 2.91/1.42 X28:$i,
% 2.91/1.42 X30:$i,
% 2.91/1.42 X32:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X32 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X28 @ X30 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X32 ) =
% 2.91/1.42 (
% 2.91/1.42 X28 ) ) |
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X32 @ X30 ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setoftrueEq ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 powersetI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 emptyinPowerset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 emptyInPowerset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 powersetE ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunionI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunionE ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subPowSU ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exuE2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 nonemptyImpWitness ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X34:$i,
% 2.91/1.42 X36:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X34 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X36 @
% 2.91/1.42 emptyset ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X34 ) =
% 2.91/1.42 (
% 2.91/1.42 X36 ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X38:$i,
% 2.91/1.42 X40:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X38 ) !=
% 2.91/1.42 (
% 2.91/1.42 X40 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 ~(
% 2.91/1.42 in @
% 2.91/1.42 X40 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X38 @
% 2.91/1.42 emptyset ) ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X42:$i,
% 2.91/1.42 X44:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X42 ) =
% 2.91/1.42 (
% 2.91/1.42 X44 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X44 @
% 2.91/1.42 emptyset ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X46:$i,
% 2.91/1.42 X48:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X46 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X48 @
% 2.91/1.42 emptyset ) ) =>
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X48 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X46 @
% 2.91/1.42 emptyset ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X50:$i,
% 2.91/1.42 X52:$i,
% 2.91/1.42 X54:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X54 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X50 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X52 @
% 2.91/1.42 emptyset ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X54 ) =
% 2.91/1.42 (
% 2.91/1.42 X50 ) ) |
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X54 ) =
% 2.91/1.42 (
% 2.91/1.42 X52 ) ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X56:$i,
% 2.91/1.42 X58:$i]:
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X56 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X56 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X58 @
% 2.91/1.42 emptyset ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X60:$i,
% 2.91/1.42 X62:$i]:
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X62 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X60 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X62 @
% 2.91/1.42 emptyset ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 emptyE1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 vacuousDall ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 quantDeMorgan1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 quantDeMorgan2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 quantDeMorgan3 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 quantDeMorgan4 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 prop2setI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 prop2set2propI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 notdexE ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 notdallE ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exuI1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exuI3 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exuI2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 inCongP ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 in__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exuE3u ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exu__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 emptyset__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X64:$i,
% 2.91/1.42 X66:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X64 ) =
% 2.91/1.42 (
% 2.91/1.42 X66 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X68:$i,
% 2.91/1.42 X70:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X68 ) =
% 2.91/1.42 (
% 2.91/1.42 X70 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X64 @ X68 ) =
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X66 @ X70 ) ) ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 powerset__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunion__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 omega__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exuEu ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 descr__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 dsetconstr__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetI1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 eqimpsubset2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 eqimpsubset1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetI2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 emptysetsubset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetE ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetE2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 notsubsetI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 notequalI1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 notequalI2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetRefl ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetTrans ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoinSub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoinSub2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subset2powerset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setextsub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetemptysetimpeq ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 powersetI1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 powersetE1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 inPowerset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 powersetsubset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 sepInPowerset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 sepSubset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binunionIL ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X72:$i,
% 2.91/1.42 X74:$i]:
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X74 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X72 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X74 @
% 2.91/1.42 emptyset ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binunionIR ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binunionEcases ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binunionE ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binunionLsub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binunionRsub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectSubset5 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectEL ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectLsub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectSubset2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectSubset3 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectER ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 disjointsetsI1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectRsub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectSubset4 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectSubset1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 bs114d ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusEL ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusER ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusSubset2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusERneg ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusELneg ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusILneg ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusIRneg ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusLsub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusSubset1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 symdiffE ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 symdiffI1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 symdiffI2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 symdiffIneg1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 symdiffIneg2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X76:$i,
% 2.91/1.42 X78:$i]:
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X78 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X76 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X78 @
% 2.91/1.42 emptyset ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setukpairIL ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setukpairIR ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 kpairiskpair ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 kpairp ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 singletonsubset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 singletoninpowerset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 singletoninpowunion ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X80:$i,
% 2.91/1.42 X82:$i,
% 2.91/1.42 X84:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X84 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X80 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X82 @
% 2.91/1.42 emptyset ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X84 ) =
% 2.91/1.42 (
% 2.91/1.42 X80 ) ) |
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X84 ) =
% 2.91/1.42 (
% 2.91/1.42 X82 ) ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 upairsubunion ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 upairinpowunion ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ubforcartprodlem1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ubforcartprodlem2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ubforcartprodlem3 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 cartprodpairin ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 cartprodmempair1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 cartprodmempair ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunionE2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunionsingleton1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunionsingleton2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunionsingleton ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 singletonprop ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ex1E1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ex1I ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ex1I2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X86:$i,
% 2.91/1.42 X88:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoin
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% 2.91/1.42 X86 @
% 2.91/1.42 emptyset ) =
% 2.91/1.42 (
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% 2.91/1.42 (
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% 2.91/1.42 (
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% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 kfstsingleton ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 theprop ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 kfstpairEq ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 cartprodfstin ) =>
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% 2.91/1.42 (
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% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setukpairinjL ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X104:$i,
% 2.91/1.42 X106:$i]:
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% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoin
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% 2.91/1.42 X104 @
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% 2.91/1.42 setadjoin
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% 2.91/1.42 (
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% 2.91/1.42 X112:$i,
% 2.91/1.42 X114:$i,
% 2.91/1.42 X116:$i,
% 2.91/1.42 X118:$i]:
% 2.91/1.42 (
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% 2.91/1.42 X112 @
% 2.91/1.42 (
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% 2.91/1.42 emptyset ) ) =
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
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% 2.91/1.42 X116 @
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% 2.91/1.42 (
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% 2.91/1.42 (
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% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X120:$i,
% 2.91/1.42 X122:$i,
% 2.91/1.42 X124:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X120 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X122 @
% 2.91/1.42 emptyset ) ) =
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X124 @
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% 2.91/1.42 (
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% 2.91/1.42 (
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% 2.91/1.42 thf(zf_stmt_4, negated_conjecture,
% 2.91/1.42 (~( ( setextAx ) =>
% 2.91/1.42 ( ( emptysetAx ) =>
% 2.91/1.42 ( ( ![X4:$i,X6:$i,X8:$i]:
% 2.91/1.42 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 2.91/1.42 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 2.91/1.42 ( ( powersetAx ) =>
% 2.91/1.42 ( ( setunionAx ) =>
% 2.91/1.42 ( ( omega0Ax ) =>
% 2.91/1.42 ( ( omegaSAx ) =>
% 2.91/1.42 ( ( omegaIndAx ) =>
% 2.91/1.42 ( ( replAx ) =>
% 2.91/1.42 ( ( foundationAx ) =>
% 2.91/1.42 ( ( wellorderingAx ) =>
% 2.91/1.42 ( ( descrp ) =>
% 2.91/1.42 ( ( dsetconstrI ) =>
% 2.91/1.42 ( ( dsetconstrEL ) =>
% 2.91/1.42 ( ( dsetconstrER ) =>
% 2.91/1.42 ( ( exuE1 ) =>
% 2.91/1.42 ( ( prop2setE ) =>
% 2.91/1.42 ( ( emptysetE ) =>
% 2.91/1.42 ( ( emptysetimpfalse ) =>
% 2.91/1.42 ( ( notinemptyset ) =>
% 2.91/1.42 ( ( exuE3e ) =>
% 2.91/1.42 ( ( setext ) =>
% 2.91/1.42 ( ( emptyI ) =>
% 2.91/1.42 ( ( noeltsimpempty ) =>
% 2.91/1.42 ( ( setbeta ) =>
% 2.91/1.42 ( ( nonemptyE1 ) =>
% 2.91/1.42 ( ( nonemptyI ) =>
% 2.91/1.42 ( ( nonemptyI1 ) =>
% 2.91/1.42 ( ( ![X10:$i,
% 2.91/1.42 X12:$i]:
% 2.91/1.42 ( in @
% 2.91/1.42 X10 @
% 2.91/1.42 ( setadjoin
% 2.91/1.42 @
% 2.91/1.42 X10 @ X12 ) ) ) =>
% 2.91/1.42 ( ( in @
% 2.91/1.42 emptyset @
% 2.91/1.42 ( setadjoin
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% 2.91/1.42 emptyset @
% 2.91/1.42 emptyset ) ) =>
% 2.91/1.42 ( ( ![
% 2.91/1.42 X14:$i,
% 2.91/1.42 X16:$i,
% 2.91/1.42 X18:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X18 @ X16 ) =>
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X18 @
% 2.91/1.42 (
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% 2.91/1.42 ( (
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% 2.91/1.42 X20:$i,
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% 2.91/1.42 X24 @
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% 2.91/1.42 X26:$o]:
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% 2.91/1.42 (
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% 2.91/1.42 (
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% 2.91/1.42 (
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% 2.91/1.42 X28:$i,
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% 2.91/1.42 (
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% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setoftrueEq ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 powersetI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 emptyinPowerset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 emptyInPowerset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
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% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunionI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunionE ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subPowSU ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exuE2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
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% 2.91/1.42 (
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% 2.91/1.42 (
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% 2.91/1.42 (
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% 2.91/1.42 (
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% 2.91/1.42 (
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% 2.91/1.42 X60:$i,
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% 2.91/1.42 (
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% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 vacuousDall ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 quantDeMorgan1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 quantDeMorgan2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 quantDeMorgan3 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 quantDeMorgan4 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 prop2setI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 prop2set2propI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 notdexE ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 notdallE ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exuI1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exuI3 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exuI2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 inCongP ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 in__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exuE3u ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exu__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 emptyset__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X64:$i,
% 2.91/1.42 X66:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X64 ) =
% 2.91/1.42 (
% 2.91/1.42 X66 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X68:$i,
% 2.91/1.42 X70:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X68 ) =
% 2.91/1.42 (
% 2.91/1.42 X70 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X64 @ X68 ) =
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X66 @ X70 ) ) ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 powerset__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunion__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 omega__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 exuEu ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 descr__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 dsetconstr__Cong ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetI1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 eqimpsubset2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 eqimpsubset1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetI2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 emptysetsubset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetE ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetE2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 notsubsetI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 notequalI1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 notequalI2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetRefl ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetTrans ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoinSub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoinSub2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subset2powerset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setextsub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 subsetemptysetimpeq ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 powersetI1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 powersetE1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 inPowerset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 powersetsubset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 sepInPowerset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 sepSubset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binunionIL ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X72:$i,
% 2.91/1.42 X74:$i]:
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X74 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X72 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X74 @
% 2.91/1.42 emptyset ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binunionIR ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binunionEcases ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binunionE ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binunionLsub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binunionRsub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectSubset5 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectEL ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectLsub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectSubset2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectSubset3 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectER ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 disjointsetsI1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectRsub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectSubset4 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 binintersectSubset1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 bs114d ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusI ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusEL ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusER ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusSubset2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusERneg ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusELneg ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusILneg ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusIRneg ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusLsub ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setminusSubset1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 symdiffE ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 symdiffI1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 symdiffI2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 symdiffIneg1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 symdiffIneg2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X76:$i,
% 2.91/1.42 X78:$i]:
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X78 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X76 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X78 @
% 2.91/1.42 emptyset ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setukpairIL ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setukpairIR ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 kpairiskpair ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 kpairp ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 singletonsubset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 singletoninpowerset ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 singletoninpowunion ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X80:$i,
% 2.91/1.42 X82:$i,
% 2.91/1.42 X84:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 X84 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X80 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X82 @
% 2.91/1.42 emptyset ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X84 ) =
% 2.91/1.42 (
% 2.91/1.42 X80 ) ) |
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X84 ) =
% 2.91/1.42 (
% 2.91/1.42 X82 ) ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 upairsubunion ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 upairinpowunion ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ubforcartprodlem1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ubforcartprodlem2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ubforcartprodlem3 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 cartprodpairin ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 cartprodmempair1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 cartprodmempair ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunionE2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunionsingleton1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunionsingleton2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setunionsingleton ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 singletonprop ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ex1E1 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ex1I ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ex1I2 ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X86:$i,
% 2.91/1.42 X88:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X86 @
% 2.91/1.42 emptyset ) =
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X88 @
% 2.91/1.42 emptyset ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X86 ) =
% 2.91/1.42 (
% 2.91/1.42 X88 ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X90:$i,
% 2.91/1.42 X92:$i,
% 2.91/1.42 X94:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 in @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X94 @
% 2.91/1.42 emptyset ) @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X90 @
% 2.91/1.42 emptyset ) @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X90 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X92 @
% 2.91/1.42 emptyset ) ) @
% 2.91/1.42 emptyset ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X90 ) =
% 2.91/1.42 (
% 2.91/1.42 X94 ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 kfstsingleton ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 theprop ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 kfstpairEq ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 cartprodfstin ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X96:$i,
% 2.91/1.42 X98:$i,
% 2.91/1.42 X100:$i,
% 2.91/1.42 X102:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X96 @
% 2.91/1.42 emptyset ) @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X96 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X98 @
% 2.91/1.42 emptyset ) ) @
% 2.91/1.42 emptyset ) ) =
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X100 @
% 2.91/1.42 emptyset ) @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X100 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X102 @
% 2.91/1.42 emptyset ) ) @
% 2.91/1.42 emptyset ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X96 ) =
% 2.91/1.42 (
% 2.91/1.42 X100 ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setukpairinjL ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X104:$i,
% 2.91/1.42 X106:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X104 ) =
% 2.91/1.42 (
% 2.91/1.42 X106 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X104 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X106 @
% 2.91/1.42 emptyset ) ) =
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X104 @
% 2.91/1.42 emptyset ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X108:$i,
% 2.91/1.42 X110:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X108 ) =
% 2.91/1.42 (
% 2.91/1.42 X110 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X108 @
% 2.91/1.42 emptyset ) @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X108 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X110 @
% 2.91/1.42 emptyset ) ) @
% 2.91/1.42 emptyset ) ) =
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X108 @
% 2.91/1.42 emptyset ) @
% 2.91/1.42 emptyset ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X112:$i,
% 2.91/1.42 X114:$i,
% 2.91/1.42 X116:$i,
% 2.91/1.42 X118:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X112 @
% 2.91/1.42 emptyset ) @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X112 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X114 @
% 2.91/1.42 emptyset ) ) @
% 2.91/1.42 emptyset ) ) =
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X116 @
% 2.91/1.42 emptyset ) @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X116 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X118 @
% 2.91/1.42 emptyset ) ) @
% 2.91/1.42 emptyset ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X116 ) =
% 2.91/1.42 (
% 2.91/1.42 X118 ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X114 ) =
% 2.91/1.42 (
% 2.91/1.42 X118 ) ) ) ) ) =>
% 2.91/1.42 (
% 2.91/1.42 ![
% 2.91/1.42 X120:$i,
% 2.91/1.42 X122:$i,
% 2.91/1.42 X124:$i]:
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X120 @
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X122 @
% 2.91/1.42 emptyset ) ) =
% 2.91/1.42 (
% 2.91/1.42 setadjoin
% 2.91/1.42 @
% 2.91/1.42 X124 @
% 2.91/1.42 emptyset ) ) =>
% 2.91/1.42 (
% 2.91/1.42 (
% 2.91/1.42 X120 ) =
% 2.91/1.42 (
% 2.91/1.42 X122 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 2.91/1.42 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 2.91/1.42 thf(zip_derived_cl26, plain,
% 2.91/1.42 (![X12 : $i, X13 : $i]:
% 2.91/1.42 (~ (in @ X12 @ (setadjoin @ X13 @ emptyset)) | ((X13) = (X12)))),
% 2.91/1.42 inference('cnf', [status(esa)], [zf_stmt_4])).
% 2.91/1.42 thf(zip_derived_cl89, plain,
% 2.91/1.42 (((setadjoin @ sk__58 @ (setadjoin @ sk__59 @ emptyset))
% 2.91/1.42 = (setadjoin @ sk__60 @ emptyset))),
% 2.91/1.42 inference('cnf', [status(esa)], [zf_stmt_4])).
% 2.91/1.42 thf(zip_derived_cl89, plain,
% 2.91/1.42 (((setadjoin @ sk__58 @ (setadjoin @ sk__59 @ emptyset))
% 2.91/1.42 = (setadjoin @ sk__60 @ emptyset))),
% 2.91/1.42 inference('cnf', [status(esa)], [zf_stmt_4])).
% 2.91/1.42 thf(zip_derived_cl18, plain,
% 2.91/1.42 (![X4 : $i, X5 : $i]: (in @ X4 @ (setadjoin @ X4 @ X5))),
% 2.91/1.42 inference('cnf', [status(esa)], [zf_stmt_4])).
% 2.91/1.42 thf(zip_derived_cl311, plain,
% 2.91/1.42 ( (in @ sk__58 @ (setadjoin @ sk__60 @ emptyset))),
% 2.91/1.42 inference('sup+', [status(thm)], [zip_derived_cl89, zip_derived_cl18])).
% 2.91/1.42 thf(zip_derived_cl26, plain,
% 2.91/1.42 (![X12 : $i, X13 : $i]:
% 2.91/1.42 (~ (in @ X12 @ (setadjoin @ X13 @ emptyset)) | ((X13) = (X12)))),
% 2.91/1.42 inference('cnf', [status(esa)], [zf_stmt_4])).
% 2.91/1.42 thf(zip_derived_cl338, plain, (((sk__60) = (sk__58))),
% 2.91/1.42 inference('sup-', [status(thm)], [zip_derived_cl311, zip_derived_cl26])).
% 2.91/1.42 thf(zip_derived_cl358, plain,
% 2.91/1.42 (((setadjoin @ sk__58 @ (setadjoin @ sk__59 @ emptyset))
% 2.91/1.42 = (setadjoin @ sk__58 @ emptyset))),
% 2.91/1.42 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl338])).
% 2.91/1.42 thf(zip_derived_cl70, plain,
% 2.91/1.42 (![X22 : $i, X23 : $i]:
% 2.91/1.42 (in @ X22 @ (setadjoin @ X23 @ (setadjoin @ X22 @ emptyset)))),
% 2.91/1.42 inference('cnf', [status(esa)], [zf_stmt_4])).
% 2.91/1.42 thf(zip_derived_cl417, plain,
% 2.91/1.42 ( (in @ sk__59 @ (setadjoin @ sk__58 @ emptyset))),
% 2.91/1.42 inference('sup+', [status(thm)], [zip_derived_cl358, zip_derived_cl70])).
% 2.91/1.42 thf(zip_derived_cl441, plain, (((sk__58) = (sk__59))),
% 2.91/1.42 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl417])).
% 2.91/1.42 thf(zip_derived_cl88, plain, (((sk__58) != (sk__59))),
% 2.91/1.42 inference('cnf', [status(esa)], [zf_stmt_4])).
% 2.91/1.42 thf(zip_derived_cl449, plain, ($false),
% 2.91/1.42 inference('simplify_reflect-', [status(thm)],
% 2.91/1.42 [zip_derived_cl441, zip_derived_cl88])).
% 2.91/1.42
% 2.91/1.42 % SZS output end Refutation
% 2.91/1.42
% 2.91/1.42
% 2.91/1.42 % Terminating...
% 3.09/1.57 % Runner terminated.
% 3.09/1.57 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------