0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fDCgsuutcO true 0.14/0.35 % Computer : n020.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1200 0.14/0.35 % WCLimit : 120 0.14/0.35 % DateTime : Tue Jul 13 15:18:36 EDT 2021 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 120 s 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.54/0.67 % Total configuration time : 828 0.54/0.67 % Estimated wc time : 983 0.54/0.67 % Estimated cpu time (8 cpus) : 122.875 0.54/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.55/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.55/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.55/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 4.33/1.15 % Solved by lams/40_c_ic.sh. 4.33/1.15 % done 277 iterations in 0.320s 4.33/1.15 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 4.33/1.15 % SZS output start Refutation 4.33/1.15 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 4.33/1.15 thf(binintersectER_type, type, binintersectER: $o). 4.33/1.15 thf(setadjoinSub_type, type, setadjoinSub: $o). 4.33/1.15 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 4.33/1.15 thf(vacuousDall_type, type, vacuousDall: $o). 4.33/1.15 thf(setadjoinIR_type, type, setadjoinIR: $o). 4.33/1.15 thf(omega0Ax_type, type, omega0Ax: $o). 4.33/1.15 thf(subsetE_type, type, subsetE: $o). 4.33/1.15 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 4.33/1.15 thf(setminusER_type, type, setminusER: $o). 4.33/1.15 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 4.33/1.15 thf(singletonsuniq_type, type, singletonsuniq: $o). 4.33/1.15 thf(binunionE_type, type, binunionE: $o). 4.33/1.15 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 4.33/1.15 thf(powersetE_type, type, powersetE: $o). 4.33/1.15 thf(binunionRsub_type, type, binunionRsub: $o). 4.33/1.15 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 4.33/1.15 thf(powerset__Cong_type, type, powerset__Cong: $o). 4.33/1.15 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 4.33/1.15 thf(upairequniteq_type, type, upairequniteq: $o). 4.33/1.15 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o). 4.33/1.15 thf(omegaIndAx_type, type, omegaIndAx: $o). 4.33/1.15 thf(uniqinunit_type, type, uniqinunit: $o). 4.33/1.15 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 4.33/1.15 thf(exu__Cong_type, type, exu__Cong: $o). 4.33/1.15 thf(subset2powerset_type, type, subset2powerset: $o). 4.33/1.15 thf(setoftrueEq_type, type, setoftrueEq: $o). 4.33/1.15 thf(singletonprop_type, type, singletonprop: $o). 4.33/1.15 thf(upairsetIL_type, type, upairsetIL: $o). 4.33/1.15 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 4.33/1.15 thf(emptyI_type, type, emptyI: $o). 4.33/1.15 thf(secondinupair_type, type, secondinupair: $o). 4.33/1.15 thf(exuI3_type, type, exuI3: $o). 4.33/1.15 thf(emptysetAx_type, type, emptysetAx: $o). 4.33/1.15 thf(setukpairIL_type, type, setukpairIL: $o). 4.33/1.15 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 4.33/1.15 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 4.33/1.15 thf(setadjoinIL_type, type, setadjoinIL: $o). 4.33/1.15 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 4.33/1.15 thf(upairsetIR_type, type, upairsetIR: $o). 4.33/1.15 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 4.33/1.15 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 4.33/1.15 thf(ex1E1_type, type, ex1E1: $o). 4.33/1.15 thf(setminusI_type, type, setminusI: $o). 4.33/1.15 thf(descrp_type, type, descrp: $o). 4.33/1.15 thf(binintersectI_type, type, binintersectI: $o). 4.33/1.15 thf(nonemptyI1_type, type, nonemptyI1: $o). 4.33/1.15 thf(emptysetsubset_type, type, emptysetsubset: $o). 4.33/1.15 thf(setunionAx_type, type, setunionAx: $o). 4.33/1.15 thf(notsubsetI_type, type, notsubsetI: $o). 4.33/1.15 thf(ex1I2_type, type, ex1I2: $o). 4.33/1.15 thf(theprop_type, type, theprop: $o). 4.33/1.15 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 4.33/1.15 thf(upairset2IR_type, type, upairset2IR: $o). 4.33/1.15 thf(binunionLsub_type, type, binunionLsub: $o). 4.33/1.15 thf(subsetRefl_type, type, subsetRefl: $o). 4.33/1.15 thf(nonemptyI_type, type, nonemptyI: $o). 4.33/1.15 thf(emptysetE_type, type, emptysetE: $o). 4.33/1.15 thf(sepInPowerset_type, type, sepInPowerset: $o). 4.33/1.15 thf(singletonsubset_type, type, singletonsubset: $o). 4.33/1.15 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 4.33/1.15 thf(setukpairinjR1_type, type, setukpairinjR1: $o). 4.33/1.15 thf(sk__62_type, type, sk__62: $i). 4.33/1.15 thf(cartprodpairin_type, type, cartprodpairin: $o). 4.33/1.15 thf(setunionsingleton_type, type, setunionsingleton: $o). 4.33/1.15 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 4.33/1.15 thf(powersetI_type, type, powersetI: $o). 4.33/1.15 thf(exuE2_type, type, exuE2: $o). 4.33/1.15 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 4.33/1.15 thf(cartprodmempair_type, type, cartprodmempair: $o). 4.33/1.15 thf(exuE3e_type, type, exuE3e: $o). 4.33/1.15 thf(setminusSubset1_type, type, setminusSubset1: $o). 4.33/1.15 thf(notequalI2_type, type, notequalI2: $o). 4.33/1.15 thf(descr__Cong_type, type, descr__Cong: $o). 4.33/1.15 thf(setextAx_type, type, setextAx: $o). 4.33/1.15 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 4.33/1.15 thf(eqinunit_type, type, eqinunit: $o). 4.33/1.15 thf(symdiffE_type, type, symdiffE: $o). 4.33/1.15 thf(upairsubunion_type, type, upairsubunion: $o). 4.33/1.15 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 4.33/1.15 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 4.33/1.15 thf(powersetAx_type, type, powersetAx: $o). 4.33/1.15 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 4.33/1.15 thf(subsetI2_type, type, subsetI2: $o). 4.33/1.15 thf(symdiffI1_type, type, symdiffI1: $o). 4.33/1.15 thf(kpairiskpair_type, type, kpairiskpair: $o). 4.33/1.15 thf(setukpairinjL_type, type, setukpairinjL: $o). 4.33/1.15 thf(subsetI1_type, type, subsetI1: $o). 4.33/1.15 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 4.33/1.15 thf(replAx_type, type, replAx: $o). 4.33/1.15 thf(subPowSU_type, type, subPowSU: $o). 4.33/1.15 thf(setunionE_type, type, setunionE: $o). 4.33/1.15 thf(kfstsingleton_type, type, kfstsingleton: $o). 4.33/1.15 thf(setunion__Cong_type, type, setunion__Cong: $o). 4.33/1.15 thf(bs114d_type, type, bs114d: $o). 4.33/1.15 thf(setminusSubset2_type, type, setminusSubset2: $o). 4.33/1.15 thf(powersetE1_type, type, powersetE1: $o). 4.33/1.15 thf(cartprodfstin_type, type, cartprodfstin: $o). 4.33/1.15 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 4.33/1.15 thf(omegaSAx_type, type, omegaSAx: $o). 4.33/1.15 thf(upairset2E_type, type, upairset2E: $o). 4.33/1.15 thf(setext_type, type, setext: $o). 4.33/1.15 thf(notequalI1_type, type, notequalI1: $o). 4.33/1.15 thf(setextsub_type, type, setextsub: $o). 4.33/1.15 thf(kfstpairEq_type, type, kfstpairEq: $o). 4.33/1.15 thf(sk__61_type, type, sk__61: $i). 4.33/1.15 thf(omega__Cong_type, type, omega__Cong: $o). 4.33/1.15 thf(ex1I_type, type, ex1I: $o). 4.33/1.15 thf(symdiffI2_type, type, symdiffI2: $o). 4.33/1.15 thf(setbeta_type, type, setbeta: $o). 4.33/1.15 thf(dsetconstrER_type, type, dsetconstrER: $o). 4.33/1.15 thf(nonemptyE1_type, type, nonemptyE1: $o). 4.33/1.15 thf(binunionIL_type, type, binunionIL: $o). 4.33/1.15 thf(sk__64_type, type, sk__64: $i). 4.33/1.15 thf(prop2setE_type, type, prop2setE: $o). 4.33/1.15 thf(prop2set2propI_type, type, prop2set2propI: $o). 4.33/1.15 thf(notdallE_type, type, notdallE: $o). 4.33/1.15 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 4.33/1.15 thf(exuEu_type, type, exuEu: $o). 4.33/1.15 thf(notinsingleton_type, type, notinsingleton: $o). 4.33/1.15 thf(upairsetE_type, type, upairsetE: $o). 4.33/1.15 thf(emptyE1_type, type, emptyE1: $o). 4.33/1.15 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 4.33/1.15 thf(binunionEcases_type, type, binunionEcases: $o). 4.33/1.15 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 4.33/1.15 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 4.33/1.15 thf(wellorderingAx_type, type, wellorderingAx: $o). 4.33/1.15 thf(binintersectLsub_type, type, binintersectLsub: $o). 4.33/1.15 thf(binintersectRsub_type, type, binintersectRsub: $o). 4.33/1.15 thf(powersetsubset_type, type, powersetsubset: $o). 4.33/1.15 thf(emptyset_type, type, emptyset: $i). 4.33/1.15 thf(upairinpowunion_type, type, upairinpowunion: $o). 4.33/1.15 thf(kpairp_type, type, kpairp: $o). 4.33/1.15 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 4.33/1.15 thf(exuE1_type, type, exuE1: $o). 4.33/1.15 thf(inPowerset_type, type, inPowerset: $o). 4.33/1.15 thf(in_type, type, in: $i > $i > $o). 4.33/1.15 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 4.33/1.15 thf(setunionI_type, type, setunionI: $o). 4.33/1.15 thf(in__Cong_type, type, in__Cong: $o). 4.33/1.15 thf(setadjoinE_type, type, setadjoinE: $o). 4.33/1.15 thf(subsetTrans_type, type, subsetTrans: $o). 4.33/1.15 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 4.33/1.15 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 4.33/1.15 thf(setminusIRneg_type, type, setminusIRneg: $o). 4.33/1.15 thf(setminusELneg_type, type, setminusELneg: $o). 4.33/1.15 thf(foundationAx_type, type, foundationAx: $o). 4.33/1.15 thf(sepSubset_type, type, sepSubset: $o). 4.33/1.15 thf(exuE3u_type, type, exuE3u: $o). 4.33/1.15 thf(setukpairIR_type, type, setukpairIR: $o). 4.33/1.15 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 4.33/1.15 thf(setadjoinOr_type, type, setadjoinOr: $o). 4.33/1.15 thf(exuI1_type, type, exuI1: $o). 4.33/1.15 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 4.33/1.15 thf(binunionIR_type, type, binunionIR: $o). 4.33/1.15 thf(inCongP_type, type, inCongP: $o). 4.33/1.15 thf(setminusLsub_type, type, setminusLsub: $o). 4.33/1.15 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 4.33/1.15 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 4.33/1.15 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 4.33/1.15 thf(sk__63_type, type, sk__63: $i). 4.33/1.15 thf(setminusERneg_type, type, setminusERneg: $o). 4.33/1.15 thf(exuI2_type, type, exuI2: $o). 4.33/1.15 thf(powersetI1_type, type, powersetI1: $o). 4.33/1.15 thf(setunionE2_type, type, setunionE2: $o). 4.33/1.15 thf(setminusILneg_type, type, setminusILneg: $o). 4.33/1.15 thf(dsetconstrI_type, type, dsetconstrI: $o). 4.33/1.15 thf(setminusEL_type, type, setminusEL: $o). 4.33/1.15 thf(subsetE2_type, type, subsetE2: $o). 4.33/1.15 thf(singletonsswitch_type, type, singletonsswitch: $o). 4.33/1.15 thf(binintersectEL_type, type, binintersectEL: $o). 4.33/1.15 thf(setadjoinAx_type, type, setadjoinAx: $o). 4.33/1.15 thf(setukpairinjR12_type, type, setukpairinjR12: $o). 4.33/1.15 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 4.33/1.15 thf(notinemptyset_type, type, notinemptyset: $o). 4.33/1.15 thf(prop2setI_type, type, prop2setI: $o). 4.33/1.15 thf(notdexE_type, type, notdexE: $o). 4.33/1.15 thf(upairequniteq, axiom, upairequniteq = 4.33/1.15 (![Xx:$i,Xy:$i,Xz:$i]: 4.33/1.15 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) = 4.33/1.15 ( setadjoin @ Xz @ emptyset ) ) => 4.33/1.15 ( ( Xx ) = ( Xy ) ) ))). 4.33/1.15 thf('0', plain, 4.33/1.15 (( upairequniteq ) = 4.33/1.15 ( ![X4:$i,X6:$i,X8:$i]: 4.33/1.15 ( ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) = 4.33/1.15 ( setadjoin @ X8 @ emptyset ) ) => 4.33/1.15 ( ( X4 ) = ( X6 ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(setukpairinjR1, axiom, setukpairinjR1 = 4.33/1.15 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]: 4.33/1.15 ( ( ( setadjoin @ 4.33/1.15 ( setadjoin @ Xx @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) = 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ Xz @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) => 4.33/1.15 ( ( ( Xz ) = ( Xu ) ) => ( ( Xy ) = ( Xu ) ) ) ))). 4.33/1.15 thf('1', plain, 4.33/1.15 (( setukpairinjR1 ) = 4.33/1.15 ( ![X4:$i,X6:$i,X8:$i,X10:$i]: 4.33/1.15 ( ( ( setadjoin @ 4.33/1.15 ( setadjoin @ X4 @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) = 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ X8 @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) => 4.33/1.15 ( ( ( X8 ) = ( X10 ) ) => ( ( X6 ) = ( X10 ) ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(setukpairinjR12, axiom, setukpairinjR12 = 4.33/1.15 (![Xx:$i,Xy:$i]: 4.33/1.15 ( ( ( Xx ) = ( Xy ) ) => 4.33/1.15 ( ( setadjoin @ 4.33/1.15 ( setadjoin @ Xx @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) = 4.33/1.15 ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ))). 4.33/1.15 thf('2', plain, 4.33/1.15 (( setukpairinjR12 ) = 4.33/1.15 ( ![X4:$i,X6:$i]: 4.33/1.15 ( ( ( X4 ) = ( X6 ) ) => 4.33/1.15 ( ( setadjoin @ 4.33/1.15 ( setadjoin @ X4 @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) = 4.33/1.15 ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ emptyset ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(setukpairinjR11, axiom, setukpairinjR11 = 4.33/1.15 (![Xx:$i,Xy:$i]: 4.33/1.15 ( ( ( Xx ) = ( Xy ) ) => 4.33/1.15 ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) = 4.33/1.15 ( setadjoin @ Xx @ emptyset ) ) ))). 4.33/1.15 thf('3', plain, 4.33/1.15 (( setukpairinjR11 ) = 4.33/1.15 ( ![X4:$i,X6:$i]: 4.33/1.15 ( ( ( X4 ) = ( X6 ) ) => 4.33/1.15 ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) = 4.33/1.15 ( setadjoin @ X4 @ emptyset ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(setukpairinjL2, axiom, setukpairinjL2 = 4.33/1.15 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]: 4.33/1.15 ( ( ( setadjoin @ 4.33/1.15 ( setadjoin @ Xx @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) = 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ Xz @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) => 4.33/1.15 ( ( Xx ) = ( Xz ) ) ))). 4.33/1.15 thf('4', plain, 4.33/1.15 (( setukpairinjL2 ) = 4.33/1.15 ( ![X4:$i,X6:$i,X8:$i,X10:$i]: 4.33/1.15 ( ( ( setadjoin @ 4.33/1.15 ( setadjoin @ X4 @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) = 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ X8 @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) => 4.33/1.15 ( ( X4 ) = ( X8 ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(setukpairinjL1, axiom, setukpairinjL1 = 4.33/1.15 (![Xx:$i,Xy:$i,Xz:$i]: 4.33/1.15 ( ( in @ 4.33/1.15 ( setadjoin @ Xz @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ Xx @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) => 4.33/1.15 ( ( Xx ) = ( Xz ) ) ))). 4.33/1.15 thf('5', plain, 4.33/1.15 (( setukpairinjL1 ) = 4.33/1.15 ( ![X4:$i,X6:$i,X8:$i]: 4.33/1.15 ( ( in @ 4.33/1.15 ( setadjoin @ X8 @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ X4 @ emptyset ) @ 4.33/1.15 ( setadjoin @ 4.33/1.15 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) => 4.33/1.15 ( ( X4 ) = ( X8 ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(singletonsuniq, axiom, singletonsuniq = 4.33/1.15 (![Xx:$i,Xy:$i]: 4.33/1.15 ( ( ( setadjoin @ Xx @ emptyset ) = ( setadjoin @ Xy @ emptyset ) ) => 4.33/1.15 ( ( Xx ) = ( Xy ) ) ))). 4.33/1.15 thf('6', plain, 4.33/1.15 (( singletonsuniq ) = 4.33/1.15 ( ![X4:$i,X6:$i]: 4.33/1.15 ( ( ( setadjoin @ X4 @ emptyset ) = ( setadjoin @ X6 @ emptyset ) ) => 4.33/1.15 ( ( X4 ) = ( X6 ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(upairset2E, axiom, upairset2E = 4.33/1.15 (![Xx:$i,Xy:$i,Xz:$i]: 4.33/1.15 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) => 4.33/1.15 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))). 4.33/1.15 thf('7', plain, 4.33/1.15 (( upairset2E ) = 4.33/1.15 ( ![X4:$i,X6:$i,X8:$i]: 4.33/1.15 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) => 4.33/1.15 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(secondinupair, axiom, secondinupair = 4.33/1.15 (![Xx:$i,Xy:$i]: 4.33/1.15 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 4.33/1.15 thf('8', plain, 4.33/1.15 (( secondinupair ) = 4.33/1.15 ( ![X4:$i,X6:$i]: 4.33/1.15 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(upairset2IR, axiom, upairset2IR = 4.33/1.15 (![Xx:$i,Xy:$i]: 4.33/1.15 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 4.33/1.15 thf('9', plain, 4.33/1.15 (( upairset2IR ) = 4.33/1.15 ( ![X4:$i,X6:$i]: 4.33/1.15 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(setadjoin__Cong, axiom, setadjoin__Cong = 4.33/1.15 (![Xx:$i,Xy:$i]: 4.33/1.15 ( ( ( Xx ) = ( Xy ) ) => 4.33/1.15 ( ![Xz:$i,Xu:$i]: 4.33/1.15 ( ( ( Xz ) = ( Xu ) ) => 4.33/1.15 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))). 4.33/1.15 thf('10', plain, 4.33/1.15 (( setadjoin__Cong ) = 4.33/1.15 ( ![X4:$i,X6:$i]: 4.33/1.15 ( ( ( X4 ) = ( X6 ) ) => 4.33/1.15 ( ![X8:$i,X10:$i]: 4.33/1.15 ( ( ( X8 ) = ( X10 ) ) => 4.33/1.15 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(upairsetIR, axiom, upairsetIR = 4.33/1.15 (![Xx:$i,Xy:$i]: 4.33/1.15 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 4.33/1.15 thf('11', plain, 4.33/1.15 (( upairsetIR ) = 4.33/1.15 ( ![X4:$i,X6:$i]: 4.33/1.15 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(upairsetIL, axiom, upairsetIL = 4.33/1.15 (![Xx:$i,Xy:$i]: 4.33/1.15 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 4.33/1.15 thf('12', plain, 4.33/1.15 (( upairsetIL ) = 4.33/1.15 ( ![X4:$i,X6:$i]: 4.33/1.15 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(upairsetE, axiom, upairsetE = 4.33/1.15 (![Xx:$i,Xy:$i,Xz:$i]: 4.33/1.15 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) => 4.33/1.15 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))). 4.33/1.15 thf('13', plain, 4.33/1.15 (( upairsetE ) = 4.33/1.15 ( ![X4:$i,X6:$i,X8:$i]: 4.33/1.15 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) => 4.33/1.15 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(singletonsswitch, axiom, singletonsswitch = 4.33/1.15 (![Xx:$i,Xy:$i]: 4.33/1.15 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => 4.33/1.15 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))). 4.33/1.15 thf('14', plain, 4.33/1.15 (( singletonsswitch ) = 4.33/1.15 ( ![X4:$i,X6:$i]: 4.33/1.15 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => 4.33/1.15 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(eqinunit, axiom, eqinunit = 4.33/1.15 (![Xx:$i,Xy:$i]: 4.33/1.15 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 4.33/1.15 thf('15', plain, 4.33/1.15 (( eqinunit ) = 4.33/1.15 ( ![X4:$i,X6:$i]: 4.33/1.15 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(notinsingleton, axiom, notinsingleton = 4.33/1.15 (![Xx:$i,Xy:$i]: 4.33/1.15 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))). 4.33/1.15 thf('16', plain, 4.33/1.15 (( notinsingleton ) = 4.33/1.15 ( ![X4:$i,X6:$i]: 4.33/1.15 ( ( ( X4 ) != ( X6 ) ) => 4.33/1.15 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(uniqinunit, axiom, uniqinunit = 4.33/1.15 (![Xx:$i,Xy:$i]: 4.33/1.15 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))). 4.33/1.15 thf('17', plain, 4.33/1.15 (( uniqinunit ) = 4.33/1.15 ( ![X4:$i,X6:$i]: 4.33/1.15 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(setadjoinOr, axiom, setadjoinOr = 4.33/1.15 (![Xx:$i,A:$i,Xy:$i]: 4.33/1.15 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) => 4.33/1.15 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))). 4.33/1.15 thf('18', plain, 4.33/1.15 (( setadjoinOr ) = 4.33/1.15 ( ![X4:$i,X6:$i,X8:$i]: 4.33/1.15 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) => 4.33/1.15 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(setadjoinE, axiom, setadjoinE = 4.33/1.15 (![Xx:$i,A:$i,Xy:$i]: 4.33/1.15 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) => 4.33/1.15 ( ![Xphi:$o]: 4.33/1.15 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) => 4.33/1.15 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))). 4.33/1.15 thf('19', plain, 4.33/1.15 (( setadjoinE ) = 4.33/1.15 ( ![X4:$i,X6:$i,X8:$i]: 4.33/1.15 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) => 4.33/1.15 ( ![X10:$o]: 4.33/1.15 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) => 4.33/1.15 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(setadjoinIR, axiom, setadjoinIR = 4.33/1.15 (![Xx:$i,A:$i,Xy:$i]: 4.33/1.15 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))). 4.33/1.15 thf('20', plain, 4.33/1.15 (( setadjoinIR ) = 4.33/1.15 ( ![X4:$i,X6:$i,X8:$i]: 4.33/1.15 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(emptyinunitempty, axiom,(( emptyinunitempty ) = 4.33/1.15 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))). 4.33/1.15 thf('21', plain, 4.33/1.15 (( emptyinunitempty ) = 4.33/1.15 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )), 4.33/1.15 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])). 4.33/1.15 thf('22', plain, 4.33/1.15 (( emptyinunitempty ) = 4.33/1.15 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(setadjoinIL, axiom, setadjoinIL = 4.33/1.15 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))). 4.33/1.15 thf('23', plain, 4.33/1.15 (( setadjoinIL ) = 4.33/1.15 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(setadjoinAx, axiom, setadjoinAx = 4.33/1.15 (![Xx:$i,A:$i,Xy:$i]: 4.33/1.15 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=> 4.33/1.15 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))). 4.33/1.15 thf('24', plain, 4.33/1.15 (( setadjoinAx ) = 4.33/1.15 ( ![X4:$i,X6:$i,X8:$i]: 4.33/1.15 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 4.33/1.15 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )), 4.33/1.15 define([status(thm)])). 4.33/1.15 thf(setukpairinjR2, conjecture, 4.33/1.15 (( setextAx ) => 4.33/1.15 ( ( emptysetAx ) => 4.33/1.15 ( ( setadjoinAx ) => 4.33/1.15 ( ( powersetAx ) => 4.33/1.15 ( ( setunionAx ) => 4.33/1.15 ( ( omega0Ax ) => 4.33/1.15 ( ( omegaSAx ) => 4.33/1.15 ( ( omegaIndAx ) => 4.33/1.15 ( ( replAx ) => 4.33/1.15 ( ( foundationAx ) => 4.33/1.15 ( ( wellorderingAx ) => 4.33/1.15 ( ( descrp ) => 4.33/1.15 ( ( dsetconstrI ) => 4.33/1.15 ( ( dsetconstrEL ) => 4.33/1.15 ( ( dsetconstrER ) => 4.33/1.15 ( ( exuE1 ) => 4.33/1.15 ( ( prop2setE ) => 4.33/1.15 ( ( emptysetE ) => 4.33/1.15 ( ( emptysetimpfalse ) => 4.33/1.15 ( ( notinemptyset ) => 4.33/1.15 ( ( exuE3e ) => 4.33/1.15 ( ( setext ) => 4.33/1.15 ( ( emptyI ) => 4.33/1.15 ( ( noeltsimpempty ) => 4.33/1.15 ( ( setbeta ) => 4.33/1.15 ( ( nonemptyE1 ) => 4.33/1.15 ( ( nonemptyI ) => 4.33/1.15 ( ( nonemptyI1 ) => 4.33/1.15 ( ( setadjoinIL ) => 4.33/1.15 ( ( emptyinunitempty ) => 4.33/1.15 ( ( setadjoinIR ) => 4.33/1.15 ( ( setadjoinE ) => 4.33/1.15 ( ( 4.33/1.15 setadjoinOr ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setoftrueEq ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyinPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyInPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subPowSU ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuE2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 nonemptyImpWitness ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 uniqinunit ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notinsingleton ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 eqinunit ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletonsswitch ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairsetE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairsetIL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairsetIR ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyE1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 vacuousDall ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan4 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 prop2setI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 prop2set2propI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notdexE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notdallE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuI3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 inCongP ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuE3u ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exu__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyset__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powerset__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunion__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 omega__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuEu ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 descr__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 dsetconstr__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 eqimpsubset2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 eqimpsubset1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptysetsubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetE2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notsubsetI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notequalI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notequalI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetRefl ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetTrans ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoinSub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoinSub2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subset2powerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setextsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetemptysetimpeq ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetE1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 inPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetsubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 sepInPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 sepSubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionIL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairset2IR ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionIR ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionEcases ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionLsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionRsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset5 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectEL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectLsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectER ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 disjointsetsI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectRsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset4 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 bs114d ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusEL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusER ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusSubset2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusERneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusELneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusILneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusIRneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusLsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusSubset1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffIneg1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffIneg2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 secondinupair ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairIL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairIR ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kpairiskpair ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kpairp ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletonsubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletoninpowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletoninpowunion ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairset2E ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairsubunion ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairinpowunion ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ubforcartprodlem1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ubforcartprodlem2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ubforcartprodlem3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodpairin ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodmempair1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodmempair ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionE2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionsingleton1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionsingleton2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionsingleton ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletonprop ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ex1E1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ex1I ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ex1I2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletonsuniq ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairinjL1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kfstsingleton ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 theprop ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kfstpairEq ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodfstin ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairinjL2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairinjL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairinjR11 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairinjR12 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairinjR1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairequniteq ) => 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 Xx:$i, 4.33/1.15 Xy:$i, 4.33/1.15 Xz:$i, 4.33/1.15 Xu:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 Xx @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 Xx @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 Xy @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 Xz @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 Xz @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 Xu @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 Xy ) = 4.33/1.15 ( 4.33/1.15 Xu ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 4.33/1.15 thf(zf_stmt_0, conjecture, 4.33/1.15 (( setextAx ) => 4.33/1.15 ( ( emptysetAx ) => 4.33/1.15 ( ( ![X4:$i,X6:$i,X8:$i]: 4.33/1.15 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 4.33/1.15 ( ( in @ X8 @ X6 ) | ( ( X8 ) = ( X4 ) ) ) ) ) => 4.33/1.15 ( ( powersetAx ) => 4.33/1.15 ( ( setunionAx ) => 4.33/1.15 ( ( omega0Ax ) => 4.33/1.15 ( ( omegaSAx ) => 4.33/1.15 ( ( omegaIndAx ) => 4.33/1.15 ( ( replAx ) => 4.33/1.15 ( ( foundationAx ) => 4.33/1.15 ( ( wellorderingAx ) => 4.33/1.15 ( ( descrp ) => 4.33/1.15 ( ( dsetconstrI ) => 4.33/1.15 ( ( dsetconstrEL ) => 4.33/1.15 ( ( dsetconstrER ) => 4.33/1.15 ( ( exuE1 ) => 4.33/1.15 ( ( prop2setE ) => 4.33/1.15 ( ( emptysetE ) => 4.33/1.15 ( ( emptysetimpfalse ) => 4.33/1.15 ( ( notinemptyset ) => 4.33/1.15 ( ( exuE3e ) => 4.33/1.15 ( ( setext ) => 4.33/1.15 ( ( emptyI ) => 4.33/1.15 ( ( noeltsimpempty ) => 4.33/1.15 ( ( setbeta ) => 4.33/1.15 ( ( nonemptyE1 ) => 4.33/1.15 ( ( nonemptyI ) => 4.33/1.15 ( ( nonemptyI1 ) => 4.33/1.15 ( ( ![X10:$i,X12:$i]: 4.33/1.15 ( in @ 4.33/1.15 X10 @ 4.33/1.15 ( setadjoin @ 4.33/1.15 X10 @ X12 ) ) ) => 4.33/1.15 ( ( in @ 4.33/1.15 emptyset @ 4.33/1.15 ( setadjoin @ 4.33/1.15 emptyset @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( ( ![X14:$i, 4.33/1.15 X16:$i, 4.33/1.15 X18:$i]: 4.33/1.15 ( ( 4.33/1.15 in @ 4.33/1.15 X18 @ X16 ) => 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X18 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X14 @ X16 ) ) ) ) => 4.33/1.15 ( ( ![ 4.33/1.15 X20:$i, 4.33/1.15 X22:$i, 4.33/1.15 X24:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X24 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X20 @ X22 ) ) => 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X26:$o]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X24 ) = 4.33/1.15 ( 4.33/1.15 X20 ) ) => 4.33/1.15 ( 4.33/1.15 X26 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X24 @ X22 ) => 4.33/1.15 ( 4.33/1.15 X26 ) ) => 4.33/1.15 ( 4.33/1.15 X26 ) ) ) ) ) ) => 4.33/1.15 ( ( 4.33/1.15 ![ 4.33/1.15 X28:$i, 4.33/1.15 X30:$i, 4.33/1.15 X32:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X32 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X28 @ X30 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X32 @ X30 ) | 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X32 ) = 4.33/1.15 ( 4.33/1.15 X28 ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setoftrueEq ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyinPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyInPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subPowSU ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuE2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 nonemptyImpWitness ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X34:$i, 4.33/1.15 X36:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X34 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X36 @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X34 ) = 4.33/1.15 ( 4.33/1.15 X36 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X38:$i, 4.33/1.15 X40:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X38 ) != 4.33/1.15 ( 4.33/1.15 X40 ) ) => 4.33/1.15 ( 4.33/1.15 ~( 4.33/1.15 in @ 4.33/1.15 X40 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X38 @ 4.33/1.15 emptyset ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X42:$i, 4.33/1.15 X44:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X42 ) = 4.33/1.15 ( 4.33/1.15 X44 ) ) => 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X42 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X44 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X46:$i, 4.33/1.15 X48:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X46 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X48 @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X48 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X46 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X50:$i, 4.33/1.15 X52:$i, 4.33/1.15 X54:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X54 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X50 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X52 @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X54 ) = 4.33/1.15 ( 4.33/1.15 X52 ) ) | 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X54 ) = 4.33/1.15 ( 4.33/1.15 X50 ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X56:$i, 4.33/1.15 X58:$i]: 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X56 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X56 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X58 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X60:$i, 4.33/1.15 X62:$i]: 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X62 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X60 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X62 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyE1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 vacuousDall ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan4 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 prop2setI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 prop2set2propI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notdexE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notdallE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuI3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 inCongP ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuE3u ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exu__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyset__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X64:$i, 4.33/1.15 X66:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X64 ) = 4.33/1.15 ( 4.33/1.15 X66 ) ) => 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X68:$i, 4.33/1.15 X70:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X68 ) = 4.33/1.15 ( 4.33/1.15 X70 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X64 @ X68 ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X66 @ X70 ) ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powerset__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunion__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 omega__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuEu ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 descr__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 dsetconstr__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 eqimpsubset2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 eqimpsubset1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptysetsubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetE2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notsubsetI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notequalI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notequalI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetRefl ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetTrans ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoinSub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoinSub2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subset2powerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setextsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetemptysetimpeq ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetE1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 inPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetsubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 sepInPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 sepSubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionIL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X72:$i, 4.33/1.15 X74:$i]: 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X74 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X72 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X74 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionIR ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionEcases ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionLsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionRsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset5 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectEL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectLsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectER ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 disjointsetsI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectRsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset4 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 bs114d ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusEL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusER ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusSubset2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusERneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusELneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusILneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusIRneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusLsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusSubset1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffIneg1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffIneg2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X76:$i, 4.33/1.15 X78:$i]: 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X78 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X76 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X78 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairIL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairIR ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kpairiskpair ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kpairp ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletonsubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletoninpowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletoninpowunion ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X80:$i, 4.33/1.15 X82:$i, 4.33/1.15 X84:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X84 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X80 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X82 @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X84 ) = 4.33/1.15 ( 4.33/1.15 X82 ) ) | 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X84 ) = 4.33/1.15 ( 4.33/1.15 X80 ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairsubunion ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairinpowunion ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ubforcartprodlem1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ubforcartprodlem2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ubforcartprodlem3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodpairin ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodmempair1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodmempair ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionE2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionsingleton1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionsingleton2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionsingleton ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletonprop ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ex1E1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ex1I ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ex1I2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X86:$i, 4.33/1.15 X88:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X86 @ 4.33/1.15 emptyset ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X88 @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X86 ) = 4.33/1.15 ( 4.33/1.15 X88 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X90:$i, 4.33/1.15 X92:$i, 4.33/1.15 X94:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X94 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X90 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X90 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X92 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X90 ) = 4.33/1.15 ( 4.33/1.15 X94 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kfstsingleton ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 theprop ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kfstpairEq ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodfstin ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X96:$i, 4.33/1.15 X98:$i, 4.33/1.15 X100:$i, 4.33/1.15 X102:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X96 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X96 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X98 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X100 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X100 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X102 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X96 ) = 4.33/1.15 ( 4.33/1.15 X100 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairinjL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X104:$i, 4.33/1.15 X106:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X104 ) = 4.33/1.15 ( 4.33/1.15 X106 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X104 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X106 @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X104 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X108:$i, 4.33/1.15 X110:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X108 ) = 4.33/1.15 ( 4.33/1.15 X110 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X108 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X108 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X110 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X108 @ 4.33/1.15 emptyset ) @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X112:$i, 4.33/1.15 X114:$i, 4.33/1.15 X116:$i, 4.33/1.15 X118:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X112 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X112 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X114 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X116 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X116 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X118 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X116 ) = 4.33/1.15 ( 4.33/1.15 X118 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X114 ) = 4.33/1.15 ( 4.33/1.15 X118 ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X120:$i, 4.33/1.15 X122:$i, 4.33/1.15 X124:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X120 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X122 @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X124 @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X120 ) = 4.33/1.15 ( 4.33/1.15 X122 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X126:$i, 4.33/1.15 X128:$i, 4.33/1.15 X130:$i, 4.33/1.15 X132:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X126 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X126 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X128 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X130 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X130 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X132 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X128 ) = 4.33/1.15 ( 4.33/1.15 X132 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 4.33/1.15 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o). 4.33/1.15 thf(zf_stmt_2, axiom, 4.33/1.15 (![X8:$i,X6:$i,X4:$i]: 4.33/1.15 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=> 4.33/1.15 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ))). 4.33/1.15 thf(zf_stmt_3, conjecture, 4.33/1.15 (( setextAx ) => 4.33/1.15 ( ( emptysetAx ) => 4.33/1.15 ( ( ![X4:$i,X6:$i,X8:$i]: 4.33/1.15 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 4.33/1.15 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) => 4.33/1.15 ( ( powersetAx ) => 4.33/1.15 ( ( setunionAx ) => 4.33/1.15 ( ( omega0Ax ) => 4.33/1.15 ( ( omegaSAx ) => 4.33/1.15 ( ( omegaIndAx ) => 4.33/1.15 ( ( replAx ) => 4.33/1.15 ( ( foundationAx ) => 4.33/1.15 ( ( wellorderingAx ) => 4.33/1.15 ( ( descrp ) => 4.33/1.15 ( ( dsetconstrI ) => 4.33/1.15 ( ( dsetconstrEL ) => 4.33/1.15 ( ( dsetconstrER ) => 4.33/1.15 ( ( exuE1 ) => 4.33/1.15 ( ( prop2setE ) => 4.33/1.15 ( ( emptysetE ) => 4.33/1.15 ( ( emptysetimpfalse ) => 4.33/1.15 ( ( notinemptyset ) => 4.33/1.15 ( ( exuE3e ) => 4.33/1.15 ( ( setext ) => 4.33/1.15 ( ( emptyI ) => 4.33/1.15 ( ( noeltsimpempty ) => 4.33/1.15 ( ( setbeta ) => 4.33/1.15 ( ( nonemptyE1 ) => 4.33/1.15 ( ( nonemptyI ) => 4.33/1.15 ( ( nonemptyI1 ) => 4.33/1.15 ( ( ![X10:$i,X12:$i]: 4.33/1.15 ( in @ 4.33/1.15 X10 @ 4.33/1.15 ( setadjoin @ 4.33/1.15 X10 @ X12 ) ) ) => 4.33/1.15 ( ( in @ 4.33/1.15 emptyset @ 4.33/1.15 ( setadjoin @ 4.33/1.15 emptyset @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( ( ![X14:$i, 4.33/1.15 X16:$i, 4.33/1.15 X18:$i]: 4.33/1.15 ( ( 4.33/1.15 in @ 4.33/1.15 X18 @ X16 ) => 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X18 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X14 @ X16 ) ) ) ) => 4.33/1.15 ( ( ![ 4.33/1.15 X20:$i, 4.33/1.15 X22:$i, 4.33/1.15 X24:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X24 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X20 @ X22 ) ) => 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X26:$o]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X24 ) = 4.33/1.15 ( 4.33/1.15 X20 ) ) => 4.33/1.15 ( 4.33/1.15 X26 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X24 @ X22 ) => 4.33/1.15 ( 4.33/1.15 X26 ) ) => 4.33/1.15 ( 4.33/1.15 X26 ) ) ) ) ) ) => 4.33/1.15 ( ( 4.33/1.15 ![ 4.33/1.15 X28:$i, 4.33/1.15 X30:$i, 4.33/1.15 X32:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X32 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X28 @ X30 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X32 ) = 4.33/1.15 ( 4.33/1.15 X28 ) ) | 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X32 @ X30 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setoftrueEq ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyinPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyInPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subPowSU ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuE2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 nonemptyImpWitness ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X34:$i, 4.33/1.15 X36:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X34 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X36 @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X34 ) = 4.33/1.15 ( 4.33/1.15 X36 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X38:$i, 4.33/1.15 X40:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X38 ) != 4.33/1.15 ( 4.33/1.15 X40 ) ) => 4.33/1.15 ( 4.33/1.15 ~( 4.33/1.15 in @ 4.33/1.15 X40 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X38 @ 4.33/1.15 emptyset ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X42:$i, 4.33/1.15 X44:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X42 ) = 4.33/1.15 ( 4.33/1.15 X44 ) ) => 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X42 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X44 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X46:$i, 4.33/1.15 X48:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X46 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X48 @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X48 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X46 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X50:$i, 4.33/1.15 X52:$i, 4.33/1.15 X54:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X54 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X50 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X52 @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X54 ) = 4.33/1.15 ( 4.33/1.15 X50 ) ) | 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X54 ) = 4.33/1.15 ( 4.33/1.15 X52 ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X56:$i, 4.33/1.15 X58:$i]: 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X56 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X56 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X58 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X60:$i, 4.33/1.15 X62:$i]: 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X62 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X60 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X62 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyE1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 vacuousDall ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan4 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 prop2setI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 prop2set2propI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notdexE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notdallE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuI3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 inCongP ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuE3u ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exu__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyset__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X64:$i, 4.33/1.15 X66:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X64 ) = 4.33/1.15 ( 4.33/1.15 X66 ) ) => 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X68:$i, 4.33/1.15 X70:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X68 ) = 4.33/1.15 ( 4.33/1.15 X70 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X64 @ X68 ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X66 @ X70 ) ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powerset__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunion__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 omega__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuEu ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 descr__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 dsetconstr__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 eqimpsubset2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 eqimpsubset1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptysetsubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetE2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notsubsetI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notequalI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notequalI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetRefl ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetTrans ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoinSub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoinSub2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subset2powerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setextsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetemptysetimpeq ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetE1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 inPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetsubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 sepInPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 sepSubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionIL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X72:$i, 4.33/1.15 X74:$i]: 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X74 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X72 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X74 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionIR ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionEcases ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionLsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionRsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset5 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectEL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectLsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectER ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 disjointsetsI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectRsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset4 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 bs114d ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusEL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusER ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusSubset2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusERneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusELneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusILneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusIRneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusLsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusSubset1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffIneg1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffIneg2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X76:$i, 4.33/1.15 X78:$i]: 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X78 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X76 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X78 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairIL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairIR ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kpairiskpair ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kpairp ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletonsubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletoninpowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletoninpowunion ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X80:$i, 4.33/1.15 X82:$i, 4.33/1.15 X84:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X84 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X80 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X82 @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X84 ) = 4.33/1.15 ( 4.33/1.15 X80 ) ) | 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X84 ) = 4.33/1.15 ( 4.33/1.15 X82 ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairsubunion ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairinpowunion ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ubforcartprodlem1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ubforcartprodlem2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ubforcartprodlem3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodpairin ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodmempair1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodmempair ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionE2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionsingleton1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionsingleton2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionsingleton ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletonprop ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ex1E1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ex1I ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ex1I2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X86:$i, 4.33/1.15 X88:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X86 @ 4.33/1.15 emptyset ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X88 @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X86 ) = 4.33/1.15 ( 4.33/1.15 X88 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X90:$i, 4.33/1.15 X92:$i, 4.33/1.15 X94:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X94 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X90 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X90 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X92 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X90 ) = 4.33/1.15 ( 4.33/1.15 X94 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kfstsingleton ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 theprop ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kfstpairEq ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodfstin ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X96:$i, 4.33/1.15 X98:$i, 4.33/1.15 X100:$i, 4.33/1.15 X102:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X96 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X96 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X98 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X100 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X100 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X102 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X96 ) = 4.33/1.15 ( 4.33/1.15 X100 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairinjL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X104:$i, 4.33/1.15 X106:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X104 ) = 4.33/1.15 ( 4.33/1.15 X106 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X104 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X106 @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X104 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X108:$i, 4.33/1.15 X110:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X108 ) = 4.33/1.15 ( 4.33/1.15 X110 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X108 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X108 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X110 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X108 @ 4.33/1.15 emptyset ) @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X112:$i, 4.33/1.15 X114:$i, 4.33/1.15 X116:$i, 4.33/1.15 X118:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X112 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X112 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X114 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X116 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X116 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X118 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X116 ) = 4.33/1.15 ( 4.33/1.15 X118 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X114 ) = 4.33/1.15 ( 4.33/1.15 X118 ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X120:$i, 4.33/1.15 X122:$i, 4.33/1.15 X124:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X120 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X122 @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X124 @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X120 ) = 4.33/1.15 ( 4.33/1.15 X122 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X126:$i, 4.33/1.15 X128:$i, 4.33/1.15 X130:$i, 4.33/1.15 X132:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X126 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X126 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X128 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X130 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X130 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X132 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X128 ) = 4.33/1.15 ( 4.33/1.15 X132 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 4.33/1.15 thf(zf_stmt_4, negated_conjecture, 4.33/1.15 (~( ( setextAx ) => 4.33/1.15 ( ( emptysetAx ) => 4.33/1.15 ( ( ![X4:$i,X6:$i,X8:$i]: 4.33/1.15 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 4.33/1.15 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) => 4.33/1.15 ( ( powersetAx ) => 4.33/1.15 ( ( setunionAx ) => 4.33/1.15 ( ( omega0Ax ) => 4.33/1.15 ( ( omegaSAx ) => 4.33/1.15 ( ( omegaIndAx ) => 4.33/1.15 ( ( replAx ) => 4.33/1.15 ( ( foundationAx ) => 4.33/1.15 ( ( wellorderingAx ) => 4.33/1.15 ( ( descrp ) => 4.33/1.15 ( ( dsetconstrI ) => 4.33/1.15 ( ( dsetconstrEL ) => 4.33/1.15 ( ( dsetconstrER ) => 4.33/1.15 ( ( exuE1 ) => 4.33/1.15 ( ( prop2setE ) => 4.33/1.15 ( ( emptysetE ) => 4.33/1.15 ( ( emptysetimpfalse ) => 4.33/1.15 ( ( notinemptyset ) => 4.33/1.15 ( ( exuE3e ) => 4.33/1.15 ( ( setext ) => 4.33/1.15 ( ( emptyI ) => 4.33/1.15 ( ( noeltsimpempty ) => 4.33/1.15 ( ( setbeta ) => 4.33/1.15 ( ( nonemptyE1 ) => 4.33/1.15 ( ( nonemptyI ) => 4.33/1.15 ( ( nonemptyI1 ) => 4.33/1.15 ( ( ![X10:$i, 4.33/1.15 X12:$i]: 4.33/1.15 ( in @ 4.33/1.15 X10 @ 4.33/1.15 ( setadjoin 4.33/1.15 @ 4.33/1.15 X10 @ X12 ) ) ) => 4.33/1.15 ( ( in @ 4.33/1.15 emptyset @ 4.33/1.15 ( setadjoin 4.33/1.15 @ 4.33/1.15 emptyset @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( ( ![ 4.33/1.15 X14:$i, 4.33/1.15 X16:$i, 4.33/1.15 X18:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X18 @ X16 ) => 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X18 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X14 @ X16 ) ) ) ) => 4.33/1.15 ( ( 4.33/1.15 ![ 4.33/1.15 X20:$i, 4.33/1.15 X22:$i, 4.33/1.15 X24:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X24 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X20 @ X22 ) ) => 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X26:$o]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X24 ) = 4.33/1.15 ( 4.33/1.15 X20 ) ) => 4.33/1.15 ( 4.33/1.15 X26 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X24 @ X22 ) => 4.33/1.15 ( 4.33/1.15 X26 ) ) => 4.33/1.15 ( 4.33/1.15 X26 ) ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X28:$i, 4.33/1.15 X30:$i, 4.33/1.15 X32:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X32 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X28 @ X30 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X32 ) = 4.33/1.15 ( 4.33/1.15 X28 ) ) | 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X32 @ X30 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setoftrueEq ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyinPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyInPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subPowSU ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuE2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 nonemptyImpWitness ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X34:$i, 4.33/1.15 X36:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X34 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X36 @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X34 ) = 4.33/1.15 ( 4.33/1.15 X36 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X38:$i, 4.33/1.15 X40:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X38 ) != 4.33/1.15 ( 4.33/1.15 X40 ) ) => 4.33/1.15 ( 4.33/1.15 ~ 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X40 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X38 @ 4.33/1.15 emptyset ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X42:$i, 4.33/1.15 X44:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X42 ) = 4.33/1.15 ( 4.33/1.15 X44 ) ) => 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X42 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X44 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X46:$i, 4.33/1.15 X48:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X46 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X48 @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X48 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X46 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X50:$i, 4.33/1.15 X52:$i, 4.33/1.15 X54:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X54 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X50 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X52 @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X54 ) = 4.33/1.15 ( 4.33/1.15 X50 ) ) | 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X54 ) = 4.33/1.15 ( 4.33/1.15 X52 ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X56:$i, 4.33/1.15 X58:$i]: 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X56 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X56 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X58 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X60:$i, 4.33/1.15 X62:$i]: 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X62 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X60 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X62 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyE1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 vacuousDall ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 quantDeMorgan4 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 prop2setI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 prop2set2propI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notdexE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notdallE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuI3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 inCongP ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuE3u ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exu__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptyset__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X64:$i, 4.33/1.15 X66:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X64 ) = 4.33/1.15 ( 4.33/1.15 X66 ) ) => 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X68:$i, 4.33/1.15 X70:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X68 ) = 4.33/1.15 ( 4.33/1.15 X70 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X64 @ X68 ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X66 @ X70 ) ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powerset__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunion__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 omega__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 exuEu ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 descr__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 dsetconstr__Cong ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 eqimpsubset2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 eqimpsubset1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 emptysetsubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetE2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notsubsetI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notequalI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 notequalI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetRefl ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetTrans ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoinSub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoinSub2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subset2powerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setextsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 subsetemptysetimpeq ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetE1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 inPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 powersetsubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 sepInPowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 sepSubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionIL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X72:$i, 4.33/1.15 X74:$i]: 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X74 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X72 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X74 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionIR ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionEcases ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionLsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binunionRsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset5 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectEL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectLsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectER ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 disjointsetsI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectRsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset4 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 binintersectSubset1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 bs114d ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusI ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusEL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusER ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusSubset2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusERneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusELneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusILneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusIRneg ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusLsub ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setminusSubset1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffE ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffI1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffI2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffIneg1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 symdiffIneg2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X76:$i, 4.33/1.15 X78:$i]: 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X78 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X76 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X78 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairIL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairIR ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kpairiskpair ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kpairp ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletonsubset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletoninpowerset ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletoninpowunion ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X80:$i, 4.33/1.15 X82:$i, 4.33/1.15 X84:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 X84 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X80 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X82 @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X84 ) = 4.33/1.15 ( 4.33/1.15 X80 ) ) | 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X84 ) = 4.33/1.15 ( 4.33/1.15 X82 ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairsubunion ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 upairinpowunion ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ubforcartprodlem1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ubforcartprodlem2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ubforcartprodlem3 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodpairin ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodmempair1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodmempair ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionE2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionsingleton1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionsingleton2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setunionsingleton ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 singletonprop ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ex1E1 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ex1I ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ex1I2 ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X86:$i, 4.33/1.15 X88:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X86 @ 4.33/1.15 emptyset ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X88 @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X86 ) = 4.33/1.15 ( 4.33/1.15 X88 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X90:$i, 4.33/1.15 X92:$i, 4.33/1.15 X94:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 in @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X94 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X90 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X90 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X92 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X90 ) = 4.33/1.15 ( 4.33/1.15 X94 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kfstsingleton ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 theprop ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 kfstpairEq ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 cartprodfstin ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X96:$i, 4.33/1.15 X98:$i, 4.33/1.15 X100:$i, 4.33/1.15 X102:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X96 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X96 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X98 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X100 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X100 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X102 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X96 ) = 4.33/1.15 ( 4.33/1.15 X100 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setukpairinjL ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X104:$i, 4.33/1.15 X106:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X104 ) = 4.33/1.15 ( 4.33/1.15 X106 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X104 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X106 @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X104 @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X108:$i, 4.33/1.15 X110:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X108 ) = 4.33/1.15 ( 4.33/1.15 X110 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X108 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X108 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X110 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X108 @ 4.33/1.15 emptyset ) @ 4.33/1.15 emptyset ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X112:$i, 4.33/1.15 X114:$i, 4.33/1.15 X116:$i, 4.33/1.15 X118:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X112 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X112 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X114 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X116 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X116 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X118 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X116 ) = 4.33/1.15 ( 4.33/1.15 X118 ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X114 ) = 4.33/1.15 ( 4.33/1.15 X118 ) ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X120:$i, 4.33/1.15 X122:$i, 4.33/1.15 X124:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X120 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X122 @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X124 @ 4.33/1.15 emptyset ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X120 ) = 4.33/1.15 ( 4.33/1.15 X122 ) ) ) ) => 4.33/1.15 ( 4.33/1.15 ![ 4.33/1.15 X126:$i, 4.33/1.15 X128:$i, 4.33/1.15 X130:$i, 4.33/1.15 X132:$i]: 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X126 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X126 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X128 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) = 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X130 @ 4.33/1.15 emptyset ) @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X130 @ 4.33/1.15 ( 4.33/1.15 setadjoin 4.33/1.15 @ 4.33/1.15 X132 @ 4.33/1.15 emptyset ) ) @ 4.33/1.15 emptyset ) ) ) => 4.33/1.15 ( 4.33/1.15 ( 4.33/1.15 X128 ) = 4.33/1.15 ( 4.33/1.15 X132 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 4.33/1.15 inference('cnf.neg', [status(esa)], [zf_stmt_3])). 4.33/1.15 thf(zip_derived_cl90, plain, 4.33/1.15 (((setadjoin @ (setadjoin @ sk__61 @ emptyset) @ 4.33/1.15 (setadjoin @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @ 4.33/1.15 emptyset)) 4.33/1.15 = (setadjoin @ (setadjoin @ sk__63 @ emptyset) @ 4.33/1.15 (setadjoin @ 4.33/1.15 (setadjoin @ sk__63 @ (setadjoin @ sk__64 @ emptyset)) @ emptyset)))), 4.33/1.15 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.15 thf(zip_derived_cl90, plain, 4.33/1.15 (((setadjoin @ (setadjoin @ sk__61 @ emptyset) @ 4.33/1.15 (setadjoin @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @ 4.33/1.15 emptyset)) 4.33/1.15 = (setadjoin @ (setadjoin @ sk__63 @ emptyset) @ 4.33/1.15 (setadjoin @ 4.33/1.15 (setadjoin @ sk__63 @ (setadjoin @ sk__64 @ emptyset)) @ emptyset)))), 4.33/1.15 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.15 thf(zip_derived_cl18, plain, 4.33/1.15 (![X4 : $i, X5 : $i]: (in @ X4 @ (setadjoin @ X4 @ X5))), 4.33/1.15 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.15 thf(zip_derived_cl468, plain, 4.33/1.15 ( (in @ (setadjoin @ sk__63 @ emptyset) @ 4.33/1.15 (setadjoin @ (setadjoin @ sk__61 @ emptyset) @ 4.33/1.15 (setadjoin @ 4.33/1.15 (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @ emptyset)))), 4.33/1.15 inference('sup+', [status(thm)], [zip_derived_cl90, zip_derived_cl18])). 4.33/1.15 thf(zip_derived_cl83, plain, 4.33/1.15 (![X27 : $i, X28 : $i, X29 : $i]: 4.33/1.15 (((X28) = (X27)) 4.33/1.15 | ~ (in @ (setadjoin @ X27 @ emptyset) @ 4.33/1.15 (setadjoin @ (setadjoin @ X28 @ emptyset) @ 4.33/1.15 (setadjoin @ 4.33/1.15 (setadjoin @ X28 @ (setadjoin @ X29 @ emptyset)) @ emptyset))))), 4.33/1.15 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.15 thf(zip_derived_cl495, plain, (((sk__61) = (sk__63))), 4.33/1.15 inference('sup-', [status(thm)], [zip_derived_cl468, zip_derived_cl83])). 4.33/1.15 thf(zip_derived_cl495, plain, (((sk__61) = (sk__63))), 4.33/1.15 inference('sup-', [status(thm)], [zip_derived_cl468, zip_derived_cl83])). 4.33/1.15 thf(zip_derived_cl521, plain, 4.33/1.15 (((setadjoin @ (setadjoin @ sk__61 @ emptyset) @ 4.33/1.15 (setadjoin @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @ 4.33/1.15 emptyset)) 4.33/1.15 = (setadjoin @ (setadjoin @ sk__61 @ emptyset) @ 4.33/1.15 (setadjoin @ 4.33/1.15 (setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset)) @ emptyset)))), 4.33/1.15 inference('demod', [status(thm)], 4.33/1.15 [zip_derived_cl90, zip_derived_cl495, zip_derived_cl495])). 4.33/1.15 thf(zip_derived_cl521, plain, 4.33/1.15 (((setadjoin @ (setadjoin @ sk__61 @ emptyset) @ 4.33/1.15 (setadjoin @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @ 4.33/1.15 emptyset)) 4.33/1.15 = (setadjoin @ (setadjoin @ sk__61 @ emptyset) @ 4.33/1.16 (setadjoin @ 4.33/1.16 (setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset)) @ emptyset)))), 4.33/1.16 inference('demod', [status(thm)], 4.33/1.16 [zip_derived_cl90, zip_derived_cl495, zip_derived_cl495])). 4.33/1.16 thf(zip_derived_cl70, plain, 4.33/1.16 (![X22 : $i, X23 : $i]: 4.33/1.16 (in @ X22 @ (setadjoin @ X23 @ (setadjoin @ X22 @ emptyset)))), 4.33/1.16 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.16 thf(zip_derived_cl527, plain, 4.33/1.16 ( (in @ (setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset)) @ 4.33/1.16 (setadjoin @ (setadjoin @ sk__61 @ emptyset) @ 4.33/1.16 (setadjoin @ 4.33/1.16 (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @ emptyset)))), 4.33/1.16 inference('sup+', [status(thm)], [zip_derived_cl521, zip_derived_cl70])). 4.33/1.16 thf(zip_derived_cl74, plain, 4.33/1.16 (![X24 : $i, X25 : $i, X26 : $i]: 4.33/1.16 (((X25) = (X24)) 4.33/1.16 | ((X25) = (X26)) 4.33/1.16 | ~ (in @ X25 @ (setadjoin @ X26 @ (setadjoin @ X24 @ emptyset))))), 4.33/1.16 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.16 thf(zip_derived_cl573, plain, 4.33/1.16 ((((setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset)) 4.33/1.16 = (setadjoin @ sk__61 @ emptyset)) 4.33/1.16 | ((setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset)) 4.33/1.16 = (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset))))), 4.33/1.16 inference('sup-', [status(thm)], [zip_derived_cl527, zip_derived_cl74])). 4.33/1.16 thf(zip_derived_cl70, plain, 4.33/1.16 (![X22 : $i, X23 : $i]: 4.33/1.16 (in @ X22 @ (setadjoin @ X23 @ (setadjoin @ X22 @ emptyset)))), 4.33/1.16 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.16 thf(zip_derived_cl607, plain, 4.33/1.16 (( (in @ sk__64 @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset))) 4.33/1.16 | ((setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset)) 4.33/1.16 = (setadjoin @ sk__61 @ emptyset)))), 4.33/1.16 inference('sup+', [status(thm)], [zip_derived_cl573, zip_derived_cl70])). 4.33/1.16 thf(zip_derived_cl74, plain, 4.33/1.16 (![X24 : $i, X25 : $i, X26 : $i]: 4.33/1.16 (((X25) = (X24)) 4.33/1.16 | ((X25) = (X26)) 4.33/1.16 | ~ (in @ X25 @ (setadjoin @ X26 @ (setadjoin @ X24 @ emptyset))))), 4.33/1.16 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.16 thf(zip_derived_cl629, plain, 4.33/1.16 ((((setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset)) 4.33/1.16 = (setadjoin @ sk__61 @ emptyset)) 4.33/1.16 | ((sk__64) = (sk__61)) 4.33/1.16 | ((sk__64) = (sk__62)))), 4.33/1.16 inference('sup-', [status(thm)], [zip_derived_cl607, zip_derived_cl74])). 4.33/1.16 thf(zip_derived_cl89, plain, (((sk__62) != (sk__64))), 4.33/1.16 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.16 thf(zip_derived_cl643, plain, 4.33/1.16 ((((setadjoin @ sk__61 @ (setadjoin @ sk__64 @ emptyset)) 4.33/1.16 = (setadjoin @ sk__61 @ emptyset)) 4.33/1.16 | ((sk__64) = (sk__61)))), 4.33/1.16 inference('simplify_reflect-', [status(thm)], 4.33/1.16 [zip_derived_cl629, zip_derived_cl89])). 4.33/1.16 thf(zip_derived_cl88, plain, 4.33/1.16 (![X32 : $i, X33 : $i, X34 : $i]: 4.33/1.16 (((X33) = (X32)) 4.33/1.16 | ((setadjoin @ X33 @ (setadjoin @ X32 @ emptyset)) 4.33/1.16 != (setadjoin @ X34 @ emptyset)))), 4.33/1.16 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.16 thf(zip_derived_cl645, plain, (((sk__64) = (sk__61))), 4.33/1.16 inference('clc', [status(thm)], [zip_derived_cl643, zip_derived_cl88])). 4.33/1.16 thf(zip_derived_cl92, plain, 4.33/1.16 (![X39 : $i, X40 : $i]: 4.33/1.16 (((setadjoin @ X39 @ (setadjoin @ X40 @ emptyset)) 4.33/1.16 = (setadjoin @ X39 @ emptyset)) 4.33/1.16 | ((X39) != (X40)))), 4.33/1.16 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.16 thf(zip_derived_cl400, plain, 4.33/1.16 (![X40 : $i]: 4.33/1.16 ((setadjoin @ X40 @ (setadjoin @ X40 @ emptyset)) 4.33/1.16 = (setadjoin @ X40 @ emptyset))), 4.33/1.16 inference('simplify', [status(thm)], [zip_derived_cl92])). 4.33/1.16 thf(zip_derived_cl400, plain, 4.33/1.16 (![X40 : $i]: 4.33/1.16 ((setadjoin @ X40 @ (setadjoin @ X40 @ emptyset)) 4.33/1.16 = (setadjoin @ X40 @ emptyset))), 4.33/1.16 inference('simplify', [status(thm)], [zip_derived_cl92])). 4.33/1.16 thf(zip_derived_cl648, plain, 4.33/1.16 (((setadjoin @ (setadjoin @ sk__61 @ emptyset) @ 4.33/1.16 (setadjoin @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @ 4.33/1.16 emptyset)) 4.33/1.16 = (setadjoin @ (setadjoin @ sk__61 @ emptyset) @ emptyset))), 4.33/1.16 inference('demod', [status(thm)], 4.33/1.16 [zip_derived_cl521, zip_derived_cl645, zip_derived_cl400, 4.33/1.16 zip_derived_cl400])). 4.33/1.16 thf(zip_derived_cl70, plain, 4.33/1.16 (![X22 : $i, X23 : $i]: 4.33/1.16 (in @ X22 @ (setadjoin @ X23 @ (setadjoin @ X22 @ emptyset)))), 4.33/1.16 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.16 thf(zip_derived_cl997, plain, 4.33/1.16 ( (in @ (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)) @ 4.33/1.16 (setadjoin @ (setadjoin @ sk__61 @ emptyset) @ emptyset))), 4.33/1.16 inference('sup+', [status(thm)], [zip_derived_cl648, zip_derived_cl70])). 4.33/1.16 thf(zip_derived_cl26, plain, 4.33/1.16 (![X12 : $i, X13 : $i]: 4.33/1.16 (~ (in @ X12 @ (setadjoin @ X13 @ emptyset)) | ((X13) = (X12)))), 4.33/1.16 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.16 thf(zip_derived_cl1050, plain, 4.33/1.16 (((setadjoin @ sk__61 @ emptyset) 4.33/1.16 = (setadjoin @ sk__61 @ (setadjoin @ sk__62 @ emptyset)))), 4.33/1.16 inference('sup-', [status(thm)], [zip_derived_cl997, zip_derived_cl26])). 4.33/1.16 thf(zip_derived_cl88, plain, 4.33/1.16 (![X32 : $i, X33 : $i, X34 : $i]: 4.33/1.16 (((X33) = (X32)) 4.33/1.16 | ((setadjoin @ X33 @ (setadjoin @ X32 @ emptyset)) 4.33/1.16 != (setadjoin @ X34 @ emptyset)))), 4.33/1.16 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.16 thf(zip_derived_cl1098, plain, 4.33/1.16 (![X0 : $i]: 4.33/1.16 (((setadjoin @ sk__61 @ emptyset) != (setadjoin @ X0 @ emptyset)) 4.33/1.16 | ((sk__61) = (sk__62)))), 4.33/1.16 inference('sup-', [status(thm)], [zip_derived_cl1050, zip_derived_cl88])). 4.33/1.16 thf(zip_derived_cl89, plain, (((sk__62) != (sk__64))), 4.33/1.16 inference('cnf', [status(esa)], [zf_stmt_4])). 4.33/1.16 thf(zip_derived_cl645, plain, (((sk__64) = (sk__61))), 4.33/1.16 inference('clc', [status(thm)], [zip_derived_cl643, zip_derived_cl88])). 4.33/1.16 thf(zip_derived_cl646, plain, (((sk__62) != (sk__61))), 4.33/1.16 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl645])). 4.33/1.16 thf(zip_derived_cl1121, plain, 4.33/1.16 (![X0 : $i]: 4.33/1.16 ((setadjoin @ sk__61 @ emptyset) != (setadjoin @ X0 @ emptyset))), 4.33/1.16 inference('simplify_reflect-', [status(thm)], 4.33/1.16 [zip_derived_cl1098, zip_derived_cl646])). 4.33/1.16 thf(zip_derived_cl1139, plain, ($false), 4.33/1.16 inference('eq_res', [status(thm)], [zip_derived_cl1121])). 4.33/1.16 4.33/1.16 % SZS output end Refutation 4.33/1.16 4.33/1.16 4.33/1.16 % Terminating... 5.16/1.28 % Runner terminated. 5.16/1.29 % Zipperpin 1.5 exiting 5.16/1.30 EOF