0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.15/0.16 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.yPePjqcuLU true 0.15/0.36 % Computer : n015.cluster.edu 0.15/0.36 % Model : x86_64 x86_64 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.36 % Memory : 8042.1875MB 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.36 % CPULimit : 1200 0.15/0.36 % WCLimit : 120 0.15/0.36 % DateTime : Tue Jul 13 15:35:19 EDT 2021 0.21/0.36 % CPUTime : 0.21/0.36 % Running portfolio for 120 s 0.21/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.21/0.37 % Number of cores: 8 0.21/0.37 % Python version: Python 3.6.8 0.21/0.37 % Running in HO mode 0.52/0.65 % Total configuration time : 828 0.52/0.65 % Estimated wc time : 983 0.52/0.65 % Estimated cpu time (8 cpus) : 122.875 0.57/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 47s 0.57/0.75 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 47s 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 18s 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 53s 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 47s 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 41s 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 35s 143.30/18.74 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 53s 206.18/27.22 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 33s 230.26/30.25 % Solved by lams/40_c_ic.sh. 230.26/30.25 % running E: timeout 27 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.yPePjqcuLU/e_input76536a --cpu-limit=25 --auto-schedule -s -p 230.26/30.25 % done 1023 iterations in 29.424s 230.26/30.25 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 230.26/30.25 % SZS output start Refutation 230.26/30.25 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 230.26/30.25 thf(binintersectER_type, type, binintersectER: $o). 230.26/30.25 thf(setadjoinSub_type, type, setadjoinSub: $o). 230.26/30.25 thf(setukpairinjR2_type, type, setukpairinjR2: $o). 230.26/30.25 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 230.26/30.25 thf(vacuousDall_type, type, vacuousDall: $o). 230.26/30.25 thf(setadjoinIR_type, type, setadjoinIR: $o). 230.26/30.25 thf(ex1E2_type, type, ex1E2: $o). 230.26/30.25 thf(omega0Ax_type, type, omega0Ax: $o). 230.26/30.25 thf(subsetE_type, type, subsetE: $o). 230.26/30.25 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 230.26/30.25 thf(setminusER_type, type, setminusER: $o). 230.26/30.25 thf(subbreln_type, type, subbreln: $o). 230.26/30.25 thf(binunionE_type, type, binunionE: $o). 230.26/30.25 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 230.26/30.25 thf(powersetE_type, type, powersetE: $o). 230.26/30.25 thf(binunionRsub_type, type, binunionRsub: $o). 230.26/30.25 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 230.26/30.25 thf(powerset__Cong_type, type, powerset__Cong: $o). 230.26/30.25 thf(lam2p_type, type, lam2p: $o). 230.26/30.25 thf(sk__103_type, type, sk__103: $i). 230.26/30.25 thf(ksndsingleton_type, type, ksndsingleton: $o). 230.26/30.25 thf(funcGraphProp2_type, type, funcGraphProp2: $o). 230.26/30.25 thf(omegaIndAx_type, type, omegaIndAx: $o). 230.26/30.25 thf(uniqinunit_type, type, uniqinunit: $o). 230.26/30.25 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 230.26/30.25 thf(exu__Cong_type, type, exu__Cong: $o). 230.26/30.25 thf(subset2powerset_type, type, subset2powerset: $o). 230.26/30.25 thf(setoftrueEq_type, type, setoftrueEq: $o). 230.26/30.25 thf(ap2p_type, type, ap2p: $o). 230.26/30.25 thf(setukpairinjR12_type, type, setukpairinjR12: $o). 230.26/30.25 thf(upairsetIL_type, type, upairsetIL: $o). 230.26/30.25 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 230.26/30.25 thf(lamp_type, type, lamp: $o). 230.26/30.25 thf(emptyI_type, type, emptyI: $o). 230.26/30.25 thf(setukpairIL_type, type, setukpairIL: $o). 230.26/30.25 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 230.26/30.25 thf(exuI3_type, type, exuI3: $o). 230.26/30.25 thf(brelnall1_type, type, brelnall1: $o). 230.26/30.25 thf(emptysetAx_type, type, emptysetAx: $o). 230.26/30.25 thf(setukpairIR_type, type, setukpairIR: $o). 230.26/30.25 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 230.26/30.25 thf(setadjoinIL_type, type, setadjoinIL: $o). 230.26/30.25 thf(upairsubunion_type, type, upairsubunion: $o). 230.26/30.25 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o). 230.26/30.25 thf(beta1_type, type, beta1: $o). 230.26/30.25 thf(ksndpairEq_type, type, ksndpairEq: $o). 230.26/30.25 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 230.26/30.25 thf(upairsetIR_type, type, upairsetIR: $o). 230.26/30.25 thf(ex1I2_type, type, ex1I2: $o). 230.26/30.25 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 230.26/30.25 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 230.26/30.25 thf(ex1I_type, type, ex1I: $o). 230.26/30.25 thf(cartprodsndin_type, type, cartprodsndin: $o). 230.26/30.25 thf(setminusI_type, type, setminusI: $o). 230.26/30.25 thf(apProp_type, type, apProp: $o). 230.26/30.25 thf(descrp_type, type, descrp: $o). 230.26/30.25 thf(binintersectI_type, type, binintersectI: $o). 230.26/30.25 thf(nonemptyI1_type, type, nonemptyI1: $o). 230.26/30.25 thf(emptysetsubset_type, type, emptysetsubset: $o). 230.26/30.25 thf(setunionAx_type, type, setunionAx: $o). 230.26/30.25 thf(notsubsetI_type, type, notsubsetI: $o). 230.26/30.25 thf(theprop_type, type, theprop: $o). 230.26/30.25 thf(iffalseProp2_type, type, iffalseProp2: $o). 230.26/30.25 thf(sk__105_type, type, sk__105: $i). 230.26/30.25 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 230.26/30.25 thf(upairset2IR_type, type, upairset2IR: $o). 230.26/30.25 thf(binunionLsub_type, type, binunionLsub: $o). 230.26/30.25 thf(subsetRefl_type, type, subsetRefl: $o). 230.26/30.25 thf(powerset_type, type, powerset: $i > $i). 230.26/30.25 thf(eta2_type, type, eta2: $o). 230.26/30.25 thf(eta1_type, type, eta1: $o). 230.26/30.25 thf(nonemptyI_type, type, nonemptyI: $o). 230.26/30.25 thf(emptysetE_type, type, emptysetE: $o). 230.26/30.25 thf(sepInPowerset_type, type, sepInPowerset: $o). 230.26/30.25 thf(upairequniteq_type, type, upairequniteq: $o). 230.26/30.25 thf(kpairsurjEq_type, type, kpairsurjEq: $o). 230.26/30.25 thf(funcext_type, type, funcext: $o). 230.26/30.25 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 230.26/30.25 thf(singletonprop_type, type, singletonprop: $o). 230.26/30.25 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 230.26/30.25 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o). 230.26/30.25 thf(powersetI_type, type, powersetI: $o). 230.26/30.25 thf(sk__108_type, type, sk__108: ($i > $o) > ($i > $o) > $i > $i > $i). 230.26/30.25 thf(exuE2_type, type, exuE2: $o). 230.26/30.25 thf(setukpairinjL_type, type, setukpairinjL: $o). 230.26/30.25 thf(exuE3e_type, type, exuE3e: $o). 230.26/30.25 thf(setminusSubset1_type, type, setminusSubset1: $o). 230.26/30.25 thf(notequalI2_type, type, notequalI2: $o). 230.26/30.25 thf(descr__Cong_type, type, descr__Cong: $o). 230.26/30.25 thf(setextAx_type, type, setextAx: $o). 230.26/30.25 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 230.26/30.25 thf(eqinunit_type, type, eqinunit: $o). 230.26/30.25 thf(symdiffE_type, type, symdiffE: $o). 230.26/30.25 thf(upairinpowunion_type, type, upairinpowunion: $o). 230.26/30.25 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 230.26/30.25 thf(powersetAx_type, type, powersetAx: $o). 230.26/30.25 thf(upairset2E_type, type, upairset2E: $o). 230.26/30.25 thf(subsetI2_type, type, subsetI2: $o). 230.26/30.25 thf(symdiffI1_type, type, symdiffI1: $o). 230.26/30.25 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 230.26/30.25 thf('#l_lift12039_type', type, '#l_lift12039': $i > $o > $i > $i > $o). 230.26/30.25 thf(subsetI1_type, type, subsetI1: $o). 230.26/30.25 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 230.26/30.25 thf(replAx_type, type, replAx: $o). 230.26/30.25 thf(subPowSU_type, type, subPowSU: $o). 230.26/30.25 thf(setunionE_type, type, setunionE: $o). 230.26/30.25 thf(setunionsingleton_type, type, setunionsingleton: $o). 230.26/30.25 thf(setunion__Cong_type, type, setunion__Cong: $o). 230.26/30.25 thf(bs114d_type, type, bs114d: $o). 230.26/30.25 thf(setminusSubset2_type, type, setminusSubset2: $o). 230.26/30.25 thf(powersetE1_type, type, powersetE1: $o). 230.26/30.25 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 230.26/30.25 thf(dpsetconstrI_type, type, dpsetconstrI: $o). 230.26/30.25 thf(omegaSAx_type, type, omegaSAx: $o). 230.26/30.25 thf(ap2apEq2_type, type, ap2apEq2: $o). 230.26/30.25 thf(setext_type, type, setext: $o). 230.26/30.25 thf(cartprodfstin_type, type, cartprodfstin: $o). 230.26/30.25 thf(notequalI1_type, type, notequalI1: $o). 230.26/30.25 thf(setextsub_type, type, setextsub: $o). 230.26/30.25 thf('#l_lift12040_type', type, '#l_lift12040': $i > $o). 230.26/30.25 thf(kpairp_type, type, kpairp: $o). 230.26/30.25 thf(funcGraphProp1_type, type, funcGraphProp1: $o). 230.26/30.25 thf(omega__Cong_type, type, omega__Cong: $o). 230.26/30.25 thf(symdiffI2_type, type, symdiffI2: $o). 230.26/30.25 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o). 230.26/30.25 thf(setbeta_type, type, setbeta: $o). 230.26/30.25 thf(ap2apEq1_type, type, ap2apEq1: $o). 230.26/30.25 thf(dsetconstrER_type, type, dsetconstrER: $o). 230.26/30.25 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o). 230.26/30.25 thf(funcGraphProp3_type, type, funcGraphProp3: $o). 230.26/30.25 thf(nonemptyE1_type, type, nonemptyE1: $o). 230.26/30.25 thf(binunionIL_type, type, binunionIL: $o). 230.26/30.25 thf(prop2setE_type, type, prop2setE: $o). 230.26/30.25 thf(prop2set2propI_type, type, prop2set2propI: $o). 230.26/30.25 thf(notdallE_type, type, notdallE: $o). 230.26/30.25 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 230.26/30.25 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o). 230.26/30.25 thf(exuEu_type, type, exuEu: $o). 230.26/30.25 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o). 230.26/30.25 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 230.26/30.25 thf(notinsingleton_type, type, notinsingleton: $o). 230.26/30.25 thf(upairsetE_type, type, upairsetE: $o). 230.26/30.25 thf(emptyE1_type, type, emptyE1: $o). 230.26/30.25 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 230.26/30.25 thf(cartprodmempair_type, type, cartprodmempair: $o). 230.26/30.25 thf(binunionEcases_type, type, binunionEcases: $o). 230.26/30.25 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o). 230.26/30.25 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 230.26/30.25 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 230.26/30.25 thf(wellorderingAx_type, type, wellorderingAx: $o). 230.26/30.25 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 230.26/30.25 thf(binintersectLsub_type, type, binintersectLsub: $o). 230.26/30.25 thf(binintersectRsub_type, type, binintersectRsub: $o). 230.26/30.25 thf(powersetsubset_type, type, powersetsubset: $o). 230.26/30.25 thf(funcextLem_type, type, funcextLem: $o). 230.26/30.25 thf(emptyset_type, type, emptyset: $i). 230.26/30.25 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 230.26/30.25 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 230.26/30.25 thf(exuE1_type, type, exuE1: $o). 230.26/30.25 thf(inPowerset_type, type, inPowerset: $o). 230.26/30.25 thf(dpsetconstrER_type, type, dpsetconstrER: $o). 230.26/30.25 thf(in_type, type, in: $i > $i > $o). 230.26/30.25 thf(cartprodpairin_type, type, cartprodpairin: $o). 230.26/30.25 thf(setunionI_type, type, setunionI: $o). 230.26/30.25 thf(in__Cong_type, type, in__Cong: $o). 230.26/30.25 thf(setadjoinE_type, type, setadjoinE: $o). 230.26/30.25 thf(subsetTrans_type, type, subsetTrans: $o). 230.26/30.25 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 230.26/30.25 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 230.26/30.25 thf(iffalseProp1_type, type, iffalseProp1: $o). 230.26/30.25 thf(funcImageSingleton_type, type, funcImageSingleton: $o). 230.26/30.25 thf(setminusIRneg_type, type, setminusIRneg: $o). 230.26/30.25 thf(setminusELneg_type, type, setminusELneg: $o). 230.26/30.25 thf(foundationAx_type, type, foundationAx: $o). 230.26/30.25 thf(sepSubset_type, type, sepSubset: $o). 230.26/30.25 thf(brelnall2_type, type, brelnall2: $o). 230.26/30.25 thf('#l_lift12044_type', type, '#l_lift12044': $i > $o). 230.26/30.25 thf(exuE3u_type, type, exuE3u: $o). 230.26/30.25 thf(kpairiskpair_type, type, kpairiskpair: $o). 230.26/30.25 thf(app_type, type, app: $o). 230.26/30.25 thf(setadjoinOr_type, type, setadjoinOr: $o). 230.26/30.25 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o). 230.26/30.25 thf(exuI1_type, type, exuI1: $o). 230.26/30.25 thf(kfstsingleton_type, type, kfstsingleton: $o). 230.26/30.25 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 230.26/30.25 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 230.26/30.25 thf(binunionIR_type, type, binunionIR: $o). 230.26/30.25 thf(inCongP_type, type, inCongP: $o). 230.26/30.25 thf('#l_lift12041_type', type, '#l_lift12041': $i > $o). 230.26/30.25 thf(beta2_type, type, beta2: $o). 230.26/30.25 thf(setminusLsub_type, type, setminusLsub: $o). 230.26/30.25 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o). 230.26/30.25 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 230.26/30.25 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 230.26/30.25 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 230.26/30.25 thf(sk__104_type, type, sk__104: $o). 230.26/30.25 thf(funcinfuncset_type, type, funcinfuncset: $o). 230.26/30.25 thf(infuncsetfunc_type, type, infuncsetfunc: $o). 230.26/30.25 thf(setukpairinjR1_type, type, setukpairinjR1: $o). 230.26/30.25 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o). 230.26/30.25 thf(setminusERneg_type, type, setminusERneg: $o). 230.26/30.25 thf(sk__106_type, type, sk__106: $i). 230.26/30.25 thf(exuI2_type, type, exuI2: $o). 230.26/30.25 thf(powersetI1_type, type, powersetI1: $o). 230.26/30.25 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o). 230.26/30.25 thf(kfstpairEq_type, type, kfstpairEq: $o). 230.26/30.25 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 230.26/30.25 thf(setminusILneg_type, type, setminusILneg: $o). 230.26/30.25 thf(eqbreln_type, type, eqbreln: $o). 230.26/30.25 thf(dsetconstrI_type, type, dsetconstrI: $o). 230.26/30.25 thf(sk__107_type, type, sk__107: ($i > $o) > ($i > $o) > $i > $i > $i). 230.26/30.25 thf(setminusEL_type, type, setminusEL: $o). 230.26/30.25 thf(singletonsubset_type, type, singletonsubset: $o). 230.26/30.25 thf(setukpairinjR_type, type, setukpairinjR: $o). 230.26/30.25 thf(secondinupair_type, type, secondinupair: $o). 230.26/30.25 thf(ex1E1_type, type, ex1E1: $o). 230.26/30.25 thf(singletonsuniq_type, type, singletonsuniq: $o). 230.26/30.25 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 230.26/30.25 thf(funcGraphProp4_type, type, funcGraphProp4: $o). 230.26/30.25 thf(iftrueProp1_type, type, iftrueProp1: $o). 230.26/30.25 thf(subsetE2_type, type, subsetE2: $o). 230.26/30.25 thf(singletonsswitch_type, type, singletonsswitch: $o). 230.26/30.25 thf(binintersectEL_type, type, binintersectEL: $o). 230.26/30.25 thf(setadjoinAx_type, type, setadjoinAx: $o). 230.26/30.25 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 230.26/30.25 thf(notinemptyset_type, type, notinemptyset: $o). 230.26/30.25 thf(prop2setI_type, type, prop2setI: $o). 230.26/30.25 thf(lamProp_type, type, lamProp: $o). 230.26/30.25 thf(lam2lamEq_type, type, lam2lamEq: $o). 230.26/30.25 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 230.26/30.25 thf(setunionE2_type, type, setunionE2: $o). 230.26/30.25 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o). 230.26/30.25 thf(subset_type, type, subset: $i > $i > $o). 230.26/30.25 thf(funcext2_type, type, funcext2: $o). 230.26/30.25 thf(notdexE_type, type, notdexE: $o). 230.26/30.25 thf(iftrueProp1, axiom, iftrueProp1 = 230.26/30.25 (![A:$i,Xphi:$o,Xx:$i]: 230.26/30.25 ( ( in @ Xx @ A ) => 230.26/30.25 ( ![Xy:$i]: 230.26/30.25 ( ( in @ Xy @ A ) => 230.26/30.25 ( ( Xphi ) => 230.26/30.25 ( in @ 230.26/30.25 Xx @ 230.26/30.25 ( dsetconstr @ 230.26/30.25 A @ 230.26/30.25 ( ^[Xz:$i]: 230.26/30.25 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) | 230.26/30.25 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) ) ) ) ) ))). 230.26/30.25 thf('0', plain, 230.26/30.25 (( iftrueProp1 ) = 230.26/30.25 ( ![X4:$i,X6:$o,X8:$i]: 230.26/30.25 ( ( in @ X8 @ X4 ) => 230.26/30.25 ( ![X10:$i]: 230.26/30.25 ( ( in @ X10 @ X4 ) => 230.26/30.25 ( ( X6 ) => 230.26/30.25 ( in @ 230.26/30.25 X8 @ 230.26/30.25 ( dsetconstr @ 230.26/30.25 X4 @ 230.26/30.25 ( ^[V_1:$i]: 230.26/30.25 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) | 230.26/30.25 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) ) ) ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(iffalseProp2, axiom, iffalseProp2 = 230.26/30.25 (![A:$i,Xphi:$o,Xx:$i]: 230.26/30.25 ( ( in @ Xx @ A ) => 230.26/30.25 ( ![Xy:$i]: 230.26/30.25 ( ( in @ Xy @ A ) => 230.26/30.25 ( ( ~( Xphi ) ) => 230.26/30.25 ( ( dsetconstr @ 230.26/30.25 A @ 230.26/30.25 ( ^[Xz:$i]: 230.26/30.25 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) | 230.26/30.25 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) = 230.26/30.25 ( setadjoin @ Xy @ emptyset ) ) ) ) ) ))). 230.26/30.25 thf('1', plain, 230.26/30.25 (( iffalseProp2 ) = 230.26/30.25 ( ![X4:$i,X6:$o,X8:$i]: 230.26/30.25 ( ( in @ X8 @ X4 ) => 230.26/30.25 ( ![X10:$i]: 230.26/30.25 ( ( in @ X10 @ X4 ) => 230.26/30.25 ( ( ~( X6 ) ) => 230.26/30.25 ( ( dsetconstr @ 230.26/30.25 X4 @ 230.26/30.25 ( ^[V_1:$i]: 230.26/30.25 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) | 230.26/30.25 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) = 230.26/30.25 ( setadjoin @ X10 @ emptyset ) ) ) ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(iffalseProp1, axiom, iffalseProp1 = 230.26/30.25 (![A:$i,Xphi:$o,Xx:$i]: 230.26/30.25 ( ( in @ Xx @ A ) => 230.26/30.25 ( ![Xy:$i]: 230.26/30.25 ( ( in @ Xy @ A ) => 230.26/30.25 ( ( ~( Xphi ) ) => 230.26/30.25 ( in @ 230.26/30.25 Xy @ 230.26/30.25 ( dsetconstr @ 230.26/30.25 A @ 230.26/30.25 ( ^[Xz:$i]: 230.26/30.25 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) | 230.26/30.25 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) ) ) ) ) ))). 230.26/30.25 thf('2', plain, 230.26/30.25 (( iffalseProp1 ) = 230.26/30.25 ( ![X4:$i,X6:$o,X8:$i]: 230.26/30.25 ( ( in @ X8 @ X4 ) => 230.26/30.25 ( ![X10:$i]: 230.26/30.25 ( ( in @ X10 @ X4 ) => 230.26/30.25 ( ( ~( X6 ) ) => 230.26/30.25 ( in @ 230.26/30.25 X10 @ 230.26/30.25 ( dsetconstr @ 230.26/30.25 X4 @ 230.26/30.25 ( ^[V_1:$i]: 230.26/30.25 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) | 230.26/30.25 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) ) ) ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setukpairinjR2, axiom, setukpairinjR2 = 230.26/30.25 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]: 230.26/30.25 ( ( ( setadjoin @ 230.26/30.25 ( setadjoin @ Xx @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) = 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ Xz @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) => 230.26/30.25 ( ( Xy ) = ( Xu ) ) ))). 230.26/30.25 thf('3', plain, 230.26/30.25 (( setukpairinjR2 ) = 230.26/30.25 ( ![X4:$i,X6:$i,X8:$i,X10:$i]: 230.26/30.25 ( ( ( setadjoin @ 230.26/30.25 ( setadjoin @ X4 @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) = 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ X8 @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) => 230.26/30.25 ( ( X6 ) = ( X10 ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(upairequniteq, axiom, upairequniteq = 230.26/30.25 (![Xx:$i,Xy:$i,Xz:$i]: 230.26/30.25 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) = 230.26/30.25 ( setadjoin @ Xz @ emptyset ) ) => 230.26/30.25 ( ( Xx ) = ( Xy ) ) ))). 230.26/30.25 thf('4', plain, 230.26/30.25 (( upairequniteq ) = 230.26/30.25 ( ![X4:$i,X6:$i,X8:$i]: 230.26/30.25 ( ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) = 230.26/30.25 ( setadjoin @ X8 @ emptyset ) ) => 230.26/30.25 ( ( X4 ) = ( X6 ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setukpairinjR1, axiom, setukpairinjR1 = 230.26/30.25 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]: 230.26/30.25 ( ( ( setadjoin @ 230.26/30.25 ( setadjoin @ Xx @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) = 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ Xz @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) => 230.26/30.25 ( ( ( Xz ) = ( Xu ) ) => ( ( Xy ) = ( Xu ) ) ) ))). 230.26/30.25 thf('5', plain, 230.26/30.25 (( setukpairinjR1 ) = 230.26/30.25 ( ![X4:$i,X6:$i,X8:$i,X10:$i]: 230.26/30.25 ( ( ( setadjoin @ 230.26/30.25 ( setadjoin @ X4 @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) = 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ X8 @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) => 230.26/30.25 ( ( ( X8 ) = ( X10 ) ) => ( ( X6 ) = ( X10 ) ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setukpairinjR12, axiom, setukpairinjR12 = 230.26/30.25 (![Xx:$i,Xy:$i]: 230.26/30.25 ( ( ( Xx ) = ( Xy ) ) => 230.26/30.25 ( ( setadjoin @ 230.26/30.25 ( setadjoin @ Xx @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) = 230.26/30.25 ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ))). 230.26/30.25 thf('6', plain, 230.26/30.25 (( setukpairinjR12 ) = 230.26/30.25 ( ![X4:$i,X6:$i]: 230.26/30.25 ( ( ( X4 ) = ( X6 ) ) => 230.26/30.25 ( ( setadjoin @ 230.26/30.25 ( setadjoin @ X4 @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) = 230.26/30.25 ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ emptyset ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setukpairinjR11, axiom, setukpairinjR11 = 230.26/30.25 (![Xx:$i,Xy:$i]: 230.26/30.25 ( ( ( Xx ) = ( Xy ) ) => 230.26/30.25 ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) = 230.26/30.25 ( setadjoin @ Xx @ emptyset ) ) ))). 230.26/30.25 thf('7', plain, 230.26/30.25 (( setukpairinjR11 ) = 230.26/30.25 ( ![X4:$i,X6:$i]: 230.26/30.25 ( ( ( X4 ) = ( X6 ) ) => 230.26/30.25 ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) = 230.26/30.25 ( setadjoin @ X4 @ emptyset ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setukpairinjL2, axiom, setukpairinjL2 = 230.26/30.25 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]: 230.26/30.25 ( ( ( setadjoin @ 230.26/30.25 ( setadjoin @ Xx @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) = 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ Xz @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) => 230.26/30.25 ( ( Xx ) = ( Xz ) ) ))). 230.26/30.25 thf('8', plain, 230.26/30.25 (( setukpairinjL2 ) = 230.26/30.25 ( ![X4:$i,X6:$i,X8:$i,X10:$i]: 230.26/30.25 ( ( ( setadjoin @ 230.26/30.25 ( setadjoin @ X4 @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) = 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ X8 @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) => 230.26/30.25 ( ( X4 ) = ( X8 ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setukpairinjL1, axiom, setukpairinjL1 = 230.26/30.25 (![Xx:$i,Xy:$i,Xz:$i]: 230.26/30.25 ( ( in @ 230.26/30.25 ( setadjoin @ Xz @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ Xx @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) => 230.26/30.25 ( ( Xx ) = ( Xz ) ) ))). 230.26/30.25 thf('9', plain, 230.26/30.25 (( setukpairinjL1 ) = 230.26/30.25 ( ![X4:$i,X6:$i,X8:$i]: 230.26/30.25 ( ( in @ 230.26/30.25 ( setadjoin @ X8 @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ X4 @ emptyset ) @ 230.26/30.25 ( setadjoin @ 230.26/30.25 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) => 230.26/30.25 ( ( X4 ) = ( X8 ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(singletonsuniq, axiom, singletonsuniq = 230.26/30.25 (![Xx:$i,Xy:$i]: 230.26/30.25 ( ( ( setadjoin @ Xx @ emptyset ) = ( setadjoin @ Xy @ emptyset ) ) => 230.26/30.25 ( ( Xx ) = ( Xy ) ) ))). 230.26/30.25 thf('10', plain, 230.26/30.25 (( singletonsuniq ) = 230.26/30.25 ( ![X4:$i,X6:$i]: 230.26/30.25 ( ( ( setadjoin @ X4 @ emptyset ) = ( setadjoin @ X6 @ emptyset ) ) => 230.26/30.25 ( ( X4 ) = ( X6 ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(upairset2E, axiom, upairset2E = 230.26/30.25 (![Xx:$i,Xy:$i,Xz:$i]: 230.26/30.25 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) => 230.26/30.25 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))). 230.26/30.25 thf('11', plain, 230.26/30.25 (( upairset2E ) = 230.26/30.25 ( ![X4:$i,X6:$i,X8:$i]: 230.26/30.25 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) => 230.26/30.25 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(secondinupair, axiom, secondinupair = 230.26/30.25 (![Xx:$i,Xy:$i]: 230.26/30.25 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 230.26/30.25 thf('12', plain, 230.26/30.25 (( secondinupair ) = 230.26/30.25 ( ![X4:$i,X6:$i]: 230.26/30.25 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(upairset2IR, axiom, upairset2IR = 230.26/30.25 (![Xx:$i,Xy:$i]: 230.26/30.25 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 230.26/30.25 thf('13', plain, 230.26/30.25 (( upairset2IR ) = 230.26/30.25 ( ![X4:$i,X6:$i]: 230.26/30.25 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(sepSubset, axiom, sepSubset = 230.26/30.25 (![A:$i,Xphi:( $i > $o )]: 230.26/30.25 ( subset @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ A ))). 230.26/30.25 thf('14', plain, 230.26/30.25 (( sepSubset ) = 230.26/30.25 ( ![X4:$i,X6:( $i > $o )]: 230.26/30.25 ( subset @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @ X4 ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(sepInPowerset, axiom, sepInPowerset = 230.26/30.25 (![A:$i,Xphi:( $i > $o )]: 230.26/30.25 ( in @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ ( powerset @ A ) ))). 230.26/30.25 thf('15', plain, 230.26/30.25 (( sepInPowerset ) = 230.26/30.25 ( ![X4:$i,X6:( $i > $o )]: 230.26/30.25 ( in @ 230.26/30.25 ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @ 230.26/30.25 ( powerset @ X4 ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(dsetconstr__Cong, axiom, dsetconstr__Cong = 230.26/30.25 (![A:$i,B:$i]: 230.26/30.25 ( ( ( A ) = ( B ) ) => 230.26/30.25 ( ![Xphi:( $i > $o ),Xpsi:( $i > $o )]: 230.26/30.25 ( ( ![Xx:$i]: 230.26/30.25 ( ( in @ Xx @ A ) => 230.26/30.25 ( ![Xy:$i]: 230.26/30.25 ( ( in @ Xy @ B ) => 230.26/30.25 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) ) ) ) => 230.26/30.25 ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) = 230.26/30.25 ( dsetconstr @ B @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ) ) ))). 230.26/30.25 thf('16', plain, 230.26/30.25 (( dsetconstr__Cong ) = 230.26/30.25 ( ![X4:$i,X6:$i]: 230.26/30.25 ( ( ( X4 ) = ( X6 ) ) => 230.26/30.25 ( ![X8:( $i > $o ),X10:( $i > $o )]: 230.26/30.25 ( ( ![X12:$i]: 230.26/30.25 ( ( in @ X12 @ X4 ) => 230.26/30.25 ( ![X14:$i]: 230.26/30.25 ( ( in @ X14 @ X6 ) => 230.26/30.25 ( ( ( X12 ) = ( X14 ) ) => 230.26/30.25 ( ( X8 @ X12 ) <=> ( X10 @ X14 ) ) ) ) ) ) ) => 230.26/30.25 ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) = 230.26/30.25 ( dsetconstr @ X6 @ ( ^[V_2:$i]: ( X10 @ V_2 ) ) ) ) ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setadjoin__Cong, axiom, setadjoin__Cong = 230.26/30.25 (![Xx:$i,Xy:$i]: 230.26/30.25 ( ( ( Xx ) = ( Xy ) ) => 230.26/30.25 ( ![Xz:$i,Xu:$i]: 230.26/30.25 ( ( ( Xz ) = ( Xu ) ) => 230.26/30.25 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))). 230.26/30.25 thf('17', plain, 230.26/30.25 (( setadjoin__Cong ) = 230.26/30.25 ( ![X4:$i,X6:$i]: 230.26/30.25 ( ( ( X4 ) = ( X6 ) ) => 230.26/30.25 ( ![X8:$i,X10:$i]: 230.26/30.25 ( ( ( X8 ) = ( X10 ) ) => 230.26/30.25 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(emptyE1, axiom, emptyE1 = 230.26/30.25 (![A:$i,Xphi:( $i > $o )]: 230.26/30.25 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) => 230.26/30.25 ( ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) = ( emptyset ) ) => 230.26/30.25 ( $false ) ) ))). 230.26/30.25 thf('18', plain, 230.26/30.25 (( emptyE1 ) = 230.26/30.25 ( ![X4:$i,X6:( $i > $o )]: 230.26/30.25 ( ( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) => 230.26/30.25 ( ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = ( emptyset ) ) => 230.26/30.25 ( $false ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(upairsetIR, axiom, upairsetIR = 230.26/30.25 (![Xx:$i,Xy:$i]: 230.26/30.25 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 230.26/30.25 thf('19', plain, 230.26/30.25 (( upairsetIR ) = 230.26/30.25 ( ![X4:$i,X6:$i]: 230.26/30.25 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(upairsetIL, axiom, upairsetIL = 230.26/30.25 (![Xx:$i,Xy:$i]: 230.26/30.25 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 230.26/30.25 thf('20', plain, 230.26/30.25 (( upairsetIL ) = 230.26/30.25 ( ![X4:$i,X6:$i]: 230.26/30.25 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(upairsetE, axiom, upairsetE = 230.26/30.25 (![Xx:$i,Xy:$i,Xz:$i]: 230.26/30.25 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) => 230.26/30.25 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))). 230.26/30.25 thf('21', plain, 230.26/30.25 (( upairsetE ) = 230.26/30.25 ( ![X4:$i,X6:$i,X8:$i]: 230.26/30.25 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) => 230.26/30.25 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(singletonsswitch, axiom, singletonsswitch = 230.26/30.25 (![Xx:$i,Xy:$i]: 230.26/30.25 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => 230.26/30.25 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))). 230.26/30.25 thf('22', plain, 230.26/30.25 (( singletonsswitch ) = 230.26/30.25 ( ![X4:$i,X6:$i]: 230.26/30.25 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => 230.26/30.25 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(eqinunit, axiom, eqinunit = 230.26/30.25 (![Xx:$i,Xy:$i]: 230.26/30.25 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 230.26/30.25 thf('23', plain, 230.26/30.25 (( eqinunit ) = 230.26/30.25 ( ![X4:$i,X6:$i]: 230.26/30.25 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(notinsingleton, axiom, notinsingleton = 230.26/30.25 (![Xx:$i,Xy:$i]: 230.26/30.25 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))). 230.26/30.25 thf('24', plain, 230.26/30.25 (( notinsingleton ) = 230.26/30.25 ( ![X4:$i,X6:$i]: 230.26/30.25 ( ( ( X4 ) != ( X6 ) ) => 230.26/30.25 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(uniqinunit, axiom, uniqinunit = 230.26/30.25 (![Xx:$i,Xy:$i]: 230.26/30.25 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))). 230.26/30.25 thf('25', plain, 230.26/30.25 (( uniqinunit ) = 230.26/30.25 ( ![X4:$i,X6:$i]: 230.26/30.25 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setoftrueEq, axiom, setoftrueEq = 230.26/30.25 (![A:$i]: ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( $true ) ) ) = ( A ) ))). 230.26/30.25 thf('26', plain, 230.26/30.25 (( setoftrueEq ) = 230.26/30.25 ( ![X4:$i]: ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( $true ) ) ) = ( X4 ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setadjoinOr, axiom, setadjoinOr = 230.26/30.25 (![Xx:$i,A:$i,Xy:$i]: 230.26/30.25 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) => 230.26/30.25 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))). 230.26/30.25 thf('27', plain, 230.26/30.25 (( setadjoinOr ) = 230.26/30.25 ( ![X4:$i,X6:$i,X8:$i]: 230.26/30.25 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) => 230.26/30.25 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setadjoinE, axiom, setadjoinE = 230.26/30.25 (![Xx:$i,A:$i,Xy:$i]: 230.26/30.25 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) => 230.26/30.25 ( ![Xphi:$o]: 230.26/30.25 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) => 230.26/30.25 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))). 230.26/30.25 thf('28', plain, 230.26/30.25 (( setadjoinE ) = 230.26/30.25 ( ![X4:$i,X6:$i,X8:$i]: 230.26/30.25 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) => 230.26/30.25 ( ![X10:$o]: 230.26/30.25 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) => 230.26/30.25 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setadjoinIR, axiom, setadjoinIR = 230.26/30.25 (![Xx:$i,A:$i,Xy:$i]: 230.26/30.25 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))). 230.26/30.25 thf('29', plain, 230.26/30.25 (( setadjoinIR ) = 230.26/30.25 ( ![X4:$i,X6:$i,X8:$i]: 230.26/30.25 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(emptyinunitempty, axiom,(( emptyinunitempty ) = 230.26/30.25 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))). 230.26/30.25 thf('30', plain, 230.26/30.25 (( emptyinunitempty ) = 230.26/30.25 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )), 230.26/30.25 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])). 230.26/30.25 thf('31', plain, 230.26/30.25 (( emptyinunitempty ) = 230.26/30.25 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setadjoinIL, axiom, setadjoinIL = 230.26/30.25 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))). 230.26/30.25 thf('32', plain, 230.26/30.25 (( setadjoinIL ) = 230.26/30.25 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setbeta, axiom, setbeta = 230.26/30.25 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 230.26/30.25 ( ( in @ Xx @ A ) => 230.26/30.25 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) <=> 230.26/30.25 ( Xphi @ Xx ) ) ))). 230.26/30.25 thf('33', plain, 230.26/30.25 (( setbeta ) = 230.26/30.25 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 230.26/30.25 ( ( in @ X8 @ X4 ) => 230.26/30.25 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=> 230.26/30.25 ( X6 @ X8 ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(dsetconstrER, axiom, dsetconstrER = 230.26/30.25 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 230.26/30.25 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) => 230.26/30.25 ( Xphi @ Xx ) ))). 230.26/30.25 thf('34', plain, 230.26/30.25 (( dsetconstrER ) = 230.26/30.25 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 230.26/30.25 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 230.26/30.25 ( X6 @ X8 ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(dsetconstrEL, axiom, dsetconstrEL = 230.26/30.25 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 230.26/30.25 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) => 230.26/30.25 ( in @ Xx @ A ) ))). 230.26/30.25 thf('35', plain, 230.26/30.25 (( dsetconstrEL ) = 230.26/30.25 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 230.26/30.25 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 230.26/30.25 ( in @ X8 @ X4 ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(dsetconstrI, axiom, dsetconstrI = 230.26/30.25 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 230.26/30.25 ( ( in @ Xx @ A ) => 230.26/30.25 ( ( Xphi @ Xx ) => 230.26/30.25 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))). 230.26/30.25 thf('36', plain, 230.26/30.25 (( dsetconstrI ) = 230.26/30.25 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 230.26/30.25 ( ( in @ X8 @ X4 ) => 230.26/30.25 ( ( X6 @ X8 ) => 230.26/30.25 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(setadjoinAx, axiom, setadjoinAx = 230.26/30.25 (![Xx:$i,A:$i,Xy:$i]: 230.26/30.25 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=> 230.26/30.25 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))). 230.26/30.25 thf('37', plain, 230.26/30.25 (( setadjoinAx ) = 230.26/30.25 ( ![X4:$i,X6:$i,X8:$i]: 230.26/30.25 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 230.26/30.25 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )), 230.26/30.25 define([status(thm)])). 230.26/30.25 thf(iftrueProp2, conjecture, 230.26/30.25 (( setextAx ) => 230.26/30.25 ( ( emptysetAx ) => 230.26/30.25 ( ( setadjoinAx ) => 230.26/30.25 ( ( powersetAx ) => 230.26/30.25 ( ( setunionAx ) => 230.26/30.25 ( ( omega0Ax ) => 230.26/30.25 ( ( omegaSAx ) => 230.26/30.25 ( ( omegaIndAx ) => 230.26/30.25 ( ( replAx ) => 230.26/30.25 ( ( foundationAx ) => 230.26/30.25 ( ( wellorderingAx ) => 230.26/30.25 ( ( descrp ) => 230.26/30.25 ( ( dsetconstrI ) => 230.26/30.25 ( ( dsetconstrEL ) => 230.26/30.25 ( ( dsetconstrER ) => 230.26/30.25 ( ( exuE1 ) => 230.26/30.25 ( ( prop2setE ) => 230.26/30.25 ( ( emptysetE ) => 230.26/30.25 ( ( emptysetimpfalse ) => 230.26/30.25 ( ( notinemptyset ) => 230.26/30.25 ( ( exuE3e ) => 230.26/30.25 ( ( setext ) => 230.26/30.25 ( ( emptyI ) => 230.26/30.25 ( ( noeltsimpempty ) => 230.26/30.25 ( ( setbeta ) => 230.26/30.25 ( ( nonemptyE1 ) => 230.26/30.25 ( ( nonemptyI ) => 230.26/30.25 ( ( nonemptyI1 ) => 230.26/30.25 ( ( setadjoinIL ) => 230.26/30.25 ( ( emptyinunitempty ) => 230.26/30.25 ( ( setadjoinIR ) => 230.26/30.25 ( ( setadjoinE ) => 230.26/30.25 ( ( 230.26/30.25 setadjoinOr ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setoftrueEq ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 powersetI ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 emptyinPowerset ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 emptyInPowerset ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 powersetE ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setunionI ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setunionE ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 subPowSU ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 exuE2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 nonemptyImpWitness ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 uniqinunit ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 notinsingleton ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 eqinunit ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 singletonsswitch ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 upairsetE ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 upairsetIL ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 upairsetIR ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 emptyE1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 vacuousDall ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 quantDeMorgan1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 quantDeMorgan2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 quantDeMorgan3 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 quantDeMorgan4 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 prop2setI ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 prop2set2propI ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 notdexE ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 notdallE ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 exuI1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 exuI3 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 exuI2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 inCongP ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 in__Cong ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 exuE3u ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 exu__Cong ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 emptyset__Cong ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setadjoin__Cong ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 powerset__Cong ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setunion__Cong ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 omega__Cong ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 exuEu ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 descr__Cong ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 dsetconstr__Cong ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 subsetI1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 eqimpsubset2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 eqimpsubset1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 subsetI2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 emptysetsubset ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 subsetE ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 subsetE2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 notsubsetI ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 notequalI1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 notequalI2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 subsetRefl ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 subsetTrans ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setadjoinSub ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setadjoinSub2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 subset2powerset ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setextsub ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 subsetemptysetimpeq ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 powersetI1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 powersetE1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 inPowerset ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 powersetsubset ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 sepInPowerset ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 sepSubset ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binunionIL ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 upairset2IR ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binunionIR ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binunionEcases ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binunionE ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binunionLsub ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binunionRsub ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binintersectI ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binintersectSubset5 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binintersectEL ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binintersectLsub ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binintersectSubset2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binintersectSubset3 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binintersectER ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 disjointsetsI1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binintersectRsub ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binintersectSubset4 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 binintersectSubset1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 bs114d ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setminusI ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setminusEL ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setminusER ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setminusSubset2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setminusERneg ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setminusELneg ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setminusILneg ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setminusIRneg ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setminusLsub ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setminusSubset1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 symdiffE ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 symdiffI1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 symdiffI2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 symdiffIneg1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 symdiffIneg2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 secondinupair ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setukpairIL ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setukpairIR ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 kpairiskpair ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 kpairp ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 singletonsubset ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 singletoninpowerset ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 singletoninpowunion ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 upairset2E ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 upairsubunion ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 upairinpowunion ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ubforcartprodlem1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ubforcartprodlem2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ubforcartprodlem3 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 cartprodpairin ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 cartprodmempair1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 cartprodmempair ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setunionE2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setunionsingleton1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setunionsingleton2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setunionsingleton ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 singletonprop ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ex1E1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ex1I ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ex1I2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 singletonsuniq ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setukpairinjL1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 kfstsingleton ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 theprop ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 kfstpairEq ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 cartprodfstin ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setukpairinjL2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setukpairinjL ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setukpairinjR11 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setukpairinjR12 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setukpairinjR1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 upairequniteq ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setukpairinjR2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setukpairinjR ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ksndsingleton ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ksndpairEq ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 kpairsurjEq ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 cartprodsndin ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 cartprodpairmemEL ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 cartprodpairmemER ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 cartprodmempaircEq ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 cartprodfstpairEq ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 cartprodsndpairEq ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 cartprodpairsurjEq ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 dpsetconstrI ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 dpsetconstrSub ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 setOfPairsIsBReln ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 dpsetconstrERa ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 dpsetconstrEL1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 dpsetconstrEL2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 dpsetconstrER ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 funcImageSingleton ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 apProp ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 app ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 infuncsetfunc ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ap2p ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 funcinfuncset ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 lamProp ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 lamp ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 lam2p ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 brelnall1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 brelnall2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ex1E2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 funcGraphProp1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 funcGraphProp3 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 funcGraphProp2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 funcextLem ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 funcGraphProp4 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 subbreln ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 eqbreln ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 funcext ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 funcext2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ap2apEq1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ap2apEq2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 beta1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 eta1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 lam2lamEq ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 beta2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 eta2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 iffalseProp1 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 iffalseProp2 ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 iftrueProp1 ) => 230.26/30.25 ( 230.26/30.25 ![ 230.26/30.25 A:$i, 230.26/30.25 Xphi:$o, 230.26/30.25 Xx:$i]: 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 in @ 230.26/30.25 Xx @ A ) => 230.26/30.25 ( 230.26/30.25 ![ 230.26/30.25 Xy:$i]: 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 in @ 230.26/30.25 Xy @ A ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 Xphi ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 dsetconstr 230.26/30.25 @ 230.26/30.25 A @ 230.26/30.25 ( 230.26/30.25 ^[ 230.26/30.25 Xz:$i]: 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 Xz ) = 230.26/30.25 ( 230.26/30.25 Xy ) ) & 230.26/30.25 ( 230.26/30.25 ~( Xphi ) ) ) | 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 Xphi ) & 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 Xz ) = 230.26/30.25 ( 230.26/30.25 Xx ) ) ) ) ) ) = 230.26/30.25 ( 230.26/30.25 setadjoin 230.26/30.25 @ 230.26/30.25 Xx @ 230.26/30.25 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 230.26/30.25 thf(zf_stmt_0, conjecture, 230.26/30.25 (( setextAx ) => 230.26/30.25 ( ( emptysetAx ) => 230.26/30.25 ( ( ![X4:$i,X6:$i,X8:$i]: 230.26/30.25 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 230.26/30.25 ( ( in @ X8 @ X6 ) | ( ( X8 ) = ( X4 ) ) ) ) ) => 230.26/30.25 ( ( powersetAx ) => 230.26/30.25 ( ( setunionAx ) => 230.26/30.25 ( ( omega0Ax ) => 230.26/30.25 ( ( omegaSAx ) => 230.26/30.25 ( ( omegaIndAx ) => 230.26/30.25 ( ( replAx ) => 230.26/30.25 ( ( foundationAx ) => 230.26/30.25 ( ( wellorderingAx ) => 230.26/30.25 ( ( descrp ) => 230.26/30.25 ( ( ![X10:$i,X12:( $i > $o ),X14:$i]: 230.26/30.25 ( ( in @ X14 @ X10 ) => 230.26/30.25 ( ( X12 @ X14 ) => 230.26/30.25 ( in @ 230.26/30.25 X14 @ 230.26/30.25 ( dsetconstr @ 230.26/30.25 X10 @ ( ^[V_1:$i]: ( X12 @ V_1 ) ) ) ) ) ) ) => 230.26/30.25 ( ( ![X16:$i,X18:( $i > $o ),X20:$i]: 230.26/30.25 ( ( in @ 230.26/30.25 X20 @ 230.26/30.25 ( dsetconstr @ 230.26/30.25 X16 @ ( ^[V_2:$i]: ( X18 @ V_2 ) ) ) ) => 230.26/30.25 ( in @ X20 @ X16 ) ) ) => 230.26/30.25 ( ( ![X22:$i,X24:( $i > $o ),X26:$i]: 230.26/30.25 ( ( in @ 230.26/30.25 X26 @ 230.26/30.25 ( dsetconstr @ 230.26/30.25 X22 @ ( ^[V_3:$i]: ( X24 @ V_3 ) ) ) ) => 230.26/30.25 ( X24 @ X26 ) ) ) => 230.26/30.25 ( ( exuE1 ) => 230.26/30.25 ( ( prop2setE ) => 230.26/30.25 ( ( emptysetE ) => 230.26/30.25 ( ( emptysetimpfalse ) => 230.26/30.25 ( ( notinemptyset ) => 230.26/30.25 ( ( exuE3e ) => 230.26/30.25 ( ( setext ) => 230.26/30.25 ( ( emptyI ) => 230.26/30.25 ( ( noeltsimpempty ) => 230.26/30.25 ( ( ![X28:$i, 230.26/30.25 X30:( $i > $o ),X32:$i]: 230.26/30.25 ( ( in @ X32 @ X28 ) => 230.26/30.25 ( ( in @ 230.26/30.25 X32 @ 230.26/30.25 ( dsetconstr @ 230.26/30.25 X28 @ 230.26/30.25 ( ^[V_4:$i]: 230.26/30.25 ( X30 @ V_4 ) ) ) ) <=> 230.26/30.25 ( X30 @ X32 ) ) ) ) => 230.26/30.25 ( ( nonemptyE1 ) => 230.26/30.25 ( ( nonemptyI ) => 230.26/30.25 ( ( nonemptyI1 ) => 230.26/30.25 ( ( ![X34:$i,X36:$i]: 230.26/30.25 ( in @ 230.26/30.25 X34 @ 230.26/30.25 ( setadjoin @ 230.26/30.25 X34 @ X36 ) ) ) => 230.26/30.25 ( ( in @ 230.26/30.25 emptyset @ 230.26/30.25 ( setadjoin @ 230.26/30.25 emptyset @ 230.26/30.25 emptyset ) ) => 230.26/30.25 ( ( ![X38:$i, 230.26/30.25 X40:$i, 230.26/30.25 X42:$i]: 230.26/30.25 ( ( 230.26/30.25 in @ 230.26/30.25 X42 @ X40 ) => 230.26/30.25 ( 230.26/30.25 in @ 230.26/30.25 X42 @ 230.26/30.25 ( 230.26/30.25 setadjoin 230.26/30.25 @ 230.26/30.25 X38 @ X40 ) ) ) ) => 230.26/30.25 ( ( ![ 230.26/30.25 X44:$i, 230.26/30.25 X46:$i, 230.26/30.25 X48:$i]: 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 in @ 230.26/30.25 X48 @ 230.26/30.25 ( 230.26/30.25 setadjoin 230.26/30.25 @ 230.26/30.25 X44 @ X46 ) ) => 230.26/30.25 ( 230.26/30.25 ![ 230.26/30.25 X50:$o]: 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 X48 ) = 230.26/30.25 ( 230.26/30.25 X44 ) ) => 230.26/30.25 ( 230.26/30.25 X50 ) ) => 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 ( 230.26/30.25 in @ 230.26/30.25 X48 @ X46 ) => 230.26/30.25 ( 230.26/30.25 X50 ) ) => 230.26/30.25 ( 230.26/30.25 X50 ) ) ) ) ) ) => 230.26/30.25 ( ( 230.26/30.25 ![ 230.26/30.25 X52:$i, 230.26/30.25 X54:$i, 230.26/30.26 X56:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X56 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X52 @ X54 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X56 @ X54 ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X56 ) = 230.26/30.26 ( 230.26/30.26 X52 ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X58:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X58 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_5:$i]: 230.26/30.26 ( 230.26/30.26 $true ) ) ) = 230.26/30.26 ( 230.26/30.26 X58 ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 emptyinPowerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 emptyInPowerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subPowSU ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuE2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 nonemptyImpWitness ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X60:$i, 230.26/30.26 X62:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X60 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X62 @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X60 ) = 230.26/30.26 ( 230.26/30.26 X62 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X64:$i, 230.26/30.26 X66:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X64 ) != 230.26/30.26 ( 230.26/30.26 X66 ) ) => 230.26/30.26 ( 230.26/30.26 ~( 230.26/30.26 in @ 230.26/30.26 X66 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X64 @ 230.26/30.26 emptyset ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X68:$i, 230.26/30.26 X70:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X68 ) = 230.26/30.26 ( 230.26/30.26 X70 ) ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X68 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X70 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X72:$i, 230.26/30.26 X74:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X72 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X74 @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X74 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X72 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X76:$i, 230.26/30.26 X78:$i, 230.26/30.26 X80:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X80 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X76 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X78 @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X80 ) = 230.26/30.26 ( 230.26/30.26 X78 ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X80 ) = 230.26/30.26 ( 230.26/30.26 X76 ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X82:$i, 230.26/30.26 X84:$i]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X82 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X82 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X84 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X86:$i, 230.26/30.26 X88:$i]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X88 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X86 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X88 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X90:$i, 230.26/30.26 X92:( 230.26/30.26 $i > $o )]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ?[ 230.26/30.26 X94:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X94 @ X90 ) & 230.26/30.26 ( 230.26/30.26 X92 @ X94 ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X90 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_6:$i]: 230.26/30.26 ( 230.26/30.26 X92 @ V_6 ) ) ) = 230.26/30.26 ( 230.26/30.26 emptyset ) ) => 230.26/30.26 ( 230.26/30.26 $false ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 vacuousDall ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 quantDeMorgan1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 quantDeMorgan2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 quantDeMorgan3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 quantDeMorgan4 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 prop2setI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 prop2set2propI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notdexE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notdallE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuI3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuI2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 inCongP ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuE3u ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exu__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 emptyset__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X96:$i, 230.26/30.26 X98:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X96 ) = 230.26/30.26 ( 230.26/30.26 X98 ) ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X100:$i, 230.26/30.26 X102:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X100 ) = 230.26/30.26 ( 230.26/30.26 X102 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X96 @ X100 ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X98 @ X102 ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powerset__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunion__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 omega__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuEu ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 descr__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X104:$i, 230.26/30.26 X106:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X104 ) = 230.26/30.26 ( 230.26/30.26 X106 ) ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X108:( 230.26/30.26 $i > $o ), 230.26/30.26 X110:( 230.26/30.26 $i > $o )]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X112:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X112 @ 230.26/30.26 X104 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X114:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X114 @ 230.26/30.26 X106 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X112 ) = 230.26/30.26 ( 230.26/30.26 X114 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X108 @ 230.26/30.26 X112 ) <=> 230.26/30.26 ( 230.26/30.26 X110 @ 230.26/30.26 X114 ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X104 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_7:$i]: 230.26/30.26 ( 230.26/30.26 X108 @ V_7 ) ) ) = 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X106 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_8:$i]: 230.26/30.26 ( 230.26/30.26 X110 @ V_8 ) ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eqimpsubset2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eqimpsubset1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetI2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 emptysetsubset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetE2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notsubsetI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notequalI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notequalI2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetRefl ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetTrans ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoinSub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoinSub2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subset2powerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setextsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetemptysetimpeq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetE1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 inPowerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetsubset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X116:$i, 230.26/30.26 X118:( 230.26/30.26 $i > $o )]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X116 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_9:$i]: 230.26/30.26 ( 230.26/30.26 X118 @ V_9 ) ) ) @ 230.26/30.26 ( 230.26/30.26 powerset @ 230.26/30.26 X116 ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X120:$i, 230.26/30.26 X122:( 230.26/30.26 $i > $o )]: 230.26/30.26 ( 230.26/30.26 subset @ 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X120 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_10:$i]: 230.26/30.26 ( 230.26/30.26 X122 @ 230.26/30.26 V_10 ) ) ) @ 230.26/30.26 X120 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionIL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X124:$i, 230.26/30.26 X126:$i]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X126 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X124 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X126 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionIR ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionEcases ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionLsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionRsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset5 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectEL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectLsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectER ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 disjointsetsI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectRsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset4 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 bs114d ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusEL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusER ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusSubset2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusERneg ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusELneg ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusILneg ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusIRneg ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusLsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusSubset1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffI2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffIneg1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffIneg2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X128:$i, 230.26/30.26 X130:$i]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X130 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X128 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X130 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setukpairIL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setukpairIR ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kpairiskpair ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kpairp ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 singletonsubset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 singletoninpowerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 singletoninpowunion ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X132:$i, 230.26/30.26 X134:$i, 230.26/30.26 X136:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X136 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X132 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X134 @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X136 ) = 230.26/30.26 ( 230.26/30.26 X134 ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X136 ) = 230.26/30.26 ( 230.26/30.26 X132 ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 upairsubunion ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 upairinpowunion ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ubforcartprodlem1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ubforcartprodlem2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ubforcartprodlem3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodpairin ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodmempair1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodmempair ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionE2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionsingleton1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionsingleton2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionsingleton ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 singletonprop ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ex1E1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ex1I ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ex1I2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X138:$i, 230.26/30.26 X140:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X138 @ 230.26/30.26 emptyset ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X140 @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X138 ) = 230.26/30.26 ( 230.26/30.26 X140 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X142:$i, 230.26/30.26 X144:$i, 230.26/30.26 X146:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X146 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X142 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X142 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X144 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X142 ) = 230.26/30.26 ( 230.26/30.26 X146 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kfstsingleton ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 theprop ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kfstpairEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodfstin ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X148:$i, 230.26/30.26 X150:$i, 230.26/30.26 X152:$i, 230.26/30.26 X154:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X148 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X148 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X150 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X152 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X152 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X154 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X148 ) = 230.26/30.26 ( 230.26/30.26 X152 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setukpairinjL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X156:$i, 230.26/30.26 X158:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X156 ) = 230.26/30.26 ( 230.26/30.26 X158 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X156 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X158 @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X156 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X160:$i, 230.26/30.26 X162:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X160 ) = 230.26/30.26 ( 230.26/30.26 X162 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X160 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X160 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X162 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X160 @ 230.26/30.26 emptyset ) @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X164:$i, 230.26/30.26 X166:$i, 230.26/30.26 X168:$i, 230.26/30.26 X170:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X164 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X164 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X166 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X168 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X168 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X170 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X168 ) = 230.26/30.26 ( 230.26/30.26 X170 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X166 ) = 230.26/30.26 ( 230.26/30.26 X170 ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X172:$i, 230.26/30.26 X174:$i, 230.26/30.26 X176:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X172 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X174 @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X176 @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X172 ) = 230.26/30.26 ( 230.26/30.26 X174 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X178:$i, 230.26/30.26 X180:$i, 230.26/30.26 X182:$i, 230.26/30.26 X184:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X178 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X178 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X180 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X182 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X182 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X184 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X180 ) = 230.26/30.26 ( 230.26/30.26 X184 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setukpairinjR ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ksndsingleton ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ksndpairEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kpairsurjEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodsndin ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodpairmemEL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodpairmemER ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodmempaircEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodfstpairEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodsndpairEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodpairsurjEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrSub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setOfPairsIsBReln ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrERa ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrEL1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrEL2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrER ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcImageSingleton ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 apProp ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 app ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 infuncsetfunc ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ap2p ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcinfuncset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 lamProp ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 lamp ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 lam2p ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 brelnall1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 brelnall2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ex1E2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcGraphProp1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcGraphProp3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcGraphProp2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcextLem ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcGraphProp4 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subbreln ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eqbreln ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcext ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcext2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ap2apEq1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ap2apEq2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 beta1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eta1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 lam2lamEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 beta2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eta2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X186:$i, 230.26/30.26 X188:$o, 230.26/30.26 X190:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X190 @ 230.26/30.26 X186 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X192:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X192 @ 230.26/30.26 X186 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ~( X188 ) ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X192 @ 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X186 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_11:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_11 ) = 230.26/30.26 ( 230.26/30.26 X192 ) ) & 230.26/30.26 ( 230.26/30.26 ~( X188 ) ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_11 ) = 230.26/30.26 ( 230.26/30.26 X190 ) ) & 230.26/30.26 ( 230.26/30.26 X188 ) ) ) ) ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X194:$i, 230.26/30.26 X196:$o, 230.26/30.26 X198:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X198 @ 230.26/30.26 X194 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X200:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X200 @ 230.26/30.26 X194 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ~( X196 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X194 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_12:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_12 ) = 230.26/30.26 ( 230.26/30.26 X200 ) ) & 230.26/30.26 ( 230.26/30.26 ~( X196 ) ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_12 ) = 230.26/30.26 ( 230.26/30.26 X198 ) ) & 230.26/30.26 ( 230.26/30.26 X196 ) ) ) ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X200 @ 230.26/30.26 emptyset ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X202:$i, 230.26/30.26 X204:$o, 230.26/30.26 X206:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X206 @ 230.26/30.26 X202 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X208:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X208 @ 230.26/30.26 X202 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X204 ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X206 @ 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X202 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_13:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_13 ) = 230.26/30.26 ( 230.26/30.26 X208 ) ) & 230.26/30.26 ( 230.26/30.26 ~( X204 ) ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_13 ) = 230.26/30.26 ( 230.26/30.26 X206 ) ) & 230.26/30.26 ( 230.26/30.26 X204 ) ) ) ) ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X210:$i, 230.26/30.26 X212:$o, 230.26/30.26 X214:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X214 @ 230.26/30.26 X210 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X216:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X216 @ 230.26/30.26 X210 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X212 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X210 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_14:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_14 ) = 230.26/30.26 ( 230.26/30.26 X214 ) ) & 230.26/30.26 ( 230.26/30.26 X212 ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ~( X212 ) ) & 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_14 ) = 230.26/30.26 ( 230.26/30.26 X216 ) ) ) ) ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X214 @ 230.26/30.26 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 230.26/30.26 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o). 230.26/30.26 thf(zf_stmt_2, axiom, 230.26/30.26 (![X8:$i,X6:$i,X4:$i]: 230.26/30.26 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=> 230.26/30.26 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ))). 230.26/30.26 thf(zf_stmt_3, conjecture, 230.26/30.26 (( setextAx ) => 230.26/30.26 ( ( emptysetAx ) => 230.26/30.26 ( ( ![X4:$i,X6:$i,X8:$i]: 230.26/30.26 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 230.26/30.26 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) => 230.26/30.26 ( ( powersetAx ) => 230.26/30.26 ( ( setunionAx ) => 230.26/30.26 ( ( omega0Ax ) => 230.26/30.26 ( ( omegaSAx ) => 230.26/30.26 ( ( omegaIndAx ) => 230.26/30.26 ( ( replAx ) => 230.26/30.26 ( ( foundationAx ) => 230.26/30.26 ( ( wellorderingAx ) => 230.26/30.26 ( ( descrp ) => 230.26/30.26 ( ( ![X10:$i,X12:( $i > $o ),X14:$i]: 230.26/30.26 ( ( in @ X14 @ X10 ) => 230.26/30.26 ( ( X12 @ X14 ) => 230.26/30.26 ( in @ 230.26/30.26 X14 @ 230.26/30.26 ( dsetconstr @ 230.26/30.26 X10 @ ( ^[V_1:$i]: ( X12 @ V_1 ) ) ) ) ) ) ) => 230.26/30.26 ( ( ![X16:$i,X18:( $i > $o ),X20:$i]: 230.26/30.26 ( ( in @ 230.26/30.26 X20 @ 230.26/30.26 ( dsetconstr @ 230.26/30.26 X16 @ ( ^[V_2:$i]: ( X18 @ V_2 ) ) ) ) => 230.26/30.26 ( in @ X20 @ X16 ) ) ) => 230.26/30.26 ( ( ![X22:$i,X24:( $i > $o ),X26:$i]: 230.26/30.26 ( ( in @ 230.26/30.26 X26 @ 230.26/30.26 ( dsetconstr @ 230.26/30.26 X22 @ ( ^[V_3:$i]: ( X24 @ V_3 ) ) ) ) => 230.26/30.26 ( X24 @ X26 ) ) ) => 230.26/30.26 ( ( exuE1 ) => 230.26/30.26 ( ( prop2setE ) => 230.26/30.26 ( ( emptysetE ) => 230.26/30.26 ( ( emptysetimpfalse ) => 230.26/30.26 ( ( notinemptyset ) => 230.26/30.26 ( ( exuE3e ) => 230.26/30.26 ( ( setext ) => 230.26/30.26 ( ( emptyI ) => 230.26/30.26 ( ( noeltsimpempty ) => 230.26/30.26 ( ( ![X28:$i, 230.26/30.26 X30:( $i > $o ),X32:$i]: 230.26/30.26 ( ( in @ X32 @ X28 ) => 230.26/30.26 ( ( in @ 230.26/30.26 X32 @ 230.26/30.26 ( dsetconstr @ 230.26/30.26 X28 @ 230.26/30.26 ( ^[V_4:$i]: 230.26/30.26 ( X30 @ V_4 ) ) ) ) <=> 230.26/30.26 ( X30 @ X32 ) ) ) ) => 230.26/30.26 ( ( nonemptyE1 ) => 230.26/30.26 ( ( nonemptyI ) => 230.26/30.26 ( ( nonemptyI1 ) => 230.26/30.26 ( ( ![X34:$i,X36:$i]: 230.26/30.26 ( in @ 230.26/30.26 X34 @ 230.26/30.26 ( setadjoin @ 230.26/30.26 X34 @ X36 ) ) ) => 230.26/30.26 ( ( in @ 230.26/30.26 emptyset @ 230.26/30.26 ( setadjoin @ 230.26/30.26 emptyset @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( ( ![X38:$i, 230.26/30.26 X40:$i, 230.26/30.26 X42:$i]: 230.26/30.26 ( ( 230.26/30.26 in @ 230.26/30.26 X42 @ X40 ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X42 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X38 @ X40 ) ) ) ) => 230.26/30.26 ( ( ![ 230.26/30.26 X44:$i, 230.26/30.26 X46:$i, 230.26/30.26 X48:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X48 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X44 @ X46 ) ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X50:$o]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X48 ) = 230.26/30.26 ( 230.26/30.26 X44 ) ) => 230.26/30.26 ( 230.26/30.26 X50 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X48 @ X46 ) => 230.26/30.26 ( 230.26/30.26 X50 ) ) => 230.26/30.26 ( 230.26/30.26 X50 ) ) ) ) ) ) => 230.26/30.26 ( ( 230.26/30.26 ![ 230.26/30.26 X52:$i, 230.26/30.26 X54:$i, 230.26/30.26 X56:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X56 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X52 @ X54 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X56 ) = 230.26/30.26 ( 230.26/30.26 X52 ) ) | 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X56 @ X54 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X58:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X58 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_5:$i]: 230.26/30.26 ( 230.26/30.26 $true ) ) ) = 230.26/30.26 ( 230.26/30.26 X58 ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 emptyinPowerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 emptyInPowerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subPowSU ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuE2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 nonemptyImpWitness ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X60:$i, 230.26/30.26 X62:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X60 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X62 @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X60 ) = 230.26/30.26 ( 230.26/30.26 X62 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X64:$i, 230.26/30.26 X66:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X64 ) != 230.26/30.26 ( 230.26/30.26 X66 ) ) => 230.26/30.26 ( 230.26/30.26 ~( 230.26/30.26 in @ 230.26/30.26 X66 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X64 @ 230.26/30.26 emptyset ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X68:$i, 230.26/30.26 X70:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X68 ) = 230.26/30.26 ( 230.26/30.26 X70 ) ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X68 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X70 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X72:$i, 230.26/30.26 X74:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X72 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X74 @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X74 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X72 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X76:$i, 230.26/30.26 X78:$i, 230.26/30.26 X80:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X80 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X76 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X78 @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X80 ) = 230.26/30.26 ( 230.26/30.26 X76 ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X80 ) = 230.26/30.26 ( 230.26/30.26 X78 ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X82:$i, 230.26/30.26 X84:$i]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X82 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X82 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X84 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X86:$i, 230.26/30.26 X88:$i]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X88 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X86 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X88 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X90:$i, 230.26/30.26 X92:( 230.26/30.26 $i > $o )]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ?[ 230.26/30.26 X94:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X92 @ X94 ) & 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X94 @ X90 ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X90 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_6:$i]: 230.26/30.26 ( 230.26/30.26 X92 @ V_6 ) ) ) != 230.26/30.26 ( 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 vacuousDall ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 quantDeMorgan1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 quantDeMorgan2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 quantDeMorgan3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 quantDeMorgan4 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 prop2setI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 prop2set2propI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notdexE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notdallE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuI3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuI2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 inCongP ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuE3u ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exu__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 emptyset__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X96:$i, 230.26/30.26 X98:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X96 ) = 230.26/30.26 ( 230.26/30.26 X98 ) ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X100:$i, 230.26/30.26 X102:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X100 ) = 230.26/30.26 ( 230.26/30.26 X102 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X96 @ X100 ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X98 @ X102 ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powerset__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunion__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 omega__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuEu ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 descr__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X104:$i, 230.26/30.26 X106:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X104 ) = 230.26/30.26 ( 230.26/30.26 X106 ) ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X108:( 230.26/30.26 $i > $o ), 230.26/30.26 X110:( 230.26/30.26 $i > $o )]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X112:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X112 @ 230.26/30.26 X104 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X114:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X114 @ 230.26/30.26 X106 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X112 ) = 230.26/30.26 ( 230.26/30.26 X114 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X108 @ 230.26/30.26 X112 ) <=> 230.26/30.26 ( 230.26/30.26 X110 @ 230.26/30.26 X114 ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X104 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_7:$i]: 230.26/30.26 ( 230.26/30.26 X108 @ V_7 ) ) ) = 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X106 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_8:$i]: 230.26/30.26 ( 230.26/30.26 X110 @ V_8 ) ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eqimpsubset2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eqimpsubset1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetI2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 emptysetsubset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetE2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notsubsetI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notequalI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notequalI2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetRefl ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetTrans ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoinSub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoinSub2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subset2powerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setextsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetemptysetimpeq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetE1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 inPowerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetsubset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X116:$i, 230.26/30.26 X118:( 230.26/30.26 $i > $o )]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X116 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_9:$i]: 230.26/30.26 ( 230.26/30.26 X118 @ V_9 ) ) ) @ 230.26/30.26 ( 230.26/30.26 powerset @ 230.26/30.26 X116 ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X120:$i, 230.26/30.26 X122:( 230.26/30.26 $i > $o )]: 230.26/30.26 ( 230.26/30.26 subset @ 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X120 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_10:$i]: 230.26/30.26 ( 230.26/30.26 X122 @ 230.26/30.26 V_10 ) ) ) @ 230.26/30.26 X120 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionIL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X124:$i, 230.26/30.26 X126:$i]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X126 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X124 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X126 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionIR ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionEcases ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionLsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionRsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset5 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectEL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectLsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectER ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 disjointsetsI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectRsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset4 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 bs114d ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusEL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusER ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusSubset2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusERneg ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusELneg ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusILneg ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusIRneg ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusLsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusSubset1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffI2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffIneg1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffIneg2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X128:$i, 230.26/30.26 X130:$i]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X130 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X128 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X130 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setukpairIL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setukpairIR ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kpairiskpair ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kpairp ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 singletonsubset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 singletoninpowerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 singletoninpowunion ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X132:$i, 230.26/30.26 X134:$i, 230.26/30.26 X136:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X136 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X132 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X134 @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X136 ) = 230.26/30.26 ( 230.26/30.26 X132 ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X136 ) = 230.26/30.26 ( 230.26/30.26 X134 ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 upairsubunion ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 upairinpowunion ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ubforcartprodlem1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ubforcartprodlem2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ubforcartprodlem3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodpairin ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodmempair1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodmempair ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionE2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionsingleton1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionsingleton2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionsingleton ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 singletonprop ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ex1E1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ex1I ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ex1I2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X138:$i, 230.26/30.26 X140:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X138 @ 230.26/30.26 emptyset ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X140 @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X138 ) = 230.26/30.26 ( 230.26/30.26 X140 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X142:$i, 230.26/30.26 X144:$i, 230.26/30.26 X146:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X146 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X142 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X142 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X144 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X142 ) = 230.26/30.26 ( 230.26/30.26 X146 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kfstsingleton ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 theprop ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kfstpairEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodfstin ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X148:$i, 230.26/30.26 X150:$i, 230.26/30.26 X152:$i, 230.26/30.26 X154:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X148 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X148 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X150 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X152 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X152 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X154 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X148 ) = 230.26/30.26 ( 230.26/30.26 X152 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setukpairinjL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X156:$i, 230.26/30.26 X158:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X156 ) = 230.26/30.26 ( 230.26/30.26 X158 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X156 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X158 @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X156 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X160:$i, 230.26/30.26 X162:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X160 ) = 230.26/30.26 ( 230.26/30.26 X162 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X160 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X160 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X162 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X160 @ 230.26/30.26 emptyset ) @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X164:$i, 230.26/30.26 X166:$i, 230.26/30.26 X168:$i, 230.26/30.26 X170:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X164 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X164 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X166 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X168 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X168 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X170 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X168 ) = 230.26/30.26 ( 230.26/30.26 X170 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X166 ) = 230.26/30.26 ( 230.26/30.26 X170 ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X172:$i, 230.26/30.26 X174:$i, 230.26/30.26 X176:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X172 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X174 @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X176 @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X172 ) = 230.26/30.26 ( 230.26/30.26 X174 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X178:$i, 230.26/30.26 X180:$i, 230.26/30.26 X182:$i, 230.26/30.26 X184:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X178 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X178 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X180 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X182 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X182 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X184 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X180 ) = 230.26/30.26 ( 230.26/30.26 X184 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setukpairinjR ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ksndsingleton ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ksndpairEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kpairsurjEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodsndin ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodpairmemEL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodpairmemER ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodmempaircEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodfstpairEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodsndpairEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodpairsurjEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrSub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setOfPairsIsBReln ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrERa ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrEL1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrEL2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrER ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcImageSingleton ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 apProp ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 app ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 infuncsetfunc ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ap2p ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcinfuncset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 lamProp ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 lamp ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 lam2p ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 brelnall1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 brelnall2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ex1E2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcGraphProp1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcGraphProp3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcGraphProp2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcextLem ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcGraphProp4 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subbreln ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eqbreln ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcext ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcext2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ap2apEq1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ap2apEq2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 beta1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eta1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 lam2lamEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 beta2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eta2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X186:$i, 230.26/30.26 X188:$o, 230.26/30.26 X190:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X190 @ 230.26/30.26 X186 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X192:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X192 @ 230.26/30.26 X186 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ~( X188 ) ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X192 @ 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X186 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_11:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_11 ) = 230.26/30.26 ( 230.26/30.26 X192 ) ) & 230.26/30.26 ( 230.26/30.26 ~( X188 ) ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_11 ) = 230.26/30.26 ( 230.26/30.26 X190 ) ) & 230.26/30.26 ( 230.26/30.26 X188 ) ) ) ) ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X194:$i, 230.26/30.26 X196:$o, 230.26/30.26 X198:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X198 @ 230.26/30.26 X194 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X200:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X200 @ 230.26/30.26 X194 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ~( X196 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X194 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_12:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_12 ) = 230.26/30.26 ( 230.26/30.26 X200 ) ) & 230.26/30.26 ( 230.26/30.26 ~( X196 ) ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_12 ) = 230.26/30.26 ( 230.26/30.26 X198 ) ) & 230.26/30.26 ( 230.26/30.26 X196 ) ) ) ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X200 @ 230.26/30.26 emptyset ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X202:$i, 230.26/30.26 X204:$o, 230.26/30.26 X206:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X206 @ 230.26/30.26 X202 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X208:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X208 @ 230.26/30.26 X202 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X204 ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X206 @ 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X202 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_13:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_13 ) = 230.26/30.26 ( 230.26/30.26 X208 ) ) & 230.26/30.26 ( 230.26/30.26 ~( X204 ) ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_13 ) = 230.26/30.26 ( 230.26/30.26 X206 ) ) & 230.26/30.26 ( 230.26/30.26 X204 ) ) ) ) ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X210:$i, 230.26/30.26 X212:$o, 230.26/30.26 X214:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X214 @ 230.26/30.26 X210 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X216:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X216 @ 230.26/30.26 X210 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X212 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X210 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_14:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_14 ) = 230.26/30.26 ( 230.26/30.26 X214 ) ) & 230.26/30.26 ( 230.26/30.26 X212 ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ~( X212 ) ) & 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_14 ) = 230.26/30.26 ( 230.26/30.26 X216 ) ) ) ) ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X214 @ 230.26/30.26 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 230.26/30.26 thf(zf_stmt_4, negated_conjecture, 230.26/30.26 (~( ( setextAx ) => 230.26/30.26 ( ( emptysetAx ) => 230.26/30.26 ( ( ![X4:$i,X6:$i,X8:$i]: 230.26/30.26 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 230.26/30.26 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) => 230.26/30.26 ( ( powersetAx ) => 230.26/30.26 ( ( setunionAx ) => 230.26/30.26 ( ( omega0Ax ) => 230.26/30.26 ( ( omegaSAx ) => 230.26/30.26 ( ( omegaIndAx ) => 230.26/30.26 ( ( replAx ) => 230.26/30.26 ( ( foundationAx ) => 230.26/30.26 ( ( wellorderingAx ) => 230.26/30.26 ( ( descrp ) => 230.26/30.26 ( ( ![X10:$i,X12:( $i > $o ),X14:$i]: 230.26/30.26 ( ( in @ X14 @ X10 ) => 230.26/30.26 ( ( X12 @ X14 ) => 230.26/30.26 ( in @ 230.26/30.26 X14 @ 230.26/30.26 ( dsetconstr @ 230.26/30.26 X10 @ ( ^[V_1:$i]: ( X12 @ V_1 ) ) ) ) ) ) ) => 230.26/30.26 ( ( ![X16:$i,X18:( $i > $o ),X20:$i]: 230.26/30.26 ( ( in @ 230.26/30.26 X20 @ 230.26/30.26 ( dsetconstr @ 230.26/30.26 X16 @ ( ^[V_2:$i]: ( X18 @ V_2 ) ) ) ) => 230.26/30.26 ( in @ X20 @ X16 ) ) ) => 230.26/30.26 ( ( ![X22:$i,X24:( $i > $o ),X26:$i]: 230.26/30.26 ( ( in @ 230.26/30.26 X26 @ 230.26/30.26 ( dsetconstr @ 230.26/30.26 X22 @ ( ^[V_3:$i]: ( X24 @ V_3 ) ) ) ) => 230.26/30.26 ( X24 @ X26 ) ) ) => 230.26/30.26 ( ( exuE1 ) => 230.26/30.26 ( ( prop2setE ) => 230.26/30.26 ( ( emptysetE ) => 230.26/30.26 ( ( emptysetimpfalse ) => 230.26/30.26 ( ( notinemptyset ) => 230.26/30.26 ( ( exuE3e ) => 230.26/30.26 ( ( setext ) => 230.26/30.26 ( ( emptyI ) => 230.26/30.26 ( ( noeltsimpempty ) => 230.26/30.26 ( ( ![X28:$i, 230.26/30.26 X30:( $i > $o ), 230.26/30.26 X32:$i]: 230.26/30.26 ( ( in @ X32 @ X28 ) => 230.26/30.26 ( ( in @ 230.26/30.26 X32 @ 230.26/30.26 ( dsetconstr @ 230.26/30.26 X28 @ 230.26/30.26 ( ^[V_4:$i]: 230.26/30.26 ( X30 @ V_4 ) ) ) ) <=> 230.26/30.26 ( X30 @ X32 ) ) ) ) => 230.26/30.26 ( ( nonemptyE1 ) => 230.26/30.26 ( ( nonemptyI ) => 230.26/30.26 ( ( nonemptyI1 ) => 230.26/30.26 ( ( ![X34:$i, 230.26/30.26 X36:$i]: 230.26/30.26 ( in @ 230.26/30.26 X34 @ 230.26/30.26 ( setadjoin 230.26/30.26 @ 230.26/30.26 X34 @ X36 ) ) ) => 230.26/30.26 ( ( in @ 230.26/30.26 emptyset @ 230.26/30.26 ( setadjoin 230.26/30.26 @ 230.26/30.26 emptyset @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( ( ![ 230.26/30.26 X38:$i, 230.26/30.26 X40:$i, 230.26/30.26 X42:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X42 @ X40 ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X42 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X38 @ X40 ) ) ) ) => 230.26/30.26 ( ( 230.26/30.26 ![ 230.26/30.26 X44:$i, 230.26/30.26 X46:$i, 230.26/30.26 X48:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X48 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X44 @ X46 ) ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X50:$o]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X48 ) = 230.26/30.26 ( 230.26/30.26 X44 ) ) => 230.26/30.26 ( 230.26/30.26 X50 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X48 @ X46 ) => 230.26/30.26 ( 230.26/30.26 X50 ) ) => 230.26/30.26 ( 230.26/30.26 X50 ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X52:$i, 230.26/30.26 X54:$i, 230.26/30.26 X56:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X56 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X52 @ X54 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X56 ) = 230.26/30.26 ( 230.26/30.26 X52 ) ) | 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X56 @ X54 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X58:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X58 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_5:$i]: 230.26/30.26 ( 230.26/30.26 $true ) ) ) = 230.26/30.26 ( 230.26/30.26 X58 ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 emptyinPowerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 emptyInPowerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subPowSU ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuE2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 nonemptyImpWitness ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X60:$i, 230.26/30.26 X62:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X60 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X62 @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X60 ) = 230.26/30.26 ( 230.26/30.26 X62 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X64:$i, 230.26/30.26 X66:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X64 ) != 230.26/30.26 ( 230.26/30.26 X66 ) ) => 230.26/30.26 ( 230.26/30.26 ~ 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X66 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X64 @ 230.26/30.26 emptyset ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X68:$i, 230.26/30.26 X70:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X68 ) = 230.26/30.26 ( 230.26/30.26 X70 ) ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X68 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X70 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X72:$i, 230.26/30.26 X74:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X72 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X74 @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X74 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X72 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X76:$i, 230.26/30.26 X78:$i, 230.26/30.26 X80:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X80 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X76 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X78 @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X80 ) = 230.26/30.26 ( 230.26/30.26 X76 ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X80 ) = 230.26/30.26 ( 230.26/30.26 X78 ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X82:$i, 230.26/30.26 X84:$i]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X82 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X82 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X84 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X86:$i, 230.26/30.26 X88:$i]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X88 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X86 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X88 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X90:$i, 230.26/30.26 X92:( 230.26/30.26 $i > $o )]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ?[ 230.26/30.26 X94:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X92 @ X94 ) & 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X94 @ X90 ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X90 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_6:$i]: 230.26/30.26 ( 230.26/30.26 X92 @ V_6 ) ) ) != 230.26/30.26 ( 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 vacuousDall ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 quantDeMorgan1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 quantDeMorgan2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 quantDeMorgan3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 quantDeMorgan4 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 prop2setI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 prop2set2propI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notdexE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notdallE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuI3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuI2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 inCongP ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuE3u ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exu__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 emptyset__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X96:$i, 230.26/30.26 X98:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X96 ) = 230.26/30.26 ( 230.26/30.26 X98 ) ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X100:$i, 230.26/30.26 X102:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X100 ) = 230.26/30.26 ( 230.26/30.26 X102 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X96 @ 230.26/30.26 X100 ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X98 @ 230.26/30.26 X102 ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powerset__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunion__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 omega__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 exuEu ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 descr__Cong ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X104:$i, 230.26/30.26 X106:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X104 ) = 230.26/30.26 ( 230.26/30.26 X106 ) ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X108:( 230.26/30.26 $i > $o ), 230.26/30.26 X110:( 230.26/30.26 $i > $o )]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X112:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X112 @ 230.26/30.26 X104 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X114:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X114 @ 230.26/30.26 X106 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X112 ) = 230.26/30.26 ( 230.26/30.26 X114 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X108 @ 230.26/30.26 X112 ) <=> 230.26/30.26 ( 230.26/30.26 X110 @ 230.26/30.26 X114 ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X104 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_7:$i]: 230.26/30.26 ( 230.26/30.26 X108 @ 230.26/30.26 V_7 ) ) ) = 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X106 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_8:$i]: 230.26/30.26 ( 230.26/30.26 X110 @ 230.26/30.26 V_8 ) ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eqimpsubset2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eqimpsubset1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetI2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 emptysetsubset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetE2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notsubsetI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notequalI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 notequalI2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetRefl ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetTrans ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoinSub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoinSub2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subset2powerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setextsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subsetemptysetimpeq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetE1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 inPowerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 powersetsubset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X116:$i, 230.26/30.26 X118:( 230.26/30.26 $i > $o )]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X116 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_9:$i]: 230.26/30.26 ( 230.26/30.26 X118 @ 230.26/30.26 V_9 ) ) ) @ 230.26/30.26 ( 230.26/30.26 powerset 230.26/30.26 @ 230.26/30.26 X116 ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X120:$i, 230.26/30.26 X122:( 230.26/30.26 $i > $o )]: 230.26/30.26 ( 230.26/30.26 subset @ 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X120 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_10:$i]: 230.26/30.26 ( 230.26/30.26 X122 @ 230.26/30.26 V_10 ) ) ) @ 230.26/30.26 X120 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionIL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X124:$i, 230.26/30.26 X126:$i]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X126 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X124 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X126 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionIR ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionEcases ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionLsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binunionRsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset5 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectEL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectLsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectER ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 disjointsetsI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectRsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset4 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 binintersectSubset1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 bs114d ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusEL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusER ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusSubset2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusERneg ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusELneg ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusILneg ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusIRneg ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusLsub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setminusSubset1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffE ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffI1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffI2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffIneg1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 symdiffIneg2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X128:$i, 230.26/30.26 X130:$i]: 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X130 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X128 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X130 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setukpairIL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setukpairIR ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kpairiskpair ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kpairp ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 singletonsubset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 singletoninpowerset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 singletoninpowunion ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X132:$i, 230.26/30.26 X134:$i, 230.26/30.26 X136:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X136 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X132 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X134 @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X136 ) = 230.26/30.26 ( 230.26/30.26 X132 ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X136 ) = 230.26/30.26 ( 230.26/30.26 X134 ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 upairsubunion ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 upairinpowunion ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ubforcartprodlem1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ubforcartprodlem2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ubforcartprodlem3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodpairin ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodmempair1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodmempair ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionE2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionsingleton1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionsingleton2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setunionsingleton ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 singletonprop ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ex1E1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ex1I ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ex1I2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X138:$i, 230.26/30.26 X140:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X138 @ 230.26/30.26 emptyset ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X140 @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X138 ) = 230.26/30.26 ( 230.26/30.26 X140 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X142:$i, 230.26/30.26 X144:$i, 230.26/30.26 X146:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X146 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X142 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X142 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X144 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X142 ) = 230.26/30.26 ( 230.26/30.26 X146 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kfstsingleton ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 theprop ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kfstpairEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodfstin ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X148:$i, 230.26/30.26 X150:$i, 230.26/30.26 X152:$i, 230.26/30.26 X154:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X148 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X148 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X150 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X152 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X152 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X154 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X148 ) = 230.26/30.26 ( 230.26/30.26 X152 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setukpairinjL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X156:$i, 230.26/30.26 X158:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X156 ) = 230.26/30.26 ( 230.26/30.26 X158 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X156 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X158 @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X156 @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X160:$i, 230.26/30.26 X162:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X160 ) = 230.26/30.26 ( 230.26/30.26 X162 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X160 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X160 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X162 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X160 @ 230.26/30.26 emptyset ) @ 230.26/30.26 emptyset ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X164:$i, 230.26/30.26 X166:$i, 230.26/30.26 X168:$i, 230.26/30.26 X170:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X164 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X164 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X166 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X168 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X168 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X170 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X168 ) = 230.26/30.26 ( 230.26/30.26 X170 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X166 ) = 230.26/30.26 ( 230.26/30.26 X170 ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X172:$i, 230.26/30.26 X174:$i, 230.26/30.26 X176:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X172 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X174 @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X176 @ 230.26/30.26 emptyset ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X172 ) = 230.26/30.26 ( 230.26/30.26 X174 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X178:$i, 230.26/30.26 X180:$i, 230.26/30.26 X182:$i, 230.26/30.26 X184:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X178 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X178 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X180 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X182 @ 230.26/30.26 emptyset ) @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X182 @ 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X184 @ 230.26/30.26 emptyset ) ) @ 230.26/30.26 emptyset ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X180 ) = 230.26/30.26 ( 230.26/30.26 X184 ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setukpairinjR ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ksndsingleton ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ksndpairEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 kpairsurjEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodsndin ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodpairmemEL ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodpairmemER ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodmempaircEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodfstpairEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodsndpairEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 cartprodpairsurjEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrI ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrSub ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 setOfPairsIsBReln ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrERa ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrEL1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrEL2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dpsetconstrER ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcImageSingleton ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 apProp ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 app ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 infuncsetfunc ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ap2p ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcinfuncset ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 lamProp ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 lamp ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 lam2p ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 brelnall1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 brelnall2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ex1E2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcGraphProp1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcGraphProp3 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcGraphProp2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcextLem ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcGraphProp4 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 subbreln ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eqbreln ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcext ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 funcext2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ap2apEq1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ap2apEq2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 beta1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eta1 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 lam2lamEq ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 beta2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 eta2 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X186:$i, 230.26/30.26 X188:$o, 230.26/30.26 X190:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X190 @ 230.26/30.26 X186 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X192:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X192 @ 230.26/30.26 X186 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ~( X188 ) ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X192 @ 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X186 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_11:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_11 ) = 230.26/30.26 ( 230.26/30.26 X192 ) ) & 230.26/30.26 ( 230.26/30.26 ~( X188 ) ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_11 ) = 230.26/30.26 ( 230.26/30.26 X190 ) ) & 230.26/30.26 ( 230.26/30.26 X188 ) ) ) ) ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X194:$i, 230.26/30.26 X196:$o, 230.26/30.26 X198:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X198 @ 230.26/30.26 X194 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X200:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X200 @ 230.26/30.26 X194 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ~( X196 ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X194 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_12:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_12 ) = 230.26/30.26 ( 230.26/30.26 X200 ) ) & 230.26/30.26 ( 230.26/30.26 ~( X196 ) ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_12 ) = 230.26/30.26 ( 230.26/30.26 X198 ) ) & 230.26/30.26 ( 230.26/30.26 X196 ) ) ) ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X200 @ 230.26/30.26 emptyset ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X202:$i, 230.26/30.26 X204:$o, 230.26/30.26 X206:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X206 @ 230.26/30.26 X202 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X208:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X208 @ 230.26/30.26 X202 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X204 ) => 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X206 @ 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X202 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_13:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_13 ) = 230.26/30.26 ( 230.26/30.26 X208 ) ) & 230.26/30.26 ( 230.26/30.26 ~( X204 ) ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_13 ) = 230.26/30.26 ( 230.26/30.26 X206 ) ) & 230.26/30.26 ( 230.26/30.26 X204 ) ) ) ) ) ) ) ) ) ) ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X210:$i, 230.26/30.26 X212:$o, 230.26/30.26 X214:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X214 @ 230.26/30.26 X210 ) => 230.26/30.26 ( 230.26/30.26 ![ 230.26/30.26 X216:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 in @ 230.26/30.26 X216 @ 230.26/30.26 X210 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 X212 ) => 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 dsetconstr 230.26/30.26 @ 230.26/30.26 X210 @ 230.26/30.26 ( 230.26/30.26 ^[ 230.26/30.26 V_14:$i]: 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_14 ) = 230.26/30.26 ( 230.26/30.26 X214 ) ) & 230.26/30.26 ( 230.26/30.26 X212 ) ) | 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 ~( X212 ) ) & 230.26/30.26 ( 230.26/30.26 ( 230.26/30.26 V_14 ) = 230.26/30.26 ( 230.26/30.26 X216 ) ) ) ) ) ) = 230.26/30.26 ( 230.26/30.26 setadjoin 230.26/30.26 @ 230.26/30.26 X214 @ 230.26/30.26 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 230.26/30.26 inference('cnf.neg', [status(esa)], [zf_stmt_3])). 230.26/30.26 thf(zip_derived_cl120, plain, 230.26/30.26 (((dsetconstr @ sk__103 @ 230.26/30.26 (^[Y0 : $i]: 230.26/30.26 (((((((Y0) = (sk__105))) & (sk__104))) | 230.26/30.26 (((((~) @ sk__104)) & (((Y0) = (sk__106))))))))) 230.26/30.26 != (setadjoin @ sk__105 @ emptyset))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl120, plain, 230.26/30.26 (((dsetconstr @ sk__103 @ 230.26/30.26 (^[Y0 : $i]: 230.26/30.26 (((((((Y0) = (sk__105))) & (sk__104))) | 230.26/30.26 (((((~) @ sk__104)) & (((Y0) = (sk__106))))))))) 230.26/30.26 != (setadjoin @ sk__105 @ emptyset))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl9945, plain, 230.26/30.26 (![X1 : $i]: 230.26/30.26 (('#l_lift12040' @ X1) 230.26/30.26 = (((((((X1) = (sk__105))) & (sk__104))) | 230.26/30.26 (((((~) @ sk__104)) & (((X1) = (sk__106))))))))), 230.26/30.26 define([status(thm)])). 230.26/30.26 thf(zip_derived_cl9946, plain, 230.26/30.26 (((dsetconstr @ sk__103 @ '#l_lift12040') 230.26/30.26 != (setadjoin @ sk__105 @ emptyset))), 230.26/30.26 inference('lambda_lifting', [status(thm)], 230.26/30.26 [zip_derived_cl120, zip_derived_cl9945])). 230.26/30.26 thf(zip_derived_cl117, plain, 230.26/30.26 (![X53 : $i, X54 : $i, X55 : $o, X56 : $i]: 230.26/30.26 (~ (in @ X53 @ X54) 230.26/30.26 | (in @ X53 @ 230.26/30.26 (dsetconstr @ X54 @ 230.26/30.26 (^[Y0 : $i]: 230.26/30.26 (((((((Y0) = (X53))) & (((~) @ X55)))) | 230.26/30.26 (((((Y0) = (X56))) & (X55)))))))) 230.26/30.26 | (X55) 230.26/30.26 | ~ (in @ X56 @ X54))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl9942, plain, 230.26/30.26 (![X53 : $i, X55 : $o, X56 : $i, X57 : $i]: 230.26/30.26 (('#l_lift12039' @ X53 @ X55 @ X56 @ X57) 230.26/30.26 = (((((((X57) = (X53))) & (((~) @ X55)))) | 230.26/30.26 (((((X57) = (X56))) & (X55))))))), 230.26/30.26 define([status(thm)])). 230.26/30.26 thf(zip_derived_cl121, plain, ( (sk__104)), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl122, plain, ( (in @ sk__105 @ sk__103)), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl1, plain, 230.26/30.26 (![X0 : $i, X1 : $i, X2 : $i]: 230.26/30.26 ( (zip_tseitin_0 @ X0 @ X1 @ X2) | ((X0) != (X2)))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_2])). 230.26/30.26 thf(zip_derived_cl241, plain, 230.26/30.26 (![X1 : $i, X2 : $i]: (zip_tseitin_0 @ X2 @ X1 @ X2)), 230.26/30.26 inference('simplify', [status(thm)], [zip_derived_cl1])). 230.26/30.26 thf(zip_derived_cl44, plain, 230.26/30.26 (![X34 : $i > $o, X35 : $i > $o, X36 : $i, X37 : $i]: 230.26/30.26 (~ (X35 @ (sk__107 @ X34 @ X35 @ X36 @ X37)) 230.26/30.26 | ~ (X34 @ (sk__108 @ X34 @ X35 @ X36 @ X37)) 230.26/30.26 | ((dsetconstr @ X37 @ (^[Y0 : $i]: (X35 @ Y0))) 230.26/30.26 = (dsetconstr @ X36 @ (^[Y0 : $i]: (X34 @ Y0)))) 230.26/30.26 | ((X37) != (X36)))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl1996, plain, 230.26/30.26 (![X34 : $i > $o, X35 : $i > $o, X36 : $i, X37 : $i]: 230.26/30.26 (~ (X35 @ (sk__107 @ X34 @ X35 @ X36 @ X37)) 230.26/30.26 | ~ (X34 @ (sk__108 @ X34 @ X35 @ X36 @ X37)) 230.26/30.26 | ((dsetconstr @ X37 @ X35) = (dsetconstr @ X36 @ X34)) 230.26/30.26 | ((X37) != (X36)))), 230.26/30.26 inference('ho_norm', [status(thm)], [zip_derived_cl44])). 230.26/30.26 thf(zip_derived_cl1997, plain, 230.26/30.26 (![X34 : $i > $o, X35 : $i > $o, X36 : $i]: 230.26/30.26 (((dsetconstr @ X36 @ X35) = (dsetconstr @ X36 @ X34)) 230.26/30.26 | ~ (X34 @ (sk__108 @ X34 @ X35 @ X36 @ X36)) 230.26/30.26 | ~ (X35 @ (sk__107 @ X34 @ X35 @ X36 @ X36)))), 230.26/30.26 inference('simplify', [status(thm)], [zip_derived_cl1996])). 230.26/30.26 thf(zip_derived_cl2089, plain, 230.26/30.26 (![X0 : $i, X1 : $i > $o]: 230.26/30.26 (~ (X1 @ 230.26/30.26 (sk__107 @ 230.26/30.26 (^[Y0 : $i]: 230.26/30.26 (zip_tseitin_0 @ ((^[Y1 : $i]: (Y1)) @ Y0) @ 230.26/30.26 ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ 230.26/30.26 X1 @ X0 @ X0)) 230.26/30.26 | ((dsetconstr @ X0 @ X1) 230.26/30.26 = (dsetconstr @ X0 @ 230.26/30.26 (^[Y0 : $i]: 230.26/30.26 (zip_tseitin_0 @ ((^[Y1 : $i]: (Y1)) @ Y0) @ 230.26/30.26 ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))))))), 230.26/30.26 inference('sup-', [status(thm)], [zip_derived_cl241, zip_derived_cl1997])). 230.26/30.26 thf(zip_derived_cl2136, plain, 230.26/30.26 (![X0 : $i, X1 : $i > $o]: 230.26/30.26 (~ (X1 @ 230.26/30.26 (sk__107 @ (^[Y0 : $i]: (zip_tseitin_0 @ Y0 @ Y0 @ Y0)) @ X1 @ 230.26/30.26 X0 @ X0)) 230.26/30.26 | ((dsetconstr @ X0 @ X1) 230.26/30.26 = (dsetconstr @ X0 @ (^[Y0 : $i]: (zip_tseitin_0 @ Y0 @ Y0 @ Y0)))))), 230.26/30.26 inference('ho_norm', [status(thm)], [zip_derived_cl2089])). 230.26/30.26 thf(zip_derived_cl5, plain, 230.26/30.26 (![X1 : $i, X2 : $i, X3 : $i]: 230.26/30.26 ( (zip_tseitin_0 @ X3 @ X2 @ X1) | ~ (in @ X3 @ (setadjoin @ X1 @ X2)))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl1997, plain, 230.26/30.26 (![X34 : $i > $o, X35 : $i > $o, X36 : $i]: 230.26/30.26 (((dsetconstr @ X36 @ X35) = (dsetconstr @ X36 @ X34)) 230.26/30.26 | ~ (X34 @ (sk__108 @ X34 @ X35 @ X36 @ X36)) 230.26/30.26 | ~ (X35 @ (sk__107 @ X34 @ X35 @ X36 @ X36)))), 230.26/30.26 inference('simplify', [status(thm)], [zip_derived_cl1996])). 230.26/30.26 thf(zip_derived_cl2409, plain, 230.26/30.26 (![X0 : $i, X1 : $i > $o]: 230.26/30.26 (~ (in @ 230.26/30.26 (sk__108 @ 230.26/30.26 (^[Y0 : $i]: 230.26/30.26 (zip_tseitin_0 @ Y0 @ ((^[Y1 : $i]: (Y1)) @ Y0) @ 230.26/30.26 ((^[Y1 : $i]: (Y1)) @ Y0))) @ 230.26/30.26 X1 @ X0 @ X0) @ 230.26/30.26 (setadjoin @ 230.26/30.26 (sk__108 @ (^[Y0 : $i]: (zip_tseitin_0 @ Y0 @ Y0 @ Y0)) @ X1 @ 230.26/30.26 X0 @ X0) @ 230.26/30.26 (sk__108 @ 230.26/30.26 (^[Y0 : $i]: 230.26/30.26 (zip_tseitin_0 @ Y0 @ Y0 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ 230.26/30.26 X1 @ X0 @ X0))) 230.26/30.26 | ~ (X1 @ 230.26/30.26 (sk__107 @ 230.26/30.26 (^[Y0 : $i]: 230.26/30.26 (zip_tseitin_0 @ ((^[Y1 : $i]: (Y1)) @ Y0) @ 230.26/30.26 ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ 230.26/30.26 X1 @ X0 @ X0)) 230.26/30.26 | ((dsetconstr @ X0 @ X1) 230.26/30.26 = (dsetconstr @ X0 @ 230.26/30.26 (^[Y0 : $i]: 230.26/30.26 (zip_tseitin_0 @ ((^[Y1 : $i]: (Y1)) @ Y0) @ 230.26/30.26 ((^[Y1 : $i]: (Y1)) @ Y0) @ ((^[Y1 : $i]: (Y1)) @ Y0))))))), 230.26/30.26 inference('sup-', [status(thm)], [zip_derived_cl5, zip_derived_cl1997])). 230.26/30.26 thf(zip_derived_cl2461, plain, 230.26/30.26 (![X0 : $i, X1 : $i > $o]: 230.26/30.26 (~ (in @ 230.26/30.26 (sk__108 @ (^[Y0 : $i]: (zip_tseitin_0 @ Y0 @ Y0 @ Y0)) @ X1 @ 230.26/30.26 X0 @ X0) @ 230.26/30.26 (setadjoin @ 230.26/30.26 (sk__108 @ (^[Y0 : $i]: (zip_tseitin_0 @ Y0 @ Y0 @ Y0)) @ X1 @ 230.26/30.26 X0 @ X0) @ 230.26/30.26 (sk__108 @ (^[Y0 : $i]: (zip_tseitin_0 @ Y0 @ Y0 @ Y0)) @ X1 @ 230.26/30.26 X0 @ X0))) 230.26/30.26 | ~ (X1 @ 230.26/30.26 (sk__107 @ (^[Y0 : $i]: (zip_tseitin_0 @ Y0 @ Y0 @ Y0)) @ X1 @ 230.26/30.26 X0 @ X0)) 230.26/30.26 | ((dsetconstr @ X0 @ X1) 230.26/30.26 = (dsetconstr @ X0 @ (^[Y0 : $i]: (zip_tseitin_0 @ Y0 @ Y0 @ Y0)))))), 230.26/30.26 inference('ho_norm', [status(thm)], [zip_derived_cl2409])). 230.26/30.26 thf(zip_derived_cl19, plain, 230.26/30.26 (![X13 : $i, X14 : $i]: (in @ X13 @ (setadjoin @ X13 @ X14))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl2462, plain, 230.26/30.26 (![X0 : $i, X1 : $i > $o]: 230.26/30.26 (~ (X1 @ 230.26/30.26 (sk__107 @ (^[Y0 : $i]: (zip_tseitin_0 @ Y0 @ Y0 @ Y0)) @ X1 @ 230.26/30.26 X0 @ X0)) 230.26/30.26 | ((dsetconstr @ X0 @ X1) 230.26/30.26 = (dsetconstr @ X0 @ (^[Y0 : $i]: (zip_tseitin_0 @ Y0 @ Y0 @ Y0)))))), 230.26/30.26 inference('demod', [status(thm)], [zip_derived_cl2461, zip_derived_cl19])). 230.26/30.26 thf(zip_derived_cl9958, plain, 230.26/30.26 (![X2 : $i]: (('#l_lift12044' @ X2) = (zip_tseitin_0 @ X2 @ X2 @ X2))), 230.26/30.26 define([status(thm)])). 230.26/30.26 thf(zip_derived_cl9958, plain, 230.26/30.26 (![X2 : $i]: (('#l_lift12044' @ X2) = (zip_tseitin_0 @ X2 @ X2 @ X2))), 230.26/30.26 define([status(thm)])). 230.26/30.26 thf(zip_derived_cl9965, plain, 230.26/30.26 (![X0 : $i, X1 : $i > $o]: 230.26/30.26 (~ (X1 @ (sk__107 @ '#l_lift12044' @ X1 @ X0 @ X0)) 230.26/30.26 | ((dsetconstr @ X0 @ X1) = (dsetconstr @ X0 @ '#l_lift12044')))), 230.26/30.26 inference('lambda_lifting', [status(thm)], 230.26/30.26 [zip_derived_cl2136, zip_derived_cl9958, zip_derived_cl9958])). 230.26/30.26 thf(zip_derived_cl123, plain, 230.26/30.26 (![X61 : $i, X62 : $i, X63 : $o, X64 : $i]: 230.26/30.26 (~ (in @ X61 @ X62) 230.26/30.26 | ((dsetconstr @ X62 @ 230.26/30.26 (^[Y0 : $i]: 230.26/30.26 (((((((Y0) = (X61))) & (((~) @ X63)))) | 230.26/30.26 (((((Y0) = (X64))) & (X63))))))) 230.26/30.26 = (setadjoin @ X61 @ emptyset)) 230.26/30.26 | (X63) 230.26/30.26 | ~ (in @ X64 @ X62))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl9942, plain, 230.26/30.26 (![X53 : $i, X55 : $o, X56 : $i, X57 : $i]: 230.26/30.26 (('#l_lift12039' @ X53 @ X55 @ X56 @ X57) 230.26/30.26 = (((((((X57) = (X53))) & (((~) @ X55)))) | 230.26/30.26 (((((X57) = (X56))) & (X55))))))), 230.26/30.26 define([status(thm)])). 230.26/30.26 thf(zip_derived_cl9947, plain, 230.26/30.26 (![X61 : $i, X62 : $i, X63 : $o, X64 : $i]: 230.26/30.26 (~ (in @ X61 @ X62) 230.26/30.26 | ((dsetconstr @ X62 @ ('#l_lift12039' @ X61 @ X63 @ X64)) 230.26/30.26 = (setadjoin @ X61 @ emptyset)) 230.26/30.26 | (X63) 230.26/30.26 | ~ (in @ X64 @ X62))), 230.26/30.26 inference('lambda_lifting', [status(thm)], 230.26/30.26 [zip_derived_cl123, zip_derived_cl9942])). 230.26/30.26 thf(zip_derived_cl9940, plain, 230.26/30.26 (![X34 : $i > $o, X35 : $i > $o, X36 : $i, X37 : $i]: 230.26/30.26 ( (in @ (sk__107 @ X34 @ X35 @ X36 @ X37) @ X37) 230.26/30.26 | ((dsetconstr @ X37 @ X35) = (dsetconstr @ X36 @ X34)) 230.26/30.26 | ((X37) != (X36)))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl9932, plain, 230.26/30.26 (![X7 : $i > $o, X8 : $i, X9 : $i]: 230.26/30.26 ( (X7 @ X8) | ~ (in @ X8 @ (dsetconstr @ X9 @ X7)))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl9945, plain, 230.26/30.26 (![X1 : $i]: 230.26/30.26 (('#l_lift12040' @ X1) 230.26/30.26 = (((((((X1) = (sk__105))) & (sk__104))) | 230.26/30.26 (((((~) @ sk__104)) & (((X1) = (sk__106))))))))), 230.26/30.26 define([status(thm)])). 230.26/30.26 thf(zip_derived_cl9958, plain, 230.26/30.26 (![X2 : $i]: (('#l_lift12044' @ X2) = (zip_tseitin_0 @ X2 @ X2 @ X2))), 230.26/30.26 define([status(thm)])). 230.26/30.26 thf(zip_derived_cl1997, plain, 230.26/30.26 (![X34 : $i > $o, X35 : $i > $o, X36 : $i]: 230.26/30.26 (((dsetconstr @ X36 @ X35) = (dsetconstr @ X36 @ X34)) 230.26/30.26 | ~ (X34 @ (sk__108 @ X34 @ X35 @ X36 @ X36)) 230.26/30.26 | ~ (X35 @ (sk__107 @ X34 @ X35 @ X36 @ X36)))), 230.26/30.26 inference('simplify', [status(thm)], [zip_derived_cl1996])). 230.26/30.26 thf(zip_derived_cl215, plain, 230.26/30.26 (![X94 : $i]: ((dsetconstr @ X94 @ (^[Y0 : $i]: ($true))) = (X94))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl2033, plain, 230.26/30.26 (![X0 : $i > $o, X1 : $i]: 230.26/30.26 (((dsetconstr @ X1 @ X0) = (X1)) 230.26/30.26 | ~ ((^[Y0 : $i]: ($true)) @ 230.26/30.26 (sk__107 @ X0 @ (^[Y0 : $i]: ($true)) @ X1 @ X1)) 230.26/30.26 | ~ (X0 @ (sk__108 @ X0 @ (^[Y0 : $i]: ($true)) @ X1 @ X1)))), 230.26/30.26 inference('sup+', [status(thm)], [zip_derived_cl1997, zip_derived_cl215])). 230.26/30.26 thf(zip_derived_cl2176, plain, 230.26/30.26 (![X0 : $i > $o, X1 : $i]: 230.26/30.26 (((dsetconstr @ X1 @ X0) = (X1)) 230.26/30.26 | ~ (X0 @ (sk__108 @ X0 @ (^[Y0 : $i]: ($true)) @ X1 @ X1)))), 230.26/30.26 inference('ho_norm', [status(thm)], [zip_derived_cl2033])). 230.26/30.26 thf(zip_derived_cl215, plain, 230.26/30.26 (![X94 : $i]: ((dsetconstr @ X94 @ (^[Y0 : $i]: ($true))) = (X94))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl9949, plain, (![X95 : $i]: ('#l_lift12041' @ X95)), 230.26/30.26 define([status(thm)])). 230.26/30.26 thf(zip_derived_cl9953, plain, 230.26/30.26 (![X0 : $i > $o, X1 : $i]: 230.26/30.26 (((dsetconstr @ X1 @ X0) = (X1)) 230.26/30.26 | ~ (X0 @ (sk__108 @ X0 @ '#l_lift12041' @ X1 @ X1)))), 230.26/30.26 inference('lambda_lifting', [status(thm)], 230.26/30.26 [zip_derived_cl2176, zip_derived_cl9949])). 230.26/30.26 thf(zip_derived_cl9933, plain, 230.26/30.26 (![X10 : $i > $o, X11 : $i, X12 : $i]: 230.26/30.26 (~ (X10 @ X11) 230.26/30.26 | (in @ X11 @ (dsetconstr @ X12 @ X10)) 230.26/30.26 | ~ (in @ X11 @ X12))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_4])). 230.26/30.26 thf(zip_derived_cl1, plain, 230.26/30.26 (![X0 : $i, X1 : $i, X2 : $i]: 230.26/30.26 ( (zip_tseitin_0 @ X0 @ X1 @ X2) | ((X0) != (X2)))), 230.26/30.26 inference('cnf', [status(esa)], [zf_stmt_2])). 230.26/30.26 thf(zip_derived_cl9967, plain, ($false), 230.26/30.26 inference('eprover', [status(thm)], 230.26/30.26 [zip_derived_cl9946, zip_derived_cl9942, zip_derived_cl121, 230.26/30.26 zip_derived_cl122, zip_derived_cl9965, zip_derived_cl9947, 230.26/30.26 zip_derived_cl9940, zip_derived_cl9932, zip_derived_cl9945, 230.26/30.26 zip_derived_cl9958, zip_derived_cl9953, zip_derived_cl9933, 230.26/30.26 zip_derived_cl1])). 230.26/30.26 230.26/30.26 % SZS output end Refutation 230.26/30.26 230.26/30.26 230.26/30.26 % /export/starexec/sandbox/solver/bin/lams/15_old_s4.sh running for 18s 230.26/30.26 % Terminating... 230.26/30.40 % Runner terminated. 230.26/30.41 % Zipperpin 1.5 exiting 230.26/30.42 EOF