0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.17 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.KpAIvkxXz6 true 0.17/0.38 % Computer : n023.cluster.edu 0.17/0.38 % Model : x86_64 x86_64 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.17/0.38 % Memory : 8042.1875MB 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64 0.17/0.38 % CPULimit : 1440 0.17/0.38 % WCLimit : 180 0.17/0.38 % DateTime : Mon Jul 3 10:53:06 EDT 2023 0.17/0.38 % CPUTime : 0.17/0.38 % Running portfolio for 1440 s 0.17/0.38 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.17/0.38 % Number of cores: 8 0.17/0.39 % Python version: Python 3.6.8 0.17/0.39 % Running in HO mode 0.57/0.71 % Total configuration time : 828 0.57/0.71 % Estimated wc time : 1656 0.57/0.71 % Estimated cpu time (8 cpus) : 207.0 0.59/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.59/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.59/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.59/0.79 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.61/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.61/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.61/0.83 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.61/0.83 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.62/0.86 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 238.56/30.98 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 395.14/52.48 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 467.50/61.90 % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s 575.51/76.41 % /export/starexec/sandbox2/solver/bin/lams/33_shallow_sine.sh running for 66s 608.97/80.65 % /export/starexec/sandbox2/solver/bin/lams/40_e_lift.sh running for 80s 611.20/81.03 % /export/starexec/sandbox2/solver/bin/lams/15_lifting1.sh running for 30s 622.19/82.41 % /export/starexec/sandbox2/solver/bin/lams/8_new_cnf.sh running for 16s 658.53/87.11 % /export/starexec/sandbox2/solver/bin/lams/10_e_short2.sh running for 20s 664.09/87.88 % Solved by lams/33_shallow_sine.sh. 664.09/87.88 % done 1493 iterations in 11.401s 664.09/87.88 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 664.09/87.88 % SZS output start Refutation 664.09/87.88 thf(setadjoinAx_type, type, setadjoinAx: $o). 664.09/87.88 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o). 664.09/87.88 thf(notdexE_type, type, notdexE: $o). 664.09/87.88 thf(setunionAx_type, type, setunionAx: $o). 664.09/87.88 thf(setminusELneg_type, type, setminusELneg: $o). 664.09/87.88 thf(kpairsurjEq_type, type, kpairsurjEq: $o). 664.09/87.88 thf(sk__138_type, type, sk__138: $i). 664.09/87.88 thf(ap2apEq2_type, type, ap2apEq2: $o). 664.09/87.88 thf(powersetE_type, type, powersetE: $o). 664.09/87.88 thf(omegaSAx_type, type, omegaSAx: $o). 664.09/87.88 thf(exuI1_type, type, exuI1: $o). 664.09/87.88 thf(exuI2_type, type, exuI2: $o). 664.09/87.88 thf(notequalI2_type, type, notequalI2: $o). 664.09/87.88 thf(kpairiskpair_type, type, kpairiskpair: $o). 664.09/87.88 thf(upairsubunion_type, type, upairsubunion: $o). 664.09/87.88 thf(powerset__Cong_type, type, powerset__Cong: $o). 664.09/87.88 thf(iftrueProp1_type, type, iftrueProp1: $o). 664.09/87.88 thf(setminusILneg_type, type, setminusILneg: $o). 664.09/87.88 thf(lam2lamEq_type, type, lam2lamEq: $o). 664.09/87.88 thf(ap2p_type, type, ap2p: $o). 664.09/87.88 thf(wellorderingAx_type, type, wellorderingAx: $o). 664.09/87.88 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 664.09/87.88 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 664.09/87.88 thf(upairinpowunion_type, type, upairinpowunion: $o). 664.09/87.88 thf(setoftrueEq_type, type, setoftrueEq: $o). 664.09/87.88 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 664.09/87.88 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o). 664.09/87.88 thf(dpsetconstrI_type, type, dpsetconstrI: $o). 664.09/87.88 thf(dpsetconstrER_type, type, dpsetconstrER: $o). 664.09/87.88 thf(sepInPowerset_type, type, sepInPowerset: $o). 664.09/87.88 thf(setukpairIR_type, type, setukpairIR: $o). 664.09/87.88 thf(binunionE_type, type, binunionE: $o). 664.09/87.88 thf(setext_type, type, setext: $o). 664.09/87.88 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 664.09/87.88 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 664.09/87.88 thf(setukpairinjR12_type, type, setukpairinjR12: $o). 664.09/87.88 thf(descr__Cong_type, type, descr__Cong: $o). 664.09/87.88 thf(iffalseProp1_type, type, iffalseProp1: $o). 664.09/87.88 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 664.09/87.88 thf(app_type, type, app: $o). 664.09/87.88 thf(in_type, type, in: $i > $i > $o). 664.09/87.88 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o). 664.09/87.88 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o). 664.09/87.88 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 664.09/87.88 thf(funcGraphProp2_type, type, funcGraphProp2: $o). 664.09/87.88 thf(setadjoinIR_type, type, setadjoinIR: $o). 664.09/87.88 thf(funcGraphProp1_type, type, funcGraphProp1: $o). 664.09/87.88 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 664.09/87.88 thf(symdiffI2_type, type, symdiffI2: $o). 664.09/87.88 thf(upairset2IR_type, type, upairset2IR: $o). 664.09/87.88 thf(subsetE_type, type, subsetE: $o). 664.09/87.88 thf(prop2set2propI_type, type, prop2set2propI: $o). 664.09/87.88 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 664.09/87.88 thf(setbeta_type, type, setbeta: $o). 664.09/87.88 thf(eqinunit_type, type, eqinunit: $o). 664.09/87.88 thf(upairsetIL_type, type, upairsetIL: $o). 664.09/87.88 thf(powersetI1_type, type, powersetI1: $o). 664.09/87.88 thf(lamProp_type, type, lamProp: $o). 664.09/87.88 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 664.09/87.88 thf(setukpairinjR_type, type, setukpairinjR: $o). 664.09/87.88 thf(cartprodfstin_type, type, cartprodfstin: $o). 664.09/87.88 thf(setminusIRneg_type, type, setminusIRneg: $o). 664.09/87.88 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o). 664.09/87.88 thf(sk__141_type, type, sk__141: $i). 664.09/87.88 thf(powersetAx_type, type, powersetAx: $o). 664.09/87.88 thf(singletonprop_type, type, singletonprop: $o). 664.09/87.88 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 664.09/87.88 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 664.09/87.88 thf(powersetI_type, type, powersetI: $o). 664.09/87.88 thf(iffalseProp2_type, type, iffalseProp2: $o). 664.09/87.88 thf(cartprodmempair_type, type, cartprodmempair: $o). 664.09/87.88 thf(upairsetIR_type, type, upairsetIR: $o). 664.09/87.88 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o). 664.09/87.88 thf(inCongP_type, type, inCongP: $o). 664.09/87.88 thf(setukpairinjL_type, type, setukpairinjL: $o). 664.09/87.88 thf(setadjoinSub_type, type, setadjoinSub: $o). 664.09/87.88 thf(exuE3e_type, type, exuE3e: $o). 664.09/87.88 thf(emptysetE_type, type, emptysetE: $o). 664.09/87.88 thf(upairequniteq_type, type, upairequniteq: $o). 664.09/87.88 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 664.09/87.88 thf(setunionI_type, type, setunionI: $o). 664.09/87.88 thf(setunion__Cong_type, type, setunion__Cong: $o). 664.09/87.88 thf(prop2setI_type, type, prop2setI: $o). 664.09/87.88 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 664.09/87.88 thf(funcinfuncset_type, type, funcinfuncset: $o). 664.09/87.88 thf(setminusER_type, type, setminusER: $o). 664.09/87.88 thf(exuE2_type, type, exuE2: $o). 664.09/87.88 thf(emptyset_type, type, emptyset: $i). 664.09/87.88 thf(powersetsubset_type, type, powersetsubset: $o). 664.09/87.88 thf(setukpairinjR1_type, type, setukpairinjR1: $o). 664.09/87.88 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o). 664.09/87.88 thf(subPowSU_type, type, subPowSU: $o). 664.09/87.88 thf(notequalI1_type, type, notequalI1: $o). 664.09/87.88 thf(notinemptyset_type, type, notinemptyset: $o). 664.09/87.88 thf(nonemptyI1_type, type, nonemptyI1: $o). 664.09/87.88 thf(subsetTrans_type, type, subsetTrans: $o). 664.09/87.88 thf(setukpairinjR2_type, type, setukpairinjR2: $o). 664.09/87.88 thf(kpairp_type, type, kpairp: $o). 664.09/87.88 thf(setminusI_type, type, setminusI: $o). 664.09/87.88 thf(binunionIL_type, type, binunionIL: $o). 664.09/87.88 thf(setunionsingleton_type, type, setunionsingleton: $o). 664.09/87.88 thf(subsetE2_type, type, subsetE2: $o). 664.09/87.88 thf(singletonsswitch_type, type, singletonsswitch: $o). 664.09/87.88 thf(kfstpairEq_type, type, kfstpairEq: $o). 664.09/87.88 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 664.09/87.88 thf(setextsub_type, type, setextsub: $o). 664.09/87.88 thf(binunionLsub_type, type, binunionLsub: $o). 664.09/87.88 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 664.09/87.88 thf(emptysetsubset_type, type, emptysetsubset: $o). 664.09/87.88 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 664.09/87.88 thf(setunionE_type, type, setunionE: $o). 664.09/87.88 thf(setminusSubset1_type, type, setminusSubset1: $o). 664.09/87.88 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 664.09/87.88 thf(binunionIR_type, type, binunionIR: $o). 664.09/87.88 thf(setadjoinE_type, type, setadjoinE: $o). 664.09/87.88 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o). 664.09/87.88 thf(subbreln_type, type, subbreln: $o). 664.09/87.88 thf(singletonsuniq_type, type, singletonsuniq: $o). 664.09/87.88 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o). 664.09/87.88 thf(setadjoinIL_type, type, setadjoinIL: $o). 664.09/87.88 thf(exuE1_type, type, exuE1: $o). 664.09/87.88 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 664.09/87.88 thf(binintersectRsub_type, type, binintersectRsub: $o). 664.09/87.88 thf(setminusLsub_type, type, setminusLsub: $o). 664.09/87.88 thf(notinsingleton_type, type, notinsingleton: $o). 664.09/87.89 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o). 664.09/87.89 thf(funcext_type, type, funcext: $o). 664.09/87.89 thf(infuncsetfunc_type, type, infuncsetfunc: $o). 664.09/87.89 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 664.09/87.89 thf(exuEu_type, type, exuEu: $o). 664.09/87.89 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 664.09/87.89 thf(ex1I2_type, type, ex1I2: $o). 664.09/87.89 thf(upairsetE_type, type, upairsetE: $o). 664.09/87.89 thf(omega0Ax_type, type, omega0Ax: $o). 664.09/87.89 thf(funcext2_type, type, funcext2: $o). 664.09/87.89 thf(notsubsetI_type, type, notsubsetI: $o). 664.09/87.89 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 664.09/87.89 thf(setextAx_type, type, setextAx: $o). 664.09/87.89 thf(powersetE1_type, type, powersetE1: $o). 664.09/87.89 thf(bs114d_type, type, bs114d: $o). 664.09/87.89 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 664.09/87.89 thf(setunion_type, type, setunion: $i > $i). 664.09/87.89 thf(eqbreln_type, type, eqbreln: $o). 664.09/87.89 thf(binintersectLsub_type, type, binintersectLsub: $o). 664.09/87.89 thf(subsetI1_type, type, subsetI1: $o). 664.09/87.89 thf(symdiffE_type, type, symdiffE: $o). 664.09/87.89 thf(descrp_type, type, descrp: $o). 664.09/87.89 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 664.09/87.89 thf(foundationAx_type, type, foundationAx: $o). 664.09/87.89 thf(brelnall1_type, type, brelnall1: $o). 664.09/87.89 thf(emptysetAx_type, type, emptysetAx: $o). 664.09/87.89 thf(emptyI_type, type, emptyI: $o). 664.09/87.89 thf(setadjoinOr_type, type, setadjoinOr: $o). 664.09/87.89 thf(binintersectEL_type, type, binintersectEL: $o). 664.09/87.89 thf(emptyE1_type, type, emptyE1: $o). 664.09/87.89 thf(ex1E2_type, type, ex1E2: $o). 664.09/87.89 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 664.09/87.89 thf(funcImageSingleton_type, type, funcImageSingleton: $o). 664.09/87.89 thf(sk__139_type, type, sk__139: $o). 664.09/87.89 thf(vacuousDall_type, type, vacuousDall: $o). 664.09/87.89 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 664.09/87.89 thf(dsetconstrER_type, type, dsetconstrER: $o). 664.09/87.89 thf(funcGraphProp3_type, type, funcGraphProp3: $o). 664.09/87.89 thf(binintersectI_type, type, binintersectI: $o). 664.09/87.89 thf(funcGraphProp4_type, type, funcGraphProp4: $o). 664.09/87.89 thf(lamp_type, type, lamp: $o). 664.09/87.89 thf(cartprodpairin_type, type, cartprodpairin: $o). 664.09/87.89 thf(eta1_type, type, eta1: $o). 664.09/87.89 thf(ex1I_type, type, ex1I: $o). 664.09/87.89 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 664.09/87.89 thf(eta2_type, type, eta2: $o). 664.09/87.89 thf(cartprodsndin_type, type, cartprodsndin: $o). 664.09/87.89 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 664.09/87.89 thf(symdiffI1_type, type, symdiffI1: $o). 664.09/87.89 thf(subsetI2_type, type, subsetI2: $o). 664.09/87.89 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o). 664.09/87.89 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 664.09/87.89 thf(theprop_type, type, theprop: $o). 664.09/87.89 thf(setminusERneg_type, type, setminusERneg: $o). 664.09/87.89 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 664.09/87.89 thf(omega__Cong_type, type, omega__Cong: $o). 664.09/87.89 thf(subsetRefl_type, type, subsetRefl: $o). 664.09/87.89 thf(uniqinunit_type, type, uniqinunit: $o). 664.09/87.89 thf(lam2p_type, type, lam2p: $o). 664.09/87.89 thf(beta1_type, type, beta1: $o). 664.09/87.89 thf(setminusSubset2_type, type, setminusSubset2: $o). 664.09/87.89 thf(prop2setE_type, type, prop2setE: $o). 664.09/87.89 thf(sk__140_type, type, sk__140: $i). 664.09/87.89 thf(binunionEcases_type, type, binunionEcases: $o). 664.09/87.89 thf(ifSingleton_type, type, ifSingleton: $o). 664.09/87.89 thf(if_type, type, if: $i > $o > $i > $i > $i). 664.09/87.89 thf(nonemptyI_type, type, nonemptyI: $o). 664.09/87.89 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 664.09/87.89 thf(exuE3u_type, type, exuE3u: $o). 664.09/87.89 thf(setminusEL_type, type, setminusEL: $o). 664.09/87.89 thf(funcextLem_type, type, funcextLem: $o). 664.09/87.89 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 664.09/87.89 thf(sepSubset_type, type, sepSubset: $o). 664.09/87.89 thf(upairset2E_type, type, upairset2E: $o). 664.09/87.89 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 664.09/87.89 thf(exuI3_type, type, exuI3: $o). 664.09/87.89 thf(notdallE_type, type, notdallE: $o). 664.09/87.89 thf(binintersectER_type, type, binintersectER: $o). 664.09/87.89 thf(ksndsingleton_type, type, ksndsingleton: $o). 664.09/87.89 thf(powerset_type, type, powerset: $i > $i). 664.09/87.89 thf(ap2apEq1_type, type, ap2apEq1: $o). 664.09/87.89 thf(beta2_type, type, beta2: $o). 664.09/87.89 thf(kfstsingleton_type, type, kfstsingleton: $o). 664.09/87.89 thf(dsetconstrI_type, type, dsetconstrI: $o). 664.09/87.89 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o). 664.09/87.89 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 664.09/87.89 thf(exu__Cong_type, type, exu__Cong: $o). 664.09/87.89 thf(ksndpairEq_type, type, ksndpairEq: $o). 664.09/87.89 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 664.09/87.89 thf(iftrueProp2_type, type, iftrueProp2: $o). 664.09/87.89 thf(ex1E1_type, type, ex1E1: $o). 664.09/87.89 thf(secondinupair_type, type, secondinupair: $o). 664.09/87.89 thf(singletonsubset_type, type, singletonsubset: $o). 664.09/87.89 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 664.09/87.89 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 664.09/87.89 thf(brelnall2_type, type, brelnall2: $o). 664.09/87.89 thf(replAx_type, type, replAx: $o). 664.09/87.89 thf(nonemptyE1_type, type, nonemptyE1: $o). 664.09/87.89 thf(omegaIndAx_type, type, omegaIndAx: $o). 664.09/87.89 thf(setukpairIL_type, type, setukpairIL: $o). 664.09/87.89 thf(setunionE2_type, type, setunionE2: $o). 664.09/87.89 thf(inPowerset_type, type, inPowerset: $o). 664.09/87.89 thf(subset_type, type, subset: $i > $i > $o). 664.09/87.89 thf(apProp_type, type, apProp: $o). 664.09/87.89 thf(in__Cong_type, type, in__Cong: $o). 664.09/87.89 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 664.09/87.89 thf(binunionRsub_type, type, binunionRsub: $o). 664.09/87.89 thf(subset2powerset_type, type, subset2powerset: $o). 664.09/87.89 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 664.09/87.89 thf(if, axiom,(( if ) = 664.09/87.89 (^[A:$i,Xphi:$o,Xx:$i,Xy:$i]: 664.09/87.89 ( setunion @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 A @ 664.09/87.89 ( ^[Xz:$i]: 664.09/87.89 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) | 664.09/87.89 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) )))). 664.09/87.89 thf('0', plain, 664.09/87.89 (( if ) = 664.09/87.89 ( ^[A:$i,Xphi:$o,Xx:$i,Xy:$i]: 664.09/87.89 ( setunion @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 A @ 664.09/87.89 ( ^[Xz:$i]: 664.09/87.89 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) | 664.09/87.89 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) ) )), 664.09/87.89 inference('simplify_rw_rule', [status(thm)], [if])). 664.09/87.89 thf('1', plain, 664.09/87.89 (( if ) = 664.09/87.89 ( ^[V_1:$i,V_2:$o,V_3:$i,V_4:$i]: 664.09/87.89 ( setunion @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 V_1 @ 664.09/87.89 ( ^[V_5:$i]: 664.09/87.89 ( ( ( V_2 ) & ( ( V_5 ) = ( V_3 ) ) ) | 664.09/87.89 ( ( ~( V_2 ) ) & ( ( V_5 ) = ( V_4 ) ) ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(iftrueProp2, axiom, iftrueProp2 = 664.09/87.89 (![A:$i,Xphi:$o,Xx:$i]: 664.09/87.89 ( ( in @ Xx @ A ) => 664.09/87.89 ( ![Xy:$i]: 664.09/87.89 ( ( in @ Xy @ A ) => 664.09/87.89 ( ( Xphi ) => 664.09/87.89 ( ( dsetconstr @ 664.09/87.89 A @ 664.09/87.89 ( ^[Xz:$i]: 664.09/87.89 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) | 664.09/87.89 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) = 664.09/87.89 ( setadjoin @ Xx @ emptyset ) ) ) ) ) ))). 664.09/87.89 thf('2', plain, 664.09/87.89 (( iftrueProp2 ) = 664.09/87.89 ( ![X4:$i,X6:$o,X8:$i]: 664.09/87.89 ( ( in @ X8 @ X4 ) => 664.09/87.89 ( ![X10:$i]: 664.09/87.89 ( ( in @ X10 @ X4 ) => 664.09/87.89 ( ( X6 ) => 664.09/87.89 ( ( dsetconstr @ 664.09/87.89 X4 @ 664.09/87.89 ( ^[V_1:$i]: 664.09/87.89 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) | 664.09/87.89 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) = 664.09/87.89 ( setadjoin @ X8 @ emptyset ) ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(iftrueProp1, axiom, iftrueProp1 = 664.09/87.89 (![A:$i,Xphi:$o,Xx:$i]: 664.09/87.89 ( ( in @ Xx @ A ) => 664.09/87.89 ( ![Xy:$i]: 664.09/87.89 ( ( in @ Xy @ A ) => 664.09/87.89 ( ( Xphi ) => 664.09/87.89 ( in @ 664.09/87.89 Xx @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 A @ 664.09/87.89 ( ^[Xz:$i]: 664.09/87.89 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) | 664.09/87.89 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) ) ) ) ) ))). 664.09/87.89 thf('3', plain, 664.09/87.89 (( iftrueProp1 ) = 664.09/87.89 ( ![X4:$i,X6:$o,X8:$i]: 664.09/87.89 ( ( in @ X8 @ X4 ) => 664.09/87.89 ( ![X10:$i]: 664.09/87.89 ( ( in @ X10 @ X4 ) => 664.09/87.89 ( ( X6 ) => 664.09/87.89 ( in @ 664.09/87.89 X8 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X4 @ 664.09/87.89 ( ^[V_1:$i]: 664.09/87.89 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) | 664.09/87.89 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(iffalseProp2, axiom, iffalseProp2 = 664.09/87.89 (![A:$i,Xphi:$o,Xx:$i]: 664.09/87.89 ( ( in @ Xx @ A ) => 664.09/87.89 ( ![Xy:$i]: 664.09/87.89 ( ( in @ Xy @ A ) => 664.09/87.89 ( ( ~( Xphi ) ) => 664.09/87.89 ( ( dsetconstr @ 664.09/87.89 A @ 664.09/87.89 ( ^[Xz:$i]: 664.09/87.89 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) | 664.09/87.89 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) = 664.09/87.89 ( setadjoin @ Xy @ emptyset ) ) ) ) ) ))). 664.09/87.89 thf('4', plain, 664.09/87.89 (( iffalseProp2 ) = 664.09/87.89 ( ![X4:$i,X6:$o,X8:$i]: 664.09/87.89 ( ( in @ X8 @ X4 ) => 664.09/87.89 ( ![X10:$i]: 664.09/87.89 ( ( in @ X10 @ X4 ) => 664.09/87.89 ( ( ~( X6 ) ) => 664.09/87.89 ( ( dsetconstr @ 664.09/87.89 X4 @ 664.09/87.89 ( ^[V_1:$i]: 664.09/87.89 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) | 664.09/87.89 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) = 664.09/87.89 ( setadjoin @ X10 @ emptyset ) ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(iffalseProp1, axiom, iffalseProp1 = 664.09/87.89 (![A:$i,Xphi:$o,Xx:$i]: 664.09/87.89 ( ( in @ Xx @ A ) => 664.09/87.89 ( ![Xy:$i]: 664.09/87.89 ( ( in @ Xy @ A ) => 664.09/87.89 ( ( ~( Xphi ) ) => 664.09/87.89 ( in @ 664.09/87.89 Xy @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 A @ 664.09/87.89 ( ^[Xz:$i]: 664.09/87.89 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) | 664.09/87.89 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) ) ) ) ) ))). 664.09/87.89 thf('5', plain, 664.09/87.89 (( iffalseProp1 ) = 664.09/87.89 ( ![X4:$i,X6:$o,X8:$i]: 664.09/87.89 ( ( in @ X8 @ X4 ) => 664.09/87.89 ( ![X10:$i]: 664.09/87.89 ( ( in @ X10 @ X4 ) => 664.09/87.89 ( ( ~( X6 ) ) => 664.09/87.89 ( in @ 664.09/87.89 X10 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X4 @ 664.09/87.89 ( ^[V_1:$i]: 664.09/87.89 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) | 664.09/87.89 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setunionsingleton, axiom, setunionsingleton = 664.09/87.89 (![Xx:$i]: ( ( setunion @ ( setadjoin @ Xx @ emptyset ) ) = ( Xx ) ))). 664.09/87.89 thf('6', plain, 664.09/87.89 (( setunionsingleton ) = 664.09/87.89 ( ![X4:$i]: ( ( setunion @ ( setadjoin @ X4 @ emptyset ) ) = ( X4 ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setunionsingleton2, axiom, setunionsingleton2 = 664.09/87.89 (![A:$i]: ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ))). 664.09/87.89 thf('7', plain, 664.09/87.89 (( setunionsingleton2 ) = 664.09/87.89 ( ![X4:$i]: 664.09/87.89 ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setunionsingleton1, axiom, setunionsingleton1 = 664.09/87.89 (![A:$i]: ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ))). 664.09/87.89 thf('8', plain, 664.09/87.89 (( setunionsingleton1 ) = 664.09/87.89 ( ![X4:$i]: 664.09/87.89 ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setunionE2, axiom, setunionE2 = 664.09/87.89 (![A:$i,Xx:$i]: 664.09/87.89 ( ( in @ Xx @ ( setunion @ A ) ) => 664.09/87.89 ( ?[X:$i]: ( ( in @ Xx @ X ) & ( in @ X @ A ) ) ) ))). 664.09/87.89 thf('9', plain, 664.09/87.89 (( setunionE2 ) = 664.09/87.89 ( ![X4:$i,X6:$i]: 664.09/87.89 ( ( in @ X6 @ ( setunion @ X4 ) ) => 664.09/87.89 ( ?[X8:$i]: ( ( in @ X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setukpairIR, axiom, setukpairIR = 664.09/87.89 (![Xx:$i,Xy:$i]: 664.09/87.89 ( in @ 664.09/87.89 Xy @ 664.09/87.89 ( setunion @ 664.09/87.89 ( setadjoin @ 664.09/87.89 ( setadjoin @ Xx @ emptyset ) @ 664.09/87.89 ( setadjoin @ 664.09/87.89 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ))). 664.09/87.89 thf('10', plain, 664.09/87.89 (( setukpairIR ) = 664.09/87.89 ( ![X4:$i,X6:$i]: 664.09/87.89 ( in @ 664.09/87.89 X6 @ 664.09/87.89 ( setunion @ 664.09/87.89 ( setadjoin @ 664.09/87.89 ( setadjoin @ X4 @ emptyset ) @ 664.09/87.89 ( setadjoin @ 664.09/87.89 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setukpairIL, axiom, setukpairIL = 664.09/87.89 (![Xx:$i,Xy:$i]: 664.09/87.89 ( in @ 664.09/87.89 Xx @ 664.09/87.89 ( setunion @ 664.09/87.89 ( setadjoin @ 664.09/87.89 ( setadjoin @ Xx @ emptyset ) @ 664.09/87.89 ( setadjoin @ 664.09/87.89 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ))). 664.09/87.89 thf('11', plain, 664.09/87.89 (( setukpairIL ) = 664.09/87.89 ( ![X4:$i,X6:$i]: 664.09/87.89 ( in @ 664.09/87.89 X4 @ 664.09/87.89 ( setunion @ 664.09/87.89 ( setadjoin @ 664.09/87.89 ( setadjoin @ X4 @ emptyset ) @ 664.09/87.89 ( setadjoin @ 664.09/87.89 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(sepSubset, axiom, sepSubset = 664.09/87.89 (![A:$i,Xphi:( $i > $o )]: 664.09/87.89 ( subset @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ A ))). 664.09/87.89 thf('12', plain, 664.09/87.89 (( sepSubset ) = 664.09/87.89 ( ![X4:$i,X6:( $i > $o )]: 664.09/87.89 ( subset @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @ X4 ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(notequalI2, axiom, notequalI2 = 664.09/87.89 (![A:$i,B:$i,Xx:$i]: 664.09/87.89 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ( A ) != ( B ) ) ) ))). 664.09/87.89 thf('13', plain, 664.09/87.89 (( notequalI2 ) = 664.09/87.89 ( ![X4:$i,X6:$i,X8:$i]: 664.09/87.89 ( ( in @ X8 @ X4 ) => 664.09/87.89 ( ( ~( in @ X8 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(dsetconstr__Cong, axiom, dsetconstr__Cong = 664.09/87.89 (![A:$i,B:$i]: 664.09/87.89 ( ( ( A ) = ( B ) ) => 664.09/87.89 ( ![Xphi:( $i > $o ),Xpsi:( $i > $o )]: 664.09/87.89 ( ( ![Xx:$i]: 664.09/87.89 ( ( in @ Xx @ A ) => 664.09/87.89 ( ![Xy:$i]: 664.09/87.89 ( ( in @ Xy @ B ) => 664.09/87.89 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) ) ) ) => 664.09/87.89 ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) = 664.09/87.89 ( dsetconstr @ B @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ) ) ))). 664.09/87.89 thf('14', plain, 664.09/87.89 (( dsetconstr__Cong ) = 664.09/87.89 ( ![X4:$i,X6:$i]: 664.09/87.89 ( ( ( X4 ) = ( X6 ) ) => 664.09/87.89 ( ![X8:( $i > $o ),X10:( $i > $o )]: 664.09/87.89 ( ( ![X12:$i]: 664.09/87.89 ( ( in @ X12 @ X4 ) => 664.09/87.89 ( ![X14:$i]: 664.09/87.89 ( ( in @ X14 @ X6 ) => 664.09/87.89 ( ( ( X12 ) = ( X14 ) ) => 664.09/87.89 ( ( X8 @ X12 ) <=> ( X10 @ X14 ) ) ) ) ) ) ) => 664.09/87.89 ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) = 664.09/87.89 ( dsetconstr @ X6 @ ( ^[V_2:$i]: ( X10 @ V_2 ) ) ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setunion__Cong, axiom, setunion__Cong = 664.09/87.89 (![A:$i,B:$i]: 664.09/87.89 ( ( ( A ) = ( B ) ) => ( ( setunion @ A ) = ( setunion @ B ) ) ))). 664.09/87.89 thf('15', plain, 664.09/87.89 (( setunion__Cong ) = 664.09/87.89 ( ![X4:$i,X6:$i]: 664.09/87.89 ( ( ( X4 ) = ( X6 ) ) => ( ( setunion @ X4 ) = ( setunion @ X6 ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(in__Cong, axiom, in__Cong = 664.09/87.89 (![A:$i,B:$i]: 664.09/87.89 ( ( ( A ) = ( B ) ) => 664.09/87.89 ( ![Xx:$i,Xy:$i]: 664.09/87.89 ( ( ( Xx ) = ( Xy ) ) => ( ( in @ Xx @ A ) <=> ( in @ Xy @ B ) ) ) ) ))). 664.09/87.89 thf('16', plain, 664.09/87.89 (( in__Cong ) = 664.09/87.89 ( ![X4:$i,X6:$i]: 664.09/87.89 ( ( ( X4 ) = ( X6 ) ) => 664.09/87.89 ( ![X8:$i,X10:$i]: 664.09/87.89 ( ( ( X8 ) = ( X10 ) ) => 664.09/87.89 ( ( in @ X8 @ X4 ) <=> ( in @ X10 @ X6 ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(inCongP, axiom, inCongP = 664.09/87.89 (![A:$i,B:$i]: 664.09/87.89 ( ( ( A ) = ( B ) ) => 664.09/87.89 ( ![Xx:$i,Xy:$i]: 664.09/87.89 ( ( ( Xx ) = ( Xy ) ) => ( ( in @ Xx @ A ) => ( in @ Xy @ B ) ) ) ) ))). 664.09/87.89 thf('17', plain, 664.09/87.89 (( inCongP ) = 664.09/87.89 ( ![X4:$i,X6:$i]: 664.09/87.89 ( ( ( X4 ) = ( X6 ) ) => 664.09/87.89 ( ![X8:$i,X10:$i]: 664.09/87.89 ( ( ( X8 ) = ( X10 ) ) => 664.09/87.89 ( ( in @ X8 @ X4 ) => ( in @ X10 @ X6 ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(notdallE, axiom, notdallE = 664.09/87.89 (![A:$i,Xphi:( $i > $o )]: 664.09/87.89 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) => 664.09/87.89 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))). 664.09/87.89 thf('18', plain, 664.09/87.89 (( notdallE ) = 664.09/87.89 ( ![X4:$i,X6:( $i > $o )]: 664.09/87.89 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) => 664.09/87.89 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(notdexE, axiom, notdexE = 664.09/87.89 (![A:$i,Xphi:( $i > $o )]: 664.09/87.89 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) => 664.09/87.89 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))). 664.09/87.89 thf('19', plain, 664.09/87.89 (( notdexE ) = 664.09/87.89 ( ![X4:$i,X6:( $i > $o )]: 664.09/87.89 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) => 664.09/87.89 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(quantDeMorgan4, axiom, quantDeMorgan4 = 664.09/87.89 (![A:$i,Xphi:( $i > $o )]: 664.09/87.89 ( ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) => 664.09/87.89 ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) ))). 664.09/87.89 thf('20', plain, 664.09/87.89 (( quantDeMorgan4 ) = 664.09/87.89 ( ![X4:$i,X6:( $i > $o )]: 664.09/87.89 ( ( ?[X8:$i]: ( ( ~( X6 @ X8 ) ) & ( in @ X8 @ X4 ) ) ) => 664.09/87.89 ( ~( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( X6 @ X10 ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(quantDeMorgan3, axiom, quantDeMorgan3 = 664.09/87.89 (![A:$i,Xphi:( $i > $o )]: 664.09/87.89 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) => 664.09/87.89 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))). 664.09/87.89 thf('21', plain, 664.09/87.89 (( quantDeMorgan3 ) = 664.09/87.89 ( ![X4:$i,X6:( $i > $o )]: 664.09/87.89 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) => 664.09/87.89 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(quantDeMorgan2, axiom, quantDeMorgan2 = 664.09/87.89 (![A:$i,Xphi:( $i > $o )]: 664.09/87.89 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) => 664.09/87.89 ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) ))). 664.09/87.89 thf('22', plain, 664.09/87.89 (( quantDeMorgan2 ) = 664.09/87.89 ( ![X4:$i,X6:( $i > $o )]: 664.09/87.89 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( ~( X6 @ X8 ) ) ) ) => 664.09/87.89 ( ~( ?[X10:$i]: ( ( X6 @ X10 ) & ( in @ X10 @ X4 ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(quantDeMorgan1, axiom, quantDeMorgan1 = 664.09/87.89 (![A:$i,Xphi:( $i > $o )]: 664.09/87.89 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) => 664.09/87.89 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))). 664.09/87.89 thf('23', plain, 664.09/87.89 (( quantDeMorgan1 ) = 664.09/87.89 ( ![X4:$i,X6:( $i > $o )]: 664.09/87.89 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) => 664.09/87.89 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(emptyE1, axiom, emptyE1 = 664.09/87.89 (![A:$i,Xphi:( $i > $o )]: 664.09/87.89 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) => 664.09/87.89 ( ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) = ( emptyset ) ) => 664.09/87.89 ( $false ) ) ))). 664.09/87.89 thf('24', plain, 664.09/87.89 (( emptyE1 ) = 664.09/87.89 ( ![X4:$i,X6:( $i > $o )]: 664.09/87.89 ( ( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) => 664.09/87.89 ( ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = ( emptyset ) ) => 664.09/87.89 ( $false ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(subPowSU, axiom, subPowSU = 664.09/87.89 (![A:$i,Xx:$i]: 664.09/87.89 ( ( in @ Xx @ A ) => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ))). 664.09/87.89 thf('25', plain, 664.09/87.89 (( subPowSU ) = 664.09/87.89 ( ![X4:$i,X6:$i]: 664.09/87.89 ( ( in @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ ( setunion @ X4 ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setunionE, axiom, setunionE = 664.09/87.89 (![A:$i,Xx:$i]: 664.09/87.89 ( ( in @ Xx @ ( setunion @ A ) ) => 664.09/87.89 ( ![Xphi:$o]: 664.09/87.89 ( ( ![B:$i]: ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( Xphi ) ) ) ) => 664.09/87.89 ( Xphi ) ) ) ))). 664.09/87.89 thf('26', plain, 664.09/87.89 (( setunionE ) = 664.09/87.89 ( ![X4:$i,X6:$i]: 664.09/87.89 ( ( in @ X6 @ ( setunion @ X4 ) ) => 664.09/87.89 ( ![X8:$o]: 664.09/87.89 ( ( ![X10:$i]: 664.09/87.89 ( ( in @ X6 @ X10 ) => ( ( in @ X10 @ X4 ) => ( X8 ) ) ) ) => 664.09/87.89 ( X8 ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setunionI, axiom, setunionI = 664.09/87.89 (![A:$i,Xx:$i,B:$i]: 664.09/87.89 ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( in @ Xx @ ( setunion @ A ) ) ) ))). 664.09/87.89 thf('27', plain, 664.09/87.89 (( setunionI ) = 664.09/87.89 ( ![X4:$i,X6:$i,X8:$i]: 664.09/87.89 ( ( in @ X6 @ X8 ) => 664.09/87.89 ( ( in @ X8 @ X4 ) => ( in @ X6 @ ( setunion @ X4 ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setoftrueEq, axiom, setoftrueEq = 664.09/87.89 (![A:$i]: ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( $true ) ) ) = ( A ) ))). 664.09/87.89 thf('28', plain, 664.09/87.89 (( setoftrueEq ) = 664.09/87.89 ( ![X4:$i]: ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( $true ) ) ) = ( X4 ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setbeta, axiom, setbeta = 664.09/87.89 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 664.09/87.89 ( ( in @ Xx @ A ) => 664.09/87.89 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) <=> 664.09/87.89 ( Xphi @ Xx ) ) ))). 664.09/87.89 thf('29', plain, 664.09/87.89 (( setbeta ) = 664.09/87.89 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 664.09/87.89 ( ( in @ X8 @ X4 ) => 664.09/87.89 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=> 664.09/87.89 ( X6 @ X8 ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setext, axiom, setext = 664.09/87.89 (![A:$i,B:$i]: 664.09/87.89 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) => 664.09/87.89 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) => 664.09/87.89 ( ( A ) = ( B ) ) ) ))). 664.09/87.89 thf('30', plain, 664.09/87.89 (( setext ) = 664.09/87.89 ( ![X4:$i,X6:$i]: 664.09/87.89 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) => 664.09/87.89 ( ( ![X10:$i]: ( ( in @ X10 @ X6 ) => ( in @ X10 @ X4 ) ) ) => 664.09/87.89 ( ( X4 ) = ( X6 ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(dsetconstrER, axiom, dsetconstrER = 664.09/87.89 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 664.09/87.89 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) => 664.09/87.89 ( Xphi @ Xx ) ))). 664.09/87.89 thf('31', plain, 664.09/87.89 (( dsetconstrER ) = 664.09/87.89 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 664.09/87.89 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 664.09/87.89 ( X6 @ X8 ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(dsetconstrEL, axiom, dsetconstrEL = 664.09/87.89 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 664.09/87.89 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) => 664.09/87.89 ( in @ Xx @ A ) ))). 664.09/87.89 thf('32', plain, 664.09/87.89 (( dsetconstrEL ) = 664.09/87.89 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 664.09/87.89 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 664.09/87.89 ( in @ X8 @ X4 ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(dsetconstrI, axiom, dsetconstrI = 664.09/87.89 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 664.09/87.89 ( ( in @ Xx @ A ) => 664.09/87.89 ( ( Xphi @ Xx ) => 664.09/87.89 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))). 664.09/87.89 thf('33', plain, 664.09/87.89 (( dsetconstrI ) = 664.09/87.89 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 664.09/87.89 ( ( in @ X8 @ X4 ) => 664.09/87.89 ( ( X6 @ X8 ) => 664.09/87.89 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(wellorderingAx, axiom, wellorderingAx = 664.09/87.89 (![A:$i]: 664.09/87.89 ( ?[B:$i]: 664.09/87.89 ( ( ![C:$i]: 664.09/87.89 ( ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) & 664.09/87.89 ( ?[Xx:$i]: ( in @ Xx @ C ) ) ) => 664.09/87.89 ( ?[D:$i,Xx:$i]: 664.09/87.89 ( ( ![E:$i]: 664.09/87.89 ( ( in @ E @ B ) => 664.09/87.89 ( ( ![Xy:$i]: ( ( in @ Xy @ E ) => ( in @ Xy @ D ) ) ) | 664.09/87.89 ( in @ Xx @ E ) ) ) ) & 664.09/87.89 ( ~( ?[Xy:$i]: ( ( in @ Xy @ C ) & ( in @ Xy @ D ) ) ) ) & 664.09/87.89 ( in @ Xx @ C ) & ( in @ D @ B ) ) ) ) ) & 664.09/87.89 ( ![C:$i,D:$i]: 664.09/87.89 ( ( ( in @ C @ B ) & ( in @ D @ B ) ) => 664.09/87.89 ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ D ) ) ) | 664.09/87.89 ( ![Xx:$i]: ( ( in @ Xx @ D ) => ( in @ Xx @ C ) ) ) ) ) ) & 664.09/87.89 ( ![Xx:$i,Xy:$i]: 664.09/87.89 ( ( ( in @ Xx @ A ) & ( in @ Xy @ A ) ) => 664.09/87.89 ( ( ![C:$i]: 664.09/87.89 ( ( in @ C @ B ) => ( ( in @ Xx @ C ) <=> ( in @ Xy @ C ) ) ) ) => 664.09/87.89 ( ( Xx ) = ( Xy ) ) ) ) ) & 664.09/87.89 ( ![C:$i]: 664.09/87.89 ( ( in @ C @ B ) => 664.09/87.89 ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) ) ) ) ))). 664.09/87.89 thf('34', plain, 664.09/87.89 (( wellorderingAx ) = 664.09/87.89 ( ![X4:$i]: 664.09/87.89 ( ?[X6:$i]: 664.09/87.89 ( ( ![X8:$i]: 664.09/87.89 ( ( ( ![X10:$i]: ( ( in @ X10 @ X8 ) => ( in @ X10 @ X4 ) ) ) & 664.09/87.89 ( ?[X12:$i]: ( in @ X12 @ X8 ) ) ) => 664.09/87.89 ( ?[X14:$i,X16:$i]: 664.09/87.89 ( ( ![X18:$i]: 664.09/87.89 ( ( in @ X18 @ X6 ) => 664.09/87.89 ( ( ![X20:$i]: 664.09/87.89 ( ( in @ X20 @ X18 ) => ( in @ X20 @ X14 ) ) ) | 664.09/87.89 ( in @ X16 @ X18 ) ) ) ) & 664.09/87.89 ( ~( ?[X22:$i]: ( ( in @ X22 @ X8 ) & ( in @ X22 @ X14 ) ) ) ) & 664.09/87.89 ( in @ X16 @ X8 ) & ( in @ X14 @ X6 ) ) ) ) ) & 664.09/87.89 ( ![X24:$i,X26:$i]: 664.09/87.89 ( ( ( in @ X24 @ X6 ) & ( in @ X26 @ X6 ) ) => 664.09/87.89 ( ( ![X28:$i]: ( ( in @ X28 @ X24 ) => ( in @ X28 @ X26 ) ) ) | 664.09/87.89 ( ![X30:$i]: ( ( in @ X30 @ X26 ) => ( in @ X30 @ X24 ) ) ) ) ) ) & 664.09/87.89 ( ![X32:$i,X34:$i]: 664.09/87.89 ( ( ( in @ X32 @ X4 ) & ( in @ X34 @ X4 ) ) => 664.09/87.89 ( ( ![X36:$i]: 664.09/87.89 ( ( in @ X36 @ X6 ) => 664.09/87.89 ( ( in @ X32 @ X36 ) <=> ( in @ X34 @ X36 ) ) ) ) => 664.09/87.89 ( ( X32 ) = ( X34 ) ) ) ) ) & 664.09/87.89 ( ![X38:$i]: 664.09/87.89 ( ( in @ X38 @ X6 ) => 664.09/87.89 ( ![X40:$i]: ( ( in @ X40 @ X38 ) => ( in @ X40 @ X4 ) ) ) ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(foundationAx, axiom, foundationAx = 664.09/87.89 (![A:$i]: 664.09/87.89 ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) => 664.09/87.89 ( ?[B:$i]: 664.09/87.89 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ A ) & ( in @ Xx @ B ) ) ) ) & 664.09/87.89 ( in @ B @ A ) ) ) ))). 664.09/87.89 thf('35', plain, 664.09/87.89 (( foundationAx ) = 664.09/87.89 ( ![X4:$i]: 664.09/87.89 ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) => 664.09/87.89 ( ?[X8:$i]: 664.09/87.89 ( ( ~( ?[X10:$i]: ( ( in @ X10 @ X4 ) & ( in @ X10 @ X8 ) ) ) ) & 664.09/87.89 ( in @ X8 @ X4 ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setunionAx, axiom, setunionAx = 664.09/87.89 (![A:$i,Xx:$i]: 664.09/87.89 ( ( in @ Xx @ ( setunion @ A ) ) <=> 664.09/87.89 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))). 664.09/87.89 thf('36', plain, 664.09/87.89 (( setunionAx ) = 664.09/87.89 ( ![X4:$i,X6:$i]: 664.09/87.89 ( ( in @ X6 @ ( setunion @ X4 ) ) <=> 664.09/87.89 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(setextAx, axiom, setextAx = 664.09/87.89 (![A:$i,B:$i]: 664.09/87.89 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) <=> ( in @ Xx @ B ) ) ) => 664.09/87.89 ( ( A ) = ( B ) ) ))). 664.09/87.89 thf('37', plain, 664.09/87.89 (( setextAx ) = 664.09/87.89 ( ![X4:$i,X6:$i]: 664.09/87.89 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) => 664.09/87.89 ( ( X4 ) = ( X6 ) ) ) )), 664.09/87.89 define([status(thm)])). 664.09/87.89 thf(ifp, conjecture, 664.09/87.89 (( setextAx ) => 664.09/87.89 ( ( emptysetAx ) => 664.09/87.89 ( ( setadjoinAx ) => 664.09/87.89 ( ( powersetAx ) => 664.09/87.89 ( ( setunionAx ) => 664.09/87.89 ( ( omega0Ax ) => 664.09/87.89 ( ( omegaSAx ) => 664.09/87.89 ( ( omegaIndAx ) => 664.09/87.89 ( ( replAx ) => 664.09/87.89 ( ( foundationAx ) => 664.09/87.89 ( ( wellorderingAx ) => 664.09/87.89 ( ( descrp ) => 664.09/87.89 ( ( dsetconstrI ) => 664.09/87.89 ( ( dsetconstrEL ) => 664.09/87.89 ( ( dsetconstrER ) => 664.09/87.89 ( ( exuE1 ) => 664.09/87.89 ( ( prop2setE ) => 664.09/87.89 ( ( emptysetE ) => 664.09/87.89 ( ( emptysetimpfalse ) => 664.09/87.89 ( ( notinemptyset ) => 664.09/87.89 ( ( exuE3e ) => 664.09/87.89 ( ( setext ) => 664.09/87.89 ( ( emptyI ) => 664.09/87.89 ( ( noeltsimpempty ) => 664.09/87.89 ( ( setbeta ) => 664.09/87.89 ( ( nonemptyE1 ) => 664.09/87.89 ( ( nonemptyI ) => 664.09/87.89 ( ( nonemptyI1 ) => 664.09/87.89 ( ( setadjoinIL ) => 664.09/87.89 ( ( emptyinunitempty ) => 664.09/87.89 ( ( setadjoinIR ) => 664.09/87.89 ( ( setadjoinE ) => 664.09/87.89 ( ( 664.09/87.89 setadjoinOr ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setoftrueEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptyinPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptyInPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setunionI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setunionE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subPowSU ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuE2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 nonemptyImpWitness ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 uniqinunit ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notinsingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqinunit ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonsswitch ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsetE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsetIL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsetIR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptyE1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 vacuousDall ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 quantDeMorgan1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 quantDeMorgan2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 quantDeMorgan3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 quantDeMorgan4 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 prop2setI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 prop2set2propI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notdexE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notdallE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuI3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuI2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 inCongP ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuE3u ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exu__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptyset__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setadjoin__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powerset__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setunion__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 omega__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuEu ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 descr__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqimpsubset2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqimpsubset1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetI2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptysetsubset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetE2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notsubsetI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notequalI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notequalI2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetRefl ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetTrans ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setadjoinSub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setadjoinSub2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subset2powerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setextsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetemptysetimpeq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetE1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 inPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetsubset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 sepInPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 sepSubset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionIL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairset2IR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionIR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionEcases ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionLsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionRsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset5 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectEL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectLsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 disjointsetsI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectRsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset4 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 bs114d ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusEL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusSubset2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusERneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusELneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusILneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusIRneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusLsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusSubset1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffI2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffIneg1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffIneg2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 secondinupair ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairIL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairIR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kpairiskpair ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kpairp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonsubset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletoninpowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletoninpowunion ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairset2E ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsubunion ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairinpowunion ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ubforcartprodlem1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ubforcartprodlem2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ubforcartprodlem3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairin ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodmempair1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodmempair ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setunionE2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setunionsingleton1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setunionsingleton2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setunionsingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonprop ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1E1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1I ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1I2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonsuniq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjL1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kfstsingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 theprop ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kfstpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodfstin ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjL2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR11 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR12 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairequniteq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ksndsingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ksndpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kpairsurjEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodsndin ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairmemEL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairmemER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodmempaircEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodfstpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodsndpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairsurjEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrSub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setOfPairsIsBReln ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrERa ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrEL1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrEL2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcImageSingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 apProp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 app ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 infuncsetfunc ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ap2p ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcinfuncset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lamProp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lamp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lam2p ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 brelnall1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 brelnall2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1E2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcextLem ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp4 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subbreln ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqbreln ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcext ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcext2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ap2apEq1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ap2apEq2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 beta1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eta1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lam2lamEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 beta2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eta2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 iffalseProp1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 iffalseProp2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 iftrueProp1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 iftrueProp2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ifSingleton ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 A:$i, 664.09/87.89 Xphi:$o, 664.09/87.89 Xx:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 Xx @ A ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 Xy:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 Xy @ A ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 ( 664.09/87.89 if @ 664.09/87.89 A @ 664.09/87.89 Xphi @ 664.09/87.89 Xx @ Xy ) @ 664.09/87.89 A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 664.09/87.89 thf(zf_stmt_0, conjecture, 664.09/87.89 (( ![X4:$i,X6:$i]: 664.09/87.89 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) => 664.09/87.89 ( ( X4 ) = ( X6 ) ) ) ) => 664.09/87.89 ( ( emptysetAx ) => 664.09/87.89 ( ( setadjoinAx ) => 664.09/87.89 ( ( powersetAx ) => 664.09/87.89 ( ( ![X10:$i,X12:$i]: 664.09/87.89 ( ( in @ X12 @ ( setunion @ X10 ) ) <=> 664.09/87.89 ( ?[X14:$i]: ( ( in @ X12 @ X14 ) & ( in @ X14 @ X10 ) ) ) ) ) => 664.09/87.89 ( ( omega0Ax ) => 664.09/87.89 ( ( omegaSAx ) => 664.09/87.89 ( ( omegaIndAx ) => 664.09/87.89 ( ( replAx ) => 664.09/87.89 ( ( ![X16:$i]: 664.09/87.89 ( ( ?[X18:$i]: ( in @ X18 @ X16 ) ) => 664.09/87.89 ( ?[X20:$i]: 664.09/87.89 ( ( in @ X20 @ X16 ) & 664.09/87.89 ( ~( ?[X22:$i]: 664.09/87.89 ( ( in @ X22 @ X20 ) & ( in @ X22 @ X16 ) ) ) ) ) ) ) ) => 664.09/87.89 ( ( ![X24:$i]: 664.09/87.89 ( ?[X26:$i]: 664.09/87.89 ( ( ![X58:$i]: 664.09/87.89 ( ( in @ X58 @ X26 ) => 664.09/87.89 ( ![X60:$i]: 664.09/87.89 ( ( in @ X60 @ X58 ) => ( in @ X60 @ X24 ) ) ) ) ) & 664.09/87.89 ( ![X52:$i,X54:$i]: 664.09/87.89 ( ( ( in @ X54 @ X24 ) & ( in @ X52 @ X24 ) ) => 664.09/87.89 ( ( ![X56:$i]: 664.09/87.89 ( ( in @ X56 @ X26 ) => 664.09/87.89 ( ( in @ X52 @ X56 ) <=> 664.09/87.89 ( in @ X54 @ X56 ) ) ) ) => 664.09/87.89 ( ( X52 ) = ( X54 ) ) ) ) ) & 664.09/87.89 ( ![X44:$i,X46:$i]: 664.09/87.89 ( ( ( in @ X46 @ X26 ) & ( in @ X44 @ X26 ) ) => 664.09/87.89 ( ( ![X50:$i]: 664.09/87.89 ( ( in @ X50 @ X46 ) => 664.09/87.89 ( in @ X50 @ X44 ) ) ) | 664.09/87.89 ( ![X48:$i]: 664.09/87.89 ( ( in @ X48 @ X44 ) => 664.09/87.89 ( in @ X48 @ X46 ) ) ) ) ) ) & 664.09/87.89 ( ![X28:$i]: 664.09/87.89 ( ( ( ?[X32:$i]: ( in @ X32 @ X28 ) ) & 664.09/87.89 ( ![X30:$i]: 664.09/87.89 ( ( in @ X30 @ X28 ) => 664.09/87.89 ( in @ X30 @ X24 ) ) ) ) => 664.09/87.89 ( ?[X34:$i,X36:$i]: 664.09/87.89 ( ( in @ X34 @ X26 ) & 664.09/87.89 ( in @ X36 @ X28 ) & 664.09/87.89 ( ~( ?[X42:$i]: 664.09/87.89 ( ( in @ X42 @ X34 ) & 664.09/87.89 ( in @ X42 @ X28 ) ) ) ) & 664.09/87.89 ( ![X38:$i]: 664.09/87.89 ( ( in @ X38 @ X26 ) => 664.09/87.89 ( ( in @ X36 @ X38 ) | 664.09/87.89 ( ![X40:$i]: 664.09/87.89 ( ( in @ X40 @ X38 ) => 664.09/87.89 ( in @ X40 @ X34 ) ) ) ) ) ) ) ) ) ) ) ) ) => 664.09/87.89 ( ( descrp ) => 664.09/87.89 ( ( ![X62:$i,X64:( $i > $o ),X66:$i]: 664.09/87.89 ( ( in @ X66 @ X62 ) => 664.09/87.89 ( ( X64 @ X66 ) => 664.09/87.89 ( in @ 664.09/87.89 X66 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X62 @ ( ^[V_1:$i]: ( X64 @ V_1 ) ) ) ) ) ) ) => 664.09/87.89 ( ( ![X68:$i,X70:( $i > $o ),X72:$i]: 664.09/87.89 ( ( in @ 664.09/87.89 X72 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X68 @ ( ^[V_2:$i]: ( X70 @ V_2 ) ) ) ) => 664.09/87.89 ( in @ X72 @ X68 ) ) ) => 664.09/87.89 ( ( ![X74:$i,X76:( $i > $o ),X78:$i]: 664.09/87.89 ( ( in @ 664.09/87.89 X78 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X74 @ ( ^[V_3:$i]: ( X76 @ V_3 ) ) ) ) => 664.09/87.89 ( X76 @ X78 ) ) ) => 664.09/87.89 ( ( exuE1 ) => 664.09/87.89 ( ( prop2setE ) => 664.09/87.89 ( ( emptysetE ) => 664.09/87.89 ( ( emptysetimpfalse ) => 664.09/87.89 ( ( notinemptyset ) => 664.09/87.89 ( ( exuE3e ) => 664.09/87.89 ( ( ![X80:$i,X82:$i]: 664.09/87.89 ( ( ![X84:$i]: 664.09/87.89 ( ( in @ X84 @ X80 ) => 664.09/87.89 ( in @ X84 @ X82 ) ) ) => 664.09/87.89 ( ( ![X86:$i]: 664.09/87.89 ( ( in @ X86 @ X82 ) => 664.09/87.89 ( in @ X86 @ X80 ) ) ) => 664.09/87.89 ( ( X80 ) = ( X82 ) ) ) ) ) => 664.09/87.89 ( ( emptyI ) => 664.09/87.89 ( ( noeltsimpempty ) => 664.09/87.89 ( ( ![X88:$i, 664.09/87.89 X90:( $i > $o ),X92:$i]: 664.09/87.89 ( ( in @ X92 @ X88 ) => 664.09/87.89 ( ( in @ 664.09/87.89 X92 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X88 @ 664.09/87.89 ( ^[V_4:$i]: 664.09/87.89 ( X90 @ V_4 ) ) ) ) <=> 664.09/87.89 ( X90 @ X92 ) ) ) ) => 664.09/87.89 ( ( nonemptyE1 ) => 664.09/87.89 ( ( nonemptyI ) => 664.09/87.89 ( ( nonemptyI1 ) => 664.09/87.89 ( ( setadjoinIL ) => 664.09/87.89 ( ( emptyinunitempty ) => 664.09/87.89 ( ( setadjoinIR ) => 664.09/87.89 ( ( setadjoinE ) => 664.09/87.89 ( ( 664.09/87.89 setadjoinOr ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X94:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X94 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_5:$i]: 664.09/87.89 ( 664.09/87.89 $true ) ) ) = 664.09/87.89 ( 664.09/87.89 X94 ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptyinPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptyInPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X96:$i, 664.09/87.89 X98:$i, 664.09/87.89 X100:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X98 @ X100 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X100 @ X96 ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X98 @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 X96 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X102:$i, 664.09/87.89 X104:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X104 @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 X102 ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X106:$o]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X108:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X104 @ 664.09/87.89 X108 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X108 @ 664.09/87.89 X102 ) => 664.09/87.89 ( 664.09/87.89 X106 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 X106 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X110:$i, 664.09/87.89 X112:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X112 @ 664.09/87.89 X110 ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X112 @ 664.09/87.89 ( 664.09/87.89 powerset @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 X110 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuE2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 nonemptyImpWitness ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 uniqinunit ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notinsingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqinunit ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonsswitch ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsetE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsetIL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsetIR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X114:$i, 664.09/87.89 X116:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X118:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X118 @ 664.09/87.89 X114 ) & 664.09/87.89 ( 664.09/87.89 X116 @ 664.09/87.89 X118 ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X114 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_6:$i]: 664.09/87.89 ( 664.09/87.89 X116 @ V_6 ) ) ) = 664.09/87.89 ( 664.09/87.89 emptyset ) ) => 664.09/87.89 ( 664.09/87.89 $false ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 vacuousDall ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X120:$i, 664.09/87.89 X122:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 ![ 664.09/87.89 X124:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X124 @ 664.09/87.89 X120 ) => 664.09/87.89 ( 664.09/87.89 X122 @ 664.09/87.89 X124 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X126:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X126 @ 664.09/87.89 X120 ) & 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 X122 @ 664.09/87.89 X126 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X128:$i, 664.09/87.89 X130:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X132:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X132 @ 664.09/87.89 X128 ) => 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 X130 @ 664.09/87.89 X132 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 ?[ 664.09/87.89 X134:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X134 @ 664.09/87.89 X128 ) & 664.09/87.89 ( 664.09/87.89 X130 @ 664.09/87.89 X134 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X136:$i, 664.09/87.89 X138:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 ?[ 664.09/87.89 X140:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X140 @ 664.09/87.89 X136 ) & 664.09/87.89 ( 664.09/87.89 X138 @ 664.09/87.89 X140 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X142:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X142 @ 664.09/87.89 X136 ) => 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 X138 @ 664.09/87.89 X142 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X144:$i, 664.09/87.89 X146:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X148:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X148 @ 664.09/87.89 X144 ) & 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 X146 @ 664.09/87.89 X148 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 ![ 664.09/87.89 X150:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X150 @ 664.09/87.89 X144 ) => 664.09/87.89 ( 664.09/87.89 X146 @ 664.09/87.89 X150 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 prop2setI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 prop2set2propI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X152:$i, 664.09/87.89 X154:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 ?[ 664.09/87.89 X156:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X156 @ 664.09/87.89 X152 ) & 664.09/87.89 ( 664.09/87.89 X154 @ 664.09/87.89 X156 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X158:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X158 @ 664.09/87.89 X152 ) => 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 X154 @ 664.09/87.89 X158 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X160:$i, 664.09/87.89 X162:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 ![ 664.09/87.89 X164:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X164 @ 664.09/87.89 X160 ) => 664.09/87.89 ( 664.09/87.89 X162 @ 664.09/87.89 X164 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X166:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X166 @ 664.09/87.89 X160 ) & 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 X162 @ 664.09/87.89 X166 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuI3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuI2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X168:$i, 664.09/87.89 X170:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X168 ) = 664.09/87.89 ( 664.09/87.89 X170 ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X172:$i, 664.09/87.89 X174:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X172 ) = 664.09/87.89 ( 664.09/87.89 X174 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X172 @ 664.09/87.89 X168 ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X174 @ 664.09/87.89 X170 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X176:$i, 664.09/87.89 X178:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X176 ) = 664.09/87.89 ( 664.09/87.89 X178 ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X180:$i, 664.09/87.89 X182:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X180 ) = 664.09/87.89 ( 664.09/87.89 X182 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X180 @ 664.09/87.89 X176 ) <=> 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X182 @ 664.09/87.89 X178 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuE3u ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exu__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptyset__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setadjoin__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powerset__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X184:$i, 664.09/87.89 X186:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X184 ) = 664.09/87.89 ( 664.09/87.89 X186 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 X184 ) = 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 X186 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 omega__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuEu ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 descr__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X188:$i, 664.09/87.89 X190:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X188 ) = 664.09/87.89 ( 664.09/87.89 X190 ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X192:( 664.09/87.89 $i > $o ), 664.09/87.89 X194:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X196:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X196 @ 664.09/87.89 X188 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X198:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X198 @ 664.09/87.89 X190 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X196 ) = 664.09/87.89 ( 664.09/87.89 X198 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X192 @ 664.09/87.89 X196 ) <=> 664.09/87.89 ( 664.09/87.89 X194 @ 664.09/87.89 X198 ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X188 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_7:$i]: 664.09/87.89 ( 664.09/87.89 X192 @ V_7 ) ) ) = 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X190 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_8:$i]: 664.09/87.89 ( 664.09/87.89 X194 @ V_8 ) ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqimpsubset2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqimpsubset1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetI2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptysetsubset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetE2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notsubsetI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notequalI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X200:$i, 664.09/87.89 X202:$i, 664.09/87.89 X204:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X204 @ 664.09/87.89 X200 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 in @ 664.09/87.89 X204 @ 664.09/87.89 X202 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X200 ) != 664.09/87.89 ( 664.09/87.89 X202 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetRefl ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetTrans ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setadjoinSub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setadjoinSub2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subset2powerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setextsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetemptysetimpeq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetE1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 inPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetsubset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 sepInPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X206:$i, 664.09/87.89 X208:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 subset @ 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X206 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_9:$i]: 664.09/87.89 ( 664.09/87.89 X208 @ V_9 ) ) ) @ 664.09/87.89 X206 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionIL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairset2IR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionIR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionEcases ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionLsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionRsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset5 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectEL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectLsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 disjointsetsI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectRsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset4 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 bs114d ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusEL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusSubset2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusERneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusELneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusILneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusIRneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusLsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusSubset1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffI2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffIneg1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffIneg2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 secondinupair ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X210:$i, 664.09/87.89 X212:$i]: 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X210 @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X210 @ 664.09/87.89 emptyset ) @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X210 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X212 @ 664.09/87.89 emptyset ) ) @ 664.09/87.89 emptyset ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X214:$i, 664.09/87.89 X216:$i]: 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X216 @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X214 @ 664.09/87.89 emptyset ) @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X214 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X216 @ 664.09/87.89 emptyset ) ) @ 664.09/87.89 emptyset ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kpairiskpair ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kpairp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonsubset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletoninpowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletoninpowunion ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairset2E ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsubunion ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairinpowunion ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ubforcartprodlem1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ubforcartprodlem2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ubforcartprodlem3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairin ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodmempair1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodmempair ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X218:$i, 664.09/87.89 X220:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X220 @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 X218 ) ) => 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X222:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X222 @ 664.09/87.89 X218 ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X220 @ 664.09/87.89 X222 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X224:$i]: 664.09/87.89 ( 664.09/87.89 subset @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X224 @ 664.09/87.89 emptyset ) ) @ 664.09/87.89 X224 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X226:$i]: 664.09/87.89 ( 664.09/87.89 subset @ 664.09/87.89 X226 @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X226 @ 664.09/87.89 emptyset ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X228:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X228 @ 664.09/87.89 emptyset ) ) = 664.09/87.89 ( 664.09/87.89 X228 ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonprop ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1E1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1I ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1I2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonsuniq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjL1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kfstsingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 theprop ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kfstpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodfstin ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjL2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR11 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR12 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairequniteq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ksndsingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ksndpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kpairsurjEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodsndin ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairmemEL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairmemER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodmempaircEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodfstpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodsndpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairsurjEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrSub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setOfPairsIsBReln ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrERa ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrEL1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrEL2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcImageSingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 apProp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 app ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 infuncsetfunc ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ap2p ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcinfuncset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lamProp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lamp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lam2p ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 brelnall1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 brelnall2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1E2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcextLem ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp4 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subbreln ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqbreln ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcext ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcext2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ap2apEq1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ap2apEq2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 beta1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eta1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lam2lamEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 beta2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eta2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X230:$i, 664.09/87.89 X232:$o, 664.09/87.89 X234:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X234 @ 664.09/87.89 X230 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X236:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X236 @ 664.09/87.89 X230 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( X232 ) ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X236 @ 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X230 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_10:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_10 ) = 664.09/87.89 ( 664.09/87.89 X236 ) ) & 664.09/87.89 ( 664.09/87.89 ~( X232 ) ) ) | 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_10 ) = 664.09/87.89 ( 664.09/87.89 X234 ) ) & 664.09/87.89 ( 664.09/87.89 X232 ) ) ) ) ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X238:$i, 664.09/87.89 X240:$o, 664.09/87.89 X242:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X242 @ 664.09/87.89 X238 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X244:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X244 @ 664.09/87.89 X238 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( X240 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X238 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_11:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_11 ) = 664.09/87.89 ( 664.09/87.89 X244 ) ) & 664.09/87.89 ( 664.09/87.89 ~( X240 ) ) ) | 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_11 ) = 664.09/87.89 ( 664.09/87.89 X242 ) ) & 664.09/87.89 ( 664.09/87.89 X240 ) ) ) ) ) = 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X244 @ 664.09/87.89 emptyset ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X246:$i, 664.09/87.89 X248:$o, 664.09/87.89 X250:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X250 @ 664.09/87.89 X246 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X252:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X252 @ 664.09/87.89 X246 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X248 ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X250 @ 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X246 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_12:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_12 ) = 664.09/87.89 ( 664.09/87.89 X252 ) ) & 664.09/87.89 ( 664.09/87.89 ~( X248 ) ) ) | 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_12 ) = 664.09/87.89 ( 664.09/87.89 X250 ) ) & 664.09/87.89 ( 664.09/87.89 X248 ) ) ) ) ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X254:$i, 664.09/87.89 X256:$o, 664.09/87.89 X258:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X258 @ 664.09/87.89 X254 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X260:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X260 @ 664.09/87.89 X254 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X256 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X254 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_13:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_13 ) = 664.09/87.89 ( 664.09/87.89 X260 ) ) & 664.09/87.89 ( 664.09/87.89 ~( X256 ) ) ) | 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_13 ) = 664.09/87.89 ( 664.09/87.89 X258 ) ) & 664.09/87.89 ( 664.09/87.89 X256 ) ) ) ) ) = 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X258 @ 664.09/87.89 emptyset ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ifSingleton ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X262:$i, 664.09/87.89 X264:$o, 664.09/87.89 X266:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X266 @ 664.09/87.89 X262 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X268:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X268 @ 664.09/87.89 X262 ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X262 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_14:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_14 ) = 664.09/87.89 ( 664.09/87.89 X268 ) ) & 664.09/87.89 ( 664.09/87.89 ~( X264 ) ) ) | 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_14 ) = 664.09/87.89 ( 664.09/87.89 X266 ) ) & 664.09/87.89 ( 664.09/87.89 X264 ) ) ) ) ) ) @ 664.09/87.89 X262 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 664.09/87.89 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o). 664.09/87.89 thf(zf_stmt_2, axiom, 664.09/87.89 (![X14:$i,X12:$i,X10:$i]: 664.09/87.89 ( ( zip_tseitin_0 @ X14 @ X12 @ X10 ) <=> 664.09/87.89 ( ( in @ X14 @ X10 ) & ( in @ X12 @ X14 ) ) ))). 664.09/87.89 thf(zf_stmt_3, conjecture, 664.09/87.89 (( ![X4:$i,X6:$i]: 664.09/87.89 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) => 664.09/87.89 ( ( X4 ) = ( X6 ) ) ) ) => 664.09/87.89 ( ( emptysetAx ) => 664.09/87.89 ( ( setadjoinAx ) => 664.09/87.89 ( ( powersetAx ) => 664.09/87.89 ( ( ![X10:$i,X12:$i]: 664.09/87.89 ( ( in @ X12 @ ( setunion @ X10 ) ) <=> 664.09/87.89 ( ?[X14:$i]: ( zip_tseitin_0 @ X14 @ X12 @ X10 ) ) ) ) => 664.09/87.89 ( ( omega0Ax ) => 664.09/87.89 ( ( omegaSAx ) => 664.09/87.89 ( ( omegaIndAx ) => 664.09/87.89 ( ( replAx ) => 664.09/87.89 ( ( ![X16:$i]: 664.09/87.89 ( ( ?[X18:$i]: ( in @ X18 @ X16 ) ) => 664.09/87.89 ( ?[X20:$i]: 664.09/87.89 ( ( ~( ?[X22:$i]: 664.09/87.89 ( ( in @ X22 @ X16 ) & ( in @ X22 @ X20 ) ) ) ) & 664.09/87.89 ( in @ X20 @ X16 ) ) ) ) ) => 664.09/87.89 ( ( ![X24:$i]: 664.09/87.89 ( ?[X26:$i]: 664.09/87.89 ( ( ![X28:$i]: 664.09/87.89 ( ( ( ![X30:$i]: 664.09/87.89 ( ( in @ X30 @ X28 ) => 664.09/87.89 ( in @ X30 @ X24 ) ) ) & 664.09/87.89 ( ?[X32:$i]: ( in @ X32 @ X28 ) ) ) => 664.09/87.89 ( ?[X34:$i,X36:$i]: 664.09/87.89 ( ( ![X38:$i]: 664.09/87.89 ( ( in @ X38 @ X26 ) => 664.09/87.89 ( ( ![X40:$i]: 664.09/87.89 ( ( in @ X40 @ X38 ) => 664.09/87.89 ( in @ X40 @ X34 ) ) ) | 664.09/87.89 ( in @ X36 @ X38 ) ) ) ) & 664.09/87.89 ( ~( ?[X42:$i]: 664.09/87.89 ( ( in @ X42 @ X28 ) & 664.09/87.89 ( in @ X42 @ X34 ) ) ) ) & 664.09/87.89 ( in @ X36 @ X28 ) & ( in @ X34 @ X26 ) ) ) ) ) & 664.09/87.89 ( ![X44:$i,X46:$i]: 664.09/87.89 ( ( ( in @ X44 @ X26 ) & ( in @ X46 @ X26 ) ) => 664.09/87.89 ( ( ![X48:$i]: 664.09/87.89 ( ( in @ X48 @ X44 ) => 664.09/87.89 ( in @ X48 @ X46 ) ) ) | 664.09/87.89 ( ![X50:$i]: 664.09/87.89 ( ( in @ X50 @ X46 ) => 664.09/87.89 ( in @ X50 @ X44 ) ) ) ) ) ) & 664.09/87.89 ( ![X52:$i,X54:$i]: 664.09/87.89 ( ( ( in @ X52 @ X24 ) & ( in @ X54 @ X24 ) ) => 664.09/87.89 ( ( ![X56:$i]: 664.09/87.89 ( ( in @ X56 @ X26 ) => 664.09/87.89 ( ( in @ X52 @ X56 ) <=> 664.09/87.89 ( in @ X54 @ X56 ) ) ) ) => 664.09/87.89 ( ( X52 ) = ( X54 ) ) ) ) ) & 664.09/87.89 ( ![X58:$i]: 664.09/87.89 ( ( in @ X58 @ X26 ) => 664.09/87.89 ( ![X60:$i]: 664.09/87.89 ( ( in @ X60 @ X58 ) => ( in @ X60 @ X24 ) ) ) ) ) ) ) ) => 664.09/87.89 ( ( descrp ) => 664.09/87.89 ( ( ![X62:$i,X64:( $i > $o ),X66:$i]: 664.09/87.89 ( ( in @ X66 @ X62 ) => 664.09/87.89 ( ( X64 @ X66 ) => 664.09/87.89 ( in @ 664.09/87.89 X66 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X62 @ ( ^[V_1:$i]: ( X64 @ V_1 ) ) ) ) ) ) ) => 664.09/87.89 ( ( ![X68:$i,X70:( $i > $o ),X72:$i]: 664.09/87.89 ( ( in @ 664.09/87.89 X72 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X68 @ ( ^[V_2:$i]: ( X70 @ V_2 ) ) ) ) => 664.09/87.89 ( in @ X72 @ X68 ) ) ) => 664.09/87.89 ( ( ![X74:$i,X76:( $i > $o ),X78:$i]: 664.09/87.89 ( ( in @ 664.09/87.89 X78 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X74 @ ( ^[V_3:$i]: ( X76 @ V_3 ) ) ) ) => 664.09/87.89 ( X76 @ X78 ) ) ) => 664.09/87.89 ( ( exuE1 ) => 664.09/87.89 ( ( prop2setE ) => 664.09/87.89 ( ( emptysetE ) => 664.09/87.89 ( ( emptysetimpfalse ) => 664.09/87.89 ( ( notinemptyset ) => 664.09/87.89 ( ( exuE3e ) => 664.09/87.89 ( ( ![X80:$i,X82:$i]: 664.09/87.89 ( ( ![X84:$i]: 664.09/87.89 ( ( in @ X84 @ X80 ) => 664.09/87.89 ( in @ X84 @ X82 ) ) ) => 664.09/87.89 ( ( ![X86:$i]: 664.09/87.89 ( ( in @ X86 @ X82 ) => 664.09/87.89 ( in @ X86 @ X80 ) ) ) => 664.09/87.89 ( ( X80 ) = ( X82 ) ) ) ) ) => 664.09/87.89 ( ( emptyI ) => 664.09/87.89 ( ( noeltsimpempty ) => 664.09/87.89 ( ( ![X88:$i, 664.09/87.89 X90:( $i > $o ),X92:$i]: 664.09/87.89 ( ( in @ X92 @ X88 ) => 664.09/87.89 ( ( in @ 664.09/87.89 X92 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X88 @ 664.09/87.89 ( ^[V_4:$i]: 664.09/87.89 ( X90 @ V_4 ) ) ) ) <=> 664.09/87.89 ( X90 @ X92 ) ) ) ) => 664.09/87.89 ( ( nonemptyE1 ) => 664.09/87.89 ( ( nonemptyI ) => 664.09/87.89 ( ( nonemptyI1 ) => 664.09/87.89 ( ( setadjoinIL ) => 664.09/87.89 ( ( emptyinunitempty ) => 664.09/87.89 ( ( setadjoinIR ) => 664.09/87.89 ( ( setadjoinE ) => 664.09/87.89 ( ( 664.09/87.89 setadjoinOr ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X94:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X94 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_5:$i]: 664.09/87.89 ( 664.09/87.89 $true ) ) ) = 664.09/87.89 ( 664.09/87.89 X94 ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptyinPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptyInPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X96:$i, 664.09/87.89 X98:$i, 664.09/87.89 X100:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X98 @ X100 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X100 @ X96 ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X98 @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 X96 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X102:$i, 664.09/87.89 X104:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X104 @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 X102 ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X106:$o]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X108:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X104 @ 664.09/87.89 X108 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X108 @ 664.09/87.89 X102 ) => 664.09/87.89 ( 664.09/87.89 X106 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 X106 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X110:$i, 664.09/87.89 X112:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X112 @ 664.09/87.89 X110 ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X112 @ 664.09/87.89 ( 664.09/87.89 powerset @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 X110 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuE2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 nonemptyImpWitness ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 uniqinunit ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notinsingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqinunit ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonsswitch ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsetE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsetIL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsetIR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X114:$i, 664.09/87.89 X116:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X118:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X116 @ 664.09/87.89 X118 ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X118 @ 664.09/87.89 X114 ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X114 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_6:$i]: 664.09/87.89 ( 664.09/87.89 X116 @ V_6 ) ) ) != 664.09/87.89 ( 664.09/87.89 emptyset ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 vacuousDall ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X120:$i, 664.09/87.89 X122:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 ![ 664.09/87.89 X124:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X124 @ 664.09/87.89 X120 ) => 664.09/87.89 ( 664.09/87.89 X122 @ 664.09/87.89 X124 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X126:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 X122 @ 664.09/87.89 X126 ) ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X126 @ 664.09/87.89 X120 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X128:$i, 664.09/87.89 X130:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X132:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X132 @ 664.09/87.89 X128 ) => 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 X130 @ 664.09/87.89 X132 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 ?[ 664.09/87.89 X134:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X130 @ 664.09/87.89 X134 ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X134 @ 664.09/87.89 X128 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X136:$i, 664.09/87.89 X138:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 ?[ 664.09/87.89 X140:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X138 @ 664.09/87.89 X140 ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X140 @ 664.09/87.89 X136 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X142:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X142 @ 664.09/87.89 X136 ) => 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 X138 @ 664.09/87.89 X142 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X144:$i, 664.09/87.89 X146:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X148:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 X146 @ 664.09/87.89 X148 ) ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X148 @ 664.09/87.89 X144 ) ) ) => 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 ![ 664.09/87.89 X150:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X150 @ 664.09/87.89 X144 ) => 664.09/87.89 ( 664.09/87.89 X146 @ 664.09/87.89 X150 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 prop2setI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 prop2set2propI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X152:$i, 664.09/87.89 X154:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 ?[ 664.09/87.89 X156:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X154 @ 664.09/87.89 X156 ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X156 @ 664.09/87.89 X152 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X158:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X158 @ 664.09/87.89 X152 ) => 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 X154 @ 664.09/87.89 X158 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X160:$i, 664.09/87.89 X162:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 ![ 664.09/87.89 X164:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X164 @ 664.09/87.89 X160 ) => 664.09/87.89 ( 664.09/87.89 X162 @ 664.09/87.89 X164 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X166:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 X162 @ 664.09/87.89 X166 ) ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X166 @ 664.09/87.89 X160 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuI3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuI2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X168:$i, 664.09/87.89 X170:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X168 ) = 664.09/87.89 ( 664.09/87.89 X170 ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X172:$i, 664.09/87.89 X174:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X172 ) = 664.09/87.89 ( 664.09/87.89 X174 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X172 @ 664.09/87.89 X168 ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X174 @ 664.09/87.89 X170 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X176:$i, 664.09/87.89 X178:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X176 ) = 664.09/87.89 ( 664.09/87.89 X178 ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X180:$i, 664.09/87.89 X182:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X180 ) = 664.09/87.89 ( 664.09/87.89 X182 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X180 @ 664.09/87.89 X176 ) <=> 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X182 @ 664.09/87.89 X178 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuE3u ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exu__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptyset__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setadjoin__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powerset__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X184:$i, 664.09/87.89 X186:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X184 ) = 664.09/87.89 ( 664.09/87.89 X186 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 X184 ) = 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 X186 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 omega__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuEu ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 descr__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X188:$i, 664.09/87.89 X190:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X188 ) = 664.09/87.89 ( 664.09/87.89 X190 ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X192:( 664.09/87.89 $i > $o ), 664.09/87.89 X194:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X196:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X196 @ 664.09/87.89 X188 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X198:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X198 @ 664.09/87.89 X190 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X196 ) = 664.09/87.89 ( 664.09/87.89 X198 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X192 @ 664.09/87.89 X196 ) <=> 664.09/87.89 ( 664.09/87.89 X194 @ 664.09/87.89 X198 ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X188 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_7:$i]: 664.09/87.89 ( 664.09/87.89 X192 @ V_7 ) ) ) = 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X190 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_8:$i]: 664.09/87.89 ( 664.09/87.89 X194 @ V_8 ) ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqimpsubset2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqimpsubset1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetI2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptysetsubset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetE2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notsubsetI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notequalI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X200:$i, 664.09/87.89 X202:$i, 664.09/87.89 X204:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X204 @ 664.09/87.89 X200 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( 664.09/87.89 in @ 664.09/87.89 X204 @ 664.09/87.89 X202 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X200 ) != 664.09/87.89 ( 664.09/87.89 X202 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetRefl ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetTrans ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setadjoinSub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setadjoinSub2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subset2powerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setextsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetemptysetimpeq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetE1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 inPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetsubset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 sepInPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X206:$i, 664.09/87.89 X208:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 subset @ 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X206 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_9:$i]: 664.09/87.89 ( 664.09/87.89 X208 @ V_9 ) ) ) @ 664.09/87.89 X206 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionIL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairset2IR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionIR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionEcases ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionLsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionRsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset5 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectEL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectLsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 disjointsetsI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectRsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset4 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 bs114d ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusEL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusSubset2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusERneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusELneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusILneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusIRneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusLsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusSubset1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffI2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffIneg1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffIneg2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 secondinupair ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X210:$i, 664.09/87.89 X212:$i]: 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X210 @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X210 @ 664.09/87.89 emptyset ) @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X210 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X212 @ 664.09/87.89 emptyset ) ) @ 664.09/87.89 emptyset ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X214:$i, 664.09/87.89 X216:$i]: 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X216 @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X214 @ 664.09/87.89 emptyset ) @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X214 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X216 @ 664.09/87.89 emptyset ) ) @ 664.09/87.89 emptyset ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kpairiskpair ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kpairp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonsubset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletoninpowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletoninpowunion ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairset2E ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsubunion ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairinpowunion ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ubforcartprodlem1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ubforcartprodlem2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ubforcartprodlem3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairin ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodmempair1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodmempair ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X218:$i, 664.09/87.89 X220:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X220 @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 X218 ) ) => 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X222:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X220 @ 664.09/87.89 X222 ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X222 @ 664.09/87.89 X218 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X224:$i]: 664.09/87.89 ( 664.09/87.89 subset @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X224 @ 664.09/87.89 emptyset ) ) @ 664.09/87.89 X224 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X226:$i]: 664.09/87.89 ( 664.09/87.89 subset @ 664.09/87.89 X226 @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X226 @ 664.09/87.89 emptyset ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X228:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X228 @ 664.09/87.89 emptyset ) ) = 664.09/87.89 ( 664.09/87.89 X228 ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonprop ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1E1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1I ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1I2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonsuniq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjL1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kfstsingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 theprop ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kfstpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodfstin ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjL2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR11 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR12 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairequniteq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ksndsingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ksndpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kpairsurjEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodsndin ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairmemEL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairmemER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodmempaircEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodfstpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodsndpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairsurjEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrSub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setOfPairsIsBReln ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrERa ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrEL1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrEL2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcImageSingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 apProp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 app ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 infuncsetfunc ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ap2p ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcinfuncset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lamProp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lamp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lam2p ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 brelnall1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 brelnall2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1E2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcextLem ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp4 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subbreln ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqbreln ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcext ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcext2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ap2apEq1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ap2apEq2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 beta1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eta1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lam2lamEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 beta2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eta2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X230:$i, 664.09/87.89 X232:$o, 664.09/87.89 X234:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X234 @ 664.09/87.89 X230 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X236:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X236 @ 664.09/87.89 X230 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( X232 ) ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X236 @ 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X230 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_10:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_10 ) = 664.09/87.89 ( 664.09/87.89 X236 ) ) & 664.09/87.89 ( 664.09/87.89 ~( X232 ) ) ) | 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_10 ) = 664.09/87.89 ( 664.09/87.89 X234 ) ) & 664.09/87.89 ( 664.09/87.89 X232 ) ) ) ) ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X238:$i, 664.09/87.89 X240:$o, 664.09/87.89 X242:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X242 @ 664.09/87.89 X238 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X244:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X244 @ 664.09/87.89 X238 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~( X240 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X238 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_11:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_11 ) = 664.09/87.89 ( 664.09/87.89 X244 ) ) & 664.09/87.89 ( 664.09/87.89 ~( X240 ) ) ) | 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_11 ) = 664.09/87.89 ( 664.09/87.89 X242 ) ) & 664.09/87.89 ( 664.09/87.89 X240 ) ) ) ) ) = 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X244 @ 664.09/87.89 emptyset ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X246:$i, 664.09/87.89 X248:$o, 664.09/87.89 X250:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X250 @ 664.09/87.89 X246 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X252:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X252 @ 664.09/87.89 X246 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X248 ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X250 @ 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X246 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_12:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_12 ) = 664.09/87.89 ( 664.09/87.89 X252 ) ) & 664.09/87.89 ( 664.09/87.89 ~( X248 ) ) ) | 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_12 ) = 664.09/87.89 ( 664.09/87.89 X250 ) ) & 664.09/87.89 ( 664.09/87.89 X248 ) ) ) ) ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X254:$i, 664.09/87.89 X256:$o, 664.09/87.89 X258:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X258 @ 664.09/87.89 X254 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X260:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X260 @ 664.09/87.89 X254 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X256 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X254 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_13:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_13 ) = 664.09/87.89 ( 664.09/87.89 X260 ) ) & 664.09/87.89 ( 664.09/87.89 ~( X256 ) ) ) | 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_13 ) = 664.09/87.89 ( 664.09/87.89 X258 ) ) & 664.09/87.89 ( 664.09/87.89 X256 ) ) ) ) ) = 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X258 @ 664.09/87.89 emptyset ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ifSingleton ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X262:$i, 664.09/87.89 X264:$o, 664.09/87.89 X266:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X266 @ 664.09/87.89 X262 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X268:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X268 @ 664.09/87.89 X262 ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 ( 664.09/87.89 setunion @ 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X262 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_14:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_14 ) = 664.09/87.89 ( 664.09/87.89 X268 ) ) & 664.09/87.89 ( 664.09/87.89 ~( X264 ) ) ) | 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 V_14 ) = 664.09/87.89 ( 664.09/87.89 X266 ) ) & 664.09/87.89 ( 664.09/87.89 X264 ) ) ) ) ) ) @ 664.09/87.89 X262 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 664.09/87.89 thf(zf_stmt_4, negated_conjecture, 664.09/87.89 (~( ( ![X4:$i,X6:$i]: 664.09/87.89 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) => 664.09/87.89 ( ( X4 ) = ( X6 ) ) ) ) => 664.09/87.89 ( ( emptysetAx ) => 664.09/87.89 ( ( setadjoinAx ) => 664.09/87.89 ( ( powersetAx ) => 664.09/87.89 ( ( ![X10:$i,X12:$i]: 664.09/87.89 ( ( in @ X12 @ ( setunion @ X10 ) ) <=> 664.09/87.89 ( ?[X14:$i]: ( zip_tseitin_0 @ X14 @ X12 @ X10 ) ) ) ) => 664.09/87.89 ( ( omega0Ax ) => 664.09/87.89 ( ( omegaSAx ) => 664.09/87.89 ( ( omegaIndAx ) => 664.09/87.89 ( ( replAx ) => 664.09/87.89 ( ( ![X16:$i]: 664.09/87.89 ( ( ?[X18:$i]: ( in @ X18 @ X16 ) ) => 664.09/87.89 ( ?[X20:$i]: 664.09/87.89 ( ( ~( ?[X22:$i]: 664.09/87.89 ( ( in @ X22 @ X16 ) & 664.09/87.89 ( in @ X22 @ X20 ) ) ) ) & 664.09/87.89 ( in @ X20 @ X16 ) ) ) ) ) => 664.09/87.89 ( ( ![X24:$i]: 664.09/87.89 ( ?[X26:$i]: 664.09/87.89 ( ( ![X28:$i]: 664.09/87.89 ( ( ( ![X30:$i]: 664.09/87.89 ( ( in @ X30 @ X28 ) => 664.09/87.89 ( in @ X30 @ X24 ) ) ) & 664.09/87.89 ( ?[X32:$i]: ( in @ X32 @ X28 ) ) ) => 664.09/87.89 ( ?[X34:$i,X36:$i]: 664.09/87.89 ( ( ![X38:$i]: 664.09/87.89 ( ( in @ X38 @ X26 ) => 664.09/87.89 ( ( ![X40:$i]: 664.09/87.89 ( ( in @ X40 @ X38 ) => 664.09/87.89 ( in @ X40 @ X34 ) ) ) | 664.09/87.89 ( in @ X36 @ X38 ) ) ) ) & 664.09/87.89 ( ~( ?[X42:$i]: 664.09/87.89 ( ( in @ X42 @ X28 ) & 664.09/87.89 ( in @ X42 @ X34 ) ) ) ) & 664.09/87.89 ( in @ X36 @ X28 ) & 664.09/87.89 ( in @ X34 @ X26 ) ) ) ) ) & 664.09/87.89 ( ![X44:$i,X46:$i]: 664.09/87.89 ( ( ( in @ X44 @ X26 ) & ( in @ X46 @ X26 ) ) => 664.09/87.89 ( ( ![X48:$i]: 664.09/87.89 ( ( in @ X48 @ X44 ) => 664.09/87.89 ( in @ X48 @ X46 ) ) ) | 664.09/87.89 ( ![X50:$i]: 664.09/87.89 ( ( in @ X50 @ X46 ) => 664.09/87.89 ( in @ X50 @ X44 ) ) ) ) ) ) & 664.09/87.89 ( ![X52:$i,X54:$i]: 664.09/87.89 ( ( ( in @ X52 @ X24 ) & ( in @ X54 @ X24 ) ) => 664.09/87.89 ( ( ![X56:$i]: 664.09/87.89 ( ( in @ X56 @ X26 ) => 664.09/87.89 ( ( in @ X52 @ X56 ) <=> 664.09/87.89 ( in @ X54 @ X56 ) ) ) ) => 664.09/87.89 ( ( X52 ) = ( X54 ) ) ) ) ) & 664.09/87.89 ( ![X58:$i]: 664.09/87.89 ( ( in @ X58 @ X26 ) => 664.09/87.89 ( ![X60:$i]: 664.09/87.89 ( ( in @ X60 @ X58 ) => 664.09/87.89 ( in @ X60 @ X24 ) ) ) ) ) ) ) ) => 664.09/87.89 ( ( descrp ) => 664.09/87.89 ( ( ![X62:$i,X64:( $i > $o ),X66:$i]: 664.09/87.89 ( ( in @ X66 @ X62 ) => 664.09/87.89 ( ( X64 @ X66 ) => 664.09/87.89 ( in @ 664.09/87.89 X66 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X62 @ ( ^[V_1:$i]: ( X64 @ V_1 ) ) ) ) ) ) ) => 664.09/87.89 ( ( ![X68:$i,X70:( $i > $o ),X72:$i]: 664.09/87.89 ( ( in @ 664.09/87.89 X72 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X68 @ ( ^[V_2:$i]: ( X70 @ V_2 ) ) ) ) => 664.09/87.89 ( in @ X72 @ X68 ) ) ) => 664.09/87.89 ( ( ![X74:$i,X76:( $i > $o ),X78:$i]: 664.09/87.89 ( ( in @ 664.09/87.89 X78 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X74 @ ( ^[V_3:$i]: ( X76 @ V_3 ) ) ) ) => 664.09/87.89 ( X76 @ X78 ) ) ) => 664.09/87.89 ( ( exuE1 ) => 664.09/87.89 ( ( prop2setE ) => 664.09/87.89 ( ( emptysetE ) => 664.09/87.89 ( ( emptysetimpfalse ) => 664.09/87.89 ( ( notinemptyset ) => 664.09/87.89 ( ( exuE3e ) => 664.09/87.89 ( ( ![X80:$i,X82:$i]: 664.09/87.89 ( ( ![X84:$i]: 664.09/87.89 ( ( in @ X84 @ X80 ) => 664.09/87.89 ( in @ X84 @ X82 ) ) ) => 664.09/87.89 ( ( ![X86:$i]: 664.09/87.89 ( ( in @ X86 @ X82 ) => 664.09/87.89 ( in @ X86 @ X80 ) ) ) => 664.09/87.89 ( ( X80 ) = ( X82 ) ) ) ) ) => 664.09/87.89 ( ( emptyI ) => 664.09/87.89 ( ( noeltsimpempty ) => 664.09/87.89 ( ( ![X88:$i, 664.09/87.89 X90:( $i > $o ), 664.09/87.89 X92:$i]: 664.09/87.89 ( ( in @ X92 @ X88 ) => 664.09/87.89 ( ( in @ 664.09/87.89 X92 @ 664.09/87.89 ( dsetconstr @ 664.09/87.89 X88 @ 664.09/87.89 ( ^[V_4:$i]: 664.09/87.89 ( X90 @ V_4 ) ) ) ) <=> 664.09/87.89 ( X90 @ X92 ) ) ) ) => 664.09/87.89 ( ( nonemptyE1 ) => 664.09/87.89 ( ( nonemptyI ) => 664.09/87.89 ( ( nonemptyI1 ) => 664.09/87.89 ( ( setadjoinIL ) => 664.09/87.89 ( ( emptyinunitempty ) => 664.09/87.89 ( ( setadjoinIR ) => 664.09/87.89 ( ( 664.09/87.89 setadjoinE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setadjoinOr ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X94:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X94 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_5:$i]: 664.09/87.89 ( 664.09/87.89 $true ) ) ) = 664.09/87.89 ( 664.09/87.89 X94 ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptyinPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptyInPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X96:$i, 664.09/87.89 X98:$i, 664.09/87.89 X100:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X98 @ 664.09/87.89 X100 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X100 @ 664.09/87.89 X96 ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X98 @ 664.09/87.89 ( 664.09/87.89 setunion 664.09/87.89 @ 664.09/87.89 X96 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X102:$i, 664.09/87.89 X104:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X104 @ 664.09/87.89 ( 664.09/87.89 setunion 664.09/87.89 @ 664.09/87.89 X102 ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X106:$o]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X108:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X104 @ 664.09/87.89 X108 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X108 @ 664.09/87.89 X102 ) => 664.09/87.89 ( 664.09/87.89 X106 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 X106 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X110:$i, 664.09/87.89 X112:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X112 @ 664.09/87.89 X110 ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X112 @ 664.09/87.89 ( 664.09/87.89 powerset 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setunion 664.09/87.89 @ 664.09/87.89 X110 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuE2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 nonemptyImpWitness ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 uniqinunit ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notinsingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqinunit ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonsswitch ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsetE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsetIL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsetIR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X114:$i, 664.09/87.89 X116:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X118:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X116 @ 664.09/87.89 X118 ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X118 @ 664.09/87.89 X114 ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X114 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_6:$i]: 664.09/87.89 ( 664.09/87.89 X116 @ 664.09/87.89 V_6 ) ) ) != 664.09/87.89 ( 664.09/87.89 emptyset ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 vacuousDall ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X120:$i, 664.09/87.89 X122:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~ 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X124:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X124 @ 664.09/87.89 X120 ) => 664.09/87.89 ( 664.09/87.89 X122 @ 664.09/87.89 X124 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X126:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~ 664.09/87.89 ( 664.09/87.89 X122 @ 664.09/87.89 X126 ) ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X126 @ 664.09/87.89 X120 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X128:$i, 664.09/87.89 X130:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X132:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X132 @ 664.09/87.89 X128 ) => 664.09/87.89 ( 664.09/87.89 ~ 664.09/87.89 ( 664.09/87.89 X130 @ 664.09/87.89 X132 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ~ 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X134:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X130 @ 664.09/87.89 X134 ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X134 @ 664.09/87.89 X128 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X136:$i, 664.09/87.89 X138:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~ 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X140:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X138 @ 664.09/87.89 X140 ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X140 @ 664.09/87.89 X136 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X142:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X142 @ 664.09/87.89 X136 ) => 664.09/87.89 ( 664.09/87.89 ~ 664.09/87.89 ( 664.09/87.89 X138 @ 664.09/87.89 X142 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X144:$i, 664.09/87.89 X146:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X148:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~ 664.09/87.89 ( 664.09/87.89 X146 @ 664.09/87.89 X148 ) ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X148 @ 664.09/87.89 X144 ) ) ) => 664.09/87.89 ( 664.09/87.89 ~ 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X150:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X150 @ 664.09/87.89 X144 ) => 664.09/87.89 ( 664.09/87.89 X146 @ 664.09/87.89 X150 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 prop2setI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 prop2set2propI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X152:$i, 664.09/87.89 X154:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~ 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X156:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X154 @ 664.09/87.89 X156 ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X156 @ 664.09/87.89 X152 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X158:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X158 @ 664.09/87.89 X152 ) => 664.09/87.89 ( 664.09/87.89 ~ 664.09/87.89 ( 664.09/87.89 X154 @ 664.09/87.89 X158 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X160:$i, 664.09/87.89 X162:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~ 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X164:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X164 @ 664.09/87.89 X160 ) => 664.09/87.89 ( 664.09/87.89 X162 @ 664.09/87.89 X164 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X166:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~ 664.09/87.89 ( 664.09/87.89 X162 @ 664.09/87.89 X166 ) ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X166 @ 664.09/87.89 X160 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuI3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuI2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X168:$i, 664.09/87.89 X170:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X168 ) = 664.09/87.89 ( 664.09/87.89 X170 ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X172:$i, 664.09/87.89 X174:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X172 ) = 664.09/87.89 ( 664.09/87.89 X174 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X172 @ 664.09/87.89 X168 ) => 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X174 @ 664.09/87.89 X170 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X176:$i, 664.09/87.89 X178:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X176 ) = 664.09/87.89 ( 664.09/87.89 X178 ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X180:$i, 664.09/87.89 X182:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X180 ) = 664.09/87.89 ( 664.09/87.89 X182 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X180 @ 664.09/87.89 X176 ) <=> 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X182 @ 664.09/87.89 X178 ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuE3u ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exu__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptyset__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setadjoin__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powerset__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X184:$i, 664.09/87.89 X186:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X184 ) = 664.09/87.89 ( 664.09/87.89 X186 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setunion 664.09/87.89 @ 664.09/87.89 X184 ) = 664.09/87.89 ( 664.09/87.89 setunion 664.09/87.89 @ 664.09/87.89 X186 ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 omega__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 exuEu ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 descr__Cong ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X188:$i, 664.09/87.89 X190:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X188 ) = 664.09/87.89 ( 664.09/87.89 X190 ) ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X192:( 664.09/87.89 $i > $o ), 664.09/87.89 X194:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X196:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X196 @ 664.09/87.89 X188 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X198:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X198 @ 664.09/87.89 X190 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X196 ) = 664.09/87.89 ( 664.09/87.89 X198 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X192 @ 664.09/87.89 X196 ) <=> 664.09/87.89 ( 664.09/87.89 X194 @ 664.09/87.89 X198 ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X188 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_7:$i]: 664.09/87.89 ( 664.09/87.89 X192 @ 664.09/87.89 V_7 ) ) ) = 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X190 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_8:$i]: 664.09/87.89 ( 664.09/87.89 X194 @ 664.09/87.89 V_8 ) ) ) ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqimpsubset2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqimpsubset1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetI2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 emptysetsubset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetE2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notsubsetI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 notequalI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X200:$i, 664.09/87.89 X202:$i, 664.09/87.89 X204:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X204 @ 664.09/87.89 X200 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ~ 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X204 @ 664.09/87.89 X202 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 X200 ) != 664.09/87.89 ( 664.09/87.89 X202 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetRefl ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetTrans ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setadjoinSub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setadjoinSub2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subset2powerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setextsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subsetemptysetimpeq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetE1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 inPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 powersetsubset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 sepInPowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X206:$i, 664.09/87.89 X208:( 664.09/87.89 $i > $o )]: 664.09/87.89 ( 664.09/87.89 subset @ 664.09/87.89 ( 664.09/87.89 dsetconstr 664.09/87.89 @ 664.09/87.89 X206 @ 664.09/87.89 ( 664.09/87.89 ^[ 664.09/87.89 V_9:$i]: 664.09/87.89 ( 664.09/87.89 X208 @ 664.09/87.89 V_9 ) ) ) @ 664.09/87.89 X206 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionIL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairset2IR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionIR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionEcases ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionLsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binunionRsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset5 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectEL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectLsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 disjointsetsI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectRsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset4 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 binintersectSubset1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 bs114d ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusEL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusSubset2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusERneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusELneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusILneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusIRneg ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusLsub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setminusSubset1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffE ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffI1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffI2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffIneg1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 symdiffIneg2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 secondinupair ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X210:$i, 664.09/87.89 X212:$i]: 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X210 @ 664.09/87.89 ( 664.09/87.89 setunion 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X210 @ 664.09/87.89 emptyset ) @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X210 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X212 @ 664.09/87.89 emptyset ) ) @ 664.09/87.89 emptyset ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X214:$i, 664.09/87.89 X216:$i]: 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X216 @ 664.09/87.89 ( 664.09/87.89 setunion 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X214 @ 664.09/87.89 emptyset ) @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X214 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X216 @ 664.09/87.89 emptyset ) ) @ 664.09/87.89 emptyset ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kpairiskpair ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kpairp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonsubset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletoninpowerset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletoninpowunion ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairset2E ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairsubunion ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairinpowunion ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ubforcartprodlem1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ubforcartprodlem2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ubforcartprodlem3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairin ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodmempair1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodmempair ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X218:$i, 664.09/87.89 X220:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X220 @ 664.09/87.89 ( 664.09/87.89 setunion 664.09/87.89 @ 664.09/87.89 X218 ) ) => 664.09/87.89 ( 664.09/87.89 ?[ 664.09/87.89 X222:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X220 @ 664.09/87.89 X222 ) & 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X222 @ 664.09/87.89 X218 ) ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X224:$i]: 664.09/87.89 ( 664.09/87.89 subset @ 664.09/87.89 ( 664.09/87.89 setunion 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X224 @ 664.09/87.89 emptyset ) ) @ 664.09/87.89 X224 ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X226:$i]: 664.09/87.89 ( 664.09/87.89 subset @ 664.09/87.89 X226 @ 664.09/87.89 ( 664.09/87.89 setunion 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X226 @ 664.09/87.89 emptyset ) ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X228:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setunion 664.09/87.89 @ 664.09/87.89 ( 664.09/87.89 setadjoin 664.09/87.89 @ 664.09/87.89 X228 @ 664.09/87.89 emptyset ) ) = 664.09/87.89 ( 664.09/87.89 X228 ) ) ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonprop ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1E1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1I ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1I2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 singletonsuniq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjL1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kfstsingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 theprop ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kfstpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodfstin ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjL2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR11 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR12 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 upairequniteq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setukpairinjR ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ksndsingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ksndpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 kpairsurjEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodsndin ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairmemEL ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairmemER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodmempaircEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodfstpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodsndpairEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 cartprodpairsurjEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrI ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrSub ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 setOfPairsIsBReln ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrERa ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrEL1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrEL2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 dpsetconstrER ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcImageSingleton ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 apProp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 app ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 infuncsetfunc ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ap2p ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcinfuncset ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lamProp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lamp ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lam2p ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 brelnall1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 brelnall2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ex1E2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp3 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcextLem ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcGraphProp4 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 subbreln ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eqbreln ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcext ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 funcext2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ap2apEq1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ap2apEq2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 beta1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eta1 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 lam2lamEq ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 beta2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 eta2 ) => 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X230:$i, 664.09/87.89 X232:$o, 664.09/87.89 X234:$i]: 664.09/87.89 ( 664.09/87.89 ( 664.09/87.89 in @ 664.09/87.89 X234 @ 664.09/87.89 X230 ) => 664.09/87.89 ( 664.09/87.89 ![ 664.09/87.89 X236:$i]: 664.09/87.89 ( 664.09/87.90 ( 664.09/87.90 in @ 664.09/87.90 X236 @ 664.09/87.90 X230 ) => 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ~( X232 ) ) => 664.09/87.90 ( 664.09/87.90 in @ 664.09/87.90 X236 @ 664.09/87.90 ( 664.09/87.90 dsetconstr 664.09/87.90 @ 664.09/87.90 X230 @ 664.09/87.90 ( 664.09/87.90 ^[ 664.09/87.90 V_10:$i]: 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 V_10 ) = 664.09/87.90 ( 664.09/87.90 X236 ) ) & 664.09/87.90 ( 664.09/87.90 ~( X232 ) ) ) | 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 V_10 ) = 664.09/87.90 ( 664.09/87.90 X234 ) ) & 664.09/87.90 ( 664.09/87.90 X232 ) ) ) ) ) ) ) ) ) ) ) => 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ![ 664.09/87.90 X238:$i, 664.09/87.90 X240:$o, 664.09/87.90 X242:$i]: 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 in @ 664.09/87.90 X242 @ 664.09/87.90 X238 ) => 664.09/87.90 ( 664.09/87.90 ![ 664.09/87.90 X244:$i]: 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 in @ 664.09/87.90 X244 @ 664.09/87.90 X238 ) => 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ~( X240 ) ) => 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 dsetconstr 664.09/87.90 @ 664.09/87.90 X238 @ 664.09/87.90 ( 664.09/87.90 ^[ 664.09/87.90 V_11:$i]: 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 V_11 ) = 664.09/87.90 ( 664.09/87.90 X244 ) ) & 664.09/87.90 ( 664.09/87.90 ~( X240 ) ) ) | 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 V_11 ) = 664.09/87.90 ( 664.09/87.90 X242 ) ) & 664.09/87.90 ( 664.09/87.90 X240 ) ) ) ) ) = 664.09/87.90 ( 664.09/87.90 setadjoin 664.09/87.90 @ 664.09/87.90 X244 @ 664.09/87.90 emptyset ) ) ) ) ) ) ) => 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ![ 664.09/87.90 X246:$i, 664.09/87.90 X248:$o, 664.09/87.90 X250:$i]: 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 in @ 664.09/87.90 X250 @ 664.09/87.90 X246 ) => 664.09/87.90 ( 664.09/87.90 ![ 664.09/87.90 X252:$i]: 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 in @ 664.09/87.90 X252 @ 664.09/87.90 X246 ) => 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 X248 ) => 664.09/87.90 ( 664.09/87.90 in @ 664.09/87.90 X250 @ 664.09/87.90 ( 664.09/87.90 dsetconstr 664.09/87.90 @ 664.09/87.90 X246 @ 664.09/87.90 ( 664.09/87.90 ^[ 664.09/87.90 V_12:$i]: 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 V_12 ) = 664.09/87.90 ( 664.09/87.90 X252 ) ) & 664.09/87.90 ( 664.09/87.90 ~( X248 ) ) ) | 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 V_12 ) = 664.09/87.90 ( 664.09/87.90 X250 ) ) & 664.09/87.90 ( 664.09/87.90 X248 ) ) ) ) ) ) ) ) ) ) ) => 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ![ 664.09/87.90 X254:$i, 664.09/87.90 X256:$o, 664.09/87.90 X258:$i]: 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 in @ 664.09/87.90 X258 @ 664.09/87.90 X254 ) => 664.09/87.90 ( 664.09/87.90 ![ 664.09/87.90 X260:$i]: 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 in @ 664.09/87.90 X260 @ 664.09/87.90 X254 ) => 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 X256 ) => 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 dsetconstr 664.09/87.90 @ 664.09/87.90 X254 @ 664.09/87.90 ( 664.09/87.90 ^[ 664.09/87.90 V_13:$i]: 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 V_13 ) = 664.09/87.90 ( 664.09/87.90 X260 ) ) & 664.09/87.90 ( 664.09/87.90 ~( X256 ) ) ) | 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 V_13 ) = 664.09/87.90 ( 664.09/87.90 X258 ) ) & 664.09/87.90 ( 664.09/87.90 X256 ) ) ) ) ) = 664.09/87.90 ( 664.09/87.90 setadjoin 664.09/87.90 @ 664.09/87.90 X258 @ 664.09/87.90 emptyset ) ) ) ) ) ) ) => 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ifSingleton ) => 664.09/87.90 ( 664.09/87.90 ![ 664.09/87.90 X262:$i, 664.09/87.90 X264:$o, 664.09/87.90 X266:$i]: 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 in @ 664.09/87.90 X266 @ 664.09/87.90 X262 ) => 664.09/87.90 ( 664.09/87.90 ![ 664.09/87.90 X268:$i]: 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 in @ 664.09/87.90 X268 @ 664.09/87.90 X262 ) => 664.09/87.90 ( 664.09/87.90 in @ 664.09/87.90 ( 664.09/87.90 setunion 664.09/87.90 @ 664.09/87.90 ( 664.09/87.90 dsetconstr 664.09/87.90 @ 664.09/87.90 X262 @ 664.09/87.90 ( 664.09/87.90 ^[ 664.09/87.90 V_14:$i]: 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 V_14 ) = 664.09/87.90 ( 664.09/87.90 X268 ) ) & 664.09/87.90 ( 664.09/87.90 ~( X264 ) ) ) | 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 ( 664.09/87.90 V_14 ) = 664.09/87.90 ( 664.09/87.90 X266 ) ) & 664.09/87.90 ( 664.09/87.90 X264 ) ) ) ) ) ) @ 664.09/87.90 X262 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 664.09/87.90 inference('cnf.neg', [status(esa)], [zf_stmt_3])). 664.09/87.90 thf(zip_derived_cl139, plain, ( (in @ sk__140 @ sk__138)), 664.09/87.90 inference('cnf', [status(esa)], [zf_stmt_4])). 664.09/87.90 thf(zip_derived_cl137, plain, ( (in @ sk__141 @ sk__138)), 664.09/87.90 inference('cnf', [status(esa)], [zf_stmt_4])). 664.09/87.90 thf(zip_derived_cl102, plain, 664.09/87.90 (![X62 : $i]: ((setunion @ (setadjoin @ X62 @ emptyset)) = (X62))), 664.09/87.90 inference('cnf', [status(esa)], [zf_stmt_4])). 664.09/87.90 thf(zip_derived_cl141, plain, 664.09/87.90 (![X75 : $i, X76 : $i, X77 : $o, X78 : $i]: 664.09/87.90 (~ (in @ X75 @ X76) 664.09/87.90 | ((dsetconstr @ X76 @ 664.09/87.90 (^[Y0 : $i]: 664.09/87.90 (((((((Y0) = (X75))) & (((~) @ X77)))) | 664.09/87.90 (((((Y0) = (X78))) & (X77))))))) 664.09/87.90 = (setadjoin @ X75 @ emptyset)) 664.09/87.90 | (X77) 664.09/87.90 | ~ (in @ X78 @ X76))), 664.09/87.90 inference('cnf', [status(esa)], [zf_stmt_4])). 664.09/87.90 thf(zip_derived_cl138, plain, 664.09/87.90 (~ (in @ 664.09/87.90 (setunion @ 664.09/87.90 (dsetconstr @ sk__138 @ 664.09/87.90 (^[Y0 : $i]: 664.09/87.90 (((((((Y0) = (sk__141))) & (((~) @ sk__139)))) | 664.09/87.90 (((((Y0) = (sk__140))) & (sk__139)))))))) @ 664.09/87.90 sk__138)), 664.09/87.90 inference('cnf', [status(esa)], [zf_stmt_4])). 664.09/87.90 thf(zip_derived_cl14375, plain, ($false), 664.09/87.90 inference('eprover', [status(thm)], 664.09/87.90 [zip_derived_cl139, zip_derived_cl137, zip_derived_cl102, 664.09/87.90 zip_derived_cl141, zip_derived_cl138])). 664.09/87.90 664.09/87.90 % SZS output end Refutation 664.09/87.90 664.09/87.90 664.09/87.90 % Terminating... 664.38/88.03 % Runner terminated. 664.38/88.03 % Zipperpin 1.5 exiting 664.38/88.04 EOF