0.03/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.16 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.VwZlafnTtJ true 0.16/0.37 % Computer : n031.cluster.edu 0.16/0.37 % Model : x86_64 x86_64 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.37 % Memory : 8042.1875MB 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.37 % CPULimit : 1920 0.16/0.37 % WCLimit : 240 0.16/0.38 % DateTime : Wed Jul 30 03:50:04 EDT 2025 0.16/0.38 % CPUTime : 0.16/0.38 % Running portfolio for 1920 s 0.16/0.38 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.16/0.38 % Number of cores: 8 0.16/0.38 % Python version: Python 3.6.8 0.16/0.38 % Running in HO mode 0.56/0.67 % Total configuration time : 828 0.56/0.67 % Estimated wc time : 1656 0.56/0.67 % Estimated cpu time (8 cpus) : 207.0 0.60/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.60/0.78 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.60/0.79 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.60/0.79 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.61/0.83 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.61/0.83 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.61/0.83 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.61/0.83 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 75.20/10.16 % Solved by lams/40_c_ic.sh. 75.20/10.16 % done 1044 iterations in 9.282s 75.20/10.16 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 75.20/10.16 % SZS output start Refutation 75.20/10.16 thf(setadjoinAx_type, type, setadjoinAx: $o). 75.20/10.16 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o). 75.20/10.16 thf(notdexE_type, type, notdexE: $o). 75.20/10.16 thf(setunionAx_type, type, setunionAx: $o). 75.20/10.16 thf(setminusELneg_type, type, setminusELneg: $o). 75.20/10.16 thf(kpairsurjEq_type, type, kpairsurjEq: $o). 75.20/10.16 thf(ap2apEq2_type, type, ap2apEq2: $o). 75.20/10.16 thf(powersetE_type, type, powersetE: $o). 75.20/10.16 thf(omegaSAx_type, type, omegaSAx: $o). 75.20/10.16 thf(sk__51_type, type, sk__51: ($i > $o) > $i > $i). 75.20/10.16 thf(exuI1_type, type, exuI1: $o). 75.20/10.16 thf(exuI2_type, type, exuI2: $o). 75.20/10.16 thf(notequalI2_type, type, notequalI2: $o). 75.20/10.16 thf(kpairiskpair_type, type, kpairiskpair: $o). 75.20/10.16 thf(upairsubunion_type, type, upairsubunion: $o). 75.20/10.16 thf(powerset__Cong_type, type, powerset__Cong: $o). 75.20/10.16 thf(iftrueProp1_type, type, iftrueProp1: $o). 75.20/10.16 thf(setminusILneg_type, type, setminusILneg: $o). 75.20/10.16 thf(lam2lamEq_type, type, lam2lamEq: $o). 75.20/10.16 thf(ap2p_type, type, ap2p: $o). 75.20/10.16 thf(wellorderingAx_type, type, wellorderingAx: $o). 75.20/10.16 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 75.20/10.16 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 75.20/10.16 thf(upairinpowunion_type, type, upairinpowunion: $o). 75.20/10.16 thf(setoftrueEq_type, type, setoftrueEq: $o). 75.20/10.16 thf(func_type, type, func: $i > $i > $i > $o). 75.20/10.16 thf(sk__53_type, type, sk__53: ($i > $o) > $i > $i). 75.20/10.16 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 75.20/10.16 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o). 75.20/10.16 thf(dpsetconstrI_type, type, dpsetconstrI: $o). 75.20/10.16 thf(dpsetconstrER_type, type, dpsetconstrER: $o). 75.20/10.16 thf(sepInPowerset_type, type, sepInPowerset: $o). 75.20/10.16 thf(setukpairIR_type, type, setukpairIR: $o). 75.20/10.16 thf(kpair_type, type, kpair: $i > $i > $i). 75.20/10.16 thf(binunionE_type, type, binunionE: $o). 75.20/10.16 thf(setext_type, type, setext: $o). 75.20/10.16 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 75.20/10.16 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 75.20/10.16 thf(setukpairinjR12_type, type, setukpairinjR12: $o). 75.20/10.16 thf(descr__Cong_type, type, descr__Cong: $o). 75.20/10.16 thf(iffalseProp1_type, type, iffalseProp1: $o). 75.20/10.16 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 75.20/10.16 thf(app_type, type, app: $o). 75.20/10.16 thf(in_type, type, in: $i > $i > $o). 75.20/10.16 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o). 75.20/10.16 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o). 75.20/10.16 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 75.20/10.16 thf(funcGraphProp2_type, type, funcGraphProp2: $o). 75.20/10.16 thf(setadjoinIR_type, type, setadjoinIR: $o). 75.20/10.16 thf(funcGraphProp1_type, type, funcGraphProp1: $o). 75.20/10.16 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 75.20/10.16 thf(symdiffI2_type, type, symdiffI2: $o). 75.20/10.16 thf(upairset2IR_type, type, upairset2IR: $o). 75.20/10.16 thf(sk__55_type, type, sk__55: $o). 75.20/10.16 thf(subsetE_type, type, subsetE: $o). 75.20/10.16 thf(prop2set2propI_type, type, prop2set2propI: $o). 75.20/10.16 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 75.20/10.16 thf(setbeta_type, type, setbeta: $o). 75.20/10.16 thf(eqinunit_type, type, eqinunit: $o). 75.20/10.16 thf(upairsetIL_type, type, upairsetIL: $o). 75.20/10.16 thf(powersetI1_type, type, powersetI1: $o). 75.20/10.16 thf(lamProp_type, type, lamProp: $o). 75.20/10.16 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 75.20/10.16 thf(setukpairinjR_type, type, setukpairinjR: $o). 75.20/10.16 thf(cartprodfstin_type, type, cartprodfstin: $o). 75.20/10.16 thf(setminusIRneg_type, type, setminusIRneg: $o). 75.20/10.16 thf(powersetAx_type, type, powersetAx: $o). 75.20/10.16 thf(singletonprop_type, type, singletonprop: $o). 75.20/10.16 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 75.20/10.16 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 75.20/10.16 thf(powersetI_type, type, powersetI: $o). 75.20/10.16 thf(iffalseProp2_type, type, iffalseProp2: $o). 75.20/10.16 thf(cartprodmempair_type, type, cartprodmempair: $o). 75.20/10.16 thf(upairsetIR_type, type, upairsetIR: $o). 75.20/10.16 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o). 75.20/10.16 thf(inCongP_type, type, inCongP: $o). 75.20/10.16 thf(setukpairinjL_type, type, setukpairinjL: $o). 75.20/10.16 thf(setadjoinSub_type, type, setadjoinSub: $o). 75.20/10.16 thf(exuE3e_type, type, exuE3e: $o). 75.20/10.16 thf(emptysetE_type, type, emptysetE: $o). 75.20/10.16 thf(upairequniteq_type, type, upairequniteq: $o). 75.20/10.16 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 75.20/10.16 thf(setunionI_type, type, setunionI: $o). 75.20/10.16 thf(setunion__Cong_type, type, setunion__Cong: $o). 75.20/10.16 thf(prop2setI_type, type, prop2setI: $o). 75.20/10.16 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 75.20/10.16 thf(funcinfuncset_type, type, funcinfuncset: $o). 75.20/10.16 thf(setminusER_type, type, setminusER: $o). 75.20/10.16 thf(exuE2_type, type, exuE2: $o). 75.20/10.16 thf(emptyset_type, type, emptyset: $i). 75.20/10.16 thf(powersetsubset_type, type, powersetsubset: $o). 75.20/10.16 thf(setukpairinjR1_type, type, setukpairinjR1: $o). 75.20/10.16 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o). 75.20/10.16 thf(subPowSU_type, type, subPowSU: $o). 75.20/10.16 thf(notequalI1_type, type, notequalI1: $o). 75.20/10.16 thf(sk__52_type, type, sk__52: ($i > $o) > $i > $i). 75.20/10.16 thf(notinemptyset_type, type, notinemptyset: $o). 75.20/10.16 thf(nonemptyI1_type, type, nonemptyI1: $o). 75.20/10.16 thf(subsetTrans_type, type, subsetTrans: $o). 75.20/10.16 thf(setukpairinjR2_type, type, setukpairinjR2: $o). 75.20/10.16 thf('#l_lift8548_type', type, '#l_lift8548': $i > $o). 75.20/10.16 thf(kpairp_type, type, kpairp: $o). 75.20/10.16 thf(setminusI_type, type, setminusI: $o). 75.20/10.16 thf(binunionIL_type, type, binunionIL: $o). 75.20/10.16 thf(setunionsingleton_type, type, setunionsingleton: $o). 75.20/10.16 thf(subsetE2_type, type, subsetE2: $o). 75.20/10.16 thf(singletonsswitch_type, type, singletonsswitch: $o). 75.20/10.16 thf(kfstpairEq_type, type, kfstpairEq: $o). 75.20/10.16 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 75.20/10.16 thf(setextsub_type, type, setextsub: $o). 75.20/10.16 thf(binunionLsub_type, type, binunionLsub: $o). 75.20/10.16 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 75.20/10.16 thf(emptysetsubset_type, type, emptysetsubset: $o). 75.20/10.16 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 75.20/10.16 thf(setunionE_type, type, setunionE: $o). 75.20/10.16 thf(setminusSubset1_type, type, setminusSubset1: $o). 75.20/10.16 thf(sk__57_type, type, sk__57: $i). 75.20/10.16 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 75.20/10.16 thf(binunionIR_type, type, binunionIR: $o). 75.20/10.16 thf(setadjoinE_type, type, setadjoinE: $o). 75.20/10.16 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o). 75.20/10.16 thf(subbreln_type, type, subbreln: $o). 75.20/10.16 thf(singletonsuniq_type, type, singletonsuniq: $o). 75.20/10.16 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o). 75.20/10.16 thf(setadjoinIL_type, type, setadjoinIL: $o). 75.20/10.16 thf(exuE1_type, type, exuE1: $o). 75.20/10.16 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 75.20/10.16 thf(binintersectRsub_type, type, binintersectRsub: $o). 75.20/10.16 thf(setminusLsub_type, type, setminusLsub: $o). 75.20/10.16 thf(notinsingleton_type, type, notinsingleton: $o). 75.20/10.16 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o). 75.20/10.16 thf(funcext_type, type, funcext: $o). 75.20/10.16 thf(infuncsetfunc_type, type, infuncsetfunc: $o). 75.20/10.16 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 75.20/10.16 thf(exuEu_type, type, exuEu: $o). 75.20/10.16 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 75.20/10.16 thf(ex1I2_type, type, ex1I2: $o). 75.20/10.16 thf(upairsetE_type, type, upairsetE: $o). 75.20/10.16 thf(omega0Ax_type, type, omega0Ax: $o). 75.20/10.16 thf(funcext2_type, type, funcext2: $o). 75.20/10.16 thf(notsubsetI_type, type, notsubsetI: $o). 75.20/10.16 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 75.20/10.16 thf(setextAx_type, type, setextAx: $o). 75.20/10.16 thf(powersetE1_type, type, powersetE1: $o). 75.20/10.16 thf(bs114d_type, type, bs114d: $o). 75.20/10.16 thf(sk__54_type, type, sk__54: $i). 75.20/10.16 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 75.20/10.16 thf(setunion_type, type, setunion: $i > $i). 75.20/10.16 thf(eqbreln_type, type, eqbreln: $o). 75.20/10.16 thf(binintersectLsub_type, type, binintersectLsub: $o). 75.20/10.16 thf(subsetI1_type, type, subsetI1: $o). 75.20/10.16 thf(symdiffE_type, type, symdiffE: $o). 75.20/10.16 thf(sk__56_type, type, sk__56: $i). 75.20/10.16 thf(descrp_type, type, descrp: $o). 75.20/10.16 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 75.20/10.16 thf(foundationAx_type, type, foundationAx: $o). 75.20/10.16 thf(brelnall1_type, type, brelnall1: $o). 75.20/10.16 thf(emptysetAx_type, type, emptysetAx: $o). 75.20/10.16 thf(emptyI_type, type, emptyI: $o). 75.20/10.16 thf(setadjoinOr_type, type, setadjoinOr: $o). 75.20/10.16 thf(binintersectEL_type, type, binintersectEL: $o). 75.20/10.16 thf(emptyE1_type, type, emptyE1: $o). 75.20/10.16 thf(ex1E2_type, type, ex1E2: $o). 75.20/10.16 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 75.20/10.16 thf(funcImageSingleton_type, type, funcImageSingleton: $o). 75.20/10.16 thf(vacuousDall_type, type, vacuousDall: $o). 75.20/10.16 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 75.20/10.16 thf(dsetconstrER_type, type, dsetconstrER: $o). 75.20/10.16 thf(funcGraphProp3_type, type, funcGraphProp3: $o). 75.20/10.16 thf(binintersectI_type, type, binintersectI: $o). 75.20/10.16 thf(funcGraphProp4_type, type, funcGraphProp4: $o). 75.20/10.16 thf(lamp_type, type, lamp: $o). 75.20/10.16 thf(cartprodpairin_type, type, cartprodpairin: $o). 75.20/10.16 thf(eta1_type, type, eta1: $o). 75.20/10.16 thf(ex1I_type, type, ex1I: $o). 75.20/10.16 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 75.20/10.16 thf(eta2_type, type, eta2: $o). 75.20/10.16 thf(cartprodsndin_type, type, cartprodsndin: $o). 75.20/10.16 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 75.20/10.16 thf(singleton_type, type, singleton: $i > $o). 75.20/10.16 thf(symdiffI1_type, type, symdiffI1: $o). 75.20/10.16 thf(subsetI2_type, type, subsetI2: $o). 75.20/10.16 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o). 75.20/10.16 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 75.20/10.16 thf(theprop_type, type, theprop: $o). 75.20/10.16 thf(setminusERneg_type, type, setminusERneg: $o). 75.20/10.16 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 75.20/10.16 thf(omega__Cong_type, type, omega__Cong: $o). 75.20/10.16 thf(subsetRefl_type, type, subsetRefl: $o). 75.20/10.16 thf(uniqinunit_type, type, uniqinunit: $o). 75.20/10.16 thf(lam2p_type, type, lam2p: $o). 75.20/10.16 thf(beta1_type, type, beta1: $o). 75.20/10.16 thf(setminusSubset2_type, type, setminusSubset2: $o). 75.20/10.16 thf(prop2setE_type, type, prop2setE: $o). 75.20/10.16 thf(binunionEcases_type, type, binunionEcases: $o). 75.20/10.16 thf(nonemptyI_type, type, nonemptyI: $o). 75.20/10.16 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 75.20/10.16 thf(exuE3u_type, type, exuE3u: $o). 75.20/10.16 thf(setminusEL_type, type, setminusEL: $o). 75.20/10.16 thf(funcextLem_type, type, funcextLem: $o). 75.20/10.16 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 75.20/10.16 thf(sepSubset_type, type, sepSubset: $o). 75.20/10.16 thf(upairset2E_type, type, upairset2E: $o). 75.20/10.16 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 75.20/10.16 thf(exuI3_type, type, exuI3: $o). 75.20/10.16 thf(notdallE_type, type, notdallE: $o). 75.20/10.16 thf(binintersectER_type, type, binintersectER: $o). 75.20/10.16 thf(ksndsingleton_type, type, ksndsingleton: $o). 75.20/10.16 thf(ap2apEq1_type, type, ap2apEq1: $o). 75.20/10.16 thf(beta2_type, type, beta2: $o). 75.20/10.16 thf(kfstsingleton_type, type, kfstsingleton: $o). 75.20/10.16 thf(dsetconstrI_type, type, dsetconstrI: $o). 75.20/10.16 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o). 75.20/10.16 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 75.20/10.16 thf(exu__Cong_type, type, exu__Cong: $o). 75.20/10.16 thf(ksndpairEq_type, type, ksndpairEq: $o). 75.20/10.16 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 75.20/10.16 thf(iftrueProp2_type, type, iftrueProp2: $o). 75.20/10.16 thf(ex1E1_type, type, ex1E1: $o). 75.20/10.16 thf(secondinupair_type, type, secondinupair: $o). 75.20/10.16 thf(singletonsubset_type, type, singletonsubset: $o). 75.20/10.16 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 75.20/10.16 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 75.20/10.16 thf(brelnall2_type, type, brelnall2: $o). 75.20/10.16 thf(replAx_type, type, replAx: $o). 75.20/10.16 thf(nonemptyE1_type, type, nonemptyE1: $o). 75.20/10.16 thf(omegaIndAx_type, type, omegaIndAx: $o). 75.20/10.16 thf(setukpairIL_type, type, setukpairIL: $o). 75.20/10.16 thf(setunionE2_type, type, setunionE2: $o). 75.20/10.16 thf(inPowerset_type, type, inPowerset: $o). 75.20/10.16 thf(subset_type, type, subset: $i > $i > $o). 75.20/10.16 thf(apProp_type, type, apProp: $o). 75.20/10.16 thf(in__Cong_type, type, in__Cong: $o). 75.20/10.16 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 75.20/10.16 thf(binunionRsub_type, type, binunionRsub: $o). 75.20/10.16 thf(subset2powerset_type, type, subset2powerset: $o). 75.20/10.16 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 75.20/10.16 thf(iftrueProp2, axiom, iftrueProp2 = 75.20/10.16 (![A:$i,Xphi:$o,Xx:$i]: 75.20/10.16 ( ( in @ Xx @ A ) => 75.20/10.16 ( ![Xy:$i]: 75.20/10.16 ( ( in @ Xy @ A ) => 75.20/10.16 ( ( Xphi ) => 75.20/10.16 ( ( dsetconstr @ 75.20/10.16 A @ 75.20/10.16 ( ^[Xz:$i]: 75.20/10.16 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) | 75.20/10.16 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) = 75.20/10.16 ( setadjoin @ Xx @ emptyset ) ) ) ) ) ))). 75.20/10.16 thf('0', plain, 75.20/10.16 (( iftrueProp2 ) = 75.20/10.16 ( ![X4:$i,X6:$o,X8:$i]: 75.20/10.16 ( ( in @ X8 @ X4 ) => 75.20/10.16 ( ![X10:$i]: 75.20/10.16 ( ( in @ X10 @ X4 ) => 75.20/10.16 ( ( X6 ) => 75.20/10.16 ( ( dsetconstr @ 75.20/10.16 X4 @ 75.20/10.16 ( ^[V_1:$i]: 75.20/10.16 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) | 75.20/10.16 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) = 75.20/10.16 ( setadjoin @ X8 @ emptyset ) ) ) ) ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(iftrueProp1, axiom, iftrueProp1 = 75.20/10.16 (![A:$i,Xphi:$o,Xx:$i]: 75.20/10.16 ( ( in @ Xx @ A ) => 75.20/10.16 ( ![Xy:$i]: 75.20/10.16 ( ( in @ Xy @ A ) => 75.20/10.16 ( ( Xphi ) => 75.20/10.16 ( in @ 75.20/10.16 Xx @ 75.20/10.16 ( dsetconstr @ 75.20/10.16 A @ 75.20/10.16 ( ^[Xz:$i]: 75.20/10.16 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) | 75.20/10.16 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) ) ) ) ) ))). 75.20/10.16 thf('1', plain, 75.20/10.16 (( iftrueProp1 ) = 75.20/10.16 ( ![X4:$i,X6:$o,X8:$i]: 75.20/10.16 ( ( in @ X8 @ X4 ) => 75.20/10.16 ( ![X10:$i]: 75.20/10.16 ( ( in @ X10 @ X4 ) => 75.20/10.16 ( ( X6 ) => 75.20/10.16 ( in @ 75.20/10.16 X8 @ 75.20/10.16 ( dsetconstr @ 75.20/10.16 X4 @ 75.20/10.16 ( ^[V_1:$i]: 75.20/10.16 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) | 75.20/10.16 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) ) ) ) ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(iffalseProp2, axiom, iffalseProp2 = 75.20/10.16 (![A:$i,Xphi:$o,Xx:$i]: 75.20/10.16 ( ( in @ Xx @ A ) => 75.20/10.16 ( ![Xy:$i]: 75.20/10.16 ( ( in @ Xy @ A ) => 75.20/10.16 ( ( ~( Xphi ) ) => 75.20/10.16 ( ( dsetconstr @ 75.20/10.16 A @ 75.20/10.16 ( ^[Xz:$i]: 75.20/10.16 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) | 75.20/10.16 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) = 75.20/10.16 ( setadjoin @ Xy @ emptyset ) ) ) ) ) ))). 75.20/10.16 thf('2', plain, 75.20/10.16 (( iffalseProp2 ) = 75.20/10.16 ( ![X4:$i,X6:$o,X8:$i]: 75.20/10.16 ( ( in @ X8 @ X4 ) => 75.20/10.16 ( ![X10:$i]: 75.20/10.16 ( ( in @ X10 @ X4 ) => 75.20/10.16 ( ( ~( X6 ) ) => 75.20/10.16 ( ( dsetconstr @ 75.20/10.16 X4 @ 75.20/10.16 ( ^[V_1:$i]: 75.20/10.16 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) | 75.20/10.16 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) = 75.20/10.16 ( setadjoin @ X10 @ emptyset ) ) ) ) ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(iffalseProp1, axiom, iffalseProp1 = 75.20/10.16 (![A:$i,Xphi:$o,Xx:$i]: 75.20/10.16 ( ( in @ Xx @ A ) => 75.20/10.16 ( ![Xy:$i]: 75.20/10.16 ( ( in @ Xy @ A ) => 75.20/10.16 ( ( ~( Xphi ) ) => 75.20/10.16 ( in @ 75.20/10.16 Xy @ 75.20/10.16 ( dsetconstr @ 75.20/10.16 A @ 75.20/10.16 ( ^[Xz:$i]: 75.20/10.16 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) | 75.20/10.16 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) ) ) ) ) ))). 75.20/10.16 thf('3', plain, 75.20/10.16 (( iffalseProp1 ) = 75.20/10.16 ( ![X4:$i,X6:$o,X8:$i]: 75.20/10.16 ( ( in @ X8 @ X4 ) => 75.20/10.16 ( ![X10:$i]: 75.20/10.16 ( ( in @ X10 @ X4 ) => 75.20/10.16 ( ( ~( X6 ) ) => 75.20/10.16 ( in @ 75.20/10.16 X10 @ 75.20/10.16 ( dsetconstr @ 75.20/10.16 X4 @ 75.20/10.16 ( ^[V_1:$i]: 75.20/10.16 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) | 75.20/10.16 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) ) ) ) ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(funcImageSingleton, axiom, funcImageSingleton = 75.20/10.16 (![A:$i,B:$i,Xf:$i]: 75.20/10.16 ( ( func @ A @ B @ Xf ) => 75.20/10.16 ( ![Xx:$i]: 75.20/10.16 ( ( in @ Xx @ A ) => 75.20/10.16 ( singleton @ 75.20/10.16 ( dsetconstr @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ))). 75.20/10.16 thf('4', plain, 75.20/10.16 (( funcImageSingleton ) = 75.20/10.16 ( ![X4:$i,X6:$i,X8:$i]: 75.20/10.16 ( ( func @ X4 @ X6 @ X8 ) => 75.20/10.16 ( ![X10:$i]: 75.20/10.16 ( ( in @ X10 @ X4 ) => 75.20/10.16 ( singleton @ 75.20/10.16 ( dsetconstr @ 75.20/10.16 X6 @ ( ^[V_1:$i]: ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) ) ) ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(theprop, axiom, theprop = 75.20/10.16 (![X:$i]: ( ( singleton @ X ) => ( in @ ( setunion @ X ) @ X ) ))). 75.20/10.16 thf('5', plain, 75.20/10.16 (( theprop ) = 75.20/10.16 ( ![X4:$i]: ( ( singleton @ X4 ) => ( in @ ( setunion @ X4 ) @ X4 ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(singletonprop, axiom, singletonprop = 75.20/10.16 (![A:$i,Xphi:( $i > $o )]: 75.20/10.16 ( ( ![Xx:$i]: 75.20/10.16 ( ( in @ Xx @ A ) => 75.20/10.16 ( ![Xy:$i]: 75.20/10.16 ( ( in @ Xy @ A ) => 75.20/10.16 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ) ) ) => 75.20/10.16 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) => 75.20/10.16 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ) ))). 75.20/10.16 thf('6', plain, 75.20/10.16 (( singletonprop ) = 75.20/10.16 ( ![X4:$i,X6:( $i > $o )]: 75.20/10.16 ( ( ![X8:$i]: 75.20/10.16 ( ( in @ X8 @ X4 ) => 75.20/10.16 ( ![X10:$i]: 75.20/10.16 ( ( in @ X10 @ X4 ) => 75.20/10.16 ( ( X6 @ X8 ) => ( ( X6 @ X10 ) => ( ( X8 ) = ( X10 ) ) ) ) ) ) ) ) => 75.20/10.16 ( ( ?[X12:$i]: ( ( X6 @ X12 ) & ( in @ X12 @ X4 ) ) ) => 75.20/10.16 ( singleton @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(singleton, axiom,(( singleton ) = 75.20/10.16 (^[A:$i]: 75.20/10.16 ( ?[Xx:$i]: 75.20/10.16 ( ( ( A ) = ( setadjoin @ Xx @ emptyset ) ) & ( in @ Xx @ A ) ) )))). 75.20/10.16 thf('7', plain, 75.20/10.16 (( singleton ) = 75.20/10.16 ( ^[A:$i]: 75.20/10.16 ( ?[Xx:$i]: 75.20/10.16 ( ( ( A ) = ( setadjoin @ Xx @ emptyset ) ) & ( in @ Xx @ A ) ) ) )), 75.20/10.16 inference('simplify_rw_rule', [status(thm)], [singleton])). 75.20/10.16 thf('8', plain, 75.20/10.16 (( singleton ) = 75.20/10.16 ( ^[V_1:$i]: 75.20/10.16 ( ?[X4:$i]: 75.20/10.16 ( ( ( V_1 ) = ( setadjoin @ X4 @ emptyset ) ) & ( in @ X4 @ V_1 ) ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(sepSubset, axiom, sepSubset = 75.20/10.16 (![A:$i,Xphi:( $i > $o )]: 75.20/10.16 ( subset @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ A ))). 75.20/10.16 thf('9', plain, 75.20/10.16 (( sepSubset ) = 75.20/10.16 ( ![X4:$i,X6:( $i > $o )]: 75.20/10.16 ( subset @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @ X4 ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(dsetconstr__Cong, axiom, dsetconstr__Cong = 75.20/10.16 (![A:$i,B:$i]: 75.20/10.16 ( ( ( A ) = ( B ) ) => 75.20/10.16 ( ![Xphi:( $i > $o ),Xpsi:( $i > $o )]: 75.20/10.16 ( ( ![Xx:$i]: 75.20/10.16 ( ( in @ Xx @ A ) => 75.20/10.16 ( ![Xy:$i]: 75.20/10.16 ( ( in @ Xy @ B ) => 75.20/10.16 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) ) ) ) => 75.20/10.16 ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) = 75.20/10.16 ( dsetconstr @ B @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ) ) ))). 75.20/10.16 thf('10', plain, 75.20/10.16 (( dsetconstr__Cong ) = 75.20/10.16 ( ![X4:$i,X6:$i]: 75.20/10.16 ( ( ( X4 ) = ( X6 ) ) => 75.20/10.16 ( ![X8:( $i > $o ),X10:( $i > $o )]: 75.20/10.16 ( ( ![X12:$i]: 75.20/10.16 ( ( in @ X12 @ X4 ) => 75.20/10.16 ( ![X14:$i]: 75.20/10.16 ( ( in @ X14 @ X6 ) => 75.20/10.16 ( ( ( X12 ) = ( X14 ) ) => 75.20/10.16 ( ( X8 @ X12 ) <=> ( X10 @ X14 ) ) ) ) ) ) ) => 75.20/10.16 ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) = 75.20/10.16 ( dsetconstr @ X6 @ ( ^[V_2:$i]: ( X10 @ V_2 ) ) ) ) ) ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(emptyE1, axiom, emptyE1 = 75.20/10.16 (![A:$i,Xphi:( $i > $o )]: 75.20/10.16 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) => 75.20/10.16 ( ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) = ( emptyset ) ) => 75.20/10.16 ( $false ) ) ))). 75.20/10.16 thf('11', plain, 75.20/10.16 (( emptyE1 ) = 75.20/10.16 ( ![X4:$i,X6:( $i > $o )]: 75.20/10.16 ( ( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) => 75.20/10.16 ( ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = ( emptyset ) ) => 75.20/10.16 ( $false ) ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(setoftrueEq, axiom, setoftrueEq = 75.20/10.16 (![A:$i]: ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( $true ) ) ) = ( A ) ))). 75.20/10.16 thf('12', plain, 75.20/10.16 (( setoftrueEq ) = 75.20/10.16 ( ![X4:$i]: ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( $true ) ) ) = ( X4 ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(setbeta, axiom, setbeta = 75.20/10.16 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 75.20/10.16 ( ( in @ Xx @ A ) => 75.20/10.16 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) <=> 75.20/10.16 ( Xphi @ Xx ) ) ))). 75.20/10.16 thf('13', plain, 75.20/10.16 (( setbeta ) = 75.20/10.16 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 75.20/10.16 ( ( in @ X8 @ X4 ) => 75.20/10.16 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=> 75.20/10.16 ( X6 @ X8 ) ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(dsetconstrER, axiom, dsetconstrER = 75.20/10.16 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 75.20/10.16 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) => 75.20/10.16 ( Xphi @ Xx ) ))). 75.20/10.16 thf('14', plain, 75.20/10.16 (( dsetconstrER ) = 75.20/10.16 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 75.20/10.16 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 75.20/10.16 ( X6 @ X8 ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(dsetconstrEL, axiom, dsetconstrEL = 75.20/10.16 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 75.20/10.16 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) => 75.20/10.16 ( in @ Xx @ A ) ))). 75.20/10.16 thf('15', plain, 75.20/10.16 (( dsetconstrEL ) = 75.20/10.16 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 75.20/10.16 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 75.20/10.16 ( in @ X8 @ X4 ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(dsetconstrI, axiom, dsetconstrI = 75.20/10.16 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 75.20/10.16 ( ( in @ Xx @ A ) => 75.20/10.16 ( ( Xphi @ Xx ) => 75.20/10.16 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))). 75.20/10.16 thf('16', plain, 75.20/10.16 (( dsetconstrI ) = 75.20/10.16 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 75.20/10.16 ( ( in @ X8 @ X4 ) => 75.20/10.16 ( ( X6 @ X8 ) => 75.20/10.16 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )), 75.20/10.16 define([status(thm)])). 75.20/10.16 thf(ifSingleton, conjecture, 75.20/10.16 (( setextAx ) => 75.20/10.16 ( ( emptysetAx ) => 75.20/10.16 ( ( setadjoinAx ) => 75.20/10.16 ( ( powersetAx ) => 75.20/10.16 ( ( setunionAx ) => 75.20/10.16 ( ( omega0Ax ) => 75.20/10.16 ( ( omegaSAx ) => 75.20/10.16 ( ( omegaIndAx ) => 75.20/10.16 ( ( replAx ) => 75.20/10.16 ( ( foundationAx ) => 75.20/10.16 ( ( wellorderingAx ) => 75.20/10.16 ( ( descrp ) => 75.20/10.16 ( ( dsetconstrI ) => 75.20/10.16 ( ( dsetconstrEL ) => 75.20/10.16 ( ( dsetconstrER ) => 75.20/10.16 ( ( exuE1 ) => 75.20/10.16 ( ( prop2setE ) => 75.20/10.16 ( ( emptysetE ) => 75.20/10.16 ( ( emptysetimpfalse ) => 75.20/10.16 ( ( notinemptyset ) => 75.20/10.16 ( ( exuE3e ) => 75.20/10.16 ( ( setext ) => 75.20/10.16 ( ( emptyI ) => 75.20/10.16 ( ( noeltsimpempty ) => 75.20/10.16 ( ( setbeta ) => 75.20/10.16 ( ( nonemptyE1 ) => 75.20/10.16 ( ( nonemptyI ) => 75.20/10.16 ( ( nonemptyI1 ) => 75.20/10.16 ( ( setadjoinIL ) => 75.20/10.16 ( ( emptyinunitempty ) => 75.20/10.16 ( ( setadjoinIR ) => 75.20/10.16 ( ( setadjoinE ) => 75.20/10.16 ( ( 75.20/10.16 setadjoinOr ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setoftrueEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 powersetI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 emptyinPowerset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 emptyInPowerset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 powersetE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunionI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunionE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subPowSU ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exuE2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 nonemptyImpWitness ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 uniqinunit ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 notinsingleton ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 eqinunit ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 singletonsswitch ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairsetE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairsetIL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairsetIR ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 emptyE1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 vacuousDall ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 quantDeMorgan1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 quantDeMorgan2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 quantDeMorgan3 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 quantDeMorgan4 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 prop2setI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 prop2set2propI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 notdexE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 notdallE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exuI1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exuI3 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exuI2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 inCongP ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 in__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exuE3u ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exu__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 emptyset__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setadjoin__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 powerset__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunion__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 omega__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exuEu ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 descr__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dsetconstr__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetI1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 eqimpsubset2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 eqimpsubset1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetI2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 emptysetsubset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetE2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 notsubsetI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 notequalI1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 notequalI2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetRefl ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetTrans ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setadjoinSub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setadjoinSub2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subset2powerset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setextsub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetemptysetimpeq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 powersetI1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 powersetE1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 inPowerset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 powersetsubset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 sepInPowerset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 sepSubset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binunionIL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairset2IR ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binunionIR ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binunionEcases ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binunionE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binunionLsub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binunionRsub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectSubset5 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectEL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectLsub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectSubset2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectSubset3 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectER ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 disjointsetsI1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectRsub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectSubset4 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectSubset1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 bs114d ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusEL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusER ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusSubset2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusERneg ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusELneg ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusILneg ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusIRneg ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusLsub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusSubset1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 symdiffE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 symdiffI1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 symdiffI2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 symdiffIneg1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 symdiffIneg2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 secondinupair ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairIL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairIR ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 kpairiskpair ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 kpairp ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 singletonsubset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 singletoninpowerset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 singletoninpowunion ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairset2E ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairsubunion ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairinpowunion ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ubforcartprodlem1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ubforcartprodlem2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ubforcartprodlem3 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodpairin ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodmempair1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodmempair ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunionE2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunionsingleton1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunionsingleton2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunionsingleton ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 singletonprop ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ex1E1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ex1I ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ex1I2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 singletonsuniq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjL1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 kfstsingleton ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 theprop ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 kfstpairEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodfstin ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjL2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjR11 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjR12 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjR1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairequniteq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjR2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjR ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ksndsingleton ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ksndpairEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 kpairsurjEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodsndin ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodpairmemEL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodpairmemER ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodmempaircEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodfstpairEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodsndpairEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodpairsurjEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dpsetconstrI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dpsetconstrSub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setOfPairsIsBReln ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dpsetconstrERa ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dpsetconstrEL1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dpsetconstrEL2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dpsetconstrER ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 funcImageSingleton ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 apProp ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 app ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 infuncsetfunc ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ap2p ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 funcinfuncset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 lamProp ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 lamp ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 lam2p ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 brelnall1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 brelnall2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ex1E2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 funcGraphProp1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 funcGraphProp3 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 funcGraphProp2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 funcextLem ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 funcGraphProp4 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subbreln ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 eqbreln ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 funcext ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 funcext2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ap2apEq1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ap2apEq2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 beta1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 eta1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 lam2lamEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 beta2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 eta2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 iffalseProp1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 iffalseProp2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 iftrueProp1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 iftrueProp2 ) => 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 A:$i, 75.20/10.16 Xphi:$o, 75.20/10.16 Xx:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 in @ 75.20/10.16 Xx @ A ) => 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 Xy:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 in @ 75.20/10.16 Xy @ A ) => 75.20/10.16 ( 75.20/10.16 singleton 75.20/10.16 @ 75.20/10.16 ( 75.20/10.16 dsetconstr 75.20/10.16 @ 75.20/10.16 A @ 75.20/10.16 ( 75.20/10.16 ^[ 75.20/10.16 Xz:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 Xphi ) & 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 Xz ) = 75.20/10.16 ( 75.20/10.16 Xx ) ) ) | 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 Xz ) = 75.20/10.16 ( 75.20/10.16 Xy ) ) & 75.20/10.16 ( 75.20/10.16 ~( Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 75.20/10.16 thf(zf_stmt_0, conjecture, 75.20/10.16 (( setextAx ) => 75.20/10.16 ( ( emptysetAx ) => 75.20/10.16 ( ( setadjoinAx ) => 75.20/10.16 ( ( powersetAx ) => 75.20/10.16 ( ( setunionAx ) => 75.20/10.16 ( ( omega0Ax ) => 75.20/10.16 ( ( omegaSAx ) => 75.20/10.16 ( ( omegaIndAx ) => 75.20/10.16 ( ( replAx ) => 75.20/10.16 ( ( foundationAx ) => 75.20/10.16 ( ( wellorderingAx ) => 75.20/10.16 ( ( descrp ) => 75.20/10.16 ( ( ![X4:$i,X6:( $i > $o ),X8:$i]: 75.20/10.16 ( ( in @ X8 @ X4 ) => 75.20/10.16 ( ( X6 @ X8 ) => 75.20/10.16 ( in @ 75.20/10.16 X8 @ 75.20/10.16 ( dsetconstr @ 75.20/10.16 X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) ) => 75.20/10.16 ( ( ![X10:$i,X12:( $i > $o ),X14:$i]: 75.20/10.16 ( ( in @ 75.20/10.16 X14 @ 75.20/10.16 ( dsetconstr @ 75.20/10.16 X10 @ ( ^[V_2:$i]: ( X12 @ V_2 ) ) ) ) => 75.20/10.16 ( in @ X14 @ X10 ) ) ) => 75.20/10.16 ( ( ![X16:$i,X18:( $i > $o ),X20:$i]: 75.20/10.16 ( ( in @ 75.20/10.16 X20 @ 75.20/10.16 ( dsetconstr @ 75.20/10.16 X16 @ ( ^[V_3:$i]: ( X18 @ V_3 ) ) ) ) => 75.20/10.16 ( X18 @ X20 ) ) ) => 75.20/10.16 ( ( exuE1 ) => 75.20/10.16 ( ( prop2setE ) => 75.20/10.16 ( ( emptysetE ) => 75.20/10.16 ( ( emptysetimpfalse ) => 75.20/10.16 ( ( notinemptyset ) => 75.20/10.16 ( ( exuE3e ) => 75.20/10.16 ( ( setext ) => 75.20/10.16 ( ( emptyI ) => 75.20/10.16 ( ( noeltsimpempty ) => 75.20/10.16 ( ( ![X22:$i, 75.20/10.16 X24:( $i > $o ),X26:$i]: 75.20/10.16 ( ( in @ X26 @ X22 ) => 75.20/10.16 ( ( in @ 75.20/10.16 X26 @ 75.20/10.16 ( dsetconstr @ 75.20/10.16 X22 @ 75.20/10.16 ( ^[V_4:$i]: 75.20/10.16 ( X24 @ V_4 ) ) ) ) <=> 75.20/10.16 ( X24 @ X26 ) ) ) ) => 75.20/10.16 ( ( nonemptyE1 ) => 75.20/10.16 ( ( nonemptyI ) => 75.20/10.16 ( ( nonemptyI1 ) => 75.20/10.16 ( ( setadjoinIL ) => 75.20/10.16 ( ( emptyinunitempty ) => 75.20/10.16 ( ( setadjoinIR ) => 75.20/10.16 ( ( setadjoinE ) => 75.20/10.16 ( ( 75.20/10.16 setadjoinOr ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 X28:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dsetconstr 75.20/10.16 @ 75.20/10.16 X28 @ 75.20/10.16 ( 75.20/10.16 ^[ 75.20/10.16 V_5:$i]: 75.20/10.16 ( 75.20/10.16 $true ) ) ) = 75.20/10.16 ( 75.20/10.16 X28 ) ) ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 powersetI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 emptyinPowerset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 emptyInPowerset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 powersetE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunionI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunionE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subPowSU ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exuE2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 nonemptyImpWitness ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 uniqinunit ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 notinsingleton ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 eqinunit ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 singletonsswitch ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairsetE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairsetIL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairsetIR ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 X30:$i, 75.20/10.16 X32:( 75.20/10.16 $i > $o )]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ?[ 75.20/10.16 X34:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 X32 @ X34 ) & 75.20/10.16 ( 75.20/10.16 in @ 75.20/10.16 X34 @ X30 ) ) ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dsetconstr 75.20/10.16 @ 75.20/10.16 X30 @ 75.20/10.16 ( 75.20/10.16 ^[ 75.20/10.16 V_6:$i]: 75.20/10.16 ( 75.20/10.16 X32 @ V_6 ) ) ) != 75.20/10.16 ( 75.20/10.16 emptyset ) ) ) ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 vacuousDall ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 quantDeMorgan1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 quantDeMorgan2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 quantDeMorgan3 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 quantDeMorgan4 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 prop2setI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 prop2set2propI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 notdexE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 notdallE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exuI1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exuI3 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exuI2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 inCongP ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 in__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exuE3u ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exu__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 emptyset__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setadjoin__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 powerset__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunion__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 omega__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 exuEu ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 descr__Cong ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 X36:$i, 75.20/10.16 X38:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 X36 ) = 75.20/10.16 ( 75.20/10.16 X38 ) ) => 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 X40:( 75.20/10.16 $i > $o ), 75.20/10.16 X42:( 75.20/10.16 $i > $o )]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 X44:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 in @ 75.20/10.16 X44 @ X36 ) => 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 X46:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 in @ 75.20/10.16 X46 @ X38 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 X44 ) = 75.20/10.16 ( 75.20/10.16 X46 ) ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 X40 @ X44 ) <=> 75.20/10.16 ( 75.20/10.16 X42 @ X46 ) ) ) ) ) ) ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dsetconstr 75.20/10.16 @ 75.20/10.16 X36 @ 75.20/10.16 ( 75.20/10.16 ^[ 75.20/10.16 V_7:$i]: 75.20/10.16 ( 75.20/10.16 X40 @ V_7 ) ) ) = 75.20/10.16 ( 75.20/10.16 dsetconstr 75.20/10.16 @ 75.20/10.16 X38 @ 75.20/10.16 ( 75.20/10.16 ^[ 75.20/10.16 V_8:$i]: 75.20/10.16 ( 75.20/10.16 X42 @ V_8 ) ) ) ) ) ) ) ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetI1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 eqimpsubset2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 eqimpsubset1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetI2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 emptysetsubset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetE2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 notsubsetI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 notequalI1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 notequalI2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetRefl ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetTrans ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setadjoinSub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setadjoinSub2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subset2powerset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setextsub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 subsetemptysetimpeq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 powersetI1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 powersetE1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 inPowerset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 powersetsubset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 sepInPowerset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 X48:$i, 75.20/10.16 X50:( 75.20/10.16 $i > $o )]: 75.20/10.16 ( 75.20/10.16 subset @ 75.20/10.16 ( 75.20/10.16 dsetconstr 75.20/10.16 @ 75.20/10.16 X48 @ 75.20/10.16 ( 75.20/10.16 ^[ 75.20/10.16 V_9:$i]: 75.20/10.16 ( 75.20/10.16 X50 @ V_9 ) ) ) @ 75.20/10.16 X48 ) ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binunionIL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairset2IR ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binunionIR ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binunionEcases ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binunionE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binunionLsub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binunionRsub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectSubset5 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectEL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectLsub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectSubset2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectSubset3 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectER ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 disjointsetsI1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectRsub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectSubset4 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 binintersectSubset1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 bs114d ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusEL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusER ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusSubset2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusERneg ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusELneg ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusILneg ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusIRneg ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusLsub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setminusSubset1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 symdiffE ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 symdiffI1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 symdiffI2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 symdiffIneg1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 symdiffIneg2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 secondinupair ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairIL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairIR ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 kpairiskpair ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 kpairp ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 singletonsubset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 singletoninpowerset ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 singletoninpowunion ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairset2E ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairsubunion ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairinpowunion ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ubforcartprodlem1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ubforcartprodlem2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ubforcartprodlem3 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodpairin ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodmempair1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodmempair ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunionE2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunionsingleton1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunionsingleton2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setunionsingleton ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 X52:$i, 75.20/10.16 X54:( 75.20/10.16 $i > $o )]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 X56:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 in @ 75.20/10.16 X56 @ X52 ) => 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 X58:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 in @ 75.20/10.16 X58 @ X52 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 X54 @ X56 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 X54 @ X58 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 X56 ) = 75.20/10.16 ( 75.20/10.16 X58 ) ) ) ) ) ) ) ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ?[ 75.20/10.16 X60:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 X54 @ X60 ) & 75.20/10.16 ( 75.20/10.16 in @ 75.20/10.16 X60 @ X52 ) ) ) => 75.20/10.16 ( 75.20/10.16 ?[ 75.20/10.16 X62:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dsetconstr 75.20/10.16 @ 75.20/10.16 X52 @ 75.20/10.16 ( 75.20/10.16 ^[ 75.20/10.16 V_10:$i]: 75.20/10.16 ( 75.20/10.16 X54 @ V_10 ) ) ) = 75.20/10.16 ( 75.20/10.16 setadjoin 75.20/10.16 @ 75.20/10.16 X62 @ 75.20/10.16 emptyset ) ) & 75.20/10.16 ( 75.20/10.16 in @ 75.20/10.16 X62 @ 75.20/10.16 ( 75.20/10.16 dsetconstr 75.20/10.16 @ 75.20/10.16 X52 @ 75.20/10.16 ( 75.20/10.16 ^[ 75.20/10.16 V_11:$i]: 75.20/10.16 ( 75.20/10.16 X54 @ V_11 ) ) ) ) ) ) ) ) ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ex1E1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ex1I ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ex1I2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 singletonsuniq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjL1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 kfstsingleton ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 X64:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ?[ 75.20/10.16 X66:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 X64 ) = 75.20/10.16 ( 75.20/10.16 setadjoin 75.20/10.16 @ 75.20/10.16 X66 @ 75.20/10.16 emptyset ) ) & 75.20/10.16 ( 75.20/10.16 in @ 75.20/10.16 X66 @ X64 ) ) ) => 75.20/10.16 ( 75.20/10.16 in @ 75.20/10.16 ( 75.20/10.16 setunion @ 75.20/10.16 X64 ) @ 75.20/10.16 X64 ) ) ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 kfstpairEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodfstin ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjL2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjR11 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjR12 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjR1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 upairequniteq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjR2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setukpairinjR ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ksndsingleton ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ksndpairEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 kpairsurjEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodsndin ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodpairmemEL ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodpairmemER ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodmempaircEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodfstpairEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodsndpairEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 cartprodpairsurjEq ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dpsetconstrI ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dpsetconstrSub ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 setOfPairsIsBReln ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dpsetconstrERa ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dpsetconstrEL1 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dpsetconstrEL2 ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 dpsetconstrER ) => 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 X68:$i, 75.20/10.16 X70:$i, 75.20/10.16 X72:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 func @ 75.20/10.16 X68 @ 75.20/10.16 X70 @ X72 ) => 75.20/10.16 ( 75.20/10.16 ![ 75.20/10.16 X74:$i]: 75.20/10.16 ( 75.20/10.16 ( 75.20/10.16 in @ 75.20/10.16 X74 @ X68 ) => 75.20/10.17 ( 75.20/10.17 ?[ 75.20/10.17 X76:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X70 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_12:$i]: 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 ( 75.20/10.17 kpair @ 75.20/10.17 X74 @ V_12 ) @ 75.20/10.17 X72 ) ) ) = 75.20/10.17 ( 75.20/10.17 setadjoin 75.20/10.17 @ 75.20/10.17 X76 @ 75.20/10.17 emptyset ) ) & 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X76 @ 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X70 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_13:$i]: 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 ( 75.20/10.17 kpair @ 75.20/10.17 X74 @ V_13 ) @ 75.20/10.17 X72 ) ) ) ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 apProp ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 app ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 infuncsetfunc ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ap2p ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcinfuncset ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 lamProp ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 lamp ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 lam2p ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 brelnall1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 brelnall2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ex1E2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcGraphProp1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcGraphProp3 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcGraphProp2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcextLem ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcGraphProp4 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 subbreln ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 eqbreln ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcext ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcext2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ap2apEq1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ap2apEq2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 beta1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 eta1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 lam2lamEq ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 beta2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 eta2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X78:$i, 75.20/10.17 X80:$o, 75.20/10.17 X82:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X82 @ X78 ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X84:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X84 @ X78 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ~( X80 ) ) => 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X84 @ 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X78 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_14:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_14 ) = 75.20/10.17 ( 75.20/10.17 X84 ) ) & 75.20/10.17 ( 75.20/10.17 ~( X80 ) ) ) | 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_14 ) = 75.20/10.17 ( 75.20/10.17 X82 ) ) & 75.20/10.17 ( 75.20/10.17 X80 ) ) ) ) ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X86:$i, 75.20/10.17 X88:$o, 75.20/10.17 X90:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X90 @ X86 ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X92:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X92 @ X86 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ~( X88 ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X86 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_15:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_15 ) = 75.20/10.17 ( 75.20/10.17 X92 ) ) & 75.20/10.17 ( 75.20/10.17 ~( X88 ) ) ) | 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_15 ) = 75.20/10.17 ( 75.20/10.17 X90 ) ) & 75.20/10.17 ( 75.20/10.17 X88 ) ) ) ) ) = 75.20/10.17 ( 75.20/10.17 setadjoin 75.20/10.17 @ 75.20/10.17 X92 @ 75.20/10.17 emptyset ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X94:$i, 75.20/10.17 X96:$o, 75.20/10.17 X98:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X98 @ X94 ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X100:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X100 @ X94 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 X96 ) => 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X98 @ 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X94 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_16:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_16 ) = 75.20/10.17 ( 75.20/10.17 X100 ) ) & 75.20/10.17 ( 75.20/10.17 ~( X96 ) ) ) | 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_16 ) = 75.20/10.17 ( 75.20/10.17 X98 ) ) & 75.20/10.17 ( 75.20/10.17 X96 ) ) ) ) ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X102:$i, 75.20/10.17 X104:$o, 75.20/10.17 X106:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X106 @ 75.20/10.17 X102 ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X108:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X108 @ 75.20/10.17 X102 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 X104 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X102 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_17:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_17 ) = 75.20/10.17 ( 75.20/10.17 X108 ) ) & 75.20/10.17 ( 75.20/10.17 ~( X104 ) ) ) | 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_17 ) = 75.20/10.17 ( 75.20/10.17 X106 ) ) & 75.20/10.17 ( 75.20/10.17 X104 ) ) ) ) ) = 75.20/10.17 ( 75.20/10.17 setadjoin 75.20/10.17 @ 75.20/10.17 X106 @ 75.20/10.17 emptyset ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X110:$i, 75.20/10.17 X112:$o, 75.20/10.17 X114:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X114 @ 75.20/10.17 X110 ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X116:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X116 @ 75.20/10.17 X110 ) => 75.20/10.17 ( 75.20/10.17 ?[ 75.20/10.17 X118:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X110 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_18:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ~( X112 ) ) & 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_18 ) = 75.20/10.17 ( 75.20/10.17 X116 ) ) ) | 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_18 ) = 75.20/10.17 ( 75.20/10.17 X114 ) ) & 75.20/10.17 ( 75.20/10.17 X112 ) ) ) ) ) = 75.20/10.17 ( 75.20/10.17 setadjoin 75.20/10.17 @ 75.20/10.17 X118 @ 75.20/10.17 emptyset ) ) & 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X118 @ 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X110 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_19:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ~( X112 ) ) & 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_19 ) = 75.20/10.17 ( 75.20/10.17 X116 ) ) ) | 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_19 ) = 75.20/10.17 ( 75.20/10.17 X114 ) ) & 75.20/10.17 ( 75.20/10.17 X112 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 75.20/10.17 thf(zf_stmt_1, negated_conjecture, 75.20/10.17 (~( ( setextAx ) => 75.20/10.17 ( ( emptysetAx ) => 75.20/10.17 ( ( setadjoinAx ) => 75.20/10.17 ( ( powersetAx ) => 75.20/10.17 ( ( setunionAx ) => 75.20/10.17 ( ( omega0Ax ) => 75.20/10.17 ( ( omegaSAx ) => 75.20/10.17 ( ( omegaIndAx ) => 75.20/10.17 ( ( replAx ) => 75.20/10.17 ( ( foundationAx ) => 75.20/10.17 ( ( wellorderingAx ) => 75.20/10.17 ( ( descrp ) => 75.20/10.17 ( ( ![X4:$i,X6:( $i > $o ),X8:$i]: 75.20/10.17 ( ( in @ X8 @ X4 ) => 75.20/10.17 ( ( X6 @ X8 ) => 75.20/10.17 ( in @ 75.20/10.17 X8 @ 75.20/10.17 ( dsetconstr @ 75.20/10.17 X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) ) => 75.20/10.17 ( ( ![X10:$i,X12:( $i > $o ),X14:$i]: 75.20/10.17 ( ( in @ 75.20/10.17 X14 @ 75.20/10.17 ( dsetconstr @ 75.20/10.17 X10 @ ( ^[V_2:$i]: ( X12 @ V_2 ) ) ) ) => 75.20/10.17 ( in @ X14 @ X10 ) ) ) => 75.20/10.17 ( ( ![X16:$i,X18:( $i > $o ),X20:$i]: 75.20/10.17 ( ( in @ 75.20/10.17 X20 @ 75.20/10.17 ( dsetconstr @ 75.20/10.17 X16 @ ( ^[V_3:$i]: ( X18 @ V_3 ) ) ) ) => 75.20/10.17 ( X18 @ X20 ) ) ) => 75.20/10.17 ( ( exuE1 ) => 75.20/10.17 ( ( prop2setE ) => 75.20/10.17 ( ( emptysetE ) => 75.20/10.17 ( ( emptysetimpfalse ) => 75.20/10.17 ( ( notinemptyset ) => 75.20/10.17 ( ( exuE3e ) => 75.20/10.17 ( ( setext ) => 75.20/10.17 ( ( emptyI ) => 75.20/10.17 ( ( noeltsimpempty ) => 75.20/10.17 ( ( ![X22:$i, 75.20/10.17 X24:( $i > $o ), 75.20/10.17 X26:$i]: 75.20/10.17 ( ( in @ X26 @ X22 ) => 75.20/10.17 ( ( in @ 75.20/10.17 X26 @ 75.20/10.17 ( dsetconstr @ 75.20/10.17 X22 @ 75.20/10.17 ( ^[V_4:$i]: 75.20/10.17 ( X24 @ V_4 ) ) ) ) <=> 75.20/10.17 ( X24 @ X26 ) ) ) ) => 75.20/10.17 ( ( nonemptyE1 ) => 75.20/10.17 ( ( nonemptyI ) => 75.20/10.17 ( ( nonemptyI1 ) => 75.20/10.17 ( ( setadjoinIL ) => 75.20/10.17 ( ( emptyinunitempty ) => 75.20/10.17 ( ( setadjoinIR ) => 75.20/10.17 ( ( 75.20/10.17 setadjoinE ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setadjoinOr ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X28:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X28 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_5:$i]: 75.20/10.17 ( 75.20/10.17 $true ) ) ) = 75.20/10.17 ( 75.20/10.17 X28 ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 powersetI ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 emptyinPowerset ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 emptyInPowerset ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 powersetE ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setunionI ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setunionE ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 subPowSU ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 exuE2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 nonemptyImpWitness ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 uniqinunit ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 notinsingleton ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 eqinunit ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 singletonsswitch ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 upairsetE ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 upairsetIL ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 upairsetIR ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X30:$i, 75.20/10.17 X32:( 75.20/10.17 $i > $o )]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ?[ 75.20/10.17 X34:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 X32 @ X34 ) & 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X34 @ X30 ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X30 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_6:$i]: 75.20/10.17 ( 75.20/10.17 X32 @ V_6 ) ) ) != 75.20/10.17 ( 75.20/10.17 emptyset ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 vacuousDall ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 quantDeMorgan1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 quantDeMorgan2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 quantDeMorgan3 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 quantDeMorgan4 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 prop2setI ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 prop2set2propI ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 notdexE ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 notdallE ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 exuI1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 exuI3 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 exuI2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 inCongP ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in__Cong ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 exuE3u ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 exu__Cong ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 emptyset__Cong ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setadjoin__Cong ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 powerset__Cong ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setunion__Cong ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 omega__Cong ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 exuEu ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 descr__Cong ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X36:$i, 75.20/10.17 X38:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 X36 ) = 75.20/10.17 ( 75.20/10.17 X38 ) ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X40:( 75.20/10.17 $i > $o ), 75.20/10.17 X42:( 75.20/10.17 $i > $o )]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X44:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X44 @ X36 ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X46:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X46 @ X38 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 X44 ) = 75.20/10.17 ( 75.20/10.17 X46 ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 X40 @ X44 ) <=> 75.20/10.17 ( 75.20/10.17 X42 @ X46 ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X36 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_7:$i]: 75.20/10.17 ( 75.20/10.17 X40 @ V_7 ) ) ) = 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X38 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_8:$i]: 75.20/10.17 ( 75.20/10.17 X42 @ V_8 ) ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 subsetI1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 eqimpsubset2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 eqimpsubset1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 subsetI2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 emptysetsubset ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 subsetE ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 subsetE2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 notsubsetI ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 notequalI1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 notequalI2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 subsetRefl ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 subsetTrans ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setadjoinSub ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setadjoinSub2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 subset2powerset ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setextsub ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 subsetemptysetimpeq ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 powersetI1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 powersetE1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 inPowerset ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 powersetsubset ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 sepInPowerset ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X48:$i, 75.20/10.17 X50:( 75.20/10.17 $i > $o )]: 75.20/10.17 ( 75.20/10.17 subset @ 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X48 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_9:$i]: 75.20/10.17 ( 75.20/10.17 X50 @ V_9 ) ) ) @ 75.20/10.17 X48 ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binunionIL ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 upairset2IR ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binunionIR ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binunionEcases ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binunionE ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binunionLsub ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binunionRsub ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binintersectI ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binintersectSubset5 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binintersectEL ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binintersectLsub ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binintersectSubset2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binintersectSubset3 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binintersectER ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 disjointsetsI1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binintersectRsub ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binintersectSubset4 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 binintersectSubset1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 bs114d ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setminusI ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setminusEL ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setminusER ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setminusSubset2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setminusERneg ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setminusELneg ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setminusILneg ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setminusIRneg ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setminusLsub ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setminusSubset1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 symdiffE ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 symdiffI1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 symdiffI2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 symdiffIneg1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 symdiffIneg2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 secondinupair ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setukpairIL ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setukpairIR ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 kpairiskpair ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 kpairp ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 singletonsubset ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 singletoninpowerset ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 singletoninpowunion ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 upairset2E ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 upairsubunion ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 upairinpowunion ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ubforcartprodlem1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ubforcartprodlem2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ubforcartprodlem3 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 cartprodpairin ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 cartprodmempair1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 cartprodmempair ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setunionE2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setunionsingleton1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setunionsingleton2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setunionsingleton ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X52:$i, 75.20/10.17 X54:( 75.20/10.17 $i > $o )]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X56:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X56 @ X52 ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X58:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X58 @ X52 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 X54 @ X56 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 X54 @ X58 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 X56 ) = 75.20/10.17 ( 75.20/10.17 X58 ) ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ?[ 75.20/10.17 X60:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 X54 @ X60 ) & 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X60 @ X52 ) ) ) => 75.20/10.17 ( 75.20/10.17 ?[ 75.20/10.17 X62:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X52 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_10:$i]: 75.20/10.17 ( 75.20/10.17 X54 @ 75.20/10.17 V_10 ) ) ) = 75.20/10.17 ( 75.20/10.17 setadjoin 75.20/10.17 @ 75.20/10.17 X62 @ 75.20/10.17 emptyset ) ) & 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X62 @ 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X52 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_11:$i]: 75.20/10.17 ( 75.20/10.17 X54 @ 75.20/10.17 V_11 ) ) ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ex1E1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ex1I ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ex1I2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 singletonsuniq ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setukpairinjL1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 kfstsingleton ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X64:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ?[ 75.20/10.17 X66:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 X64 ) = 75.20/10.17 ( 75.20/10.17 setadjoin 75.20/10.17 @ 75.20/10.17 X66 @ 75.20/10.17 emptyset ) ) & 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X66 @ X64 ) ) ) => 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 ( 75.20/10.17 setunion 75.20/10.17 @ 75.20/10.17 X64 ) @ 75.20/10.17 X64 ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 kfstpairEq ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 cartprodfstin ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setukpairinjL2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setukpairinjL ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setukpairinjR11 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setukpairinjR12 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setukpairinjR1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 upairequniteq ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setukpairinjR2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setukpairinjR ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ksndsingleton ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ksndpairEq ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 kpairsurjEq ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 cartprodsndin ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 cartprodpairmemEL ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 cartprodpairmemER ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 cartprodmempaircEq ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 cartprodfstpairEq ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 cartprodsndpairEq ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 cartprodpairsurjEq ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dpsetconstrI ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dpsetconstrSub ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 setOfPairsIsBReln ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dpsetconstrERa ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dpsetconstrEL1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dpsetconstrEL2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dpsetconstrER ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X68:$i, 75.20/10.17 X70:$i, 75.20/10.17 X72:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 func @ 75.20/10.17 X68 @ 75.20/10.17 X70 @ X72 ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X74:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X74 @ X68 ) => 75.20/10.17 ( 75.20/10.17 ?[ 75.20/10.17 X76:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X70 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_12:$i]: 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 ( 75.20/10.17 kpair @ 75.20/10.17 X74 @ 75.20/10.17 V_12 ) @ 75.20/10.17 X72 ) ) ) = 75.20/10.17 ( 75.20/10.17 setadjoin 75.20/10.17 @ 75.20/10.17 X76 @ 75.20/10.17 emptyset ) ) & 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X76 @ 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X70 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_13:$i]: 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 ( 75.20/10.17 kpair @ 75.20/10.17 X74 @ 75.20/10.17 V_13 ) @ 75.20/10.17 X72 ) ) ) ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 apProp ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 app ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 infuncsetfunc ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ap2p ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcinfuncset ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 lamProp ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 lamp ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 lam2p ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 brelnall1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 brelnall2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ex1E2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcGraphProp1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcGraphProp3 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcGraphProp2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcextLem ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcGraphProp4 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 subbreln ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 eqbreln ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcext ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 funcext2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ap2apEq1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ap2apEq2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 beta1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 eta1 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 lam2lamEq ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 beta2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 eta2 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X78:$i, 75.20/10.17 X80:$o, 75.20/10.17 X82:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X82 @ X78 ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X84:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X84 @ X78 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ~( X80 ) ) => 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X84 @ 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X78 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_14:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_14 ) = 75.20/10.17 ( 75.20/10.17 X84 ) ) & 75.20/10.17 ( 75.20/10.17 ~( X80 ) ) ) | 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_14 ) = 75.20/10.17 ( 75.20/10.17 X82 ) ) & 75.20/10.17 ( 75.20/10.17 X80 ) ) ) ) ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X86:$i, 75.20/10.17 X88:$o, 75.20/10.17 X90:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X90 @ X86 ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X92:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X92 @ X86 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ~( X88 ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X86 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_15:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_15 ) = 75.20/10.17 ( 75.20/10.17 X92 ) ) & 75.20/10.17 ( 75.20/10.17 ~( X88 ) ) ) | 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_15 ) = 75.20/10.17 ( 75.20/10.17 X90 ) ) & 75.20/10.17 ( 75.20/10.17 X88 ) ) ) ) ) = 75.20/10.17 ( 75.20/10.17 setadjoin 75.20/10.17 @ 75.20/10.17 X92 @ 75.20/10.17 emptyset ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X94:$i, 75.20/10.17 X96:$o, 75.20/10.17 X98:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X98 @ X94 ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X100:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X100 @ 75.20/10.17 X94 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 X96 ) => 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X98 @ 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X94 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_16:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_16 ) = 75.20/10.17 ( 75.20/10.17 X100 ) ) & 75.20/10.17 ( 75.20/10.17 ~( X96 ) ) ) | 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_16 ) = 75.20/10.17 ( 75.20/10.17 X98 ) ) & 75.20/10.17 ( 75.20/10.17 X96 ) ) ) ) ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X102:$i, 75.20/10.17 X104:$o, 75.20/10.17 X106:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X106 @ 75.20/10.17 X102 ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X108:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X108 @ 75.20/10.17 X102 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 X104 ) => 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X102 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_17:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_17 ) = 75.20/10.17 ( 75.20/10.17 X108 ) ) & 75.20/10.17 ( 75.20/10.17 ~( X104 ) ) ) | 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_17 ) = 75.20/10.17 ( 75.20/10.17 X106 ) ) & 75.20/10.17 ( 75.20/10.17 X104 ) ) ) ) ) = 75.20/10.17 ( 75.20/10.17 setadjoin 75.20/10.17 @ 75.20/10.17 X106 @ 75.20/10.17 emptyset ) ) ) ) ) ) ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X110:$i, 75.20/10.17 X112:$o, 75.20/10.17 X114:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X114 @ 75.20/10.17 X110 ) => 75.20/10.17 ( 75.20/10.17 ![ 75.20/10.17 X116:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X116 @ 75.20/10.17 X110 ) => 75.20/10.17 ( 75.20/10.17 ?[ 75.20/10.17 X118:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X110 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_18:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ~( X112 ) ) & 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_18 ) = 75.20/10.17 ( 75.20/10.17 X116 ) ) ) | 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_18 ) = 75.20/10.17 ( 75.20/10.17 X114 ) ) & 75.20/10.17 ( 75.20/10.17 X112 ) ) ) ) ) = 75.20/10.17 ( 75.20/10.17 setadjoin 75.20/10.17 @ 75.20/10.17 X118 @ 75.20/10.17 emptyset ) ) & 75.20/10.17 ( 75.20/10.17 in @ 75.20/10.17 X118 @ 75.20/10.17 ( 75.20/10.17 dsetconstr 75.20/10.17 @ 75.20/10.17 X110 @ 75.20/10.17 ( 75.20/10.17 ^[ 75.20/10.17 V_19:$i]: 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ~( X112 ) ) & 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_19 ) = 75.20/10.17 ( 75.20/10.17 X116 ) ) ) | 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 ( 75.20/10.17 V_19 ) = 75.20/10.17 ( 75.20/10.17 X114 ) ) & 75.20/10.17 ( 75.20/10.17 X112 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 75.20/10.17 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 75.20/10.17 thf(zip_derived_cl7764, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | (in @ (sk__51 @ X41 @ X40) @ (dsetconstr @ X40 @ X41)) 75.20/10.17 | ((sk__52 @ X41 @ X40) != (sk__53 @ X41 @ X40)))), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl116, plain, ( (in @ sk__57 @ sk__54)), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl118, plain, ( (in @ sk__56 @ sk__54)), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl7759, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | ((dsetconstr @ X40 @ X41) 75.20/10.17 = (setadjoin @ (sk__51 @ X41 @ X40) @ emptyset)) 75.20/10.17 | ((sk__52 @ X41 @ X40) != (sk__53 @ X41 @ X40)))), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl116, plain, ( (in @ sk__57 @ sk__54)), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl155, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | ((dsetconstr @ X40 @ (^[Y0 : $i]: (X41 @ Y0))) 75.20/10.17 = (setadjoin @ (sk__51 @ X41 @ X40) @ emptyset)) 75.20/10.17 | (X41 @ (sk__52 @ X41 @ X40)))), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl3628, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | ((dsetconstr @ X40 @ X41) 75.20/10.17 = (setadjoin @ (sk__51 @ X41 @ X40) @ emptyset)) 75.20/10.17 | (X41 @ (sk__52 @ X41 @ X40)))), 75.20/10.17 inference('ho_norm', [status(thm)], [zip_derived_cl155])). 75.20/10.17 thf(zip_derived_cl3631, plain, 75.20/10.17 (![X0 : $i > $o]: 75.20/10.17 ( (X0 @ (sk__52 @ X0 @ sk__54)) 75.20/10.17 | ((dsetconstr @ sk__54 @ X0) 75.20/10.17 = (setadjoin @ (sk__51 @ X0 @ sk__54) @ emptyset)) 75.20/10.17 | ~ (X0 @ sk__57))), 75.20/10.17 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl3628])). 75.20/10.17 thf(zip_derived_cl116, plain, ( (in @ sk__57 @ sk__54)), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl153, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | ((dsetconstr @ X40 @ (^[Y0 : $i]: (X41 @ Y0))) 75.20/10.17 = (setadjoin @ (sk__51 @ X41 @ X40) @ emptyset)) 75.20/10.17 | (X41 @ (sk__53 @ X41 @ X40)))), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl3477, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | ((dsetconstr @ X40 @ X41) 75.20/10.17 = (setadjoin @ (sk__51 @ X41 @ X40) @ emptyset)) 75.20/10.17 | (X41 @ (sk__53 @ X41 @ X40)))), 75.20/10.17 inference('ho_norm', [status(thm)], [zip_derived_cl153])). 75.20/10.17 thf(zip_derived_cl3480, plain, 75.20/10.17 (![X0 : $i > $o]: 75.20/10.17 ( (X0 @ (sk__53 @ X0 @ sk__54)) 75.20/10.17 | ((dsetconstr @ sk__54 @ X0) 75.20/10.17 = (setadjoin @ (sk__51 @ X0 @ sk__54) @ emptyset)) 75.20/10.17 | ~ (X0 @ sk__57))), 75.20/10.17 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl3477])). 75.20/10.17 thf(zip_derived_cl118, plain, ( (in @ sk__56 @ sk__54)), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl3628, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | ((dsetconstr @ X40 @ X41) 75.20/10.17 = (setadjoin @ (sk__51 @ X41 @ X40) @ emptyset)) 75.20/10.17 | (X41 @ (sk__52 @ X41 @ X40)))), 75.20/10.17 inference('ho_norm', [status(thm)], [zip_derived_cl155])). 75.20/10.17 thf(zip_derived_cl3633, plain, 75.20/10.17 (![X0 : $i > $o]: 75.20/10.17 ( (X0 @ (sk__52 @ X0 @ sk__54)) 75.20/10.17 | ((dsetconstr @ sk__54 @ X0) 75.20/10.17 = (setadjoin @ (sk__51 @ X0 @ sk__54) @ emptyset)) 75.20/10.17 | ~ (X0 @ sk__56))), 75.20/10.17 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl3628])). 75.20/10.17 thf(zip_derived_cl118, plain, ( (in @ sk__56 @ sk__54)), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl3477, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | ((dsetconstr @ X40 @ X41) 75.20/10.17 = (setadjoin @ (sk__51 @ X41 @ X40) @ emptyset)) 75.20/10.17 | (X41 @ (sk__53 @ X41 @ X40)))), 75.20/10.17 inference('ho_norm', [status(thm)], [zip_derived_cl153])). 75.20/10.17 thf(zip_derived_cl3482, plain, 75.20/10.17 (![X0 : $i > $o]: 75.20/10.17 ( (X0 @ (sk__53 @ X0 @ sk__54)) 75.20/10.17 | ((dsetconstr @ sk__54 @ X0) 75.20/10.17 = (setadjoin @ (sk__51 @ X0 @ sk__54) @ emptyset)) 75.20/10.17 | ~ (X0 @ sk__56))), 75.20/10.17 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl3477])). 75.20/10.17 thf(zip_derived_cl116, plain, ( (in @ sk__57 @ sk__54)), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl160, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | (in @ (sk__51 @ X41 @ X40) @ 75.20/10.17 (dsetconstr @ X40 @ (^[Y0 : $i]: (X41 @ Y0)))) 75.20/10.17 | (X41 @ (sk__52 @ X41 @ X40)))), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl4225, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | (in @ (sk__51 @ X41 @ X40) @ (dsetconstr @ X40 @ X41)) 75.20/10.17 | (X41 @ (sk__52 @ X41 @ X40)))), 75.20/10.17 inference('ho_norm', [status(thm)], [zip_derived_cl160])). 75.20/10.17 thf(zip_derived_cl4230, plain, 75.20/10.17 (![X0 : $i > $o]: 75.20/10.17 ( (X0 @ (sk__52 @ X0 @ sk__54)) 75.20/10.17 | (in @ (sk__51 @ X0 @ sk__54) @ (dsetconstr @ sk__54 @ X0)) 75.20/10.17 | ~ (X0 @ sk__57))), 75.20/10.17 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl4225])). 75.20/10.17 thf(zip_derived_cl116, plain, ( (in @ sk__57 @ sk__54)), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl158, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | (in @ (sk__51 @ X41 @ X40) @ 75.20/10.17 (dsetconstr @ X40 @ (^[Y0 : $i]: (X41 @ Y0)))) 75.20/10.17 | (X41 @ (sk__53 @ X41 @ X40)))), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl4161, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | (in @ (sk__51 @ X41 @ X40) @ (dsetconstr @ X40 @ X41)) 75.20/10.17 | (X41 @ (sk__53 @ X41 @ X40)))), 75.20/10.17 inference('ho_norm', [status(thm)], [zip_derived_cl158])). 75.20/10.17 thf(zip_derived_cl4166, plain, 75.20/10.17 (![X0 : $i > $o]: 75.20/10.17 ( (X0 @ (sk__53 @ X0 @ sk__54)) 75.20/10.17 | (in @ (sk__51 @ X0 @ sk__54) @ (dsetconstr @ sk__54 @ X0)) 75.20/10.17 | ~ (X0 @ sk__57))), 75.20/10.17 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl4161])). 75.20/10.17 thf(zip_derived_cl118, plain, ( (in @ sk__56 @ sk__54)), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl4225, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | (in @ (sk__51 @ X41 @ X40) @ (dsetconstr @ X40 @ X41)) 75.20/10.17 | (X41 @ (sk__52 @ X41 @ X40)))), 75.20/10.17 inference('ho_norm', [status(thm)], [zip_derived_cl160])). 75.20/10.17 thf(zip_derived_cl4232, plain, 75.20/10.17 (![X0 : $i > $o]: 75.20/10.17 ( (X0 @ (sk__52 @ X0 @ sk__54)) 75.20/10.17 | (in @ (sk__51 @ X0 @ sk__54) @ (dsetconstr @ sk__54 @ X0)) 75.20/10.17 | ~ (X0 @ sk__56))), 75.20/10.17 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl4225])). 75.20/10.17 thf(zip_derived_cl117, plain, 75.20/10.17 (![X30 : $i]: 75.20/10.17 (((dsetconstr @ sk__54 @ 75.20/10.17 (^[Y0 : $i]: 75.20/10.17 (((((((~) @ sk__55)) & (((Y0) = (sk__57))))) | 75.20/10.17 (((((Y0) = (sk__56))) & (sk__55))))))) 75.20/10.17 != (setadjoin @ X30 @ emptyset)) 75.20/10.17 | ~ (in @ X30 @ 75.20/10.17 (dsetconstr @ sk__54 @ 75.20/10.17 (^[Y0 : $i]: 75.20/10.17 (((((((~) @ sk__55)) & (((Y0) = (sk__57))))) | 75.20/10.17 (((((Y0) = (sk__56))) & (sk__55)))))))))), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl7753, plain, 75.20/10.17 (![X31 : $i]: 75.20/10.17 (('#l_lift8548' @ X31) 75.20/10.17 = (((((((~) @ sk__55)) & (((X31) = (sk__57))))) | 75.20/10.17 (((((X31) = (sk__56))) & (sk__55))))))), 75.20/10.17 define([status(thm)])). 75.20/10.17 thf(zip_derived_cl118, plain, ( (in @ sk__56 @ sk__54)), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl4161, plain, 75.20/10.17 (![X39 : $i, X40 : $i, X41 : $i > $o]: 75.20/10.17 (~ (in @ X39 @ X40) 75.20/10.17 | ~ (X41 @ X39) 75.20/10.17 | (in @ (sk__51 @ X41 @ X40) @ (dsetconstr @ X40 @ X41)) 75.20/10.17 | (X41 @ (sk__53 @ X41 @ X40)))), 75.20/10.17 inference('ho_norm', [status(thm)], [zip_derived_cl158])). 75.20/10.17 thf(zip_derived_cl4168, plain, 75.20/10.17 (![X0 : $i > $o]: 75.20/10.17 ( (X0 @ (sk__53 @ X0 @ sk__54)) 75.20/10.17 | (in @ (sk__51 @ X0 @ sk__54) @ (dsetconstr @ sk__54 @ X0)) 75.20/10.17 | ~ (X0 @ sk__56))), 75.20/10.17 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl4161])). 75.20/10.17 thf(zip_derived_cl117, plain, 75.20/10.17 (![X30 : $i]: 75.20/10.17 (((dsetconstr @ sk__54 @ 75.20/10.17 (^[Y0 : $i]: 75.20/10.17 (((((((~) @ sk__55)) & (((Y0) = (sk__57))))) | 75.20/10.17 (((((Y0) = (sk__56))) & (sk__55))))))) 75.20/10.17 != (setadjoin @ X30 @ emptyset)) 75.20/10.17 | ~ (in @ X30 @ 75.20/10.17 (dsetconstr @ sk__54 @ 75.20/10.17 (^[Y0 : $i]: 75.20/10.17 (((((((~) @ sk__55)) & (((Y0) = (sk__57))))) | 75.20/10.17 (((((Y0) = (sk__56))) & (sk__55)))))))))), 75.20/10.17 inference('cnf', [status(esa)], [zf_stmt_1])). 75.20/10.17 thf(zip_derived_cl7753, plain, 75.20/10.17 (![X31 : $i]: 75.20/10.17 (('#l_lift8548' @ X31) 75.20/10.17 = (((((((~) @ sk__55)) & (((X31) = (sk__57))))) | 75.20/10.17 (((((X31) = (sk__56))) & (sk__55))))))), 75.20/10.17 define([status(thm)])). 75.20/10.17 thf(zip_derived_cl7753, plain, 75.20/10.17 (![X31 : $i]: 75.20/10.17 (('#l_lift8548' @ X31) 75.20/10.17 = (((((((~) @ sk__55)) & (((X31) = (sk__57))))) | 75.20/10.17 (((((X31) = (sk__56))) & (sk__55))))))), 75.20/10.17 define([status(thm)])). 75.20/10.17 thf(zip_derived_cl7754, plain, 75.20/10.17 (![X30 : $i]: 75.20/10.17 (((dsetconstr @ sk__54 @ '#l_lift8548') 75.20/10.17 != (setadjoin @ X30 @ emptyset)) 75.20/10.17 | ~ (in @ X30 @ (dsetconstr @ sk__54 @ '#l_lift8548')))), 75.20/10.17 inference('lambda_lifting', [status(thm)], 75.20/10.17 [zip_derived_cl117, zip_derived_cl7753, zip_derived_cl7753])). 75.20/10.17 thf(zip_derived_cl7780, plain, ($false), 75.20/10.17 inference('eprover', [status(thm)], 75.20/10.17 [zip_derived_cl7764, zip_derived_cl116, zip_derived_cl118, 75.20/10.17 zip_derived_cl7759, zip_derived_cl3631, zip_derived_cl3480, 75.20/10.17 zip_derived_cl3633, zip_derived_cl3482, zip_derived_cl4230, 75.20/10.17 zip_derived_cl4166, zip_derived_cl4232, zip_derived_cl7753, 75.20/10.17 zip_derived_cl4168, zip_derived_cl7754])). 75.20/10.17 75.20/10.17 % SZS output end Refutation 75.20/10.17 75.20/10.17 75.20/10.17 % Terminating... 75.20/10.27 % Runner terminated. 75.20/10.28 % Zipperpin 1.5 exiting 75.20/10.29 EOF