0.11/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.hYjbwzjgdN true 0.14/0.35 % Computer : n009.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1200 0.14/0.35 % WCLimit : 120 0.14/0.35 % DateTime : Tue Jul 13 12:20:13 EDT 2021 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 120 s 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.35 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.51/0.63 % Total configuration time : 828 0.51/0.63 % Estimated wc time : 983 0.51/0.63 % Estimated cpu time (8 cpus) : 122.875 0.53/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.53/0.75 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.53/0.75 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 39.97/5.67 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 53s 39.97/5.67 % Solved by lams/40_c_ic.sh. 39.97/5.67 % running E: timeout 27 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.hYjbwzjgdN/e_inputcdaf95 --cpu-limit=25 --auto-schedule -s -p 39.97/5.67 % done 508 iterations in 4.822s 39.97/5.67 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 39.97/5.67 % SZS output start Refutation 39.97/5.67 thf(binintersectER_type, type, binintersectER: $o). 39.97/5.67 thf(setadjoinSub_type, type, setadjoinSub: $o). 39.97/5.67 thf(ex1_type, type, ex1: $i > ($i > $o) > $o). 39.97/5.67 thf(setukpairinjR2_type, type, setukpairinjR2: $o). 39.97/5.67 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 39.97/5.67 thf(setunion_type, type, setunion: $i > $i). 39.97/5.67 thf(vacuousDall_type, type, vacuousDall: $o). 39.97/5.67 thf(setadjoinIR_type, type, setadjoinIR: $o). 39.97/5.67 thf(omega0Ax_type, type, omega0Ax: $o). 39.97/5.67 thf(subsetE_type, type, subsetE: $o). 39.97/5.67 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 39.97/5.67 thf(setminusER_type, type, setminusER: $o). 39.97/5.67 thf(sk__43_type, type, sk__43: $i). 39.97/5.67 thf(binunionE_type, type, binunionE: $o). 39.97/5.67 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 39.97/5.67 thf(powersetE_type, type, powersetE: $o). 39.97/5.67 thf(binunionRsub_type, type, binunionRsub: $o). 39.97/5.67 thf(infuncsetfunc_type, type, infuncsetfunc: $o). 39.97/5.67 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 39.97/5.67 thf(powerset__Cong_type, type, powerset__Cong: $o). 39.97/5.67 thf(ksndsingleton_type, type, ksndsingleton: $o). 39.97/5.67 thf(funcGraphProp1_type, type, funcGraphProp1: $o). 39.97/5.67 thf(omegaIndAx_type, type, omegaIndAx: $o). 39.97/5.67 thf(uniqinunit_type, type, uniqinunit: $o). 39.97/5.67 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 39.97/5.67 thf(exu__Cong_type, type, exu__Cong: $o). 39.97/5.67 thf(subset2powerset_type, type, subset2powerset: $o). 39.97/5.67 thf(setoftrueEq_type, type, setoftrueEq: $o). 39.97/5.67 thf(setukpairinjR12_type, type, setukpairinjR12: $o). 39.97/5.67 thf(upairsetIL_type, type, upairsetIL: $o). 39.97/5.67 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 39.97/5.67 thf(sk__40_type, type, sk__40: $i). 39.97/5.67 thf(emptyI_type, type, emptyI: $o). 39.97/5.67 thf(setukpairIL_type, type, setukpairIL: $o). 39.97/5.67 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 39.97/5.67 thf(func_type, type, func: $i > $i > $i > $o). 39.97/5.67 thf(exuI3_type, type, exuI3: $o). 39.97/5.67 thf(emptysetAx_type, type, emptysetAx: $o). 39.97/5.67 thf(setukpairIR_type, type, setukpairIR: $o). 39.97/5.67 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 39.97/5.67 thf(lam2p_type, type, lam2p: $o). 39.97/5.67 thf(setadjoinIL_type, type, setadjoinIL: $o). 39.97/5.67 thf(upairsubunion_type, type, upairsubunion: $o). 39.97/5.67 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o). 39.97/5.67 thf(ksndpairEq_type, type, ksndpairEq: $o). 39.97/5.67 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 39.97/5.67 thf(upairsetIR_type, type, upairsetIR: $o). 39.97/5.67 thf('#l_lift1180_type', type, '#l_lift1180': $i > $i > $i > $i > $o). 39.97/5.67 thf(ex1I2_type, type, ex1I2: $o). 39.97/5.67 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 39.97/5.67 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 39.97/5.67 thf(sk__41_type, type, sk__41: $i). 39.97/5.67 thf(funcGraphProp2_type, type, funcGraphProp2: $o). 39.97/5.67 thf(ex1I_type, type, ex1I: $o). 39.97/5.67 thf(sk__38_type, type, sk__38: $i > $i > $i > $i). 39.97/5.67 thf(cartprodsndin_type, type, cartprodsndin: $o). 39.97/5.67 thf(setminusI_type, type, setminusI: $o). 39.97/5.67 thf(descrp_type, type, descrp: $o). 39.97/5.67 thf(binintersectI_type, type, binintersectI: $o). 39.97/5.67 thf(nonemptyI1_type, type, nonemptyI1: $o). 39.97/5.67 thf(emptysetsubset_type, type, emptysetsubset: $o). 39.97/5.67 thf(setunionAx_type, type, setunionAx: $o). 39.97/5.67 thf(notsubsetI_type, type, notsubsetI: $o). 39.97/5.67 thf(theprop_type, type, theprop: $o). 39.97/5.67 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 39.97/5.67 thf(upairset2IR_type, type, upairset2IR: $o). 39.97/5.67 thf(binunionLsub_type, type, binunionLsub: $o). 39.97/5.67 thf(subsetRefl_type, type, subsetRefl: $o). 39.97/5.67 thf(nonemptyI_type, type, nonemptyI: $o). 39.97/5.67 thf(emptysetE_type, type, emptysetE: $o). 39.97/5.67 thf(sepInPowerset_type, type, sepInPowerset: $o). 39.97/5.67 thf(lamProp_type, type, lamProp: $o). 39.97/5.67 thf(upairequniteq_type, type, upairequniteq: $o). 39.97/5.67 thf(kpairsurjEq_type, type, kpairsurjEq: $o). 39.97/5.67 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 39.97/5.67 thf(singletonprop_type, type, singletonprop: $o). 39.97/5.67 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 39.97/5.67 thf('#l_lift1185_type', type, '#l_lift1185': $i > $i > $i > $o). 39.97/5.67 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o). 39.97/5.67 thf(powersetI_type, type, powersetI: $o). 39.97/5.67 thf(exuE2_type, type, exuE2: $o). 39.97/5.67 thf(setukpairinjL_type, type, setukpairinjL: $o). 39.97/5.67 thf(exuE3e_type, type, exuE3e: $o). 39.97/5.67 thf(setminusSubset1_type, type, setminusSubset1: $o). 39.97/5.67 thf(sk__44_type, type, sk__44: $i). 39.97/5.67 thf(notequalI2_type, type, notequalI2: $o). 39.97/5.67 thf(descr__Cong_type, type, descr__Cong: $o). 39.97/5.67 thf(setextAx_type, type, setextAx: $o). 39.97/5.67 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 39.97/5.67 thf(eqinunit_type, type, eqinunit: $o). 39.97/5.67 thf(symdiffE_type, type, symdiffE: $o). 39.97/5.67 thf('#l_lift1181_type', type, '#l_lift1181': $i > $i > $i > $i > $o). 39.97/5.67 thf(upairinpowunion_type, type, upairinpowunion: $o). 39.97/5.67 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 39.97/5.67 thf(powersetAx_type, type, powersetAx: $o). 39.97/5.67 thf(upairset2E_type, type, upairset2E: $o). 39.97/5.67 thf(subsetI2_type, type, subsetI2: $o). 39.97/5.67 thf(symdiffI1_type, type, symdiffI1: $o). 39.97/5.67 thf(kpair_type, type, kpair: $i > $i > $i). 39.97/5.67 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 39.97/5.67 thf(subsetI1_type, type, subsetI1: $o). 39.97/5.67 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 39.97/5.67 thf(breln_type, type, breln: $i > $i > $i > $o). 39.97/5.67 thf(replAx_type, type, replAx: $o). 39.97/5.67 thf(subPowSU_type, type, subPowSU: $o). 39.97/5.67 thf(setunionE_type, type, setunionE: $o). 39.97/5.67 thf(setunionsingleton_type, type, setunionsingleton: $o). 39.97/5.67 thf(setunion__Cong_type, type, setunion__Cong: $o). 39.97/5.67 thf(sk__45_type, type, sk__45: $i > $i > $i > $i). 39.97/5.67 thf(bs114d_type, type, bs114d: $o). 39.97/5.67 thf(setminusSubset2_type, type, setminusSubset2: $o). 39.97/5.67 thf(powersetE1_type, type, powersetE1: $o). 39.97/5.67 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 39.97/5.67 thf(dpsetconstrI_type, type, dpsetconstrI: $o). 39.97/5.67 thf(omegaSAx_type, type, omegaSAx: $o). 39.97/5.67 thf('#l_lift1183_type', type, '#l_lift1183': $i > $i > $o). 39.97/5.67 thf(setext_type, type, setext: $o). 39.97/5.67 thf(cartprodfstin_type, type, cartprodfstin: $o). 39.97/5.67 thf(notequalI1_type, type, notequalI1: $o). 39.97/5.67 thf(setextsub_type, type, setextsub: $o). 39.97/5.67 thf(kpairp_type, type, kpairp: $o). 39.97/5.67 thf(ap_type, type, ap: $i > $i > $i > $i > $i). 39.97/5.67 thf(omega__Cong_type, type, omega__Cong: $o). 39.97/5.67 thf(symdiffI2_type, type, symdiffI2: $o). 39.97/5.67 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o). 39.97/5.67 thf(brelnall2_type, type, brelnall2: $o). 39.97/5.67 thf(funcSet_type, type, funcSet: $i > $i > $i). 39.97/5.67 thf(sk__39_type, type, sk__39: $i). 39.97/5.67 thf(setbeta_type, type, setbeta: $o). 39.97/5.67 thf(dsetconstrER_type, type, dsetconstrER: $o). 39.97/5.67 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o). 39.97/5.67 thf(apProp_type, type, apProp: $o). 39.97/5.67 thf(nonemptyE1_type, type, nonemptyE1: $o). 39.97/5.67 thf(binunionIL_type, type, binunionIL: $o). 39.97/5.67 thf(prop2setE_type, type, prop2setE: $o). 39.97/5.67 thf(prop2set2propI_type, type, prop2set2propI: $o). 39.97/5.67 thf(notdallE_type, type, notdallE: $o). 39.97/5.67 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 39.97/5.67 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o). 39.97/5.67 thf(exuEu_type, type, exuEu: $o). 39.97/5.67 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o). 39.97/5.67 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 39.97/5.67 thf(notinsingleton_type, type, notinsingleton: $o). 39.97/5.67 thf(upairsetE_type, type, upairsetE: $o). 39.97/5.67 thf(emptyE1_type, type, emptyE1: $o). 39.97/5.67 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 39.97/5.67 thf(cartprodmempair_type, type, cartprodmempair: $o). 39.97/5.67 thf(binunionEcases_type, type, binunionEcases: $o). 39.97/5.67 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o). 39.97/5.67 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 39.97/5.67 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 39.97/5.67 thf(wellorderingAx_type, type, wellorderingAx: $o). 39.97/5.67 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 39.97/5.67 thf(binintersectLsub_type, type, binintersectLsub: $o). 39.97/5.67 thf(binintersectRsub_type, type, binintersectRsub: $o). 39.97/5.67 thf(powersetsubset_type, type, powersetsubset: $o). 39.97/5.67 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 39.97/5.67 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 39.97/5.67 thf(exuE1_type, type, exuE1: $o). 39.97/5.67 thf(ex1E2_type, type, ex1E2: $o). 39.97/5.67 thf(inPowerset_type, type, inPowerset: $o). 39.97/5.67 thf(brelnall1_type, type, brelnall1: $o). 39.97/5.67 thf(dpsetconstrER_type, type, dpsetconstrER: $o). 39.97/5.67 thf(in_type, type, in: $i > $i > $o). 39.97/5.67 thf(lamp_type, type, lamp: $o). 39.97/5.67 thf(cartprodpairin_type, type, cartprodpairin: $o). 39.97/5.67 thf(setunionI_type, type, setunionI: $o). 39.97/5.67 thf(in__Cong_type, type, in__Cong: $o). 39.97/5.67 thf(setadjoinE_type, type, setadjoinE: $o). 39.97/5.67 thf(subsetTrans_type, type, subsetTrans: $o). 39.97/5.67 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 39.97/5.67 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 39.97/5.67 thf(setminusIRneg_type, type, setminusIRneg: $o). 39.97/5.67 thf(setminusELneg_type, type, setminusELneg: $o). 39.97/5.67 thf(foundationAx_type, type, foundationAx: $o). 39.97/5.67 thf(sepSubset_type, type, sepSubset: $o). 39.97/5.67 thf(exuE3u_type, type, exuE3u: $o). 39.97/5.67 thf(kpairiskpair_type, type, kpairiskpair: $o). 39.97/5.67 thf(setadjoinOr_type, type, setadjoinOr: $o). 39.97/5.67 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o). 39.97/5.67 thf(exuI1_type, type, exuI1: $o). 39.97/5.67 thf(kfstsingleton_type, type, kfstsingleton: $o). 39.97/5.67 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 39.97/5.67 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 39.97/5.67 thf(binunionIR_type, type, binunionIR: $o). 39.97/5.67 thf(inCongP_type, type, inCongP: $o). 39.97/5.67 thf(setminusLsub_type, type, setminusLsub: $o). 39.97/5.67 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o). 39.97/5.67 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 39.97/5.67 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 39.97/5.67 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 39.97/5.67 thf(ap2p_type, type, ap2p: $o). 39.97/5.67 thf(app_type, type, app: $o). 39.97/5.67 thf(setukpairinjR1_type, type, setukpairinjR1: $o). 39.97/5.67 thf(setminusERneg_type, type, setminusERneg: $o). 39.97/5.67 thf(sk__42_type, type, sk__42: $i). 39.97/5.67 thf(exuI2_type, type, exuI2: $o). 39.97/5.67 thf(powersetI1_type, type, powersetI1: $o). 39.97/5.67 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o). 39.97/5.67 thf(funcGraphProp3_type, type, funcGraphProp3: $o). 39.97/5.67 thf(kfstpairEq_type, type, kfstpairEq: $o). 39.97/5.67 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 39.97/5.67 thf(setminusILneg_type, type, setminusILneg: $o). 39.97/5.67 thf(dsetconstrI_type, type, dsetconstrI: $o). 39.97/5.67 thf('#l_lift1182_type', type, '#l_lift1182': $i > $i > $o). 39.97/5.67 thf(setminusEL_type, type, setminusEL: $o). 39.97/5.67 thf(singletonsubset_type, type, singletonsubset: $o). 39.97/5.67 thf(setukpairinjR_type, type, setukpairinjR: $o). 39.97/5.67 thf(secondinupair_type, type, secondinupair: $o). 39.97/5.67 thf(ex1E1_type, type, ex1E1: $o). 39.97/5.67 thf(singletonsuniq_type, type, singletonsuniq: $o). 39.97/5.67 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 39.97/5.67 thf(funcinfuncset_type, type, funcinfuncset: $o). 39.97/5.67 thf(subsetE2_type, type, subsetE2: $o). 39.97/5.67 thf(singletonsswitch_type, type, singletonsswitch: $o). 39.97/5.67 thf(sk__46_type, type, sk__46: $i > $i > $i > $i). 39.97/5.67 thf(binintersectEL_type, type, binintersectEL: $o). 39.97/5.67 thf(setadjoinAx_type, type, setadjoinAx: $o). 39.97/5.67 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 39.97/5.67 thf(notinemptyset_type, type, notinemptyset: $o). 39.97/5.67 thf(prop2setI_type, type, prop2setI: $o). 39.97/5.67 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 39.97/5.67 thf(setunionE2_type, type, setunionE2: $o). 39.97/5.67 thf(funcImageSingleton_type, type, funcImageSingleton: $o). 39.97/5.67 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o). 39.97/5.67 thf(notdexE_type, type, notdexE: $o). 39.97/5.67 thf(funcGraphProp2, axiom, funcGraphProp2 = 39.97/5.67 (![A:$i,B:$i,Xf:$i]: 39.97/5.67 ( ( func @ A @ B @ Xf ) => 39.97/5.67 ( ![Xx:$i]: 39.97/5.67 ( ( in @ Xx @ A ) => 39.97/5.67 ( ![Xy:$i]: 39.97/5.67 ( ( in @ Xy @ B ) => 39.97/5.67 ( ( in @ ( kpair @ Xx @ Xy ) @ Xf ) => 39.97/5.67 ( ( ap @ A @ B @ Xf @ Xx ) = ( Xy ) ) ) ) ) ) ) ))). 39.97/5.67 thf('0', plain, 39.97/5.67 (( funcGraphProp2 ) = 39.97/5.67 ( ![X4:$i,X6:$i,X8:$i]: 39.97/5.67 ( ( func @ X4 @ X6 @ X8 ) => 39.97/5.67 ( ![X10:$i]: 39.97/5.67 ( ( in @ X10 @ X4 ) => 39.97/5.67 ( ![X12:$i]: 39.97/5.67 ( ( in @ X12 @ X6 ) => 39.97/5.67 ( ( in @ ( kpair @ X10 @ X12 ) @ X8 ) => 39.97/5.67 ( ( ap @ X4 @ X6 @ X8 @ X10 ) = ( X12 ) ) ) ) ) ) ) ) )), 39.97/5.67 define([status(thm)])). 39.97/5.67 thf(funcGraphProp3, axiom, funcGraphProp3 = 39.97/5.67 (![A:$i,B:$i,Xf:$i]: 39.97/5.67 ( ( in @ Xf @ ( funcSet @ A @ B ) ) => 39.97/5.67 ( ![Xx:$i]: 39.97/5.67 ( ( in @ Xx @ A ) => 39.97/5.67 ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ))). 39.97/5.67 thf('1', plain, 39.97/5.67 (( funcGraphProp3 ) = 39.97/5.67 ( ![X4:$i,X6:$i,X8:$i]: 39.97/5.67 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) => 39.97/5.67 ( ![X10:$i]: 39.97/5.67 ( ( in @ X10 @ X4 ) => 39.97/5.67 ( in @ ( kpair @ X10 @ ( ap @ X4 @ X6 @ X8 @ X10 ) ) @ X8 ) ) ) ) )), 39.97/5.67 define([status(thm)])). 39.97/5.67 thf(funcGraphProp1, axiom, funcGraphProp1 = 39.97/5.67 (![A:$i,B:$i,Xf:$i]: 39.97/5.67 ( ( func @ A @ B @ Xf ) => 39.97/5.67 ( ![Xx:$i]: 39.97/5.67 ( ( in @ Xx @ A ) => 39.97/5.67 ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ))). 39.97/5.67 thf('2', plain, 39.97/5.67 (( funcGraphProp1 ) = 39.97/5.67 ( ![X4:$i,X6:$i,X8:$i]: 39.97/5.67 ( ( func @ X4 @ X6 @ X8 ) => 39.97/5.67 ( ![X10:$i]: 39.97/5.67 ( ( in @ X10 @ X4 ) => 39.97/5.67 ( in @ ( kpair @ X10 @ ( ap @ X4 @ X6 @ X8 @ X10 ) ) @ X8 ) ) ) ) )), 39.97/5.67 define([status(thm)])). 39.97/5.67 thf(ap2p, axiom, ap2p = 39.97/5.67 (![A:$i,B:$i,Xf:$i]: 39.97/5.67 ( ( in @ Xf @ ( funcSet @ A @ B ) ) => 39.97/5.67 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ))). 39.97/5.67 thf('3', plain, 39.97/5.67 (( ap2p ) = 39.97/5.67 ( ![X4:$i,X6:$i,X8:$i]: 39.97/5.67 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) => 39.97/5.67 ( ![X10:$i]: 39.97/5.67 ( ( in @ X10 @ X4 ) => ( in @ ( ap @ X4 @ X6 @ X8 @ X10 ) @ X6 ) ) ) ) )), 39.97/5.67 define([status(thm)])). 39.97/5.67 thf(app, axiom, app = 39.97/5.67 (![A:$i,B:$i,Xf:$i]: 39.97/5.67 ( ( func @ A @ B @ Xf ) => 39.97/5.67 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ))). 39.97/5.67 thf('4', plain, 39.97/5.67 (( app ) = 39.97/5.67 ( ![X4:$i,X6:$i,X8:$i]: 39.97/5.67 ( ( func @ X4 @ X6 @ X8 ) => 39.97/5.67 ( ![X10:$i]: 39.97/5.67 ( ( in @ X10 @ X4 ) => ( in @ ( ap @ X4 @ X6 @ X8 @ X10 ) @ X6 ) ) ) ) )), 39.97/5.67 define([status(thm)])). 39.97/5.67 thf(apProp, axiom, apProp = 39.97/5.67 (![A:$i,B:$i,Xf:$i]: 39.97/5.67 ( ( func @ A @ B @ Xf ) => 39.97/5.67 ( ![Xx:$i]: 39.97/5.67 ( ( in @ Xx @ A ) => 39.97/5.67 ( in @ 39.97/5.67 ( setunion @ 39.97/5.67 ( dsetconstr @ 39.97/5.67 B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) @ 39.97/5.67 B ) ) ) ))). 39.97/5.67 thf('5', plain, 39.97/5.67 (( apProp ) = 39.97/5.67 ( ![X4:$i,X6:$i,X8:$i]: 39.97/5.67 ( ( func @ X4 @ X6 @ X8 ) => 39.97/5.67 ( ![X10:$i]: 39.97/5.67 ( ( in @ X10 @ X4 ) => 39.97/5.67 ( in @ 39.97/5.67 ( setunion @ 39.97/5.67 ( dsetconstr @ 39.97/5.67 X6 @ ( ^[V_1:$i]: ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) ) @ 39.97/5.67 X6 ) ) ) ) )), 39.97/5.67 define([status(thm)])). 39.97/5.67 thf(func, axiom,(( func ) = 39.97/5.67 (^[A:$i,B:$i,R:$i]: 39.97/5.67 ( ( breln @ A @ B @ R ) & 39.97/5.67 ( ![Xx:$i]: 39.97/5.67 ( ( in @ Xx @ A ) => 39.97/5.67 ( ex1 @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )))). 39.97/5.67 thf('6', plain, 39.97/5.67 (( func ) = 39.97/5.67 ( ^[A:$i,B:$i,R:$i]: 39.97/5.67 ( ( breln @ A @ B @ R ) & 39.97/5.67 ( ![Xx:$i]: 39.97/5.67 ( ( in @ Xx @ A ) => 39.97/5.67 ( ex1 @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) )), 39.97/5.67 inference('simplify_rw_rule', [status(thm)], [func])). 39.97/5.67 thf('7', plain, 39.97/5.67 (( func ) = 39.97/5.67 ( ^[V_1:$i,V_2:$i,V_3:$i]: 39.97/5.67 ( ( breln @ V_1 @ V_2 @ V_3 ) & 39.97/5.67 ( ![X4:$i]: 39.97/5.67 ( ( in @ X4 @ V_1 ) => 39.97/5.67 ( ex1 @ V_2 @ ( ^[V_4:$i]: ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ) )), 39.97/5.67 define([status(thm)])). 39.97/5.67 thf(cartprodmempaircEq, axiom, cartprodmempaircEq = 39.97/5.67 (![A:$i,B:$i,Xx:$i]: 39.97/5.67 ( ( in @ Xx @ A ) => 39.97/5.67 ( ![Xy:$i]: 39.97/5.67 ( ( in @ Xy @ B ) => ( ( kpair @ Xx @ Xy ) = ( kpair @ Xx @ Xy ) ) ) ) ))). 39.97/5.67 thf('8', plain, 39.97/5.67 (( cartprodmempaircEq ) = 39.97/5.67 ( ![X4:$i,X6:$i,X8:$i]: 39.97/5.67 ( ( in @ X8 @ X4 ) => 39.97/5.67 ( ![X10:$i]: 39.97/5.67 ( ( in @ X10 @ X6 ) => 39.97/5.67 ( ( kpair @ X8 @ X10 ) = ( kpair @ X8 @ X10 ) ) ) ) ) )), 39.97/5.67 define([status(thm)])). 39.97/5.67 thf(setukpairinjR, axiom, setukpairinjR = 39.97/5.67 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]: 39.97/5.67 ( ( ( kpair @ Xx @ Xy ) = ( kpair @ Xz @ Xu ) ) => ( ( Xy ) = ( Xu ) ) ))). 39.97/5.67 thf('9', plain, 39.97/5.67 (( setukpairinjR ) = 39.97/5.67 ( ![X4:$i,X6:$i,X8:$i,X10:$i]: 39.97/5.67 ( ( ( kpair @ X4 @ X6 ) = ( kpair @ X8 @ X10 ) ) => 39.97/5.67 ( ( X6 ) = ( X10 ) ) ) )), 39.97/5.67 define([status(thm)])). 39.97/5.67 thf(setukpairinjL, axiom, setukpairinjL = 39.97/5.67 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]: 39.97/5.67 ( ( ( kpair @ Xx @ Xy ) = ( kpair @ Xz @ Xu ) ) => ( ( Xx ) = ( Xz ) ) ))). 39.97/5.67 thf('10', plain, 39.97/5.67 (( setukpairinjL ) = 39.97/5.67 ( ![X4:$i,X6:$i,X8:$i,X10:$i]: 39.97/5.67 ( ( ( kpair @ X4 @ X6 ) = ( kpair @ X8 @ X10 ) ) => 39.97/5.67 ( ( X4 ) = ( X8 ) ) ) )), 39.97/5.67 define([status(thm)])). 39.97/5.67 thf(funcextLem, conjecture, 39.97/5.67 (( setextAx ) => 39.97/5.67 ( ( emptysetAx ) => 39.97/5.67 ( ( setadjoinAx ) => 39.97/5.67 ( ( powersetAx ) => 39.97/5.67 ( ( setunionAx ) => 39.97/5.67 ( ( omega0Ax ) => 39.97/5.67 ( ( omegaSAx ) => 39.97/5.67 ( ( omegaIndAx ) => 39.97/5.67 ( ( replAx ) => 39.97/5.67 ( ( foundationAx ) => 39.97/5.67 ( ( wellorderingAx ) => 39.97/5.67 ( ( descrp ) => 39.97/5.67 ( ( dsetconstrI ) => 39.97/5.67 ( ( dsetconstrEL ) => 39.97/5.67 ( ( dsetconstrER ) => 39.97/5.67 ( ( exuE1 ) => 39.97/5.67 ( ( prop2setE ) => 39.97/5.67 ( ( emptysetE ) => 39.97/5.67 ( ( emptysetimpfalse ) => 39.97/5.67 ( ( notinemptyset ) => 39.97/5.67 ( ( exuE3e ) => 39.97/5.67 ( ( setext ) => 39.97/5.67 ( ( emptyI ) => 39.97/5.67 ( ( noeltsimpempty ) => 39.97/5.67 ( ( setbeta ) => 39.97/5.67 ( ( nonemptyE1 ) => 39.97/5.67 ( ( nonemptyI ) => 39.97/5.67 ( ( nonemptyI1 ) => 39.97/5.67 ( ( setadjoinIL ) => 39.97/5.67 ( ( emptyinunitempty ) => 39.97/5.67 ( ( setadjoinIR ) => 39.97/5.67 ( ( setadjoinE ) => 39.97/5.67 ( ( 39.97/5.67 setadjoinOr ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setoftrueEq ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 powersetI ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 emptyinPowerset ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 emptyInPowerset ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 powersetE ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setunionI ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setunionE ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 subPowSU ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 exuE2 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 nonemptyImpWitness ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 uniqinunit ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 notinsingleton ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 eqinunit ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 singletonsswitch ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 upairsetE ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 upairsetIL ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 upairsetIR ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 emptyE1 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 vacuousDall ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 quantDeMorgan1 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 quantDeMorgan2 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 quantDeMorgan3 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 quantDeMorgan4 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 prop2setI ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 prop2set2propI ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 notdexE ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 notdallE ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 exuI1 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 exuI3 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 exuI2 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 inCongP ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 in__Cong ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 exuE3u ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 exu__Cong ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 emptyset__Cong ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setadjoin__Cong ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 powerset__Cong ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setunion__Cong ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 omega__Cong ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 exuEu ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 descr__Cong ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 dsetconstr__Cong ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 subsetI1 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 eqimpsubset2 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 eqimpsubset1 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 subsetI2 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 emptysetsubset ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 subsetE ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 subsetE2 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 notsubsetI ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 notequalI1 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 notequalI2 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 subsetRefl ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 subsetTrans ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setadjoinSub ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setadjoinSub2 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 subset2powerset ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setextsub ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 subsetemptysetimpeq ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 powersetI1 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 powersetE1 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 inPowerset ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 powersetsubset ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 sepInPowerset ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 sepSubset ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binunionIL ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 upairset2IR ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binunionIR ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binunionEcases ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binunionE ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binunionLsub ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binunionRsub ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binintersectI ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binintersectSubset5 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binintersectEL ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binintersectLsub ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binintersectSubset2 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binintersectSubset3 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binintersectER ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 disjointsetsI1 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binintersectRsub ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binintersectSubset4 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 binintersectSubset1 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 bs114d ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setminusI ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setminusEL ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setminusER ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setminusSubset2 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setminusERneg ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setminusELneg ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setminusILneg ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setminusIRneg ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setminusLsub ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setminusSubset1 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 symdiffE ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 symdiffI1 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 symdiffI2 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 symdiffIneg1 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 symdiffIneg2 ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 secondinupair ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setukpairIL ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 setukpairIR ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 kpairiskpair ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 kpairp ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 singletonsubset ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 singletoninpowerset ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 singletoninpowunion ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 upairset2E ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 upairsubunion ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 upairinpowunion ) => 39.97/5.67 ( 39.97/5.67 ( 39.97/5.67 ubforcartprodlem1 ) => 39.97/5.67 ( 39.97/5.68 ( 39.97/5.68 ubforcartprodlem2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ubforcartprodlem3 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodpairin ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodmempair1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodmempair ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionE2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionsingleton1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionsingleton2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionsingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletonprop ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ex1E1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ex1I ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ex1I2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletonsuniq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjL1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kfstsingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 theprop ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kfstpairEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodfstin ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjL2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjR11 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjR12 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjR1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairequniteq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjR2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjR ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ksndsingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ksndpairEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kpairsurjEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodsndin ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodpairmemEL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodpairmemER ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodmempaircEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodfstpairEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodsndpairEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodpairsurjEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrSub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setOfPairsIsBReln ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrERa ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrEL1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrEL2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrER ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 funcImageSingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 apProp ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 app ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 infuncsetfunc ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ap2p ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 funcinfuncset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 lamProp ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 lamp ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 lam2p ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 brelnall1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 brelnall2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ex1E2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 funcGraphProp1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 funcGraphProp3 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 funcGraphProp2 ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 A:$i,B:$i, 39.97/5.68 Xf:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 func @ 39.97/5.68 A @ B @ Xf ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 Xg:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 func @ 39.97/5.68 A @ B @ Xg ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 Xx:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 Xx @ A ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 A @ B @ 39.97/5.68 Xf @ Xx ) = 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 A @ B @ 39.97/5.68 Xg @ Xx ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 Xx:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 Xx @ A ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 Xy:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 Xy @ B ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 Xx @ Xy ) @ 39.97/5.68 Xg ) => 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 Xx @ Xy ) @ 39.97/5.68 Xf ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 39.97/5.68 thf(zf_stmt_0, conjecture, 39.97/5.68 (( setextAx ) => 39.97/5.68 ( ( emptysetAx ) => 39.97/5.68 ( ( setadjoinAx ) => 39.97/5.68 ( ( powersetAx ) => 39.97/5.68 ( ( setunionAx ) => 39.97/5.68 ( ( omega0Ax ) => 39.97/5.68 ( ( omegaSAx ) => 39.97/5.68 ( ( omegaIndAx ) => 39.97/5.68 ( ( replAx ) => 39.97/5.68 ( ( foundationAx ) => 39.97/5.68 ( ( wellorderingAx ) => 39.97/5.68 ( ( descrp ) => 39.97/5.68 ( ( dsetconstrI ) => 39.97/5.68 ( ( dsetconstrEL ) => 39.97/5.68 ( ( dsetconstrER ) => 39.97/5.68 ( ( exuE1 ) => 39.97/5.68 ( ( prop2setE ) => 39.97/5.68 ( ( emptysetE ) => 39.97/5.68 ( ( emptysetimpfalse ) => 39.97/5.68 ( ( notinemptyset ) => 39.97/5.68 ( ( exuE3e ) => 39.97/5.68 ( ( setext ) => 39.97/5.68 ( ( emptyI ) => 39.97/5.68 ( ( noeltsimpempty ) => 39.97/5.68 ( ( setbeta ) => 39.97/5.68 ( ( nonemptyE1 ) => 39.97/5.68 ( ( nonemptyI ) => 39.97/5.68 ( ( nonemptyI1 ) => 39.97/5.68 ( ( setadjoinIL ) => 39.97/5.68 ( ( emptyinunitempty ) => 39.97/5.68 ( ( setadjoinIR ) => 39.97/5.68 ( ( setadjoinE ) => 39.97/5.68 ( ( 39.97/5.68 setadjoinOr ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setoftrueEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 powersetI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 emptyinPowerset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 emptyInPowerset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 powersetE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subPowSU ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exuE2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 nonemptyImpWitness ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 uniqinunit ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 notinsingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 eqinunit ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletonsswitch ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairsetE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairsetIL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairsetIR ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 emptyE1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 vacuousDall ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 quantDeMorgan1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 quantDeMorgan2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 quantDeMorgan3 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 quantDeMorgan4 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 prop2setI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 prop2set2propI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 notdexE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 notdallE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exuI1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exuI3 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exuI2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 inCongP ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exuE3u ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exu__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 emptyset__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setadjoin__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 powerset__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunion__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 omega__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exuEu ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 descr__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dsetconstr__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetI1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 eqimpsubset2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 eqimpsubset1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetI2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 emptysetsubset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetE2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 notsubsetI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 notequalI1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 notequalI2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetRefl ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetTrans ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setadjoinSub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setadjoinSub2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subset2powerset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setextsub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetemptysetimpeq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 powersetI1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 powersetE1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 inPowerset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 powersetsubset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 sepInPowerset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 sepSubset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binunionIL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairset2IR ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binunionIR ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binunionEcases ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binunionE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binunionLsub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binunionRsub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectSubset5 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectEL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectLsub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectSubset2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectSubset3 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectER ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 disjointsetsI1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectRsub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectSubset4 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectSubset1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 bs114d ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusEL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusER ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusSubset2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusERneg ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusELneg ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusILneg ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusIRneg ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusLsub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusSubset1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 symdiffE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 symdiffI1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 symdiffI2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 symdiffIneg1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 symdiffIneg2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 secondinupair ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairIL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairIR ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kpairiskpair ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kpairp ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletonsubset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletoninpowerset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletoninpowunion ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairset2E ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairsubunion ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairinpowunion ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ubforcartprodlem1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ubforcartprodlem2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ubforcartprodlem3 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodpairin ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodmempair1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodmempair ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionE2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionsingleton1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionsingleton2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionsingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletonprop ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ex1E1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ex1I ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ex1I2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletonsuniq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjL1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kfstsingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 theprop ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kfstpairEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodfstin ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjL2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X4:$i, 39.97/5.68 X6:$i, 39.97/5.68 X8:$i, 39.97/5.68 X10:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X4 @ X6 ) = 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X8 @ X10 ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 X4 ) = 39.97/5.68 ( 39.97/5.68 X8 ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjR11 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjR12 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjR1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairequniteq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjR2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X12:$i, 39.97/5.68 X14:$i, 39.97/5.68 X16:$i, 39.97/5.68 X18:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X12 @ X14 ) = 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X16 @ X18 ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 X14 ) = 39.97/5.68 ( 39.97/5.68 X18 ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ksndsingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ksndpairEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kpairsurjEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodsndin ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodpairmemEL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodpairmemER ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X20:$i, 39.97/5.68 X22:$i, 39.97/5.68 X24:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X24 @ X20 ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X26:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X26 @ X22 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X24 @ X26 ) = 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X24 @ X26 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodfstpairEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodsndpairEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodpairsurjEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrSub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setOfPairsIsBReln ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrERa ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrEL1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrEL2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrER ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 funcImageSingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X28:$i, 39.97/5.68 X30:$i, 39.97/5.68 X32:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 breln @ 39.97/5.68 X28 @ 39.97/5.68 X30 @ X32 ) & 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X34:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X34 @ X28 ) => 39.97/5.68 ( 39.97/5.68 ex1 @ 39.97/5.68 X30 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_1:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X34 @ V_1 ) @ 39.97/5.68 X32 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X36:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X36 @ X28 ) => 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 setunion @ 39.97/5.68 ( 39.97/5.68 dsetconstr 39.97/5.68 @ 39.97/5.68 X30 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_2:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X36 @ V_2 ) @ 39.97/5.68 X32 ) ) ) ) @ 39.97/5.68 X30 ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X38:$i, 39.97/5.68 X40:$i, 39.97/5.68 X42:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 breln @ 39.97/5.68 X38 @ 39.97/5.68 X40 @ X42 ) & 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X44:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X44 @ X38 ) => 39.97/5.68 ( 39.97/5.68 ex1 @ 39.97/5.68 X40 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_3:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X44 @ V_3 ) @ 39.97/5.68 X42 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X46:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X46 @ X38 ) => 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X38 @ 39.97/5.68 X40 @ 39.97/5.68 X42 @ X46 ) @ 39.97/5.68 X40 ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 infuncsetfunc ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X48:$i, 39.97/5.68 X50:$i, 39.97/5.68 X52:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X52 @ 39.97/5.68 ( 39.97/5.68 funcSet @ 39.97/5.68 X48 @ X50 ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X54:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X54 @ X48 ) => 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X48 @ 39.97/5.68 X50 @ 39.97/5.68 X52 @ X54 ) @ 39.97/5.68 X50 ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 funcinfuncset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 lamProp ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 lamp ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 lam2p ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 brelnall1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 brelnall2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ex1E2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X56:$i, 39.97/5.68 X58:$i, 39.97/5.68 X60:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 breln @ 39.97/5.68 X56 @ 39.97/5.68 X58 @ X60 ) & 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X62:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X62 @ X56 ) => 39.97/5.68 ( 39.97/5.68 ex1 @ 39.97/5.68 X58 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_4:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X62 @ V_4 ) @ 39.97/5.68 X60 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X64:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X64 @ X56 ) => 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X64 @ 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X56 @ 39.97/5.68 X58 @ 39.97/5.68 X60 @ X64 ) ) @ 39.97/5.68 X60 ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X66:$i, 39.97/5.68 X68:$i, 39.97/5.68 X70:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X70 @ 39.97/5.68 ( 39.97/5.68 funcSet @ 39.97/5.68 X66 @ X68 ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X72:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X72 @ X66 ) => 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X72 @ 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X66 @ 39.97/5.68 X68 @ 39.97/5.68 X70 @ X72 ) ) @ 39.97/5.68 X70 ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X74:$i, 39.97/5.68 X76:$i, 39.97/5.68 X78:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 breln @ 39.97/5.68 X74 @ 39.97/5.68 X76 @ X78 ) & 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X80:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X80 @ X74 ) => 39.97/5.68 ( 39.97/5.68 ex1 @ 39.97/5.68 X76 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_5:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X80 @ V_5 ) @ 39.97/5.68 X78 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X82:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X82 @ X74 ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X84:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X84 @ X76 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X82 @ X84 ) @ 39.97/5.68 X78 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X74 @ 39.97/5.68 X76 @ 39.97/5.68 X78 @ X82 ) = 39.97/5.68 ( 39.97/5.68 X84 ) ) ) ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X86:$i, 39.97/5.68 X88:$i, 39.97/5.68 X90:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 breln @ 39.97/5.68 X86 @ 39.97/5.68 X88 @ X90 ) & 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X92:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X92 @ X86 ) => 39.97/5.68 ( 39.97/5.68 ex1 @ 39.97/5.68 X88 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_6:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X92 @ V_6 ) @ 39.97/5.68 X90 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X94:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 breln @ 39.97/5.68 X86 @ 39.97/5.68 X88 @ X94 ) & 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X96:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X96 @ X86 ) => 39.97/5.68 ( 39.97/5.68 ex1 @ 39.97/5.68 X88 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_7:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X96 @ V_7 ) @ 39.97/5.68 X94 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X98:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X98 @ X86 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X86 @ 39.97/5.68 X88 @ 39.97/5.68 X90 @ X98 ) = 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X86 @ 39.97/5.68 X88 @ 39.97/5.68 X94 @ X98 ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X100:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X100 @ X86 ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X102:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X102 @ X88 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X100 @ 39.97/5.68 X102 ) @ 39.97/5.68 X94 ) => 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X100 @ 39.97/5.68 X102 ) @ 39.97/5.68 X90 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 39.97/5.68 thf(zf_stmt_1, negated_conjecture, 39.97/5.68 (~( ( setextAx ) => 39.97/5.68 ( ( emptysetAx ) => 39.97/5.68 ( ( setadjoinAx ) => 39.97/5.68 ( ( powersetAx ) => 39.97/5.68 ( ( setunionAx ) => 39.97/5.68 ( ( omega0Ax ) => 39.97/5.68 ( ( omegaSAx ) => 39.97/5.68 ( ( omegaIndAx ) => 39.97/5.68 ( ( replAx ) => 39.97/5.68 ( ( foundationAx ) => 39.97/5.68 ( ( wellorderingAx ) => 39.97/5.68 ( ( descrp ) => 39.97/5.68 ( ( dsetconstrI ) => 39.97/5.68 ( ( dsetconstrEL ) => 39.97/5.68 ( ( dsetconstrER ) => 39.97/5.68 ( ( exuE1 ) => 39.97/5.68 ( ( prop2setE ) => 39.97/5.68 ( ( emptysetE ) => 39.97/5.68 ( ( emptysetimpfalse ) => 39.97/5.68 ( ( notinemptyset ) => 39.97/5.68 ( ( exuE3e ) => 39.97/5.68 ( ( setext ) => 39.97/5.68 ( ( emptyI ) => 39.97/5.68 ( ( noeltsimpempty ) => 39.97/5.68 ( ( setbeta ) => 39.97/5.68 ( ( nonemptyE1 ) => 39.97/5.68 ( ( nonemptyI ) => 39.97/5.68 ( ( nonemptyI1 ) => 39.97/5.68 ( ( setadjoinIL ) => 39.97/5.68 ( ( emptyinunitempty ) => 39.97/5.68 ( ( setadjoinIR ) => 39.97/5.68 ( ( 39.97/5.68 setadjoinE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setadjoinOr ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setoftrueEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 powersetI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 emptyinPowerset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 emptyInPowerset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 powersetE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subPowSU ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exuE2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 nonemptyImpWitness ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 uniqinunit ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 notinsingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 eqinunit ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletonsswitch ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairsetE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairsetIL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairsetIR ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 emptyE1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 vacuousDall ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 quantDeMorgan1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 quantDeMorgan2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 quantDeMorgan3 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 quantDeMorgan4 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 prop2setI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 prop2set2propI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 notdexE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 notdallE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exuI1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exuI3 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exuI2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 inCongP ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exuE3u ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exu__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 emptyset__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setadjoin__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 powerset__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunion__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 omega__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 exuEu ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 descr__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dsetconstr__Cong ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetI1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 eqimpsubset2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 eqimpsubset1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetI2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 emptysetsubset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetE2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 notsubsetI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 notequalI1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 notequalI2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetRefl ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetTrans ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setadjoinSub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setadjoinSub2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subset2powerset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setextsub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 subsetemptysetimpeq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 powersetI1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 powersetE1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 inPowerset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 powersetsubset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 sepInPowerset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 sepSubset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binunionIL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairset2IR ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binunionIR ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binunionEcases ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binunionE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binunionLsub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binunionRsub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectSubset5 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectEL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectLsub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectSubset2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectSubset3 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectER ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 disjointsetsI1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectRsub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectSubset4 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 binintersectSubset1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 bs114d ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusEL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusER ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusSubset2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusERneg ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusELneg ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusILneg ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusIRneg ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusLsub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setminusSubset1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 symdiffE ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 symdiffI1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 symdiffI2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 symdiffIneg1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 symdiffIneg2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 secondinupair ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairIL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairIR ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kpairiskpair ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kpairp ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletonsubset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletoninpowerset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletoninpowunion ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairset2E ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairsubunion ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairinpowunion ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ubforcartprodlem1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ubforcartprodlem2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ubforcartprodlem3 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodpairin ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodmempair1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodmempair ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionE2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionsingleton1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionsingleton2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setunionsingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletonprop ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ex1E1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ex1I ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ex1I2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 singletonsuniq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjL1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kfstsingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 theprop ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kfstpairEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodfstin ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjL2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X4:$i, 39.97/5.68 X6:$i, 39.97/5.68 X8:$i, 39.97/5.68 X10:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X4 @ X6 ) = 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X8 @ X10 ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 X4 ) = 39.97/5.68 ( 39.97/5.68 X8 ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjR11 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjR12 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjR1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 upairequniteq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setukpairinjR2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X12:$i, 39.97/5.68 X14:$i, 39.97/5.68 X16:$i, 39.97/5.68 X18:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X12 @ X14 ) = 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X16 @ X18 ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 X14 ) = 39.97/5.68 ( 39.97/5.68 X18 ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ksndsingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ksndpairEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kpairsurjEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodsndin ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodpairmemEL ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodpairmemER ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X20:$i, 39.97/5.68 X22:$i, 39.97/5.68 X24:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X24 @ X20 ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X26:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X26 @ X22 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X24 @ X26 ) = 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X24 @ X26 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodfstpairEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodsndpairEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 cartprodpairsurjEq ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrI ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrSub ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 setOfPairsIsBReln ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrERa ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrEL1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrEL2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 dpsetconstrER ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 funcImageSingleton ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X28:$i, 39.97/5.68 X30:$i, 39.97/5.68 X32:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 breln @ 39.97/5.68 X28 @ 39.97/5.68 X30 @ X32 ) & 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X34:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X34 @ X28 ) => 39.97/5.68 ( 39.97/5.68 ex1 @ 39.97/5.68 X30 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_1:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X34 @ V_1 ) @ 39.97/5.68 X32 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X36:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X36 @ X28 ) => 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 setunion 39.97/5.68 @ 39.97/5.68 ( 39.97/5.68 dsetconstr 39.97/5.68 @ 39.97/5.68 X30 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_2:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X36 @ V_2 ) @ 39.97/5.68 X32 ) ) ) ) @ 39.97/5.68 X30 ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X38:$i, 39.97/5.68 X40:$i, 39.97/5.68 X42:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 breln @ 39.97/5.68 X38 @ 39.97/5.68 X40 @ X42 ) & 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X44:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X44 @ X38 ) => 39.97/5.68 ( 39.97/5.68 ex1 @ 39.97/5.68 X40 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_3:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X44 @ V_3 ) @ 39.97/5.68 X42 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X46:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X46 @ X38 ) => 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X38 @ 39.97/5.68 X40 @ 39.97/5.68 X42 @ X46 ) @ 39.97/5.68 X40 ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 infuncsetfunc ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X48:$i, 39.97/5.68 X50:$i, 39.97/5.68 X52:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X52 @ 39.97/5.68 ( 39.97/5.68 funcSet @ 39.97/5.68 X48 @ X50 ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X54:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X54 @ X48 ) => 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X48 @ 39.97/5.68 X50 @ 39.97/5.68 X52 @ X54 ) @ 39.97/5.68 X50 ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 funcinfuncset ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 lamProp ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 lamp ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 lam2p ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 brelnall1 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 brelnall2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ex1E2 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X56:$i, 39.97/5.68 X58:$i, 39.97/5.68 X60:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 breln @ 39.97/5.68 X56 @ 39.97/5.68 X58 @ X60 ) & 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X62:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X62 @ X56 ) => 39.97/5.68 ( 39.97/5.68 ex1 @ 39.97/5.68 X58 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_4:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X62 @ V_4 ) @ 39.97/5.68 X60 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X64:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X64 @ X56 ) => 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X64 @ 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X56 @ 39.97/5.68 X58 @ 39.97/5.68 X60 @ X64 ) ) @ 39.97/5.68 X60 ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X66:$i, 39.97/5.68 X68:$i, 39.97/5.68 X70:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X70 @ 39.97/5.68 ( 39.97/5.68 funcSet @ 39.97/5.68 X66 @ X68 ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X72:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X72 @ X66 ) => 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X72 @ 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X66 @ 39.97/5.68 X68 @ 39.97/5.68 X70 @ X72 ) ) @ 39.97/5.68 X70 ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X74:$i, 39.97/5.68 X76:$i, 39.97/5.68 X78:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 breln @ 39.97/5.68 X74 @ 39.97/5.68 X76 @ X78 ) & 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X80:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X80 @ X74 ) => 39.97/5.68 ( 39.97/5.68 ex1 @ 39.97/5.68 X76 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_5:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X80 @ V_5 ) @ 39.97/5.68 X78 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X82:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X82 @ X74 ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X84:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X84 @ X76 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X82 @ X84 ) @ 39.97/5.68 X78 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X74 @ 39.97/5.68 X76 @ 39.97/5.68 X78 @ X82 ) = 39.97/5.68 ( 39.97/5.68 X84 ) ) ) ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X86:$i, 39.97/5.68 X88:$i, 39.97/5.68 X90:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 breln @ 39.97/5.68 X86 @ 39.97/5.68 X88 @ X90 ) & 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X92:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X92 @ X86 ) => 39.97/5.68 ( 39.97/5.68 ex1 @ 39.97/5.68 X88 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_6:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X92 @ V_6 ) @ 39.97/5.68 X90 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X94:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 breln @ 39.97/5.68 X86 @ 39.97/5.68 X88 @ X94 ) & 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X96:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X96 @ X86 ) => 39.97/5.68 ( 39.97/5.68 ex1 @ 39.97/5.68 X88 @ 39.97/5.68 ( 39.97/5.68 ^[ 39.97/5.68 V_7:$i]: 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X96 @ V_7 ) @ 39.97/5.68 X94 ) ) ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X98:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X98 @ X86 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X86 @ 39.97/5.68 X88 @ 39.97/5.68 X90 @ X98 ) = 39.97/5.68 ( 39.97/5.68 ap @ 39.97/5.68 X86 @ 39.97/5.68 X88 @ 39.97/5.68 X94 @ X98 ) ) ) ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X100:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X100 @ 39.97/5.68 X86 ) => 39.97/5.68 ( 39.97/5.68 ![ 39.97/5.68 X102:$i]: 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 X102 @ 39.97/5.68 X88 ) => 39.97/5.68 ( 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X100 @ 39.97/5.68 X102 ) @ 39.97/5.68 X94 ) => 39.97/5.68 ( 39.97/5.68 in @ 39.97/5.68 ( 39.97/5.68 kpair @ 39.97/5.68 X100 @ 39.97/5.68 X102 ) @ 39.97/5.68 X90 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 39.97/5.68 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 39.97/5.68 thf(zip_derived_cl108, plain, (~ (in @ (kpair @ sk__43 @ sk__44) @ sk__41)), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl120, plain, 39.97/5.68 (![X32 : $i, X33 : $i, X34 : $i, X35 : $i]: 39.97/5.68 (~ (in @ X32 @ X33) 39.97/5.68 | (in @ 39.97/5.68 (setunion @ 39.97/5.68 (dsetconstr @ X34 @ 39.97/5.68 (^[Y0 : $i]: (in @ (kpair @ X32 @ Y0) @ X35)))) @ 39.97/5.68 X34) 39.97/5.68 | ~ (ex1 @ X34 @ 39.97/5.68 (^[Y0 : $i]: 39.97/5.68 (in @ (kpair @ (sk__38 @ X35 @ X34 @ X33) @ Y0) @ X35))) 39.97/5.68 | ~ (breln @ X33 @ X34 @ X35))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl101, plain, 39.97/5.68 (![X16 : $i, X17 : $i, X18 : $i, X19 : $i]: 39.97/5.68 (~ (in @ X16 @ X17) 39.97/5.68 | (in @ (kpair @ X16 @ (ap @ X17 @ X18 @ X19 @ X16)) @ X19) 39.97/5.68 | ~ (ex1 @ X18 @ 39.97/5.68 (^[Y0 : $i]: 39.97/5.68 (in @ (kpair @ (sk__46 @ X19 @ X18 @ X17) @ Y0) @ X19))) 39.97/5.68 | ~ (breln @ X17 @ X18 @ X19))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl5583, plain, 39.97/5.68 (![X17 : $i, X18 : $i, X19 : $i, X20 : $i]: 39.97/5.68 (('#l_lift1180' @ X17 @ X18 @ X19 @ X20) 39.97/5.68 = (in @ (kpair @ (sk__46 @ X19 @ X18 @ X17) @ X20) @ X19))), 39.97/5.68 define([status(thm)])). 39.97/5.68 thf(zip_derived_cl5595, plain, 39.97/5.68 (![X0 : $i, X1 : $i, X2 : $i]: 39.97/5.68 (('#l_lift1185' @ (sk__46 @ X0 @ X1 @ X2) @ X0) 39.97/5.68 = ('#l_lift1180' @ X2 @ X1 @ X0))), 39.97/5.68 define([status(thm)])). 39.97/5.68 thf(zip_derived_cl101, plain, 39.97/5.68 (![X16 : $i, X17 : $i, X18 : $i, X19 : $i]: 39.97/5.68 (~ (in @ X16 @ X17) 39.97/5.68 | (in @ (kpair @ X16 @ (ap @ X17 @ X18 @ X19 @ X16)) @ X19) 39.97/5.68 | ~ (ex1 @ X18 @ 39.97/5.68 (^[Y0 : $i]: 39.97/5.68 (in @ (kpair @ (sk__46 @ X19 @ X18 @ X17) @ Y0) @ X19))) 39.97/5.68 | ~ (breln @ X17 @ X18 @ X19))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl5583, plain, 39.97/5.68 (![X17 : $i, X18 : $i, X19 : $i, X20 : $i]: 39.97/5.68 (('#l_lift1180' @ X17 @ X18 @ X19 @ X20) 39.97/5.68 = (in @ (kpair @ (sk__46 @ X19 @ X18 @ X17) @ X20) @ X19))), 39.97/5.68 define([status(thm)])). 39.97/5.68 thf(zip_derived_cl5584, plain, 39.97/5.68 (![X16 : $i, X17 : $i, X18 : $i, X19 : $i]: 39.97/5.68 (~ (in @ X16 @ X17) 39.97/5.68 | (in @ (kpair @ X16 @ (ap @ X17 @ X18 @ X19 @ X16)) @ X19) 39.97/5.68 | ~ (ex1 @ X18 @ ('#l_lift1180' @ X17 @ X18 @ X19)) 39.97/5.68 | ~ (breln @ X17 @ X18 @ X19))), 39.97/5.68 inference('lambda_lifting', [status(thm)], 39.97/5.68 [zip_derived_cl101, zip_derived_cl5583])). 39.97/5.68 thf(zip_derived_cl110, plain, ( (in @ sk__43 @ sk__39)), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl107, plain, ( (in @ sk__44 @ sk__40)), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl105, plain, ( (breln @ sk__39 @ sk__40 @ sk__42)), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl111, plain, 39.97/5.68 (![X26 : $i]: 39.97/5.68 (((ap @ sk__39 @ sk__40 @ sk__41 @ X26) 39.97/5.68 = (ap @ sk__39 @ sk__40 @ sk__42 @ X26)) 39.97/5.68 | ~ (in @ X26 @ sk__39))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl113, plain, ( (breln @ sk__39 @ sk__40 @ sk__41)), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl120, plain, 39.97/5.68 (![X32 : $i, X33 : $i, X34 : $i, X35 : $i]: 39.97/5.68 (~ (in @ X32 @ X33) 39.97/5.68 | (in @ 39.97/5.68 (setunion @ 39.97/5.68 (dsetconstr @ X34 @ 39.97/5.68 (^[Y0 : $i]: (in @ (kpair @ X32 @ Y0) @ X35)))) @ 39.97/5.68 X34) 39.97/5.68 | ~ (ex1 @ X34 @ 39.97/5.68 (^[Y0 : $i]: 39.97/5.68 (in @ (kpair @ (sk__38 @ X35 @ X34 @ X33) @ Y0) @ X35))) 39.97/5.68 | ~ (breln @ X33 @ X34 @ X35))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl112, plain, 39.97/5.68 (![X27 : $i]: 39.97/5.68 ( (ex1 @ sk__40 @ (^[Y0 : $i]: (in @ (kpair @ X27 @ Y0) @ sk__41))) 39.97/5.68 | ~ (in @ X27 @ sk__39))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl5589, plain, 39.97/5.68 (![X27 : $i, X28 : $i]: 39.97/5.68 (('#l_lift1183' @ X27 @ X28) = (in @ (kpair @ X27 @ X28) @ sk__41))), 39.97/5.68 define([status(thm)])). 39.97/5.68 thf(zip_derived_cl5597, plain, 39.97/5.68 (![X0 : $i]: (('#l_lift1185' @ X0 @ sk__41) = ('#l_lift1183' @ X0))), 39.97/5.68 define([status(thm)])). 39.97/5.68 thf(zip_derived_cl109, plain, ( (in @ (kpair @ sk__43 @ sk__44) @ sk__42)), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl112, plain, 39.97/5.68 (![X27 : $i]: 39.97/5.68 ( (ex1 @ sk__40 @ (^[Y0 : $i]: (in @ (kpair @ X27 @ Y0) @ sk__41))) 39.97/5.68 | ~ (in @ X27 @ sk__39))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl5589, plain, 39.97/5.68 (![X27 : $i, X28 : $i]: 39.97/5.68 (('#l_lift1183' @ X27 @ X28) = (in @ (kpair @ X27 @ X28) @ sk__41))), 39.97/5.68 define([status(thm)])). 39.97/5.68 thf(zip_derived_cl5590, plain, 39.97/5.68 (![X27 : $i]: 39.97/5.68 ( (ex1 @ sk__40 @ ('#l_lift1183' @ X27)) | ~ (in @ X27 @ sk__39))), 39.97/5.68 inference('lambda_lifting', [status(thm)], 39.97/5.68 [zip_derived_cl112, zip_derived_cl5589])). 39.97/5.68 thf(zip_derived_cl120, plain, 39.97/5.68 (![X32 : $i, X33 : $i, X34 : $i, X35 : $i]: 39.97/5.68 (~ (in @ X32 @ X33) 39.97/5.68 | (in @ 39.97/5.68 (setunion @ 39.97/5.68 (dsetconstr @ X34 @ 39.97/5.68 (^[Y0 : $i]: (in @ (kpair @ X32 @ Y0) @ X35)))) @ 39.97/5.68 X34) 39.97/5.68 | ~ (ex1 @ X34 @ 39.97/5.68 (^[Y0 : $i]: 39.97/5.68 (in @ (kpair @ (sk__38 @ X35 @ X34 @ X33) @ Y0) @ X35))) 39.97/5.68 | ~ (breln @ X33 @ X34 @ X35))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl103, plain, 39.97/5.68 (![X20 : $i, X21 : $i, X22 : $i, X23 : $i, X24 : $i]: 39.97/5.68 (~ (in @ X20 @ X21) 39.97/5.68 | ~ (in @ (kpair @ X20 @ X22) @ X23) 39.97/5.68 | ((ap @ X21 @ X24 @ X23 @ X20) = (X22)) 39.97/5.68 | ~ (in @ X22 @ X24) 39.97/5.68 | ~ (ex1 @ X24 @ 39.97/5.68 (^[Y0 : $i]: 39.97/5.68 (in @ (kpair @ (sk__45 @ X23 @ X24 @ X21) @ Y0) @ X23))) 39.97/5.68 | ~ (breln @ X21 @ X24 @ X23))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl5585, plain, 39.97/5.68 (![X21 : $i, X23 : $i, X24 : $i, X25 : $i]: 39.97/5.68 (('#l_lift1181' @ X21 @ X23 @ X24 @ X25) 39.97/5.68 = (in @ (kpair @ (sk__45 @ X23 @ X24 @ X21) @ X25) @ X23))), 39.97/5.68 define([status(thm)])). 39.97/5.68 thf(zip_derived_cl5594, plain, 39.97/5.68 (![X0 : $i, X1 : $i, X2 : $i]: 39.97/5.68 (('#l_lift1185' @ (sk__45 @ X1 @ X0 @ X2) @ X1) 39.97/5.68 = ('#l_lift1181' @ X2 @ X1 @ X0))), 39.97/5.68 define([status(thm)])). 39.97/5.68 thf(zip_derived_cl103, plain, 39.97/5.68 (![X20 : $i, X21 : $i, X22 : $i, X23 : $i, X24 : $i]: 39.97/5.68 (~ (in @ X20 @ X21) 39.97/5.68 | ~ (in @ (kpair @ X20 @ X22) @ X23) 39.97/5.68 | ((ap @ X21 @ X24 @ X23 @ X20) = (X22)) 39.97/5.68 | ~ (in @ X22 @ X24) 39.97/5.68 | ~ (ex1 @ X24 @ 39.97/5.68 (^[Y0 : $i]: 39.97/5.68 (in @ (kpair @ (sk__45 @ X23 @ X24 @ X21) @ Y0) @ X23))) 39.97/5.68 | ~ (breln @ X21 @ X24 @ X23))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl5585, plain, 39.97/5.68 (![X21 : $i, X23 : $i, X24 : $i, X25 : $i]: 39.97/5.68 (('#l_lift1181' @ X21 @ X23 @ X24 @ X25) 39.97/5.68 = (in @ (kpair @ (sk__45 @ X23 @ X24 @ X21) @ X25) @ X23))), 39.97/5.68 define([status(thm)])). 39.97/5.68 thf(zip_derived_cl5586, plain, 39.97/5.68 (![X20 : $i, X21 : $i, X22 : $i, X23 : $i, X24 : $i]: 39.97/5.68 (~ (in @ X20 @ X21) 39.97/5.68 | ~ (in @ (kpair @ X20 @ X22) @ X23) 39.97/5.68 | ((ap @ X21 @ X24 @ X23 @ X20) = (X22)) 39.97/5.68 | ~ (in @ X22 @ X24) 39.97/5.68 | ~ (ex1 @ X24 @ ('#l_lift1181' @ X21 @ X23 @ X24)) 39.97/5.68 | ~ (breln @ X21 @ X24 @ X23))), 39.97/5.68 inference('lambda_lifting', [status(thm)], 39.97/5.68 [zip_derived_cl103, zip_derived_cl5585])). 39.97/5.68 thf(zip_derived_cl102, plain, 39.97/5.68 (![X16 : $i, X17 : $i, X18 : $i, X19 : $i]: 39.97/5.68 (~ (in @ X16 @ X17) 39.97/5.68 | (in @ (kpair @ X16 @ (ap @ X17 @ X18 @ X19 @ X16)) @ X19) 39.97/5.68 | (in @ (sk__46 @ X19 @ X18 @ X17) @ X17) 39.97/5.68 | ~ (breln @ X17 @ X18 @ X19))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl104, plain, 39.97/5.68 (![X20 : $i, X21 : $i, X22 : $i, X23 : $i, X24 : $i]: 39.97/5.68 (~ (in @ X20 @ X21) 39.97/5.68 | ~ (in @ (kpair @ X20 @ X22) @ X23) 39.97/5.68 | ((ap @ X21 @ X24 @ X23 @ X20) = (X22)) 39.97/5.68 | ~ (in @ X22 @ X24) 39.97/5.68 | (in @ (sk__45 @ X23 @ X24 @ X21) @ X21) 39.97/5.68 | ~ (breln @ X21 @ X24 @ X23))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl120, plain, 39.97/5.68 (![X32 : $i, X33 : $i, X34 : $i, X35 : $i]: 39.97/5.68 (~ (in @ X32 @ X33) 39.97/5.68 | (in @ 39.97/5.68 (setunion @ 39.97/5.68 (dsetconstr @ X34 @ 39.97/5.68 (^[Y0 : $i]: (in @ (kpair @ X32 @ Y0) @ X35)))) @ 39.97/5.68 X34) 39.97/5.68 | ~ (ex1 @ X34 @ 39.97/5.68 (^[Y0 : $i]: 39.97/5.68 (in @ (kpair @ (sk__38 @ X35 @ X34 @ X33) @ Y0) @ X35))) 39.97/5.68 | ~ (breln @ X33 @ X34 @ X35))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl106, plain, 39.97/5.68 (![X25 : $i]: 39.97/5.68 ( (ex1 @ sk__40 @ (^[Y0 : $i]: (in @ (kpair @ X25 @ Y0) @ sk__42))) 39.97/5.68 | ~ (in @ X25 @ sk__39))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl5587, plain, 39.97/5.68 (![X25 : $i, X26 : $i]: 39.97/5.68 (('#l_lift1182' @ X25 @ X26) = (in @ (kpair @ X25 @ X26) @ sk__42))), 39.97/5.68 define([status(thm)])). 39.97/5.68 thf(zip_derived_cl5598, plain, 39.97/5.68 (![X0 : $i]: (('#l_lift1185' @ X0 @ sk__42) = ('#l_lift1182' @ X0))), 39.97/5.68 define([status(thm)])). 39.97/5.68 thf(zip_derived_cl106, plain, 39.97/5.68 (![X25 : $i]: 39.97/5.68 ( (ex1 @ sk__40 @ (^[Y0 : $i]: (in @ (kpair @ X25 @ Y0) @ sk__42))) 39.97/5.68 | ~ (in @ X25 @ sk__39))), 39.97/5.68 inference('cnf', [status(esa)], [zf_stmt_1])). 39.97/5.68 thf(zip_derived_cl5587, plain, 39.97/5.68 (![X25 : $i, X26 : $i]: 39.97/5.68 (('#l_lift1182' @ X25 @ X26) = (in @ (kpair @ X25 @ X26) @ sk__42))), 39.97/5.68 define([status(thm)])). 39.97/5.68 thf(zip_derived_cl5588, plain, 39.97/5.68 (![X25 : $i]: 39.97/5.68 ( (ex1 @ sk__40 @ ('#l_lift1182' @ X25)) | ~ (in @ X25 @ sk__39))), 39.97/5.68 inference('lambda_lifting', [status(thm)], 39.97/5.68 [zip_derived_cl106, zip_derived_cl5587])). 39.97/5.68 thf(zip_derived_cl5601, plain, ($false), 39.97/5.68 inference('eprover', [status(thm)], 39.97/5.68 [zip_derived_cl108, zip_derived_cl5595, zip_derived_cl5584, 39.97/5.68 zip_derived_cl110, zip_derived_cl107, zip_derived_cl105, 39.97/5.68 zip_derived_cl111, zip_derived_cl113, zip_derived_cl5597, 39.97/5.68 zip_derived_cl109, zip_derived_cl5590, zip_derived_cl5594, 39.97/5.68 zip_derived_cl5586, zip_derived_cl102, zip_derived_cl104, 39.97/5.68 zip_derived_cl5598, zip_derived_cl5588])). 39.97/5.68 39.97/5.68 % SZS output end Refutation 39.97/5.68 39.97/5.68 39.97/5.68 % Terminating... 40.65/5.82 % Runner terminated. 40.65/5.85 % Zipperpin 1.5 exiting 40.65/5.86 EOF