0.13/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.18 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.8GmuPYANLY true 0.18/0.39 % Computer : n005.cluster.edu 0.18/0.39 % Model : x86_64 x86_64 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.18/0.39 % Memory : 8042.1875MB 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64 0.18/0.39 % CPULimit : 1200 0.18/0.39 % WCLimit : 120 0.18/0.39 % DateTime : Tue Jul 13 12:18:03 EDT 2021 0.18/0.40 % CPUTime : 0.18/0.40 % Running portfolio for 120 s 0.18/0.40 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.18/0.40 % Number of cores: 8 0.18/0.40 % Python version: Python 3.6.8 0.18/0.40 % Running in HO mode 0.38/0.69 % Total configuration time : 828 0.38/0.69 % Estimated wc time : 983 0.38/0.69 % Estimated cpu time (8 cpus) : 122.875 0.41/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 47s 0.41/0.79 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 47s 0.41/0.79 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 47s 0.41/0.81 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 18s 0.41/0.81 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 53s 0.41/0.82 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 41s 0.41/0.83 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.41/0.84 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 35s 70.90/9.67 % Solved by lams/40_b.comb.sh. 70.90/9.67 % running E: timeout 28 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.8GmuPYANLY/e_input547da1 --cpu-limit=26 --auto-schedule -s -p 70.90/9.67 % done 0 iterations in 8.438s 70.90/9.67 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 70.90/9.67 % SZS output start Refutation 70.90/9.67 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 70.90/9.67 thf(binintersectER_type, type, binintersectER: $o). 70.90/9.67 thf(setadjoinSub_type, type, setadjoinSub: $o). 70.90/9.67 thf(breln1compE_type, type, breln1compE: $o). 70.90/9.67 thf(setukpairinjR_type, type, setukpairinjR: $o). 70.90/9.67 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 70.90/9.67 thf(vacuousDall_type, type, vacuousDall: $o). 70.90/9.67 thf(complementT_lem_type, type, complementT_lem: $o). 70.90/9.67 thf(setadjoinIR_type, type, setadjoinIR: $o). 70.90/9.67 thf(ex1I2_type, type, ex1I2: $o). 70.90/9.67 thf(omega0Ax_type, type, omega0Ax: $o). 70.90/9.67 thf(subsetE_type, type, subsetE: $o). 70.90/9.67 thf(ifp_type, type, ifp: $o). 70.90/9.67 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 70.90/9.67 thf(setminusER_type, type, setminusER: $o). 70.90/9.67 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o). 70.90/9.67 thf(binunionE_type, type, binunionE: $o). 70.90/9.67 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 70.90/9.67 thf(powersetE_type, type, powersetE: $o). 70.90/9.67 thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o). 70.90/9.67 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o). 70.90/9.67 thf(binunionRsub_type, type, binunionRsub: $o). 70.90/9.67 thf(powersetTE1_type, type, powersetTE1: $o). 70.90/9.67 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 70.90/9.67 thf(brelnall2_type, type, brelnall2: $o). 70.90/9.67 thf(powerset__Cong_type, type, powerset__Cong: $o). 70.90/9.67 thf(singletonprop_type, type, singletonprop: $o). 70.90/9.67 thf('#sk43_type', type, '#sk43': $i). 70.90/9.67 thf(breln1invprop_type, type, breln1invprop: $o). 70.90/9.67 thf(demorgan2b2_type, type, demorgan2b2: $o). 70.90/9.67 thf(omegaIndAx_type, type, omegaIndAx: $o). 70.90/9.67 thf(uniqinunit_type, type, uniqinunit: $o). 70.90/9.67 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 70.90/9.67 thf(exu__Cong_type, type, exu__Cong: $o). 70.90/9.67 thf(subset2powerset_type, type, subset2powerset: $o). 70.90/9.67 thf(setoftrueEq_type, type, setoftrueEq: $o). 70.90/9.67 thf('#sk45_type', type, '#sk45': $i). 70.90/9.67 thf(lam2p_type, type, lam2p: $o). 70.90/9.67 thf(funcinfuncset_type, type, funcinfuncset: $o). 70.90/9.67 thf(eqbreln1_type, type, eqbreln1: $o). 70.90/9.67 thf(upairsetIL_type, type, upairsetIL: $o). 70.90/9.67 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 70.90/9.67 thf(complementTE1_type, type, complementTE1: $o). 70.90/9.67 thf(woz13rule3_type, type, woz13rule3: $o). 70.90/9.67 thf(kpairsurjEq_type, type, kpairsurjEq: $o). 70.90/9.67 thf(emptyI_type, type, emptyI: $o). 70.90/9.67 thf(setukpairIL_type, type, setukpairIL: $o). 70.90/9.67 thf(exuI3_type, type, exuI3: $o). 70.90/9.67 thf(singletonsuniq_type, type, singletonsuniq: $o). 70.90/9.67 thf(emptysetAx_type, type, emptysetAx: $o). 70.90/9.67 thf(setukpairIR_type, type, setukpairIR: $o). 70.90/9.67 thf(doubleComplementEq_type, type, doubleComplementEq: $o). 70.90/9.67 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 70.90/9.67 thf(setadjoinIL_type, type, setadjoinIL: $o). 70.90/9.67 thf(upairsubunion_type, type, upairsubunion: $o). 70.90/9.67 thf(iftrue_type, type, iftrue: $o). 70.90/9.67 thf(cartprodsndin_type, type, cartprodsndin: $o). 70.90/9.67 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 70.90/9.67 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect: 70.90/9.67 $o). 70.90/9.67 thf(upairsetIR_type, type, upairsetIR: $o). 70.90/9.67 thf(setukpairinjR12_type, type, setukpairinjR12: $o). 70.90/9.67 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 70.90/9.67 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 70.90/9.67 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o). 70.90/9.67 thf(setminusI_type, type, setminusI: $o). 70.90/9.67 thf(brelnall1_type, type, brelnall1: $o). 70.90/9.67 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 70.90/9.67 thf(woz13rule0_type, type, woz13rule0: $o). 70.90/9.67 thf(descrp_type, type, descrp: $o). 70.90/9.67 thf(binintersectI_type, type, binintersectI: $o). 70.90/9.67 thf(nonemptyI1_type, type, nonemptyI1: $o). 70.90/9.67 thf(emptysetsubset_type, type, emptysetsubset: $o). 70.90/9.67 thf(setunionAx_type, type, setunionAx: $o). 70.90/9.67 thf(iffalse_type, type, iffalse: $o). 70.90/9.67 thf(notsubsetI_type, type, notsubsetI: $o). 70.90/9.67 thf(breln1compI_type, type, breln1compI: $o). 70.90/9.67 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 70.90/9.67 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 70.90/9.67 thf(upairset2IR_type, type, upairset2IR: $o). 70.90/9.67 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o). 70.90/9.67 thf(binunionLsub_type, type, binunionLsub: $o). 70.90/9.67 thf(subsetRefl_type, type, subsetRefl: $o). 70.90/9.67 thf(cartprodfstin_type, type, cartprodfstin: $o). 70.90/9.67 thf(powerset_type, type, powerset: $i > $i). 70.90/9.67 thf(powersetTI1_type, type, powersetTI1: $o). 70.90/9.67 thf(iffalseProp1_type, type, iffalseProp1: $o). 70.90/9.67 thf(lam2lamEq_type, type, lam2lamEq: $o). 70.90/9.67 thf(nonemptyI_type, type, nonemptyI: $o). 70.90/9.67 thf(emptysetE_type, type, emptysetE: $o). 70.90/9.67 thf(sepInPowerset_type, type, sepInPowerset: $o). 70.90/9.67 thf(funcGraphProp1_type, type, funcGraphProp1: $o). 70.90/9.67 thf(breln1_type, type, breln1: $i > $i > $o). 70.90/9.67 thf(contrasubsetT1_type, type, contrasubsetT1: $o). 70.90/9.67 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect: 70.90/9.67 $o). 70.90/9.67 thf(doubleComplementE1_type, type, doubleComplementE1: $o). 70.90/9.67 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 70.90/9.67 thf(powersetT_lem_type, type, powersetT_lem: $o). 70.90/9.67 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 70.90/9.67 thf(powersetI_type, type, powersetI: $o). 70.90/9.67 thf(setukpairinjR2_type, type, setukpairinjR2: $o). 70.90/9.67 thf(exuE2_type, type, exuE2: $o). 70.90/9.67 thf(breln1invI_type, type, breln1invI: $o). 70.90/9.67 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 70.90/9.67 thf(exuE3e_type, type, exuE3e: $o). 70.90/9.67 thf(ifSingleton_type, type, ifSingleton: $o). 70.90/9.67 thf(setminusSubset1_type, type, setminusSubset1: $o). 70.90/9.67 thf(ap2apEq1_type, type, ap2apEq1: $o). 70.90/9.67 thf(notequalI2_type, type, notequalI2: $o). 70.90/9.67 thf(lamProp_type, type, lamProp: $o). 70.90/9.67 thf(woz1_3_type, type, woz1_3: $o). 70.90/9.67 thf(descr__Cong_type, type, descr__Cong: $o). 70.90/9.67 thf(woz1_1_type, type, woz1_1: $o). 70.90/9.67 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1: 70.90/9.67 $o). 70.90/9.67 thf(setextAx_type, type, setextAx: $o). 70.90/9.67 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o). 70.90/9.67 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 70.90/9.67 thf(eqinunit_type, type, eqinunit: $o). 70.90/9.67 thf(symdiffE_type, type, symdiffE: $o). 70.90/9.67 thf(upairinpowunion_type, type, upairinpowunion: $o). 70.90/9.67 thf(breln1invE_type, type, breln1invE: $o). 70.90/9.67 thf(ex1E1_type, type, ex1E1: $o). 70.90/9.67 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 70.90/9.67 thf(powersetAx_type, type, powersetAx: $o). 70.90/9.67 thf(upairset2E_type, type, upairset2E: $o). 70.90/9.67 thf(kfstpairEq_type, type, kfstpairEq: $o). 70.90/9.67 thf(subbreln_type, type, subbreln: $o). 70.90/9.67 thf(apProp_type, type, apProp: $o). 70.90/9.67 thf(subsetI2_type, type, subsetI2: $o). 70.90/9.67 thf(symdiffI1_type, type, symdiffI1: $o). 70.90/9.67 thf(binunion_type, type, binunion: $i > $i > $i). 70.90/9.67 thf(subsetI1_type, type, subsetI1: $o). 70.90/9.67 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions: 70.90/9.67 $o). 70.90/9.67 thf(iftrueProp2_type, type, iftrueProp2: $o). 70.90/9.67 thf(funcextLem_type, type, funcextLem: $o). 70.90/9.67 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 70.90/9.67 thf(dpsetconstrI_type, type, dpsetconstrI: $o). 70.90/9.67 thf(replAx_type, type, replAx: $o). 70.90/9.67 thf(subPowSU_type, type, subPowSU: $o). 70.90/9.67 thf(demorgan2a2_type, type, demorgan2a2: $o). 70.90/9.67 thf(app_type, type, app: $o). 70.90/9.67 thf(setunionE_type, type, setunionE: $o). 70.90/9.67 thf('#sk44_type', type, '#sk44': $i). 70.90/9.67 thf(setextT_type, type, setextT: $o). 70.90/9.67 thf(eta2_type, type, eta2: $o). 70.90/9.67 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o). 70.90/9.67 thf(setunionsingleton_type, type, setunionsingleton: $o). 70.90/9.67 thf(setunion__Cong_type, type, setunion__Cong: $o). 70.90/9.67 thf(bs114d_type, type, bs114d: $o). 70.90/9.67 thf(woz13rule4_type, type, woz13rule4: $o). 70.90/9.67 thf(setminusSubset2_type, type, setminusSubset2: $o). 70.90/9.67 thf(powersetE1_type, type, powersetE1: $o). 70.90/9.67 thf(eta1_type, type, eta1: $o). 70.90/9.67 thf(beta2_type, type, beta2: $o). 70.90/9.67 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 70.90/9.67 thf(setminusT_lem_type, type, setminusT_lem: $o). 70.90/9.67 thf(omegaSAx_type, type, omegaSAx: $o). 70.90/9.67 thf(beta1_type, type, beta1: $o). 70.90/9.67 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o). 70.90/9.67 thf(subbreln1_type, type, subbreln1: $o). 70.90/9.67 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions: 70.90/9.67 $o). 70.90/9.67 thf(demorgan1b_type, type, demorgan1b: $o). 70.90/9.67 thf(setext_type, type, setext: $o). 70.90/9.67 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o). 70.90/9.67 thf(notequalI1_type, type, notequalI1: $o). 70.90/9.67 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o). 70.90/9.67 thf(setextsub_type, type, setextsub: $o). 70.90/9.67 thf(breln1all2_type, type, breln1all2: $o). 70.90/9.67 thf(doubleComplementI1_type, type, doubleComplementI1: $o). 70.90/9.67 thf(kpairp_type, type, kpairp: $o). 70.90/9.67 thf(funcGraphProp3_type, type, funcGraphProp3: $o). 70.90/9.67 thf(demorgan2a1_type, type, demorgan2a1: $o). 70.90/9.67 thf(ap2p_type, type, ap2p: $o). 70.90/9.67 thf(omega__Cong_type, type, omega__Cong: $o). 70.90/9.67 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o). 70.90/9.67 thf(symdiffI2_type, type, symdiffI2: $o). 70.90/9.67 thf(omega_type, type, omega: $i). 70.90/9.67 thf(woz1_2_type, type, woz1_2: $o). 70.90/9.67 thf(setbeta_type, type, setbeta: $o). 70.90/9.67 thf(ap2apEq2_type, type, ap2apEq2: $o). 70.90/9.67 thf(dsetconstrER_type, type, dsetconstrER: $o). 70.90/9.67 thf(funcGraphProp2_type, type, funcGraphProp2: $o). 70.90/9.67 thf(nonemptyE1_type, type, nonemptyE1: $o). 70.90/9.67 thf(binunionIL_type, type, binunionIL: $o). 70.90/9.67 thf(binunionT_lem_type, type, binunionT_lem: $o). 70.90/9.67 thf(prop2setE_type, type, prop2setE: $o). 70.90/9.67 thf(prop2set2propI_type, type, prop2set2propI: $o). 70.90/9.67 thf(notdallE_type, type, notdallE: $o). 70.90/9.67 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o). 70.90/9.67 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 70.90/9.67 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o). 70.90/9.67 thf(exuEu_type, type, exuEu: $o). 70.90/9.67 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 70.90/9.67 thf(notinsingleton_type, type, notinsingleton: $o). 70.90/9.67 thf(iftrueorfalse_type, type, iftrueorfalse: $o). 70.90/9.67 thf(upairsetE_type, type, upairsetE: $o). 70.90/9.67 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o). 70.90/9.67 thf(dpsetconstrER_type, type, dpsetconstrER: $o). 70.90/9.67 thf(complementTI1_type, type, complementTI1: $o). 70.90/9.67 thf(emptyE1_type, type, emptyE1: $o). 70.90/9.67 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 70.90/9.67 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect: 70.90/9.67 $o). 70.90/9.67 thf(cartprodmempair_type, type, cartprodmempair: $o). 70.90/9.67 thf(binunionEcases_type, type, binunionEcases: $o). 70.90/9.67 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o). 70.90/9.67 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 70.90/9.67 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 70.90/9.67 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o). 70.90/9.67 thf(wellorderingAx_type, type, wellorderingAx: $o). 70.90/9.67 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 70.90/9.67 thf(binintersectLsub_type, type, binintersectLsub: $o). 70.90/9.67 thf(binintersectRsub_type, type, binintersectRsub: $o). 70.90/9.67 thf(powersetsubset_type, type, powersetsubset: $o). 70.90/9.67 thf(emptyset_type, type, emptyset: $i). 70.90/9.67 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 70.90/9.67 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 70.90/9.67 thf(woz13rule1_type, type, woz13rule1: $o). 70.90/9.67 thf(exuE1_type, type, exuE1: $o). 70.90/9.67 thf(demorgan1_type, type, demorgan1: $o). 70.90/9.67 thf(inPowerset_type, type, inPowerset: $o). 70.90/9.67 thf(ex1E2_type, type, ex1E2: $o). 70.90/9.67 thf(in_type, type, in: $i > $i > $o). 70.90/9.67 thf(cartprodpairin_type, type, cartprodpairin: $o). 70.90/9.67 thf(setunionI_type, type, setunionI: $o). 70.90/9.67 thf(in__Cong_type, type, in__Cong: $o). 70.90/9.67 thf(demorgan1a_type, type, demorgan1a: $o). 70.90/9.67 thf(setadjoinE_type, type, setadjoinE: $o). 70.90/9.67 thf(subsetTrans_type, type, subsetTrans: $o). 70.90/9.67 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 70.90/9.67 thf(woz1_5_type, type, woz1_5: $o). 70.90/9.67 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 70.90/9.67 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o). 70.90/9.67 thf(contrasubsetT_type, type, contrasubsetT: $o). 70.90/9.67 thf(funcImageSingleton_type, type, funcImageSingleton: $o). 70.90/9.67 thf(setminusIRneg_type, type, setminusIRneg: $o). 70.90/9.67 thf(setminusELneg_type, type, setminusELneg: $o). 70.90/9.67 thf(foundationAx_type, type, foundationAx: $o). 70.90/9.67 thf(iftrueProp1_type, type, iftrueProp1: $o). 70.90/9.67 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement: 70.90/9.67 $o). 70.90/9.67 thf(sepSubset_type, type, sepSubset: $o). 70.90/9.67 thf(breln1compprop_type, type, breln1compprop: $o). 70.90/9.67 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o). 70.90/9.67 thf(iffalseProp2_type, type, iffalseProp2: $o). 70.90/9.67 thf(exuE3u_type, type, exuE3u: $o). 70.90/9.67 thf(kpairiskpair_type, type, kpairiskpair: $o). 70.90/9.67 thf(infuncsetfunc_type, type, infuncsetfunc: $o). 70.90/9.67 thf(binunionTEcontra_type, type, binunionTEcontra: $o). 70.90/9.67 thf(contrasubsetT3_type, type, contrasubsetT3: $o). 70.90/9.67 thf(binintersectT_lem_type, type, binintersectT_lem: $o). 70.90/9.67 thf(setadjoinOr_type, type, setadjoinOr: $o). 70.90/9.67 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o). 70.90/9.67 thf(exuI1_type, type, exuI1: $o). 70.90/9.67 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o). 70.90/9.67 thf(setukpairinjR1_type, type, setukpairinjR1: $o). 70.90/9.67 thf(setukpairinjL_type, type, setukpairinjL: $o). 70.90/9.67 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 70.90/9.67 thf(binunionIR_type, type, binunionIR: $o). 70.90/9.67 thf(inCongP_type, type, inCongP: $o). 70.90/9.67 thf(setminusLsub_type, type, setminusLsub: $o). 70.90/9.67 thf(demorgan2b_type, type, demorgan2b: $o). 70.90/9.67 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o). 70.90/9.67 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 70.90/9.67 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 70.90/9.67 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 70.90/9.67 thf(funcext2_type, type, funcext2: $o). 70.90/9.67 thf(upairequniteq_type, type, upairequniteq: $o). 70.90/9.67 thf(setminusERneg_type, type, setminusERneg: $o). 70.90/9.67 thf(lamp_type, type, lamp: $o). 70.90/9.67 thf(exuI2_type, type, exuI2: $o). 70.90/9.67 thf(powersetI1_type, type, powersetI1: $o). 70.90/9.67 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o). 70.90/9.67 thf(theeq_type, type, theeq: $o). 70.90/9.67 thf(breln1compEex_type, type, breln1compEex: $o). 70.90/9.67 thf(woz1_4_type, type, woz1_4: $o). 70.90/9.67 thf(funcGraphProp4_type, type, funcGraphProp4: $o). 70.90/9.67 thf(breln1all1_type, type, breln1all1: $o). 70.90/9.67 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 70.90/9.67 thf(setminusILneg_type, type, setminusILneg: $o). 70.90/9.67 thf(dsetconstrI_type, type, dsetconstrI: $o). 70.90/9.67 thf(ksndpairEq_type, type, ksndpairEq: $o). 70.90/9.67 thf(setminusEL_type, type, setminusEL: $o). 70.90/9.67 thf(singletonsubset_type, type, singletonsubset: $o). 70.90/9.67 thf(ksndsingleton_type, type, ksndsingleton: $o). 70.90/9.67 thf(theprop_type, type, theprop: $o). 70.90/9.67 thf(secondinupair_type, type, secondinupair: $o). 70.90/9.67 thf(demorgan2_type, type, demorgan2: $o). 70.90/9.67 thf(ex1I_type, type, ex1I: $o). 70.90/9.67 thf(breln_type, type, breln: $i > $i > $i > $o). 70.90/9.67 thf(woz13rule2_type, type, woz13rule2: $o). 70.90/9.67 thf(eqbreln_type, type, eqbreln: $o). 70.90/9.67 thf(subsetTI_type, type, subsetTI: $o). 70.90/9.67 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o). 70.90/9.67 thf(subsetE2_type, type, subsetE2: $o). 70.90/9.67 thf(singletonsswitch_type, type, singletonsswitch: $o). 70.90/9.67 thf(binunionTE_type, type, binunionTE: $o). 70.90/9.67 thf(cartprod_type, type, cartprod: $i > $i > $i). 70.90/9.67 thf(binunionTILcontra_type, type, binunionTILcontra: $o). 70.90/9.67 thf(funcext_type, type, funcext: $o). 70.90/9.67 thf(binintersectEL_type, type, binintersectEL: $o). 70.90/9.67 thf(setadjoinAx_type, type, setadjoinAx: $o). 70.90/9.67 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 70.90/9.67 thf(notinemptyset_type, type, notinemptyset: $o). 70.90/9.67 thf(prop2setI_type, type, prop2setI: $o). 70.90/9.67 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o). 70.90/9.67 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o). 70.90/9.67 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 70.90/9.67 thf(contrasubsetT2_type, type, contrasubsetT2: $o). 70.90/9.67 thf(demorgan2a_type, type, demorgan2a: $o). 70.90/9.67 thf(setunionE2_type, type, setunionE2: $o). 70.90/9.67 thf(subset_type, type, subset: $i > $i > $o). 70.90/9.67 thf(notdexE_type, type, notdexE: $o). 70.90/9.67 thf(kfstsingleton_type, type, kfstsingleton: $o). 70.90/9.67 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 70.90/9.67 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 70.90/9.67 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 70.90/9.67 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 70.90/9.67 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 70.90/9.67 thf(breln1unionprop, conjecture, 70.90/9.67 (( setextAx ) => 70.90/9.67 ( ( emptysetAx ) => 70.90/9.67 ( ( setadjoinAx ) => 70.90/9.67 ( ( powersetAx ) => 70.90/9.67 ( ( setunionAx ) => 70.90/9.67 ( ( omega0Ax ) => 70.90/9.67 ( ( omegaSAx ) => 70.90/9.67 ( ( omegaIndAx ) => 70.90/9.67 ( ( replAx ) => 70.90/9.67 ( ( foundationAx ) => 70.90/9.67 ( ( wellorderingAx ) => 70.90/9.67 ( ( descrp ) => 70.90/9.67 ( ( dsetconstrI ) => 70.90/9.67 ( ( dsetconstrEL ) => 70.90/9.67 ( ( dsetconstrER ) => 70.90/9.67 ( ( exuE1 ) => 70.90/9.67 ( ( prop2setE ) => 70.90/9.67 ( ( emptysetE ) => 70.90/9.67 ( ( emptysetimpfalse ) => 70.90/9.67 ( ( notinemptyset ) => 70.90/9.67 ( ( exuE3e ) => 70.90/9.67 ( ( setext ) => 70.90/9.67 ( ( emptyI ) => 70.90/9.67 ( ( noeltsimpempty ) => 70.90/9.67 ( ( setbeta ) => 70.90/9.67 ( ( nonemptyE1 ) => 70.90/9.67 ( ( nonemptyI ) => 70.90/9.67 ( ( nonemptyI1 ) => 70.90/9.67 ( ( setadjoinIL ) => 70.90/9.67 ( ( emptyinunitempty ) => 70.90/9.67 ( ( setadjoinIR ) => 70.90/9.67 ( ( setadjoinE ) => 70.90/9.67 ( ( 70.90/9.67 setadjoinOr ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setoftrueEq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 powersetI ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 emptyinPowerset ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 emptyInPowerset ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 powersetE ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setunionI ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setunionE ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 subPowSU ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 exuE2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 nonemptyImpWitness ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 uniqinunit ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 notinsingleton ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 eqinunit ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 singletonsswitch ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 upairsetE ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 upairsetIL ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 upairsetIR ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 emptyE1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 vacuousDall ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 quantDeMorgan1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 quantDeMorgan2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 quantDeMorgan3 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 quantDeMorgan4 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 prop2setI ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 prop2set2propI ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 notdexE ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 notdallE ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 exuI1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 exuI3 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 exuI2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 inCongP ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 in__Cong ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 exuE3u ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 exu__Cong ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 emptyset__Cong ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setadjoin__Cong ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 powerset__Cong ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setunion__Cong ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 omega__Cong ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 exuEu ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 descr__Cong ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 dsetconstr__Cong ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 subsetI1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 eqimpsubset2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 eqimpsubset1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 subsetI2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 emptysetsubset ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 subsetE ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 subsetE2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 notsubsetI ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 notequalI1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 notequalI2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 subsetRefl ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 subsetTrans ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setadjoinSub ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setadjoinSub2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 subset2powerset ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setextsub ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 subsetemptysetimpeq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 powersetI1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 powersetE1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 inPowerset ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 powersetsubset ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 sepInPowerset ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 sepSubset ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binunionIL ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 upairset2IR ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binunionIR ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binunionEcases ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binunionE ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binunionLsub ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binunionRsub ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binintersectI ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binintersectSubset5 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binintersectEL ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binintersectLsub ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binintersectSubset2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binintersectSubset3 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binintersectER ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 disjointsetsI1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binintersectRsub ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binintersectSubset4 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binintersectSubset1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 bs114d ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setminusI ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setminusEL ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setminusER ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setminusSubset2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setminusERneg ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setminusELneg ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setminusILneg ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setminusIRneg ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setminusLsub ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setminusSubset1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 symdiffE ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 symdiffI1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 symdiffI2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 symdiffIneg1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 symdiffIneg2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 secondinupair ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setukpairIL ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setukpairIR ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 kpairiskpair ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 kpairp ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 singletonsubset ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 singletoninpowerset ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 singletoninpowunion ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 upairset2E ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 upairsubunion ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 upairinpowunion ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ubforcartprodlem1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ubforcartprodlem2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ubforcartprodlem3 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 cartprodpairin ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 cartprodmempair1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 cartprodmempair ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setunionE2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setunionsingleton1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setunionsingleton2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setunionsingleton ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 singletonprop ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ex1E1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ex1I ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ex1I2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 singletonsuniq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setukpairinjL1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 kfstsingleton ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 theprop ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 kfstpairEq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 cartprodfstin ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setukpairinjL2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setukpairinjL ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setukpairinjR11 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setukpairinjR12 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setukpairinjR1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 upairequniteq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setukpairinjR2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setukpairinjR ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ksndsingleton ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ksndpairEq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 kpairsurjEq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 cartprodsndin ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 cartprodpairmemEL ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 cartprodpairmemER ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 cartprodmempaircEq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 cartprodfstpairEq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 cartprodsndpairEq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 cartprodpairsurjEq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 dpsetconstrI ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 dpsetconstrSub ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setOfPairsIsBReln ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 dpsetconstrERa ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 dpsetconstrEL1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 dpsetconstrEL2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 dpsetconstrER ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 funcImageSingleton ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 apProp ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 app ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 infuncsetfunc ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ap2p ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 funcinfuncset ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 lamProp ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 lamp ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 lam2p ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 brelnall1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 brelnall2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ex1E2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 funcGraphProp1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 funcGraphProp3 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 funcGraphProp2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 funcextLem ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 funcGraphProp4 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 subbreln ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 eqbreln ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 funcext ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 funcext2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ap2apEq1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ap2apEq2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 beta1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 eta1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 lam2lamEq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 beta2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 eta2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 iffalseProp1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 iffalseProp2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 iftrueProp1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 iftrueProp2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ifSingleton ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 ifp ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 theeq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 iftrue ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 iffalse ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 iftrueorfalse ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binintersectT_lem ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binunionT_lem ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 powersetT_lem ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setminusT_lem ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 complementT_lem ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setextT ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 subsetTI ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 powersetTI1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 powersetTE1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 complementTI1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 complementTE1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binintersectTELcontra ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binintersectTERcontra ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 contrasubsetT ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 contrasubsetT1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 contrasubsetT2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 contrasubsetT3 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 doubleComplementI1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 doubleComplementE1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 doubleComplementSub1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 doubleComplementSub2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 doubleComplementEq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 complementTnotintersectT ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 complementImpComplementIntersect ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 complementSubsetComplementIntersect ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 complementInPowersetComplementIntersect ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 contraSubsetComplement ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 complementTcontraSubset ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binunionTILcontra ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binunionTIRcontra ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 inIntersectImpInUnion ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 inIntersectImpInUnion2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 inIntersectImpInIntersectUnions ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 intersectInPowersetIntersectUnions ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 inComplementUnionImpNotIn1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 inComplementUnionImpInComplement1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binunionTE ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 binunionTEcontra ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 demorgan2a1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 complementUnionInPowersetComplement ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 demorgan2a2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 demorgan1a ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 demorgan1b ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 demorgan1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 demorgan2a ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 demorgan2b2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 demorgan2b ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 demorgan2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 woz13rule0 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 woz13rule1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 woz13rule2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 woz13rule3 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 woz13rule4 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 woz1_1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 woz1_2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 woz1_3 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 woz1_4 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 woz1_5 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 breln1all2 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 breln1SetBreln1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 choice2fnsingleton ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setOfPairsIsBReln1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 breln1all1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 subbreln1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 eqbreln1 ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 breln1invprop ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 breln1invI ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 breln1invE ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 breln1compprop ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 breln1compI ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 breln1compE ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 breln1compEex ) => 70.90/9.67 ( 70.90/9.67 ![ 70.90/9.67 A:$i,R:$i]: 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 breln1 @ 70.90/9.67 A @ R ) => 70.90/9.67 ( 70.90/9.67 ![ 70.90/9.67 S:$i]: 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 breln1 @ 70.90/9.67 A @ S ) => 70.90/9.67 ( 70.90/9.67 breln1 @ 70.90/9.67 A @ 70.90/9.67 ( 70.90/9.67 binunion @ 70.90/9.67 R @ S ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 70.90/9.67 thf(zf_stmt_0, negated_conjecture, 70.90/9.67 (~( ( setextAx ) => 70.90/9.67 ( ( emptysetAx ) => 70.90/9.67 ( ( setadjoinAx ) => 70.90/9.67 ( ( powersetAx ) => 70.90/9.67 ( ( setunionAx ) => 70.90/9.67 ( ( omega0Ax ) => 70.90/9.67 ( ( omegaSAx ) => 70.90/9.67 ( ( omegaIndAx ) => 70.90/9.67 ( ( replAx ) => 70.90/9.67 ( ( foundationAx ) => 70.90/9.67 ( ( wellorderingAx ) => 70.90/9.67 ( ( descrp ) => 70.90/9.67 ( ( dsetconstrI ) => 70.90/9.67 ( ( dsetconstrEL ) => 70.90/9.67 ( ( dsetconstrER ) => 70.90/9.67 ( ( exuE1 ) => 70.90/9.67 ( ( prop2setE ) => 70.90/9.67 ( ( emptysetE ) => 70.90/9.67 ( ( emptysetimpfalse ) => 70.90/9.67 ( ( notinemptyset ) => 70.90/9.67 ( ( exuE3e ) => 70.90/9.67 ( ( setext ) => 70.90/9.67 ( ( emptyI ) => 70.90/9.67 ( ( noeltsimpempty ) => 70.90/9.67 ( ( setbeta ) => 70.90/9.67 ( ( nonemptyE1 ) => 70.90/9.67 ( ( nonemptyI ) => 70.90/9.67 ( ( nonemptyI1 ) => 70.90/9.67 ( ( setadjoinIL ) => 70.90/9.67 ( ( emptyinunitempty ) => 70.90/9.67 ( ( setadjoinIR ) => 70.90/9.67 ( ( 70.90/9.67 setadjoinE ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setadjoinOr ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.67 setoftrueEq ) => 70.90/9.67 ( 70.90/9.67 ( 70.90/9.68 powersetI ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 emptyinPowerset ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 emptyInPowerset ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 powersetE ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setunionI ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setunionE ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 subPowSU ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 exuE2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 nonemptyImpWitness ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 uniqinunit ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 notinsingleton ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 eqinunit ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 singletonsswitch ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 upairsetE ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 upairsetIL ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 upairsetIR ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 emptyE1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 vacuousDall ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 quantDeMorgan1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 quantDeMorgan2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 quantDeMorgan3 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 quantDeMorgan4 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 prop2setI ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 prop2set2propI ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 notdexE ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 notdallE ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 exuI1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 exuI3 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 exuI2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 inCongP ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 in__Cong ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 exuE3u ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 exu__Cong ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 emptyset__Cong ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setadjoin__Cong ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 powerset__Cong ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setunion__Cong ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 omega__Cong ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 exuEu ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 descr__Cong ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 dsetconstr__Cong ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 subsetI1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 eqimpsubset2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 eqimpsubset1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 subsetI2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 emptysetsubset ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 subsetE ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 subsetE2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 notsubsetI ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 notequalI1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 notequalI2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 subsetRefl ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 subsetTrans ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setadjoinSub ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setadjoinSub2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 subset2powerset ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setextsub ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 subsetemptysetimpeq ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 powersetI1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 powersetE1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 inPowerset ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 powersetsubset ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 sepInPowerset ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 sepSubset ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binunionIL ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 upairset2IR ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binunionIR ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binunionEcases ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binunionE ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binunionLsub ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binunionRsub ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binintersectI ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binintersectSubset5 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binintersectEL ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binintersectLsub ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binintersectSubset2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binintersectSubset3 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binintersectER ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 disjointsetsI1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binintersectRsub ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binintersectSubset4 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binintersectSubset1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 bs114d ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setminusI ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setminusEL ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setminusER ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setminusSubset2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setminusERneg ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setminusELneg ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setminusILneg ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setminusIRneg ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setminusLsub ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setminusSubset1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 symdiffE ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 symdiffI1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 symdiffI2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 symdiffIneg1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 symdiffIneg2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 secondinupair ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setukpairIL ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setukpairIR ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 kpairiskpair ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 kpairp ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 singletonsubset ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 singletoninpowerset ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 singletoninpowunion ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 upairset2E ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 upairsubunion ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 upairinpowunion ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ubforcartprodlem1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ubforcartprodlem2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ubforcartprodlem3 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 cartprodpairin ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 cartprodmempair1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 cartprodmempair ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setunionE2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setunionsingleton1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setunionsingleton2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setunionsingleton ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 singletonprop ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ex1E1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ex1I ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ex1I2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 singletonsuniq ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setukpairinjL1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 kfstsingleton ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 theprop ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 kfstpairEq ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 cartprodfstin ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setukpairinjL2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setukpairinjL ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setukpairinjR11 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setukpairinjR12 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setukpairinjR1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 upairequniteq ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setukpairinjR2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setukpairinjR ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ksndsingleton ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ksndpairEq ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 kpairsurjEq ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 cartprodsndin ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 cartprodpairmemEL ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 cartprodpairmemER ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 cartprodmempaircEq ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 cartprodfstpairEq ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 cartprodsndpairEq ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 cartprodpairsurjEq ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 dpsetconstrI ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 dpsetconstrSub ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setOfPairsIsBReln ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 dpsetconstrERa ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 dpsetconstrEL1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 dpsetconstrEL2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 dpsetconstrER ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 funcImageSingleton ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 apProp ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 app ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 infuncsetfunc ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ap2p ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 funcinfuncset ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 lamProp ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 lamp ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 lam2p ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 brelnall1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 brelnall2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ex1E2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 funcGraphProp1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 funcGraphProp3 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 funcGraphProp2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 funcextLem ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 funcGraphProp4 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 subbreln ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 eqbreln ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 funcext ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 funcext2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ap2apEq1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ap2apEq2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 beta1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 eta1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 lam2lamEq ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 beta2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 eta2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 iffalseProp1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 iffalseProp2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 iftrueProp1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 iftrueProp2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ifSingleton ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 ifp ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 theeq ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 iftrue ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 iffalse ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 iftrueorfalse ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binintersectT_lem ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binunionT_lem ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 powersetT_lem ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setminusT_lem ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 complementT_lem ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 setextT ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 subsetTI ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 powersetTI1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 powersetTE1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 complementTI1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 complementTE1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binintersectTELcontra ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binintersectTERcontra ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 contrasubsetT ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 contrasubsetT1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 contrasubsetT2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 contrasubsetT3 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 doubleComplementI1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 doubleComplementE1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 doubleComplementSub1 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 doubleComplementSub2 ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 doubleComplementEq ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 complementTnotintersectT ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 complementImpComplementIntersect ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 complementSubsetComplementIntersect ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 complementInPowersetComplementIntersect ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 contraSubsetComplement ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 complementTcontraSubset ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binunionTILcontra ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 binunionTIRcontra ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 inIntersectImpInUnion ) => 70.90/9.68 ( 70.90/9.68 ( 70.90/9.68 inIntersectImpInUnion2 ) => 70.90/9.68 ( 70.90/9.68 ( 71.20/9.68 inIntersectImpInIntersectUnions ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 intersectInPowersetIntersectUnions ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 inComplementUnionImpNotIn1 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 inComplementUnionImpInComplement1 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 binunionTE ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 binunionTEcontra ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 demorgan2a1 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 complementUnionInPowersetComplement ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 demorgan2a2 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 demorgan1a ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 demorgan1b ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 demorgan1 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 demorgan2a ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 demorgan2b2 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 demorgan2b ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 demorgan2 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 woz13rule0 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 woz13rule1 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 woz13rule2 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 woz13rule3 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 woz13rule4 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 woz1_1 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 woz1_2 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 woz1_3 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 woz1_4 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 woz1_5 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 breln1all2 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 breln1SetBreln1 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 choice2fnsingleton ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 setOfPairsIsBReln1 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 breln1all1 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 subbreln1 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 eqbreln1 ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 breln1invprop ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 breln1invI ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 breln1invE ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 breln1compprop ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 breln1compI ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 breln1compE ) => 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 breln1compEex ) => 71.20/9.68 ( 71.20/9.68 ![ 71.20/9.68 A:$i,R:$i]: 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 breln1 @ 71.20/9.68 A @ R ) => 71.20/9.68 ( 71.20/9.68 ![ 71.20/9.68 S:$i]: 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 breln1 @ 71.20/9.68 A @ S ) => 71.20/9.68 ( 71.20/9.68 breln1 @ 71.20/9.68 A @ 71.20/9.68 ( 71.20/9.68 binunion 71.20/9.68 @ 71.20/9.68 R @ S ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 71.20/9.68 inference('cnf.neg', [status(esa)], [breln1unionprop])). 71.20/9.68 thf(zip_derived_cl0, plain, 71.20/9.68 (~ (((setextAx) => 71.20/9.68 (((emptysetAx) => 71.20/9.68 (((setadjoinAx) => 71.20/9.68 (((powersetAx) => 71.20/9.68 (((setunionAx) => 71.20/9.68 (((omega0Ax) => 71.20/9.68 (((omegaSAx) => 71.20/9.68 (((omegaIndAx) => 71.20/9.68 (((replAx) => 71.20/9.68 (((foundationAx) => 71.20/9.68 (((wellorderingAx) => 71.20/9.68 (((descrp) => 71.20/9.68 (((dsetconstrI) => 71.20/9.68 (((dsetconstrEL) => 71.20/9.68 (((dsetconstrER) => 71.20/9.68 (((exuE1) => 71.20/9.68 (((prop2setE) => 71.20/9.68 (((emptysetE) => 71.20/9.68 (((emptysetimpfalse) => 71.20/9.68 (((notinemptyset) => 71.20/9.68 (((exuE3e) => 71.20/9.68 (((setext) => 71.20/9.68 (((emptyI) => 71.20/9.68 (((noeltsimpempty) => 71.20/9.68 (((setbeta) => 71.20/9.68 (((nonemptyE1) => 71.20/9.68 (((nonemptyI) => 71.20/9.68 (((nonemptyI1) => 71.20/9.68 (((setadjoinIL) => 71.20/9.68 (((emptyinunitempty) => 71.20/9.68 (( 71.20/9.68 (setadjoinIR) => 71.20/9.68 (( 71.20/9.68 (setadjoinE) => 71.20/9.68 (( 71.20/9.68 (setadjoinOr) => 71.20/9.68 (( 71.20/9.68 (setoftrueEq) => 71.20/9.68 (( 71.20/9.68 (powersetI) => 71.20/9.68 (( 71.20/9.68 (emptyinPowerset) => 71.20/9.68 (( 71.20/9.68 (emptyInPowerset) => 71.20/9.68 (( 71.20/9.68 (powersetE) => 71.20/9.68 (( 71.20/9.68 (setunionI) => 71.20/9.68 (( 71.20/9.68 (setunionE) => 71.20/9.68 (( 71.20/9.68 (subPowSU) => 71.20/9.68 (( 71.20/9.68 (exuE2) => 71.20/9.68 (( 71.20/9.68 (nonemptyImpWitness) => 71.20/9.68 (( 71.20/9.68 (uniqinunit) => 71.20/9.68 (( 71.20/9.68 (notinsingleton) => 71.20/9.68 (( 71.20/9.68 (eqinunit) => 71.20/9.68 (( 71.20/9.68 (singletonsswitch) => 71.20/9.68 (( 71.20/9.68 (upairsetE) => 71.20/9.68 (( 71.20/9.68 (upairsetIL) => 71.20/9.68 (( 71.20/9.68 (upairsetIR) => 71.20/9.68 (( 71.20/9.68 (emptyE1) => 71.20/9.68 (( 71.20/9.68 (vacuousDall) => 71.20/9.68 (( 71.20/9.68 (quantDeMorgan1) => 71.20/9.68 (( 71.20/9.68 (quantDeMorgan2) => 71.20/9.68 (( 71.20/9.68 (quantDeMorgan3) => 71.20/9.68 (( 71.20/9.68 (quantDeMorgan4) => 71.20/9.68 (( 71.20/9.68 (prop2setI) => 71.20/9.68 (( 71.20/9.68 (prop2set2propI) => 71.20/9.68 (( 71.20/9.68 (notdexE) => 71.20/9.68 (( 71.20/9.68 (notdallE) => 71.20/9.68 (( 71.20/9.68 (exuI1) => 71.20/9.68 (( 71.20/9.68 (exuI3) => 71.20/9.68 (( 71.20/9.68 (exuI2) => 71.20/9.68 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71.20/9.68 (((wellorderingAx) => 71.20/9.68 (((descrp) => 71.20/9.68 (((dsetconstrI) => 71.20/9.68 (((dsetconstrEL) => 71.20/9.68 (((dsetconstrER) => 71.20/9.68 (((exuE1) => 71.20/9.68 (((prop2setE) => 71.20/9.68 (((emptysetE) => 71.20/9.68 (((emptysetimpfalse) => 71.20/9.68 (((notinemptyset) => 71.20/9.68 (((exuE3e) => 71.20/9.68 (((setext) => 71.20/9.68 (((emptyI) => 71.20/9.68 (((noeltsimpempty) => 71.20/9.68 (((setbeta) => 71.20/9.68 (((nonemptyE1) => 71.20/9.68 (((nonemptyI) => 71.20/9.68 (((nonemptyI1) => 71.20/9.68 (((setadjoinIL) => 71.20/9.68 (((emptyinunitempty) => 71.20/9.68 (( 71.20/9.68 (setadjoinIR) => 71.20/9.68 (( 71.20/9.68 (setadjoinE) => 71.20/9.68 (( 71.20/9.68 (setadjoinOr) => 71.20/9.68 (( 71.20/9.68 (setoftrueEq) => 71.20/9.68 (( 71.20/9.68 (powersetI) => 71.20/9.68 (( 71.20/9.68 (emptyinPowerset) => 71.20/9.68 (( 71.20/9.68 (emptyInPowerset) => 71.20/9.68 (( 71.20/9.68 (powersetE) => 71.20/9.68 (( 71.20/9.68 (setunionI) => 71.20/9.68 (( 71.20/9.68 (setunionE) => 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71.20/9.68 (in__Cong) => 71.20/9.68 (( 71.20/9.68 (exuE3u) => 71.20/9.68 (( 71.20/9.68 (exu__Cong) => 71.20/9.68 (( 71.20/9.68 (emptyset__Cong) => 71.20/9.68 (( 71.20/9.68 (setadjoin__Cong) => 71.20/9.68 (( 71.20/9.68 (powerset__Cong) => 71.20/9.68 (( 71.20/9.68 (setunion__Cong) => 71.20/9.68 (( 71.20/9.68 (omega__Cong) => 71.20/9.68 (( 71.20/9.68 (exuEu) => 71.20/9.68 (( 71.20/9.68 (descr__Cong) => 71.20/9.68 (( 71.20/9.68 (dsetconstr__Cong) => 71.20/9.68 (( 71.20/9.68 (subsetI1) => 71.20/9.68 (( 71.20/9.68 (eqimpsubset2) => 71.20/9.68 (( 71.20/9.68 (eqimpsubset1) => 71.20/9.68 (( 71.20/9.68 (subsetI2) => 71.20/9.68 (( 71.20/9.68 (emptysetsubset) => 71.20/9.68 (( 71.20/9.68 (subsetE) => 71.20/9.68 (( 71.20/9.68 (subsetE2) => 71.20/9.68 (( 71.20/9.68 (notsubsetI) => 71.20/9.68 (( 71.20/9.68 (notequalI1) => 71.20/9.68 (( 71.20/9.68 (notequalI2) => 71.20/9.68 (( 71.20/9.68 (subsetRefl) => 71.20/9.68 (( 71.20/9.68 (subsetTrans) => 71.20/9.68 (( 71.20/9.68 (setadjoinSub) => 71.20/9.68 (( 71.20/9.68 (setadjoinSub2) => 71.20/9.68 (( 71.20/9.68 (subset2powerset) => 71.20/9.68 (( 71.20/9.68 (setextsub) => 71.20/9.68 (( 71.20/9.68 (subsetemptysetimpeq) => 71.20/9.68 (( 71.20/9.68 (powersetI1) => 71.20/9.68 (( 71.20/9.68 (powersetE1) => 71.20/9.68 (( 71.20/9.68 (inPowerset) => 71.20/9.68 (( 71.20/9.68 (powersetsubset) => 71.20/9.68 (( 71.20/9.68 (sepInPowerset) => 71.20/9.68 (( 71.20/9.68 (sepSubset) => 71.20/9.68 (( 71.20/9.68 (binunionIL) => 71.20/9.68 (( 71.20/9.68 (upairset2IR) => 71.20/9.68 (( 71.20/9.68 (binunionIR) => 71.20/9.68 (( 71.20/9.68 (binunionEcases) => 71.20/9.68 (( 71.20/9.68 (binunionE) => 71.20/9.68 (( 71.20/9.68 (binunionLsub) => 71.20/9.68 (( 71.20/9.68 (binunionRsub) => 71.20/9.68 (( 71.20/9.68 (binintersectI) => 71.20/9.68 (( 71.20/9.68 (binintersectSubset5) => 71.20/9.68 (( 71.20/9.68 (binintersectEL) => 71.20/9.68 (( 71.20/9.68 (binintersectLsub) => 71.20/9.68 (( 71.20/9.68 (binintersectSubset2) => 71.20/9.68 (( 71.20/9.68 (binintersectSubset3) => 71.20/9.68 (( 71.20/9.68 (binintersectER) => 71.20/9.68 (( 71.20/9.68 (disjointsetsI1) => 71.20/9.68 (( 71.20/9.68 (binintersectRsub) => 71.20/9.68 (( 71.20/9.68 (binintersectSubset4) => 71.20/9.68 (( 71.20/9.68 (binintersectSubset1) => 71.20/9.68 (( 71.20/9.68 (bs114d) => 71.20/9.68 (( 71.20/9.68 (setminusI) => 71.20/9.68 (( 71.20/9.68 (setminusEL) => 71.20/9.68 (( 71.20/9.68 (setminusER) => 71.20/9.68 (( 71.20/9.68 (setminusSubset2) => 71.20/9.68 (( 71.20/9.68 (setminusERneg) => 71.20/9.68 (( 71.20/9.68 (setminusELneg) => 71.20/9.68 (( 71.20/9.68 (setminusILneg) => 71.20/9.68 (( 71.20/9.68 (setminusIRneg) => 71.20/9.68 (( 71.20/9.68 (setminusLsub) => 71.20/9.68 (( 71.20/9.68 (setminusSubset1) => 71.20/9.68 (( 71.20/9.68 (symdiffE) => 71.20/9.68 (( 71.20/9.68 (symdiffI1) => 71.20/9.68 (( 71.20/9.68 (symdiffI2) => 71.20/9.68 (( 71.20/9.68 (symdiffIneg1) => 71.20/9.68 (( 71.20/9.68 (symdiffIneg2) => 71.20/9.68 (( 71.20/9.68 (secondinupair) => 71.20/9.68 (( 71.20/9.68 (setukpairIL) => 71.20/9.68 (( 71.20/9.68 (setukpairIR) => 71.20/9.68 (( 71.20/9.68 (kpairiskpair) => 71.20/9.68 (( 71.20/9.68 (kpairp) => 71.20/9.68 (( 71.20/9.68 (singletonsubset) => 71.20/9.68 (( 71.20/9.68 (singletoninpowerset) => 71.20/9.68 (( 71.20/9.68 (singletoninpowunion) => 71.20/9.68 (( 71.20/9.68 (upairset2E) => 71.20/9.68 (( 71.20/9.68 (upairsubunion) => 71.20/9.68 (( 71.20/9.68 (upairinpowunion) => 71.20/9.68 (( 71.20/9.68 (ubforcartprodlem1) => 71.20/9.68 (( 71.20/9.68 (ubforcartprodlem2) => 71.20/9.68 (( 71.20/9.68 (ubforcartprodlem3) => 71.20/9.68 (( 71.20/9.68 (cartprodpairin) => 71.20/9.68 (( 71.20/9.68 (cartprodmempair1) => 71.20/9.68 (( 71.20/9.68 (cartprodmempair) => 71.20/9.68 (( 71.20/9.68 (setunionE2) => 71.20/9.68 (( 71.20/9.68 (setunionsingleton1) => 71.20/9.68 (( 71.20/9.68 (setunionsingleton2) => 71.20/9.68 (( 71.20/9.68 (setunionsingleton) => 71.20/9.68 (( 71.20/9.68 (singletonprop) => 71.20/9.68 (( 71.20/9.68 (ex1E1) => 71.20/9.68 (( 71.20/9.68 (ex1I) => 71.20/9.68 (( 71.20/9.68 (ex1I2) => 71.20/9.68 (( 71.20/9.68 (singletonsuniq) => 71.20/9.68 (( 71.20/9.68 (setukpairinjL1) => 71.20/9.68 (( 71.20/9.68 (kfstsingleton) => 71.20/9.68 (( 71.20/9.68 (theprop) => 71.20/9.68 (( 71.20/9.68 (kfstpairEq) => 71.20/9.68 (( 71.20/9.68 (cartprodfstin) => 71.20/9.68 (( 71.20/9.68 (setukpairinjL2) => 71.20/9.68 (( 71.20/9.68 (setukpairinjL) => 71.20/9.68 (( 71.20/9.68 (setukpairinjR11) => 71.20/9.68 (( 71.20/9.68 (setukpairinjR12) => 71.20/9.68 (( 71.20/9.68 (setukpairinjR1) => 71.20/9.68 (( 71.20/9.68 (upairequniteq) => 71.20/9.68 (( 71.20/9.68 (setukpairinjR2) => 71.20/9.68 (( 71.20/9.68 (setukpairinjR) => 71.20/9.68 (( 71.20/9.68 (ksndsingleton) => 71.20/9.68 (( 71.20/9.68 (ksndpairEq) => 71.20/9.68 (( 71.20/9.68 (kpairsurjEq) => 71.20/9.68 (( 71.20/9.68 (cartprodsndin) => 71.20/9.68 (( 71.20/9.68 (cartprodpairmemEL) => 71.20/9.68 (( 71.20/9.68 (cartprodpairmemER) => 71.20/9.68 (( 71.20/9.68 (cartprodmempaircEq) => 71.20/9.68 (( 71.20/9.68 (cartprodfstpairEq) => 71.20/9.68 (( 71.20/9.68 (cartprodsndpairEq) => 71.20/9.68 (( 71.20/9.68 (cartprodpairsurjEq) => 71.20/9.68 (( 71.20/9.68 (dpsetconstrI) => 71.20/9.68 (( 71.20/9.68 (dpsetconstrSub) => 71.20/9.68 (( 71.20/9.68 (setOfPairsIsBReln) => 71.20/9.68 (( 71.20/9.68 (dpsetconstrERa) => 71.20/9.68 (( 71.20/9.68 (dpsetconstrEL1) => 71.20/9.68 (( 71.20/9.68 (dpsetconstrEL2) => 71.20/9.68 (( 71.20/9.68 (dpsetconstrER) => 71.20/9.68 (( 71.20/9.68 (funcImageSingleton) => 71.20/9.68 (( 71.20/9.68 (apProp) => 71.20/9.68 (( 71.20/9.68 (app) => 71.20/9.68 (( 71.20/9.68 (infuncsetfunc) => 71.20/9.68 (( 71.20/9.68 (ap2p) => 71.20/9.68 (( 71.20/9.68 (funcinfuncset) => 71.20/9.68 (( 71.20/9.68 (lamProp) => 71.20/9.68 (( 71.20/9.68 (lamp) => 71.20/9.68 (( 71.20/9.68 (lam2p) => 71.20/9.68 (( 71.20/9.68 (brelnall1) => 71.20/9.68 (( 71.20/9.68 (brelnall2) => 71.20/9.68 (( 71.20/9.68 (ex1E2) => 71.20/9.68 (( 71.20/9.68 (funcGraphProp1) => 71.20/9.68 (( 71.20/9.68 (funcGraphProp3) => 71.20/9.68 (( 71.20/9.68 (funcGraphProp2) => 71.20/9.68 (( 71.20/9.68 (funcextLem) => 71.20/9.68 (( 71.20/9.68 (funcGraphProp4) => 71.20/9.68 (( 71.20/9.68 (subbreln) => 71.20/9.68 (( 71.20/9.68 (eqbreln) => 71.20/9.68 (( 71.20/9.68 (funcext) => 71.20/9.68 (( 71.20/9.68 (funcext2) => 71.20/9.68 (( 71.20/9.68 (ap2apEq1) => 71.20/9.68 (( 71.20/9.68 (ap2apEq2) => 71.20/9.68 (( 71.20/9.68 (beta1) => 71.20/9.68 (( 71.20/9.68 (eta1) => 71.20/9.68 (( 71.20/9.68 (lam2lamEq) => 71.20/9.68 (( 71.20/9.68 (beta2) => 71.20/9.68 (( 71.20/9.68 (eta2) => 71.20/9.68 (( 71.20/9.68 (iffalseProp1) => 71.20/9.68 (( 71.20/9.68 (iffalseProp2) => 71.20/9.68 (( 71.20/9.68 (iftrueProp1) => 71.20/9.68 (( 71.20/9.68 (iftrueProp2) => 71.20/9.68 (( 71.20/9.68 (ifSingleton) => 71.20/9.68 (( 71.20/9.68 (ifp) => 71.20/9.68 (( 71.20/9.68 (theeq) => 71.20/9.68 (( 71.20/9.68 (iftrue) => 71.20/9.68 (( 71.20/9.68 (iffalse) => 71.20/9.68 (( 71.20/9.68 (iftrueorfalse) => 71.20/9.68 (( 71.20/9.68 (binintersectT_lem) => 71.20/9.68 (( 71.20/9.68 (binunionT_lem) => 71.20/9.68 (( 71.20/9.68 (powersetT_lem) => 71.20/9.68 (( 71.20/9.68 (setminusT_lem) => 71.20/9.68 (( 71.20/9.68 (complementT_lem) => 71.20/9.68 (( 71.20/9.68 (setextT) => 71.20/9.68 (( 71.20/9.68 (subsetTI) => 71.20/9.68 (( 71.20/9.68 (powersetTI1) => 71.20/9.68 (( 71.20/9.68 (powersetTE1) => 71.20/9.68 (( 71.20/9.68 (complementTI1) => 71.20/9.68 (( 71.20/9.68 (complementTE1) => 71.20/9.68 (( 71.20/9.68 (binintersectTELcontra) => 71.20/9.68 (( 71.20/9.68 (binintersectTERcontra) => 71.20/9.68 (( 71.20/9.68 (contrasubsetT) => 71.20/9.68 (( 71.20/9.68 (contrasubsetT1) => 71.20/9.68 (( 71.20/9.68 (contrasubsetT2) => 71.20/9.68 (( 71.20/9.68 (contrasubsetT3) => 71.20/9.68 (( 71.20/9.68 (doubleComplementI1) => 71.20/9.68 (( 71.20/9.68 (doubleComplementE1) => 71.20/9.68 (( 71.20/9.68 (doubleComplementSub1) => 71.20/9.68 (( 71.20/9.68 (doubleComplementSub2) => 71.20/9.68 (( 71.20/9.68 (doubleComplementEq) => 71.20/9.68 (( 71.20/9.68 (complementTnotintersectT) => 71.20/9.68 (( 71.20/9.68 (complementImpComplementIntersect) => 71.20/9.68 (( 71.20/9.68 (complementSubsetComplementIntersect) => 71.20/9.68 (( 71.20/9.68 (complementInPowersetComplementIntersect) => 71.20/9.68 (( 71.20/9.68 (contraSubsetComplement) => 71.20/9.68 (( 71.20/9.68 (complementTcontraSubset) => 71.20/9.68 (( 71.20/9.68 (binunionTILcontra) => 71.20/9.68 (( 71.20/9.68 (binunionTIRcontra) => 71.20/9.68 (( 71.20/9.68 (inIntersectImpInUnion) => 71.20/9.68 (( 71.20/9.68 (inIntersectImpInUnion2) => 71.20/9.68 (( 71.20/9.68 (inIntersectImpInIntersectUnions) => 71.20/9.68 (( 71.20/9.68 (intersectInPowersetIntersectUnions) => 71.20/9.68 (( 71.20/9.68 (inComplementUnionImpNotIn1) => 71.20/9.68 (( 71.20/9.68 (inComplementUnionImpInComplement1) => 71.20/9.68 (( 71.20/9.68 (binunionTE) => 71.20/9.68 (( 71.20/9.68 (binunionTEcontra) => 71.20/9.68 (( 71.20/9.68 (demorgan2a1) => 71.20/9.68 (( 71.20/9.68 (complementUnionInPowersetComplement) => 71.20/9.68 (( 71.20/9.68 (demorgan2a2) => 71.20/9.68 (( 71.20/9.68 (demorgan1a) => 71.20/9.68 (( 71.20/9.68 (demorgan1b) => 71.20/9.68 (( 71.20/9.68 (demorgan1) => 71.20/9.68 (( 71.20/9.68 (demorgan2a) => 71.20/9.68 (( 71.20/9.68 (demorgan2b2) => 71.20/9.68 (( 71.20/9.68 (demorgan2b) => 71.20/9.68 (( 71.20/9.68 (demorgan2) => 71.20/9.68 (( 71.20/9.68 (woz13rule0) => 71.20/9.68 (( 71.20/9.68 (woz13rule1) => 71.20/9.68 (( 71.20/9.68 (woz13rule2) => 71.20/9.68 (( 71.20/9.68 (woz13rule3) => 71.20/9.68 (( 71.20/9.68 (woz13rule4) => 71.20/9.68 (( 71.20/9.68 (woz1_1) => 71.20/9.68 (( 71.20/9.68 (woz1_2) => 71.20/9.68 (( 71.20/9.68 (woz1_3) => 71.20/9.68 (( 71.20/9.68 (woz1_4) => 71.20/9.68 (( 71.20/9.68 (woz1_5) => 71.20/9.68 (( 71.20/9.68 (breln1all2) => 71.20/9.68 (( 71.20/9.68 (breln1SetBreln1) => 71.20/9.68 (( 71.20/9.68 (choice2fnsingleton) => 71.20/9.68 (( 71.20/9.68 (setOfPairsIsBReln1) => 71.20/9.68 (( 71.20/9.68 (breln1all1) => 71.20/9.68 (( 71.20/9.68 (subbreln1) => 71.20/9.68 (( 71.20/9.68 (eqbreln1) => 71.20/9.68 (( 71.20/9.68 (breln1invprop) => 71.20/9.68 (( 71.20/9.68 (breln1invI) => 71.20/9.68 (( 71.20/9.68 (breln1invE) => 71.20/9.68 (( 71.20/9.68 (breln1compprop) => 71.20/9.68 (( 71.20/9.68 (breln1compI) => 71.20/9.68 (( 71.20/9.68 (breln1compE) => 71.20/9.68 (( 71.20/9.68 (breln1compEex) => 71.20/9.68 (( 71.20/9.68 (!!) @ ( 71.20/9.68 (('#B') @ ( 71.20/9.68 !!) @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#S') @ ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 '#S') @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 =>))) @ 71.20/9.68 breln1)))) @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 !!))) @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#S') @ ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 '#B') @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 '#S') @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 =>))) @ 71.20/9.68 breln1)))))) @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#C') @ ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 '#B') @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 '#B') @ 71.20/9.68 breln1)))) @ 71.20/9.68 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.68 inference('lams2combs', [status(thm)], [zip_derived_cl0])). 71.20/9.68 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))). 71.20/9.68 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )), 71.20/9.68 define([status(thm)])). 71.20/9.68 thf(emptyinunitempty, axiom,(( emptyinunitempty ) = 71.20/9.68 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))). 71.20/9.68 thf('1', plain, 71.20/9.68 (( emptyinunitempty ) = 71.20/9.68 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )), 71.20/9.68 define([status(thm)])). 71.20/9.68 thf(emptyset__Cong, axiom,(( emptyset__Cong ) = 71.20/9.68 ((((emptyset) = (emptyset)))))). 71.20/9.68 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )), 71.20/9.68 define([status(thm)])). 71.20/9.68 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))). 71.20/9.68 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )), 71.20/9.68 define([status(thm)])). 71.20/9.68 thf(zip_derived_cl2, plain, 71.20/9.68 (~ (((setextAx) => 71.20/9.68 (((emptysetAx) => 71.20/9.68 (((setadjoinAx) => 71.20/9.68 (((powersetAx) => 71.20/9.68 (((setunionAx) => 71.20/9.68 (((in @ emptyset @ omega) => 71.20/9.68 (((omegaSAx) => 71.20/9.68 (((omegaIndAx) => 71.20/9.68 (((replAx) => 71.20/9.68 (((foundationAx) => 71.20/9.68 (((wellorderingAx) => 71.20/9.68 (((descrp) => 71.20/9.68 (((dsetconstrI) => 71.20/9.68 (((dsetconstrEL) => 71.20/9.68 (((dsetconstrER) => 71.20/9.68 (((exuE1) => 71.20/9.68 (((prop2setE) => 71.20/9.68 (((emptysetE) => 71.20/9.68 (((emptysetimpfalse) => 71.20/9.68 (((notinemptyset) => 71.20/9.68 (((exuE3e) => 71.20/9.68 (((setext) => 71.20/9.68 (((emptyI) => 71.20/9.68 (((noeltsimpempty) => 71.20/9.68 (((setbeta) => 71.20/9.68 (((nonemptyE1) => 71.20/9.68 (((nonemptyI) => 71.20/9.68 (((nonemptyI1) => 71.20/9.68 (((setadjoinIL) => 71.20/9.68 (((in @ 71.20/9.68 emptyset @ 71.20/9.68 (setadjoin @ 71.20/9.68 emptyset @ 71.20/9.68 emptyset)) => 71.20/9.68 (( 71.20/9.68 (setadjoinIR) => 71.20/9.68 (( 71.20/9.68 (setadjoinE) => 71.20/9.68 (( 71.20/9.68 (setadjoinOr) => 71.20/9.68 (( 71.20/9.68 (setoftrueEq) => 71.20/9.68 (( 71.20/9.68 (powersetI) => 71.20/9.68 (( 71.20/9.68 (emptyinPowerset) => 71.20/9.68 (( 71.20/9.68 (emptyInPowerset) => 71.20/9.68 (( 71.20/9.68 (powersetE) => 71.20/9.68 (( 71.20/9.68 (setunionI) => 71.20/9.68 (( 71.20/9.68 (setunionE) => 71.20/9.68 (( 71.20/9.68 (subPowSU) => 71.20/9.68 (( 71.20/9.68 (exuE2) => 71.20/9.68 (( 71.20/9.68 (nonemptyImpWitness) => 71.20/9.68 (( 71.20/9.68 (uniqinunit) => 71.20/9.68 (( 71.20/9.68 (notinsingleton) => 71.20/9.68 (( 71.20/9.68 (eqinunit) => 71.20/9.68 (( 71.20/9.68 (singletonsswitch) => 71.20/9.68 (( 71.20/9.68 (upairsetE) => 71.20/9.68 (( 71.20/9.68 (upairsetIL) => 71.20/9.68 (( 71.20/9.68 (upairsetIR) => 71.20/9.68 (( 71.20/9.68 (emptyE1) => 71.20/9.68 (( 71.20/9.68 (vacuousDall) => 71.20/9.68 (( 71.20/9.68 (quantDeMorgan1) => 71.20/9.68 (( 71.20/9.68 (quantDeMorgan2) => 71.20/9.68 (( 71.20/9.68 (quantDeMorgan3) => 71.20/9.68 (( 71.20/9.68 (quantDeMorgan4) => 71.20/9.68 (( 71.20/9.68 (prop2setI) => 71.20/9.68 (( 71.20/9.68 (prop2set2propI) => 71.20/9.68 (( 71.20/9.68 (notdexE) => 71.20/9.68 (( 71.20/9.68 (notdallE) => 71.20/9.68 (( 71.20/9.68 (exuI1) => 71.20/9.68 (( 71.20/9.68 (exuI3) => 71.20/9.68 (( 71.20/9.68 (exuI2) => 71.20/9.68 (( 71.20/9.68 (inCongP) => 71.20/9.68 (( 71.20/9.68 (in__Cong) => 71.20/9.68 (( 71.20/9.68 (exuE3u) => 71.20/9.68 (( 71.20/9.68 (exu__Cong) => 71.20/9.68 (( 71.20/9.68 (( 71.20/9.68 (emptyset) = 71.20/9.68 (emptyset))) => 71.20/9.68 (( 71.20/9.68 (setadjoin__Cong) => 71.20/9.68 (( 71.20/9.68 (powerset__Cong) => 71.20/9.68 (( 71.20/9.68 (setunion__Cong) => 71.20/9.68 (( 71.20/9.68 (( 71.20/9.68 (omega) = 71.20/9.68 (omega))) => 71.20/9.68 (( 71.20/9.68 (exuEu) => 71.20/9.68 (( 71.20/9.68 (descr__Cong) => 71.20/9.68 (( 71.20/9.68 (dsetconstr__Cong) => 71.20/9.68 (( 71.20/9.68 (subsetI1) => 71.20/9.68 (( 71.20/9.68 (eqimpsubset2) => 71.20/9.68 (( 71.20/9.68 (eqimpsubset1) => 71.20/9.68 (( 71.20/9.68 (subsetI2) => 71.20/9.68 (( 71.20/9.68 (emptysetsubset) => 71.20/9.68 (( 71.20/9.68 (subsetE) => 71.20/9.68 (( 71.20/9.68 (subsetE2) => 71.20/9.68 (( 71.20/9.68 (notsubsetI) => 71.20/9.68 (( 71.20/9.68 (notequalI1) => 71.20/9.68 (( 71.20/9.68 (notequalI2) => 71.20/9.68 (( 71.20/9.68 (subsetRefl) => 71.20/9.68 (( 71.20/9.68 (subsetTrans) => 71.20/9.68 (( 71.20/9.68 (setadjoinSub) => 71.20/9.68 (( 71.20/9.68 (setadjoinSub2) => 71.20/9.68 (( 71.20/9.68 (subset2powerset) => 71.20/9.68 (( 71.20/9.68 (setextsub) => 71.20/9.68 (( 71.20/9.68 (subsetemptysetimpeq) => 71.20/9.68 (( 71.20/9.68 (powersetI1) => 71.20/9.68 (( 71.20/9.68 (powersetE1) => 71.20/9.68 (( 71.20/9.68 (inPowerset) => 71.20/9.68 (( 71.20/9.68 (powersetsubset) => 71.20/9.68 (( 71.20/9.68 (sepInPowerset) => 71.20/9.68 (( 71.20/9.68 (sepSubset) => 71.20/9.68 (( 71.20/9.68 (binunionIL) => 71.20/9.68 (( 71.20/9.68 (upairset2IR) => 71.20/9.68 (( 71.20/9.68 (binunionIR) => 71.20/9.68 (( 71.20/9.68 (binunionEcases) => 71.20/9.68 (( 71.20/9.68 (binunionE) => 71.20/9.68 (( 71.20/9.68 (binunionLsub) => 71.20/9.68 (( 71.20/9.68 (binunionRsub) => 71.20/9.68 (( 71.20/9.68 (binintersectI) => 71.20/9.68 (( 71.20/9.68 (binintersectSubset5) => 71.20/9.68 (( 71.20/9.68 (binintersectEL) => 71.20/9.68 (( 71.20/9.68 (binintersectLsub) => 71.20/9.68 (( 71.20/9.68 (binintersectSubset2) => 71.20/9.68 (( 71.20/9.68 (binintersectSubset3) => 71.20/9.68 (( 71.20/9.68 (binintersectER) => 71.20/9.68 (( 71.20/9.68 (disjointsetsI1) => 71.20/9.68 (( 71.20/9.68 (binintersectRsub) => 71.20/9.68 (( 71.20/9.68 (binintersectSubset4) => 71.20/9.68 (( 71.20/9.68 (binintersectSubset1) => 71.20/9.68 (( 71.20/9.68 (bs114d) => 71.20/9.68 (( 71.20/9.68 (setminusI) => 71.20/9.68 (( 71.20/9.68 (setminusEL) => 71.20/9.68 (( 71.20/9.68 (setminusER) => 71.20/9.68 (( 71.20/9.68 (setminusSubset2) => 71.20/9.68 (( 71.20/9.68 (setminusERneg) => 71.20/9.68 (( 71.20/9.68 (setminusELneg) => 71.20/9.68 (( 71.20/9.68 (setminusILneg) => 71.20/9.68 (( 71.20/9.68 (setminusIRneg) => 71.20/9.68 (( 71.20/9.68 (setminusLsub) => 71.20/9.68 (( 71.20/9.68 (setminusSubset1) => 71.20/9.68 (( 71.20/9.68 (symdiffE) => 71.20/9.68 (( 71.20/9.68 (symdiffI1) => 71.20/9.68 (( 71.20/9.68 (symdiffI2) => 71.20/9.68 (( 71.20/9.68 (symdiffIneg1) => 71.20/9.68 (( 71.20/9.68 (symdiffIneg2) => 71.20/9.68 (( 71.20/9.68 (secondinupair) => 71.20/9.68 (( 71.20/9.68 (setukpairIL) => 71.20/9.68 (( 71.20/9.68 (setukpairIR) => 71.20/9.68 (( 71.20/9.68 (kpairiskpair) => 71.20/9.68 (( 71.20/9.68 (kpairp) => 71.20/9.68 (( 71.20/9.68 (singletonsubset) => 71.20/9.68 (( 71.20/9.68 (singletoninpowerset) => 71.20/9.68 (( 71.20/9.68 (singletoninpowunion) => 71.20/9.68 (( 71.20/9.68 (upairset2E) => 71.20/9.68 (( 71.20/9.68 (upairsubunion) => 71.20/9.68 (( 71.20/9.68 (upairinpowunion) => 71.20/9.68 (( 71.20/9.68 (ubforcartprodlem1) => 71.20/9.68 (( 71.20/9.68 (ubforcartprodlem2) => 71.20/9.68 (( 71.20/9.68 (ubforcartprodlem3) => 71.20/9.68 (( 71.20/9.68 (cartprodpairin) => 71.20/9.68 (( 71.20/9.68 (cartprodmempair1) => 71.20/9.68 (( 71.20/9.68 (cartprodmempair) => 71.20/9.68 (( 71.20/9.68 (setunionE2) => 71.20/9.68 (( 71.20/9.68 (setunionsingleton1) => 71.20/9.68 (( 71.20/9.68 (setunionsingleton2) => 71.20/9.68 (( 71.20/9.68 (setunionsingleton) => 71.20/9.68 (( 71.20/9.68 (singletonprop) => 71.20/9.68 (( 71.20/9.68 (ex1E1) => 71.20/9.68 (( 71.20/9.68 (ex1I) => 71.20/9.68 (( 71.20/9.68 (ex1I2) => 71.20/9.68 (( 71.20/9.68 (singletonsuniq) => 71.20/9.68 (( 71.20/9.68 (setukpairinjL1) => 71.20/9.68 (( 71.20/9.68 (kfstsingleton) => 71.20/9.68 (( 71.20/9.68 (theprop) => 71.20/9.68 (( 71.20/9.68 (kfstpairEq) => 71.20/9.68 (( 71.20/9.68 (cartprodfstin) => 71.20/9.68 (( 71.20/9.68 (setukpairinjL2) => 71.20/9.68 (( 71.20/9.68 (setukpairinjL) => 71.20/9.68 (( 71.20/9.68 (setukpairinjR11) => 71.20/9.68 (( 71.20/9.68 (setukpairinjR12) => 71.20/9.68 (( 71.20/9.68 (setukpairinjR1) => 71.20/9.68 (( 71.20/9.68 (upairequniteq) => 71.20/9.68 (( 71.20/9.68 (setukpairinjR2) => 71.20/9.68 (( 71.20/9.68 (setukpairinjR) => 71.20/9.68 (( 71.20/9.68 (ksndsingleton) => 71.20/9.68 (( 71.20/9.68 (ksndpairEq) => 71.20/9.68 (( 71.20/9.68 (kpairsurjEq) => 71.20/9.68 (( 71.20/9.68 (cartprodsndin) => 71.20/9.68 (( 71.20/9.68 (cartprodpairmemEL) => 71.20/9.68 (( 71.20/9.68 (cartprodpairmemER) => 71.20/9.68 (( 71.20/9.68 (cartprodmempaircEq) => 71.20/9.68 (( 71.20/9.68 (cartprodfstpairEq) => 71.20/9.68 (( 71.20/9.68 (cartprodsndpairEq) => 71.20/9.68 (( 71.20/9.68 (cartprodpairsurjEq) => 71.20/9.68 (( 71.20/9.68 (dpsetconstrI) => 71.20/9.68 (( 71.20/9.68 (dpsetconstrSub) => 71.20/9.68 (( 71.20/9.68 (setOfPairsIsBReln) => 71.20/9.68 (( 71.20/9.68 (dpsetconstrERa) => 71.20/9.68 (( 71.20/9.68 (dpsetconstrEL1) => 71.20/9.68 (( 71.20/9.68 (dpsetconstrEL2) => 71.20/9.68 (( 71.20/9.68 (dpsetconstrER) => 71.20/9.68 (( 71.20/9.68 (funcImageSingleton) => 71.20/9.68 (( 71.20/9.68 (apProp) => 71.20/9.68 (( 71.20/9.68 (app) => 71.20/9.68 (( 71.20/9.68 (infuncsetfunc) => 71.20/9.68 (( 71.20/9.68 (ap2p) => 71.20/9.68 (( 71.20/9.68 (funcinfuncset) => 71.20/9.68 (( 71.20/9.68 (lamProp) => 71.20/9.68 (( 71.20/9.68 (lamp) => 71.20/9.68 (( 71.20/9.68 (lam2p) => 71.20/9.68 (( 71.20/9.68 (brelnall1) => 71.20/9.68 (( 71.20/9.68 (brelnall2) => 71.20/9.68 (( 71.20/9.68 (ex1E2) => 71.20/9.68 (( 71.20/9.68 (funcGraphProp1) => 71.20/9.68 (( 71.20/9.68 (funcGraphProp3) => 71.20/9.68 (( 71.20/9.68 (funcGraphProp2) => 71.20/9.68 (( 71.20/9.68 (funcextLem) => 71.20/9.68 (( 71.20/9.68 (funcGraphProp4) => 71.20/9.68 (( 71.20/9.68 (subbreln) => 71.20/9.68 (( 71.20/9.68 (eqbreln) => 71.20/9.68 (( 71.20/9.68 (funcext) => 71.20/9.68 (( 71.20/9.68 (funcext2) => 71.20/9.68 (( 71.20/9.68 (ap2apEq1) => 71.20/9.68 (( 71.20/9.68 (ap2apEq2) => 71.20/9.68 (( 71.20/9.68 (beta1) => 71.20/9.68 (( 71.20/9.68 (eta1) => 71.20/9.68 (( 71.20/9.68 (lam2lamEq) => 71.20/9.68 (( 71.20/9.68 (beta2) => 71.20/9.68 (( 71.20/9.68 (eta2) => 71.20/9.68 (( 71.20/9.68 (iffalseProp1) => 71.20/9.68 (( 71.20/9.68 (iffalseProp2) => 71.20/9.68 (( 71.20/9.68 (iftrueProp1) => 71.20/9.68 (( 71.20/9.68 (iftrueProp2) => 71.20/9.68 (( 71.20/9.68 (ifSingleton) => 71.20/9.68 (( 71.20/9.68 (ifp) => 71.20/9.68 (( 71.20/9.68 (theeq) => 71.20/9.68 (( 71.20/9.68 (iftrue) => 71.20/9.68 (( 71.20/9.68 (iffalse) => 71.20/9.68 (( 71.20/9.68 (iftrueorfalse) => 71.20/9.68 (( 71.20/9.68 (binintersectT_lem) => 71.20/9.68 (( 71.20/9.68 (binunionT_lem) => 71.20/9.68 (( 71.20/9.68 (powersetT_lem) => 71.20/9.68 (( 71.20/9.68 (setminusT_lem) => 71.20/9.68 (( 71.20/9.68 (complementT_lem) => 71.20/9.68 (( 71.20/9.68 (setextT) => 71.20/9.68 (( 71.20/9.68 (subsetTI) => 71.20/9.68 (( 71.20/9.68 (powersetTI1) => 71.20/9.68 (( 71.20/9.68 (powersetTE1) => 71.20/9.68 (( 71.20/9.68 (complementTI1) => 71.20/9.68 (( 71.20/9.68 (complementTE1) => 71.20/9.68 (( 71.20/9.68 (binintersectTELcontra) => 71.20/9.68 (( 71.20/9.68 (binintersectTERcontra) => 71.20/9.68 (( 71.20/9.68 (contrasubsetT) => 71.20/9.68 (( 71.20/9.68 (contrasubsetT1) => 71.20/9.68 (( 71.20/9.68 (contrasubsetT2) => 71.20/9.68 (( 71.20/9.68 (contrasubsetT3) => 71.20/9.68 (( 71.20/9.68 (doubleComplementI1) => 71.20/9.68 (( 71.20/9.68 (doubleComplementE1) => 71.20/9.68 (( 71.20/9.68 (doubleComplementSub1) => 71.20/9.68 (( 71.20/9.68 (doubleComplementSub2) => 71.20/9.68 (( 71.20/9.68 (doubleComplementEq) => 71.20/9.68 (( 71.20/9.68 (complementTnotintersectT) => 71.20/9.68 (( 71.20/9.68 (complementImpComplementIntersect) => 71.20/9.68 (( 71.20/9.68 (complementSubsetComplementIntersect) => 71.20/9.68 (( 71.20/9.68 (complementInPowersetComplementIntersect) => 71.20/9.68 (( 71.20/9.68 (contraSubsetComplement) => 71.20/9.68 (( 71.20/9.68 (complementTcontraSubset) => 71.20/9.68 (( 71.20/9.68 (binunionTILcontra) => 71.20/9.68 (( 71.20/9.68 (binunionTIRcontra) => 71.20/9.68 (( 71.20/9.68 (inIntersectImpInUnion) => 71.20/9.68 (( 71.20/9.68 (inIntersectImpInUnion2) => 71.20/9.68 (( 71.20/9.68 (inIntersectImpInIntersectUnions) => 71.20/9.68 (( 71.20/9.68 (intersectInPowersetIntersectUnions) => 71.20/9.68 (( 71.20/9.68 (inComplementUnionImpNotIn1) => 71.20/9.68 (( 71.20/9.68 (inComplementUnionImpInComplement1) => 71.20/9.68 (( 71.20/9.68 (binunionTE) => 71.20/9.68 (( 71.20/9.68 (binunionTEcontra) => 71.20/9.68 (( 71.20/9.68 (demorgan2a1) => 71.20/9.68 (( 71.20/9.68 (complementUnionInPowersetComplement) => 71.20/9.68 (( 71.20/9.68 (demorgan2a2) => 71.20/9.68 (( 71.20/9.68 (demorgan1a) => 71.20/9.68 (( 71.20/9.68 (demorgan1b) => 71.20/9.68 (( 71.20/9.68 (demorgan1) => 71.20/9.68 (( 71.20/9.68 (demorgan2a) => 71.20/9.68 (( 71.20/9.68 (demorgan2b2) => 71.20/9.68 (( 71.20/9.68 (demorgan2b) => 71.20/9.68 (( 71.20/9.68 (demorgan2) => 71.20/9.68 (( 71.20/9.68 (woz13rule0) => 71.20/9.68 (( 71.20/9.68 (woz13rule1) => 71.20/9.68 (( 71.20/9.68 (woz13rule2) => 71.20/9.68 (( 71.20/9.68 (woz13rule3) => 71.20/9.68 (( 71.20/9.68 (woz13rule4) => 71.20/9.68 (( 71.20/9.68 (woz1_1) => 71.20/9.68 (( 71.20/9.68 (woz1_2) => 71.20/9.68 (( 71.20/9.68 (woz1_3) => 71.20/9.68 (( 71.20/9.68 (woz1_4) => 71.20/9.68 (( 71.20/9.68 (woz1_5) => 71.20/9.68 (( 71.20/9.68 (breln1all2) => 71.20/9.68 (( 71.20/9.68 (breln1SetBreln1) => 71.20/9.68 (( 71.20/9.68 (choice2fnsingleton) => 71.20/9.68 (( 71.20/9.68 (setOfPairsIsBReln1) => 71.20/9.68 (( 71.20/9.68 (breln1all1) => 71.20/9.68 (( 71.20/9.68 (subbreln1) => 71.20/9.68 (( 71.20/9.68 (eqbreln1) => 71.20/9.68 (( 71.20/9.68 (breln1invprop) => 71.20/9.68 (( 71.20/9.68 (breln1invI) => 71.20/9.68 (( 71.20/9.68 (breln1invE) => 71.20/9.68 (( 71.20/9.68 (breln1compprop) => 71.20/9.68 (( 71.20/9.68 (breln1compI) => 71.20/9.68 (( 71.20/9.68 (breln1compE) => 71.20/9.68 (( 71.20/9.68 (breln1compEex) => 71.20/9.68 (( 71.20/9.68 (!!) @ ( 71.20/9.68 (('#B') @ ( 71.20/9.68 !!) @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#S') @ ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 '#S') @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 =>))) @ 71.20/9.68 breln1)))) @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 !!))) @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#S') @ ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 '#B') @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 '#S') @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 =>))) @ 71.20/9.68 breln1)))))) @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#C') @ ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 '#B') @ 71.20/9.68 ( 71.20/9.68 ( 71.20/9.68 ('#B') @ ( 71.20/9.68 '#B') @ 71.20/9.68 breln1)))) @ 71.20/9.68 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.68 inference('rw', [status(thm)], [zip_derived_cl1, '0', '1', '2', '3'])). 71.20/9.68 thf(zip_derived_cl3, plain, 71.20/9.68 (~ (((setextAx) => 71.20/9.68 (((emptysetAx) => 71.20/9.68 (((setadjoinAx) => 71.20/9.68 (((powersetAx) => 71.20/9.68 (((setunionAx) => 71.20/9.68 (((in @ emptyset @ omega) => 71.20/9.68 (((omegaSAx) => 71.20/9.68 (((omegaIndAx) => 71.20/9.68 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=> 71.20/9.68 (( 71.20/9.68 (powersetE) => 71.20/9.68 (( 71.20/9.68 (setunionI) => 71.20/9.68 (( 71.20/9.68 (setunionE) => 71.20/9.68 (( 71.20/9.68 (subPowSU) => 71.20/9.68 (( 71.20/9.68 (exuE2) => 71.20/9.68 (( 71.20/9.68 (nonemptyImpWitness) => 71.20/9.68 (( 71.20/9.68 (uniqinunit) => 71.20/9.68 (( 71.20/9.68 (notinsingleton) => 71.20/9.68 (( 71.20/9.68 (eqinunit) => 71.20/9.68 (( 71.20/9.68 (singletonsswitch) => 71.20/9.68 (( 71.20/9.68 (upairsetE) => 71.20/9.68 (( 71.20/9.68 (upairsetIL) => 71.20/9.68 (( 71.20/9.68 (upairsetIR) => 71.20/9.68 (( 71.20/9.68 (emptyE1) => 71.20/9.68 (( 71.20/9.68 (vacuousDall) => 71.20/9.68 (( 71.20/9.68 (quantDeMorgan1) => 71.20/9.68 (( 71.20/9.68 (quantDeMorgan2) => 71.20/9.68 (( 71.20/9.68 (quantDeMorgan3) => 71.20/9.68 (( 71.20/9.68 (quantDeMorgan4) => 71.20/9.68 (( 71.20/9.68 (prop2setI) => 71.20/9.68 (( 71.20/9.68 (prop2set2propI) => 71.20/9.68 (( 71.20/9.68 (notdexE) => 71.20/9.68 (( 71.20/9.68 (notdallE) => 71.20/9.68 (( 71.20/9.68 (exuI1) => 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(secondinupair) => 71.20/9.68 (( 71.20/9.68 (setukpairIL) => 71.20/9.68 (( 71.20/9.68 (setukpairIR) => 71.20/9.68 (( 71.20/9.68 (kpairiskpair) => 71.20/9.68 (( 71.20/9.68 (kpairp) => 71.20/9.68 (( 71.20/9.68 (singletonsubset) => 71.20/9.68 (( 71.20/9.68 (singletoninpowerset) => 71.20/9.68 (( 71.20/9.68 (singletoninpowunion) => 71.20/9.68 (( 71.20/9.68 (upairset2E) => 71.20/9.68 (( 71.20/9.68 (upairsubunion) => 71.20/9.68 (( 71.20/9.68 (upairinpowunion) => 71.20/9.68 (( 71.20/9.68 (ubforcartprodlem1) => 71.20/9.68 (( 71.20/9.68 (ubforcartprodlem2) => 71.20/9.68 (( 71.20/9.68 (ubforcartprodlem3) => 71.20/9.68 (( 71.20/9.68 (cartprodpairin) => 71.20/9.68 (( 71.20/9.68 (cartprodmempair1) => 71.20/9.68 (( 71.20/9.68 (cartprodmempair) => 71.20/9.68 (( 71.20/9.68 (setunionE2) => 71.20/9.68 (( 71.20/9.68 (setunionsingleton1) => 71.20/9.68 (( 71.20/9.68 (setunionsingleton2) => 71.20/9.68 (( 71.20/9.68 (setunionsingleton) => 71.20/9.68 (( 71.20/9.68 (singletonprop) => 71.20/9.68 (( 71.20/9.68 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(doubleComplementEq) => 71.20/9.68 (( 71.20/9.68 (complementTnotintersectT) => 71.20/9.68 (( 71.20/9.68 (complementImpComplementIntersect) => 71.20/9.68 (( 71.20/9.68 (complementSubsetComplementIntersect) => 71.20/9.68 (( 71.20/9.68 (complementInPowersetComplementIntersect) => 71.20/9.68 (( 71.20/9.68 (contraSubsetComplement) => 71.20/9.68 (( 71.20/9.68 (complementTcontraSubset) => 71.20/9.68 (( 71.20/9.68 (binunionTILcontra) => 71.20/9.68 (( 71.20/9.68 (binunionTIRcontra) => 71.20/9.68 (( 71.20/9.68 (inIntersectImpInUnion) => 71.20/9.68 (( 71.20/9.68 (inIntersectImpInUnion2) => 71.20/9.68 (( 71.20/9.68 (inIntersectImpInIntersectUnions) => 71.20/9.68 (( 71.20/9.68 (intersectInPowersetIntersectUnions) => 71.20/9.68 (( 71.20/9.68 (inComplementUnionImpNotIn1) => 71.20/9.68 (( 71.20/9.68 (inComplementUnionImpInComplement1) => 71.20/9.68 (( 71.20/9.68 (binunionTE) => 71.20/9.68 (( 71.20/9.68 (binunionTEcontra) => 71.20/9.68 (( 71.20/9.68 (demorgan2a1) => 71.20/9.68 (( 71.20/9.68 (complementUnionInPowersetComplement) => 71.20/9.68 (( 71.20/9.68 (demorgan2a2) => 71.20/9.68 (( 71.20/9.68 (demorgan1a) => 71.20/9.68 (( 71.20/9.68 (demorgan1b) => 71.20/9.68 (( 71.20/9.68 (demorgan1) => 71.20/9.68 (( 71.20/9.68 (demorgan2a) => 71.20/9.68 (( 71.20/9.68 (demorgan2b2) => 71.20/9.68 (( 71.20/9.68 (demorgan2b) => 71.20/9.68 (( 71.20/9.68 (demorgan2) => 71.20/9.68 (( 71.20/9.68 (woz13rule0) => 71.20/9.68 (( 71.20/9.68 (woz13rule1) => 71.20/9.68 (( 71.20/9.68 (woz13rule2) => 71.20/9.68 (( 71.20/9.68 (woz13rule3) => 71.20/9.68 (( 71.20/9.68 (woz13rule4) => 71.20/9.68 (( 71.20/9.68 (woz1_1) => 71.20/9.68 (( 71.20/9.68 (woz1_2) => 71.20/9.68 (( 71.20/9.68 (woz1_3) => 71.20/9.68 (( 71.20/9.68 (woz1_4) => 71.20/9.68 (( 71.20/9.68 (woz1_5) => 71.20/9.68 (( 71.20/9.68 (breln1all2) => 71.20/9.68 (( 71.20/9.68 (breln1SetBreln1) => 71.20/9.68 (( 71.20/9.68 (choice2fnsingleton) => 71.20/9.68 (( 71.20/9.68 (setOfPairsIsBReln1) => 71.20/9.68 (( 71.20/9.68 (breln1all1) => 71.20/9.68 (( 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71.20/9.70 ( 71.20/9.70 ('#B') @ ( 71.20/9.70 ( 71.20/9.70 ('#B') @ ( 71.20/9.70 =>))) @ 71.20/9.70 breln1)))))) @ 71.20/9.70 ( 71.20/9.70 ( 71.20/9.70 ('#C') @ ( 71.20/9.70 ( 71.20/9.70 ('#B') @ ( 71.20/9.70 '#B') @ 71.20/9.70 ( 71.20/9.70 ( 71.20/9.70 ('#B') @ ( 71.20/9.70 '#B') @ 71.20/9.70 breln1)))) @ 71.20/9.70 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 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(emptyInPowerset) => 71.20/9.70 (( 71.20/9.70 (powersetE) => 71.20/9.70 (( 71.20/9.70 (setunionI) => 71.20/9.70 (( 71.20/9.70 (setunionE) => 71.20/9.70 (( 71.20/9.70 (subPowSU) => 71.20/9.70 (( 71.20/9.70 (exuE2) => 71.20/9.70 (( 71.20/9.70 (nonemptyImpWitness) => 71.20/9.70 (( 71.20/9.70 (uniqinunit) => 71.20/9.70 (( 71.20/9.70 (notinsingleton) => 71.20/9.70 (( 71.20/9.70 (eqinunit) => 71.20/9.70 (( 71.20/9.70 (singletonsswitch) => 71.20/9.70 (( 71.20/9.70 (upairsetE) => 71.20/9.70 (( 71.20/9.70 (upairsetIL) => 71.20/9.70 (( 71.20/9.70 (upairsetIR) => 71.20/9.70 (( 71.20/9.70 (emptyE1) => 71.20/9.70 (( 71.20/9.70 (vacuousDall) => 71.20/9.70 (( 71.20/9.70 (quantDeMorgan1) => 71.20/9.70 (( 71.20/9.70 (quantDeMorgan2) => 71.20/9.70 (( 71.20/9.70 (quantDeMorgan3) => 71.20/9.70 (( 71.20/9.70 (quantDeMorgan4) => 71.20/9.70 (( 71.20/9.70 (prop2setI) => 71.20/9.70 (( 71.20/9.70 (prop2set2propI) => 71.20/9.70 (( 71.20/9.70 (notdexE) => 71.20/9.70 (( 71.20/9.70 (notdallE) => 71.20/9.70 (( 71.20/9.70 (exuI1) => 71.20/9.70 (( 71.20/9.70 (exuI3) => 71.20/9.70 (( 71.20/9.70 (exuI2) => 71.20/9.70 (( 71.20/9.70 (inCongP) => 71.20/9.70 (( 71.20/9.70 (in__Cong) => 71.20/9.70 (( 71.20/9.70 (exuE3u) => 71.20/9.70 (( 71.20/9.70 (exu__Cong) => 71.20/9.70 (( 71.20/9.70 (setadjoin__Cong) => 71.20/9.70 (( 71.20/9.70 (powerset__Cong) => 71.20/9.70 (( 71.20/9.70 (setunion__Cong) => 71.20/9.70 (( 71.20/9.70 (exuEu) => 71.20/9.70 (( 71.20/9.70 (descr__Cong) => 71.20/9.70 (( 71.20/9.70 (dsetconstr__Cong) => 71.20/9.70 (( 71.20/9.70 (subsetI1) => 71.20/9.70 (( 71.20/9.70 (eqimpsubset2) => 71.20/9.70 (( 71.20/9.70 (eqimpsubset1) => 71.20/9.70 (( 71.20/9.70 (subsetI2) => 71.20/9.70 (( 71.20/9.70 (emptysetsubset) => 71.20/9.70 (( 71.20/9.70 (subsetE) => 71.20/9.70 (( 71.20/9.70 (subsetE2) => 71.20/9.70 (( 71.20/9.70 (notsubsetI) => 71.20/9.71 (( 71.20/9.71 (notequalI1) => 71.20/9.71 (( 71.20/9.71 (notequalI2) => 71.20/9.71 (( 71.20/9.71 (subsetRefl) => 71.20/9.71 (( 71.20/9.71 (subsetTrans) => 71.20/9.71 (( 71.20/9.71 (setadjoinSub) => 71.20/9.71 (( 71.20/9.71 (setadjoinSub2) => 71.20/9.71 (( 71.20/9.71 (subset2powerset) => 71.20/9.71 (( 71.20/9.71 (setextsub) => 71.20/9.71 (( 71.20/9.71 (subsetemptysetimpeq) => 71.20/9.71 (( 71.20/9.71 (powersetI1) => 71.20/9.71 (( 71.20/9.71 (powersetE1) => 71.20/9.71 (( 71.20/9.71 (inPowerset) => 71.20/9.71 (( 71.20/9.71 (powersetsubset) => 71.20/9.71 (( 71.20/9.71 (sepInPowerset) => 71.20/9.71 (( 71.20/9.71 (sepSubset) => 71.20/9.71 (( 71.20/9.71 (binunionIL) => 71.20/9.71 (( 71.20/9.71 (upairset2IR) => 71.20/9.71 (( 71.20/9.71 (binunionIR) => 71.20/9.71 (( 71.20/9.71 (binunionEcases) => 71.20/9.71 (( 71.20/9.71 (binunionE) => 71.20/9.71 (( 71.20/9.71 (binunionLsub) => 71.20/9.71 (( 71.20/9.71 (binunionRsub) => 71.20/9.71 (( 71.20/9.71 (binintersectI) => 71.20/9.71 (( 71.20/9.71 (binintersectSubset5) => 71.20/9.71 (( 71.20/9.71 (binintersectEL) => 71.20/9.71 (( 71.20/9.71 (binintersectLsub) => 71.20/9.71 (( 71.20/9.71 (binintersectSubset2) => 71.20/9.71 (( 71.20/9.71 (binintersectSubset3) => 71.20/9.71 (( 71.20/9.71 (binintersectER) => 71.20/9.71 (( 71.20/9.71 (disjointsetsI1) => 71.20/9.71 (( 71.20/9.71 (binintersectRsub) => 71.20/9.71 (( 71.20/9.71 (binintersectSubset4) => 71.20/9.71 (( 71.20/9.71 (binintersectSubset1) => 71.20/9.71 (( 71.20/9.71 (bs114d) => 71.20/9.71 (( 71.20/9.71 (setminusI) => 71.20/9.71 (( 71.20/9.71 (setminusEL) => 71.20/9.71 (( 71.20/9.71 (setminusER) => 71.20/9.71 (( 71.20/9.71 (setminusSubset2) => 71.20/9.71 (( 71.20/9.71 (setminusERneg) => 71.20/9.71 (( 71.20/9.71 (setminusELneg) => 71.20/9.71 (( 71.20/9.71 (setminusILneg) => 71.20/9.71 (( 71.20/9.71 (setminusIRneg) => 71.20/9.71 (( 71.20/9.71 (setminusLsub) => 71.20/9.71 (( 71.20/9.71 (setminusSubset1) => 71.20/9.71 (( 71.20/9.71 (symdiffE) => 71.20/9.71 (( 71.20/9.71 (symdiffI1) => 71.20/9.71 (( 71.20/9.71 (symdiffI2) => 71.20/9.71 (( 71.20/9.71 (symdiffIneg1) => 71.20/9.71 (( 71.20/9.71 (symdiffIneg2) => 71.20/9.71 (( 71.20/9.71 (secondinupair) => 71.20/9.71 (( 71.20/9.71 (setukpairIL) => 71.20/9.71 (( 71.20/9.71 (setukpairIR) => 71.20/9.71 (( 71.20/9.71 (kpairiskpair) => 71.20/9.71 (( 71.20/9.71 (kpairp) => 71.20/9.71 (( 71.20/9.71 (singletonsubset) => 71.20/9.71 (( 71.20/9.71 (singletoninpowerset) => 71.20/9.71 (( 71.20/9.71 (singletoninpowunion) => 71.20/9.71 (( 71.20/9.71 (upairset2E) => 71.20/9.71 (( 71.20/9.71 (upairsubunion) => 71.20/9.71 (( 71.20/9.71 (upairinpowunion) => 71.20/9.71 (( 71.20/9.71 (ubforcartprodlem1) => 71.20/9.71 (( 71.20/9.71 (ubforcartprodlem2) => 71.20/9.71 (( 71.20/9.71 (ubforcartprodlem3) => 71.20/9.71 (( 71.20/9.71 (cartprodpairin) => 71.20/9.71 (( 71.20/9.71 (cartprodmempair1) => 71.20/9.71 (( 71.20/9.71 (cartprodmempair) => 71.20/9.71 (( 71.20/9.71 (setunionE2) => 71.20/9.71 (( 71.20/9.71 (setunionsingleton1) => 71.20/9.71 (( 71.20/9.71 (setunionsingleton2) => 71.20/9.71 (( 71.20/9.71 (setunionsingleton) => 71.20/9.71 (( 71.20/9.71 (singletonprop) => 71.20/9.71 (( 71.20/9.71 (ex1E1) => 71.20/9.71 (( 71.20/9.71 (ex1I) => 71.20/9.71 (( 71.20/9.71 (ex1I2) => 71.20/9.71 (( 71.20/9.71 (singletonsuniq) => 71.20/9.71 (( 71.20/9.71 (setukpairinjL1) => 71.20/9.71 (( 71.20/9.71 (kfstsingleton) => 71.20/9.71 (( 71.20/9.71 (theprop) => 71.20/9.71 (( 71.20/9.71 (kfstpairEq) => 71.20/9.71 (( 71.20/9.71 (cartprodfstin) => 71.20/9.71 (( 71.20/9.71 (setukpairinjL2) => 71.20/9.71 (( 71.20/9.71 (setukpairinjL) => 71.20/9.71 (( 71.20/9.71 (setukpairinjR11) => 71.20/9.71 (( 71.20/9.71 (setukpairinjR12) => 71.20/9.71 (( 71.20/9.71 (setukpairinjR1) => 71.20/9.71 (( 71.20/9.71 (upairequniteq) => 71.20/9.71 (( 71.20/9.71 (setukpairinjR2) => 71.20/9.71 (( 71.20/9.71 (setukpairinjR) => 71.20/9.71 (( 71.20/9.71 (ksndsingleton) => 71.20/9.71 (( 71.20/9.71 (ksndpairEq) => 71.20/9.71 (( 71.20/9.71 (kpairsurjEq) => 71.20/9.71 (( 71.20/9.71 (cartprodsndin) => 71.20/9.71 (( 71.20/9.71 (cartprodpairmemEL) => 71.20/9.71 (( 71.20/9.71 (cartprodpairmemER) => 71.20/9.71 (( 71.20/9.71 (cartprodmempaircEq) => 71.20/9.71 (( 71.20/9.71 (cartprodfstpairEq) => 71.20/9.71 (( 71.20/9.71 (cartprodsndpairEq) => 71.20/9.71 (( 71.20/9.71 (cartprodpairsurjEq) => 71.20/9.71 (( 71.20/9.71 (dpsetconstrI) => 71.20/9.71 (( 71.20/9.71 (dpsetconstrSub) => 71.20/9.71 (( 71.20/9.71 (setOfPairsIsBReln) => 71.20/9.71 (( 71.20/9.71 (dpsetconstrERa) => 71.20/9.71 (( 71.20/9.71 (dpsetconstrEL1) => 71.20/9.71 (( 71.20/9.71 (dpsetconstrEL2) => 71.20/9.71 (( 71.20/9.71 (dpsetconstrER) => 71.20/9.71 (( 71.20/9.71 (funcImageSingleton) => 71.20/9.71 (( 71.20/9.71 (apProp) => 71.20/9.71 (( 71.20/9.71 (app) => 71.20/9.71 (( 71.20/9.71 (infuncsetfunc) => 71.20/9.71 (( 71.20/9.71 (ap2p) => 71.20/9.71 (( 71.20/9.71 (funcinfuncset) => 71.20/9.71 (( 71.20/9.71 (lamProp) => 71.20/9.71 (( 71.20/9.71 (lamp) => 71.20/9.71 (( 71.20/9.71 (lam2p) => 71.20/9.71 (( 71.20/9.71 (brelnall1) => 71.20/9.71 (( 71.20/9.71 (brelnall2) => 71.20/9.71 (( 71.20/9.71 (ex1E2) => 71.20/9.71 (( 71.20/9.71 (funcGraphProp1) => 71.20/9.71 (( 71.20/9.71 (funcGraphProp3) => 71.20/9.71 (( 71.20/9.71 (funcGraphProp2) => 71.20/9.71 (( 71.20/9.71 (funcextLem) => 71.20/9.71 (( 71.20/9.71 (funcGraphProp4) => 71.20/9.71 (( 71.20/9.71 (subbreln) => 71.20/9.71 (( 71.20/9.71 (eqbreln) => 71.20/9.71 (( 71.20/9.71 (funcext) => 71.20/9.71 (( 71.20/9.71 (funcext2) => 71.20/9.71 (( 71.20/9.71 (ap2apEq1) => 71.20/9.71 (( 71.20/9.71 (ap2apEq2) => 71.20/9.71 (( 71.20/9.71 (beta1) => 71.20/9.71 (( 71.20/9.71 (eta1) => 71.20/9.71 (( 71.20/9.71 (lam2lamEq) => 71.20/9.71 (( 71.20/9.71 (beta2) => 71.20/9.71 (( 71.20/9.71 (eta2) => 71.20/9.71 (( 71.20/9.71 (iffalseProp1) => 71.20/9.71 (( 71.20/9.71 (iffalseProp2) => 71.20/9.71 (( 71.20/9.71 (iftrueProp1) => 71.20/9.71 (( 71.20/9.71 (iftrueProp2) => 71.20/9.71 (( 71.20/9.71 (ifSingleton) => 71.20/9.71 (( 71.20/9.71 (ifp) => 71.20/9.71 (( 71.20/9.71 (theeq) => 71.20/9.71 (( 71.20/9.71 (iftrue) => 71.20/9.71 (( 71.20/9.71 (iffalse) => 71.20/9.71 (( 71.20/9.71 (iftrueorfalse) => 71.20/9.71 (( 71.20/9.71 (binintersectT_lem) => 71.20/9.71 (( 71.20/9.71 (binunionT_lem) => 71.20/9.71 (( 71.20/9.71 (powersetT_lem) => 71.20/9.71 (( 71.20/9.71 (setminusT_lem) => 71.20/9.71 (( 71.20/9.71 (complementT_lem) => 71.20/9.71 (( 71.20/9.71 (setextT) => 71.20/9.71 (( 71.20/9.71 (subsetTI) => 71.20/9.71 (( 71.20/9.71 (powersetTI1) => 71.20/9.71 (( 71.20/9.71 (powersetTE1) => 71.20/9.71 (( 71.20/9.71 (complementTI1) => 71.20/9.71 (( 71.20/9.71 (complementTE1) => 71.20/9.71 (( 71.20/9.71 (binintersectTELcontra) => 71.20/9.71 (( 71.20/9.71 (binintersectTERcontra) => 71.20/9.71 (( 71.20/9.71 (contrasubsetT) => 71.20/9.71 (( 71.20/9.71 (contrasubsetT1) => 71.20/9.71 (( 71.20/9.71 (contrasubsetT2) => 71.20/9.71 (( 71.20/9.71 (contrasubsetT3) => 71.20/9.71 (( 71.20/9.71 (doubleComplementI1) => 71.20/9.71 (( 71.20/9.71 (doubleComplementE1) => 71.20/9.71 (( 71.20/9.71 (doubleComplementSub1) => 71.20/9.71 (( 71.20/9.71 (doubleComplementSub2) => 71.20/9.71 (( 71.20/9.71 (doubleComplementEq) => 71.20/9.71 (( 71.20/9.71 (complementTnotintersectT) => 71.20/9.71 (( 71.20/9.71 (complementImpComplementIntersect) => 71.20/9.71 (( 71.20/9.71 (complementSubsetComplementIntersect) => 71.20/9.71 (( 71.20/9.71 (complementInPowersetComplementIntersect) => 71.20/9.71 (( 71.20/9.71 (contraSubsetComplement) => 71.20/9.71 (( 71.20/9.71 (complementTcontraSubset) => 71.20/9.71 (( 71.20/9.71 (binunionTILcontra) => 71.20/9.71 (( 71.20/9.71 (binunionTIRcontra) => 71.20/9.71 (( 71.20/9.71 (inIntersectImpInUnion) => 71.20/9.71 (( 71.20/9.71 (inIntersectImpInUnion2) => 71.20/9.71 (( 71.20/9.71 (inIntersectImpInIntersectUnions) => 71.20/9.71 (( 71.20/9.71 (intersectInPowersetIntersectUnions) => 71.20/9.71 (( 71.20/9.71 (inComplementUnionImpNotIn1) => 71.20/9.71 (( 71.20/9.71 (inComplementUnionImpInComplement1) => 71.20/9.71 (( 71.20/9.71 (binunionTE) => 71.20/9.71 (( 71.20/9.71 (binunionTEcontra) => 71.20/9.71 (( 71.20/9.71 (demorgan2a1) => 71.20/9.71 (( 71.20/9.71 (complementUnionInPowersetComplement) => 71.20/9.71 (( 71.20/9.71 (demorgan2a2) => 71.20/9.71 (( 71.20/9.71 (demorgan1a) => 71.20/9.71 (( 71.20/9.71 (demorgan1b) => 71.20/9.71 (( 71.20/9.71 (demorgan1) => 71.20/9.71 (( 71.20/9.71 (demorgan2a) => 71.20/9.71 (( 71.20/9.71 (demorgan2b2) => 71.20/9.71 (( 71.20/9.71 (demorgan2b) => 71.20/9.71 (( 71.20/9.71 (demorgan2) => 71.20/9.71 (( 71.20/9.71 (woz13rule0) => 71.20/9.71 (( 71.20/9.71 (woz13rule1) => 71.20/9.71 (( 71.20/9.71 (woz13rule2) => 71.20/9.71 (( 71.20/9.71 (woz13rule3) => 71.20/9.71 (( 71.20/9.71 (woz13rule4) => 71.20/9.71 (( 71.20/9.71 (woz1_1) => 71.20/9.71 (( 71.20/9.71 (woz1_2) => 71.20/9.71 (( 71.20/9.71 (woz1_3) => 71.20/9.71 (( 71.20/9.71 (woz1_4) => 71.20/9.71 (( 71.20/9.71 (woz1_5) => 71.20/9.71 (( 71.20/9.71 (breln1all2) => 71.20/9.71 (( 71.20/9.71 (breln1SetBreln1) => 71.20/9.71 (( 71.20/9.71 (choice2fnsingleton) => 71.20/9.71 (( 71.20/9.71 (setOfPairsIsBReln1) => 71.20/9.71 (( 71.20/9.71 (breln1all1) => 71.20/9.71 (( 71.20/9.71 (subbreln1) => 71.20/9.71 (( 71.20/9.71 (eqbreln1) => 71.20/9.71 (( 71.20/9.71 (breln1invprop) => 71.20/9.71 (( 71.20/9.71 (breln1invI) => 71.20/9.71 (( 71.20/9.71 (breln1invE) => 71.20/9.71 (( 71.20/9.71 (breln1compprop) => 71.20/9.71 (( 71.20/9.71 (breln1compI) => 71.20/9.71 (( 71.20/9.71 (breln1compE) => 71.20/9.71 (( 71.20/9.71 (breln1compEex) => 71.20/9.71 (( 71.20/9.71 (!!) @ ( 71.20/9.71 (('#B') @ ( 71.20/9.71 !!) @ 71.20/9.71 ( 71.20/9.71 ( 71.20/9.71 ('#S') @ ( 71.20/9.71 ( 71.20/9.71 ('#B') @ ( 71.20/9.71 '#S') @ 71.20/9.71 ( 71.20/9.71 ( 71.20/9.71 ('#B') @ ( 71.20/9.71 ( 71.20/9.71 ('#B') @ ( 71.20/9.71 =>))) @ 71.20/9.71 breln1)))) @ 71.20/9.71 ( 71.20/9.71 ( 71.20/9.71 ('#B') @ ( 71.20/9.71 ( 71.20/9.71 ('#B') @ ( 71.20/9.71 !!))) @ 71.20/9.71 ( 71.20/9.71 ( 71.20/9.71 ('#S') @ ( 71.20/9.71 ( 71.20/9.71 ('#B') @ ( 71.20/9.71 '#B') @ 71.20/9.71 ( 71.20/9.71 ( 71.20/9.71 ('#B') @ ( 71.20/9.71 '#S') @ 71.20/9.71 ( 71.20/9.71 ( 71.20/9.71 ('#B') @ ( 71.20/9.71 ( 71.20/9.71 ('#B') @ ( 71.20/9.71 =>))) @ 71.20/9.71 breln1)))))) @ 71.20/9.71 ( 71.20/9.71 ( 71.20/9.71 ('#C') @ ( 71.20/9.71 ( 71.20/9.71 ('#B') @ ( 71.20/9.71 '#B') @ 71.20/9.71 ( 71.20/9.71 ( 71.20/9.71 ('#B') @ ( 71.20/9.71 '#B') @ 71.20/9.71 breln1)))) @ 71.20/9.71 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 71.20/9.71 thf(zip_derived_cl40, plain, 71.20/9.71 (~ (((omegaIndAx) => 71.20/9.71 (((replAx) => 71.20/9.71 (((foundationAx) => 71.20/9.71 (((wellorderingAx) => 71.20/9.71 (((descrp) => 71.20/9.71 (((dsetconstrI) => 71.20/9.71 (((dsetconstrEL) => 71.20/9.71 (((dsetconstrER) => 71.20/9.71 (((exuE1) => 71.20/9.71 (((prop2setE) => 71.20/9.71 (((emptysetE) => 71.20/9.71 (((emptysetimpfalse) => 71.20/9.71 (((notinemptyset) => 71.20/9.71 (((exuE3e) => 71.20/9.71 (((setext) => 71.20/9.71 (((emptyI) => 71.20/9.71 (((noeltsimpempty) => 71.20/9.71 (((setbeta) => 71.20/9.71 (((nonemptyE1) => 71.20/9.71 (((nonemptyI) => 71.20/9.71 (((nonemptyI1) => 71.20/9.71 (((setadjoinIL) => 71.20/9.71 (((in @ emptyset @ 71.20/9.71 (setadjoin @ emptyset @ 71.20/9.71 emptyset)) => 71.20/9.71 (((setadjoinIR) => 71.20/9.71 (((setadjoinE) => 71.20/9.71 (((setadjoinOr) => 71.20/9.71 (((setoftrueEq) => 71.20/9.71 (((powersetI) => 71.20/9.71 (((emptyinPowerset) => 71.20/9.71 (((emptyInPowerset) => 71.20/9.71 (( 71.20/9.71 (powersetE) => 71.20/9.71 (( 71.20/9.71 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=> 71.20/9.71 (( 71.20/9.71 (inCongP) => 71.20/9.71 (( 71.20/9.71 (in__Cong) => 71.20/9.71 (( 71.20/9.71 (exuE3u) => 71.20/9.71 (( 71.20/9.71 (exu__Cong) => 71.20/9.71 (( 71.20/9.71 (setadjoin__Cong) => 71.20/9.71 (( 71.20/9.71 (powerset__Cong) => 71.20/9.71 (( 71.20/9.71 (setunion__Cong) => 71.20/9.71 (( 71.20/9.71 (exuEu) => 71.20/9.71 (( 71.20/9.71 (descr__Cong) => 71.20/9.71 (( 71.20/9.71 (dsetconstr__Cong) => 71.20/9.71 (( 71.20/9.71 (subsetI1) => 71.20/9.71 (( 71.20/9.71 (eqimpsubset2) => 71.20/9.71 (( 71.20/9.71 (eqimpsubset1) => 71.20/9.71 (( 71.20/9.71 (subsetI2) => 71.20/9.71 (( 71.20/9.71 (emptysetsubset) => 71.20/9.71 (( 71.20/9.71 (subsetE) => 71.20/9.71 (( 71.20/9.71 (subsetE2) => 71.20/9.71 (( 71.20/9.71 (notsubsetI) => 71.20/9.71 (( 71.20/9.71 (notequalI1) => 71.20/9.71 (( 71.20/9.71 (notequalI2) => 71.20/9.71 (( 71.20/9.71 (subsetRefl) => 71.20/9.71 (( 71.20/9.71 (subsetTrans) => 71.20/9.71 (( 71.20/9.71 (setadjoinSub) => 71.20/9.71 (( 71.20/9.71 (setadjoinSub2) => 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@ ( 71.20/9.71 ( 71.20/9.71 ('#B') @ ( 71.20/9.71 '#B') @ 71.20/9.71 ( 71.20/9.71 ( 71.20/9.71 ('#B') @ ( 71.20/9.71 '#B') @ 71.20/9.71 breln1)))) @ 71.20/9.71 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 71.20/9.71 thf(zip_derived_cl46, plain, 71.20/9.71 (~ (((replAx) => 71.20/9.71 (((foundationAx) => 71.20/9.71 (((wellorderingAx) => 71.20/9.71 (((descrp) => 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=> 71.20/9.71 (( 71.20/9.71 (singletoninpowerset) => 71.20/9.71 (( 71.20/9.71 (singletoninpowunion) => 71.20/9.71 (( 71.20/9.71 (upairset2E) => 71.20/9.71 (( 71.20/9.71 (upairsubunion) => 71.20/9.71 (( 71.20/9.71 (upairinpowunion) => 71.20/9.71 (( 71.20/9.71 (ubforcartprodlem1) => 71.20/9.71 (( 71.20/9.71 (ubforcartprodlem2) => 71.20/9.71 (( 71.20/9.71 (ubforcartprodlem3) => 71.20/9.71 (( 71.20/9.71 (cartprodpairin) => 71.20/9.71 (( 71.20/9.71 (cartprodmempair1) => 71.20/9.71 (( 71.20/9.71 (cartprodmempair) => 71.20/9.71 (( 71.20/9.71 (setunionE2) => 71.20/9.71 (( 71.20/9.71 (setunionsingleton1) => 71.20/9.71 (( 71.20/9.71 (setunionsingleton2) => 71.20/9.71 (( 71.20/9.71 (setunionsingleton) => 71.20/9.71 (( 71.20/9.71 (singletonprop) => 71.20/9.71 (( 71.20/9.71 (ex1E1) => 71.20/9.71 (( 71.20/9.71 (ex1I) => 71.20/9.71 (( 71.20/9.71 (ex1I2) => 71.20/9.71 (( 71.20/9.71 (singletonsuniq) => 71.20/9.71 (( 71.20/9.71 (setukpairinjL1) => 71.20/9.71 (( 71.20/9.71 (kfstsingleton) => 71.20/9.71 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=> 71.20/9.71 (( 71.20/9.71 (demorgan2b2) => 71.20/9.71 (( 71.20/9.71 (demorgan2b) => 71.20/9.71 (( 71.20/9.71 (demorgan2) => 71.20/9.71 (( 71.20/9.71 (woz13rule0) => 71.20/9.71 (( 71.20/9.71 (woz13rule1) => 71.20/9.71 (( 71.20/9.71 (woz13rule2) => 71.20/9.71 (( 71.20/9.71 (woz13rule3) => 71.20/9.71 (( 71.20/9.71 (woz13rule4) => 71.20/9.71 (( 71.20/9.71 (woz1_1) => 71.20/9.71 (( 71.20/9.71 (woz1_2) => 71.20/9.71 (( 71.20/9.71 (woz1_3) => 71.20/9.71 (( 71.20/9.71 (woz1_4) => 71.20/9.71 (( 71.20/9.71 (woz1_5) => 71.20/9.71 (( 71.20/9.71 (breln1all2) => 71.20/9.71 (( 71.20/9.71 (breln1SetBreln1) => 71.20/9.71 (( 71.20/9.71 (choice2fnsingleton) => 71.20/9.71 (( 71.20/9.71 (setOfPairsIsBReln1) => 71.20/9.71 (( 71.20/9.71 (breln1all1) => 71.20/9.71 (( 71.20/9.71 (subbreln1) => 71.20/9.71 (( 71.20/9.71 (eqbreln1) => 71.20/9.71 (( 71.20/9.71 (breln1invprop) => 71.20/9.71 (( 71.20/9.71 (breln1invI) => 71.20/9.71 (( 71.20/9.71 (breln1invE) => 71.20/9.71 (( 71.20/9.71 (breln1compprop) => 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71.20/9.72 !!))) @ 71.20/9.72 ( 71.20/9.72 ( 71.20/9.72 ('#S') @ ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 '#B') @ 71.20/9.72 ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 '#S') @ 71.20/9.72 ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 =>))) @ 71.20/9.72 breln1)))))) @ 71.20/9.72 ( 71.20/9.72 ( 71.20/9.72 ('#C') @ ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 '#B') @ 71.20/9.72 ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 '#B') @ 71.20/9.72 breln1)))) @ 71.20/9.72 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 71.20/9.72 thf(zip_derived_cl142, plain, 71.20/9.72 (~ (((emptysetE) => 71.20/9.72 (((emptysetimpfalse) => 71.20/9.72 (((notinemptyset) => 71.20/9.72 (((exuE3e) => 71.20/9.72 (((setext) => 71.20/9.72 (((emptyI) => 71.20/9.72 (((noeltsimpempty) => 71.20/9.72 (((setbeta) => 71.20/9.72 (((nonemptyE1) => 71.20/9.72 (((nonemptyI) => 71.20/9.72 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(quantDeMorgan4) => 71.20/9.72 (( 71.20/9.72 (prop2setI) => 71.20/9.72 (( 71.20/9.72 (prop2set2propI) => 71.20/9.72 (( 71.20/9.72 (notdexE) => 71.20/9.72 (( 71.20/9.72 (notdallE) => 71.20/9.72 (( 71.20/9.72 (exuI1) => 71.20/9.72 (( 71.20/9.72 (exuI3) => 71.20/9.72 (( 71.20/9.72 (exuI2) => 71.20/9.72 (( 71.20/9.72 (inCongP) => 71.20/9.72 (( 71.20/9.72 (in__Cong) => 71.20/9.72 (( 71.20/9.72 (exuE3u) => 71.20/9.72 (( 71.20/9.72 (exu__Cong) => 71.20/9.72 (( 71.20/9.72 (setadjoin__Cong) => 71.20/9.72 (( 71.20/9.72 (powerset__Cong) => 71.20/9.72 (( 71.20/9.72 (setunion__Cong) => 71.20/9.72 (( 71.20/9.72 (exuEu) => 71.20/9.72 (( 71.20/9.72 (descr__Cong) => 71.20/9.72 (( 71.20/9.72 (dsetconstr__Cong) => 71.20/9.72 (( 71.20/9.72 (subsetI1) => 71.20/9.72 (( 71.20/9.72 (eqimpsubset2) => 71.20/9.72 (( 71.20/9.72 (eqimpsubset1) => 71.20/9.72 (( 71.20/9.72 (subsetI2) => 71.20/9.72 (( 71.20/9.72 (emptysetsubset) => 71.20/9.72 (( 71.20/9.72 (subsetE) => 71.20/9.72 (( 71.20/9.72 (subsetE2) => 71.20/9.72 (( 71.20/9.72 (notsubsetI) => 71.20/9.72 (( 71.20/9.72 (notequalI1) => 71.20/9.72 (( 71.20/9.72 (notequalI2) => 71.20/9.72 (( 71.20/9.72 (subsetRefl) => 71.20/9.72 (( 71.20/9.72 (subsetTrans) => 71.20/9.72 (( 71.20/9.72 (setadjoinSub) => 71.20/9.72 (( 71.20/9.72 (setadjoinSub2) => 71.20/9.72 (( 71.20/9.72 (subset2powerset) => 71.20/9.72 (( 71.20/9.72 (setextsub) => 71.20/9.72 (( 71.20/9.72 (subsetemptysetimpeq) => 71.20/9.72 (( 71.20/9.72 (powersetI1) => 71.20/9.72 (( 71.20/9.72 (powersetE1) => 71.20/9.72 (( 71.20/9.72 (inPowerset) => 71.20/9.72 (( 71.20/9.72 (powersetsubset) => 71.20/9.72 (( 71.20/9.72 (sepInPowerset) => 71.20/9.72 (( 71.20/9.72 (sepSubset) => 71.20/9.72 (( 71.20/9.72 (binunionIL) => 71.20/9.72 (( 71.20/9.72 (upairset2IR) => 71.20/9.72 (( 71.20/9.72 (binunionIR) => 71.20/9.72 (( 71.20/9.72 (binunionEcases) => 71.20/9.72 (( 71.20/9.72 (binunionE) => 71.20/9.72 (( 71.20/9.72 (binunionLsub) => 71.20/9.72 (( 71.20/9.72 (binunionRsub) => 71.20/9.72 (( 71.20/9.72 (binintersectI) => 71.20/9.72 (( 71.20/9.72 (binintersectSubset5) => 71.20/9.72 (( 71.20/9.72 (binintersectEL) => 71.20/9.72 (( 71.20/9.72 (binintersectLsub) => 71.20/9.72 (( 71.20/9.72 (binintersectSubset2) => 71.20/9.72 (( 71.20/9.72 (binintersectSubset3) => 71.20/9.72 (( 71.20/9.72 (binintersectER) => 71.20/9.72 (( 71.20/9.72 (disjointsetsI1) => 71.20/9.72 (( 71.20/9.72 (binintersectRsub) => 71.20/9.72 (( 71.20/9.72 (binintersectSubset4) => 71.20/9.72 (( 71.20/9.72 (binintersectSubset1) => 71.20/9.72 (( 71.20/9.72 (bs114d) => 71.20/9.72 (( 71.20/9.72 (setminusI) => 71.20/9.72 (( 71.20/9.72 (setminusEL) => 71.20/9.72 (( 71.20/9.72 (setminusER) => 71.20/9.72 (( 71.20/9.72 (setminusSubset2) => 71.20/9.72 (( 71.20/9.72 (setminusERneg) => 71.20/9.72 (( 71.20/9.72 (setminusELneg) => 71.20/9.72 (( 71.20/9.72 (setminusILneg) => 71.20/9.72 (( 71.20/9.72 (setminusIRneg) => 71.20/9.72 (( 71.20/9.72 (setminusLsub) => 71.20/9.72 (( 71.20/9.72 (setminusSubset1) => 71.20/9.72 (( 71.20/9.72 (symdiffE) => 71.20/9.72 (( 71.20/9.72 (symdiffI1) => 71.20/9.72 (( 71.20/9.72 (symdiffI2) => 71.20/9.72 (( 71.20/9.72 (symdiffIneg1) => 71.20/9.72 (( 71.20/9.72 (symdiffIneg2) => 71.20/9.72 (( 71.20/9.72 (secondinupair) => 71.20/9.72 (( 71.20/9.72 (setukpairIL) => 71.20/9.72 (( 71.20/9.72 (setukpairIR) => 71.20/9.72 (( 71.20/9.72 (kpairiskpair) => 71.20/9.72 (( 71.20/9.72 (kpairp) => 71.20/9.72 (( 71.20/9.72 (singletonsubset) => 71.20/9.72 (( 71.20/9.72 (singletoninpowerset) => 71.20/9.72 (( 71.20/9.72 (singletoninpowunion) => 71.20/9.72 (( 71.20/9.72 (upairset2E) => 71.20/9.72 (( 71.20/9.72 (upairsubunion) => 71.20/9.72 (( 71.20/9.72 (upairinpowunion) => 71.20/9.72 (( 71.20/9.72 (ubforcartprodlem1) => 71.20/9.72 (( 71.20/9.72 (ubforcartprodlem2) => 71.20/9.72 (( 71.20/9.72 (ubforcartprodlem3) => 71.20/9.72 (( 71.20/9.72 (cartprodpairin) => 71.20/9.72 (( 71.20/9.72 (cartprodmempair1) => 71.20/9.72 (( 71.20/9.72 (cartprodmempair) => 71.20/9.72 (( 71.20/9.72 (setunionE2) => 71.20/9.72 (( 71.20/9.72 (setunionsingleton1) => 71.20/9.72 (( 71.20/9.72 (setunionsingleton2) => 71.20/9.72 (( 71.20/9.72 (setunionsingleton) => 71.20/9.72 (( 71.20/9.72 (singletonprop) => 71.20/9.72 (( 71.20/9.72 (ex1E1) => 71.20/9.72 (( 71.20/9.72 (ex1I) => 71.20/9.72 (( 71.20/9.72 (ex1I2) => 71.20/9.72 (( 71.20/9.72 (singletonsuniq) => 71.20/9.72 (( 71.20/9.72 (setukpairinjL1) => 71.20/9.72 (( 71.20/9.72 (kfstsingleton) => 71.20/9.72 (( 71.20/9.72 (theprop) => 71.20/9.72 (( 71.20/9.72 (kfstpairEq) => 71.20/9.72 (( 71.20/9.72 (cartprodfstin) => 71.20/9.72 (( 71.20/9.72 (setukpairinjL2) => 71.20/9.72 (( 71.20/9.72 (setukpairinjL) => 71.20/9.72 (( 71.20/9.72 (setukpairinjR11) => 71.20/9.72 (( 71.20/9.72 (setukpairinjR12) => 71.20/9.72 (( 71.20/9.72 (setukpairinjR1) => 71.20/9.72 (( 71.20/9.72 (upairequniteq) => 71.20/9.72 (( 71.20/9.72 (setukpairinjR2) => 71.20/9.72 (( 71.20/9.72 (setukpairinjR) => 71.20/9.72 (( 71.20/9.72 (ksndsingleton) => 71.20/9.72 (( 71.20/9.72 (ksndpairEq) => 71.20/9.72 (( 71.20/9.72 (kpairsurjEq) => 71.20/9.72 (( 71.20/9.72 (cartprodsndin) => 71.20/9.72 (( 71.20/9.72 (cartprodpairmemEL) => 71.20/9.72 (( 71.20/9.72 (cartprodpairmemER) => 71.20/9.72 (( 71.20/9.72 (cartprodmempaircEq) => 71.20/9.72 (( 71.20/9.72 (cartprodfstpairEq) => 71.20/9.72 (( 71.20/9.72 (cartprodsndpairEq) => 71.20/9.72 (( 71.20/9.72 (cartprodpairsurjEq) => 71.20/9.72 (( 71.20/9.72 (dpsetconstrI) => 71.20/9.72 (( 71.20/9.72 (dpsetconstrSub) => 71.20/9.72 (( 71.20/9.72 (setOfPairsIsBReln) => 71.20/9.72 (( 71.20/9.72 (dpsetconstrERa) => 71.20/9.72 (( 71.20/9.72 (dpsetconstrEL1) => 71.20/9.72 (( 71.20/9.72 (dpsetconstrEL2) => 71.20/9.72 (( 71.20/9.72 (dpsetconstrER) => 71.20/9.72 (( 71.20/9.72 (funcImageSingleton) => 71.20/9.72 (( 71.20/9.72 (apProp) => 71.20/9.72 (( 71.20/9.72 (app) => 71.20/9.72 (( 71.20/9.72 (infuncsetfunc) => 71.20/9.72 (( 71.20/9.72 (ap2p) => 71.20/9.72 (( 71.20/9.72 (funcinfuncset) => 71.20/9.72 (( 71.20/9.72 (lamProp) => 71.20/9.72 (( 71.20/9.72 (lamp) => 71.20/9.72 (( 71.20/9.72 (lam2p) => 71.20/9.72 (( 71.20/9.72 (brelnall1) => 71.20/9.72 (( 71.20/9.72 (brelnall2) => 71.20/9.72 (( 71.20/9.72 (ex1E2) => 71.20/9.72 (( 71.20/9.72 (funcGraphProp1) => 71.20/9.72 (( 71.20/9.72 (funcGraphProp3) => 71.20/9.72 (( 71.20/9.72 (funcGraphProp2) => 71.20/9.72 (( 71.20/9.72 (funcextLem) => 71.20/9.72 (( 71.20/9.72 (funcGraphProp4) => 71.20/9.72 (( 71.20/9.72 (subbreln) => 71.20/9.72 (( 71.20/9.72 (eqbreln) => 71.20/9.72 (( 71.20/9.72 (funcext) => 71.20/9.72 (( 71.20/9.72 (funcext2) => 71.20/9.72 (( 71.20/9.72 (ap2apEq1) => 71.20/9.72 (( 71.20/9.72 (ap2apEq2) => 71.20/9.72 (( 71.20/9.72 (beta1) => 71.20/9.72 (( 71.20/9.72 (eta1) => 71.20/9.72 (( 71.20/9.72 (lam2lamEq) => 71.20/9.72 (( 71.20/9.72 (beta2) => 71.20/9.72 (( 71.20/9.72 (eta2) => 71.20/9.72 (( 71.20/9.72 (iffalseProp1) => 71.20/9.72 (( 71.20/9.72 (iffalseProp2) => 71.20/9.72 (( 71.20/9.72 (iftrueProp1) => 71.20/9.72 (( 71.20/9.72 (iftrueProp2) => 71.20/9.72 (( 71.20/9.72 (ifSingleton) => 71.20/9.72 (( 71.20/9.72 (ifp) => 71.20/9.72 (( 71.20/9.72 (theeq) => 71.20/9.72 (( 71.20/9.72 (iftrue) => 71.20/9.72 (( 71.20/9.72 (iffalse) => 71.20/9.72 (( 71.20/9.72 (iftrueorfalse) => 71.20/9.72 (( 71.20/9.72 (binintersectT_lem) => 71.20/9.72 (( 71.20/9.72 (binunionT_lem) => 71.20/9.72 (( 71.20/9.72 (powersetT_lem) => 71.20/9.72 (( 71.20/9.72 (setminusT_lem) => 71.20/9.72 (( 71.20/9.72 (complementT_lem) => 71.20/9.72 (( 71.20/9.72 (setextT) => 71.20/9.72 (( 71.20/9.72 (subsetTI) => 71.20/9.72 (( 71.20/9.72 (powersetTI1) => 71.20/9.72 (( 71.20/9.72 (powersetTE1) => 71.20/9.72 (( 71.20/9.72 (complementTI1) => 71.20/9.72 (( 71.20/9.72 (complementTE1) => 71.20/9.72 (( 71.20/9.72 (binintersectTELcontra) => 71.20/9.72 (( 71.20/9.72 (binintersectTERcontra) => 71.20/9.72 (( 71.20/9.72 (contrasubsetT) => 71.20/9.72 (( 71.20/9.72 (contrasubsetT1) => 71.20/9.72 (( 71.20/9.72 (contrasubsetT2) => 71.20/9.72 (( 71.20/9.72 (contrasubsetT3) => 71.20/9.72 (( 71.20/9.72 (doubleComplementI1) => 71.20/9.72 (( 71.20/9.72 (doubleComplementE1) => 71.20/9.72 (( 71.20/9.72 (doubleComplementSub1) => 71.20/9.72 (( 71.20/9.72 (doubleComplementSub2) => 71.20/9.72 (( 71.20/9.72 (doubleComplementEq) => 71.20/9.72 (( 71.20/9.72 (complementTnotintersectT) => 71.20/9.72 (( 71.20/9.72 (complementImpComplementIntersect) => 71.20/9.72 (( 71.20/9.72 (complementSubsetComplementIntersect) => 71.20/9.72 (( 71.20/9.72 (complementInPowersetComplementIntersect) => 71.20/9.72 (( 71.20/9.72 (contraSubsetComplement) => 71.20/9.72 (( 71.20/9.72 (complementTcontraSubset) => 71.20/9.72 (( 71.20/9.72 (binunionTILcontra) => 71.20/9.72 (( 71.20/9.72 (binunionTIRcontra) => 71.20/9.72 (( 71.20/9.72 (inIntersectImpInUnion) => 71.20/9.72 (( 71.20/9.72 (inIntersectImpInUnion2) => 71.20/9.72 (( 71.20/9.72 (inIntersectImpInIntersectUnions) => 71.20/9.72 (( 71.20/9.72 (intersectInPowersetIntersectUnions) => 71.20/9.72 (( 71.20/9.72 (inComplementUnionImpNotIn1) => 71.20/9.72 (( 71.20/9.72 (inComplementUnionImpInComplement1) => 71.20/9.72 (( 71.20/9.72 (binunionTE) => 71.20/9.72 (( 71.20/9.72 (binunionTEcontra) => 71.20/9.72 (( 71.20/9.72 (demorgan2a1) => 71.20/9.72 (( 71.20/9.72 (complementUnionInPowersetComplement) => 71.20/9.72 (( 71.20/9.72 (demorgan2a2) => 71.20/9.72 (( 71.20/9.72 (demorgan1a) => 71.20/9.72 (( 71.20/9.72 (demorgan1b) => 71.20/9.72 (( 71.20/9.72 (demorgan1) => 71.20/9.72 (( 71.20/9.72 (demorgan2a) => 71.20/9.72 (( 71.20/9.72 (demorgan2b2) => 71.20/9.72 (( 71.20/9.72 (demorgan2b) => 71.20/9.72 (( 71.20/9.72 (demorgan2) => 71.20/9.72 (( 71.20/9.72 (woz13rule0) => 71.20/9.72 (( 71.20/9.72 (woz13rule1) => 71.20/9.72 (( 71.20/9.72 (woz13rule2) => 71.20/9.72 (( 71.20/9.72 (woz13rule3) => 71.20/9.72 (( 71.20/9.72 (woz13rule4) => 71.20/9.72 (( 71.20/9.72 (woz1_1) => 71.20/9.72 (( 71.20/9.72 (woz1_2) => 71.20/9.72 (( 71.20/9.72 (woz1_3) => 71.20/9.72 (( 71.20/9.72 (woz1_4) => 71.20/9.72 (( 71.20/9.72 (woz1_5) => 71.20/9.72 (( 71.20/9.72 (breln1all2) => 71.20/9.72 (( 71.20/9.72 (breln1SetBreln1) => 71.20/9.72 (( 71.20/9.72 (choice2fnsingleton) => 71.20/9.72 (( 71.20/9.72 (setOfPairsIsBReln1) => 71.20/9.72 (( 71.20/9.72 (breln1all1) => 71.20/9.72 (( 71.20/9.72 (subbreln1) => 71.20/9.72 (( 71.20/9.72 (eqbreln1) => 71.20/9.72 (( 71.20/9.72 (breln1invprop) => 71.20/9.72 (( 71.20/9.72 (breln1invI) => 71.20/9.72 (( 71.20/9.72 (breln1invE) => 71.20/9.72 (( 71.20/9.72 (breln1compprop) => 71.20/9.72 (( 71.20/9.72 (breln1compI) => 71.20/9.72 (( 71.20/9.72 (breln1compE) => 71.20/9.72 (( 71.20/9.72 (breln1compEex) => 71.20/9.72 (( 71.20/9.72 (!!) @ ( 71.20/9.72 (('#B') @ ( 71.20/9.72 !!) @ 71.20/9.72 ( 71.20/9.72 ( 71.20/9.72 ('#S') @ ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 '#S') @ 71.20/9.72 ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 =>))) @ 71.20/9.72 breln1)))) @ 71.20/9.72 ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 !!))) @ 71.20/9.72 ( 71.20/9.72 ( 71.20/9.72 ('#S') @ ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 '#B') @ 71.20/9.72 ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 '#S') @ 71.20/9.72 ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 =>))) @ 71.20/9.72 breln1)))))) @ 71.20/9.72 ( 71.20/9.72 ( 71.20/9.72 ('#C') @ ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 '#B') @ 71.20/9.72 ( 71.20/9.72 ( 71.20/9.72 ('#B') @ ( 71.20/9.72 '#B') @ 71.20/9.72 breln1)))) @ 71.20/9.72 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])). 71.20/9.72 thf(zip_derived_cl158, plain, 71.20/9.72 (~ (((emptysetimpfalse) => 71.20/9.72 (((notinemptyset) => 71.20/9.72 (((exuE3e) => 71.20/9.72 (((setext) => 71.20/9.72 (((emptyI) => 71.20/9.72 (((noeltsimpempty) => 71.20/9.72 (((setbeta) => 71.20/9.72 (((nonemptyE1) => 71.20/9.72 (((nonemptyI) => 71.20/9.72 (((nonemptyI1) => 71.20/9.72 (((setadjoinIL) => 71.20/9.72 (((in @ emptyset @ 71.20/9.72 (setadjoin @ emptyset @ emptyset)) => 71.20/9.72 (((setadjoinIR) => 71.20/9.72 (((setadjoinE) => 71.20/9.72 (((setadjoinOr) => 71.20/9.72 (((setoftrueEq) => 71.20/9.72 (((powersetI) => 71.20/9.72 (((emptyinPowerset) => 71.20/9.72 (((emptyInPowerset) => 71.20/9.72 (((powersetE) => 71.20/9.72 (((setunionI) => 71.20/9.72 (((setunionE) => 71.20/9.72 (((subPowSU) => 71.20/9.72 (((exuE2) => 71.20/9.72 (((nonemptyImpWitness) => 71.20/9.72 (((uniqinunit) => 71.20/9.72 (((notinsingleton) => 71.20/9.72 (((eqinunit) => 71.20/9.72 (((singletonsswitch) => 71.20/9.72 (((upairsetE) => 71.20/9.72 (( 71.20/9.72 (upairsetIL) => 71.20/9.72 (( 71.20/9.72 (upairsetIR) => 71.20/9.72 (( 71.20/9.72 (emptyE1) => 71.20/9.72 (( 71.20/9.72 (vacuousDall) => 71.20/9.72 (( 71.20/9.72 (quantDeMorgan1) => 71.20/9.72 (( 71.20/9.72 (quantDeMorgan2) => 71.20/9.72 (( 71.20/9.72 (quantDeMorgan3) => 71.20/9.72 (( 71.20/9.72 (quantDeMorgan4) => 71.20/9.72 (( 71.20/9.72 (prop2setI) => 71.20/9.72 (( 71.20/9.72 (prop2set2propI) => 71.20/9.72 (( 71.20/9.72 (notdexE) => 71.20/9.72 (( 71.20/9.72 (notdallE) => 71.20/9.72 (( 71.20/9.72 (exuI1) => 71.20/9.72 (( 71.20/9.72 (exuI3) => 71.20/9.72 (( 71.20/9.72 (exuI2) => 71.20/9.72 (( 71.20/9.72 (inCongP) => 71.20/9.72 (( 71.20/9.72 (in__Cong) => 71.20/9.72 (( 71.20/9.72 (exuE3u) => 71.20/9.72 (( 71.20/9.72 (exu__Cong) => 71.20/9.72 (( 71.20/9.72 (setadjoin__Cong) => 71.20/9.72 (( 71.20/9.72 (powerset__Cong) => 71.20/9.72 (( 71.20/9.72 (setunion__Cong) => 71.20/9.72 (( 71.20/9.72 (exuEu) => 71.20/9.72 (( 71.20/9.72 (descr__Cong) => 71.20/9.72 (( 71.20/9.72 (dsetconstr__Cong) => 71.20/9.72 (( 71.20/9.72 (subsetI1) => 71.20/9.72 (( 71.20/9.72 (eqimpsubset2) => 71.20/9.72 (( 71.20/9.72 (eqimpsubset1) => 71.20/9.72 (( 71.20/9.72 (subsetI2) => 71.20/9.72 (( 71.20/9.72 (emptysetsubset) => 71.20/9.72 (( 71.20/9.72 (subsetE) => 71.20/9.72 (( 71.20/9.72 (subsetE2) => 71.20/9.72 (( 71.20/9.72 (notsubsetI) => 71.20/9.72 (( 71.20/9.72 (notequalI1) => 71.20/9.72 (( 71.20/9.72 (notequalI2) => 71.20/9.72 (( 71.20/9.72 (subsetRefl) => 71.20/9.72 (( 71.20/9.72 (subsetTrans) => 71.20/9.72 (( 71.20/9.72 (setadjoinSub) => 71.20/9.72 (( 71.20/9.72 (setadjoinSub2) => 71.20/9.72 (( 71.20/9.72 (subset2powerset) => 71.20/9.72 (( 71.20/9.72 (setextsub) => 71.20/9.72 (( 71.20/9.72 (subsetemptysetimpeq) => 71.20/9.72 (( 71.20/9.72 (powersetI1) => 71.20/9.72 (( 71.20/9.72 (powersetE1) => 71.20/9.72 (( 71.20/9.72 (inPowerset) => 71.20/9.72 (( 71.20/9.72 (powersetsubset) => 71.20/9.72 (( 71.20/9.72 (sepInPowerset) => 71.20/9.72 (( 71.20/9.72 (sepSubset) => 71.20/9.72 (( 71.20/9.72 (binunionIL) => 71.20/9.72 (( 71.20/9.72 (upairset2IR) => 71.20/9.72 (( 71.20/9.72 (binunionIR) => 71.20/9.72 (( 71.20/9.72 (binunionEcases) => 71.20/9.72 (( 71.20/9.72 (binunionE) => 71.20/9.72 (( 71.20/9.72 (binunionLsub) => 71.20/9.72 (( 71.20/9.72 (binunionRsub) => 71.20/9.72 (( 71.20/9.72 (binintersectI) => 71.20/9.72 (( 71.20/9.72 (binintersectSubset5) => 71.20/9.72 (( 71.20/9.72 (binintersectEL) => 71.20/9.72 (( 71.20/9.72 (binintersectLsub) => 71.20/9.72 (( 71.20/9.72 (binintersectSubset2) => 71.20/9.72 (( 71.20/9.72 (binintersectSubset3) => 71.20/9.72 (( 71.20/9.72 (binintersectER) => 71.20/9.72 (( 71.20/9.72 (disjointsetsI1) => 71.20/9.72 (( 71.20/9.72 (binintersectRsub) => 71.20/9.72 (( 71.20/9.72 (binintersectSubset4) => 71.20/9.72 (( 71.20/9.72 (binintersectSubset1) => 71.20/9.72 (( 71.20/9.72 (bs114d) => 71.20/9.72 (( 71.20/9.72 (setminusI) => 71.20/9.72 (( 71.20/9.72 (setminusEL) => 71.20/9.72 (( 71.20/9.72 (setminusER) => 71.20/9.72 (( 71.20/9.72 (setminusSubset2) => 71.20/9.72 (( 71.20/9.72 (setminusERneg) => 71.20/9.72 (( 71.20/9.72 (setminusELneg) => 71.20/9.72 (( 71.20/9.72 (setminusILneg) => 71.20/9.72 (( 71.20/9.72 (setminusIRneg) => 71.20/9.72 (( 71.20/9.72 (setminusLsub) => 71.20/9.72 (( 71.20/9.72 (setminusSubset1) => 71.20/9.72 (( 71.20/9.72 (symdiffE) => 71.20/9.72 (( 71.20/9.72 (symdiffI1) => 71.20/9.72 (( 71.20/9.72 (symdiffI2) => 71.20/9.72 (( 71.20/9.72 (symdiffIneg1) => 71.20/9.72 (( 71.20/9.72 (symdiffIneg2) => 71.20/9.72 (( 71.20/9.72 (secondinupair) => 71.20/9.72 (( 71.20/9.72 (setukpairIL) => 71.20/9.72 (( 71.20/9.72 (setukpairIR) => 71.20/9.72 (( 71.20/9.72 (kpairiskpair) => 71.20/9.72 (( 71.20/9.72 (kpairp) => 71.20/9.72 (( 71.20/9.72 (singletonsubset) => 71.20/9.72 (( 71.20/9.72 (singletoninpowerset) => 71.20/9.72 (( 71.20/9.72 (singletoninpowunion) => 71.20/9.72 (( 71.20/9.72 (upairset2E) => 71.20/9.72 (( 71.20/9.72 (upairsubunion) => 71.20/9.72 (( 71.20/9.72 (upairinpowunion) => 71.20/9.72 (( 71.20/9.72 (ubforcartprodlem1) => 71.20/9.72 (( 71.20/9.72 (ubforcartprodlem2) => 71.20/9.72 (( 71.20/9.72 (ubforcartprodlem3) => 71.20/9.72 (( 71.20/9.72 (cartprodpairin) => 71.20/9.72 (( 71.20/9.72 (cartprodmempair1) => 71.20/9.72 (( 71.20/9.72 (cartprodmempair) => 71.20/9.72 (( 71.20/9.72 (setunionE2) => 71.20/9.72 (( 71.20/9.72 (setunionsingleton1) => 71.20/9.72 (( 71.20/9.72 (setunionsingleton2) => 71.20/9.72 (( 71.20/9.72 (setunionsingleton) => 71.20/9.72 (( 71.20/9.72 (singletonprop) => 71.20/9.72 (( 71.20/9.72 (ex1E1) => 71.20/9.72 (( 71.20/9.72 (ex1I) => 71.20/9.72 (( 71.20/9.72 (ex1I2) => 71.20/9.72 (( 71.20/9.72 (singletonsuniq) => 71.20/9.72 (( 71.20/9.72 (setukpairinjL1) => 71.20/9.72 (( 71.20/9.72 (kfstsingleton) => 71.20/9.72 (( 71.20/9.72 (theprop) => 71.20/9.72 (( 71.20/9.72 (kfstpairEq) => 71.20/9.72 (( 71.20/9.72 (cartprodfstin) => 71.20/9.72 (( 71.20/9.72 (setukpairinjL2) => 71.20/9.72 (( 71.20/9.72 (setukpairinjL) => 71.20/9.72 (( 71.20/9.72 (setukpairinjR11) => 71.20/9.72 (( 71.20/9.72 (setukpairinjR12) => 71.20/9.72 (( 71.20/9.72 (setukpairinjR1) => 71.20/9.72 (( 71.20/9.72 (upairequniteq) => 71.20/9.72 (( 71.20/9.72 (setukpairinjR2) => 71.20/9.72 (( 71.20/9.72 (setukpairinjR) => 71.20/9.72 (( 71.20/9.72 (ksndsingleton) => 71.20/9.72 (( 71.20/9.72 (ksndpairEq) => 71.20/9.72 (( 71.20/9.72 (kpairsurjEq) => 71.20/9.72 (( 71.20/9.72 (cartprodsndin) => 71.20/9.72 (( 71.20/9.72 (cartprodpairmemEL) => 71.20/9.72 (( 71.20/9.72 (cartprodpairmemER) => 71.20/9.72 (( 71.20/9.72 (cartprodmempaircEq) => 71.20/9.72 (( 71.20/9.72 (cartprodfstpairEq) => 71.20/9.72 (( 71.20/9.72 (cartprodsndpairEq) => 71.20/9.72 (( 71.20/9.72 (cartprodpairsurjEq) => 71.20/9.72 (( 71.20/9.72 (dpsetconstrI) => 71.20/9.72 (( 71.20/9.72 (dpsetconstrSub) => 71.20/9.72 (( 71.20/9.72 (setOfPairsIsBReln) => 71.20/9.72 (( 71.20/9.72 (dpsetconstrERa) => 71.20/9.72 (( 71.20/9.72 (dpsetconstrEL1) => 71.20/9.72 (( 71.20/9.72 (dpsetconstrEL2) => 71.20/9.72 (( 71.20/9.72 (dpsetconstrER) => 71.20/9.72 (( 71.20/9.72 (funcImageSingleton) => 71.20/9.72 (( 71.20/9.72 (apProp) => 71.20/9.72 (( 71.20/9.72 (app) => 71.20/9.72 (( 71.20/9.72 (infuncsetfunc) => 71.20/9.72 (( 71.20/9.72 (ap2p) => 71.20/9.72 (( 71.20/9.72 (funcinfuncset) => 71.20/9.72 (( 71.20/9.72 (lamProp) => 71.20/9.72 (( 71.20/9.72 (lamp) => 71.20/9.72 (( 71.20/9.72 (lam2p) => 71.20/9.72 (( 71.20/9.72 (brelnall1) => 71.20/9.72 (( 71.20/9.72 (brelnall2) => 71.20/9.72 (( 71.20/9.72 (ex1E2) => 71.20/9.72 (( 71.20/9.72 (funcGraphProp1) => 71.20/9.72 (( 71.20/9.72 (funcGraphProp3) => 71.20/9.72 (( 71.20/9.72 (funcGraphProp2) => 71.20/9.72 (( 71.20/9.72 (funcextLem) => 71.20/9.72 (( 71.20/9.72 (funcGraphProp4) => 71.20/9.72 (( 71.20/9.72 (subbreln) => 71.20/9.72 (( 71.20/9.72 (eqbreln) => 71.20/9.72 (( 71.20/9.72 (funcext) => 71.20/9.73 (( 71.20/9.73 (funcext2) => 71.20/9.73 (( 71.20/9.73 (ap2apEq1) => 71.20/9.73 (( 71.20/9.73 (ap2apEq2) => 71.20/9.73 (( 71.20/9.73 (beta1) => 71.20/9.73 (( 71.20/9.73 (eta1) => 71.20/9.73 (( 71.20/9.73 (lam2lamEq) => 71.20/9.73 (( 71.20/9.73 (beta2) => 71.20/9.73 (( 71.20/9.73 (eta2) => 71.20/9.73 (( 71.20/9.73 (iffalseProp1) => 71.20/9.73 (( 71.20/9.73 (iffalseProp2) => 71.20/9.73 (( 71.20/9.73 (iftrueProp1) => 71.20/9.73 (( 71.20/9.73 (iftrueProp2) => 71.20/9.73 (( 71.20/9.73 (ifSingleton) => 71.20/9.73 (( 71.20/9.73 (ifp) => 71.20/9.73 (( 71.20/9.73 (theeq) => 71.20/9.73 (( 71.20/9.73 (iftrue) => 71.20/9.73 (( 71.20/9.73 (iffalse) => 71.20/9.73 (( 71.20/9.73 (iftrueorfalse) => 71.20/9.73 (( 71.20/9.73 (binintersectT_lem) => 71.20/9.73 (( 71.20/9.73 (binunionT_lem) => 71.20/9.73 (( 71.20/9.73 (powersetT_lem) => 71.20/9.73 (( 71.20/9.73 (setminusT_lem) => 71.20/9.73 (( 71.20/9.73 (complementT_lem) => 71.20/9.73 (( 71.20/9.73 (setextT) => 71.20/9.73 (( 71.20/9.73 (subsetTI) => 71.20/9.73 (( 71.20/9.73 (powersetTI1) => 71.20/9.73 (( 71.20/9.73 (powersetTE1) => 71.20/9.73 (( 71.20/9.73 (complementTI1) => 71.20/9.73 (( 71.20/9.73 (complementTE1) => 71.20/9.73 (( 71.20/9.73 (binintersectTELcontra) => 71.20/9.73 (( 71.20/9.73 (binintersectTERcontra) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT1) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT2) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT3) => 71.20/9.73 (( 71.20/9.73 (doubleComplementI1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementE1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementSub1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementSub2) => 71.20/9.73 (( 71.20/9.73 (doubleComplementEq) => 71.20/9.73 (( 71.20/9.73 (complementTnotintersectT) => 71.20/9.73 (( 71.20/9.73 (complementImpComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (complementSubsetComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (complementInPowersetComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (contraSubsetComplement) => 71.20/9.73 (( 71.20/9.73 (complementTcontraSubset) => 71.20/9.73 (( 71.20/9.73 (binunionTILcontra) => 71.20/9.73 (( 71.20/9.73 (binunionTIRcontra) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInUnion) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInUnion2) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInIntersectUnions) => 71.20/9.73 (( 71.20/9.73 (intersectInPowersetIntersectUnions) => 71.20/9.73 (( 71.20/9.73 (inComplementUnionImpNotIn1) => 71.20/9.73 (( 71.20/9.73 (inComplementUnionImpInComplement1) => 71.20/9.73 (( 71.20/9.73 (binunionTE) => 71.20/9.73 (( 71.20/9.73 (binunionTEcontra) => 71.20/9.73 (( 71.20/9.73 (demorgan2a1) => 71.20/9.73 (( 71.20/9.73 (complementUnionInPowersetComplement) => 71.20/9.73 (( 71.20/9.73 (demorgan2a2) => 71.20/9.73 (( 71.20/9.73 (demorgan1a) => 71.20/9.73 (( 71.20/9.73 (demorgan1b) => 71.20/9.73 (( 71.20/9.73 (demorgan1) => 71.20/9.73 (( 71.20/9.73 (demorgan2a) => 71.20/9.73 (( 71.20/9.73 (demorgan2b2) => 71.20/9.73 (( 71.20/9.73 (demorgan2b) => 71.20/9.73 (( 71.20/9.73 (demorgan2) => 71.20/9.73 (( 71.20/9.73 (woz13rule0) => 71.20/9.73 (( 71.20/9.73 (woz13rule1) => 71.20/9.73 (( 71.20/9.73 (woz13rule2) => 71.20/9.73 (( 71.20/9.73 (woz13rule3) => 71.20/9.73 (( 71.20/9.73 (woz13rule4) => 71.20/9.73 (( 71.20/9.73 (woz1_1) => 71.20/9.73 (( 71.20/9.73 (woz1_2) => 71.20/9.73 (( 71.20/9.73 (woz1_3) => 71.20/9.73 (( 71.20/9.73 (woz1_4) => 71.20/9.73 (( 71.20/9.73 (woz1_5) => 71.20/9.73 (( 71.20/9.73 (breln1all2) => 71.20/9.73 (( 71.20/9.73 (breln1SetBreln1) => 71.20/9.73 (( 71.20/9.73 (choice2fnsingleton) => 71.20/9.73 (( 71.20/9.73 (setOfPairsIsBReln1) => 71.20/9.73 (( 71.20/9.73 (breln1all1) => 71.20/9.73 (( 71.20/9.73 (subbreln1) => 71.20/9.73 (( 71.20/9.73 (eqbreln1) => 71.20/9.73 (( 71.20/9.73 (breln1invprop) => 71.20/9.73 (( 71.20/9.73 (breln1invI) => 71.20/9.73 (( 71.20/9.73 (breln1invE) => 71.20/9.73 (( 71.20/9.73 (breln1compprop) => 71.20/9.73 (( 71.20/9.73 (breln1compI) => 71.20/9.73 (( 71.20/9.73 (breln1compE) => 71.20/9.73 (( 71.20/9.73 (breln1compEex) => 71.20/9.73 (( 71.20/9.73 (!!) @ ( 71.20/9.73 (('#B') @ ( 71.20/9.73 !!) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#S') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#S') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 =>))) @ 71.20/9.73 breln1)))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 !!))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#S') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#S') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 =>))) @ 71.20/9.73 breln1)))))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#C') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 breln1)))) @ 71.20/9.73 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])). 71.20/9.73 thf(zip_derived_cl174, plain, 71.20/9.73 (~ (((notinemptyset) => 71.20/9.73 (((exuE3e) => 71.20/9.73 (((setext) => 71.20/9.73 (((emptyI) => 71.20/9.73 (((noeltsimpempty) => 71.20/9.73 (((setbeta) => 71.20/9.73 (((nonemptyE1) => 71.20/9.73 (((nonemptyI) => 71.20/9.73 (((nonemptyI1) => 71.20/9.73 (((setadjoinIL) => 71.20/9.73 (((in @ emptyset @ 71.20/9.73 (setadjoin @ emptyset @ emptyset)) => 71.20/9.73 (((setadjoinIR) => 71.20/9.73 (((setadjoinE) => 71.20/9.73 (((setadjoinOr) => 71.20/9.73 (((setoftrueEq) => 71.20/9.73 (((powersetI) => 71.20/9.73 (((emptyinPowerset) => 71.20/9.73 (((emptyInPowerset) => 71.20/9.73 (((powersetE) => 71.20/9.73 (((setunionI) => 71.20/9.73 (((setunionE) => 71.20/9.73 (((subPowSU) => 71.20/9.73 (((exuE2) => 71.20/9.73 (((nonemptyImpWitness) => 71.20/9.73 (((uniqinunit) => 71.20/9.73 (((notinsingleton) => 71.20/9.73 (((eqinunit) => 71.20/9.73 (((singletonsswitch) => 71.20/9.73 (((upairsetE) => 71.20/9.73 (((upairsetIL) => 71.20/9.73 (( 71.20/9.73 (upairsetIR) => 71.20/9.73 (( 71.20/9.73 (emptyE1) => 71.20/9.73 (( 71.20/9.73 (vacuousDall) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan1) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan2) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan3) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan4) => 71.20/9.73 (( 71.20/9.73 (prop2setI) => 71.20/9.73 (( 71.20/9.73 (prop2set2propI) => 71.20/9.73 (( 71.20/9.73 (notdexE) => 71.20/9.73 (( 71.20/9.73 (notdallE) => 71.20/9.73 (( 71.20/9.73 (exuI1) => 71.20/9.73 (( 71.20/9.73 (exuI3) => 71.20/9.73 (( 71.20/9.73 (exuI2) => 71.20/9.73 (( 71.20/9.73 (inCongP) => 71.20/9.73 (( 71.20/9.73 (in__Cong) => 71.20/9.73 (( 71.20/9.73 (exuE3u) => 71.20/9.73 (( 71.20/9.73 (exu__Cong) => 71.20/9.73 (( 71.20/9.73 (setadjoin__Cong) => 71.20/9.73 (( 71.20/9.73 (powerset__Cong) => 71.20/9.73 (( 71.20/9.73 (setunion__Cong) => 71.20/9.73 (( 71.20/9.73 (exuEu) => 71.20/9.73 (( 71.20/9.73 (descr__Cong) => 71.20/9.73 (( 71.20/9.73 (dsetconstr__Cong) => 71.20/9.73 (( 71.20/9.73 (subsetI1) => 71.20/9.73 (( 71.20/9.73 (eqimpsubset2) => 71.20/9.73 (( 71.20/9.73 (eqimpsubset1) => 71.20/9.73 (( 71.20/9.73 (subsetI2) => 71.20/9.73 (( 71.20/9.73 (emptysetsubset) => 71.20/9.73 (( 71.20/9.73 (subsetE) => 71.20/9.73 (( 71.20/9.73 (subsetE2) => 71.20/9.73 (( 71.20/9.73 (notsubsetI) => 71.20/9.73 (( 71.20/9.73 (notequalI1) => 71.20/9.73 (( 71.20/9.73 (notequalI2) => 71.20/9.73 (( 71.20/9.73 (subsetRefl) => 71.20/9.73 (( 71.20/9.73 (subsetTrans) => 71.20/9.73 (( 71.20/9.73 (setadjoinSub) => 71.20/9.73 (( 71.20/9.73 (setadjoinSub2) => 71.20/9.73 (( 71.20/9.73 (subset2powerset) => 71.20/9.73 (( 71.20/9.73 (setextsub) => 71.20/9.73 (( 71.20/9.73 (subsetemptysetimpeq) => 71.20/9.73 (( 71.20/9.73 (powersetI1) => 71.20/9.73 (( 71.20/9.73 (powersetE1) => 71.20/9.73 (( 71.20/9.73 (inPowerset) => 71.20/9.73 (( 71.20/9.73 (powersetsubset) => 71.20/9.73 (( 71.20/9.73 (sepInPowerset) => 71.20/9.73 (( 71.20/9.73 (sepSubset) => 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71.20/9.73 (setminusSubset2) => 71.20/9.73 (( 71.20/9.73 (setminusERneg) => 71.20/9.73 (( 71.20/9.73 (setminusELneg) => 71.20/9.73 (( 71.20/9.73 (setminusILneg) => 71.20/9.73 (( 71.20/9.73 (setminusIRneg) => 71.20/9.73 (( 71.20/9.73 (setminusLsub) => 71.20/9.73 (( 71.20/9.73 (setminusSubset1) => 71.20/9.73 (( 71.20/9.73 (symdiffE) => 71.20/9.73 (( 71.20/9.73 (symdiffI1) => 71.20/9.73 (( 71.20/9.73 (symdiffI2) => 71.20/9.73 (( 71.20/9.73 (symdiffIneg1) => 71.20/9.73 (( 71.20/9.73 (symdiffIneg2) => 71.20/9.73 (( 71.20/9.73 (secondinupair) => 71.20/9.73 (( 71.20/9.73 (setukpairIL) => 71.20/9.73 (( 71.20/9.73 (setukpairIR) => 71.20/9.73 (( 71.20/9.73 (kpairiskpair) => 71.20/9.73 (( 71.20/9.73 (kpairp) => 71.20/9.73 (( 71.20/9.73 (singletonsubset) => 71.20/9.73 (( 71.20/9.73 (singletoninpowerset) => 71.20/9.73 (( 71.20/9.73 (singletoninpowunion) => 71.20/9.73 (( 71.20/9.73 (upairset2E) => 71.20/9.73 (( 71.20/9.73 (upairsubunion) => 71.20/9.73 (( 71.20/9.73 (upairinpowunion) => 71.20/9.73 (( 71.20/9.73 (ubforcartprodlem1) => 71.20/9.73 (( 71.20/9.73 (ubforcartprodlem2) => 71.20/9.73 (( 71.20/9.73 (ubforcartprodlem3) => 71.20/9.73 (( 71.20/9.73 (cartprodpairin) => 71.20/9.73 (( 71.20/9.73 (cartprodmempair1) => 71.20/9.73 (( 71.20/9.73 (cartprodmempair) => 71.20/9.73 (( 71.20/9.73 (setunionE2) => 71.20/9.73 (( 71.20/9.73 (setunionsingleton1) => 71.20/9.73 (( 71.20/9.73 (setunionsingleton2) => 71.20/9.73 (( 71.20/9.73 (setunionsingleton) => 71.20/9.73 (( 71.20/9.73 (singletonprop) => 71.20/9.73 (( 71.20/9.73 (ex1E1) => 71.20/9.73 (( 71.20/9.73 (ex1I) => 71.20/9.73 (( 71.20/9.73 (ex1I2) => 71.20/9.73 (( 71.20/9.73 (singletonsuniq) => 71.20/9.73 (( 71.20/9.73 (setukpairinjL1) => 71.20/9.73 (( 71.20/9.73 (kfstsingleton) => 71.20/9.73 (( 71.20/9.73 (theprop) => 71.20/9.73 (( 71.20/9.73 (kfstpairEq) => 71.20/9.73 (( 71.20/9.73 (cartprodfstin) => 71.20/9.73 (( 71.20/9.73 (setukpairinjL2) => 71.20/9.73 (( 71.20/9.73 (setukpairinjL) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR11) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR12) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR1) => 71.20/9.73 (( 71.20/9.73 (upairequniteq) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR2) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR) => 71.20/9.73 (( 71.20/9.73 (ksndsingleton) => 71.20/9.73 (( 71.20/9.73 (ksndpairEq) => 71.20/9.73 (( 71.20/9.73 (kpairsurjEq) => 71.20/9.73 (( 71.20/9.73 (cartprodsndin) => 71.20/9.73 (( 71.20/9.73 (cartprodpairmemEL) => 71.20/9.73 (( 71.20/9.73 (cartprodpairmemER) => 71.20/9.73 (( 71.20/9.73 (cartprodmempaircEq) => 71.20/9.73 (( 71.20/9.73 (cartprodfstpairEq) => 71.20/9.73 (( 71.20/9.73 (cartprodsndpairEq) => 71.20/9.73 (( 71.20/9.73 (cartprodpairsurjEq) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrI) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrSub) => 71.20/9.73 (( 71.20/9.73 (setOfPairsIsBReln) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrERa) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrEL1) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrEL2) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrER) => 71.20/9.73 (( 71.20/9.73 (funcImageSingleton) => 71.20/9.73 (( 71.20/9.73 (apProp) => 71.20/9.73 (( 71.20/9.73 (app) => 71.20/9.73 (( 71.20/9.73 (infuncsetfunc) => 71.20/9.73 (( 71.20/9.73 (ap2p) => 71.20/9.73 (( 71.20/9.73 (funcinfuncset) => 71.20/9.73 (( 71.20/9.73 (lamProp) => 71.20/9.73 (( 71.20/9.73 (lamp) => 71.20/9.73 (( 71.20/9.73 (lam2p) => 71.20/9.73 (( 71.20/9.73 (brelnall1) => 71.20/9.73 (( 71.20/9.73 (brelnall2) => 71.20/9.73 (( 71.20/9.73 (ex1E2) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp1) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp3) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp2) => 71.20/9.73 (( 71.20/9.73 (funcextLem) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp4) => 71.20/9.73 (( 71.20/9.73 (subbreln) => 71.20/9.73 (( 71.20/9.73 (eqbreln) => 71.20/9.73 (( 71.20/9.73 (funcext) => 71.20/9.73 (( 71.20/9.73 (funcext2) => 71.20/9.73 (( 71.20/9.73 (ap2apEq1) => 71.20/9.73 (( 71.20/9.73 (ap2apEq2) => 71.20/9.73 (( 71.20/9.73 (beta1) => 71.20/9.73 (( 71.20/9.73 (eta1) => 71.20/9.73 (( 71.20/9.73 (lam2lamEq) => 71.20/9.73 (( 71.20/9.73 (beta2) => 71.20/9.73 (( 71.20/9.73 (eta2) => 71.20/9.73 (( 71.20/9.73 (iffalseProp1) => 71.20/9.73 (( 71.20/9.73 (iffalseProp2) => 71.20/9.73 (( 71.20/9.73 (iftrueProp1) => 71.20/9.73 (( 71.20/9.73 (iftrueProp2) => 71.20/9.73 (( 71.20/9.73 (ifSingleton) => 71.20/9.73 (( 71.20/9.73 (ifp) => 71.20/9.73 (( 71.20/9.73 (theeq) => 71.20/9.73 (( 71.20/9.73 (iftrue) => 71.20/9.73 (( 71.20/9.73 (iffalse) => 71.20/9.73 (( 71.20/9.73 (iftrueorfalse) => 71.20/9.73 (( 71.20/9.73 (binintersectT_lem) => 71.20/9.73 (( 71.20/9.73 (binunionT_lem) => 71.20/9.73 (( 71.20/9.73 (powersetT_lem) => 71.20/9.73 (( 71.20/9.73 (setminusT_lem) => 71.20/9.73 (( 71.20/9.73 (complementT_lem) => 71.20/9.73 (( 71.20/9.73 (setextT) => 71.20/9.73 (( 71.20/9.73 (subsetTI) => 71.20/9.73 (( 71.20/9.73 (powersetTI1) => 71.20/9.73 (( 71.20/9.73 (powersetTE1) => 71.20/9.73 (( 71.20/9.73 (complementTI1) => 71.20/9.73 (( 71.20/9.73 (complementTE1) => 71.20/9.73 (( 71.20/9.73 (binintersectTELcontra) => 71.20/9.73 (( 71.20/9.73 (binintersectTERcontra) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT1) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT2) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT3) => 71.20/9.73 (( 71.20/9.73 (doubleComplementI1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementE1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementSub1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementSub2) => 71.20/9.73 (( 71.20/9.73 (doubleComplementEq) => 71.20/9.73 (( 71.20/9.73 (complementTnotintersectT) => 71.20/9.73 (( 71.20/9.73 (complementImpComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (complementSubsetComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (complementInPowersetComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (contraSubsetComplement) => 71.20/9.73 (( 71.20/9.73 (complementTcontraSubset) => 71.20/9.73 (( 71.20/9.73 (binunionTILcontra) => 71.20/9.73 (( 71.20/9.73 (binunionTIRcontra) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInUnion) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInUnion2) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInIntersectUnions) => 71.20/9.73 (( 71.20/9.73 (intersectInPowersetIntersectUnions) => 71.20/9.73 (( 71.20/9.73 (inComplementUnionImpNotIn1) => 71.20/9.73 (( 71.20/9.73 (inComplementUnionImpInComplement1) => 71.20/9.73 (( 71.20/9.73 (binunionTE) => 71.20/9.73 (( 71.20/9.73 (binunionTEcontra) => 71.20/9.73 (( 71.20/9.73 (demorgan2a1) => 71.20/9.73 (( 71.20/9.73 (complementUnionInPowersetComplement) => 71.20/9.73 (( 71.20/9.73 (demorgan2a2) => 71.20/9.73 (( 71.20/9.73 (demorgan1a) => 71.20/9.73 (( 71.20/9.73 (demorgan1b) => 71.20/9.73 (( 71.20/9.73 (demorgan1) => 71.20/9.73 (( 71.20/9.73 (demorgan2a) => 71.20/9.73 (( 71.20/9.73 (demorgan2b2) => 71.20/9.73 (( 71.20/9.73 (demorgan2b) => 71.20/9.73 (( 71.20/9.73 (demorgan2) => 71.20/9.73 (( 71.20/9.73 (woz13rule0) => 71.20/9.73 (( 71.20/9.73 (woz13rule1) => 71.20/9.73 (( 71.20/9.73 (woz13rule2) => 71.20/9.73 (( 71.20/9.73 (woz13rule3) => 71.20/9.73 (( 71.20/9.73 (woz13rule4) => 71.20/9.73 (( 71.20/9.73 (woz1_1) => 71.20/9.73 (( 71.20/9.73 (woz1_2) => 71.20/9.73 (( 71.20/9.73 (woz1_3) => 71.20/9.73 (( 71.20/9.73 (woz1_4) => 71.20/9.73 (( 71.20/9.73 (woz1_5) => 71.20/9.73 (( 71.20/9.73 (breln1all2) => 71.20/9.73 (( 71.20/9.73 (breln1SetBreln1) => 71.20/9.73 (( 71.20/9.73 (choice2fnsingleton) => 71.20/9.73 (( 71.20/9.73 (setOfPairsIsBReln1) => 71.20/9.73 (( 71.20/9.73 (breln1all1) => 71.20/9.73 (( 71.20/9.73 (subbreln1) => 71.20/9.73 (( 71.20/9.73 (eqbreln1) => 71.20/9.73 (( 71.20/9.73 (breln1invprop) => 71.20/9.73 (( 71.20/9.73 (breln1invI) => 71.20/9.73 (( 71.20/9.73 (breln1invE) => 71.20/9.73 (( 71.20/9.73 (breln1compprop) => 71.20/9.73 (( 71.20/9.73 (breln1compI) => 71.20/9.73 (( 71.20/9.73 (breln1compE) => 71.20/9.73 (( 71.20/9.73 (breln1compEex) => 71.20/9.73 (( 71.20/9.73 (!!) @ ( 71.20/9.73 (('#B') @ ( 71.20/9.73 !!) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#S') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#S') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 =>))) @ 71.20/9.73 breln1)))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 !!))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#S') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#S') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 =>))) @ 71.20/9.73 breln1)))))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#C') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 breln1)))) @ 71.20/9.73 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])). 71.20/9.73 thf(zip_derived_cl189, plain, 71.20/9.73 (~ (((exuE3e) => 71.20/9.73 (((setext) => 71.20/9.73 (((emptyI) => 71.20/9.73 (((noeltsimpempty) => 71.20/9.73 (((setbeta) => 71.20/9.73 (((nonemptyE1) => 71.20/9.73 (((nonemptyI) => 71.20/9.73 (((nonemptyI1) => 71.20/9.73 (((setadjoinIL) => 71.20/9.73 (((in @ emptyset @ 71.20/9.73 (setadjoin @ emptyset @ emptyset)) => 71.20/9.73 (((setadjoinIR) => 71.20/9.73 (((setadjoinE) => 71.20/9.73 (((setadjoinOr) => 71.20/9.73 (((setoftrueEq) => 71.20/9.73 (((powersetI) => 71.20/9.73 (((emptyinPowerset) => 71.20/9.73 (((emptyInPowerset) => 71.20/9.73 (((powersetE) => 71.20/9.73 (((setunionI) => 71.20/9.73 (((setunionE) => 71.20/9.73 (((subPowSU) => 71.20/9.73 (((exuE2) => 71.20/9.73 (((nonemptyImpWitness) => 71.20/9.73 (((uniqinunit) => 71.20/9.73 (((notinsingleton) => 71.20/9.73 (((eqinunit) => 71.20/9.73 (((singletonsswitch) => 71.20/9.73 (((upairsetE) => 71.20/9.73 (((upairsetIL) => 71.20/9.73 (((upairsetIR) => 71.20/9.73 (( 71.20/9.73 (emptyE1) => 71.20/9.73 (( 71.20/9.73 (vacuousDall) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan1) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan2) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan3) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan4) => 71.20/9.73 (( 71.20/9.73 (prop2setI) => 71.20/9.73 (( 71.20/9.73 (prop2set2propI) => 71.20/9.73 (( 71.20/9.73 (notdexE) => 71.20/9.73 (( 71.20/9.73 (notdallE) => 71.20/9.73 (( 71.20/9.73 (exuI1) => 71.20/9.73 (( 71.20/9.73 (exuI3) => 71.20/9.73 (( 71.20/9.73 (exuI2) => 71.20/9.73 (( 71.20/9.73 (inCongP) => 71.20/9.73 (( 71.20/9.73 (in__Cong) => 71.20/9.73 (( 71.20/9.73 (exuE3u) => 71.20/9.73 (( 71.20/9.73 (exu__Cong) => 71.20/9.73 (( 71.20/9.73 (setadjoin__Cong) => 71.20/9.73 (( 71.20/9.73 (powerset__Cong) => 71.20/9.73 (( 71.20/9.73 (setunion__Cong) => 71.20/9.73 (( 71.20/9.73 (exuEu) => 71.20/9.73 (( 71.20/9.73 (descr__Cong) => 71.20/9.73 (( 71.20/9.73 (dsetconstr__Cong) => 71.20/9.73 (( 71.20/9.73 (subsetI1) => 71.20/9.73 (( 71.20/9.73 (eqimpsubset2) => 71.20/9.73 (( 71.20/9.73 (eqimpsubset1) => 71.20/9.73 (( 71.20/9.73 (subsetI2) => 71.20/9.73 (( 71.20/9.73 (emptysetsubset) => 71.20/9.73 (( 71.20/9.73 (subsetE) => 71.20/9.73 (( 71.20/9.73 (subsetE2) => 71.20/9.73 (( 71.20/9.73 (notsubsetI) => 71.20/9.73 (( 71.20/9.73 (notequalI1) => 71.20/9.73 (( 71.20/9.73 (notequalI2) => 71.20/9.73 (( 71.20/9.73 (subsetRefl) => 71.20/9.73 (( 71.20/9.73 (subsetTrans) => 71.20/9.73 (( 71.20/9.73 (setadjoinSub) => 71.20/9.73 (( 71.20/9.73 (setadjoinSub2) => 71.20/9.73 (( 71.20/9.73 (subset2powerset) => 71.20/9.73 (( 71.20/9.73 (setextsub) => 71.20/9.73 (( 71.20/9.73 (subsetemptysetimpeq) => 71.20/9.73 (( 71.20/9.73 (powersetI1) => 71.20/9.73 (( 71.20/9.73 (powersetE1) => 71.20/9.73 (( 71.20/9.73 (inPowerset) => 71.20/9.73 (( 71.20/9.73 (powersetsubset) => 71.20/9.73 (( 71.20/9.73 (sepInPowerset) => 71.20/9.73 (( 71.20/9.73 (sepSubset) => 71.20/9.73 (( 71.20/9.73 (binunionIL) => 71.20/9.73 (( 71.20/9.73 (upairset2IR) => 71.20/9.73 (( 71.20/9.73 (binunionIR) => 71.20/9.73 (( 71.20/9.73 (binunionEcases) => 71.20/9.73 (( 71.20/9.73 (binunionE) => 71.20/9.73 (( 71.20/9.73 (binunionLsub) => 71.20/9.73 (( 71.20/9.73 (binunionRsub) => 71.20/9.73 (( 71.20/9.73 (binintersectI) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset5) => 71.20/9.73 (( 71.20/9.73 (binintersectEL) => 71.20/9.73 (( 71.20/9.73 (binintersectLsub) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset2) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset3) => 71.20/9.73 (( 71.20/9.73 (binintersectER) => 71.20/9.73 (( 71.20/9.73 (disjointsetsI1) => 71.20/9.73 (( 71.20/9.73 (binintersectRsub) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset4) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset1) => 71.20/9.73 (( 71.20/9.73 (bs114d) => 71.20/9.73 (( 71.20/9.73 (setminusI) => 71.20/9.73 (( 71.20/9.73 (setminusEL) => 71.20/9.73 (( 71.20/9.73 (setminusER) => 71.20/9.73 (( 71.20/9.73 (setminusSubset2) => 71.20/9.73 (( 71.20/9.73 (setminusERneg) => 71.20/9.73 (( 71.20/9.73 (setminusELneg) => 71.20/9.73 (( 71.20/9.73 (setminusILneg) => 71.20/9.73 (( 71.20/9.73 (setminusIRneg) => 71.20/9.73 (( 71.20/9.73 (setminusLsub) => 71.20/9.73 (( 71.20/9.73 (setminusSubset1) => 71.20/9.73 (( 71.20/9.73 (symdiffE) => 71.20/9.73 (( 71.20/9.73 (symdiffI1) => 71.20/9.73 (( 71.20/9.73 (symdiffI2) => 71.20/9.73 (( 71.20/9.73 (symdiffIneg1) => 71.20/9.73 (( 71.20/9.73 (symdiffIneg2) => 71.20/9.73 (( 71.20/9.73 (secondinupair) => 71.20/9.73 (( 71.20/9.73 (setukpairIL) => 71.20/9.73 (( 71.20/9.73 (setukpairIR) => 71.20/9.73 (( 71.20/9.73 (kpairiskpair) => 71.20/9.73 (( 71.20/9.73 (kpairp) => 71.20/9.73 (( 71.20/9.73 (singletonsubset) => 71.20/9.73 (( 71.20/9.73 (singletoninpowerset) => 71.20/9.73 (( 71.20/9.73 (singletoninpowunion) => 71.20/9.73 (( 71.20/9.73 (upairset2E) => 71.20/9.73 (( 71.20/9.73 (upairsubunion) => 71.20/9.73 (( 71.20/9.73 (upairinpowunion) => 71.20/9.73 (( 71.20/9.73 (ubforcartprodlem1) => 71.20/9.73 (( 71.20/9.73 (ubforcartprodlem2) => 71.20/9.73 (( 71.20/9.73 (ubforcartprodlem3) => 71.20/9.73 (( 71.20/9.73 (cartprodpairin) => 71.20/9.73 (( 71.20/9.73 (cartprodmempair1) => 71.20/9.73 (( 71.20/9.73 (cartprodmempair) => 71.20/9.73 (( 71.20/9.73 (setunionE2) => 71.20/9.73 (( 71.20/9.73 (setunionsingleton1) => 71.20/9.73 (( 71.20/9.73 (setunionsingleton2) => 71.20/9.73 (( 71.20/9.73 (setunionsingleton) => 71.20/9.73 (( 71.20/9.73 (singletonprop) => 71.20/9.73 (( 71.20/9.73 (ex1E1) => 71.20/9.73 (( 71.20/9.73 (ex1I) => 71.20/9.73 (( 71.20/9.73 (ex1I2) => 71.20/9.73 (( 71.20/9.73 (singletonsuniq) => 71.20/9.73 (( 71.20/9.73 (setukpairinjL1) => 71.20/9.73 (( 71.20/9.73 (kfstsingleton) => 71.20/9.73 (( 71.20/9.73 (theprop) => 71.20/9.73 (( 71.20/9.73 (kfstpairEq) => 71.20/9.73 (( 71.20/9.73 (cartprodfstin) => 71.20/9.73 (( 71.20/9.73 (setukpairinjL2) => 71.20/9.73 (( 71.20/9.73 (setukpairinjL) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR11) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR12) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR1) => 71.20/9.73 (( 71.20/9.73 (upairequniteq) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR2) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR) => 71.20/9.73 (( 71.20/9.73 (ksndsingleton) => 71.20/9.73 (( 71.20/9.73 (ksndpairEq) => 71.20/9.73 (( 71.20/9.73 (kpairsurjEq) => 71.20/9.73 (( 71.20/9.73 (cartprodsndin) => 71.20/9.73 (( 71.20/9.73 (cartprodpairmemEL) => 71.20/9.73 (( 71.20/9.73 (cartprodpairmemER) => 71.20/9.73 (( 71.20/9.73 (cartprodmempaircEq) => 71.20/9.73 (( 71.20/9.73 (cartprodfstpairEq) => 71.20/9.73 (( 71.20/9.73 (cartprodsndpairEq) => 71.20/9.73 (( 71.20/9.73 (cartprodpairsurjEq) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrI) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrSub) => 71.20/9.73 (( 71.20/9.73 (setOfPairsIsBReln) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrERa) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrEL1) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrEL2) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrER) => 71.20/9.73 (( 71.20/9.73 (funcImageSingleton) => 71.20/9.73 (( 71.20/9.73 (apProp) => 71.20/9.73 (( 71.20/9.73 (app) => 71.20/9.73 (( 71.20/9.73 (infuncsetfunc) => 71.20/9.73 (( 71.20/9.73 (ap2p) => 71.20/9.73 (( 71.20/9.73 (funcinfuncset) => 71.20/9.73 (( 71.20/9.73 (lamProp) => 71.20/9.73 (( 71.20/9.73 (lamp) => 71.20/9.73 (( 71.20/9.73 (lam2p) => 71.20/9.73 (( 71.20/9.73 (brelnall1) => 71.20/9.73 (( 71.20/9.73 (brelnall2) => 71.20/9.73 (( 71.20/9.73 (ex1E2) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp1) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp3) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp2) => 71.20/9.73 (( 71.20/9.73 (funcextLem) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp4) => 71.20/9.73 (( 71.20/9.73 (subbreln) => 71.20/9.73 (( 71.20/9.73 (eqbreln) => 71.20/9.73 (( 71.20/9.73 (funcext) => 71.20/9.73 (( 71.20/9.73 (funcext2) => 71.20/9.73 (( 71.20/9.73 (ap2apEq1) => 71.20/9.73 (( 71.20/9.73 (ap2apEq2) => 71.20/9.73 (( 71.20/9.73 (beta1) => 71.20/9.73 (( 71.20/9.73 (eta1) => 71.20/9.73 (( 71.20/9.73 (lam2lamEq) => 71.20/9.73 (( 71.20/9.73 (beta2) => 71.20/9.73 (( 71.20/9.73 (eta2) => 71.20/9.73 (( 71.20/9.73 (iffalseProp1) => 71.20/9.73 (( 71.20/9.73 (iffalseProp2) => 71.20/9.73 (( 71.20/9.73 (iftrueProp1) => 71.20/9.73 (( 71.20/9.73 (iftrueProp2) => 71.20/9.73 (( 71.20/9.73 (ifSingleton) => 71.20/9.73 (( 71.20/9.73 (ifp) => 71.20/9.73 (( 71.20/9.73 (theeq) => 71.20/9.73 (( 71.20/9.73 (iftrue) => 71.20/9.73 (( 71.20/9.73 (iffalse) => 71.20/9.73 (( 71.20/9.73 (iftrueorfalse) => 71.20/9.73 (( 71.20/9.73 (binintersectT_lem) => 71.20/9.73 (( 71.20/9.73 (binunionT_lem) => 71.20/9.73 (( 71.20/9.73 (powersetT_lem) => 71.20/9.73 (( 71.20/9.73 (setminusT_lem) => 71.20/9.73 (( 71.20/9.73 (complementT_lem) => 71.20/9.73 (( 71.20/9.73 (setextT) => 71.20/9.73 (( 71.20/9.73 (subsetTI) => 71.20/9.73 (( 71.20/9.73 (powersetTI1) => 71.20/9.73 (( 71.20/9.73 (powersetTE1) => 71.20/9.73 (( 71.20/9.73 (complementTI1) => 71.20/9.73 (( 71.20/9.73 (complementTE1) => 71.20/9.73 (( 71.20/9.73 (binintersectTELcontra) => 71.20/9.73 (( 71.20/9.73 (binintersectTERcontra) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT1) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT2) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT3) => 71.20/9.73 (( 71.20/9.73 (doubleComplementI1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementE1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementSub1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementSub2) => 71.20/9.73 (( 71.20/9.73 (doubleComplementEq) => 71.20/9.73 (( 71.20/9.73 (complementTnotintersectT) => 71.20/9.73 (( 71.20/9.73 (complementImpComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (complementSubsetComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (complementInPowersetComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (contraSubsetComplement) => 71.20/9.73 (( 71.20/9.73 (complementTcontraSubset) => 71.20/9.73 (( 71.20/9.73 (binunionTILcontra) => 71.20/9.73 (( 71.20/9.73 (binunionTIRcontra) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInUnion) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInUnion2) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInIntersectUnions) => 71.20/9.73 (( 71.20/9.73 (intersectInPowersetIntersectUnions) => 71.20/9.73 (( 71.20/9.73 (inComplementUnionImpNotIn1) => 71.20/9.73 (( 71.20/9.73 (inComplementUnionImpInComplement1) => 71.20/9.73 (( 71.20/9.73 (binunionTE) => 71.20/9.73 (( 71.20/9.73 (binunionTEcontra) => 71.20/9.73 (( 71.20/9.73 (demorgan2a1) => 71.20/9.73 (( 71.20/9.73 (complementUnionInPowersetComplement) => 71.20/9.73 (( 71.20/9.73 (demorgan2a2) => 71.20/9.73 (( 71.20/9.73 (demorgan1a) => 71.20/9.73 (( 71.20/9.73 (demorgan1b) => 71.20/9.73 (( 71.20/9.73 (demorgan1) => 71.20/9.73 (( 71.20/9.73 (demorgan2a) => 71.20/9.73 (( 71.20/9.73 (demorgan2b2) => 71.20/9.73 (( 71.20/9.73 (demorgan2b) => 71.20/9.73 (( 71.20/9.73 (demorgan2) => 71.20/9.73 (( 71.20/9.73 (woz13rule0) => 71.20/9.73 (( 71.20/9.73 (woz13rule1) => 71.20/9.73 (( 71.20/9.73 (woz13rule2) => 71.20/9.73 (( 71.20/9.73 (woz13rule3) => 71.20/9.73 (( 71.20/9.73 (woz13rule4) => 71.20/9.73 (( 71.20/9.73 (woz1_1) => 71.20/9.73 (( 71.20/9.73 (woz1_2) => 71.20/9.73 (( 71.20/9.73 (woz1_3) => 71.20/9.73 (( 71.20/9.73 (woz1_4) => 71.20/9.73 (( 71.20/9.73 (woz1_5) => 71.20/9.73 (( 71.20/9.73 (breln1all2) => 71.20/9.73 (( 71.20/9.73 (breln1SetBreln1) => 71.20/9.73 (( 71.20/9.73 (choice2fnsingleton) => 71.20/9.73 (( 71.20/9.73 (setOfPairsIsBReln1) => 71.20/9.73 (( 71.20/9.73 (breln1all1) => 71.20/9.73 (( 71.20/9.73 (subbreln1) => 71.20/9.73 (( 71.20/9.73 (eqbreln1) => 71.20/9.73 (( 71.20/9.73 (breln1invprop) => 71.20/9.73 (( 71.20/9.73 (breln1invI) => 71.20/9.73 (( 71.20/9.73 (breln1invE) => 71.20/9.73 (( 71.20/9.73 (breln1compprop) => 71.20/9.73 (( 71.20/9.73 (breln1compI) => 71.20/9.73 (( 71.20/9.73 (breln1compE) => 71.20/9.73 (( 71.20/9.73 (breln1compEex) => 71.20/9.73 (( 71.20/9.73 (!!) @ ( 71.20/9.73 (('#B') @ ( 71.20/9.73 !!) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#S') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#S') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 =>))) @ 71.20/9.73 breln1)))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 !!))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#S') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#S') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 =>))) @ 71.20/9.73 breln1)))))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#C') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 breln1)))) @ 71.20/9.73 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl174])). 71.20/9.73 thf(zip_derived_cl206, plain, 71.20/9.73 (~ (((setext) => 71.20/9.73 (((emptyI) => 71.20/9.73 (((noeltsimpempty) => 71.20/9.73 (((setbeta) => 71.20/9.73 (((nonemptyE1) => 71.20/9.73 (((nonemptyI) => 71.20/9.73 (((nonemptyI1) => 71.20/9.73 (((setadjoinIL) => 71.20/9.73 (((in @ emptyset @ 71.20/9.73 (setadjoin @ emptyset @ emptyset)) => 71.20/9.73 (((setadjoinIR) => 71.20/9.73 (((setadjoinE) => 71.20/9.73 (((setadjoinOr) => 71.20/9.73 (((setoftrueEq) => 71.20/9.73 (((powersetI) => 71.20/9.73 (((emptyinPowerset) => 71.20/9.73 (((emptyInPowerset) => 71.20/9.73 (((powersetE) => 71.20/9.73 (((setunionI) => 71.20/9.73 (((setunionE) => 71.20/9.73 (((subPowSU) => 71.20/9.73 (((exuE2) => 71.20/9.73 (((nonemptyImpWitness) => 71.20/9.73 (((uniqinunit) => 71.20/9.73 (((notinsingleton) => 71.20/9.73 (((eqinunit) => 71.20/9.73 (((singletonsswitch) => 71.20/9.73 (((upairsetE) => 71.20/9.73 (((upairsetIL) => 71.20/9.73 (((upairsetIR) => 71.20/9.73 (((emptyE1) => 71.20/9.73 (( 71.20/9.73 (vacuousDall) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan1) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan2) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan3) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan4) => 71.20/9.73 (( 71.20/9.73 (prop2setI) => 71.20/9.73 (( 71.20/9.73 (prop2set2propI) => 71.20/9.73 (( 71.20/9.73 (notdexE) => 71.20/9.73 (( 71.20/9.73 (notdallE) => 71.20/9.73 (( 71.20/9.73 (exuI1) => 71.20/9.73 (( 71.20/9.73 (exuI3) => 71.20/9.73 (( 71.20/9.73 (exuI2) => 71.20/9.73 (( 71.20/9.73 (inCongP) => 71.20/9.73 (( 71.20/9.73 (in__Cong) => 71.20/9.73 (( 71.20/9.73 (exuE3u) => 71.20/9.73 (( 71.20/9.73 (exu__Cong) => 71.20/9.73 (( 71.20/9.73 (setadjoin__Cong) => 71.20/9.73 (( 71.20/9.73 (powerset__Cong) => 71.20/9.73 (( 71.20/9.73 (setunion__Cong) => 71.20/9.73 (( 71.20/9.73 (exuEu) => 71.20/9.73 (( 71.20/9.73 (descr__Cong) => 71.20/9.73 (( 71.20/9.73 (dsetconstr__Cong) => 71.20/9.73 (( 71.20/9.73 (subsetI1) => 71.20/9.73 (( 71.20/9.73 (eqimpsubset2) => 71.20/9.73 (( 71.20/9.73 (eqimpsubset1) => 71.20/9.73 (( 71.20/9.73 (subsetI2) => 71.20/9.73 (( 71.20/9.73 (emptysetsubset) => 71.20/9.73 (( 71.20/9.73 (subsetE) => 71.20/9.73 (( 71.20/9.73 (subsetE2) => 71.20/9.73 (( 71.20/9.73 (notsubsetI) => 71.20/9.73 (( 71.20/9.73 (notequalI1) => 71.20/9.73 (( 71.20/9.73 (notequalI2) => 71.20/9.73 (( 71.20/9.73 (subsetRefl) => 71.20/9.73 (( 71.20/9.73 (subsetTrans) => 71.20/9.73 (( 71.20/9.73 (setadjoinSub) => 71.20/9.73 (( 71.20/9.73 (setadjoinSub2) => 71.20/9.73 (( 71.20/9.73 (subset2powerset) => 71.20/9.73 (( 71.20/9.73 (setextsub) => 71.20/9.73 (( 71.20/9.73 (subsetemptysetimpeq) => 71.20/9.73 (( 71.20/9.73 (powersetI1) => 71.20/9.73 (( 71.20/9.73 (powersetE1) => 71.20/9.73 (( 71.20/9.73 (inPowerset) => 71.20/9.73 (( 71.20/9.73 (powersetsubset) => 71.20/9.73 (( 71.20/9.73 (sepInPowerset) => 71.20/9.73 (( 71.20/9.73 (sepSubset) => 71.20/9.73 (( 71.20/9.73 (binunionIL) => 71.20/9.73 (( 71.20/9.73 (upairset2IR) => 71.20/9.73 (( 71.20/9.73 (binunionIR) => 71.20/9.73 (( 71.20/9.73 (binunionEcases) => 71.20/9.73 (( 71.20/9.73 (binunionE) => 71.20/9.73 (( 71.20/9.73 (binunionLsub) => 71.20/9.73 (( 71.20/9.73 (binunionRsub) => 71.20/9.73 (( 71.20/9.73 (binintersectI) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset5) => 71.20/9.73 (( 71.20/9.73 (binintersectEL) => 71.20/9.73 (( 71.20/9.73 (binintersectLsub) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset2) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset3) => 71.20/9.73 (( 71.20/9.73 (binintersectER) => 71.20/9.73 (( 71.20/9.73 (disjointsetsI1) => 71.20/9.73 (( 71.20/9.73 (binintersectRsub) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset4) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset1) => 71.20/9.73 (( 71.20/9.73 (bs114d) => 71.20/9.73 (( 71.20/9.73 (setminusI) => 71.20/9.73 (( 71.20/9.73 (setminusEL) => 71.20/9.73 (( 71.20/9.73 (setminusER) => 71.20/9.73 (( 71.20/9.73 (setminusSubset2) => 71.20/9.73 (( 71.20/9.73 (setminusERneg) => 71.20/9.73 (( 71.20/9.73 (setminusELneg) => 71.20/9.73 (( 71.20/9.73 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breln1)))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 !!))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#S') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#S') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 =>))) @ 71.20/9.73 breln1)))))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#C') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 breln1)))) @ 71.20/9.73 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])). 71.20/9.73 thf(zip_derived_cl222, plain, 71.20/9.73 (~ (((emptyI) => 71.20/9.73 (((noeltsimpempty) => 71.20/9.73 (((setbeta) => 71.20/9.73 (((nonemptyE1) => 71.20/9.73 (((nonemptyI) => 71.20/9.73 (((nonemptyI1) => 71.20/9.73 (((setadjoinIL) => 71.20/9.73 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 71.20/9.73 (((setadjoinIR) => 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71.20/9.73 ('#B') @ ( 71.20/9.73 =>))) @ 71.20/9.73 breln1)))))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#C') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 breln1)))) @ 71.20/9.73 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])). 71.20/9.73 thf(zip_derived_cl236, plain, 71.20/9.73 (~ (((noeltsimpempty) => 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=> 71.20/9.73 (( 71.20/9.73 (notsubsetI) => 71.20/9.73 (( 71.20/9.73 (notequalI1) => 71.20/9.73 (( 71.20/9.73 (notequalI2) => 71.20/9.73 (( 71.20/9.73 (subsetRefl) => 71.20/9.73 (( 71.20/9.73 (subsetTrans) => 71.20/9.73 (( 71.20/9.73 (setadjoinSub) => 71.20/9.73 (( 71.20/9.73 (setadjoinSub2) => 71.20/9.73 (( 71.20/9.73 (subset2powerset) => 71.20/9.73 (( 71.20/9.73 (setextsub) => 71.20/9.73 (( 71.20/9.73 (subsetemptysetimpeq) => 71.20/9.73 (( 71.20/9.73 (powersetI1) => 71.20/9.73 (( 71.20/9.73 (powersetE1) => 71.20/9.73 (( 71.20/9.73 (inPowerset) => 71.20/9.73 (( 71.20/9.73 (powersetsubset) => 71.20/9.73 (( 71.20/9.73 (sepInPowerset) => 71.20/9.73 (( 71.20/9.73 (sepSubset) => 71.20/9.73 (( 71.20/9.73 (binunionIL) => 71.20/9.73 (( 71.20/9.73 (upairset2IR) => 71.20/9.73 (( 71.20/9.73 (binunionIR) => 71.20/9.73 (( 71.20/9.73 (binunionEcases) => 71.20/9.73 (( 71.20/9.73 (binunionE) => 71.20/9.73 (( 71.20/9.73 (binunionLsub) => 71.20/9.73 (( 71.20/9.73 (binunionRsub) => 71.20/9.73 (( 71.20/9.73 (binintersectI) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset5) => 71.20/9.73 (( 71.20/9.73 (binintersectEL) => 71.20/9.73 (( 71.20/9.73 (binintersectLsub) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset2) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset3) => 71.20/9.73 (( 71.20/9.73 (binintersectER) => 71.20/9.73 (( 71.20/9.73 (disjointsetsI1) => 71.20/9.73 (( 71.20/9.73 (binintersectRsub) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset4) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset1) => 71.20/9.73 (( 71.20/9.73 (bs114d) => 71.20/9.73 (( 71.20/9.73 (setminusI) => 71.20/9.73 (( 71.20/9.73 (setminusEL) => 71.20/9.73 (( 71.20/9.73 (setminusER) => 71.20/9.73 (( 71.20/9.73 (setminusSubset2) => 71.20/9.73 (( 71.20/9.73 (setminusERneg) => 71.20/9.73 (( 71.20/9.73 (setminusELneg) => 71.20/9.73 (( 71.20/9.73 (setminusILneg) => 71.20/9.73 (( 71.20/9.73 (setminusIRneg) => 71.20/9.73 (( 71.20/9.73 (setminusLsub) => 71.20/9.73 (( 71.20/9.73 (setminusSubset1) => 71.20/9.73 (( 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71.20/9.73 (( 71.20/9.73 (setunionsingleton1) => 71.20/9.73 (( 71.20/9.73 (setunionsingleton2) => 71.20/9.73 (( 71.20/9.73 (setunionsingleton) => 71.20/9.73 (( 71.20/9.73 (singletonprop) => 71.20/9.73 (( 71.20/9.73 (ex1E1) => 71.20/9.73 (( 71.20/9.73 (ex1I) => 71.20/9.73 (( 71.20/9.73 (ex1I2) => 71.20/9.73 (( 71.20/9.73 (singletonsuniq) => 71.20/9.73 (( 71.20/9.73 (setukpairinjL1) => 71.20/9.73 (( 71.20/9.73 (kfstsingleton) => 71.20/9.73 (( 71.20/9.73 (theprop) => 71.20/9.73 (( 71.20/9.73 (kfstpairEq) => 71.20/9.73 (( 71.20/9.73 (cartprodfstin) => 71.20/9.73 (( 71.20/9.73 (setukpairinjL2) => 71.20/9.73 (( 71.20/9.73 (setukpairinjL) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR11) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR12) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR1) => 71.20/9.73 (( 71.20/9.73 (upairequniteq) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR2) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR) => 71.20/9.73 (( 71.20/9.73 (ksndsingleton) => 71.20/9.73 (( 71.20/9.73 (ksndpairEq) => 71.20/9.73 (( 71.20/9.73 (kpairsurjEq) => 71.20/9.73 (( 71.20/9.73 (cartprodsndin) => 71.20/9.73 (( 71.20/9.73 (cartprodpairmemEL) => 71.20/9.73 (( 71.20/9.73 (cartprodpairmemER) => 71.20/9.73 (( 71.20/9.73 (cartprodmempaircEq) => 71.20/9.73 (( 71.20/9.73 (cartprodfstpairEq) => 71.20/9.73 (( 71.20/9.73 (cartprodsndpairEq) => 71.20/9.73 (( 71.20/9.73 (cartprodpairsurjEq) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrI) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrSub) => 71.20/9.73 (( 71.20/9.73 (setOfPairsIsBReln) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrERa) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrEL1) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrEL2) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrER) => 71.20/9.73 (( 71.20/9.73 (funcImageSingleton) => 71.20/9.73 (( 71.20/9.73 (apProp) => 71.20/9.73 (( 71.20/9.73 (app) => 71.20/9.73 (( 71.20/9.73 (infuncsetfunc) => 71.20/9.73 (( 71.20/9.73 (ap2p) => 71.20/9.73 (( 71.20/9.73 (funcinfuncset) => 71.20/9.73 (( 71.20/9.73 (lamProp) => 71.20/9.73 (( 71.20/9.73 (lamp) => 71.20/9.73 (( 71.20/9.73 (lam2p) => 71.20/9.73 (( 71.20/9.73 (brelnall1) => 71.20/9.73 (( 71.20/9.73 (brelnall2) => 71.20/9.73 (( 71.20/9.73 (ex1E2) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp1) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp3) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp2) => 71.20/9.73 (( 71.20/9.73 (funcextLem) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp4) => 71.20/9.73 (( 71.20/9.73 (subbreln) => 71.20/9.73 (( 71.20/9.73 (eqbreln) => 71.20/9.73 (( 71.20/9.73 (funcext) => 71.20/9.73 (( 71.20/9.73 (funcext2) => 71.20/9.73 (( 71.20/9.73 (ap2apEq1) => 71.20/9.73 (( 71.20/9.73 (ap2apEq2) => 71.20/9.73 (( 71.20/9.73 (beta1) => 71.20/9.73 (( 71.20/9.73 (eta1) => 71.20/9.73 (( 71.20/9.73 (lam2lamEq) => 71.20/9.73 (( 71.20/9.73 (beta2) => 71.20/9.73 (( 71.20/9.73 (eta2) => 71.20/9.73 (( 71.20/9.73 (iffalseProp1) => 71.20/9.73 (( 71.20/9.73 (iffalseProp2) => 71.20/9.73 (( 71.20/9.73 (iftrueProp1) => 71.20/9.73 (( 71.20/9.73 (iftrueProp2) => 71.20/9.73 (( 71.20/9.73 (ifSingleton) => 71.20/9.73 (( 71.20/9.73 (ifp) => 71.20/9.73 (( 71.20/9.73 (theeq) => 71.20/9.73 (( 71.20/9.73 (iftrue) => 71.20/9.73 (( 71.20/9.73 (iffalse) => 71.20/9.73 (( 71.20/9.73 (iftrueorfalse) => 71.20/9.73 (( 71.20/9.73 (binintersectT_lem) => 71.20/9.73 (( 71.20/9.73 (binunionT_lem) => 71.20/9.73 (( 71.20/9.73 (powersetT_lem) => 71.20/9.73 (( 71.20/9.73 (setminusT_lem) => 71.20/9.73 (( 71.20/9.73 (complementT_lem) => 71.20/9.73 (( 71.20/9.73 (setextT) => 71.20/9.73 (( 71.20/9.73 (subsetTI) => 71.20/9.73 (( 71.20/9.73 (powersetTI1) => 71.20/9.73 (( 71.20/9.73 (powersetTE1) => 71.20/9.73 (( 71.20/9.73 (complementTI1) => 71.20/9.73 (( 71.20/9.73 (complementTE1) => 71.20/9.73 (( 71.20/9.73 (binintersectTELcontra) => 71.20/9.73 (( 71.20/9.73 (binintersectTERcontra) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT1) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT2) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT3) => 71.20/9.73 (( 71.20/9.73 (doubleComplementI1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementE1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementSub1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementSub2) => 71.20/9.73 (( 71.20/9.73 (doubleComplementEq) => 71.20/9.73 (( 71.20/9.73 (complementTnotintersectT) => 71.20/9.73 (( 71.20/9.73 (complementImpComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (complementSubsetComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (complementInPowersetComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (contraSubsetComplement) => 71.20/9.73 (( 71.20/9.73 (complementTcontraSubset) => 71.20/9.73 (( 71.20/9.73 (binunionTILcontra) => 71.20/9.73 (( 71.20/9.73 (binunionTIRcontra) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInUnion) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInUnion2) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInIntersectUnions) => 71.20/9.73 (( 71.20/9.73 (intersectInPowersetIntersectUnions) => 71.20/9.73 (( 71.20/9.73 (inComplementUnionImpNotIn1) => 71.20/9.73 (( 71.20/9.73 (inComplementUnionImpInComplement1) => 71.20/9.73 (( 71.20/9.73 (binunionTE) => 71.20/9.73 (( 71.20/9.73 (binunionTEcontra) => 71.20/9.73 (( 71.20/9.73 (demorgan2a1) => 71.20/9.73 (( 71.20/9.73 (complementUnionInPowersetComplement) => 71.20/9.73 (( 71.20/9.73 (demorgan2a2) => 71.20/9.73 (( 71.20/9.73 (demorgan1a) => 71.20/9.73 (( 71.20/9.73 (demorgan1b) => 71.20/9.73 (( 71.20/9.73 (demorgan1) => 71.20/9.73 (( 71.20/9.73 (demorgan2a) => 71.20/9.73 (( 71.20/9.73 (demorgan2b2) => 71.20/9.73 (( 71.20/9.73 (demorgan2b) => 71.20/9.73 (( 71.20/9.73 (demorgan2) => 71.20/9.73 (( 71.20/9.73 (woz13rule0) => 71.20/9.73 (( 71.20/9.73 (woz13rule1) => 71.20/9.73 (( 71.20/9.73 (woz13rule2) => 71.20/9.73 (( 71.20/9.73 (woz13rule3) => 71.20/9.73 (( 71.20/9.73 (woz13rule4) => 71.20/9.73 (( 71.20/9.73 (woz1_1) => 71.20/9.73 (( 71.20/9.73 (woz1_2) => 71.20/9.73 (( 71.20/9.73 (woz1_3) => 71.20/9.73 (( 71.20/9.73 (woz1_4) => 71.20/9.73 (( 71.20/9.73 (woz1_5) => 71.20/9.73 (( 71.20/9.73 (breln1all2) => 71.20/9.73 (( 71.20/9.73 (breln1SetBreln1) => 71.20/9.73 (( 71.20/9.73 (choice2fnsingleton) => 71.20/9.73 (( 71.20/9.73 (setOfPairsIsBReln1) => 71.20/9.73 (( 71.20/9.73 (breln1all1) => 71.20/9.73 (( 71.20/9.73 (subbreln1) => 71.20/9.73 (( 71.20/9.73 (eqbreln1) => 71.20/9.73 (( 71.20/9.73 (breln1invprop) => 71.20/9.73 (( 71.20/9.73 (breln1invI) => 71.20/9.73 (( 71.20/9.73 (breln1invE) => 71.20/9.73 (( 71.20/9.73 (breln1compprop) => 71.20/9.73 (( 71.20/9.73 (breln1compI) => 71.20/9.73 (( 71.20/9.73 (breln1compE) => 71.20/9.73 (( 71.20/9.73 (breln1compEex) => 71.20/9.73 (( 71.20/9.73 (!!) @ ( 71.20/9.73 (('#B') @ ( 71.20/9.73 !!) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#S') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#S') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 =>))) @ 71.20/9.73 breln1)))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 !!))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#S') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#S') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 =>))) @ 71.20/9.73 breln1)))))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#C') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 breln1)))) @ 71.20/9.73 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])). 71.20/9.73 thf(zip_derived_cl251, plain, 71.20/9.73 (~ (((setbeta) => 71.20/9.73 (((nonemptyE1) => 71.20/9.73 (((nonemptyI) => 71.20/9.73 (((nonemptyI1) => 71.20/9.73 (((setadjoinIL) => 71.20/9.73 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 71.20/9.73 (((setadjoinIR) => 71.20/9.73 (((setadjoinE) => 71.20/9.73 (((setadjoinOr) => 71.20/9.73 (((setoftrueEq) => 71.20/9.73 (((powersetI) => 71.20/9.73 (((emptyinPowerset) => 71.20/9.73 (((emptyInPowerset) => 71.20/9.73 (((powersetE) => 71.20/9.73 (((setunionI) => 71.20/9.73 (((setunionE) => 71.20/9.73 (((subPowSU) => 71.20/9.73 (((exuE2) => 71.20/9.73 (((nonemptyImpWitness) => 71.20/9.73 (((uniqinunit) => 71.20/9.73 (((notinsingleton) => 71.20/9.73 (((eqinunit) => 71.20/9.73 (((singletonsswitch) => 71.20/9.73 (((upairsetE) => 71.20/9.73 (((upairsetIL) => 71.20/9.73 (((upairsetIR) => 71.20/9.73 (((emptyE1) => 71.20/9.73 (((vacuousDall) => 71.20/9.73 (((quantDeMorgan1) => 71.20/9.73 (((quantDeMorgan2) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan3) => 71.20/9.73 (( 71.20/9.73 (quantDeMorgan4) => 71.20/9.73 (( 71.20/9.73 (prop2setI) => 71.20/9.73 (( 71.20/9.73 (prop2set2propI) => 71.20/9.73 (( 71.20/9.73 (notdexE) => 71.20/9.73 (( 71.20/9.73 (notdallE) => 71.20/9.73 (( 71.20/9.73 (exuI1) => 71.20/9.73 (( 71.20/9.73 (exuI3) => 71.20/9.73 (( 71.20/9.73 (exuI2) => 71.20/9.73 (( 71.20/9.73 (inCongP) => 71.20/9.73 (( 71.20/9.73 (in__Cong) => 71.20/9.73 (( 71.20/9.73 (exuE3u) => 71.20/9.73 (( 71.20/9.73 (exu__Cong) => 71.20/9.73 (( 71.20/9.73 (setadjoin__Cong) => 71.20/9.73 (( 71.20/9.73 (powerset__Cong) => 71.20/9.73 (( 71.20/9.73 (setunion__Cong) => 71.20/9.73 (( 71.20/9.73 (exuEu) => 71.20/9.73 (( 71.20/9.73 (descr__Cong) => 71.20/9.73 (( 71.20/9.73 (dsetconstr__Cong) => 71.20/9.73 (( 71.20/9.73 (subsetI1) => 71.20/9.73 (( 71.20/9.73 (eqimpsubset2) => 71.20/9.73 (( 71.20/9.73 (eqimpsubset1) => 71.20/9.73 (( 71.20/9.73 (subsetI2) => 71.20/9.73 (( 71.20/9.73 (emptysetsubset) => 71.20/9.73 (( 71.20/9.73 (subsetE) => 71.20/9.73 (( 71.20/9.73 (subsetE2) => 71.20/9.73 (( 71.20/9.73 (notsubsetI) => 71.20/9.73 (( 71.20/9.73 (notequalI1) => 71.20/9.73 (( 71.20/9.73 (notequalI2) => 71.20/9.73 (( 71.20/9.73 (subsetRefl) => 71.20/9.73 (( 71.20/9.73 (subsetTrans) => 71.20/9.73 (( 71.20/9.73 (setadjoinSub) => 71.20/9.73 (( 71.20/9.73 (setadjoinSub2) => 71.20/9.73 (( 71.20/9.73 (subset2powerset) => 71.20/9.73 (( 71.20/9.73 (setextsub) => 71.20/9.73 (( 71.20/9.73 (subsetemptysetimpeq) => 71.20/9.73 (( 71.20/9.73 (powersetI1) => 71.20/9.73 (( 71.20/9.73 (powersetE1) => 71.20/9.73 (( 71.20/9.73 (inPowerset) => 71.20/9.73 (( 71.20/9.73 (powersetsubset) => 71.20/9.73 (( 71.20/9.73 (sepInPowerset) => 71.20/9.73 (( 71.20/9.73 (sepSubset) => 71.20/9.73 (( 71.20/9.73 (binunionIL) => 71.20/9.73 (( 71.20/9.73 (upairset2IR) => 71.20/9.73 (( 71.20/9.73 (binunionIR) => 71.20/9.73 (( 71.20/9.73 (binunionEcases) => 71.20/9.73 (( 71.20/9.73 (binunionE) => 71.20/9.73 (( 71.20/9.73 (binunionLsub) => 71.20/9.73 (( 71.20/9.73 (binunionRsub) => 71.20/9.73 (( 71.20/9.73 (binintersectI) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset5) => 71.20/9.73 (( 71.20/9.73 (binintersectEL) => 71.20/9.73 (( 71.20/9.73 (binintersectLsub) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset2) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset3) => 71.20/9.73 (( 71.20/9.73 (binintersectER) => 71.20/9.73 (( 71.20/9.73 (disjointsetsI1) => 71.20/9.73 (( 71.20/9.73 (binintersectRsub) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset4) => 71.20/9.73 (( 71.20/9.73 (binintersectSubset1) => 71.20/9.73 (( 71.20/9.73 (bs114d) => 71.20/9.73 (( 71.20/9.73 (setminusI) => 71.20/9.73 (( 71.20/9.73 (setminusEL) => 71.20/9.73 (( 71.20/9.73 (setminusER) => 71.20/9.73 (( 71.20/9.73 (setminusSubset2) => 71.20/9.73 (( 71.20/9.73 (setminusERneg) => 71.20/9.73 (( 71.20/9.73 (setminusELneg) => 71.20/9.73 (( 71.20/9.73 (setminusILneg) => 71.20/9.73 (( 71.20/9.73 (setminusIRneg) => 71.20/9.73 (( 71.20/9.73 (setminusLsub) => 71.20/9.73 (( 71.20/9.73 (setminusSubset1) => 71.20/9.73 (( 71.20/9.73 (symdiffE) => 71.20/9.73 (( 71.20/9.73 (symdiffI1) => 71.20/9.73 (( 71.20/9.73 (symdiffI2) => 71.20/9.73 (( 71.20/9.73 (symdiffIneg1) => 71.20/9.73 (( 71.20/9.73 (symdiffIneg2) => 71.20/9.73 (( 71.20/9.73 (secondinupair) => 71.20/9.73 (( 71.20/9.73 (setukpairIL) => 71.20/9.73 (( 71.20/9.73 (setukpairIR) => 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71.20/9.73 (singletonsuniq) => 71.20/9.73 (( 71.20/9.73 (setukpairinjL1) => 71.20/9.73 (( 71.20/9.73 (kfstsingleton) => 71.20/9.73 (( 71.20/9.73 (theprop) => 71.20/9.73 (( 71.20/9.73 (kfstpairEq) => 71.20/9.73 (( 71.20/9.73 (cartprodfstin) => 71.20/9.73 (( 71.20/9.73 (setukpairinjL2) => 71.20/9.73 (( 71.20/9.73 (setukpairinjL) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR11) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR12) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR1) => 71.20/9.73 (( 71.20/9.73 (upairequniteq) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR2) => 71.20/9.73 (( 71.20/9.73 (setukpairinjR) => 71.20/9.73 (( 71.20/9.73 (ksndsingleton) => 71.20/9.73 (( 71.20/9.73 (ksndpairEq) => 71.20/9.73 (( 71.20/9.73 (kpairsurjEq) => 71.20/9.73 (( 71.20/9.73 (cartprodsndin) => 71.20/9.73 (( 71.20/9.73 (cartprodpairmemEL) => 71.20/9.73 (( 71.20/9.73 (cartprodpairmemER) => 71.20/9.73 (( 71.20/9.73 (cartprodmempaircEq) => 71.20/9.73 (( 71.20/9.73 (cartprodfstpairEq) => 71.20/9.73 (( 71.20/9.73 (cartprodsndpairEq) => 71.20/9.73 (( 71.20/9.73 (cartprodpairsurjEq) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrI) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrSub) => 71.20/9.73 (( 71.20/9.73 (setOfPairsIsBReln) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrERa) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrEL1) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrEL2) => 71.20/9.73 (( 71.20/9.73 (dpsetconstrER) => 71.20/9.73 (( 71.20/9.73 (funcImageSingleton) => 71.20/9.73 (( 71.20/9.73 (apProp) => 71.20/9.73 (( 71.20/9.73 (app) => 71.20/9.73 (( 71.20/9.73 (infuncsetfunc) => 71.20/9.73 (( 71.20/9.73 (ap2p) => 71.20/9.73 (( 71.20/9.73 (funcinfuncset) => 71.20/9.73 (( 71.20/9.73 (lamProp) => 71.20/9.73 (( 71.20/9.73 (lamp) => 71.20/9.73 (( 71.20/9.73 (lam2p) => 71.20/9.73 (( 71.20/9.73 (brelnall1) => 71.20/9.73 (( 71.20/9.73 (brelnall2) => 71.20/9.73 (( 71.20/9.73 (ex1E2) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp1) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp3) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp2) => 71.20/9.73 (( 71.20/9.73 (funcextLem) => 71.20/9.73 (( 71.20/9.73 (funcGraphProp4) => 71.20/9.73 (( 71.20/9.73 (subbreln) => 71.20/9.73 (( 71.20/9.73 (eqbreln) => 71.20/9.73 (( 71.20/9.73 (funcext) => 71.20/9.73 (( 71.20/9.73 (funcext2) => 71.20/9.73 (( 71.20/9.73 (ap2apEq1) => 71.20/9.73 (( 71.20/9.73 (ap2apEq2) => 71.20/9.73 (( 71.20/9.73 (beta1) => 71.20/9.73 (( 71.20/9.73 (eta1) => 71.20/9.73 (( 71.20/9.73 (lam2lamEq) => 71.20/9.73 (( 71.20/9.73 (beta2) => 71.20/9.73 (( 71.20/9.73 (eta2) => 71.20/9.73 (( 71.20/9.73 (iffalseProp1) => 71.20/9.73 (( 71.20/9.73 (iffalseProp2) => 71.20/9.73 (( 71.20/9.73 (iftrueProp1) => 71.20/9.73 (( 71.20/9.73 (iftrueProp2) => 71.20/9.73 (( 71.20/9.73 (ifSingleton) => 71.20/9.73 (( 71.20/9.73 (ifp) => 71.20/9.73 (( 71.20/9.73 (theeq) => 71.20/9.73 (( 71.20/9.73 (iftrue) => 71.20/9.73 (( 71.20/9.73 (iffalse) => 71.20/9.73 (( 71.20/9.73 (iftrueorfalse) => 71.20/9.73 (( 71.20/9.73 (binintersectT_lem) => 71.20/9.73 (( 71.20/9.73 (binunionT_lem) => 71.20/9.73 (( 71.20/9.73 (powersetT_lem) => 71.20/9.73 (( 71.20/9.73 (setminusT_lem) => 71.20/9.73 (( 71.20/9.73 (complementT_lem) => 71.20/9.73 (( 71.20/9.73 (setextT) => 71.20/9.73 (( 71.20/9.73 (subsetTI) => 71.20/9.73 (( 71.20/9.73 (powersetTI1) => 71.20/9.73 (( 71.20/9.73 (powersetTE1) => 71.20/9.73 (( 71.20/9.73 (complementTI1) => 71.20/9.73 (( 71.20/9.73 (complementTE1) => 71.20/9.73 (( 71.20/9.73 (binintersectTELcontra) => 71.20/9.73 (( 71.20/9.73 (binintersectTERcontra) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT1) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT2) => 71.20/9.73 (( 71.20/9.73 (contrasubsetT3) => 71.20/9.73 (( 71.20/9.73 (doubleComplementI1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementE1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementSub1) => 71.20/9.73 (( 71.20/9.73 (doubleComplementSub2) => 71.20/9.73 (( 71.20/9.73 (doubleComplementEq) => 71.20/9.73 (( 71.20/9.73 (complementTnotintersectT) => 71.20/9.73 (( 71.20/9.73 (complementImpComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (complementSubsetComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (complementInPowersetComplementIntersect) => 71.20/9.73 (( 71.20/9.73 (contraSubsetComplement) => 71.20/9.73 (( 71.20/9.73 (complementTcontraSubset) => 71.20/9.73 (( 71.20/9.73 (binunionTILcontra) => 71.20/9.73 (( 71.20/9.73 (binunionTIRcontra) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInUnion) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInUnion2) => 71.20/9.73 (( 71.20/9.73 (inIntersectImpInIntersectUnions) => 71.20/9.73 (( 71.20/9.73 (intersectInPowersetIntersectUnions) => 71.20/9.73 (( 71.20/9.73 (inComplementUnionImpNotIn1) => 71.20/9.73 (( 71.20/9.73 (inComplementUnionImpInComplement1) => 71.20/9.73 (( 71.20/9.73 (binunionTE) => 71.20/9.73 (( 71.20/9.73 (binunionTEcontra) => 71.20/9.73 (( 71.20/9.73 (demorgan2a1) => 71.20/9.73 (( 71.20/9.73 (complementUnionInPowersetComplement) => 71.20/9.73 (( 71.20/9.73 (demorgan2a2) => 71.20/9.73 (( 71.20/9.73 (demorgan1a) => 71.20/9.73 (( 71.20/9.73 (demorgan1b) => 71.20/9.73 (( 71.20/9.73 (demorgan1) => 71.20/9.73 (( 71.20/9.73 (demorgan2a) => 71.20/9.73 (( 71.20/9.73 (demorgan2b2) => 71.20/9.73 (( 71.20/9.73 (demorgan2b) => 71.20/9.73 (( 71.20/9.73 (demorgan2) => 71.20/9.73 (( 71.20/9.73 (woz13rule0) => 71.20/9.73 (( 71.20/9.73 (woz13rule1) => 71.20/9.73 (( 71.20/9.73 (woz13rule2) => 71.20/9.73 (( 71.20/9.73 (woz13rule3) => 71.20/9.73 (( 71.20/9.73 (woz13rule4) => 71.20/9.73 (( 71.20/9.73 (woz1_1) => 71.20/9.73 (( 71.20/9.73 (woz1_2) => 71.20/9.73 (( 71.20/9.73 (woz1_3) => 71.20/9.73 (( 71.20/9.73 (woz1_4) => 71.20/9.73 (( 71.20/9.73 (woz1_5) => 71.20/9.73 (( 71.20/9.73 (breln1all2) => 71.20/9.73 (( 71.20/9.73 (breln1SetBreln1) => 71.20/9.73 (( 71.20/9.73 (choice2fnsingleton) => 71.20/9.73 (( 71.20/9.73 (setOfPairsIsBReln1) => 71.20/9.73 (( 71.20/9.73 (breln1all1) => 71.20/9.73 (( 71.20/9.73 (subbreln1) => 71.20/9.73 (( 71.20/9.73 (eqbreln1) => 71.20/9.73 (( 71.20/9.73 (breln1invprop) => 71.20/9.73 (( 71.20/9.73 (breln1invI) => 71.20/9.73 (( 71.20/9.73 (breln1invE) => 71.20/9.73 (( 71.20/9.73 (breln1compprop) => 71.20/9.73 (( 71.20/9.73 (breln1compI) => 71.20/9.73 (( 71.20/9.73 (breln1compE) => 71.20/9.73 (( 71.20/9.73 (breln1compEex) => 71.20/9.73 (( 71.20/9.73 (!!) @ ( 71.20/9.73 (('#B') @ ( 71.20/9.73 !!) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#S') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#S') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 =>))) @ 71.20/9.73 breln1)))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 !!))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#S') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#S') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 =>))) @ 71.20/9.73 breln1)))))) @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#C') @ ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 ( 71.20/9.73 ( 71.20/9.73 ('#B') @ ( 71.20/9.73 '#B') @ 71.20/9.73 breln1)))) @ 71.20/9.73 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])). 71.20/9.73 thf(zip_derived_cl264, plain, 71.20/9.73 (~ (((nonemptyE1) => 71.20/9.73 (((nonemptyI) => 71.20/9.73 (((nonemptyI1) => 71.20/9.73 (((setadjoinIL) => 71.20/9.73 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 71.20/9.73 (((setadjoinIR) => 71.20/9.73 (((setadjoinE) => 71.20/9.73 (((setadjoinOr) => 71.20/9.73 (((setoftrueEq) => 71.20/9.73 (((powersetI) => 71.20/9.73 (((emptyinPowerset) => 71.20/9.73 (((emptyInPowerset) => 71.20/9.73 (((powersetE) => 71.20/9.73 (((setunionI) => 71.20/9.73 (((setunionE) => 71.20/9.73 (((subPowSU) => 71.20/9.73 (((exuE2) => 71.20/9.73 (((nonemptyImpWitness) => 71.20/9.73 (((uniqinunit) => 71.20/9.73 (((notinsingleton) => 71.20/9.73 (((eqinunit) => 71.20/9.73 (((singletonsswitch) => 71.20/9.73 (((upairsetE) => 71.20/9.73 (((upairsetIL) => 71.20/9.73 (((upairsetIR) => 71.20/9.74 (((emptyE1) => 71.20/9.74 (((vacuousDall) => 71.20/9.74 (((quantDeMorgan1) => 71.20/9.74 (((quantDeMorgan2) => 71.20/9.74 (((quantDeMorgan3) => 71.20/9.74 (( 71.20/9.74 (quantDeMorgan4) => 71.20/9.74 (( 71.20/9.74 (prop2setI) => 71.20/9.74 (( 71.20/9.74 (prop2set2propI) => 71.20/9.74 (( 71.20/9.74 (notdexE) => 71.20/9.74 (( 71.20/9.74 (notdallE) => 71.20/9.74 (( 71.20/9.74 (exuI1) => 71.20/9.74 (( 71.20/9.74 (exuI3) => 71.20/9.74 (( 71.20/9.74 (exuI2) => 71.20/9.74 (( 71.20/9.74 (inCongP) => 71.20/9.74 (( 71.20/9.74 (in__Cong) => 71.20/9.74 (( 71.20/9.74 (exuE3u) => 71.20/9.74 (( 71.20/9.74 (exu__Cong) => 71.20/9.74 (( 71.20/9.74 (setadjoin__Cong) => 71.20/9.74 (( 71.20/9.74 (powerset__Cong) => 71.20/9.74 (( 71.20/9.74 (setunion__Cong) => 71.20/9.74 (( 71.20/9.74 (exuEu) => 71.20/9.74 (( 71.20/9.74 (descr__Cong) => 71.20/9.74 (( 71.20/9.74 (dsetconstr__Cong) => 71.20/9.74 (( 71.20/9.74 (subsetI1) => 71.20/9.74 (( 71.20/9.74 (eqimpsubset2) => 71.20/9.74 (( 71.20/9.74 (eqimpsubset1) => 71.20/9.74 (( 71.20/9.74 (subsetI2) => 71.20/9.74 (( 71.20/9.74 (emptysetsubset) => 71.20/9.74 (( 71.20/9.74 (subsetE) => 71.20/9.74 (( 71.20/9.74 (subsetE2) => 71.20/9.74 (( 71.20/9.74 (notsubsetI) => 71.20/9.74 (( 71.20/9.74 (notequalI1) => 71.20/9.74 (( 71.20/9.74 (notequalI2) => 71.20/9.74 (( 71.20/9.74 (subsetRefl) => 71.20/9.74 (( 71.20/9.74 (subsetTrans) => 71.20/9.74 (( 71.20/9.74 (setadjoinSub) => 71.20/9.74 (( 71.20/9.74 (setadjoinSub2) => 71.20/9.74 (( 71.20/9.74 (subset2powerset) => 71.20/9.74 (( 71.20/9.74 (setextsub) => 71.20/9.74 (( 71.20/9.74 (subsetemptysetimpeq) => 71.20/9.74 (( 71.20/9.74 (powersetI1) => 71.20/9.74 (( 71.20/9.74 (powersetE1) => 71.20/9.74 (( 71.20/9.74 (inPowerset) => 71.20/9.74 (( 71.20/9.74 (powersetsubset) => 71.20/9.74 (( 71.20/9.74 (sepInPowerset) => 71.20/9.74 (( 71.20/9.74 (sepSubset) => 71.20/9.74 (( 71.20/9.74 (binunionIL) => 71.20/9.74 (( 71.20/9.74 (upairset2IR) => 71.20/9.74 (( 71.20/9.74 (binunionIR) => 71.20/9.74 (( 71.20/9.74 (binunionEcases) => 71.20/9.74 (( 71.20/9.74 (binunionE) => 71.20/9.74 (( 71.20/9.74 (binunionLsub) => 71.20/9.74 (( 71.20/9.74 (binunionRsub) => 71.20/9.74 (( 71.20/9.74 (binintersectI) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset5) => 71.20/9.74 (( 71.20/9.74 (binintersectEL) => 71.20/9.74 (( 71.20/9.74 (binintersectLsub) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset2) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset3) => 71.20/9.74 (( 71.20/9.74 (binintersectER) => 71.20/9.74 (( 71.20/9.74 (disjointsetsI1) => 71.20/9.74 (( 71.20/9.74 (binintersectRsub) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset4) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset1) => 71.20/9.74 (( 71.20/9.74 (bs114d) => 71.20/9.74 (( 71.20/9.74 (setminusI) => 71.20/9.74 (( 71.20/9.74 (setminusEL) => 71.20/9.74 (( 71.20/9.74 (setminusER) => 71.20/9.74 (( 71.20/9.74 (setminusSubset2) => 71.20/9.74 (( 71.20/9.74 (setminusERneg) => 71.20/9.74 (( 71.20/9.74 (setminusELneg) => 71.20/9.74 (( 71.20/9.74 (setminusILneg) => 71.20/9.74 (( 71.20/9.74 (setminusIRneg) => 71.20/9.74 (( 71.20/9.74 (setminusLsub) => 71.20/9.74 (( 71.20/9.74 (setminusSubset1) => 71.20/9.74 (( 71.20/9.74 (symdiffE) => 71.20/9.74 (( 71.20/9.74 (symdiffI1) => 71.20/9.74 (( 71.20/9.74 (symdiffI2) => 71.20/9.74 (( 71.20/9.74 (symdiffIneg1) => 71.20/9.74 (( 71.20/9.74 (symdiffIneg2) => 71.20/9.74 (( 71.20/9.74 (secondinupair) => 71.20/9.74 (( 71.20/9.74 (setukpairIL) => 71.20/9.74 (( 71.20/9.74 (setukpairIR) => 71.20/9.74 (( 71.20/9.74 (kpairiskpair) => 71.20/9.74 (( 71.20/9.74 (kpairp) => 71.20/9.74 (( 71.20/9.74 (singletonsubset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowerset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowunion) => 71.20/9.74 (( 71.20/9.74 (upairset2E) => 71.20/9.74 (( 71.20/9.74 (upairsubunion) => 71.20/9.74 (( 71.20/9.74 (upairinpowunion) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem1) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem2) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem3) => 71.20/9.74 (( 71.20/9.74 (cartprodpairin) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair1) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair) => 71.20/9.74 (( 71.20/9.74 (setunionE2) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton1) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton2) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton) => 71.20/9.74 (( 71.20/9.74 (singletonprop) => 71.20/9.74 (( 71.20/9.74 (ex1E1) => 71.20/9.74 (( 71.20/9.74 (ex1I) => 71.20/9.74 (( 71.20/9.74 (ex1I2) => 71.20/9.74 (( 71.20/9.74 (singletonsuniq) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL1) => 71.20/9.74 (( 71.20/9.74 (kfstsingleton) => 71.20/9.74 (( 71.20/9.74 (theprop) => 71.20/9.74 (( 71.20/9.74 (kfstpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodfstin) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL2) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR11) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR12) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR1) => 71.20/9.74 (( 71.20/9.74 (upairequniteq) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR2) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR) => 71.20/9.74 (( 71.20/9.74 (ksndsingleton) => 71.20/9.74 (( 71.20/9.74 (ksndpairEq) => 71.20/9.74 (( 71.20/9.74 (kpairsurjEq) => 71.20/9.74 (( 71.20/9.74 (cartprodsndin) => 71.20/9.74 (( 71.20/9.74 (cartprodpairmemEL) => 71.20/9.74 (( 71.20/9.74 (cartprodpairmemER) => 71.20/9.74 (( 71.20/9.74 (cartprodmempaircEq) => 71.20/9.74 (( 71.20/9.74 (cartprodfstpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodsndpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodpairsurjEq) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrI) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrSub) => 71.20/9.74 (( 71.20/9.74 (setOfPairsIsBReln) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrERa) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrEL1) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrEL2) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrER) => 71.20/9.74 (( 71.20/9.74 (funcImageSingleton) => 71.20/9.74 (( 71.20/9.74 (apProp) => 71.20/9.74 (( 71.20/9.74 (app) => 71.20/9.74 (( 71.20/9.74 (infuncsetfunc) => 71.20/9.74 (( 71.20/9.74 (ap2p) => 71.20/9.74 (( 71.20/9.74 (funcinfuncset) => 71.20/9.74 (( 71.20/9.74 (lamProp) => 71.20/9.74 (( 71.20/9.74 (lamp) => 71.20/9.74 (( 71.20/9.74 (lam2p) => 71.20/9.74 (( 71.20/9.74 (brelnall1) => 71.20/9.74 (( 71.20/9.74 (brelnall2) => 71.20/9.74 (( 71.20/9.74 (ex1E2) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp1) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp3) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp2) => 71.20/9.74 (( 71.20/9.74 (funcextLem) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp4) => 71.20/9.74 (( 71.20/9.74 (subbreln) => 71.20/9.74 (( 71.20/9.74 (eqbreln) => 71.20/9.74 (( 71.20/9.74 (funcext) => 71.20/9.74 (( 71.20/9.74 (funcext2) => 71.20/9.74 (( 71.20/9.74 (ap2apEq1) => 71.20/9.74 (( 71.20/9.74 (ap2apEq2) => 71.20/9.74 (( 71.20/9.74 (beta1) => 71.20/9.74 (( 71.20/9.74 (eta1) => 71.20/9.74 (( 71.20/9.74 (lam2lamEq) => 71.20/9.74 (( 71.20/9.74 (beta2) => 71.20/9.74 (( 71.20/9.74 (eta2) => 71.20/9.74 (( 71.20/9.74 (iffalseProp1) => 71.20/9.74 (( 71.20/9.74 (iffalseProp2) => 71.20/9.74 (( 71.20/9.74 (iftrueProp1) => 71.20/9.74 (( 71.20/9.74 (iftrueProp2) => 71.20/9.74 (( 71.20/9.74 (ifSingleton) => 71.20/9.74 (( 71.20/9.74 (ifp) => 71.20/9.74 (( 71.20/9.74 (theeq) => 71.20/9.74 (( 71.20/9.74 (iftrue) => 71.20/9.74 (( 71.20/9.74 (iffalse) => 71.20/9.74 (( 71.20/9.74 (iftrueorfalse) => 71.20/9.74 (( 71.20/9.74 (binintersectT_lem) => 71.20/9.74 (( 71.20/9.74 (binunionT_lem) => 71.20/9.74 (( 71.20/9.74 (powersetT_lem) => 71.20/9.74 (( 71.20/9.74 (setminusT_lem) => 71.20/9.74 (( 71.20/9.74 (complementT_lem) => 71.20/9.74 (( 71.20/9.74 (setextT) => 71.20/9.74 (( 71.20/9.74 (subsetTI) => 71.20/9.74 (( 71.20/9.74 (powersetTI1) => 71.20/9.74 (( 71.20/9.74 (powersetTE1) => 71.20/9.74 (( 71.20/9.74 (complementTI1) => 71.20/9.74 (( 71.20/9.74 (complementTE1) => 71.20/9.74 (( 71.20/9.74 (binintersectTELcontra) => 71.20/9.74 (( 71.20/9.74 (binintersectTERcontra) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT1) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT2) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT3) => 71.20/9.74 (( 71.20/9.74 (doubleComplementI1) => 71.20/9.74 (( 71.20/9.74 (doubleComplementE1) => 71.20/9.74 (( 71.20/9.74 (doubleComplementSub1) => 71.20/9.74 (( 71.20/9.74 (doubleComplementSub2) => 71.20/9.74 (( 71.20/9.74 (doubleComplementEq) => 71.20/9.74 (( 71.20/9.74 (complementTnotintersectT) => 71.20/9.74 (( 71.20/9.74 (complementImpComplementIntersect) => 71.20/9.74 (( 71.20/9.74 (complementSubsetComplementIntersect) => 71.20/9.74 (( 71.20/9.74 (complementInPowersetComplementIntersect) => 71.20/9.74 (( 71.20/9.74 (contraSubsetComplement) => 71.20/9.74 (( 71.20/9.74 (complementTcontraSubset) => 71.20/9.74 (( 71.20/9.74 (binunionTILcontra) => 71.20/9.74 (( 71.20/9.74 (binunionTIRcontra) => 71.20/9.74 (( 71.20/9.74 (inIntersectImpInUnion) => 71.20/9.74 (( 71.20/9.74 (inIntersectImpInUnion2) => 71.20/9.74 (( 71.20/9.74 (inIntersectImpInIntersectUnions) => 71.20/9.74 (( 71.20/9.74 (intersectInPowersetIntersectUnions) => 71.20/9.74 (( 71.20/9.74 (inComplementUnionImpNotIn1) => 71.20/9.74 (( 71.20/9.74 (inComplementUnionImpInComplement1) => 71.20/9.74 (( 71.20/9.74 (binunionTE) => 71.20/9.74 (( 71.20/9.74 (binunionTEcontra) => 71.20/9.74 (( 71.20/9.74 (demorgan2a1) => 71.20/9.74 (( 71.20/9.74 (complementUnionInPowersetComplement) => 71.20/9.74 (( 71.20/9.74 (demorgan2a2) => 71.20/9.74 (( 71.20/9.74 (demorgan1a) => 71.20/9.74 (( 71.20/9.74 (demorgan1b) => 71.20/9.74 (( 71.20/9.74 (demorgan1) => 71.20/9.74 (( 71.20/9.74 (demorgan2a) => 71.20/9.74 (( 71.20/9.74 (demorgan2b2) => 71.20/9.74 (( 71.20/9.74 (demorgan2b) => 71.20/9.74 (( 71.20/9.74 (demorgan2) => 71.20/9.74 (( 71.20/9.74 (woz13rule0) => 71.20/9.74 (( 71.20/9.74 (woz13rule1) => 71.20/9.74 (( 71.20/9.74 (woz13rule2) => 71.20/9.74 (( 71.20/9.74 (woz13rule3) => 71.20/9.74 (( 71.20/9.74 (woz13rule4) => 71.20/9.74 (( 71.20/9.74 (woz1_1) => 71.20/9.74 (( 71.20/9.74 (woz1_2) => 71.20/9.74 (( 71.20/9.74 (woz1_3) => 71.20/9.74 (( 71.20/9.74 (woz1_4) => 71.20/9.74 (( 71.20/9.74 (woz1_5) => 71.20/9.74 (( 71.20/9.74 (breln1all2) => 71.20/9.74 (( 71.20/9.74 (breln1SetBreln1) => 71.20/9.74 (( 71.20/9.74 (choice2fnsingleton) => 71.20/9.74 (( 71.20/9.74 (setOfPairsIsBReln1) => 71.20/9.74 (( 71.20/9.74 (breln1all1) => 71.20/9.74 (( 71.20/9.74 (subbreln1) => 71.20/9.74 (( 71.20/9.74 (eqbreln1) => 71.20/9.74 (( 71.20/9.74 (breln1invprop) => 71.20/9.74 (( 71.20/9.74 (breln1invI) => 71.20/9.74 (( 71.20/9.74 (breln1invE) => 71.20/9.74 (( 71.20/9.74 (breln1compprop) => 71.20/9.74 (( 71.20/9.74 (breln1compI) => 71.20/9.74 (( 71.20/9.74 (breln1compE) => 71.20/9.74 (( 71.20/9.74 (breln1compEex) => 71.20/9.74 (( 71.20/9.74 (!!) @ ( 71.20/9.74 (('#B') @ ( 71.20/9.74 !!) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#S') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#S') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 =>))) @ 71.20/9.74 breln1)))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 !!))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#S') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#S') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 =>))) @ 71.20/9.74 breln1)))))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#C') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 breln1)))) @ 71.20/9.74 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl251])). 71.20/9.74 thf(zip_derived_cl280, plain, 71.20/9.74 (~ (((nonemptyI) => 71.20/9.74 (((nonemptyI1) => 71.20/9.74 (((setadjoinIL) => 71.20/9.74 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 71.20/9.74 (((setadjoinIR) => 71.20/9.74 (((setadjoinE) => 71.20/9.74 (((setadjoinOr) => 71.20/9.74 (((setoftrueEq) => 71.20/9.74 (((powersetI) => 71.20/9.74 (((emptyinPowerset) => 71.20/9.74 (((emptyInPowerset) => 71.20/9.74 (((powersetE) => 71.20/9.74 (((setunionI) => 71.20/9.74 (((setunionE) => 71.20/9.74 (((subPowSU) => 71.20/9.74 (((exuE2) => 71.20/9.74 (((nonemptyImpWitness) => 71.20/9.74 (((uniqinunit) => 71.20/9.74 (((notinsingleton) => 71.20/9.74 (((eqinunit) => 71.20/9.74 (((singletonsswitch) => 71.20/9.74 (((upairsetE) => 71.20/9.74 (((upairsetIL) => 71.20/9.74 (((upairsetIR) => 71.20/9.74 (((emptyE1) => 71.20/9.74 (((vacuousDall) => 71.20/9.74 (((quantDeMorgan1) => 71.20/9.74 (((quantDeMorgan2) => 71.20/9.74 (((quantDeMorgan3) => 71.20/9.74 (((quantDeMorgan4) => 71.20/9.74 (( 71.20/9.74 (prop2setI) => 71.20/9.74 (( 71.20/9.74 (prop2set2propI) => 71.20/9.74 (( 71.20/9.74 (notdexE) => 71.20/9.74 (( 71.20/9.74 (notdallE) => 71.20/9.74 (( 71.20/9.74 (exuI1) => 71.20/9.74 (( 71.20/9.74 (exuI3) => 71.20/9.74 (( 71.20/9.74 (exuI2) => 71.20/9.74 (( 71.20/9.74 (inCongP) => 71.20/9.74 (( 71.20/9.74 (in__Cong) => 71.20/9.74 (( 71.20/9.74 (exuE3u) => 71.20/9.74 (( 71.20/9.74 (exu__Cong) => 71.20/9.74 (( 71.20/9.74 (setadjoin__Cong) => 71.20/9.74 (( 71.20/9.74 (powerset__Cong) => 71.20/9.74 (( 71.20/9.74 (setunion__Cong) => 71.20/9.74 (( 71.20/9.74 (exuEu) => 71.20/9.74 (( 71.20/9.74 (descr__Cong) => 71.20/9.74 (( 71.20/9.74 (dsetconstr__Cong) => 71.20/9.74 (( 71.20/9.74 (subsetI1) => 71.20/9.74 (( 71.20/9.74 (eqimpsubset2) => 71.20/9.74 (( 71.20/9.74 (eqimpsubset1) => 71.20/9.74 (( 71.20/9.74 (subsetI2) => 71.20/9.74 (( 71.20/9.74 (emptysetsubset) => 71.20/9.74 (( 71.20/9.74 (subsetE) => 71.20/9.74 (( 71.20/9.74 (subsetE2) => 71.20/9.74 (( 71.20/9.74 (notsubsetI) => 71.20/9.74 (( 71.20/9.74 (notequalI1) => 71.20/9.74 (( 71.20/9.74 (notequalI2) => 71.20/9.74 (( 71.20/9.74 (subsetRefl) => 71.20/9.74 (( 71.20/9.74 (subsetTrans) => 71.20/9.74 (( 71.20/9.74 (setadjoinSub) => 71.20/9.74 (( 71.20/9.74 (setadjoinSub2) => 71.20/9.74 (( 71.20/9.74 (subset2powerset) => 71.20/9.74 (( 71.20/9.74 (setextsub) => 71.20/9.74 (( 71.20/9.74 (subsetemptysetimpeq) => 71.20/9.74 (( 71.20/9.74 (powersetI1) => 71.20/9.74 (( 71.20/9.74 (powersetE1) => 71.20/9.74 (( 71.20/9.74 (inPowerset) => 71.20/9.74 (( 71.20/9.74 (powersetsubset) => 71.20/9.74 (( 71.20/9.74 (sepInPowerset) => 71.20/9.74 (( 71.20/9.74 (sepSubset) => 71.20/9.74 (( 71.20/9.74 (binunionIL) => 71.20/9.74 (( 71.20/9.74 (upairset2IR) => 71.20/9.74 (( 71.20/9.74 (binunionIR) => 71.20/9.74 (( 71.20/9.74 (binunionEcases) => 71.20/9.74 (( 71.20/9.74 (binunionE) => 71.20/9.74 (( 71.20/9.74 (binunionLsub) => 71.20/9.74 (( 71.20/9.74 (binunionRsub) => 71.20/9.74 (( 71.20/9.74 (binintersectI) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset5) => 71.20/9.74 (( 71.20/9.74 (binintersectEL) => 71.20/9.74 (( 71.20/9.74 (binintersectLsub) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset2) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset3) => 71.20/9.74 (( 71.20/9.74 (binintersectER) => 71.20/9.74 (( 71.20/9.74 (disjointsetsI1) => 71.20/9.74 (( 71.20/9.74 (binintersectRsub) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset4) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset1) => 71.20/9.74 (( 71.20/9.74 (bs114d) => 71.20/9.74 (( 71.20/9.74 (setminusI) => 71.20/9.74 (( 71.20/9.74 (setminusEL) => 71.20/9.74 (( 71.20/9.74 (setminusER) => 71.20/9.74 (( 71.20/9.74 (setminusSubset2) => 71.20/9.74 (( 71.20/9.74 (setminusERneg) => 71.20/9.74 (( 71.20/9.74 (setminusELneg) => 71.20/9.74 (( 71.20/9.74 (setminusILneg) => 71.20/9.74 (( 71.20/9.74 (setminusIRneg) => 71.20/9.74 (( 71.20/9.74 (setminusLsub) => 71.20/9.74 (( 71.20/9.74 (setminusSubset1) => 71.20/9.74 (( 71.20/9.74 (symdiffE) => 71.20/9.74 (( 71.20/9.74 (symdiffI1) => 71.20/9.74 (( 71.20/9.74 (symdiffI2) => 71.20/9.74 (( 71.20/9.74 (symdiffIneg1) => 71.20/9.74 (( 71.20/9.74 (symdiffIneg2) => 71.20/9.74 (( 71.20/9.74 (secondinupair) => 71.20/9.74 (( 71.20/9.74 (setukpairIL) => 71.20/9.74 (( 71.20/9.74 (setukpairIR) => 71.20/9.74 (( 71.20/9.74 (kpairiskpair) => 71.20/9.74 (( 71.20/9.74 (kpairp) => 71.20/9.74 (( 71.20/9.74 (singletonsubset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowerset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowunion) => 71.20/9.74 (( 71.20/9.74 (upairset2E) => 71.20/9.74 (( 71.20/9.74 (upairsubunion) => 71.20/9.74 (( 71.20/9.74 (upairinpowunion) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem1) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem2) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem3) => 71.20/9.74 (( 71.20/9.74 (cartprodpairin) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair1) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair) => 71.20/9.74 (( 71.20/9.74 (setunionE2) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton1) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton2) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton) => 71.20/9.74 (( 71.20/9.74 (singletonprop) => 71.20/9.74 (( 71.20/9.74 (ex1E1) => 71.20/9.74 (( 71.20/9.74 (ex1I) => 71.20/9.74 (( 71.20/9.74 (ex1I2) => 71.20/9.74 (( 71.20/9.74 (singletonsuniq) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL1) => 71.20/9.74 (( 71.20/9.74 (kfstsingleton) => 71.20/9.74 (( 71.20/9.74 (theprop) => 71.20/9.74 (( 71.20/9.74 (kfstpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodfstin) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL2) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR11) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR12) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR1) => 71.20/9.74 (( 71.20/9.74 (upairequniteq) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR2) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR) => 71.20/9.74 (( 71.20/9.74 (ksndsingleton) => 71.20/9.74 (( 71.20/9.74 (ksndpairEq) => 71.20/9.74 (( 71.20/9.74 (kpairsurjEq) => 71.20/9.74 (( 71.20/9.74 (cartprodsndin) => 71.20/9.74 (( 71.20/9.74 (cartprodpairmemEL) => 71.20/9.74 (( 71.20/9.74 (cartprodpairmemER) => 71.20/9.74 (( 71.20/9.74 (cartprodmempaircEq) => 71.20/9.74 (( 71.20/9.74 (cartprodfstpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodsndpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodpairsurjEq) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrI) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrSub) => 71.20/9.74 (( 71.20/9.74 (setOfPairsIsBReln) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrERa) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrEL1) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrEL2) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrER) => 71.20/9.74 (( 71.20/9.74 (funcImageSingleton) => 71.20/9.74 (( 71.20/9.74 (apProp) => 71.20/9.74 (( 71.20/9.74 (app) => 71.20/9.74 (( 71.20/9.74 (infuncsetfunc) => 71.20/9.74 (( 71.20/9.74 (ap2p) => 71.20/9.74 (( 71.20/9.74 (funcinfuncset) => 71.20/9.74 (( 71.20/9.74 (lamProp) => 71.20/9.74 (( 71.20/9.74 (lamp) => 71.20/9.74 (( 71.20/9.74 (lam2p) => 71.20/9.74 (( 71.20/9.74 (brelnall1) => 71.20/9.74 (( 71.20/9.74 (brelnall2) => 71.20/9.74 (( 71.20/9.74 (ex1E2) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp1) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp3) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp2) => 71.20/9.74 (( 71.20/9.74 (funcextLem) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp4) => 71.20/9.74 (( 71.20/9.74 (subbreln) => 71.20/9.74 (( 71.20/9.74 (eqbreln) => 71.20/9.74 (( 71.20/9.74 (funcext) => 71.20/9.74 (( 71.20/9.74 (funcext2) => 71.20/9.74 (( 71.20/9.74 (ap2apEq1) => 71.20/9.74 (( 71.20/9.74 (ap2apEq2) => 71.20/9.74 (( 71.20/9.74 (beta1) => 71.20/9.74 (( 71.20/9.74 (eta1) => 71.20/9.74 (( 71.20/9.74 (lam2lamEq) => 71.20/9.74 (( 71.20/9.74 (beta2) => 71.20/9.74 (( 71.20/9.74 (eta2) => 71.20/9.74 (( 71.20/9.74 (iffalseProp1) => 71.20/9.74 (( 71.20/9.74 (iffalseProp2) => 71.20/9.74 (( 71.20/9.74 (iftrueProp1) => 71.20/9.74 (( 71.20/9.74 (iftrueProp2) => 71.20/9.74 (( 71.20/9.74 (ifSingleton) => 71.20/9.74 (( 71.20/9.74 (ifp) => 71.20/9.74 (( 71.20/9.74 (theeq) => 71.20/9.74 (( 71.20/9.74 (iftrue) => 71.20/9.74 (( 71.20/9.74 (iffalse) => 71.20/9.74 (( 71.20/9.74 (iftrueorfalse) => 71.20/9.74 (( 71.20/9.74 (binintersectT_lem) => 71.20/9.74 (( 71.20/9.74 (binunionT_lem) => 71.20/9.74 (( 71.20/9.74 (powersetT_lem) => 71.20/9.74 (( 71.20/9.74 (setminusT_lem) => 71.20/9.74 (( 71.20/9.74 (complementT_lem) => 71.20/9.74 (( 71.20/9.74 (setextT) => 71.20/9.74 (( 71.20/9.74 (subsetTI) => 71.20/9.74 (( 71.20/9.74 (powersetTI1) => 71.20/9.74 (( 71.20/9.74 (powersetTE1) => 71.20/9.74 (( 71.20/9.74 (complementTI1) => 71.20/9.74 (( 71.20/9.74 (complementTE1) => 71.20/9.74 (( 71.20/9.74 (binintersectTELcontra) => 71.20/9.74 (( 71.20/9.74 (binintersectTERcontra) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT1) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT2) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT3) => 71.20/9.74 (( 71.20/9.74 (doubleComplementI1) => 71.20/9.74 (( 71.20/9.74 (doubleComplementE1) => 71.20/9.74 (( 71.20/9.74 (doubleComplementSub1) => 71.20/9.74 (( 71.20/9.74 (doubleComplementSub2) => 71.20/9.74 (( 71.20/9.74 (doubleComplementEq) => 71.20/9.74 (( 71.20/9.74 (complementTnotintersectT) => 71.20/9.74 (( 71.20/9.74 (complementImpComplementIntersect) => 71.20/9.74 (( 71.20/9.74 (complementSubsetComplementIntersect) => 71.20/9.74 (( 71.20/9.74 (complementInPowersetComplementIntersect) => 71.20/9.74 (( 71.20/9.74 (contraSubsetComplement) => 71.20/9.74 (( 71.20/9.74 (complementTcontraSubset) => 71.20/9.74 (( 71.20/9.74 (binunionTILcontra) => 71.20/9.74 (( 71.20/9.74 (binunionTIRcontra) => 71.20/9.74 (( 71.20/9.74 (inIntersectImpInUnion) => 71.20/9.74 (( 71.20/9.74 (inIntersectImpInUnion2) => 71.20/9.74 (( 71.20/9.74 (inIntersectImpInIntersectUnions) => 71.20/9.74 (( 71.20/9.74 (intersectInPowersetIntersectUnions) => 71.20/9.74 (( 71.20/9.74 (inComplementUnionImpNotIn1) => 71.20/9.74 (( 71.20/9.74 (inComplementUnionImpInComplement1) => 71.20/9.74 (( 71.20/9.74 (binunionTE) => 71.20/9.74 (( 71.20/9.74 (binunionTEcontra) => 71.20/9.74 (( 71.20/9.74 (demorgan2a1) => 71.20/9.74 (( 71.20/9.74 (complementUnionInPowersetComplement) => 71.20/9.74 (( 71.20/9.74 (demorgan2a2) => 71.20/9.74 (( 71.20/9.74 (demorgan1a) => 71.20/9.74 (( 71.20/9.74 (demorgan1b) => 71.20/9.74 (( 71.20/9.74 (demorgan1) => 71.20/9.74 (( 71.20/9.74 (demorgan2a) => 71.20/9.74 (( 71.20/9.74 (demorgan2b2) => 71.20/9.74 (( 71.20/9.74 (demorgan2b) => 71.20/9.74 (( 71.20/9.74 (demorgan2) => 71.20/9.74 (( 71.20/9.74 (woz13rule0) => 71.20/9.74 (( 71.20/9.74 (woz13rule1) => 71.20/9.74 (( 71.20/9.74 (woz13rule2) => 71.20/9.74 (( 71.20/9.74 (woz13rule3) => 71.20/9.74 (( 71.20/9.74 (woz13rule4) => 71.20/9.74 (( 71.20/9.74 (woz1_1) => 71.20/9.74 (( 71.20/9.74 (woz1_2) => 71.20/9.74 (( 71.20/9.74 (woz1_3) => 71.20/9.74 (( 71.20/9.74 (woz1_4) => 71.20/9.74 (( 71.20/9.74 (woz1_5) => 71.20/9.74 (( 71.20/9.74 (breln1all2) => 71.20/9.74 (( 71.20/9.74 (breln1SetBreln1) => 71.20/9.74 (( 71.20/9.74 (choice2fnsingleton) => 71.20/9.74 (( 71.20/9.74 (setOfPairsIsBReln1) => 71.20/9.74 (( 71.20/9.74 (breln1all1) => 71.20/9.74 (( 71.20/9.74 (subbreln1) => 71.20/9.74 (( 71.20/9.74 (eqbreln1) => 71.20/9.74 (( 71.20/9.74 (breln1invprop) => 71.20/9.74 (( 71.20/9.74 (breln1invI) => 71.20/9.74 (( 71.20/9.74 (breln1invE) => 71.20/9.74 (( 71.20/9.74 (breln1compprop) => 71.20/9.74 (( 71.20/9.74 (breln1compI) => 71.20/9.74 (( 71.20/9.74 (breln1compE) => 71.20/9.74 (( 71.20/9.74 (breln1compEex) => 71.20/9.74 (( 71.20/9.74 (!!) @ ( 71.20/9.74 (('#B') @ ( 71.20/9.74 !!) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#S') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#S') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 =>))) @ 71.20/9.74 breln1)))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 !!))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#S') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#S') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 =>))) @ 71.20/9.74 breln1)))))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#C') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 breln1)))) @ 71.20/9.74 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl264])). 71.20/9.74 thf(zip_derived_cl293, plain, 71.20/9.74 (~ (((nonemptyI1) => 71.20/9.74 (((setadjoinIL) => 71.20/9.74 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 71.20/9.74 (((setadjoinIR) => 71.20/9.74 (((setadjoinE) => 71.20/9.74 (((setadjoinOr) => 71.20/9.74 (((setoftrueEq) => 71.20/9.74 (((powersetI) => 71.20/9.74 (((emptyinPowerset) => 71.20/9.74 (((emptyInPowerset) => 71.20/9.74 (((powersetE) => 71.20/9.74 (((setunionI) => 71.20/9.74 (((setunionE) => 71.20/9.74 (((subPowSU) => 71.20/9.74 (((exuE2) => 71.20/9.74 (((nonemptyImpWitness) => 71.20/9.74 (((uniqinunit) => 71.20/9.74 (((notinsingleton) => 71.20/9.74 (((eqinunit) => 71.20/9.74 (((singletonsswitch) => 71.20/9.74 (((upairsetE) => 71.20/9.74 (((upairsetIL) => 71.20/9.74 (((upairsetIR) => 71.20/9.74 (((emptyE1) => 71.20/9.74 (((vacuousDall) => 71.20/9.74 (((quantDeMorgan1) => 71.20/9.74 (((quantDeMorgan2) => 71.20/9.74 (((quantDeMorgan3) => 71.20/9.74 (((quantDeMorgan4) => 71.20/9.74 (((prop2setI) => 71.20/9.74 (( 71.20/9.74 (prop2set2propI) => 71.20/9.74 (( 71.20/9.74 (notdexE) => 71.20/9.74 (( 71.20/9.74 (notdallE) => 71.20/9.74 (( 71.20/9.74 (exuI1) => 71.20/9.74 (( 71.20/9.74 (exuI3) => 71.20/9.74 (( 71.20/9.74 (exuI2) => 71.20/9.74 (( 71.20/9.74 (inCongP) => 71.20/9.74 (( 71.20/9.74 (in__Cong) => 71.20/9.74 (( 71.20/9.74 (exuE3u) => 71.20/9.74 (( 71.20/9.74 (exu__Cong) => 71.20/9.74 (( 71.20/9.74 (setadjoin__Cong) => 71.20/9.74 (( 71.20/9.74 (powerset__Cong) => 71.20/9.74 (( 71.20/9.74 (setunion__Cong) => 71.20/9.74 (( 71.20/9.74 (exuEu) => 71.20/9.74 (( 71.20/9.74 (descr__Cong) => 71.20/9.74 (( 71.20/9.74 (dsetconstr__Cong) => 71.20/9.74 (( 71.20/9.74 (subsetI1) => 71.20/9.74 (( 71.20/9.74 (eqimpsubset2) => 71.20/9.74 (( 71.20/9.74 (eqimpsubset1) => 71.20/9.74 (( 71.20/9.74 (subsetI2) => 71.20/9.74 (( 71.20/9.74 (emptysetsubset) => 71.20/9.74 (( 71.20/9.74 (subsetE) => 71.20/9.74 (( 71.20/9.74 (subsetE2) => 71.20/9.74 (( 71.20/9.74 (notsubsetI) => 71.20/9.74 (( 71.20/9.74 (notequalI1) => 71.20/9.74 (( 71.20/9.74 (notequalI2) => 71.20/9.74 (( 71.20/9.74 (subsetRefl) => 71.20/9.74 (( 71.20/9.74 (subsetTrans) => 71.20/9.74 (( 71.20/9.74 (setadjoinSub) => 71.20/9.74 (( 71.20/9.74 (setadjoinSub2) => 71.20/9.74 (( 71.20/9.74 (subset2powerset) => 71.20/9.74 (( 71.20/9.74 (setextsub) => 71.20/9.74 (( 71.20/9.74 (subsetemptysetimpeq) => 71.20/9.74 (( 71.20/9.74 (powersetI1) => 71.20/9.74 (( 71.20/9.74 (powersetE1) => 71.20/9.74 (( 71.20/9.74 (inPowerset) => 71.20/9.74 (( 71.20/9.74 (powersetsubset) => 71.20/9.74 (( 71.20/9.74 (sepInPowerset) => 71.20/9.74 (( 71.20/9.74 (sepSubset) => 71.20/9.74 (( 71.20/9.74 (binunionIL) => 71.20/9.74 (( 71.20/9.74 (upairset2IR) => 71.20/9.74 (( 71.20/9.74 (binunionIR) => 71.20/9.74 (( 71.20/9.74 (binunionEcases) => 71.20/9.74 (( 71.20/9.74 (binunionE) => 71.20/9.74 (( 71.20/9.74 (binunionLsub) => 71.20/9.74 (( 71.20/9.74 (binunionRsub) => 71.20/9.74 (( 71.20/9.74 (binintersectI) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset5) => 71.20/9.74 (( 71.20/9.74 (binintersectEL) => 71.20/9.74 (( 71.20/9.74 (binintersectLsub) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset2) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset3) => 71.20/9.74 (( 71.20/9.74 (binintersectER) => 71.20/9.74 (( 71.20/9.74 (disjointsetsI1) => 71.20/9.74 (( 71.20/9.74 (binintersectRsub) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset4) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset1) => 71.20/9.74 (( 71.20/9.74 (bs114d) => 71.20/9.74 (( 71.20/9.74 (setminusI) => 71.20/9.74 (( 71.20/9.74 (setminusEL) => 71.20/9.74 (( 71.20/9.74 (setminusER) => 71.20/9.74 (( 71.20/9.74 (setminusSubset2) => 71.20/9.74 (( 71.20/9.74 (setminusERneg) => 71.20/9.74 (( 71.20/9.74 (setminusELneg) => 71.20/9.74 (( 71.20/9.74 (setminusILneg) => 71.20/9.74 (( 71.20/9.74 (setminusIRneg) => 71.20/9.74 (( 71.20/9.74 (setminusLsub) => 71.20/9.74 (( 71.20/9.74 (setminusSubset1) => 71.20/9.74 (( 71.20/9.74 (symdiffE) => 71.20/9.74 (( 71.20/9.74 (symdiffI1) => 71.20/9.74 (( 71.20/9.74 (symdiffI2) => 71.20/9.74 (( 71.20/9.74 (symdiffIneg1) => 71.20/9.74 (( 71.20/9.74 (symdiffIneg2) => 71.20/9.74 (( 71.20/9.74 (secondinupair) => 71.20/9.74 (( 71.20/9.74 (setukpairIL) => 71.20/9.74 (( 71.20/9.74 (setukpairIR) => 71.20/9.74 (( 71.20/9.74 (kpairiskpair) => 71.20/9.74 (( 71.20/9.74 (kpairp) => 71.20/9.74 (( 71.20/9.74 (singletonsubset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowerset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowunion) => 71.20/9.74 (( 71.20/9.74 (upairset2E) => 71.20/9.74 (( 71.20/9.74 (upairsubunion) => 71.20/9.74 (( 71.20/9.74 (upairinpowunion) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem1) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem2) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem3) => 71.20/9.74 (( 71.20/9.74 (cartprodpairin) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair1) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair) => 71.20/9.74 (( 71.20/9.74 (setunionE2) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton1) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton2) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton) => 71.20/9.74 (( 71.20/9.74 (singletonprop) => 71.20/9.74 (( 71.20/9.74 (ex1E1) => 71.20/9.74 (( 71.20/9.74 (ex1I) => 71.20/9.74 (( 71.20/9.74 (ex1I2) => 71.20/9.74 (( 71.20/9.74 (singletonsuniq) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL1) => 71.20/9.74 (( 71.20/9.74 (kfstsingleton) => 71.20/9.74 (( 71.20/9.74 (theprop) => 71.20/9.74 (( 71.20/9.74 (kfstpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodfstin) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL2) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR11) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR12) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR1) => 71.20/9.74 (( 71.20/9.74 (upairequniteq) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR2) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR) => 71.20/9.74 (( 71.20/9.74 (ksndsingleton) => 71.20/9.74 (( 71.20/9.74 (ksndpairEq) => 71.20/9.74 (( 71.20/9.74 (kpairsurjEq) => 71.20/9.74 (( 71.20/9.74 (cartprodsndin) => 71.20/9.74 (( 71.20/9.74 (cartprodpairmemEL) => 71.20/9.74 (( 71.20/9.74 (cartprodpairmemER) => 71.20/9.74 (( 71.20/9.74 (cartprodmempaircEq) => 71.20/9.74 (( 71.20/9.74 (cartprodfstpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodsndpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodpairsurjEq) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrI) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrSub) => 71.20/9.74 (( 71.20/9.74 (setOfPairsIsBReln) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrERa) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrEL1) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrEL2) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrER) => 71.20/9.74 (( 71.20/9.74 (funcImageSingleton) => 71.20/9.74 (( 71.20/9.74 (apProp) => 71.20/9.74 (( 71.20/9.74 (app) => 71.20/9.74 (( 71.20/9.74 (infuncsetfunc) => 71.20/9.74 (( 71.20/9.74 (ap2p) => 71.20/9.74 (( 71.20/9.74 (funcinfuncset) => 71.20/9.74 (( 71.20/9.74 (lamProp) => 71.20/9.74 (( 71.20/9.74 (lamp) => 71.20/9.74 (( 71.20/9.74 (lam2p) => 71.20/9.74 (( 71.20/9.74 (brelnall1) => 71.20/9.74 (( 71.20/9.74 (brelnall2) => 71.20/9.74 (( 71.20/9.74 (ex1E2) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp1) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp3) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp2) => 71.20/9.74 (( 71.20/9.74 (funcextLem) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp4) => 71.20/9.74 (( 71.20/9.74 (subbreln) => 71.20/9.74 (( 71.20/9.74 (eqbreln) => 71.20/9.74 (( 71.20/9.74 (funcext) => 71.20/9.74 (( 71.20/9.74 (funcext2) => 71.20/9.74 (( 71.20/9.74 (ap2apEq1) => 71.20/9.74 (( 71.20/9.74 (ap2apEq2) => 71.20/9.74 (( 71.20/9.74 (beta1) => 71.20/9.74 (( 71.20/9.74 (eta1) => 71.20/9.74 (( 71.20/9.74 (lam2lamEq) => 71.20/9.74 (( 71.20/9.74 (beta2) => 71.20/9.74 (( 71.20/9.74 (eta2) => 71.20/9.74 (( 71.20/9.74 (iffalseProp1) => 71.20/9.74 (( 71.20/9.74 (iffalseProp2) => 71.20/9.74 (( 71.20/9.74 (iftrueProp1) => 71.20/9.74 (( 71.20/9.74 (iftrueProp2) => 71.20/9.74 (( 71.20/9.74 (ifSingleton) => 71.20/9.74 (( 71.20/9.74 (ifp) => 71.20/9.74 (( 71.20/9.74 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71.20/9.74 ('#B') @ ( 71.20/9.74 '#S') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 =>))) @ 71.20/9.74 breln1)))))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#C') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 breln1)))) @ 71.20/9.74 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])). 71.20/9.74 thf(zip_derived_cl307, plain, 71.20/9.74 (~ (((setadjoinIL) => 71.20/9.74 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 71.20/9.74 (((setadjoinIR) => 71.20/9.74 (((setadjoinE) => 71.20/9.74 (((setadjoinOr) => 71.20/9.74 (((setoftrueEq) => 71.20/9.74 (((powersetI) => 71.20/9.74 (((emptyinPowerset) => 71.20/9.74 (((emptyInPowerset) => 71.20/9.74 (((powersetE) => 71.20/9.74 (((setunionI) => 71.20/9.74 (((setunionE) => 71.20/9.74 (((subPowSU) => 71.20/9.74 (((exuE2) => 71.20/9.74 (((nonemptyImpWitness) => 71.20/9.74 (((uniqinunit) => 71.20/9.74 (((notinsingleton) => 71.20/9.74 (((eqinunit) => 71.20/9.74 (((singletonsswitch) => 71.20/9.74 (((upairsetE) => 71.20/9.74 (((upairsetIL) => 71.20/9.74 (((upairsetIR) => 71.20/9.74 (((emptyE1) => 71.20/9.74 (((vacuousDall) => 71.20/9.74 (((quantDeMorgan1) => 71.20/9.74 (((quantDeMorgan2) => 71.20/9.74 (((quantDeMorgan3) => 71.20/9.74 (((quantDeMorgan4) => 71.20/9.74 (((prop2setI) => 71.20/9.74 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=> 71.20/9.74 (( 71.20/9.74 (symdiffIneg1) => 71.20/9.74 (( 71.20/9.74 (symdiffIneg2) => 71.20/9.74 (( 71.20/9.74 (secondinupair) => 71.20/9.74 (( 71.20/9.74 (setukpairIL) => 71.20/9.74 (( 71.20/9.74 (setukpairIR) => 71.20/9.74 (( 71.20/9.74 (kpairiskpair) => 71.20/9.74 (( 71.20/9.74 (kpairp) => 71.20/9.74 (( 71.20/9.74 (singletonsubset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowerset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowunion) => 71.20/9.74 (( 71.20/9.74 (upairset2E) => 71.20/9.74 (( 71.20/9.74 (upairsubunion) => 71.20/9.74 (( 71.20/9.74 (upairinpowunion) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem1) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem2) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem3) => 71.20/9.74 (( 71.20/9.74 (cartprodpairin) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair1) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair) => 71.20/9.74 (( 71.20/9.74 (setunionE2) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton1) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton2) => 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71.20/9.74 (binunionTEcontra) => 71.20/9.74 (( 71.20/9.74 (demorgan2a1) => 71.20/9.74 (( 71.20/9.74 (complementUnionInPowersetComplement) => 71.20/9.74 (( 71.20/9.74 (demorgan2a2) => 71.20/9.74 (( 71.20/9.74 (demorgan1a) => 71.20/9.74 (( 71.20/9.74 (demorgan1b) => 71.20/9.74 (( 71.20/9.74 (demorgan1) => 71.20/9.74 (( 71.20/9.74 (demorgan2a) => 71.20/9.74 (( 71.20/9.74 (demorgan2b2) => 71.20/9.74 (( 71.20/9.74 (demorgan2b) => 71.20/9.74 (( 71.20/9.74 (demorgan2) => 71.20/9.74 (( 71.20/9.74 (woz13rule0) => 71.20/9.74 (( 71.20/9.74 (woz13rule1) => 71.20/9.74 (( 71.20/9.74 (woz13rule2) => 71.20/9.74 (( 71.20/9.74 (woz13rule3) => 71.20/9.74 (( 71.20/9.74 (woz13rule4) => 71.20/9.74 (( 71.20/9.74 (woz1_1) => 71.20/9.74 (( 71.20/9.74 (woz1_2) => 71.20/9.74 (( 71.20/9.74 (woz1_3) => 71.20/9.74 (( 71.20/9.74 (woz1_4) => 71.20/9.74 (( 71.20/9.74 (woz1_5) => 71.20/9.74 (( 71.20/9.74 (breln1all2) => 71.20/9.74 (( 71.20/9.74 (breln1SetBreln1) => 71.20/9.74 (( 71.20/9.74 (choice2fnsingleton) => 71.20/9.74 (( 71.20/9.74 (setOfPairsIsBReln1) => 71.20/9.74 (( 71.20/9.74 (breln1all1) => 71.20/9.74 (( 71.20/9.74 (subbreln1) => 71.20/9.74 (( 71.20/9.74 (eqbreln1) => 71.20/9.74 (( 71.20/9.74 (breln1invprop) => 71.20/9.74 (( 71.20/9.74 (breln1invI) => 71.20/9.74 (( 71.20/9.74 (breln1invE) => 71.20/9.74 (( 71.20/9.74 (breln1compprop) => 71.20/9.74 (( 71.20/9.74 (breln1compI) => 71.20/9.74 (( 71.20/9.74 (breln1compE) => 71.20/9.74 (( 71.20/9.74 (breln1compEex) => 71.20/9.74 (( 71.20/9.74 (!!) @ ( 71.20/9.74 (('#B') @ ( 71.20/9.74 !!) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#S') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#S') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 =>))) @ 71.20/9.74 breln1)))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 !!))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#S') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#S') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 =>))) @ 71.20/9.74 breln1)))))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#C') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 breln1)))) @ 71.20/9.74 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])). 71.20/9.74 thf(zip_derived_cl322, plain, 71.20/9.74 (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => 71.20/9.74 (((setadjoinIR) => 71.20/9.74 (((setadjoinE) => 71.20/9.74 (((setadjoinOr) => 71.20/9.74 (((setoftrueEq) => 71.20/9.74 (((powersetI) => 71.20/9.74 (((emptyinPowerset) => 71.20/9.74 (((emptyInPowerset) => 71.20/9.74 (((powersetE) => 71.20/9.74 (((setunionI) => 71.20/9.74 (((setunionE) => 71.20/9.74 (((subPowSU) => 71.20/9.74 (((exuE2) => 71.20/9.74 (((nonemptyImpWitness) => 71.20/9.74 (((uniqinunit) => 71.20/9.74 (((notinsingleton) => 71.20/9.74 (((eqinunit) => 71.20/9.74 (((singletonsswitch) => 71.20/9.74 (((upairsetE) => 71.20/9.74 (((upairsetIL) => 71.20/9.74 (((upairsetIR) => 71.20/9.74 (((emptyE1) => 71.20/9.74 (((vacuousDall) => 71.20/9.74 (((quantDeMorgan1) => 71.20/9.74 (((quantDeMorgan2) => 71.20/9.74 (((quantDeMorgan3) => 71.20/9.74 (((quantDeMorgan4) => 71.20/9.74 (((prop2setI) => 71.20/9.74 (((prop2set2propI) => 71.20/9.74 (((notdexE) => 71.20/9.74 (( 71.20/9.74 (notdallE) => 71.20/9.74 (( 71.20/9.74 (exuI1) => 71.20/9.74 (( 71.20/9.74 (exuI3) => 71.20/9.74 (( 71.20/9.74 (exuI2) => 71.20/9.74 (( 71.20/9.74 (inCongP) => 71.20/9.74 (( 71.20/9.74 (in__Cong) => 71.20/9.74 (( 71.20/9.74 (exuE3u) => 71.20/9.74 (( 71.20/9.74 (exu__Cong) => 71.20/9.74 (( 71.20/9.74 (setadjoin__Cong) => 71.20/9.74 (( 71.20/9.74 (powerset__Cong) => 71.20/9.74 (( 71.20/9.74 (setunion__Cong) => 71.20/9.74 (( 71.20/9.74 (exuEu) => 71.20/9.74 (( 71.20/9.74 (descr__Cong) => 71.20/9.74 (( 71.20/9.74 (dsetconstr__Cong) => 71.20/9.74 (( 71.20/9.74 (subsetI1) => 71.20/9.74 (( 71.20/9.74 (eqimpsubset2) => 71.20/9.74 (( 71.20/9.74 (eqimpsubset1) => 71.20/9.74 (( 71.20/9.74 (subsetI2) => 71.20/9.74 (( 71.20/9.74 (emptysetsubset) => 71.20/9.74 (( 71.20/9.74 (subsetE) => 71.20/9.74 (( 71.20/9.74 (subsetE2) => 71.20/9.74 (( 71.20/9.74 (notsubsetI) => 71.20/9.74 (( 71.20/9.74 (notequalI1) => 71.20/9.74 (( 71.20/9.74 (notequalI2) => 71.20/9.74 (( 71.20/9.74 (subsetRefl) => 71.20/9.74 (( 71.20/9.74 (subsetTrans) => 71.20/9.74 (( 71.20/9.74 (setadjoinSub) => 71.20/9.74 (( 71.20/9.74 (setadjoinSub2) => 71.20/9.74 (( 71.20/9.74 (subset2powerset) => 71.20/9.74 (( 71.20/9.74 (setextsub) => 71.20/9.74 (( 71.20/9.74 (subsetemptysetimpeq) => 71.20/9.74 (( 71.20/9.74 (powersetI1) => 71.20/9.74 (( 71.20/9.74 (powersetE1) => 71.20/9.74 (( 71.20/9.74 (inPowerset) => 71.20/9.74 (( 71.20/9.74 (powersetsubset) => 71.20/9.74 (( 71.20/9.74 (sepInPowerset) => 71.20/9.74 (( 71.20/9.74 (sepSubset) => 71.20/9.74 (( 71.20/9.74 (binunionIL) => 71.20/9.74 (( 71.20/9.74 (upairset2IR) => 71.20/9.74 (( 71.20/9.74 (binunionIR) => 71.20/9.74 (( 71.20/9.74 (binunionEcases) => 71.20/9.74 (( 71.20/9.74 (binunionE) => 71.20/9.74 (( 71.20/9.74 (binunionLsub) => 71.20/9.74 (( 71.20/9.74 (binunionRsub) => 71.20/9.74 (( 71.20/9.74 (binintersectI) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset5) => 71.20/9.74 (( 71.20/9.74 (binintersectEL) => 71.20/9.74 (( 71.20/9.74 (binintersectLsub) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset2) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset3) => 71.20/9.74 (( 71.20/9.74 (binintersectER) => 71.20/9.74 (( 71.20/9.74 (disjointsetsI1) => 71.20/9.74 (( 71.20/9.74 (binintersectRsub) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset4) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset1) => 71.20/9.74 (( 71.20/9.74 (bs114d) => 71.20/9.74 (( 71.20/9.74 (setminusI) => 71.20/9.74 (( 71.20/9.74 (setminusEL) => 71.20/9.74 (( 71.20/9.74 (setminusER) => 71.20/9.74 (( 71.20/9.74 (setminusSubset2) => 71.20/9.74 (( 71.20/9.74 (setminusERneg) => 71.20/9.74 (( 71.20/9.74 (setminusELneg) => 71.20/9.74 (( 71.20/9.74 (setminusILneg) => 71.20/9.74 (( 71.20/9.74 (setminusIRneg) => 71.20/9.74 (( 71.20/9.74 (setminusLsub) => 71.20/9.74 (( 71.20/9.74 (setminusSubset1) => 71.20/9.74 (( 71.20/9.74 (symdiffE) => 71.20/9.74 (( 71.20/9.74 (symdiffI1) => 71.20/9.74 (( 71.20/9.74 (symdiffI2) => 71.20/9.74 (( 71.20/9.74 (symdiffIneg1) => 71.20/9.74 (( 71.20/9.74 (symdiffIneg2) => 71.20/9.74 (( 71.20/9.74 (secondinupair) => 71.20/9.74 (( 71.20/9.74 (setukpairIL) => 71.20/9.74 (( 71.20/9.74 (setukpairIR) => 71.20/9.74 (( 71.20/9.74 (kpairiskpair) => 71.20/9.74 (( 71.20/9.74 (kpairp) => 71.20/9.74 (( 71.20/9.74 (singletonsubset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowerset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowunion) => 71.20/9.74 (( 71.20/9.74 (upairset2E) => 71.20/9.74 (( 71.20/9.74 (upairsubunion) => 71.20/9.74 (( 71.20/9.74 (upairinpowunion) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem1) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem2) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem3) => 71.20/9.74 (( 71.20/9.74 (cartprodpairin) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair1) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair) => 71.20/9.74 (( 71.20/9.74 (setunionE2) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton1) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton2) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton) => 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71.20/9.74 (cartprodpairmemER) => 71.20/9.74 (( 71.20/9.74 (cartprodmempaircEq) => 71.20/9.74 (( 71.20/9.74 (cartprodfstpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodsndpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodpairsurjEq) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrI) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrSub) => 71.20/9.74 (( 71.20/9.74 (setOfPairsIsBReln) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrERa) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrEL1) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrEL2) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrER) => 71.20/9.74 (( 71.20/9.74 (funcImageSingleton) => 71.20/9.74 (( 71.20/9.74 (apProp) => 71.20/9.74 (( 71.20/9.74 (app) => 71.20/9.74 (( 71.20/9.74 (infuncsetfunc) => 71.20/9.74 (( 71.20/9.74 (ap2p) => 71.20/9.74 (( 71.20/9.74 (funcinfuncset) => 71.20/9.74 (( 71.20/9.74 (lamProp) => 71.20/9.74 (( 71.20/9.74 (lamp) => 71.20/9.74 (( 71.20/9.74 (lam2p) => 71.20/9.74 (( 71.20/9.74 (brelnall1) => 71.20/9.74 (( 71.20/9.74 (brelnall2) => 71.20/9.74 (( 71.20/9.74 (ex1E2) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp1) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp3) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp2) => 71.20/9.74 (( 71.20/9.74 (funcextLem) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp4) => 71.20/9.74 (( 71.20/9.74 (subbreln) => 71.20/9.74 (( 71.20/9.74 (eqbreln) => 71.20/9.74 (( 71.20/9.74 (funcext) => 71.20/9.74 (( 71.20/9.74 (funcext2) => 71.20/9.74 (( 71.20/9.74 (ap2apEq1) => 71.20/9.74 (( 71.20/9.74 (ap2apEq2) => 71.20/9.74 (( 71.20/9.74 (beta1) => 71.20/9.74 (( 71.20/9.74 (eta1) => 71.20/9.74 (( 71.20/9.74 (lam2lamEq) => 71.20/9.74 (( 71.20/9.74 (beta2) => 71.20/9.74 (( 71.20/9.74 (eta2) => 71.20/9.74 (( 71.20/9.74 (iffalseProp1) => 71.20/9.74 (( 71.20/9.74 (iffalseProp2) => 71.20/9.74 (( 71.20/9.74 (iftrueProp1) => 71.20/9.74 (( 71.20/9.74 (iftrueProp2) => 71.20/9.74 (( 71.20/9.74 (ifSingleton) => 71.20/9.74 (( 71.20/9.74 (ifp) => 71.20/9.74 (( 71.20/9.74 (theeq) => 71.20/9.74 (( 71.20/9.74 (iftrue) => 71.20/9.74 (( 71.20/9.74 (iffalse) => 71.20/9.74 (( 71.20/9.74 (iftrueorfalse) => 71.20/9.74 (( 71.20/9.74 (binintersectT_lem) => 71.20/9.74 (( 71.20/9.74 (binunionT_lem) => 71.20/9.74 (( 71.20/9.74 (powersetT_lem) => 71.20/9.74 (( 71.20/9.74 (setminusT_lem) => 71.20/9.74 (( 71.20/9.74 (complementT_lem) => 71.20/9.74 (( 71.20/9.74 (setextT) => 71.20/9.74 (( 71.20/9.74 (subsetTI) => 71.20/9.74 (( 71.20/9.74 (powersetTI1) => 71.20/9.74 (( 71.20/9.74 (powersetTE1) => 71.20/9.74 (( 71.20/9.74 (complementTI1) => 71.20/9.74 (( 71.20/9.74 (complementTE1) => 71.20/9.74 (( 71.20/9.74 (binintersectTELcontra) => 71.20/9.74 (( 71.20/9.74 (binintersectTERcontra) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT1) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT2) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT3) => 71.20/9.74 (( 71.20/9.74 (doubleComplementI1) => 71.20/9.74 (( 71.20/9.74 (doubleComplementE1) => 71.20/9.74 (( 71.20/9.74 (doubleComplementSub1) => 71.20/9.74 (( 71.20/9.74 (doubleComplementSub2) => 71.20/9.74 (( 71.20/9.74 (doubleComplementEq) => 71.20/9.74 (( 71.20/9.74 (complementTnotintersectT) => 71.20/9.74 (( 71.20/9.74 (complementImpComplementIntersect) => 71.20/9.74 (( 71.20/9.74 (complementSubsetComplementIntersect) => 71.20/9.74 (( 71.20/9.74 (complementInPowersetComplementIntersect) => 71.20/9.74 (( 71.20/9.74 (contraSubsetComplement) => 71.20/9.74 (( 71.20/9.74 (complementTcontraSubset) => 71.20/9.74 (( 71.20/9.74 (binunionTILcontra) => 71.20/9.74 (( 71.20/9.74 (binunionTIRcontra) => 71.20/9.74 (( 71.20/9.74 (inIntersectImpInUnion) => 71.20/9.74 (( 71.20/9.74 (inIntersectImpInUnion2) => 71.20/9.74 (( 71.20/9.74 (inIntersectImpInIntersectUnions) => 71.20/9.74 (( 71.20/9.74 (intersectInPowersetIntersectUnions) => 71.20/9.74 (( 71.20/9.74 (inComplementUnionImpNotIn1) => 71.20/9.74 (( 71.20/9.74 (inComplementUnionImpInComplement1) => 71.20/9.74 (( 71.20/9.74 (binunionTE) => 71.20/9.74 (( 71.20/9.74 (binunionTEcontra) => 71.20/9.74 (( 71.20/9.74 (demorgan2a1) => 71.20/9.74 (( 71.20/9.74 (complementUnionInPowersetComplement) => 71.20/9.74 (( 71.20/9.74 (demorgan2a2) => 71.20/9.74 (( 71.20/9.74 (demorgan1a) => 71.20/9.74 (( 71.20/9.74 (demorgan1b) => 71.20/9.74 (( 71.20/9.74 (demorgan1) => 71.20/9.74 (( 71.20/9.74 (demorgan2a) => 71.20/9.74 (( 71.20/9.74 (demorgan2b2) => 71.20/9.74 (( 71.20/9.74 (demorgan2b) => 71.20/9.74 (( 71.20/9.74 (demorgan2) => 71.20/9.74 (( 71.20/9.74 (woz13rule0) => 71.20/9.74 (( 71.20/9.74 (woz13rule1) => 71.20/9.74 (( 71.20/9.74 (woz13rule2) => 71.20/9.74 (( 71.20/9.74 (woz13rule3) => 71.20/9.74 (( 71.20/9.74 (woz13rule4) => 71.20/9.74 (( 71.20/9.74 (woz1_1) => 71.20/9.74 (( 71.20/9.74 (woz1_2) => 71.20/9.74 (( 71.20/9.74 (woz1_3) => 71.20/9.74 (( 71.20/9.74 (woz1_4) => 71.20/9.74 (( 71.20/9.74 (woz1_5) => 71.20/9.74 (( 71.20/9.74 (breln1all2) => 71.20/9.74 (( 71.20/9.74 (breln1SetBreln1) => 71.20/9.74 (( 71.20/9.74 (choice2fnsingleton) => 71.20/9.74 (( 71.20/9.74 (setOfPairsIsBReln1) => 71.20/9.74 (( 71.20/9.74 (breln1all1) => 71.20/9.74 (( 71.20/9.74 (subbreln1) => 71.20/9.74 (( 71.20/9.74 (eqbreln1) => 71.20/9.74 (( 71.20/9.74 (breln1invprop) => 71.20/9.74 (( 71.20/9.74 (breln1invI) => 71.20/9.74 (( 71.20/9.74 (breln1invE) => 71.20/9.74 (( 71.20/9.74 (breln1compprop) => 71.20/9.74 (( 71.20/9.74 (breln1compI) => 71.20/9.74 (( 71.20/9.74 (breln1compE) => 71.20/9.74 (( 71.20/9.74 (breln1compEex) => 71.20/9.74 (( 71.20/9.74 (!!) @ ( 71.20/9.74 (('#B') @ ( 71.20/9.74 !!) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#S') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#S') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 =>))) @ 71.20/9.74 breln1)))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 !!))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#S') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#S') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 =>))) @ 71.20/9.74 breln1)))))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#C') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 breln1)))) @ 71.20/9.74 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])). 71.20/9.74 thf(zip_derived_cl337, plain, 71.20/9.74 (~ (((setadjoinIR) => 71.20/9.74 (((setadjoinE) => 71.20/9.74 (((setadjoinOr) => 71.20/9.74 (((setoftrueEq) => 71.20/9.74 (((powersetI) => 71.20/9.74 (((emptyinPowerset) => 71.20/9.74 (((emptyInPowerset) => 71.20/9.74 (((powersetE) => 71.20/9.74 (((setunionI) => 71.20/9.74 (((setunionE) => 71.20/9.74 (((subPowSU) => 71.20/9.74 (((exuE2) => 71.20/9.74 (((nonemptyImpWitness) => 71.20/9.74 (((uniqinunit) => 71.20/9.74 (((notinsingleton) => 71.20/9.74 (((eqinunit) => 71.20/9.74 (((singletonsswitch) => 71.20/9.74 (((upairsetE) => 71.20/9.74 (((upairsetIL) => 71.20/9.74 (((upairsetIR) => 71.20/9.74 (((emptyE1) => 71.20/9.74 (((vacuousDall) => 71.20/9.74 (((quantDeMorgan1) => 71.20/9.74 (((quantDeMorgan2) => 71.20/9.74 (((quantDeMorgan3) => 71.20/9.74 (((quantDeMorgan4) => 71.20/9.74 (((prop2setI) => 71.20/9.74 (((prop2set2propI) => 71.20/9.74 (((notdexE) => 71.20/9.74 (((notdallE) => 71.20/9.74 (( 71.20/9.74 (exuI1) => 71.20/9.74 (( 71.20/9.74 (exuI3) => 71.20/9.74 (( 71.20/9.74 (exuI2) => 71.20/9.74 (( 71.20/9.74 (inCongP) => 71.20/9.74 (( 71.20/9.74 (in__Cong) => 71.20/9.74 (( 71.20/9.74 (exuE3u) => 71.20/9.74 (( 71.20/9.74 (exu__Cong) => 71.20/9.74 (( 71.20/9.74 (setadjoin__Cong) => 71.20/9.74 (( 71.20/9.74 (powerset__Cong) => 71.20/9.74 (( 71.20/9.74 (setunion__Cong) => 71.20/9.74 (( 71.20/9.74 (exuEu) => 71.20/9.74 (( 71.20/9.74 (descr__Cong) => 71.20/9.74 (( 71.20/9.74 (dsetconstr__Cong) => 71.20/9.74 (( 71.20/9.74 (subsetI1) => 71.20/9.74 (( 71.20/9.74 (eqimpsubset2) => 71.20/9.74 (( 71.20/9.74 (eqimpsubset1) => 71.20/9.74 (( 71.20/9.74 (subsetI2) => 71.20/9.74 (( 71.20/9.74 (emptysetsubset) => 71.20/9.74 (( 71.20/9.74 (subsetE) => 71.20/9.74 (( 71.20/9.74 (subsetE2) => 71.20/9.74 (( 71.20/9.74 (notsubsetI) => 71.20/9.74 (( 71.20/9.74 (notequalI1) => 71.20/9.74 (( 71.20/9.74 (notequalI2) => 71.20/9.74 (( 71.20/9.74 (subsetRefl) => 71.20/9.74 (( 71.20/9.74 (subsetTrans) => 71.20/9.74 (( 71.20/9.74 (setadjoinSub) => 71.20/9.74 (( 71.20/9.74 (setadjoinSub2) => 71.20/9.74 (( 71.20/9.74 (subset2powerset) => 71.20/9.74 (( 71.20/9.74 (setextsub) => 71.20/9.74 (( 71.20/9.74 (subsetemptysetimpeq) => 71.20/9.74 (( 71.20/9.74 (powersetI1) => 71.20/9.74 (( 71.20/9.74 (powersetE1) => 71.20/9.74 (( 71.20/9.74 (inPowerset) => 71.20/9.74 (( 71.20/9.74 (powersetsubset) => 71.20/9.74 (( 71.20/9.74 (sepInPowerset) => 71.20/9.74 (( 71.20/9.74 (sepSubset) => 71.20/9.74 (( 71.20/9.74 (binunionIL) => 71.20/9.74 (( 71.20/9.74 (upairset2IR) => 71.20/9.74 (( 71.20/9.74 (binunionIR) => 71.20/9.74 (( 71.20/9.74 (binunionEcases) => 71.20/9.74 (( 71.20/9.74 (binunionE) => 71.20/9.74 (( 71.20/9.74 (binunionLsub) => 71.20/9.74 (( 71.20/9.74 (binunionRsub) => 71.20/9.74 (( 71.20/9.74 (binintersectI) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset5) => 71.20/9.74 (( 71.20/9.74 (binintersectEL) => 71.20/9.74 (( 71.20/9.74 (binintersectLsub) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset2) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset3) => 71.20/9.74 (( 71.20/9.74 (binintersectER) => 71.20/9.74 (( 71.20/9.74 (disjointsetsI1) => 71.20/9.74 (( 71.20/9.74 (binintersectRsub) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset4) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset1) => 71.20/9.74 (( 71.20/9.74 (bs114d) => 71.20/9.74 (( 71.20/9.74 (setminusI) => 71.20/9.74 (( 71.20/9.74 (setminusEL) => 71.20/9.74 (( 71.20/9.74 (setminusER) => 71.20/9.74 (( 71.20/9.74 (setminusSubset2) => 71.20/9.74 (( 71.20/9.74 (setminusERneg) => 71.20/9.74 (( 71.20/9.74 (setminusELneg) => 71.20/9.74 (( 71.20/9.74 (setminusILneg) => 71.20/9.74 (( 71.20/9.74 (setminusIRneg) => 71.20/9.74 (( 71.20/9.74 (setminusLsub) => 71.20/9.74 (( 71.20/9.74 (setminusSubset1) => 71.20/9.74 (( 71.20/9.74 (symdiffE) => 71.20/9.74 (( 71.20/9.74 (symdiffI1) => 71.20/9.74 (( 71.20/9.74 (symdiffI2) => 71.20/9.74 (( 71.20/9.74 (symdiffIneg1) => 71.20/9.74 (( 71.20/9.74 (symdiffIneg2) => 71.20/9.74 (( 71.20/9.74 (secondinupair) => 71.20/9.74 (( 71.20/9.74 (setukpairIL) => 71.20/9.74 (( 71.20/9.74 (setukpairIR) => 71.20/9.74 (( 71.20/9.74 (kpairiskpair) => 71.20/9.74 (( 71.20/9.74 (kpairp) => 71.20/9.74 (( 71.20/9.74 (singletonsubset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowerset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowunion) => 71.20/9.74 (( 71.20/9.74 (upairset2E) => 71.20/9.74 (( 71.20/9.74 (upairsubunion) => 71.20/9.74 (( 71.20/9.74 (upairinpowunion) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem1) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem2) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem3) => 71.20/9.74 (( 71.20/9.74 (cartprodpairin) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair1) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair) => 71.20/9.74 (( 71.20/9.74 (setunionE2) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton1) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton2) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton) => 71.20/9.74 (( 71.20/9.74 (singletonprop) => 71.20/9.74 (( 71.20/9.74 (ex1E1) => 71.20/9.74 (( 71.20/9.74 (ex1I) => 71.20/9.74 (( 71.20/9.74 (ex1I2) => 71.20/9.74 (( 71.20/9.74 (singletonsuniq) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL1) => 71.20/9.74 (( 71.20/9.74 (kfstsingleton) => 71.20/9.74 (( 71.20/9.74 (theprop) => 71.20/9.74 (( 71.20/9.74 (kfstpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodfstin) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL2) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR11) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR12) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR1) => 71.20/9.74 (( 71.20/9.74 (upairequniteq) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR2) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR) => 71.20/9.74 (( 71.20/9.74 (ksndsingleton) => 71.20/9.74 (( 71.20/9.74 (ksndpairEq) => 71.20/9.74 (( 71.20/9.74 (kpairsurjEq) => 71.20/9.74 (( 71.20/9.74 (cartprodsndin) => 71.20/9.74 (( 71.20/9.74 (cartprodpairmemEL) => 71.20/9.74 (( 71.20/9.74 (cartprodpairmemER) => 71.20/9.74 (( 71.20/9.74 (cartprodmempaircEq) => 71.20/9.74 (( 71.20/9.74 (cartprodfstpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodsndpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodpairsurjEq) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrI) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrSub) => 71.20/9.74 (( 71.20/9.74 (setOfPairsIsBReln) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrERa) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrEL1) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrEL2) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrER) => 71.20/9.74 (( 71.20/9.74 (funcImageSingleton) => 71.20/9.74 (( 71.20/9.74 (apProp) => 71.20/9.74 (( 71.20/9.74 (app) => 71.20/9.74 (( 71.20/9.74 (infuncsetfunc) => 71.20/9.74 (( 71.20/9.74 (ap2p) => 71.20/9.74 (( 71.20/9.74 (funcinfuncset) => 71.20/9.74 (( 71.20/9.74 (lamProp) => 71.20/9.74 (( 71.20/9.74 (lamp) => 71.20/9.74 (( 71.20/9.74 (lam2p) => 71.20/9.74 (( 71.20/9.74 (brelnall1) => 71.20/9.74 (( 71.20/9.74 (brelnall2) => 71.20/9.74 (( 71.20/9.74 (ex1E2) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp1) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp3) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp2) => 71.20/9.74 (( 71.20/9.74 (funcextLem) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp4) => 71.20/9.74 (( 71.20/9.74 (subbreln) => 71.20/9.74 (( 71.20/9.74 (eqbreln) => 71.20/9.74 (( 71.20/9.74 (funcext) => 71.20/9.74 (( 71.20/9.74 (funcext2) => 71.20/9.74 (( 71.20/9.74 (ap2apEq1) => 71.20/9.74 (( 71.20/9.74 (ap2apEq2) => 71.20/9.74 (( 71.20/9.74 (beta1) => 71.20/9.74 (( 71.20/9.74 (eta1) => 71.20/9.74 (( 71.20/9.74 (lam2lamEq) => 71.20/9.74 (( 71.20/9.74 (beta2) => 71.20/9.74 (( 71.20/9.74 (eta2) => 71.20/9.74 (( 71.20/9.74 (iffalseProp1) => 71.20/9.74 (( 71.20/9.74 (iffalseProp2) => 71.20/9.74 (( 71.20/9.74 (iftrueProp1) => 71.20/9.74 (( 71.20/9.74 (iftrueProp2) => 71.20/9.74 (( 71.20/9.74 (ifSingleton) => 71.20/9.74 (( 71.20/9.74 (ifp) => 71.20/9.74 (( 71.20/9.74 (theeq) => 71.20/9.74 (( 71.20/9.74 (iftrue) => 71.20/9.74 (( 71.20/9.74 (iffalse) => 71.20/9.74 (( 71.20/9.74 (iftrueorfalse) => 71.20/9.74 (( 71.20/9.74 (binintersectT_lem) => 71.20/9.74 (( 71.20/9.74 (binunionT_lem) => 71.20/9.74 (( 71.20/9.74 (powersetT_lem) => 71.20/9.74 (( 71.20/9.74 (setminusT_lem) => 71.20/9.74 (( 71.20/9.74 (complementT_lem) => 71.20/9.74 (( 71.20/9.74 (setextT) => 71.20/9.74 (( 71.20/9.74 (subsetTI) => 71.20/9.74 (( 71.20/9.74 (powersetTI1) => 71.20/9.74 (( 71.20/9.74 (powersetTE1) => 71.20/9.74 (( 71.20/9.74 (complementTI1) => 71.20/9.74 (( 71.20/9.74 (complementTE1) => 71.20/9.74 (( 71.20/9.74 (binintersectTELcontra) => 71.20/9.74 (( 71.20/9.74 (binintersectTERcontra) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT1) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT2) => 71.20/9.74 (( 71.20/9.74 (contrasubsetT3) => 71.20/9.74 (( 71.20/9.74 (doubleComplementI1) => 71.20/9.74 (( 71.20/9.74 (doubleComplementE1) => 71.20/9.74 (( 71.20/9.74 (doubleComplementSub1) => 71.20/9.74 (( 71.20/9.74 (doubleComplementSub2) => 71.20/9.74 (( 71.20/9.74 (doubleComplementEq) => 71.20/9.74 (( 71.20/9.74 (complementTnotintersectT) => 71.20/9.74 (( 71.20/9.74 (complementImpComplementIntersect) => 71.20/9.74 (( 71.20/9.74 (complementSubsetComplementIntersect) => 71.20/9.74 (( 71.20/9.74 (complementInPowersetComplementIntersect) => 71.20/9.74 (( 71.20/9.74 (contraSubsetComplement) => 71.20/9.74 (( 71.20/9.74 (complementTcontraSubset) => 71.20/9.74 (( 71.20/9.74 (binunionTILcontra) => 71.20/9.74 (( 71.20/9.74 (binunionTIRcontra) => 71.20/9.74 (( 71.20/9.74 (inIntersectImpInUnion) => 71.20/9.74 (( 71.20/9.74 (inIntersectImpInUnion2) => 71.20/9.74 (( 71.20/9.74 (inIntersectImpInIntersectUnions) => 71.20/9.74 (( 71.20/9.74 (intersectInPowersetIntersectUnions) => 71.20/9.74 (( 71.20/9.74 (inComplementUnionImpNotIn1) => 71.20/9.74 (( 71.20/9.74 (inComplementUnionImpInComplement1) => 71.20/9.74 (( 71.20/9.74 (binunionTE) => 71.20/9.74 (( 71.20/9.74 (binunionTEcontra) => 71.20/9.74 (( 71.20/9.74 (demorgan2a1) => 71.20/9.74 (( 71.20/9.74 (complementUnionInPowersetComplement) => 71.20/9.74 (( 71.20/9.74 (demorgan2a2) => 71.20/9.74 (( 71.20/9.74 (demorgan1a) => 71.20/9.74 (( 71.20/9.74 (demorgan1b) => 71.20/9.74 (( 71.20/9.74 (demorgan1) => 71.20/9.74 (( 71.20/9.74 (demorgan2a) => 71.20/9.74 (( 71.20/9.74 (demorgan2b2) => 71.20/9.74 (( 71.20/9.74 (demorgan2b) => 71.20/9.74 (( 71.20/9.74 (demorgan2) => 71.20/9.74 (( 71.20/9.74 (woz13rule0) => 71.20/9.74 (( 71.20/9.74 (woz13rule1) => 71.20/9.74 (( 71.20/9.74 (woz13rule2) => 71.20/9.74 (( 71.20/9.74 (woz13rule3) => 71.20/9.74 (( 71.20/9.74 (woz13rule4) => 71.20/9.74 (( 71.20/9.74 (woz1_1) => 71.20/9.74 (( 71.20/9.74 (woz1_2) => 71.20/9.74 (( 71.20/9.74 (woz1_3) => 71.20/9.74 (( 71.20/9.74 (woz1_4) => 71.20/9.74 (( 71.20/9.74 (woz1_5) => 71.20/9.74 (( 71.20/9.74 (breln1all2) => 71.20/9.74 (( 71.20/9.74 (breln1SetBreln1) => 71.20/9.74 (( 71.20/9.74 (choice2fnsingleton) => 71.20/9.74 (( 71.20/9.74 (setOfPairsIsBReln1) => 71.20/9.74 (( 71.20/9.74 (breln1all1) => 71.20/9.74 (( 71.20/9.74 (subbreln1) => 71.20/9.74 (( 71.20/9.74 (eqbreln1) => 71.20/9.74 (( 71.20/9.74 (breln1invprop) => 71.20/9.74 (( 71.20/9.74 (breln1invI) => 71.20/9.74 (( 71.20/9.74 (breln1invE) => 71.20/9.74 (( 71.20/9.74 (breln1compprop) => 71.20/9.74 (( 71.20/9.74 (breln1compI) => 71.20/9.74 (( 71.20/9.74 (breln1compE) => 71.20/9.74 (( 71.20/9.74 (breln1compEex) => 71.20/9.74 (( 71.20/9.74 (!!) @ ( 71.20/9.74 (('#B') @ ( 71.20/9.74 !!) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#S') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#S') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 =>))) @ 71.20/9.74 breln1)))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 !!))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#S') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#S') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 =>))) @ 71.20/9.74 breln1)))))) @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#C') @ ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 ( 71.20/9.74 ( 71.20/9.74 ('#B') @ ( 71.20/9.74 '#B') @ 71.20/9.74 breln1)))) @ 71.20/9.74 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl322])). 71.20/9.74 thf(zip_derived_cl349, plain, 71.20/9.74 (~ (((setadjoinE) => 71.20/9.74 (((setadjoinOr) => 71.20/9.74 (((setoftrueEq) => 71.20/9.74 (((powersetI) => 71.20/9.74 (((emptyinPowerset) => 71.20/9.74 (((emptyInPowerset) => 71.20/9.74 (((powersetE) => 71.20/9.74 (((setunionI) => 71.20/9.74 (((setunionE) => 71.20/9.74 (((subPowSU) => 71.20/9.74 (((exuE2) => 71.20/9.74 (((nonemptyImpWitness) => 71.20/9.74 (((uniqinunit) => 71.20/9.74 (((notinsingleton) => 71.20/9.74 (((eqinunit) => 71.20/9.74 (((singletonsswitch) => 71.20/9.74 (((upairsetE) => 71.20/9.74 (((upairsetIL) => 71.20/9.74 (((upairsetIR) => 71.20/9.74 (((emptyE1) => 71.20/9.74 (((vacuousDall) => 71.20/9.74 (((quantDeMorgan1) => 71.20/9.74 (((quantDeMorgan2) => 71.20/9.74 (((quantDeMorgan3) => 71.20/9.74 (((quantDeMorgan4) => 71.20/9.74 (((prop2setI) => 71.20/9.74 (((prop2set2propI) => 71.20/9.74 (((notdexE) => 71.20/9.74 (((notdallE) => 71.20/9.74 (((exuI1) => 71.20/9.74 (( 71.20/9.74 (exuI3) => 71.20/9.74 (( 71.20/9.74 (exuI2) => 71.20/9.74 (( 71.20/9.74 (inCongP) => 71.20/9.74 (( 71.20/9.74 (in__Cong) => 71.20/9.74 (( 71.20/9.74 (exuE3u) => 71.20/9.74 (( 71.20/9.74 (exu__Cong) => 71.20/9.74 (( 71.20/9.74 (setadjoin__Cong) => 71.20/9.74 (( 71.20/9.74 (powerset__Cong) => 71.20/9.74 (( 71.20/9.74 (setunion__Cong) => 71.20/9.74 (( 71.20/9.74 (exuEu) => 71.20/9.74 (( 71.20/9.74 (descr__Cong) => 71.20/9.74 (( 71.20/9.74 (dsetconstr__Cong) => 71.20/9.74 (( 71.20/9.74 (subsetI1) => 71.20/9.74 (( 71.20/9.74 (eqimpsubset2) => 71.20/9.74 (( 71.20/9.74 (eqimpsubset1) => 71.20/9.74 (( 71.20/9.74 (subsetI2) => 71.20/9.74 (( 71.20/9.74 (emptysetsubset) => 71.20/9.74 (( 71.20/9.74 (subsetE) => 71.20/9.74 (( 71.20/9.74 (subsetE2) => 71.20/9.74 (( 71.20/9.74 (notsubsetI) => 71.20/9.74 (( 71.20/9.74 (notequalI1) => 71.20/9.74 (( 71.20/9.74 (notequalI2) => 71.20/9.74 (( 71.20/9.74 (subsetRefl) => 71.20/9.74 (( 71.20/9.74 (subsetTrans) => 71.20/9.74 (( 71.20/9.74 (setadjoinSub) => 71.20/9.74 (( 71.20/9.74 (setadjoinSub2) => 71.20/9.74 (( 71.20/9.74 (subset2powerset) => 71.20/9.74 (( 71.20/9.74 (setextsub) => 71.20/9.74 (( 71.20/9.74 (subsetemptysetimpeq) => 71.20/9.74 (( 71.20/9.74 (powersetI1) => 71.20/9.74 (( 71.20/9.74 (powersetE1) => 71.20/9.74 (( 71.20/9.74 (inPowerset) => 71.20/9.74 (( 71.20/9.74 (powersetsubset) => 71.20/9.74 (( 71.20/9.74 (sepInPowerset) => 71.20/9.74 (( 71.20/9.74 (sepSubset) => 71.20/9.74 (( 71.20/9.74 (binunionIL) => 71.20/9.74 (( 71.20/9.74 (upairset2IR) => 71.20/9.74 (( 71.20/9.74 (binunionIR) => 71.20/9.74 (( 71.20/9.74 (binunionEcases) => 71.20/9.74 (( 71.20/9.74 (binunionE) => 71.20/9.74 (( 71.20/9.74 (binunionLsub) => 71.20/9.74 (( 71.20/9.74 (binunionRsub) => 71.20/9.74 (( 71.20/9.74 (binintersectI) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset5) => 71.20/9.74 (( 71.20/9.74 (binintersectEL) => 71.20/9.74 (( 71.20/9.74 (binintersectLsub) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset2) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset3) => 71.20/9.74 (( 71.20/9.74 (binintersectER) => 71.20/9.74 (( 71.20/9.74 (disjointsetsI1) => 71.20/9.74 (( 71.20/9.74 (binintersectRsub) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset4) => 71.20/9.74 (( 71.20/9.74 (binintersectSubset1) => 71.20/9.74 (( 71.20/9.74 (bs114d) => 71.20/9.74 (( 71.20/9.74 (setminusI) => 71.20/9.74 (( 71.20/9.74 (setminusEL) => 71.20/9.74 (( 71.20/9.74 (setminusER) => 71.20/9.74 (( 71.20/9.74 (setminusSubset2) => 71.20/9.74 (( 71.20/9.74 (setminusERneg) => 71.20/9.74 (( 71.20/9.74 (setminusELneg) => 71.20/9.74 (( 71.20/9.74 (setminusILneg) => 71.20/9.74 (( 71.20/9.74 (setminusIRneg) => 71.20/9.74 (( 71.20/9.74 (setminusLsub) => 71.20/9.74 (( 71.20/9.74 (setminusSubset1) => 71.20/9.74 (( 71.20/9.74 (symdiffE) => 71.20/9.74 (( 71.20/9.74 (symdiffI1) => 71.20/9.74 (( 71.20/9.74 (symdiffI2) => 71.20/9.74 (( 71.20/9.74 (symdiffIneg1) => 71.20/9.74 (( 71.20/9.74 (symdiffIneg2) => 71.20/9.74 (( 71.20/9.74 (secondinupair) => 71.20/9.74 (( 71.20/9.74 (setukpairIL) => 71.20/9.74 (( 71.20/9.74 (setukpairIR) => 71.20/9.74 (( 71.20/9.74 (kpairiskpair) => 71.20/9.74 (( 71.20/9.74 (kpairp) => 71.20/9.74 (( 71.20/9.74 (singletonsubset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowerset) => 71.20/9.74 (( 71.20/9.74 (singletoninpowunion) => 71.20/9.74 (( 71.20/9.74 (upairset2E) => 71.20/9.74 (( 71.20/9.74 (upairsubunion) => 71.20/9.74 (( 71.20/9.74 (upairinpowunion) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem1) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem2) => 71.20/9.74 (( 71.20/9.74 (ubforcartprodlem3) => 71.20/9.74 (( 71.20/9.74 (cartprodpairin) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair1) => 71.20/9.74 (( 71.20/9.74 (cartprodmempair) => 71.20/9.74 (( 71.20/9.74 (setunionE2) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton1) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton2) => 71.20/9.74 (( 71.20/9.74 (setunionsingleton) => 71.20/9.74 (( 71.20/9.74 (singletonprop) => 71.20/9.74 (( 71.20/9.74 (ex1E1) => 71.20/9.74 (( 71.20/9.74 (ex1I) => 71.20/9.74 (( 71.20/9.74 (ex1I2) => 71.20/9.74 (( 71.20/9.74 (singletonsuniq) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL1) => 71.20/9.74 (( 71.20/9.74 (kfstsingleton) => 71.20/9.74 (( 71.20/9.74 (theprop) => 71.20/9.74 (( 71.20/9.74 (kfstpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodfstin) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL2) => 71.20/9.74 (( 71.20/9.74 (setukpairinjL) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR11) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR12) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR1) => 71.20/9.74 (( 71.20/9.74 (upairequniteq) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR2) => 71.20/9.74 (( 71.20/9.74 (setukpairinjR) => 71.20/9.74 (( 71.20/9.74 (ksndsingleton) => 71.20/9.74 (( 71.20/9.74 (ksndpairEq) => 71.20/9.74 (( 71.20/9.74 (kpairsurjEq) => 71.20/9.74 (( 71.20/9.74 (cartprodsndin) => 71.20/9.74 (( 71.20/9.74 (cartprodpairmemEL) => 71.20/9.74 (( 71.20/9.74 (cartprodpairmemER) => 71.20/9.74 (( 71.20/9.74 (cartprodmempaircEq) => 71.20/9.74 (( 71.20/9.74 (cartprodfstpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodsndpairEq) => 71.20/9.74 (( 71.20/9.74 (cartprodpairsurjEq) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrI) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrSub) => 71.20/9.74 (( 71.20/9.74 (setOfPairsIsBReln) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrERa) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrEL1) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrEL2) => 71.20/9.74 (( 71.20/9.74 (dpsetconstrER) => 71.20/9.74 (( 71.20/9.74 (funcImageSingleton) => 71.20/9.74 (( 71.20/9.74 (apProp) => 71.20/9.74 (( 71.20/9.74 (app) => 71.20/9.74 (( 71.20/9.74 (infuncsetfunc) => 71.20/9.74 (( 71.20/9.74 (ap2p) => 71.20/9.74 (( 71.20/9.74 (funcinfuncset) => 71.20/9.74 (( 71.20/9.74 (lamProp) => 71.20/9.74 (( 71.20/9.74 (lamp) => 71.20/9.74 (( 71.20/9.74 (lam2p) => 71.20/9.74 (( 71.20/9.74 (brelnall1) => 71.20/9.74 (( 71.20/9.74 (brelnall2) => 71.20/9.74 (( 71.20/9.74 (ex1E2) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp1) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp3) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp2) => 71.20/9.74 (( 71.20/9.74 (funcextLem) => 71.20/9.74 (( 71.20/9.74 (funcGraphProp4) => 71.20/9.74 (( 71.20/9.74 (subbreln) => 71.20/9.74 (( 71.20/9.74 (eqbreln) => 71.20/9.74 (( 71.20/9.74 (funcext) => 71.20/9.74 (( 71.20/9.74 (funcext2) => 71.20/9.74 (( 71.20/9.74 (ap2apEq1) => 71.20/9.74 (( 71.20/9.74 (ap2apEq2) => 71.20/9.74 (( 71.20/9.74 (beta1) => 71.20/9.74 (( 71.20/9.74 (eta1) => 71.20/9.74 (( 71.20/9.74 (lam2lamEq) => 71.20/9.74 (( 71.20/9.74 (beta2) => 71.20/9.74 (( 71.20/9.74 (eta2) => 71.20/9.74 (( 71.20/9.74 (iffalseProp1) => 71.20/9.74 (( 71.20/9.74 (iffalseProp2) => 71.20/9.74 (( 71.20/9.74 (iftrueProp1) => 71.20/9.74 (( 71.20/9.74 (iftrueProp2) => 71.20/9.74 (( 71.20/9.74 (ifSingleton) => 71.20/9.74 (( 71.20/9.74 (ifp) => 71.20/9.74 (( 71.20/9.74 (theeq) => 71.20/9.74 (( 71.20/9.74 (iftrue) => 71.20/9.74 (( 71.20/9.74 (iffalse) => 71.20/9.74 (( 71.20/9.74 (iftrueorfalse) => 71.20/9.75 (( 71.20/9.75 (binintersectT_lem) => 71.20/9.75 (( 71.20/9.75 (binunionT_lem) => 71.20/9.75 (( 71.20/9.75 (powersetT_lem) => 71.20/9.75 (( 71.20/9.75 (setminusT_lem) => 71.20/9.75 (( 71.20/9.75 (complementT_lem) => 71.20/9.75 (( 71.20/9.75 (setextT) => 71.20/9.75 (( 71.20/9.75 (subsetTI) => 71.20/9.75 (( 71.20/9.75 (powersetTI1) => 71.20/9.75 (( 71.20/9.75 (powersetTE1) => 71.20/9.75 (( 71.20/9.75 (complementTI1) => 71.20/9.75 (( 71.20/9.75 (complementTE1) => 71.20/9.75 (( 71.20/9.75 (binintersectTELcontra) => 71.20/9.75 (( 71.20/9.75 (binintersectTERcontra) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT1) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT2) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT3) => 71.20/9.75 (( 71.20/9.75 (doubleComplementI1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementE1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub2) => 71.20/9.75 (( 71.20/9.75 (doubleComplementEq) => 71.20/9.75 (( 71.20/9.75 (complementTnotintersectT) => 71.20/9.75 (( 71.20/9.75 (complementImpComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementSubsetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementInPowersetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (contraSubsetComplement) => 71.20/9.75 (( 71.20/9.75 (complementTcontraSubset) => 71.20/9.75 (( 71.20/9.75 (binunionTILcontra) => 71.20/9.75 (( 71.20/9.75 (binunionTIRcontra) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion2) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (intersectInPowersetIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpNotIn1) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpInComplement1) => 71.20/9.75 (( 71.20/9.75 (binunionTE) => 71.20/9.75 (( 71.20/9.75 (binunionTEcontra) => 71.20/9.75 (( 71.20/9.75 (demorgan2a1) => 71.20/9.75 (( 71.20/9.75 (complementUnionInPowersetComplement) => 71.20/9.75 (( 71.20/9.75 (demorgan2a2) => 71.20/9.75 (( 71.20/9.75 (demorgan1a) => 71.20/9.75 (( 71.20/9.75 (demorgan1b) => 71.20/9.75 (( 71.20/9.75 (demorgan1) => 71.20/9.75 (( 71.20/9.75 (demorgan2a) => 71.20/9.75 (( 71.20/9.75 (demorgan2b2) => 71.20/9.75 (( 71.20/9.75 (demorgan2b) => 71.20/9.75 (( 71.20/9.75 (demorgan2) => 71.20/9.75 (( 71.20/9.75 (woz13rule0) => 71.20/9.75 (( 71.20/9.75 (woz13rule1) => 71.20/9.75 (( 71.20/9.75 (woz13rule2) => 71.20/9.75 (( 71.20/9.75 (woz13rule3) => 71.20/9.75 (( 71.20/9.75 (woz13rule4) => 71.20/9.75 (( 71.20/9.75 (woz1_1) => 71.20/9.75 (( 71.20/9.75 (woz1_2) => 71.20/9.75 (( 71.20/9.75 (woz1_3) => 71.20/9.75 (( 71.20/9.75 (woz1_4) => 71.20/9.75 (( 71.20/9.75 (woz1_5) => 71.20/9.75 (( 71.20/9.75 (breln1all2) => 71.20/9.75 (( 71.20/9.75 (breln1SetBreln1) => 71.20/9.75 (( 71.20/9.75 (choice2fnsingleton) => 71.20/9.75 (( 71.20/9.75 (setOfPairsIsBReln1) => 71.20/9.75 (( 71.20/9.75 (breln1all1) => 71.20/9.75 (( 71.20/9.75 (subbreln1) => 71.20/9.75 (( 71.20/9.75 (eqbreln1) => 71.20/9.75 (( 71.20/9.75 (breln1invprop) => 71.20/9.75 (( 71.20/9.75 (breln1invI) => 71.20/9.75 (( 71.20/9.75 (breln1invE) => 71.20/9.75 (( 71.20/9.75 (breln1compprop) => 71.20/9.75 (( 71.20/9.75 (breln1compI) => 71.20/9.75 (( 71.20/9.75 (breln1compE) => 71.20/9.75 (( 71.20/9.75 (breln1compEex) => 71.20/9.75 (( 71.20/9.75 (!!) @ ( 71.20/9.75 (('#B') @ ( 71.20/9.75 !!) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 !!))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#C') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 breln1)))) @ 71.20/9.75 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])). 71.20/9.75 thf(zip_derived_cl355, plain, 71.20/9.75 (~ (((setadjoinOr) => 71.20/9.75 (((setoftrueEq) => 71.20/9.75 (((powersetI) => 71.20/9.75 (((emptyinPowerset) => 71.20/9.75 (((emptyInPowerset) => 71.20/9.75 (((powersetE) => 71.20/9.75 (((setunionI) => 71.20/9.75 (((setunionE) => 71.20/9.75 (((subPowSU) => 71.20/9.75 (((exuE2) => 71.20/9.75 (((nonemptyImpWitness) => 71.20/9.75 (((uniqinunit) => 71.20/9.75 (((notinsingleton) => 71.20/9.75 (((eqinunit) => 71.20/9.75 (((singletonsswitch) => 71.20/9.75 (((upairsetE) => 71.20/9.75 (((upairsetIL) => 71.20/9.75 (((upairsetIR) => 71.20/9.75 (((emptyE1) => 71.20/9.75 (((vacuousDall) => 71.20/9.75 (((quantDeMorgan1) => 71.20/9.75 (((quantDeMorgan2) => 71.20/9.75 (((quantDeMorgan3) => 71.20/9.75 (((quantDeMorgan4) => 71.20/9.75 (((prop2setI) => 71.20/9.75 (((prop2set2propI) => 71.20/9.75 (((notdexE) => 71.20/9.75 (((notdallE) => 71.20/9.75 (((exuI1) => 71.20/9.75 (((exuI3) => 71.20/9.75 (( 71.20/9.75 (exuI2) => 71.20/9.75 (( 71.20/9.75 (inCongP) => 71.20/9.75 (( 71.20/9.75 (in__Cong) => 71.20/9.75 (( 71.20/9.75 (exuE3u) => 71.20/9.75 (( 71.20/9.75 (exu__Cong) => 71.20/9.75 (( 71.20/9.75 (setadjoin__Cong) => 71.20/9.75 (( 71.20/9.75 (powerset__Cong) => 71.20/9.75 (( 71.20/9.75 (setunion__Cong) => 71.20/9.75 (( 71.20/9.75 (exuEu) => 71.20/9.75 (( 71.20/9.75 (descr__Cong) => 71.20/9.75 (( 71.20/9.75 (dsetconstr__Cong) => 71.20/9.75 (( 71.20/9.75 (subsetI1) => 71.20/9.75 (( 71.20/9.75 (eqimpsubset2) => 71.20/9.75 (( 71.20/9.75 (eqimpsubset1) => 71.20/9.75 (( 71.20/9.75 (subsetI2) => 71.20/9.75 (( 71.20/9.75 (emptysetsubset) => 71.20/9.75 (( 71.20/9.75 (subsetE) => 71.20/9.75 (( 71.20/9.75 (subsetE2) => 71.20/9.75 (( 71.20/9.75 (notsubsetI) => 71.20/9.75 (( 71.20/9.75 (notequalI1) => 71.20/9.75 (( 71.20/9.75 (notequalI2) => 71.20/9.75 (( 71.20/9.75 (subsetRefl) => 71.20/9.75 (( 71.20/9.75 (subsetTrans) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub2) => 71.20/9.75 (( 71.20/9.75 (subset2powerset) => 71.20/9.75 (( 71.20/9.75 (setextsub) => 71.20/9.75 (( 71.20/9.75 (subsetemptysetimpeq) => 71.20/9.75 (( 71.20/9.75 (powersetI1) => 71.20/9.75 (( 71.20/9.75 (powersetE1) => 71.20/9.75 (( 71.20/9.75 (inPowerset) => 71.20/9.75 (( 71.20/9.75 (powersetsubset) => 71.20/9.75 (( 71.20/9.75 (sepInPowerset) => 71.20/9.75 (( 71.20/9.75 (sepSubset) => 71.20/9.75 (( 71.20/9.75 (binunionIL) => 71.20/9.75 (( 71.20/9.75 (upairset2IR) => 71.20/9.75 (( 71.20/9.75 (binunionIR) => 71.20/9.75 (( 71.20/9.75 (binunionEcases) => 71.20/9.75 (( 71.20/9.75 (binunionE) => 71.20/9.75 (( 71.20/9.75 (binunionLsub) => 71.20/9.75 (( 71.20/9.75 (binunionRsub) => 71.20/9.75 (( 71.20/9.75 (binintersectI) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset5) => 71.20/9.75 (( 71.20/9.75 (binintersectEL) => 71.20/9.75 (( 71.20/9.75 (binintersectLsub) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset2) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset3) => 71.20/9.75 (( 71.20/9.75 (binintersectER) => 71.20/9.75 (( 71.20/9.75 (disjointsetsI1) => 71.20/9.75 (( 71.20/9.75 (binintersectRsub) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset4) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset1) => 71.20/9.75 (( 71.20/9.75 (bs114d) => 71.20/9.75 (( 71.20/9.75 (setminusI) => 71.20/9.75 (( 71.20/9.75 (setminusEL) => 71.20/9.75 (( 71.20/9.75 (setminusER) => 71.20/9.75 (( 71.20/9.75 (setminusSubset2) => 71.20/9.75 (( 71.20/9.75 (setminusERneg) => 71.20/9.75 (( 71.20/9.75 (setminusELneg) => 71.20/9.75 (( 71.20/9.75 (setminusILneg) => 71.20/9.75 (( 71.20/9.75 (setminusIRneg) => 71.20/9.75 (( 71.20/9.75 (setminusLsub) => 71.20/9.75 (( 71.20/9.75 (setminusSubset1) => 71.20/9.75 (( 71.20/9.75 (symdiffE) => 71.20/9.75 (( 71.20/9.75 (symdiffI1) => 71.20/9.75 (( 71.20/9.75 (symdiffI2) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg1) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg2) => 71.20/9.75 (( 71.20/9.75 (secondinupair) => 71.20/9.75 (( 71.20/9.75 (setukpairIL) => 71.20/9.75 (( 71.20/9.75 (setukpairIR) => 71.20/9.75 (( 71.20/9.75 (kpairiskpair) => 71.20/9.75 (( 71.20/9.75 (kpairp) => 71.20/9.75 (( 71.20/9.75 (singletonsubset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowerset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowunion) => 71.20/9.75 (( 71.20/9.75 (upairset2E) => 71.20/9.75 (( 71.20/9.75 (upairsubunion) => 71.20/9.75 (( 71.20/9.75 (upairinpowunion) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem1) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem2) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem3) => 71.20/9.75 (( 71.20/9.75 (cartprodpairin) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair1) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair) => 71.20/9.75 (( 71.20/9.75 (setunionE2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton1) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton) => 71.20/9.75 (( 71.20/9.75 (singletonprop) => 71.20/9.75 (( 71.20/9.75 (ex1E1) => 71.20/9.75 (( 71.20/9.75 (ex1I) => 71.20/9.75 (( 71.20/9.75 (ex1I2) => 71.20/9.75 (( 71.20/9.75 (singletonsuniq) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL1) => 71.20/9.75 (( 71.20/9.75 (kfstsingleton) => 71.20/9.75 (( 71.20/9.75 (theprop) => 71.20/9.75 (( 71.20/9.75 (kfstpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodfstin) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL2) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR11) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR12) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR1) => 71.20/9.75 (( 71.20/9.75 (upairequniteq) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR2) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR) => 71.20/9.75 (( 71.20/9.75 (ksndsingleton) => 71.20/9.75 (( 71.20/9.75 (ksndpairEq) => 71.20/9.75 (( 71.20/9.75 (kpairsurjEq) => 71.20/9.75 (( 71.20/9.75 (cartprodsndin) => 71.20/9.75 (( 71.20/9.75 (cartprodpairmemEL) => 71.20/9.75 (( 71.20/9.75 (cartprodpairmemER) => 71.20/9.75 (( 71.20/9.75 (cartprodmempaircEq) => 71.20/9.75 (( 71.20/9.75 (cartprodfstpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodsndpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodpairsurjEq) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrI) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrSub) => 71.20/9.75 (( 71.20/9.75 (setOfPairsIsBReln) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrERa) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrEL1) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrEL2) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrER) => 71.20/9.75 (( 71.20/9.75 (funcImageSingleton) => 71.20/9.75 (( 71.20/9.75 (apProp) => 71.20/9.75 (( 71.20/9.75 (app) => 71.20/9.75 (( 71.20/9.75 (infuncsetfunc) => 71.20/9.75 (( 71.20/9.75 (ap2p) => 71.20/9.75 (( 71.20/9.75 (funcinfuncset) => 71.20/9.75 (( 71.20/9.75 (lamProp) => 71.20/9.75 (( 71.20/9.75 (lamp) => 71.20/9.75 (( 71.20/9.75 (lam2p) => 71.20/9.75 (( 71.20/9.75 (brelnall1) => 71.20/9.75 (( 71.20/9.75 (brelnall2) => 71.20/9.75 (( 71.20/9.75 (ex1E2) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp1) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp3) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp2) => 71.20/9.75 (( 71.20/9.75 (funcextLem) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp4) => 71.20/9.75 (( 71.20/9.75 (subbreln) => 71.20/9.75 (( 71.20/9.75 (eqbreln) => 71.20/9.75 (( 71.20/9.75 (funcext) => 71.20/9.75 (( 71.20/9.75 (funcext2) => 71.20/9.75 (( 71.20/9.75 (ap2apEq1) => 71.20/9.75 (( 71.20/9.75 (ap2apEq2) => 71.20/9.75 (( 71.20/9.75 (beta1) => 71.20/9.75 (( 71.20/9.75 (eta1) => 71.20/9.75 (( 71.20/9.75 (lam2lamEq) => 71.20/9.75 (( 71.20/9.75 (beta2) => 71.20/9.75 (( 71.20/9.75 (eta2) => 71.20/9.75 (( 71.20/9.75 (iffalseProp1) => 71.20/9.75 (( 71.20/9.75 (iffalseProp2) => 71.20/9.75 (( 71.20/9.75 (iftrueProp1) => 71.20/9.75 (( 71.20/9.75 (iftrueProp2) => 71.20/9.75 (( 71.20/9.75 (ifSingleton) => 71.20/9.75 (( 71.20/9.75 (ifp) => 71.20/9.75 (( 71.20/9.75 (theeq) => 71.20/9.75 (( 71.20/9.75 (iftrue) => 71.20/9.75 (( 71.20/9.75 (iffalse) => 71.20/9.75 (( 71.20/9.75 (iftrueorfalse) => 71.20/9.75 (( 71.20/9.75 (binintersectT_lem) => 71.20/9.75 (( 71.20/9.75 (binunionT_lem) => 71.20/9.75 (( 71.20/9.75 (powersetT_lem) => 71.20/9.75 (( 71.20/9.75 (setminusT_lem) => 71.20/9.75 (( 71.20/9.75 (complementT_lem) => 71.20/9.75 (( 71.20/9.75 (setextT) => 71.20/9.75 (( 71.20/9.75 (subsetTI) => 71.20/9.75 (( 71.20/9.75 (powersetTI1) => 71.20/9.75 (( 71.20/9.75 (powersetTE1) => 71.20/9.75 (( 71.20/9.75 (complementTI1) => 71.20/9.75 (( 71.20/9.75 (complementTE1) => 71.20/9.75 (( 71.20/9.75 (binintersectTELcontra) => 71.20/9.75 (( 71.20/9.75 (binintersectTERcontra) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT1) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT2) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT3) => 71.20/9.75 (( 71.20/9.75 (doubleComplementI1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementE1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub2) => 71.20/9.75 (( 71.20/9.75 (doubleComplementEq) => 71.20/9.75 (( 71.20/9.75 (complementTnotintersectT) => 71.20/9.75 (( 71.20/9.75 (complementImpComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementSubsetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementInPowersetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (contraSubsetComplement) => 71.20/9.75 (( 71.20/9.75 (complementTcontraSubset) => 71.20/9.75 (( 71.20/9.75 (binunionTILcontra) => 71.20/9.75 (( 71.20/9.75 (binunionTIRcontra) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion2) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (intersectInPowersetIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpNotIn1) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpInComplement1) => 71.20/9.75 (( 71.20/9.75 (binunionTE) => 71.20/9.75 (( 71.20/9.75 (binunionTEcontra) => 71.20/9.75 (( 71.20/9.75 (demorgan2a1) => 71.20/9.75 (( 71.20/9.75 (complementUnionInPowersetComplement) => 71.20/9.75 (( 71.20/9.75 (demorgan2a2) => 71.20/9.75 (( 71.20/9.75 (demorgan1a) => 71.20/9.75 (( 71.20/9.75 (demorgan1b) => 71.20/9.75 (( 71.20/9.75 (demorgan1) => 71.20/9.75 (( 71.20/9.75 (demorgan2a) => 71.20/9.75 (( 71.20/9.75 (demorgan2b2) => 71.20/9.75 (( 71.20/9.75 (demorgan2b) => 71.20/9.75 (( 71.20/9.75 (demorgan2) => 71.20/9.75 (( 71.20/9.75 (woz13rule0) => 71.20/9.75 (( 71.20/9.75 (woz13rule1) => 71.20/9.75 (( 71.20/9.75 (woz13rule2) => 71.20/9.75 (( 71.20/9.75 (woz13rule3) => 71.20/9.75 (( 71.20/9.75 (woz13rule4) => 71.20/9.75 (( 71.20/9.75 (woz1_1) => 71.20/9.75 (( 71.20/9.75 (woz1_2) => 71.20/9.75 (( 71.20/9.75 (woz1_3) => 71.20/9.75 (( 71.20/9.75 (woz1_4) => 71.20/9.75 (( 71.20/9.75 (woz1_5) => 71.20/9.75 (( 71.20/9.75 (breln1all2) => 71.20/9.75 (( 71.20/9.75 (breln1SetBreln1) => 71.20/9.75 (( 71.20/9.75 (choice2fnsingleton) => 71.20/9.75 (( 71.20/9.75 (setOfPairsIsBReln1) => 71.20/9.75 (( 71.20/9.75 (breln1all1) => 71.20/9.75 (( 71.20/9.75 (subbreln1) => 71.20/9.75 (( 71.20/9.75 (eqbreln1) => 71.20/9.75 (( 71.20/9.75 (breln1invprop) => 71.20/9.75 (( 71.20/9.75 (breln1invI) => 71.20/9.75 (( 71.20/9.75 (breln1invE) => 71.20/9.75 (( 71.20/9.75 (breln1compprop) => 71.20/9.75 (( 71.20/9.75 (breln1compI) => 71.20/9.75 (( 71.20/9.75 (breln1compE) => 71.20/9.75 (( 71.20/9.75 (breln1compEex) => 71.20/9.75 (( 71.20/9.75 (!!) @ ( 71.20/9.75 (('#B') @ ( 71.20/9.75 !!) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 !!))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#C') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 breln1)))) @ 71.20/9.75 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl349])). 71.20/9.75 thf(zip_derived_cl362, plain, 71.20/9.75 (~ (((setoftrueEq) => 71.20/9.75 (((powersetI) => 71.20/9.75 (((emptyinPowerset) => 71.20/9.75 (((emptyInPowerset) => 71.20/9.75 (((powersetE) => 71.20/9.75 (((setunionI) => 71.20/9.75 (((setunionE) => 71.20/9.75 (((subPowSU) => 71.20/9.75 (((exuE2) => 71.20/9.75 (((nonemptyImpWitness) => 71.20/9.75 (((uniqinunit) => 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(subsetI1) => 71.20/9.75 (( 71.20/9.75 (eqimpsubset2) => 71.20/9.75 (( 71.20/9.75 (eqimpsubset1) => 71.20/9.75 (( 71.20/9.75 (subsetI2) => 71.20/9.75 (( 71.20/9.75 (emptysetsubset) => 71.20/9.75 (( 71.20/9.75 (subsetE) => 71.20/9.75 (( 71.20/9.75 (subsetE2) => 71.20/9.75 (( 71.20/9.75 (notsubsetI) => 71.20/9.75 (( 71.20/9.75 (notequalI1) => 71.20/9.75 (( 71.20/9.75 (notequalI2) => 71.20/9.75 (( 71.20/9.75 (subsetRefl) => 71.20/9.75 (( 71.20/9.75 (subsetTrans) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub2) => 71.20/9.75 (( 71.20/9.75 (subset2powerset) => 71.20/9.75 (( 71.20/9.75 (setextsub) => 71.20/9.75 (( 71.20/9.75 (subsetemptysetimpeq) => 71.20/9.75 (( 71.20/9.75 (powersetI1) => 71.20/9.75 (( 71.20/9.75 (powersetE1) => 71.20/9.75 (( 71.20/9.75 (inPowerset) => 71.20/9.75 (( 71.20/9.75 (powersetsubset) => 71.20/9.75 (( 71.20/9.75 (sepInPowerset) => 71.20/9.75 (( 71.20/9.75 (sepSubset) => 71.20/9.75 (( 71.20/9.75 (binunionIL) => 71.20/9.75 (( 71.20/9.75 (upairset2IR) => 71.20/9.75 (( 71.20/9.75 (binunionIR) => 71.20/9.75 (( 71.20/9.75 (binunionEcases) => 71.20/9.75 (( 71.20/9.75 (binunionE) => 71.20/9.75 (( 71.20/9.75 (binunionLsub) => 71.20/9.75 (( 71.20/9.75 (binunionRsub) => 71.20/9.75 (( 71.20/9.75 (binintersectI) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset5) => 71.20/9.75 (( 71.20/9.75 (binintersectEL) => 71.20/9.75 (( 71.20/9.75 (binintersectLsub) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset2) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset3) => 71.20/9.75 (( 71.20/9.75 (binintersectER) => 71.20/9.75 (( 71.20/9.75 (disjointsetsI1) => 71.20/9.75 (( 71.20/9.75 (binintersectRsub) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset4) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset1) => 71.20/9.75 (( 71.20/9.75 (bs114d) => 71.20/9.75 (( 71.20/9.75 (setminusI) => 71.20/9.75 (( 71.20/9.75 (setminusEL) => 71.20/9.75 (( 71.20/9.75 (setminusER) => 71.20/9.75 (( 71.20/9.75 (setminusSubset2) => 71.20/9.75 (( 71.20/9.75 (setminusERneg) => 71.20/9.75 (( 71.20/9.75 (setminusELneg) => 71.20/9.75 (( 71.20/9.75 (setminusILneg) => 71.20/9.75 (( 71.20/9.75 (setminusIRneg) => 71.20/9.75 (( 71.20/9.75 (setminusLsub) => 71.20/9.75 (( 71.20/9.75 (setminusSubset1) => 71.20/9.75 (( 71.20/9.75 (symdiffE) => 71.20/9.75 (( 71.20/9.75 (symdiffI1) => 71.20/9.75 (( 71.20/9.75 (symdiffI2) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg1) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg2) => 71.20/9.75 (( 71.20/9.75 (secondinupair) => 71.20/9.75 (( 71.20/9.75 (setukpairIL) => 71.20/9.75 (( 71.20/9.75 (setukpairIR) => 71.20/9.75 (( 71.20/9.75 (kpairiskpair) => 71.20/9.75 (( 71.20/9.75 (kpairp) => 71.20/9.75 (( 71.20/9.75 (singletonsubset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowerset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowunion) => 71.20/9.75 (( 71.20/9.75 (upairset2E) => 71.20/9.75 (( 71.20/9.75 (upairsubunion) => 71.20/9.75 (( 71.20/9.75 (upairinpowunion) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem1) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem2) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem3) => 71.20/9.75 (( 71.20/9.75 (cartprodpairin) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair1) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair) => 71.20/9.75 (( 71.20/9.75 (setunionE2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton1) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton) => 71.20/9.75 (( 71.20/9.75 (singletonprop) => 71.20/9.75 (( 71.20/9.75 (ex1E1) => 71.20/9.75 (( 71.20/9.75 (ex1I) => 71.20/9.75 (( 71.20/9.75 (ex1I2) => 71.20/9.75 (( 71.20/9.75 (singletonsuniq) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL1) => 71.20/9.75 (( 71.20/9.75 (kfstsingleton) => 71.20/9.75 (( 71.20/9.75 (theprop) => 71.20/9.75 (( 71.20/9.75 (kfstpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodfstin) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL2) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR11) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR12) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR1) => 71.20/9.75 (( 71.20/9.75 (upairequniteq) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR2) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR) => 71.20/9.75 (( 71.20/9.75 (ksndsingleton) => 71.20/9.75 (( 71.20/9.75 (ksndpairEq) => 71.20/9.75 (( 71.20/9.75 (kpairsurjEq) => 71.20/9.75 (( 71.20/9.75 (cartprodsndin) => 71.20/9.75 (( 71.20/9.75 (cartprodpairmemEL) => 71.20/9.75 (( 71.20/9.75 (cartprodpairmemER) => 71.20/9.75 (( 71.20/9.75 (cartprodmempaircEq) => 71.20/9.75 (( 71.20/9.75 (cartprodfstpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodsndpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodpairsurjEq) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrI) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrSub) => 71.20/9.75 (( 71.20/9.75 (setOfPairsIsBReln) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrERa) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrEL1) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrEL2) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrER) => 71.20/9.75 (( 71.20/9.75 (funcImageSingleton) => 71.20/9.75 (( 71.20/9.75 (apProp) => 71.20/9.75 (( 71.20/9.75 (app) => 71.20/9.75 (( 71.20/9.75 (infuncsetfunc) => 71.20/9.75 (( 71.20/9.75 (ap2p) => 71.20/9.75 (( 71.20/9.75 (funcinfuncset) => 71.20/9.75 (( 71.20/9.75 (lamProp) => 71.20/9.75 (( 71.20/9.75 (lamp) => 71.20/9.75 (( 71.20/9.75 (lam2p) => 71.20/9.75 (( 71.20/9.75 (brelnall1) => 71.20/9.75 (( 71.20/9.75 (brelnall2) => 71.20/9.75 (( 71.20/9.75 (ex1E2) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp1) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp3) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp2) => 71.20/9.75 (( 71.20/9.75 (funcextLem) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp4) => 71.20/9.75 (( 71.20/9.75 (subbreln) => 71.20/9.75 (( 71.20/9.75 (eqbreln) => 71.20/9.75 (( 71.20/9.75 (funcext) => 71.20/9.75 (( 71.20/9.75 (funcext2) => 71.20/9.75 (( 71.20/9.75 (ap2apEq1) => 71.20/9.75 (( 71.20/9.75 (ap2apEq2) => 71.20/9.75 (( 71.20/9.75 (beta1) => 71.20/9.75 (( 71.20/9.75 (eta1) => 71.20/9.75 (( 71.20/9.75 (lam2lamEq) => 71.20/9.75 (( 71.20/9.75 (beta2) => 71.20/9.75 (( 71.20/9.75 (eta2) => 71.20/9.75 (( 71.20/9.75 (iffalseProp1) => 71.20/9.75 (( 71.20/9.75 (iffalseProp2) => 71.20/9.75 (( 71.20/9.75 (iftrueProp1) => 71.20/9.75 (( 71.20/9.75 (iftrueProp2) => 71.20/9.75 (( 71.20/9.75 (ifSingleton) => 71.20/9.75 (( 71.20/9.75 (ifp) => 71.20/9.75 (( 71.20/9.75 (theeq) => 71.20/9.75 (( 71.20/9.75 (iftrue) => 71.20/9.75 (( 71.20/9.75 (iffalse) => 71.20/9.75 (( 71.20/9.75 (iftrueorfalse) => 71.20/9.75 (( 71.20/9.75 (binintersectT_lem) => 71.20/9.75 (( 71.20/9.75 (binunionT_lem) => 71.20/9.75 (( 71.20/9.75 (powersetT_lem) => 71.20/9.75 (( 71.20/9.75 (setminusT_lem) => 71.20/9.75 (( 71.20/9.75 (complementT_lem) => 71.20/9.75 (( 71.20/9.75 (setextT) => 71.20/9.75 (( 71.20/9.75 (subsetTI) => 71.20/9.75 (( 71.20/9.75 (powersetTI1) => 71.20/9.75 (( 71.20/9.75 (powersetTE1) => 71.20/9.75 (( 71.20/9.75 (complementTI1) => 71.20/9.75 (( 71.20/9.75 (complementTE1) => 71.20/9.75 (( 71.20/9.75 (binintersectTELcontra) => 71.20/9.75 (( 71.20/9.75 (binintersectTERcontra) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT1) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT2) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT3) => 71.20/9.75 (( 71.20/9.75 (doubleComplementI1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementE1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub2) => 71.20/9.75 (( 71.20/9.75 (doubleComplementEq) => 71.20/9.75 (( 71.20/9.75 (complementTnotintersectT) => 71.20/9.75 (( 71.20/9.75 (complementImpComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementSubsetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementInPowersetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (contraSubsetComplement) => 71.20/9.75 (( 71.20/9.75 (complementTcontraSubset) => 71.20/9.75 (( 71.20/9.75 (binunionTILcontra) => 71.20/9.75 (( 71.20/9.75 (binunionTIRcontra) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion2) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (intersectInPowersetIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpNotIn1) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpInComplement1) => 71.20/9.75 (( 71.20/9.75 (binunionTE) => 71.20/9.75 (( 71.20/9.75 (binunionTEcontra) => 71.20/9.75 (( 71.20/9.75 (demorgan2a1) => 71.20/9.75 (( 71.20/9.75 (complementUnionInPowersetComplement) => 71.20/9.75 (( 71.20/9.75 (demorgan2a2) => 71.20/9.75 (( 71.20/9.75 (demorgan1a) => 71.20/9.75 (( 71.20/9.75 (demorgan1b) => 71.20/9.75 (( 71.20/9.75 (demorgan1) => 71.20/9.75 (( 71.20/9.75 (demorgan2a) => 71.20/9.75 (( 71.20/9.75 (demorgan2b2) => 71.20/9.75 (( 71.20/9.75 (demorgan2b) => 71.20/9.75 (( 71.20/9.75 (demorgan2) => 71.20/9.75 (( 71.20/9.75 (woz13rule0) => 71.20/9.75 (( 71.20/9.75 (woz13rule1) => 71.20/9.75 (( 71.20/9.75 (woz13rule2) => 71.20/9.75 (( 71.20/9.75 (woz13rule3) => 71.20/9.75 (( 71.20/9.75 (woz13rule4) => 71.20/9.75 (( 71.20/9.75 (woz1_1) => 71.20/9.75 (( 71.20/9.75 (woz1_2) => 71.20/9.75 (( 71.20/9.75 (woz1_3) => 71.20/9.75 (( 71.20/9.75 (woz1_4) => 71.20/9.75 (( 71.20/9.75 (woz1_5) => 71.20/9.75 (( 71.20/9.75 (breln1all2) => 71.20/9.75 (( 71.20/9.75 (breln1SetBreln1) => 71.20/9.75 (( 71.20/9.75 (choice2fnsingleton) => 71.20/9.75 (( 71.20/9.75 (setOfPairsIsBReln1) => 71.20/9.75 (( 71.20/9.75 (breln1all1) => 71.20/9.75 (( 71.20/9.75 (subbreln1) => 71.20/9.75 (( 71.20/9.75 (eqbreln1) => 71.20/9.75 (( 71.20/9.75 (breln1invprop) => 71.20/9.75 (( 71.20/9.75 (breln1invI) => 71.20/9.75 (( 71.20/9.75 (breln1invE) => 71.20/9.75 (( 71.20/9.75 (breln1compprop) => 71.20/9.75 (( 71.20/9.75 (breln1compI) => 71.20/9.75 (( 71.20/9.75 (breln1compE) => 71.20/9.75 (( 71.20/9.75 (breln1compEex) => 71.20/9.75 (( 71.20/9.75 (!!) @ ( 71.20/9.75 (('#B') @ ( 71.20/9.75 !!) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 !!))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#C') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 breln1)))) @ 71.20/9.75 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl355])). 71.20/9.75 thf(zip_derived_cl369, plain, 71.20/9.75 (~ (((powersetI) => 71.20/9.75 (((emptyinPowerset) => 71.20/9.75 (((emptyInPowerset) => 71.20/9.75 (((powersetE) => 71.20/9.75 (((setunionI) => 71.20/9.75 (((setunionE) => 71.20/9.75 (((subPowSU) => 71.20/9.75 (((exuE2) => 71.20/9.75 (((nonemptyImpWitness) => 71.20/9.75 (((uniqinunit) => 71.20/9.75 (((notinsingleton) => 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(eqimpsubset2) => 71.20/9.75 (( 71.20/9.75 (eqimpsubset1) => 71.20/9.75 (( 71.20/9.75 (subsetI2) => 71.20/9.75 (( 71.20/9.75 (emptysetsubset) => 71.20/9.75 (( 71.20/9.75 (subsetE) => 71.20/9.75 (( 71.20/9.75 (subsetE2) => 71.20/9.75 (( 71.20/9.75 (notsubsetI) => 71.20/9.75 (( 71.20/9.75 (notequalI1) => 71.20/9.75 (( 71.20/9.75 (notequalI2) => 71.20/9.75 (( 71.20/9.75 (subsetRefl) => 71.20/9.75 (( 71.20/9.75 (subsetTrans) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub2) => 71.20/9.75 (( 71.20/9.75 (subset2powerset) => 71.20/9.75 (( 71.20/9.75 (setextsub) => 71.20/9.75 (( 71.20/9.75 (subsetemptysetimpeq) => 71.20/9.75 (( 71.20/9.75 (powersetI1) => 71.20/9.75 (( 71.20/9.75 (powersetE1) => 71.20/9.75 (( 71.20/9.75 (inPowerset) => 71.20/9.75 (( 71.20/9.75 (powersetsubset) => 71.20/9.75 (( 71.20/9.75 (sepInPowerset) => 71.20/9.75 (( 71.20/9.75 (sepSubset) => 71.20/9.75 (( 71.20/9.75 (binunionIL) => 71.20/9.75 (( 71.20/9.75 (upairset2IR) => 71.20/9.75 (( 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(setminusELneg) => 71.20/9.75 (( 71.20/9.75 (setminusILneg) => 71.20/9.75 (( 71.20/9.75 (setminusIRneg) => 71.20/9.75 (( 71.20/9.75 (setminusLsub) => 71.20/9.75 (( 71.20/9.75 (setminusSubset1) => 71.20/9.75 (( 71.20/9.75 (symdiffE) => 71.20/9.75 (( 71.20/9.75 (symdiffI1) => 71.20/9.75 (( 71.20/9.75 (symdiffI2) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg1) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg2) => 71.20/9.75 (( 71.20/9.75 (secondinupair) => 71.20/9.75 (( 71.20/9.75 (setukpairIL) => 71.20/9.75 (( 71.20/9.75 (setukpairIR) => 71.20/9.75 (( 71.20/9.75 (kpairiskpair) => 71.20/9.75 (( 71.20/9.75 (kpairp) => 71.20/9.75 (( 71.20/9.75 (singletonsubset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowerset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowunion) => 71.20/9.75 (( 71.20/9.75 (upairset2E) => 71.20/9.75 (( 71.20/9.75 (upairsubunion) => 71.20/9.75 (( 71.20/9.75 (upairinpowunion) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem1) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem2) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem3) => 71.20/9.75 (( 71.20/9.75 (cartprodpairin) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair1) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair) => 71.20/9.75 (( 71.20/9.75 (setunionE2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton1) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton) => 71.20/9.75 (( 71.20/9.75 (singletonprop) => 71.20/9.75 (( 71.20/9.75 (ex1E1) => 71.20/9.75 (( 71.20/9.75 (ex1I) => 71.20/9.75 (( 71.20/9.75 (ex1I2) => 71.20/9.75 (( 71.20/9.75 (singletonsuniq) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL1) => 71.20/9.75 (( 71.20/9.75 (kfstsingleton) => 71.20/9.75 (( 71.20/9.75 (theprop) => 71.20/9.75 (( 71.20/9.75 (kfstpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodfstin) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL2) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR11) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR12) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR1) => 71.20/9.75 (( 71.20/9.75 (upairequniteq) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR2) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR) => 71.20/9.75 (( 71.20/9.75 (ksndsingleton) => 71.20/9.75 (( 71.20/9.75 (ksndpairEq) => 71.20/9.75 (( 71.20/9.75 (kpairsurjEq) => 71.20/9.75 (( 71.20/9.75 (cartprodsndin) => 71.20/9.75 (( 71.20/9.75 (cartprodpairmemEL) => 71.20/9.75 (( 71.20/9.75 (cartprodpairmemER) => 71.20/9.75 (( 71.20/9.75 (cartprodmempaircEq) => 71.20/9.75 (( 71.20/9.75 (cartprodfstpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodsndpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodpairsurjEq) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrI) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrSub) => 71.20/9.75 (( 71.20/9.75 (setOfPairsIsBReln) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrERa) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrEL1) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrEL2) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrER) => 71.20/9.75 (( 71.20/9.75 (funcImageSingleton) => 71.20/9.75 (( 71.20/9.75 (apProp) => 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71.20/9.75 (eta2) => 71.20/9.75 (( 71.20/9.75 (iffalseProp1) => 71.20/9.75 (( 71.20/9.75 (iffalseProp2) => 71.20/9.75 (( 71.20/9.75 (iftrueProp1) => 71.20/9.75 (( 71.20/9.75 (iftrueProp2) => 71.20/9.75 (( 71.20/9.75 (ifSingleton) => 71.20/9.75 (( 71.20/9.75 (ifp) => 71.20/9.75 (( 71.20/9.75 (theeq) => 71.20/9.75 (( 71.20/9.75 (iftrue) => 71.20/9.75 (( 71.20/9.75 (iffalse) => 71.20/9.75 (( 71.20/9.75 (iftrueorfalse) => 71.20/9.75 (( 71.20/9.75 (binintersectT_lem) => 71.20/9.75 (( 71.20/9.75 (binunionT_lem) => 71.20/9.75 (( 71.20/9.75 (powersetT_lem) => 71.20/9.75 (( 71.20/9.75 (setminusT_lem) => 71.20/9.75 (( 71.20/9.75 (complementT_lem) => 71.20/9.75 (( 71.20/9.75 (setextT) => 71.20/9.75 (( 71.20/9.75 (subsetTI) => 71.20/9.75 (( 71.20/9.75 (powersetTI1) => 71.20/9.75 (( 71.20/9.75 (powersetTE1) => 71.20/9.75 (( 71.20/9.75 (complementTI1) => 71.20/9.75 (( 71.20/9.75 (complementTE1) => 71.20/9.75 (( 71.20/9.75 (binintersectTELcontra) => 71.20/9.75 (( 71.20/9.75 (binintersectTERcontra) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT1) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT2) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT3) => 71.20/9.75 (( 71.20/9.75 (doubleComplementI1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementE1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub2) => 71.20/9.75 (( 71.20/9.75 (doubleComplementEq) => 71.20/9.75 (( 71.20/9.75 (complementTnotintersectT) => 71.20/9.75 (( 71.20/9.75 (complementImpComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementSubsetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementInPowersetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (contraSubsetComplement) => 71.20/9.75 (( 71.20/9.75 (complementTcontraSubset) => 71.20/9.75 (( 71.20/9.75 (binunionTILcontra) => 71.20/9.75 (( 71.20/9.75 (binunionTIRcontra) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion2) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (intersectInPowersetIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpNotIn1) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpInComplement1) => 71.20/9.75 (( 71.20/9.75 (binunionTE) => 71.20/9.75 (( 71.20/9.75 (binunionTEcontra) => 71.20/9.75 (( 71.20/9.75 (demorgan2a1) => 71.20/9.75 (( 71.20/9.75 (complementUnionInPowersetComplement) => 71.20/9.75 (( 71.20/9.75 (demorgan2a2) => 71.20/9.75 (( 71.20/9.75 (demorgan1a) => 71.20/9.75 (( 71.20/9.75 (demorgan1b) => 71.20/9.75 (( 71.20/9.75 (demorgan1) => 71.20/9.75 (( 71.20/9.75 (demorgan2a) => 71.20/9.75 (( 71.20/9.75 (demorgan2b2) => 71.20/9.75 (( 71.20/9.75 (demorgan2b) => 71.20/9.75 (( 71.20/9.75 (demorgan2) => 71.20/9.75 (( 71.20/9.75 (woz13rule0) => 71.20/9.75 (( 71.20/9.75 (woz13rule1) => 71.20/9.75 (( 71.20/9.75 (woz13rule2) => 71.20/9.75 (( 71.20/9.75 (woz13rule3) => 71.20/9.75 (( 71.20/9.75 (woz13rule4) => 71.20/9.75 (( 71.20/9.75 (woz1_1) => 71.20/9.75 (( 71.20/9.75 (woz1_2) => 71.20/9.75 (( 71.20/9.75 (woz1_3) => 71.20/9.75 (( 71.20/9.75 (woz1_4) => 71.20/9.75 (( 71.20/9.75 (woz1_5) => 71.20/9.75 (( 71.20/9.75 (breln1all2) => 71.20/9.75 (( 71.20/9.75 (breln1SetBreln1) => 71.20/9.75 (( 71.20/9.75 (choice2fnsingleton) => 71.20/9.75 (( 71.20/9.75 (setOfPairsIsBReln1) => 71.20/9.75 (( 71.20/9.75 (breln1all1) => 71.20/9.75 (( 71.20/9.75 (subbreln1) => 71.20/9.75 (( 71.20/9.75 (eqbreln1) => 71.20/9.75 (( 71.20/9.75 (breln1invprop) => 71.20/9.75 (( 71.20/9.75 (breln1invI) => 71.20/9.75 (( 71.20/9.75 (breln1invE) => 71.20/9.75 (( 71.20/9.75 (breln1compprop) => 71.20/9.75 (( 71.20/9.75 (breln1compI) => 71.20/9.75 (( 71.20/9.75 (breln1compE) => 71.20/9.75 (( 71.20/9.75 (breln1compEex) => 71.20/9.75 (( 71.20/9.75 (!!) @ ( 71.20/9.75 (('#B') @ ( 71.20/9.75 !!) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 !!))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#C') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 breln1)))) @ 71.20/9.75 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])). 71.20/9.75 thf(zip_derived_cl376, plain, 71.20/9.75 (~ (((emptyinPowerset) => 71.20/9.75 (((emptyInPowerset) => 71.20/9.75 (((powersetE) => 71.20/9.75 (((setunionI) => 71.20/9.75 (((setunionE) => 71.20/9.75 (((subPowSU) => 71.20/9.75 (((exuE2) => 71.20/9.75 (((nonemptyImpWitness) => 71.20/9.75 (((uniqinunit) => 71.20/9.75 (((notinsingleton) => 71.20/9.75 (((eqinunit) => 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(eqimpsubset1) => 71.20/9.75 (( 71.20/9.75 (subsetI2) => 71.20/9.75 (( 71.20/9.75 (emptysetsubset) => 71.20/9.75 (( 71.20/9.75 (subsetE) => 71.20/9.75 (( 71.20/9.75 (subsetE2) => 71.20/9.75 (( 71.20/9.75 (notsubsetI) => 71.20/9.75 (( 71.20/9.75 (notequalI1) => 71.20/9.75 (( 71.20/9.75 (notequalI2) => 71.20/9.75 (( 71.20/9.75 (subsetRefl) => 71.20/9.75 (( 71.20/9.75 (subsetTrans) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub2) => 71.20/9.75 (( 71.20/9.75 (subset2powerset) => 71.20/9.75 (( 71.20/9.75 (setextsub) => 71.20/9.75 (( 71.20/9.75 (subsetemptysetimpeq) => 71.20/9.75 (( 71.20/9.75 (powersetI1) => 71.20/9.75 (( 71.20/9.75 (powersetE1) => 71.20/9.75 (( 71.20/9.75 (inPowerset) => 71.20/9.75 (( 71.20/9.75 (powersetsubset) => 71.20/9.75 (( 71.20/9.75 (sepInPowerset) => 71.20/9.75 (( 71.20/9.75 (sepSubset) => 71.20/9.75 (( 71.20/9.75 (binunionIL) => 71.20/9.75 (( 71.20/9.75 (upairset2IR) => 71.20/9.75 (( 71.20/9.75 (binunionIR) => 71.20/9.75 (( 71.20/9.75 (binunionEcases) => 71.20/9.75 (( 71.20/9.75 (binunionE) => 71.20/9.75 (( 71.20/9.75 (binunionLsub) => 71.20/9.75 (( 71.20/9.75 (binunionRsub) => 71.20/9.75 (( 71.20/9.75 (binintersectI) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset5) => 71.20/9.75 (( 71.20/9.75 (binintersectEL) => 71.20/9.75 (( 71.20/9.75 (binintersectLsub) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset2) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset3) => 71.20/9.75 (( 71.20/9.75 (binintersectER) => 71.20/9.75 (( 71.20/9.75 (disjointsetsI1) => 71.20/9.75 (( 71.20/9.75 (binintersectRsub) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset4) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset1) => 71.20/9.75 (( 71.20/9.75 (bs114d) => 71.20/9.75 (( 71.20/9.75 (setminusI) => 71.20/9.75 (( 71.20/9.75 (setminusEL) => 71.20/9.75 (( 71.20/9.75 (setminusER) => 71.20/9.75 (( 71.20/9.75 (setminusSubset2) => 71.20/9.75 (( 71.20/9.75 (setminusERneg) => 71.20/9.75 (( 71.20/9.75 (setminusELneg) => 71.20/9.75 (( 71.20/9.75 (setminusILneg) => 71.20/9.75 (( 71.20/9.75 (setminusIRneg) => 71.20/9.75 (( 71.20/9.75 (setminusLsub) => 71.20/9.75 (( 71.20/9.75 (setminusSubset1) => 71.20/9.75 (( 71.20/9.75 (symdiffE) => 71.20/9.75 (( 71.20/9.75 (symdiffI1) => 71.20/9.75 (( 71.20/9.75 (symdiffI2) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg1) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg2) => 71.20/9.75 (( 71.20/9.75 (secondinupair) => 71.20/9.75 (( 71.20/9.75 (setukpairIL) => 71.20/9.75 (( 71.20/9.75 (setukpairIR) => 71.20/9.75 (( 71.20/9.75 (kpairiskpair) => 71.20/9.75 (( 71.20/9.75 (kpairp) => 71.20/9.75 (( 71.20/9.75 (singletonsubset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowerset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowunion) => 71.20/9.75 (( 71.20/9.75 (upairset2E) => 71.20/9.75 (( 71.20/9.75 (upairsubunion) => 71.20/9.75 (( 71.20/9.75 (upairinpowunion) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem1) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem2) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem3) => 71.20/9.75 (( 71.20/9.75 (cartprodpairin) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair1) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair) => 71.20/9.75 (( 71.20/9.75 (setunionE2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton1) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton) => 71.20/9.75 (( 71.20/9.75 (singletonprop) => 71.20/9.75 (( 71.20/9.75 (ex1E1) => 71.20/9.75 (( 71.20/9.75 (ex1I) => 71.20/9.75 (( 71.20/9.75 (ex1I2) => 71.20/9.75 (( 71.20/9.75 (singletonsuniq) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL1) => 71.20/9.75 (( 71.20/9.75 (kfstsingleton) => 71.20/9.75 (( 71.20/9.75 (theprop) => 71.20/9.75 (( 71.20/9.75 (kfstpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodfstin) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL2) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR11) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR12) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR1) => 71.20/9.75 (( 71.20/9.75 (upairequniteq) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR2) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR) => 71.20/9.75 (( 71.20/9.75 (ksndsingleton) => 71.20/9.75 (( 71.20/9.75 (ksndpairEq) => 71.20/9.75 (( 71.20/9.75 (kpairsurjEq) => 71.20/9.75 (( 71.20/9.75 (cartprodsndin) => 71.20/9.75 (( 71.20/9.75 (cartprodpairmemEL) => 71.20/9.75 (( 71.20/9.75 (cartprodpairmemER) => 71.20/9.75 (( 71.20/9.75 (cartprodmempaircEq) => 71.20/9.75 (( 71.20/9.75 (cartprodfstpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodsndpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodpairsurjEq) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrI) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrSub) => 71.20/9.75 (( 71.20/9.75 (setOfPairsIsBReln) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrERa) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrEL1) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrEL2) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrER) => 71.20/9.75 (( 71.20/9.75 (funcImageSingleton) => 71.20/9.75 (( 71.20/9.75 (apProp) => 71.20/9.75 (( 71.20/9.75 (app) => 71.20/9.75 (( 71.20/9.75 (infuncsetfunc) => 71.20/9.75 (( 71.20/9.75 (ap2p) => 71.20/9.75 (( 71.20/9.75 (funcinfuncset) => 71.20/9.75 (( 71.20/9.75 (lamProp) => 71.20/9.75 (( 71.20/9.75 (lamp) => 71.20/9.75 (( 71.20/9.75 (lam2p) => 71.20/9.75 (( 71.20/9.75 (brelnall1) => 71.20/9.75 (( 71.20/9.75 (brelnall2) => 71.20/9.75 (( 71.20/9.75 (ex1E2) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp1) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp3) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp2) => 71.20/9.75 (( 71.20/9.75 (funcextLem) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp4) => 71.20/9.75 (( 71.20/9.75 (subbreln) => 71.20/9.75 (( 71.20/9.75 (eqbreln) => 71.20/9.75 (( 71.20/9.75 (funcext) => 71.20/9.75 (( 71.20/9.75 (funcext2) => 71.20/9.75 (( 71.20/9.75 (ap2apEq1) => 71.20/9.75 (( 71.20/9.75 (ap2apEq2) => 71.20/9.75 (( 71.20/9.75 (beta1) => 71.20/9.75 (( 71.20/9.75 (eta1) => 71.20/9.75 (( 71.20/9.75 (lam2lamEq) => 71.20/9.75 (( 71.20/9.75 (beta2) => 71.20/9.75 (( 71.20/9.75 (eta2) => 71.20/9.75 (( 71.20/9.75 (iffalseProp1) => 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71.20/9.75 (contrasubsetT1) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT2) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT3) => 71.20/9.75 (( 71.20/9.75 (doubleComplementI1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementE1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub2) => 71.20/9.75 (( 71.20/9.75 (doubleComplementEq) => 71.20/9.75 (( 71.20/9.75 (complementTnotintersectT) => 71.20/9.75 (( 71.20/9.75 (complementImpComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementSubsetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementInPowersetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (contraSubsetComplement) => 71.20/9.75 (( 71.20/9.75 (complementTcontraSubset) => 71.20/9.75 (( 71.20/9.75 (binunionTILcontra) => 71.20/9.75 (( 71.20/9.75 (binunionTIRcontra) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion2) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (intersectInPowersetIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpNotIn1) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpInComplement1) => 71.20/9.75 (( 71.20/9.75 (binunionTE) => 71.20/9.75 (( 71.20/9.75 (binunionTEcontra) => 71.20/9.75 (( 71.20/9.75 (demorgan2a1) => 71.20/9.75 (( 71.20/9.75 (complementUnionInPowersetComplement) => 71.20/9.75 (( 71.20/9.75 (demorgan2a2) => 71.20/9.75 (( 71.20/9.75 (demorgan1a) => 71.20/9.75 (( 71.20/9.75 (demorgan1b) => 71.20/9.75 (( 71.20/9.75 (demorgan1) => 71.20/9.75 (( 71.20/9.75 (demorgan2a) => 71.20/9.75 (( 71.20/9.75 (demorgan2b2) => 71.20/9.75 (( 71.20/9.75 (demorgan2b) => 71.20/9.75 (( 71.20/9.75 (demorgan2) => 71.20/9.75 (( 71.20/9.75 (woz13rule0) => 71.20/9.75 (( 71.20/9.75 (woz13rule1) => 71.20/9.75 (( 71.20/9.75 (woz13rule2) => 71.20/9.75 (( 71.20/9.75 (woz13rule3) => 71.20/9.75 (( 71.20/9.75 (woz13rule4) => 71.20/9.75 (( 71.20/9.75 (woz1_1) => 71.20/9.75 (( 71.20/9.75 (woz1_2) => 71.20/9.75 (( 71.20/9.75 (woz1_3) => 71.20/9.75 (( 71.20/9.75 (woz1_4) => 71.20/9.75 (( 71.20/9.75 (woz1_5) => 71.20/9.75 (( 71.20/9.75 (breln1all2) => 71.20/9.75 (( 71.20/9.75 (breln1SetBreln1) => 71.20/9.75 (( 71.20/9.75 (choice2fnsingleton) => 71.20/9.75 (( 71.20/9.75 (setOfPairsIsBReln1) => 71.20/9.75 (( 71.20/9.75 (breln1all1) => 71.20/9.75 (( 71.20/9.75 (subbreln1) => 71.20/9.75 (( 71.20/9.75 (eqbreln1) => 71.20/9.75 (( 71.20/9.75 (breln1invprop) => 71.20/9.75 (( 71.20/9.75 (breln1invI) => 71.20/9.75 (( 71.20/9.75 (breln1invE) => 71.20/9.75 (( 71.20/9.75 (breln1compprop) => 71.20/9.75 (( 71.20/9.75 (breln1compI) => 71.20/9.75 (( 71.20/9.75 (breln1compE) => 71.20/9.75 (( 71.20/9.75 (breln1compEex) => 71.20/9.75 (( 71.20/9.75 (!!) @ ( 71.20/9.75 (('#B') @ ( 71.20/9.75 !!) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 !!))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#C') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 breln1)))) @ 71.20/9.75 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl369])). 71.20/9.75 thf(zip_derived_cl384, plain, 71.20/9.75 (~ (((emptyInPowerset) => 71.20/9.75 (((powersetE) => 71.20/9.75 (((setunionI) => 71.20/9.75 (((setunionE) => 71.20/9.75 (((subPowSU) => 71.20/9.75 (((exuE2) => 71.20/9.75 (((nonemptyImpWitness) => 71.20/9.75 (((uniqinunit) => 71.20/9.75 (((notinsingleton) => 71.20/9.75 (((eqinunit) => 71.20/9.75 (((singletonsswitch) => 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=> 71.20/9.75 (( 71.20/9.75 (emptysetsubset) => 71.20/9.75 (( 71.20/9.75 (subsetE) => 71.20/9.75 (( 71.20/9.75 (subsetE2) => 71.20/9.75 (( 71.20/9.75 (notsubsetI) => 71.20/9.75 (( 71.20/9.75 (notequalI1) => 71.20/9.75 (( 71.20/9.75 (notequalI2) => 71.20/9.75 (( 71.20/9.75 (subsetRefl) => 71.20/9.75 (( 71.20/9.75 (subsetTrans) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub2) => 71.20/9.75 (( 71.20/9.75 (subset2powerset) => 71.20/9.75 (( 71.20/9.75 (setextsub) => 71.20/9.75 (( 71.20/9.75 (subsetemptysetimpeq) => 71.20/9.75 (( 71.20/9.75 (powersetI1) => 71.20/9.75 (( 71.20/9.75 (powersetE1) => 71.20/9.75 (( 71.20/9.75 (inPowerset) => 71.20/9.75 (( 71.20/9.75 (powersetsubset) => 71.20/9.75 (( 71.20/9.75 (sepInPowerset) => 71.20/9.75 (( 71.20/9.75 (sepSubset) => 71.20/9.75 (( 71.20/9.75 (binunionIL) => 71.20/9.75 (( 71.20/9.75 (upairset2IR) => 71.20/9.75 (( 71.20/9.75 (binunionIR) => 71.20/9.75 (( 71.20/9.75 (binunionEcases) => 71.20/9.75 (( 71.20/9.75 (binunionE) => 71.20/9.75 (( 71.20/9.75 (binunionLsub) => 71.20/9.75 (( 71.20/9.75 (binunionRsub) => 71.20/9.75 (( 71.20/9.75 (binintersectI) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset5) => 71.20/9.75 (( 71.20/9.75 (binintersectEL) => 71.20/9.75 (( 71.20/9.75 (binintersectLsub) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset2) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset3) => 71.20/9.75 (( 71.20/9.75 (binintersectER) => 71.20/9.75 (( 71.20/9.75 (disjointsetsI1) => 71.20/9.75 (( 71.20/9.75 (binintersectRsub) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset4) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset1) => 71.20/9.75 (( 71.20/9.75 (bs114d) => 71.20/9.75 (( 71.20/9.75 (setminusI) => 71.20/9.75 (( 71.20/9.75 (setminusEL) => 71.20/9.75 (( 71.20/9.75 (setminusER) => 71.20/9.75 (( 71.20/9.75 (setminusSubset2) => 71.20/9.75 (( 71.20/9.75 (setminusERneg) => 71.20/9.75 (( 71.20/9.75 (setminusELneg) => 71.20/9.75 (( 71.20/9.75 (setminusILneg) => 71.20/9.75 (( 71.20/9.75 (setminusIRneg) => 71.20/9.75 (( 71.20/9.75 (setminusLsub) => 71.20/9.75 (( 71.20/9.75 (setminusSubset1) => 71.20/9.75 (( 71.20/9.75 (symdiffE) => 71.20/9.75 (( 71.20/9.75 (symdiffI1) => 71.20/9.75 (( 71.20/9.75 (symdiffI2) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg1) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg2) => 71.20/9.75 (( 71.20/9.75 (secondinupair) => 71.20/9.75 (( 71.20/9.75 (setukpairIL) => 71.20/9.75 (( 71.20/9.75 (setukpairIR) => 71.20/9.75 (( 71.20/9.75 (kpairiskpair) => 71.20/9.75 (( 71.20/9.75 (kpairp) => 71.20/9.75 (( 71.20/9.75 (singletonsubset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowerset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowunion) => 71.20/9.75 (( 71.20/9.75 (upairset2E) => 71.20/9.75 (( 71.20/9.75 (upairsubunion) => 71.20/9.75 (( 71.20/9.75 (upairinpowunion) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem1) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem2) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem3) => 71.20/9.75 (( 71.20/9.75 (cartprodpairin) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair1) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair) => 71.20/9.75 (( 71.20/9.75 (setunionE2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton1) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton) => 71.20/9.75 (( 71.20/9.75 (singletonprop) => 71.20/9.75 (( 71.20/9.75 (ex1E1) => 71.20/9.75 (( 71.20/9.75 (ex1I) => 71.20/9.75 (( 71.20/9.75 (ex1I2) => 71.20/9.75 (( 71.20/9.75 (singletonsuniq) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL1) => 71.20/9.75 (( 71.20/9.75 (kfstsingleton) => 71.20/9.75 (( 71.20/9.75 (theprop) => 71.20/9.75 (( 71.20/9.75 (kfstpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodfstin) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL2) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR11) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR12) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR1) => 71.20/9.75 (( 71.20/9.75 (upairequniteq) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR2) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR) => 71.20/9.75 (( 71.20/9.75 (ksndsingleton) => 71.20/9.75 (( 71.20/9.75 (ksndpairEq) => 71.20/9.75 (( 71.20/9.75 (kpairsurjEq) => 71.20/9.75 (( 71.20/9.75 (cartprodsndin) => 71.20/9.75 (( 71.20/9.75 (cartprodpairmemEL) => 71.20/9.75 (( 71.20/9.75 (cartprodpairmemER) => 71.20/9.75 (( 71.20/9.75 (cartprodmempaircEq) => 71.20/9.75 (( 71.20/9.75 (cartprodfstpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodsndpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodpairsurjEq) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrI) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrSub) => 71.20/9.75 (( 71.20/9.75 (setOfPairsIsBReln) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrERa) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrEL1) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrEL2) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrER) => 71.20/9.75 (( 71.20/9.75 (funcImageSingleton) => 71.20/9.75 (( 71.20/9.75 (apProp) => 71.20/9.75 (( 71.20/9.75 (app) => 71.20/9.75 (( 71.20/9.75 (infuncsetfunc) => 71.20/9.75 (( 71.20/9.75 (ap2p) => 71.20/9.75 (( 71.20/9.75 (funcinfuncset) => 71.20/9.75 (( 71.20/9.75 (lamProp) => 71.20/9.75 (( 71.20/9.75 (lamp) => 71.20/9.75 (( 71.20/9.75 (lam2p) => 71.20/9.75 (( 71.20/9.75 (brelnall1) => 71.20/9.75 (( 71.20/9.75 (brelnall2) => 71.20/9.75 (( 71.20/9.75 (ex1E2) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp1) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp3) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp2) => 71.20/9.75 (( 71.20/9.75 (funcextLem) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp4) => 71.20/9.75 (( 71.20/9.75 (subbreln) => 71.20/9.75 (( 71.20/9.75 (eqbreln) => 71.20/9.75 (( 71.20/9.75 (funcext) => 71.20/9.75 (( 71.20/9.75 (funcext2) => 71.20/9.75 (( 71.20/9.75 (ap2apEq1) => 71.20/9.75 (( 71.20/9.75 (ap2apEq2) => 71.20/9.75 (( 71.20/9.75 (beta1) => 71.20/9.75 (( 71.20/9.75 (eta1) => 71.20/9.75 (( 71.20/9.75 (lam2lamEq) => 71.20/9.75 (( 71.20/9.75 (beta2) => 71.20/9.75 (( 71.20/9.75 (eta2) => 71.20/9.75 (( 71.20/9.75 (iffalseProp1) => 71.20/9.75 (( 71.20/9.75 (iffalseProp2) => 71.20/9.75 (( 71.20/9.75 (iftrueProp1) => 71.20/9.75 (( 71.20/9.75 (iftrueProp2) => 71.20/9.75 (( 71.20/9.75 (ifSingleton) => 71.20/9.75 (( 71.20/9.75 (ifp) => 71.20/9.75 (( 71.20/9.75 (theeq) => 71.20/9.75 (( 71.20/9.75 (iftrue) => 71.20/9.75 (( 71.20/9.75 (iffalse) => 71.20/9.75 (( 71.20/9.75 (iftrueorfalse) => 71.20/9.75 (( 71.20/9.75 (binintersectT_lem) => 71.20/9.75 (( 71.20/9.75 (binunionT_lem) => 71.20/9.75 (( 71.20/9.75 (powersetT_lem) => 71.20/9.75 (( 71.20/9.75 (setminusT_lem) => 71.20/9.75 (( 71.20/9.75 (complementT_lem) => 71.20/9.75 (( 71.20/9.75 (setextT) => 71.20/9.75 (( 71.20/9.75 (subsetTI) => 71.20/9.75 (( 71.20/9.75 (powersetTI1) => 71.20/9.75 (( 71.20/9.75 (powersetTE1) => 71.20/9.75 (( 71.20/9.75 (complementTI1) => 71.20/9.75 (( 71.20/9.75 (complementTE1) => 71.20/9.75 (( 71.20/9.75 (binintersectTELcontra) => 71.20/9.75 (( 71.20/9.75 (binintersectTERcontra) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT1) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT2) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT3) => 71.20/9.75 (( 71.20/9.75 (doubleComplementI1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementE1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub2) => 71.20/9.75 (( 71.20/9.75 (doubleComplementEq) => 71.20/9.75 (( 71.20/9.75 (complementTnotintersectT) => 71.20/9.75 (( 71.20/9.75 (complementImpComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementSubsetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementInPowersetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (contraSubsetComplement) => 71.20/9.75 (( 71.20/9.75 (complementTcontraSubset) => 71.20/9.75 (( 71.20/9.75 (binunionTILcontra) => 71.20/9.75 (( 71.20/9.75 (binunionTIRcontra) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion2) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (intersectInPowersetIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpNotIn1) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpInComplement1) => 71.20/9.75 (( 71.20/9.75 (binunionTE) => 71.20/9.75 (( 71.20/9.75 (binunionTEcontra) => 71.20/9.75 (( 71.20/9.75 (demorgan2a1) => 71.20/9.75 (( 71.20/9.75 (complementUnionInPowersetComplement) => 71.20/9.75 (( 71.20/9.75 (demorgan2a2) => 71.20/9.75 (( 71.20/9.75 (demorgan1a) => 71.20/9.75 (( 71.20/9.75 (demorgan1b) => 71.20/9.75 (( 71.20/9.75 (demorgan1) => 71.20/9.75 (( 71.20/9.75 (demorgan2a) => 71.20/9.75 (( 71.20/9.75 (demorgan2b2) => 71.20/9.75 (( 71.20/9.75 (demorgan2b) => 71.20/9.75 (( 71.20/9.75 (demorgan2) => 71.20/9.75 (( 71.20/9.75 (woz13rule0) => 71.20/9.75 (( 71.20/9.75 (woz13rule1) => 71.20/9.75 (( 71.20/9.75 (woz13rule2) => 71.20/9.75 (( 71.20/9.75 (woz13rule3) => 71.20/9.75 (( 71.20/9.75 (woz13rule4) => 71.20/9.75 (( 71.20/9.75 (woz1_1) => 71.20/9.75 (( 71.20/9.75 (woz1_2) => 71.20/9.75 (( 71.20/9.75 (woz1_3) => 71.20/9.75 (( 71.20/9.75 (woz1_4) => 71.20/9.75 (( 71.20/9.75 (woz1_5) => 71.20/9.75 (( 71.20/9.75 (breln1all2) => 71.20/9.75 (( 71.20/9.75 (breln1SetBreln1) => 71.20/9.75 (( 71.20/9.75 (choice2fnsingleton) => 71.20/9.75 (( 71.20/9.75 (setOfPairsIsBReln1) => 71.20/9.75 (( 71.20/9.75 (breln1all1) => 71.20/9.75 (( 71.20/9.75 (subbreln1) => 71.20/9.75 (( 71.20/9.75 (eqbreln1) => 71.20/9.75 (( 71.20/9.75 (breln1invprop) => 71.20/9.75 (( 71.20/9.75 (breln1invI) => 71.20/9.75 (( 71.20/9.75 (breln1invE) => 71.20/9.75 (( 71.20/9.75 (breln1compprop) => 71.20/9.75 (( 71.20/9.75 (breln1compI) => 71.20/9.75 (( 71.20/9.75 (breln1compE) => 71.20/9.75 (( 71.20/9.75 (breln1compEex) => 71.20/9.75 (( 71.20/9.75 (!!) @ ( 71.20/9.75 (('#B') @ ( 71.20/9.75 !!) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 !!))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#C') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 breln1)))) @ 71.20/9.75 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl376])). 71.20/9.75 thf(zip_derived_cl392, plain, 71.20/9.75 (~ (((powersetE) => 71.20/9.75 (((setunionI) => 71.20/9.75 (((setunionE) => 71.20/9.75 (((subPowSU) => 71.20/9.75 (((exuE2) => 71.20/9.75 (((nonemptyImpWitness) => 71.20/9.75 (((uniqinunit) => 71.20/9.75 (((notinsingleton) => 71.20/9.75 (((eqinunit) => 71.20/9.75 (((singletonsswitch) => 71.20/9.75 (((upairsetE) => 71.20/9.75 (((upairsetIL) => 71.20/9.75 (((upairsetIR) => 71.20/9.75 (((emptyE1) => 71.20/9.75 (((vacuousDall) => 71.20/9.75 (((quantDeMorgan1) => 71.20/9.75 (((quantDeMorgan2) => 71.20/9.75 (((quantDeMorgan3) => 71.20/9.75 (((quantDeMorgan4) => 71.20/9.75 (((prop2setI) => 71.20/9.75 (((prop2set2propI) => 71.20/9.75 (((notdexE) => 71.20/9.75 (((notdallE) => 71.20/9.75 (((exuI1) => 71.20/9.75 (((exuI3) => 71.20/9.75 (((exuI2) => 71.20/9.75 (((inCongP) => 71.20/9.75 (((in__Cong) => 71.20/9.75 (((exuE3u) => 71.20/9.75 (((exu__Cong) => 71.20/9.75 (( 71.20/9.75 (setadjoin__Cong) => 71.20/9.75 (( 71.20/9.75 (powerset__Cong) => 71.20/9.75 (( 71.20/9.75 (setunion__Cong) => 71.20/9.75 (( 71.20/9.75 (exuEu) => 71.20/9.75 (( 71.20/9.75 (descr__Cong) => 71.20/9.75 (( 71.20/9.75 (dsetconstr__Cong) => 71.20/9.75 (( 71.20/9.75 (subsetI1) => 71.20/9.75 (( 71.20/9.75 (eqimpsubset2) => 71.20/9.75 (( 71.20/9.75 (eqimpsubset1) => 71.20/9.75 (( 71.20/9.75 (subsetI2) => 71.20/9.75 (( 71.20/9.75 (emptysetsubset) => 71.20/9.75 (( 71.20/9.75 (subsetE) => 71.20/9.75 (( 71.20/9.75 (subsetE2) => 71.20/9.75 (( 71.20/9.75 (notsubsetI) => 71.20/9.75 (( 71.20/9.75 (notequalI1) => 71.20/9.75 (( 71.20/9.75 (notequalI2) => 71.20/9.75 (( 71.20/9.75 (subsetRefl) => 71.20/9.75 (( 71.20/9.75 (subsetTrans) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub2) => 71.20/9.75 (( 71.20/9.75 (subset2powerset) => 71.20/9.75 (( 71.20/9.75 (setextsub) => 71.20/9.75 (( 71.20/9.75 (subsetemptysetimpeq) => 71.20/9.75 (( 71.20/9.75 (powersetI1) => 71.20/9.75 (( 71.20/9.75 (powersetE1) => 71.20/9.75 (( 71.20/9.75 (inPowerset) => 71.20/9.75 (( 71.20/9.75 (powersetsubset) => 71.20/9.75 (( 71.20/9.75 (sepInPowerset) => 71.20/9.75 (( 71.20/9.75 (sepSubset) => 71.20/9.75 (( 71.20/9.75 (binunionIL) => 71.20/9.75 (( 71.20/9.75 (upairset2IR) => 71.20/9.75 (( 71.20/9.75 (binunionIR) => 71.20/9.75 (( 71.20/9.75 (binunionEcases) => 71.20/9.75 (( 71.20/9.75 (binunionE) => 71.20/9.75 (( 71.20/9.75 (binunionLsub) => 71.20/9.75 (( 71.20/9.75 (binunionRsub) => 71.20/9.75 (( 71.20/9.75 (binintersectI) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset5) => 71.20/9.75 (( 71.20/9.75 (binintersectEL) => 71.20/9.75 (( 71.20/9.75 (binintersectLsub) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset2) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset3) => 71.20/9.75 (( 71.20/9.75 (binintersectER) => 71.20/9.75 (( 71.20/9.75 (disjointsetsI1) => 71.20/9.75 (( 71.20/9.75 (binintersectRsub) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset4) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset1) => 71.20/9.75 (( 71.20/9.75 (bs114d) => 71.20/9.75 (( 71.20/9.75 (setminusI) => 71.20/9.75 (( 71.20/9.75 (setminusEL) => 71.20/9.75 (( 71.20/9.75 (setminusER) => 71.20/9.75 (( 71.20/9.75 (setminusSubset2) => 71.20/9.75 (( 71.20/9.75 (setminusERneg) => 71.20/9.75 (( 71.20/9.75 (setminusELneg) => 71.20/9.75 (( 71.20/9.75 (setminusILneg) => 71.20/9.75 (( 71.20/9.75 (setminusIRneg) => 71.20/9.75 (( 71.20/9.75 (setminusLsub) => 71.20/9.75 (( 71.20/9.75 (setminusSubset1) => 71.20/9.75 (( 71.20/9.75 (symdiffE) => 71.20/9.75 (( 71.20/9.75 (symdiffI1) => 71.20/9.75 (( 71.20/9.75 (symdiffI2) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg1) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg2) => 71.20/9.75 (( 71.20/9.75 (secondinupair) => 71.20/9.75 (( 71.20/9.75 (setukpairIL) => 71.20/9.75 (( 71.20/9.75 (setukpairIR) => 71.20/9.75 (( 71.20/9.75 (kpairiskpair) => 71.20/9.75 (( 71.20/9.75 (kpairp) => 71.20/9.75 (( 71.20/9.75 (singletonsubset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowerset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowunion) => 71.20/9.75 (( 71.20/9.75 (upairset2E) => 71.20/9.75 (( 71.20/9.75 (upairsubunion) => 71.20/9.75 (( 71.20/9.75 (upairinpowunion) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem1) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem2) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem3) => 71.20/9.75 (( 71.20/9.75 (cartprodpairin) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair1) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair) => 71.20/9.75 (( 71.20/9.75 (setunionE2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton1) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton) => 71.20/9.75 (( 71.20/9.75 (singletonprop) => 71.20/9.75 (( 71.20/9.75 (ex1E1) => 71.20/9.75 (( 71.20/9.75 (ex1I) => 71.20/9.75 (( 71.20/9.75 (ex1I2) => 71.20/9.75 (( 71.20/9.75 (singletonsuniq) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL1) => 71.20/9.75 (( 71.20/9.75 (kfstsingleton) => 71.20/9.75 (( 71.20/9.75 (theprop) => 71.20/9.75 (( 71.20/9.75 (kfstpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodfstin) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL2) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR11) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR12) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR1) => 71.20/9.75 (( 71.20/9.75 (upairequniteq) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR2) => 71.20/9.75 (( 71.20/9.75 (setukpairinjR) => 71.20/9.75 (( 71.20/9.75 (ksndsingleton) => 71.20/9.75 (( 71.20/9.75 (ksndpairEq) => 71.20/9.75 (( 71.20/9.75 (kpairsurjEq) => 71.20/9.75 (( 71.20/9.75 (cartprodsndin) => 71.20/9.75 (( 71.20/9.75 (cartprodpairmemEL) => 71.20/9.75 (( 71.20/9.75 (cartprodpairmemER) => 71.20/9.75 (( 71.20/9.75 (cartprodmempaircEq) => 71.20/9.75 (( 71.20/9.75 (cartprodfstpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodsndpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodpairsurjEq) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrI) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrSub) => 71.20/9.75 (( 71.20/9.75 (setOfPairsIsBReln) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrERa) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrEL1) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrEL2) => 71.20/9.75 (( 71.20/9.75 (dpsetconstrER) => 71.20/9.75 (( 71.20/9.75 (funcImageSingleton) => 71.20/9.75 (( 71.20/9.75 (apProp) => 71.20/9.75 (( 71.20/9.75 (app) => 71.20/9.75 (( 71.20/9.75 (infuncsetfunc) => 71.20/9.75 (( 71.20/9.75 (ap2p) => 71.20/9.75 (( 71.20/9.75 (funcinfuncset) => 71.20/9.75 (( 71.20/9.75 (lamProp) => 71.20/9.75 (( 71.20/9.75 (lamp) => 71.20/9.75 (( 71.20/9.75 (lam2p) => 71.20/9.75 (( 71.20/9.75 (brelnall1) => 71.20/9.75 (( 71.20/9.75 (brelnall2) => 71.20/9.75 (( 71.20/9.75 (ex1E2) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp1) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp3) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp2) => 71.20/9.75 (( 71.20/9.75 (funcextLem) => 71.20/9.75 (( 71.20/9.75 (funcGraphProp4) => 71.20/9.75 (( 71.20/9.75 (subbreln) => 71.20/9.75 (( 71.20/9.75 (eqbreln) => 71.20/9.75 (( 71.20/9.75 (funcext) => 71.20/9.75 (( 71.20/9.75 (funcext2) => 71.20/9.75 (( 71.20/9.75 (ap2apEq1) => 71.20/9.75 (( 71.20/9.75 (ap2apEq2) => 71.20/9.75 (( 71.20/9.75 (beta1) => 71.20/9.75 (( 71.20/9.75 (eta1) => 71.20/9.75 (( 71.20/9.75 (lam2lamEq) => 71.20/9.75 (( 71.20/9.75 (beta2) => 71.20/9.75 (( 71.20/9.75 (eta2) => 71.20/9.75 (( 71.20/9.75 (iffalseProp1) => 71.20/9.75 (( 71.20/9.75 (iffalseProp2) => 71.20/9.75 (( 71.20/9.75 (iftrueProp1) => 71.20/9.75 (( 71.20/9.75 (iftrueProp2) => 71.20/9.75 (( 71.20/9.75 (ifSingleton) => 71.20/9.75 (( 71.20/9.75 (ifp) => 71.20/9.75 (( 71.20/9.75 (theeq) => 71.20/9.75 (( 71.20/9.75 (iftrue) => 71.20/9.75 (( 71.20/9.75 (iffalse) => 71.20/9.75 (( 71.20/9.75 (iftrueorfalse) => 71.20/9.75 (( 71.20/9.75 (binintersectT_lem) => 71.20/9.75 (( 71.20/9.75 (binunionT_lem) => 71.20/9.75 (( 71.20/9.75 (powersetT_lem) => 71.20/9.75 (( 71.20/9.75 (setminusT_lem) => 71.20/9.75 (( 71.20/9.75 (complementT_lem) => 71.20/9.75 (( 71.20/9.75 (setextT) => 71.20/9.75 (( 71.20/9.75 (subsetTI) => 71.20/9.75 (( 71.20/9.75 (powersetTI1) => 71.20/9.75 (( 71.20/9.75 (powersetTE1) => 71.20/9.75 (( 71.20/9.75 (complementTI1) => 71.20/9.75 (( 71.20/9.75 (complementTE1) => 71.20/9.75 (( 71.20/9.75 (binintersectTELcontra) => 71.20/9.75 (( 71.20/9.75 (binintersectTERcontra) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT1) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT2) => 71.20/9.75 (( 71.20/9.75 (contrasubsetT3) => 71.20/9.75 (( 71.20/9.75 (doubleComplementI1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementE1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub1) => 71.20/9.75 (( 71.20/9.75 (doubleComplementSub2) => 71.20/9.75 (( 71.20/9.75 (doubleComplementEq) => 71.20/9.75 (( 71.20/9.75 (complementTnotintersectT) => 71.20/9.75 (( 71.20/9.75 (complementImpComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementSubsetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (complementInPowersetComplementIntersect) => 71.20/9.75 (( 71.20/9.75 (contraSubsetComplement) => 71.20/9.75 (( 71.20/9.75 (complementTcontraSubset) => 71.20/9.75 (( 71.20/9.75 (binunionTILcontra) => 71.20/9.75 (( 71.20/9.75 (binunionTIRcontra) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInUnion2) => 71.20/9.75 (( 71.20/9.75 (inIntersectImpInIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (intersectInPowersetIntersectUnions) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpNotIn1) => 71.20/9.75 (( 71.20/9.75 (inComplementUnionImpInComplement1) => 71.20/9.75 (( 71.20/9.75 (binunionTE) => 71.20/9.75 (( 71.20/9.75 (binunionTEcontra) => 71.20/9.75 (( 71.20/9.75 (demorgan2a1) => 71.20/9.75 (( 71.20/9.75 (complementUnionInPowersetComplement) => 71.20/9.75 (( 71.20/9.75 (demorgan2a2) => 71.20/9.75 (( 71.20/9.75 (demorgan1a) => 71.20/9.75 (( 71.20/9.75 (demorgan1b) => 71.20/9.75 (( 71.20/9.75 (demorgan1) => 71.20/9.75 (( 71.20/9.75 (demorgan2a) => 71.20/9.75 (( 71.20/9.75 (demorgan2b2) => 71.20/9.75 (( 71.20/9.75 (demorgan2b) => 71.20/9.75 (( 71.20/9.75 (demorgan2) => 71.20/9.75 (( 71.20/9.75 (woz13rule0) => 71.20/9.75 (( 71.20/9.75 (woz13rule1) => 71.20/9.75 (( 71.20/9.75 (woz13rule2) => 71.20/9.75 (( 71.20/9.75 (woz13rule3) => 71.20/9.75 (( 71.20/9.75 (woz13rule4) => 71.20/9.75 (( 71.20/9.75 (woz1_1) => 71.20/9.75 (( 71.20/9.75 (woz1_2) => 71.20/9.75 (( 71.20/9.75 (woz1_3) => 71.20/9.75 (( 71.20/9.75 (woz1_4) => 71.20/9.75 (( 71.20/9.75 (woz1_5) => 71.20/9.75 (( 71.20/9.75 (breln1all2) => 71.20/9.75 (( 71.20/9.75 (breln1SetBreln1) => 71.20/9.75 (( 71.20/9.75 (choice2fnsingleton) => 71.20/9.75 (( 71.20/9.75 (setOfPairsIsBReln1) => 71.20/9.75 (( 71.20/9.75 (breln1all1) => 71.20/9.75 (( 71.20/9.75 (subbreln1) => 71.20/9.75 (( 71.20/9.75 (eqbreln1) => 71.20/9.75 (( 71.20/9.75 (breln1invprop) => 71.20/9.75 (( 71.20/9.75 (breln1invI) => 71.20/9.75 (( 71.20/9.75 (breln1invE) => 71.20/9.75 (( 71.20/9.75 (breln1compprop) => 71.20/9.75 (( 71.20/9.75 (breln1compI) => 71.20/9.75 (( 71.20/9.75 (breln1compE) => 71.20/9.75 (( 71.20/9.75 (breln1compEex) => 71.20/9.75 (( 71.20/9.75 (!!) @ ( 71.20/9.75 (('#B') @ ( 71.20/9.75 !!) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 !!))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#S') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#S') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 =>))) @ 71.20/9.75 breln1)))))) @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#C') @ ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 ( 71.20/9.75 ( 71.20/9.75 ('#B') @ ( 71.20/9.75 '#B') @ 71.20/9.75 breln1)))) @ 71.20/9.75 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])). 71.20/9.75 thf(zip_derived_cl400, plain, 71.20/9.75 (~ (((setunionI) => 71.20/9.75 (((setunionE) => 71.20/9.75 (((subPowSU) => 71.20/9.75 (((exuE2) => 71.20/9.75 (((nonemptyImpWitness) => 71.20/9.75 (((uniqinunit) => 71.20/9.75 (((notinsingleton) => 71.20/9.75 (((eqinunit) => 71.20/9.75 (((singletonsswitch) => 71.20/9.75 (((upairsetE) => 71.20/9.75 (((upairsetIL) => 71.20/9.75 (((upairsetIR) => 71.20/9.75 (((emptyE1) => 71.20/9.75 (((vacuousDall) => 71.20/9.75 (((quantDeMorgan1) => 71.20/9.75 (((quantDeMorgan2) => 71.20/9.75 (((quantDeMorgan3) => 71.20/9.75 (((quantDeMorgan4) => 71.20/9.75 (((prop2setI) => 71.20/9.75 (((prop2set2propI) => 71.20/9.75 (((notdexE) => 71.20/9.75 (((notdallE) => 71.20/9.75 (((exuI1) => 71.20/9.75 (((exuI3) => 71.20/9.75 (((exuI2) => 71.20/9.75 (((inCongP) => 71.20/9.75 (((in__Cong) => 71.20/9.75 (((exuE3u) => 71.20/9.75 (((exu__Cong) => 71.20/9.75 (((setadjoin__Cong) => 71.20/9.75 (( 71.20/9.75 (powerset__Cong) => 71.20/9.75 (( 71.20/9.75 (setunion__Cong) => 71.20/9.75 (( 71.20/9.75 (exuEu) => 71.20/9.75 (( 71.20/9.75 (descr__Cong) => 71.20/9.75 (( 71.20/9.75 (dsetconstr__Cong) => 71.20/9.75 (( 71.20/9.75 (subsetI1) => 71.20/9.75 (( 71.20/9.75 (eqimpsubset2) => 71.20/9.75 (( 71.20/9.75 (eqimpsubset1) => 71.20/9.75 (( 71.20/9.75 (subsetI2) => 71.20/9.75 (( 71.20/9.75 (emptysetsubset) => 71.20/9.75 (( 71.20/9.75 (subsetE) => 71.20/9.75 (( 71.20/9.75 (subsetE2) => 71.20/9.75 (( 71.20/9.75 (notsubsetI) => 71.20/9.75 (( 71.20/9.75 (notequalI1) => 71.20/9.75 (( 71.20/9.75 (notequalI2) => 71.20/9.75 (( 71.20/9.75 (subsetRefl) => 71.20/9.75 (( 71.20/9.75 (subsetTrans) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub) => 71.20/9.75 (( 71.20/9.75 (setadjoinSub2) => 71.20/9.75 (( 71.20/9.75 (subset2powerset) => 71.20/9.75 (( 71.20/9.75 (setextsub) => 71.20/9.75 (( 71.20/9.75 (subsetemptysetimpeq) => 71.20/9.75 (( 71.20/9.75 (powersetI1) => 71.20/9.75 (( 71.20/9.75 (powersetE1) => 71.20/9.75 (( 71.20/9.75 (inPowerset) => 71.20/9.75 (( 71.20/9.75 (powersetsubset) => 71.20/9.75 (( 71.20/9.75 (sepInPowerset) => 71.20/9.75 (( 71.20/9.75 (sepSubset) => 71.20/9.75 (( 71.20/9.75 (binunionIL) => 71.20/9.75 (( 71.20/9.75 (upairset2IR) => 71.20/9.75 (( 71.20/9.75 (binunionIR) => 71.20/9.75 (( 71.20/9.75 (binunionEcases) => 71.20/9.75 (( 71.20/9.75 (binunionE) => 71.20/9.75 (( 71.20/9.75 (binunionLsub) => 71.20/9.75 (( 71.20/9.75 (binunionRsub) => 71.20/9.75 (( 71.20/9.75 (binintersectI) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset5) => 71.20/9.75 (( 71.20/9.75 (binintersectEL) => 71.20/9.75 (( 71.20/9.75 (binintersectLsub) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset2) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset3) => 71.20/9.75 (( 71.20/9.75 (binintersectER) => 71.20/9.75 (( 71.20/9.75 (disjointsetsI1) => 71.20/9.75 (( 71.20/9.75 (binintersectRsub) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset4) => 71.20/9.75 (( 71.20/9.75 (binintersectSubset1) => 71.20/9.75 (( 71.20/9.75 (bs114d) => 71.20/9.75 (( 71.20/9.75 (setminusI) => 71.20/9.75 (( 71.20/9.75 (setminusEL) => 71.20/9.75 (( 71.20/9.75 (setminusER) => 71.20/9.75 (( 71.20/9.75 (setminusSubset2) => 71.20/9.75 (( 71.20/9.75 (setminusERneg) => 71.20/9.75 (( 71.20/9.75 (setminusELneg) => 71.20/9.75 (( 71.20/9.75 (setminusILneg) => 71.20/9.75 (( 71.20/9.75 (setminusIRneg) => 71.20/9.75 (( 71.20/9.75 (setminusLsub) => 71.20/9.75 (( 71.20/9.75 (setminusSubset1) => 71.20/9.75 (( 71.20/9.75 (symdiffE) => 71.20/9.75 (( 71.20/9.75 (symdiffI1) => 71.20/9.75 (( 71.20/9.75 (symdiffI2) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg1) => 71.20/9.75 (( 71.20/9.75 (symdiffIneg2) => 71.20/9.75 (( 71.20/9.75 (secondinupair) => 71.20/9.75 (( 71.20/9.75 (setukpairIL) => 71.20/9.75 (( 71.20/9.75 (setukpairIR) => 71.20/9.75 (( 71.20/9.75 (kpairiskpair) => 71.20/9.75 (( 71.20/9.75 (kpairp) => 71.20/9.75 (( 71.20/9.75 (singletonsubset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowerset) => 71.20/9.75 (( 71.20/9.75 (singletoninpowunion) => 71.20/9.75 (( 71.20/9.75 (upairset2E) => 71.20/9.75 (( 71.20/9.75 (upairsubunion) => 71.20/9.75 (( 71.20/9.75 (upairinpowunion) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem1) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem2) => 71.20/9.75 (( 71.20/9.75 (ubforcartprodlem3) => 71.20/9.75 (( 71.20/9.75 (cartprodpairin) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair1) => 71.20/9.75 (( 71.20/9.75 (cartprodmempair) => 71.20/9.75 (( 71.20/9.75 (setunionE2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton1) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton2) => 71.20/9.75 (( 71.20/9.75 (setunionsingleton) => 71.20/9.75 (( 71.20/9.75 (singletonprop) => 71.20/9.75 (( 71.20/9.75 (ex1E1) => 71.20/9.75 (( 71.20/9.75 (ex1I) => 71.20/9.75 (( 71.20/9.75 (ex1I2) => 71.20/9.75 (( 71.20/9.75 (singletonsuniq) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL1) => 71.20/9.75 (( 71.20/9.75 (kfstsingleton) => 71.20/9.75 (( 71.20/9.75 (theprop) => 71.20/9.75 (( 71.20/9.75 (kfstpairEq) => 71.20/9.75 (( 71.20/9.75 (cartprodfstin) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL2) => 71.20/9.75 (( 71.20/9.75 (setukpairinjL) => 71.20/9.76 (( 71.20/9.76 (setukpairinjR11) => 71.20/9.76 (( 71.20/9.76 (setukpairinjR12) => 71.20/9.76 (( 71.20/9.76 (setukpairinjR1) => 71.20/9.76 (( 71.20/9.76 (upairequniteq) => 71.20/9.76 (( 71.20/9.76 (setukpairinjR2) => 71.20/9.76 (( 71.20/9.76 (setukpairinjR) => 71.20/9.76 (( 71.20/9.76 (ksndsingleton) => 71.20/9.76 (( 71.20/9.76 (ksndpairEq) => 71.20/9.76 (( 71.20/9.76 (kpairsurjEq) => 71.20/9.76 (( 71.20/9.76 (cartprodsndin) => 71.20/9.76 (( 71.20/9.76 (cartprodpairmemEL) => 71.20/9.76 (( 71.20/9.76 (cartprodpairmemER) => 71.20/9.76 (( 71.20/9.76 (cartprodmempaircEq) => 71.20/9.76 (( 71.20/9.76 (cartprodfstpairEq) => 71.20/9.76 (( 71.20/9.76 (cartprodsndpairEq) => 71.20/9.76 (( 71.20/9.76 (cartprodpairsurjEq) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrI) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrSub) => 71.20/9.76 (( 71.20/9.76 (setOfPairsIsBReln) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrERa) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrEL1) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrEL2) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrER) => 71.20/9.76 (( 71.20/9.76 (funcImageSingleton) => 71.20/9.76 (( 71.20/9.76 (apProp) => 71.20/9.76 (( 71.20/9.76 (app) => 71.20/9.76 (( 71.20/9.76 (infuncsetfunc) => 71.20/9.76 (( 71.20/9.76 (ap2p) => 71.20/9.76 (( 71.20/9.76 (funcinfuncset) => 71.20/9.76 (( 71.20/9.76 (lamProp) => 71.20/9.76 (( 71.20/9.76 (lamp) => 71.20/9.76 (( 71.20/9.76 (lam2p) => 71.20/9.76 (( 71.20/9.76 (brelnall1) => 71.20/9.76 (( 71.20/9.76 (brelnall2) => 71.20/9.76 (( 71.20/9.76 (ex1E2) => 71.20/9.76 (( 71.20/9.76 (funcGraphProp1) => 71.20/9.76 (( 71.20/9.76 (funcGraphProp3) => 71.20/9.76 (( 71.20/9.76 (funcGraphProp2) => 71.20/9.76 (( 71.20/9.76 (funcextLem) => 71.20/9.76 (( 71.20/9.76 (funcGraphProp4) => 71.20/9.76 (( 71.20/9.76 (subbreln) => 71.20/9.76 (( 71.20/9.76 (eqbreln) => 71.20/9.76 (( 71.20/9.76 (funcext) => 71.20/9.76 (( 71.20/9.76 (funcext2) => 71.20/9.76 (( 71.20/9.76 (ap2apEq1) => 71.20/9.76 (( 71.20/9.76 (ap2apEq2) => 71.20/9.76 (( 71.20/9.76 (beta1) => 71.20/9.76 (( 71.20/9.76 (eta1) => 71.20/9.76 (( 71.20/9.76 (lam2lamEq) => 71.20/9.76 (( 71.20/9.76 (beta2) => 71.20/9.76 (( 71.20/9.76 (eta2) => 71.20/9.76 (( 71.20/9.76 (iffalseProp1) => 71.20/9.76 (( 71.20/9.76 (iffalseProp2) => 71.20/9.76 (( 71.20/9.76 (iftrueProp1) => 71.20/9.76 (( 71.20/9.76 (iftrueProp2) => 71.20/9.76 (( 71.20/9.76 (ifSingleton) => 71.20/9.76 (( 71.20/9.76 (ifp) => 71.20/9.76 (( 71.20/9.76 (theeq) => 71.20/9.76 (( 71.20/9.76 (iftrue) => 71.20/9.76 (( 71.20/9.76 (iffalse) => 71.20/9.76 (( 71.20/9.76 (iftrueorfalse) => 71.20/9.76 (( 71.20/9.76 (binintersectT_lem) => 71.20/9.76 (( 71.20/9.76 (binunionT_lem) => 71.20/9.76 (( 71.20/9.76 (powersetT_lem) => 71.20/9.76 (( 71.20/9.76 (setminusT_lem) => 71.20/9.76 (( 71.20/9.76 (complementT_lem) => 71.20/9.76 (( 71.20/9.76 (setextT) => 71.20/9.76 (( 71.20/9.76 (subsetTI) => 71.20/9.76 (( 71.20/9.76 (powersetTI1) => 71.20/9.76 (( 71.20/9.76 (powersetTE1) => 71.20/9.76 (( 71.20/9.76 (complementTI1) => 71.20/9.76 (( 71.20/9.76 (complementTE1) => 71.20/9.76 (( 71.20/9.76 (binintersectTELcontra) => 71.20/9.76 (( 71.20/9.76 (binintersectTERcontra) => 71.20/9.76 (( 71.20/9.76 (contrasubsetT) => 71.20/9.76 (( 71.20/9.76 (contrasubsetT1) => 71.20/9.76 (( 71.20/9.76 (contrasubsetT2) => 71.20/9.76 (( 71.20/9.76 (contrasubsetT3) => 71.20/9.76 (( 71.20/9.76 (doubleComplementI1) => 71.20/9.76 (( 71.20/9.76 (doubleComplementE1) => 71.20/9.76 (( 71.20/9.76 (doubleComplementSub1) => 71.20/9.76 (( 71.20/9.76 (doubleComplementSub2) => 71.20/9.76 (( 71.20/9.76 (doubleComplementEq) => 71.20/9.76 (( 71.20/9.76 (complementTnotintersectT) => 71.20/9.76 (( 71.20/9.76 (complementImpComplementIntersect) => 71.20/9.76 (( 71.20/9.76 (complementSubsetComplementIntersect) => 71.20/9.76 (( 71.20/9.76 (complementInPowersetComplementIntersect) => 71.20/9.76 (( 71.20/9.76 (contraSubsetComplement) => 71.20/9.76 (( 71.20/9.76 (complementTcontraSubset) => 71.20/9.76 (( 71.20/9.76 (binunionTILcontra) => 71.20/9.76 (( 71.20/9.76 (binunionTIRcontra) => 71.20/9.76 (( 71.20/9.76 (inIntersectImpInUnion) => 71.20/9.76 (( 71.20/9.76 (inIntersectImpInUnion2) => 71.20/9.76 (( 71.20/9.76 (inIntersectImpInIntersectUnions) => 71.20/9.76 (( 71.20/9.76 (intersectInPowersetIntersectUnions) => 71.20/9.76 (( 71.20/9.76 (inComplementUnionImpNotIn1) => 71.20/9.76 (( 71.20/9.76 (inComplementUnionImpInComplement1) => 71.20/9.76 (( 71.20/9.76 (binunionTE) => 71.20/9.76 (( 71.20/9.76 (binunionTEcontra) => 71.20/9.76 (( 71.20/9.76 (demorgan2a1) => 71.20/9.76 (( 71.20/9.76 (complementUnionInPowersetComplement) => 71.20/9.76 (( 71.20/9.76 (demorgan2a2) => 71.20/9.76 (( 71.20/9.76 (demorgan1a) => 71.20/9.76 (( 71.20/9.76 (demorgan1b) => 71.20/9.76 (( 71.20/9.76 (demorgan1) => 71.20/9.76 (( 71.20/9.76 (demorgan2a) => 71.20/9.76 (( 71.20/9.76 (demorgan2b2) => 71.20/9.76 (( 71.20/9.76 (demorgan2b) => 71.20/9.76 (( 71.20/9.76 (demorgan2) => 71.20/9.76 (( 71.20/9.76 (woz13rule0) => 71.20/9.76 (( 71.20/9.76 (woz13rule1) => 71.20/9.76 (( 71.20/9.76 (woz13rule2) => 71.20/9.76 (( 71.20/9.76 (woz13rule3) => 71.20/9.76 (( 71.20/9.76 (woz13rule4) => 71.20/9.76 (( 71.20/9.76 (woz1_1) => 71.20/9.76 (( 71.20/9.76 (woz1_2) => 71.20/9.76 (( 71.20/9.76 (woz1_3) => 71.20/9.76 (( 71.20/9.76 (woz1_4) => 71.20/9.76 (( 71.20/9.76 (woz1_5) => 71.20/9.76 (( 71.20/9.76 (breln1all2) => 71.20/9.76 (( 71.20/9.76 (breln1SetBreln1) => 71.20/9.76 (( 71.20/9.76 (choice2fnsingleton) => 71.20/9.76 (( 71.20/9.76 (setOfPairsIsBReln1) => 71.20/9.76 (( 71.20/9.76 (breln1all1) => 71.20/9.76 (( 71.20/9.76 (subbreln1) => 71.20/9.76 (( 71.20/9.76 (eqbreln1) => 71.20/9.76 (( 71.20/9.76 (breln1invprop) => 71.20/9.76 (( 71.20/9.76 (breln1invI) => 71.20/9.76 (( 71.20/9.76 (breln1invE) => 71.20/9.76 (( 71.20/9.76 (breln1compprop) => 71.20/9.76 (( 71.20/9.76 (breln1compI) => 71.20/9.76 (( 71.20/9.76 (breln1compE) => 71.20/9.76 (( 71.20/9.76 (breln1compEex) => 71.20/9.76 (( 71.20/9.76 (!!) @ ( 71.20/9.76 (('#B') @ ( 71.20/9.76 !!) @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#S') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#S') @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 =>))) @ 71.20/9.76 breln1)))) @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 !!))) @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#S') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#B') @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#S') @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 =>))) @ 71.20/9.76 breln1)))))) @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#C') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#B') @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#B') @ 71.20/9.76 breln1)))) @ 71.20/9.76 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])). 71.20/9.76 thf(zip_derived_cl408, plain, 71.20/9.76 (~ (((setunionE) => 71.20/9.76 (((subPowSU) => 71.20/9.76 (((exuE2) => 71.20/9.76 (((nonemptyImpWitness) => 71.20/9.76 (((uniqinunit) => 71.20/9.76 (((notinsingleton) => 71.20/9.76 (((eqinunit) => 71.20/9.76 (((singletonsswitch) => 71.20/9.76 (((upairsetE) => 71.20/9.76 (((upairsetIL) => 71.20/9.76 (((upairsetIR) => 71.20/9.76 (((emptyE1) => 71.20/9.76 (((vacuousDall) => 71.20/9.76 (((quantDeMorgan1) => 71.20/9.76 (((quantDeMorgan2) => 71.20/9.76 (((quantDeMorgan3) => 71.20/9.76 (((quantDeMorgan4) => 71.20/9.76 (((prop2setI) => 71.20/9.76 (((prop2set2propI) => 71.20/9.76 (((notdexE) => 71.20/9.76 (((notdallE) => 71.20/9.76 (((exuI1) => 71.20/9.76 (((exuI3) => 71.20/9.76 (((exuI2) => 71.20/9.76 (((inCongP) => 71.20/9.76 (((in__Cong) => 71.20/9.76 (((exuE3u) => 71.20/9.76 (((exu__Cong) => 71.20/9.76 (((setadjoin__Cong) => 71.20/9.76 (((powerset__Cong) => 71.20/9.76 (( 71.20/9.76 (setunion__Cong) => 71.20/9.76 (( 71.20/9.76 (exuEu) => 71.20/9.76 (( 71.20/9.76 (descr__Cong) => 71.20/9.76 (( 71.20/9.76 (dsetconstr__Cong) => 71.20/9.76 (( 71.20/9.76 (subsetI1) => 71.20/9.76 (( 71.20/9.76 (eqimpsubset2) => 71.20/9.76 (( 71.20/9.76 (eqimpsubset1) => 71.20/9.76 (( 71.20/9.76 (subsetI2) => 71.20/9.76 (( 71.20/9.76 (emptysetsubset) => 71.20/9.76 (( 71.20/9.76 (subsetE) => 71.20/9.76 (( 71.20/9.76 (subsetE2) => 71.20/9.76 (( 71.20/9.76 (notsubsetI) => 71.20/9.76 (( 71.20/9.76 (notequalI1) => 71.20/9.76 (( 71.20/9.76 (notequalI2) => 71.20/9.76 (( 71.20/9.76 (subsetRefl) => 71.20/9.76 (( 71.20/9.76 (subsetTrans) => 71.20/9.76 (( 71.20/9.76 (setadjoinSub) => 71.20/9.76 (( 71.20/9.76 (setadjoinSub2) => 71.20/9.76 (( 71.20/9.76 (subset2powerset) => 71.20/9.76 (( 71.20/9.76 (setextsub) => 71.20/9.76 (( 71.20/9.76 (subsetemptysetimpeq) => 71.20/9.76 (( 71.20/9.76 (powersetI1) => 71.20/9.76 (( 71.20/9.76 (powersetE1) => 71.20/9.76 (( 71.20/9.76 (inPowerset) => 71.20/9.76 (( 71.20/9.76 (powersetsubset) => 71.20/9.76 (( 71.20/9.76 (sepInPowerset) => 71.20/9.76 (( 71.20/9.76 (sepSubset) => 71.20/9.76 (( 71.20/9.76 (binunionIL) => 71.20/9.76 (( 71.20/9.76 (upairset2IR) => 71.20/9.76 (( 71.20/9.76 (binunionIR) => 71.20/9.76 (( 71.20/9.76 (binunionEcases) => 71.20/9.76 (( 71.20/9.76 (binunionE) => 71.20/9.76 (( 71.20/9.76 (binunionLsub) => 71.20/9.76 (( 71.20/9.76 (binunionRsub) => 71.20/9.76 (( 71.20/9.76 (binintersectI) => 71.20/9.76 (( 71.20/9.76 (binintersectSubset5) => 71.20/9.76 (( 71.20/9.76 (binintersectEL) => 71.20/9.76 (( 71.20/9.76 (binintersectLsub) => 71.20/9.76 (( 71.20/9.76 (binintersectSubset2) => 71.20/9.76 (( 71.20/9.76 (binintersectSubset3) => 71.20/9.76 (( 71.20/9.76 (binintersectER) => 71.20/9.76 (( 71.20/9.76 (disjointsetsI1) => 71.20/9.76 (( 71.20/9.76 (binintersectRsub) => 71.20/9.76 (( 71.20/9.76 (binintersectSubset4) => 71.20/9.76 (( 71.20/9.76 (binintersectSubset1) => 71.20/9.76 (( 71.20/9.76 (bs114d) => 71.20/9.76 (( 71.20/9.76 (setminusI) => 71.20/9.76 (( 71.20/9.76 (setminusEL) => 71.20/9.76 (( 71.20/9.76 (setminusER) => 71.20/9.76 (( 71.20/9.76 (setminusSubset2) => 71.20/9.76 (( 71.20/9.76 (setminusERneg) => 71.20/9.76 (( 71.20/9.76 (setminusELneg) => 71.20/9.76 (( 71.20/9.76 (setminusILneg) => 71.20/9.76 (( 71.20/9.76 (setminusIRneg) => 71.20/9.76 (( 71.20/9.76 (setminusLsub) => 71.20/9.76 (( 71.20/9.76 (setminusSubset1) => 71.20/9.76 (( 71.20/9.76 (symdiffE) => 71.20/9.76 (( 71.20/9.76 (symdiffI1) => 71.20/9.76 (( 71.20/9.76 (symdiffI2) => 71.20/9.76 (( 71.20/9.76 (symdiffIneg1) => 71.20/9.76 (( 71.20/9.76 (symdiffIneg2) => 71.20/9.76 (( 71.20/9.76 (secondinupair) => 71.20/9.76 (( 71.20/9.76 (setukpairIL) => 71.20/9.76 (( 71.20/9.76 (setukpairIR) => 71.20/9.76 (( 71.20/9.76 (kpairiskpair) => 71.20/9.76 (( 71.20/9.76 (kpairp) => 71.20/9.76 (( 71.20/9.76 (singletonsubset) => 71.20/9.76 (( 71.20/9.76 (singletoninpowerset) => 71.20/9.76 (( 71.20/9.76 (singletoninpowunion) => 71.20/9.76 (( 71.20/9.76 (upairset2E) => 71.20/9.76 (( 71.20/9.76 (upairsubunion) => 71.20/9.76 (( 71.20/9.76 (upairinpowunion) => 71.20/9.76 (( 71.20/9.76 (ubforcartprodlem1) => 71.20/9.76 (( 71.20/9.76 (ubforcartprodlem2) => 71.20/9.76 (( 71.20/9.76 (ubforcartprodlem3) => 71.20/9.76 (( 71.20/9.76 (cartprodpairin) => 71.20/9.76 (( 71.20/9.76 (cartprodmempair1) => 71.20/9.76 (( 71.20/9.76 (cartprodmempair) => 71.20/9.76 (( 71.20/9.76 (setunionE2) => 71.20/9.76 (( 71.20/9.76 (setunionsingleton1) => 71.20/9.76 (( 71.20/9.76 (setunionsingleton2) => 71.20/9.76 (( 71.20/9.76 (setunionsingleton) => 71.20/9.76 (( 71.20/9.76 (singletonprop) => 71.20/9.76 (( 71.20/9.76 (ex1E1) => 71.20/9.76 (( 71.20/9.76 (ex1I) => 71.20/9.76 (( 71.20/9.76 (ex1I2) => 71.20/9.76 (( 71.20/9.76 (singletonsuniq) => 71.20/9.76 (( 71.20/9.76 (setukpairinjL1) => 71.20/9.76 (( 71.20/9.76 (kfstsingleton) => 71.20/9.76 (( 71.20/9.76 (theprop) => 71.20/9.76 (( 71.20/9.76 (kfstpairEq) => 71.20/9.76 (( 71.20/9.76 (cartprodfstin) => 71.20/9.76 (( 71.20/9.76 (setukpairinjL2) => 71.20/9.76 (( 71.20/9.76 (setukpairinjL) => 71.20/9.76 (( 71.20/9.76 (setukpairinjR11) => 71.20/9.76 (( 71.20/9.76 (setukpairinjR12) => 71.20/9.76 (( 71.20/9.76 (setukpairinjR1) => 71.20/9.76 (( 71.20/9.76 (upairequniteq) => 71.20/9.76 (( 71.20/9.76 (setukpairinjR2) => 71.20/9.76 (( 71.20/9.76 (setukpairinjR) => 71.20/9.76 (( 71.20/9.76 (ksndsingleton) => 71.20/9.76 (( 71.20/9.76 (ksndpairEq) => 71.20/9.76 (( 71.20/9.76 (kpairsurjEq) => 71.20/9.76 (( 71.20/9.76 (cartprodsndin) => 71.20/9.76 (( 71.20/9.76 (cartprodpairmemEL) => 71.20/9.76 (( 71.20/9.76 (cartprodpairmemER) => 71.20/9.76 (( 71.20/9.76 (cartprodmempaircEq) => 71.20/9.76 (( 71.20/9.76 (cartprodfstpairEq) => 71.20/9.76 (( 71.20/9.76 (cartprodsndpairEq) => 71.20/9.76 (( 71.20/9.76 (cartprodpairsurjEq) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrI) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrSub) => 71.20/9.76 (( 71.20/9.76 (setOfPairsIsBReln) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrERa) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrEL1) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrEL2) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrER) => 71.20/9.76 (( 71.20/9.76 (funcImageSingleton) => 71.20/9.76 (( 71.20/9.76 (apProp) => 71.20/9.76 (( 71.20/9.76 (app) => 71.20/9.76 (( 71.20/9.76 (infuncsetfunc) => 71.20/9.76 (( 71.20/9.76 (ap2p) => 71.20/9.76 (( 71.20/9.76 (funcinfuncset) => 71.20/9.76 (( 71.20/9.76 (lamProp) => 71.20/9.76 (( 71.20/9.76 (lamp) => 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71.20/9.76 (( 71.20/9.76 (doubleComplementE1) => 71.20/9.76 (( 71.20/9.76 (doubleComplementSub1) => 71.20/9.76 (( 71.20/9.76 (doubleComplementSub2) => 71.20/9.76 (( 71.20/9.76 (doubleComplementEq) => 71.20/9.76 (( 71.20/9.76 (complementTnotintersectT) => 71.20/9.76 (( 71.20/9.76 (complementImpComplementIntersect) => 71.20/9.76 (( 71.20/9.76 (complementSubsetComplementIntersect) => 71.20/9.76 (( 71.20/9.76 (complementInPowersetComplementIntersect) => 71.20/9.76 (( 71.20/9.76 (contraSubsetComplement) => 71.20/9.76 (( 71.20/9.76 (complementTcontraSubset) => 71.20/9.76 (( 71.20/9.76 (binunionTILcontra) => 71.20/9.76 (( 71.20/9.76 (binunionTIRcontra) => 71.20/9.76 (( 71.20/9.76 (inIntersectImpInUnion) => 71.20/9.76 (( 71.20/9.76 (inIntersectImpInUnion2) => 71.20/9.76 (( 71.20/9.76 (inIntersectImpInIntersectUnions) => 71.20/9.76 (( 71.20/9.76 (intersectInPowersetIntersectUnions) => 71.20/9.76 (( 71.20/9.76 (inComplementUnionImpNotIn1) => 71.20/9.76 (( 71.20/9.76 (inComplementUnionImpInComplement1) => 71.20/9.76 (( 71.20/9.76 (binunionTE) => 71.20/9.76 (( 71.20/9.76 (binunionTEcontra) => 71.20/9.76 (( 71.20/9.76 (demorgan2a1) => 71.20/9.76 (( 71.20/9.76 (complementUnionInPowersetComplement) => 71.20/9.76 (( 71.20/9.76 (demorgan2a2) => 71.20/9.76 (( 71.20/9.76 (demorgan1a) => 71.20/9.76 (( 71.20/9.76 (demorgan1b) => 71.20/9.76 (( 71.20/9.76 (demorgan1) => 71.20/9.76 (( 71.20/9.76 (demorgan2a) => 71.20/9.76 (( 71.20/9.76 (demorgan2b2) => 71.20/9.76 (( 71.20/9.76 (demorgan2b) => 71.20/9.76 (( 71.20/9.76 (demorgan2) => 71.20/9.76 (( 71.20/9.76 (woz13rule0) => 71.20/9.76 (( 71.20/9.76 (woz13rule1) => 71.20/9.76 (( 71.20/9.76 (woz13rule2) => 71.20/9.76 (( 71.20/9.76 (woz13rule3) => 71.20/9.76 (( 71.20/9.76 (woz13rule4) => 71.20/9.76 (( 71.20/9.76 (woz1_1) => 71.20/9.76 (( 71.20/9.76 (woz1_2) => 71.20/9.76 (( 71.20/9.76 (woz1_3) => 71.20/9.76 (( 71.20/9.76 (woz1_4) => 71.20/9.76 (( 71.20/9.76 (woz1_5) => 71.20/9.76 (( 71.20/9.76 (breln1all2) => 71.20/9.76 (( 71.20/9.76 (breln1SetBreln1) => 71.20/9.76 (( 71.20/9.76 (choice2fnsingleton) => 71.20/9.76 (( 71.20/9.76 (setOfPairsIsBReln1) => 71.20/9.76 (( 71.20/9.76 (breln1all1) => 71.20/9.76 (( 71.20/9.76 (subbreln1) => 71.20/9.76 (( 71.20/9.76 (eqbreln1) => 71.20/9.76 (( 71.20/9.76 (breln1invprop) => 71.20/9.76 (( 71.20/9.76 (breln1invI) => 71.20/9.76 (( 71.20/9.76 (breln1invE) => 71.20/9.76 (( 71.20/9.76 (breln1compprop) => 71.20/9.76 (( 71.20/9.76 (breln1compI) => 71.20/9.76 (( 71.20/9.76 (breln1compE) => 71.20/9.76 (( 71.20/9.76 (breln1compEex) => 71.20/9.76 (( 71.20/9.76 (!!) @ ( 71.20/9.76 (('#B') @ ( 71.20/9.76 !!) @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#S') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#S') @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 =>))) @ 71.20/9.76 breln1)))) @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 !!))) @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#S') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#B') @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#S') @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 =>))) @ 71.20/9.76 breln1)))))) @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#C') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#B') @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#B') @ 71.20/9.76 breln1)))) @ 71.20/9.76 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])). 71.20/9.76 thf(zip_derived_cl417, plain, 71.20/9.76 (~ (((subPowSU) => 71.20/9.76 (((exuE2) => 71.20/9.76 (((nonemptyImpWitness) => 71.20/9.76 (((uniqinunit) => 71.20/9.76 (((notinsingleton) => 71.20/9.76 (((eqinunit) => 71.20/9.76 (((singletonsswitch) => 71.20/9.76 (((upairsetE) => 71.20/9.76 (((upairsetIL) => 71.20/9.76 (((upairsetIR) => 71.20/9.76 (((emptyE1) => 71.20/9.76 (((vacuousDall) => 71.20/9.76 (((quantDeMorgan1) => 71.20/9.76 (((quantDeMorgan2) => 71.20/9.76 (((quantDeMorgan3) => 71.20/9.76 (((quantDeMorgan4) => 71.20/9.76 (((prop2setI) => 71.20/9.76 (((prop2set2propI) => 71.20/9.76 (((notdexE) => 71.20/9.76 (((notdallE) => 71.20/9.76 (((exuI1) => 71.20/9.76 (((exuI3) => 71.20/9.76 (((exuI2) => 71.20/9.76 (((inCongP) => 71.20/9.76 (((in__Cong) => 71.20/9.76 (((exuE3u) => 71.20/9.76 (((exu__Cong) => 71.20/9.76 (((setadjoin__Cong) => 71.20/9.76 (((powerset__Cong) => 71.20/9.76 (((setunion__Cong) => 71.20/9.76 (( 71.20/9.76 (exuEu) => 71.20/9.76 (( 71.20/9.76 (descr__Cong) => 71.20/9.76 (( 71.20/9.76 (dsetconstr__Cong) => 71.20/9.76 (( 71.20/9.76 (subsetI1) => 71.20/9.76 (( 71.20/9.76 (eqimpsubset2) => 71.20/9.76 (( 71.20/9.76 (eqimpsubset1) => 71.20/9.76 (( 71.20/9.76 (subsetI2) => 71.20/9.76 (( 71.20/9.76 (emptysetsubset) => 71.20/9.76 (( 71.20/9.76 (subsetE) => 71.20/9.76 (( 71.20/9.76 (subsetE2) => 71.20/9.76 (( 71.20/9.76 (notsubsetI) => 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71.20/9.76 (binintersectSubset5) => 71.20/9.76 (( 71.20/9.76 (binintersectEL) => 71.20/9.76 (( 71.20/9.76 (binintersectLsub) => 71.20/9.76 (( 71.20/9.76 (binintersectSubset2) => 71.20/9.76 (( 71.20/9.76 (binintersectSubset3) => 71.20/9.76 (( 71.20/9.76 (binintersectER) => 71.20/9.76 (( 71.20/9.76 (disjointsetsI1) => 71.20/9.76 (( 71.20/9.76 (binintersectRsub) => 71.20/9.76 (( 71.20/9.76 (binintersectSubset4) => 71.20/9.76 (( 71.20/9.76 (binintersectSubset1) => 71.20/9.76 (( 71.20/9.76 (bs114d) => 71.20/9.76 (( 71.20/9.76 (setminusI) => 71.20/9.76 (( 71.20/9.76 (setminusEL) => 71.20/9.76 (( 71.20/9.76 (setminusER) => 71.20/9.76 (( 71.20/9.76 (setminusSubset2) => 71.20/9.76 (( 71.20/9.76 (setminusERneg) => 71.20/9.76 (( 71.20/9.76 (setminusELneg) => 71.20/9.76 (( 71.20/9.76 (setminusILneg) => 71.20/9.76 (( 71.20/9.76 (setminusIRneg) => 71.20/9.76 (( 71.20/9.76 (setminusLsub) => 71.20/9.76 (( 71.20/9.76 (setminusSubset1) => 71.20/9.76 (( 71.20/9.76 (symdiffE) => 71.20/9.76 (( 71.20/9.76 (symdiffI1) => 71.20/9.76 (( 71.20/9.76 (symdiffI2) => 71.20/9.76 (( 71.20/9.76 (symdiffIneg1) => 71.20/9.76 (( 71.20/9.76 (symdiffIneg2) => 71.20/9.76 (( 71.20/9.76 (secondinupair) => 71.20/9.76 (( 71.20/9.76 (setukpairIL) => 71.20/9.76 (( 71.20/9.76 (setukpairIR) => 71.20/9.76 (( 71.20/9.76 (kpairiskpair) => 71.20/9.76 (( 71.20/9.76 (kpairp) => 71.20/9.76 (( 71.20/9.76 (singletonsubset) => 71.20/9.76 (( 71.20/9.76 (singletoninpowerset) => 71.20/9.76 (( 71.20/9.76 (singletoninpowunion) => 71.20/9.76 (( 71.20/9.76 (upairset2E) => 71.20/9.76 (( 71.20/9.76 (upairsubunion) => 71.20/9.76 (( 71.20/9.76 (upairinpowunion) => 71.20/9.76 (( 71.20/9.76 (ubforcartprodlem1) => 71.20/9.76 (( 71.20/9.76 (ubforcartprodlem2) => 71.20/9.76 (( 71.20/9.76 (ubforcartprodlem3) => 71.20/9.76 (( 71.20/9.76 (cartprodpairin) => 71.20/9.76 (( 71.20/9.76 (cartprodmempair1) => 71.20/9.76 (( 71.20/9.76 (cartprodmempair) => 71.20/9.76 (( 71.20/9.76 (setunionE2) => 71.20/9.76 (( 71.20/9.76 (setunionsingleton1) => 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71.20/9.76 (( 71.20/9.76 (cartprodsndin) => 71.20/9.76 (( 71.20/9.76 (cartprodpairmemEL) => 71.20/9.76 (( 71.20/9.76 (cartprodpairmemER) => 71.20/9.76 (( 71.20/9.76 (cartprodmempaircEq) => 71.20/9.76 (( 71.20/9.76 (cartprodfstpairEq) => 71.20/9.76 (( 71.20/9.76 (cartprodsndpairEq) => 71.20/9.76 (( 71.20/9.76 (cartprodpairsurjEq) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrI) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrSub) => 71.20/9.76 (( 71.20/9.76 (setOfPairsIsBReln) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrERa) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrEL1) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrEL2) => 71.20/9.76 (( 71.20/9.76 (dpsetconstrER) => 71.20/9.76 (( 71.20/9.76 (funcImageSingleton) => 71.20/9.76 (( 71.20/9.76 (apProp) => 71.20/9.76 (( 71.20/9.76 (app) => 71.20/9.76 (( 71.20/9.76 (infuncsetfunc) => 71.20/9.76 (( 71.20/9.76 (ap2p) => 71.20/9.76 (( 71.20/9.76 (funcinfuncset) => 71.20/9.76 (( 71.20/9.76 (lamProp) => 71.20/9.76 (( 71.20/9.76 (lamp) => 71.20/9.76 (( 71.20/9.76 (lam2p) => 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(doubleComplementE1) => 71.20/9.76 (( 71.20/9.76 (doubleComplementSub1) => 71.20/9.76 (( 71.20/9.76 (doubleComplementSub2) => 71.20/9.76 (( 71.20/9.76 (doubleComplementEq) => 71.20/9.76 (( 71.20/9.76 (complementTnotintersectT) => 71.20/9.76 (( 71.20/9.76 (complementImpComplementIntersect) => 71.20/9.76 (( 71.20/9.76 (complementSubsetComplementIntersect) => 71.20/9.76 (( 71.20/9.76 (complementInPowersetComplementIntersect) => 71.20/9.76 (( 71.20/9.76 (contraSubsetComplement) => 71.20/9.76 (( 71.20/9.76 (complementTcontraSubset) => 71.20/9.76 (( 71.20/9.76 (binunionTILcontra) => 71.20/9.76 (( 71.20/9.76 (binunionTIRcontra) => 71.20/9.76 (( 71.20/9.76 (inIntersectImpInUnion) => 71.20/9.76 (( 71.20/9.76 (inIntersectImpInUnion2) => 71.20/9.76 (( 71.20/9.76 (inIntersectImpInIntersectUnions) => 71.20/9.76 (( 71.20/9.76 (intersectInPowersetIntersectUnions) => 71.20/9.76 (( 71.20/9.76 (inComplementUnionImpNotIn1) => 71.20/9.76 (( 71.20/9.76 (inComplementUnionImpInComplement1) => 71.20/9.76 (( 71.20/9.76 (binunionTE) => 71.20/9.76 (( 71.20/9.76 (binunionTEcontra) => 71.20/9.76 (( 71.20/9.76 (demorgan2a1) => 71.20/9.76 (( 71.20/9.76 (complementUnionInPowersetComplement) => 71.20/9.76 (( 71.20/9.76 (demorgan2a2) => 71.20/9.76 (( 71.20/9.76 (demorgan1a) => 71.20/9.76 (( 71.20/9.76 (demorgan1b) => 71.20/9.76 (( 71.20/9.76 (demorgan1) => 71.20/9.76 (( 71.20/9.76 (demorgan2a) => 71.20/9.76 (( 71.20/9.76 (demorgan2b2) => 71.20/9.76 (( 71.20/9.76 (demorgan2b) => 71.20/9.76 (( 71.20/9.76 (demorgan2) => 71.20/9.76 (( 71.20/9.76 (woz13rule0) => 71.20/9.76 (( 71.20/9.76 (woz13rule1) => 71.20/9.76 (( 71.20/9.76 (woz13rule2) => 71.20/9.76 (( 71.20/9.76 (woz13rule3) => 71.20/9.76 (( 71.20/9.76 (woz13rule4) => 71.20/9.76 (( 71.20/9.76 (woz1_1) => 71.20/9.76 (( 71.20/9.76 (woz1_2) => 71.20/9.76 (( 71.20/9.76 (woz1_3) => 71.20/9.76 (( 71.20/9.76 (woz1_4) => 71.20/9.76 (( 71.20/9.76 (woz1_5) => 71.20/9.76 (( 71.20/9.76 (breln1all2) => 71.20/9.76 (( 71.20/9.76 (breln1SetBreln1) => 71.20/9.76 (( 71.20/9.76 (choice2fnsingleton) => 71.20/9.76 (( 71.20/9.76 (setOfPairsIsBReln1) => 71.20/9.76 (( 71.20/9.76 (breln1all1) => 71.20/9.76 (( 71.20/9.76 (subbreln1) => 71.20/9.76 (( 71.20/9.76 (eqbreln1) => 71.20/9.76 (( 71.20/9.76 (breln1invprop) => 71.20/9.76 (( 71.20/9.76 (breln1invI) => 71.20/9.76 (( 71.20/9.76 (breln1invE) => 71.20/9.76 (( 71.20/9.76 (breln1compprop) => 71.20/9.76 (( 71.20/9.76 (breln1compI) => 71.20/9.76 (( 71.20/9.76 (breln1compE) => 71.20/9.76 (( 71.20/9.76 (breln1compEex) => 71.20/9.76 (( 71.20/9.76 (!!) @ ( 71.20/9.76 (('#B') @ ( 71.20/9.76 !!) @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#S') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#S') @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 =>))) @ 71.20/9.76 breln1)))) @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 !!))) @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#S') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#B') @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#S') @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 =>))) @ 71.20/9.76 breln1)))))) @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#C') @ ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#B') @ 71.20/9.76 ( 71.20/9.76 ( 71.20/9.76 ('#B') @ ( 71.20/9.76 '#B') @ 71.20/9.76 breln1)))) @ 71.20/9.76 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.20/9.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])). 71.20/9.76 thf(zip_derived_cl428, plain, 71.20/9.76 (~ (((exuE2) => 71.20/9.76 (((nonemptyImpWitness) => 71.20/9.76 (((uniqinunit) => 71.20/9.76 (((notinsingleton) => 71.20/9.76 (((eqinunit) => 71.20/9.76 (((singletonsswitch) => 71.20/9.76 (((upairsetE) => 71.20/9.76 (((upairsetIL) => 71.20/9.76 (((upairsetIR) => 71.20/9.76 (((emptyE1) => 71.20/9.76 (((vacuousDall) => 71.20/9.76 (((quantDeMorgan1) => 71.20/9.76 (((quantDeMorgan2) => 71.20/9.76 (((quantDeMorgan3) => 71.20/9.76 (((quantDeMorgan4) => 71.20/9.76 (((prop2setI) => 71.20/9.76 (((prop2set2propI) => 71.20/9.76 (((notdexE) => 71.20/9.76 (((notdallE) => 71.20/9.76 (((exuI1) => 71.20/9.76 (((exuI3) => 71.20/9.76 (((exuI2) => 71.20/9.76 (((inCongP) => 71.20/9.76 (((in__Cong) => 71.20/9.76 (((exuE3u) => 71.20/9.76 (((exu__Cong) => 71.20/9.76 (((setadjoin__Cong) => 71.77/9.76 (((powerset__Cong) => 71.77/9.76 (((setunion__Cong) => 71.77/9.76 (((exuEu) => 71.77/9.76 (( 71.77/9.76 (descr__Cong) => 71.77/9.76 (( 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71.77/9.76 (setminusSubset2) => 71.77/9.76 (( 71.77/9.76 (setminusERneg) => 71.77/9.76 (( 71.77/9.76 (setminusELneg) => 71.77/9.76 (( 71.77/9.76 (setminusILneg) => 71.77/9.76 (( 71.77/9.76 (setminusIRneg) => 71.77/9.76 (( 71.77/9.76 (setminusLsub) => 71.77/9.76 (( 71.77/9.76 (setminusSubset1) => 71.77/9.76 (( 71.77/9.76 (symdiffE) => 71.77/9.76 (( 71.77/9.76 (symdiffI1) => 71.77/9.76 (( 71.77/9.76 (symdiffI2) => 71.77/9.76 (( 71.77/9.76 (symdiffIneg1) => 71.77/9.76 (( 71.77/9.76 (symdiffIneg2) => 71.77/9.76 (( 71.77/9.76 (secondinupair) => 71.77/9.76 (( 71.77/9.76 (setukpairIL) => 71.77/9.76 (( 71.77/9.76 (setukpairIR) => 71.77/9.76 (( 71.77/9.76 (kpairiskpair) => 71.77/9.76 (( 71.77/9.76 (kpairp) => 71.77/9.76 (( 71.77/9.76 (singletonsubset) => 71.77/9.76 (( 71.77/9.76 (singletoninpowerset) => 71.77/9.76 (( 71.77/9.76 (singletoninpowunion) => 71.77/9.76 (( 71.77/9.76 (upairset2E) => 71.77/9.76 (( 71.77/9.76 (upairsubunion) => 71.77/9.76 (( 71.77/9.76 (upairinpowunion) => 71.77/9.76 (( 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71.77/9.76 (( 71.77/9.76 (funcImageSingleton) => 71.77/9.76 (( 71.77/9.76 (apProp) => 71.77/9.76 (( 71.77/9.76 (app) => 71.77/9.76 (( 71.77/9.76 (infuncsetfunc) => 71.77/9.76 (( 71.77/9.76 (ap2p) => 71.77/9.76 (( 71.77/9.76 (funcinfuncset) => 71.77/9.76 (( 71.77/9.76 (lamProp) => 71.77/9.76 (( 71.77/9.76 (lamp) => 71.77/9.76 (( 71.77/9.76 (lam2p) => 71.77/9.76 (( 71.77/9.76 (brelnall1) => 71.77/9.76 (( 71.77/9.76 (brelnall2) => 71.77/9.76 (( 71.77/9.76 (ex1E2) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp1) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp3) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp2) => 71.77/9.76 (( 71.77/9.76 (funcextLem) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp4) => 71.77/9.76 (( 71.77/9.76 (subbreln) => 71.77/9.76 (( 71.77/9.76 (eqbreln) => 71.77/9.76 (( 71.77/9.76 (funcext) => 71.77/9.76 (( 71.77/9.76 (funcext2) => 71.77/9.76 (( 71.77/9.76 (ap2apEq1) => 71.77/9.76 (( 71.77/9.76 (ap2apEq2) => 71.77/9.76 (( 71.77/9.76 (beta1) => 71.77/9.76 (( 71.77/9.76 (eta1) => 71.77/9.76 (( 71.77/9.76 (lam2lamEq) => 71.77/9.76 (( 71.77/9.76 (beta2) => 71.77/9.76 (( 71.77/9.76 (eta2) => 71.77/9.76 (( 71.77/9.76 (iffalseProp1) => 71.77/9.76 (( 71.77/9.76 (iffalseProp2) => 71.77/9.76 (( 71.77/9.76 (iftrueProp1) => 71.77/9.76 (( 71.77/9.76 (iftrueProp2) => 71.77/9.76 (( 71.77/9.76 (ifSingleton) => 71.77/9.76 (( 71.77/9.76 (ifp) => 71.77/9.76 (( 71.77/9.76 (theeq) => 71.77/9.76 (( 71.77/9.76 (iftrue) => 71.77/9.76 (( 71.77/9.76 (iffalse) => 71.77/9.76 (( 71.77/9.76 (iftrueorfalse) => 71.77/9.76 (( 71.77/9.76 (binintersectT_lem) => 71.77/9.76 (( 71.77/9.76 (binunionT_lem) => 71.77/9.76 (( 71.77/9.76 (powersetT_lem) => 71.77/9.76 (( 71.77/9.76 (setminusT_lem) => 71.77/9.76 (( 71.77/9.76 (complementT_lem) => 71.77/9.76 (( 71.77/9.76 (setextT) => 71.77/9.76 (( 71.77/9.76 (subsetTI) => 71.77/9.76 (( 71.77/9.76 (powersetTI1) => 71.77/9.76 (( 71.77/9.76 (powersetTE1) => 71.77/9.76 (( 71.77/9.76 (complementTI1) => 71.77/9.76 (( 71.77/9.76 (complementTE1) => 71.77/9.76 (( 71.77/9.76 (binintersectTELcontra) => 71.77/9.76 (( 71.77/9.76 (binintersectTERcontra) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT1) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT2) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT3) => 71.77/9.76 (( 71.77/9.76 (doubleComplementI1) => 71.77/9.76 (( 71.77/9.76 (doubleComplementE1) => 71.77/9.76 (( 71.77/9.76 (doubleComplementSub1) => 71.77/9.76 (( 71.77/9.76 (doubleComplementSub2) => 71.77/9.76 (( 71.77/9.76 (doubleComplementEq) => 71.77/9.76 (( 71.77/9.76 (complementTnotintersectT) => 71.77/9.76 (( 71.77/9.76 (complementImpComplementIntersect) => 71.77/9.76 (( 71.77/9.76 (complementSubsetComplementIntersect) => 71.77/9.76 (( 71.77/9.76 (complementInPowersetComplementIntersect) => 71.77/9.76 (( 71.77/9.76 (contraSubsetComplement) => 71.77/9.76 (( 71.77/9.76 (complementTcontraSubset) => 71.77/9.76 (( 71.77/9.76 (binunionTILcontra) => 71.77/9.76 (( 71.77/9.76 (binunionTIRcontra) => 71.77/9.76 (( 71.77/9.76 (inIntersectImpInUnion) => 71.77/9.76 (( 71.77/9.76 (inIntersectImpInUnion2) => 71.77/9.76 (( 71.77/9.76 (inIntersectImpInIntersectUnions) => 71.77/9.76 (( 71.77/9.76 (intersectInPowersetIntersectUnions) => 71.77/9.76 (( 71.77/9.76 (inComplementUnionImpNotIn1) => 71.77/9.76 (( 71.77/9.76 (inComplementUnionImpInComplement1) => 71.77/9.76 (( 71.77/9.76 (binunionTE) => 71.77/9.76 (( 71.77/9.76 (binunionTEcontra) => 71.77/9.76 (( 71.77/9.76 (demorgan2a1) => 71.77/9.76 (( 71.77/9.76 (complementUnionInPowersetComplement) => 71.77/9.76 (( 71.77/9.76 (demorgan2a2) => 71.77/9.76 (( 71.77/9.76 (demorgan1a) => 71.77/9.76 (( 71.77/9.76 (demorgan1b) => 71.77/9.76 (( 71.77/9.76 (demorgan1) => 71.77/9.76 (( 71.77/9.76 (demorgan2a) => 71.77/9.76 (( 71.77/9.76 (demorgan2b2) => 71.77/9.76 (( 71.77/9.76 (demorgan2b) => 71.77/9.76 (( 71.77/9.76 (demorgan2) => 71.77/9.76 (( 71.77/9.76 (woz13rule0) => 71.77/9.76 (( 71.77/9.76 (woz13rule1) => 71.77/9.76 (( 71.77/9.76 (woz13rule2) => 71.77/9.76 (( 71.77/9.76 (woz13rule3) => 71.77/9.76 (( 71.77/9.76 (woz13rule4) => 71.77/9.76 (( 71.77/9.76 (woz1_1) => 71.77/9.76 (( 71.77/9.76 (woz1_2) => 71.77/9.76 (( 71.77/9.76 (woz1_3) => 71.77/9.76 (( 71.77/9.76 (woz1_4) => 71.77/9.76 (( 71.77/9.76 (woz1_5) => 71.77/9.76 (( 71.77/9.76 (breln1all2) => 71.77/9.76 (( 71.77/9.76 (breln1SetBreln1) => 71.77/9.76 (( 71.77/9.76 (choice2fnsingleton) => 71.77/9.76 (( 71.77/9.76 (setOfPairsIsBReln1) => 71.77/9.76 (( 71.77/9.76 (breln1all1) => 71.77/9.76 (( 71.77/9.76 (subbreln1) => 71.77/9.76 (( 71.77/9.76 (eqbreln1) => 71.77/9.76 (( 71.77/9.76 (breln1invprop) => 71.77/9.76 (( 71.77/9.76 (breln1invI) => 71.77/9.76 (( 71.77/9.76 (breln1invE) => 71.77/9.76 (( 71.77/9.76 (breln1compprop) => 71.77/9.76 (( 71.77/9.76 (breln1compI) => 71.77/9.76 (( 71.77/9.76 (breln1compE) => 71.77/9.76 (( 71.77/9.76 (breln1compEex) => 71.77/9.76 (( 71.77/9.76 (!!) @ ( 71.77/9.76 (('#B') @ ( 71.77/9.76 !!) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#S') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#S') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 =>))) @ 71.77/9.76 breln1)))) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 !!))) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#S') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#B') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#S') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 =>))) @ 71.77/9.76 breln1)))))) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#C') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#B') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#B') @ 71.77/9.76 breln1)))) @ 71.77/9.76 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])). 71.77/9.76 thf(zip_derived_cl439, plain, 71.77/9.76 (~ (((nonemptyImpWitness) => 71.77/9.76 (((uniqinunit) => 71.77/9.76 (((notinsingleton) => 71.77/9.76 (((eqinunit) => 71.77/9.76 (((singletonsswitch) => 71.77/9.76 (((upairsetE) => 71.77/9.76 (((upairsetIL) => 71.77/9.76 (((upairsetIR) => 71.77/9.76 (((emptyE1) => 71.77/9.76 (((vacuousDall) => 71.77/9.76 (((quantDeMorgan1) => 71.77/9.76 (((quantDeMorgan2) => 71.77/9.76 (((quantDeMorgan3) => 71.77/9.76 (((quantDeMorgan4) => 71.77/9.76 (((prop2setI) => 71.77/9.76 (((prop2set2propI) => 71.77/9.76 (((notdexE) => 71.77/9.76 (((notdallE) => 71.77/9.76 (((exuI1) => 71.77/9.76 (((exuI3) => 71.77/9.76 (((exuI2) => 71.77/9.76 (((inCongP) => 71.77/9.76 (((in__Cong) => 71.77/9.76 (((exuE3u) => 71.77/9.76 (((exu__Cong) => 71.77/9.76 (((setadjoin__Cong) => 71.77/9.76 (((powerset__Cong) => 71.77/9.76 (((setunion__Cong) => 71.77/9.76 (((exuEu) => 71.77/9.76 (((descr__Cong) => 71.77/9.76 (( 71.77/9.76 (dsetconstr__Cong) => 71.77/9.76 (( 71.77/9.76 (subsetI1) => 71.77/9.76 (( 71.77/9.76 (eqimpsubset2) => 71.77/9.76 (( 71.77/9.76 (eqimpsubset1) => 71.77/9.76 (( 71.77/9.76 (subsetI2) => 71.77/9.76 (( 71.77/9.76 (emptysetsubset) => 71.77/9.76 (( 71.77/9.76 (subsetE) => 71.77/9.76 (( 71.77/9.76 (subsetE2) => 71.77/9.76 (( 71.77/9.76 (notsubsetI) => 71.77/9.76 (( 71.77/9.76 (notequalI1) => 71.77/9.76 (( 71.77/9.76 (notequalI2) => 71.77/9.76 (( 71.77/9.76 (subsetRefl) => 71.77/9.76 (( 71.77/9.76 (subsetTrans) => 71.77/9.76 (( 71.77/9.76 (setadjoinSub) => 71.77/9.76 (( 71.77/9.76 (setadjoinSub2) => 71.77/9.76 (( 71.77/9.76 (subset2powerset) => 71.77/9.76 (( 71.77/9.76 (setextsub) => 71.77/9.76 (( 71.77/9.76 (subsetemptysetimpeq) => 71.77/9.76 (( 71.77/9.76 (powersetI1) => 71.77/9.76 (( 71.77/9.76 (powersetE1) => 71.77/9.76 (( 71.77/9.76 (inPowerset) => 71.77/9.76 (( 71.77/9.76 (powersetsubset) => 71.77/9.76 (( 71.77/9.76 (sepInPowerset) => 71.77/9.76 (( 71.77/9.76 (sepSubset) => 71.77/9.76 (( 71.77/9.76 (binunionIL) => 71.77/9.76 (( 71.77/9.76 (upairset2IR) => 71.77/9.76 (( 71.77/9.76 (binunionIR) => 71.77/9.76 (( 71.77/9.76 (binunionEcases) => 71.77/9.76 (( 71.77/9.76 (binunionE) => 71.77/9.76 (( 71.77/9.76 (binunionLsub) => 71.77/9.76 (( 71.77/9.76 (binunionRsub) => 71.77/9.76 (( 71.77/9.76 (binintersectI) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset5) => 71.77/9.76 (( 71.77/9.76 (binintersectEL) => 71.77/9.76 (( 71.77/9.76 (binintersectLsub) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset2) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset3) => 71.77/9.76 (( 71.77/9.76 (binintersectER) => 71.77/9.76 (( 71.77/9.76 (disjointsetsI1) => 71.77/9.76 (( 71.77/9.76 (binintersectRsub) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset4) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset1) => 71.77/9.76 (( 71.77/9.76 (bs114d) => 71.77/9.76 (( 71.77/9.76 (setminusI) => 71.77/9.76 (( 71.77/9.76 (setminusEL) => 71.77/9.76 (( 71.77/9.76 (setminusER) => 71.77/9.76 (( 71.77/9.76 (setminusSubset2) => 71.77/9.76 (( 71.77/9.76 (setminusERneg) => 71.77/9.76 (( 71.77/9.76 (setminusELneg) => 71.77/9.76 (( 71.77/9.76 (setminusILneg) => 71.77/9.76 (( 71.77/9.76 (setminusIRneg) => 71.77/9.76 (( 71.77/9.76 (setminusLsub) => 71.77/9.76 (( 71.77/9.76 (setminusSubset1) => 71.77/9.76 (( 71.77/9.76 (symdiffE) => 71.77/9.76 (( 71.77/9.76 (symdiffI1) => 71.77/9.76 (( 71.77/9.76 (symdiffI2) => 71.77/9.76 (( 71.77/9.76 (symdiffIneg1) => 71.77/9.76 (( 71.77/9.76 (symdiffIneg2) => 71.77/9.76 (( 71.77/9.76 (secondinupair) => 71.77/9.76 (( 71.77/9.76 (setukpairIL) => 71.77/9.76 (( 71.77/9.76 (setukpairIR) => 71.77/9.76 (( 71.77/9.76 (kpairiskpair) => 71.77/9.76 (( 71.77/9.76 (kpairp) => 71.77/9.76 (( 71.77/9.76 (singletonsubset) => 71.77/9.76 (( 71.77/9.76 (singletoninpowerset) => 71.77/9.76 (( 71.77/9.76 (singletoninpowunion) => 71.77/9.76 (( 71.77/9.76 (upairset2E) => 71.77/9.76 (( 71.77/9.76 (upairsubunion) => 71.77/9.76 (( 71.77/9.76 (upairinpowunion) => 71.77/9.76 (( 71.77/9.76 (ubforcartprodlem1) => 71.77/9.76 (( 71.77/9.76 (ubforcartprodlem2) => 71.77/9.76 (( 71.77/9.76 (ubforcartprodlem3) => 71.77/9.76 (( 71.77/9.76 (cartprodpairin) => 71.77/9.76 (( 71.77/9.76 (cartprodmempair1) => 71.77/9.76 (( 71.77/9.76 (cartprodmempair) => 71.77/9.76 (( 71.77/9.76 (setunionE2) => 71.77/9.76 (( 71.77/9.76 (setunionsingleton1) => 71.77/9.76 (( 71.77/9.76 (setunionsingleton2) => 71.77/9.76 (( 71.77/9.76 (setunionsingleton) => 71.77/9.76 (( 71.77/9.76 (singletonprop) => 71.77/9.76 (( 71.77/9.76 (ex1E1) => 71.77/9.76 (( 71.77/9.76 (ex1I) => 71.77/9.76 (( 71.77/9.76 (ex1I2) => 71.77/9.76 (( 71.77/9.76 (singletonsuniq) => 71.77/9.76 (( 71.77/9.76 (setukpairinjL1) => 71.77/9.76 (( 71.77/9.76 (kfstsingleton) => 71.77/9.76 (( 71.77/9.76 (theprop) => 71.77/9.76 (( 71.77/9.76 (kfstpairEq) => 71.77/9.76 (( 71.77/9.76 (cartprodfstin) => 71.77/9.76 (( 71.77/9.76 (setukpairinjL2) => 71.77/9.76 (( 71.77/9.76 (setukpairinjL) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR11) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR12) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR1) => 71.77/9.76 (( 71.77/9.76 (upairequniteq) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR2) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR) => 71.77/9.76 (( 71.77/9.76 (ksndsingleton) => 71.77/9.76 (( 71.77/9.76 (ksndpairEq) => 71.77/9.76 (( 71.77/9.76 (kpairsurjEq) => 71.77/9.76 (( 71.77/9.76 (cartprodsndin) => 71.77/9.76 (( 71.77/9.76 (cartprodpairmemEL) => 71.77/9.76 (( 71.77/9.76 (cartprodpairmemER) => 71.77/9.76 (( 71.77/9.76 (cartprodmempaircEq) => 71.77/9.76 (( 71.77/9.76 (cartprodfstpairEq) => 71.77/9.76 (( 71.77/9.76 (cartprodsndpairEq) => 71.77/9.76 (( 71.77/9.76 (cartprodpairsurjEq) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrI) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrSub) => 71.77/9.76 (( 71.77/9.76 (setOfPairsIsBReln) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrERa) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrEL1) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrEL2) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrER) => 71.77/9.76 (( 71.77/9.76 (funcImageSingleton) => 71.77/9.76 (( 71.77/9.76 (apProp) => 71.77/9.76 (( 71.77/9.76 (app) => 71.77/9.76 (( 71.77/9.76 (infuncsetfunc) => 71.77/9.76 (( 71.77/9.76 (ap2p) => 71.77/9.76 (( 71.77/9.76 (funcinfuncset) => 71.77/9.76 (( 71.77/9.76 (lamProp) => 71.77/9.76 (( 71.77/9.76 (lamp) => 71.77/9.76 (( 71.77/9.76 (lam2p) => 71.77/9.76 (( 71.77/9.76 (brelnall1) => 71.77/9.76 (( 71.77/9.76 (brelnall2) => 71.77/9.76 (( 71.77/9.76 (ex1E2) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp1) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp3) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp2) => 71.77/9.76 (( 71.77/9.76 (funcextLem) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp4) => 71.77/9.76 (( 71.77/9.76 (subbreln) => 71.77/9.76 (( 71.77/9.76 (eqbreln) => 71.77/9.76 (( 71.77/9.76 (funcext) => 71.77/9.76 (( 71.77/9.76 (funcext2) => 71.77/9.76 (( 71.77/9.76 (ap2apEq1) => 71.77/9.76 (( 71.77/9.76 (ap2apEq2) => 71.77/9.76 (( 71.77/9.76 (beta1) => 71.77/9.76 (( 71.77/9.76 (eta1) => 71.77/9.76 (( 71.77/9.76 (lam2lamEq) => 71.77/9.76 (( 71.77/9.76 (beta2) => 71.77/9.76 (( 71.77/9.76 (eta2) => 71.77/9.76 (( 71.77/9.76 (iffalseProp1) => 71.77/9.76 (( 71.77/9.76 (iffalseProp2) => 71.77/9.76 (( 71.77/9.76 (iftrueProp1) => 71.77/9.76 (( 71.77/9.76 (iftrueProp2) => 71.77/9.76 (( 71.77/9.76 (ifSingleton) => 71.77/9.76 (( 71.77/9.76 (ifp) => 71.77/9.76 (( 71.77/9.76 (theeq) => 71.77/9.76 (( 71.77/9.76 (iftrue) => 71.77/9.76 (( 71.77/9.76 (iffalse) => 71.77/9.76 (( 71.77/9.76 (iftrueorfalse) => 71.77/9.76 (( 71.77/9.76 (binintersectT_lem) => 71.77/9.76 (( 71.77/9.76 (binunionT_lem) => 71.77/9.76 (( 71.77/9.76 (powersetT_lem) => 71.77/9.76 (( 71.77/9.76 (setminusT_lem) => 71.77/9.76 (( 71.77/9.76 (complementT_lem) => 71.77/9.76 (( 71.77/9.76 (setextT) => 71.77/9.76 (( 71.77/9.76 (subsetTI) => 71.77/9.76 (( 71.77/9.76 (powersetTI1) => 71.77/9.76 (( 71.77/9.76 (powersetTE1) => 71.77/9.76 (( 71.77/9.76 (complementTI1) => 71.77/9.76 (( 71.77/9.76 (complementTE1) => 71.77/9.76 (( 71.77/9.76 (binintersectTELcontra) => 71.77/9.76 (( 71.77/9.76 (binintersectTERcontra) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT1) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT2) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT3) => 71.77/9.76 (( 71.77/9.76 (doubleComplementI1) => 71.77/9.76 (( 71.77/9.76 (doubleComplementE1) => 71.77/9.76 (( 71.77/9.76 (doubleComplementSub1) => 71.77/9.76 (( 71.77/9.76 (doubleComplementSub2) => 71.77/9.76 (( 71.77/9.76 (doubleComplementEq) => 71.77/9.76 (( 71.77/9.76 (complementTnotintersectT) => 71.77/9.76 (( 71.77/9.76 (complementImpComplementIntersect) => 71.77/9.76 (( 71.77/9.76 (complementSubsetComplementIntersect) => 71.77/9.76 (( 71.77/9.76 (complementInPowersetComplementIntersect) => 71.77/9.76 (( 71.77/9.76 (contraSubsetComplement) => 71.77/9.76 (( 71.77/9.76 (complementTcontraSubset) => 71.77/9.76 (( 71.77/9.76 (binunionTILcontra) => 71.77/9.76 (( 71.77/9.76 (binunionTIRcontra) => 71.77/9.76 (( 71.77/9.76 (inIntersectImpInUnion) => 71.77/9.76 (( 71.77/9.76 (inIntersectImpInUnion2) => 71.77/9.76 (( 71.77/9.76 (inIntersectImpInIntersectUnions) => 71.77/9.76 (( 71.77/9.76 (intersectInPowersetIntersectUnions) => 71.77/9.76 (( 71.77/9.76 (inComplementUnionImpNotIn1) => 71.77/9.76 (( 71.77/9.76 (inComplementUnionImpInComplement1) => 71.77/9.76 (( 71.77/9.76 (binunionTE) => 71.77/9.76 (( 71.77/9.76 (binunionTEcontra) => 71.77/9.76 (( 71.77/9.76 (demorgan2a1) => 71.77/9.76 (( 71.77/9.76 (complementUnionInPowersetComplement) => 71.77/9.76 (( 71.77/9.76 (demorgan2a2) => 71.77/9.76 (( 71.77/9.76 (demorgan1a) => 71.77/9.76 (( 71.77/9.76 (demorgan1b) => 71.77/9.76 (( 71.77/9.76 (demorgan1) => 71.77/9.76 (( 71.77/9.76 (demorgan2a) => 71.77/9.76 (( 71.77/9.76 (demorgan2b2) => 71.77/9.76 (( 71.77/9.76 (demorgan2b) => 71.77/9.76 (( 71.77/9.76 (demorgan2) => 71.77/9.76 (( 71.77/9.76 (woz13rule0) => 71.77/9.76 (( 71.77/9.76 (woz13rule1) => 71.77/9.76 (( 71.77/9.76 (woz13rule2) => 71.77/9.76 (( 71.77/9.76 (woz13rule3) => 71.77/9.76 (( 71.77/9.76 (woz13rule4) => 71.77/9.76 (( 71.77/9.76 (woz1_1) => 71.77/9.76 (( 71.77/9.76 (woz1_2) => 71.77/9.76 (( 71.77/9.76 (woz1_3) => 71.77/9.76 (( 71.77/9.76 (woz1_4) => 71.77/9.76 (( 71.77/9.76 (woz1_5) => 71.77/9.76 (( 71.77/9.76 (breln1all2) => 71.77/9.76 (( 71.77/9.76 (breln1SetBreln1) => 71.77/9.76 (( 71.77/9.76 (choice2fnsingleton) => 71.77/9.76 (( 71.77/9.76 (setOfPairsIsBReln1) => 71.77/9.76 (( 71.77/9.76 (breln1all1) => 71.77/9.76 (( 71.77/9.76 (subbreln1) => 71.77/9.76 (( 71.77/9.76 (eqbreln1) => 71.77/9.76 (( 71.77/9.76 (breln1invprop) => 71.77/9.76 (( 71.77/9.76 (breln1invI) => 71.77/9.76 (( 71.77/9.76 (breln1invE) => 71.77/9.76 (( 71.77/9.76 (breln1compprop) => 71.77/9.76 (( 71.77/9.76 (breln1compI) => 71.77/9.76 (( 71.77/9.76 (breln1compE) => 71.77/9.76 (( 71.77/9.76 (breln1compEex) => 71.77/9.76 (( 71.77/9.76 (!!) @ ( 71.77/9.76 (('#B') @ ( 71.77/9.76 !!) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#S') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#S') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 =>))) @ 71.77/9.76 breln1)))) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 !!))) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#S') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#B') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#S') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 =>))) @ 71.77/9.76 breln1)))))) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#C') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#B') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#B') @ 71.77/9.76 breln1)))) @ 71.77/9.76 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])). 71.77/9.76 thf(zip_derived_cl449, plain, 71.77/9.76 (~ (((uniqinunit) => 71.77/9.76 (((notinsingleton) => 71.77/9.76 (((eqinunit) => 71.77/9.76 (((singletonsswitch) => 71.77/9.76 (((upairsetE) => 71.77/9.76 (((upairsetIL) => 71.77/9.76 (((upairsetIR) => 71.77/9.76 (((emptyE1) => 71.77/9.76 (((vacuousDall) => 71.77/9.76 (((quantDeMorgan1) => 71.77/9.76 (((quantDeMorgan2) => 71.77/9.76 (((quantDeMorgan3) => 71.77/9.76 (((quantDeMorgan4) => 71.77/9.76 (((prop2setI) => 71.77/9.76 (((prop2set2propI) => 71.77/9.76 (((notdexE) => 71.77/9.76 (((notdallE) => 71.77/9.76 (((exuI1) => 71.77/9.76 (((exuI3) => 71.77/9.76 (((exuI2) => 71.77/9.76 (((inCongP) => 71.77/9.76 (((in__Cong) => 71.77/9.76 (((exuE3u) => 71.77/9.76 (((exu__Cong) => 71.77/9.76 (((setadjoin__Cong) => 71.77/9.76 (((powerset__Cong) => 71.77/9.76 (((setunion__Cong) => 71.77/9.76 (((exuEu) => 71.77/9.76 (((descr__Cong) => 71.77/9.76 (((dsetconstr__Cong) => 71.77/9.76 (( 71.77/9.76 (subsetI1) => 71.77/9.76 (( 71.77/9.76 (eqimpsubset2) => 71.77/9.76 (( 71.77/9.76 (eqimpsubset1) => 71.77/9.76 (( 71.77/9.76 (subsetI2) => 71.77/9.76 (( 71.77/9.76 (emptysetsubset) => 71.77/9.76 (( 71.77/9.76 (subsetE) => 71.77/9.76 (( 71.77/9.76 (subsetE2) => 71.77/9.76 (( 71.77/9.76 (notsubsetI) => 71.77/9.76 (( 71.77/9.76 (notequalI1) => 71.77/9.76 (( 71.77/9.76 (notequalI2) => 71.77/9.76 (( 71.77/9.76 (subsetRefl) => 71.77/9.76 (( 71.77/9.76 (subsetTrans) => 71.77/9.76 (( 71.77/9.76 (setadjoinSub) => 71.77/9.76 (( 71.77/9.76 (setadjoinSub2) => 71.77/9.76 (( 71.77/9.76 (subset2powerset) => 71.77/9.76 (( 71.77/9.76 (setextsub) => 71.77/9.76 (( 71.77/9.76 (subsetemptysetimpeq) => 71.77/9.76 (( 71.77/9.76 (powersetI1) => 71.77/9.76 (( 71.77/9.76 (powersetE1) => 71.77/9.76 (( 71.77/9.76 (inPowerset) => 71.77/9.76 (( 71.77/9.76 (powersetsubset) => 71.77/9.76 (( 71.77/9.76 (sepInPowerset) => 71.77/9.76 (( 71.77/9.76 (sepSubset) => 71.77/9.76 (( 71.77/9.76 (binunionIL) => 71.77/9.76 (( 71.77/9.76 (upairset2IR) => 71.77/9.76 (( 71.77/9.76 (binunionIR) => 71.77/9.76 (( 71.77/9.76 (binunionEcases) => 71.77/9.76 (( 71.77/9.76 (binunionE) => 71.77/9.76 (( 71.77/9.76 (binunionLsub) => 71.77/9.76 (( 71.77/9.76 (binunionRsub) => 71.77/9.76 (( 71.77/9.76 (binintersectI) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset5) => 71.77/9.76 (( 71.77/9.76 (binintersectEL) => 71.77/9.76 (( 71.77/9.76 (binintersectLsub) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset2) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset3) => 71.77/9.76 (( 71.77/9.76 (binintersectER) => 71.77/9.76 (( 71.77/9.76 (disjointsetsI1) => 71.77/9.76 (( 71.77/9.76 (binintersectRsub) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset4) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset1) => 71.77/9.76 (( 71.77/9.76 (bs114d) => 71.77/9.76 (( 71.77/9.76 (setminusI) => 71.77/9.76 (( 71.77/9.76 (setminusEL) => 71.77/9.76 (( 71.77/9.76 (setminusER) => 71.77/9.76 (( 71.77/9.76 (setminusSubset2) => 71.77/9.76 (( 71.77/9.76 (setminusERneg) => 71.77/9.76 (( 71.77/9.76 (setminusELneg) => 71.77/9.76 (( 71.77/9.76 (setminusILneg) => 71.77/9.76 (( 71.77/9.76 (setminusIRneg) => 71.77/9.76 (( 71.77/9.76 (setminusLsub) => 71.77/9.76 (( 71.77/9.76 (setminusSubset1) => 71.77/9.76 (( 71.77/9.76 (symdiffE) => 71.77/9.76 (( 71.77/9.76 (symdiffI1) => 71.77/9.76 (( 71.77/9.76 (symdiffI2) => 71.77/9.76 (( 71.77/9.76 (symdiffIneg1) => 71.77/9.76 (( 71.77/9.76 (symdiffIneg2) => 71.77/9.76 (( 71.77/9.76 (secondinupair) => 71.77/9.76 (( 71.77/9.76 (setukpairIL) => 71.77/9.76 (( 71.77/9.76 (setukpairIR) => 71.77/9.76 (( 71.77/9.76 (kpairiskpair) => 71.77/9.76 (( 71.77/9.76 (kpairp) => 71.77/9.76 (( 71.77/9.76 (singletonsubset) => 71.77/9.76 (( 71.77/9.76 (singletoninpowerset) => 71.77/9.76 (( 71.77/9.76 (singletoninpowunion) => 71.77/9.76 (( 71.77/9.76 (upairset2E) => 71.77/9.76 (( 71.77/9.76 (upairsubunion) => 71.77/9.76 (( 71.77/9.76 (upairinpowunion) => 71.77/9.76 (( 71.77/9.76 (ubforcartprodlem1) => 71.77/9.76 (( 71.77/9.76 (ubforcartprodlem2) => 71.77/9.76 (( 71.77/9.76 (ubforcartprodlem3) => 71.77/9.76 (( 71.77/9.76 (cartprodpairin) => 71.77/9.76 (( 71.77/9.76 (cartprodmempair1) => 71.77/9.76 (( 71.77/9.76 (cartprodmempair) => 71.77/9.76 (( 71.77/9.76 (setunionE2) => 71.77/9.76 (( 71.77/9.76 (setunionsingleton1) => 71.77/9.76 (( 71.77/9.76 (setunionsingleton2) => 71.77/9.76 (( 71.77/9.76 (setunionsingleton) => 71.77/9.76 (( 71.77/9.76 (singletonprop) => 71.77/9.76 (( 71.77/9.76 (ex1E1) => 71.77/9.76 (( 71.77/9.76 (ex1I) => 71.77/9.76 (( 71.77/9.76 (ex1I2) => 71.77/9.76 (( 71.77/9.76 (singletonsuniq) => 71.77/9.76 (( 71.77/9.76 (setukpairinjL1) => 71.77/9.76 (( 71.77/9.76 (kfstsingleton) => 71.77/9.76 (( 71.77/9.76 (theprop) => 71.77/9.76 (( 71.77/9.76 (kfstpairEq) => 71.77/9.76 (( 71.77/9.76 (cartprodfstin) => 71.77/9.76 (( 71.77/9.76 (setukpairinjL2) => 71.77/9.76 (( 71.77/9.76 (setukpairinjL) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR11) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR12) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR1) => 71.77/9.76 (( 71.77/9.76 (upairequniteq) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR2) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR) => 71.77/9.76 (( 71.77/9.76 (ksndsingleton) => 71.77/9.76 (( 71.77/9.76 (ksndpairEq) => 71.77/9.76 (( 71.77/9.76 (kpairsurjEq) => 71.77/9.76 (( 71.77/9.76 (cartprodsndin) => 71.77/9.76 (( 71.77/9.76 (cartprodpairmemEL) => 71.77/9.76 (( 71.77/9.76 (cartprodpairmemER) => 71.77/9.76 (( 71.77/9.76 (cartprodmempaircEq) => 71.77/9.76 (( 71.77/9.76 (cartprodfstpairEq) => 71.77/9.76 (( 71.77/9.76 (cartprodsndpairEq) => 71.77/9.76 (( 71.77/9.76 (cartprodpairsurjEq) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrI) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrSub) => 71.77/9.76 (( 71.77/9.76 (setOfPairsIsBReln) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrERa) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrEL1) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrEL2) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrER) => 71.77/9.76 (( 71.77/9.76 (funcImageSingleton) => 71.77/9.76 (( 71.77/9.76 (apProp) => 71.77/9.76 (( 71.77/9.76 (app) => 71.77/9.76 (( 71.77/9.76 (infuncsetfunc) => 71.77/9.76 (( 71.77/9.76 (ap2p) => 71.77/9.76 (( 71.77/9.76 (funcinfuncset) => 71.77/9.76 (( 71.77/9.76 (lamProp) => 71.77/9.76 (( 71.77/9.76 (lamp) => 71.77/9.76 (( 71.77/9.76 (lam2p) => 71.77/9.76 (( 71.77/9.76 (brelnall1) => 71.77/9.76 (( 71.77/9.76 (brelnall2) => 71.77/9.76 (( 71.77/9.76 (ex1E2) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp1) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp3) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp2) => 71.77/9.76 (( 71.77/9.76 (funcextLem) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp4) => 71.77/9.76 (( 71.77/9.76 (subbreln) => 71.77/9.76 (( 71.77/9.76 (eqbreln) => 71.77/9.76 (( 71.77/9.76 (funcext) => 71.77/9.76 (( 71.77/9.76 (funcext2) => 71.77/9.76 (( 71.77/9.76 (ap2apEq1) => 71.77/9.76 (( 71.77/9.76 (ap2apEq2) => 71.77/9.76 (( 71.77/9.76 (beta1) => 71.77/9.76 (( 71.77/9.76 (eta1) => 71.77/9.76 (( 71.77/9.76 (lam2lamEq) => 71.77/9.76 (( 71.77/9.76 (beta2) => 71.77/9.76 (( 71.77/9.76 (eta2) => 71.77/9.76 (( 71.77/9.76 (iffalseProp1) => 71.77/9.76 (( 71.77/9.76 (iffalseProp2) => 71.77/9.76 (( 71.77/9.76 (iftrueProp1) => 71.77/9.76 (( 71.77/9.76 (iftrueProp2) => 71.77/9.76 (( 71.77/9.76 (ifSingleton) => 71.77/9.76 (( 71.77/9.76 (ifp) => 71.77/9.76 (( 71.77/9.76 (theeq) => 71.77/9.76 (( 71.77/9.76 (iftrue) => 71.77/9.76 (( 71.77/9.76 (iffalse) => 71.77/9.76 (( 71.77/9.76 (iftrueorfalse) => 71.77/9.76 (( 71.77/9.76 (binintersectT_lem) => 71.77/9.76 (( 71.77/9.76 (binunionT_lem) => 71.77/9.76 (( 71.77/9.76 (powersetT_lem) => 71.77/9.76 (( 71.77/9.76 (setminusT_lem) => 71.77/9.76 (( 71.77/9.76 (complementT_lem) => 71.77/9.76 (( 71.77/9.76 (setextT) => 71.77/9.76 (( 71.77/9.76 (subsetTI) => 71.77/9.76 (( 71.77/9.76 (powersetTI1) => 71.77/9.76 (( 71.77/9.76 (powersetTE1) => 71.77/9.76 (( 71.77/9.76 (complementTI1) => 71.77/9.76 (( 71.77/9.76 (complementTE1) => 71.77/9.76 (( 71.77/9.76 (binintersectTELcontra) => 71.77/9.76 (( 71.77/9.76 (binintersectTERcontra) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT1) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT2) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT3) => 71.77/9.76 (( 71.77/9.76 (doubleComplementI1) => 71.77/9.76 (( 71.77/9.76 (doubleComplementE1) => 71.77/9.76 (( 71.77/9.76 (doubleComplementSub1) => 71.77/9.76 (( 71.77/9.76 (doubleComplementSub2) => 71.77/9.76 (( 71.77/9.76 (doubleComplementEq) => 71.77/9.76 (( 71.77/9.76 (complementTnotintersectT) => 71.77/9.76 (( 71.77/9.76 (complementImpComplementIntersect) => 71.77/9.76 (( 71.77/9.76 (complementSubsetComplementIntersect) => 71.77/9.76 (( 71.77/9.76 (complementInPowersetComplementIntersect) => 71.77/9.76 (( 71.77/9.76 (contraSubsetComplement) => 71.77/9.76 (( 71.77/9.76 (complementTcontraSubset) => 71.77/9.76 (( 71.77/9.76 (binunionTILcontra) => 71.77/9.76 (( 71.77/9.76 (binunionTIRcontra) => 71.77/9.76 (( 71.77/9.76 (inIntersectImpInUnion) => 71.77/9.76 (( 71.77/9.76 (inIntersectImpInUnion2) => 71.77/9.76 (( 71.77/9.76 (inIntersectImpInIntersectUnions) => 71.77/9.76 (( 71.77/9.76 (intersectInPowersetIntersectUnions) => 71.77/9.76 (( 71.77/9.76 (inComplementUnionImpNotIn1) => 71.77/9.76 (( 71.77/9.76 (inComplementUnionImpInComplement1) => 71.77/9.76 (( 71.77/9.76 (binunionTE) => 71.77/9.76 (( 71.77/9.76 (binunionTEcontra) => 71.77/9.76 (( 71.77/9.76 (demorgan2a1) => 71.77/9.76 (( 71.77/9.76 (complementUnionInPowersetComplement) => 71.77/9.76 (( 71.77/9.76 (demorgan2a2) => 71.77/9.76 (( 71.77/9.76 (demorgan1a) => 71.77/9.76 (( 71.77/9.76 (demorgan1b) => 71.77/9.76 (( 71.77/9.76 (demorgan1) => 71.77/9.76 (( 71.77/9.76 (demorgan2a) => 71.77/9.76 (( 71.77/9.76 (demorgan2b2) => 71.77/9.76 (( 71.77/9.76 (demorgan2b) => 71.77/9.76 (( 71.77/9.76 (demorgan2) => 71.77/9.76 (( 71.77/9.76 (woz13rule0) => 71.77/9.76 (( 71.77/9.76 (woz13rule1) => 71.77/9.76 (( 71.77/9.76 (woz13rule2) => 71.77/9.76 (( 71.77/9.76 (woz13rule3) => 71.77/9.76 (( 71.77/9.76 (woz13rule4) => 71.77/9.76 (( 71.77/9.76 (woz1_1) => 71.77/9.76 (( 71.77/9.76 (woz1_2) => 71.77/9.76 (( 71.77/9.76 (woz1_3) => 71.77/9.76 (( 71.77/9.76 (woz1_4) => 71.77/9.76 (( 71.77/9.76 (woz1_5) => 71.77/9.76 (( 71.77/9.76 (breln1all2) => 71.77/9.76 (( 71.77/9.76 (breln1SetBreln1) => 71.77/9.76 (( 71.77/9.76 (choice2fnsingleton) => 71.77/9.76 (( 71.77/9.76 (setOfPairsIsBReln1) => 71.77/9.76 (( 71.77/9.76 (breln1all1) => 71.77/9.76 (( 71.77/9.76 (subbreln1) => 71.77/9.76 (( 71.77/9.76 (eqbreln1) => 71.77/9.76 (( 71.77/9.76 (breln1invprop) => 71.77/9.76 (( 71.77/9.76 (breln1invI) => 71.77/9.76 (( 71.77/9.76 (breln1invE) => 71.77/9.76 (( 71.77/9.76 (breln1compprop) => 71.77/9.76 (( 71.77/9.76 (breln1compI) => 71.77/9.76 (( 71.77/9.76 (breln1compE) => 71.77/9.76 (( 71.77/9.76 (breln1compEex) => 71.77/9.76 (( 71.77/9.76 (!!) @ ( 71.77/9.76 (('#B') @ ( 71.77/9.76 !!) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#S') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#S') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 =>))) @ 71.77/9.76 breln1)))) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 !!))) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#S') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#B') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#S') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 =>))) @ 71.77/9.76 breln1)))))) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#C') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#B') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#B') @ 71.77/9.76 breln1)))) @ 71.77/9.76 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])). 71.77/9.76 thf(zip_derived_cl458, plain, 71.77/9.76 (~ (((notinsingleton) => 71.77/9.76 (((eqinunit) => 71.77/9.76 (((singletonsswitch) => 71.77/9.76 (((upairsetE) => 71.77/9.76 (((upairsetIL) => 71.77/9.76 (((upairsetIR) => 71.77/9.76 (((emptyE1) => 71.77/9.76 (((vacuousDall) => 71.77/9.76 (((quantDeMorgan1) => 71.77/9.76 (((quantDeMorgan2) => 71.77/9.76 (((quantDeMorgan3) => 71.77/9.76 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71.77/9.76 (( 71.77/9.76 (binintersectSubset3) => 71.77/9.76 (( 71.77/9.76 (binintersectER) => 71.77/9.76 (( 71.77/9.76 (disjointsetsI1) => 71.77/9.76 (( 71.77/9.76 (binintersectRsub) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset4) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset1) => 71.77/9.76 (( 71.77/9.76 (bs114d) => 71.77/9.76 (( 71.77/9.76 (setminusI) => 71.77/9.76 (( 71.77/9.76 (setminusEL) => 71.77/9.76 (( 71.77/9.76 (setminusER) => 71.77/9.76 (( 71.77/9.76 (setminusSubset2) => 71.77/9.76 (( 71.77/9.76 (setminusERneg) => 71.77/9.76 (( 71.77/9.76 (setminusELneg) => 71.77/9.76 (( 71.77/9.76 (setminusILneg) => 71.77/9.76 (( 71.77/9.76 (setminusIRneg) => 71.77/9.76 (( 71.77/9.76 (setminusLsub) => 71.77/9.76 (( 71.77/9.76 (setminusSubset1) => 71.77/9.76 (( 71.77/9.76 (symdiffE) => 71.77/9.76 (( 71.77/9.76 (symdiffI1) => 71.77/9.76 (( 71.77/9.76 (symdiffI2) => 71.77/9.76 (( 71.77/9.76 (symdiffIneg1) => 71.77/9.76 (( 71.77/9.76 (symdiffIneg2) => 71.77/9.76 (( 71.77/9.76 (secondinupair) => 71.77/9.76 (( 71.77/9.76 (setukpairIL) => 71.77/9.76 (( 71.77/9.76 (setukpairIR) => 71.77/9.76 (( 71.77/9.76 (kpairiskpair) => 71.77/9.76 (( 71.77/9.76 (kpairp) => 71.77/9.76 (( 71.77/9.76 (singletonsubset) => 71.77/9.76 (( 71.77/9.76 (singletoninpowerset) => 71.77/9.76 (( 71.77/9.76 (singletoninpowunion) => 71.77/9.76 (( 71.77/9.76 (upairset2E) => 71.77/9.76 (( 71.77/9.76 (upairsubunion) => 71.77/9.76 (( 71.77/9.76 (upairinpowunion) => 71.77/9.76 (( 71.77/9.76 (ubforcartprodlem1) => 71.77/9.76 (( 71.77/9.76 (ubforcartprodlem2) => 71.77/9.76 (( 71.77/9.76 (ubforcartprodlem3) => 71.77/9.76 (( 71.77/9.76 (cartprodpairin) => 71.77/9.76 (( 71.77/9.76 (cartprodmempair1) => 71.77/9.76 (( 71.77/9.76 (cartprodmempair) => 71.77/9.76 (( 71.77/9.76 (setunionE2) => 71.77/9.76 (( 71.77/9.76 (setunionsingleton1) => 71.77/9.76 (( 71.77/9.76 (setunionsingleton2) => 71.77/9.76 (( 71.77/9.76 (setunionsingleton) => 71.77/9.76 (( 71.77/9.76 (singletonprop) => 71.77/9.76 (( 71.77/9.76 (ex1E1) => 71.77/9.76 (( 71.77/9.76 (ex1I) => 71.77/9.76 (( 71.77/9.76 (ex1I2) => 71.77/9.76 (( 71.77/9.76 (singletonsuniq) => 71.77/9.76 (( 71.77/9.76 (setukpairinjL1) => 71.77/9.76 (( 71.77/9.76 (kfstsingleton) => 71.77/9.76 (( 71.77/9.76 (theprop) => 71.77/9.76 (( 71.77/9.76 (kfstpairEq) => 71.77/9.76 (( 71.77/9.76 (cartprodfstin) => 71.77/9.76 (( 71.77/9.76 (setukpairinjL2) => 71.77/9.76 (( 71.77/9.76 (setukpairinjL) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR11) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR12) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR1) => 71.77/9.76 (( 71.77/9.76 (upairequniteq) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR2) => 71.77/9.76 (( 71.77/9.76 (setukpairinjR) => 71.77/9.76 (( 71.77/9.76 (ksndsingleton) => 71.77/9.76 (( 71.77/9.76 (ksndpairEq) => 71.77/9.76 (( 71.77/9.76 (kpairsurjEq) => 71.77/9.76 (( 71.77/9.76 (cartprodsndin) => 71.77/9.76 (( 71.77/9.76 (cartprodpairmemEL) => 71.77/9.76 (( 71.77/9.76 (cartprodpairmemER) => 71.77/9.76 (( 71.77/9.76 (cartprodmempaircEq) => 71.77/9.76 (( 71.77/9.76 (cartprodfstpairEq) => 71.77/9.76 (( 71.77/9.76 (cartprodsndpairEq) => 71.77/9.76 (( 71.77/9.76 (cartprodpairsurjEq) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrI) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrSub) => 71.77/9.76 (( 71.77/9.76 (setOfPairsIsBReln) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrERa) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrEL1) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrEL2) => 71.77/9.76 (( 71.77/9.76 (dpsetconstrER) => 71.77/9.76 (( 71.77/9.76 (funcImageSingleton) => 71.77/9.76 (( 71.77/9.76 (apProp) => 71.77/9.76 (( 71.77/9.76 (app) => 71.77/9.76 (( 71.77/9.76 (infuncsetfunc) => 71.77/9.76 (( 71.77/9.76 (ap2p) => 71.77/9.76 (( 71.77/9.76 (funcinfuncset) => 71.77/9.76 (( 71.77/9.76 (lamProp) => 71.77/9.76 (( 71.77/9.76 (lamp) => 71.77/9.76 (( 71.77/9.76 (lam2p) => 71.77/9.76 (( 71.77/9.76 (brelnall1) => 71.77/9.76 (( 71.77/9.76 (brelnall2) => 71.77/9.76 (( 71.77/9.76 (ex1E2) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp1) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp3) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp2) => 71.77/9.76 (( 71.77/9.76 (funcextLem) => 71.77/9.76 (( 71.77/9.76 (funcGraphProp4) => 71.77/9.76 (( 71.77/9.76 (subbreln) => 71.77/9.76 (( 71.77/9.76 (eqbreln) => 71.77/9.76 (( 71.77/9.76 (funcext) => 71.77/9.76 (( 71.77/9.76 (funcext2) => 71.77/9.76 (( 71.77/9.76 (ap2apEq1) => 71.77/9.76 (( 71.77/9.76 (ap2apEq2) => 71.77/9.76 (( 71.77/9.76 (beta1) => 71.77/9.76 (( 71.77/9.76 (eta1) => 71.77/9.76 (( 71.77/9.76 (lam2lamEq) => 71.77/9.76 (( 71.77/9.76 (beta2) => 71.77/9.76 (( 71.77/9.76 (eta2) => 71.77/9.76 (( 71.77/9.76 (iffalseProp1) => 71.77/9.76 (( 71.77/9.76 (iffalseProp2) => 71.77/9.76 (( 71.77/9.76 (iftrueProp1) => 71.77/9.76 (( 71.77/9.76 (iftrueProp2) => 71.77/9.76 (( 71.77/9.76 (ifSingleton) => 71.77/9.76 (( 71.77/9.76 (ifp) => 71.77/9.76 (( 71.77/9.76 (theeq) => 71.77/9.76 (( 71.77/9.76 (iftrue) => 71.77/9.76 (( 71.77/9.76 (iffalse) => 71.77/9.76 (( 71.77/9.76 (iftrueorfalse) => 71.77/9.76 (( 71.77/9.76 (binintersectT_lem) => 71.77/9.76 (( 71.77/9.76 (binunionT_lem) => 71.77/9.76 (( 71.77/9.76 (powersetT_lem) => 71.77/9.76 (( 71.77/9.76 (setminusT_lem) => 71.77/9.76 (( 71.77/9.76 (complementT_lem) => 71.77/9.76 (( 71.77/9.76 (setextT) => 71.77/9.76 (( 71.77/9.76 (subsetTI) => 71.77/9.76 (( 71.77/9.76 (powersetTI1) => 71.77/9.76 (( 71.77/9.76 (powersetTE1) => 71.77/9.76 (( 71.77/9.76 (complementTI1) => 71.77/9.76 (( 71.77/9.76 (complementTE1) => 71.77/9.76 (( 71.77/9.76 (binintersectTELcontra) => 71.77/9.76 (( 71.77/9.76 (binintersectTERcontra) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT1) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT2) => 71.77/9.76 (( 71.77/9.76 (contrasubsetT3) => 71.77/9.76 (( 71.77/9.76 (doubleComplementI1) => 71.77/9.76 (( 71.77/9.76 (doubleComplementE1) => 71.77/9.76 (( 71.77/9.76 (doubleComplementSub1) => 71.77/9.76 (( 71.77/9.76 (doubleComplementSub2) => 71.77/9.76 (( 71.77/9.76 (doubleComplementEq) => 71.77/9.76 (( 71.77/9.76 (complementTnotintersectT) => 71.77/9.76 (( 71.77/9.76 (complementImpComplementIntersect) => 71.77/9.76 (( 71.77/9.76 (complementSubsetComplementIntersect) => 71.77/9.76 (( 71.77/9.76 (complementInPowersetComplementIntersect) => 71.77/9.76 (( 71.77/9.76 (contraSubsetComplement) => 71.77/9.76 (( 71.77/9.76 (complementTcontraSubset) => 71.77/9.76 (( 71.77/9.76 (binunionTILcontra) => 71.77/9.76 (( 71.77/9.76 (binunionTIRcontra) => 71.77/9.76 (( 71.77/9.76 (inIntersectImpInUnion) => 71.77/9.76 (( 71.77/9.76 (inIntersectImpInUnion2) => 71.77/9.76 (( 71.77/9.76 (inIntersectImpInIntersectUnions) => 71.77/9.76 (( 71.77/9.76 (intersectInPowersetIntersectUnions) => 71.77/9.76 (( 71.77/9.76 (inComplementUnionImpNotIn1) => 71.77/9.76 (( 71.77/9.76 (inComplementUnionImpInComplement1) => 71.77/9.76 (( 71.77/9.76 (binunionTE) => 71.77/9.76 (( 71.77/9.76 (binunionTEcontra) => 71.77/9.76 (( 71.77/9.76 (demorgan2a1) => 71.77/9.76 (( 71.77/9.76 (complementUnionInPowersetComplement) => 71.77/9.76 (( 71.77/9.76 (demorgan2a2) => 71.77/9.76 (( 71.77/9.76 (demorgan1a) => 71.77/9.76 (( 71.77/9.76 (demorgan1b) => 71.77/9.76 (( 71.77/9.76 (demorgan1) => 71.77/9.76 (( 71.77/9.76 (demorgan2a) => 71.77/9.76 (( 71.77/9.76 (demorgan2b2) => 71.77/9.76 (( 71.77/9.76 (demorgan2b) => 71.77/9.76 (( 71.77/9.76 (demorgan2) => 71.77/9.76 (( 71.77/9.76 (woz13rule0) => 71.77/9.76 (( 71.77/9.76 (woz13rule1) => 71.77/9.76 (( 71.77/9.76 (woz13rule2) => 71.77/9.76 (( 71.77/9.76 (woz13rule3) => 71.77/9.76 (( 71.77/9.76 (woz13rule4) => 71.77/9.76 (( 71.77/9.76 (woz1_1) => 71.77/9.76 (( 71.77/9.76 (woz1_2) => 71.77/9.76 (( 71.77/9.76 (woz1_3) => 71.77/9.76 (( 71.77/9.76 (woz1_4) => 71.77/9.76 (( 71.77/9.76 (woz1_5) => 71.77/9.76 (( 71.77/9.76 (breln1all2) => 71.77/9.76 (( 71.77/9.76 (breln1SetBreln1) => 71.77/9.76 (( 71.77/9.76 (choice2fnsingleton) => 71.77/9.76 (( 71.77/9.76 (setOfPairsIsBReln1) => 71.77/9.76 (( 71.77/9.76 (breln1all1) => 71.77/9.76 (( 71.77/9.76 (subbreln1) => 71.77/9.76 (( 71.77/9.76 (eqbreln1) => 71.77/9.76 (( 71.77/9.76 (breln1invprop) => 71.77/9.76 (( 71.77/9.76 (breln1invI) => 71.77/9.76 (( 71.77/9.76 (breln1invE) => 71.77/9.76 (( 71.77/9.76 (breln1compprop) => 71.77/9.76 (( 71.77/9.76 (breln1compI) => 71.77/9.76 (( 71.77/9.76 (breln1compE) => 71.77/9.76 (( 71.77/9.76 (breln1compEex) => 71.77/9.76 (( 71.77/9.76 (!!) @ ( 71.77/9.76 (('#B') @ ( 71.77/9.76 !!) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#S') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#S') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 =>))) @ 71.77/9.76 breln1)))) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 !!))) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#S') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#B') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#S') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 =>))) @ 71.77/9.76 breln1)))))) @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#C') @ ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#B') @ 71.77/9.76 ( 71.77/9.76 ( 71.77/9.76 ('#B') @ ( 71.77/9.76 '#B') @ 71.77/9.76 breln1)))) @ 71.77/9.76 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])). 71.77/9.76 thf(zip_derived_cl467, plain, 71.77/9.76 (~ (((eqinunit) => 71.77/9.76 (((singletonsswitch) => 71.77/9.76 (((upairsetE) => 71.77/9.76 (((upairsetIL) => 71.77/9.76 (((upairsetIR) => 71.77/9.76 (((emptyE1) => 71.77/9.76 (((vacuousDall) => 71.77/9.76 (((quantDeMorgan1) => 71.77/9.76 (((quantDeMorgan2) => 71.77/9.76 (((quantDeMorgan3) => 71.77/9.76 (((quantDeMorgan4) => 71.77/9.76 (((prop2setI) => 71.77/9.76 (((prop2set2propI) => 71.77/9.76 (((notdexE) => 71.77/9.76 (((notdallE) => 71.77/9.76 (((exuI1) => 71.77/9.76 (((exuI3) => 71.77/9.76 (((exuI2) => 71.77/9.76 (((inCongP) => 71.77/9.76 (((in__Cong) => 71.77/9.76 (((exuE3u) => 71.77/9.76 (((exu__Cong) => 71.77/9.76 (((setadjoin__Cong) => 71.77/9.76 (((powerset__Cong) => 71.77/9.76 (((setunion__Cong) => 71.77/9.76 (((exuEu) => 71.77/9.76 (((descr__Cong) => 71.77/9.76 (((dsetconstr__Cong) => 71.77/9.76 (((subsetI1) => 71.77/9.76 (((eqimpsubset2) => 71.77/9.76 (( 71.77/9.76 (eqimpsubset1) => 71.77/9.76 (( 71.77/9.76 (subsetI2) => 71.77/9.76 (( 71.77/9.76 (emptysetsubset) => 71.77/9.76 (( 71.77/9.76 (subsetE) => 71.77/9.76 (( 71.77/9.76 (subsetE2) => 71.77/9.76 (( 71.77/9.76 (notsubsetI) => 71.77/9.76 (( 71.77/9.76 (notequalI1) => 71.77/9.76 (( 71.77/9.76 (notequalI2) => 71.77/9.76 (( 71.77/9.76 (subsetRefl) => 71.77/9.76 (( 71.77/9.76 (subsetTrans) => 71.77/9.76 (( 71.77/9.76 (setadjoinSub) => 71.77/9.76 (( 71.77/9.76 (setadjoinSub2) => 71.77/9.76 (( 71.77/9.76 (subset2powerset) => 71.77/9.76 (( 71.77/9.76 (setextsub) => 71.77/9.76 (( 71.77/9.76 (subsetemptysetimpeq) => 71.77/9.76 (( 71.77/9.76 (powersetI1) => 71.77/9.76 (( 71.77/9.76 (powersetE1) => 71.77/9.76 (( 71.77/9.76 (inPowerset) => 71.77/9.76 (( 71.77/9.76 (powersetsubset) => 71.77/9.76 (( 71.77/9.76 (sepInPowerset) => 71.77/9.76 (( 71.77/9.76 (sepSubset) => 71.77/9.76 (( 71.77/9.76 (binunionIL) => 71.77/9.76 (( 71.77/9.76 (upairset2IR) => 71.77/9.76 (( 71.77/9.76 (binunionIR) => 71.77/9.76 (( 71.77/9.76 (binunionEcases) => 71.77/9.76 (( 71.77/9.76 (binunionE) => 71.77/9.76 (( 71.77/9.76 (binunionLsub) => 71.77/9.76 (( 71.77/9.76 (binunionRsub) => 71.77/9.76 (( 71.77/9.76 (binintersectI) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset5) => 71.77/9.76 (( 71.77/9.76 (binintersectEL) => 71.77/9.76 (( 71.77/9.76 (binintersectLsub) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset2) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset3) => 71.77/9.76 (( 71.77/9.76 (binintersectER) => 71.77/9.76 (( 71.77/9.76 (disjointsetsI1) => 71.77/9.76 (( 71.77/9.76 (binintersectRsub) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset4) => 71.77/9.76 (( 71.77/9.76 (binintersectSubset1) => 71.77/9.76 (( 71.77/9.76 (bs114d) => 71.77/9.76 (( 71.77/9.76 (setminusI) => 71.77/9.76 (( 71.77/9.76 (setminusEL) => 71.77/9.76 (( 71.77/9.76 (setminusER) => 71.77/9.76 (( 71.77/9.76 (setminusSubset2) => 71.77/9.76 (( 71.77/9.76 (setminusERneg) => 71.77/9.76 (( 71.77/9.76 (setminusELneg) => 71.77/9.76 (( 71.77/9.76 (setminusILneg) => 71.77/9.76 (( 71.77/9.76 (setminusIRneg) => 71.77/9.76 (( 71.77/9.76 (setminusLsub) => 71.77/9.76 (( 71.77/9.76 (setminusSubset1) => 71.77/9.76 (( 71.77/9.76 (symdiffE) => 71.77/9.76 (( 71.77/9.76 (symdiffI1) => 71.77/9.76 (( 71.77/9.76 (symdiffI2) => 71.77/9.76 (( 71.77/9.76 (symdiffIneg1) => 71.77/9.76 (( 71.77/9.76 (symdiffIneg2) => 71.77/9.76 (( 71.77/9.76 (secondinupair) => 71.77/9.76 (( 71.77/9.76 (setukpairIL) => 71.77/9.77 (( 71.77/9.77 (setukpairIR) => 71.77/9.77 (( 71.77/9.77 (kpairiskpair) => 71.77/9.77 (( 71.77/9.77 (kpairp) => 71.77/9.77 (( 71.77/9.77 (singletonsubset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowerset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowunion) => 71.77/9.77 (( 71.77/9.77 (upairset2E) => 71.77/9.77 (( 71.77/9.77 (upairsubunion) => 71.77/9.77 (( 71.77/9.77 (upairinpowunion) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem1) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem2) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem3) => 71.77/9.77 (( 71.77/9.77 (cartprodpairin) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair1) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair) => 71.77/9.77 (( 71.77/9.77 (setunionE2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton1) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton) => 71.77/9.77 (( 71.77/9.77 (singletonprop) => 71.77/9.77 (( 71.77/9.77 (ex1E1) => 71.77/9.77 (( 71.77/9.77 (ex1I) => 71.77/9.77 (( 71.77/9.77 (ex1I2) => 71.77/9.77 (( 71.77/9.77 (singletonsuniq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL1) => 71.77/9.77 (( 71.77/9.77 (kfstsingleton) => 71.77/9.77 (( 71.77/9.77 (theprop) => 71.77/9.77 (( 71.77/9.77 (kfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstin) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR11) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR12) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR1) => 71.77/9.77 (( 71.77/9.77 (upairequniteq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR) => 71.77/9.77 (( 71.77/9.77 (ksndsingleton) => 71.77/9.77 (( 71.77/9.77 (ksndpairEq) => 71.77/9.77 (( 71.77/9.77 (kpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndin) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemEL) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemER) => 71.77/9.77 (( 71.77/9.77 (cartprodmempaircEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrI) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrSub) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrERa) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL1) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL2) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrER) => 71.77/9.77 (( 71.77/9.77 (funcImageSingleton) => 71.77/9.77 (( 71.77/9.77 (apProp) => 71.77/9.77 (( 71.77/9.77 (app) => 71.77/9.77 (( 71.77/9.77 (infuncsetfunc) => 71.77/9.77 (( 71.77/9.77 (ap2p) => 71.77/9.77 (( 71.77/9.77 (funcinfuncset) => 71.77/9.77 (( 71.77/9.77 (lamProp) => 71.77/9.77 (( 71.77/9.77 (lamp) => 71.77/9.77 (( 71.77/9.77 (lam2p) => 71.77/9.77 (( 71.77/9.77 (brelnall1) => 71.77/9.77 (( 71.77/9.77 (brelnall2) => 71.77/9.77 (( 71.77/9.77 (ex1E2) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp1) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp3) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp2) => 71.77/9.77 (( 71.77/9.77 (funcextLem) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp4) => 71.77/9.77 (( 71.77/9.77 (subbreln) => 71.77/9.77 (( 71.77/9.77 (eqbreln) => 71.77/9.77 (( 71.77/9.77 (funcext) => 71.77/9.77 (( 71.77/9.77 (funcext2) => 71.77/9.77 (( 71.77/9.77 (ap2apEq1) => 71.77/9.77 (( 71.77/9.77 (ap2apEq2) => 71.77/9.77 (( 71.77/9.77 (beta1) => 71.77/9.77 (( 71.77/9.77 (eta1) => 71.77/9.77 (( 71.77/9.77 (lam2lamEq) => 71.77/9.77 (( 71.77/9.77 (beta2) => 71.77/9.77 (( 71.77/9.77 (eta2) => 71.77/9.77 (( 71.77/9.77 (iffalseProp1) => 71.77/9.77 (( 71.77/9.77 (iffalseProp2) => 71.77/9.77 (( 71.77/9.77 (iftrueProp1) => 71.77/9.77 (( 71.77/9.77 (iftrueProp2) => 71.77/9.77 (( 71.77/9.77 (ifSingleton) => 71.77/9.77 (( 71.77/9.77 (ifp) => 71.77/9.77 (( 71.77/9.77 (theeq) => 71.77/9.77 (( 71.77/9.77 (iftrue) => 71.77/9.77 (( 71.77/9.77 (iffalse) => 71.77/9.77 (( 71.77/9.77 (iftrueorfalse) => 71.77/9.77 (( 71.77/9.77 (binintersectT_lem) => 71.77/9.77 (( 71.77/9.77 (binunionT_lem) => 71.77/9.77 (( 71.77/9.77 (powersetT_lem) => 71.77/9.77 (( 71.77/9.77 (setminusT_lem) => 71.77/9.77 (( 71.77/9.77 (complementT_lem) => 71.77/9.77 (( 71.77/9.77 (setextT) => 71.77/9.77 (( 71.77/9.77 (subsetTI) => 71.77/9.77 (( 71.77/9.77 (powersetTI1) => 71.77/9.77 (( 71.77/9.77 (powersetTE1) => 71.77/9.77 (( 71.77/9.77 (complementTI1) => 71.77/9.77 (( 71.77/9.77 (complementTE1) => 71.77/9.77 (( 71.77/9.77 (binintersectTELcontra) => 71.77/9.77 (( 71.77/9.77 (binintersectTERcontra) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT1) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT2) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT3) => 71.77/9.77 (( 71.77/9.77 (doubleComplementI1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementE1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub2) => 71.77/9.77 (( 71.77/9.77 (doubleComplementEq) => 71.77/9.77 (( 71.77/9.77 (complementTnotintersectT) => 71.77/9.77 (( 71.77/9.77 (complementImpComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementSubsetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementInPowersetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (contraSubsetComplement) => 71.77/9.77 (( 71.77/9.77 (complementTcontraSubset) => 71.77/9.77 (( 71.77/9.77 (binunionTILcontra) => 71.77/9.77 (( 71.77/9.77 (binunionTIRcontra) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion2) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (intersectInPowersetIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpNotIn1) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpInComplement1) => 71.77/9.77 (( 71.77/9.77 (binunionTE) => 71.77/9.77 (( 71.77/9.77 (binunionTEcontra) => 71.77/9.77 (( 71.77/9.77 (demorgan2a1) => 71.77/9.77 (( 71.77/9.77 (complementUnionInPowersetComplement) => 71.77/9.77 (( 71.77/9.77 (demorgan2a2) => 71.77/9.77 (( 71.77/9.77 (demorgan1a) => 71.77/9.77 (( 71.77/9.77 (demorgan1b) => 71.77/9.77 (( 71.77/9.77 (demorgan1) => 71.77/9.77 (( 71.77/9.77 (demorgan2a) => 71.77/9.77 (( 71.77/9.77 (demorgan2b2) => 71.77/9.77 (( 71.77/9.77 (demorgan2b) => 71.77/9.77 (( 71.77/9.77 (demorgan2) => 71.77/9.77 (( 71.77/9.77 (woz13rule0) => 71.77/9.77 (( 71.77/9.77 (woz13rule1) => 71.77/9.77 (( 71.77/9.77 (woz13rule2) => 71.77/9.77 (( 71.77/9.77 (woz13rule3) => 71.77/9.77 (( 71.77/9.77 (woz13rule4) => 71.77/9.77 (( 71.77/9.77 (woz1_1) => 71.77/9.77 (( 71.77/9.77 (woz1_2) => 71.77/9.77 (( 71.77/9.77 (woz1_3) => 71.77/9.77 (( 71.77/9.77 (woz1_4) => 71.77/9.77 (( 71.77/9.77 (woz1_5) => 71.77/9.77 (( 71.77/9.77 (breln1all2) => 71.77/9.77 (( 71.77/9.77 (breln1SetBreln1) => 71.77/9.77 (( 71.77/9.77 (choice2fnsingleton) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln1) => 71.77/9.77 (( 71.77/9.77 (breln1all1) => 71.77/9.77 (( 71.77/9.77 (subbreln1) => 71.77/9.77 (( 71.77/9.77 (eqbreln1) => 71.77/9.77 (( 71.77/9.77 (breln1invprop) => 71.77/9.77 (( 71.77/9.77 (breln1invI) => 71.77/9.77 (( 71.77/9.77 (breln1invE) => 71.77/9.77 (( 71.77/9.77 (breln1compprop) => 71.77/9.77 (( 71.77/9.77 (breln1compI) => 71.77/9.77 (( 71.77/9.77 (breln1compE) => 71.77/9.77 (( 71.77/9.77 (breln1compEex) => 71.77/9.77 (( 71.77/9.77 (!!) @ ( 71.77/9.77 (('#B') @ ( 71.77/9.77 !!) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 !!))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#C') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 breln1)))) @ 71.77/9.77 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl458])). 71.77/9.77 thf(zip_derived_cl475, plain, 71.77/9.77 (~ (((singletonsswitch) => 71.77/9.77 (((upairsetE) => 71.77/9.77 (((upairsetIL) => 71.77/9.77 (((upairsetIR) => 71.77/9.77 (((emptyE1) => 71.77/9.77 (((vacuousDall) => 71.77/9.77 (((quantDeMorgan1) => 71.77/9.77 (((quantDeMorgan2) => 71.77/9.77 (((quantDeMorgan3) => 71.77/9.77 (((quantDeMorgan4) => 71.77/9.77 (((prop2setI) => 71.77/9.77 (((prop2set2propI) => 71.77/9.77 (((notdexE) => 71.77/9.77 (((notdallE) => 71.77/9.77 (((exuI1) => 71.77/9.77 (((exuI3) => 71.77/9.77 (((exuI2) => 71.77/9.77 (((inCongP) => 71.77/9.77 (((in__Cong) => 71.77/9.77 (((exuE3u) => 71.77/9.77 (((exu__Cong) => 71.77/9.77 (((setadjoin__Cong) => 71.77/9.77 (((powerset__Cong) => 71.77/9.77 (((setunion__Cong) => 71.77/9.77 (((exuEu) => 71.77/9.77 (((descr__Cong) => 71.77/9.77 (((dsetconstr__Cong) => 71.77/9.77 (((subsetI1) => 71.77/9.77 (((eqimpsubset2) => 71.77/9.77 (((eqimpsubset1) => 71.77/9.77 (( 71.77/9.77 (subsetI2) => 71.77/9.77 (( 71.77/9.77 (emptysetsubset) => 71.77/9.77 (( 71.77/9.77 (subsetE) => 71.77/9.77 (( 71.77/9.77 (subsetE2) => 71.77/9.77 (( 71.77/9.77 (notsubsetI) => 71.77/9.77 (( 71.77/9.77 (notequalI1) => 71.77/9.77 (( 71.77/9.77 (notequalI2) => 71.77/9.77 (( 71.77/9.77 (subsetRefl) => 71.77/9.77 (( 71.77/9.77 (subsetTrans) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub2) => 71.77/9.77 (( 71.77/9.77 (subset2powerset) => 71.77/9.77 (( 71.77/9.77 (setextsub) => 71.77/9.77 (( 71.77/9.77 (subsetemptysetimpeq) => 71.77/9.77 (( 71.77/9.77 (powersetI1) => 71.77/9.77 (( 71.77/9.77 (powersetE1) => 71.77/9.77 (( 71.77/9.77 (inPowerset) => 71.77/9.77 (( 71.77/9.77 (powersetsubset) => 71.77/9.77 (( 71.77/9.77 (sepInPowerset) => 71.77/9.77 (( 71.77/9.77 (sepSubset) => 71.77/9.77 (( 71.77/9.77 (binunionIL) => 71.77/9.77 (( 71.77/9.77 (upairset2IR) => 71.77/9.77 (( 71.77/9.77 (binunionIR) => 71.77/9.77 (( 71.77/9.77 (binunionEcases) => 71.77/9.77 (( 71.77/9.77 (binunionE) => 71.77/9.77 (( 71.77/9.77 (binunionLsub) => 71.77/9.77 (( 71.77/9.77 (binunionRsub) => 71.77/9.77 (( 71.77/9.77 (binintersectI) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset5) => 71.77/9.77 (( 71.77/9.77 (binintersectEL) => 71.77/9.77 (( 71.77/9.77 (binintersectLsub) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset2) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset3) => 71.77/9.77 (( 71.77/9.77 (binintersectER) => 71.77/9.77 (( 71.77/9.77 (disjointsetsI1) => 71.77/9.77 (( 71.77/9.77 (binintersectRsub) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset4) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset1) => 71.77/9.77 (( 71.77/9.77 (bs114d) => 71.77/9.77 (( 71.77/9.77 (setminusI) => 71.77/9.77 (( 71.77/9.77 (setminusEL) => 71.77/9.77 (( 71.77/9.77 (setminusER) => 71.77/9.77 (( 71.77/9.77 (setminusSubset2) => 71.77/9.77 (( 71.77/9.77 (setminusERneg) => 71.77/9.77 (( 71.77/9.77 (setminusELneg) => 71.77/9.77 (( 71.77/9.77 (setminusILneg) => 71.77/9.77 (( 71.77/9.77 (setminusIRneg) => 71.77/9.77 (( 71.77/9.77 (setminusLsub) => 71.77/9.77 (( 71.77/9.77 (setminusSubset1) => 71.77/9.77 (( 71.77/9.77 (symdiffE) => 71.77/9.77 (( 71.77/9.77 (symdiffI1) => 71.77/9.77 (( 71.77/9.77 (symdiffI2) => 71.77/9.77 (( 71.77/9.77 (symdiffIneg1) => 71.77/9.77 (( 71.77/9.77 (symdiffIneg2) => 71.77/9.77 (( 71.77/9.77 (secondinupair) => 71.77/9.77 (( 71.77/9.77 (setukpairIL) => 71.77/9.77 (( 71.77/9.77 (setukpairIR) => 71.77/9.77 (( 71.77/9.77 (kpairiskpair) => 71.77/9.77 (( 71.77/9.77 (kpairp) => 71.77/9.77 (( 71.77/9.77 (singletonsubset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowerset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowunion) => 71.77/9.77 (( 71.77/9.77 (upairset2E) => 71.77/9.77 (( 71.77/9.77 (upairsubunion) => 71.77/9.77 (( 71.77/9.77 (upairinpowunion) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem1) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem2) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem3) => 71.77/9.77 (( 71.77/9.77 (cartprodpairin) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair1) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair) => 71.77/9.77 (( 71.77/9.77 (setunionE2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton1) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton) => 71.77/9.77 (( 71.77/9.77 (singletonprop) => 71.77/9.77 (( 71.77/9.77 (ex1E1) => 71.77/9.77 (( 71.77/9.77 (ex1I) => 71.77/9.77 (( 71.77/9.77 (ex1I2) => 71.77/9.77 (( 71.77/9.77 (singletonsuniq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL1) => 71.77/9.77 (( 71.77/9.77 (kfstsingleton) => 71.77/9.77 (( 71.77/9.77 (theprop) => 71.77/9.77 (( 71.77/9.77 (kfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstin) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR11) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR12) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR1) => 71.77/9.77 (( 71.77/9.77 (upairequniteq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR) => 71.77/9.77 (( 71.77/9.77 (ksndsingleton) => 71.77/9.77 (( 71.77/9.77 (ksndpairEq) => 71.77/9.77 (( 71.77/9.77 (kpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndin) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemEL) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemER) => 71.77/9.77 (( 71.77/9.77 (cartprodmempaircEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrI) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrSub) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrERa) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL1) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL2) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrER) => 71.77/9.77 (( 71.77/9.77 (funcImageSingleton) => 71.77/9.77 (( 71.77/9.77 (apProp) => 71.77/9.77 (( 71.77/9.77 (app) => 71.77/9.77 (( 71.77/9.77 (infuncsetfunc) => 71.77/9.77 (( 71.77/9.77 (ap2p) => 71.77/9.77 (( 71.77/9.77 (funcinfuncset) => 71.77/9.77 (( 71.77/9.77 (lamProp) => 71.77/9.77 (( 71.77/9.77 (lamp) => 71.77/9.77 (( 71.77/9.77 (lam2p) => 71.77/9.77 (( 71.77/9.77 (brelnall1) => 71.77/9.77 (( 71.77/9.77 (brelnall2) => 71.77/9.77 (( 71.77/9.77 (ex1E2) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp1) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp3) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp2) => 71.77/9.77 (( 71.77/9.77 (funcextLem) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp4) => 71.77/9.77 (( 71.77/9.77 (subbreln) => 71.77/9.77 (( 71.77/9.77 (eqbreln) => 71.77/9.77 (( 71.77/9.77 (funcext) => 71.77/9.77 (( 71.77/9.77 (funcext2) => 71.77/9.77 (( 71.77/9.77 (ap2apEq1) => 71.77/9.77 (( 71.77/9.77 (ap2apEq2) => 71.77/9.77 (( 71.77/9.77 (beta1) => 71.77/9.77 (( 71.77/9.77 (eta1) => 71.77/9.77 (( 71.77/9.77 (lam2lamEq) => 71.77/9.77 (( 71.77/9.77 (beta2) => 71.77/9.77 (( 71.77/9.77 (eta2) => 71.77/9.77 (( 71.77/9.77 (iffalseProp1) => 71.77/9.77 (( 71.77/9.77 (iffalseProp2) => 71.77/9.77 (( 71.77/9.77 (iftrueProp1) => 71.77/9.77 (( 71.77/9.77 (iftrueProp2) => 71.77/9.77 (( 71.77/9.77 (ifSingleton) => 71.77/9.77 (( 71.77/9.77 (ifp) => 71.77/9.77 (( 71.77/9.77 (theeq) => 71.77/9.77 (( 71.77/9.77 (iftrue) => 71.77/9.77 (( 71.77/9.77 (iffalse) => 71.77/9.77 (( 71.77/9.77 (iftrueorfalse) => 71.77/9.77 (( 71.77/9.77 (binintersectT_lem) => 71.77/9.77 (( 71.77/9.77 (binunionT_lem) => 71.77/9.77 (( 71.77/9.77 (powersetT_lem) => 71.77/9.77 (( 71.77/9.77 (setminusT_lem) => 71.77/9.77 (( 71.77/9.77 (complementT_lem) => 71.77/9.77 (( 71.77/9.77 (setextT) => 71.77/9.77 (( 71.77/9.77 (subsetTI) => 71.77/9.77 (( 71.77/9.77 (powersetTI1) => 71.77/9.77 (( 71.77/9.77 (powersetTE1) => 71.77/9.77 (( 71.77/9.77 (complementTI1) => 71.77/9.77 (( 71.77/9.77 (complementTE1) => 71.77/9.77 (( 71.77/9.77 (binintersectTELcontra) => 71.77/9.77 (( 71.77/9.77 (binintersectTERcontra) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT1) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT2) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT3) => 71.77/9.77 (( 71.77/9.77 (doubleComplementI1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementE1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub2) => 71.77/9.77 (( 71.77/9.77 (doubleComplementEq) => 71.77/9.77 (( 71.77/9.77 (complementTnotintersectT) => 71.77/9.77 (( 71.77/9.77 (complementImpComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementSubsetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementInPowersetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (contraSubsetComplement) => 71.77/9.77 (( 71.77/9.77 (complementTcontraSubset) => 71.77/9.77 (( 71.77/9.77 (binunionTILcontra) => 71.77/9.77 (( 71.77/9.77 (binunionTIRcontra) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion2) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (intersectInPowersetIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpNotIn1) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpInComplement1) => 71.77/9.77 (( 71.77/9.77 (binunionTE) => 71.77/9.77 (( 71.77/9.77 (binunionTEcontra) => 71.77/9.77 (( 71.77/9.77 (demorgan2a1) => 71.77/9.77 (( 71.77/9.77 (complementUnionInPowersetComplement) => 71.77/9.77 (( 71.77/9.77 (demorgan2a2) => 71.77/9.77 (( 71.77/9.77 (demorgan1a) => 71.77/9.77 (( 71.77/9.77 (demorgan1b) => 71.77/9.77 (( 71.77/9.77 (demorgan1) => 71.77/9.77 (( 71.77/9.77 (demorgan2a) => 71.77/9.77 (( 71.77/9.77 (demorgan2b2) => 71.77/9.77 (( 71.77/9.77 (demorgan2b) => 71.77/9.77 (( 71.77/9.77 (demorgan2) => 71.77/9.77 (( 71.77/9.77 (woz13rule0) => 71.77/9.77 (( 71.77/9.77 (woz13rule1) => 71.77/9.77 (( 71.77/9.77 (woz13rule2) => 71.77/9.77 (( 71.77/9.77 (woz13rule3) => 71.77/9.77 (( 71.77/9.77 (woz13rule4) => 71.77/9.77 (( 71.77/9.77 (woz1_1) => 71.77/9.77 (( 71.77/9.77 (woz1_2) => 71.77/9.77 (( 71.77/9.77 (woz1_3) => 71.77/9.77 (( 71.77/9.77 (woz1_4) => 71.77/9.77 (( 71.77/9.77 (woz1_5) => 71.77/9.77 (( 71.77/9.77 (breln1all2) => 71.77/9.77 (( 71.77/9.77 (breln1SetBreln1) => 71.77/9.77 (( 71.77/9.77 (choice2fnsingleton) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln1) => 71.77/9.77 (( 71.77/9.77 (breln1all1) => 71.77/9.77 (( 71.77/9.77 (subbreln1) => 71.77/9.77 (( 71.77/9.77 (eqbreln1) => 71.77/9.77 (( 71.77/9.77 (breln1invprop) => 71.77/9.77 (( 71.77/9.77 (breln1invI) => 71.77/9.77 (( 71.77/9.77 (breln1invE) => 71.77/9.77 (( 71.77/9.77 (breln1compprop) => 71.77/9.77 (( 71.77/9.77 (breln1compI) => 71.77/9.77 (( 71.77/9.77 (breln1compE) => 71.77/9.77 (( 71.77/9.77 (breln1compEex) => 71.77/9.77 (( 71.77/9.77 (!!) @ ( 71.77/9.77 (('#B') @ ( 71.77/9.77 !!) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 !!))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#C') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 breln1)))) @ 71.77/9.77 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])). 71.77/9.77 thf(zip_derived_cl485, plain, 71.77/9.77 (~ (((upairsetE) => 71.77/9.77 (((upairsetIL) => 71.77/9.77 (((upairsetIR) => 71.77/9.77 (((emptyE1) => 71.77/9.77 (((vacuousDall) => 71.77/9.77 (((quantDeMorgan1) => 71.77/9.77 (((quantDeMorgan2) => 71.77/9.77 (((quantDeMorgan3) => 71.77/9.77 (((quantDeMorgan4) => 71.77/9.77 (((prop2setI) => 71.77/9.77 (((prop2set2propI) => 71.77/9.77 (((notdexE) => 71.77/9.77 (((notdallE) => 71.77/9.77 (((exuI1) => 71.77/9.77 (((exuI3) => 71.77/9.77 (((exuI2) => 71.77/9.77 (((inCongP) => 71.77/9.77 (((in__Cong) => 71.77/9.77 (((exuE3u) => 71.77/9.77 (((exu__Cong) => 71.77/9.77 (((setadjoin__Cong) => 71.77/9.77 (((powerset__Cong) => 71.77/9.77 (((setunion__Cong) => 71.77/9.77 (((exuEu) => 71.77/9.77 (((descr__Cong) => 71.77/9.77 (((dsetconstr__Cong) => 71.77/9.77 (((subsetI1) => 71.77/9.77 (((eqimpsubset2) => 71.77/9.77 (((eqimpsubset1) => 71.77/9.77 (((subsetI2) => 71.77/9.77 (( 71.77/9.77 (emptysetsubset) => 71.77/9.77 (( 71.77/9.77 (subsetE) => 71.77/9.77 (( 71.77/9.77 (subsetE2) => 71.77/9.77 (( 71.77/9.77 (notsubsetI) => 71.77/9.77 (( 71.77/9.77 (notequalI1) => 71.77/9.77 (( 71.77/9.77 (notequalI2) => 71.77/9.77 (( 71.77/9.77 (subsetRefl) => 71.77/9.77 (( 71.77/9.77 (subsetTrans) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub2) => 71.77/9.77 (( 71.77/9.77 (subset2powerset) => 71.77/9.77 (( 71.77/9.77 (setextsub) => 71.77/9.77 (( 71.77/9.77 (subsetemptysetimpeq) => 71.77/9.77 (( 71.77/9.77 (powersetI1) => 71.77/9.77 (( 71.77/9.77 (powersetE1) => 71.77/9.77 (( 71.77/9.77 (inPowerset) => 71.77/9.77 (( 71.77/9.77 (powersetsubset) => 71.77/9.77 (( 71.77/9.77 (sepInPowerset) => 71.77/9.77 (( 71.77/9.77 (sepSubset) => 71.77/9.77 (( 71.77/9.77 (binunionIL) => 71.77/9.77 (( 71.77/9.77 (upairset2IR) => 71.77/9.77 (( 71.77/9.77 (binunionIR) => 71.77/9.77 (( 71.77/9.77 (binunionEcases) => 71.77/9.77 (( 71.77/9.77 (binunionE) => 71.77/9.77 (( 71.77/9.77 (binunionLsub) => 71.77/9.77 (( 71.77/9.77 (binunionRsub) => 71.77/9.77 (( 71.77/9.77 (binintersectI) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset5) => 71.77/9.77 (( 71.77/9.77 (binintersectEL) => 71.77/9.77 (( 71.77/9.77 (binintersectLsub) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset2) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset3) => 71.77/9.77 (( 71.77/9.77 (binintersectER) => 71.77/9.77 (( 71.77/9.77 (disjointsetsI1) => 71.77/9.77 (( 71.77/9.77 (binintersectRsub) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset4) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset1) => 71.77/9.77 (( 71.77/9.77 (bs114d) => 71.77/9.77 (( 71.77/9.77 (setminusI) => 71.77/9.77 (( 71.77/9.77 (setminusEL) => 71.77/9.77 (( 71.77/9.77 (setminusER) => 71.77/9.77 (( 71.77/9.77 (setminusSubset2) => 71.77/9.77 (( 71.77/9.77 (setminusERneg) => 71.77/9.77 (( 71.77/9.77 (setminusELneg) => 71.77/9.77 (( 71.77/9.77 (setminusILneg) => 71.77/9.77 (( 71.77/9.77 (setminusIRneg) => 71.77/9.77 (( 71.77/9.77 (setminusLsub) => 71.77/9.77 (( 71.77/9.77 (setminusSubset1) => 71.77/9.77 (( 71.77/9.77 (symdiffE) => 71.77/9.77 (( 71.77/9.77 (symdiffI1) => 71.77/9.77 (( 71.77/9.77 (symdiffI2) => 71.77/9.77 (( 71.77/9.77 (symdiffIneg1) => 71.77/9.77 (( 71.77/9.77 (symdiffIneg2) => 71.77/9.77 (( 71.77/9.77 (secondinupair) => 71.77/9.77 (( 71.77/9.77 (setukpairIL) => 71.77/9.77 (( 71.77/9.77 (setukpairIR) => 71.77/9.77 (( 71.77/9.77 (kpairiskpair) => 71.77/9.77 (( 71.77/9.77 (kpairp) => 71.77/9.77 (( 71.77/9.77 (singletonsubset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowerset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowunion) => 71.77/9.77 (( 71.77/9.77 (upairset2E) => 71.77/9.77 (( 71.77/9.77 (upairsubunion) => 71.77/9.77 (( 71.77/9.77 (upairinpowunion) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem1) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem2) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem3) => 71.77/9.77 (( 71.77/9.77 (cartprodpairin) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair1) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair) => 71.77/9.77 (( 71.77/9.77 (setunionE2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton1) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton) => 71.77/9.77 (( 71.77/9.77 (singletonprop) => 71.77/9.77 (( 71.77/9.77 (ex1E1) => 71.77/9.77 (( 71.77/9.77 (ex1I) => 71.77/9.77 (( 71.77/9.77 (ex1I2) => 71.77/9.77 (( 71.77/9.77 (singletonsuniq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL1) => 71.77/9.77 (( 71.77/9.77 (kfstsingleton) => 71.77/9.77 (( 71.77/9.77 (theprop) => 71.77/9.77 (( 71.77/9.77 (kfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstin) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR11) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR12) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR1) => 71.77/9.77 (( 71.77/9.77 (upairequniteq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR) => 71.77/9.77 (( 71.77/9.77 (ksndsingleton) => 71.77/9.77 (( 71.77/9.77 (ksndpairEq) => 71.77/9.77 (( 71.77/9.77 (kpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndin) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemEL) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemER) => 71.77/9.77 (( 71.77/9.77 (cartprodmempaircEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrI) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrSub) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrERa) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL1) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL2) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrER) => 71.77/9.77 (( 71.77/9.77 (funcImageSingleton) => 71.77/9.77 (( 71.77/9.77 (apProp) => 71.77/9.77 (( 71.77/9.77 (app) => 71.77/9.77 (( 71.77/9.77 (infuncsetfunc) => 71.77/9.77 (( 71.77/9.77 (ap2p) => 71.77/9.77 (( 71.77/9.77 (funcinfuncset) => 71.77/9.77 (( 71.77/9.77 (lamProp) => 71.77/9.77 (( 71.77/9.77 (lamp) => 71.77/9.77 (( 71.77/9.77 (lam2p) => 71.77/9.77 (( 71.77/9.77 (brelnall1) => 71.77/9.77 (( 71.77/9.77 (brelnall2) => 71.77/9.77 (( 71.77/9.77 (ex1E2) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp1) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp3) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp2) => 71.77/9.77 (( 71.77/9.77 (funcextLem) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp4) => 71.77/9.77 (( 71.77/9.77 (subbreln) => 71.77/9.77 (( 71.77/9.77 (eqbreln) => 71.77/9.77 (( 71.77/9.77 (funcext) => 71.77/9.77 (( 71.77/9.77 (funcext2) => 71.77/9.77 (( 71.77/9.77 (ap2apEq1) => 71.77/9.77 (( 71.77/9.77 (ap2apEq2) => 71.77/9.77 (( 71.77/9.77 (beta1) => 71.77/9.77 (( 71.77/9.77 (eta1) => 71.77/9.77 (( 71.77/9.77 (lam2lamEq) => 71.77/9.77 (( 71.77/9.77 (beta2) => 71.77/9.77 (( 71.77/9.77 (eta2) => 71.77/9.77 (( 71.77/9.77 (iffalseProp1) => 71.77/9.77 (( 71.77/9.77 (iffalseProp2) => 71.77/9.77 (( 71.77/9.77 (iftrueProp1) => 71.77/9.77 (( 71.77/9.77 (iftrueProp2) => 71.77/9.77 (( 71.77/9.77 (ifSingleton) => 71.77/9.77 (( 71.77/9.77 (ifp) => 71.77/9.77 (( 71.77/9.77 (theeq) => 71.77/9.77 (( 71.77/9.77 (iftrue) => 71.77/9.77 (( 71.77/9.77 (iffalse) => 71.77/9.77 (( 71.77/9.77 (iftrueorfalse) => 71.77/9.77 (( 71.77/9.77 (binintersectT_lem) => 71.77/9.77 (( 71.77/9.77 (binunionT_lem) => 71.77/9.77 (( 71.77/9.77 (powersetT_lem) => 71.77/9.77 (( 71.77/9.77 (setminusT_lem) => 71.77/9.77 (( 71.77/9.77 (complementT_lem) => 71.77/9.77 (( 71.77/9.77 (setextT) => 71.77/9.77 (( 71.77/9.77 (subsetTI) => 71.77/9.77 (( 71.77/9.77 (powersetTI1) => 71.77/9.77 (( 71.77/9.77 (powersetTE1) => 71.77/9.77 (( 71.77/9.77 (complementTI1) => 71.77/9.77 (( 71.77/9.77 (complementTE1) => 71.77/9.77 (( 71.77/9.77 (binintersectTELcontra) => 71.77/9.77 (( 71.77/9.77 (binintersectTERcontra) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT1) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT2) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT3) => 71.77/9.77 (( 71.77/9.77 (doubleComplementI1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementE1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub2) => 71.77/9.77 (( 71.77/9.77 (doubleComplementEq) => 71.77/9.77 (( 71.77/9.77 (complementTnotintersectT) => 71.77/9.77 (( 71.77/9.77 (complementImpComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementSubsetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementInPowersetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (contraSubsetComplement) => 71.77/9.77 (( 71.77/9.77 (complementTcontraSubset) => 71.77/9.77 (( 71.77/9.77 (binunionTILcontra) => 71.77/9.77 (( 71.77/9.77 (binunionTIRcontra) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion2) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (intersectInPowersetIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpNotIn1) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpInComplement1) => 71.77/9.77 (( 71.77/9.77 (binunionTE) => 71.77/9.77 (( 71.77/9.77 (binunionTEcontra) => 71.77/9.77 (( 71.77/9.77 (demorgan2a1) => 71.77/9.77 (( 71.77/9.77 (complementUnionInPowersetComplement) => 71.77/9.77 (( 71.77/9.77 (demorgan2a2) => 71.77/9.77 (( 71.77/9.77 (demorgan1a) => 71.77/9.77 (( 71.77/9.77 (demorgan1b) => 71.77/9.77 (( 71.77/9.77 (demorgan1) => 71.77/9.77 (( 71.77/9.77 (demorgan2a) => 71.77/9.77 (( 71.77/9.77 (demorgan2b2) => 71.77/9.77 (( 71.77/9.77 (demorgan2b) => 71.77/9.77 (( 71.77/9.77 (demorgan2) => 71.77/9.77 (( 71.77/9.77 (woz13rule0) => 71.77/9.77 (( 71.77/9.77 (woz13rule1) => 71.77/9.77 (( 71.77/9.77 (woz13rule2) => 71.77/9.77 (( 71.77/9.77 (woz13rule3) => 71.77/9.77 (( 71.77/9.77 (woz13rule4) => 71.77/9.77 (( 71.77/9.77 (woz1_1) => 71.77/9.77 (( 71.77/9.77 (woz1_2) => 71.77/9.77 (( 71.77/9.77 (woz1_3) => 71.77/9.77 (( 71.77/9.77 (woz1_4) => 71.77/9.77 (( 71.77/9.77 (woz1_5) => 71.77/9.77 (( 71.77/9.77 (breln1all2) => 71.77/9.77 (( 71.77/9.77 (breln1SetBreln1) => 71.77/9.77 (( 71.77/9.77 (choice2fnsingleton) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln1) => 71.77/9.77 (( 71.77/9.77 (breln1all1) => 71.77/9.77 (( 71.77/9.77 (subbreln1) => 71.77/9.77 (( 71.77/9.77 (eqbreln1) => 71.77/9.77 (( 71.77/9.77 (breln1invprop) => 71.77/9.77 (( 71.77/9.77 (breln1invI) => 71.77/9.77 (( 71.77/9.77 (breln1invE) => 71.77/9.77 (( 71.77/9.77 (breln1compprop) => 71.77/9.77 (( 71.77/9.77 (breln1compI) => 71.77/9.77 (( 71.77/9.77 (breln1compE) => 71.77/9.77 (( 71.77/9.77 (breln1compEex) => 71.77/9.77 (( 71.77/9.77 (!!) @ ( 71.77/9.77 (('#B') @ ( 71.77/9.77 !!) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 !!))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#C') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 breln1)))) @ 71.77/9.77 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl475])). 71.77/9.77 thf(zip_derived_cl496, plain, 71.77/9.77 (~ (((upairsetIL) => 71.77/9.77 (((upairsetIR) => 71.77/9.77 (((emptyE1) => 71.77/9.77 (((vacuousDall) => 71.77/9.77 (((quantDeMorgan1) => 71.77/9.77 (((quantDeMorgan2) => 71.77/9.77 (((quantDeMorgan3) => 71.77/9.77 (((quantDeMorgan4) => 71.77/9.77 (((prop2setI) => 71.77/9.77 (((prop2set2propI) => 71.77/9.77 (((notdexE) => 71.77/9.77 (((notdallE) => 71.77/9.77 (((exuI1) => 71.77/9.77 (((exuI3) => 71.77/9.77 (((exuI2) => 71.77/9.77 (((inCongP) => 71.77/9.77 (((in__Cong) => 71.77/9.77 (((exuE3u) => 71.77/9.77 (((exu__Cong) => 71.77/9.77 (((setadjoin__Cong) => 71.77/9.77 (((powerset__Cong) => 71.77/9.77 (((setunion__Cong) => 71.77/9.77 (((exuEu) => 71.77/9.77 (((descr__Cong) => 71.77/9.77 (((dsetconstr__Cong) => 71.77/9.77 (((subsetI1) => 71.77/9.77 (((eqimpsubset2) => 71.77/9.77 (((eqimpsubset1) => 71.77/9.77 (((subsetI2) => 71.77/9.77 (((emptysetsubset) => 71.77/9.77 (( 71.77/9.77 (subsetE) => 71.77/9.77 (( 71.77/9.77 (subsetE2) => 71.77/9.77 (( 71.77/9.77 (notsubsetI) => 71.77/9.77 (( 71.77/9.77 (notequalI1) => 71.77/9.77 (( 71.77/9.77 (notequalI2) => 71.77/9.77 (( 71.77/9.77 (subsetRefl) => 71.77/9.77 (( 71.77/9.77 (subsetTrans) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub2) => 71.77/9.77 (( 71.77/9.77 (subset2powerset) => 71.77/9.77 (( 71.77/9.77 (setextsub) => 71.77/9.77 (( 71.77/9.77 (subsetemptysetimpeq) => 71.77/9.77 (( 71.77/9.77 (powersetI1) => 71.77/9.77 (( 71.77/9.77 (powersetE1) => 71.77/9.77 (( 71.77/9.77 (inPowerset) => 71.77/9.77 (( 71.77/9.77 (powersetsubset) => 71.77/9.77 (( 71.77/9.77 (sepInPowerset) => 71.77/9.77 (( 71.77/9.77 (sepSubset) => 71.77/9.77 (( 71.77/9.77 (binunionIL) => 71.77/9.77 (( 71.77/9.77 (upairset2IR) => 71.77/9.77 (( 71.77/9.77 (binunionIR) => 71.77/9.77 (( 71.77/9.77 (binunionEcases) => 71.77/9.77 (( 71.77/9.77 (binunionE) => 71.77/9.77 (( 71.77/9.77 (binunionLsub) => 71.77/9.77 (( 71.77/9.77 (binunionRsub) => 71.77/9.77 (( 71.77/9.77 (binintersectI) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset5) => 71.77/9.77 (( 71.77/9.77 (binintersectEL) => 71.77/9.77 (( 71.77/9.77 (binintersectLsub) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset2) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset3) => 71.77/9.77 (( 71.77/9.77 (binintersectER) => 71.77/9.77 (( 71.77/9.77 (disjointsetsI1) => 71.77/9.77 (( 71.77/9.77 (binintersectRsub) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset4) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset1) => 71.77/9.77 (( 71.77/9.77 (bs114d) => 71.77/9.77 (( 71.77/9.77 (setminusI) => 71.77/9.77 (( 71.77/9.77 (setminusEL) => 71.77/9.77 (( 71.77/9.77 (setminusER) => 71.77/9.77 (( 71.77/9.77 (setminusSubset2) => 71.77/9.77 (( 71.77/9.77 (setminusERneg) => 71.77/9.77 (( 71.77/9.77 (setminusELneg) => 71.77/9.77 (( 71.77/9.77 (setminusILneg) => 71.77/9.77 (( 71.77/9.77 (setminusIRneg) => 71.77/9.77 (( 71.77/9.77 (setminusLsub) => 71.77/9.77 (( 71.77/9.77 (setminusSubset1) => 71.77/9.77 (( 71.77/9.77 (symdiffE) => 71.77/9.77 (( 71.77/9.77 (symdiffI1) => 71.77/9.77 (( 71.77/9.77 (symdiffI2) => 71.77/9.77 (( 71.77/9.77 (symdiffIneg1) => 71.77/9.77 (( 71.77/9.77 (symdiffIneg2) => 71.77/9.77 (( 71.77/9.77 (secondinupair) => 71.77/9.77 (( 71.77/9.77 (setukpairIL) => 71.77/9.77 (( 71.77/9.77 (setukpairIR) => 71.77/9.77 (( 71.77/9.77 (kpairiskpair) => 71.77/9.77 (( 71.77/9.77 (kpairp) => 71.77/9.77 (( 71.77/9.77 (singletonsubset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowerset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowunion) => 71.77/9.77 (( 71.77/9.77 (upairset2E) => 71.77/9.77 (( 71.77/9.77 (upairsubunion) => 71.77/9.77 (( 71.77/9.77 (upairinpowunion) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem1) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem2) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem3) => 71.77/9.77 (( 71.77/9.77 (cartprodpairin) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair1) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair) => 71.77/9.77 (( 71.77/9.77 (setunionE2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton1) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton) => 71.77/9.77 (( 71.77/9.77 (singletonprop) => 71.77/9.77 (( 71.77/9.77 (ex1E1) => 71.77/9.77 (( 71.77/9.77 (ex1I) => 71.77/9.77 (( 71.77/9.77 (ex1I2) => 71.77/9.77 (( 71.77/9.77 (singletonsuniq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL1) => 71.77/9.77 (( 71.77/9.77 (kfstsingleton) => 71.77/9.77 (( 71.77/9.77 (theprop) => 71.77/9.77 (( 71.77/9.77 (kfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstin) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR11) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR12) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR1) => 71.77/9.77 (( 71.77/9.77 (upairequniteq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR) => 71.77/9.77 (( 71.77/9.77 (ksndsingleton) => 71.77/9.77 (( 71.77/9.77 (ksndpairEq) => 71.77/9.77 (( 71.77/9.77 (kpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndin) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemEL) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemER) => 71.77/9.77 (( 71.77/9.77 (cartprodmempaircEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrI) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrSub) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrERa) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL1) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL2) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrER) => 71.77/9.77 (( 71.77/9.77 (funcImageSingleton) => 71.77/9.77 (( 71.77/9.77 (apProp) => 71.77/9.77 (( 71.77/9.77 (app) => 71.77/9.77 (( 71.77/9.77 (infuncsetfunc) => 71.77/9.77 (( 71.77/9.77 (ap2p) => 71.77/9.77 (( 71.77/9.77 (funcinfuncset) => 71.77/9.77 (( 71.77/9.77 (lamProp) => 71.77/9.77 (( 71.77/9.77 (lamp) => 71.77/9.77 (( 71.77/9.77 (lam2p) => 71.77/9.77 (( 71.77/9.77 (brelnall1) => 71.77/9.77 (( 71.77/9.77 (brelnall2) => 71.77/9.77 (( 71.77/9.77 (ex1E2) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp1) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp3) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp2) => 71.77/9.77 (( 71.77/9.77 (funcextLem) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp4) => 71.77/9.77 (( 71.77/9.77 (subbreln) => 71.77/9.77 (( 71.77/9.77 (eqbreln) => 71.77/9.77 (( 71.77/9.77 (funcext) => 71.77/9.77 (( 71.77/9.77 (funcext2) => 71.77/9.77 (( 71.77/9.77 (ap2apEq1) => 71.77/9.77 (( 71.77/9.77 (ap2apEq2) => 71.77/9.77 (( 71.77/9.77 (beta1) => 71.77/9.77 (( 71.77/9.77 (eta1) => 71.77/9.77 (( 71.77/9.77 (lam2lamEq) => 71.77/9.77 (( 71.77/9.77 (beta2) => 71.77/9.77 (( 71.77/9.77 (eta2) => 71.77/9.77 (( 71.77/9.77 (iffalseProp1) => 71.77/9.77 (( 71.77/9.77 (iffalseProp2) => 71.77/9.77 (( 71.77/9.77 (iftrueProp1) => 71.77/9.77 (( 71.77/9.77 (iftrueProp2) => 71.77/9.77 (( 71.77/9.77 (ifSingleton) => 71.77/9.77 (( 71.77/9.77 (ifp) => 71.77/9.77 (( 71.77/9.77 (theeq) => 71.77/9.77 (( 71.77/9.77 (iftrue) => 71.77/9.77 (( 71.77/9.77 (iffalse) => 71.77/9.77 (( 71.77/9.77 (iftrueorfalse) => 71.77/9.77 (( 71.77/9.77 (binintersectT_lem) => 71.77/9.77 (( 71.77/9.77 (binunionT_lem) => 71.77/9.77 (( 71.77/9.77 (powersetT_lem) => 71.77/9.77 (( 71.77/9.77 (setminusT_lem) => 71.77/9.77 (( 71.77/9.77 (complementT_lem) => 71.77/9.77 (( 71.77/9.77 (setextT) => 71.77/9.77 (( 71.77/9.77 (subsetTI) => 71.77/9.77 (( 71.77/9.77 (powersetTI1) => 71.77/9.77 (( 71.77/9.77 (powersetTE1) => 71.77/9.77 (( 71.77/9.77 (complementTI1) => 71.77/9.77 (( 71.77/9.77 (complementTE1) => 71.77/9.77 (( 71.77/9.77 (binintersectTELcontra) => 71.77/9.77 (( 71.77/9.77 (binintersectTERcontra) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT1) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT2) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT3) => 71.77/9.77 (( 71.77/9.77 (doubleComplementI1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementE1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub2) => 71.77/9.77 (( 71.77/9.77 (doubleComplementEq) => 71.77/9.77 (( 71.77/9.77 (complementTnotintersectT) => 71.77/9.77 (( 71.77/9.77 (complementImpComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementSubsetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementInPowersetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (contraSubsetComplement) => 71.77/9.77 (( 71.77/9.77 (complementTcontraSubset) => 71.77/9.77 (( 71.77/9.77 (binunionTILcontra) => 71.77/9.77 (( 71.77/9.77 (binunionTIRcontra) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion2) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (intersectInPowersetIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpNotIn1) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpInComplement1) => 71.77/9.77 (( 71.77/9.77 (binunionTE) => 71.77/9.77 (( 71.77/9.77 (binunionTEcontra) => 71.77/9.77 (( 71.77/9.77 (demorgan2a1) => 71.77/9.77 (( 71.77/9.77 (complementUnionInPowersetComplement) => 71.77/9.77 (( 71.77/9.77 (demorgan2a2) => 71.77/9.77 (( 71.77/9.77 (demorgan1a) => 71.77/9.77 (( 71.77/9.77 (demorgan1b) => 71.77/9.77 (( 71.77/9.77 (demorgan1) => 71.77/9.77 (( 71.77/9.77 (demorgan2a) => 71.77/9.77 (( 71.77/9.77 (demorgan2b2) => 71.77/9.77 (( 71.77/9.77 (demorgan2b) => 71.77/9.77 (( 71.77/9.77 (demorgan2) => 71.77/9.77 (( 71.77/9.77 (woz13rule0) => 71.77/9.77 (( 71.77/9.77 (woz13rule1) => 71.77/9.77 (( 71.77/9.77 (woz13rule2) => 71.77/9.77 (( 71.77/9.77 (woz13rule3) => 71.77/9.77 (( 71.77/9.77 (woz13rule4) => 71.77/9.77 (( 71.77/9.77 (woz1_1) => 71.77/9.77 (( 71.77/9.77 (woz1_2) => 71.77/9.77 (( 71.77/9.77 (woz1_3) => 71.77/9.77 (( 71.77/9.77 (woz1_4) => 71.77/9.77 (( 71.77/9.77 (woz1_5) => 71.77/9.77 (( 71.77/9.77 (breln1all2) => 71.77/9.77 (( 71.77/9.77 (breln1SetBreln1) => 71.77/9.77 (( 71.77/9.77 (choice2fnsingleton) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln1) => 71.77/9.77 (( 71.77/9.77 (breln1all1) => 71.77/9.77 (( 71.77/9.77 (subbreln1) => 71.77/9.77 (( 71.77/9.77 (eqbreln1) => 71.77/9.77 (( 71.77/9.77 (breln1invprop) => 71.77/9.77 (( 71.77/9.77 (breln1invI) => 71.77/9.77 (( 71.77/9.77 (breln1invE) => 71.77/9.77 (( 71.77/9.77 (breln1compprop) => 71.77/9.77 (( 71.77/9.77 (breln1compI) => 71.77/9.77 (( 71.77/9.77 (breln1compE) => 71.77/9.77 (( 71.77/9.77 (breln1compEex) => 71.77/9.77 (( 71.77/9.77 (!!) @ ( 71.77/9.77 (('#B') @ ( 71.77/9.77 !!) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 !!))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#C') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 breln1)))) @ 71.77/9.77 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])). 71.77/9.77 thf(zip_derived_cl507, plain, 71.77/9.77 (~ (((upairsetIR) => 71.77/9.77 (((emptyE1) => 71.77/9.77 (((vacuousDall) => 71.77/9.77 (((quantDeMorgan1) => 71.77/9.77 (((quantDeMorgan2) => 71.77/9.77 (((quantDeMorgan3) => 71.77/9.77 (((quantDeMorgan4) => 71.77/9.77 (((prop2setI) => 71.77/9.77 (((prop2set2propI) => 71.77/9.77 (((notdexE) => 71.77/9.77 (((notdallE) => 71.77/9.77 (((exuI1) => 71.77/9.77 (((exuI3) => 71.77/9.77 (((exuI2) => 71.77/9.77 (((inCongP) => 71.77/9.77 (((in__Cong) => 71.77/9.77 (((exuE3u) => 71.77/9.77 (((exu__Cong) => 71.77/9.77 (((setadjoin__Cong) => 71.77/9.77 (((powerset__Cong) => 71.77/9.77 (((setunion__Cong) => 71.77/9.77 (((exuEu) => 71.77/9.77 (((descr__Cong) => 71.77/9.77 (((dsetconstr__Cong) => 71.77/9.77 (((subsetI1) => 71.77/9.77 (((eqimpsubset2) => 71.77/9.77 (((eqimpsubset1) => 71.77/9.77 (((subsetI2) => 71.77/9.77 (((emptysetsubset) => 71.77/9.77 (((subsetE) => 71.77/9.77 (( 71.77/9.77 (subsetE2) => 71.77/9.77 (( 71.77/9.77 (notsubsetI) => 71.77/9.77 (( 71.77/9.77 (notequalI1) => 71.77/9.77 (( 71.77/9.77 (notequalI2) => 71.77/9.77 (( 71.77/9.77 (subsetRefl) => 71.77/9.77 (( 71.77/9.77 (subsetTrans) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub2) => 71.77/9.77 (( 71.77/9.77 (subset2powerset) => 71.77/9.77 (( 71.77/9.77 (setextsub) => 71.77/9.77 (( 71.77/9.77 (subsetemptysetimpeq) => 71.77/9.77 (( 71.77/9.77 (powersetI1) => 71.77/9.77 (( 71.77/9.77 (powersetE1) => 71.77/9.77 (( 71.77/9.77 (inPowerset) => 71.77/9.77 (( 71.77/9.77 (powersetsubset) => 71.77/9.77 (( 71.77/9.77 (sepInPowerset) => 71.77/9.77 (( 71.77/9.77 (sepSubset) => 71.77/9.77 (( 71.77/9.77 (binunionIL) => 71.77/9.77 (( 71.77/9.77 (upairset2IR) => 71.77/9.77 (( 71.77/9.77 (binunionIR) => 71.77/9.77 (( 71.77/9.77 (binunionEcases) => 71.77/9.77 (( 71.77/9.77 (binunionE) => 71.77/9.77 (( 71.77/9.77 (binunionLsub) => 71.77/9.77 (( 71.77/9.77 (binunionRsub) => 71.77/9.77 (( 71.77/9.77 (binintersectI) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset5) => 71.77/9.77 (( 71.77/9.77 (binintersectEL) => 71.77/9.77 (( 71.77/9.77 (binintersectLsub) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset2) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset3) => 71.77/9.77 (( 71.77/9.77 (binintersectER) => 71.77/9.77 (( 71.77/9.77 (disjointsetsI1) => 71.77/9.77 (( 71.77/9.77 (binintersectRsub) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset4) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset1) => 71.77/9.77 (( 71.77/9.77 (bs114d) => 71.77/9.77 (( 71.77/9.77 (setminusI) => 71.77/9.77 (( 71.77/9.77 (setminusEL) => 71.77/9.77 (( 71.77/9.77 (setminusER) => 71.77/9.77 (( 71.77/9.77 (setminusSubset2) => 71.77/9.77 (( 71.77/9.77 (setminusERneg) => 71.77/9.77 (( 71.77/9.77 (setminusELneg) => 71.77/9.77 (( 71.77/9.77 (setminusILneg) => 71.77/9.77 (( 71.77/9.77 (setminusIRneg) => 71.77/9.77 (( 71.77/9.77 (setminusLsub) => 71.77/9.77 (( 71.77/9.77 (setminusSubset1) => 71.77/9.77 (( 71.77/9.77 (symdiffE) => 71.77/9.77 (( 71.77/9.77 (symdiffI1) => 71.77/9.77 (( 71.77/9.77 (symdiffI2) => 71.77/9.77 (( 71.77/9.77 (symdiffIneg1) => 71.77/9.77 (( 71.77/9.77 (symdiffIneg2) => 71.77/9.77 (( 71.77/9.77 (secondinupair) => 71.77/9.77 (( 71.77/9.77 (setukpairIL) => 71.77/9.77 (( 71.77/9.77 (setukpairIR) => 71.77/9.77 (( 71.77/9.77 (kpairiskpair) => 71.77/9.77 (( 71.77/9.77 (kpairp) => 71.77/9.77 (( 71.77/9.77 (singletonsubset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowerset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowunion) => 71.77/9.77 (( 71.77/9.77 (upairset2E) => 71.77/9.77 (( 71.77/9.77 (upairsubunion) => 71.77/9.77 (( 71.77/9.77 (upairinpowunion) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem1) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem2) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem3) => 71.77/9.77 (( 71.77/9.77 (cartprodpairin) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair1) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair) => 71.77/9.77 (( 71.77/9.77 (setunionE2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton1) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton) => 71.77/9.77 (( 71.77/9.77 (singletonprop) => 71.77/9.77 (( 71.77/9.77 (ex1E1) => 71.77/9.77 (( 71.77/9.77 (ex1I) => 71.77/9.77 (( 71.77/9.77 (ex1I2) => 71.77/9.77 (( 71.77/9.77 (singletonsuniq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL1) => 71.77/9.77 (( 71.77/9.77 (kfstsingleton) => 71.77/9.77 (( 71.77/9.77 (theprop) => 71.77/9.77 (( 71.77/9.77 (kfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstin) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR11) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR12) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR1) => 71.77/9.77 (( 71.77/9.77 (upairequniteq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR) => 71.77/9.77 (( 71.77/9.77 (ksndsingleton) => 71.77/9.77 (( 71.77/9.77 (ksndpairEq) => 71.77/9.77 (( 71.77/9.77 (kpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndin) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemEL) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemER) => 71.77/9.77 (( 71.77/9.77 (cartprodmempaircEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrI) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrSub) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrERa) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL1) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL2) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrER) => 71.77/9.77 (( 71.77/9.77 (funcImageSingleton) => 71.77/9.77 (( 71.77/9.77 (apProp) => 71.77/9.77 (( 71.77/9.77 (app) => 71.77/9.77 (( 71.77/9.77 (infuncsetfunc) => 71.77/9.77 (( 71.77/9.77 (ap2p) => 71.77/9.77 (( 71.77/9.77 (funcinfuncset) => 71.77/9.77 (( 71.77/9.77 (lamProp) => 71.77/9.77 (( 71.77/9.77 (lamp) => 71.77/9.77 (( 71.77/9.77 (lam2p) => 71.77/9.77 (( 71.77/9.77 (brelnall1) => 71.77/9.77 (( 71.77/9.77 (brelnall2) => 71.77/9.77 (( 71.77/9.77 (ex1E2) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp1) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp3) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp2) => 71.77/9.77 (( 71.77/9.77 (funcextLem) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp4) => 71.77/9.77 (( 71.77/9.77 (subbreln) => 71.77/9.77 (( 71.77/9.77 (eqbreln) => 71.77/9.77 (( 71.77/9.77 (funcext) => 71.77/9.77 (( 71.77/9.77 (funcext2) => 71.77/9.77 (( 71.77/9.77 (ap2apEq1) => 71.77/9.77 (( 71.77/9.77 (ap2apEq2) => 71.77/9.77 (( 71.77/9.77 (beta1) => 71.77/9.77 (( 71.77/9.77 (eta1) => 71.77/9.77 (( 71.77/9.77 (lam2lamEq) => 71.77/9.77 (( 71.77/9.77 (beta2) => 71.77/9.77 (( 71.77/9.77 (eta2) => 71.77/9.77 (( 71.77/9.77 (iffalseProp1) => 71.77/9.77 (( 71.77/9.77 (iffalseProp2) => 71.77/9.77 (( 71.77/9.77 (iftrueProp1) => 71.77/9.77 (( 71.77/9.77 (iftrueProp2) => 71.77/9.77 (( 71.77/9.77 (ifSingleton) => 71.77/9.77 (( 71.77/9.77 (ifp) => 71.77/9.77 (( 71.77/9.77 (theeq) => 71.77/9.77 (( 71.77/9.77 (iftrue) => 71.77/9.77 (( 71.77/9.77 (iffalse) => 71.77/9.77 (( 71.77/9.77 (iftrueorfalse) => 71.77/9.77 (( 71.77/9.77 (binintersectT_lem) => 71.77/9.77 (( 71.77/9.77 (binunionT_lem) => 71.77/9.77 (( 71.77/9.77 (powersetT_lem) => 71.77/9.77 (( 71.77/9.77 (setminusT_lem) => 71.77/9.77 (( 71.77/9.77 (complementT_lem) => 71.77/9.77 (( 71.77/9.77 (setextT) => 71.77/9.77 (( 71.77/9.77 (subsetTI) => 71.77/9.77 (( 71.77/9.77 (powersetTI1) => 71.77/9.77 (( 71.77/9.77 (powersetTE1) => 71.77/9.77 (( 71.77/9.77 (complementTI1) => 71.77/9.77 (( 71.77/9.77 (complementTE1) => 71.77/9.77 (( 71.77/9.77 (binintersectTELcontra) => 71.77/9.77 (( 71.77/9.77 (binintersectTERcontra) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT1) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT2) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT3) => 71.77/9.77 (( 71.77/9.77 (doubleComplementI1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementE1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub2) => 71.77/9.77 (( 71.77/9.77 (doubleComplementEq) => 71.77/9.77 (( 71.77/9.77 (complementTnotintersectT) => 71.77/9.77 (( 71.77/9.77 (complementImpComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementSubsetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementInPowersetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (contraSubsetComplement) => 71.77/9.77 (( 71.77/9.77 (complementTcontraSubset) => 71.77/9.77 (( 71.77/9.77 (binunionTILcontra) => 71.77/9.77 (( 71.77/9.77 (binunionTIRcontra) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion2) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (intersectInPowersetIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpNotIn1) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpInComplement1) => 71.77/9.77 (( 71.77/9.77 (binunionTE) => 71.77/9.77 (( 71.77/9.77 (binunionTEcontra) => 71.77/9.77 (( 71.77/9.77 (demorgan2a1) => 71.77/9.77 (( 71.77/9.77 (complementUnionInPowersetComplement) => 71.77/9.77 (( 71.77/9.77 (demorgan2a2) => 71.77/9.77 (( 71.77/9.77 (demorgan1a) => 71.77/9.77 (( 71.77/9.77 (demorgan1b) => 71.77/9.77 (( 71.77/9.77 (demorgan1) => 71.77/9.77 (( 71.77/9.77 (demorgan2a) => 71.77/9.77 (( 71.77/9.77 (demorgan2b2) => 71.77/9.77 (( 71.77/9.77 (demorgan2b) => 71.77/9.77 (( 71.77/9.77 (demorgan2) => 71.77/9.77 (( 71.77/9.77 (woz13rule0) => 71.77/9.77 (( 71.77/9.77 (woz13rule1) => 71.77/9.77 (( 71.77/9.77 (woz13rule2) => 71.77/9.77 (( 71.77/9.77 (woz13rule3) => 71.77/9.77 (( 71.77/9.77 (woz13rule4) => 71.77/9.77 (( 71.77/9.77 (woz1_1) => 71.77/9.77 (( 71.77/9.77 (woz1_2) => 71.77/9.77 (( 71.77/9.77 (woz1_3) => 71.77/9.77 (( 71.77/9.77 (woz1_4) => 71.77/9.77 (( 71.77/9.77 (woz1_5) => 71.77/9.77 (( 71.77/9.77 (breln1all2) => 71.77/9.77 (( 71.77/9.77 (breln1SetBreln1) => 71.77/9.77 (( 71.77/9.77 (choice2fnsingleton) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln1) => 71.77/9.77 (( 71.77/9.77 (breln1all1) => 71.77/9.77 (( 71.77/9.77 (subbreln1) => 71.77/9.77 (( 71.77/9.77 (eqbreln1) => 71.77/9.77 (( 71.77/9.77 (breln1invprop) => 71.77/9.77 (( 71.77/9.77 (breln1invI) => 71.77/9.77 (( 71.77/9.77 (breln1invE) => 71.77/9.77 (( 71.77/9.77 (breln1compprop) => 71.77/9.77 (( 71.77/9.77 (breln1compI) => 71.77/9.77 (( 71.77/9.77 (breln1compE) => 71.77/9.77 (( 71.77/9.77 (breln1compEex) => 71.77/9.77 (( 71.77/9.77 (!!) @ ( 71.77/9.77 (('#B') @ ( 71.77/9.77 !!) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 !!))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#C') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 breln1)))) @ 71.77/9.77 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl496])). 71.77/9.77 thf(zip_derived_cl517, plain, 71.77/9.77 (~ (((emptyE1) => 71.77/9.77 (((vacuousDall) => 71.77/9.77 (((quantDeMorgan1) => 71.77/9.77 (((quantDeMorgan2) => 71.77/9.77 (((quantDeMorgan3) => 71.77/9.77 (((quantDeMorgan4) => 71.77/9.77 (((prop2setI) => 71.77/9.77 (((prop2set2propI) => 71.77/9.77 (((notdexE) => 71.77/9.77 (((notdallE) => 71.77/9.77 (((exuI1) => 71.77/9.77 (((exuI3) => 71.77/9.77 (((exuI2) => 71.77/9.77 (((inCongP) => 71.77/9.77 (((in__Cong) => 71.77/9.77 (((exuE3u) => 71.77/9.77 (((exu__Cong) => 71.77/9.77 (((setadjoin__Cong) => 71.77/9.77 (((powerset__Cong) => 71.77/9.77 (((setunion__Cong) => 71.77/9.77 (((exuEu) => 71.77/9.77 (((descr__Cong) => 71.77/9.77 (((dsetconstr__Cong) => 71.77/9.77 (((subsetI1) => 71.77/9.77 (((eqimpsubset2) => 71.77/9.77 (((eqimpsubset1) => 71.77/9.77 (((subsetI2) => 71.77/9.77 (((emptysetsubset) => 71.77/9.77 (((subsetE) => 71.77/9.77 (((subsetE2) => 71.77/9.77 (( 71.77/9.77 (notsubsetI) => 71.77/9.77 (( 71.77/9.77 (notequalI1) => 71.77/9.77 (( 71.77/9.77 (notequalI2) => 71.77/9.77 (( 71.77/9.77 (subsetRefl) => 71.77/9.77 (( 71.77/9.77 (subsetTrans) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub2) => 71.77/9.77 (( 71.77/9.77 (subset2powerset) => 71.77/9.77 (( 71.77/9.77 (setextsub) => 71.77/9.77 (( 71.77/9.77 (subsetemptysetimpeq) => 71.77/9.77 (( 71.77/9.77 (powersetI1) => 71.77/9.77 (( 71.77/9.77 (powersetE1) => 71.77/9.77 (( 71.77/9.77 (inPowerset) => 71.77/9.77 (( 71.77/9.77 (powersetsubset) => 71.77/9.77 (( 71.77/9.77 (sepInPowerset) => 71.77/9.77 (( 71.77/9.77 (sepSubset) => 71.77/9.77 (( 71.77/9.77 (binunionIL) => 71.77/9.77 (( 71.77/9.77 (upairset2IR) => 71.77/9.77 (( 71.77/9.77 (binunionIR) => 71.77/9.77 (( 71.77/9.77 (binunionEcases) => 71.77/9.77 (( 71.77/9.77 (binunionE) => 71.77/9.77 (( 71.77/9.77 (binunionLsub) => 71.77/9.77 (( 71.77/9.77 (binunionRsub) => 71.77/9.77 (( 71.77/9.77 (binintersectI) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset5) => 71.77/9.77 (( 71.77/9.77 (binintersectEL) => 71.77/9.77 (( 71.77/9.77 (binintersectLsub) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset2) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset3) => 71.77/9.77 (( 71.77/9.77 (binintersectER) => 71.77/9.77 (( 71.77/9.77 (disjointsetsI1) => 71.77/9.77 (( 71.77/9.77 (binintersectRsub) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset4) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset1) => 71.77/9.77 (( 71.77/9.77 (bs114d) => 71.77/9.77 (( 71.77/9.77 (setminusI) => 71.77/9.77 (( 71.77/9.77 (setminusEL) => 71.77/9.77 (( 71.77/9.77 (setminusER) => 71.77/9.77 (( 71.77/9.77 (setminusSubset2) => 71.77/9.77 (( 71.77/9.77 (setminusERneg) => 71.77/9.77 (( 71.77/9.77 (setminusELneg) => 71.77/9.77 (( 71.77/9.77 (setminusILneg) => 71.77/9.77 (( 71.77/9.77 (setminusIRneg) => 71.77/9.77 (( 71.77/9.77 (setminusLsub) => 71.77/9.77 (( 71.77/9.77 (setminusSubset1) => 71.77/9.77 (( 71.77/9.77 (symdiffE) => 71.77/9.77 (( 71.77/9.77 (symdiffI1) => 71.77/9.77 (( 71.77/9.77 (symdiffI2) => 71.77/9.77 (( 71.77/9.77 (symdiffIneg1) => 71.77/9.77 (( 71.77/9.77 (symdiffIneg2) => 71.77/9.77 (( 71.77/9.77 (secondinupair) => 71.77/9.77 (( 71.77/9.77 (setukpairIL) => 71.77/9.77 (( 71.77/9.77 (setukpairIR) => 71.77/9.77 (( 71.77/9.77 (kpairiskpair) => 71.77/9.77 (( 71.77/9.77 (kpairp) => 71.77/9.77 (( 71.77/9.77 (singletonsubset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowerset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowunion) => 71.77/9.77 (( 71.77/9.77 (upairset2E) => 71.77/9.77 (( 71.77/9.77 (upairsubunion) => 71.77/9.77 (( 71.77/9.77 (upairinpowunion) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem1) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem2) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem3) => 71.77/9.77 (( 71.77/9.77 (cartprodpairin) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair1) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair) => 71.77/9.77 (( 71.77/9.77 (setunionE2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton1) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton) => 71.77/9.77 (( 71.77/9.77 (singletonprop) => 71.77/9.77 (( 71.77/9.77 (ex1E1) => 71.77/9.77 (( 71.77/9.77 (ex1I) => 71.77/9.77 (( 71.77/9.77 (ex1I2) => 71.77/9.77 (( 71.77/9.77 (singletonsuniq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL1) => 71.77/9.77 (( 71.77/9.77 (kfstsingleton) => 71.77/9.77 (( 71.77/9.77 (theprop) => 71.77/9.77 (( 71.77/9.77 (kfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstin) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR11) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR12) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR1) => 71.77/9.77 (( 71.77/9.77 (upairequniteq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR) => 71.77/9.77 (( 71.77/9.77 (ksndsingleton) => 71.77/9.77 (( 71.77/9.77 (ksndpairEq) => 71.77/9.77 (( 71.77/9.77 (kpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndin) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemEL) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemER) => 71.77/9.77 (( 71.77/9.77 (cartprodmempaircEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrI) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrSub) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrERa) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL1) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL2) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrER) => 71.77/9.77 (( 71.77/9.77 (funcImageSingleton) => 71.77/9.77 (( 71.77/9.77 (apProp) => 71.77/9.77 (( 71.77/9.77 (app) => 71.77/9.77 (( 71.77/9.77 (infuncsetfunc) => 71.77/9.77 (( 71.77/9.77 (ap2p) => 71.77/9.77 (( 71.77/9.77 (funcinfuncset) => 71.77/9.77 (( 71.77/9.77 (lamProp) => 71.77/9.77 (( 71.77/9.77 (lamp) => 71.77/9.77 (( 71.77/9.77 (lam2p) => 71.77/9.77 (( 71.77/9.77 (brelnall1) => 71.77/9.77 (( 71.77/9.77 (brelnall2) => 71.77/9.77 (( 71.77/9.77 (ex1E2) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp1) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp3) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp2) => 71.77/9.77 (( 71.77/9.77 (funcextLem) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp4) => 71.77/9.77 (( 71.77/9.77 (subbreln) => 71.77/9.77 (( 71.77/9.77 (eqbreln) => 71.77/9.77 (( 71.77/9.77 (funcext) => 71.77/9.77 (( 71.77/9.77 (funcext2) => 71.77/9.77 (( 71.77/9.77 (ap2apEq1) => 71.77/9.77 (( 71.77/9.77 (ap2apEq2) => 71.77/9.77 (( 71.77/9.77 (beta1) => 71.77/9.77 (( 71.77/9.77 (eta1) => 71.77/9.77 (( 71.77/9.77 (lam2lamEq) => 71.77/9.77 (( 71.77/9.77 (beta2) => 71.77/9.77 (( 71.77/9.77 (eta2) => 71.77/9.77 (( 71.77/9.77 (iffalseProp1) => 71.77/9.77 (( 71.77/9.77 (iffalseProp2) => 71.77/9.77 (( 71.77/9.77 (iftrueProp1) => 71.77/9.77 (( 71.77/9.77 (iftrueProp2) => 71.77/9.77 (( 71.77/9.77 (ifSingleton) => 71.77/9.77 (( 71.77/9.77 (ifp) => 71.77/9.77 (( 71.77/9.77 (theeq) => 71.77/9.77 (( 71.77/9.77 (iftrue) => 71.77/9.77 (( 71.77/9.77 (iffalse) => 71.77/9.77 (( 71.77/9.77 (iftrueorfalse) => 71.77/9.77 (( 71.77/9.77 (binintersectT_lem) => 71.77/9.77 (( 71.77/9.77 (binunionT_lem) => 71.77/9.77 (( 71.77/9.77 (powersetT_lem) => 71.77/9.77 (( 71.77/9.77 (setminusT_lem) => 71.77/9.77 (( 71.77/9.77 (complementT_lem) => 71.77/9.77 (( 71.77/9.77 (setextT) => 71.77/9.77 (( 71.77/9.77 (subsetTI) => 71.77/9.77 (( 71.77/9.77 (powersetTI1) => 71.77/9.77 (( 71.77/9.77 (powersetTE1) => 71.77/9.77 (( 71.77/9.77 (complementTI1) => 71.77/9.77 (( 71.77/9.77 (complementTE1) => 71.77/9.77 (( 71.77/9.77 (binintersectTELcontra) => 71.77/9.77 (( 71.77/9.77 (binintersectTERcontra) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT1) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT2) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT3) => 71.77/9.77 (( 71.77/9.77 (doubleComplementI1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementE1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub2) => 71.77/9.77 (( 71.77/9.77 (doubleComplementEq) => 71.77/9.77 (( 71.77/9.77 (complementTnotintersectT) => 71.77/9.77 (( 71.77/9.77 (complementImpComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementSubsetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementInPowersetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (contraSubsetComplement) => 71.77/9.77 (( 71.77/9.77 (complementTcontraSubset) => 71.77/9.77 (( 71.77/9.77 (binunionTILcontra) => 71.77/9.77 (( 71.77/9.77 (binunionTIRcontra) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion2) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (intersectInPowersetIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpNotIn1) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpInComplement1) => 71.77/9.77 (( 71.77/9.77 (binunionTE) => 71.77/9.77 (( 71.77/9.77 (binunionTEcontra) => 71.77/9.77 (( 71.77/9.77 (demorgan2a1) => 71.77/9.77 (( 71.77/9.77 (complementUnionInPowersetComplement) => 71.77/9.77 (( 71.77/9.77 (demorgan2a2) => 71.77/9.77 (( 71.77/9.77 (demorgan1a) => 71.77/9.77 (( 71.77/9.77 (demorgan1b) => 71.77/9.77 (( 71.77/9.77 (demorgan1) => 71.77/9.77 (( 71.77/9.77 (demorgan2a) => 71.77/9.77 (( 71.77/9.77 (demorgan2b2) => 71.77/9.77 (( 71.77/9.77 (demorgan2b) => 71.77/9.77 (( 71.77/9.77 (demorgan2) => 71.77/9.77 (( 71.77/9.77 (woz13rule0) => 71.77/9.77 (( 71.77/9.77 (woz13rule1) => 71.77/9.77 (( 71.77/9.77 (woz13rule2) => 71.77/9.77 (( 71.77/9.77 (woz13rule3) => 71.77/9.77 (( 71.77/9.77 (woz13rule4) => 71.77/9.77 (( 71.77/9.77 (woz1_1) => 71.77/9.77 (( 71.77/9.77 (woz1_2) => 71.77/9.77 (( 71.77/9.77 (woz1_3) => 71.77/9.77 (( 71.77/9.77 (woz1_4) => 71.77/9.77 (( 71.77/9.77 (woz1_5) => 71.77/9.77 (( 71.77/9.77 (breln1all2) => 71.77/9.77 (( 71.77/9.77 (breln1SetBreln1) => 71.77/9.77 (( 71.77/9.77 (choice2fnsingleton) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln1) => 71.77/9.77 (( 71.77/9.77 (breln1all1) => 71.77/9.77 (( 71.77/9.77 (subbreln1) => 71.77/9.77 (( 71.77/9.77 (eqbreln1) => 71.77/9.77 (( 71.77/9.77 (breln1invprop) => 71.77/9.77 (( 71.77/9.77 (breln1invI) => 71.77/9.77 (( 71.77/9.77 (breln1invE) => 71.77/9.77 (( 71.77/9.77 (breln1compprop) => 71.77/9.77 (( 71.77/9.77 (breln1compI) => 71.77/9.77 (( 71.77/9.77 (breln1compE) => 71.77/9.77 (( 71.77/9.77 (breln1compEex) => 71.77/9.77 (( 71.77/9.77 (!!) @ ( 71.77/9.77 (('#B') @ ( 71.77/9.77 !!) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 !!))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#C') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 breln1)))) @ 71.77/9.77 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl507])). 71.77/9.77 thf(zip_derived_cl528, plain, 71.77/9.77 (~ (((vacuousDall) => 71.77/9.77 (((quantDeMorgan1) => 71.77/9.77 (((quantDeMorgan2) => 71.77/9.77 (((quantDeMorgan3) => 71.77/9.77 (((quantDeMorgan4) => 71.77/9.77 (((prop2setI) => 71.77/9.77 (((prop2set2propI) => 71.77/9.77 (((notdexE) => 71.77/9.77 (((notdallE) => 71.77/9.77 (((exuI1) => 71.77/9.77 (((exuI3) => 71.77/9.77 (((exuI2) => 71.77/9.77 (((inCongP) => 71.77/9.77 (((in__Cong) => 71.77/9.77 (((exuE3u) => 71.77/9.77 (((exu__Cong) => 71.77/9.77 (((setadjoin__Cong) => 71.77/9.77 (((powerset__Cong) => 71.77/9.77 (((setunion__Cong) => 71.77/9.77 (((exuEu) => 71.77/9.77 (((descr__Cong) => 71.77/9.77 (((dsetconstr__Cong) => 71.77/9.77 (((subsetI1) => 71.77/9.77 (((eqimpsubset2) => 71.77/9.77 (((eqimpsubset1) => 71.77/9.77 (((subsetI2) => 71.77/9.77 (((emptysetsubset) => 71.77/9.77 (((subsetE) => 71.77/9.77 (((subsetE2) => 71.77/9.77 (((notsubsetI) => 71.77/9.77 (( 71.77/9.77 (notequalI1) => 71.77/9.77 (( 71.77/9.77 (notequalI2) => 71.77/9.77 (( 71.77/9.77 (subsetRefl) => 71.77/9.77 (( 71.77/9.77 (subsetTrans) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub2) => 71.77/9.77 (( 71.77/9.77 (subset2powerset) => 71.77/9.77 (( 71.77/9.77 (setextsub) => 71.77/9.77 (( 71.77/9.77 (subsetemptysetimpeq) => 71.77/9.77 (( 71.77/9.77 (powersetI1) => 71.77/9.77 (( 71.77/9.77 (powersetE1) => 71.77/9.77 (( 71.77/9.77 (inPowerset) => 71.77/9.77 (( 71.77/9.77 (powersetsubset) => 71.77/9.77 (( 71.77/9.77 (sepInPowerset) => 71.77/9.77 (( 71.77/9.77 (sepSubset) => 71.77/9.77 (( 71.77/9.77 (binunionIL) => 71.77/9.77 (( 71.77/9.77 (upairset2IR) => 71.77/9.77 (( 71.77/9.77 (binunionIR) => 71.77/9.77 (( 71.77/9.77 (binunionEcases) => 71.77/9.77 (( 71.77/9.77 (binunionE) => 71.77/9.77 (( 71.77/9.77 (binunionLsub) => 71.77/9.77 (( 71.77/9.77 (binunionRsub) => 71.77/9.77 (( 71.77/9.77 (binintersectI) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset5) => 71.77/9.77 (( 71.77/9.77 (binintersectEL) => 71.77/9.77 (( 71.77/9.77 (binintersectLsub) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset2) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset3) => 71.77/9.77 (( 71.77/9.77 (binintersectER) => 71.77/9.77 (( 71.77/9.77 (disjointsetsI1) => 71.77/9.77 (( 71.77/9.77 (binintersectRsub) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset4) => 71.77/9.77 (( 71.77/9.77 (binintersectSubset1) => 71.77/9.77 (( 71.77/9.77 (bs114d) => 71.77/9.77 (( 71.77/9.77 (setminusI) => 71.77/9.77 (( 71.77/9.77 (setminusEL) => 71.77/9.77 (( 71.77/9.77 (setminusER) => 71.77/9.77 (( 71.77/9.77 (setminusSubset2) => 71.77/9.77 (( 71.77/9.77 (setminusERneg) => 71.77/9.77 (( 71.77/9.77 (setminusELneg) => 71.77/9.77 (( 71.77/9.77 (setminusILneg) => 71.77/9.77 (( 71.77/9.77 (setminusIRneg) => 71.77/9.77 (( 71.77/9.77 (setminusLsub) => 71.77/9.77 (( 71.77/9.77 (setminusSubset1) => 71.77/9.77 (( 71.77/9.77 (symdiffE) => 71.77/9.77 (( 71.77/9.77 (symdiffI1) => 71.77/9.77 (( 71.77/9.77 (symdiffI2) => 71.77/9.77 (( 71.77/9.77 (symdiffIneg1) => 71.77/9.77 (( 71.77/9.77 (symdiffIneg2) => 71.77/9.77 (( 71.77/9.77 (secondinupair) => 71.77/9.77 (( 71.77/9.77 (setukpairIL) => 71.77/9.77 (( 71.77/9.77 (setukpairIR) => 71.77/9.77 (( 71.77/9.77 (kpairiskpair) => 71.77/9.77 (( 71.77/9.77 (kpairp) => 71.77/9.77 (( 71.77/9.77 (singletonsubset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowerset) => 71.77/9.77 (( 71.77/9.77 (singletoninpowunion) => 71.77/9.77 (( 71.77/9.77 (upairset2E) => 71.77/9.77 (( 71.77/9.77 (upairsubunion) => 71.77/9.77 (( 71.77/9.77 (upairinpowunion) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem1) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem2) => 71.77/9.77 (( 71.77/9.77 (ubforcartprodlem3) => 71.77/9.77 (( 71.77/9.77 (cartprodpairin) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair1) => 71.77/9.77 (( 71.77/9.77 (cartprodmempair) => 71.77/9.77 (( 71.77/9.77 (setunionE2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton1) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton2) => 71.77/9.77 (( 71.77/9.77 (setunionsingleton) => 71.77/9.77 (( 71.77/9.77 (singletonprop) => 71.77/9.77 (( 71.77/9.77 (ex1E1) => 71.77/9.77 (( 71.77/9.77 (ex1I) => 71.77/9.77 (( 71.77/9.77 (ex1I2) => 71.77/9.77 (( 71.77/9.77 (singletonsuniq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL1) => 71.77/9.77 (( 71.77/9.77 (kfstsingleton) => 71.77/9.77 (( 71.77/9.77 (theprop) => 71.77/9.77 (( 71.77/9.77 (kfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstin) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjL) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR11) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR12) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR1) => 71.77/9.77 (( 71.77/9.77 (upairequniteq) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR2) => 71.77/9.77 (( 71.77/9.77 (setukpairinjR) => 71.77/9.77 (( 71.77/9.77 (ksndsingleton) => 71.77/9.77 (( 71.77/9.77 (ksndpairEq) => 71.77/9.77 (( 71.77/9.77 (kpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndin) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemEL) => 71.77/9.77 (( 71.77/9.77 (cartprodpairmemER) => 71.77/9.77 (( 71.77/9.77 (cartprodmempaircEq) => 71.77/9.77 (( 71.77/9.77 (cartprodfstpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodsndpairEq) => 71.77/9.77 (( 71.77/9.77 (cartprodpairsurjEq) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrI) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrSub) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrERa) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL1) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrEL2) => 71.77/9.77 (( 71.77/9.77 (dpsetconstrER) => 71.77/9.77 (( 71.77/9.77 (funcImageSingleton) => 71.77/9.77 (( 71.77/9.77 (apProp) => 71.77/9.77 (( 71.77/9.77 (app) => 71.77/9.77 (( 71.77/9.77 (infuncsetfunc) => 71.77/9.77 (( 71.77/9.77 (ap2p) => 71.77/9.77 (( 71.77/9.77 (funcinfuncset) => 71.77/9.77 (( 71.77/9.77 (lamProp) => 71.77/9.77 (( 71.77/9.77 (lamp) => 71.77/9.77 (( 71.77/9.77 (lam2p) => 71.77/9.77 (( 71.77/9.77 (brelnall1) => 71.77/9.77 (( 71.77/9.77 (brelnall2) => 71.77/9.77 (( 71.77/9.77 (ex1E2) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp1) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp3) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp2) => 71.77/9.77 (( 71.77/9.77 (funcextLem) => 71.77/9.77 (( 71.77/9.77 (funcGraphProp4) => 71.77/9.77 (( 71.77/9.77 (subbreln) => 71.77/9.77 (( 71.77/9.77 (eqbreln) => 71.77/9.77 (( 71.77/9.77 (funcext) => 71.77/9.77 (( 71.77/9.77 (funcext2) => 71.77/9.77 (( 71.77/9.77 (ap2apEq1) => 71.77/9.77 (( 71.77/9.77 (ap2apEq2) => 71.77/9.77 (( 71.77/9.77 (beta1) => 71.77/9.77 (( 71.77/9.77 (eta1) => 71.77/9.77 (( 71.77/9.77 (lam2lamEq) => 71.77/9.77 (( 71.77/9.77 (beta2) => 71.77/9.77 (( 71.77/9.77 (eta2) => 71.77/9.77 (( 71.77/9.77 (iffalseProp1) => 71.77/9.77 (( 71.77/9.77 (iffalseProp2) => 71.77/9.77 (( 71.77/9.77 (iftrueProp1) => 71.77/9.77 (( 71.77/9.77 (iftrueProp2) => 71.77/9.77 (( 71.77/9.77 (ifSingleton) => 71.77/9.77 (( 71.77/9.77 (ifp) => 71.77/9.77 (( 71.77/9.77 (theeq) => 71.77/9.77 (( 71.77/9.77 (iftrue) => 71.77/9.77 (( 71.77/9.77 (iffalse) => 71.77/9.77 (( 71.77/9.77 (iftrueorfalse) => 71.77/9.77 (( 71.77/9.77 (binintersectT_lem) => 71.77/9.77 (( 71.77/9.77 (binunionT_lem) => 71.77/9.77 (( 71.77/9.77 (powersetT_lem) => 71.77/9.77 (( 71.77/9.77 (setminusT_lem) => 71.77/9.77 (( 71.77/9.77 (complementT_lem) => 71.77/9.77 (( 71.77/9.77 (setextT) => 71.77/9.77 (( 71.77/9.77 (subsetTI) => 71.77/9.77 (( 71.77/9.77 (powersetTI1) => 71.77/9.77 (( 71.77/9.77 (powersetTE1) => 71.77/9.77 (( 71.77/9.77 (complementTI1) => 71.77/9.77 (( 71.77/9.77 (complementTE1) => 71.77/9.77 (( 71.77/9.77 (binintersectTELcontra) => 71.77/9.77 (( 71.77/9.77 (binintersectTERcontra) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT1) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT2) => 71.77/9.77 (( 71.77/9.77 (contrasubsetT3) => 71.77/9.77 (( 71.77/9.77 (doubleComplementI1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementE1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub1) => 71.77/9.77 (( 71.77/9.77 (doubleComplementSub2) => 71.77/9.77 (( 71.77/9.77 (doubleComplementEq) => 71.77/9.77 (( 71.77/9.77 (complementTnotintersectT) => 71.77/9.77 (( 71.77/9.77 (complementImpComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementSubsetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (complementInPowersetComplementIntersect) => 71.77/9.77 (( 71.77/9.77 (contraSubsetComplement) => 71.77/9.77 (( 71.77/9.77 (complementTcontraSubset) => 71.77/9.77 (( 71.77/9.77 (binunionTILcontra) => 71.77/9.77 (( 71.77/9.77 (binunionTIRcontra) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInUnion2) => 71.77/9.77 (( 71.77/9.77 (inIntersectImpInIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (intersectInPowersetIntersectUnions) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpNotIn1) => 71.77/9.77 (( 71.77/9.77 (inComplementUnionImpInComplement1) => 71.77/9.77 (( 71.77/9.77 (binunionTE) => 71.77/9.77 (( 71.77/9.77 (binunionTEcontra) => 71.77/9.77 (( 71.77/9.77 (demorgan2a1) => 71.77/9.77 (( 71.77/9.77 (complementUnionInPowersetComplement) => 71.77/9.77 (( 71.77/9.77 (demorgan2a2) => 71.77/9.77 (( 71.77/9.77 (demorgan1a) => 71.77/9.77 (( 71.77/9.77 (demorgan1b) => 71.77/9.77 (( 71.77/9.77 (demorgan1) => 71.77/9.77 (( 71.77/9.77 (demorgan2a) => 71.77/9.77 (( 71.77/9.77 (demorgan2b2) => 71.77/9.77 (( 71.77/9.77 (demorgan2b) => 71.77/9.77 (( 71.77/9.77 (demorgan2) => 71.77/9.77 (( 71.77/9.77 (woz13rule0) => 71.77/9.77 (( 71.77/9.77 (woz13rule1) => 71.77/9.77 (( 71.77/9.77 (woz13rule2) => 71.77/9.77 (( 71.77/9.77 (woz13rule3) => 71.77/9.77 (( 71.77/9.77 (woz13rule4) => 71.77/9.77 (( 71.77/9.77 (woz1_1) => 71.77/9.77 (( 71.77/9.77 (woz1_2) => 71.77/9.77 (( 71.77/9.77 (woz1_3) => 71.77/9.77 (( 71.77/9.77 (woz1_4) => 71.77/9.77 (( 71.77/9.77 (woz1_5) => 71.77/9.77 (( 71.77/9.77 (breln1all2) => 71.77/9.77 (( 71.77/9.77 (breln1SetBreln1) => 71.77/9.77 (( 71.77/9.77 (choice2fnsingleton) => 71.77/9.77 (( 71.77/9.77 (setOfPairsIsBReln1) => 71.77/9.77 (( 71.77/9.77 (breln1all1) => 71.77/9.77 (( 71.77/9.77 (subbreln1) => 71.77/9.77 (( 71.77/9.77 (eqbreln1) => 71.77/9.77 (( 71.77/9.77 (breln1invprop) => 71.77/9.77 (( 71.77/9.77 (breln1invI) => 71.77/9.77 (( 71.77/9.77 (breln1invE) => 71.77/9.77 (( 71.77/9.77 (breln1compprop) => 71.77/9.77 (( 71.77/9.77 (breln1compI) => 71.77/9.77 (( 71.77/9.77 (breln1compE) => 71.77/9.77 (( 71.77/9.77 (breln1compEex) => 71.77/9.77 (( 71.77/9.77 (!!) @ ( 71.77/9.77 (('#B') @ ( 71.77/9.77 !!) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 !!))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#S') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#S') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 =>))) @ 71.77/9.77 breln1)))))) @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#C') @ ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 ( 71.77/9.77 ( 71.77/9.77 ('#B') @ ( 71.77/9.77 '#B') @ 71.77/9.77 breln1)))) @ 71.77/9.77 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl517])). 71.77/9.77 thf(zip_derived_cl537, plain, 71.77/9.77 (~ (((quantDeMorgan1) => 71.77/9.77 (((quantDeMorgan2) => 71.77/9.77 (((quantDeMorgan3) => 71.77/9.77 (((quantDeMorgan4) => 71.77/9.77 (((prop2setI) => 71.77/9.77 (((prop2set2propI) => 71.77/9.77 (((notdexE) => 71.77/9.77 (((notdallE) => 71.77/9.77 (((exuI1) => 71.77/9.77 (((exuI3) => 71.77/9.77 (((exuI2) => 71.77/9.77 (((inCongP) => 71.77/9.77 (((in__Cong) => 71.77/9.77 (((exuE3u) => 71.77/9.77 (((exu__Cong) => 71.77/9.77 (((setadjoin__Cong) => 71.77/9.77 (((powerset__Cong) => 71.77/9.77 (((setunion__Cong) => 71.77/9.77 (((exuEu) => 71.77/9.77 (((descr__Cong) => 71.77/9.77 (((dsetconstr__Cong) => 71.77/9.77 (((subsetI1) => 71.77/9.77 (((eqimpsubset2) => 71.77/9.77 (((eqimpsubset1) => 71.77/9.77 (((subsetI2) => 71.77/9.77 (((emptysetsubset) => 71.77/9.77 (((subsetE) => 71.77/9.77 (((subsetE2) => 71.77/9.77 (((notsubsetI) => 71.77/9.77 (((notequalI1) => 71.77/9.77 (( 71.77/9.77 (notequalI2) => 71.77/9.77 (( 71.77/9.77 (subsetRefl) => 71.77/9.77 (( 71.77/9.77 (subsetTrans) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub) => 71.77/9.77 (( 71.77/9.77 (setadjoinSub2) => 71.77/9.77 (( 71.77/9.77 (subset2powerset) => 71.77/9.77 (( 71.77/9.77 (setextsub) => 71.77/9.77 (( 71.77/9.77 (subsetemptysetimpeq) => 71.77/9.77 (( 71.77/9.77 (powersetI1) => 71.77/9.77 (( 71.77/9.77 (powersetE1) => 71.77/9.77 (( 71.77/9.77 (inPowerset) => 71.77/9.77 (( 71.77/9.77 (powersetsubset) => 71.77/9.77 (( 71.77/9.77 (sepInPowerset) => 71.77/9.77 (( 71.77/9.77 (sepSubset) => 71.77/9.77 (( 71.77/9.77 (binunionIL) => 71.77/9.77 (( 71.77/9.77 (upairset2IR) => 71.77/9.77 (( 71.77/9.77 (binunionIR) => 71.77/9.77 (( 71.77/9.77 (binunionEcases) => 71.77/9.77 (( 71.77/9.77 (binunionE) => 71.77/9.77 (( 71.77/9.77 (binunionLsub) => 71.77/9.77 (( 71.77/9.77 (binunionRsub) => 71.77/9.77 (( 71.77/9.77 (binintersectI) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset5) => 71.77/9.78 (( 71.77/9.78 (binintersectEL) => 71.77/9.78 (( 71.77/9.78 (binintersectLsub) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset2) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset3) => 71.77/9.78 (( 71.77/9.78 (binintersectER) => 71.77/9.78 (( 71.77/9.78 (disjointsetsI1) => 71.77/9.78 (( 71.77/9.78 (binintersectRsub) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset4) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset1) => 71.77/9.78 (( 71.77/9.78 (bs114d) => 71.77/9.78 (( 71.77/9.78 (setminusI) => 71.77/9.78 (( 71.77/9.78 (setminusEL) => 71.77/9.78 (( 71.77/9.78 (setminusER) => 71.77/9.78 (( 71.77/9.78 (setminusSubset2) => 71.77/9.78 (( 71.77/9.78 (setminusERneg) => 71.77/9.78 (( 71.77/9.78 (setminusELneg) => 71.77/9.78 (( 71.77/9.78 (setminusILneg) => 71.77/9.78 (( 71.77/9.78 (setminusIRneg) => 71.77/9.78 (( 71.77/9.78 (setminusLsub) => 71.77/9.78 (( 71.77/9.78 (setminusSubset1) => 71.77/9.78 (( 71.77/9.78 (symdiffE) => 71.77/9.78 (( 71.77/9.78 (symdiffI1) => 71.77/9.78 (( 71.77/9.78 (symdiffI2) => 71.77/9.78 (( 71.77/9.78 (symdiffIneg1) => 71.77/9.78 (( 71.77/9.78 (symdiffIneg2) => 71.77/9.78 (( 71.77/9.78 (secondinupair) => 71.77/9.78 (( 71.77/9.78 (setukpairIL) => 71.77/9.78 (( 71.77/9.78 (setukpairIR) => 71.77/9.78 (( 71.77/9.78 (kpairiskpair) => 71.77/9.78 (( 71.77/9.78 (kpairp) => 71.77/9.78 (( 71.77/9.78 (singletonsubset) => 71.77/9.78 (( 71.77/9.78 (singletoninpowerset) => 71.77/9.78 (( 71.77/9.78 (singletoninpowunion) => 71.77/9.78 (( 71.77/9.78 (upairset2E) => 71.77/9.78 (( 71.77/9.78 (upairsubunion) => 71.77/9.78 (( 71.77/9.78 (upairinpowunion) => 71.77/9.78 (( 71.77/9.78 (ubforcartprodlem1) => 71.77/9.78 (( 71.77/9.78 (ubforcartprodlem2) => 71.77/9.78 (( 71.77/9.78 (ubforcartprodlem3) => 71.77/9.78 (( 71.77/9.78 (cartprodpairin) => 71.77/9.78 (( 71.77/9.78 (cartprodmempair1) => 71.77/9.78 (( 71.77/9.78 (cartprodmempair) => 71.77/9.78 (( 71.77/9.78 (setunionE2) => 71.77/9.78 (( 71.77/9.78 (setunionsingleton1) => 71.77/9.78 (( 71.77/9.78 (setunionsingleton2) => 71.77/9.78 (( 71.77/9.78 (setunionsingleton) => 71.77/9.78 (( 71.77/9.78 (singletonprop) => 71.77/9.78 (( 71.77/9.78 (ex1E1) => 71.77/9.78 (( 71.77/9.78 (ex1I) => 71.77/9.78 (( 71.77/9.78 (ex1I2) => 71.77/9.78 (( 71.77/9.78 (singletonsuniq) => 71.77/9.78 (( 71.77/9.78 (setukpairinjL1) => 71.77/9.78 (( 71.77/9.78 (kfstsingleton) => 71.77/9.78 (( 71.77/9.78 (theprop) => 71.77/9.78 (( 71.77/9.78 (kfstpairEq) => 71.77/9.78 (( 71.77/9.78 (cartprodfstin) => 71.77/9.78 (( 71.77/9.78 (setukpairinjL2) => 71.77/9.78 (( 71.77/9.78 (setukpairinjL) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR11) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR12) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR1) => 71.77/9.78 (( 71.77/9.78 (upairequniteq) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR2) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR) => 71.77/9.78 (( 71.77/9.78 (ksndsingleton) => 71.77/9.78 (( 71.77/9.78 (ksndpairEq) => 71.77/9.78 (( 71.77/9.78 (kpairsurjEq) => 71.77/9.78 (( 71.77/9.78 (cartprodsndin) => 71.77/9.78 (( 71.77/9.78 (cartprodpairmemEL) => 71.77/9.78 (( 71.77/9.78 (cartprodpairmemER) => 71.77/9.78 (( 71.77/9.78 (cartprodmempaircEq) => 71.77/9.78 (( 71.77/9.78 (cartprodfstpairEq) => 71.77/9.78 (( 71.77/9.78 (cartprodsndpairEq) => 71.77/9.78 (( 71.77/9.78 (cartprodpairsurjEq) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrI) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrSub) => 71.77/9.78 (( 71.77/9.78 (setOfPairsIsBReln) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrERa) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrEL1) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrEL2) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrER) => 71.77/9.78 (( 71.77/9.78 (funcImageSingleton) => 71.77/9.78 (( 71.77/9.78 (apProp) => 71.77/9.78 (( 71.77/9.78 (app) => 71.77/9.78 (( 71.77/9.78 (infuncsetfunc) => 71.77/9.78 (( 71.77/9.78 (ap2p) => 71.77/9.78 (( 71.77/9.78 (funcinfuncset) => 71.77/9.78 (( 71.77/9.78 (lamProp) => 71.77/9.78 (( 71.77/9.78 (lamp) => 71.77/9.78 (( 71.77/9.78 (lam2p) => 71.77/9.78 (( 71.77/9.78 (brelnall1) => 71.77/9.78 (( 71.77/9.78 (brelnall2) => 71.77/9.78 (( 71.77/9.78 (ex1E2) => 71.77/9.78 (( 71.77/9.78 (funcGraphProp1) => 71.77/9.78 (( 71.77/9.78 (funcGraphProp3) => 71.77/9.78 (( 71.77/9.78 (funcGraphProp2) => 71.77/9.78 (( 71.77/9.78 (funcextLem) => 71.77/9.78 (( 71.77/9.78 (funcGraphProp4) => 71.77/9.78 (( 71.77/9.78 (subbreln) => 71.77/9.78 (( 71.77/9.78 (eqbreln) => 71.77/9.78 (( 71.77/9.78 (funcext) => 71.77/9.78 (( 71.77/9.78 (funcext2) => 71.77/9.78 (( 71.77/9.78 (ap2apEq1) => 71.77/9.78 (( 71.77/9.78 (ap2apEq2) => 71.77/9.78 (( 71.77/9.78 (beta1) => 71.77/9.78 (( 71.77/9.78 (eta1) => 71.77/9.78 (( 71.77/9.78 (lam2lamEq) => 71.77/9.78 (( 71.77/9.78 (beta2) => 71.77/9.78 (( 71.77/9.78 (eta2) => 71.77/9.78 (( 71.77/9.78 (iffalseProp1) => 71.77/9.78 (( 71.77/9.78 (iffalseProp2) => 71.77/9.78 (( 71.77/9.78 (iftrueProp1) => 71.77/9.78 (( 71.77/9.78 (iftrueProp2) => 71.77/9.78 (( 71.77/9.78 (ifSingleton) => 71.77/9.78 (( 71.77/9.78 (ifp) => 71.77/9.78 (( 71.77/9.78 (theeq) => 71.77/9.78 (( 71.77/9.78 (iftrue) => 71.77/9.78 (( 71.77/9.78 (iffalse) => 71.77/9.78 (( 71.77/9.78 (iftrueorfalse) => 71.77/9.78 (( 71.77/9.78 (binintersectT_lem) => 71.77/9.78 (( 71.77/9.78 (binunionT_lem) => 71.77/9.78 (( 71.77/9.78 (powersetT_lem) => 71.77/9.78 (( 71.77/9.78 (setminusT_lem) => 71.77/9.78 (( 71.77/9.78 (complementT_lem) => 71.77/9.78 (( 71.77/9.78 (setextT) => 71.77/9.78 (( 71.77/9.78 (subsetTI) => 71.77/9.78 (( 71.77/9.78 (powersetTI1) => 71.77/9.78 (( 71.77/9.78 (powersetTE1) => 71.77/9.78 (( 71.77/9.78 (complementTI1) => 71.77/9.78 (( 71.77/9.78 (complementTE1) => 71.77/9.78 (( 71.77/9.78 (binintersectTELcontra) => 71.77/9.78 (( 71.77/9.78 (binintersectTERcontra) => 71.77/9.78 (( 71.77/9.78 (contrasubsetT) => 71.77/9.78 (( 71.77/9.78 (contrasubsetT1) => 71.77/9.78 (( 71.77/9.78 (contrasubsetT2) => 71.77/9.78 (( 71.77/9.78 (contrasubsetT3) => 71.77/9.78 (( 71.77/9.78 (doubleComplementI1) => 71.77/9.78 (( 71.77/9.78 (doubleComplementE1) => 71.77/9.78 (( 71.77/9.78 (doubleComplementSub1) => 71.77/9.78 (( 71.77/9.78 (doubleComplementSub2) => 71.77/9.78 (( 71.77/9.78 (doubleComplementEq) => 71.77/9.78 (( 71.77/9.78 (complementTnotintersectT) => 71.77/9.78 (( 71.77/9.78 (complementImpComplementIntersect) => 71.77/9.78 (( 71.77/9.78 (complementSubsetComplementIntersect) => 71.77/9.78 (( 71.77/9.78 (complementInPowersetComplementIntersect) => 71.77/9.78 (( 71.77/9.78 (contraSubsetComplement) => 71.77/9.78 (( 71.77/9.78 (complementTcontraSubset) => 71.77/9.78 (( 71.77/9.78 (binunionTILcontra) => 71.77/9.78 (( 71.77/9.78 (binunionTIRcontra) => 71.77/9.78 (( 71.77/9.78 (inIntersectImpInUnion) => 71.77/9.78 (( 71.77/9.78 (inIntersectImpInUnion2) => 71.77/9.78 (( 71.77/9.78 (inIntersectImpInIntersectUnions) => 71.77/9.78 (( 71.77/9.78 (intersectInPowersetIntersectUnions) => 71.77/9.78 (( 71.77/9.78 (inComplementUnionImpNotIn1) => 71.77/9.78 (( 71.77/9.78 (inComplementUnionImpInComplement1) => 71.77/9.78 (( 71.77/9.78 (binunionTE) => 71.77/9.78 (( 71.77/9.78 (binunionTEcontra) => 71.77/9.78 (( 71.77/9.78 (demorgan2a1) => 71.77/9.78 (( 71.77/9.78 (complementUnionInPowersetComplement) => 71.77/9.78 (( 71.77/9.78 (demorgan2a2) => 71.77/9.78 (( 71.77/9.78 (demorgan1a) => 71.77/9.78 (( 71.77/9.78 (demorgan1b) => 71.77/9.78 (( 71.77/9.78 (demorgan1) => 71.77/9.78 (( 71.77/9.78 (demorgan2a) => 71.77/9.78 (( 71.77/9.78 (demorgan2b2) => 71.77/9.78 (( 71.77/9.78 (demorgan2b) => 71.77/9.78 (( 71.77/9.78 (demorgan2) => 71.77/9.78 (( 71.77/9.78 (woz13rule0) => 71.77/9.78 (( 71.77/9.78 (woz13rule1) => 71.77/9.78 (( 71.77/9.78 (woz13rule2) => 71.77/9.78 (( 71.77/9.78 (woz13rule3) => 71.77/9.78 (( 71.77/9.78 (woz13rule4) => 71.77/9.78 (( 71.77/9.78 (woz1_1) => 71.77/9.78 (( 71.77/9.78 (woz1_2) => 71.77/9.78 (( 71.77/9.78 (woz1_3) => 71.77/9.78 (( 71.77/9.78 (woz1_4) => 71.77/9.78 (( 71.77/9.78 (woz1_5) => 71.77/9.78 (( 71.77/9.78 (breln1all2) => 71.77/9.78 (( 71.77/9.78 (breln1SetBreln1) => 71.77/9.78 (( 71.77/9.78 (choice2fnsingleton) => 71.77/9.78 (( 71.77/9.78 (setOfPairsIsBReln1) => 71.77/9.78 (( 71.77/9.78 (breln1all1) => 71.77/9.78 (( 71.77/9.78 (subbreln1) => 71.77/9.78 (( 71.77/9.78 (eqbreln1) => 71.77/9.78 (( 71.77/9.78 (breln1invprop) => 71.77/9.78 (( 71.77/9.78 (breln1invI) => 71.77/9.78 (( 71.77/9.78 (breln1invE) => 71.77/9.78 (( 71.77/9.78 (breln1compprop) => 71.77/9.78 (( 71.77/9.78 (breln1compI) => 71.77/9.78 (( 71.77/9.78 (breln1compE) => 71.77/9.78 (( 71.77/9.78 (breln1compEex) => 71.77/9.78 (( 71.77/9.78 (!!) @ ( 71.77/9.78 (('#B') @ ( 71.77/9.78 !!) @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#S') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#S') @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 =>))) @ 71.77/9.78 breln1)))) @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 !!))) @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#S') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#B') @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#S') @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 =>))) @ 71.77/9.78 breln1)))))) @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#C') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#B') @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#B') @ 71.77/9.78 breln1)))) @ 71.77/9.78 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])). 71.77/9.78 thf(zip_derived_cl546, plain, 71.77/9.78 (~ (((quantDeMorgan2) => 71.77/9.78 (((quantDeMorgan3) => 71.77/9.78 (((quantDeMorgan4) => 71.77/9.78 (((prop2setI) => 71.77/9.78 (((prop2set2propI) => 71.77/9.78 (((notdexE) => 71.77/9.78 (((notdallE) => 71.77/9.78 (((exuI1) => 71.77/9.78 (((exuI3) => 71.77/9.78 (((exuI2) => 71.77/9.78 (((inCongP) => 71.77/9.78 (((in__Cong) => 71.77/9.78 (((exuE3u) => 71.77/9.78 (((exu__Cong) => 71.77/9.78 (((setadjoin__Cong) => 71.77/9.78 (((powerset__Cong) => 71.77/9.78 (((setunion__Cong) => 71.77/9.78 (((exuEu) => 71.77/9.78 (((descr__Cong) => 71.77/9.78 (((dsetconstr__Cong) => 71.77/9.78 (((subsetI1) => 71.77/9.78 (((eqimpsubset2) => 71.77/9.78 (((eqimpsubset1) => 71.77/9.78 (((subsetI2) => 71.77/9.78 (((emptysetsubset) => 71.77/9.78 (((subsetE) => 71.77/9.78 (((subsetE2) => 71.77/9.78 (((notsubsetI) => 71.77/9.78 (((notequalI1) => 71.77/9.78 (((notequalI2) => 71.77/9.78 (( 71.77/9.78 (subsetRefl) => 71.77/9.78 (( 71.77/9.78 (subsetTrans) => 71.77/9.78 (( 71.77/9.78 (setadjoinSub) => 71.77/9.78 (( 71.77/9.78 (setadjoinSub2) => 71.77/9.78 (( 71.77/9.78 (subset2powerset) => 71.77/9.78 (( 71.77/9.78 (setextsub) => 71.77/9.78 (( 71.77/9.78 (subsetemptysetimpeq) => 71.77/9.78 (( 71.77/9.78 (powersetI1) => 71.77/9.78 (( 71.77/9.78 (powersetE1) => 71.77/9.78 (( 71.77/9.78 (inPowerset) => 71.77/9.78 (( 71.77/9.78 (powersetsubset) => 71.77/9.78 (( 71.77/9.78 (sepInPowerset) => 71.77/9.78 (( 71.77/9.78 (sepSubset) => 71.77/9.78 (( 71.77/9.78 (binunionIL) => 71.77/9.78 (( 71.77/9.78 (upairset2IR) => 71.77/9.78 (( 71.77/9.78 (binunionIR) => 71.77/9.78 (( 71.77/9.78 (binunionEcases) => 71.77/9.78 (( 71.77/9.78 (binunionE) => 71.77/9.78 (( 71.77/9.78 (binunionLsub) => 71.77/9.78 (( 71.77/9.78 (binunionRsub) => 71.77/9.78 (( 71.77/9.78 (binintersectI) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset5) => 71.77/9.78 (( 71.77/9.78 (binintersectEL) => 71.77/9.78 (( 71.77/9.78 (binintersectLsub) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset2) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset3) => 71.77/9.78 (( 71.77/9.78 (binintersectER) => 71.77/9.78 (( 71.77/9.78 (disjointsetsI1) => 71.77/9.78 (( 71.77/9.78 (binintersectRsub) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset4) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset1) => 71.77/9.78 (( 71.77/9.78 (bs114d) => 71.77/9.78 (( 71.77/9.78 (setminusI) => 71.77/9.78 (( 71.77/9.78 (setminusEL) => 71.77/9.78 (( 71.77/9.78 (setminusER) => 71.77/9.78 (( 71.77/9.78 (setminusSubset2) => 71.77/9.78 (( 71.77/9.78 (setminusERneg) => 71.77/9.78 (( 71.77/9.78 (setminusELneg) => 71.77/9.78 (( 71.77/9.78 (setminusILneg) => 71.77/9.78 (( 71.77/9.78 (setminusIRneg) => 71.77/9.78 (( 71.77/9.78 (setminusLsub) => 71.77/9.78 (( 71.77/9.78 (setminusSubset1) => 71.77/9.78 (( 71.77/9.78 (symdiffE) => 71.77/9.78 (( 71.77/9.78 (symdiffI1) => 71.77/9.78 (( 71.77/9.78 (symdiffI2) => 71.77/9.78 (( 71.77/9.78 (symdiffIneg1) => 71.77/9.78 (( 71.77/9.78 (symdiffIneg2) => 71.77/9.78 (( 71.77/9.78 (secondinupair) => 71.77/9.78 (( 71.77/9.78 (setukpairIL) => 71.77/9.78 (( 71.77/9.78 (setukpairIR) => 71.77/9.78 (( 71.77/9.78 (kpairiskpair) => 71.77/9.78 (( 71.77/9.78 (kpairp) => 71.77/9.78 (( 71.77/9.78 (singletonsubset) => 71.77/9.78 (( 71.77/9.78 (singletoninpowerset) => 71.77/9.78 (( 71.77/9.78 (singletoninpowunion) => 71.77/9.78 (( 71.77/9.78 (upairset2E) => 71.77/9.78 (( 71.77/9.78 (upairsubunion) => 71.77/9.78 (( 71.77/9.78 (upairinpowunion) => 71.77/9.78 (( 71.77/9.78 (ubforcartprodlem1) => 71.77/9.78 (( 71.77/9.78 (ubforcartprodlem2) => 71.77/9.78 (( 71.77/9.78 (ubforcartprodlem3) => 71.77/9.78 (( 71.77/9.78 (cartprodpairin) => 71.77/9.78 (( 71.77/9.78 (cartprodmempair1) => 71.77/9.78 (( 71.77/9.78 (cartprodmempair) => 71.77/9.78 (( 71.77/9.78 (setunionE2) => 71.77/9.78 (( 71.77/9.78 (setunionsingleton1) => 71.77/9.78 (( 71.77/9.78 (setunionsingleton2) => 71.77/9.78 (( 71.77/9.78 (setunionsingleton) => 71.77/9.78 (( 71.77/9.78 (singletonprop) => 71.77/9.78 (( 71.77/9.78 (ex1E1) => 71.77/9.78 (( 71.77/9.78 (ex1I) => 71.77/9.78 (( 71.77/9.78 (ex1I2) => 71.77/9.78 (( 71.77/9.78 (singletonsuniq) => 71.77/9.78 (( 71.77/9.78 (setukpairinjL1) => 71.77/9.78 (( 71.77/9.78 (kfstsingleton) => 71.77/9.78 (( 71.77/9.78 (theprop) => 71.77/9.78 (( 71.77/9.78 (kfstpairEq) => 71.77/9.78 (( 71.77/9.78 (cartprodfstin) => 71.77/9.78 (( 71.77/9.78 (setukpairinjL2) => 71.77/9.78 (( 71.77/9.78 (setukpairinjL) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR11) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR12) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR1) => 71.77/9.78 (( 71.77/9.78 (upairequniteq) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR2) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR) => 71.77/9.78 (( 71.77/9.78 (ksndsingleton) => 71.77/9.78 (( 71.77/9.78 (ksndpairEq) => 71.77/9.78 (( 71.77/9.78 (kpairsurjEq) => 71.77/9.78 (( 71.77/9.78 (cartprodsndin) => 71.77/9.78 (( 71.77/9.78 (cartprodpairmemEL) => 71.77/9.78 (( 71.77/9.78 (cartprodpairmemER) => 71.77/9.78 (( 71.77/9.78 (cartprodmempaircEq) => 71.77/9.78 (( 71.77/9.78 (cartprodfstpairEq) => 71.77/9.78 (( 71.77/9.78 (cartprodsndpairEq) => 71.77/9.78 (( 71.77/9.78 (cartprodpairsurjEq) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrI) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrSub) => 71.77/9.78 (( 71.77/9.78 (setOfPairsIsBReln) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrERa) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrEL1) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrEL2) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrER) => 71.77/9.78 (( 71.77/9.78 (funcImageSingleton) => 71.77/9.78 (( 71.77/9.78 (apProp) => 71.77/9.78 (( 71.77/9.78 (app) => 71.77/9.78 (( 71.77/9.78 (infuncsetfunc) => 71.77/9.78 (( 71.77/9.78 (ap2p) => 71.77/9.78 (( 71.77/9.78 (funcinfuncset) => 71.77/9.78 (( 71.77/9.78 (lamProp) => 71.77/9.78 (( 71.77/9.78 (lamp) => 71.77/9.78 (( 71.77/9.78 (lam2p) => 71.77/9.78 (( 71.77/9.78 (brelnall1) => 71.77/9.78 (( 71.77/9.78 (brelnall2) => 71.77/9.78 (( 71.77/9.78 (ex1E2) => 71.77/9.78 (( 71.77/9.78 (funcGraphProp1) => 71.77/9.78 (( 71.77/9.78 (funcGraphProp3) => 71.77/9.78 (( 71.77/9.78 (funcGraphProp2) => 71.77/9.78 (( 71.77/9.78 (funcextLem) => 71.77/9.78 (( 71.77/9.78 (funcGraphProp4) => 71.77/9.78 (( 71.77/9.78 (subbreln) => 71.77/9.78 (( 71.77/9.78 (eqbreln) => 71.77/9.78 (( 71.77/9.78 (funcext) => 71.77/9.78 (( 71.77/9.78 (funcext2) => 71.77/9.78 (( 71.77/9.78 (ap2apEq1) => 71.77/9.78 (( 71.77/9.78 (ap2apEq2) => 71.77/9.78 (( 71.77/9.78 (beta1) => 71.77/9.78 (( 71.77/9.78 (eta1) => 71.77/9.78 (( 71.77/9.78 (lam2lamEq) => 71.77/9.78 (( 71.77/9.78 (beta2) => 71.77/9.78 (( 71.77/9.78 (eta2) => 71.77/9.78 (( 71.77/9.78 (iffalseProp1) => 71.77/9.78 (( 71.77/9.78 (iffalseProp2) => 71.77/9.78 (( 71.77/9.78 (iftrueProp1) => 71.77/9.78 (( 71.77/9.78 (iftrueProp2) => 71.77/9.78 (( 71.77/9.78 (ifSingleton) => 71.77/9.78 (( 71.77/9.78 (ifp) => 71.77/9.78 (( 71.77/9.78 (theeq) => 71.77/9.78 (( 71.77/9.78 (iftrue) => 71.77/9.78 (( 71.77/9.78 (iffalse) => 71.77/9.78 (( 71.77/9.78 (iftrueorfalse) => 71.77/9.78 (( 71.77/9.78 (binintersectT_lem) => 71.77/9.78 (( 71.77/9.78 (binunionT_lem) => 71.77/9.78 (( 71.77/9.78 (powersetT_lem) => 71.77/9.78 (( 71.77/9.78 (setminusT_lem) => 71.77/9.78 (( 71.77/9.78 (complementT_lem) => 71.77/9.78 (( 71.77/9.78 (setextT) => 71.77/9.78 (( 71.77/9.78 (subsetTI) => 71.77/9.78 (( 71.77/9.78 (powersetTI1) => 71.77/9.78 (( 71.77/9.78 (powersetTE1) => 71.77/9.78 (( 71.77/9.78 (complementTI1) => 71.77/9.78 (( 71.77/9.78 (complementTE1) => 71.77/9.78 (( 71.77/9.78 (binintersectTELcontra) => 71.77/9.78 (( 71.77/9.78 (binintersectTERcontra) => 71.77/9.78 (( 71.77/9.78 (contrasubsetT) => 71.77/9.78 (( 71.77/9.78 (contrasubsetT1) => 71.77/9.78 (( 71.77/9.78 (contrasubsetT2) => 71.77/9.78 (( 71.77/9.78 (contrasubsetT3) => 71.77/9.78 (( 71.77/9.78 (doubleComplementI1) => 71.77/9.78 (( 71.77/9.78 (doubleComplementE1) => 71.77/9.78 (( 71.77/9.78 (doubleComplementSub1) => 71.77/9.78 (( 71.77/9.78 (doubleComplementSub2) => 71.77/9.78 (( 71.77/9.78 (doubleComplementEq) => 71.77/9.78 (( 71.77/9.78 (complementTnotintersectT) => 71.77/9.78 (( 71.77/9.78 (complementImpComplementIntersect) => 71.77/9.78 (( 71.77/9.78 (complementSubsetComplementIntersect) => 71.77/9.78 (( 71.77/9.78 (complementInPowersetComplementIntersect) => 71.77/9.78 (( 71.77/9.78 (contraSubsetComplement) => 71.77/9.78 (( 71.77/9.78 (complementTcontraSubset) => 71.77/9.78 (( 71.77/9.78 (binunionTILcontra) => 71.77/9.78 (( 71.77/9.78 (binunionTIRcontra) => 71.77/9.78 (( 71.77/9.78 (inIntersectImpInUnion) => 71.77/9.78 (( 71.77/9.78 (inIntersectImpInUnion2) => 71.77/9.78 (( 71.77/9.78 (inIntersectImpInIntersectUnions) => 71.77/9.78 (( 71.77/9.78 (intersectInPowersetIntersectUnions) => 71.77/9.78 (( 71.77/9.78 (inComplementUnionImpNotIn1) => 71.77/9.78 (( 71.77/9.78 (inComplementUnionImpInComplement1) => 71.77/9.78 (( 71.77/9.78 (binunionTE) => 71.77/9.78 (( 71.77/9.78 (binunionTEcontra) => 71.77/9.78 (( 71.77/9.78 (demorgan2a1) => 71.77/9.78 (( 71.77/9.78 (complementUnionInPowersetComplement) => 71.77/9.78 (( 71.77/9.78 (demorgan2a2) => 71.77/9.78 (( 71.77/9.78 (demorgan1a) => 71.77/9.78 (( 71.77/9.78 (demorgan1b) => 71.77/9.78 (( 71.77/9.78 (demorgan1) => 71.77/9.78 (( 71.77/9.78 (demorgan2a) => 71.77/9.78 (( 71.77/9.78 (demorgan2b2) => 71.77/9.78 (( 71.77/9.78 (demorgan2b) => 71.77/9.78 (( 71.77/9.78 (demorgan2) => 71.77/9.78 (( 71.77/9.78 (woz13rule0) => 71.77/9.78 (( 71.77/9.78 (woz13rule1) => 71.77/9.78 (( 71.77/9.78 (woz13rule2) => 71.77/9.78 (( 71.77/9.78 (woz13rule3) => 71.77/9.78 (( 71.77/9.78 (woz13rule4) => 71.77/9.78 (( 71.77/9.78 (woz1_1) => 71.77/9.78 (( 71.77/9.78 (woz1_2) => 71.77/9.78 (( 71.77/9.78 (woz1_3) => 71.77/9.78 (( 71.77/9.78 (woz1_4) => 71.77/9.78 (( 71.77/9.78 (woz1_5) => 71.77/9.78 (( 71.77/9.78 (breln1all2) => 71.77/9.78 (( 71.77/9.78 (breln1SetBreln1) => 71.77/9.78 (( 71.77/9.78 (choice2fnsingleton) => 71.77/9.78 (( 71.77/9.78 (setOfPairsIsBReln1) => 71.77/9.78 (( 71.77/9.78 (breln1all1) => 71.77/9.78 (( 71.77/9.78 (subbreln1) => 71.77/9.78 (( 71.77/9.78 (eqbreln1) => 71.77/9.78 (( 71.77/9.78 (breln1invprop) => 71.77/9.78 (( 71.77/9.78 (breln1invI) => 71.77/9.78 (( 71.77/9.78 (breln1invE) => 71.77/9.78 (( 71.77/9.78 (breln1compprop) => 71.77/9.78 (( 71.77/9.78 (breln1compI) => 71.77/9.78 (( 71.77/9.78 (breln1compE) => 71.77/9.78 (( 71.77/9.78 (breln1compEex) => 71.77/9.78 (( 71.77/9.78 (!!) @ ( 71.77/9.78 (('#B') @ ( 71.77/9.78 !!) @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#S') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#S') @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 =>))) @ 71.77/9.78 breln1)))) @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 !!))) @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#S') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#B') @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#S') @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 =>))) @ 71.77/9.78 breln1)))))) @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#C') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#B') @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#B') @ 71.77/9.78 breln1)))) @ 71.77/9.78 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])). 71.77/9.78 thf(zip_derived_cl553, plain, 71.77/9.78 (~ (((quantDeMorgan3) => 71.77/9.78 (((quantDeMorgan4) => 71.77/9.78 (((prop2setI) => 71.77/9.78 (((prop2set2propI) => 71.77/9.78 (((notdexE) => 71.77/9.78 (((notdallE) => 71.77/9.78 (((exuI1) => 71.77/9.78 (((exuI3) => 71.77/9.78 (((exuI2) => 71.77/9.78 (((inCongP) => 71.77/9.78 (((in__Cong) => 71.77/9.78 (((exuE3u) => 71.77/9.78 (((exu__Cong) => 71.77/9.78 (((setadjoin__Cong) => 71.77/9.78 (((powerset__Cong) => 71.77/9.78 (((setunion__Cong) => 71.77/9.78 (((exuEu) => 71.77/9.78 (((descr__Cong) => 71.77/9.78 (((dsetconstr__Cong) => 71.77/9.78 (((subsetI1) => 71.77/9.78 (((eqimpsubset2) => 71.77/9.78 (((eqimpsubset1) => 71.77/9.78 (((subsetI2) => 71.77/9.78 (((emptysetsubset) => 71.77/9.78 (((subsetE) => 71.77/9.78 (((subsetE2) => 71.77/9.78 (((notsubsetI) => 71.77/9.78 (((notequalI1) => 71.77/9.78 (((notequalI2) => 71.77/9.78 (((subsetRefl) => 71.77/9.78 (( 71.77/9.78 (subsetTrans) => 71.77/9.78 (( 71.77/9.78 (setadjoinSub) => 71.77/9.78 (( 71.77/9.78 (setadjoinSub2) => 71.77/9.78 (( 71.77/9.78 (subset2powerset) => 71.77/9.78 (( 71.77/9.78 (setextsub) => 71.77/9.78 (( 71.77/9.78 (subsetemptysetimpeq) => 71.77/9.78 (( 71.77/9.78 (powersetI1) => 71.77/9.78 (( 71.77/9.78 (powersetE1) => 71.77/9.78 (( 71.77/9.78 (inPowerset) => 71.77/9.78 (( 71.77/9.78 (powersetsubset) => 71.77/9.78 (( 71.77/9.78 (sepInPowerset) => 71.77/9.78 (( 71.77/9.78 (sepSubset) => 71.77/9.78 (( 71.77/9.78 (binunionIL) => 71.77/9.78 (( 71.77/9.78 (upairset2IR) => 71.77/9.78 (( 71.77/9.78 (binunionIR) => 71.77/9.78 (( 71.77/9.78 (binunionEcases) => 71.77/9.78 (( 71.77/9.78 (binunionE) => 71.77/9.78 (( 71.77/9.78 (binunionLsub) => 71.77/9.78 (( 71.77/9.78 (binunionRsub) => 71.77/9.78 (( 71.77/9.78 (binintersectI) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset5) => 71.77/9.78 (( 71.77/9.78 (binintersectEL) => 71.77/9.78 (( 71.77/9.78 (binintersectLsub) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset2) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset3) => 71.77/9.78 (( 71.77/9.78 (binintersectER) => 71.77/9.78 (( 71.77/9.78 (disjointsetsI1) => 71.77/9.78 (( 71.77/9.78 (binintersectRsub) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset4) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset1) => 71.77/9.78 (( 71.77/9.78 (bs114d) => 71.77/9.78 (( 71.77/9.78 (setminusI) => 71.77/9.78 (( 71.77/9.78 (setminusEL) => 71.77/9.78 (( 71.77/9.78 (setminusER) => 71.77/9.78 (( 71.77/9.78 (setminusSubset2) => 71.77/9.78 (( 71.77/9.78 (setminusERneg) => 71.77/9.78 (( 71.77/9.78 (setminusELneg) => 71.77/9.78 (( 71.77/9.78 (setminusILneg) => 71.77/9.78 (( 71.77/9.78 (setminusIRneg) => 71.77/9.78 (( 71.77/9.78 (setminusLsub) => 71.77/9.78 (( 71.77/9.78 (setminusSubset1) => 71.77/9.78 (( 71.77/9.78 (symdiffE) => 71.77/9.78 (( 71.77/9.78 (symdiffI1) => 71.77/9.78 (( 71.77/9.78 (symdiffI2) => 71.77/9.78 (( 71.77/9.78 (symdiffIneg1) => 71.77/9.78 (( 71.77/9.78 (symdiffIneg2) => 71.77/9.78 (( 71.77/9.78 (secondinupair) => 71.77/9.78 (( 71.77/9.78 (setukpairIL) => 71.77/9.78 (( 71.77/9.78 (setukpairIR) => 71.77/9.78 (( 71.77/9.78 (kpairiskpair) => 71.77/9.78 (( 71.77/9.78 (kpairp) => 71.77/9.78 (( 71.77/9.78 (singletonsubset) => 71.77/9.78 (( 71.77/9.78 (singletoninpowerset) => 71.77/9.78 (( 71.77/9.78 (singletoninpowunion) => 71.77/9.78 (( 71.77/9.78 (upairset2E) => 71.77/9.78 (( 71.77/9.78 (upairsubunion) => 71.77/9.78 (( 71.77/9.78 (upairinpowunion) => 71.77/9.78 (( 71.77/9.78 (ubforcartprodlem1) => 71.77/9.78 (( 71.77/9.78 (ubforcartprodlem2) => 71.77/9.78 (( 71.77/9.78 (ubforcartprodlem3) => 71.77/9.78 (( 71.77/9.78 (cartprodpairin) => 71.77/9.78 (( 71.77/9.78 (cartprodmempair1) => 71.77/9.78 (( 71.77/9.78 (cartprodmempair) => 71.77/9.78 (( 71.77/9.78 (setunionE2) => 71.77/9.78 (( 71.77/9.78 (setunionsingleton1) => 71.77/9.78 (( 71.77/9.78 (setunionsingleton2) => 71.77/9.78 (( 71.77/9.78 (setunionsingleton) => 71.77/9.78 (( 71.77/9.78 (singletonprop) => 71.77/9.78 (( 71.77/9.78 (ex1E1) => 71.77/9.78 (( 71.77/9.78 (ex1I) => 71.77/9.78 (( 71.77/9.78 (ex1I2) => 71.77/9.78 (( 71.77/9.78 (singletonsuniq) => 71.77/9.78 (( 71.77/9.78 (setukpairinjL1) => 71.77/9.78 (( 71.77/9.78 (kfstsingleton) => 71.77/9.78 (( 71.77/9.78 (theprop) => 71.77/9.78 (( 71.77/9.78 (kfstpairEq) => 71.77/9.78 (( 71.77/9.78 (cartprodfstin) => 71.77/9.78 (( 71.77/9.78 (setukpairinjL2) => 71.77/9.78 (( 71.77/9.78 (setukpairinjL) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR11) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR12) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR1) => 71.77/9.78 (( 71.77/9.78 (upairequniteq) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR2) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR) => 71.77/9.78 (( 71.77/9.78 (ksndsingleton) => 71.77/9.78 (( 71.77/9.78 (ksndpairEq) => 71.77/9.78 (( 71.77/9.78 (kpairsurjEq) => 71.77/9.78 (( 71.77/9.78 (cartprodsndin) => 71.77/9.78 (( 71.77/9.78 (cartprodpairmemEL) => 71.77/9.78 (( 71.77/9.78 (cartprodpairmemER) => 71.77/9.78 (( 71.77/9.78 (cartprodmempaircEq) => 71.77/9.78 (( 71.77/9.78 (cartprodfstpairEq) => 71.77/9.78 (( 71.77/9.78 (cartprodsndpairEq) => 71.77/9.78 (( 71.77/9.78 (cartprodpairsurjEq) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrI) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrSub) => 71.77/9.78 (( 71.77/9.78 (setOfPairsIsBReln) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrERa) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrEL1) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrEL2) => 71.77/9.78 (( 71.77/9.78 (dpsetconstrER) => 71.77/9.78 (( 71.77/9.78 (funcImageSingleton) => 71.77/9.78 (( 71.77/9.78 (apProp) => 71.77/9.78 (( 71.77/9.78 (app) => 71.77/9.78 (( 71.77/9.78 (infuncsetfunc) => 71.77/9.78 (( 71.77/9.78 (ap2p) => 71.77/9.78 (( 71.77/9.78 (funcinfuncset) => 71.77/9.78 (( 71.77/9.78 (lamProp) => 71.77/9.78 (( 71.77/9.78 (lamp) => 71.77/9.78 (( 71.77/9.78 (lam2p) => 71.77/9.78 (( 71.77/9.78 (brelnall1) => 71.77/9.78 (( 71.77/9.78 (brelnall2) => 71.77/9.78 (( 71.77/9.78 (ex1E2) => 71.77/9.78 (( 71.77/9.78 (funcGraphProp1) => 71.77/9.78 (( 71.77/9.78 (funcGraphProp3) => 71.77/9.78 (( 71.77/9.78 (funcGraphProp2) => 71.77/9.78 (( 71.77/9.78 (funcextLem) => 71.77/9.78 (( 71.77/9.78 (funcGraphProp4) => 71.77/9.78 (( 71.77/9.78 (subbreln) => 71.77/9.78 (( 71.77/9.78 (eqbreln) => 71.77/9.78 (( 71.77/9.78 (funcext) => 71.77/9.78 (( 71.77/9.78 (funcext2) => 71.77/9.78 (( 71.77/9.78 (ap2apEq1) => 71.77/9.78 (( 71.77/9.78 (ap2apEq2) => 71.77/9.78 (( 71.77/9.78 (beta1) => 71.77/9.78 (( 71.77/9.78 (eta1) => 71.77/9.78 (( 71.77/9.78 (lam2lamEq) => 71.77/9.78 (( 71.77/9.78 (beta2) => 71.77/9.78 (( 71.77/9.78 (eta2) => 71.77/9.78 (( 71.77/9.78 (iffalseProp1) => 71.77/9.78 (( 71.77/9.78 (iffalseProp2) => 71.77/9.78 (( 71.77/9.78 (iftrueProp1) => 71.77/9.78 (( 71.77/9.78 (iftrueProp2) => 71.77/9.78 (( 71.77/9.78 (ifSingleton) => 71.77/9.78 (( 71.77/9.78 (ifp) => 71.77/9.78 (( 71.77/9.78 (theeq) => 71.77/9.78 (( 71.77/9.78 (iftrue) => 71.77/9.78 (( 71.77/9.78 (iffalse) => 71.77/9.78 (( 71.77/9.78 (iftrueorfalse) => 71.77/9.78 (( 71.77/9.78 (binintersectT_lem) => 71.77/9.78 (( 71.77/9.78 (binunionT_lem) => 71.77/9.78 (( 71.77/9.78 (powersetT_lem) => 71.77/9.78 (( 71.77/9.78 (setminusT_lem) => 71.77/9.78 (( 71.77/9.78 (complementT_lem) => 71.77/9.78 (( 71.77/9.78 (setextT) => 71.77/9.78 (( 71.77/9.78 (subsetTI) => 71.77/9.78 (( 71.77/9.78 (powersetTI1) => 71.77/9.78 (( 71.77/9.78 (powersetTE1) => 71.77/9.78 (( 71.77/9.78 (complementTI1) => 71.77/9.78 (( 71.77/9.78 (complementTE1) => 71.77/9.78 (( 71.77/9.78 (binintersectTELcontra) => 71.77/9.78 (( 71.77/9.78 (binintersectTERcontra) => 71.77/9.78 (( 71.77/9.78 (contrasubsetT) => 71.77/9.78 (( 71.77/9.78 (contrasubsetT1) => 71.77/9.78 (( 71.77/9.78 (contrasubsetT2) => 71.77/9.78 (( 71.77/9.78 (contrasubsetT3) => 71.77/9.78 (( 71.77/9.78 (doubleComplementI1) => 71.77/9.78 (( 71.77/9.78 (doubleComplementE1) => 71.77/9.78 (( 71.77/9.78 (doubleComplementSub1) => 71.77/9.78 (( 71.77/9.78 (doubleComplementSub2) => 71.77/9.78 (( 71.77/9.78 (doubleComplementEq) => 71.77/9.78 (( 71.77/9.78 (complementTnotintersectT) => 71.77/9.78 (( 71.77/9.78 (complementImpComplementIntersect) => 71.77/9.78 (( 71.77/9.78 (complementSubsetComplementIntersect) => 71.77/9.78 (( 71.77/9.78 (complementInPowersetComplementIntersect) => 71.77/9.78 (( 71.77/9.78 (contraSubsetComplement) => 71.77/9.78 (( 71.77/9.78 (complementTcontraSubset) => 71.77/9.78 (( 71.77/9.78 (binunionTILcontra) => 71.77/9.78 (( 71.77/9.78 (binunionTIRcontra) => 71.77/9.78 (( 71.77/9.78 (inIntersectImpInUnion) => 71.77/9.78 (( 71.77/9.78 (inIntersectImpInUnion2) => 71.77/9.78 (( 71.77/9.78 (inIntersectImpInIntersectUnions) => 71.77/9.78 (( 71.77/9.78 (intersectInPowersetIntersectUnions) => 71.77/9.78 (( 71.77/9.78 (inComplementUnionImpNotIn1) => 71.77/9.78 (( 71.77/9.78 (inComplementUnionImpInComplement1) => 71.77/9.78 (( 71.77/9.78 (binunionTE) => 71.77/9.78 (( 71.77/9.78 (binunionTEcontra) => 71.77/9.78 (( 71.77/9.78 (demorgan2a1) => 71.77/9.78 (( 71.77/9.78 (complementUnionInPowersetComplement) => 71.77/9.78 (( 71.77/9.78 (demorgan2a2) => 71.77/9.78 (( 71.77/9.78 (demorgan1a) => 71.77/9.78 (( 71.77/9.78 (demorgan1b) => 71.77/9.78 (( 71.77/9.78 (demorgan1) => 71.77/9.78 (( 71.77/9.78 (demorgan2a) => 71.77/9.78 (( 71.77/9.78 (demorgan2b2) => 71.77/9.78 (( 71.77/9.78 (demorgan2b) => 71.77/9.78 (( 71.77/9.78 (demorgan2) => 71.77/9.78 (( 71.77/9.78 (woz13rule0) => 71.77/9.78 (( 71.77/9.78 (woz13rule1) => 71.77/9.78 (( 71.77/9.78 (woz13rule2) => 71.77/9.78 (( 71.77/9.78 (woz13rule3) => 71.77/9.78 (( 71.77/9.78 (woz13rule4) => 71.77/9.78 (( 71.77/9.78 (woz1_1) => 71.77/9.78 (( 71.77/9.78 (woz1_2) => 71.77/9.78 (( 71.77/9.78 (woz1_3) => 71.77/9.78 (( 71.77/9.78 (woz1_4) => 71.77/9.78 (( 71.77/9.78 (woz1_5) => 71.77/9.78 (( 71.77/9.78 (breln1all2) => 71.77/9.78 (( 71.77/9.78 (breln1SetBreln1) => 71.77/9.78 (( 71.77/9.78 (choice2fnsingleton) => 71.77/9.78 (( 71.77/9.78 (setOfPairsIsBReln1) => 71.77/9.78 (( 71.77/9.78 (breln1all1) => 71.77/9.78 (( 71.77/9.78 (subbreln1) => 71.77/9.78 (( 71.77/9.78 (eqbreln1) => 71.77/9.78 (( 71.77/9.78 (breln1invprop) => 71.77/9.78 (( 71.77/9.78 (breln1invI) => 71.77/9.78 (( 71.77/9.78 (breln1invE) => 71.77/9.78 (( 71.77/9.78 (breln1compprop) => 71.77/9.78 (( 71.77/9.78 (breln1compI) => 71.77/9.78 (( 71.77/9.78 (breln1compE) => 71.77/9.78 (( 71.77/9.78 (breln1compEex) => 71.77/9.78 (( 71.77/9.78 (!!) @ ( 71.77/9.78 (('#B') @ ( 71.77/9.78 !!) @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#S') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#S') @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 =>))) @ 71.77/9.78 breln1)))) @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 !!))) @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#S') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#B') @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#S') @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 =>))) @ 71.77/9.78 breln1)))))) @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#C') @ ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#B') @ 71.77/9.78 ( 71.77/9.78 ( 71.77/9.78 ('#B') @ ( 71.77/9.78 '#B') @ 71.77/9.78 breln1)))) @ 71.77/9.78 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.77/9.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl546])). 71.77/9.78 thf(zip_derived_cl561, plain, 71.77/9.78 (~ (((quantDeMorgan4) => 71.77/9.78 (((prop2setI) => 71.77/9.78 (((prop2set2propI) => 71.77/9.78 (((notdexE) => 71.77/9.78 (((notdallE) => 71.77/9.78 (((exuI1) => 71.77/9.78 (((exuI3) => 71.77/9.78 (((exuI2) => 71.77/9.78 (((inCongP) => 71.77/9.78 (((in__Cong) => 71.77/9.78 (((exuE3u) => 71.77/9.78 (((exu__Cong) => 71.77/9.78 (((setadjoin__Cong) => 71.77/9.78 (((powerset__Cong) => 71.77/9.78 (((setunion__Cong) => 71.77/9.78 (((exuEu) => 71.77/9.78 (((descr__Cong) => 71.77/9.78 (((dsetconstr__Cong) => 71.77/9.78 (((subsetI1) => 71.77/9.78 (((eqimpsubset2) => 71.77/9.78 (((eqimpsubset1) => 71.77/9.78 (((subsetI2) => 71.77/9.78 (((emptysetsubset) => 71.77/9.78 (((subsetE) => 71.77/9.78 (((subsetE2) => 71.77/9.78 (((notsubsetI) => 71.77/9.78 (((notequalI1) => 71.77/9.78 (((notequalI2) => 71.77/9.78 (((subsetRefl) => 71.77/9.78 (((subsetTrans) => 71.77/9.78 (( 71.77/9.78 (setadjoinSub) => 71.77/9.78 (( 71.77/9.78 (setadjoinSub2) => 71.77/9.78 (( 71.77/9.78 (subset2powerset) => 71.77/9.78 (( 71.77/9.78 (setextsub) => 71.77/9.78 (( 71.77/9.78 (subsetemptysetimpeq) => 71.77/9.78 (( 71.77/9.78 (powersetI1) => 71.77/9.78 (( 71.77/9.78 (powersetE1) => 71.77/9.78 (( 71.77/9.78 (inPowerset) => 71.77/9.78 (( 71.77/9.78 (powersetsubset) => 71.77/9.78 (( 71.77/9.78 (sepInPowerset) => 71.77/9.78 (( 71.77/9.78 (sepSubset) => 71.77/9.78 (( 71.77/9.78 (binunionIL) => 71.77/9.78 (( 71.77/9.78 (upairset2IR) => 71.77/9.78 (( 71.77/9.78 (binunionIR) => 71.77/9.78 (( 71.77/9.78 (binunionEcases) => 71.77/9.78 (( 71.77/9.78 (binunionE) => 71.77/9.78 (( 71.77/9.78 (binunionLsub) => 71.77/9.78 (( 71.77/9.78 (binunionRsub) => 71.77/9.78 (( 71.77/9.78 (binintersectI) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset5) => 71.77/9.78 (( 71.77/9.78 (binintersectEL) => 71.77/9.78 (( 71.77/9.78 (binintersectLsub) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset2) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset3) => 71.77/9.78 (( 71.77/9.78 (binintersectER) => 71.77/9.78 (( 71.77/9.78 (disjointsetsI1) => 71.77/9.78 (( 71.77/9.78 (binintersectRsub) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset4) => 71.77/9.78 (( 71.77/9.78 (binintersectSubset1) => 71.77/9.78 (( 71.77/9.78 (bs114d) => 71.77/9.78 (( 71.77/9.78 (setminusI) => 71.77/9.78 (( 71.77/9.78 (setminusEL) => 71.77/9.78 (( 71.77/9.78 (setminusER) => 71.77/9.78 (( 71.77/9.78 (setminusSubset2) => 71.77/9.78 (( 71.77/9.78 (setminusERneg) => 71.77/9.78 (( 71.77/9.78 (setminusELneg) => 71.77/9.78 (( 71.77/9.78 (setminusILneg) => 71.77/9.78 (( 71.77/9.78 (setminusIRneg) => 71.77/9.78 (( 71.77/9.78 (setminusLsub) => 71.77/9.78 (( 71.77/9.78 (setminusSubset1) => 71.77/9.78 (( 71.77/9.78 (symdiffE) => 71.77/9.78 (( 71.77/9.78 (symdiffI1) => 71.77/9.78 (( 71.77/9.78 (symdiffI2) => 71.77/9.78 (( 71.77/9.78 (symdiffIneg1) => 71.77/9.78 (( 71.77/9.78 (symdiffIneg2) => 71.77/9.78 (( 71.77/9.78 (secondinupair) => 71.77/9.78 (( 71.77/9.78 (setukpairIL) => 71.77/9.78 (( 71.77/9.78 (setukpairIR) => 71.77/9.78 (( 71.77/9.78 (kpairiskpair) => 71.77/9.78 (( 71.77/9.78 (kpairp) => 71.77/9.78 (( 71.77/9.78 (singletonsubset) => 71.77/9.78 (( 71.77/9.78 (singletoninpowerset) => 71.77/9.78 (( 71.77/9.78 (singletoninpowunion) => 71.77/9.78 (( 71.77/9.78 (upairset2E) => 71.77/9.78 (( 71.77/9.78 (upairsubunion) => 71.77/9.78 (( 71.77/9.78 (upairinpowunion) => 71.77/9.78 (( 71.77/9.78 (ubforcartprodlem1) => 71.77/9.78 (( 71.77/9.78 (ubforcartprodlem2) => 71.77/9.78 (( 71.77/9.78 (ubforcartprodlem3) => 71.77/9.78 (( 71.77/9.78 (cartprodpairin) => 71.77/9.78 (( 71.77/9.78 (cartprodmempair1) => 71.77/9.78 (( 71.77/9.78 (cartprodmempair) => 71.77/9.78 (( 71.77/9.78 (setunionE2) => 71.77/9.78 (( 71.77/9.78 (setunionsingleton1) => 71.77/9.78 (( 71.77/9.78 (setunionsingleton2) => 71.77/9.78 (( 71.77/9.78 (setunionsingleton) => 71.77/9.78 (( 71.77/9.78 (singletonprop) => 71.77/9.78 (( 71.77/9.78 (ex1E1) => 71.77/9.78 (( 71.77/9.78 (ex1I) => 71.77/9.78 (( 71.77/9.78 (ex1I2) => 71.77/9.78 (( 71.77/9.78 (singletonsuniq) => 71.77/9.78 (( 71.77/9.78 (setukpairinjL1) => 71.77/9.78 (( 71.77/9.78 (kfstsingleton) => 71.77/9.78 (( 71.77/9.78 (theprop) => 71.77/9.78 (( 71.77/9.78 (kfstpairEq) => 71.77/9.78 (( 71.77/9.78 (cartprodfstin) => 71.77/9.78 (( 71.77/9.78 (setukpairinjL2) => 71.77/9.78 (( 71.77/9.78 (setukpairinjL) => 71.77/9.78 (( 71.77/9.78 (setukpairinjR11) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR12) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR1) => 71.92/9.78 (( 71.92/9.78 (upairequniteq) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR2) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR) => 71.92/9.78 (( 71.92/9.78 (ksndsingleton) => 71.92/9.78 (( 71.92/9.78 (ksndpairEq) => 71.92/9.78 (( 71.92/9.78 (kpairsurjEq) => 71.92/9.78 (( 71.92/9.78 (cartprodsndin) => 71.92/9.78 (( 71.92/9.78 (cartprodpairmemEL) => 71.92/9.78 (( 71.92/9.78 (cartprodpairmemER) => 71.92/9.78 (( 71.92/9.78 (cartprodmempaircEq) => 71.92/9.78 (( 71.92/9.78 (cartprodfstpairEq) => 71.92/9.78 (( 71.92/9.78 (cartprodsndpairEq) => 71.92/9.78 (( 71.92/9.78 (cartprodpairsurjEq) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrI) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrSub) => 71.92/9.78 (( 71.92/9.78 (setOfPairsIsBReln) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrERa) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrEL1) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrEL2) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrER) => 71.92/9.78 (( 71.92/9.78 (funcImageSingleton) => 71.92/9.78 (( 71.92/9.78 (apProp) => 71.92/9.78 (( 71.92/9.78 (app) => 71.92/9.78 (( 71.92/9.78 (infuncsetfunc) => 71.92/9.78 (( 71.92/9.78 (ap2p) => 71.92/9.78 (( 71.92/9.78 (funcinfuncset) => 71.92/9.78 (( 71.92/9.78 (lamProp) => 71.92/9.78 (( 71.92/9.78 (lamp) => 71.92/9.78 (( 71.92/9.78 (lam2p) => 71.92/9.78 (( 71.92/9.78 (brelnall1) => 71.92/9.78 (( 71.92/9.78 (brelnall2) => 71.92/9.78 (( 71.92/9.78 (ex1E2) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp1) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp3) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp2) => 71.92/9.78 (( 71.92/9.78 (funcextLem) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp4) => 71.92/9.78 (( 71.92/9.78 (subbreln) => 71.92/9.78 (( 71.92/9.78 (eqbreln) => 71.92/9.78 (( 71.92/9.78 (funcext) => 71.92/9.78 (( 71.92/9.78 (funcext2) => 71.92/9.78 (( 71.92/9.78 (ap2apEq1) => 71.92/9.78 (( 71.92/9.78 (ap2apEq2) => 71.92/9.78 (( 71.92/9.78 (beta1) => 71.92/9.78 (( 71.92/9.78 (eta1) => 71.92/9.78 (( 71.92/9.78 (lam2lamEq) => 71.92/9.78 (( 71.92/9.78 (beta2) => 71.92/9.78 (( 71.92/9.78 (eta2) => 71.92/9.78 (( 71.92/9.78 (iffalseProp1) => 71.92/9.78 (( 71.92/9.78 (iffalseProp2) => 71.92/9.78 (( 71.92/9.78 (iftrueProp1) => 71.92/9.78 (( 71.92/9.78 (iftrueProp2) => 71.92/9.78 (( 71.92/9.78 (ifSingleton) => 71.92/9.78 (( 71.92/9.78 (ifp) => 71.92/9.78 (( 71.92/9.78 (theeq) => 71.92/9.78 (( 71.92/9.78 (iftrue) => 71.92/9.78 (( 71.92/9.78 (iffalse) => 71.92/9.78 (( 71.92/9.78 (iftrueorfalse) => 71.92/9.78 (( 71.92/9.78 (binintersectT_lem) => 71.92/9.78 (( 71.92/9.78 (binunionT_lem) => 71.92/9.78 (( 71.92/9.78 (powersetT_lem) => 71.92/9.78 (( 71.92/9.78 (setminusT_lem) => 71.92/9.78 (( 71.92/9.78 (complementT_lem) => 71.92/9.78 (( 71.92/9.78 (setextT) => 71.92/9.78 (( 71.92/9.78 (subsetTI) => 71.92/9.78 (( 71.92/9.78 (powersetTI1) => 71.92/9.78 (( 71.92/9.78 (powersetTE1) => 71.92/9.78 (( 71.92/9.78 (complementTI1) => 71.92/9.78 (( 71.92/9.78 (complementTE1) => 71.92/9.78 (( 71.92/9.78 (binintersectTELcontra) => 71.92/9.78 (( 71.92/9.78 (binintersectTERcontra) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT1) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT2) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT3) => 71.92/9.78 (( 71.92/9.78 (doubleComplementI1) => 71.92/9.78 (( 71.92/9.78 (doubleComplementE1) => 71.92/9.78 (( 71.92/9.78 (doubleComplementSub1) => 71.92/9.78 (( 71.92/9.78 (doubleComplementSub2) => 71.92/9.78 (( 71.92/9.78 (doubleComplementEq) => 71.92/9.78 (( 71.92/9.78 (complementTnotintersectT) => 71.92/9.78 (( 71.92/9.78 (complementImpComplementIntersect) => 71.92/9.78 (( 71.92/9.78 (complementSubsetComplementIntersect) => 71.92/9.78 (( 71.92/9.78 (complementInPowersetComplementIntersect) => 71.92/9.78 (( 71.92/9.78 (contraSubsetComplement) => 71.92/9.78 (( 71.92/9.78 (complementTcontraSubset) => 71.92/9.78 (( 71.92/9.78 (binunionTILcontra) => 71.92/9.78 (( 71.92/9.78 (binunionTIRcontra) => 71.92/9.78 (( 71.92/9.78 (inIntersectImpInUnion) => 71.92/9.78 (( 71.92/9.78 (inIntersectImpInUnion2) => 71.92/9.78 (( 71.92/9.78 (inIntersectImpInIntersectUnions) => 71.92/9.78 (( 71.92/9.78 (intersectInPowersetIntersectUnions) => 71.92/9.78 (( 71.92/9.78 (inComplementUnionImpNotIn1) => 71.92/9.78 (( 71.92/9.78 (inComplementUnionImpInComplement1) => 71.92/9.78 (( 71.92/9.78 (binunionTE) => 71.92/9.78 (( 71.92/9.78 (binunionTEcontra) => 71.92/9.78 (( 71.92/9.78 (demorgan2a1) => 71.92/9.78 (( 71.92/9.78 (complementUnionInPowersetComplement) => 71.92/9.78 (( 71.92/9.78 (demorgan2a2) => 71.92/9.78 (( 71.92/9.78 (demorgan1a) => 71.92/9.78 (( 71.92/9.78 (demorgan1b) => 71.92/9.78 (( 71.92/9.78 (demorgan1) => 71.92/9.78 (( 71.92/9.78 (demorgan2a) => 71.92/9.78 (( 71.92/9.78 (demorgan2b2) => 71.92/9.78 (( 71.92/9.78 (demorgan2b) => 71.92/9.78 (( 71.92/9.78 (demorgan2) => 71.92/9.78 (( 71.92/9.78 (woz13rule0) => 71.92/9.78 (( 71.92/9.78 (woz13rule1) => 71.92/9.78 (( 71.92/9.78 (woz13rule2) => 71.92/9.78 (( 71.92/9.78 (woz13rule3) => 71.92/9.78 (( 71.92/9.78 (woz13rule4) => 71.92/9.78 (( 71.92/9.78 (woz1_1) => 71.92/9.78 (( 71.92/9.78 (woz1_2) => 71.92/9.78 (( 71.92/9.78 (woz1_3) => 71.92/9.78 (( 71.92/9.78 (woz1_4) => 71.92/9.78 (( 71.92/9.78 (woz1_5) => 71.92/9.78 (( 71.92/9.78 (breln1all2) => 71.92/9.78 (( 71.92/9.78 (breln1SetBreln1) => 71.92/9.78 (( 71.92/9.78 (choice2fnsingleton) => 71.92/9.78 (( 71.92/9.78 (setOfPairsIsBReln1) => 71.92/9.78 (( 71.92/9.78 (breln1all1) => 71.92/9.78 (( 71.92/9.78 (subbreln1) => 71.92/9.78 (( 71.92/9.78 (eqbreln1) => 71.92/9.78 (( 71.92/9.78 (breln1invprop) => 71.92/9.78 (( 71.92/9.78 (breln1invI) => 71.92/9.78 (( 71.92/9.78 (breln1invE) => 71.92/9.78 (( 71.92/9.78 (breln1compprop) => 71.92/9.78 (( 71.92/9.78 (breln1compI) => 71.92/9.78 (( 71.92/9.78 (breln1compE) => 71.92/9.78 (( 71.92/9.78 (breln1compEex) => 71.92/9.78 (( 71.92/9.78 (!!) @ ( 71.92/9.78 (('#B') @ ( 71.92/9.78 !!) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#S') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#S') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 =>))) @ 71.92/9.78 breln1)))) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 !!))) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#S') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#B') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#S') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 =>))) @ 71.92/9.78 breln1)))))) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#C') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#B') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#B') @ 71.92/9.78 breln1)))) @ 71.92/9.78 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl553])). 71.92/9.78 thf(zip_derived_cl570, plain, 71.92/9.78 (~ (((prop2setI) => 71.92/9.78 (((prop2set2propI) => 71.92/9.78 (((notdexE) => 71.92/9.78 (((notdallE) => 71.92/9.78 (((exuI1) => 71.92/9.78 (((exuI3) => 71.92/9.78 (((exuI2) => 71.92/9.78 (((inCongP) => 71.92/9.78 (((in__Cong) => 71.92/9.78 (((exuE3u) => 71.92/9.78 (((exu__Cong) => 71.92/9.78 (((setadjoin__Cong) => 71.92/9.78 (((powerset__Cong) => 71.92/9.78 (((setunion__Cong) => 71.92/9.78 (((exuEu) => 71.92/9.78 (((descr__Cong) => 71.92/9.78 (((dsetconstr__Cong) => 71.92/9.78 (((subsetI1) => 71.92/9.78 (((eqimpsubset2) => 71.92/9.78 (((eqimpsubset1) => 71.92/9.78 (((subsetI2) => 71.92/9.78 (((emptysetsubset) => 71.92/9.78 (((subsetE) => 71.92/9.78 (((subsetE2) => 71.92/9.78 (((notsubsetI) => 71.92/9.78 (((notequalI1) => 71.92/9.78 (((notequalI2) => 71.92/9.78 (((subsetRefl) => 71.92/9.78 (((subsetTrans) => 71.92/9.78 (((setadjoinSub) => 71.92/9.78 (( 71.92/9.78 (setadjoinSub2) => 71.92/9.78 (( 71.92/9.78 (subset2powerset) => 71.92/9.78 (( 71.92/9.78 (setextsub) => 71.92/9.78 (( 71.92/9.78 (subsetemptysetimpeq) => 71.92/9.78 (( 71.92/9.78 (powersetI1) => 71.92/9.78 (( 71.92/9.78 (powersetE1) => 71.92/9.78 (( 71.92/9.78 (inPowerset) => 71.92/9.78 (( 71.92/9.78 (powersetsubset) => 71.92/9.78 (( 71.92/9.78 (sepInPowerset) => 71.92/9.78 (( 71.92/9.78 (sepSubset) => 71.92/9.78 (( 71.92/9.78 (binunionIL) => 71.92/9.78 (( 71.92/9.78 (upairset2IR) => 71.92/9.78 (( 71.92/9.78 (binunionIR) => 71.92/9.78 (( 71.92/9.78 (binunionEcases) => 71.92/9.78 (( 71.92/9.78 (binunionE) => 71.92/9.78 (( 71.92/9.78 (binunionLsub) => 71.92/9.78 (( 71.92/9.78 (binunionRsub) => 71.92/9.78 (( 71.92/9.78 (binintersectI) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset5) => 71.92/9.78 (( 71.92/9.78 (binintersectEL) => 71.92/9.78 (( 71.92/9.78 (binintersectLsub) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset2) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset3) => 71.92/9.78 (( 71.92/9.78 (binintersectER) => 71.92/9.78 (( 71.92/9.78 (disjointsetsI1) => 71.92/9.78 (( 71.92/9.78 (binintersectRsub) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset4) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset1) => 71.92/9.78 (( 71.92/9.78 (bs114d) => 71.92/9.78 (( 71.92/9.78 (setminusI) => 71.92/9.78 (( 71.92/9.78 (setminusEL) => 71.92/9.78 (( 71.92/9.78 (setminusER) => 71.92/9.78 (( 71.92/9.78 (setminusSubset2) => 71.92/9.78 (( 71.92/9.78 (setminusERneg) => 71.92/9.78 (( 71.92/9.78 (setminusELneg) => 71.92/9.78 (( 71.92/9.78 (setminusILneg) => 71.92/9.78 (( 71.92/9.78 (setminusIRneg) => 71.92/9.78 (( 71.92/9.78 (setminusLsub) => 71.92/9.78 (( 71.92/9.78 (setminusSubset1) => 71.92/9.78 (( 71.92/9.78 (symdiffE) => 71.92/9.78 (( 71.92/9.78 (symdiffI1) => 71.92/9.78 (( 71.92/9.78 (symdiffI2) => 71.92/9.78 (( 71.92/9.78 (symdiffIneg1) => 71.92/9.78 (( 71.92/9.78 (symdiffIneg2) => 71.92/9.78 (( 71.92/9.78 (secondinupair) => 71.92/9.78 (( 71.92/9.78 (setukpairIL) => 71.92/9.78 (( 71.92/9.78 (setukpairIR) => 71.92/9.78 (( 71.92/9.78 (kpairiskpair) => 71.92/9.78 (( 71.92/9.78 (kpairp) => 71.92/9.78 (( 71.92/9.78 (singletonsubset) => 71.92/9.78 (( 71.92/9.78 (singletoninpowerset) => 71.92/9.78 (( 71.92/9.78 (singletoninpowunion) => 71.92/9.78 (( 71.92/9.78 (upairset2E) => 71.92/9.78 (( 71.92/9.78 (upairsubunion) => 71.92/9.78 (( 71.92/9.78 (upairinpowunion) => 71.92/9.78 (( 71.92/9.78 (ubforcartprodlem1) => 71.92/9.78 (( 71.92/9.78 (ubforcartprodlem2) => 71.92/9.78 (( 71.92/9.78 (ubforcartprodlem3) => 71.92/9.78 (( 71.92/9.78 (cartprodpairin) => 71.92/9.78 (( 71.92/9.78 (cartprodmempair1) => 71.92/9.78 (( 71.92/9.78 (cartprodmempair) => 71.92/9.78 (( 71.92/9.78 (setunionE2) => 71.92/9.78 (( 71.92/9.78 (setunionsingleton1) => 71.92/9.78 (( 71.92/9.78 (setunionsingleton2) => 71.92/9.78 (( 71.92/9.78 (setunionsingleton) => 71.92/9.78 (( 71.92/9.78 (singletonprop) => 71.92/9.78 (( 71.92/9.78 (ex1E1) => 71.92/9.78 (( 71.92/9.78 (ex1I) => 71.92/9.78 (( 71.92/9.78 (ex1I2) => 71.92/9.78 (( 71.92/9.78 (singletonsuniq) => 71.92/9.78 (( 71.92/9.78 (setukpairinjL1) => 71.92/9.78 (( 71.92/9.78 (kfstsingleton) => 71.92/9.78 (( 71.92/9.78 (theprop) => 71.92/9.78 (( 71.92/9.78 (kfstpairEq) => 71.92/9.78 (( 71.92/9.78 (cartprodfstin) => 71.92/9.78 (( 71.92/9.78 (setukpairinjL2) => 71.92/9.78 (( 71.92/9.78 (setukpairinjL) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR11) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR12) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR1) => 71.92/9.78 (( 71.92/9.78 (upairequniteq) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR2) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR) => 71.92/9.78 (( 71.92/9.78 (ksndsingleton) => 71.92/9.78 (( 71.92/9.78 (ksndpairEq) => 71.92/9.78 (( 71.92/9.78 (kpairsurjEq) => 71.92/9.78 (( 71.92/9.78 (cartprodsndin) => 71.92/9.78 (( 71.92/9.78 (cartprodpairmemEL) => 71.92/9.78 (( 71.92/9.78 (cartprodpairmemER) => 71.92/9.78 (( 71.92/9.78 (cartprodmempaircEq) => 71.92/9.78 (( 71.92/9.78 (cartprodfstpairEq) => 71.92/9.78 (( 71.92/9.78 (cartprodsndpairEq) => 71.92/9.78 (( 71.92/9.78 (cartprodpairsurjEq) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrI) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrSub) => 71.92/9.78 (( 71.92/9.78 (setOfPairsIsBReln) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrERa) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrEL1) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrEL2) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrER) => 71.92/9.78 (( 71.92/9.78 (funcImageSingleton) => 71.92/9.78 (( 71.92/9.78 (apProp) => 71.92/9.78 (( 71.92/9.78 (app) => 71.92/9.78 (( 71.92/9.78 (infuncsetfunc) => 71.92/9.78 (( 71.92/9.78 (ap2p) => 71.92/9.78 (( 71.92/9.78 (funcinfuncset) => 71.92/9.78 (( 71.92/9.78 (lamProp) => 71.92/9.78 (( 71.92/9.78 (lamp) => 71.92/9.78 (( 71.92/9.78 (lam2p) => 71.92/9.78 (( 71.92/9.78 (brelnall1) => 71.92/9.78 (( 71.92/9.78 (brelnall2) => 71.92/9.78 (( 71.92/9.78 (ex1E2) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp1) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp3) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp2) => 71.92/9.78 (( 71.92/9.78 (funcextLem) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp4) => 71.92/9.78 (( 71.92/9.78 (subbreln) => 71.92/9.78 (( 71.92/9.78 (eqbreln) => 71.92/9.78 (( 71.92/9.78 (funcext) => 71.92/9.78 (( 71.92/9.78 (funcext2) => 71.92/9.78 (( 71.92/9.78 (ap2apEq1) => 71.92/9.78 (( 71.92/9.78 (ap2apEq2) => 71.92/9.78 (( 71.92/9.78 (beta1) => 71.92/9.78 (( 71.92/9.78 (eta1) => 71.92/9.78 (( 71.92/9.78 (lam2lamEq) => 71.92/9.78 (( 71.92/9.78 (beta2) => 71.92/9.78 (( 71.92/9.78 (eta2) => 71.92/9.78 (( 71.92/9.78 (iffalseProp1) => 71.92/9.78 (( 71.92/9.78 (iffalseProp2) => 71.92/9.78 (( 71.92/9.78 (iftrueProp1) => 71.92/9.78 (( 71.92/9.78 (iftrueProp2) => 71.92/9.78 (( 71.92/9.78 (ifSingleton) => 71.92/9.78 (( 71.92/9.78 (ifp) => 71.92/9.78 (( 71.92/9.78 (theeq) => 71.92/9.78 (( 71.92/9.78 (iftrue) => 71.92/9.78 (( 71.92/9.78 (iffalse) => 71.92/9.78 (( 71.92/9.78 (iftrueorfalse) => 71.92/9.78 (( 71.92/9.78 (binintersectT_lem) => 71.92/9.78 (( 71.92/9.78 (binunionT_lem) => 71.92/9.78 (( 71.92/9.78 (powersetT_lem) => 71.92/9.78 (( 71.92/9.78 (setminusT_lem) => 71.92/9.78 (( 71.92/9.78 (complementT_lem) => 71.92/9.78 (( 71.92/9.78 (setextT) => 71.92/9.78 (( 71.92/9.78 (subsetTI) => 71.92/9.78 (( 71.92/9.78 (powersetTI1) => 71.92/9.78 (( 71.92/9.78 (powersetTE1) => 71.92/9.78 (( 71.92/9.78 (complementTI1) => 71.92/9.78 (( 71.92/9.78 (complementTE1) => 71.92/9.78 (( 71.92/9.78 (binintersectTELcontra) => 71.92/9.78 (( 71.92/9.78 (binintersectTERcontra) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT1) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT2) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT3) => 71.92/9.78 (( 71.92/9.78 (doubleComplementI1) => 71.92/9.78 (( 71.92/9.78 (doubleComplementE1) => 71.92/9.78 (( 71.92/9.78 (doubleComplementSub1) => 71.92/9.78 (( 71.92/9.78 (doubleComplementSub2) => 71.92/9.78 (( 71.92/9.78 (doubleComplementEq) => 71.92/9.78 (( 71.92/9.78 (complementTnotintersectT) => 71.92/9.78 (( 71.92/9.78 (complementImpComplementIntersect) => 71.92/9.78 (( 71.92/9.78 (complementSubsetComplementIntersect) => 71.92/9.78 (( 71.92/9.78 (complementInPowersetComplementIntersect) => 71.92/9.78 (( 71.92/9.78 (contraSubsetComplement) => 71.92/9.78 (( 71.92/9.78 (complementTcontraSubset) => 71.92/9.78 (( 71.92/9.78 (binunionTILcontra) => 71.92/9.78 (( 71.92/9.78 (binunionTIRcontra) => 71.92/9.78 (( 71.92/9.78 (inIntersectImpInUnion) => 71.92/9.78 (( 71.92/9.78 (inIntersectImpInUnion2) => 71.92/9.78 (( 71.92/9.78 (inIntersectImpInIntersectUnions) => 71.92/9.78 (( 71.92/9.78 (intersectInPowersetIntersectUnions) => 71.92/9.78 (( 71.92/9.78 (inComplementUnionImpNotIn1) => 71.92/9.78 (( 71.92/9.78 (inComplementUnionImpInComplement1) => 71.92/9.78 (( 71.92/9.78 (binunionTE) => 71.92/9.78 (( 71.92/9.78 (binunionTEcontra) => 71.92/9.78 (( 71.92/9.78 (demorgan2a1) => 71.92/9.78 (( 71.92/9.78 (complementUnionInPowersetComplement) => 71.92/9.78 (( 71.92/9.78 (demorgan2a2) => 71.92/9.78 (( 71.92/9.78 (demorgan1a) => 71.92/9.78 (( 71.92/9.78 (demorgan1b) => 71.92/9.78 (( 71.92/9.78 (demorgan1) => 71.92/9.78 (( 71.92/9.78 (demorgan2a) => 71.92/9.78 (( 71.92/9.78 (demorgan2b2) => 71.92/9.78 (( 71.92/9.78 (demorgan2b) => 71.92/9.78 (( 71.92/9.78 (demorgan2) => 71.92/9.78 (( 71.92/9.78 (woz13rule0) => 71.92/9.78 (( 71.92/9.78 (woz13rule1) => 71.92/9.78 (( 71.92/9.78 (woz13rule2) => 71.92/9.78 (( 71.92/9.78 (woz13rule3) => 71.92/9.78 (( 71.92/9.78 (woz13rule4) => 71.92/9.78 (( 71.92/9.78 (woz1_1) => 71.92/9.78 (( 71.92/9.78 (woz1_2) => 71.92/9.78 (( 71.92/9.78 (woz1_3) => 71.92/9.78 (( 71.92/9.78 (woz1_4) => 71.92/9.78 (( 71.92/9.78 (woz1_5) => 71.92/9.78 (( 71.92/9.78 (breln1all2) => 71.92/9.78 (( 71.92/9.78 (breln1SetBreln1) => 71.92/9.78 (( 71.92/9.78 (choice2fnsingleton) => 71.92/9.78 (( 71.92/9.78 (setOfPairsIsBReln1) => 71.92/9.78 (( 71.92/9.78 (breln1all1) => 71.92/9.78 (( 71.92/9.78 (subbreln1) => 71.92/9.78 (( 71.92/9.78 (eqbreln1) => 71.92/9.78 (( 71.92/9.78 (breln1invprop) => 71.92/9.78 (( 71.92/9.78 (breln1invI) => 71.92/9.78 (( 71.92/9.78 (breln1invE) => 71.92/9.78 (( 71.92/9.78 (breln1compprop) => 71.92/9.78 (( 71.92/9.78 (breln1compI) => 71.92/9.78 (( 71.92/9.78 (breln1compE) => 71.92/9.78 (( 71.92/9.78 (breln1compEex) => 71.92/9.78 (( 71.92/9.78 (!!) @ ( 71.92/9.78 (('#B') @ ( 71.92/9.78 !!) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#S') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#S') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 =>))) @ 71.92/9.78 breln1)))) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 !!))) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#S') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#B') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#S') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 =>))) @ 71.92/9.78 breln1)))))) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#C') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#B') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#B') @ 71.92/9.78 breln1)))) @ 71.92/9.78 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])). 71.92/9.78 thf(zip_derived_cl578, plain, 71.92/9.78 (~ (((prop2set2propI) => 71.92/9.78 (((notdexE) => 71.92/9.78 (((notdallE) => 71.92/9.78 (((exuI1) => 71.92/9.78 (((exuI3) => 71.92/9.78 (((exuI2) => 71.92/9.78 (((inCongP) => 71.92/9.78 (((in__Cong) => 71.92/9.78 (((exuE3u) => 71.92/9.78 (((exu__Cong) => 71.92/9.78 (((setadjoin__Cong) => 71.92/9.78 (((powerset__Cong) => 71.92/9.78 (((setunion__Cong) => 71.92/9.78 (((exuEu) => 71.92/9.78 (((descr__Cong) => 71.92/9.78 (((dsetconstr__Cong) => 71.92/9.78 (((subsetI1) => 71.92/9.78 (((eqimpsubset2) => 71.92/9.78 (((eqimpsubset1) => 71.92/9.78 (((subsetI2) => 71.92/9.78 (((emptysetsubset) => 71.92/9.78 (((subsetE) => 71.92/9.78 (((subsetE2) => 71.92/9.78 (((notsubsetI) => 71.92/9.78 (((notequalI1) => 71.92/9.78 (((notequalI2) => 71.92/9.78 (((subsetRefl) => 71.92/9.78 (((subsetTrans) => 71.92/9.78 (((setadjoinSub) => 71.92/9.78 (((setadjoinSub2) => 71.92/9.78 (( 71.92/9.78 (subset2powerset) => 71.92/9.78 (( 71.92/9.78 (setextsub) => 71.92/9.78 (( 71.92/9.78 (subsetemptysetimpeq) => 71.92/9.78 (( 71.92/9.78 (powersetI1) => 71.92/9.78 (( 71.92/9.78 (powersetE1) => 71.92/9.78 (( 71.92/9.78 (inPowerset) => 71.92/9.78 (( 71.92/9.78 (powersetsubset) => 71.92/9.78 (( 71.92/9.78 (sepInPowerset) => 71.92/9.78 (( 71.92/9.78 (sepSubset) => 71.92/9.78 (( 71.92/9.78 (binunionIL) => 71.92/9.78 (( 71.92/9.78 (upairset2IR) => 71.92/9.78 (( 71.92/9.78 (binunionIR) => 71.92/9.78 (( 71.92/9.78 (binunionEcases) => 71.92/9.78 (( 71.92/9.78 (binunionE) => 71.92/9.78 (( 71.92/9.78 (binunionLsub) => 71.92/9.78 (( 71.92/9.78 (binunionRsub) => 71.92/9.78 (( 71.92/9.78 (binintersectI) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset5) => 71.92/9.78 (( 71.92/9.78 (binintersectEL) => 71.92/9.78 (( 71.92/9.78 (binintersectLsub) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset2) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset3) => 71.92/9.78 (( 71.92/9.78 (binintersectER) => 71.92/9.78 (( 71.92/9.78 (disjointsetsI1) => 71.92/9.78 (( 71.92/9.78 (binintersectRsub) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset4) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset1) => 71.92/9.78 (( 71.92/9.78 (bs114d) => 71.92/9.78 (( 71.92/9.78 (setminusI) => 71.92/9.78 (( 71.92/9.78 (setminusEL) => 71.92/9.78 (( 71.92/9.78 (setminusER) => 71.92/9.78 (( 71.92/9.78 (setminusSubset2) => 71.92/9.78 (( 71.92/9.78 (setminusERneg) => 71.92/9.78 (( 71.92/9.78 (setminusELneg) => 71.92/9.78 (( 71.92/9.78 (setminusILneg) => 71.92/9.78 (( 71.92/9.78 (setminusIRneg) => 71.92/9.78 (( 71.92/9.78 (setminusLsub) => 71.92/9.78 (( 71.92/9.78 (setminusSubset1) => 71.92/9.78 (( 71.92/9.78 (symdiffE) => 71.92/9.78 (( 71.92/9.78 (symdiffI1) => 71.92/9.78 (( 71.92/9.78 (symdiffI2) => 71.92/9.78 (( 71.92/9.78 (symdiffIneg1) => 71.92/9.78 (( 71.92/9.78 (symdiffIneg2) => 71.92/9.78 (( 71.92/9.78 (secondinupair) => 71.92/9.78 (( 71.92/9.78 (setukpairIL) => 71.92/9.78 (( 71.92/9.78 (setukpairIR) => 71.92/9.78 (( 71.92/9.78 (kpairiskpair) => 71.92/9.78 (( 71.92/9.78 (kpairp) => 71.92/9.78 (( 71.92/9.78 (singletonsubset) => 71.92/9.78 (( 71.92/9.78 (singletoninpowerset) => 71.92/9.78 (( 71.92/9.78 (singletoninpowunion) => 71.92/9.78 (( 71.92/9.78 (upairset2E) => 71.92/9.78 (( 71.92/9.78 (upairsubunion) => 71.92/9.78 (( 71.92/9.78 (upairinpowunion) => 71.92/9.78 (( 71.92/9.78 (ubforcartprodlem1) => 71.92/9.78 (( 71.92/9.78 (ubforcartprodlem2) => 71.92/9.78 (( 71.92/9.78 (ubforcartprodlem3) => 71.92/9.78 (( 71.92/9.78 (cartprodpairin) => 71.92/9.78 (( 71.92/9.78 (cartprodmempair1) => 71.92/9.78 (( 71.92/9.78 (cartprodmempair) => 71.92/9.78 (( 71.92/9.78 (setunionE2) => 71.92/9.78 (( 71.92/9.78 (setunionsingleton1) => 71.92/9.78 (( 71.92/9.78 (setunionsingleton2) => 71.92/9.78 (( 71.92/9.78 (setunionsingleton) => 71.92/9.78 (( 71.92/9.78 (singletonprop) => 71.92/9.78 (( 71.92/9.78 (ex1E1) => 71.92/9.78 (( 71.92/9.78 (ex1I) => 71.92/9.78 (( 71.92/9.78 (ex1I2) => 71.92/9.78 (( 71.92/9.78 (singletonsuniq) => 71.92/9.78 (( 71.92/9.78 (setukpairinjL1) => 71.92/9.78 (( 71.92/9.78 (kfstsingleton) => 71.92/9.78 (( 71.92/9.78 (theprop) => 71.92/9.78 (( 71.92/9.78 (kfstpairEq) => 71.92/9.78 (( 71.92/9.78 (cartprodfstin) => 71.92/9.78 (( 71.92/9.78 (setukpairinjL2) => 71.92/9.78 (( 71.92/9.78 (setukpairinjL) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR11) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR12) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR1) => 71.92/9.78 (( 71.92/9.78 (upairequniteq) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR2) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR) => 71.92/9.78 (( 71.92/9.78 (ksndsingleton) => 71.92/9.78 (( 71.92/9.78 (ksndpairEq) => 71.92/9.78 (( 71.92/9.78 (kpairsurjEq) => 71.92/9.78 (( 71.92/9.78 (cartprodsndin) => 71.92/9.78 (( 71.92/9.78 (cartprodpairmemEL) => 71.92/9.78 (( 71.92/9.78 (cartprodpairmemER) => 71.92/9.78 (( 71.92/9.78 (cartprodmempaircEq) => 71.92/9.78 (( 71.92/9.78 (cartprodfstpairEq) => 71.92/9.78 (( 71.92/9.78 (cartprodsndpairEq) => 71.92/9.78 (( 71.92/9.78 (cartprodpairsurjEq) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrI) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrSub) => 71.92/9.78 (( 71.92/9.78 (setOfPairsIsBReln) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrERa) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrEL1) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrEL2) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrER) => 71.92/9.78 (( 71.92/9.78 (funcImageSingleton) => 71.92/9.78 (( 71.92/9.78 (apProp) => 71.92/9.78 (( 71.92/9.78 (app) => 71.92/9.78 (( 71.92/9.78 (infuncsetfunc) => 71.92/9.78 (( 71.92/9.78 (ap2p) => 71.92/9.78 (( 71.92/9.78 (funcinfuncset) => 71.92/9.78 (( 71.92/9.78 (lamProp) => 71.92/9.78 (( 71.92/9.78 (lamp) => 71.92/9.78 (( 71.92/9.78 (lam2p) => 71.92/9.78 (( 71.92/9.78 (brelnall1) => 71.92/9.78 (( 71.92/9.78 (brelnall2) => 71.92/9.78 (( 71.92/9.78 (ex1E2) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp1) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp3) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp2) => 71.92/9.78 (( 71.92/9.78 (funcextLem) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp4) => 71.92/9.78 (( 71.92/9.78 (subbreln) => 71.92/9.78 (( 71.92/9.78 (eqbreln) => 71.92/9.78 (( 71.92/9.78 (funcext) => 71.92/9.78 (( 71.92/9.78 (funcext2) => 71.92/9.78 (( 71.92/9.78 (ap2apEq1) => 71.92/9.78 (( 71.92/9.78 (ap2apEq2) => 71.92/9.78 (( 71.92/9.78 (beta1) => 71.92/9.78 (( 71.92/9.78 (eta1) => 71.92/9.78 (( 71.92/9.78 (lam2lamEq) => 71.92/9.78 (( 71.92/9.78 (beta2) => 71.92/9.78 (( 71.92/9.78 (eta2) => 71.92/9.78 (( 71.92/9.78 (iffalseProp1) => 71.92/9.78 (( 71.92/9.78 (iffalseProp2) => 71.92/9.78 (( 71.92/9.78 (iftrueProp1) => 71.92/9.78 (( 71.92/9.78 (iftrueProp2) => 71.92/9.78 (( 71.92/9.78 (ifSingleton) => 71.92/9.78 (( 71.92/9.78 (ifp) => 71.92/9.78 (( 71.92/9.78 (theeq) => 71.92/9.78 (( 71.92/9.78 (iftrue) => 71.92/9.78 (( 71.92/9.78 (iffalse) => 71.92/9.78 (( 71.92/9.78 (iftrueorfalse) => 71.92/9.78 (( 71.92/9.78 (binintersectT_lem) => 71.92/9.78 (( 71.92/9.78 (binunionT_lem) => 71.92/9.78 (( 71.92/9.78 (powersetT_lem) => 71.92/9.78 (( 71.92/9.78 (setminusT_lem) => 71.92/9.78 (( 71.92/9.78 (complementT_lem) => 71.92/9.78 (( 71.92/9.78 (setextT) => 71.92/9.78 (( 71.92/9.78 (subsetTI) => 71.92/9.78 (( 71.92/9.78 (powersetTI1) => 71.92/9.78 (( 71.92/9.78 (powersetTE1) => 71.92/9.78 (( 71.92/9.78 (complementTI1) => 71.92/9.78 (( 71.92/9.78 (complementTE1) => 71.92/9.78 (( 71.92/9.78 (binintersectTELcontra) => 71.92/9.78 (( 71.92/9.78 (binintersectTERcontra) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT1) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT2) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT3) => 71.92/9.78 (( 71.92/9.78 (doubleComplementI1) => 71.92/9.78 (( 71.92/9.78 (doubleComplementE1) => 71.92/9.78 (( 71.92/9.78 (doubleComplementSub1) => 71.92/9.78 (( 71.92/9.78 (doubleComplementSub2) => 71.92/9.78 (( 71.92/9.78 (doubleComplementEq) => 71.92/9.78 (( 71.92/9.78 (complementTnotintersectT) => 71.92/9.78 (( 71.92/9.78 (complementImpComplementIntersect) => 71.92/9.78 (( 71.92/9.78 (complementSubsetComplementIntersect) => 71.92/9.78 (( 71.92/9.78 (complementInPowersetComplementIntersect) => 71.92/9.78 (( 71.92/9.78 (contraSubsetComplement) => 71.92/9.78 (( 71.92/9.78 (complementTcontraSubset) => 71.92/9.78 (( 71.92/9.78 (binunionTILcontra) => 71.92/9.78 (( 71.92/9.78 (binunionTIRcontra) => 71.92/9.78 (( 71.92/9.78 (inIntersectImpInUnion) => 71.92/9.78 (( 71.92/9.78 (inIntersectImpInUnion2) => 71.92/9.78 (( 71.92/9.78 (inIntersectImpInIntersectUnions) => 71.92/9.78 (( 71.92/9.78 (intersectInPowersetIntersectUnions) => 71.92/9.78 (( 71.92/9.78 (inComplementUnionImpNotIn1) => 71.92/9.78 (( 71.92/9.78 (inComplementUnionImpInComplement1) => 71.92/9.78 (( 71.92/9.78 (binunionTE) => 71.92/9.78 (( 71.92/9.78 (binunionTEcontra) => 71.92/9.78 (( 71.92/9.78 (demorgan2a1) => 71.92/9.78 (( 71.92/9.78 (complementUnionInPowersetComplement) => 71.92/9.78 (( 71.92/9.78 (demorgan2a2) => 71.92/9.78 (( 71.92/9.78 (demorgan1a) => 71.92/9.78 (( 71.92/9.78 (demorgan1b) => 71.92/9.78 (( 71.92/9.78 (demorgan1) => 71.92/9.78 (( 71.92/9.78 (demorgan2a) => 71.92/9.78 (( 71.92/9.78 (demorgan2b2) => 71.92/9.78 (( 71.92/9.78 (demorgan2b) => 71.92/9.78 (( 71.92/9.78 (demorgan2) => 71.92/9.78 (( 71.92/9.78 (woz13rule0) => 71.92/9.78 (( 71.92/9.78 (woz13rule1) => 71.92/9.78 (( 71.92/9.78 (woz13rule2) => 71.92/9.78 (( 71.92/9.78 (woz13rule3) => 71.92/9.78 (( 71.92/9.78 (woz13rule4) => 71.92/9.78 (( 71.92/9.78 (woz1_1) => 71.92/9.78 (( 71.92/9.78 (woz1_2) => 71.92/9.78 (( 71.92/9.78 (woz1_3) => 71.92/9.78 (( 71.92/9.78 (woz1_4) => 71.92/9.78 (( 71.92/9.78 (woz1_5) => 71.92/9.78 (( 71.92/9.78 (breln1all2) => 71.92/9.78 (( 71.92/9.78 (breln1SetBreln1) => 71.92/9.78 (( 71.92/9.78 (choice2fnsingleton) => 71.92/9.78 (( 71.92/9.78 (setOfPairsIsBReln1) => 71.92/9.78 (( 71.92/9.78 (breln1all1) => 71.92/9.78 (( 71.92/9.78 (subbreln1) => 71.92/9.78 (( 71.92/9.78 (eqbreln1) => 71.92/9.78 (( 71.92/9.78 (breln1invprop) => 71.92/9.78 (( 71.92/9.78 (breln1invI) => 71.92/9.78 (( 71.92/9.78 (breln1invE) => 71.92/9.78 (( 71.92/9.78 (breln1compprop) => 71.92/9.78 (( 71.92/9.78 (breln1compI) => 71.92/9.78 (( 71.92/9.78 (breln1compE) => 71.92/9.78 (( 71.92/9.78 (breln1compEex) => 71.92/9.78 (( 71.92/9.78 (!!) @ ( 71.92/9.78 (('#B') @ ( 71.92/9.78 !!) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#S') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#S') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 =>))) @ 71.92/9.78 breln1)))) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 !!))) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#S') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#B') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#S') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 =>))) @ 71.92/9.78 breln1)))))) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#C') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#B') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#B') @ 71.92/9.78 breln1)))) @ 71.92/9.78 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl570])). 71.92/9.78 thf(zip_derived_cl586, plain, 71.92/9.78 (~ (((notdexE) => 71.92/9.78 (((notdallE) => 71.92/9.78 (((exuI1) => 71.92/9.78 (((exuI3) => 71.92/9.78 (((exuI2) => 71.92/9.78 (((inCongP) => 71.92/9.78 (((in__Cong) => 71.92/9.78 (((exuE3u) => 71.92/9.78 (((exu__Cong) => 71.92/9.78 (((setadjoin__Cong) => 71.92/9.78 (((powerset__Cong) => 71.92/9.78 (((setunion__Cong) => 71.92/9.78 (((exuEu) => 71.92/9.78 (((descr__Cong) => 71.92/9.78 (((dsetconstr__Cong) => 71.92/9.78 (((subsetI1) => 71.92/9.78 (((eqimpsubset2) => 71.92/9.78 (((eqimpsubset1) => 71.92/9.78 (((subsetI2) => 71.92/9.78 (((emptysetsubset) => 71.92/9.78 (((subsetE) => 71.92/9.78 (((subsetE2) => 71.92/9.78 (((notsubsetI) => 71.92/9.78 (((notequalI1) => 71.92/9.78 (((notequalI2) => 71.92/9.78 (((subsetRefl) => 71.92/9.78 (((subsetTrans) => 71.92/9.78 (((setadjoinSub) => 71.92/9.78 (((setadjoinSub2) => 71.92/9.78 (((subset2powerset) => 71.92/9.78 (( 71.92/9.78 (setextsub) => 71.92/9.78 (( 71.92/9.78 (subsetemptysetimpeq) => 71.92/9.78 (( 71.92/9.78 (powersetI1) => 71.92/9.78 (( 71.92/9.78 (powersetE1) => 71.92/9.78 (( 71.92/9.78 (inPowerset) => 71.92/9.78 (( 71.92/9.78 (powersetsubset) => 71.92/9.78 (( 71.92/9.78 (sepInPowerset) => 71.92/9.78 (( 71.92/9.78 (sepSubset) => 71.92/9.78 (( 71.92/9.78 (binunionIL) => 71.92/9.78 (( 71.92/9.78 (upairset2IR) => 71.92/9.78 (( 71.92/9.78 (binunionIR) => 71.92/9.78 (( 71.92/9.78 (binunionEcases) => 71.92/9.78 (( 71.92/9.78 (binunionE) => 71.92/9.78 (( 71.92/9.78 (binunionLsub) => 71.92/9.78 (( 71.92/9.78 (binunionRsub) => 71.92/9.78 (( 71.92/9.78 (binintersectI) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset5) => 71.92/9.78 (( 71.92/9.78 (binintersectEL) => 71.92/9.78 (( 71.92/9.78 (binintersectLsub) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset2) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset3) => 71.92/9.78 (( 71.92/9.78 (binintersectER) => 71.92/9.78 (( 71.92/9.78 (disjointsetsI1) => 71.92/9.78 (( 71.92/9.78 (binintersectRsub) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset4) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset1) => 71.92/9.78 (( 71.92/9.78 (bs114d) => 71.92/9.78 (( 71.92/9.78 (setminusI) => 71.92/9.78 (( 71.92/9.78 (setminusEL) => 71.92/9.78 (( 71.92/9.78 (setminusER) => 71.92/9.78 (( 71.92/9.78 (setminusSubset2) => 71.92/9.78 (( 71.92/9.78 (setminusERneg) => 71.92/9.78 (( 71.92/9.78 (setminusELneg) => 71.92/9.78 (( 71.92/9.78 (setminusILneg) => 71.92/9.78 (( 71.92/9.78 (setminusIRneg) => 71.92/9.78 (( 71.92/9.78 (setminusLsub) => 71.92/9.78 (( 71.92/9.78 (setminusSubset1) => 71.92/9.78 (( 71.92/9.78 (symdiffE) => 71.92/9.78 (( 71.92/9.78 (symdiffI1) => 71.92/9.78 (( 71.92/9.78 (symdiffI2) => 71.92/9.78 (( 71.92/9.78 (symdiffIneg1) => 71.92/9.78 (( 71.92/9.78 (symdiffIneg2) => 71.92/9.78 (( 71.92/9.78 (secondinupair) => 71.92/9.78 (( 71.92/9.78 (setukpairIL) => 71.92/9.78 (( 71.92/9.78 (setukpairIR) => 71.92/9.78 (( 71.92/9.78 (kpairiskpair) => 71.92/9.78 (( 71.92/9.78 (kpairp) => 71.92/9.78 (( 71.92/9.78 (singletonsubset) => 71.92/9.78 (( 71.92/9.78 (singletoninpowerset) => 71.92/9.78 (( 71.92/9.78 (singletoninpowunion) => 71.92/9.78 (( 71.92/9.78 (upairset2E) => 71.92/9.78 (( 71.92/9.78 (upairsubunion) => 71.92/9.78 (( 71.92/9.78 (upairinpowunion) => 71.92/9.78 (( 71.92/9.78 (ubforcartprodlem1) => 71.92/9.78 (( 71.92/9.78 (ubforcartprodlem2) => 71.92/9.78 (( 71.92/9.78 (ubforcartprodlem3) => 71.92/9.78 (( 71.92/9.78 (cartprodpairin) => 71.92/9.78 (( 71.92/9.78 (cartprodmempair1) => 71.92/9.78 (( 71.92/9.78 (cartprodmempair) => 71.92/9.78 (( 71.92/9.78 (setunionE2) => 71.92/9.78 (( 71.92/9.78 (setunionsingleton1) => 71.92/9.78 (( 71.92/9.78 (setunionsingleton2) => 71.92/9.78 (( 71.92/9.78 (setunionsingleton) => 71.92/9.78 (( 71.92/9.78 (singletonprop) => 71.92/9.78 (( 71.92/9.78 (ex1E1) => 71.92/9.78 (( 71.92/9.78 (ex1I) => 71.92/9.78 (( 71.92/9.78 (ex1I2) => 71.92/9.78 (( 71.92/9.78 (singletonsuniq) => 71.92/9.78 (( 71.92/9.78 (setukpairinjL1) => 71.92/9.78 (( 71.92/9.78 (kfstsingleton) => 71.92/9.78 (( 71.92/9.78 (theprop) => 71.92/9.78 (( 71.92/9.78 (kfstpairEq) => 71.92/9.78 (( 71.92/9.78 (cartprodfstin) => 71.92/9.78 (( 71.92/9.78 (setukpairinjL2) => 71.92/9.78 (( 71.92/9.78 (setukpairinjL) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR11) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR12) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR1) => 71.92/9.78 (( 71.92/9.78 (upairequniteq) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR2) => 71.92/9.78 (( 71.92/9.78 (setukpairinjR) => 71.92/9.78 (( 71.92/9.78 (ksndsingleton) => 71.92/9.78 (( 71.92/9.78 (ksndpairEq) => 71.92/9.78 (( 71.92/9.78 (kpairsurjEq) => 71.92/9.78 (( 71.92/9.78 (cartprodsndin) => 71.92/9.78 (( 71.92/9.78 (cartprodpairmemEL) => 71.92/9.78 (( 71.92/9.78 (cartprodpairmemER) => 71.92/9.78 (( 71.92/9.78 (cartprodmempaircEq) => 71.92/9.78 (( 71.92/9.78 (cartprodfstpairEq) => 71.92/9.78 (( 71.92/9.78 (cartprodsndpairEq) => 71.92/9.78 (( 71.92/9.78 (cartprodpairsurjEq) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrI) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrSub) => 71.92/9.78 (( 71.92/9.78 (setOfPairsIsBReln) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrERa) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrEL1) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrEL2) => 71.92/9.78 (( 71.92/9.78 (dpsetconstrER) => 71.92/9.78 (( 71.92/9.78 (funcImageSingleton) => 71.92/9.78 (( 71.92/9.78 (apProp) => 71.92/9.78 (( 71.92/9.78 (app) => 71.92/9.78 (( 71.92/9.78 (infuncsetfunc) => 71.92/9.78 (( 71.92/9.78 (ap2p) => 71.92/9.78 (( 71.92/9.78 (funcinfuncset) => 71.92/9.78 (( 71.92/9.78 (lamProp) => 71.92/9.78 (( 71.92/9.78 (lamp) => 71.92/9.78 (( 71.92/9.78 (lam2p) => 71.92/9.78 (( 71.92/9.78 (brelnall1) => 71.92/9.78 (( 71.92/9.78 (brelnall2) => 71.92/9.78 (( 71.92/9.78 (ex1E2) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp1) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp3) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp2) => 71.92/9.78 (( 71.92/9.78 (funcextLem) => 71.92/9.78 (( 71.92/9.78 (funcGraphProp4) => 71.92/9.78 (( 71.92/9.78 (subbreln) => 71.92/9.78 (( 71.92/9.78 (eqbreln) => 71.92/9.78 (( 71.92/9.78 (funcext) => 71.92/9.78 (( 71.92/9.78 (funcext2) => 71.92/9.78 (( 71.92/9.78 (ap2apEq1) => 71.92/9.78 (( 71.92/9.78 (ap2apEq2) => 71.92/9.78 (( 71.92/9.78 (beta1) => 71.92/9.78 (( 71.92/9.78 (eta1) => 71.92/9.78 (( 71.92/9.78 (lam2lamEq) => 71.92/9.78 (( 71.92/9.78 (beta2) => 71.92/9.78 (( 71.92/9.78 (eta2) => 71.92/9.78 (( 71.92/9.78 (iffalseProp1) => 71.92/9.78 (( 71.92/9.78 (iffalseProp2) => 71.92/9.78 (( 71.92/9.78 (iftrueProp1) => 71.92/9.78 (( 71.92/9.78 (iftrueProp2) => 71.92/9.78 (( 71.92/9.78 (ifSingleton) => 71.92/9.78 (( 71.92/9.78 (ifp) => 71.92/9.78 (( 71.92/9.78 (theeq) => 71.92/9.78 (( 71.92/9.78 (iftrue) => 71.92/9.78 (( 71.92/9.78 (iffalse) => 71.92/9.78 (( 71.92/9.78 (iftrueorfalse) => 71.92/9.78 (( 71.92/9.78 (binintersectT_lem) => 71.92/9.78 (( 71.92/9.78 (binunionT_lem) => 71.92/9.78 (( 71.92/9.78 (powersetT_lem) => 71.92/9.78 (( 71.92/9.78 (setminusT_lem) => 71.92/9.78 (( 71.92/9.78 (complementT_lem) => 71.92/9.78 (( 71.92/9.78 (setextT) => 71.92/9.78 (( 71.92/9.78 (subsetTI) => 71.92/9.78 (( 71.92/9.78 (powersetTI1) => 71.92/9.78 (( 71.92/9.78 (powersetTE1) => 71.92/9.78 (( 71.92/9.78 (complementTI1) => 71.92/9.78 (( 71.92/9.78 (complementTE1) => 71.92/9.78 (( 71.92/9.78 (binintersectTELcontra) => 71.92/9.78 (( 71.92/9.78 (binintersectTERcontra) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT1) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT2) => 71.92/9.78 (( 71.92/9.78 (contrasubsetT3) => 71.92/9.78 (( 71.92/9.78 (doubleComplementI1) => 71.92/9.78 (( 71.92/9.78 (doubleComplementE1) => 71.92/9.78 (( 71.92/9.78 (doubleComplementSub1) => 71.92/9.78 (( 71.92/9.78 (doubleComplementSub2) => 71.92/9.78 (( 71.92/9.78 (doubleComplementEq) => 71.92/9.78 (( 71.92/9.78 (complementTnotintersectT) => 71.92/9.78 (( 71.92/9.78 (complementImpComplementIntersect) => 71.92/9.78 (( 71.92/9.78 (complementSubsetComplementIntersect) => 71.92/9.78 (( 71.92/9.78 (complementInPowersetComplementIntersect) => 71.92/9.78 (( 71.92/9.78 (contraSubsetComplement) => 71.92/9.78 (( 71.92/9.78 (complementTcontraSubset) => 71.92/9.78 (( 71.92/9.78 (binunionTILcontra) => 71.92/9.78 (( 71.92/9.78 (binunionTIRcontra) => 71.92/9.78 (( 71.92/9.78 (inIntersectImpInUnion) => 71.92/9.78 (( 71.92/9.78 (inIntersectImpInUnion2) => 71.92/9.78 (( 71.92/9.78 (inIntersectImpInIntersectUnions) => 71.92/9.78 (( 71.92/9.78 (intersectInPowersetIntersectUnions) => 71.92/9.78 (( 71.92/9.78 (inComplementUnionImpNotIn1) => 71.92/9.78 (( 71.92/9.78 (inComplementUnionImpInComplement1) => 71.92/9.78 (( 71.92/9.78 (binunionTE) => 71.92/9.78 (( 71.92/9.78 (binunionTEcontra) => 71.92/9.78 (( 71.92/9.78 (demorgan2a1) => 71.92/9.78 (( 71.92/9.78 (complementUnionInPowersetComplement) => 71.92/9.78 (( 71.92/9.78 (demorgan2a2) => 71.92/9.78 (( 71.92/9.78 (demorgan1a) => 71.92/9.78 (( 71.92/9.78 (demorgan1b) => 71.92/9.78 (( 71.92/9.78 (demorgan1) => 71.92/9.78 (( 71.92/9.78 (demorgan2a) => 71.92/9.78 (( 71.92/9.78 (demorgan2b2) => 71.92/9.78 (( 71.92/9.78 (demorgan2b) => 71.92/9.78 (( 71.92/9.78 (demorgan2) => 71.92/9.78 (( 71.92/9.78 (woz13rule0) => 71.92/9.78 (( 71.92/9.78 (woz13rule1) => 71.92/9.78 (( 71.92/9.78 (woz13rule2) => 71.92/9.78 (( 71.92/9.78 (woz13rule3) => 71.92/9.78 (( 71.92/9.78 (woz13rule4) => 71.92/9.78 (( 71.92/9.78 (woz1_1) => 71.92/9.78 (( 71.92/9.78 (woz1_2) => 71.92/9.78 (( 71.92/9.78 (woz1_3) => 71.92/9.78 (( 71.92/9.78 (woz1_4) => 71.92/9.78 (( 71.92/9.78 (woz1_5) => 71.92/9.78 (( 71.92/9.78 (breln1all2) => 71.92/9.78 (( 71.92/9.78 (breln1SetBreln1) => 71.92/9.78 (( 71.92/9.78 (choice2fnsingleton) => 71.92/9.78 (( 71.92/9.78 (setOfPairsIsBReln1) => 71.92/9.78 (( 71.92/9.78 (breln1all1) => 71.92/9.78 (( 71.92/9.78 (subbreln1) => 71.92/9.78 (( 71.92/9.78 (eqbreln1) => 71.92/9.78 (( 71.92/9.78 (breln1invprop) => 71.92/9.78 (( 71.92/9.78 (breln1invI) => 71.92/9.78 (( 71.92/9.78 (breln1invE) => 71.92/9.78 (( 71.92/9.78 (breln1compprop) => 71.92/9.78 (( 71.92/9.78 (breln1compI) => 71.92/9.78 (( 71.92/9.78 (breln1compE) => 71.92/9.78 (( 71.92/9.78 (breln1compEex) => 71.92/9.78 (( 71.92/9.78 (!!) @ ( 71.92/9.78 (('#B') @ ( 71.92/9.78 !!) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#S') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#S') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 =>))) @ 71.92/9.78 breln1)))) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 !!))) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#S') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#B') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#S') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 =>))) @ 71.92/9.78 breln1)))))) @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#C') @ ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#B') @ 71.92/9.78 ( 71.92/9.78 ( 71.92/9.78 ('#B') @ ( 71.92/9.78 '#B') @ 71.92/9.78 breln1)))) @ 71.92/9.78 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])). 71.92/9.78 thf(zip_derived_cl595, plain, 71.92/9.78 (~ (((notdallE) => 71.92/9.78 (((exuI1) => 71.92/9.78 (((exuI3) => 71.92/9.78 (((exuI2) => 71.92/9.78 (((inCongP) => 71.92/9.78 (((in__Cong) => 71.92/9.78 (((exuE3u) => 71.92/9.78 (((exu__Cong) => 71.92/9.78 (((setadjoin__Cong) => 71.92/9.78 (((powerset__Cong) => 71.92/9.78 (((setunion__Cong) => 71.92/9.78 (((exuEu) => 71.92/9.78 (((descr__Cong) => 71.92/9.78 (((dsetconstr__Cong) => 71.92/9.78 (((subsetI1) => 71.92/9.78 (((eqimpsubset2) => 71.92/9.78 (((eqimpsubset1) => 71.92/9.78 (((subsetI2) => 71.92/9.78 (((emptysetsubset) => 71.92/9.78 (((subsetE) => 71.92/9.78 (((subsetE2) => 71.92/9.78 (((notsubsetI) => 71.92/9.78 (((notequalI1) => 71.92/9.78 (((notequalI2) => 71.92/9.78 (((subsetRefl) => 71.92/9.78 (((subsetTrans) => 71.92/9.78 (((setadjoinSub) => 71.92/9.78 (((setadjoinSub2) => 71.92/9.78 (((subset2powerset) => 71.92/9.78 (((setextsub) => 71.92/9.78 (( 71.92/9.78 (subsetemptysetimpeq) => 71.92/9.78 (( 71.92/9.78 (powersetI1) => 71.92/9.78 (( 71.92/9.78 (powersetE1) => 71.92/9.78 (( 71.92/9.78 (inPowerset) => 71.92/9.78 (( 71.92/9.78 (powersetsubset) => 71.92/9.78 (( 71.92/9.78 (sepInPowerset) => 71.92/9.78 (( 71.92/9.78 (sepSubset) => 71.92/9.78 (( 71.92/9.78 (binunionIL) => 71.92/9.78 (( 71.92/9.78 (upairset2IR) => 71.92/9.78 (( 71.92/9.78 (binunionIR) => 71.92/9.78 (( 71.92/9.78 (binunionEcases) => 71.92/9.78 (( 71.92/9.78 (binunionE) => 71.92/9.78 (( 71.92/9.78 (binunionLsub) => 71.92/9.78 (( 71.92/9.78 (binunionRsub) => 71.92/9.78 (( 71.92/9.78 (binintersectI) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset5) => 71.92/9.78 (( 71.92/9.78 (binintersectEL) => 71.92/9.78 (( 71.92/9.78 (binintersectLsub) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset2) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset3) => 71.92/9.78 (( 71.92/9.78 (binintersectER) => 71.92/9.78 (( 71.92/9.78 (disjointsetsI1) => 71.92/9.78 (( 71.92/9.78 (binintersectRsub) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset4) => 71.92/9.78 (( 71.92/9.78 (binintersectSubset1) => 71.92/9.78 (( 71.92/9.78 (bs114d) => 71.92/9.78 (( 71.92/9.78 (setminusI) => 71.92/9.78 (( 71.92/9.78 (setminusEL) => 71.92/9.78 (( 71.92/9.78 (setminusER) => 71.92/9.78 (( 71.92/9.78 (setminusSubset2) => 71.92/9.78 (( 71.92/9.78 (setminusERneg) => 71.92/9.78 (( 71.92/9.78 (setminusELneg) => 71.92/9.78 (( 71.92/9.78 (setminusILneg) => 71.92/9.78 (( 71.92/9.78 (setminusIRneg) => 71.92/9.78 (( 71.92/9.78 (setminusLsub) => 71.92/9.78 (( 71.92/9.78 (setminusSubset1) => 71.92/9.78 (( 71.92/9.78 (symdiffE) => 71.92/9.78 (( 71.92/9.78 (symdiffI1) => 71.92/9.78 (( 71.92/9.78 (symdiffI2) => 71.92/9.78 (( 71.92/9.78 (symdiffIneg1) => 71.92/9.78 (( 71.92/9.78 (symdiffIneg2) => 71.92/9.78 (( 71.92/9.78 (secondinupair) => 71.92/9.78 (( 71.92/9.78 (setukpairIL) => 71.92/9.79 (( 71.92/9.79 (setukpairIR) => 71.92/9.79 (( 71.92/9.79 (kpairiskpair) => 71.92/9.79 (( 71.92/9.79 (kpairp) => 71.92/9.79 (( 71.92/9.79 (singletonsubset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowerset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowunion) => 71.92/9.79 (( 71.92/9.79 (upairset2E) => 71.92/9.79 (( 71.92/9.79 (upairsubunion) => 71.92/9.79 (( 71.92/9.79 (upairinpowunion) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem1) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem2) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem3) => 71.92/9.79 (( 71.92/9.79 (cartprodpairin) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair1) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair) => 71.92/9.79 (( 71.92/9.79 (setunionE2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton1) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton) => 71.92/9.79 (( 71.92/9.79 (singletonprop) => 71.92/9.79 (( 71.92/9.79 (ex1E1) => 71.92/9.79 (( 71.92/9.79 (ex1I) => 71.92/9.79 (( 71.92/9.79 (ex1I2) => 71.92/9.79 (( 71.92/9.79 (singletonsuniq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL1) => 71.92/9.79 (( 71.92/9.79 (kfstsingleton) => 71.92/9.79 (( 71.92/9.79 (theprop) => 71.92/9.79 (( 71.92/9.79 (kfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstin) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR11) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR12) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR1) => 71.92/9.79 (( 71.92/9.79 (upairequniteq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR) => 71.92/9.79 (( 71.92/9.79 (ksndsingleton) => 71.92/9.79 (( 71.92/9.79 (ksndpairEq) => 71.92/9.79 (( 71.92/9.79 (kpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndin) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemEL) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemER) => 71.92/9.79 (( 71.92/9.79 (cartprodmempaircEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrI) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrSub) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrERa) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL1) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL2) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrER) => 71.92/9.79 (( 71.92/9.79 (funcImageSingleton) => 71.92/9.79 (( 71.92/9.79 (apProp) => 71.92/9.79 (( 71.92/9.79 (app) => 71.92/9.79 (( 71.92/9.79 (infuncsetfunc) => 71.92/9.79 (( 71.92/9.79 (ap2p) => 71.92/9.79 (( 71.92/9.79 (funcinfuncset) => 71.92/9.79 (( 71.92/9.79 (lamProp) => 71.92/9.79 (( 71.92/9.79 (lamp) => 71.92/9.79 (( 71.92/9.79 (lam2p) => 71.92/9.79 (( 71.92/9.79 (brelnall1) => 71.92/9.79 (( 71.92/9.79 (brelnall2) => 71.92/9.79 (( 71.92/9.79 (ex1E2) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp1) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp3) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp2) => 71.92/9.79 (( 71.92/9.79 (funcextLem) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp4) => 71.92/9.79 (( 71.92/9.79 (subbreln) => 71.92/9.79 (( 71.92/9.79 (eqbreln) => 71.92/9.79 (( 71.92/9.79 (funcext) => 71.92/9.79 (( 71.92/9.79 (funcext2) => 71.92/9.79 (( 71.92/9.79 (ap2apEq1) => 71.92/9.79 (( 71.92/9.79 (ap2apEq2) => 71.92/9.79 (( 71.92/9.79 (beta1) => 71.92/9.79 (( 71.92/9.79 (eta1) => 71.92/9.79 (( 71.92/9.79 (lam2lamEq) => 71.92/9.79 (( 71.92/9.79 (beta2) => 71.92/9.79 (( 71.92/9.79 (eta2) => 71.92/9.79 (( 71.92/9.79 (iffalseProp1) => 71.92/9.79 (( 71.92/9.79 (iffalseProp2) => 71.92/9.79 (( 71.92/9.79 (iftrueProp1) => 71.92/9.79 (( 71.92/9.79 (iftrueProp2) => 71.92/9.79 (( 71.92/9.79 (ifSingleton) => 71.92/9.79 (( 71.92/9.79 (ifp) => 71.92/9.79 (( 71.92/9.79 (theeq) => 71.92/9.79 (( 71.92/9.79 (iftrue) => 71.92/9.79 (( 71.92/9.79 (iffalse) => 71.92/9.79 (( 71.92/9.79 (iftrueorfalse) => 71.92/9.79 (( 71.92/9.79 (binintersectT_lem) => 71.92/9.79 (( 71.92/9.79 (binunionT_lem) => 71.92/9.79 (( 71.92/9.79 (powersetT_lem) => 71.92/9.79 (( 71.92/9.79 (setminusT_lem) => 71.92/9.79 (( 71.92/9.79 (complementT_lem) => 71.92/9.79 (( 71.92/9.79 (setextT) => 71.92/9.79 (( 71.92/9.79 (subsetTI) => 71.92/9.79 (( 71.92/9.79 (powersetTI1) => 71.92/9.79 (( 71.92/9.79 (powersetTE1) => 71.92/9.79 (( 71.92/9.79 (complementTI1) => 71.92/9.79 (( 71.92/9.79 (complementTE1) => 71.92/9.79 (( 71.92/9.79 (binintersectTELcontra) => 71.92/9.79 (( 71.92/9.79 (binintersectTERcontra) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT1) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT2) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT3) => 71.92/9.79 (( 71.92/9.79 (doubleComplementI1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementE1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub2) => 71.92/9.79 (( 71.92/9.79 (doubleComplementEq) => 71.92/9.79 (( 71.92/9.79 (complementTnotintersectT) => 71.92/9.79 (( 71.92/9.79 (complementImpComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementSubsetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementInPowersetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (contraSubsetComplement) => 71.92/9.79 (( 71.92/9.79 (complementTcontraSubset) => 71.92/9.79 (( 71.92/9.79 (binunionTILcontra) => 71.92/9.79 (( 71.92/9.79 (binunionTIRcontra) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion2) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (intersectInPowersetIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpNotIn1) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpInComplement1) => 71.92/9.79 (( 71.92/9.79 (binunionTE) => 71.92/9.79 (( 71.92/9.79 (binunionTEcontra) => 71.92/9.79 (( 71.92/9.79 (demorgan2a1) => 71.92/9.79 (( 71.92/9.79 (complementUnionInPowersetComplement) => 71.92/9.79 (( 71.92/9.79 (demorgan2a2) => 71.92/9.79 (( 71.92/9.79 (demorgan1a) => 71.92/9.79 (( 71.92/9.79 (demorgan1b) => 71.92/9.79 (( 71.92/9.79 (demorgan1) => 71.92/9.79 (( 71.92/9.79 (demorgan2a) => 71.92/9.79 (( 71.92/9.79 (demorgan2b2) => 71.92/9.79 (( 71.92/9.79 (demorgan2b) => 71.92/9.79 (( 71.92/9.79 (demorgan2) => 71.92/9.79 (( 71.92/9.79 (woz13rule0) => 71.92/9.79 (( 71.92/9.79 (woz13rule1) => 71.92/9.79 (( 71.92/9.79 (woz13rule2) => 71.92/9.79 (( 71.92/9.79 (woz13rule3) => 71.92/9.79 (( 71.92/9.79 (woz13rule4) => 71.92/9.79 (( 71.92/9.79 (woz1_1) => 71.92/9.79 (( 71.92/9.79 (woz1_2) => 71.92/9.79 (( 71.92/9.79 (woz1_3) => 71.92/9.79 (( 71.92/9.79 (woz1_4) => 71.92/9.79 (( 71.92/9.79 (woz1_5) => 71.92/9.79 (( 71.92/9.79 (breln1all2) => 71.92/9.79 (( 71.92/9.79 (breln1SetBreln1) => 71.92/9.79 (( 71.92/9.79 (choice2fnsingleton) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln1) => 71.92/9.79 (( 71.92/9.79 (breln1all1) => 71.92/9.79 (( 71.92/9.79 (subbreln1) => 71.92/9.79 (( 71.92/9.79 (eqbreln1) => 71.92/9.79 (( 71.92/9.79 (breln1invprop) => 71.92/9.79 (( 71.92/9.79 (breln1invI) => 71.92/9.79 (( 71.92/9.79 (breln1invE) => 71.92/9.79 (( 71.92/9.79 (breln1compprop) => 71.92/9.79 (( 71.92/9.79 (breln1compI) => 71.92/9.79 (( 71.92/9.79 (breln1compE) => 71.92/9.79 (( 71.92/9.79 (breln1compEex) => 71.92/9.79 (( 71.92/9.79 (!!) @ ( 71.92/9.79 (('#B') @ ( 71.92/9.79 !!) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 !!))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#C') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 breln1)))) @ 71.92/9.79 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl586])). 71.92/9.79 thf(zip_derived_cl606, plain, 71.92/9.79 (~ (((exuI1) => 71.92/9.79 (((exuI3) => 71.92/9.79 (((exuI2) => 71.92/9.79 (((inCongP) => 71.92/9.79 (((in__Cong) => 71.92/9.79 (((exuE3u) => 71.92/9.79 (((exu__Cong) => 71.92/9.79 (((setadjoin__Cong) => 71.92/9.79 (((powerset__Cong) => 71.92/9.79 (((setunion__Cong) => 71.92/9.79 (((exuEu) => 71.92/9.79 (((descr__Cong) => 71.92/9.79 (((dsetconstr__Cong) => 71.92/9.79 (((subsetI1) => 71.92/9.79 (((eqimpsubset2) => 71.92/9.79 (((eqimpsubset1) => 71.92/9.79 (((subsetI2) => 71.92/9.79 (((emptysetsubset) => 71.92/9.79 (((subsetE) => 71.92/9.79 (((subsetE2) => 71.92/9.79 (((notsubsetI) => 71.92/9.79 (((notequalI1) => 71.92/9.79 (((notequalI2) => 71.92/9.79 (((subsetRefl) => 71.92/9.79 (((subsetTrans) => 71.92/9.79 (((setadjoinSub) => 71.92/9.79 (((setadjoinSub2) => 71.92/9.79 (((subset2powerset) => 71.92/9.79 (((setextsub) => 71.92/9.79 (((subsetemptysetimpeq) => 71.92/9.79 (( 71.92/9.79 (powersetI1) => 71.92/9.79 (( 71.92/9.79 (powersetE1) => 71.92/9.79 (( 71.92/9.79 (inPowerset) => 71.92/9.79 (( 71.92/9.79 (powersetsubset) => 71.92/9.79 (( 71.92/9.79 (sepInPowerset) => 71.92/9.79 (( 71.92/9.79 (sepSubset) => 71.92/9.79 (( 71.92/9.79 (binunionIL) => 71.92/9.79 (( 71.92/9.79 (upairset2IR) => 71.92/9.79 (( 71.92/9.79 (binunionIR) => 71.92/9.79 (( 71.92/9.79 (binunionEcases) => 71.92/9.79 (( 71.92/9.79 (binunionE) => 71.92/9.79 (( 71.92/9.79 (binunionLsub) => 71.92/9.79 (( 71.92/9.79 (binunionRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectI) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset5) => 71.92/9.79 (( 71.92/9.79 (binintersectEL) => 71.92/9.79 (( 71.92/9.79 (binintersectLsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset2) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset3) => 71.92/9.79 (( 71.92/9.79 (binintersectER) => 71.92/9.79 (( 71.92/9.79 (disjointsetsI1) => 71.92/9.79 (( 71.92/9.79 (binintersectRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset4) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset1) => 71.92/9.79 (( 71.92/9.79 (bs114d) => 71.92/9.79 (( 71.92/9.79 (setminusI) => 71.92/9.79 (( 71.92/9.79 (setminusEL) => 71.92/9.79 (( 71.92/9.79 (setminusER) => 71.92/9.79 (( 71.92/9.79 (setminusSubset2) => 71.92/9.79 (( 71.92/9.79 (setminusERneg) => 71.92/9.79 (( 71.92/9.79 (setminusELneg) => 71.92/9.79 (( 71.92/9.79 (setminusILneg) => 71.92/9.79 (( 71.92/9.79 (setminusIRneg) => 71.92/9.79 (( 71.92/9.79 (setminusLsub) => 71.92/9.79 (( 71.92/9.79 (setminusSubset1) => 71.92/9.79 (( 71.92/9.79 (symdiffE) => 71.92/9.79 (( 71.92/9.79 (symdiffI1) => 71.92/9.79 (( 71.92/9.79 (symdiffI2) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg1) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg2) => 71.92/9.79 (( 71.92/9.79 (secondinupair) => 71.92/9.79 (( 71.92/9.79 (setukpairIL) => 71.92/9.79 (( 71.92/9.79 (setukpairIR) => 71.92/9.79 (( 71.92/9.79 (kpairiskpair) => 71.92/9.79 (( 71.92/9.79 (kpairp) => 71.92/9.79 (( 71.92/9.79 (singletonsubset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowerset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowunion) => 71.92/9.79 (( 71.92/9.79 (upairset2E) => 71.92/9.79 (( 71.92/9.79 (upairsubunion) => 71.92/9.79 (( 71.92/9.79 (upairinpowunion) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem1) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem2) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem3) => 71.92/9.79 (( 71.92/9.79 (cartprodpairin) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair1) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair) => 71.92/9.79 (( 71.92/9.79 (setunionE2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton1) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton) => 71.92/9.79 (( 71.92/9.79 (singletonprop) => 71.92/9.79 (( 71.92/9.79 (ex1E1) => 71.92/9.79 (( 71.92/9.79 (ex1I) => 71.92/9.79 (( 71.92/9.79 (ex1I2) => 71.92/9.79 (( 71.92/9.79 (singletonsuniq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL1) => 71.92/9.79 (( 71.92/9.79 (kfstsingleton) => 71.92/9.79 (( 71.92/9.79 (theprop) => 71.92/9.79 (( 71.92/9.79 (kfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstin) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR11) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR12) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR1) => 71.92/9.79 (( 71.92/9.79 (upairequniteq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR) => 71.92/9.79 (( 71.92/9.79 (ksndsingleton) => 71.92/9.79 (( 71.92/9.79 (ksndpairEq) => 71.92/9.79 (( 71.92/9.79 (kpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndin) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemEL) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemER) => 71.92/9.79 (( 71.92/9.79 (cartprodmempaircEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrI) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrSub) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrERa) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL1) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL2) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrER) => 71.92/9.79 (( 71.92/9.79 (funcImageSingleton) => 71.92/9.79 (( 71.92/9.79 (apProp) => 71.92/9.79 (( 71.92/9.79 (app) => 71.92/9.79 (( 71.92/9.79 (infuncsetfunc) => 71.92/9.79 (( 71.92/9.79 (ap2p) => 71.92/9.79 (( 71.92/9.79 (funcinfuncset) => 71.92/9.79 (( 71.92/9.79 (lamProp) => 71.92/9.79 (( 71.92/9.79 (lamp) => 71.92/9.79 (( 71.92/9.79 (lam2p) => 71.92/9.79 (( 71.92/9.79 (brelnall1) => 71.92/9.79 (( 71.92/9.79 (brelnall2) => 71.92/9.79 (( 71.92/9.79 (ex1E2) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp1) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp3) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp2) => 71.92/9.79 (( 71.92/9.79 (funcextLem) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp4) => 71.92/9.79 (( 71.92/9.79 (subbreln) => 71.92/9.79 (( 71.92/9.79 (eqbreln) => 71.92/9.79 (( 71.92/9.79 (funcext) => 71.92/9.79 (( 71.92/9.79 (funcext2) => 71.92/9.79 (( 71.92/9.79 (ap2apEq1) => 71.92/9.79 (( 71.92/9.79 (ap2apEq2) => 71.92/9.79 (( 71.92/9.79 (beta1) => 71.92/9.79 (( 71.92/9.79 (eta1) => 71.92/9.79 (( 71.92/9.79 (lam2lamEq) => 71.92/9.79 (( 71.92/9.79 (beta2) => 71.92/9.79 (( 71.92/9.79 (eta2) => 71.92/9.79 (( 71.92/9.79 (iffalseProp1) => 71.92/9.79 (( 71.92/9.79 (iffalseProp2) => 71.92/9.79 (( 71.92/9.79 (iftrueProp1) => 71.92/9.79 (( 71.92/9.79 (iftrueProp2) => 71.92/9.79 (( 71.92/9.79 (ifSingleton) => 71.92/9.79 (( 71.92/9.79 (ifp) => 71.92/9.79 (( 71.92/9.79 (theeq) => 71.92/9.79 (( 71.92/9.79 (iftrue) => 71.92/9.79 (( 71.92/9.79 (iffalse) => 71.92/9.79 (( 71.92/9.79 (iftrueorfalse) => 71.92/9.79 (( 71.92/9.79 (binintersectT_lem) => 71.92/9.79 (( 71.92/9.79 (binunionT_lem) => 71.92/9.79 (( 71.92/9.79 (powersetT_lem) => 71.92/9.79 (( 71.92/9.79 (setminusT_lem) => 71.92/9.79 (( 71.92/9.79 (complementT_lem) => 71.92/9.79 (( 71.92/9.79 (setextT) => 71.92/9.79 (( 71.92/9.79 (subsetTI) => 71.92/9.79 (( 71.92/9.79 (powersetTI1) => 71.92/9.79 (( 71.92/9.79 (powersetTE1) => 71.92/9.79 (( 71.92/9.79 (complementTI1) => 71.92/9.79 (( 71.92/9.79 (complementTE1) => 71.92/9.79 (( 71.92/9.79 (binintersectTELcontra) => 71.92/9.79 (( 71.92/9.79 (binintersectTERcontra) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT1) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT2) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT3) => 71.92/9.79 (( 71.92/9.79 (doubleComplementI1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementE1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub2) => 71.92/9.79 (( 71.92/9.79 (doubleComplementEq) => 71.92/9.79 (( 71.92/9.79 (complementTnotintersectT) => 71.92/9.79 (( 71.92/9.79 (complementImpComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementSubsetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementInPowersetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (contraSubsetComplement) => 71.92/9.79 (( 71.92/9.79 (complementTcontraSubset) => 71.92/9.79 (( 71.92/9.79 (binunionTILcontra) => 71.92/9.79 (( 71.92/9.79 (binunionTIRcontra) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion2) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (intersectInPowersetIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpNotIn1) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpInComplement1) => 71.92/9.79 (( 71.92/9.79 (binunionTE) => 71.92/9.79 (( 71.92/9.79 (binunionTEcontra) => 71.92/9.79 (( 71.92/9.79 (demorgan2a1) => 71.92/9.79 (( 71.92/9.79 (complementUnionInPowersetComplement) => 71.92/9.79 (( 71.92/9.79 (demorgan2a2) => 71.92/9.79 (( 71.92/9.79 (demorgan1a) => 71.92/9.79 (( 71.92/9.79 (demorgan1b) => 71.92/9.79 (( 71.92/9.79 (demorgan1) => 71.92/9.79 (( 71.92/9.79 (demorgan2a) => 71.92/9.79 (( 71.92/9.79 (demorgan2b2) => 71.92/9.79 (( 71.92/9.79 (demorgan2b) => 71.92/9.79 (( 71.92/9.79 (demorgan2) => 71.92/9.79 (( 71.92/9.79 (woz13rule0) => 71.92/9.79 (( 71.92/9.79 (woz13rule1) => 71.92/9.79 (( 71.92/9.79 (woz13rule2) => 71.92/9.79 (( 71.92/9.79 (woz13rule3) => 71.92/9.79 (( 71.92/9.79 (woz13rule4) => 71.92/9.79 (( 71.92/9.79 (woz1_1) => 71.92/9.79 (( 71.92/9.79 (woz1_2) => 71.92/9.79 (( 71.92/9.79 (woz1_3) => 71.92/9.79 (( 71.92/9.79 (woz1_4) => 71.92/9.79 (( 71.92/9.79 (woz1_5) => 71.92/9.79 (( 71.92/9.79 (breln1all2) => 71.92/9.79 (( 71.92/9.79 (breln1SetBreln1) => 71.92/9.79 (( 71.92/9.79 (choice2fnsingleton) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln1) => 71.92/9.79 (( 71.92/9.79 (breln1all1) => 71.92/9.79 (( 71.92/9.79 (subbreln1) => 71.92/9.79 (( 71.92/9.79 (eqbreln1) => 71.92/9.79 (( 71.92/9.79 (breln1invprop) => 71.92/9.79 (( 71.92/9.79 (breln1invI) => 71.92/9.79 (( 71.92/9.79 (breln1invE) => 71.92/9.79 (( 71.92/9.79 (breln1compprop) => 71.92/9.79 (( 71.92/9.79 (breln1compI) => 71.92/9.79 (( 71.92/9.79 (breln1compE) => 71.92/9.79 (( 71.92/9.79 (breln1compEex) => 71.92/9.79 (( 71.92/9.79 (!!) @ ( 71.92/9.79 (('#B') @ ( 71.92/9.79 !!) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 !!))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#C') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 breln1)))) @ 71.92/9.79 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])). 71.92/9.79 thf(zip_derived_cl619, plain, 71.92/9.79 (~ (((exuI3) => 71.92/9.79 (((exuI2) => 71.92/9.79 (((inCongP) => 71.92/9.79 (((in__Cong) => 71.92/9.79 (((exuE3u) => 71.92/9.79 (((exu__Cong) => 71.92/9.79 (((setadjoin__Cong) => 71.92/9.79 (((powerset__Cong) => 71.92/9.79 (((setunion__Cong) => 71.92/9.79 (((exuEu) => 71.92/9.79 (((descr__Cong) => 71.92/9.79 (((dsetconstr__Cong) => 71.92/9.79 (((subsetI1) => 71.92/9.79 (((eqimpsubset2) => 71.92/9.79 (((eqimpsubset1) => 71.92/9.79 (((subsetI2) => 71.92/9.79 (((emptysetsubset) => 71.92/9.79 (((subsetE) => 71.92/9.79 (((subsetE2) => 71.92/9.79 (((notsubsetI) => 71.92/9.79 (((notequalI1) => 71.92/9.79 (((notequalI2) => 71.92/9.79 (((subsetRefl) => 71.92/9.79 (((subsetTrans) => 71.92/9.79 (((setadjoinSub) => 71.92/9.79 (((setadjoinSub2) => 71.92/9.79 (((subset2powerset) => 71.92/9.79 (((setextsub) => 71.92/9.79 (((subsetemptysetimpeq) => 71.92/9.79 (((powersetI1) => 71.92/9.79 (( 71.92/9.79 (powersetE1) => 71.92/9.79 (( 71.92/9.79 (inPowerset) => 71.92/9.79 (( 71.92/9.79 (powersetsubset) => 71.92/9.79 (( 71.92/9.79 (sepInPowerset) => 71.92/9.79 (( 71.92/9.79 (sepSubset) => 71.92/9.79 (( 71.92/9.79 (binunionIL) => 71.92/9.79 (( 71.92/9.79 (upairset2IR) => 71.92/9.79 (( 71.92/9.79 (binunionIR) => 71.92/9.79 (( 71.92/9.79 (binunionEcases) => 71.92/9.79 (( 71.92/9.79 (binunionE) => 71.92/9.79 (( 71.92/9.79 (binunionLsub) => 71.92/9.79 (( 71.92/9.79 (binunionRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectI) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset5) => 71.92/9.79 (( 71.92/9.79 (binintersectEL) => 71.92/9.79 (( 71.92/9.79 (binintersectLsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset2) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset3) => 71.92/9.79 (( 71.92/9.79 (binintersectER) => 71.92/9.79 (( 71.92/9.79 (disjointsetsI1) => 71.92/9.79 (( 71.92/9.79 (binintersectRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset4) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset1) => 71.92/9.79 (( 71.92/9.79 (bs114d) => 71.92/9.79 (( 71.92/9.79 (setminusI) => 71.92/9.79 (( 71.92/9.79 (setminusEL) => 71.92/9.79 (( 71.92/9.79 (setminusER) => 71.92/9.79 (( 71.92/9.79 (setminusSubset2) => 71.92/9.79 (( 71.92/9.79 (setminusERneg) => 71.92/9.79 (( 71.92/9.79 (setminusELneg) => 71.92/9.79 (( 71.92/9.79 (setminusILneg) => 71.92/9.79 (( 71.92/9.79 (setminusIRneg) => 71.92/9.79 (( 71.92/9.79 (setminusLsub) => 71.92/9.79 (( 71.92/9.79 (setminusSubset1) => 71.92/9.79 (( 71.92/9.79 (symdiffE) => 71.92/9.79 (( 71.92/9.79 (symdiffI1) => 71.92/9.79 (( 71.92/9.79 (symdiffI2) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg1) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg2) => 71.92/9.79 (( 71.92/9.79 (secondinupair) => 71.92/9.79 (( 71.92/9.79 (setukpairIL) => 71.92/9.79 (( 71.92/9.79 (setukpairIR) => 71.92/9.79 (( 71.92/9.79 (kpairiskpair) => 71.92/9.79 (( 71.92/9.79 (kpairp) => 71.92/9.79 (( 71.92/9.79 (singletonsubset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowerset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowunion) => 71.92/9.79 (( 71.92/9.79 (upairset2E) => 71.92/9.79 (( 71.92/9.79 (upairsubunion) => 71.92/9.79 (( 71.92/9.79 (upairinpowunion) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem1) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem2) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem3) => 71.92/9.79 (( 71.92/9.79 (cartprodpairin) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair1) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair) => 71.92/9.79 (( 71.92/9.79 (setunionE2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton1) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton) => 71.92/9.79 (( 71.92/9.79 (singletonprop) => 71.92/9.79 (( 71.92/9.79 (ex1E1) => 71.92/9.79 (( 71.92/9.79 (ex1I) => 71.92/9.79 (( 71.92/9.79 (ex1I2) => 71.92/9.79 (( 71.92/9.79 (singletonsuniq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL1) => 71.92/9.79 (( 71.92/9.79 (kfstsingleton) => 71.92/9.79 (( 71.92/9.79 (theprop) => 71.92/9.79 (( 71.92/9.79 (kfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstin) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR11) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR12) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR1) => 71.92/9.79 (( 71.92/9.79 (upairequniteq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR) => 71.92/9.79 (( 71.92/9.79 (ksndsingleton) => 71.92/9.79 (( 71.92/9.79 (ksndpairEq) => 71.92/9.79 (( 71.92/9.79 (kpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndin) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemEL) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemER) => 71.92/9.79 (( 71.92/9.79 (cartprodmempaircEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrI) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrSub) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrERa) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL1) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL2) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrER) => 71.92/9.79 (( 71.92/9.79 (funcImageSingleton) => 71.92/9.79 (( 71.92/9.79 (apProp) => 71.92/9.79 (( 71.92/9.79 (app) => 71.92/9.79 (( 71.92/9.79 (infuncsetfunc) => 71.92/9.79 (( 71.92/9.79 (ap2p) => 71.92/9.79 (( 71.92/9.79 (funcinfuncset) => 71.92/9.79 (( 71.92/9.79 (lamProp) => 71.92/9.79 (( 71.92/9.79 (lamp) => 71.92/9.79 (( 71.92/9.79 (lam2p) => 71.92/9.79 (( 71.92/9.79 (brelnall1) => 71.92/9.79 (( 71.92/9.79 (brelnall2) => 71.92/9.79 (( 71.92/9.79 (ex1E2) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp1) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp3) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp2) => 71.92/9.79 (( 71.92/9.79 (funcextLem) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp4) => 71.92/9.79 (( 71.92/9.79 (subbreln) => 71.92/9.79 (( 71.92/9.79 (eqbreln) => 71.92/9.79 (( 71.92/9.79 (funcext) => 71.92/9.79 (( 71.92/9.79 (funcext2) => 71.92/9.79 (( 71.92/9.79 (ap2apEq1) => 71.92/9.79 (( 71.92/9.79 (ap2apEq2) => 71.92/9.79 (( 71.92/9.79 (beta1) => 71.92/9.79 (( 71.92/9.79 (eta1) => 71.92/9.79 (( 71.92/9.79 (lam2lamEq) => 71.92/9.79 (( 71.92/9.79 (beta2) => 71.92/9.79 (( 71.92/9.79 (eta2) => 71.92/9.79 (( 71.92/9.79 (iffalseProp1) => 71.92/9.79 (( 71.92/9.79 (iffalseProp2) => 71.92/9.79 (( 71.92/9.79 (iftrueProp1) => 71.92/9.79 (( 71.92/9.79 (iftrueProp2) => 71.92/9.79 (( 71.92/9.79 (ifSingleton) => 71.92/9.79 (( 71.92/9.79 (ifp) => 71.92/9.79 (( 71.92/9.79 (theeq) => 71.92/9.79 (( 71.92/9.79 (iftrue) => 71.92/9.79 (( 71.92/9.79 (iffalse) => 71.92/9.79 (( 71.92/9.79 (iftrueorfalse) => 71.92/9.79 (( 71.92/9.79 (binintersectT_lem) => 71.92/9.79 (( 71.92/9.79 (binunionT_lem) => 71.92/9.79 (( 71.92/9.79 (powersetT_lem) => 71.92/9.79 (( 71.92/9.79 (setminusT_lem) => 71.92/9.79 (( 71.92/9.79 (complementT_lem) => 71.92/9.79 (( 71.92/9.79 (setextT) => 71.92/9.79 (( 71.92/9.79 (subsetTI) => 71.92/9.79 (( 71.92/9.79 (powersetTI1) => 71.92/9.79 (( 71.92/9.79 (powersetTE1) => 71.92/9.79 (( 71.92/9.79 (complementTI1) => 71.92/9.79 (( 71.92/9.79 (complementTE1) => 71.92/9.79 (( 71.92/9.79 (binintersectTELcontra) => 71.92/9.79 (( 71.92/9.79 (binintersectTERcontra) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT1) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT2) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT3) => 71.92/9.79 (( 71.92/9.79 (doubleComplementI1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementE1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub2) => 71.92/9.79 (( 71.92/9.79 (doubleComplementEq) => 71.92/9.79 (( 71.92/9.79 (complementTnotintersectT) => 71.92/9.79 (( 71.92/9.79 (complementImpComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementSubsetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementInPowersetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (contraSubsetComplement) => 71.92/9.79 (( 71.92/9.79 (complementTcontraSubset) => 71.92/9.79 (( 71.92/9.79 (binunionTILcontra) => 71.92/9.79 (( 71.92/9.79 (binunionTIRcontra) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion2) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (intersectInPowersetIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpNotIn1) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpInComplement1) => 71.92/9.79 (( 71.92/9.79 (binunionTE) => 71.92/9.79 (( 71.92/9.79 (binunionTEcontra) => 71.92/9.79 (( 71.92/9.79 (demorgan2a1) => 71.92/9.79 (( 71.92/9.79 (complementUnionInPowersetComplement) => 71.92/9.79 (( 71.92/9.79 (demorgan2a2) => 71.92/9.79 (( 71.92/9.79 (demorgan1a) => 71.92/9.79 (( 71.92/9.79 (demorgan1b) => 71.92/9.79 (( 71.92/9.79 (demorgan1) => 71.92/9.79 (( 71.92/9.79 (demorgan2a) => 71.92/9.79 (( 71.92/9.79 (demorgan2b2) => 71.92/9.79 (( 71.92/9.79 (demorgan2b) => 71.92/9.79 (( 71.92/9.79 (demorgan2) => 71.92/9.79 (( 71.92/9.79 (woz13rule0) => 71.92/9.79 (( 71.92/9.79 (woz13rule1) => 71.92/9.79 (( 71.92/9.79 (woz13rule2) => 71.92/9.79 (( 71.92/9.79 (woz13rule3) => 71.92/9.79 (( 71.92/9.79 (woz13rule4) => 71.92/9.79 (( 71.92/9.79 (woz1_1) => 71.92/9.79 (( 71.92/9.79 (woz1_2) => 71.92/9.79 (( 71.92/9.79 (woz1_3) => 71.92/9.79 (( 71.92/9.79 (woz1_4) => 71.92/9.79 (( 71.92/9.79 (woz1_5) => 71.92/9.79 (( 71.92/9.79 (breln1all2) => 71.92/9.79 (( 71.92/9.79 (breln1SetBreln1) => 71.92/9.79 (( 71.92/9.79 (choice2fnsingleton) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln1) => 71.92/9.79 (( 71.92/9.79 (breln1all1) => 71.92/9.79 (( 71.92/9.79 (subbreln1) => 71.92/9.79 (( 71.92/9.79 (eqbreln1) => 71.92/9.79 (( 71.92/9.79 (breln1invprop) => 71.92/9.79 (( 71.92/9.79 (breln1invI) => 71.92/9.79 (( 71.92/9.79 (breln1invE) => 71.92/9.79 (( 71.92/9.79 (breln1compprop) => 71.92/9.79 (( 71.92/9.79 (breln1compI) => 71.92/9.79 (( 71.92/9.79 (breln1compE) => 71.92/9.79 (( 71.92/9.79 (breln1compEex) => 71.92/9.79 (( 71.92/9.79 (!!) @ ( 71.92/9.79 (('#B') @ ( 71.92/9.79 !!) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 !!))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#C') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 breln1)))) @ 71.92/9.79 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])). 71.92/9.79 thf(zip_derived_cl630, plain, 71.92/9.79 (~ (((exuI2) => 71.92/9.79 (((inCongP) => 71.92/9.79 (((in__Cong) => 71.92/9.79 (((exuE3u) => 71.92/9.79 (((exu__Cong) => 71.92/9.79 (((setadjoin__Cong) => 71.92/9.79 (((powerset__Cong) => 71.92/9.79 (((setunion__Cong) => 71.92/9.79 (((exuEu) => 71.92/9.79 (((descr__Cong) => 71.92/9.79 (((dsetconstr__Cong) => 71.92/9.79 (((subsetI1) => 71.92/9.79 (((eqimpsubset2) => 71.92/9.79 (((eqimpsubset1) => 71.92/9.79 (((subsetI2) => 71.92/9.79 (((emptysetsubset) => 71.92/9.79 (((subsetE) => 71.92/9.79 (((subsetE2) => 71.92/9.79 (((notsubsetI) => 71.92/9.79 (((notequalI1) => 71.92/9.79 (((notequalI2) => 71.92/9.79 (((subsetRefl) => 71.92/9.79 (((subsetTrans) => 71.92/9.79 (((setadjoinSub) => 71.92/9.79 (((setadjoinSub2) => 71.92/9.79 (((subset2powerset) => 71.92/9.79 (((setextsub) => 71.92/9.79 (((subsetemptysetimpeq) => 71.92/9.79 (((powersetI1) => 71.92/9.79 (((powersetE1) => 71.92/9.79 (( 71.92/9.79 (inPowerset) => 71.92/9.79 (( 71.92/9.79 (powersetsubset) => 71.92/9.79 (( 71.92/9.79 (sepInPowerset) => 71.92/9.79 (( 71.92/9.79 (sepSubset) => 71.92/9.79 (( 71.92/9.79 (binunionIL) => 71.92/9.79 (( 71.92/9.79 (upairset2IR) => 71.92/9.79 (( 71.92/9.79 (binunionIR) => 71.92/9.79 (( 71.92/9.79 (binunionEcases) => 71.92/9.79 (( 71.92/9.79 (binunionE) => 71.92/9.79 (( 71.92/9.79 (binunionLsub) => 71.92/9.79 (( 71.92/9.79 (binunionRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectI) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset5) => 71.92/9.79 (( 71.92/9.79 (binintersectEL) => 71.92/9.79 (( 71.92/9.79 (binintersectLsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset2) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset3) => 71.92/9.79 (( 71.92/9.79 (binintersectER) => 71.92/9.79 (( 71.92/9.79 (disjointsetsI1) => 71.92/9.79 (( 71.92/9.79 (binintersectRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset4) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset1) => 71.92/9.79 (( 71.92/9.79 (bs114d) => 71.92/9.79 (( 71.92/9.79 (setminusI) => 71.92/9.79 (( 71.92/9.79 (setminusEL) => 71.92/9.79 (( 71.92/9.79 (setminusER) => 71.92/9.79 (( 71.92/9.79 (setminusSubset2) => 71.92/9.79 (( 71.92/9.79 (setminusERneg) => 71.92/9.79 (( 71.92/9.79 (setminusELneg) => 71.92/9.79 (( 71.92/9.79 (setminusILneg) => 71.92/9.79 (( 71.92/9.79 (setminusIRneg) => 71.92/9.79 (( 71.92/9.79 (setminusLsub) => 71.92/9.79 (( 71.92/9.79 (setminusSubset1) => 71.92/9.79 (( 71.92/9.79 (symdiffE) => 71.92/9.79 (( 71.92/9.79 (symdiffI1) => 71.92/9.79 (( 71.92/9.79 (symdiffI2) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg1) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg2) => 71.92/9.79 (( 71.92/9.79 (secondinupair) => 71.92/9.79 (( 71.92/9.79 (setukpairIL) => 71.92/9.79 (( 71.92/9.79 (setukpairIR) => 71.92/9.79 (( 71.92/9.79 (kpairiskpair) => 71.92/9.79 (( 71.92/9.79 (kpairp) => 71.92/9.79 (( 71.92/9.79 (singletonsubset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowerset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowunion) => 71.92/9.79 (( 71.92/9.79 (upairset2E) => 71.92/9.79 (( 71.92/9.79 (upairsubunion) => 71.92/9.79 (( 71.92/9.79 (upairinpowunion) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem1) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem2) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem3) => 71.92/9.79 (( 71.92/9.79 (cartprodpairin) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair1) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair) => 71.92/9.79 (( 71.92/9.79 (setunionE2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton1) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton) => 71.92/9.79 (( 71.92/9.79 (singletonprop) => 71.92/9.79 (( 71.92/9.79 (ex1E1) => 71.92/9.79 (( 71.92/9.79 (ex1I) => 71.92/9.79 (( 71.92/9.79 (ex1I2) => 71.92/9.79 (( 71.92/9.79 (singletonsuniq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL1) => 71.92/9.79 (( 71.92/9.79 (kfstsingleton) => 71.92/9.79 (( 71.92/9.79 (theprop) => 71.92/9.79 (( 71.92/9.79 (kfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstin) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR11) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR12) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR1) => 71.92/9.79 (( 71.92/9.79 (upairequniteq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR) => 71.92/9.79 (( 71.92/9.79 (ksndsingleton) => 71.92/9.79 (( 71.92/9.79 (ksndpairEq) => 71.92/9.79 (( 71.92/9.79 (kpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndin) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemEL) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemER) => 71.92/9.79 (( 71.92/9.79 (cartprodmempaircEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrI) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrSub) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrERa) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL1) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL2) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrER) => 71.92/9.79 (( 71.92/9.79 (funcImageSingleton) => 71.92/9.79 (( 71.92/9.79 (apProp) => 71.92/9.79 (( 71.92/9.79 (app) => 71.92/9.79 (( 71.92/9.79 (infuncsetfunc) => 71.92/9.79 (( 71.92/9.79 (ap2p) => 71.92/9.79 (( 71.92/9.79 (funcinfuncset) => 71.92/9.79 (( 71.92/9.79 (lamProp) => 71.92/9.79 (( 71.92/9.79 (lamp) => 71.92/9.79 (( 71.92/9.79 (lam2p) => 71.92/9.79 (( 71.92/9.79 (brelnall1) => 71.92/9.79 (( 71.92/9.79 (brelnall2) => 71.92/9.79 (( 71.92/9.79 (ex1E2) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp1) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp3) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp2) => 71.92/9.79 (( 71.92/9.79 (funcextLem) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp4) => 71.92/9.79 (( 71.92/9.79 (subbreln) => 71.92/9.79 (( 71.92/9.79 (eqbreln) => 71.92/9.79 (( 71.92/9.79 (funcext) => 71.92/9.79 (( 71.92/9.79 (funcext2) => 71.92/9.79 (( 71.92/9.79 (ap2apEq1) => 71.92/9.79 (( 71.92/9.79 (ap2apEq2) => 71.92/9.79 (( 71.92/9.79 (beta1) => 71.92/9.79 (( 71.92/9.79 (eta1) => 71.92/9.79 (( 71.92/9.79 (lam2lamEq) => 71.92/9.79 (( 71.92/9.79 (beta2) => 71.92/9.79 (( 71.92/9.79 (eta2) => 71.92/9.79 (( 71.92/9.79 (iffalseProp1) => 71.92/9.79 (( 71.92/9.79 (iffalseProp2) => 71.92/9.79 (( 71.92/9.79 (iftrueProp1) => 71.92/9.79 (( 71.92/9.79 (iftrueProp2) => 71.92/9.79 (( 71.92/9.79 (ifSingleton) => 71.92/9.79 (( 71.92/9.79 (ifp) => 71.92/9.79 (( 71.92/9.79 (theeq) => 71.92/9.79 (( 71.92/9.79 (iftrue) => 71.92/9.79 (( 71.92/9.79 (iffalse) => 71.92/9.79 (( 71.92/9.79 (iftrueorfalse) => 71.92/9.79 (( 71.92/9.79 (binintersectT_lem) => 71.92/9.79 (( 71.92/9.79 (binunionT_lem) => 71.92/9.79 (( 71.92/9.79 (powersetT_lem) => 71.92/9.79 (( 71.92/9.79 (setminusT_lem) => 71.92/9.79 (( 71.92/9.79 (complementT_lem) => 71.92/9.79 (( 71.92/9.79 (setextT) => 71.92/9.79 (( 71.92/9.79 (subsetTI) => 71.92/9.79 (( 71.92/9.79 (powersetTI1) => 71.92/9.79 (( 71.92/9.79 (powersetTE1) => 71.92/9.79 (( 71.92/9.79 (complementTI1) => 71.92/9.79 (( 71.92/9.79 (complementTE1) => 71.92/9.79 (( 71.92/9.79 (binintersectTELcontra) => 71.92/9.79 (( 71.92/9.79 (binintersectTERcontra) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT1) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT2) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT3) => 71.92/9.79 (( 71.92/9.79 (doubleComplementI1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementE1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub2) => 71.92/9.79 (( 71.92/9.79 (doubleComplementEq) => 71.92/9.79 (( 71.92/9.79 (complementTnotintersectT) => 71.92/9.79 (( 71.92/9.79 (complementImpComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementSubsetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementInPowersetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (contraSubsetComplement) => 71.92/9.79 (( 71.92/9.79 (complementTcontraSubset) => 71.92/9.79 (( 71.92/9.79 (binunionTILcontra) => 71.92/9.79 (( 71.92/9.79 (binunionTIRcontra) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion2) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (intersectInPowersetIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpNotIn1) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpInComplement1) => 71.92/9.79 (( 71.92/9.79 (binunionTE) => 71.92/9.79 (( 71.92/9.79 (binunionTEcontra) => 71.92/9.79 (( 71.92/9.79 (demorgan2a1) => 71.92/9.79 (( 71.92/9.79 (complementUnionInPowersetComplement) => 71.92/9.79 (( 71.92/9.79 (demorgan2a2) => 71.92/9.79 (( 71.92/9.79 (demorgan1a) => 71.92/9.79 (( 71.92/9.79 (demorgan1b) => 71.92/9.79 (( 71.92/9.79 (demorgan1) => 71.92/9.79 (( 71.92/9.79 (demorgan2a) => 71.92/9.79 (( 71.92/9.79 (demorgan2b2) => 71.92/9.79 (( 71.92/9.79 (demorgan2b) => 71.92/9.79 (( 71.92/9.79 (demorgan2) => 71.92/9.79 (( 71.92/9.79 (woz13rule0) => 71.92/9.79 (( 71.92/9.79 (woz13rule1) => 71.92/9.79 (( 71.92/9.79 (woz13rule2) => 71.92/9.79 (( 71.92/9.79 (woz13rule3) => 71.92/9.79 (( 71.92/9.79 (woz13rule4) => 71.92/9.79 (( 71.92/9.79 (woz1_1) => 71.92/9.79 (( 71.92/9.79 (woz1_2) => 71.92/9.79 (( 71.92/9.79 (woz1_3) => 71.92/9.79 (( 71.92/9.79 (woz1_4) => 71.92/9.79 (( 71.92/9.79 (woz1_5) => 71.92/9.79 (( 71.92/9.79 (breln1all2) => 71.92/9.79 (( 71.92/9.79 (breln1SetBreln1) => 71.92/9.79 (( 71.92/9.79 (choice2fnsingleton) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln1) => 71.92/9.79 (( 71.92/9.79 (breln1all1) => 71.92/9.79 (( 71.92/9.79 (subbreln1) => 71.92/9.79 (( 71.92/9.79 (eqbreln1) => 71.92/9.79 (( 71.92/9.79 (breln1invprop) => 71.92/9.79 (( 71.92/9.79 (breln1invI) => 71.92/9.79 (( 71.92/9.79 (breln1invE) => 71.92/9.79 (( 71.92/9.79 (breln1compprop) => 71.92/9.79 (( 71.92/9.79 (breln1compI) => 71.92/9.79 (( 71.92/9.79 (breln1compE) => 71.92/9.79 (( 71.92/9.79 (breln1compEex) => 71.92/9.79 (( 71.92/9.79 (!!) @ ( 71.92/9.79 (('#B') @ ( 71.92/9.79 !!) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 !!))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#C') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 breln1)))) @ 71.92/9.79 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl619])). 71.92/9.79 thf(zip_derived_cl640, plain, 71.92/9.79 (~ (((inCongP) => 71.92/9.79 (((in__Cong) => 71.92/9.79 (((exuE3u) => 71.92/9.79 (((exu__Cong) => 71.92/9.79 (((setadjoin__Cong) => 71.92/9.79 (((powerset__Cong) => 71.92/9.79 (((setunion__Cong) => 71.92/9.79 (((exuEu) => 71.92/9.79 (((descr__Cong) => 71.92/9.79 (((dsetconstr__Cong) => 71.92/9.79 (((subsetI1) => 71.92/9.79 (((eqimpsubset2) => 71.92/9.79 (((eqimpsubset1) => 71.92/9.79 (((subsetI2) => 71.92/9.79 (((emptysetsubset) => 71.92/9.79 (((subsetE) => 71.92/9.79 (((subsetE2) => 71.92/9.79 (((notsubsetI) => 71.92/9.79 (((notequalI1) => 71.92/9.79 (((notequalI2) => 71.92/9.79 (((subsetRefl) => 71.92/9.79 (((subsetTrans) => 71.92/9.79 (((setadjoinSub) => 71.92/9.79 (((setadjoinSub2) => 71.92/9.79 (((subset2powerset) => 71.92/9.79 (((setextsub) => 71.92/9.79 (((subsetemptysetimpeq) => 71.92/9.79 (((powersetI1) => 71.92/9.79 (((powersetE1) => 71.92/9.79 (((inPowerset) => 71.92/9.79 (( 71.92/9.79 (powersetsubset) => 71.92/9.79 (( 71.92/9.79 (sepInPowerset) => 71.92/9.79 (( 71.92/9.79 (sepSubset) => 71.92/9.79 (( 71.92/9.79 (binunionIL) => 71.92/9.79 (( 71.92/9.79 (upairset2IR) => 71.92/9.79 (( 71.92/9.79 (binunionIR) => 71.92/9.79 (( 71.92/9.79 (binunionEcases) => 71.92/9.79 (( 71.92/9.79 (binunionE) => 71.92/9.79 (( 71.92/9.79 (binunionLsub) => 71.92/9.79 (( 71.92/9.79 (binunionRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectI) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset5) => 71.92/9.79 (( 71.92/9.79 (binintersectEL) => 71.92/9.79 (( 71.92/9.79 (binintersectLsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset2) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset3) => 71.92/9.79 (( 71.92/9.79 (binintersectER) => 71.92/9.79 (( 71.92/9.79 (disjointsetsI1) => 71.92/9.79 (( 71.92/9.79 (binintersectRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset4) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset1) => 71.92/9.79 (( 71.92/9.79 (bs114d) => 71.92/9.79 (( 71.92/9.79 (setminusI) => 71.92/9.79 (( 71.92/9.79 (setminusEL) => 71.92/9.79 (( 71.92/9.79 (setminusER) => 71.92/9.79 (( 71.92/9.79 (setminusSubset2) => 71.92/9.79 (( 71.92/9.79 (setminusERneg) => 71.92/9.79 (( 71.92/9.79 (setminusELneg) => 71.92/9.79 (( 71.92/9.79 (setminusILneg) => 71.92/9.79 (( 71.92/9.79 (setminusIRneg) => 71.92/9.79 (( 71.92/9.79 (setminusLsub) => 71.92/9.79 (( 71.92/9.79 (setminusSubset1) => 71.92/9.79 (( 71.92/9.79 (symdiffE) => 71.92/9.79 (( 71.92/9.79 (symdiffI1) => 71.92/9.79 (( 71.92/9.79 (symdiffI2) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg1) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg2) => 71.92/9.79 (( 71.92/9.79 (secondinupair) => 71.92/9.79 (( 71.92/9.79 (setukpairIL) => 71.92/9.79 (( 71.92/9.79 (setukpairIR) => 71.92/9.79 (( 71.92/9.79 (kpairiskpair) => 71.92/9.79 (( 71.92/9.79 (kpairp) => 71.92/9.79 (( 71.92/9.79 (singletonsubset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowerset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowunion) => 71.92/9.79 (( 71.92/9.79 (upairset2E) => 71.92/9.79 (( 71.92/9.79 (upairsubunion) => 71.92/9.79 (( 71.92/9.79 (upairinpowunion) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem1) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem2) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem3) => 71.92/9.79 (( 71.92/9.79 (cartprodpairin) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair1) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair) => 71.92/9.79 (( 71.92/9.79 (setunionE2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton1) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton) => 71.92/9.79 (( 71.92/9.79 (singletonprop) => 71.92/9.79 (( 71.92/9.79 (ex1E1) => 71.92/9.79 (( 71.92/9.79 (ex1I) => 71.92/9.79 (( 71.92/9.79 (ex1I2) => 71.92/9.79 (( 71.92/9.79 (singletonsuniq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL1) => 71.92/9.79 (( 71.92/9.79 (kfstsingleton) => 71.92/9.79 (( 71.92/9.79 (theprop) => 71.92/9.79 (( 71.92/9.79 (kfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstin) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR11) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR12) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR1) => 71.92/9.79 (( 71.92/9.79 (upairequniteq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR) => 71.92/9.79 (( 71.92/9.79 (ksndsingleton) => 71.92/9.79 (( 71.92/9.79 (ksndpairEq) => 71.92/9.79 (( 71.92/9.79 (kpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndin) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemEL) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemER) => 71.92/9.79 (( 71.92/9.79 (cartprodmempaircEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrI) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrSub) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrERa) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL1) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL2) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrER) => 71.92/9.79 (( 71.92/9.79 (funcImageSingleton) => 71.92/9.79 (( 71.92/9.79 (apProp) => 71.92/9.79 (( 71.92/9.79 (app) => 71.92/9.79 (( 71.92/9.79 (infuncsetfunc) => 71.92/9.79 (( 71.92/9.79 (ap2p) => 71.92/9.79 (( 71.92/9.79 (funcinfuncset) => 71.92/9.79 (( 71.92/9.79 (lamProp) => 71.92/9.79 (( 71.92/9.79 (lamp) => 71.92/9.79 (( 71.92/9.79 (lam2p) => 71.92/9.79 (( 71.92/9.79 (brelnall1) => 71.92/9.79 (( 71.92/9.79 (brelnall2) => 71.92/9.79 (( 71.92/9.79 (ex1E2) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp1) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp3) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp2) => 71.92/9.79 (( 71.92/9.79 (funcextLem) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp4) => 71.92/9.79 (( 71.92/9.79 (subbreln) => 71.92/9.79 (( 71.92/9.79 (eqbreln) => 71.92/9.79 (( 71.92/9.79 (funcext) => 71.92/9.79 (( 71.92/9.79 (funcext2) => 71.92/9.79 (( 71.92/9.79 (ap2apEq1) => 71.92/9.79 (( 71.92/9.79 (ap2apEq2) => 71.92/9.79 (( 71.92/9.79 (beta1) => 71.92/9.79 (( 71.92/9.79 (eta1) => 71.92/9.79 (( 71.92/9.79 (lam2lamEq) => 71.92/9.79 (( 71.92/9.79 (beta2) => 71.92/9.79 (( 71.92/9.79 (eta2) => 71.92/9.79 (( 71.92/9.79 (iffalseProp1) => 71.92/9.79 (( 71.92/9.79 (iffalseProp2) => 71.92/9.79 (( 71.92/9.79 (iftrueProp1) => 71.92/9.79 (( 71.92/9.79 (iftrueProp2) => 71.92/9.79 (( 71.92/9.79 (ifSingleton) => 71.92/9.79 (( 71.92/9.79 (ifp) => 71.92/9.79 (( 71.92/9.79 (theeq) => 71.92/9.79 (( 71.92/9.79 (iftrue) => 71.92/9.79 (( 71.92/9.79 (iffalse) => 71.92/9.79 (( 71.92/9.79 (iftrueorfalse) => 71.92/9.79 (( 71.92/9.79 (binintersectT_lem) => 71.92/9.79 (( 71.92/9.79 (binunionT_lem) => 71.92/9.79 (( 71.92/9.79 (powersetT_lem) => 71.92/9.79 (( 71.92/9.79 (setminusT_lem) => 71.92/9.79 (( 71.92/9.79 (complementT_lem) => 71.92/9.79 (( 71.92/9.79 (setextT) => 71.92/9.79 (( 71.92/9.79 (subsetTI) => 71.92/9.79 (( 71.92/9.79 (powersetTI1) => 71.92/9.79 (( 71.92/9.79 (powersetTE1) => 71.92/9.79 (( 71.92/9.79 (complementTI1) => 71.92/9.79 (( 71.92/9.79 (complementTE1) => 71.92/9.79 (( 71.92/9.79 (binintersectTELcontra) => 71.92/9.79 (( 71.92/9.79 (binintersectTERcontra) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT1) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT2) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT3) => 71.92/9.79 (( 71.92/9.79 (doubleComplementI1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementE1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub2) => 71.92/9.79 (( 71.92/9.79 (doubleComplementEq) => 71.92/9.79 (( 71.92/9.79 (complementTnotintersectT) => 71.92/9.79 (( 71.92/9.79 (complementImpComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementSubsetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementInPowersetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (contraSubsetComplement) => 71.92/9.79 (( 71.92/9.79 (complementTcontraSubset) => 71.92/9.79 (( 71.92/9.79 (binunionTILcontra) => 71.92/9.79 (( 71.92/9.79 (binunionTIRcontra) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion2) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (intersectInPowersetIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpNotIn1) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpInComplement1) => 71.92/9.79 (( 71.92/9.79 (binunionTE) => 71.92/9.79 (( 71.92/9.79 (binunionTEcontra) => 71.92/9.79 (( 71.92/9.79 (demorgan2a1) => 71.92/9.79 (( 71.92/9.79 (complementUnionInPowersetComplement) => 71.92/9.79 (( 71.92/9.79 (demorgan2a2) => 71.92/9.79 (( 71.92/9.79 (demorgan1a) => 71.92/9.79 (( 71.92/9.79 (demorgan1b) => 71.92/9.79 (( 71.92/9.79 (demorgan1) => 71.92/9.79 (( 71.92/9.79 (demorgan2a) => 71.92/9.79 (( 71.92/9.79 (demorgan2b2) => 71.92/9.79 (( 71.92/9.79 (demorgan2b) => 71.92/9.79 (( 71.92/9.79 (demorgan2) => 71.92/9.79 (( 71.92/9.79 (woz13rule0) => 71.92/9.79 (( 71.92/9.79 (woz13rule1) => 71.92/9.79 (( 71.92/9.79 (woz13rule2) => 71.92/9.79 (( 71.92/9.79 (woz13rule3) => 71.92/9.79 (( 71.92/9.79 (woz13rule4) => 71.92/9.79 (( 71.92/9.79 (woz1_1) => 71.92/9.79 (( 71.92/9.79 (woz1_2) => 71.92/9.79 (( 71.92/9.79 (woz1_3) => 71.92/9.79 (( 71.92/9.79 (woz1_4) => 71.92/9.79 (( 71.92/9.79 (woz1_5) => 71.92/9.79 (( 71.92/9.79 (breln1all2) => 71.92/9.79 (( 71.92/9.79 (breln1SetBreln1) => 71.92/9.79 (( 71.92/9.79 (choice2fnsingleton) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln1) => 71.92/9.79 (( 71.92/9.79 (breln1all1) => 71.92/9.79 (( 71.92/9.79 (subbreln1) => 71.92/9.79 (( 71.92/9.79 (eqbreln1) => 71.92/9.79 (( 71.92/9.79 (breln1invprop) => 71.92/9.79 (( 71.92/9.79 (breln1invI) => 71.92/9.79 (( 71.92/9.79 (breln1invE) => 71.92/9.79 (( 71.92/9.79 (breln1compprop) => 71.92/9.79 (( 71.92/9.79 (breln1compI) => 71.92/9.79 (( 71.92/9.79 (breln1compE) => 71.92/9.79 (( 71.92/9.79 (breln1compEex) => 71.92/9.79 (( 71.92/9.79 (!!) @ ( 71.92/9.79 (('#B') @ ( 71.92/9.79 !!) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 !!))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#C') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 breln1)))) @ 71.92/9.79 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl630])). 71.92/9.79 thf(zip_derived_cl650, plain, 71.92/9.79 (~ (((in__Cong) => 71.92/9.79 (((exuE3u) => 71.92/9.79 (((exu__Cong) => 71.92/9.79 (((setadjoin__Cong) => 71.92/9.79 (((powerset__Cong) => 71.92/9.79 (((setunion__Cong) => 71.92/9.79 (((exuEu) => 71.92/9.79 (((descr__Cong) => 71.92/9.79 (((dsetconstr__Cong) => 71.92/9.79 (((subsetI1) => 71.92/9.79 (((eqimpsubset2) => 71.92/9.79 (((eqimpsubset1) => 71.92/9.79 (((subsetI2) => 71.92/9.79 (((emptysetsubset) => 71.92/9.79 (((subsetE) => 71.92/9.79 (((subsetE2) => 71.92/9.79 (((notsubsetI) => 71.92/9.79 (((notequalI1) => 71.92/9.79 (((notequalI2) => 71.92/9.79 (((subsetRefl) => 71.92/9.79 (((subsetTrans) => 71.92/9.79 (((setadjoinSub) => 71.92/9.79 (((setadjoinSub2) => 71.92/9.79 (((subset2powerset) => 71.92/9.79 (((setextsub) => 71.92/9.79 (((subsetemptysetimpeq) => 71.92/9.79 (((powersetI1) => 71.92/9.79 (((powersetE1) => 71.92/9.79 (((inPowerset) => 71.92/9.79 (((powersetsubset) => 71.92/9.79 (( 71.92/9.79 (sepInPowerset) => 71.92/9.79 (( 71.92/9.79 (sepSubset) => 71.92/9.79 (( 71.92/9.79 (binunionIL) => 71.92/9.79 (( 71.92/9.79 (upairset2IR) => 71.92/9.79 (( 71.92/9.79 (binunionIR) => 71.92/9.79 (( 71.92/9.79 (binunionEcases) => 71.92/9.79 (( 71.92/9.79 (binunionE) => 71.92/9.79 (( 71.92/9.79 (binunionLsub) => 71.92/9.79 (( 71.92/9.79 (binunionRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectI) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset5) => 71.92/9.79 (( 71.92/9.79 (binintersectEL) => 71.92/9.79 (( 71.92/9.79 (binintersectLsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset2) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset3) => 71.92/9.79 (( 71.92/9.79 (binintersectER) => 71.92/9.79 (( 71.92/9.79 (disjointsetsI1) => 71.92/9.79 (( 71.92/9.79 (binintersectRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset4) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset1) => 71.92/9.79 (( 71.92/9.79 (bs114d) => 71.92/9.79 (( 71.92/9.79 (setminusI) => 71.92/9.79 (( 71.92/9.79 (setminusEL) => 71.92/9.79 (( 71.92/9.79 (setminusER) => 71.92/9.79 (( 71.92/9.79 (setminusSubset2) => 71.92/9.79 (( 71.92/9.79 (setminusERneg) => 71.92/9.79 (( 71.92/9.79 (setminusELneg) => 71.92/9.79 (( 71.92/9.79 (setminusILneg) => 71.92/9.79 (( 71.92/9.79 (setminusIRneg) => 71.92/9.79 (( 71.92/9.79 (setminusLsub) => 71.92/9.79 (( 71.92/9.79 (setminusSubset1) => 71.92/9.79 (( 71.92/9.79 (symdiffE) => 71.92/9.79 (( 71.92/9.79 (symdiffI1) => 71.92/9.79 (( 71.92/9.79 (symdiffI2) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg1) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg2) => 71.92/9.79 (( 71.92/9.79 (secondinupair) => 71.92/9.79 (( 71.92/9.79 (setukpairIL) => 71.92/9.79 (( 71.92/9.79 (setukpairIR) => 71.92/9.79 (( 71.92/9.79 (kpairiskpair) => 71.92/9.79 (( 71.92/9.79 (kpairp) => 71.92/9.79 (( 71.92/9.79 (singletonsubset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowerset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowunion) => 71.92/9.79 (( 71.92/9.79 (upairset2E) => 71.92/9.79 (( 71.92/9.79 (upairsubunion) => 71.92/9.79 (( 71.92/9.79 (upairinpowunion) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem1) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem2) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem3) => 71.92/9.79 (( 71.92/9.79 (cartprodpairin) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair1) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair) => 71.92/9.79 (( 71.92/9.79 (setunionE2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton1) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton) => 71.92/9.79 (( 71.92/9.79 (singletonprop) => 71.92/9.79 (( 71.92/9.79 (ex1E1) => 71.92/9.79 (( 71.92/9.79 (ex1I) => 71.92/9.79 (( 71.92/9.79 (ex1I2) => 71.92/9.79 (( 71.92/9.79 (singletonsuniq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL1) => 71.92/9.79 (( 71.92/9.79 (kfstsingleton) => 71.92/9.79 (( 71.92/9.79 (theprop) => 71.92/9.79 (( 71.92/9.79 (kfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstin) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR11) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR12) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR1) => 71.92/9.79 (( 71.92/9.79 (upairequniteq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR) => 71.92/9.79 (( 71.92/9.79 (ksndsingleton) => 71.92/9.79 (( 71.92/9.79 (ksndpairEq) => 71.92/9.79 (( 71.92/9.79 (kpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndin) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemEL) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemER) => 71.92/9.79 (( 71.92/9.79 (cartprodmempaircEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrI) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrSub) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrERa) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL1) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL2) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrER) => 71.92/9.79 (( 71.92/9.79 (funcImageSingleton) => 71.92/9.79 (( 71.92/9.79 (apProp) => 71.92/9.79 (( 71.92/9.79 (app) => 71.92/9.79 (( 71.92/9.79 (infuncsetfunc) => 71.92/9.79 (( 71.92/9.79 (ap2p) => 71.92/9.79 (( 71.92/9.79 (funcinfuncset) => 71.92/9.79 (( 71.92/9.79 (lamProp) => 71.92/9.79 (( 71.92/9.79 (lamp) => 71.92/9.79 (( 71.92/9.79 (lam2p) => 71.92/9.79 (( 71.92/9.79 (brelnall1) => 71.92/9.79 (( 71.92/9.79 (brelnall2) => 71.92/9.79 (( 71.92/9.79 (ex1E2) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp1) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp3) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp2) => 71.92/9.79 (( 71.92/9.79 (funcextLem) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp4) => 71.92/9.79 (( 71.92/9.79 (subbreln) => 71.92/9.79 (( 71.92/9.79 (eqbreln) => 71.92/9.79 (( 71.92/9.79 (funcext) => 71.92/9.79 (( 71.92/9.79 (funcext2) => 71.92/9.79 (( 71.92/9.79 (ap2apEq1) => 71.92/9.79 (( 71.92/9.79 (ap2apEq2) => 71.92/9.79 (( 71.92/9.79 (beta1) => 71.92/9.79 (( 71.92/9.79 (eta1) => 71.92/9.79 (( 71.92/9.79 (lam2lamEq) => 71.92/9.79 (( 71.92/9.79 (beta2) => 71.92/9.79 (( 71.92/9.79 (eta2) => 71.92/9.79 (( 71.92/9.79 (iffalseProp1) => 71.92/9.79 (( 71.92/9.79 (iffalseProp2) => 71.92/9.79 (( 71.92/9.79 (iftrueProp1) => 71.92/9.79 (( 71.92/9.79 (iftrueProp2) => 71.92/9.79 (( 71.92/9.79 (ifSingleton) => 71.92/9.79 (( 71.92/9.79 (ifp) => 71.92/9.79 (( 71.92/9.79 (theeq) => 71.92/9.79 (( 71.92/9.79 (iftrue) => 71.92/9.79 (( 71.92/9.79 (iffalse) => 71.92/9.79 (( 71.92/9.79 (iftrueorfalse) => 71.92/9.79 (( 71.92/9.79 (binintersectT_lem) => 71.92/9.79 (( 71.92/9.79 (binunionT_lem) => 71.92/9.79 (( 71.92/9.79 (powersetT_lem) => 71.92/9.79 (( 71.92/9.79 (setminusT_lem) => 71.92/9.79 (( 71.92/9.79 (complementT_lem) => 71.92/9.79 (( 71.92/9.79 (setextT) => 71.92/9.79 (( 71.92/9.79 (subsetTI) => 71.92/9.79 (( 71.92/9.79 (powersetTI1) => 71.92/9.79 (( 71.92/9.79 (powersetTE1) => 71.92/9.79 (( 71.92/9.79 (complementTI1) => 71.92/9.79 (( 71.92/9.79 (complementTE1) => 71.92/9.79 (( 71.92/9.79 (binintersectTELcontra) => 71.92/9.79 (( 71.92/9.79 (binintersectTERcontra) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT1) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT2) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT3) => 71.92/9.79 (( 71.92/9.79 (doubleComplementI1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementE1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub2) => 71.92/9.79 (( 71.92/9.79 (doubleComplementEq) => 71.92/9.79 (( 71.92/9.79 (complementTnotintersectT) => 71.92/9.79 (( 71.92/9.79 (complementImpComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementSubsetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementInPowersetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (contraSubsetComplement) => 71.92/9.79 (( 71.92/9.79 (complementTcontraSubset) => 71.92/9.79 (( 71.92/9.79 (binunionTILcontra) => 71.92/9.79 (( 71.92/9.79 (binunionTIRcontra) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion2) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (intersectInPowersetIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpNotIn1) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpInComplement1) => 71.92/9.79 (( 71.92/9.79 (binunionTE) => 71.92/9.79 (( 71.92/9.79 (binunionTEcontra) => 71.92/9.79 (( 71.92/9.79 (demorgan2a1) => 71.92/9.79 (( 71.92/9.79 (complementUnionInPowersetComplement) => 71.92/9.79 (( 71.92/9.79 (demorgan2a2) => 71.92/9.79 (( 71.92/9.79 (demorgan1a) => 71.92/9.79 (( 71.92/9.79 (demorgan1b) => 71.92/9.79 (( 71.92/9.79 (demorgan1) => 71.92/9.79 (( 71.92/9.79 (demorgan2a) => 71.92/9.79 (( 71.92/9.79 (demorgan2b2) => 71.92/9.79 (( 71.92/9.79 (demorgan2b) => 71.92/9.79 (( 71.92/9.79 (demorgan2) => 71.92/9.79 (( 71.92/9.79 (woz13rule0) => 71.92/9.79 (( 71.92/9.79 (woz13rule1) => 71.92/9.79 (( 71.92/9.79 (woz13rule2) => 71.92/9.79 (( 71.92/9.79 (woz13rule3) => 71.92/9.79 (( 71.92/9.79 (woz13rule4) => 71.92/9.79 (( 71.92/9.79 (woz1_1) => 71.92/9.79 (( 71.92/9.79 (woz1_2) => 71.92/9.79 (( 71.92/9.79 (woz1_3) => 71.92/9.79 (( 71.92/9.79 (woz1_4) => 71.92/9.79 (( 71.92/9.79 (woz1_5) => 71.92/9.79 (( 71.92/9.79 (breln1all2) => 71.92/9.79 (( 71.92/9.79 (breln1SetBreln1) => 71.92/9.79 (( 71.92/9.79 (choice2fnsingleton) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln1) => 71.92/9.79 (( 71.92/9.79 (breln1all1) => 71.92/9.79 (( 71.92/9.79 (subbreln1) => 71.92/9.79 (( 71.92/9.79 (eqbreln1) => 71.92/9.79 (( 71.92/9.79 (breln1invprop) => 71.92/9.79 (( 71.92/9.79 (breln1invI) => 71.92/9.79 (( 71.92/9.79 (breln1invE) => 71.92/9.79 (( 71.92/9.79 (breln1compprop) => 71.92/9.79 (( 71.92/9.79 (breln1compI) => 71.92/9.79 (( 71.92/9.79 (breln1compE) => 71.92/9.79 (( 71.92/9.79 (breln1compEex) => 71.92/9.79 (( 71.92/9.79 (!!) @ ( 71.92/9.79 (('#B') @ ( 71.92/9.79 !!) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 !!))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#C') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 breln1)))) @ 71.92/9.79 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])). 71.92/9.79 thf(zip_derived_cl660, plain, 71.92/9.79 (~ (((exuE3u) => 71.92/9.79 (((exu__Cong) => 71.92/9.79 (((setadjoin__Cong) => 71.92/9.79 (((powerset__Cong) => 71.92/9.79 (((setunion__Cong) => 71.92/9.79 (((exuEu) => 71.92/9.79 (((descr__Cong) => 71.92/9.79 (((dsetconstr__Cong) => 71.92/9.79 (((subsetI1) => 71.92/9.79 (((eqimpsubset2) => 71.92/9.79 (((eqimpsubset1) => 71.92/9.79 (((subsetI2) => 71.92/9.79 (((emptysetsubset) => 71.92/9.79 (((subsetE) => 71.92/9.79 (((subsetE2) => 71.92/9.79 (((notsubsetI) => 71.92/9.79 (((notequalI1) => 71.92/9.79 (((notequalI2) => 71.92/9.79 (((subsetRefl) => 71.92/9.79 (((subsetTrans) => 71.92/9.79 (((setadjoinSub) => 71.92/9.79 (((setadjoinSub2) => 71.92/9.79 (((subset2powerset) => 71.92/9.79 (((setextsub) => 71.92/9.79 (((subsetemptysetimpeq) => 71.92/9.79 (((powersetI1) => 71.92/9.79 (((powersetE1) => 71.92/9.79 (((inPowerset) => 71.92/9.79 (((powersetsubset) => 71.92/9.79 (((sepInPowerset) => 71.92/9.79 (( 71.92/9.79 (sepSubset) => 71.92/9.79 (( 71.92/9.79 (binunionIL) => 71.92/9.79 (( 71.92/9.79 (upairset2IR) => 71.92/9.79 (( 71.92/9.79 (binunionIR) => 71.92/9.79 (( 71.92/9.79 (binunionEcases) => 71.92/9.79 (( 71.92/9.79 (binunionE) => 71.92/9.79 (( 71.92/9.79 (binunionLsub) => 71.92/9.79 (( 71.92/9.79 (binunionRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectI) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset5) => 71.92/9.79 (( 71.92/9.79 (binintersectEL) => 71.92/9.79 (( 71.92/9.79 (binintersectLsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset2) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset3) => 71.92/9.79 (( 71.92/9.79 (binintersectER) => 71.92/9.79 (( 71.92/9.79 (disjointsetsI1) => 71.92/9.79 (( 71.92/9.79 (binintersectRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset4) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset1) => 71.92/9.79 (( 71.92/9.79 (bs114d) => 71.92/9.79 (( 71.92/9.79 (setminusI) => 71.92/9.79 (( 71.92/9.79 (setminusEL) => 71.92/9.79 (( 71.92/9.79 (setminusER) => 71.92/9.79 (( 71.92/9.79 (setminusSubset2) => 71.92/9.79 (( 71.92/9.79 (setminusERneg) => 71.92/9.79 (( 71.92/9.79 (setminusELneg) => 71.92/9.79 (( 71.92/9.79 (setminusILneg) => 71.92/9.79 (( 71.92/9.79 (setminusIRneg) => 71.92/9.79 (( 71.92/9.79 (setminusLsub) => 71.92/9.79 (( 71.92/9.79 (setminusSubset1) => 71.92/9.79 (( 71.92/9.79 (symdiffE) => 71.92/9.79 (( 71.92/9.79 (symdiffI1) => 71.92/9.79 (( 71.92/9.79 (symdiffI2) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg1) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg2) => 71.92/9.79 (( 71.92/9.79 (secondinupair) => 71.92/9.79 (( 71.92/9.79 (setukpairIL) => 71.92/9.79 (( 71.92/9.79 (setukpairIR) => 71.92/9.79 (( 71.92/9.79 (kpairiskpair) => 71.92/9.79 (( 71.92/9.79 (kpairp) => 71.92/9.79 (( 71.92/9.79 (singletonsubset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowerset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowunion) => 71.92/9.79 (( 71.92/9.79 (upairset2E) => 71.92/9.79 (( 71.92/9.79 (upairsubunion) => 71.92/9.79 (( 71.92/9.79 (upairinpowunion) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem1) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem2) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem3) => 71.92/9.79 (( 71.92/9.79 (cartprodpairin) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair1) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair) => 71.92/9.79 (( 71.92/9.79 (setunionE2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton1) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton) => 71.92/9.79 (( 71.92/9.79 (singletonprop) => 71.92/9.79 (( 71.92/9.79 (ex1E1) => 71.92/9.79 (( 71.92/9.79 (ex1I) => 71.92/9.79 (( 71.92/9.79 (ex1I2) => 71.92/9.79 (( 71.92/9.79 (singletonsuniq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL1) => 71.92/9.79 (( 71.92/9.79 (kfstsingleton) => 71.92/9.79 (( 71.92/9.79 (theprop) => 71.92/9.79 (( 71.92/9.79 (kfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstin) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR11) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR12) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR1) => 71.92/9.79 (( 71.92/9.79 (upairequniteq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR) => 71.92/9.79 (( 71.92/9.79 (ksndsingleton) => 71.92/9.79 (( 71.92/9.79 (ksndpairEq) => 71.92/9.79 (( 71.92/9.79 (kpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndin) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemEL) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemER) => 71.92/9.79 (( 71.92/9.79 (cartprodmempaircEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrI) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrSub) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrERa) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL1) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL2) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrER) => 71.92/9.79 (( 71.92/9.79 (funcImageSingleton) => 71.92/9.79 (( 71.92/9.79 (apProp) => 71.92/9.79 (( 71.92/9.79 (app) => 71.92/9.79 (( 71.92/9.79 (infuncsetfunc) => 71.92/9.79 (( 71.92/9.79 (ap2p) => 71.92/9.79 (( 71.92/9.79 (funcinfuncset) => 71.92/9.79 (( 71.92/9.79 (lamProp) => 71.92/9.79 (( 71.92/9.79 (lamp) => 71.92/9.79 (( 71.92/9.79 (lam2p) => 71.92/9.79 (( 71.92/9.79 (brelnall1) => 71.92/9.79 (( 71.92/9.79 (brelnall2) => 71.92/9.79 (( 71.92/9.79 (ex1E2) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp1) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp3) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp2) => 71.92/9.79 (( 71.92/9.79 (funcextLem) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp4) => 71.92/9.79 (( 71.92/9.79 (subbreln) => 71.92/9.79 (( 71.92/9.79 (eqbreln) => 71.92/9.79 (( 71.92/9.79 (funcext) => 71.92/9.79 (( 71.92/9.79 (funcext2) => 71.92/9.79 (( 71.92/9.79 (ap2apEq1) => 71.92/9.79 (( 71.92/9.79 (ap2apEq2) => 71.92/9.79 (( 71.92/9.79 (beta1) => 71.92/9.79 (( 71.92/9.79 (eta1) => 71.92/9.79 (( 71.92/9.79 (lam2lamEq) => 71.92/9.79 (( 71.92/9.79 (beta2) => 71.92/9.79 (( 71.92/9.79 (eta2) => 71.92/9.79 (( 71.92/9.79 (iffalseProp1) => 71.92/9.79 (( 71.92/9.79 (iffalseProp2) => 71.92/9.79 (( 71.92/9.79 (iftrueProp1) => 71.92/9.79 (( 71.92/9.79 (iftrueProp2) => 71.92/9.79 (( 71.92/9.79 (ifSingleton) => 71.92/9.79 (( 71.92/9.79 (ifp) => 71.92/9.79 (( 71.92/9.79 (theeq) => 71.92/9.79 (( 71.92/9.79 (iftrue) => 71.92/9.79 (( 71.92/9.79 (iffalse) => 71.92/9.79 (( 71.92/9.79 (iftrueorfalse) => 71.92/9.79 (( 71.92/9.79 (binintersectT_lem) => 71.92/9.79 (( 71.92/9.79 (binunionT_lem) => 71.92/9.79 (( 71.92/9.79 (powersetT_lem) => 71.92/9.79 (( 71.92/9.79 (setminusT_lem) => 71.92/9.79 (( 71.92/9.79 (complementT_lem) => 71.92/9.79 (( 71.92/9.79 (setextT) => 71.92/9.79 (( 71.92/9.79 (subsetTI) => 71.92/9.79 (( 71.92/9.79 (powersetTI1) => 71.92/9.79 (( 71.92/9.79 (powersetTE1) => 71.92/9.79 (( 71.92/9.79 (complementTI1) => 71.92/9.79 (( 71.92/9.79 (complementTE1) => 71.92/9.79 (( 71.92/9.79 (binintersectTELcontra) => 71.92/9.79 (( 71.92/9.79 (binintersectTERcontra) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT1) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT2) => 71.92/9.79 (( 71.92/9.79 (contrasubsetT3) => 71.92/9.79 (( 71.92/9.79 (doubleComplementI1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementE1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub1) => 71.92/9.79 (( 71.92/9.79 (doubleComplementSub2) => 71.92/9.79 (( 71.92/9.79 (doubleComplementEq) => 71.92/9.79 (( 71.92/9.79 (complementTnotintersectT) => 71.92/9.79 (( 71.92/9.79 (complementImpComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementSubsetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (complementInPowersetComplementIntersect) => 71.92/9.79 (( 71.92/9.79 (contraSubsetComplement) => 71.92/9.79 (( 71.92/9.79 (complementTcontraSubset) => 71.92/9.79 (( 71.92/9.79 (binunionTILcontra) => 71.92/9.79 (( 71.92/9.79 (binunionTIRcontra) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInUnion2) => 71.92/9.79 (( 71.92/9.79 (inIntersectImpInIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (intersectInPowersetIntersectUnions) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpNotIn1) => 71.92/9.79 (( 71.92/9.79 (inComplementUnionImpInComplement1) => 71.92/9.79 (( 71.92/9.79 (binunionTE) => 71.92/9.79 (( 71.92/9.79 (binunionTEcontra) => 71.92/9.79 (( 71.92/9.79 (demorgan2a1) => 71.92/9.79 (( 71.92/9.79 (complementUnionInPowersetComplement) => 71.92/9.79 (( 71.92/9.79 (demorgan2a2) => 71.92/9.79 (( 71.92/9.79 (demorgan1a) => 71.92/9.79 (( 71.92/9.79 (demorgan1b) => 71.92/9.79 (( 71.92/9.79 (demorgan1) => 71.92/9.79 (( 71.92/9.79 (demorgan2a) => 71.92/9.79 (( 71.92/9.79 (demorgan2b2) => 71.92/9.79 (( 71.92/9.79 (demorgan2b) => 71.92/9.79 (( 71.92/9.79 (demorgan2) => 71.92/9.79 (( 71.92/9.79 (woz13rule0) => 71.92/9.79 (( 71.92/9.79 (woz13rule1) => 71.92/9.79 (( 71.92/9.79 (woz13rule2) => 71.92/9.79 (( 71.92/9.79 (woz13rule3) => 71.92/9.79 (( 71.92/9.79 (woz13rule4) => 71.92/9.79 (( 71.92/9.79 (woz1_1) => 71.92/9.79 (( 71.92/9.79 (woz1_2) => 71.92/9.79 (( 71.92/9.79 (woz1_3) => 71.92/9.79 (( 71.92/9.79 (woz1_4) => 71.92/9.79 (( 71.92/9.79 (woz1_5) => 71.92/9.79 (( 71.92/9.79 (breln1all2) => 71.92/9.79 (( 71.92/9.79 (breln1SetBreln1) => 71.92/9.79 (( 71.92/9.79 (choice2fnsingleton) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln1) => 71.92/9.79 (( 71.92/9.79 (breln1all1) => 71.92/9.79 (( 71.92/9.79 (subbreln1) => 71.92/9.79 (( 71.92/9.79 (eqbreln1) => 71.92/9.79 (( 71.92/9.79 (breln1invprop) => 71.92/9.79 (( 71.92/9.79 (breln1invI) => 71.92/9.79 (( 71.92/9.79 (breln1invE) => 71.92/9.79 (( 71.92/9.79 (breln1compprop) => 71.92/9.79 (( 71.92/9.79 (breln1compI) => 71.92/9.79 (( 71.92/9.79 (breln1compE) => 71.92/9.79 (( 71.92/9.79 (breln1compEex) => 71.92/9.79 (( 71.92/9.79 (!!) @ ( 71.92/9.79 (('#B') @ ( 71.92/9.79 !!) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 !!))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#S') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#S') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 =>))) @ 71.92/9.79 breln1)))))) @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#C') @ ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 ( 71.92/9.79 ( 71.92/9.79 ('#B') @ ( 71.92/9.79 '#B') @ 71.92/9.79 breln1)))) @ 71.92/9.79 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])). 71.92/9.79 thf(zip_derived_cl672, plain, 71.92/9.79 (~ (((exu__Cong) => 71.92/9.79 (((setadjoin__Cong) => 71.92/9.79 (((powerset__Cong) => 71.92/9.79 (((setunion__Cong) => 71.92/9.79 (((exuEu) => 71.92/9.79 (((descr__Cong) => 71.92/9.79 (((dsetconstr__Cong) => 71.92/9.79 (((subsetI1) => 71.92/9.79 (((eqimpsubset2) => 71.92/9.79 (((eqimpsubset1) => 71.92/9.79 (((subsetI2) => 71.92/9.79 (((emptysetsubset) => 71.92/9.79 (((subsetE) => 71.92/9.79 (((subsetE2) => 71.92/9.79 (((notsubsetI) => 71.92/9.79 (((notequalI1) => 71.92/9.79 (((notequalI2) => 71.92/9.79 (((subsetRefl) => 71.92/9.79 (((subsetTrans) => 71.92/9.79 (((setadjoinSub) => 71.92/9.79 (((setadjoinSub2) => 71.92/9.79 (((subset2powerset) => 71.92/9.79 (((setextsub) => 71.92/9.79 (((subsetemptysetimpeq) => 71.92/9.79 (((powersetI1) => 71.92/9.79 (((powersetE1) => 71.92/9.79 (((inPowerset) => 71.92/9.79 (((powersetsubset) => 71.92/9.79 (((sepInPowerset) => 71.92/9.79 (((sepSubset) => 71.92/9.79 (( 71.92/9.79 (binunionIL) => 71.92/9.79 (( 71.92/9.79 (upairset2IR) => 71.92/9.79 (( 71.92/9.79 (binunionIR) => 71.92/9.79 (( 71.92/9.79 (binunionEcases) => 71.92/9.79 (( 71.92/9.79 (binunionE) => 71.92/9.79 (( 71.92/9.79 (binunionLsub) => 71.92/9.79 (( 71.92/9.79 (binunionRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectI) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset5) => 71.92/9.79 (( 71.92/9.79 (binintersectEL) => 71.92/9.79 (( 71.92/9.79 (binintersectLsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset2) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset3) => 71.92/9.79 (( 71.92/9.79 (binintersectER) => 71.92/9.79 (( 71.92/9.79 (disjointsetsI1) => 71.92/9.79 (( 71.92/9.79 (binintersectRsub) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset4) => 71.92/9.79 (( 71.92/9.79 (binintersectSubset1) => 71.92/9.79 (( 71.92/9.79 (bs114d) => 71.92/9.79 (( 71.92/9.79 (setminusI) => 71.92/9.79 (( 71.92/9.79 (setminusEL) => 71.92/9.79 (( 71.92/9.79 (setminusER) => 71.92/9.79 (( 71.92/9.79 (setminusSubset2) => 71.92/9.79 (( 71.92/9.79 (setminusERneg) => 71.92/9.79 (( 71.92/9.79 (setminusELneg) => 71.92/9.79 (( 71.92/9.79 (setminusILneg) => 71.92/9.79 (( 71.92/9.79 (setminusIRneg) => 71.92/9.79 (( 71.92/9.79 (setminusLsub) => 71.92/9.79 (( 71.92/9.79 (setminusSubset1) => 71.92/9.79 (( 71.92/9.79 (symdiffE) => 71.92/9.79 (( 71.92/9.79 (symdiffI1) => 71.92/9.79 (( 71.92/9.79 (symdiffI2) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg1) => 71.92/9.79 (( 71.92/9.79 (symdiffIneg2) => 71.92/9.79 (( 71.92/9.79 (secondinupair) => 71.92/9.79 (( 71.92/9.79 (setukpairIL) => 71.92/9.79 (( 71.92/9.79 (setukpairIR) => 71.92/9.79 (( 71.92/9.79 (kpairiskpair) => 71.92/9.79 (( 71.92/9.79 (kpairp) => 71.92/9.79 (( 71.92/9.79 (singletonsubset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowerset) => 71.92/9.79 (( 71.92/9.79 (singletoninpowunion) => 71.92/9.79 (( 71.92/9.79 (upairset2E) => 71.92/9.79 (( 71.92/9.79 (upairsubunion) => 71.92/9.79 (( 71.92/9.79 (upairinpowunion) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem1) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem2) => 71.92/9.79 (( 71.92/9.79 (ubforcartprodlem3) => 71.92/9.79 (( 71.92/9.79 (cartprodpairin) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair1) => 71.92/9.79 (( 71.92/9.79 (cartprodmempair) => 71.92/9.79 (( 71.92/9.79 (setunionE2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton1) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton2) => 71.92/9.79 (( 71.92/9.79 (setunionsingleton) => 71.92/9.79 (( 71.92/9.79 (singletonprop) => 71.92/9.79 (( 71.92/9.79 (ex1E1) => 71.92/9.79 (( 71.92/9.79 (ex1I) => 71.92/9.79 (( 71.92/9.79 (ex1I2) => 71.92/9.79 (( 71.92/9.79 (singletonsuniq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL1) => 71.92/9.79 (( 71.92/9.79 (kfstsingleton) => 71.92/9.79 (( 71.92/9.79 (theprop) => 71.92/9.79 (( 71.92/9.79 (kfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstin) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjL) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR11) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR12) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR1) => 71.92/9.79 (( 71.92/9.79 (upairequniteq) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR2) => 71.92/9.79 (( 71.92/9.79 (setukpairinjR) => 71.92/9.79 (( 71.92/9.79 (ksndsingleton) => 71.92/9.79 (( 71.92/9.79 (ksndpairEq) => 71.92/9.79 (( 71.92/9.79 (kpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndin) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemEL) => 71.92/9.79 (( 71.92/9.79 (cartprodpairmemER) => 71.92/9.79 (( 71.92/9.79 (cartprodmempaircEq) => 71.92/9.79 (( 71.92/9.79 (cartprodfstpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodsndpairEq) => 71.92/9.79 (( 71.92/9.79 (cartprodpairsurjEq) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrI) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrSub) => 71.92/9.79 (( 71.92/9.79 (setOfPairsIsBReln) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrERa) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL1) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrEL2) => 71.92/9.79 (( 71.92/9.79 (dpsetconstrER) => 71.92/9.79 (( 71.92/9.79 (funcImageSingleton) => 71.92/9.79 (( 71.92/9.79 (apProp) => 71.92/9.79 (( 71.92/9.79 (app) => 71.92/9.79 (( 71.92/9.79 (infuncsetfunc) => 71.92/9.79 (( 71.92/9.79 (ap2p) => 71.92/9.79 (( 71.92/9.79 (funcinfuncset) => 71.92/9.79 (( 71.92/9.79 (lamProp) => 71.92/9.79 (( 71.92/9.79 (lamp) => 71.92/9.79 (( 71.92/9.79 (lam2p) => 71.92/9.79 (( 71.92/9.79 (brelnall1) => 71.92/9.79 (( 71.92/9.79 (brelnall2) => 71.92/9.79 (( 71.92/9.79 (ex1E2) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp1) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp3) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp2) => 71.92/9.79 (( 71.92/9.79 (funcextLem) => 71.92/9.79 (( 71.92/9.79 (funcGraphProp4) => 71.92/9.79 (( 71.92/9.79 (subbreln) => 71.92/9.79 (( 71.92/9.79 (eqbreln) => 71.92/9.79 (( 71.92/9.79 (funcext) => 71.92/9.79 (( 71.92/9.79 (funcext2) => 71.92/9.79 (( 71.92/9.79 (ap2apEq1) => 71.92/9.79 (( 71.92/9.79 (ap2apEq2) => 71.92/9.79 (( 71.92/9.79 (beta1) => 71.92/9.79 (( 71.92/9.79 (eta1) => 71.92/9.79 (( 71.92/9.79 (lam2lamEq) => 71.92/9.79 (( 71.92/9.79 (beta2) => 71.92/9.79 (( 71.92/9.79 (eta2) => 71.92/9.79 (( 71.92/9.79 (iffalseProp1) => 71.92/9.79 (( 71.92/9.79 (iffalseProp2) => 71.92/9.79 (( 71.92/9.79 (iftrueProp1) => 71.92/9.79 (( 71.92/9.79 (iftrueProp2) => 71.92/9.79 (( 71.92/9.79 (ifSingleton) => 71.92/9.79 (( 71.92/9.79 (ifp) => 71.92/9.79 (( 71.92/9.79 (theeq) => 71.92/9.79 (( 71.92/9.80 (iftrue) => 71.92/9.80 (( 71.92/9.80 (iffalse) => 71.92/9.80 (( 71.92/9.80 (iftrueorfalse) => 71.92/9.80 (( 71.92/9.80 (binintersectT_lem) => 71.92/9.80 (( 71.92/9.80 (binunionT_lem) => 71.92/9.80 (( 71.92/9.80 (powersetT_lem) => 71.92/9.80 (( 71.92/9.80 (setminusT_lem) => 71.92/9.80 (( 71.92/9.80 (complementT_lem) => 71.92/9.80 (( 71.92/9.80 (setextT) => 71.92/9.80 (( 71.92/9.80 (subsetTI) => 71.92/9.80 (( 71.92/9.80 (powersetTI1) => 71.92/9.80 (( 71.92/9.80 (powersetTE1) => 71.92/9.80 (( 71.92/9.80 (complementTI1) => 71.92/9.80 (( 71.92/9.80 (complementTE1) => 71.92/9.80 (( 71.92/9.80 (binintersectTELcontra) => 71.92/9.80 (( 71.92/9.80 (binintersectTERcontra) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT1) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT2) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT3) => 71.92/9.80 (( 71.92/9.80 (doubleComplementI1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementE1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementSub1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementSub2) => 71.92/9.80 (( 71.92/9.80 (doubleComplementEq) => 71.92/9.80 (( 71.92/9.80 (complementTnotintersectT) => 71.92/9.80 (( 71.92/9.80 (complementImpComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (complementSubsetComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (complementInPowersetComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (contraSubsetComplement) => 71.92/9.80 (( 71.92/9.80 (complementTcontraSubset) => 71.92/9.80 (( 71.92/9.80 (binunionTILcontra) => 71.92/9.80 (( 71.92/9.80 (binunionTIRcontra) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInUnion) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInUnion2) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInIntersectUnions) => 71.92/9.80 (( 71.92/9.80 (intersectInPowersetIntersectUnions) => 71.92/9.80 (( 71.92/9.80 (inComplementUnionImpNotIn1) => 71.92/9.80 (( 71.92/9.80 (inComplementUnionImpInComplement1) => 71.92/9.80 (( 71.92/9.80 (binunionTE) => 71.92/9.80 (( 71.92/9.80 (binunionTEcontra) => 71.92/9.80 (( 71.92/9.80 (demorgan2a1) => 71.92/9.80 (( 71.92/9.80 (complementUnionInPowersetComplement) => 71.92/9.80 (( 71.92/9.80 (demorgan2a2) => 71.92/9.80 (( 71.92/9.80 (demorgan1a) => 71.92/9.80 (( 71.92/9.80 (demorgan1b) => 71.92/9.80 (( 71.92/9.80 (demorgan1) => 71.92/9.80 (( 71.92/9.80 (demorgan2a) => 71.92/9.80 (( 71.92/9.80 (demorgan2b2) => 71.92/9.80 (( 71.92/9.80 (demorgan2b) => 71.92/9.80 (( 71.92/9.80 (demorgan2) => 71.92/9.80 (( 71.92/9.80 (woz13rule0) => 71.92/9.80 (( 71.92/9.80 (woz13rule1) => 71.92/9.80 (( 71.92/9.80 (woz13rule2) => 71.92/9.80 (( 71.92/9.80 (woz13rule3) => 71.92/9.80 (( 71.92/9.80 (woz13rule4) => 71.92/9.80 (( 71.92/9.80 (woz1_1) => 71.92/9.80 (( 71.92/9.80 (woz1_2) => 71.92/9.80 (( 71.92/9.80 (woz1_3) => 71.92/9.80 (( 71.92/9.80 (woz1_4) => 71.92/9.80 (( 71.92/9.80 (woz1_5) => 71.92/9.80 (( 71.92/9.80 (breln1all2) => 71.92/9.80 (( 71.92/9.80 (breln1SetBreln1) => 71.92/9.80 (( 71.92/9.80 (choice2fnsingleton) => 71.92/9.80 (( 71.92/9.80 (setOfPairsIsBReln1) => 71.92/9.80 (( 71.92/9.80 (breln1all1) => 71.92/9.80 (( 71.92/9.80 (subbreln1) => 71.92/9.80 (( 71.92/9.80 (eqbreln1) => 71.92/9.80 (( 71.92/9.80 (breln1invprop) => 71.92/9.80 (( 71.92/9.80 (breln1invI) => 71.92/9.80 (( 71.92/9.80 (breln1invE) => 71.92/9.80 (( 71.92/9.80 (breln1compprop) => 71.92/9.80 (( 71.92/9.80 (breln1compI) => 71.92/9.80 (( 71.92/9.80 (breln1compE) => 71.92/9.80 (( 71.92/9.80 (breln1compEex) => 71.92/9.80 (( 71.92/9.80 (!!) @ ( 71.92/9.80 (('#B') @ ( 71.92/9.80 !!) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#S') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#S') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 =>))) @ 71.92/9.80 breln1)))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 !!))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#S') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#S') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 =>))) @ 71.92/9.80 breln1)))))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#C') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 breln1)))) @ 71.92/9.80 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])). 71.92/9.80 thf(zip_derived_cl685, plain, 71.92/9.80 (~ (((setadjoin__Cong) => 71.92/9.80 (((powerset__Cong) => 71.92/9.80 (((setunion__Cong) => 71.92/9.80 (((exuEu) => 71.92/9.80 (((descr__Cong) => 71.92/9.80 (((dsetconstr__Cong) => 71.92/9.80 (((subsetI1) => 71.92/9.80 (((eqimpsubset2) => 71.92/9.80 (((eqimpsubset1) => 71.92/9.80 (((subsetI2) => 71.92/9.80 (((emptysetsubset) => 71.92/9.80 (((subsetE) => 71.92/9.80 (((subsetE2) => 71.92/9.80 (((notsubsetI) => 71.92/9.80 (((notequalI1) => 71.92/9.80 (((notequalI2) => 71.92/9.80 (((subsetRefl) => 71.92/9.80 (((subsetTrans) => 71.92/9.80 (((setadjoinSub) => 71.92/9.80 (((setadjoinSub2) => 71.92/9.80 (((subset2powerset) => 71.92/9.80 (((setextsub) => 71.92/9.80 (((subsetemptysetimpeq) => 71.92/9.80 (((powersetI1) => 71.92/9.80 (((powersetE1) => 71.92/9.80 (((inPowerset) => 71.92/9.80 (((powersetsubset) => 71.92/9.80 (((sepInPowerset) => 71.92/9.80 (((sepSubset) => 71.92/9.80 (((binunionIL) => 71.92/9.80 (( 71.92/9.80 (upairset2IR) => 71.92/9.80 (( 71.92/9.80 (binunionIR) => 71.92/9.80 (( 71.92/9.80 (binunionEcases) => 71.92/9.80 (( 71.92/9.80 (binunionE) => 71.92/9.80 (( 71.92/9.80 (binunionLsub) => 71.92/9.80 (( 71.92/9.80 (binunionRsub) => 71.92/9.80 (( 71.92/9.80 (binintersectI) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset5) => 71.92/9.80 (( 71.92/9.80 (binintersectEL) => 71.92/9.80 (( 71.92/9.80 (binintersectLsub) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset2) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset3) => 71.92/9.80 (( 71.92/9.80 (binintersectER) => 71.92/9.80 (( 71.92/9.80 (disjointsetsI1) => 71.92/9.80 (( 71.92/9.80 (binintersectRsub) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset4) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset1) => 71.92/9.80 (( 71.92/9.80 (bs114d) => 71.92/9.80 (( 71.92/9.80 (setminusI) => 71.92/9.80 (( 71.92/9.80 (setminusEL) => 71.92/9.80 (( 71.92/9.80 (setminusER) => 71.92/9.80 (( 71.92/9.80 (setminusSubset2) => 71.92/9.80 (( 71.92/9.80 (setminusERneg) => 71.92/9.80 (( 71.92/9.80 (setminusELneg) => 71.92/9.80 (( 71.92/9.80 (setminusILneg) => 71.92/9.80 (( 71.92/9.80 (setminusIRneg) => 71.92/9.80 (( 71.92/9.80 (setminusLsub) => 71.92/9.80 (( 71.92/9.80 (setminusSubset1) => 71.92/9.80 (( 71.92/9.80 (symdiffE) => 71.92/9.80 (( 71.92/9.80 (symdiffI1) => 71.92/9.80 (( 71.92/9.80 (symdiffI2) => 71.92/9.80 (( 71.92/9.80 (symdiffIneg1) => 71.92/9.80 (( 71.92/9.80 (symdiffIneg2) => 71.92/9.80 (( 71.92/9.80 (secondinupair) => 71.92/9.80 (( 71.92/9.80 (setukpairIL) => 71.92/9.80 (( 71.92/9.80 (setukpairIR) => 71.92/9.80 (( 71.92/9.80 (kpairiskpair) => 71.92/9.80 (( 71.92/9.80 (kpairp) => 71.92/9.80 (( 71.92/9.80 (singletonsubset) => 71.92/9.80 (( 71.92/9.80 (singletoninpowerset) => 71.92/9.80 (( 71.92/9.80 (singletoninpowunion) => 71.92/9.80 (( 71.92/9.80 (upairset2E) => 71.92/9.80 (( 71.92/9.80 (upairsubunion) => 71.92/9.80 (( 71.92/9.80 (upairinpowunion) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem1) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem2) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem3) => 71.92/9.80 (( 71.92/9.80 (cartprodpairin) => 71.92/9.80 (( 71.92/9.80 (cartprodmempair1) => 71.92/9.80 (( 71.92/9.80 (cartprodmempair) => 71.92/9.80 (( 71.92/9.80 (setunionE2) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton1) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton2) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton) => 71.92/9.80 (( 71.92/9.80 (singletonprop) => 71.92/9.80 (( 71.92/9.80 (ex1E1) => 71.92/9.80 (( 71.92/9.80 (ex1I) => 71.92/9.80 (( 71.92/9.80 (ex1I2) => 71.92/9.80 (( 71.92/9.80 (singletonsuniq) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL1) => 71.92/9.80 (( 71.92/9.80 (kfstsingleton) => 71.92/9.80 (( 71.92/9.80 (theprop) => 71.92/9.80 (( 71.92/9.80 (kfstpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodfstin) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL2) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR11) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR12) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR1) => 71.92/9.80 (( 71.92/9.80 (upairequniteq) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR2) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR) => 71.92/9.80 (( 71.92/9.80 (ksndsingleton) => 71.92/9.80 (( 71.92/9.80 (ksndpairEq) => 71.92/9.80 (( 71.92/9.80 (kpairsurjEq) => 71.92/9.80 (( 71.92/9.80 (cartprodsndin) => 71.92/9.80 (( 71.92/9.80 (cartprodpairmemEL) => 71.92/9.80 (( 71.92/9.80 (cartprodpairmemER) => 71.92/9.80 (( 71.92/9.80 (cartprodmempaircEq) => 71.92/9.80 (( 71.92/9.80 (cartprodfstpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodsndpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodpairsurjEq) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrI) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrSub) => 71.92/9.80 (( 71.92/9.80 (setOfPairsIsBReln) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrERa) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrEL1) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrEL2) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrER) => 71.92/9.80 (( 71.92/9.80 (funcImageSingleton) => 71.92/9.80 (( 71.92/9.80 (apProp) => 71.92/9.80 (( 71.92/9.80 (app) => 71.92/9.80 (( 71.92/9.80 (infuncsetfunc) => 71.92/9.80 (( 71.92/9.80 (ap2p) => 71.92/9.80 (( 71.92/9.80 (funcinfuncset) => 71.92/9.80 (( 71.92/9.80 (lamProp) => 71.92/9.80 (( 71.92/9.80 (lamp) => 71.92/9.80 (( 71.92/9.80 (lam2p) => 71.92/9.80 (( 71.92/9.80 (brelnall1) => 71.92/9.80 (( 71.92/9.80 (brelnall2) => 71.92/9.80 (( 71.92/9.80 (ex1E2) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp1) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp3) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp2) => 71.92/9.80 (( 71.92/9.80 (funcextLem) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp4) => 71.92/9.80 (( 71.92/9.80 (subbreln) => 71.92/9.80 (( 71.92/9.80 (eqbreln) => 71.92/9.80 (( 71.92/9.80 (funcext) => 71.92/9.80 (( 71.92/9.80 (funcext2) => 71.92/9.80 (( 71.92/9.80 (ap2apEq1) => 71.92/9.80 (( 71.92/9.80 (ap2apEq2) => 71.92/9.80 (( 71.92/9.80 (beta1) => 71.92/9.80 (( 71.92/9.80 (eta1) => 71.92/9.80 (( 71.92/9.80 (lam2lamEq) => 71.92/9.80 (( 71.92/9.80 (beta2) => 71.92/9.80 (( 71.92/9.80 (eta2) => 71.92/9.80 (( 71.92/9.80 (iffalseProp1) => 71.92/9.80 (( 71.92/9.80 (iffalseProp2) => 71.92/9.80 (( 71.92/9.80 (iftrueProp1) => 71.92/9.80 (( 71.92/9.80 (iftrueProp2) => 71.92/9.80 (( 71.92/9.80 (ifSingleton) => 71.92/9.80 (( 71.92/9.80 (ifp) => 71.92/9.80 (( 71.92/9.80 (theeq) => 71.92/9.80 (( 71.92/9.80 (iftrue) => 71.92/9.80 (( 71.92/9.80 (iffalse) => 71.92/9.80 (( 71.92/9.80 (iftrueorfalse) => 71.92/9.80 (( 71.92/9.80 (binintersectT_lem) => 71.92/9.80 (( 71.92/9.80 (binunionT_lem) => 71.92/9.80 (( 71.92/9.80 (powersetT_lem) => 71.92/9.80 (( 71.92/9.80 (setminusT_lem) => 71.92/9.80 (( 71.92/9.80 (complementT_lem) => 71.92/9.80 (( 71.92/9.80 (setextT) => 71.92/9.80 (( 71.92/9.80 (subsetTI) => 71.92/9.80 (( 71.92/9.80 (powersetTI1) => 71.92/9.80 (( 71.92/9.80 (powersetTE1) => 71.92/9.80 (( 71.92/9.80 (complementTI1) => 71.92/9.80 (( 71.92/9.80 (complementTE1) => 71.92/9.80 (( 71.92/9.80 (binintersectTELcontra) => 71.92/9.80 (( 71.92/9.80 (binintersectTERcontra) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT1) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT2) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT3) => 71.92/9.80 (( 71.92/9.80 (doubleComplementI1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementE1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementSub1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementSub2) => 71.92/9.80 (( 71.92/9.80 (doubleComplementEq) => 71.92/9.80 (( 71.92/9.80 (complementTnotintersectT) => 71.92/9.80 (( 71.92/9.80 (complementImpComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (complementSubsetComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (complementInPowersetComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (contraSubsetComplement) => 71.92/9.80 (( 71.92/9.80 (complementTcontraSubset) => 71.92/9.80 (( 71.92/9.80 (binunionTILcontra) => 71.92/9.80 (( 71.92/9.80 (binunionTIRcontra) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInUnion) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInUnion2) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInIntersectUnions) => 71.92/9.80 (( 71.92/9.80 (intersectInPowersetIntersectUnions) => 71.92/9.80 (( 71.92/9.80 (inComplementUnionImpNotIn1) => 71.92/9.80 (( 71.92/9.80 (inComplementUnionImpInComplement1) => 71.92/9.80 (( 71.92/9.80 (binunionTE) => 71.92/9.80 (( 71.92/9.80 (binunionTEcontra) => 71.92/9.80 (( 71.92/9.80 (demorgan2a1) => 71.92/9.80 (( 71.92/9.80 (complementUnionInPowersetComplement) => 71.92/9.80 (( 71.92/9.80 (demorgan2a2) => 71.92/9.80 (( 71.92/9.80 (demorgan1a) => 71.92/9.80 (( 71.92/9.80 (demorgan1b) => 71.92/9.80 (( 71.92/9.80 (demorgan1) => 71.92/9.80 (( 71.92/9.80 (demorgan2a) => 71.92/9.80 (( 71.92/9.80 (demorgan2b2) => 71.92/9.80 (( 71.92/9.80 (demorgan2b) => 71.92/9.80 (( 71.92/9.80 (demorgan2) => 71.92/9.80 (( 71.92/9.80 (woz13rule0) => 71.92/9.80 (( 71.92/9.80 (woz13rule1) => 71.92/9.80 (( 71.92/9.80 (woz13rule2) => 71.92/9.80 (( 71.92/9.80 (woz13rule3) => 71.92/9.80 (( 71.92/9.80 (woz13rule4) => 71.92/9.80 (( 71.92/9.80 (woz1_1) => 71.92/9.80 (( 71.92/9.80 (woz1_2) => 71.92/9.80 (( 71.92/9.80 (woz1_3) => 71.92/9.80 (( 71.92/9.80 (woz1_4) => 71.92/9.80 (( 71.92/9.80 (woz1_5) => 71.92/9.80 (( 71.92/9.80 (breln1all2) => 71.92/9.80 (( 71.92/9.80 (breln1SetBreln1) => 71.92/9.80 (( 71.92/9.80 (choice2fnsingleton) => 71.92/9.80 (( 71.92/9.80 (setOfPairsIsBReln1) => 71.92/9.80 (( 71.92/9.80 (breln1all1) => 71.92/9.80 (( 71.92/9.80 (subbreln1) => 71.92/9.80 (( 71.92/9.80 (eqbreln1) => 71.92/9.80 (( 71.92/9.80 (breln1invprop) => 71.92/9.80 (( 71.92/9.80 (breln1invI) => 71.92/9.80 (( 71.92/9.80 (breln1invE) => 71.92/9.80 (( 71.92/9.80 (breln1compprop) => 71.92/9.80 (( 71.92/9.80 (breln1compI) => 71.92/9.80 (( 71.92/9.80 (breln1compE) => 71.92/9.80 (( 71.92/9.80 (breln1compEex) => 71.92/9.80 (( 71.92/9.80 (!!) @ ( 71.92/9.80 (('#B') @ ( 71.92/9.80 !!) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#S') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#S') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 =>))) @ 71.92/9.80 breln1)))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 !!))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#S') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#S') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 =>))) @ 71.92/9.80 breln1)))))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#C') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 breln1)))) @ 71.92/9.80 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])). 71.92/9.80 thf(zip_derived_cl699, plain, 71.92/9.80 (~ (((powerset__Cong) => 71.92/9.80 (((setunion__Cong) => 71.92/9.80 (((exuEu) => 71.92/9.80 (((descr__Cong) => 71.92/9.80 (((dsetconstr__Cong) => 71.92/9.80 (((subsetI1) => 71.92/9.80 (((eqimpsubset2) => 71.92/9.80 (((eqimpsubset1) => 71.92/9.80 (((subsetI2) => 71.92/9.80 (((emptysetsubset) => 71.92/9.80 (((subsetE) => 71.92/9.80 (((subsetE2) => 71.92/9.80 (((notsubsetI) => 71.92/9.80 (((notequalI1) => 71.92/9.80 (((notequalI2) => 71.92/9.80 (((subsetRefl) => 71.92/9.80 (((subsetTrans) => 71.92/9.80 (((setadjoinSub) => 71.92/9.80 (((setadjoinSub2) => 71.92/9.80 (((subset2powerset) => 71.92/9.80 (((setextsub) => 71.92/9.80 (((subsetemptysetimpeq) => 71.92/9.80 (((powersetI1) => 71.92/9.80 (((powersetE1) => 71.92/9.80 (((inPowerset) => 71.92/9.80 (((powersetsubset) => 71.92/9.80 (((sepInPowerset) => 71.92/9.80 (((sepSubset) => 71.92/9.80 (((binunionIL) => 71.92/9.80 (((upairset2IR) => 71.92/9.80 (( 71.92/9.80 (binunionIR) => 71.92/9.80 (( 71.92/9.80 (binunionEcases) => 71.92/9.80 (( 71.92/9.80 (binunionE) => 71.92/9.80 (( 71.92/9.80 (binunionLsub) => 71.92/9.80 (( 71.92/9.80 (binunionRsub) => 71.92/9.80 (( 71.92/9.80 (binintersectI) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset5) => 71.92/9.80 (( 71.92/9.80 (binintersectEL) => 71.92/9.80 (( 71.92/9.80 (binintersectLsub) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset2) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset3) => 71.92/9.80 (( 71.92/9.80 (binintersectER) => 71.92/9.80 (( 71.92/9.80 (disjointsetsI1) => 71.92/9.80 (( 71.92/9.80 (binintersectRsub) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset4) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset1) => 71.92/9.80 (( 71.92/9.80 (bs114d) => 71.92/9.80 (( 71.92/9.80 (setminusI) => 71.92/9.80 (( 71.92/9.80 (setminusEL) => 71.92/9.80 (( 71.92/9.80 (setminusER) => 71.92/9.80 (( 71.92/9.80 (setminusSubset2) => 71.92/9.80 (( 71.92/9.80 (setminusERneg) => 71.92/9.80 (( 71.92/9.80 (setminusELneg) => 71.92/9.80 (( 71.92/9.80 (setminusILneg) => 71.92/9.80 (( 71.92/9.80 (setminusIRneg) => 71.92/9.80 (( 71.92/9.80 (setminusLsub) => 71.92/9.80 (( 71.92/9.80 (setminusSubset1) => 71.92/9.80 (( 71.92/9.80 (symdiffE) => 71.92/9.80 (( 71.92/9.80 (symdiffI1) => 71.92/9.80 (( 71.92/9.80 (symdiffI2) => 71.92/9.80 (( 71.92/9.80 (symdiffIneg1) => 71.92/9.80 (( 71.92/9.80 (symdiffIneg2) => 71.92/9.80 (( 71.92/9.80 (secondinupair) => 71.92/9.80 (( 71.92/9.80 (setukpairIL) => 71.92/9.80 (( 71.92/9.80 (setukpairIR) => 71.92/9.80 (( 71.92/9.80 (kpairiskpair) => 71.92/9.80 (( 71.92/9.80 (kpairp) => 71.92/9.80 (( 71.92/9.80 (singletonsubset) => 71.92/9.80 (( 71.92/9.80 (singletoninpowerset) => 71.92/9.80 (( 71.92/9.80 (singletoninpowunion) => 71.92/9.80 (( 71.92/9.80 (upairset2E) => 71.92/9.80 (( 71.92/9.80 (upairsubunion) => 71.92/9.80 (( 71.92/9.80 (upairinpowunion) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem1) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem2) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem3) => 71.92/9.80 (( 71.92/9.80 (cartprodpairin) => 71.92/9.80 (( 71.92/9.80 (cartprodmempair1) => 71.92/9.80 (( 71.92/9.80 (cartprodmempair) => 71.92/9.80 (( 71.92/9.80 (setunionE2) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton1) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton2) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton) => 71.92/9.80 (( 71.92/9.80 (singletonprop) => 71.92/9.80 (( 71.92/9.80 (ex1E1) => 71.92/9.80 (( 71.92/9.80 (ex1I) => 71.92/9.80 (( 71.92/9.80 (ex1I2) => 71.92/9.80 (( 71.92/9.80 (singletonsuniq) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL1) => 71.92/9.80 (( 71.92/9.80 (kfstsingleton) => 71.92/9.80 (( 71.92/9.80 (theprop) => 71.92/9.80 (( 71.92/9.80 (kfstpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodfstin) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL2) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR11) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR12) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR1) => 71.92/9.80 (( 71.92/9.80 (upairequniteq) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR2) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR) => 71.92/9.80 (( 71.92/9.80 (ksndsingleton) => 71.92/9.80 (( 71.92/9.80 (ksndpairEq) => 71.92/9.80 (( 71.92/9.80 (kpairsurjEq) => 71.92/9.80 (( 71.92/9.80 (cartprodsndin) => 71.92/9.80 (( 71.92/9.80 (cartprodpairmemEL) => 71.92/9.80 (( 71.92/9.80 (cartprodpairmemER) => 71.92/9.80 (( 71.92/9.80 (cartprodmempaircEq) => 71.92/9.80 (( 71.92/9.80 (cartprodfstpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodsndpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodpairsurjEq) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrI) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrSub) => 71.92/9.80 (( 71.92/9.80 (setOfPairsIsBReln) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrERa) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrEL1) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrEL2) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrER) => 71.92/9.80 (( 71.92/9.80 (funcImageSingleton) => 71.92/9.80 (( 71.92/9.80 (apProp) => 71.92/9.80 (( 71.92/9.80 (app) => 71.92/9.80 (( 71.92/9.80 (infuncsetfunc) => 71.92/9.80 (( 71.92/9.80 (ap2p) => 71.92/9.80 (( 71.92/9.80 (funcinfuncset) => 71.92/9.80 (( 71.92/9.80 (lamProp) => 71.92/9.80 (( 71.92/9.80 (lamp) => 71.92/9.80 (( 71.92/9.80 (lam2p) => 71.92/9.80 (( 71.92/9.80 (brelnall1) => 71.92/9.80 (( 71.92/9.80 (brelnall2) => 71.92/9.80 (( 71.92/9.80 (ex1E2) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp1) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp3) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp2) => 71.92/9.80 (( 71.92/9.80 (funcextLem) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp4) => 71.92/9.80 (( 71.92/9.80 (subbreln) => 71.92/9.80 (( 71.92/9.80 (eqbreln) => 71.92/9.80 (( 71.92/9.80 (funcext) => 71.92/9.80 (( 71.92/9.80 (funcext2) => 71.92/9.80 (( 71.92/9.80 (ap2apEq1) => 71.92/9.80 (( 71.92/9.80 (ap2apEq2) => 71.92/9.80 (( 71.92/9.80 (beta1) => 71.92/9.80 (( 71.92/9.80 (eta1) => 71.92/9.80 (( 71.92/9.80 (lam2lamEq) => 71.92/9.80 (( 71.92/9.80 (beta2) => 71.92/9.80 (( 71.92/9.80 (eta2) => 71.92/9.80 (( 71.92/9.80 (iffalseProp1) => 71.92/9.80 (( 71.92/9.80 (iffalseProp2) => 71.92/9.80 (( 71.92/9.80 (iftrueProp1) => 71.92/9.80 (( 71.92/9.80 (iftrueProp2) => 71.92/9.80 (( 71.92/9.80 (ifSingleton) => 71.92/9.80 (( 71.92/9.80 (ifp) => 71.92/9.80 (( 71.92/9.80 (theeq) => 71.92/9.80 (( 71.92/9.80 (iftrue) => 71.92/9.80 (( 71.92/9.80 (iffalse) => 71.92/9.80 (( 71.92/9.80 (iftrueorfalse) => 71.92/9.80 (( 71.92/9.80 (binintersectT_lem) => 71.92/9.80 (( 71.92/9.80 (binunionT_lem) => 71.92/9.80 (( 71.92/9.80 (powersetT_lem) => 71.92/9.80 (( 71.92/9.80 (setminusT_lem) => 71.92/9.80 (( 71.92/9.80 (complementT_lem) => 71.92/9.80 (( 71.92/9.80 (setextT) => 71.92/9.80 (( 71.92/9.80 (subsetTI) => 71.92/9.80 (( 71.92/9.80 (powersetTI1) => 71.92/9.80 (( 71.92/9.80 (powersetTE1) => 71.92/9.80 (( 71.92/9.80 (complementTI1) => 71.92/9.80 (( 71.92/9.80 (complementTE1) => 71.92/9.80 (( 71.92/9.80 (binintersectTELcontra) => 71.92/9.80 (( 71.92/9.80 (binintersectTERcontra) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT1) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT2) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT3) => 71.92/9.80 (( 71.92/9.80 (doubleComplementI1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementE1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementSub1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementSub2) => 71.92/9.80 (( 71.92/9.80 (doubleComplementEq) => 71.92/9.80 (( 71.92/9.80 (complementTnotintersectT) => 71.92/9.80 (( 71.92/9.80 (complementImpComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (complementSubsetComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (complementInPowersetComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (contraSubsetComplement) => 71.92/9.80 (( 71.92/9.80 (complementTcontraSubset) => 71.92/9.80 (( 71.92/9.80 (binunionTILcontra) => 71.92/9.80 (( 71.92/9.80 (binunionTIRcontra) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInUnion) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInUnion2) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInIntersectUnions) => 71.92/9.80 (( 71.92/9.80 (intersectInPowersetIntersectUnions) => 71.92/9.80 (( 71.92/9.80 (inComplementUnionImpNotIn1) => 71.92/9.80 (( 71.92/9.80 (inComplementUnionImpInComplement1) => 71.92/9.80 (( 71.92/9.80 (binunionTE) => 71.92/9.80 (( 71.92/9.80 (binunionTEcontra) => 71.92/9.80 (( 71.92/9.80 (demorgan2a1) => 71.92/9.80 (( 71.92/9.80 (complementUnionInPowersetComplement) => 71.92/9.80 (( 71.92/9.80 (demorgan2a2) => 71.92/9.80 (( 71.92/9.80 (demorgan1a) => 71.92/9.80 (( 71.92/9.80 (demorgan1b) => 71.92/9.80 (( 71.92/9.80 (demorgan1) => 71.92/9.80 (( 71.92/9.80 (demorgan2a) => 71.92/9.80 (( 71.92/9.80 (demorgan2b2) => 71.92/9.80 (( 71.92/9.80 (demorgan2b) => 71.92/9.80 (( 71.92/9.80 (demorgan2) => 71.92/9.80 (( 71.92/9.80 (woz13rule0) => 71.92/9.80 (( 71.92/9.80 (woz13rule1) => 71.92/9.80 (( 71.92/9.80 (woz13rule2) => 71.92/9.80 (( 71.92/9.80 (woz13rule3) => 71.92/9.80 (( 71.92/9.80 (woz13rule4) => 71.92/9.80 (( 71.92/9.80 (woz1_1) => 71.92/9.80 (( 71.92/9.80 (woz1_2) => 71.92/9.80 (( 71.92/9.80 (woz1_3) => 71.92/9.80 (( 71.92/9.80 (woz1_4) => 71.92/9.80 (( 71.92/9.80 (woz1_5) => 71.92/9.80 (( 71.92/9.80 (breln1all2) => 71.92/9.80 (( 71.92/9.80 (breln1SetBreln1) => 71.92/9.80 (( 71.92/9.80 (choice2fnsingleton) => 71.92/9.80 (( 71.92/9.80 (setOfPairsIsBReln1) => 71.92/9.80 (( 71.92/9.80 (breln1all1) => 71.92/9.80 (( 71.92/9.80 (subbreln1) => 71.92/9.80 (( 71.92/9.80 (eqbreln1) => 71.92/9.80 (( 71.92/9.80 (breln1invprop) => 71.92/9.80 (( 71.92/9.80 (breln1invI) => 71.92/9.80 (( 71.92/9.80 (breln1invE) => 71.92/9.80 (( 71.92/9.80 (breln1compprop) => 71.92/9.80 (( 71.92/9.80 (breln1compI) => 71.92/9.80 (( 71.92/9.80 (breln1compE) => 71.92/9.80 (( 71.92/9.80 (breln1compEex) => 71.92/9.80 (( 71.92/9.80 (!!) @ ( 71.92/9.80 (('#B') @ ( 71.92/9.80 !!) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#S') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#S') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 =>))) @ 71.92/9.80 breln1)))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 !!))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#S') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#S') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 =>))) @ 71.92/9.80 breln1)))))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#C') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 breln1)))) @ 71.92/9.80 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl685])). 71.92/9.80 thf(zip_derived_cl714, plain, 71.92/9.80 (~ (((setunion__Cong) => 71.92/9.80 (((exuEu) => 71.92/9.80 (((descr__Cong) => 71.92/9.80 (((dsetconstr__Cong) => 71.92/9.80 (((subsetI1) => 71.92/9.80 (((eqimpsubset2) => 71.92/9.80 (((eqimpsubset1) => 71.92/9.80 (((subsetI2) => 71.92/9.80 (((emptysetsubset) => 71.92/9.80 (((subsetE) => 71.92/9.80 (((subsetE2) => 71.92/9.80 (((notsubsetI) => 71.92/9.80 (((notequalI1) => 71.92/9.80 (((notequalI2) => 71.92/9.80 (((subsetRefl) => 71.92/9.80 (((subsetTrans) => 71.92/9.80 (((setadjoinSub) => 71.92/9.80 (((setadjoinSub2) => 71.92/9.80 (((subset2powerset) => 71.92/9.80 (((setextsub) => 71.92/9.80 (((subsetemptysetimpeq) => 71.92/9.80 (((powersetI1) => 71.92/9.80 (((powersetE1) => 71.92/9.80 (((inPowerset) => 71.92/9.80 (((powersetsubset) => 71.92/9.80 (((sepInPowerset) => 71.92/9.80 (((sepSubset) => 71.92/9.80 (((binunionIL) => 71.92/9.80 (((upairset2IR) => 71.92/9.80 (((binunionIR) => 71.92/9.80 (( 71.92/9.80 (binunionEcases) => 71.92/9.80 (( 71.92/9.80 (binunionE) => 71.92/9.80 (( 71.92/9.80 (binunionLsub) => 71.92/9.80 (( 71.92/9.80 (binunionRsub) => 71.92/9.80 (( 71.92/9.80 (binintersectI) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset5) => 71.92/9.80 (( 71.92/9.80 (binintersectEL) => 71.92/9.80 (( 71.92/9.80 (binintersectLsub) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset2) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset3) => 71.92/9.80 (( 71.92/9.80 (binintersectER) => 71.92/9.80 (( 71.92/9.80 (disjointsetsI1) => 71.92/9.80 (( 71.92/9.80 (binintersectRsub) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset4) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset1) => 71.92/9.80 (( 71.92/9.80 (bs114d) => 71.92/9.80 (( 71.92/9.80 (setminusI) => 71.92/9.80 (( 71.92/9.80 (setminusEL) => 71.92/9.80 (( 71.92/9.80 (setminusER) => 71.92/9.80 (( 71.92/9.80 (setminusSubset2) => 71.92/9.80 (( 71.92/9.80 (setminusERneg) => 71.92/9.80 (( 71.92/9.80 (setminusELneg) => 71.92/9.80 (( 71.92/9.80 (setminusILneg) => 71.92/9.80 (( 71.92/9.80 (setminusIRneg) => 71.92/9.80 (( 71.92/9.80 (setminusLsub) => 71.92/9.80 (( 71.92/9.80 (setminusSubset1) => 71.92/9.80 (( 71.92/9.80 (symdiffE) => 71.92/9.80 (( 71.92/9.80 (symdiffI1) => 71.92/9.80 (( 71.92/9.80 (symdiffI2) => 71.92/9.80 (( 71.92/9.80 (symdiffIneg1) => 71.92/9.80 (( 71.92/9.80 (symdiffIneg2) => 71.92/9.80 (( 71.92/9.80 (secondinupair) => 71.92/9.80 (( 71.92/9.80 (setukpairIL) => 71.92/9.80 (( 71.92/9.80 (setukpairIR) => 71.92/9.80 (( 71.92/9.80 (kpairiskpair) => 71.92/9.80 (( 71.92/9.80 (kpairp) => 71.92/9.80 (( 71.92/9.80 (singletonsubset) => 71.92/9.80 (( 71.92/9.80 (singletoninpowerset) => 71.92/9.80 (( 71.92/9.80 (singletoninpowunion) => 71.92/9.80 (( 71.92/9.80 (upairset2E) => 71.92/9.80 (( 71.92/9.80 (upairsubunion) => 71.92/9.80 (( 71.92/9.80 (upairinpowunion) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem1) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem2) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem3) => 71.92/9.80 (( 71.92/9.80 (cartprodpairin) => 71.92/9.80 (( 71.92/9.80 (cartprodmempair1) => 71.92/9.80 (( 71.92/9.80 (cartprodmempair) => 71.92/9.80 (( 71.92/9.80 (setunionE2) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton1) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton2) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton) => 71.92/9.80 (( 71.92/9.80 (singletonprop) => 71.92/9.80 (( 71.92/9.80 (ex1E1) => 71.92/9.80 (( 71.92/9.80 (ex1I) => 71.92/9.80 (( 71.92/9.80 (ex1I2) => 71.92/9.80 (( 71.92/9.80 (singletonsuniq) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL1) => 71.92/9.80 (( 71.92/9.80 (kfstsingleton) => 71.92/9.80 (( 71.92/9.80 (theprop) => 71.92/9.80 (( 71.92/9.80 (kfstpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodfstin) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL2) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR11) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR12) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR1) => 71.92/9.80 (( 71.92/9.80 (upairequniteq) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR2) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR) => 71.92/9.80 (( 71.92/9.80 (ksndsingleton) => 71.92/9.80 (( 71.92/9.80 (ksndpairEq) => 71.92/9.80 (( 71.92/9.80 (kpairsurjEq) => 71.92/9.80 (( 71.92/9.80 (cartprodsndin) => 71.92/9.80 (( 71.92/9.80 (cartprodpairmemEL) => 71.92/9.80 (( 71.92/9.80 (cartprodpairmemER) => 71.92/9.80 (( 71.92/9.80 (cartprodmempaircEq) => 71.92/9.80 (( 71.92/9.80 (cartprodfstpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodsndpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodpairsurjEq) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrI) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrSub) => 71.92/9.80 (( 71.92/9.80 (setOfPairsIsBReln) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrERa) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrEL1) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrEL2) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrER) => 71.92/9.80 (( 71.92/9.80 (funcImageSingleton) => 71.92/9.80 (( 71.92/9.80 (apProp) => 71.92/9.80 (( 71.92/9.80 (app) => 71.92/9.80 (( 71.92/9.80 (infuncsetfunc) => 71.92/9.80 (( 71.92/9.80 (ap2p) => 71.92/9.80 (( 71.92/9.80 (funcinfuncset) => 71.92/9.80 (( 71.92/9.80 (lamProp) => 71.92/9.80 (( 71.92/9.80 (lamp) => 71.92/9.80 (( 71.92/9.80 (lam2p) => 71.92/9.80 (( 71.92/9.80 (brelnall1) => 71.92/9.80 (( 71.92/9.80 (brelnall2) => 71.92/9.80 (( 71.92/9.80 (ex1E2) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp1) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp3) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp2) => 71.92/9.80 (( 71.92/9.80 (funcextLem) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp4) => 71.92/9.80 (( 71.92/9.80 (subbreln) => 71.92/9.80 (( 71.92/9.80 (eqbreln) => 71.92/9.80 (( 71.92/9.80 (funcext) => 71.92/9.80 (( 71.92/9.80 (funcext2) => 71.92/9.80 (( 71.92/9.80 (ap2apEq1) => 71.92/9.80 (( 71.92/9.80 (ap2apEq2) => 71.92/9.80 (( 71.92/9.80 (beta1) => 71.92/9.80 (( 71.92/9.80 (eta1) => 71.92/9.80 (( 71.92/9.80 (lam2lamEq) => 71.92/9.80 (( 71.92/9.80 (beta2) => 71.92/9.80 (( 71.92/9.80 (eta2) => 71.92/9.80 (( 71.92/9.80 (iffalseProp1) => 71.92/9.80 (( 71.92/9.80 (iffalseProp2) => 71.92/9.80 (( 71.92/9.80 (iftrueProp1) => 71.92/9.80 (( 71.92/9.80 (iftrueProp2) => 71.92/9.80 (( 71.92/9.80 (ifSingleton) => 71.92/9.80 (( 71.92/9.80 (ifp) => 71.92/9.80 (( 71.92/9.80 (theeq) => 71.92/9.80 (( 71.92/9.80 (iftrue) => 71.92/9.80 (( 71.92/9.80 (iffalse) => 71.92/9.80 (( 71.92/9.80 (iftrueorfalse) => 71.92/9.80 (( 71.92/9.80 (binintersectT_lem) => 71.92/9.80 (( 71.92/9.80 (binunionT_lem) => 71.92/9.80 (( 71.92/9.80 (powersetT_lem) => 71.92/9.80 (( 71.92/9.80 (setminusT_lem) => 71.92/9.80 (( 71.92/9.80 (complementT_lem) => 71.92/9.80 (( 71.92/9.80 (setextT) => 71.92/9.80 (( 71.92/9.80 (subsetTI) => 71.92/9.80 (( 71.92/9.80 (powersetTI1) => 71.92/9.80 (( 71.92/9.80 (powersetTE1) => 71.92/9.80 (( 71.92/9.80 (complementTI1) => 71.92/9.80 (( 71.92/9.80 (complementTE1) => 71.92/9.80 (( 71.92/9.80 (binintersectTELcontra) => 71.92/9.80 (( 71.92/9.80 (binintersectTERcontra) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT1) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT2) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT3) => 71.92/9.80 (( 71.92/9.80 (doubleComplementI1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementE1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementSub1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementSub2) => 71.92/9.80 (( 71.92/9.80 (doubleComplementEq) => 71.92/9.80 (( 71.92/9.80 (complementTnotintersectT) => 71.92/9.80 (( 71.92/9.80 (complementImpComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (complementSubsetComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (complementInPowersetComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (contraSubsetComplement) => 71.92/9.80 (( 71.92/9.80 (complementTcontraSubset) => 71.92/9.80 (( 71.92/9.80 (binunionTILcontra) => 71.92/9.80 (( 71.92/9.80 (binunionTIRcontra) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInUnion) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInUnion2) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInIntersectUnions) => 71.92/9.80 (( 71.92/9.80 (intersectInPowersetIntersectUnions) => 71.92/9.80 (( 71.92/9.80 (inComplementUnionImpNotIn1) => 71.92/9.80 (( 71.92/9.80 (inComplementUnionImpInComplement1) => 71.92/9.80 (( 71.92/9.80 (binunionTE) => 71.92/9.80 (( 71.92/9.80 (binunionTEcontra) => 71.92/9.80 (( 71.92/9.80 (demorgan2a1) => 71.92/9.80 (( 71.92/9.80 (complementUnionInPowersetComplement) => 71.92/9.80 (( 71.92/9.80 (demorgan2a2) => 71.92/9.80 (( 71.92/9.80 (demorgan1a) => 71.92/9.80 (( 71.92/9.80 (demorgan1b) => 71.92/9.80 (( 71.92/9.80 (demorgan1) => 71.92/9.80 (( 71.92/9.80 (demorgan2a) => 71.92/9.80 (( 71.92/9.80 (demorgan2b2) => 71.92/9.80 (( 71.92/9.80 (demorgan2b) => 71.92/9.80 (( 71.92/9.80 (demorgan2) => 71.92/9.80 (( 71.92/9.80 (woz13rule0) => 71.92/9.80 (( 71.92/9.80 (woz13rule1) => 71.92/9.80 (( 71.92/9.80 (woz13rule2) => 71.92/9.80 (( 71.92/9.80 (woz13rule3) => 71.92/9.80 (( 71.92/9.80 (woz13rule4) => 71.92/9.80 (( 71.92/9.80 (woz1_1) => 71.92/9.80 (( 71.92/9.80 (woz1_2) => 71.92/9.80 (( 71.92/9.80 (woz1_3) => 71.92/9.80 (( 71.92/9.80 (woz1_4) => 71.92/9.80 (( 71.92/9.80 (woz1_5) => 71.92/9.80 (( 71.92/9.80 (breln1all2) => 71.92/9.80 (( 71.92/9.80 (breln1SetBreln1) => 71.92/9.80 (( 71.92/9.80 (choice2fnsingleton) => 71.92/9.80 (( 71.92/9.80 (setOfPairsIsBReln1) => 71.92/9.80 (( 71.92/9.80 (breln1all1) => 71.92/9.80 (( 71.92/9.80 (subbreln1) => 71.92/9.80 (( 71.92/9.80 (eqbreln1) => 71.92/9.80 (( 71.92/9.80 (breln1invprop) => 71.92/9.80 (( 71.92/9.80 (breln1invI) => 71.92/9.80 (( 71.92/9.80 (breln1invE) => 71.92/9.80 (( 71.92/9.80 (breln1compprop) => 71.92/9.80 (( 71.92/9.80 (breln1compI) => 71.92/9.80 (( 71.92/9.80 (breln1compE) => 71.92/9.80 (( 71.92/9.80 (breln1compEex) => 71.92/9.80 (( 71.92/9.80 (!!) @ ( 71.92/9.80 (('#B') @ ( 71.92/9.80 !!) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#S') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#S') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 =>))) @ 71.92/9.80 breln1)))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 !!))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#S') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#S') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 =>))) @ 71.92/9.80 breln1)))))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#C') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 breln1)))) @ 71.92/9.80 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl699])). 71.92/9.80 thf(zip_derived_cl731, plain, 71.92/9.80 (~ (((exuEu) => 71.92/9.80 (((descr__Cong) => 71.92/9.80 (((dsetconstr__Cong) => 71.92/9.80 (((subsetI1) => 71.92/9.80 (((eqimpsubset2) => 71.92/9.80 (((eqimpsubset1) => 71.92/9.80 (((subsetI2) => 71.92/9.80 (((emptysetsubset) => 71.92/9.80 (((subsetE) => 71.92/9.80 (((subsetE2) => 71.92/9.80 (((notsubsetI) => 71.92/9.80 (((notequalI1) => 71.92/9.80 (((notequalI2) => 71.92/9.80 (((subsetRefl) => 71.92/9.80 (((subsetTrans) => 71.92/9.80 (((setadjoinSub) => 71.92/9.80 (((setadjoinSub2) => 71.92/9.80 (((subset2powerset) => 71.92/9.80 (((setextsub) => 71.92/9.80 (((subsetemptysetimpeq) => 71.92/9.80 (((powersetI1) => 71.92/9.80 (((powersetE1) => 71.92/9.80 (((inPowerset) => 71.92/9.80 (((powersetsubset) => 71.92/9.80 (((sepInPowerset) => 71.92/9.80 (((sepSubset) => 71.92/9.80 (((binunionIL) => 71.92/9.80 (((upairset2IR) => 71.92/9.80 (((binunionIR) => 71.92/9.80 (((binunionEcases) => 71.92/9.80 (( 71.92/9.80 (binunionE) => 71.92/9.80 (( 71.92/9.80 (binunionLsub) => 71.92/9.80 (( 71.92/9.80 (binunionRsub) => 71.92/9.80 (( 71.92/9.80 (binintersectI) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset5) => 71.92/9.80 (( 71.92/9.80 (binintersectEL) => 71.92/9.80 (( 71.92/9.80 (binintersectLsub) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset2) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset3) => 71.92/9.80 (( 71.92/9.80 (binintersectER) => 71.92/9.80 (( 71.92/9.80 (disjointsetsI1) => 71.92/9.80 (( 71.92/9.80 (binintersectRsub) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset4) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset1) => 71.92/9.80 (( 71.92/9.80 (bs114d) => 71.92/9.80 (( 71.92/9.80 (setminusI) => 71.92/9.80 (( 71.92/9.80 (setminusEL) => 71.92/9.80 (( 71.92/9.80 (setminusER) => 71.92/9.80 (( 71.92/9.80 (setminusSubset2) => 71.92/9.80 (( 71.92/9.80 (setminusERneg) => 71.92/9.80 (( 71.92/9.80 (setminusELneg) => 71.92/9.80 (( 71.92/9.80 (setminusILneg) => 71.92/9.80 (( 71.92/9.80 (setminusIRneg) => 71.92/9.80 (( 71.92/9.80 (setminusLsub) => 71.92/9.80 (( 71.92/9.80 (setminusSubset1) => 71.92/9.80 (( 71.92/9.80 (symdiffE) => 71.92/9.80 (( 71.92/9.80 (symdiffI1) => 71.92/9.80 (( 71.92/9.80 (symdiffI2) => 71.92/9.80 (( 71.92/9.80 (symdiffIneg1) => 71.92/9.80 (( 71.92/9.80 (symdiffIneg2) => 71.92/9.80 (( 71.92/9.80 (secondinupair) => 71.92/9.80 (( 71.92/9.80 (setukpairIL) => 71.92/9.80 (( 71.92/9.80 (setukpairIR) => 71.92/9.80 (( 71.92/9.80 (kpairiskpair) => 71.92/9.80 (( 71.92/9.80 (kpairp) => 71.92/9.80 (( 71.92/9.80 (singletonsubset) => 71.92/9.80 (( 71.92/9.80 (singletoninpowerset) => 71.92/9.80 (( 71.92/9.80 (singletoninpowunion) => 71.92/9.80 (( 71.92/9.80 (upairset2E) => 71.92/9.80 (( 71.92/9.80 (upairsubunion) => 71.92/9.80 (( 71.92/9.80 (upairinpowunion) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem1) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem2) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem3) => 71.92/9.80 (( 71.92/9.80 (cartprodpairin) => 71.92/9.80 (( 71.92/9.80 (cartprodmempair1) => 71.92/9.80 (( 71.92/9.80 (cartprodmempair) => 71.92/9.80 (( 71.92/9.80 (setunionE2) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton1) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton2) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton) => 71.92/9.80 (( 71.92/9.80 (singletonprop) => 71.92/9.80 (( 71.92/9.80 (ex1E1) => 71.92/9.80 (( 71.92/9.80 (ex1I) => 71.92/9.80 (( 71.92/9.80 (ex1I2) => 71.92/9.80 (( 71.92/9.80 (singletonsuniq) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL1) => 71.92/9.80 (( 71.92/9.80 (kfstsingleton) => 71.92/9.80 (( 71.92/9.80 (theprop) => 71.92/9.80 (( 71.92/9.80 (kfstpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodfstin) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL2) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR11) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR12) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR1) => 71.92/9.80 (( 71.92/9.80 (upairequniteq) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR2) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR) => 71.92/9.80 (( 71.92/9.80 (ksndsingleton) => 71.92/9.80 (( 71.92/9.80 (ksndpairEq) => 71.92/9.80 (( 71.92/9.80 (kpairsurjEq) => 71.92/9.80 (( 71.92/9.80 (cartprodsndin) => 71.92/9.80 (( 71.92/9.80 (cartprodpairmemEL) => 71.92/9.80 (( 71.92/9.80 (cartprodpairmemER) => 71.92/9.80 (( 71.92/9.80 (cartprodmempaircEq) => 71.92/9.80 (( 71.92/9.80 (cartprodfstpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodsndpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodpairsurjEq) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrI) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrSub) => 71.92/9.80 (( 71.92/9.80 (setOfPairsIsBReln) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrERa) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrEL1) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrEL2) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrER) => 71.92/9.80 (( 71.92/9.80 (funcImageSingleton) => 71.92/9.80 (( 71.92/9.80 (apProp) => 71.92/9.80 (( 71.92/9.80 (app) => 71.92/9.80 (( 71.92/9.80 (infuncsetfunc) => 71.92/9.80 (( 71.92/9.80 (ap2p) => 71.92/9.80 (( 71.92/9.80 (funcinfuncset) => 71.92/9.80 (( 71.92/9.80 (lamProp) => 71.92/9.80 (( 71.92/9.80 (lamp) => 71.92/9.80 (( 71.92/9.80 (lam2p) => 71.92/9.80 (( 71.92/9.80 (brelnall1) => 71.92/9.80 (( 71.92/9.80 (brelnall2) => 71.92/9.80 (( 71.92/9.80 (ex1E2) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp1) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp3) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp2) => 71.92/9.80 (( 71.92/9.80 (funcextLem) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp4) => 71.92/9.80 (( 71.92/9.80 (subbreln) => 71.92/9.80 (( 71.92/9.80 (eqbreln) => 71.92/9.80 (( 71.92/9.80 (funcext) => 71.92/9.80 (( 71.92/9.80 (funcext2) => 71.92/9.80 (( 71.92/9.80 (ap2apEq1) => 71.92/9.80 (( 71.92/9.80 (ap2apEq2) => 71.92/9.80 (( 71.92/9.80 (beta1) => 71.92/9.80 (( 71.92/9.80 (eta1) => 71.92/9.80 (( 71.92/9.80 (lam2lamEq) => 71.92/9.80 (( 71.92/9.80 (beta2) => 71.92/9.80 (( 71.92/9.80 (eta2) => 71.92/9.80 (( 71.92/9.80 (iffalseProp1) => 71.92/9.80 (( 71.92/9.80 (iffalseProp2) => 71.92/9.80 (( 71.92/9.80 (iftrueProp1) => 71.92/9.80 (( 71.92/9.80 (iftrueProp2) => 71.92/9.80 (( 71.92/9.80 (ifSingleton) => 71.92/9.80 (( 71.92/9.80 (ifp) => 71.92/9.80 (( 71.92/9.80 (theeq) => 71.92/9.80 (( 71.92/9.80 (iftrue) => 71.92/9.80 (( 71.92/9.80 (iffalse) => 71.92/9.80 (( 71.92/9.80 (iftrueorfalse) => 71.92/9.80 (( 71.92/9.80 (binintersectT_lem) => 71.92/9.80 (( 71.92/9.80 (binunionT_lem) => 71.92/9.80 (( 71.92/9.80 (powersetT_lem) => 71.92/9.80 (( 71.92/9.80 (setminusT_lem) => 71.92/9.80 (( 71.92/9.80 (complementT_lem) => 71.92/9.80 (( 71.92/9.80 (setextT) => 71.92/9.80 (( 71.92/9.80 (subsetTI) => 71.92/9.80 (( 71.92/9.80 (powersetTI1) => 71.92/9.80 (( 71.92/9.80 (powersetTE1) => 71.92/9.80 (( 71.92/9.80 (complementTI1) => 71.92/9.80 (( 71.92/9.80 (complementTE1) => 71.92/9.80 (( 71.92/9.80 (binintersectTELcontra) => 71.92/9.80 (( 71.92/9.80 (binintersectTERcontra) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT1) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT2) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT3) => 71.92/9.80 (( 71.92/9.80 (doubleComplementI1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementE1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementSub1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementSub2) => 71.92/9.80 (( 71.92/9.80 (doubleComplementEq) => 71.92/9.80 (( 71.92/9.80 (complementTnotintersectT) => 71.92/9.80 (( 71.92/9.80 (complementImpComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (complementSubsetComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (complementInPowersetComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (contraSubsetComplement) => 71.92/9.80 (( 71.92/9.80 (complementTcontraSubset) => 71.92/9.80 (( 71.92/9.80 (binunionTILcontra) => 71.92/9.80 (( 71.92/9.80 (binunionTIRcontra) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInUnion) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInUnion2) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInIntersectUnions) => 71.92/9.80 (( 71.92/9.80 (intersectInPowersetIntersectUnions) => 71.92/9.80 (( 71.92/9.80 (inComplementUnionImpNotIn1) => 71.92/9.80 (( 71.92/9.80 (inComplementUnionImpInComplement1) => 71.92/9.80 (( 71.92/9.80 (binunionTE) => 71.92/9.80 (( 71.92/9.80 (binunionTEcontra) => 71.92/9.80 (( 71.92/9.80 (demorgan2a1) => 71.92/9.80 (( 71.92/9.80 (complementUnionInPowersetComplement) => 71.92/9.80 (( 71.92/9.80 (demorgan2a2) => 71.92/9.80 (( 71.92/9.80 (demorgan1a) => 71.92/9.80 (( 71.92/9.80 (demorgan1b) => 71.92/9.80 (( 71.92/9.80 (demorgan1) => 71.92/9.80 (( 71.92/9.80 (demorgan2a) => 71.92/9.80 (( 71.92/9.80 (demorgan2b2) => 71.92/9.80 (( 71.92/9.80 (demorgan2b) => 71.92/9.80 (( 71.92/9.80 (demorgan2) => 71.92/9.80 (( 71.92/9.80 (woz13rule0) => 71.92/9.80 (( 71.92/9.80 (woz13rule1) => 71.92/9.80 (( 71.92/9.80 (woz13rule2) => 71.92/9.80 (( 71.92/9.80 (woz13rule3) => 71.92/9.80 (( 71.92/9.80 (woz13rule4) => 71.92/9.80 (( 71.92/9.80 (woz1_1) => 71.92/9.80 (( 71.92/9.80 (woz1_2) => 71.92/9.80 (( 71.92/9.80 (woz1_3) => 71.92/9.80 (( 71.92/9.80 (woz1_4) => 71.92/9.80 (( 71.92/9.80 (woz1_5) => 71.92/9.80 (( 71.92/9.80 (breln1all2) => 71.92/9.80 (( 71.92/9.80 (breln1SetBreln1) => 71.92/9.80 (( 71.92/9.80 (choice2fnsingleton) => 71.92/9.80 (( 71.92/9.80 (setOfPairsIsBReln1) => 71.92/9.80 (( 71.92/9.80 (breln1all1) => 71.92/9.80 (( 71.92/9.80 (subbreln1) => 71.92/9.80 (( 71.92/9.80 (eqbreln1) => 71.92/9.80 (( 71.92/9.80 (breln1invprop) => 71.92/9.80 (( 71.92/9.80 (breln1invI) => 71.92/9.80 (( 71.92/9.80 (breln1invE) => 71.92/9.80 (( 71.92/9.80 (breln1compprop) => 71.92/9.80 (( 71.92/9.80 (breln1compI) => 71.92/9.80 (( 71.92/9.80 (breln1compE) => 71.92/9.80 (( 71.92/9.80 (breln1compEex) => 71.92/9.80 (( 71.92/9.80 (!!) @ ( 71.92/9.80 (('#B') @ ( 71.92/9.80 !!) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#S') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#S') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 =>))) @ 71.92/9.80 breln1)))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 !!))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#S') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#S') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 =>))) @ 71.92/9.80 breln1)))))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#C') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 breln1)))) @ 71.92/9.80 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl714])). 71.92/9.80 thf(zip_derived_cl749, plain, 71.92/9.80 (~ (((descr__Cong) => 71.92/9.80 (((dsetconstr__Cong) => 71.92/9.80 (((subsetI1) => 71.92/9.80 (((eqimpsubset2) => 71.92/9.80 (((eqimpsubset1) => 71.92/9.80 (((subsetI2) => 71.92/9.80 (((emptysetsubset) => 71.92/9.80 (((subsetE) => 71.92/9.80 (((subsetE2) => 71.92/9.80 (((notsubsetI) => 71.92/9.80 (((notequalI1) => 71.92/9.80 (((notequalI2) => 71.92/9.80 (((subsetRefl) => 71.92/9.80 (((subsetTrans) => 71.92/9.80 (((setadjoinSub) => 71.92/9.80 (((setadjoinSub2) => 71.92/9.80 (((subset2powerset) => 71.92/9.80 (((setextsub) => 71.92/9.80 (((subsetemptysetimpeq) => 71.92/9.80 (((powersetI1) => 71.92/9.80 (((powersetE1) => 71.92/9.80 (((inPowerset) => 71.92/9.80 (((powersetsubset) => 71.92/9.80 (((sepInPowerset) => 71.92/9.80 (((sepSubset) => 71.92/9.80 (((binunionIL) => 71.92/9.80 (((upairset2IR) => 71.92/9.80 (((binunionIR) => 71.92/9.80 (((binunionEcases) => 71.92/9.80 (((binunionE) => 71.92/9.80 (( 71.92/9.80 (binunionLsub) => 71.92/9.80 (( 71.92/9.80 (binunionRsub) => 71.92/9.80 (( 71.92/9.80 (binintersectI) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset5) => 71.92/9.80 (( 71.92/9.80 (binintersectEL) => 71.92/9.80 (( 71.92/9.80 (binintersectLsub) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset2) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset3) => 71.92/9.80 (( 71.92/9.80 (binintersectER) => 71.92/9.80 (( 71.92/9.80 (disjointsetsI1) => 71.92/9.80 (( 71.92/9.80 (binintersectRsub) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset4) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset1) => 71.92/9.80 (( 71.92/9.80 (bs114d) => 71.92/9.80 (( 71.92/9.80 (setminusI) => 71.92/9.80 (( 71.92/9.80 (setminusEL) => 71.92/9.80 (( 71.92/9.80 (setminusER) => 71.92/9.80 (( 71.92/9.80 (setminusSubset2) => 71.92/9.80 (( 71.92/9.80 (setminusERneg) => 71.92/9.80 (( 71.92/9.80 (setminusELneg) => 71.92/9.80 (( 71.92/9.80 (setminusILneg) => 71.92/9.80 (( 71.92/9.80 (setminusIRneg) => 71.92/9.80 (( 71.92/9.80 (setminusLsub) => 71.92/9.80 (( 71.92/9.80 (setminusSubset1) => 71.92/9.80 (( 71.92/9.80 (symdiffE) => 71.92/9.80 (( 71.92/9.80 (symdiffI1) => 71.92/9.80 (( 71.92/9.80 (symdiffI2) => 71.92/9.80 (( 71.92/9.80 (symdiffIneg1) => 71.92/9.80 (( 71.92/9.80 (symdiffIneg2) => 71.92/9.80 (( 71.92/9.80 (secondinupair) => 71.92/9.80 (( 71.92/9.80 (setukpairIL) => 71.92/9.80 (( 71.92/9.80 (setukpairIR) => 71.92/9.80 (( 71.92/9.80 (kpairiskpair) => 71.92/9.80 (( 71.92/9.80 (kpairp) => 71.92/9.80 (( 71.92/9.80 (singletonsubset) => 71.92/9.80 (( 71.92/9.80 (singletoninpowerset) => 71.92/9.80 (( 71.92/9.80 (singletoninpowunion) => 71.92/9.80 (( 71.92/9.80 (upairset2E) => 71.92/9.80 (( 71.92/9.80 (upairsubunion) => 71.92/9.80 (( 71.92/9.80 (upairinpowunion) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem1) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem2) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem3) => 71.92/9.80 (( 71.92/9.80 (cartprodpairin) => 71.92/9.80 (( 71.92/9.80 (cartprodmempair1) => 71.92/9.80 (( 71.92/9.80 (cartprodmempair) => 71.92/9.80 (( 71.92/9.80 (setunionE2) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton1) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton2) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton) => 71.92/9.80 (( 71.92/9.80 (singletonprop) => 71.92/9.80 (( 71.92/9.80 (ex1E1) => 71.92/9.80 (( 71.92/9.80 (ex1I) => 71.92/9.80 (( 71.92/9.80 (ex1I2) => 71.92/9.80 (( 71.92/9.80 (singletonsuniq) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL1) => 71.92/9.80 (( 71.92/9.80 (kfstsingleton) => 71.92/9.80 (( 71.92/9.80 (theprop) => 71.92/9.80 (( 71.92/9.80 (kfstpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodfstin) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL2) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR11) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR12) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR1) => 71.92/9.80 (( 71.92/9.80 (upairequniteq) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR2) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR) => 71.92/9.80 (( 71.92/9.80 (ksndsingleton) => 71.92/9.80 (( 71.92/9.80 (ksndpairEq) => 71.92/9.80 (( 71.92/9.80 (kpairsurjEq) => 71.92/9.80 (( 71.92/9.80 (cartprodsndin) => 71.92/9.80 (( 71.92/9.80 (cartprodpairmemEL) => 71.92/9.80 (( 71.92/9.80 (cartprodpairmemER) => 71.92/9.80 (( 71.92/9.80 (cartprodmempaircEq) => 71.92/9.80 (( 71.92/9.80 (cartprodfstpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodsndpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodpairsurjEq) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrI) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrSub) => 71.92/9.80 (( 71.92/9.80 (setOfPairsIsBReln) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrERa) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrEL1) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrEL2) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrER) => 71.92/9.80 (( 71.92/9.80 (funcImageSingleton) => 71.92/9.80 (( 71.92/9.80 (apProp) => 71.92/9.80 (( 71.92/9.80 (app) => 71.92/9.80 (( 71.92/9.80 (infuncsetfunc) => 71.92/9.80 (( 71.92/9.80 (ap2p) => 71.92/9.80 (( 71.92/9.80 (funcinfuncset) => 71.92/9.80 (( 71.92/9.80 (lamProp) => 71.92/9.80 (( 71.92/9.80 (lamp) => 71.92/9.80 (( 71.92/9.80 (lam2p) => 71.92/9.80 (( 71.92/9.80 (brelnall1) => 71.92/9.80 (( 71.92/9.80 (brelnall2) => 71.92/9.80 (( 71.92/9.80 (ex1E2) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp1) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp3) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp2) => 71.92/9.80 (( 71.92/9.80 (funcextLem) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp4) => 71.92/9.80 (( 71.92/9.80 (subbreln) => 71.92/9.80 (( 71.92/9.80 (eqbreln) => 71.92/9.80 (( 71.92/9.80 (funcext) => 71.92/9.80 (( 71.92/9.80 (funcext2) => 71.92/9.80 (( 71.92/9.80 (ap2apEq1) => 71.92/9.80 (( 71.92/9.80 (ap2apEq2) => 71.92/9.80 (( 71.92/9.80 (beta1) => 71.92/9.80 (( 71.92/9.80 (eta1) => 71.92/9.80 (( 71.92/9.80 (lam2lamEq) => 71.92/9.80 (( 71.92/9.80 (beta2) => 71.92/9.80 (( 71.92/9.80 (eta2) => 71.92/9.80 (( 71.92/9.80 (iffalseProp1) => 71.92/9.80 (( 71.92/9.80 (iffalseProp2) => 71.92/9.80 (( 71.92/9.80 (iftrueProp1) => 71.92/9.80 (( 71.92/9.80 (iftrueProp2) => 71.92/9.80 (( 71.92/9.80 (ifSingleton) => 71.92/9.80 (( 71.92/9.80 (ifp) => 71.92/9.80 (( 71.92/9.80 (theeq) => 71.92/9.80 (( 71.92/9.80 (iftrue) => 71.92/9.80 (( 71.92/9.80 (iffalse) => 71.92/9.80 (( 71.92/9.80 (iftrueorfalse) => 71.92/9.80 (( 71.92/9.80 (binintersectT_lem) => 71.92/9.80 (( 71.92/9.80 (binunionT_lem) => 71.92/9.80 (( 71.92/9.80 (powersetT_lem) => 71.92/9.80 (( 71.92/9.80 (setminusT_lem) => 71.92/9.80 (( 71.92/9.80 (complementT_lem) => 71.92/9.80 (( 71.92/9.80 (setextT) => 71.92/9.80 (( 71.92/9.80 (subsetTI) => 71.92/9.80 (( 71.92/9.80 (powersetTI1) => 71.92/9.80 (( 71.92/9.80 (powersetTE1) => 71.92/9.80 (( 71.92/9.80 (complementTI1) => 71.92/9.80 (( 71.92/9.80 (complementTE1) => 71.92/9.80 (( 71.92/9.80 (binintersectTELcontra) => 71.92/9.80 (( 71.92/9.80 (binintersectTERcontra) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT1) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT2) => 71.92/9.80 (( 71.92/9.80 (contrasubsetT3) => 71.92/9.80 (( 71.92/9.80 (doubleComplementI1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementE1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementSub1) => 71.92/9.80 (( 71.92/9.80 (doubleComplementSub2) => 71.92/9.80 (( 71.92/9.80 (doubleComplementEq) => 71.92/9.80 (( 71.92/9.80 (complementTnotintersectT) => 71.92/9.80 (( 71.92/9.80 (complementImpComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (complementSubsetComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (complementInPowersetComplementIntersect) => 71.92/9.80 (( 71.92/9.80 (contraSubsetComplement) => 71.92/9.80 (( 71.92/9.80 (complementTcontraSubset) => 71.92/9.80 (( 71.92/9.80 (binunionTILcontra) => 71.92/9.80 (( 71.92/9.80 (binunionTIRcontra) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInUnion) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInUnion2) => 71.92/9.80 (( 71.92/9.80 (inIntersectImpInIntersectUnions) => 71.92/9.80 (( 71.92/9.80 (intersectInPowersetIntersectUnions) => 71.92/9.80 (( 71.92/9.80 (inComplementUnionImpNotIn1) => 71.92/9.80 (( 71.92/9.80 (inComplementUnionImpInComplement1) => 71.92/9.80 (( 71.92/9.80 (binunionTE) => 71.92/9.80 (( 71.92/9.80 (binunionTEcontra) => 71.92/9.80 (( 71.92/9.80 (demorgan2a1) => 71.92/9.80 (( 71.92/9.80 (complementUnionInPowersetComplement) => 71.92/9.80 (( 71.92/9.80 (demorgan2a2) => 71.92/9.80 (( 71.92/9.80 (demorgan1a) => 71.92/9.80 (( 71.92/9.80 (demorgan1b) => 71.92/9.80 (( 71.92/9.80 (demorgan1) => 71.92/9.80 (( 71.92/9.80 (demorgan2a) => 71.92/9.80 (( 71.92/9.80 (demorgan2b2) => 71.92/9.80 (( 71.92/9.80 (demorgan2b) => 71.92/9.80 (( 71.92/9.80 (demorgan2) => 71.92/9.80 (( 71.92/9.80 (woz13rule0) => 71.92/9.80 (( 71.92/9.80 (woz13rule1) => 71.92/9.80 (( 71.92/9.80 (woz13rule2) => 71.92/9.80 (( 71.92/9.80 (woz13rule3) => 71.92/9.80 (( 71.92/9.80 (woz13rule4) => 71.92/9.80 (( 71.92/9.80 (woz1_1) => 71.92/9.80 (( 71.92/9.80 (woz1_2) => 71.92/9.80 (( 71.92/9.80 (woz1_3) => 71.92/9.80 (( 71.92/9.80 (woz1_4) => 71.92/9.80 (( 71.92/9.80 (woz1_5) => 71.92/9.80 (( 71.92/9.80 (breln1all2) => 71.92/9.80 (( 71.92/9.80 (breln1SetBreln1) => 71.92/9.80 (( 71.92/9.80 (choice2fnsingleton) => 71.92/9.80 (( 71.92/9.80 (setOfPairsIsBReln1) => 71.92/9.80 (( 71.92/9.80 (breln1all1) => 71.92/9.80 (( 71.92/9.80 (subbreln1) => 71.92/9.80 (( 71.92/9.80 (eqbreln1) => 71.92/9.80 (( 71.92/9.80 (breln1invprop) => 71.92/9.80 (( 71.92/9.80 (breln1invI) => 71.92/9.80 (( 71.92/9.80 (breln1invE) => 71.92/9.80 (( 71.92/9.80 (breln1compprop) => 71.92/9.80 (( 71.92/9.80 (breln1compI) => 71.92/9.80 (( 71.92/9.80 (breln1compE) => 71.92/9.80 (( 71.92/9.80 (breln1compEex) => 71.92/9.80 (( 71.92/9.80 (!!) @ ( 71.92/9.80 (('#B') @ ( 71.92/9.80 !!) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#S') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#S') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 =>))) @ 71.92/9.80 breln1)))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 !!))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#S') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#S') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 =>))) @ 71.92/9.80 breln1)))))) @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#C') @ ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 ( 71.92/9.80 ( 71.92/9.80 ('#B') @ ( 71.92/9.80 '#B') @ 71.92/9.80 breln1)))) @ 71.92/9.80 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl731])). 71.92/9.80 thf(zip_derived_cl769, plain, 71.92/9.80 (~ (((dsetconstr__Cong) => 71.92/9.80 (((subsetI1) => 71.92/9.80 (((eqimpsubset2) => 71.92/9.80 (((eqimpsubset1) => 71.92/9.80 (((subsetI2) => 71.92/9.80 (((emptysetsubset) => 71.92/9.80 (((subsetE) => 71.92/9.80 (((subsetE2) => 71.92/9.80 (((notsubsetI) => 71.92/9.80 (((notequalI1) => 71.92/9.80 (((notequalI2) => 71.92/9.80 (((subsetRefl) => 71.92/9.80 (((subsetTrans) => 71.92/9.80 (((setadjoinSub) => 71.92/9.80 (((setadjoinSub2) => 71.92/9.80 (((subset2powerset) => 71.92/9.80 (((setextsub) => 71.92/9.80 (((subsetemptysetimpeq) => 71.92/9.80 (((powersetI1) => 71.92/9.80 (((powersetE1) => 71.92/9.80 (((inPowerset) => 71.92/9.80 (((powersetsubset) => 71.92/9.80 (((sepInPowerset) => 71.92/9.80 (((sepSubset) => 71.92/9.80 (((binunionIL) => 71.92/9.80 (((upairset2IR) => 71.92/9.80 (((binunionIR) => 71.92/9.80 (((binunionEcases) => 71.92/9.80 (((binunionE) => 71.92/9.80 (((binunionLsub) => 71.92/9.80 (( 71.92/9.80 (binunionRsub) => 71.92/9.80 (( 71.92/9.80 (binintersectI) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset5) => 71.92/9.80 (( 71.92/9.80 (binintersectEL) => 71.92/9.80 (( 71.92/9.80 (binintersectLsub) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset2) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset3) => 71.92/9.80 (( 71.92/9.80 (binintersectER) => 71.92/9.80 (( 71.92/9.80 (disjointsetsI1) => 71.92/9.80 (( 71.92/9.80 (binintersectRsub) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset4) => 71.92/9.80 (( 71.92/9.80 (binintersectSubset1) => 71.92/9.80 (( 71.92/9.80 (bs114d) => 71.92/9.80 (( 71.92/9.80 (setminusI) => 71.92/9.80 (( 71.92/9.80 (setminusEL) => 71.92/9.80 (( 71.92/9.80 (setminusER) => 71.92/9.80 (( 71.92/9.80 (setminusSubset2) => 71.92/9.80 (( 71.92/9.80 (setminusERneg) => 71.92/9.80 (( 71.92/9.80 (setminusELneg) => 71.92/9.80 (( 71.92/9.80 (setminusILneg) => 71.92/9.80 (( 71.92/9.80 (setminusIRneg) => 71.92/9.80 (( 71.92/9.80 (setminusLsub) => 71.92/9.80 (( 71.92/9.80 (setminusSubset1) => 71.92/9.80 (( 71.92/9.80 (symdiffE) => 71.92/9.80 (( 71.92/9.80 (symdiffI1) => 71.92/9.80 (( 71.92/9.80 (symdiffI2) => 71.92/9.80 (( 71.92/9.80 (symdiffIneg1) => 71.92/9.80 (( 71.92/9.80 (symdiffIneg2) => 71.92/9.80 (( 71.92/9.80 (secondinupair) => 71.92/9.80 (( 71.92/9.80 (setukpairIL) => 71.92/9.80 (( 71.92/9.80 (setukpairIR) => 71.92/9.80 (( 71.92/9.80 (kpairiskpair) => 71.92/9.80 (( 71.92/9.80 (kpairp) => 71.92/9.80 (( 71.92/9.80 (singletonsubset) => 71.92/9.80 (( 71.92/9.80 (singletoninpowerset) => 71.92/9.80 (( 71.92/9.80 (singletoninpowunion) => 71.92/9.80 (( 71.92/9.80 (upairset2E) => 71.92/9.80 (( 71.92/9.80 (upairsubunion) => 71.92/9.80 (( 71.92/9.80 (upairinpowunion) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem1) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem2) => 71.92/9.80 (( 71.92/9.80 (ubforcartprodlem3) => 71.92/9.80 (( 71.92/9.80 (cartprodpairin) => 71.92/9.80 (( 71.92/9.80 (cartprodmempair1) => 71.92/9.80 (( 71.92/9.80 (cartprodmempair) => 71.92/9.80 (( 71.92/9.80 (setunionE2) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton1) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton2) => 71.92/9.80 (( 71.92/9.80 (setunionsingleton) => 71.92/9.80 (( 71.92/9.80 (singletonprop) => 71.92/9.80 (( 71.92/9.80 (ex1E1) => 71.92/9.80 (( 71.92/9.80 (ex1I) => 71.92/9.80 (( 71.92/9.80 (ex1I2) => 71.92/9.80 (( 71.92/9.80 (singletonsuniq) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL1) => 71.92/9.80 (( 71.92/9.80 (kfstsingleton) => 71.92/9.80 (( 71.92/9.80 (theprop) => 71.92/9.80 (( 71.92/9.80 (kfstpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodfstin) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL2) => 71.92/9.80 (( 71.92/9.80 (setukpairinjL) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR11) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR12) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR1) => 71.92/9.80 (( 71.92/9.80 (upairequniteq) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR2) => 71.92/9.80 (( 71.92/9.80 (setukpairinjR) => 71.92/9.80 (( 71.92/9.80 (ksndsingleton) => 71.92/9.80 (( 71.92/9.80 (ksndpairEq) => 71.92/9.80 (( 71.92/9.80 (kpairsurjEq) => 71.92/9.80 (( 71.92/9.80 (cartprodsndin) => 71.92/9.80 (( 71.92/9.80 (cartprodpairmemEL) => 71.92/9.80 (( 71.92/9.80 (cartprodpairmemER) => 71.92/9.80 (( 71.92/9.80 (cartprodmempaircEq) => 71.92/9.80 (( 71.92/9.80 (cartprodfstpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodsndpairEq) => 71.92/9.80 (( 71.92/9.80 (cartprodpairsurjEq) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrI) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrSub) => 71.92/9.80 (( 71.92/9.80 (setOfPairsIsBReln) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrERa) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrEL1) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrEL2) => 71.92/9.80 (( 71.92/9.80 (dpsetconstrER) => 71.92/9.80 (( 71.92/9.80 (funcImageSingleton) => 71.92/9.80 (( 71.92/9.80 (apProp) => 71.92/9.80 (( 71.92/9.80 (app) => 71.92/9.80 (( 71.92/9.80 (infuncsetfunc) => 71.92/9.80 (( 71.92/9.80 (ap2p) => 71.92/9.80 (( 71.92/9.80 (funcinfuncset) => 71.92/9.80 (( 71.92/9.80 (lamProp) => 71.92/9.80 (( 71.92/9.80 (lamp) => 71.92/9.80 (( 71.92/9.80 (lam2p) => 71.92/9.80 (( 71.92/9.80 (brelnall1) => 71.92/9.80 (( 71.92/9.80 (brelnall2) => 71.92/9.80 (( 71.92/9.80 (ex1E2) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp1) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp3) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp2) => 71.92/9.80 (( 71.92/9.80 (funcextLem) => 71.92/9.80 (( 71.92/9.80 (funcGraphProp4) => 71.92/9.80 (( 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71.92/9.80 '#B') @ 71.92/9.80 breln1)))) @ 71.92/9.80 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl749])). 71.92/9.80 thf(zip_derived_cl789, plain, 71.92/9.80 (~ (((subsetI1) => 71.92/9.80 (((eqimpsubset2) => 71.92/9.80 (((eqimpsubset1) => 71.92/9.80 (((subsetI2) => 71.92/9.80 (((emptysetsubset) => 71.92/9.80 (((subsetE) => 71.92/9.80 (((subsetE2) => 71.92/9.80 (((notsubsetI) => 71.92/9.80 (((notequalI1) => 71.92/9.80 (((notequalI2) => 71.92/9.80 (((subsetRefl) => 71.92/9.80 (((subsetTrans) => 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=> 71.92/9.81 (( 71.92/9.81 (subsetTI) => 71.92/9.81 (( 71.92/9.81 (powersetTI1) => 71.92/9.81 (( 71.92/9.81 (powersetTE1) => 71.92/9.81 (( 71.92/9.81 (complementTI1) => 71.92/9.81 (( 71.92/9.81 (complementTE1) => 71.92/9.81 (( 71.92/9.81 (binintersectTELcontra) => 71.92/9.81 (( 71.92/9.81 (binintersectTERcontra) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT1) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT2) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT3) => 71.92/9.81 (( 71.92/9.81 (doubleComplementI1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementE1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub2) => 71.92/9.81 (( 71.92/9.81 (doubleComplementEq) => 71.92/9.81 (( 71.92/9.81 (complementTnotintersectT) => 71.92/9.81 (( 71.92/9.81 (complementImpComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementSubsetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementInPowersetComplementIntersect) => 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(( 71.92/9.81 (breln1compE) => 71.92/9.81 (( 71.92/9.81 (breln1compEex) => 71.92/9.81 (( 71.92/9.81 (!!) @ ( 71.92/9.81 (('#B') @ ( 71.92/9.81 !!) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 !!))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#C') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 breln1)))) @ 71.92/9.81 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl789])). 71.92/9.81 thf(zip_derived_cl824, plain, 71.92/9.81 (~ (((eqimpsubset1) => 71.92/9.81 (((subsetI2) => 71.92/9.81 (((emptysetsubset) => 71.92/9.81 (((subsetE) => 71.92/9.81 (((subsetE2) => 71.92/9.81 (((notsubsetI) => 71.92/9.81 (((notequalI1) => 71.92/9.81 (((notequalI2) => 71.92/9.81 (((subsetRefl) => 71.92/9.81 (((subsetTrans) => 71.92/9.81 (((setadjoinSub) => 71.92/9.81 (((setadjoinSub2) => 71.92/9.81 (((subset2powerset) => 71.92/9.81 (((setextsub) => 71.92/9.81 (((subsetemptysetimpeq) => 71.92/9.81 (((powersetI1) => 71.92/9.81 (((powersetE1) => 71.92/9.81 (((inPowerset) => 71.92/9.81 (((powersetsubset) => 71.92/9.81 (((sepInPowerset) => 71.92/9.81 (((sepSubset) => 71.92/9.81 (((binunionIL) => 71.92/9.81 (((upairset2IR) => 71.92/9.81 (((binunionIR) => 71.92/9.81 (((binunionEcases) => 71.92/9.81 (((binunionE) => 71.92/9.81 (((binunionLsub) => 71.92/9.81 (((binunionRsub) => 71.92/9.81 (((binintersectI) => 71.92/9.81 (((binintersectSubset5) => 71.92/9.81 (( 71.92/9.81 (binintersectEL) => 71.92/9.81 (( 71.92/9.81 (binintersectLsub) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset2) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset3) => 71.92/9.81 (( 71.92/9.81 (binintersectER) => 71.92/9.81 (( 71.92/9.81 (disjointsetsI1) => 71.92/9.81 (( 71.92/9.81 (binintersectRsub) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset4) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset1) => 71.92/9.81 (( 71.92/9.81 (bs114d) => 71.92/9.81 (( 71.92/9.81 (setminusI) => 71.92/9.81 (( 71.92/9.81 (setminusEL) => 71.92/9.81 (( 71.92/9.81 (setminusER) => 71.92/9.81 (( 71.92/9.81 (setminusSubset2) => 71.92/9.81 (( 71.92/9.81 (setminusERneg) => 71.92/9.81 (( 71.92/9.81 (setminusELneg) => 71.92/9.81 (( 71.92/9.81 (setminusILneg) => 71.92/9.81 (( 71.92/9.81 (setminusIRneg) => 71.92/9.81 (( 71.92/9.81 (setminusLsub) => 71.92/9.81 (( 71.92/9.81 (setminusSubset1) => 71.92/9.81 (( 71.92/9.81 (symdiffE) => 71.92/9.81 (( 71.92/9.81 (symdiffI1) => 71.92/9.81 (( 71.92/9.81 (symdiffI2) => 71.92/9.81 (( 71.92/9.81 (symdiffIneg1) => 71.92/9.81 (( 71.92/9.81 (symdiffIneg2) => 71.92/9.81 (( 71.92/9.81 (secondinupair) => 71.92/9.81 (( 71.92/9.81 (setukpairIL) => 71.92/9.81 (( 71.92/9.81 (setukpairIR) => 71.92/9.81 (( 71.92/9.81 (kpairiskpair) => 71.92/9.81 (( 71.92/9.81 (kpairp) => 71.92/9.81 (( 71.92/9.81 (singletonsubset) => 71.92/9.81 (( 71.92/9.81 (singletoninpowerset) => 71.92/9.81 (( 71.92/9.81 (singletoninpowunion) => 71.92/9.81 (( 71.92/9.81 (upairset2E) => 71.92/9.81 (( 71.92/9.81 (upairsubunion) => 71.92/9.81 (( 71.92/9.81 (upairinpowunion) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem1) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem2) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem3) => 71.92/9.81 (( 71.92/9.81 (cartprodpairin) => 71.92/9.81 (( 71.92/9.81 (cartprodmempair1) => 71.92/9.81 (( 71.92/9.81 (cartprodmempair) => 71.92/9.81 (( 71.92/9.81 (setunionE2) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton1) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton2) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton) => 71.92/9.81 (( 71.92/9.81 (singletonprop) => 71.92/9.81 (( 71.92/9.81 (ex1E1) => 71.92/9.81 (( 71.92/9.81 (ex1I) => 71.92/9.81 (( 71.92/9.81 (ex1I2) => 71.92/9.81 (( 71.92/9.81 (singletonsuniq) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL1) => 71.92/9.81 (( 71.92/9.81 (kfstsingleton) => 71.92/9.81 (( 71.92/9.81 (theprop) => 71.92/9.81 (( 71.92/9.81 (kfstpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodfstin) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL2) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR11) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR12) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR1) => 71.92/9.81 (( 71.92/9.81 (upairequniteq) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR2) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR) => 71.92/9.81 (( 71.92/9.81 (ksndsingleton) => 71.92/9.81 (( 71.92/9.81 (ksndpairEq) => 71.92/9.81 (( 71.92/9.81 (kpairsurjEq) => 71.92/9.81 (( 71.92/9.81 (cartprodsndin) => 71.92/9.81 (( 71.92/9.81 (cartprodpairmemEL) => 71.92/9.81 (( 71.92/9.81 (cartprodpairmemER) => 71.92/9.81 (( 71.92/9.81 (cartprodmempaircEq) => 71.92/9.81 (( 71.92/9.81 (cartprodfstpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodsndpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodpairsurjEq) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrI) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrSub) => 71.92/9.81 (( 71.92/9.81 (setOfPairsIsBReln) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrERa) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrEL1) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrEL2) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrER) => 71.92/9.81 (( 71.92/9.81 (funcImageSingleton) => 71.92/9.81 (( 71.92/9.81 (apProp) => 71.92/9.81 (( 71.92/9.81 (app) => 71.92/9.81 (( 71.92/9.81 (infuncsetfunc) => 71.92/9.81 (( 71.92/9.81 (ap2p) => 71.92/9.81 (( 71.92/9.81 (funcinfuncset) => 71.92/9.81 (( 71.92/9.81 (lamProp) => 71.92/9.81 (( 71.92/9.81 (lamp) => 71.92/9.81 (( 71.92/9.81 (lam2p) => 71.92/9.81 (( 71.92/9.81 (brelnall1) => 71.92/9.81 (( 71.92/9.81 (brelnall2) => 71.92/9.81 (( 71.92/9.81 (ex1E2) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp1) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp3) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp2) => 71.92/9.81 (( 71.92/9.81 (funcextLem) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp4) => 71.92/9.81 (( 71.92/9.81 (subbreln) => 71.92/9.81 (( 71.92/9.81 (eqbreln) => 71.92/9.81 (( 71.92/9.81 (funcext) => 71.92/9.81 (( 71.92/9.81 (funcext2) => 71.92/9.81 (( 71.92/9.81 (ap2apEq1) => 71.92/9.81 (( 71.92/9.81 (ap2apEq2) => 71.92/9.81 (( 71.92/9.81 (beta1) => 71.92/9.81 (( 71.92/9.81 (eta1) => 71.92/9.81 (( 71.92/9.81 (lam2lamEq) => 71.92/9.81 (( 71.92/9.81 (beta2) => 71.92/9.81 (( 71.92/9.81 (eta2) => 71.92/9.81 (( 71.92/9.81 (iffalseProp1) => 71.92/9.81 (( 71.92/9.81 (iffalseProp2) => 71.92/9.81 (( 71.92/9.81 (iftrueProp1) => 71.92/9.81 (( 71.92/9.81 (iftrueProp2) => 71.92/9.81 (( 71.92/9.81 (ifSingleton) => 71.92/9.81 (( 71.92/9.81 (ifp) => 71.92/9.81 (( 71.92/9.81 (theeq) => 71.92/9.81 (( 71.92/9.81 (iftrue) => 71.92/9.81 (( 71.92/9.81 (iffalse) => 71.92/9.81 (( 71.92/9.81 (iftrueorfalse) => 71.92/9.81 (( 71.92/9.81 (binintersectT_lem) => 71.92/9.81 (( 71.92/9.81 (binunionT_lem) => 71.92/9.81 (( 71.92/9.81 (powersetT_lem) => 71.92/9.81 (( 71.92/9.81 (setminusT_lem) => 71.92/9.81 (( 71.92/9.81 (complementT_lem) => 71.92/9.81 (( 71.92/9.81 (setextT) => 71.92/9.81 (( 71.92/9.81 (subsetTI) => 71.92/9.81 (( 71.92/9.81 (powersetTI1) => 71.92/9.81 (( 71.92/9.81 (powersetTE1) => 71.92/9.81 (( 71.92/9.81 (complementTI1) => 71.92/9.81 (( 71.92/9.81 (complementTE1) => 71.92/9.81 (( 71.92/9.81 (binintersectTELcontra) => 71.92/9.81 (( 71.92/9.81 (binintersectTERcontra) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT1) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT2) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT3) => 71.92/9.81 (( 71.92/9.81 (doubleComplementI1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementE1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub2) => 71.92/9.81 (( 71.92/9.81 (doubleComplementEq) => 71.92/9.81 (( 71.92/9.81 (complementTnotintersectT) => 71.92/9.81 (( 71.92/9.81 (complementImpComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementSubsetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementInPowersetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (contraSubsetComplement) => 71.92/9.81 (( 71.92/9.81 (complementTcontraSubset) => 71.92/9.81 (( 71.92/9.81 (binunionTILcontra) => 71.92/9.81 (( 71.92/9.81 (binunionTIRcontra) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion2) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (intersectInPowersetIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpNotIn1) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpInComplement1) => 71.92/9.81 (( 71.92/9.81 (binunionTE) => 71.92/9.81 (( 71.92/9.81 (binunionTEcontra) => 71.92/9.81 (( 71.92/9.81 (demorgan2a1) => 71.92/9.81 (( 71.92/9.81 (complementUnionInPowersetComplement) => 71.92/9.81 (( 71.92/9.81 (demorgan2a2) => 71.92/9.81 (( 71.92/9.81 (demorgan1a) => 71.92/9.81 (( 71.92/9.81 (demorgan1b) => 71.92/9.81 (( 71.92/9.81 (demorgan1) => 71.92/9.81 (( 71.92/9.81 (demorgan2a) => 71.92/9.81 (( 71.92/9.81 (demorgan2b2) => 71.92/9.81 (( 71.92/9.81 (demorgan2b) => 71.92/9.81 (( 71.92/9.81 (demorgan2) => 71.92/9.81 (( 71.92/9.81 (woz13rule0) => 71.92/9.81 (( 71.92/9.81 (woz13rule1) => 71.92/9.81 (( 71.92/9.81 (woz13rule2) => 71.92/9.81 (( 71.92/9.81 (woz13rule3) => 71.92/9.81 (( 71.92/9.81 (woz13rule4) => 71.92/9.81 (( 71.92/9.81 (woz1_1) => 71.92/9.81 (( 71.92/9.81 (woz1_2) => 71.92/9.81 (( 71.92/9.81 (woz1_3) => 71.92/9.81 (( 71.92/9.81 (woz1_4) => 71.92/9.81 (( 71.92/9.81 (woz1_5) => 71.92/9.81 (( 71.92/9.81 (breln1all2) => 71.92/9.81 (( 71.92/9.81 (breln1SetBreln1) => 71.92/9.81 (( 71.92/9.81 (choice2fnsingleton) => 71.92/9.81 (( 71.92/9.81 (setOfPairsIsBReln1) => 71.92/9.81 (( 71.92/9.81 (breln1all1) => 71.92/9.81 (( 71.92/9.81 (subbreln1) => 71.92/9.81 (( 71.92/9.81 (eqbreln1) => 71.92/9.81 (( 71.92/9.81 (breln1invprop) => 71.92/9.81 (( 71.92/9.81 (breln1invI) => 71.92/9.81 (( 71.92/9.81 (breln1invE) => 71.92/9.81 (( 71.92/9.81 (breln1compprop) => 71.92/9.81 (( 71.92/9.81 (breln1compI) => 71.92/9.81 (( 71.92/9.81 (breln1compE) => 71.92/9.81 (( 71.92/9.81 (breln1compEex) => 71.92/9.81 (( 71.92/9.81 (!!) @ ( 71.92/9.81 (('#B') @ ( 71.92/9.81 !!) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 !!))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#C') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 breln1)))) @ 71.92/9.81 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl807])). 71.92/9.81 thf(zip_derived_cl838, plain, 71.92/9.81 (~ (((subsetI2) => 71.92/9.81 (((emptysetsubset) => 71.92/9.81 (((subsetE) => 71.92/9.81 (((subsetE2) => 71.92/9.81 (((notsubsetI) => 71.92/9.81 (((notequalI1) => 71.92/9.81 (((notequalI2) => 71.92/9.81 (((subsetRefl) => 71.92/9.81 (((subsetTrans) => 71.92/9.81 (((setadjoinSub) => 71.92/9.81 (((setadjoinSub2) => 71.92/9.81 (((subset2powerset) => 71.92/9.81 (((setextsub) => 71.92/9.81 (((subsetemptysetimpeq) => 71.92/9.81 (((powersetI1) => 71.92/9.81 (((powersetE1) => 71.92/9.81 (((inPowerset) => 71.92/9.81 (((powersetsubset) => 71.92/9.81 (((sepInPowerset) => 71.92/9.81 (((sepSubset) => 71.92/9.81 (((binunionIL) => 71.92/9.81 (((upairset2IR) => 71.92/9.81 (((binunionIR) => 71.92/9.81 (((binunionEcases) => 71.92/9.81 (((binunionE) => 71.92/9.81 (((binunionLsub) => 71.92/9.81 (((binunionRsub) => 71.92/9.81 (((binintersectI) => 71.92/9.81 (((binintersectSubset5) => 71.92/9.81 (((binintersectEL) => 71.92/9.81 (( 71.92/9.81 (binintersectLsub) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset2) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset3) => 71.92/9.81 (( 71.92/9.81 (binintersectER) => 71.92/9.81 (( 71.92/9.81 (disjointsetsI1) => 71.92/9.81 (( 71.92/9.81 (binintersectRsub) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset4) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset1) => 71.92/9.81 (( 71.92/9.81 (bs114d) => 71.92/9.81 (( 71.92/9.81 (setminusI) => 71.92/9.81 (( 71.92/9.81 (setminusEL) => 71.92/9.81 (( 71.92/9.81 (setminusER) => 71.92/9.81 (( 71.92/9.81 (setminusSubset2) => 71.92/9.81 (( 71.92/9.81 (setminusERneg) => 71.92/9.81 (( 71.92/9.81 (setminusELneg) => 71.92/9.81 (( 71.92/9.81 (setminusILneg) => 71.92/9.81 (( 71.92/9.81 (setminusIRneg) => 71.92/9.81 (( 71.92/9.81 (setminusLsub) => 71.92/9.81 (( 71.92/9.81 (setminusSubset1) => 71.92/9.81 (( 71.92/9.81 (symdiffE) => 71.92/9.81 (( 71.92/9.81 (symdiffI1) => 71.92/9.81 (( 71.92/9.81 (symdiffI2) => 71.92/9.81 (( 71.92/9.81 (symdiffIneg1) => 71.92/9.81 (( 71.92/9.81 (symdiffIneg2) => 71.92/9.81 (( 71.92/9.81 (secondinupair) => 71.92/9.81 (( 71.92/9.81 (setukpairIL) => 71.92/9.81 (( 71.92/9.81 (setukpairIR) => 71.92/9.81 (( 71.92/9.81 (kpairiskpair) => 71.92/9.81 (( 71.92/9.81 (kpairp) => 71.92/9.81 (( 71.92/9.81 (singletonsubset) => 71.92/9.81 (( 71.92/9.81 (singletoninpowerset) => 71.92/9.81 (( 71.92/9.81 (singletoninpowunion) => 71.92/9.81 (( 71.92/9.81 (upairset2E) => 71.92/9.81 (( 71.92/9.81 (upairsubunion) => 71.92/9.81 (( 71.92/9.81 (upairinpowunion) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem1) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem2) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem3) => 71.92/9.81 (( 71.92/9.81 (cartprodpairin) => 71.92/9.81 (( 71.92/9.81 (cartprodmempair1) => 71.92/9.81 (( 71.92/9.81 (cartprodmempair) => 71.92/9.81 (( 71.92/9.81 (setunionE2) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton1) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton2) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton) => 71.92/9.81 (( 71.92/9.81 (singletonprop) => 71.92/9.81 (( 71.92/9.81 (ex1E1) => 71.92/9.81 (( 71.92/9.81 (ex1I) => 71.92/9.81 (( 71.92/9.81 (ex1I2) => 71.92/9.81 (( 71.92/9.81 (singletonsuniq) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL1) => 71.92/9.81 (( 71.92/9.81 (kfstsingleton) => 71.92/9.81 (( 71.92/9.81 (theprop) => 71.92/9.81 (( 71.92/9.81 (kfstpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodfstin) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL2) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR11) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR12) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR1) => 71.92/9.81 (( 71.92/9.81 (upairequniteq) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR2) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR) => 71.92/9.81 (( 71.92/9.81 (ksndsingleton) => 71.92/9.81 (( 71.92/9.81 (ksndpairEq) => 71.92/9.81 (( 71.92/9.81 (kpairsurjEq) => 71.92/9.81 (( 71.92/9.81 (cartprodsndin) => 71.92/9.81 (( 71.92/9.81 (cartprodpairmemEL) => 71.92/9.81 (( 71.92/9.81 (cartprodpairmemER) => 71.92/9.81 (( 71.92/9.81 (cartprodmempaircEq) => 71.92/9.81 (( 71.92/9.81 (cartprodfstpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodsndpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodpairsurjEq) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrI) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrSub) => 71.92/9.81 (( 71.92/9.81 (setOfPairsIsBReln) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrERa) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrEL1) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrEL2) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrER) => 71.92/9.81 (( 71.92/9.81 (funcImageSingleton) => 71.92/9.81 (( 71.92/9.81 (apProp) => 71.92/9.81 (( 71.92/9.81 (app) => 71.92/9.81 (( 71.92/9.81 (infuncsetfunc) => 71.92/9.81 (( 71.92/9.81 (ap2p) => 71.92/9.81 (( 71.92/9.81 (funcinfuncset) => 71.92/9.81 (( 71.92/9.81 (lamProp) => 71.92/9.81 (( 71.92/9.81 (lamp) => 71.92/9.81 (( 71.92/9.81 (lam2p) => 71.92/9.81 (( 71.92/9.81 (brelnall1) => 71.92/9.81 (( 71.92/9.81 (brelnall2) => 71.92/9.81 (( 71.92/9.81 (ex1E2) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp1) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp3) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp2) => 71.92/9.81 (( 71.92/9.81 (funcextLem) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp4) => 71.92/9.81 (( 71.92/9.81 (subbreln) => 71.92/9.81 (( 71.92/9.81 (eqbreln) => 71.92/9.81 (( 71.92/9.81 (funcext) => 71.92/9.81 (( 71.92/9.81 (funcext2) => 71.92/9.81 (( 71.92/9.81 (ap2apEq1) => 71.92/9.81 (( 71.92/9.81 (ap2apEq2) => 71.92/9.81 (( 71.92/9.81 (beta1) => 71.92/9.81 (( 71.92/9.81 (eta1) => 71.92/9.81 (( 71.92/9.81 (lam2lamEq) => 71.92/9.81 (( 71.92/9.81 (beta2) => 71.92/9.81 (( 71.92/9.81 (eta2) => 71.92/9.81 (( 71.92/9.81 (iffalseProp1) => 71.92/9.81 (( 71.92/9.81 (iffalseProp2) => 71.92/9.81 (( 71.92/9.81 (iftrueProp1) => 71.92/9.81 (( 71.92/9.81 (iftrueProp2) => 71.92/9.81 (( 71.92/9.81 (ifSingleton) => 71.92/9.81 (( 71.92/9.81 (ifp) => 71.92/9.81 (( 71.92/9.81 (theeq) => 71.92/9.81 (( 71.92/9.81 (iftrue) => 71.92/9.81 (( 71.92/9.81 (iffalse) => 71.92/9.81 (( 71.92/9.81 (iftrueorfalse) => 71.92/9.81 (( 71.92/9.81 (binintersectT_lem) => 71.92/9.81 (( 71.92/9.81 (binunionT_lem) => 71.92/9.81 (( 71.92/9.81 (powersetT_lem) => 71.92/9.81 (( 71.92/9.81 (setminusT_lem) => 71.92/9.81 (( 71.92/9.81 (complementT_lem) => 71.92/9.81 (( 71.92/9.81 (setextT) => 71.92/9.81 (( 71.92/9.81 (subsetTI) => 71.92/9.81 (( 71.92/9.81 (powersetTI1) => 71.92/9.81 (( 71.92/9.81 (powersetTE1) => 71.92/9.81 (( 71.92/9.81 (complementTI1) => 71.92/9.81 (( 71.92/9.81 (complementTE1) => 71.92/9.81 (( 71.92/9.81 (binintersectTELcontra) => 71.92/9.81 (( 71.92/9.81 (binintersectTERcontra) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT1) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT2) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT3) => 71.92/9.81 (( 71.92/9.81 (doubleComplementI1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementE1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub2) => 71.92/9.81 (( 71.92/9.81 (doubleComplementEq) => 71.92/9.81 (( 71.92/9.81 (complementTnotintersectT) => 71.92/9.81 (( 71.92/9.81 (complementImpComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementSubsetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementInPowersetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (contraSubsetComplement) => 71.92/9.81 (( 71.92/9.81 (complementTcontraSubset) => 71.92/9.81 (( 71.92/9.81 (binunionTILcontra) => 71.92/9.81 (( 71.92/9.81 (binunionTIRcontra) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion2) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (intersectInPowersetIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpNotIn1) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpInComplement1) => 71.92/9.81 (( 71.92/9.81 (binunionTE) => 71.92/9.81 (( 71.92/9.81 (binunionTEcontra) => 71.92/9.81 (( 71.92/9.81 (demorgan2a1) => 71.92/9.81 (( 71.92/9.81 (complementUnionInPowersetComplement) => 71.92/9.81 (( 71.92/9.81 (demorgan2a2) => 71.92/9.81 (( 71.92/9.81 (demorgan1a) => 71.92/9.81 (( 71.92/9.81 (demorgan1b) => 71.92/9.81 (( 71.92/9.81 (demorgan1) => 71.92/9.81 (( 71.92/9.81 (demorgan2a) => 71.92/9.81 (( 71.92/9.81 (demorgan2b2) => 71.92/9.81 (( 71.92/9.81 (demorgan2b) => 71.92/9.81 (( 71.92/9.81 (demorgan2) => 71.92/9.81 (( 71.92/9.81 (woz13rule0) => 71.92/9.81 (( 71.92/9.81 (woz13rule1) => 71.92/9.81 (( 71.92/9.81 (woz13rule2) => 71.92/9.81 (( 71.92/9.81 (woz13rule3) => 71.92/9.81 (( 71.92/9.81 (woz13rule4) => 71.92/9.81 (( 71.92/9.81 (woz1_1) => 71.92/9.81 (( 71.92/9.81 (woz1_2) => 71.92/9.81 (( 71.92/9.81 (woz1_3) => 71.92/9.81 (( 71.92/9.81 (woz1_4) => 71.92/9.81 (( 71.92/9.81 (woz1_5) => 71.92/9.81 (( 71.92/9.81 (breln1all2) => 71.92/9.81 (( 71.92/9.81 (breln1SetBreln1) => 71.92/9.81 (( 71.92/9.81 (choice2fnsingleton) => 71.92/9.81 (( 71.92/9.81 (setOfPairsIsBReln1) => 71.92/9.81 (( 71.92/9.81 (breln1all1) => 71.92/9.81 (( 71.92/9.81 (subbreln1) => 71.92/9.81 (( 71.92/9.81 (eqbreln1) => 71.92/9.81 (( 71.92/9.81 (breln1invprop) => 71.92/9.81 (( 71.92/9.81 (breln1invI) => 71.92/9.81 (( 71.92/9.81 (breln1invE) => 71.92/9.81 (( 71.92/9.81 (breln1compprop) => 71.92/9.81 (( 71.92/9.81 (breln1compI) => 71.92/9.81 (( 71.92/9.81 (breln1compE) => 71.92/9.81 (( 71.92/9.81 (breln1compEex) => 71.92/9.81 (( 71.92/9.81 (!!) @ ( 71.92/9.81 (('#B') @ ( 71.92/9.81 !!) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 !!))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#C') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 breln1)))) @ 71.92/9.81 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl824])). 71.92/9.81 thf(zip_derived_cl850, plain, 71.92/9.81 (~ (((emptysetsubset) => 71.92/9.81 (((subsetE) => 71.92/9.81 (((subsetE2) => 71.92/9.81 (((notsubsetI) => 71.92/9.81 (((notequalI1) => 71.92/9.81 (((notequalI2) => 71.92/9.81 (((subsetRefl) => 71.92/9.81 (((subsetTrans) => 71.92/9.81 (((setadjoinSub) => 71.92/9.81 (((setadjoinSub2) => 71.92/9.81 (((subset2powerset) => 71.92/9.81 (((setextsub) => 71.92/9.81 (((subsetemptysetimpeq) => 71.92/9.81 (((powersetI1) => 71.92/9.81 (((powersetE1) => 71.92/9.81 (((inPowerset) => 71.92/9.81 (((powersetsubset) => 71.92/9.81 (((sepInPowerset) => 71.92/9.81 (((sepSubset) => 71.92/9.81 (((binunionIL) => 71.92/9.81 (((upairset2IR) => 71.92/9.81 (((binunionIR) => 71.92/9.81 (((binunionEcases) => 71.92/9.81 (((binunionE) => 71.92/9.81 (((binunionLsub) => 71.92/9.81 (((binunionRsub) => 71.92/9.81 (((binintersectI) => 71.92/9.81 (((binintersectSubset5) => 71.92/9.81 (((binintersectEL) => 71.92/9.81 (((binintersectLsub) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset2) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset3) => 71.92/9.81 (( 71.92/9.81 (binintersectER) => 71.92/9.81 (( 71.92/9.81 (disjointsetsI1) => 71.92/9.81 (( 71.92/9.81 (binintersectRsub) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset4) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset1) => 71.92/9.81 (( 71.92/9.81 (bs114d) => 71.92/9.81 (( 71.92/9.81 (setminusI) => 71.92/9.81 (( 71.92/9.81 (setminusEL) => 71.92/9.81 (( 71.92/9.81 (setminusER) => 71.92/9.81 (( 71.92/9.81 (setminusSubset2) => 71.92/9.81 (( 71.92/9.81 (setminusERneg) => 71.92/9.81 (( 71.92/9.81 (setminusELneg) => 71.92/9.81 (( 71.92/9.81 (setminusILneg) => 71.92/9.81 (( 71.92/9.81 (setminusIRneg) => 71.92/9.81 (( 71.92/9.81 (setminusLsub) => 71.92/9.81 (( 71.92/9.81 (setminusSubset1) => 71.92/9.81 (( 71.92/9.81 (symdiffE) => 71.92/9.81 (( 71.92/9.81 (symdiffI1) => 71.92/9.81 (( 71.92/9.81 (symdiffI2) => 71.92/9.81 (( 71.92/9.81 (symdiffIneg1) => 71.92/9.81 (( 71.92/9.81 (symdiffIneg2) => 71.92/9.81 (( 71.92/9.81 (secondinupair) => 71.92/9.81 (( 71.92/9.81 (setukpairIL) => 71.92/9.81 (( 71.92/9.81 (setukpairIR) => 71.92/9.81 (( 71.92/9.81 (kpairiskpair) => 71.92/9.81 (( 71.92/9.81 (kpairp) => 71.92/9.81 (( 71.92/9.81 (singletonsubset) => 71.92/9.81 (( 71.92/9.81 (singletoninpowerset) => 71.92/9.81 (( 71.92/9.81 (singletoninpowunion) => 71.92/9.81 (( 71.92/9.81 (upairset2E) => 71.92/9.81 (( 71.92/9.81 (upairsubunion) => 71.92/9.81 (( 71.92/9.81 (upairinpowunion) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem1) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem2) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem3) => 71.92/9.81 (( 71.92/9.81 (cartprodpairin) => 71.92/9.81 (( 71.92/9.81 (cartprodmempair1) => 71.92/9.81 (( 71.92/9.81 (cartprodmempair) => 71.92/9.81 (( 71.92/9.81 (setunionE2) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton1) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton2) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton) => 71.92/9.81 (( 71.92/9.81 (singletonprop) => 71.92/9.81 (( 71.92/9.81 (ex1E1) => 71.92/9.81 (( 71.92/9.81 (ex1I) => 71.92/9.81 (( 71.92/9.81 (ex1I2) => 71.92/9.81 (( 71.92/9.81 (singletonsuniq) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL1) => 71.92/9.81 (( 71.92/9.81 (kfstsingleton) => 71.92/9.81 (( 71.92/9.81 (theprop) => 71.92/9.81 (( 71.92/9.81 (kfstpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodfstin) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL2) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR11) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR12) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR1) => 71.92/9.81 (( 71.92/9.81 (upairequniteq) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR2) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR) => 71.92/9.81 (( 71.92/9.81 (ksndsingleton) => 71.92/9.81 (( 71.92/9.81 (ksndpairEq) => 71.92/9.81 (( 71.92/9.81 (kpairsurjEq) => 71.92/9.81 (( 71.92/9.81 (cartprodsndin) => 71.92/9.81 (( 71.92/9.81 (cartprodpairmemEL) => 71.92/9.81 (( 71.92/9.81 (cartprodpairmemER) => 71.92/9.81 (( 71.92/9.81 (cartprodmempaircEq) => 71.92/9.81 (( 71.92/9.81 (cartprodfstpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodsndpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodpairsurjEq) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrI) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrSub) => 71.92/9.81 (( 71.92/9.81 (setOfPairsIsBReln) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrERa) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrEL1) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrEL2) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrER) => 71.92/9.81 (( 71.92/9.81 (funcImageSingleton) => 71.92/9.81 (( 71.92/9.81 (apProp) => 71.92/9.81 (( 71.92/9.81 (app) => 71.92/9.81 (( 71.92/9.81 (infuncsetfunc) => 71.92/9.81 (( 71.92/9.81 (ap2p) => 71.92/9.81 (( 71.92/9.81 (funcinfuncset) => 71.92/9.81 (( 71.92/9.81 (lamProp) => 71.92/9.81 (( 71.92/9.81 (lamp) => 71.92/9.81 (( 71.92/9.81 (lam2p) => 71.92/9.81 (( 71.92/9.81 (brelnall1) => 71.92/9.81 (( 71.92/9.81 (brelnall2) => 71.92/9.81 (( 71.92/9.81 (ex1E2) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp1) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp3) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp2) => 71.92/9.81 (( 71.92/9.81 (funcextLem) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp4) => 71.92/9.81 (( 71.92/9.81 (subbreln) => 71.92/9.81 (( 71.92/9.81 (eqbreln) => 71.92/9.81 (( 71.92/9.81 (funcext) => 71.92/9.81 (( 71.92/9.81 (funcext2) => 71.92/9.81 (( 71.92/9.81 (ap2apEq1) => 71.92/9.81 (( 71.92/9.81 (ap2apEq2) => 71.92/9.81 (( 71.92/9.81 (beta1) => 71.92/9.81 (( 71.92/9.81 (eta1) => 71.92/9.81 (( 71.92/9.81 (lam2lamEq) => 71.92/9.81 (( 71.92/9.81 (beta2) => 71.92/9.81 (( 71.92/9.81 (eta2) => 71.92/9.81 (( 71.92/9.81 (iffalseProp1) => 71.92/9.81 (( 71.92/9.81 (iffalseProp2) => 71.92/9.81 (( 71.92/9.81 (iftrueProp1) => 71.92/9.81 (( 71.92/9.81 (iftrueProp2) => 71.92/9.81 (( 71.92/9.81 (ifSingleton) => 71.92/9.81 (( 71.92/9.81 (ifp) => 71.92/9.81 (( 71.92/9.81 (theeq) => 71.92/9.81 (( 71.92/9.81 (iftrue) => 71.92/9.81 (( 71.92/9.81 (iffalse) => 71.92/9.81 (( 71.92/9.81 (iftrueorfalse) => 71.92/9.81 (( 71.92/9.81 (binintersectT_lem) => 71.92/9.81 (( 71.92/9.81 (binunionT_lem) => 71.92/9.81 (( 71.92/9.81 (powersetT_lem) => 71.92/9.81 (( 71.92/9.81 (setminusT_lem) => 71.92/9.81 (( 71.92/9.81 (complementT_lem) => 71.92/9.81 (( 71.92/9.81 (setextT) => 71.92/9.81 (( 71.92/9.81 (subsetTI) => 71.92/9.81 (( 71.92/9.81 (powersetTI1) => 71.92/9.81 (( 71.92/9.81 (powersetTE1) => 71.92/9.81 (( 71.92/9.81 (complementTI1) => 71.92/9.81 (( 71.92/9.81 (complementTE1) => 71.92/9.81 (( 71.92/9.81 (binintersectTELcontra) => 71.92/9.81 (( 71.92/9.81 (binintersectTERcontra) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT1) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT2) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT3) => 71.92/9.81 (( 71.92/9.81 (doubleComplementI1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementE1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub2) => 71.92/9.81 (( 71.92/9.81 (doubleComplementEq) => 71.92/9.81 (( 71.92/9.81 (complementTnotintersectT) => 71.92/9.81 (( 71.92/9.81 (complementImpComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementSubsetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementInPowersetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (contraSubsetComplement) => 71.92/9.81 (( 71.92/9.81 (complementTcontraSubset) => 71.92/9.81 (( 71.92/9.81 (binunionTILcontra) => 71.92/9.81 (( 71.92/9.81 (binunionTIRcontra) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion2) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (intersectInPowersetIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpNotIn1) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpInComplement1) => 71.92/9.81 (( 71.92/9.81 (binunionTE) => 71.92/9.81 (( 71.92/9.81 (binunionTEcontra) => 71.92/9.81 (( 71.92/9.81 (demorgan2a1) => 71.92/9.81 (( 71.92/9.81 (complementUnionInPowersetComplement) => 71.92/9.81 (( 71.92/9.81 (demorgan2a2) => 71.92/9.81 (( 71.92/9.81 (demorgan1a) => 71.92/9.81 (( 71.92/9.81 (demorgan1b) => 71.92/9.81 (( 71.92/9.81 (demorgan1) => 71.92/9.81 (( 71.92/9.81 (demorgan2a) => 71.92/9.81 (( 71.92/9.81 (demorgan2b2) => 71.92/9.81 (( 71.92/9.81 (demorgan2b) => 71.92/9.81 (( 71.92/9.81 (demorgan2) => 71.92/9.81 (( 71.92/9.81 (woz13rule0) => 71.92/9.81 (( 71.92/9.81 (woz13rule1) => 71.92/9.81 (( 71.92/9.81 (woz13rule2) => 71.92/9.81 (( 71.92/9.81 (woz13rule3) => 71.92/9.81 (( 71.92/9.81 (woz13rule4) => 71.92/9.81 (( 71.92/9.81 (woz1_1) => 71.92/9.81 (( 71.92/9.81 (woz1_2) => 71.92/9.81 (( 71.92/9.81 (woz1_3) => 71.92/9.81 (( 71.92/9.81 (woz1_4) => 71.92/9.81 (( 71.92/9.81 (woz1_5) => 71.92/9.81 (( 71.92/9.81 (breln1all2) => 71.92/9.81 (( 71.92/9.81 (breln1SetBreln1) => 71.92/9.81 (( 71.92/9.81 (choice2fnsingleton) => 71.92/9.81 (( 71.92/9.81 (setOfPairsIsBReln1) => 71.92/9.81 (( 71.92/9.81 (breln1all1) => 71.92/9.81 (( 71.92/9.81 (subbreln1) => 71.92/9.81 (( 71.92/9.81 (eqbreln1) => 71.92/9.81 (( 71.92/9.81 (breln1invprop) => 71.92/9.81 (( 71.92/9.81 (breln1invI) => 71.92/9.81 (( 71.92/9.81 (breln1invE) => 71.92/9.81 (( 71.92/9.81 (breln1compprop) => 71.92/9.81 (( 71.92/9.81 (breln1compI) => 71.92/9.81 (( 71.92/9.81 (breln1compE) => 71.92/9.81 (( 71.92/9.81 (breln1compEex) => 71.92/9.81 (( 71.92/9.81 (!!) @ ( 71.92/9.81 (('#B') @ ( 71.92/9.81 !!) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 !!))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#C') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 breln1)))) @ 71.92/9.81 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl838])). 71.92/9.81 thf(zip_derived_cl863, plain, 71.92/9.81 (~ (((subsetE) => 71.92/9.81 (((subsetE2) => 71.92/9.81 (((notsubsetI) => 71.92/9.81 (((notequalI1) => 71.92/9.81 (((notequalI2) => 71.92/9.81 (((subsetRefl) => 71.92/9.81 (((subsetTrans) => 71.92/9.81 (((setadjoinSub) => 71.92/9.81 (((setadjoinSub2) => 71.92/9.81 (((subset2powerset) => 71.92/9.81 (((setextsub) => 71.92/9.81 (((subsetemptysetimpeq) => 71.92/9.81 (((powersetI1) => 71.92/9.81 (((powersetE1) => 71.92/9.81 (((inPowerset) => 71.92/9.81 (((powersetsubset) => 71.92/9.81 (((sepInPowerset) => 71.92/9.81 (((sepSubset) => 71.92/9.81 (((binunionIL) => 71.92/9.81 (((upairset2IR) => 71.92/9.81 (((binunionIR) => 71.92/9.81 (((binunionEcases) => 71.92/9.81 (((binunionE) => 71.92/9.81 (((binunionLsub) => 71.92/9.81 (((binunionRsub) => 71.92/9.81 (((binintersectI) => 71.92/9.81 (((binintersectSubset5) => 71.92/9.81 (((binintersectEL) => 71.92/9.81 (((binintersectLsub) => 71.92/9.81 (((binintersectSubset2) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset3) => 71.92/9.81 (( 71.92/9.81 (binintersectER) => 71.92/9.81 (( 71.92/9.81 (disjointsetsI1) => 71.92/9.81 (( 71.92/9.81 (binintersectRsub) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset4) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset1) => 71.92/9.81 (( 71.92/9.81 (bs114d) => 71.92/9.81 (( 71.92/9.81 (setminusI) => 71.92/9.81 (( 71.92/9.81 (setminusEL) => 71.92/9.81 (( 71.92/9.81 (setminusER) => 71.92/9.81 (( 71.92/9.81 (setminusSubset2) => 71.92/9.81 (( 71.92/9.81 (setminusERneg) => 71.92/9.81 (( 71.92/9.81 (setminusELneg) => 71.92/9.81 (( 71.92/9.81 (setminusILneg) => 71.92/9.81 (( 71.92/9.81 (setminusIRneg) => 71.92/9.81 (( 71.92/9.81 (setminusLsub) => 71.92/9.81 (( 71.92/9.81 (setminusSubset1) => 71.92/9.81 (( 71.92/9.81 (symdiffE) => 71.92/9.81 (( 71.92/9.81 (symdiffI1) => 71.92/9.81 (( 71.92/9.81 (symdiffI2) => 71.92/9.81 (( 71.92/9.81 (symdiffIneg1) => 71.92/9.81 (( 71.92/9.81 (symdiffIneg2) => 71.92/9.81 (( 71.92/9.81 (secondinupair) => 71.92/9.81 (( 71.92/9.81 (setukpairIL) => 71.92/9.81 (( 71.92/9.81 (setukpairIR) => 71.92/9.81 (( 71.92/9.81 (kpairiskpair) => 71.92/9.81 (( 71.92/9.81 (kpairp) => 71.92/9.81 (( 71.92/9.81 (singletonsubset) => 71.92/9.81 (( 71.92/9.81 (singletoninpowerset) => 71.92/9.81 (( 71.92/9.81 (singletoninpowunion) => 71.92/9.81 (( 71.92/9.81 (upairset2E) => 71.92/9.81 (( 71.92/9.81 (upairsubunion) => 71.92/9.81 (( 71.92/9.81 (upairinpowunion) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem1) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem2) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem3) => 71.92/9.81 (( 71.92/9.81 (cartprodpairin) => 71.92/9.81 (( 71.92/9.81 (cartprodmempair1) => 71.92/9.81 (( 71.92/9.81 (cartprodmempair) => 71.92/9.81 (( 71.92/9.81 (setunionE2) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton1) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton2) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton) => 71.92/9.81 (( 71.92/9.81 (singletonprop) => 71.92/9.81 (( 71.92/9.81 (ex1E1) => 71.92/9.81 (( 71.92/9.81 (ex1I) => 71.92/9.81 (( 71.92/9.81 (ex1I2) => 71.92/9.81 (( 71.92/9.81 (singletonsuniq) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL1) => 71.92/9.81 (( 71.92/9.81 (kfstsingleton) => 71.92/9.81 (( 71.92/9.81 (theprop) => 71.92/9.81 (( 71.92/9.81 (kfstpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodfstin) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL2) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR11) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR12) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR1) => 71.92/9.81 (( 71.92/9.81 (upairequniteq) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR2) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR) => 71.92/9.81 (( 71.92/9.81 (ksndsingleton) => 71.92/9.81 (( 71.92/9.81 (ksndpairEq) => 71.92/9.81 (( 71.92/9.81 (kpairsurjEq) => 71.92/9.81 (( 71.92/9.81 (cartprodsndin) => 71.92/9.81 (( 71.92/9.81 (cartprodpairmemEL) => 71.92/9.81 (( 71.92/9.81 (cartprodpairmemER) => 71.92/9.81 (( 71.92/9.81 (cartprodmempaircEq) => 71.92/9.81 (( 71.92/9.81 (cartprodfstpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodsndpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodpairsurjEq) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrI) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrSub) => 71.92/9.81 (( 71.92/9.81 (setOfPairsIsBReln) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrERa) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrEL1) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrEL2) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrER) => 71.92/9.81 (( 71.92/9.81 (funcImageSingleton) => 71.92/9.81 (( 71.92/9.81 (apProp) => 71.92/9.81 (( 71.92/9.81 (app) => 71.92/9.81 (( 71.92/9.81 (infuncsetfunc) => 71.92/9.81 (( 71.92/9.81 (ap2p) => 71.92/9.81 (( 71.92/9.81 (funcinfuncset) => 71.92/9.81 (( 71.92/9.81 (lamProp) => 71.92/9.81 (( 71.92/9.81 (lamp) => 71.92/9.81 (( 71.92/9.81 (lam2p) => 71.92/9.81 (( 71.92/9.81 (brelnall1) => 71.92/9.81 (( 71.92/9.81 (brelnall2) => 71.92/9.81 (( 71.92/9.81 (ex1E2) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp1) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp3) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp2) => 71.92/9.81 (( 71.92/9.81 (funcextLem) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp4) => 71.92/9.81 (( 71.92/9.81 (subbreln) => 71.92/9.81 (( 71.92/9.81 (eqbreln) => 71.92/9.81 (( 71.92/9.81 (funcext) => 71.92/9.81 (( 71.92/9.81 (funcext2) => 71.92/9.81 (( 71.92/9.81 (ap2apEq1) => 71.92/9.81 (( 71.92/9.81 (ap2apEq2) => 71.92/9.81 (( 71.92/9.81 (beta1) => 71.92/9.81 (( 71.92/9.81 (eta1) => 71.92/9.81 (( 71.92/9.81 (lam2lamEq) => 71.92/9.81 (( 71.92/9.81 (beta2) => 71.92/9.81 (( 71.92/9.81 (eta2) => 71.92/9.81 (( 71.92/9.81 (iffalseProp1) => 71.92/9.81 (( 71.92/9.81 (iffalseProp2) => 71.92/9.81 (( 71.92/9.81 (iftrueProp1) => 71.92/9.81 (( 71.92/9.81 (iftrueProp2) => 71.92/9.81 (( 71.92/9.81 (ifSingleton) => 71.92/9.81 (( 71.92/9.81 (ifp) => 71.92/9.81 (( 71.92/9.81 (theeq) => 71.92/9.81 (( 71.92/9.81 (iftrue) => 71.92/9.81 (( 71.92/9.81 (iffalse) => 71.92/9.81 (( 71.92/9.81 (iftrueorfalse) => 71.92/9.81 (( 71.92/9.81 (binintersectT_lem) => 71.92/9.81 (( 71.92/9.81 (binunionT_lem) => 71.92/9.81 (( 71.92/9.81 (powersetT_lem) => 71.92/9.81 (( 71.92/9.81 (setminusT_lem) => 71.92/9.81 (( 71.92/9.81 (complementT_lem) => 71.92/9.81 (( 71.92/9.81 (setextT) => 71.92/9.81 (( 71.92/9.81 (subsetTI) => 71.92/9.81 (( 71.92/9.81 (powersetTI1) => 71.92/9.81 (( 71.92/9.81 (powersetTE1) => 71.92/9.81 (( 71.92/9.81 (complementTI1) => 71.92/9.81 (( 71.92/9.81 (complementTE1) => 71.92/9.81 (( 71.92/9.81 (binintersectTELcontra) => 71.92/9.81 (( 71.92/9.81 (binintersectTERcontra) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT1) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT2) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT3) => 71.92/9.81 (( 71.92/9.81 (doubleComplementI1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementE1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub2) => 71.92/9.81 (( 71.92/9.81 (doubleComplementEq) => 71.92/9.81 (( 71.92/9.81 (complementTnotintersectT) => 71.92/9.81 (( 71.92/9.81 (complementImpComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementSubsetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementInPowersetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (contraSubsetComplement) => 71.92/9.81 (( 71.92/9.81 (complementTcontraSubset) => 71.92/9.81 (( 71.92/9.81 (binunionTILcontra) => 71.92/9.81 (( 71.92/9.81 (binunionTIRcontra) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion2) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (intersectInPowersetIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpNotIn1) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpInComplement1) => 71.92/9.81 (( 71.92/9.81 (binunionTE) => 71.92/9.81 (( 71.92/9.81 (binunionTEcontra) => 71.92/9.81 (( 71.92/9.81 (demorgan2a1) => 71.92/9.81 (( 71.92/9.81 (complementUnionInPowersetComplement) => 71.92/9.81 (( 71.92/9.81 (demorgan2a2) => 71.92/9.81 (( 71.92/9.81 (demorgan1a) => 71.92/9.81 (( 71.92/9.81 (demorgan1b) => 71.92/9.81 (( 71.92/9.81 (demorgan1) => 71.92/9.81 (( 71.92/9.81 (demorgan2a) => 71.92/9.81 (( 71.92/9.81 (demorgan2b2) => 71.92/9.81 (( 71.92/9.81 (demorgan2b) => 71.92/9.81 (( 71.92/9.81 (demorgan2) => 71.92/9.81 (( 71.92/9.81 (woz13rule0) => 71.92/9.81 (( 71.92/9.81 (woz13rule1) => 71.92/9.81 (( 71.92/9.81 (woz13rule2) => 71.92/9.81 (( 71.92/9.81 (woz13rule3) => 71.92/9.81 (( 71.92/9.81 (woz13rule4) => 71.92/9.81 (( 71.92/9.81 (woz1_1) => 71.92/9.81 (( 71.92/9.81 (woz1_2) => 71.92/9.81 (( 71.92/9.81 (woz1_3) => 71.92/9.81 (( 71.92/9.81 (woz1_4) => 71.92/9.81 (( 71.92/9.81 (woz1_5) => 71.92/9.81 (( 71.92/9.81 (breln1all2) => 71.92/9.81 (( 71.92/9.81 (breln1SetBreln1) => 71.92/9.81 (( 71.92/9.81 (choice2fnsingleton) => 71.92/9.81 (( 71.92/9.81 (setOfPairsIsBReln1) => 71.92/9.81 (( 71.92/9.81 (breln1all1) => 71.92/9.81 (( 71.92/9.81 (subbreln1) => 71.92/9.81 (( 71.92/9.81 (eqbreln1) => 71.92/9.81 (( 71.92/9.81 (breln1invprop) => 71.92/9.81 (( 71.92/9.81 (breln1invI) => 71.92/9.81 (( 71.92/9.81 (breln1invE) => 71.92/9.81 (( 71.92/9.81 (breln1compprop) => 71.92/9.81 (( 71.92/9.81 (breln1compI) => 71.92/9.81 (( 71.92/9.81 (breln1compE) => 71.92/9.81 (( 71.92/9.81 (breln1compEex) => 71.92/9.81 (( 71.92/9.81 (!!) @ ( 71.92/9.81 (('#B') @ ( 71.92/9.81 !!) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 !!))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#C') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 breln1)))) @ 71.92/9.81 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl850])). 71.92/9.81 thf(zip_derived_cl878, plain, 71.92/9.81 (~ (((subsetE2) => 71.92/9.81 (((notsubsetI) => 71.92/9.81 (((notequalI1) => 71.92/9.81 (((notequalI2) => 71.92/9.81 (((subsetRefl) => 71.92/9.81 (((subsetTrans) => 71.92/9.81 (((setadjoinSub) => 71.92/9.81 (((setadjoinSub2) => 71.92/9.81 (((subset2powerset) => 71.92/9.81 (((setextsub) => 71.92/9.81 (((subsetemptysetimpeq) => 71.92/9.81 (((powersetI1) => 71.92/9.81 (((powersetE1) => 71.92/9.81 (((inPowerset) 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=> 71.92/9.81 (( 71.92/9.81 (apProp) => 71.92/9.81 (( 71.92/9.81 (app) => 71.92/9.81 (( 71.92/9.81 (infuncsetfunc) => 71.92/9.81 (( 71.92/9.81 (ap2p) => 71.92/9.81 (( 71.92/9.81 (funcinfuncset) => 71.92/9.81 (( 71.92/9.81 (lamProp) => 71.92/9.81 (( 71.92/9.81 (lamp) => 71.92/9.81 (( 71.92/9.81 (lam2p) => 71.92/9.81 (( 71.92/9.81 (brelnall1) => 71.92/9.81 (( 71.92/9.81 (brelnall2) => 71.92/9.81 (( 71.92/9.81 (ex1E2) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp1) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp3) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp2) => 71.92/9.81 (( 71.92/9.81 (funcextLem) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp4) => 71.92/9.81 (( 71.92/9.81 (subbreln) => 71.92/9.81 (( 71.92/9.81 (eqbreln) => 71.92/9.81 (( 71.92/9.81 (funcext) => 71.92/9.81 (( 71.92/9.81 (funcext2) => 71.92/9.81 (( 71.92/9.81 (ap2apEq1) => 71.92/9.81 (( 71.92/9.81 (ap2apEq2) => 71.92/9.81 (( 71.92/9.81 (beta1) => 71.92/9.81 (( 71.92/9.81 (eta1) => 71.92/9.81 (( 71.92/9.81 (lam2lamEq) => 71.92/9.81 (( 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71.92/9.81 (binintersectTERcontra) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT1) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT2) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT3) => 71.92/9.81 (( 71.92/9.81 (doubleComplementI1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementE1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub2) => 71.92/9.81 (( 71.92/9.81 (doubleComplementEq) => 71.92/9.81 (( 71.92/9.81 (complementTnotintersectT) => 71.92/9.81 (( 71.92/9.81 (complementImpComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementSubsetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementInPowersetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (contraSubsetComplement) => 71.92/9.81 (( 71.92/9.81 (complementTcontraSubset) => 71.92/9.81 (( 71.92/9.81 (binunionTILcontra) => 71.92/9.81 (( 71.92/9.81 (binunionTIRcontra) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion2) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (intersectInPowersetIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpNotIn1) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpInComplement1) => 71.92/9.81 (( 71.92/9.81 (binunionTE) => 71.92/9.81 (( 71.92/9.81 (binunionTEcontra) => 71.92/9.81 (( 71.92/9.81 (demorgan2a1) => 71.92/9.81 (( 71.92/9.81 (complementUnionInPowersetComplement) => 71.92/9.81 (( 71.92/9.81 (demorgan2a2) => 71.92/9.81 (( 71.92/9.81 (demorgan1a) => 71.92/9.81 (( 71.92/9.81 (demorgan1b) => 71.92/9.81 (( 71.92/9.81 (demorgan1) => 71.92/9.81 (( 71.92/9.81 (demorgan2a) => 71.92/9.81 (( 71.92/9.81 (demorgan2b2) => 71.92/9.81 (( 71.92/9.81 (demorgan2b) => 71.92/9.81 (( 71.92/9.81 (demorgan2) => 71.92/9.81 (( 71.92/9.81 (woz13rule0) => 71.92/9.81 (( 71.92/9.81 (woz13rule1) => 71.92/9.81 (( 71.92/9.81 (woz13rule2) => 71.92/9.81 (( 71.92/9.81 (woz13rule3) => 71.92/9.81 (( 71.92/9.81 (woz13rule4) => 71.92/9.81 (( 71.92/9.81 (woz1_1) => 71.92/9.81 (( 71.92/9.81 (woz1_2) => 71.92/9.81 (( 71.92/9.81 (woz1_3) => 71.92/9.81 (( 71.92/9.81 (woz1_4) => 71.92/9.81 (( 71.92/9.81 (woz1_5) => 71.92/9.81 (( 71.92/9.81 (breln1all2) => 71.92/9.81 (( 71.92/9.81 (breln1SetBreln1) => 71.92/9.81 (( 71.92/9.81 (choice2fnsingleton) => 71.92/9.81 (( 71.92/9.81 (setOfPairsIsBReln1) => 71.92/9.81 (( 71.92/9.81 (breln1all1) => 71.92/9.81 (( 71.92/9.81 (subbreln1) => 71.92/9.81 (( 71.92/9.81 (eqbreln1) => 71.92/9.81 (( 71.92/9.81 (breln1invprop) => 71.92/9.81 (( 71.92/9.81 (breln1invI) => 71.92/9.81 (( 71.92/9.81 (breln1invE) => 71.92/9.81 (( 71.92/9.81 (breln1compprop) => 71.92/9.81 (( 71.92/9.81 (breln1compI) => 71.92/9.81 (( 71.92/9.81 (breln1compE) => 71.92/9.81 (( 71.92/9.81 (breln1compEex) => 71.92/9.81 (( 71.92/9.81 (!!) @ ( 71.92/9.81 (('#B') @ ( 71.92/9.81 !!) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 !!))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#C') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 breln1)))) @ 71.92/9.81 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(beta2) => 71.92/9.81 (( 71.92/9.81 (eta2) => 71.92/9.81 (( 71.92/9.81 (iffalseProp1) => 71.92/9.81 (( 71.92/9.81 (iffalseProp2) => 71.92/9.81 (( 71.92/9.81 (iftrueProp1) => 71.92/9.81 (( 71.92/9.81 (iftrueProp2) => 71.92/9.81 (( 71.92/9.81 (ifSingleton) => 71.92/9.81 (( 71.92/9.81 (ifp) => 71.92/9.81 (( 71.92/9.81 (theeq) => 71.92/9.81 (( 71.92/9.81 (iftrue) => 71.92/9.81 (( 71.92/9.81 (iffalse) => 71.92/9.81 (( 71.92/9.81 (iftrueorfalse) => 71.92/9.81 (( 71.92/9.81 (binintersectT_lem) => 71.92/9.81 (( 71.92/9.81 (binunionT_lem) => 71.92/9.81 (( 71.92/9.81 (powersetT_lem) => 71.92/9.81 (( 71.92/9.81 (setminusT_lem) => 71.92/9.81 (( 71.92/9.81 (complementT_lem) => 71.92/9.81 (( 71.92/9.81 (setextT) => 71.92/9.81 (( 71.92/9.81 (subsetTI) => 71.92/9.81 (( 71.92/9.81 (powersetTI1) => 71.92/9.81 (( 71.92/9.81 (powersetTE1) => 71.92/9.81 (( 71.92/9.81 (complementTI1) => 71.92/9.81 (( 71.92/9.81 (complementTE1) => 71.92/9.81 (( 71.92/9.81 (binintersectTELcontra) => 71.92/9.81 (( 71.92/9.81 (binintersectTERcontra) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT1) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT2) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT3) => 71.92/9.81 (( 71.92/9.81 (doubleComplementI1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementE1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub2) => 71.92/9.81 (( 71.92/9.81 (doubleComplementEq) => 71.92/9.81 (( 71.92/9.81 (complementTnotintersectT) => 71.92/9.81 (( 71.92/9.81 (complementImpComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementSubsetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementInPowersetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (contraSubsetComplement) => 71.92/9.81 (( 71.92/9.81 (complementTcontraSubset) => 71.92/9.81 (( 71.92/9.81 (binunionTILcontra) => 71.92/9.81 (( 71.92/9.81 (binunionTIRcontra) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion2) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (intersectInPowersetIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpNotIn1) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpInComplement1) => 71.92/9.81 (( 71.92/9.81 (binunionTE) => 71.92/9.81 (( 71.92/9.81 (binunionTEcontra) => 71.92/9.81 (( 71.92/9.81 (demorgan2a1) => 71.92/9.81 (( 71.92/9.81 (complementUnionInPowersetComplement) => 71.92/9.81 (( 71.92/9.81 (demorgan2a2) => 71.92/9.81 (( 71.92/9.81 (demorgan1a) => 71.92/9.81 (( 71.92/9.81 (demorgan1b) => 71.92/9.81 (( 71.92/9.81 (demorgan1) => 71.92/9.81 (( 71.92/9.81 (demorgan2a) => 71.92/9.81 (( 71.92/9.81 (demorgan2b2) => 71.92/9.81 (( 71.92/9.81 (demorgan2b) => 71.92/9.81 (( 71.92/9.81 (demorgan2) => 71.92/9.81 (( 71.92/9.81 (woz13rule0) => 71.92/9.81 (( 71.92/9.81 (woz13rule1) => 71.92/9.81 (( 71.92/9.81 (woz13rule2) => 71.92/9.81 (( 71.92/9.81 (woz13rule3) => 71.92/9.81 (( 71.92/9.81 (woz13rule4) => 71.92/9.81 (( 71.92/9.81 (woz1_1) => 71.92/9.81 (( 71.92/9.81 (woz1_2) => 71.92/9.81 (( 71.92/9.81 (woz1_3) => 71.92/9.81 (( 71.92/9.81 (woz1_4) => 71.92/9.81 (( 71.92/9.81 (woz1_5) => 71.92/9.81 (( 71.92/9.81 (breln1all2) => 71.92/9.81 (( 71.92/9.81 (breln1SetBreln1) => 71.92/9.81 (( 71.92/9.81 (choice2fnsingleton) => 71.92/9.81 (( 71.92/9.81 (setOfPairsIsBReln1) => 71.92/9.81 (( 71.92/9.81 (breln1all1) => 71.92/9.81 (( 71.92/9.81 (subbreln1) => 71.92/9.81 (( 71.92/9.81 (eqbreln1) => 71.92/9.81 (( 71.92/9.81 (breln1invprop) => 71.92/9.81 (( 71.92/9.81 (breln1invI) => 71.92/9.81 (( 71.92/9.81 (breln1invE) => 71.92/9.81 (( 71.92/9.81 (breln1compprop) => 71.92/9.81 (( 71.92/9.81 (breln1compI) => 71.92/9.81 (( 71.92/9.81 (breln1compE) => 71.92/9.81 (( 71.92/9.81 (breln1compEex) => 71.92/9.81 (( 71.92/9.81 (!!) @ ( 71.92/9.81 (('#B') @ ( 71.92/9.81 !!) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 !!))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#C') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 breln1)))) @ 71.92/9.81 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl878])). 71.92/9.81 thf(zip_derived_cl909, plain, 71.92/9.81 (~ (((notequalI1) => 71.92/9.81 (((notequalI2) => 71.92/9.81 (((subsetRefl) => 71.92/9.81 (((subsetTrans) => 71.92/9.81 (((setadjoinSub) => 71.92/9.81 (((setadjoinSub2) => 71.92/9.81 (((subset2powerset) => 71.92/9.81 (((setextsub) => 71.92/9.81 (((subsetemptysetimpeq) => 71.92/9.81 (((powersetI1) => 71.92/9.81 (((powersetE1) => 71.92/9.81 (((inPowerset) => 71.92/9.81 (((powersetsubset) => 71.92/9.81 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71.92/9.81 (( 71.92/9.81 (cartprodpairin) => 71.92/9.81 (( 71.92/9.81 (cartprodmempair1) => 71.92/9.81 (( 71.92/9.81 (cartprodmempair) => 71.92/9.81 (( 71.92/9.81 (setunionE2) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton1) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton2) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton) => 71.92/9.81 (( 71.92/9.81 (singletonprop) => 71.92/9.81 (( 71.92/9.81 (ex1E1) => 71.92/9.81 (( 71.92/9.81 (ex1I) => 71.92/9.81 (( 71.92/9.81 (ex1I2) => 71.92/9.81 (( 71.92/9.81 (singletonsuniq) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL1) => 71.92/9.81 (( 71.92/9.81 (kfstsingleton) => 71.92/9.81 (( 71.92/9.81 (theprop) => 71.92/9.81 (( 71.92/9.81 (kfstpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodfstin) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL2) => 71.92/9.81 (( 71.92/9.81 (setukpairinjL) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR11) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR12) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR1) => 71.92/9.81 (( 71.92/9.81 (upairequniteq) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR2) => 71.92/9.81 (( 71.92/9.81 (setukpairinjR) => 71.92/9.81 (( 71.92/9.81 (ksndsingleton) => 71.92/9.81 (( 71.92/9.81 (ksndpairEq) => 71.92/9.81 (( 71.92/9.81 (kpairsurjEq) => 71.92/9.81 (( 71.92/9.81 (cartprodsndin) => 71.92/9.81 (( 71.92/9.81 (cartprodpairmemEL) => 71.92/9.81 (( 71.92/9.81 (cartprodpairmemER) => 71.92/9.81 (( 71.92/9.81 (cartprodmempaircEq) => 71.92/9.81 (( 71.92/9.81 (cartprodfstpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodsndpairEq) => 71.92/9.81 (( 71.92/9.81 (cartprodpairsurjEq) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrI) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrSub) => 71.92/9.81 (( 71.92/9.81 (setOfPairsIsBReln) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrERa) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrEL1) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrEL2) => 71.92/9.81 (( 71.92/9.81 (dpsetconstrER) => 71.92/9.81 (( 71.92/9.81 (funcImageSingleton) => 71.92/9.81 (( 71.92/9.81 (apProp) => 71.92/9.81 (( 71.92/9.81 (app) => 71.92/9.81 (( 71.92/9.81 (infuncsetfunc) => 71.92/9.81 (( 71.92/9.81 (ap2p) => 71.92/9.81 (( 71.92/9.81 (funcinfuncset) => 71.92/9.81 (( 71.92/9.81 (lamProp) => 71.92/9.81 (( 71.92/9.81 (lamp) => 71.92/9.81 (( 71.92/9.81 (lam2p) => 71.92/9.81 (( 71.92/9.81 (brelnall1) => 71.92/9.81 (( 71.92/9.81 (brelnall2) => 71.92/9.81 (( 71.92/9.81 (ex1E2) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp1) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp3) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp2) => 71.92/9.81 (( 71.92/9.81 (funcextLem) => 71.92/9.81 (( 71.92/9.81 (funcGraphProp4) => 71.92/9.81 (( 71.92/9.81 (subbreln) => 71.92/9.81 (( 71.92/9.81 (eqbreln) => 71.92/9.81 (( 71.92/9.81 (funcext) => 71.92/9.81 (( 71.92/9.81 (funcext2) => 71.92/9.81 (( 71.92/9.81 (ap2apEq1) => 71.92/9.81 (( 71.92/9.81 (ap2apEq2) => 71.92/9.81 (( 71.92/9.81 (beta1) => 71.92/9.81 (( 71.92/9.81 (eta1) => 71.92/9.81 (( 71.92/9.81 (lam2lamEq) => 71.92/9.81 (( 71.92/9.81 (beta2) => 71.92/9.81 (( 71.92/9.81 (eta2) => 71.92/9.81 (( 71.92/9.81 (iffalseProp1) => 71.92/9.81 (( 71.92/9.81 (iffalseProp2) => 71.92/9.81 (( 71.92/9.81 (iftrueProp1) => 71.92/9.81 (( 71.92/9.81 (iftrueProp2) => 71.92/9.81 (( 71.92/9.81 (ifSingleton) => 71.92/9.81 (( 71.92/9.81 (ifp) => 71.92/9.81 (( 71.92/9.81 (theeq) => 71.92/9.81 (( 71.92/9.81 (iftrue) => 71.92/9.81 (( 71.92/9.81 (iffalse) => 71.92/9.81 (( 71.92/9.81 (iftrueorfalse) => 71.92/9.81 (( 71.92/9.81 (binintersectT_lem) => 71.92/9.81 (( 71.92/9.81 (binunionT_lem) => 71.92/9.81 (( 71.92/9.81 (powersetT_lem) => 71.92/9.81 (( 71.92/9.81 (setminusT_lem) => 71.92/9.81 (( 71.92/9.81 (complementT_lem) => 71.92/9.81 (( 71.92/9.81 (setextT) => 71.92/9.81 (( 71.92/9.81 (subsetTI) => 71.92/9.81 (( 71.92/9.81 (powersetTI1) => 71.92/9.81 (( 71.92/9.81 (powersetTE1) => 71.92/9.81 (( 71.92/9.81 (complementTI1) => 71.92/9.81 (( 71.92/9.81 (complementTE1) => 71.92/9.81 (( 71.92/9.81 (binintersectTELcontra) => 71.92/9.81 (( 71.92/9.81 (binintersectTERcontra) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT1) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT2) => 71.92/9.81 (( 71.92/9.81 (contrasubsetT3) => 71.92/9.81 (( 71.92/9.81 (doubleComplementI1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementE1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub1) => 71.92/9.81 (( 71.92/9.81 (doubleComplementSub2) => 71.92/9.81 (( 71.92/9.81 (doubleComplementEq) => 71.92/9.81 (( 71.92/9.81 (complementTnotintersectT) => 71.92/9.81 (( 71.92/9.81 (complementImpComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementSubsetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (complementInPowersetComplementIntersect) => 71.92/9.81 (( 71.92/9.81 (contraSubsetComplement) => 71.92/9.81 (( 71.92/9.81 (complementTcontraSubset) => 71.92/9.81 (( 71.92/9.81 (binunionTILcontra) => 71.92/9.81 (( 71.92/9.81 (binunionTIRcontra) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInUnion2) => 71.92/9.81 (( 71.92/9.81 (inIntersectImpInIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (intersectInPowersetIntersectUnions) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpNotIn1) => 71.92/9.81 (( 71.92/9.81 (inComplementUnionImpInComplement1) => 71.92/9.81 (( 71.92/9.81 (binunionTE) => 71.92/9.81 (( 71.92/9.81 (binunionTEcontra) => 71.92/9.81 (( 71.92/9.81 (demorgan2a1) => 71.92/9.81 (( 71.92/9.81 (complementUnionInPowersetComplement) => 71.92/9.81 (( 71.92/9.81 (demorgan2a2) => 71.92/9.81 (( 71.92/9.81 (demorgan1a) => 71.92/9.81 (( 71.92/9.81 (demorgan1b) => 71.92/9.81 (( 71.92/9.81 (demorgan1) => 71.92/9.81 (( 71.92/9.81 (demorgan2a) => 71.92/9.81 (( 71.92/9.81 (demorgan2b2) => 71.92/9.81 (( 71.92/9.81 (demorgan2b) => 71.92/9.81 (( 71.92/9.81 (demorgan2) => 71.92/9.81 (( 71.92/9.81 (woz13rule0) => 71.92/9.81 (( 71.92/9.81 (woz13rule1) => 71.92/9.81 (( 71.92/9.81 (woz13rule2) => 71.92/9.81 (( 71.92/9.81 (woz13rule3) => 71.92/9.81 (( 71.92/9.81 (woz13rule4) => 71.92/9.81 (( 71.92/9.81 (woz1_1) => 71.92/9.81 (( 71.92/9.81 (woz1_2) => 71.92/9.81 (( 71.92/9.81 (woz1_3) => 71.92/9.81 (( 71.92/9.81 (woz1_4) => 71.92/9.81 (( 71.92/9.81 (woz1_5) => 71.92/9.81 (( 71.92/9.81 (breln1all2) => 71.92/9.81 (( 71.92/9.81 (breln1SetBreln1) => 71.92/9.81 (( 71.92/9.81 (choice2fnsingleton) => 71.92/9.81 (( 71.92/9.81 (setOfPairsIsBReln1) => 71.92/9.81 (( 71.92/9.81 (breln1all1) => 71.92/9.81 (( 71.92/9.81 (subbreln1) => 71.92/9.81 (( 71.92/9.81 (eqbreln1) => 71.92/9.81 (( 71.92/9.81 (breln1invprop) => 71.92/9.81 (( 71.92/9.81 (breln1invI) => 71.92/9.81 (( 71.92/9.81 (breln1invE) => 71.92/9.81 (( 71.92/9.81 (breln1compprop) => 71.92/9.81 (( 71.92/9.81 (breln1compI) => 71.92/9.81 (( 71.92/9.81 (breln1compE) => 71.92/9.81 (( 71.92/9.81 (breln1compEex) => 71.92/9.81 (( 71.92/9.81 (!!) @ ( 71.92/9.81 (('#B') @ ( 71.92/9.81 !!) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 !!))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#S') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#S') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 =>))) @ 71.92/9.81 breln1)))))) @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#C') @ ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 ( 71.92/9.81 ( 71.92/9.81 ('#B') @ ( 71.92/9.81 '#B') @ 71.92/9.81 breln1)))) @ 71.92/9.81 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl896])). 71.92/9.81 thf(zip_derived_cl924, plain, 71.92/9.81 (~ (((notequalI2) => 71.92/9.81 (((subsetRefl) => 71.92/9.81 (((subsetTrans) => 71.92/9.81 (((setadjoinSub) => 71.92/9.81 (((setadjoinSub2) => 71.92/9.81 (((subset2powerset) => 71.92/9.81 (((setextsub) => 71.92/9.81 (((subsetemptysetimpeq) => 71.92/9.81 (((powersetI1) => 71.92/9.81 (((powersetE1) => 71.92/9.81 (((inPowerset) => 71.92/9.81 (((powersetsubset) => 71.92/9.81 (((sepInPowerset) => 71.92/9.81 (((sepSubset) => 71.92/9.81 (((binunionIL) => 71.92/9.81 (((upairset2IR) => 71.92/9.81 (((binunionIR) => 71.92/9.81 (((binunionEcases) => 71.92/9.81 (((binunionE) => 71.92/9.81 (((binunionLsub) => 71.92/9.81 (((binunionRsub) => 71.92/9.81 (((binintersectI) => 71.92/9.81 (((binintersectSubset5) => 71.92/9.81 (((binintersectEL) => 71.92/9.81 (((binintersectLsub) => 71.92/9.81 (((binintersectSubset2) => 71.92/9.81 (((binintersectSubset3) => 71.92/9.81 (((binintersectER) => 71.92/9.81 (((disjointsetsI1) => 71.92/9.81 (((binintersectRsub) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset4) => 71.92/9.81 (( 71.92/9.81 (binintersectSubset1) => 71.92/9.81 (( 71.92/9.81 (bs114d) => 71.92/9.81 (( 71.92/9.81 (setminusI) => 71.92/9.81 (( 71.92/9.81 (setminusEL) => 71.92/9.81 (( 71.92/9.81 (setminusER) => 71.92/9.81 (( 71.92/9.81 (setminusSubset2) => 71.92/9.81 (( 71.92/9.81 (setminusERneg) => 71.92/9.81 (( 71.92/9.81 (setminusELneg) => 71.92/9.81 (( 71.92/9.81 (setminusILneg) => 71.92/9.81 (( 71.92/9.81 (setminusIRneg) => 71.92/9.81 (( 71.92/9.81 (setminusLsub) => 71.92/9.81 (( 71.92/9.81 (setminusSubset1) => 71.92/9.81 (( 71.92/9.81 (symdiffE) => 71.92/9.81 (( 71.92/9.81 (symdiffI1) => 71.92/9.81 (( 71.92/9.81 (symdiffI2) => 71.92/9.81 (( 71.92/9.81 (symdiffIneg1) => 71.92/9.81 (( 71.92/9.81 (symdiffIneg2) => 71.92/9.81 (( 71.92/9.81 (secondinupair) => 71.92/9.81 (( 71.92/9.81 (setukpairIL) => 71.92/9.81 (( 71.92/9.81 (setukpairIR) => 71.92/9.81 (( 71.92/9.81 (kpairiskpair) => 71.92/9.81 (( 71.92/9.81 (kpairp) => 71.92/9.81 (( 71.92/9.81 (singletonsubset) => 71.92/9.81 (( 71.92/9.81 (singletoninpowerset) => 71.92/9.81 (( 71.92/9.81 (singletoninpowunion) => 71.92/9.81 (( 71.92/9.81 (upairset2E) => 71.92/9.81 (( 71.92/9.81 (upairsubunion) => 71.92/9.81 (( 71.92/9.81 (upairinpowunion) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem1) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem2) => 71.92/9.81 (( 71.92/9.81 (ubforcartprodlem3) => 71.92/9.81 (( 71.92/9.81 (cartprodpairin) => 71.92/9.81 (( 71.92/9.81 (cartprodmempair1) => 71.92/9.81 (( 71.92/9.81 (cartprodmempair) => 71.92/9.81 (( 71.92/9.81 (setunionE2) => 71.92/9.81 (( 71.92/9.81 (setunionsingleton1) => 71.92/9.81 (( 71.92/9.82 (setunionsingleton2) => 71.92/9.82 (( 71.92/9.82 (setunionsingleton) => 71.92/9.82 (( 71.92/9.82 (singletonprop) => 71.92/9.82 (( 71.92/9.82 (ex1E1) => 71.92/9.82 (( 71.92/9.82 (ex1I) => 71.92/9.82 (( 71.92/9.82 (ex1I2) => 71.92/9.82 (( 71.92/9.82 (singletonsuniq) => 71.92/9.82 (( 71.92/9.82 (setukpairinjL1) => 71.92/9.82 (( 71.92/9.82 (kfstsingleton) => 71.92/9.82 (( 71.92/9.82 (theprop) => 71.92/9.82 (( 71.92/9.82 (kfstpairEq) => 71.92/9.82 (( 71.92/9.82 (cartprodfstin) => 71.92/9.82 (( 71.92/9.82 (setukpairinjL2) => 71.92/9.82 (( 71.92/9.82 (setukpairinjL) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR11) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR12) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR1) => 71.92/9.82 (( 71.92/9.82 (upairequniteq) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR2) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR) => 71.92/9.82 (( 71.92/9.82 (ksndsingleton) => 71.92/9.82 (( 71.92/9.82 (ksndpairEq) => 71.92/9.82 (( 71.92/9.82 (kpairsurjEq) => 71.92/9.82 (( 71.92/9.82 (cartprodsndin) => 71.92/9.82 (( 71.92/9.82 (cartprodpairmemEL) => 71.92/9.82 (( 71.92/9.82 (cartprodpairmemER) => 71.92/9.82 (( 71.92/9.82 (cartprodmempaircEq) => 71.92/9.82 (( 71.92/9.82 (cartprodfstpairEq) => 71.92/9.82 (( 71.92/9.82 (cartprodsndpairEq) => 71.92/9.82 (( 71.92/9.82 (cartprodpairsurjEq) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrI) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrSub) => 71.92/9.82 (( 71.92/9.82 (setOfPairsIsBReln) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrERa) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrEL1) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrEL2) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrER) => 71.92/9.82 (( 71.92/9.82 (funcImageSingleton) => 71.92/9.82 (( 71.92/9.82 (apProp) => 71.92/9.82 (( 71.92/9.82 (app) => 71.92/9.82 (( 71.92/9.82 (infuncsetfunc) => 71.92/9.82 (( 71.92/9.82 (ap2p) => 71.92/9.82 (( 71.92/9.82 (funcinfuncset) => 71.92/9.82 (( 71.92/9.82 (lamProp) => 71.92/9.82 (( 71.92/9.82 (lamp) => 71.92/9.82 (( 71.92/9.82 (lam2p) => 71.92/9.82 (( 71.92/9.82 (brelnall1) => 71.92/9.82 (( 71.92/9.82 (brelnall2) => 71.92/9.82 (( 71.92/9.82 (ex1E2) => 71.92/9.82 (( 71.92/9.82 (funcGraphProp1) => 71.92/9.82 (( 71.92/9.82 (funcGraphProp3) => 71.92/9.82 (( 71.92/9.82 (funcGraphProp2) => 71.92/9.82 (( 71.92/9.82 (funcextLem) => 71.92/9.82 (( 71.92/9.82 (funcGraphProp4) => 71.92/9.82 (( 71.92/9.82 (subbreln) => 71.92/9.82 (( 71.92/9.82 (eqbreln) => 71.92/9.82 (( 71.92/9.82 (funcext) => 71.92/9.82 (( 71.92/9.82 (funcext2) => 71.92/9.82 (( 71.92/9.82 (ap2apEq1) => 71.92/9.82 (( 71.92/9.82 (ap2apEq2) => 71.92/9.82 (( 71.92/9.82 (beta1) => 71.92/9.82 (( 71.92/9.82 (eta1) => 71.92/9.82 (( 71.92/9.82 (lam2lamEq) => 71.92/9.82 (( 71.92/9.82 (beta2) => 71.92/9.82 (( 71.92/9.82 (eta2) => 71.92/9.82 (( 71.92/9.82 (iffalseProp1) => 71.92/9.82 (( 71.92/9.82 (iffalseProp2) => 71.92/9.82 (( 71.92/9.82 (iftrueProp1) => 71.92/9.82 (( 71.92/9.82 (iftrueProp2) => 71.92/9.82 (( 71.92/9.82 (ifSingleton) => 71.92/9.82 (( 71.92/9.82 (ifp) => 71.92/9.82 (( 71.92/9.82 (theeq) => 71.92/9.82 (( 71.92/9.82 (iftrue) => 71.92/9.82 (( 71.92/9.82 (iffalse) => 71.92/9.82 (( 71.92/9.82 (iftrueorfalse) => 71.92/9.82 (( 71.92/9.82 (binintersectT_lem) => 71.92/9.82 (( 71.92/9.82 (binunionT_lem) => 71.92/9.82 (( 71.92/9.82 (powersetT_lem) => 71.92/9.82 (( 71.92/9.82 (setminusT_lem) => 71.92/9.82 (( 71.92/9.82 (complementT_lem) => 71.92/9.82 (( 71.92/9.82 (setextT) => 71.92/9.82 (( 71.92/9.82 (subsetTI) => 71.92/9.82 (( 71.92/9.82 (powersetTI1) => 71.92/9.82 (( 71.92/9.82 (powersetTE1) => 71.92/9.82 (( 71.92/9.82 (complementTI1) => 71.92/9.82 (( 71.92/9.82 (complementTE1) => 71.92/9.82 (( 71.92/9.82 (binintersectTELcontra) => 71.92/9.82 (( 71.92/9.82 (binintersectTERcontra) => 71.92/9.82 (( 71.92/9.82 (contrasubsetT) => 71.92/9.82 (( 71.92/9.82 (contrasubsetT1) => 71.92/9.82 (( 71.92/9.82 (contrasubsetT2) => 71.92/9.82 (( 71.92/9.82 (contrasubsetT3) => 71.92/9.82 (( 71.92/9.82 (doubleComplementI1) => 71.92/9.82 (( 71.92/9.82 (doubleComplementE1) => 71.92/9.82 (( 71.92/9.82 (doubleComplementSub1) => 71.92/9.82 (( 71.92/9.82 (doubleComplementSub2) => 71.92/9.82 (( 71.92/9.82 (doubleComplementEq) => 71.92/9.82 (( 71.92/9.82 (complementTnotintersectT) => 71.92/9.82 (( 71.92/9.82 (complementImpComplementIntersect) => 71.92/9.82 (( 71.92/9.82 (complementSubsetComplementIntersect) => 71.92/9.82 (( 71.92/9.82 (complementInPowersetComplementIntersect) => 71.92/9.82 (( 71.92/9.82 (contraSubsetComplement) => 71.92/9.82 (( 71.92/9.82 (complementTcontraSubset) => 71.92/9.82 (( 71.92/9.82 (binunionTILcontra) => 71.92/9.82 (( 71.92/9.82 (binunionTIRcontra) => 71.92/9.82 (( 71.92/9.82 (inIntersectImpInUnion) => 71.92/9.82 (( 71.92/9.82 (inIntersectImpInUnion2) => 71.92/9.82 (( 71.92/9.82 (inIntersectImpInIntersectUnions) => 71.92/9.82 (( 71.92/9.82 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71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 !!))) @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#S') @ ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 '#B') @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 '#S') @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 =>))) @ 71.92/9.82 breln1)))))) @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#C') @ ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 '#B') @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 '#B') @ 71.92/9.82 breln1)))) @ 71.92/9.82 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl909])). 71.92/9.82 thf(zip_derived_cl938, plain, 71.92/9.82 (~ (((subsetRefl) => 71.92/9.82 (((subsetTrans) => 71.92/9.82 (((setadjoinSub) => 71.92/9.82 (((setadjoinSub2) => 71.92/9.82 (((subset2powerset) => 71.92/9.82 (((setextsub) => 71.92/9.82 (((subsetemptysetimpeq) => 71.92/9.82 (((powersetI1) => 71.92/9.82 (((powersetE1) => 71.92/9.82 (((inPowerset) => 71.92/9.82 (((powersetsubset) => 71.92/9.82 (((sepInPowerset) => 71.92/9.82 (((sepSubset) => 71.92/9.82 (((binunionIL) => 71.92/9.82 (((upairset2IR) => 71.92/9.82 (((binunionIR) => 71.92/9.82 (((binunionEcases) => 71.92/9.82 (((binunionE) => 71.92/9.82 (((binunionLsub) => 71.92/9.82 (((binunionRsub) => 71.92/9.82 (((binintersectI) => 71.92/9.82 (((binintersectSubset5) => 71.92/9.82 (((binintersectEL) => 71.92/9.82 (((binintersectLsub) => 71.92/9.82 (((binintersectSubset2) => 71.92/9.82 (((binintersectSubset3) => 71.92/9.82 (((binintersectER) => 71.92/9.82 (((disjointsetsI1) => 71.92/9.82 (((binintersectRsub) => 71.92/9.82 (((binintersectSubset4) => 71.92/9.82 (( 71.92/9.82 (binintersectSubset1) => 71.92/9.82 (( 71.92/9.82 (bs114d) => 71.92/9.82 (( 71.92/9.82 (setminusI) => 71.92/9.82 (( 71.92/9.82 (setminusEL) => 71.92/9.82 (( 71.92/9.82 (setminusER) => 71.92/9.82 (( 71.92/9.82 (setminusSubset2) => 71.92/9.82 (( 71.92/9.82 (setminusERneg) => 71.92/9.82 (( 71.92/9.82 (setminusELneg) => 71.92/9.82 (( 71.92/9.82 (setminusILneg) => 71.92/9.82 (( 71.92/9.82 (setminusIRneg) => 71.92/9.82 (( 71.92/9.82 (setminusLsub) => 71.92/9.82 (( 71.92/9.82 (setminusSubset1) => 71.92/9.82 (( 71.92/9.82 (symdiffE) => 71.92/9.82 (( 71.92/9.82 (symdiffI1) => 71.92/9.82 (( 71.92/9.82 (symdiffI2) => 71.92/9.82 (( 71.92/9.82 (symdiffIneg1) => 71.92/9.82 (( 71.92/9.82 (symdiffIneg2) => 71.92/9.82 (( 71.92/9.82 (secondinupair) => 71.92/9.82 (( 71.92/9.82 (setukpairIL) => 71.92/9.82 (( 71.92/9.82 (setukpairIR) => 71.92/9.82 (( 71.92/9.82 (kpairiskpair) => 71.92/9.82 (( 71.92/9.82 (kpairp) => 71.92/9.82 (( 71.92/9.82 (singletonsubset) => 71.92/9.82 (( 71.92/9.82 (singletoninpowerset) => 71.92/9.82 (( 71.92/9.82 (singletoninpowunion) => 71.92/9.82 (( 71.92/9.82 (upairset2E) => 71.92/9.82 (( 71.92/9.82 (upairsubunion) => 71.92/9.82 (( 71.92/9.82 (upairinpowunion) => 71.92/9.82 (( 71.92/9.82 (ubforcartprodlem1) => 71.92/9.82 (( 71.92/9.82 (ubforcartprodlem2) => 71.92/9.82 (( 71.92/9.82 (ubforcartprodlem3) => 71.92/9.82 (( 71.92/9.82 (cartprodpairin) => 71.92/9.82 (( 71.92/9.82 (cartprodmempair1) => 71.92/9.82 (( 71.92/9.82 (cartprodmempair) => 71.92/9.82 (( 71.92/9.82 (setunionE2) => 71.92/9.82 (( 71.92/9.82 (setunionsingleton1) => 71.92/9.82 (( 71.92/9.82 (setunionsingleton2) => 71.92/9.82 (( 71.92/9.82 (setunionsingleton) => 71.92/9.82 (( 71.92/9.82 (singletonprop) => 71.92/9.82 (( 71.92/9.82 (ex1E1) => 71.92/9.82 (( 71.92/9.82 (ex1I) => 71.92/9.82 (( 71.92/9.82 (ex1I2) => 71.92/9.82 (( 71.92/9.82 (singletonsuniq) => 71.92/9.82 (( 71.92/9.82 (setukpairinjL1) => 71.92/9.82 (( 71.92/9.82 (kfstsingleton) => 71.92/9.82 (( 71.92/9.82 (theprop) => 71.92/9.82 (( 71.92/9.82 (kfstpairEq) => 71.92/9.82 (( 71.92/9.82 (cartprodfstin) => 71.92/9.82 (( 71.92/9.82 (setukpairinjL2) => 71.92/9.82 (( 71.92/9.82 (setukpairinjL) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR11) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR12) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR1) => 71.92/9.82 (( 71.92/9.82 (upairequniteq) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR2) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR) => 71.92/9.82 (( 71.92/9.82 (ksndsingleton) => 71.92/9.82 (( 71.92/9.82 (ksndpairEq) => 71.92/9.82 (( 71.92/9.82 (kpairsurjEq) => 71.92/9.82 (( 71.92/9.82 (cartprodsndin) => 71.92/9.82 (( 71.92/9.82 (cartprodpairmemEL) => 71.92/9.82 (( 71.92/9.82 (cartprodpairmemER) => 71.92/9.82 (( 71.92/9.82 (cartprodmempaircEq) => 71.92/9.82 (( 71.92/9.82 (cartprodfstpairEq) => 71.92/9.82 (( 71.92/9.82 (cartprodsndpairEq) => 71.92/9.82 (( 71.92/9.82 (cartprodpairsurjEq) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrI) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrSub) => 71.92/9.82 (( 71.92/9.82 (setOfPairsIsBReln) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrERa) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrEL1) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrEL2) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrER) => 71.92/9.82 (( 71.92/9.82 (funcImageSingleton) => 71.92/9.82 (( 71.92/9.82 (apProp) => 71.92/9.82 (( 71.92/9.82 (app) => 71.92/9.82 (( 71.92/9.82 (infuncsetfunc) => 71.92/9.82 (( 71.92/9.82 (ap2p) => 71.92/9.82 (( 71.92/9.82 (funcinfuncset) => 71.92/9.82 (( 71.92/9.82 (lamProp) => 71.92/9.82 (( 71.92/9.82 (lamp) => 71.92/9.82 (( 71.92/9.82 (lam2p) => 71.92/9.82 (( 71.92/9.82 (brelnall1) => 71.92/9.82 (( 71.92/9.82 (brelnall2) => 71.92/9.82 (( 71.92/9.82 (ex1E2) => 71.92/9.82 (( 71.92/9.82 (funcGraphProp1) => 71.92/9.82 (( 71.92/9.82 (funcGraphProp3) => 71.92/9.82 (( 71.92/9.82 (funcGraphProp2) => 71.92/9.82 (( 71.92/9.82 (funcextLem) => 71.92/9.82 (( 71.92/9.82 (funcGraphProp4) => 71.92/9.82 (( 71.92/9.82 (subbreln) => 71.92/9.82 (( 71.92/9.82 (eqbreln) => 71.92/9.82 (( 71.92/9.82 (funcext) => 71.92/9.82 (( 71.92/9.82 (funcext2) => 71.92/9.82 (( 71.92/9.82 (ap2apEq1) => 71.92/9.82 (( 71.92/9.82 (ap2apEq2) => 71.92/9.82 (( 71.92/9.82 (beta1) => 71.92/9.82 (( 71.92/9.82 (eta1) => 71.92/9.82 (( 71.92/9.82 (lam2lamEq) => 71.92/9.82 (( 71.92/9.82 (beta2) => 71.92/9.82 (( 71.92/9.82 (eta2) => 71.92/9.82 (( 71.92/9.82 (iffalseProp1) => 71.92/9.82 (( 71.92/9.82 (iffalseProp2) => 71.92/9.82 (( 71.92/9.82 (iftrueProp1) => 71.92/9.82 (( 71.92/9.82 (iftrueProp2) => 71.92/9.82 (( 71.92/9.82 (ifSingleton) => 71.92/9.82 (( 71.92/9.82 (ifp) => 71.92/9.82 (( 71.92/9.82 (theeq) => 71.92/9.82 (( 71.92/9.82 (iftrue) => 71.92/9.82 (( 71.92/9.82 (iffalse) => 71.92/9.82 (( 71.92/9.82 (iftrueorfalse) => 71.92/9.82 (( 71.92/9.82 (binintersectT_lem) => 71.92/9.82 (( 71.92/9.82 (binunionT_lem) => 71.92/9.82 (( 71.92/9.82 (powersetT_lem) => 71.92/9.82 (( 71.92/9.82 (setminusT_lem) => 71.92/9.82 (( 71.92/9.82 (complementT_lem) => 71.92/9.82 (( 71.92/9.82 (setextT) => 71.92/9.82 (( 71.92/9.82 (subsetTI) => 71.92/9.82 (( 71.92/9.82 (powersetTI1) => 71.92/9.82 (( 71.92/9.82 (powersetTE1) => 71.92/9.82 (( 71.92/9.82 (complementTI1) => 71.92/9.82 (( 71.92/9.82 (complementTE1) => 71.92/9.82 (( 71.92/9.82 (binintersectTELcontra) => 71.92/9.82 (( 71.92/9.82 (binintersectTERcontra) => 71.92/9.82 (( 71.92/9.82 (contrasubsetT) => 71.92/9.82 (( 71.92/9.82 (contrasubsetT1) => 71.92/9.82 (( 71.92/9.82 (contrasubsetT2) => 71.92/9.82 (( 71.92/9.82 (contrasubsetT3) => 71.92/9.82 (( 71.92/9.82 (doubleComplementI1) => 71.92/9.82 (( 71.92/9.82 (doubleComplementE1) => 71.92/9.82 (( 71.92/9.82 (doubleComplementSub1) => 71.92/9.82 (( 71.92/9.82 (doubleComplementSub2) => 71.92/9.82 (( 71.92/9.82 (doubleComplementEq) => 71.92/9.82 (( 71.92/9.82 (complementTnotintersectT) => 71.92/9.82 (( 71.92/9.82 (complementImpComplementIntersect) => 71.92/9.82 (( 71.92/9.82 (complementSubsetComplementIntersect) => 71.92/9.82 (( 71.92/9.82 (complementInPowersetComplementIntersect) => 71.92/9.82 (( 71.92/9.82 (contraSubsetComplement) => 71.92/9.82 (( 71.92/9.82 (complementTcontraSubset) => 71.92/9.82 (( 71.92/9.82 (binunionTILcontra) => 71.92/9.82 (( 71.92/9.82 (binunionTIRcontra) => 71.92/9.82 (( 71.92/9.82 (inIntersectImpInUnion) => 71.92/9.82 (( 71.92/9.82 (inIntersectImpInUnion2) => 71.92/9.82 (( 71.92/9.82 (inIntersectImpInIntersectUnions) => 71.92/9.82 (( 71.92/9.82 (intersectInPowersetIntersectUnions) => 71.92/9.82 (( 71.92/9.82 (inComplementUnionImpNotIn1) => 71.92/9.82 (( 71.92/9.82 (inComplementUnionImpInComplement1) => 71.92/9.82 (( 71.92/9.82 (binunionTE) => 71.92/9.82 (( 71.92/9.82 (binunionTEcontra) => 71.92/9.82 (( 71.92/9.82 (demorgan2a1) => 71.92/9.82 (( 71.92/9.82 (complementUnionInPowersetComplement) => 71.92/9.82 (( 71.92/9.82 (demorgan2a2) => 71.92/9.82 (( 71.92/9.82 (demorgan1a) => 71.92/9.82 (( 71.92/9.82 (demorgan1b) => 71.92/9.82 (( 71.92/9.82 (demorgan1) => 71.92/9.82 (( 71.92/9.82 (demorgan2a) => 71.92/9.82 (( 71.92/9.82 (demorgan2b2) => 71.92/9.82 (( 71.92/9.82 (demorgan2b) => 71.92/9.82 (( 71.92/9.82 (demorgan2) => 71.92/9.82 (( 71.92/9.82 (woz13rule0) => 71.92/9.82 (( 71.92/9.82 (woz13rule1) => 71.92/9.82 (( 71.92/9.82 (woz13rule2) => 71.92/9.82 (( 71.92/9.82 (woz13rule3) => 71.92/9.82 (( 71.92/9.82 (woz13rule4) => 71.92/9.82 (( 71.92/9.82 (woz1_1) => 71.92/9.82 (( 71.92/9.82 (woz1_2) => 71.92/9.82 (( 71.92/9.82 (woz1_3) => 71.92/9.82 (( 71.92/9.82 (woz1_4) => 71.92/9.82 (( 71.92/9.82 (woz1_5) => 71.92/9.82 (( 71.92/9.82 (breln1all2) => 71.92/9.82 (( 71.92/9.82 (breln1SetBreln1) => 71.92/9.82 (( 71.92/9.82 (choice2fnsingleton) => 71.92/9.82 (( 71.92/9.82 (setOfPairsIsBReln1) => 71.92/9.82 (( 71.92/9.82 (breln1all1) => 71.92/9.82 (( 71.92/9.82 (subbreln1) => 71.92/9.82 (( 71.92/9.82 (eqbreln1) => 71.92/9.82 (( 71.92/9.82 (breln1invprop) => 71.92/9.82 (( 71.92/9.82 (breln1invI) => 71.92/9.82 (( 71.92/9.82 (breln1invE) => 71.92/9.82 (( 71.92/9.82 (breln1compprop) => 71.92/9.82 (( 71.92/9.82 (breln1compI) => 71.92/9.82 (( 71.92/9.82 (breln1compE) => 71.92/9.82 (( 71.92/9.82 (breln1compEex) => 71.92/9.82 (( 71.92/9.82 (!!) @ ( 71.92/9.82 (('#B') @ ( 71.92/9.82 !!) @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#S') @ ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 '#S') @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 =>))) @ 71.92/9.82 breln1)))) @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 !!))) @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#S') @ ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 '#B') @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 '#S') @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 =>))) @ 71.92/9.82 breln1)))))) @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#C') @ ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 '#B') @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 '#B') @ 71.92/9.82 breln1)))) @ 71.92/9.82 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 71.92/9.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl924])). 71.92/9.82 thf(zip_derived_cl952, plain, 71.92/9.82 (~ (((subsetTrans) => 71.92/9.82 (((setadjoinSub) => 71.92/9.82 (((setadjoinSub2) => 71.92/9.82 (((subset2powerset) => 71.92/9.82 (((setextsub) => 71.92/9.82 (((subsetemptysetimpeq) => 71.92/9.82 (((powersetI1) => 71.92/9.82 (((powersetE1) => 71.92/9.82 (((inPowerset) => 71.92/9.82 (((powersetsubset) => 71.92/9.82 (((sepInPowerset) => 71.92/9.82 (((sepSubset) => 71.92/9.82 (((binunionIL) => 71.92/9.82 (((upairset2IR) => 71.92/9.82 (((binunionIR) => 71.92/9.82 (((binunionEcases) => 71.92/9.82 (((binunionE) => 71.92/9.82 (((binunionLsub) => 71.92/9.82 (((binunionRsub) => 71.92/9.82 (((binintersectI) => 71.92/9.82 (((binintersectSubset5) => 71.92/9.82 (((binintersectEL) => 71.92/9.82 (((binintersectLsub) => 71.92/9.82 (((binintersectSubset2) => 71.92/9.82 (((binintersectSubset3) => 71.92/9.82 (((binintersectER) => 71.92/9.82 (((disjointsetsI1) => 71.92/9.82 (((binintersectRsub) => 71.92/9.82 (((binintersectSubset4) => 71.92/9.82 (((binintersectSubset1) => 71.92/9.82 (( 71.92/9.82 (bs114d) => 71.92/9.82 (( 71.92/9.82 (setminusI) => 71.92/9.82 (( 71.92/9.82 (setminusEL) => 71.92/9.82 (( 71.92/9.82 (setminusER) => 71.92/9.82 (( 71.92/9.82 (setminusSubset2) => 71.92/9.82 (( 71.92/9.82 (setminusERneg) => 71.92/9.82 (( 71.92/9.82 (setminusELneg) => 71.92/9.82 (( 71.92/9.82 (setminusILneg) => 71.92/9.82 (( 71.92/9.82 (setminusIRneg) => 71.92/9.82 (( 71.92/9.82 (setminusLsub) => 71.92/9.82 (( 71.92/9.82 (setminusSubset1) => 71.92/9.82 (( 71.92/9.82 (symdiffE) => 71.92/9.82 (( 71.92/9.82 (symdiffI1) => 71.92/9.82 (( 71.92/9.82 (symdiffI2) => 71.92/9.82 (( 71.92/9.82 (symdiffIneg1) => 71.92/9.82 (( 71.92/9.82 (symdiffIneg2) => 71.92/9.82 (( 71.92/9.82 (secondinupair) => 71.92/9.82 (( 71.92/9.82 (setukpairIL) => 71.92/9.82 (( 71.92/9.82 (setukpairIR) => 71.92/9.82 (( 71.92/9.82 (kpairiskpair) => 71.92/9.82 (( 71.92/9.82 (kpairp) => 71.92/9.82 (( 71.92/9.82 (singletonsubset) => 71.92/9.82 (( 71.92/9.82 (singletoninpowerset) => 71.92/9.82 (( 71.92/9.82 (singletoninpowunion) => 71.92/9.82 (( 71.92/9.82 (upairset2E) => 71.92/9.82 (( 71.92/9.82 (upairsubunion) => 71.92/9.82 (( 71.92/9.82 (upairinpowunion) => 71.92/9.82 (( 71.92/9.82 (ubforcartprodlem1) => 71.92/9.82 (( 71.92/9.82 (ubforcartprodlem2) => 71.92/9.82 (( 71.92/9.82 (ubforcartprodlem3) => 71.92/9.82 (( 71.92/9.82 (cartprodpairin) => 71.92/9.82 (( 71.92/9.82 (cartprodmempair1) => 71.92/9.82 (( 71.92/9.82 (cartprodmempair) => 71.92/9.82 (( 71.92/9.82 (setunionE2) => 71.92/9.82 (( 71.92/9.82 (setunionsingleton1) => 71.92/9.82 (( 71.92/9.82 (setunionsingleton2) => 71.92/9.82 (( 71.92/9.82 (setunionsingleton) => 71.92/9.82 (( 71.92/9.82 (singletonprop) => 71.92/9.82 (( 71.92/9.82 (ex1E1) => 71.92/9.82 (( 71.92/9.82 (ex1I) => 71.92/9.82 (( 71.92/9.82 (ex1I2) => 71.92/9.82 (( 71.92/9.82 (singletonsuniq) => 71.92/9.82 (( 71.92/9.82 (setukpairinjL1) => 71.92/9.82 (( 71.92/9.82 (kfstsingleton) => 71.92/9.82 (( 71.92/9.82 (theprop) => 71.92/9.82 (( 71.92/9.82 (kfstpairEq) => 71.92/9.82 (( 71.92/9.82 (cartprodfstin) => 71.92/9.82 (( 71.92/9.82 (setukpairinjL2) => 71.92/9.82 (( 71.92/9.82 (setukpairinjL) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR11) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR12) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR1) => 71.92/9.82 (( 71.92/9.82 (upairequniteq) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR2) => 71.92/9.82 (( 71.92/9.82 (setukpairinjR) => 71.92/9.82 (( 71.92/9.82 (ksndsingleton) => 71.92/9.82 (( 71.92/9.82 (ksndpairEq) => 71.92/9.82 (( 71.92/9.82 (kpairsurjEq) => 71.92/9.82 (( 71.92/9.82 (cartprodsndin) => 71.92/9.82 (( 71.92/9.82 (cartprodpairmemEL) => 71.92/9.82 (( 71.92/9.82 (cartprodpairmemER) => 71.92/9.82 (( 71.92/9.82 (cartprodmempaircEq) => 71.92/9.82 (( 71.92/9.82 (cartprodfstpairEq) => 71.92/9.82 (( 71.92/9.82 (cartprodsndpairEq) => 71.92/9.82 (( 71.92/9.82 (cartprodpairsurjEq) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrI) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrSub) => 71.92/9.82 (( 71.92/9.82 (setOfPairsIsBReln) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrERa) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrEL1) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrEL2) => 71.92/9.82 (( 71.92/9.82 (dpsetconstrER) => 71.92/9.82 (( 71.92/9.82 (funcImageSingleton) => 71.92/9.82 (( 71.92/9.82 (apProp) => 71.92/9.82 (( 71.92/9.82 (app) => 71.92/9.82 (( 71.92/9.82 (infuncsetfunc) => 71.92/9.82 (( 71.92/9.82 (ap2p) => 71.92/9.82 (( 71.92/9.82 (funcinfuncset) => 71.92/9.82 (( 71.92/9.82 (lamProp) => 71.92/9.82 (( 71.92/9.82 (lamp) => 71.92/9.82 (( 71.92/9.82 (lam2p) => 71.92/9.82 (( 71.92/9.82 (brelnall1) => 71.92/9.82 (( 71.92/9.82 (brelnall2) => 71.92/9.82 (( 71.92/9.82 (ex1E2) => 71.92/9.82 (( 71.92/9.82 (funcGraphProp1) => 71.92/9.82 (( 71.92/9.82 (funcGraphProp3) => 71.92/9.82 (( 71.92/9.82 (funcGraphProp2) => 71.92/9.82 (( 71.92/9.82 (funcextLem) => 71.92/9.82 (( 71.92/9.82 (funcGraphProp4) => 71.92/9.82 (( 71.92/9.82 (subbreln) => 71.92/9.82 (( 71.92/9.82 (eqbreln) => 71.92/9.82 (( 71.92/9.82 (funcext) => 71.92/9.82 (( 71.92/9.82 (funcext2) => 71.92/9.82 (( 71.92/9.82 (ap2apEq1) => 71.92/9.82 (( 71.92/9.82 (ap2apEq2) => 71.92/9.82 (( 71.92/9.82 (beta1) => 71.92/9.82 (( 71.92/9.82 (eta1) => 71.92/9.82 (( 71.92/9.82 (lam2lamEq) => 71.92/9.82 (( 71.92/9.82 (beta2) => 71.92/9.82 (( 71.92/9.82 (eta2) => 71.92/9.82 (( 71.92/9.82 (iffalseProp1) => 71.92/9.82 (( 71.92/9.82 (iffalseProp2) => 71.92/9.82 (( 71.92/9.82 (iftrueProp1) => 71.92/9.82 (( 71.92/9.82 (iftrueProp2) => 71.92/9.82 (( 71.92/9.82 (ifSingleton) => 71.92/9.82 (( 71.92/9.82 (ifp) => 71.92/9.82 (( 71.92/9.82 (theeq) => 71.92/9.82 (( 71.92/9.82 (iftrue) => 71.92/9.82 (( 71.92/9.82 (iffalse) => 71.92/9.82 (( 71.92/9.82 (iftrueorfalse) => 71.92/9.82 (( 71.92/9.82 (binintersectT_lem) => 71.92/9.82 (( 71.92/9.82 (binunionT_lem) => 71.92/9.82 (( 71.92/9.82 (powersetT_lem) => 71.92/9.82 (( 71.92/9.82 (setminusT_lem) => 71.92/9.82 (( 71.92/9.82 (complementT_lem) => 71.92/9.82 (( 71.92/9.82 (setextT) => 71.92/9.82 (( 71.92/9.82 (subsetTI) => 71.92/9.82 (( 71.92/9.82 (powersetTI1) => 71.92/9.82 (( 71.92/9.82 (powersetTE1) => 71.92/9.82 (( 71.92/9.82 (complementTI1) => 71.92/9.82 (( 71.92/9.82 (complementTE1) => 71.92/9.82 (( 71.92/9.82 (binintersectTELcontra) => 71.92/9.82 (( 71.92/9.82 (binintersectTERcontra) => 71.92/9.82 (( 71.92/9.82 (contrasubsetT) => 71.92/9.82 (( 71.92/9.82 (contrasubsetT1) => 71.92/9.82 (( 71.92/9.82 (contrasubsetT2) => 71.92/9.82 (( 71.92/9.82 (contrasubsetT3) => 71.92/9.82 (( 71.92/9.82 (doubleComplementI1) => 71.92/9.82 (( 71.92/9.82 (doubleComplementE1) => 71.92/9.82 (( 71.92/9.82 (doubleComplementSub1) => 71.92/9.82 (( 71.92/9.82 (doubleComplementSub2) => 71.92/9.82 (( 71.92/9.82 (doubleComplementEq) => 71.92/9.82 (( 71.92/9.82 (complementTnotintersectT) => 71.92/9.82 (( 71.92/9.82 (complementImpComplementIntersect) => 71.92/9.82 (( 71.92/9.82 (complementSubsetComplementIntersect) => 71.92/9.82 (( 71.92/9.82 (complementInPowersetComplementIntersect) => 71.92/9.82 (( 71.92/9.82 (contraSubsetComplement) => 71.92/9.82 (( 71.92/9.82 (complementTcontraSubset) => 71.92/9.82 (( 71.92/9.82 (binunionTILcontra) => 71.92/9.82 (( 71.92/9.82 (binunionTIRcontra) => 71.92/9.82 (( 71.92/9.82 (inIntersectImpInUnion) => 71.92/9.82 (( 71.92/9.82 (inIntersectImpInUnion2) => 71.92/9.82 (( 71.92/9.82 (inIntersectImpInIntersectUnions) => 71.92/9.82 (( 71.92/9.82 (intersectInPowersetIntersectUnions) => 71.92/9.82 (( 71.92/9.82 (inComplementUnionImpNotIn1) => 71.92/9.82 (( 71.92/9.82 (inComplementUnionImpInComplement1) => 71.92/9.82 (( 71.92/9.82 (binunionTE) => 71.92/9.82 (( 71.92/9.82 (binunionTEcontra) => 71.92/9.82 (( 71.92/9.82 (demorgan2a1) => 71.92/9.82 (( 71.92/9.82 (complementUnionInPowersetComplement) => 71.92/9.82 (( 71.92/9.82 (demorgan2a2) => 71.92/9.82 (( 71.92/9.82 (demorgan1a) => 71.92/9.82 (( 71.92/9.82 (demorgan1b) => 71.92/9.82 (( 71.92/9.82 (demorgan1) => 71.92/9.82 (( 71.92/9.82 (demorgan2a) => 71.92/9.82 (( 71.92/9.82 (demorgan2b2) => 71.92/9.82 (( 71.92/9.82 (demorgan2b) => 71.92/9.82 (( 71.92/9.82 (demorgan2) => 71.92/9.82 (( 71.92/9.82 (woz13rule0) => 71.92/9.82 (( 71.92/9.82 (woz13rule1) => 71.92/9.82 (( 71.92/9.82 (woz13rule2) => 71.92/9.82 (( 71.92/9.82 (woz13rule3) => 71.92/9.82 (( 71.92/9.82 (woz13rule4) => 71.92/9.82 (( 71.92/9.82 (woz1_1) => 71.92/9.82 (( 71.92/9.82 (woz1_2) => 71.92/9.82 (( 71.92/9.82 (woz1_3) => 71.92/9.82 (( 71.92/9.82 (woz1_4) => 71.92/9.82 (( 71.92/9.82 (woz1_5) => 71.92/9.82 (( 71.92/9.82 (breln1all2) => 71.92/9.82 (( 71.92/9.82 (breln1SetBreln1) => 71.92/9.82 (( 71.92/9.82 (choice2fnsingleton) => 71.92/9.82 (( 71.92/9.82 (setOfPairsIsBReln1) => 71.92/9.82 (( 71.92/9.82 (breln1all1) => 71.92/9.82 (( 71.92/9.82 (subbreln1) => 71.92/9.82 (( 71.92/9.82 (eqbreln1) => 71.92/9.82 (( 71.92/9.82 (breln1invprop) => 71.92/9.82 (( 71.92/9.82 (breln1invI) => 71.92/9.82 (( 71.92/9.82 (breln1invE) => 71.92/9.82 (( 71.92/9.82 (breln1compprop) => 71.92/9.82 (( 71.92/9.82 (breln1compI) => 71.92/9.82 (( 71.92/9.82 (breln1compE) => 71.92/9.82 (( 71.92/9.82 (breln1compEex) => 71.92/9.82 (( 71.92/9.82 (!!) @ ( 71.92/9.82 (('#B') @ ( 71.92/9.82 !!) @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#S') @ ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 '#S') @ 71.92/9.82 ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 71.92/9.82 ( 71.92/9.82 ('#B') @ ( 72.19/9.82 =>))) @ 72.19/9.82 breln1)))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 !!))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#S') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#S') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 =>))) @ 72.19/9.82 breln1)))))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#C') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 breln1)))) @ 72.19/9.82 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.19/9.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl938])). 72.19/9.82 thf(zip_derived_cl967, plain, 72.19/9.82 (~ (((setadjoinSub) => 72.19/9.82 (((setadjoinSub2) => 72.19/9.82 (((subset2powerset) => 72.19/9.82 (((setextsub) => 72.19/9.82 (((subsetemptysetimpeq) => 72.19/9.82 (((powersetI1) => 72.19/9.82 (((powersetE1) => 72.19/9.82 (((inPowerset) => 72.19/9.82 (((powersetsubset) => 72.19/9.82 (((sepInPowerset) => 72.19/9.82 (((sepSubset) => 72.19/9.82 (((binunionIL) => 72.19/9.82 (((upairset2IR) => 72.19/9.82 (((binunionIR) => 72.19/9.82 (((binunionEcases) => 72.19/9.82 (((binunionE) => 72.19/9.82 (((binunionLsub) => 72.19/9.82 (((binunionRsub) => 72.19/9.82 (((binintersectI) => 72.19/9.82 (((binintersectSubset5) => 72.19/9.82 (((binintersectEL) => 72.19/9.82 (((binintersectLsub) => 72.19/9.82 (((binintersectSubset2) => 72.19/9.82 (((binintersectSubset3) => 72.19/9.82 (((binintersectER) => 72.19/9.82 (((disjointsetsI1) => 72.19/9.82 (((binintersectRsub) => 72.19/9.82 (((binintersectSubset4) => 72.19/9.82 (((binintersectSubset1) => 72.19/9.82 (((bs114d) => 72.19/9.82 (( 72.19/9.82 (setminusI) => 72.19/9.82 (( 72.19/9.82 (setminusEL) => 72.19/9.82 (( 72.19/9.82 (setminusER) => 72.19/9.82 (( 72.19/9.82 (setminusSubset2) => 72.19/9.82 (( 72.19/9.82 (setminusERneg) => 72.19/9.82 (( 72.19/9.82 (setminusELneg) => 72.19/9.82 (( 72.19/9.82 (setminusILneg) => 72.19/9.82 (( 72.19/9.82 (setminusIRneg) => 72.19/9.82 (( 72.19/9.82 (setminusLsub) => 72.19/9.82 (( 72.19/9.82 (setminusSubset1) => 72.19/9.82 (( 72.19/9.82 (symdiffE) => 72.19/9.82 (( 72.19/9.82 (symdiffI1) => 72.19/9.82 (( 72.19/9.82 (symdiffI2) => 72.19/9.82 (( 72.19/9.82 (symdiffIneg1) => 72.19/9.82 (( 72.19/9.82 (symdiffIneg2) => 72.19/9.82 (( 72.19/9.82 (secondinupair) => 72.19/9.82 (( 72.19/9.82 (setukpairIL) => 72.19/9.82 (( 72.19/9.82 (setukpairIR) => 72.19/9.82 (( 72.19/9.82 (kpairiskpair) => 72.19/9.82 (( 72.19/9.82 (kpairp) => 72.19/9.82 (( 72.19/9.82 (singletonsubset) => 72.19/9.82 (( 72.19/9.82 (singletoninpowerset) => 72.19/9.82 (( 72.19/9.82 (singletoninpowunion) => 72.19/9.82 (( 72.19/9.82 (upairset2E) => 72.19/9.82 (( 72.19/9.82 (upairsubunion) => 72.19/9.82 (( 72.19/9.82 (upairinpowunion) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem1) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem2) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem3) => 72.19/9.82 (( 72.19/9.82 (cartprodpairin) => 72.19/9.82 (( 72.19/9.82 (cartprodmempair1) => 72.19/9.82 (( 72.19/9.82 (cartprodmempair) => 72.19/9.82 (( 72.19/9.82 (setunionE2) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton1) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton2) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton) => 72.19/9.82 (( 72.19/9.82 (singletonprop) => 72.19/9.82 (( 72.19/9.82 (ex1E1) => 72.19/9.82 (( 72.19/9.82 (ex1I) => 72.19/9.82 (( 72.19/9.82 (ex1I2) => 72.19/9.82 (( 72.19/9.82 (singletonsuniq) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL1) => 72.19/9.82 (( 72.19/9.82 (kfstsingleton) => 72.19/9.82 (( 72.19/9.82 (theprop) => 72.19/9.82 (( 72.19/9.82 (kfstpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodfstin) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL2) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR11) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR12) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR1) => 72.19/9.82 (( 72.19/9.82 (upairequniteq) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR2) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR) => 72.19/9.82 (( 72.19/9.82 (ksndsingleton) => 72.19/9.82 (( 72.19/9.82 (ksndpairEq) => 72.19/9.82 (( 72.19/9.82 (kpairsurjEq) => 72.19/9.82 (( 72.19/9.82 (cartprodsndin) => 72.19/9.82 (( 72.19/9.82 (cartprodpairmemEL) => 72.19/9.82 (( 72.19/9.82 (cartprodpairmemER) => 72.19/9.82 (( 72.19/9.82 (cartprodmempaircEq) => 72.19/9.82 (( 72.19/9.82 (cartprodfstpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodsndpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodpairsurjEq) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrI) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrSub) => 72.19/9.82 (( 72.19/9.82 (setOfPairsIsBReln) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrERa) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrEL1) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrEL2) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrER) => 72.19/9.82 (( 72.19/9.82 (funcImageSingleton) => 72.19/9.82 (( 72.19/9.82 (apProp) => 72.19/9.82 (( 72.19/9.82 (app) => 72.19/9.82 (( 72.19/9.82 (infuncsetfunc) => 72.19/9.82 (( 72.19/9.82 (ap2p) => 72.19/9.82 (( 72.19/9.82 (funcinfuncset) => 72.19/9.82 (( 72.19/9.82 (lamProp) => 72.19/9.82 (( 72.19/9.82 (lamp) => 72.19/9.82 (( 72.19/9.82 (lam2p) => 72.19/9.82 (( 72.19/9.82 (brelnall1) => 72.19/9.82 (( 72.19/9.82 (brelnall2) => 72.19/9.82 (( 72.19/9.82 (ex1E2) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp1) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp3) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp2) => 72.19/9.82 (( 72.19/9.82 (funcextLem) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp4) => 72.19/9.82 (( 72.19/9.82 (subbreln) => 72.19/9.82 (( 72.19/9.82 (eqbreln) => 72.19/9.82 (( 72.19/9.82 (funcext) => 72.19/9.82 (( 72.19/9.82 (funcext2) => 72.19/9.82 (( 72.19/9.82 (ap2apEq1) => 72.19/9.82 (( 72.19/9.82 (ap2apEq2) => 72.19/9.82 (( 72.19/9.82 (beta1) => 72.19/9.82 (( 72.19/9.82 (eta1) => 72.19/9.82 (( 72.19/9.82 (lam2lamEq) => 72.19/9.82 (( 72.19/9.82 (beta2) => 72.19/9.82 (( 72.19/9.82 (eta2) => 72.19/9.82 (( 72.19/9.82 (iffalseProp1) => 72.19/9.82 (( 72.19/9.82 (iffalseProp2) => 72.19/9.82 (( 72.19/9.82 (iftrueProp1) => 72.19/9.82 (( 72.19/9.82 (iftrueProp2) => 72.19/9.82 (( 72.19/9.82 (ifSingleton) => 72.19/9.82 (( 72.19/9.82 (ifp) => 72.19/9.82 (( 72.19/9.82 (theeq) => 72.19/9.82 (( 72.19/9.82 (iftrue) => 72.19/9.82 (( 72.19/9.82 (iffalse) => 72.19/9.82 (( 72.19/9.82 (iftrueorfalse) => 72.19/9.82 (( 72.19/9.82 (binintersectT_lem) => 72.19/9.82 (( 72.19/9.82 (binunionT_lem) => 72.19/9.82 (( 72.19/9.82 (powersetT_lem) => 72.19/9.82 (( 72.19/9.82 (setminusT_lem) => 72.19/9.82 (( 72.19/9.82 (complementT_lem) => 72.19/9.82 (( 72.19/9.82 (setextT) => 72.19/9.82 (( 72.19/9.82 (subsetTI) => 72.19/9.82 (( 72.19/9.82 (powersetTI1) => 72.19/9.82 (( 72.19/9.82 (powersetTE1) => 72.19/9.82 (( 72.19/9.82 (complementTI1) => 72.19/9.82 (( 72.19/9.82 (complementTE1) => 72.19/9.82 (( 72.19/9.82 (binintersectTELcontra) => 72.19/9.82 (( 72.19/9.82 (binintersectTERcontra) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT1) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT2) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT3) => 72.19/9.82 (( 72.19/9.82 (doubleComplementI1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementE1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementSub1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementSub2) => 72.19/9.82 (( 72.19/9.82 (doubleComplementEq) => 72.19/9.82 (( 72.19/9.82 (complementTnotintersectT) => 72.19/9.82 (( 72.19/9.82 (complementImpComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (complementSubsetComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (complementInPowersetComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (contraSubsetComplement) => 72.19/9.82 (( 72.19/9.82 (complementTcontraSubset) => 72.19/9.82 (( 72.19/9.82 (binunionTILcontra) => 72.19/9.82 (( 72.19/9.82 (binunionTIRcontra) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInUnion) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInUnion2) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInIntersectUnions) => 72.19/9.82 (( 72.19/9.82 (intersectInPowersetIntersectUnions) => 72.19/9.82 (( 72.19/9.82 (inComplementUnionImpNotIn1) => 72.19/9.82 (( 72.19/9.82 (inComplementUnionImpInComplement1) => 72.19/9.82 (( 72.19/9.82 (binunionTE) => 72.19/9.82 (( 72.19/9.82 (binunionTEcontra) => 72.19/9.82 (( 72.19/9.82 (demorgan2a1) => 72.19/9.82 (( 72.19/9.82 (complementUnionInPowersetComplement) => 72.19/9.82 (( 72.19/9.82 (demorgan2a2) => 72.19/9.82 (( 72.19/9.82 (demorgan1a) => 72.19/9.82 (( 72.19/9.82 (demorgan1b) => 72.19/9.82 (( 72.19/9.82 (demorgan1) => 72.19/9.82 (( 72.19/9.82 (demorgan2a) => 72.19/9.82 (( 72.19/9.82 (demorgan2b2) => 72.19/9.82 (( 72.19/9.82 (demorgan2b) => 72.19/9.82 (( 72.19/9.82 (demorgan2) => 72.19/9.82 (( 72.19/9.82 (woz13rule0) => 72.19/9.82 (( 72.19/9.82 (woz13rule1) => 72.19/9.82 (( 72.19/9.82 (woz13rule2) => 72.19/9.82 (( 72.19/9.82 (woz13rule3) => 72.19/9.82 (( 72.19/9.82 (woz13rule4) => 72.19/9.82 (( 72.19/9.82 (woz1_1) => 72.19/9.82 (( 72.19/9.82 (woz1_2) => 72.19/9.82 (( 72.19/9.82 (woz1_3) => 72.19/9.82 (( 72.19/9.82 (woz1_4) => 72.19/9.82 (( 72.19/9.82 (woz1_5) => 72.19/9.82 (( 72.19/9.82 (breln1all2) => 72.19/9.82 (( 72.19/9.82 (breln1SetBreln1) => 72.19/9.82 (( 72.19/9.82 (choice2fnsingleton) => 72.19/9.82 (( 72.19/9.82 (setOfPairsIsBReln1) => 72.19/9.82 (( 72.19/9.82 (breln1all1) => 72.19/9.82 (( 72.19/9.82 (subbreln1) => 72.19/9.82 (( 72.19/9.82 (eqbreln1) => 72.19/9.82 (( 72.19/9.82 (breln1invprop) => 72.19/9.82 (( 72.19/9.82 (breln1invI) => 72.19/9.82 (( 72.19/9.82 (breln1invE) => 72.19/9.82 (( 72.19/9.82 (breln1compprop) => 72.19/9.82 (( 72.19/9.82 (breln1compI) => 72.19/9.82 (( 72.19/9.82 (breln1compE) => 72.19/9.82 (( 72.19/9.82 (breln1compEex) => 72.19/9.82 (( 72.19/9.82 (!!) @ ( 72.19/9.82 (('#B') @ ( 72.19/9.82 !!) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#S') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#S') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 =>))) @ 72.19/9.82 breln1)))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 !!))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#S') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#S') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 =>))) @ 72.19/9.82 breln1)))))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#C') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 breln1)))) @ 72.19/9.82 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.19/9.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl952])). 72.19/9.82 thf(zip_derived_cl984, plain, 72.19/9.82 (~ (((setadjoinSub2) => 72.19/9.82 (((subset2powerset) => 72.19/9.82 (((setextsub) => 72.19/9.82 (((subsetemptysetimpeq) => 72.19/9.82 (((powersetI1) => 72.19/9.82 (((powersetE1) => 72.19/9.82 (((inPowerset) => 72.19/9.82 (((powersetsubset) => 72.19/9.82 (((sepInPowerset) => 72.19/9.82 (((sepSubset) => 72.19/9.82 (((binunionIL) => 72.19/9.82 (((upairset2IR) => 72.19/9.82 (((binunionIR) => 72.19/9.82 (((binunionEcases) => 72.19/9.82 (((binunionE) => 72.19/9.82 (((binunionLsub) => 72.19/9.82 (((binunionRsub) => 72.19/9.82 (((binintersectI) => 72.19/9.82 (((binintersectSubset5) => 72.19/9.82 (((binintersectEL) => 72.19/9.82 (((binintersectLsub) => 72.19/9.82 (((binintersectSubset2) => 72.19/9.82 (((binintersectSubset3) => 72.19/9.82 (((binintersectER) => 72.19/9.82 (((disjointsetsI1) => 72.19/9.82 (((binintersectRsub) => 72.19/9.82 (((binintersectSubset4) => 72.19/9.82 (((binintersectSubset1) => 72.19/9.82 (((bs114d) => 72.19/9.82 (((setminusI) => 72.19/9.82 (( 72.19/9.82 (setminusEL) => 72.19/9.82 (( 72.19/9.82 (setminusER) => 72.19/9.82 (( 72.19/9.82 (setminusSubset2) => 72.19/9.82 (( 72.19/9.82 (setminusERneg) => 72.19/9.82 (( 72.19/9.82 (setminusELneg) => 72.19/9.82 (( 72.19/9.82 (setminusILneg) => 72.19/9.82 (( 72.19/9.82 (setminusIRneg) => 72.19/9.82 (( 72.19/9.82 (setminusLsub) => 72.19/9.82 (( 72.19/9.82 (setminusSubset1) => 72.19/9.82 (( 72.19/9.82 (symdiffE) => 72.19/9.82 (( 72.19/9.82 (symdiffI1) => 72.19/9.82 (( 72.19/9.82 (symdiffI2) => 72.19/9.82 (( 72.19/9.82 (symdiffIneg1) => 72.19/9.82 (( 72.19/9.82 (symdiffIneg2) => 72.19/9.82 (( 72.19/9.82 (secondinupair) => 72.19/9.82 (( 72.19/9.82 (setukpairIL) => 72.19/9.82 (( 72.19/9.82 (setukpairIR) => 72.19/9.82 (( 72.19/9.82 (kpairiskpair) => 72.19/9.82 (( 72.19/9.82 (kpairp) => 72.19/9.82 (( 72.19/9.82 (singletonsubset) => 72.19/9.82 (( 72.19/9.82 (singletoninpowerset) => 72.19/9.82 (( 72.19/9.82 (singletoninpowunion) => 72.19/9.82 (( 72.19/9.82 (upairset2E) => 72.19/9.82 (( 72.19/9.82 (upairsubunion) => 72.19/9.82 (( 72.19/9.82 (upairinpowunion) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem1) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem2) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem3) => 72.19/9.82 (( 72.19/9.82 (cartprodpairin) => 72.19/9.82 (( 72.19/9.82 (cartprodmempair1) => 72.19/9.82 (( 72.19/9.82 (cartprodmempair) => 72.19/9.82 (( 72.19/9.82 (setunionE2) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton1) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton2) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton) => 72.19/9.82 (( 72.19/9.82 (singletonprop) => 72.19/9.82 (( 72.19/9.82 (ex1E1) => 72.19/9.82 (( 72.19/9.82 (ex1I) => 72.19/9.82 (( 72.19/9.82 (ex1I2) => 72.19/9.82 (( 72.19/9.82 (singletonsuniq) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL1) => 72.19/9.82 (( 72.19/9.82 (kfstsingleton) => 72.19/9.82 (( 72.19/9.82 (theprop) => 72.19/9.82 (( 72.19/9.82 (kfstpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodfstin) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL2) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR11) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR12) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR1) => 72.19/9.82 (( 72.19/9.82 (upairequniteq) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR2) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR) => 72.19/9.82 (( 72.19/9.82 (ksndsingleton) => 72.19/9.82 (( 72.19/9.82 (ksndpairEq) => 72.19/9.82 (( 72.19/9.82 (kpairsurjEq) => 72.19/9.82 (( 72.19/9.82 (cartprodsndin) => 72.19/9.82 (( 72.19/9.82 (cartprodpairmemEL) => 72.19/9.82 (( 72.19/9.82 (cartprodpairmemER) => 72.19/9.82 (( 72.19/9.82 (cartprodmempaircEq) => 72.19/9.82 (( 72.19/9.82 (cartprodfstpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodsndpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodpairsurjEq) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrI) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrSub) => 72.19/9.82 (( 72.19/9.82 (setOfPairsIsBReln) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrERa) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrEL1) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrEL2) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrER) => 72.19/9.82 (( 72.19/9.82 (funcImageSingleton) => 72.19/9.82 (( 72.19/9.82 (apProp) => 72.19/9.82 (( 72.19/9.82 (app) => 72.19/9.82 (( 72.19/9.82 (infuncsetfunc) => 72.19/9.82 (( 72.19/9.82 (ap2p) => 72.19/9.82 (( 72.19/9.82 (funcinfuncset) => 72.19/9.82 (( 72.19/9.82 (lamProp) => 72.19/9.82 (( 72.19/9.82 (lamp) => 72.19/9.82 (( 72.19/9.82 (lam2p) => 72.19/9.82 (( 72.19/9.82 (brelnall1) => 72.19/9.82 (( 72.19/9.82 (brelnall2) => 72.19/9.82 (( 72.19/9.82 (ex1E2) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp1) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp3) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp2) => 72.19/9.82 (( 72.19/9.82 (funcextLem) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp4) => 72.19/9.82 (( 72.19/9.82 (subbreln) => 72.19/9.82 (( 72.19/9.82 (eqbreln) => 72.19/9.82 (( 72.19/9.82 (funcext) => 72.19/9.82 (( 72.19/9.82 (funcext2) => 72.19/9.82 (( 72.19/9.82 (ap2apEq1) => 72.19/9.82 (( 72.19/9.82 (ap2apEq2) => 72.19/9.82 (( 72.19/9.82 (beta1) => 72.19/9.82 (( 72.19/9.82 (eta1) => 72.19/9.82 (( 72.19/9.82 (lam2lamEq) => 72.19/9.82 (( 72.19/9.82 (beta2) => 72.19/9.82 (( 72.19/9.82 (eta2) => 72.19/9.82 (( 72.19/9.82 (iffalseProp1) => 72.19/9.82 (( 72.19/9.82 (iffalseProp2) => 72.19/9.82 (( 72.19/9.82 (iftrueProp1) => 72.19/9.82 (( 72.19/9.82 (iftrueProp2) => 72.19/9.82 (( 72.19/9.82 (ifSingleton) => 72.19/9.82 (( 72.19/9.82 (ifp) => 72.19/9.82 (( 72.19/9.82 (theeq) => 72.19/9.82 (( 72.19/9.82 (iftrue) => 72.19/9.82 (( 72.19/9.82 (iffalse) => 72.19/9.82 (( 72.19/9.82 (iftrueorfalse) => 72.19/9.82 (( 72.19/9.82 (binintersectT_lem) => 72.19/9.82 (( 72.19/9.82 (binunionT_lem) => 72.19/9.82 (( 72.19/9.82 (powersetT_lem) => 72.19/9.82 (( 72.19/9.82 (setminusT_lem) => 72.19/9.82 (( 72.19/9.82 (complementT_lem) => 72.19/9.82 (( 72.19/9.82 (setextT) => 72.19/9.82 (( 72.19/9.82 (subsetTI) => 72.19/9.82 (( 72.19/9.82 (powersetTI1) => 72.19/9.82 (( 72.19/9.82 (powersetTE1) => 72.19/9.82 (( 72.19/9.82 (complementTI1) => 72.19/9.82 (( 72.19/9.82 (complementTE1) => 72.19/9.82 (( 72.19/9.82 (binintersectTELcontra) => 72.19/9.82 (( 72.19/9.82 (binintersectTERcontra) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT1) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT2) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT3) => 72.19/9.82 (( 72.19/9.82 (doubleComplementI1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementE1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementSub1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementSub2) => 72.19/9.82 (( 72.19/9.82 (doubleComplementEq) => 72.19/9.82 (( 72.19/9.82 (complementTnotintersectT) => 72.19/9.82 (( 72.19/9.82 (complementImpComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (complementSubsetComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (complementInPowersetComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (contraSubsetComplement) => 72.19/9.82 (( 72.19/9.82 (complementTcontraSubset) => 72.19/9.82 (( 72.19/9.82 (binunionTILcontra) => 72.19/9.82 (( 72.19/9.82 (binunionTIRcontra) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInUnion) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInUnion2) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInIntersectUnions) => 72.19/9.82 (( 72.19/9.82 (intersectInPowersetIntersectUnions) => 72.19/9.82 (( 72.19/9.82 (inComplementUnionImpNotIn1) => 72.19/9.82 (( 72.19/9.82 (inComplementUnionImpInComplement1) => 72.19/9.82 (( 72.19/9.82 (binunionTE) => 72.19/9.82 (( 72.19/9.82 (binunionTEcontra) => 72.19/9.82 (( 72.19/9.82 (demorgan2a1) => 72.19/9.82 (( 72.19/9.82 (complementUnionInPowersetComplement) => 72.19/9.82 (( 72.19/9.82 (demorgan2a2) => 72.19/9.82 (( 72.19/9.82 (demorgan1a) => 72.19/9.82 (( 72.19/9.82 (demorgan1b) => 72.19/9.82 (( 72.19/9.82 (demorgan1) => 72.19/9.82 (( 72.19/9.82 (demorgan2a) => 72.19/9.82 (( 72.19/9.82 (demorgan2b2) => 72.19/9.82 (( 72.19/9.82 (demorgan2b) => 72.19/9.82 (( 72.19/9.82 (demorgan2) => 72.19/9.82 (( 72.19/9.82 (woz13rule0) => 72.19/9.82 (( 72.19/9.82 (woz13rule1) => 72.19/9.82 (( 72.19/9.82 (woz13rule2) => 72.19/9.82 (( 72.19/9.82 (woz13rule3) => 72.19/9.82 (( 72.19/9.82 (woz13rule4) => 72.19/9.82 (( 72.19/9.82 (woz1_1) => 72.19/9.82 (( 72.19/9.82 (woz1_2) => 72.19/9.82 (( 72.19/9.82 (woz1_3) => 72.19/9.82 (( 72.19/9.82 (woz1_4) => 72.19/9.82 (( 72.19/9.82 (woz1_5) => 72.19/9.82 (( 72.19/9.82 (breln1all2) => 72.19/9.82 (( 72.19/9.82 (breln1SetBreln1) => 72.19/9.82 (( 72.19/9.82 (choice2fnsingleton) => 72.19/9.82 (( 72.19/9.82 (setOfPairsIsBReln1) => 72.19/9.82 (( 72.19/9.82 (breln1all1) => 72.19/9.82 (( 72.19/9.82 (subbreln1) => 72.19/9.82 (( 72.19/9.82 (eqbreln1) => 72.19/9.82 (( 72.19/9.82 (breln1invprop) => 72.19/9.82 (( 72.19/9.82 (breln1invI) => 72.19/9.82 (( 72.19/9.82 (breln1invE) => 72.19/9.82 (( 72.19/9.82 (breln1compprop) => 72.19/9.82 (( 72.19/9.82 (breln1compI) => 72.19/9.82 (( 72.19/9.82 (breln1compE) => 72.19/9.82 (( 72.19/9.82 (breln1compEex) => 72.19/9.82 (( 72.19/9.82 (!!) @ ( 72.19/9.82 (('#B') @ ( 72.19/9.82 !!) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#S') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#S') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 =>))) @ 72.19/9.82 breln1)))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 !!))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#S') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#S') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 =>))) @ 72.19/9.82 breln1)))))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#C') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 breln1)))) @ 72.19/9.82 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.19/9.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl967])). 72.19/9.82 thf(zip_derived_cl1000, plain, 72.19/9.82 (~ (((subset2powerset) => 72.19/9.82 (((setextsub) => 72.19/9.82 (((subsetemptysetimpeq) => 72.19/9.82 (((powersetI1) => 72.19/9.82 (((powersetE1) => 72.19/9.82 (((inPowerset) => 72.19/9.82 (((powersetsubset) => 72.19/9.82 (((sepInPowerset) => 72.19/9.82 (((sepSubset) => 72.19/9.82 (((binunionIL) => 72.19/9.82 (((upairset2IR) => 72.19/9.82 (((binunionIR) => 72.19/9.82 (((binunionEcases) => 72.19/9.82 (((binunionE) => 72.19/9.82 (((binunionLsub) => 72.19/9.82 (((binunionRsub) => 72.19/9.82 (((binintersectI) => 72.19/9.82 (((binintersectSubset5) => 72.19/9.82 (((binintersectEL) => 72.19/9.82 (((binintersectLsub) => 72.19/9.82 (((binintersectSubset2) => 72.19/9.82 (((binintersectSubset3) => 72.19/9.82 (((binintersectER) => 72.19/9.82 (((disjointsetsI1) => 72.19/9.82 (((binintersectRsub) => 72.19/9.82 (((binintersectSubset4) => 72.19/9.82 (((binintersectSubset1) => 72.19/9.82 (((bs114d) => 72.19/9.82 (((setminusI) => 72.19/9.82 (((setminusEL) => 72.19/9.82 (( 72.19/9.82 (setminusER) => 72.19/9.82 (( 72.19/9.82 (setminusSubset2) => 72.19/9.82 (( 72.19/9.82 (setminusERneg) => 72.19/9.82 (( 72.19/9.82 (setminusELneg) => 72.19/9.82 (( 72.19/9.82 (setminusILneg) => 72.19/9.82 (( 72.19/9.82 (setminusIRneg) => 72.19/9.82 (( 72.19/9.82 (setminusLsub) => 72.19/9.82 (( 72.19/9.82 (setminusSubset1) => 72.19/9.82 (( 72.19/9.82 (symdiffE) => 72.19/9.82 (( 72.19/9.82 (symdiffI1) => 72.19/9.82 (( 72.19/9.82 (symdiffI2) => 72.19/9.82 (( 72.19/9.82 (symdiffIneg1) => 72.19/9.82 (( 72.19/9.82 (symdiffIneg2) => 72.19/9.82 (( 72.19/9.82 (secondinupair) => 72.19/9.82 (( 72.19/9.82 (setukpairIL) => 72.19/9.82 (( 72.19/9.82 (setukpairIR) => 72.19/9.82 (( 72.19/9.82 (kpairiskpair) => 72.19/9.82 (( 72.19/9.82 (kpairp) => 72.19/9.82 (( 72.19/9.82 (singletonsubset) => 72.19/9.82 (( 72.19/9.82 (singletoninpowerset) => 72.19/9.82 (( 72.19/9.82 (singletoninpowunion) => 72.19/9.82 (( 72.19/9.82 (upairset2E) => 72.19/9.82 (( 72.19/9.82 (upairsubunion) => 72.19/9.82 (( 72.19/9.82 (upairinpowunion) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem1) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem2) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem3) => 72.19/9.82 (( 72.19/9.82 (cartprodpairin) => 72.19/9.82 (( 72.19/9.82 (cartprodmempair1) => 72.19/9.82 (( 72.19/9.82 (cartprodmempair) => 72.19/9.82 (( 72.19/9.82 (setunionE2) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton1) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton2) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton) => 72.19/9.82 (( 72.19/9.82 (singletonprop) => 72.19/9.82 (( 72.19/9.82 (ex1E1) => 72.19/9.82 (( 72.19/9.82 (ex1I) => 72.19/9.82 (( 72.19/9.82 (ex1I2) => 72.19/9.82 (( 72.19/9.82 (singletonsuniq) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL1) => 72.19/9.82 (( 72.19/9.82 (kfstsingleton) => 72.19/9.82 (( 72.19/9.82 (theprop) => 72.19/9.82 (( 72.19/9.82 (kfstpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodfstin) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL2) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR11) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR12) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR1) => 72.19/9.82 (( 72.19/9.82 (upairequniteq) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR2) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR) => 72.19/9.82 (( 72.19/9.82 (ksndsingleton) => 72.19/9.82 (( 72.19/9.82 (ksndpairEq) => 72.19/9.82 (( 72.19/9.82 (kpairsurjEq) => 72.19/9.82 (( 72.19/9.82 (cartprodsndin) => 72.19/9.82 (( 72.19/9.82 (cartprodpairmemEL) => 72.19/9.82 (( 72.19/9.82 (cartprodpairmemER) => 72.19/9.82 (( 72.19/9.82 (cartprodmempaircEq) => 72.19/9.82 (( 72.19/9.82 (cartprodfstpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodsndpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodpairsurjEq) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrI) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrSub) => 72.19/9.82 (( 72.19/9.82 (setOfPairsIsBReln) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrERa) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrEL1) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrEL2) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrER) => 72.19/9.82 (( 72.19/9.82 (funcImageSingleton) => 72.19/9.82 (( 72.19/9.82 (apProp) => 72.19/9.82 (( 72.19/9.82 (app) => 72.19/9.82 (( 72.19/9.82 (infuncsetfunc) => 72.19/9.82 (( 72.19/9.82 (ap2p) => 72.19/9.82 (( 72.19/9.82 (funcinfuncset) => 72.19/9.82 (( 72.19/9.82 (lamProp) => 72.19/9.82 (( 72.19/9.82 (lamp) => 72.19/9.82 (( 72.19/9.82 (lam2p) => 72.19/9.82 (( 72.19/9.82 (brelnall1) => 72.19/9.82 (( 72.19/9.82 (brelnall2) => 72.19/9.82 (( 72.19/9.82 (ex1E2) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp1) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp3) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp2) => 72.19/9.82 (( 72.19/9.82 (funcextLem) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp4) => 72.19/9.82 (( 72.19/9.82 (subbreln) => 72.19/9.82 (( 72.19/9.82 (eqbreln) => 72.19/9.82 (( 72.19/9.82 (funcext) => 72.19/9.82 (( 72.19/9.82 (funcext2) => 72.19/9.82 (( 72.19/9.82 (ap2apEq1) => 72.19/9.82 (( 72.19/9.82 (ap2apEq2) => 72.19/9.82 (( 72.19/9.82 (beta1) => 72.19/9.82 (( 72.19/9.82 (eta1) => 72.19/9.82 (( 72.19/9.82 (lam2lamEq) => 72.19/9.82 (( 72.19/9.82 (beta2) => 72.19/9.82 (( 72.19/9.82 (eta2) => 72.19/9.82 (( 72.19/9.82 (iffalseProp1) => 72.19/9.82 (( 72.19/9.82 (iffalseProp2) => 72.19/9.82 (( 72.19/9.82 (iftrueProp1) => 72.19/9.82 (( 72.19/9.82 (iftrueProp2) => 72.19/9.82 (( 72.19/9.82 (ifSingleton) => 72.19/9.82 (( 72.19/9.82 (ifp) => 72.19/9.82 (( 72.19/9.82 (theeq) => 72.19/9.82 (( 72.19/9.82 (iftrue) => 72.19/9.82 (( 72.19/9.82 (iffalse) => 72.19/9.82 (( 72.19/9.82 (iftrueorfalse) => 72.19/9.82 (( 72.19/9.82 (binintersectT_lem) => 72.19/9.82 (( 72.19/9.82 (binunionT_lem) => 72.19/9.82 (( 72.19/9.82 (powersetT_lem) => 72.19/9.82 (( 72.19/9.82 (setminusT_lem) => 72.19/9.82 (( 72.19/9.82 (complementT_lem) => 72.19/9.82 (( 72.19/9.82 (setextT) => 72.19/9.82 (( 72.19/9.82 (subsetTI) => 72.19/9.82 (( 72.19/9.82 (powersetTI1) => 72.19/9.82 (( 72.19/9.82 (powersetTE1) => 72.19/9.82 (( 72.19/9.82 (complementTI1) => 72.19/9.82 (( 72.19/9.82 (complementTE1) => 72.19/9.82 (( 72.19/9.82 (binintersectTELcontra) => 72.19/9.82 (( 72.19/9.82 (binintersectTERcontra) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT1) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT2) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT3) => 72.19/9.82 (( 72.19/9.82 (doubleComplementI1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementE1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementSub1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementSub2) => 72.19/9.82 (( 72.19/9.82 (doubleComplementEq) => 72.19/9.82 (( 72.19/9.82 (complementTnotintersectT) => 72.19/9.82 (( 72.19/9.82 (complementImpComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (complementSubsetComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (complementInPowersetComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (contraSubsetComplement) => 72.19/9.82 (( 72.19/9.82 (complementTcontraSubset) => 72.19/9.82 (( 72.19/9.82 (binunionTILcontra) => 72.19/9.82 (( 72.19/9.82 (binunionTIRcontra) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInUnion) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInUnion2) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInIntersectUnions) => 72.19/9.82 (( 72.19/9.82 (intersectInPowersetIntersectUnions) => 72.19/9.82 (( 72.19/9.82 (inComplementUnionImpNotIn1) => 72.19/9.82 (( 72.19/9.82 (inComplementUnionImpInComplement1) => 72.19/9.82 (( 72.19/9.82 (binunionTE) => 72.19/9.82 (( 72.19/9.82 (binunionTEcontra) => 72.19/9.82 (( 72.19/9.82 (demorgan2a1) => 72.19/9.82 (( 72.19/9.82 (complementUnionInPowersetComplement) => 72.19/9.82 (( 72.19/9.82 (demorgan2a2) => 72.19/9.82 (( 72.19/9.82 (demorgan1a) => 72.19/9.82 (( 72.19/9.82 (demorgan1b) => 72.19/9.82 (( 72.19/9.82 (demorgan1) => 72.19/9.82 (( 72.19/9.82 (demorgan2a) => 72.19/9.82 (( 72.19/9.82 (demorgan2b2) => 72.19/9.82 (( 72.19/9.82 (demorgan2b) => 72.19/9.82 (( 72.19/9.82 (demorgan2) => 72.19/9.82 (( 72.19/9.82 (woz13rule0) => 72.19/9.82 (( 72.19/9.82 (woz13rule1) => 72.19/9.82 (( 72.19/9.82 (woz13rule2) => 72.19/9.82 (( 72.19/9.82 (woz13rule3) => 72.19/9.82 (( 72.19/9.82 (woz13rule4) => 72.19/9.82 (( 72.19/9.82 (woz1_1) => 72.19/9.82 (( 72.19/9.82 (woz1_2) => 72.19/9.82 (( 72.19/9.82 (woz1_3) => 72.19/9.82 (( 72.19/9.82 (woz1_4) => 72.19/9.82 (( 72.19/9.82 (woz1_5) => 72.19/9.82 (( 72.19/9.82 (breln1all2) => 72.19/9.82 (( 72.19/9.82 (breln1SetBreln1) => 72.19/9.82 (( 72.19/9.82 (choice2fnsingleton) => 72.19/9.82 (( 72.19/9.82 (setOfPairsIsBReln1) => 72.19/9.82 (( 72.19/9.82 (breln1all1) => 72.19/9.82 (( 72.19/9.82 (subbreln1) => 72.19/9.82 (( 72.19/9.82 (eqbreln1) => 72.19/9.82 (( 72.19/9.82 (breln1invprop) => 72.19/9.82 (( 72.19/9.82 (breln1invI) => 72.19/9.82 (( 72.19/9.82 (breln1invE) => 72.19/9.82 (( 72.19/9.82 (breln1compprop) => 72.19/9.82 (( 72.19/9.82 (breln1compI) => 72.19/9.82 (( 72.19/9.82 (breln1compE) => 72.19/9.82 (( 72.19/9.82 (breln1compEex) => 72.19/9.82 (( 72.19/9.82 (!!) @ ( 72.19/9.82 (('#B') @ ( 72.19/9.82 !!) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#S') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#S') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 =>))) @ 72.19/9.82 breln1)))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 !!))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#S') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#S') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 =>))) @ 72.19/9.82 breln1)))))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#C') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 breln1)))) @ 72.19/9.82 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.19/9.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl984])). 72.19/9.82 thf(zip_derived_cl1015, plain, 72.19/9.82 (~ (((setextsub) => 72.19/9.82 (((subsetemptysetimpeq) => 72.19/9.82 (((powersetI1) => 72.19/9.82 (((powersetE1) => 72.19/9.82 (((inPowerset) => 72.19/9.82 (((powersetsubset) => 72.19/9.82 (((sepInPowerset) => 72.19/9.82 (((sepSubset) => 72.19/9.82 (((binunionIL) => 72.19/9.82 (((upairset2IR) => 72.19/9.82 (((binunionIR) => 72.19/9.82 (((binunionEcases) => 72.19/9.82 (((binunionE) => 72.19/9.82 (((binunionLsub) => 72.19/9.82 (((binunionRsub) => 72.19/9.82 (((binintersectI) => 72.19/9.82 (((binintersectSubset5) => 72.19/9.82 (((binintersectEL) => 72.19/9.82 (((binintersectLsub) => 72.19/9.82 (((binintersectSubset2) => 72.19/9.82 (((binintersectSubset3) => 72.19/9.82 (((binintersectER) => 72.19/9.82 (((disjointsetsI1) => 72.19/9.82 (((binintersectRsub) => 72.19/9.82 (((binintersectSubset4) => 72.19/9.82 (((binintersectSubset1) => 72.19/9.82 (((bs114d) => 72.19/9.82 (((setminusI) => 72.19/9.82 (((setminusEL) => 72.19/9.82 (((setminusER) => 72.19/9.82 (( 72.19/9.82 (setminusSubset2) => 72.19/9.82 (( 72.19/9.82 (setminusERneg) => 72.19/9.82 (( 72.19/9.82 (setminusELneg) => 72.19/9.82 (( 72.19/9.82 (setminusILneg) => 72.19/9.82 (( 72.19/9.82 (setminusIRneg) => 72.19/9.82 (( 72.19/9.82 (setminusLsub) => 72.19/9.82 (( 72.19/9.82 (setminusSubset1) => 72.19/9.82 (( 72.19/9.82 (symdiffE) => 72.19/9.82 (( 72.19/9.82 (symdiffI1) => 72.19/9.82 (( 72.19/9.82 (symdiffI2) => 72.19/9.82 (( 72.19/9.82 (symdiffIneg1) => 72.19/9.82 (( 72.19/9.82 (symdiffIneg2) => 72.19/9.82 (( 72.19/9.82 (secondinupair) => 72.19/9.82 (( 72.19/9.82 (setukpairIL) => 72.19/9.82 (( 72.19/9.82 (setukpairIR) => 72.19/9.82 (( 72.19/9.82 (kpairiskpair) => 72.19/9.82 (( 72.19/9.82 (kpairp) => 72.19/9.82 (( 72.19/9.82 (singletonsubset) => 72.19/9.82 (( 72.19/9.82 (singletoninpowerset) => 72.19/9.82 (( 72.19/9.82 (singletoninpowunion) => 72.19/9.82 (( 72.19/9.82 (upairset2E) => 72.19/9.82 (( 72.19/9.82 (upairsubunion) => 72.19/9.82 (( 72.19/9.82 (upairinpowunion) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem1) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem2) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem3) => 72.19/9.82 (( 72.19/9.82 (cartprodpairin) => 72.19/9.82 (( 72.19/9.82 (cartprodmempair1) => 72.19/9.82 (( 72.19/9.82 (cartprodmempair) => 72.19/9.82 (( 72.19/9.82 (setunionE2) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton1) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton2) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton) => 72.19/9.82 (( 72.19/9.82 (singletonprop) => 72.19/9.82 (( 72.19/9.82 (ex1E1) => 72.19/9.82 (( 72.19/9.82 (ex1I) => 72.19/9.82 (( 72.19/9.82 (ex1I2) => 72.19/9.82 (( 72.19/9.82 (singletonsuniq) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL1) => 72.19/9.82 (( 72.19/9.82 (kfstsingleton) => 72.19/9.82 (( 72.19/9.82 (theprop) => 72.19/9.82 (( 72.19/9.82 (kfstpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodfstin) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL2) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR11) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR12) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR1) => 72.19/9.82 (( 72.19/9.82 (upairequniteq) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR2) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR) => 72.19/9.82 (( 72.19/9.82 (ksndsingleton) => 72.19/9.82 (( 72.19/9.82 (ksndpairEq) => 72.19/9.82 (( 72.19/9.82 (kpairsurjEq) => 72.19/9.82 (( 72.19/9.82 (cartprodsndin) => 72.19/9.82 (( 72.19/9.82 (cartprodpairmemEL) => 72.19/9.82 (( 72.19/9.82 (cartprodpairmemER) => 72.19/9.82 (( 72.19/9.82 (cartprodmempaircEq) => 72.19/9.82 (( 72.19/9.82 (cartprodfstpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodsndpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodpairsurjEq) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrI) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrSub) => 72.19/9.82 (( 72.19/9.82 (setOfPairsIsBReln) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrERa) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrEL1) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrEL2) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrER) => 72.19/9.82 (( 72.19/9.82 (funcImageSingleton) => 72.19/9.82 (( 72.19/9.82 (apProp) => 72.19/9.82 (( 72.19/9.82 (app) => 72.19/9.82 (( 72.19/9.82 (infuncsetfunc) => 72.19/9.82 (( 72.19/9.82 (ap2p) => 72.19/9.82 (( 72.19/9.82 (funcinfuncset) => 72.19/9.82 (( 72.19/9.82 (lamProp) => 72.19/9.82 (( 72.19/9.82 (lamp) => 72.19/9.82 (( 72.19/9.82 (lam2p) => 72.19/9.82 (( 72.19/9.82 (brelnall1) => 72.19/9.82 (( 72.19/9.82 (brelnall2) => 72.19/9.82 (( 72.19/9.82 (ex1E2) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp1) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp3) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp2) => 72.19/9.82 (( 72.19/9.82 (funcextLem) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp4) => 72.19/9.82 (( 72.19/9.82 (subbreln) => 72.19/9.82 (( 72.19/9.82 (eqbreln) => 72.19/9.82 (( 72.19/9.82 (funcext) => 72.19/9.82 (( 72.19/9.82 (funcext2) => 72.19/9.82 (( 72.19/9.82 (ap2apEq1) => 72.19/9.82 (( 72.19/9.82 (ap2apEq2) => 72.19/9.82 (( 72.19/9.82 (beta1) => 72.19/9.82 (( 72.19/9.82 (eta1) => 72.19/9.82 (( 72.19/9.82 (lam2lamEq) => 72.19/9.82 (( 72.19/9.82 (beta2) => 72.19/9.82 (( 72.19/9.82 (eta2) => 72.19/9.82 (( 72.19/9.82 (iffalseProp1) => 72.19/9.82 (( 72.19/9.82 (iffalseProp2) => 72.19/9.82 (( 72.19/9.82 (iftrueProp1) => 72.19/9.82 (( 72.19/9.82 (iftrueProp2) => 72.19/9.82 (( 72.19/9.82 (ifSingleton) => 72.19/9.82 (( 72.19/9.82 (ifp) => 72.19/9.82 (( 72.19/9.82 (theeq) => 72.19/9.82 (( 72.19/9.82 (iftrue) => 72.19/9.82 (( 72.19/9.82 (iffalse) => 72.19/9.82 (( 72.19/9.82 (iftrueorfalse) => 72.19/9.82 (( 72.19/9.82 (binintersectT_lem) => 72.19/9.82 (( 72.19/9.82 (binunionT_lem) => 72.19/9.82 (( 72.19/9.82 (powersetT_lem) => 72.19/9.82 (( 72.19/9.82 (setminusT_lem) => 72.19/9.82 (( 72.19/9.82 (complementT_lem) => 72.19/9.82 (( 72.19/9.82 (setextT) => 72.19/9.82 (( 72.19/9.82 (subsetTI) => 72.19/9.82 (( 72.19/9.82 (powersetTI1) => 72.19/9.82 (( 72.19/9.82 (powersetTE1) => 72.19/9.82 (( 72.19/9.82 (complementTI1) => 72.19/9.82 (( 72.19/9.82 (complementTE1) => 72.19/9.82 (( 72.19/9.82 (binintersectTELcontra) => 72.19/9.82 (( 72.19/9.82 (binintersectTERcontra) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT1) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT2) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT3) => 72.19/9.82 (( 72.19/9.82 (doubleComplementI1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementE1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementSub1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementSub2) => 72.19/9.82 (( 72.19/9.82 (doubleComplementEq) => 72.19/9.82 (( 72.19/9.82 (complementTnotintersectT) => 72.19/9.82 (( 72.19/9.82 (complementImpComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (complementSubsetComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (complementInPowersetComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (contraSubsetComplement) => 72.19/9.82 (( 72.19/9.82 (complementTcontraSubset) => 72.19/9.82 (( 72.19/9.82 (binunionTILcontra) => 72.19/9.82 (( 72.19/9.82 (binunionTIRcontra) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInUnion) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInUnion2) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInIntersectUnions) => 72.19/9.82 (( 72.19/9.82 (intersectInPowersetIntersectUnions) => 72.19/9.82 (( 72.19/9.82 (inComplementUnionImpNotIn1) => 72.19/9.82 (( 72.19/9.82 (inComplementUnionImpInComplement1) => 72.19/9.82 (( 72.19/9.82 (binunionTE) => 72.19/9.82 (( 72.19/9.82 (binunionTEcontra) => 72.19/9.82 (( 72.19/9.82 (demorgan2a1) => 72.19/9.82 (( 72.19/9.82 (complementUnionInPowersetComplement) => 72.19/9.82 (( 72.19/9.82 (demorgan2a2) => 72.19/9.82 (( 72.19/9.82 (demorgan1a) => 72.19/9.82 (( 72.19/9.82 (demorgan1b) => 72.19/9.82 (( 72.19/9.82 (demorgan1) => 72.19/9.82 (( 72.19/9.82 (demorgan2a) => 72.19/9.82 (( 72.19/9.82 (demorgan2b2) => 72.19/9.82 (( 72.19/9.82 (demorgan2b) => 72.19/9.82 (( 72.19/9.82 (demorgan2) => 72.19/9.82 (( 72.19/9.82 (woz13rule0) => 72.19/9.82 (( 72.19/9.82 (woz13rule1) => 72.19/9.82 (( 72.19/9.82 (woz13rule2) => 72.19/9.82 (( 72.19/9.82 (woz13rule3) => 72.19/9.82 (( 72.19/9.82 (woz13rule4) => 72.19/9.82 (( 72.19/9.82 (woz1_1) => 72.19/9.82 (( 72.19/9.82 (woz1_2) => 72.19/9.82 (( 72.19/9.82 (woz1_3) => 72.19/9.82 (( 72.19/9.82 (woz1_4) => 72.19/9.82 (( 72.19/9.82 (woz1_5) => 72.19/9.82 (( 72.19/9.82 (breln1all2) => 72.19/9.82 (( 72.19/9.82 (breln1SetBreln1) => 72.19/9.82 (( 72.19/9.82 (choice2fnsingleton) => 72.19/9.82 (( 72.19/9.82 (setOfPairsIsBReln1) => 72.19/9.82 (( 72.19/9.82 (breln1all1) => 72.19/9.82 (( 72.19/9.82 (subbreln1) => 72.19/9.82 (( 72.19/9.82 (eqbreln1) => 72.19/9.82 (( 72.19/9.82 (breln1invprop) => 72.19/9.82 (( 72.19/9.82 (breln1invI) => 72.19/9.82 (( 72.19/9.82 (breln1invE) => 72.19/9.82 (( 72.19/9.82 (breln1compprop) => 72.19/9.82 (( 72.19/9.82 (breln1compI) => 72.19/9.82 (( 72.19/9.82 (breln1compE) => 72.19/9.82 (( 72.19/9.82 (breln1compEex) => 72.19/9.82 (( 72.19/9.82 (!!) @ ( 72.19/9.82 (('#B') @ ( 72.19/9.82 !!) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#S') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#S') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 =>))) @ 72.19/9.82 breln1)))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 !!))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#S') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#S') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 =>))) @ 72.19/9.82 breln1)))))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#C') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 breln1)))) @ 72.19/9.82 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.19/9.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])). 72.19/9.82 thf(zip_derived_cl1027, plain, 72.19/9.82 (~ (((subsetemptysetimpeq) => 72.19/9.82 (((powersetI1) => 72.19/9.82 (((powersetE1) => 72.19/9.82 (((inPowerset) => 72.19/9.82 (((powersetsubset) => 72.19/9.82 (((sepInPowerset) => 72.19/9.82 (((sepSubset) => 72.19/9.82 (((binunionIL) => 72.19/9.82 (((upairset2IR) => 72.19/9.82 (((binunionIR) => 72.19/9.82 (((binunionEcases) => 72.19/9.82 (((binunionE) => 72.19/9.82 (((binunionLsub) => 72.19/9.82 (((binunionRsub) => 72.19/9.82 (((binintersectI) => 72.19/9.82 (((binintersectSubset5) => 72.19/9.82 (((binintersectEL) => 72.19/9.82 (((binintersectLsub) => 72.19/9.82 (((binintersectSubset2) => 72.19/9.82 (((binintersectSubset3) => 72.19/9.82 (((binintersectER) => 72.19/9.82 (((disjointsetsI1) => 72.19/9.82 (((binintersectRsub) => 72.19/9.82 (((binintersectSubset4) => 72.19/9.82 (((binintersectSubset1) => 72.19/9.82 (((bs114d) => 72.19/9.82 (((setminusI) => 72.19/9.82 (((setminusEL) => 72.19/9.82 (((setminusER) => 72.19/9.82 (((setminusSubset2) => 72.19/9.82 (( 72.19/9.82 (setminusERneg) => 72.19/9.82 (( 72.19/9.82 (setminusELneg) => 72.19/9.82 (( 72.19/9.82 (setminusILneg) => 72.19/9.82 (( 72.19/9.82 (setminusIRneg) => 72.19/9.82 (( 72.19/9.82 (setminusLsub) => 72.19/9.82 (( 72.19/9.82 (setminusSubset1) => 72.19/9.82 (( 72.19/9.82 (symdiffE) => 72.19/9.82 (( 72.19/9.82 (symdiffI1) => 72.19/9.82 (( 72.19/9.82 (symdiffI2) => 72.19/9.82 (( 72.19/9.82 (symdiffIneg1) => 72.19/9.82 (( 72.19/9.82 (symdiffIneg2) => 72.19/9.82 (( 72.19/9.82 (secondinupair) => 72.19/9.82 (( 72.19/9.82 (setukpairIL) => 72.19/9.82 (( 72.19/9.82 (setukpairIR) => 72.19/9.82 (( 72.19/9.82 (kpairiskpair) => 72.19/9.82 (( 72.19/9.82 (kpairp) => 72.19/9.82 (( 72.19/9.82 (singletonsubset) => 72.19/9.82 (( 72.19/9.82 (singletoninpowerset) => 72.19/9.82 (( 72.19/9.82 (singletoninpowunion) => 72.19/9.82 (( 72.19/9.82 (upairset2E) => 72.19/9.82 (( 72.19/9.82 (upairsubunion) => 72.19/9.82 (( 72.19/9.82 (upairinpowunion) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem1) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem2) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem3) => 72.19/9.82 (( 72.19/9.82 (cartprodpairin) => 72.19/9.82 (( 72.19/9.82 (cartprodmempair1) => 72.19/9.82 (( 72.19/9.82 (cartprodmempair) => 72.19/9.82 (( 72.19/9.82 (setunionE2) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton1) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton2) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton) => 72.19/9.82 (( 72.19/9.82 (singletonprop) => 72.19/9.82 (( 72.19/9.82 (ex1E1) => 72.19/9.82 (( 72.19/9.82 (ex1I) => 72.19/9.82 (( 72.19/9.82 (ex1I2) => 72.19/9.82 (( 72.19/9.82 (singletonsuniq) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL1) => 72.19/9.82 (( 72.19/9.82 (kfstsingleton) => 72.19/9.82 (( 72.19/9.82 (theprop) => 72.19/9.82 (( 72.19/9.82 (kfstpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodfstin) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL2) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR11) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR12) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR1) => 72.19/9.82 (( 72.19/9.82 (upairequniteq) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR2) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR) => 72.19/9.82 (( 72.19/9.82 (ksndsingleton) => 72.19/9.82 (( 72.19/9.82 (ksndpairEq) => 72.19/9.82 (( 72.19/9.82 (kpairsurjEq) => 72.19/9.82 (( 72.19/9.82 (cartprodsndin) => 72.19/9.82 (( 72.19/9.82 (cartprodpairmemEL) => 72.19/9.82 (( 72.19/9.82 (cartprodpairmemER) => 72.19/9.82 (( 72.19/9.82 (cartprodmempaircEq) => 72.19/9.82 (( 72.19/9.82 (cartprodfstpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodsndpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodpairsurjEq) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrI) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrSub) => 72.19/9.82 (( 72.19/9.82 (setOfPairsIsBReln) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrERa) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrEL1) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrEL2) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrER) => 72.19/9.82 (( 72.19/9.82 (funcImageSingleton) => 72.19/9.82 (( 72.19/9.82 (apProp) => 72.19/9.82 (( 72.19/9.82 (app) => 72.19/9.82 (( 72.19/9.82 (infuncsetfunc) => 72.19/9.82 (( 72.19/9.82 (ap2p) => 72.19/9.82 (( 72.19/9.82 (funcinfuncset) => 72.19/9.82 (( 72.19/9.82 (lamProp) => 72.19/9.82 (( 72.19/9.82 (lamp) => 72.19/9.82 (( 72.19/9.82 (lam2p) => 72.19/9.82 (( 72.19/9.82 (brelnall1) => 72.19/9.82 (( 72.19/9.82 (brelnall2) => 72.19/9.82 (( 72.19/9.82 (ex1E2) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp1) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp3) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp2) => 72.19/9.82 (( 72.19/9.82 (funcextLem) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp4) => 72.19/9.82 (( 72.19/9.82 (subbreln) => 72.19/9.82 (( 72.19/9.82 (eqbreln) => 72.19/9.82 (( 72.19/9.82 (funcext) => 72.19/9.82 (( 72.19/9.82 (funcext2) => 72.19/9.82 (( 72.19/9.82 (ap2apEq1) => 72.19/9.82 (( 72.19/9.82 (ap2apEq2) => 72.19/9.82 (( 72.19/9.82 (beta1) => 72.19/9.82 (( 72.19/9.82 (eta1) => 72.19/9.82 (( 72.19/9.82 (lam2lamEq) => 72.19/9.82 (( 72.19/9.82 (beta2) => 72.19/9.82 (( 72.19/9.82 (eta2) => 72.19/9.82 (( 72.19/9.82 (iffalseProp1) => 72.19/9.82 (( 72.19/9.82 (iffalseProp2) => 72.19/9.82 (( 72.19/9.82 (iftrueProp1) => 72.19/9.82 (( 72.19/9.82 (iftrueProp2) => 72.19/9.82 (( 72.19/9.82 (ifSingleton) => 72.19/9.82 (( 72.19/9.82 (ifp) => 72.19/9.82 (( 72.19/9.82 (theeq) => 72.19/9.82 (( 72.19/9.82 (iftrue) => 72.19/9.82 (( 72.19/9.82 (iffalse) => 72.19/9.82 (( 72.19/9.82 (iftrueorfalse) => 72.19/9.82 (( 72.19/9.82 (binintersectT_lem) => 72.19/9.82 (( 72.19/9.82 (binunionT_lem) => 72.19/9.82 (( 72.19/9.82 (powersetT_lem) => 72.19/9.82 (( 72.19/9.82 (setminusT_lem) => 72.19/9.82 (( 72.19/9.82 (complementT_lem) => 72.19/9.82 (( 72.19/9.82 (setextT) => 72.19/9.82 (( 72.19/9.82 (subsetTI) => 72.19/9.82 (( 72.19/9.82 (powersetTI1) => 72.19/9.82 (( 72.19/9.82 (powersetTE1) => 72.19/9.82 (( 72.19/9.82 (complementTI1) => 72.19/9.82 (( 72.19/9.82 (complementTE1) => 72.19/9.82 (( 72.19/9.82 (binintersectTELcontra) => 72.19/9.82 (( 72.19/9.82 (binintersectTERcontra) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT1) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT2) => 72.19/9.82 (( 72.19/9.82 (contrasubsetT3) => 72.19/9.82 (( 72.19/9.82 (doubleComplementI1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementE1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementSub1) => 72.19/9.82 (( 72.19/9.82 (doubleComplementSub2) => 72.19/9.82 (( 72.19/9.82 (doubleComplementEq) => 72.19/9.82 (( 72.19/9.82 (complementTnotintersectT) => 72.19/9.82 (( 72.19/9.82 (complementImpComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (complementSubsetComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (complementInPowersetComplementIntersect) => 72.19/9.82 (( 72.19/9.82 (contraSubsetComplement) => 72.19/9.82 (( 72.19/9.82 (complementTcontraSubset) => 72.19/9.82 (( 72.19/9.82 (binunionTILcontra) => 72.19/9.82 (( 72.19/9.82 (binunionTIRcontra) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInUnion) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInUnion2) => 72.19/9.82 (( 72.19/9.82 (inIntersectImpInIntersectUnions) => 72.19/9.82 (( 72.19/9.82 (intersectInPowersetIntersectUnions) => 72.19/9.82 (( 72.19/9.82 (inComplementUnionImpNotIn1) => 72.19/9.82 (( 72.19/9.82 (inComplementUnionImpInComplement1) => 72.19/9.82 (( 72.19/9.82 (binunionTE) => 72.19/9.82 (( 72.19/9.82 (binunionTEcontra) => 72.19/9.82 (( 72.19/9.82 (demorgan2a1) => 72.19/9.82 (( 72.19/9.82 (complementUnionInPowersetComplement) => 72.19/9.82 (( 72.19/9.82 (demorgan2a2) => 72.19/9.82 (( 72.19/9.82 (demorgan1a) => 72.19/9.82 (( 72.19/9.82 (demorgan1b) => 72.19/9.82 (( 72.19/9.82 (demorgan1) => 72.19/9.82 (( 72.19/9.82 (demorgan2a) => 72.19/9.82 (( 72.19/9.82 (demorgan2b2) => 72.19/9.82 (( 72.19/9.82 (demorgan2b) => 72.19/9.82 (( 72.19/9.82 (demorgan2) => 72.19/9.82 (( 72.19/9.82 (woz13rule0) => 72.19/9.82 (( 72.19/9.82 (woz13rule1) => 72.19/9.82 (( 72.19/9.82 (woz13rule2) => 72.19/9.82 (( 72.19/9.82 (woz13rule3) => 72.19/9.82 (( 72.19/9.82 (woz13rule4) => 72.19/9.82 (( 72.19/9.82 (woz1_1) => 72.19/9.82 (( 72.19/9.82 (woz1_2) => 72.19/9.82 (( 72.19/9.82 (woz1_3) => 72.19/9.82 (( 72.19/9.82 (woz1_4) => 72.19/9.82 (( 72.19/9.82 (woz1_5) => 72.19/9.82 (( 72.19/9.82 (breln1all2) => 72.19/9.82 (( 72.19/9.82 (breln1SetBreln1) => 72.19/9.82 (( 72.19/9.82 (choice2fnsingleton) => 72.19/9.82 (( 72.19/9.82 (setOfPairsIsBReln1) => 72.19/9.82 (( 72.19/9.82 (breln1all1) => 72.19/9.82 (( 72.19/9.82 (subbreln1) => 72.19/9.82 (( 72.19/9.82 (eqbreln1) => 72.19/9.82 (( 72.19/9.82 (breln1invprop) => 72.19/9.82 (( 72.19/9.82 (breln1invI) => 72.19/9.82 (( 72.19/9.82 (breln1invE) => 72.19/9.82 (( 72.19/9.82 (breln1compprop) => 72.19/9.82 (( 72.19/9.82 (breln1compI) => 72.19/9.82 (( 72.19/9.82 (breln1compE) => 72.19/9.82 (( 72.19/9.82 (breln1compEex) => 72.19/9.82 (( 72.19/9.82 (!!) @ ( 72.19/9.82 (('#B') @ ( 72.19/9.82 !!) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#S') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#S') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 =>))) @ 72.19/9.82 breln1)))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 !!))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#S') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#S') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 =>))) @ 72.19/9.82 breln1)))))) @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#C') @ ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 ( 72.19/9.82 ( 72.19/9.82 ('#B') @ ( 72.19/9.82 '#B') @ 72.19/9.82 breln1)))) @ 72.19/9.82 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.19/9.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1015])). 72.19/9.82 thf(zip_derived_cl1039, plain, 72.19/9.82 (~ (((powersetI1) => 72.19/9.82 (((powersetE1) => 72.19/9.82 (((inPowerset) => 72.19/9.82 (((powersetsubset) => 72.19/9.82 (((sepInPowerset) => 72.19/9.82 (((sepSubset) => 72.19/9.82 (((binunionIL) => 72.19/9.82 (((upairset2IR) => 72.19/9.82 (((binunionIR) => 72.19/9.82 (((binunionEcases) => 72.19/9.82 (((binunionE) => 72.19/9.82 (((binunionLsub) => 72.19/9.82 (((binunionRsub) => 72.19/9.82 (((binintersectI) => 72.19/9.82 (((binintersectSubset5) => 72.19/9.82 (((binintersectEL) => 72.19/9.82 (((binintersectLsub) => 72.19/9.82 (((binintersectSubset2) => 72.19/9.82 (((binintersectSubset3) => 72.19/9.82 (((binintersectER) => 72.19/9.82 (((disjointsetsI1) => 72.19/9.82 (((binintersectRsub) => 72.19/9.82 (((binintersectSubset4) => 72.19/9.82 (((binintersectSubset1) => 72.19/9.82 (((bs114d) => 72.19/9.82 (((setminusI) => 72.19/9.82 (((setminusEL) => 72.19/9.82 (((setminusER) => 72.19/9.82 (((setminusSubset2) => 72.19/9.82 (((setminusERneg) => 72.19/9.82 (( 72.19/9.82 (setminusELneg) => 72.19/9.82 (( 72.19/9.82 (setminusILneg) => 72.19/9.82 (( 72.19/9.82 (setminusIRneg) => 72.19/9.82 (( 72.19/9.82 (setminusLsub) => 72.19/9.82 (( 72.19/9.82 (setminusSubset1) => 72.19/9.82 (( 72.19/9.82 (symdiffE) => 72.19/9.82 (( 72.19/9.82 (symdiffI1) => 72.19/9.82 (( 72.19/9.82 (symdiffI2) => 72.19/9.82 (( 72.19/9.82 (symdiffIneg1) => 72.19/9.82 (( 72.19/9.82 (symdiffIneg2) => 72.19/9.82 (( 72.19/9.82 (secondinupair) => 72.19/9.82 (( 72.19/9.82 (setukpairIL) => 72.19/9.82 (( 72.19/9.82 (setukpairIR) => 72.19/9.82 (( 72.19/9.82 (kpairiskpair) => 72.19/9.82 (( 72.19/9.82 (kpairp) => 72.19/9.82 (( 72.19/9.82 (singletonsubset) => 72.19/9.82 (( 72.19/9.82 (singletoninpowerset) => 72.19/9.82 (( 72.19/9.82 (singletoninpowunion) => 72.19/9.82 (( 72.19/9.82 (upairset2E) => 72.19/9.82 (( 72.19/9.82 (upairsubunion) => 72.19/9.82 (( 72.19/9.82 (upairinpowunion) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem1) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem2) => 72.19/9.82 (( 72.19/9.82 (ubforcartprodlem3) => 72.19/9.82 (( 72.19/9.82 (cartprodpairin) => 72.19/9.82 (( 72.19/9.82 (cartprodmempair1) => 72.19/9.82 (( 72.19/9.82 (cartprodmempair) => 72.19/9.82 (( 72.19/9.82 (setunionE2) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton1) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton2) => 72.19/9.82 (( 72.19/9.82 (setunionsingleton) => 72.19/9.82 (( 72.19/9.82 (singletonprop) => 72.19/9.82 (( 72.19/9.82 (ex1E1) => 72.19/9.82 (( 72.19/9.82 (ex1I) => 72.19/9.82 (( 72.19/9.82 (ex1I2) => 72.19/9.82 (( 72.19/9.82 (singletonsuniq) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL1) => 72.19/9.82 (( 72.19/9.82 (kfstsingleton) => 72.19/9.82 (( 72.19/9.82 (theprop) => 72.19/9.82 (( 72.19/9.82 (kfstpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodfstin) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL2) => 72.19/9.82 (( 72.19/9.82 (setukpairinjL) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR11) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR12) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR1) => 72.19/9.82 (( 72.19/9.82 (upairequniteq) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR2) => 72.19/9.82 (( 72.19/9.82 (setukpairinjR) => 72.19/9.82 (( 72.19/9.82 (ksndsingleton) => 72.19/9.82 (( 72.19/9.82 (ksndpairEq) => 72.19/9.82 (( 72.19/9.82 (kpairsurjEq) => 72.19/9.82 (( 72.19/9.82 (cartprodsndin) => 72.19/9.82 (( 72.19/9.82 (cartprodpairmemEL) => 72.19/9.82 (( 72.19/9.82 (cartprodpairmemER) => 72.19/9.82 (( 72.19/9.82 (cartprodmempaircEq) => 72.19/9.82 (( 72.19/9.82 (cartprodfstpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodsndpairEq) => 72.19/9.82 (( 72.19/9.82 (cartprodpairsurjEq) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrI) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrSub) => 72.19/9.82 (( 72.19/9.82 (setOfPairsIsBReln) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrERa) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrEL1) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrEL2) => 72.19/9.82 (( 72.19/9.82 (dpsetconstrER) => 72.19/9.82 (( 72.19/9.82 (funcImageSingleton) => 72.19/9.82 (( 72.19/9.82 (apProp) => 72.19/9.82 (( 72.19/9.82 (app) => 72.19/9.82 (( 72.19/9.82 (infuncsetfunc) => 72.19/9.82 (( 72.19/9.82 (ap2p) => 72.19/9.82 (( 72.19/9.82 (funcinfuncset) => 72.19/9.82 (( 72.19/9.82 (lamProp) => 72.19/9.82 (( 72.19/9.82 (lamp) => 72.19/9.82 (( 72.19/9.82 (lam2p) => 72.19/9.82 (( 72.19/9.82 (brelnall1) => 72.19/9.82 (( 72.19/9.82 (brelnall2) => 72.19/9.82 (( 72.19/9.82 (ex1E2) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp1) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp3) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp2) => 72.19/9.82 (( 72.19/9.82 (funcextLem) => 72.19/9.82 (( 72.19/9.82 (funcGraphProp4) => 72.19/9.82 (( 72.19/9.82 (subbreln) => 72.19/9.82 (( 72.19/9.82 (eqbreln) => 72.19/9.82 (( 72.19/9.82 (funcext) => 72.19/9.82 (( 72.19/9.82 (funcext2) => 72.19/9.82 (( 72.19/9.82 (ap2apEq1) => 72.19/9.82 (( 72.19/9.82 (ap2apEq2) => 72.19/9.82 (( 72.19/9.82 (beta1) => 72.19/9.82 (( 72.19/9.82 (eta1) => 72.19/9.82 (( 72.19/9.82 (lam2lamEq) => 72.19/9.82 (( 72.19/9.82 (beta2) => 72.19/9.82 (( 72.19/9.82 (eta2) => 72.19/9.82 (( 72.19/9.82 (iffalseProp1) => 72.19/9.82 (( 72.19/9.82 (iffalseProp2) => 72.19/9.82 (( 72.19/9.82 (iftrueProp1) => 72.19/9.82 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72.19/9.83 (( 72.19/9.83 (funcGraphProp3) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp2) => 72.19/9.83 (( 72.19/9.83 (funcextLem) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp4) => 72.19/9.83 (( 72.19/9.83 (subbreln) => 72.19/9.83 (( 72.19/9.83 (eqbreln) => 72.19/9.83 (( 72.19/9.83 (funcext) => 72.19/9.83 (( 72.19/9.83 (funcext2) => 72.19/9.83 (( 72.19/9.83 (ap2apEq1) => 72.19/9.83 (( 72.19/9.83 (ap2apEq2) => 72.19/9.83 (( 72.19/9.83 (beta1) => 72.19/9.83 (( 72.19/9.83 (eta1) => 72.19/9.83 (( 72.19/9.83 (lam2lamEq) => 72.19/9.83 (( 72.19/9.83 (beta2) => 72.19/9.83 (( 72.19/9.83 (eta2) => 72.19/9.83 (( 72.19/9.83 (iffalseProp1) => 72.19/9.83 (( 72.19/9.83 (iffalseProp2) => 72.19/9.83 (( 72.19/9.83 (iftrueProp1) => 72.19/9.83 (( 72.19/9.83 (iftrueProp2) => 72.19/9.83 (( 72.19/9.83 (ifSingleton) => 72.19/9.83 (( 72.19/9.83 (ifp) => 72.19/9.83 (( 72.19/9.83 (theeq) => 72.19/9.83 (( 72.19/9.83 (iftrue) => 72.19/9.83 (( 72.19/9.83 (iffalse) => 72.19/9.83 (( 72.19/9.83 (iftrueorfalse) => 72.19/9.83 (( 72.19/9.83 (binintersectT_lem) => 72.19/9.83 (( 72.19/9.83 (binunionT_lem) => 72.19/9.83 (( 72.19/9.83 (powersetT_lem) => 72.19/9.83 (( 72.19/9.83 (setminusT_lem) => 72.19/9.83 (( 72.19/9.83 (complementT_lem) => 72.19/9.83 (( 72.19/9.83 (setextT) => 72.19/9.83 (( 72.19/9.83 (subsetTI) => 72.19/9.83 (( 72.19/9.83 (powersetTI1) => 72.19/9.83 (( 72.19/9.83 (powersetTE1) => 72.19/9.83 (( 72.19/9.83 (complementTI1) => 72.19/9.83 (( 72.19/9.83 (complementTE1) => 72.19/9.83 (( 72.19/9.83 (binintersectTELcontra) => 72.19/9.83 (( 72.19/9.83 (binintersectTERcontra) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT1) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT2) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT3) => 72.19/9.83 (( 72.19/9.83 (doubleComplementI1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementE1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementSub1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementSub2) => 72.19/9.83 (( 72.19/9.83 (doubleComplementEq) => 72.19/9.83 (( 72.19/9.83 (complementTnotintersectT) => 72.19/9.83 (( 72.19/9.83 (complementImpComplementIntersect) => 72.19/9.83 (( 72.19/9.83 (complementSubsetComplementIntersect) => 72.19/9.83 (( 72.19/9.83 (complementInPowersetComplementIntersect) => 72.19/9.83 (( 72.19/9.83 (contraSubsetComplement) => 72.19/9.83 (( 72.19/9.83 (complementTcontraSubset) => 72.19/9.83 (( 72.19/9.83 (binunionTILcontra) => 72.19/9.83 (( 72.19/9.83 (binunionTIRcontra) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInUnion) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInUnion2) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInIntersectUnions) => 72.19/9.83 (( 72.19/9.83 (intersectInPowersetIntersectUnions) => 72.19/9.83 (( 72.19/9.83 (inComplementUnionImpNotIn1) => 72.19/9.83 (( 72.19/9.83 (inComplementUnionImpInComplement1) => 72.19/9.83 (( 72.19/9.83 (binunionTE) => 72.19/9.83 (( 72.19/9.83 (binunionTEcontra) => 72.19/9.83 (( 72.19/9.83 (demorgan2a1) => 72.19/9.83 (( 72.19/9.83 (complementUnionInPowersetComplement) => 72.19/9.83 (( 72.19/9.83 (demorgan2a2) => 72.19/9.83 (( 72.19/9.83 (demorgan1a) => 72.19/9.83 (( 72.19/9.83 (demorgan1b) => 72.19/9.83 (( 72.19/9.83 (demorgan1) => 72.19/9.83 (( 72.19/9.83 (demorgan2a) => 72.19/9.83 (( 72.19/9.83 (demorgan2b2) => 72.19/9.83 (( 72.19/9.83 (demorgan2b) => 72.19/9.83 (( 72.19/9.83 (demorgan2) => 72.19/9.83 (( 72.19/9.83 (woz13rule0) => 72.19/9.83 (( 72.19/9.83 (woz13rule1) => 72.19/9.83 (( 72.19/9.83 (woz13rule2) => 72.19/9.83 (( 72.19/9.83 (woz13rule3) => 72.19/9.83 (( 72.19/9.83 (woz13rule4) => 72.19/9.83 (( 72.19/9.83 (woz1_1) => 72.19/9.83 (( 72.19/9.83 (woz1_2) => 72.19/9.83 (( 72.19/9.83 (woz1_3) => 72.19/9.83 (( 72.19/9.83 (woz1_4) => 72.19/9.83 (( 72.19/9.83 (woz1_5) => 72.19/9.83 (( 72.19/9.83 (breln1all2) => 72.19/9.83 (( 72.19/9.83 (breln1SetBreln1) => 72.19/9.83 (( 72.19/9.83 (choice2fnsingleton) => 72.19/9.83 (( 72.19/9.83 (setOfPairsIsBReln1) => 72.19/9.83 (( 72.19/9.83 (breln1all1) => 72.19/9.83 (( 72.19/9.83 (subbreln1) => 72.19/9.83 (( 72.19/9.83 (eqbreln1) => 72.19/9.83 (( 72.19/9.83 (breln1invprop) => 72.19/9.83 (( 72.19/9.83 (breln1invI) => 72.19/9.83 (( 72.19/9.83 (breln1invE) => 72.19/9.83 (( 72.19/9.83 (breln1compprop) => 72.19/9.83 (( 72.19/9.83 (breln1compI) => 72.19/9.83 (( 72.19/9.83 (breln1compE) => 72.19/9.83 (( 72.19/9.83 (breln1compEex) => 72.19/9.83 (( 72.19/9.83 (!!) @ ( 72.19/9.83 (('#B') @ ( 72.19/9.83 !!) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#S') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#S') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 =>))) @ 72.19/9.83 breln1)))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 !!))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#S') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#S') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 =>))) @ 72.19/9.83 breln1)))))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#C') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 breln1)))) @ 72.19/9.83 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.19/9.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1067])). 72.19/9.83 thf(zip_derived_cl1082, plain, 72.19/9.83 (~ (((sepInPowerset) => 72.19/9.83 (((sepSubset) => 72.19/9.83 (((binunionIL) => 72.19/9.83 (((upairset2IR) => 72.19/9.83 (((binunionIR) => 72.19/9.83 (((binunionEcases) => 72.19/9.83 (((binunionE) => 72.19/9.83 (((binunionLsub) => 72.19/9.83 (((binunionRsub) => 72.19/9.83 (((binintersectI) => 72.19/9.83 (((binintersectSubset5) => 72.19/9.83 (((binintersectEL) => 72.19/9.83 (((binintersectLsub) => 72.19/9.83 (((binintersectSubset2) => 72.19/9.83 (((binintersectSubset3) => 72.19/9.83 (((binintersectER) => 72.19/9.83 (((disjointsetsI1) => 72.19/9.83 (((binintersectRsub) => 72.19/9.83 (((binintersectSubset4) => 72.19/9.83 (((binintersectSubset1) => 72.19/9.83 (((bs114d) => 72.19/9.83 (((setminusI) => 72.19/9.83 (((setminusEL) => 72.19/9.83 (((setminusER) => 72.19/9.83 (((setminusSubset2) => 72.19/9.83 (((setminusERneg) => 72.19/9.83 (((setminusELneg) => 72.19/9.83 (((setminusILneg) => 72.19/9.83 (((setminusIRneg) => 72.19/9.83 (((setminusLsub) => 72.19/9.83 (( 72.19/9.83 (setminusSubset1) => 72.19/9.83 (( 72.19/9.83 (symdiffE) => 72.19/9.83 (( 72.19/9.83 (symdiffI1) => 72.19/9.83 (( 72.19/9.83 (symdiffI2) => 72.19/9.83 (( 72.19/9.83 (symdiffIneg1) => 72.19/9.83 (( 72.19/9.83 (symdiffIneg2) => 72.19/9.83 (( 72.19/9.83 (secondinupair) => 72.19/9.83 (( 72.19/9.83 (setukpairIL) => 72.19/9.83 (( 72.19/9.83 (setukpairIR) => 72.19/9.83 (( 72.19/9.83 (kpairiskpair) => 72.19/9.83 (( 72.19/9.83 (kpairp) => 72.19/9.83 (( 72.19/9.83 (singletonsubset) => 72.19/9.83 (( 72.19/9.83 (singletoninpowerset) => 72.19/9.83 (( 72.19/9.83 (singletoninpowunion) => 72.19/9.83 (( 72.19/9.83 (upairset2E) => 72.19/9.83 (( 72.19/9.83 (upairsubunion) => 72.19/9.83 (( 72.19/9.83 (upairinpowunion) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem1) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem2) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem3) => 72.19/9.83 (( 72.19/9.83 (cartprodpairin) => 72.19/9.83 (( 72.19/9.83 (cartprodmempair1) => 72.19/9.83 (( 72.19/9.83 (cartprodmempair) => 72.19/9.83 (( 72.19/9.83 (setunionE2) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton1) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton2) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton) => 72.19/9.83 (( 72.19/9.83 (singletonprop) => 72.19/9.83 (( 72.19/9.83 (ex1E1) => 72.19/9.83 (( 72.19/9.83 (ex1I) => 72.19/9.83 (( 72.19/9.83 (ex1I2) => 72.19/9.83 (( 72.19/9.83 (singletonsuniq) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL1) => 72.19/9.83 (( 72.19/9.83 (kfstsingleton) => 72.19/9.83 (( 72.19/9.83 (theprop) => 72.19/9.83 (( 72.19/9.83 (kfstpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodfstin) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL2) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR11) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR12) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR1) => 72.19/9.83 (( 72.19/9.83 (upairequniteq) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR2) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR) => 72.19/9.83 (( 72.19/9.83 (ksndsingleton) => 72.19/9.83 (( 72.19/9.83 (ksndpairEq) => 72.19/9.83 (( 72.19/9.83 (kpairsurjEq) => 72.19/9.83 (( 72.19/9.83 (cartprodsndin) => 72.19/9.83 (( 72.19/9.83 (cartprodpairmemEL) => 72.19/9.83 (( 72.19/9.83 (cartprodpairmemER) => 72.19/9.83 (( 72.19/9.83 (cartprodmempaircEq) => 72.19/9.83 (( 72.19/9.83 (cartprodfstpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodsndpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodpairsurjEq) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrI) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrSub) => 72.19/9.83 (( 72.19/9.83 (setOfPairsIsBReln) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrERa) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrEL1) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrEL2) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrER) => 72.19/9.83 (( 72.19/9.83 (funcImageSingleton) => 72.19/9.83 (( 72.19/9.83 (apProp) => 72.19/9.83 (( 72.19/9.83 (app) => 72.19/9.83 (( 72.19/9.83 (infuncsetfunc) => 72.19/9.83 (( 72.19/9.83 (ap2p) => 72.19/9.83 (( 72.19/9.83 (funcinfuncset) => 72.19/9.83 (( 72.19/9.83 (lamProp) => 72.19/9.83 (( 72.19/9.83 (lamp) => 72.19/9.83 (( 72.19/9.83 (lam2p) => 72.19/9.83 (( 72.19/9.83 (brelnall1) => 72.19/9.83 (( 72.19/9.83 (brelnall2) => 72.19/9.83 (( 72.19/9.83 (ex1E2) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp1) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp3) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp2) => 72.19/9.83 (( 72.19/9.83 (funcextLem) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp4) => 72.19/9.83 (( 72.19/9.83 (subbreln) => 72.19/9.83 (( 72.19/9.83 (eqbreln) => 72.19/9.83 (( 72.19/9.83 (funcext) => 72.19/9.83 (( 72.19/9.83 (funcext2) => 72.19/9.83 (( 72.19/9.83 (ap2apEq1) => 72.19/9.83 (( 72.19/9.83 (ap2apEq2) => 72.19/9.83 (( 72.19/9.83 (beta1) => 72.19/9.83 (( 72.19/9.83 (eta1) => 72.19/9.83 (( 72.19/9.83 (lam2lamEq) => 72.19/9.83 (( 72.19/9.83 (beta2) => 72.19/9.83 (( 72.19/9.83 (eta2) => 72.19/9.83 (( 72.19/9.83 (iffalseProp1) => 72.19/9.83 (( 72.19/9.83 (iffalseProp2) => 72.19/9.83 (( 72.19/9.83 (iftrueProp1) => 72.19/9.83 (( 72.19/9.83 (iftrueProp2) => 72.19/9.83 (( 72.19/9.83 (ifSingleton) => 72.19/9.83 (( 72.19/9.83 (ifp) => 72.19/9.83 (( 72.19/9.83 (theeq) => 72.19/9.83 (( 72.19/9.83 (iftrue) => 72.19/9.83 (( 72.19/9.83 (iffalse) => 72.19/9.83 (( 72.19/9.83 (iftrueorfalse) => 72.19/9.83 (( 72.19/9.83 (binintersectT_lem) => 72.19/9.83 (( 72.19/9.83 (binunionT_lem) => 72.19/9.83 (( 72.19/9.83 (powersetT_lem) => 72.19/9.83 (( 72.19/9.83 (setminusT_lem) => 72.19/9.83 (( 72.19/9.83 (complementT_lem) => 72.19/9.83 (( 72.19/9.83 (setextT) => 72.19/9.83 (( 72.19/9.83 (subsetTI) => 72.19/9.83 (( 72.19/9.83 (powersetTI1) => 72.19/9.83 (( 72.19/9.83 (powersetTE1) => 72.19/9.83 (( 72.19/9.83 (complementTI1) => 72.19/9.83 (( 72.19/9.83 (complementTE1) => 72.19/9.83 (( 72.19/9.83 (binintersectTELcontra) => 72.19/9.83 (( 72.19/9.83 (binintersectTERcontra) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT1) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT2) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT3) => 72.19/9.83 (( 72.19/9.83 (doubleComplementI1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementE1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementSub1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementSub2) => 72.19/9.83 (( 72.19/9.83 (doubleComplementEq) => 72.19/9.83 (( 72.19/9.83 (complementTnotintersectT) => 72.19/9.83 (( 72.19/9.83 (complementImpComplementIntersect) => 72.19/9.83 (( 72.19/9.83 (complementSubsetComplementIntersect) => 72.19/9.83 (( 72.19/9.83 (complementInPowersetComplementIntersect) => 72.19/9.83 (( 72.19/9.83 (contraSubsetComplement) => 72.19/9.83 (( 72.19/9.83 (complementTcontraSubset) => 72.19/9.83 (( 72.19/9.83 (binunionTILcontra) => 72.19/9.83 (( 72.19/9.83 (binunionTIRcontra) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInUnion) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInUnion2) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInIntersectUnions) => 72.19/9.83 (( 72.19/9.83 (intersectInPowersetIntersectUnions) => 72.19/9.83 (( 72.19/9.83 (inComplementUnionImpNotIn1) => 72.19/9.83 (( 72.19/9.83 (inComplementUnionImpInComplement1) => 72.19/9.83 (( 72.19/9.83 (binunionTE) => 72.19/9.83 (( 72.19/9.83 (binunionTEcontra) => 72.19/9.83 (( 72.19/9.83 (demorgan2a1) => 72.19/9.83 (( 72.19/9.83 (complementUnionInPowersetComplement) => 72.19/9.83 (( 72.19/9.83 (demorgan2a2) => 72.19/9.83 (( 72.19/9.83 (demorgan1a) => 72.19/9.83 (( 72.19/9.83 (demorgan1b) => 72.19/9.83 (( 72.19/9.83 (demorgan1) => 72.19/9.83 (( 72.19/9.83 (demorgan2a) => 72.19/9.83 (( 72.19/9.83 (demorgan2b2) => 72.19/9.83 (( 72.19/9.83 (demorgan2b) => 72.19/9.83 (( 72.19/9.83 (demorgan2) => 72.19/9.83 (( 72.19/9.83 (woz13rule0) => 72.19/9.83 (( 72.19/9.83 (woz13rule1) => 72.19/9.83 (( 72.19/9.83 (woz13rule2) => 72.19/9.83 (( 72.19/9.83 (woz13rule3) => 72.19/9.83 (( 72.19/9.83 (woz13rule4) => 72.19/9.83 (( 72.19/9.83 (woz1_1) => 72.19/9.83 (( 72.19/9.83 (woz1_2) => 72.19/9.83 (( 72.19/9.83 (woz1_3) => 72.19/9.83 (( 72.19/9.83 (woz1_4) => 72.19/9.83 (( 72.19/9.83 (woz1_5) => 72.19/9.83 (( 72.19/9.83 (breln1all2) => 72.19/9.83 (( 72.19/9.83 (breln1SetBreln1) => 72.19/9.83 (( 72.19/9.83 (choice2fnsingleton) => 72.19/9.83 (( 72.19/9.83 (setOfPairsIsBReln1) => 72.19/9.83 (( 72.19/9.83 (breln1all1) => 72.19/9.83 (( 72.19/9.83 (subbreln1) => 72.19/9.83 (( 72.19/9.83 (eqbreln1) => 72.19/9.83 (( 72.19/9.83 (breln1invprop) => 72.19/9.83 (( 72.19/9.83 (breln1invI) => 72.19/9.83 (( 72.19/9.83 (breln1invE) => 72.19/9.83 (( 72.19/9.83 (breln1compprop) => 72.19/9.83 (( 72.19/9.83 (breln1compI) => 72.19/9.83 (( 72.19/9.83 (breln1compE) => 72.19/9.83 (( 72.19/9.83 (breln1compEex) => 72.19/9.83 (( 72.19/9.83 (!!) @ ( 72.19/9.83 (('#B') @ ( 72.19/9.83 !!) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#S') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#S') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 =>))) @ 72.19/9.83 breln1)))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 !!))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#S') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#S') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 =>))) @ 72.19/9.83 breln1)))))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#C') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 breln1)))) @ 72.19/9.83 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.19/9.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1074])). 72.19/9.83 thf(zip_derived_cl1090, plain, 72.19/9.83 (~ (((sepSubset) => 72.19/9.83 (((binunionIL) => 72.19/9.83 (((upairset2IR) => 72.19/9.83 (((binunionIR) => 72.19/9.83 (((binunionEcases) => 72.19/9.83 (((binunionE) => 72.19/9.83 (((binunionLsub) => 72.19/9.83 (((binunionRsub) => 72.19/9.83 (((binintersectI) => 72.19/9.83 (((binintersectSubset5) => 72.19/9.83 (((binintersectEL) => 72.19/9.83 (((binintersectLsub) => 72.19/9.83 (((binintersectSubset2) => 72.19/9.83 (((binintersectSubset3) => 72.19/9.83 (((binintersectER) => 72.19/9.83 (((disjointsetsI1) => 72.19/9.83 (((binintersectRsub) => 72.19/9.83 (((binintersectSubset4) => 72.19/9.83 (((binintersectSubset1) => 72.19/9.83 (((bs114d) => 72.19/9.83 (((setminusI) => 72.19/9.83 (((setminusEL) => 72.19/9.83 (((setminusER) => 72.19/9.83 (((setminusSubset2) => 72.19/9.83 (((setminusERneg) => 72.19/9.83 (((setminusELneg) => 72.19/9.83 (((setminusILneg) => 72.19/9.83 (((setminusIRneg) => 72.19/9.83 (((setminusLsub) => 72.19/9.83 (((setminusSubset1) => 72.19/9.83 (( 72.19/9.83 (symdiffE) => 72.19/9.83 (( 72.19/9.83 (symdiffI1) => 72.19/9.83 (( 72.19/9.83 (symdiffI2) => 72.19/9.83 (( 72.19/9.83 (symdiffIneg1) => 72.19/9.83 (( 72.19/9.83 (symdiffIneg2) => 72.19/9.83 (( 72.19/9.83 (secondinupair) => 72.19/9.83 (( 72.19/9.83 (setukpairIL) => 72.19/9.83 (( 72.19/9.83 (setukpairIR) => 72.19/9.83 (( 72.19/9.83 (kpairiskpair) => 72.19/9.83 (( 72.19/9.83 (kpairp) => 72.19/9.83 (( 72.19/9.83 (singletonsubset) => 72.19/9.83 (( 72.19/9.83 (singletoninpowerset) => 72.19/9.83 (( 72.19/9.83 (singletoninpowunion) => 72.19/9.83 (( 72.19/9.83 (upairset2E) => 72.19/9.83 (( 72.19/9.83 (upairsubunion) => 72.19/9.83 (( 72.19/9.83 (upairinpowunion) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem1) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem2) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem3) => 72.19/9.83 (( 72.19/9.83 (cartprodpairin) => 72.19/9.83 (( 72.19/9.83 (cartprodmempair1) => 72.19/9.83 (( 72.19/9.83 (cartprodmempair) => 72.19/9.83 (( 72.19/9.83 (setunionE2) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton1) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton2) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton) => 72.19/9.83 (( 72.19/9.83 (singletonprop) => 72.19/9.83 (( 72.19/9.83 (ex1E1) => 72.19/9.83 (( 72.19/9.83 (ex1I) => 72.19/9.83 (( 72.19/9.83 (ex1I2) => 72.19/9.83 (( 72.19/9.83 (singletonsuniq) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL1) => 72.19/9.83 (( 72.19/9.83 (kfstsingleton) => 72.19/9.83 (( 72.19/9.83 (theprop) => 72.19/9.83 (( 72.19/9.83 (kfstpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodfstin) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL2) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR11) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR12) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR1) => 72.19/9.83 (( 72.19/9.83 (upairequniteq) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR2) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR) => 72.19/9.83 (( 72.19/9.83 (ksndsingleton) => 72.19/9.83 (( 72.19/9.83 (ksndpairEq) => 72.19/9.83 (( 72.19/9.83 (kpairsurjEq) => 72.19/9.83 (( 72.19/9.83 (cartprodsndin) => 72.19/9.83 (( 72.19/9.83 (cartprodpairmemEL) => 72.19/9.83 (( 72.19/9.83 (cartprodpairmemER) => 72.19/9.83 (( 72.19/9.83 (cartprodmempaircEq) => 72.19/9.83 (( 72.19/9.83 (cartprodfstpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodsndpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodpairsurjEq) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrI) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrSub) => 72.19/9.83 (( 72.19/9.83 (setOfPairsIsBReln) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrERa) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrEL1) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrEL2) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrER) => 72.19/9.83 (( 72.19/9.83 (funcImageSingleton) => 72.19/9.83 (( 72.19/9.83 (apProp) => 72.19/9.83 (( 72.19/9.83 (app) => 72.19/9.83 (( 72.19/9.83 (infuncsetfunc) => 72.19/9.83 (( 72.19/9.83 (ap2p) => 72.19/9.83 (( 72.19/9.83 (funcinfuncset) => 72.19/9.83 (( 72.19/9.83 (lamProp) => 72.19/9.83 (( 72.19/9.83 (lamp) => 72.19/9.83 (( 72.19/9.83 (lam2p) => 72.19/9.83 (( 72.19/9.83 (brelnall1) => 72.19/9.83 (( 72.19/9.83 (brelnall2) => 72.19/9.83 (( 72.19/9.83 (ex1E2) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp1) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp3) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp2) => 72.19/9.83 (( 72.19/9.83 (funcextLem) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp4) => 72.19/9.83 (( 72.19/9.83 (subbreln) => 72.19/9.83 (( 72.19/9.83 (eqbreln) => 72.19/9.83 (( 72.19/9.83 (funcext) => 72.19/9.83 (( 72.19/9.83 (funcext2) => 72.19/9.83 (( 72.19/9.83 (ap2apEq1) => 72.19/9.83 (( 72.19/9.83 (ap2apEq2) => 72.19/9.83 (( 72.19/9.83 (beta1) => 72.19/9.83 (( 72.19/9.83 (eta1) => 72.19/9.83 (( 72.19/9.83 (lam2lamEq) => 72.19/9.83 (( 72.19/9.83 (beta2) => 72.19/9.83 (( 72.19/9.83 (eta2) => 72.19/9.83 (( 72.19/9.83 (iffalseProp1) => 72.19/9.83 (( 72.19/9.83 (iffalseProp2) => 72.19/9.83 (( 72.19/9.83 (iftrueProp1) => 72.19/9.83 (( 72.19/9.83 (iftrueProp2) => 72.19/9.83 (( 72.19/9.83 (ifSingleton) => 72.19/9.83 (( 72.19/9.83 (ifp) => 72.19/9.83 (( 72.19/9.83 (theeq) => 72.19/9.83 (( 72.19/9.83 (iftrue) => 72.19/9.83 (( 72.19/9.83 (iffalse) => 72.19/9.83 (( 72.19/9.83 (iftrueorfalse) => 72.19/9.83 (( 72.19/9.83 (binintersectT_lem) => 72.19/9.83 (( 72.19/9.83 (binunionT_lem) => 72.19/9.83 (( 72.19/9.83 (powersetT_lem) => 72.19/9.83 (( 72.19/9.83 (setminusT_lem) => 72.19/9.83 (( 72.19/9.83 (complementT_lem) => 72.19/9.83 (( 72.19/9.83 (setextT) => 72.19/9.83 (( 72.19/9.83 (subsetTI) => 72.19/9.83 (( 72.19/9.83 (powersetTI1) => 72.19/9.83 (( 72.19/9.83 (powersetTE1) => 72.19/9.83 (( 72.19/9.83 (complementTI1) => 72.19/9.83 (( 72.19/9.83 (complementTE1) => 72.19/9.83 (( 72.19/9.83 (binintersectTELcontra) => 72.19/9.83 (( 72.19/9.83 (binintersectTERcontra) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT1) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT2) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT3) => 72.19/9.83 (( 72.19/9.83 (doubleComplementI1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementE1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementSub1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementSub2) => 72.19/9.83 (( 72.19/9.83 (doubleComplementEq) => 72.19/9.83 (( 72.19/9.83 (complementTnotintersectT) => 72.19/9.83 (( 72.19/9.83 (complementImpComplementIntersect) => 72.19/9.83 (( 72.19/9.83 (complementSubsetComplementIntersect) => 72.19/9.83 (( 72.19/9.83 (complementInPowersetComplementIntersect) => 72.19/9.83 (( 72.19/9.83 (contraSubsetComplement) => 72.19/9.83 (( 72.19/9.83 (complementTcontraSubset) => 72.19/9.83 (( 72.19/9.83 (binunionTILcontra) => 72.19/9.83 (( 72.19/9.83 (binunionTIRcontra) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInUnion) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInUnion2) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInIntersectUnions) => 72.19/9.83 (( 72.19/9.83 (intersectInPowersetIntersectUnions) => 72.19/9.83 (( 72.19/9.83 (inComplementUnionImpNotIn1) => 72.19/9.83 (( 72.19/9.83 (inComplementUnionImpInComplement1) => 72.19/9.83 (( 72.19/9.83 (binunionTE) => 72.19/9.83 (( 72.19/9.83 (binunionTEcontra) => 72.19/9.83 (( 72.19/9.83 (demorgan2a1) => 72.19/9.83 (( 72.19/9.83 (complementUnionInPowersetComplement) => 72.19/9.83 (( 72.19/9.83 (demorgan2a2) => 72.19/9.83 (( 72.19/9.83 (demorgan1a) => 72.19/9.83 (( 72.19/9.83 (demorgan1b) => 72.19/9.83 (( 72.19/9.83 (demorgan1) => 72.19/9.83 (( 72.19/9.83 (demorgan2a) => 72.19/9.83 (( 72.19/9.83 (demorgan2b2) => 72.19/9.83 (( 72.19/9.83 (demorgan2b) => 72.19/9.83 (( 72.19/9.83 (demorgan2) => 72.19/9.83 (( 72.19/9.83 (woz13rule0) => 72.19/9.83 (( 72.19/9.83 (woz13rule1) => 72.19/9.83 (( 72.19/9.83 (woz13rule2) => 72.19/9.83 (( 72.19/9.83 (woz13rule3) => 72.19/9.83 (( 72.19/9.83 (woz13rule4) => 72.19/9.83 (( 72.19/9.83 (woz1_1) => 72.19/9.83 (( 72.19/9.83 (woz1_2) => 72.19/9.83 (( 72.19/9.83 (woz1_3) => 72.19/9.83 (( 72.19/9.83 (woz1_4) => 72.19/9.83 (( 72.19/9.83 (woz1_5) => 72.19/9.83 (( 72.19/9.83 (breln1all2) => 72.19/9.83 (( 72.19/9.83 (breln1SetBreln1) => 72.19/9.83 (( 72.19/9.83 (choice2fnsingleton) => 72.19/9.83 (( 72.19/9.83 (setOfPairsIsBReln1) => 72.19/9.83 (( 72.19/9.83 (breln1all1) => 72.19/9.83 (( 72.19/9.83 (subbreln1) => 72.19/9.83 (( 72.19/9.83 (eqbreln1) => 72.19/9.83 (( 72.19/9.83 (breln1invprop) => 72.19/9.83 (( 72.19/9.83 (breln1invI) => 72.19/9.83 (( 72.19/9.83 (breln1invE) => 72.19/9.83 (( 72.19/9.83 (breln1compprop) => 72.19/9.83 (( 72.19/9.83 (breln1compI) => 72.19/9.83 (( 72.19/9.83 (breln1compE) => 72.19/9.83 (( 72.19/9.83 (breln1compEex) => 72.19/9.83 (( 72.19/9.83 (!!) @ ( 72.19/9.83 (('#B') @ ( 72.19/9.83 !!) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#S') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#S') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 =>))) @ 72.19/9.83 breln1)))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 !!))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#S') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#S') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 =>))) @ 72.19/9.83 breln1)))))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#C') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 breln1)))) @ 72.19/9.83 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.19/9.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])). 72.19/9.83 thf(zip_derived_cl1096, plain, 72.19/9.83 (~ (((binunionIL) => 72.19/9.83 (((upairset2IR) => 72.19/9.83 (((binunionIR) => 72.19/9.83 (((binunionEcases) => 72.19/9.83 (((binunionE) => 72.19/9.83 (((binunionLsub) => 72.19/9.83 (((binunionRsub) => 72.19/9.83 (((binintersectI) => 72.19/9.83 (((binintersectSubset5) => 72.19/9.83 (((binintersectEL) => 72.19/9.83 (((binintersectLsub) => 72.19/9.83 (((binintersectSubset2) => 72.19/9.83 (((binintersectSubset3) => 72.19/9.83 (((binintersectER) => 72.19/9.83 (((disjointsetsI1) => 72.19/9.83 (((binintersectRsub) => 72.19/9.83 (((binintersectSubset4) => 72.19/9.83 (((binintersectSubset1) => 72.19/9.83 (((bs114d) => 72.19/9.83 (((setminusI) => 72.19/9.83 (((setminusEL) => 72.19/9.83 (((setminusER) => 72.19/9.83 (((setminusSubset2) => 72.19/9.83 (((setminusERneg) => 72.19/9.83 (((setminusELneg) => 72.19/9.83 (((setminusILneg) => 72.19/9.83 (((setminusIRneg) => 72.19/9.83 (((setminusLsub) => 72.19/9.83 (((setminusSubset1) => 72.19/9.83 (((symdiffE) => 72.19/9.83 (( 72.19/9.83 (symdiffI1) => 72.19/9.83 (( 72.19/9.83 (symdiffI2) => 72.19/9.83 (( 72.19/9.83 (symdiffIneg1) => 72.19/9.83 (( 72.19/9.83 (symdiffIneg2) => 72.19/9.83 (( 72.19/9.83 (secondinupair) => 72.19/9.83 (( 72.19/9.83 (setukpairIL) => 72.19/9.83 (( 72.19/9.83 (setukpairIR) => 72.19/9.83 (( 72.19/9.83 (kpairiskpair) => 72.19/9.83 (( 72.19/9.83 (kpairp) => 72.19/9.83 (( 72.19/9.83 (singletonsubset) => 72.19/9.83 (( 72.19/9.83 (singletoninpowerset) => 72.19/9.83 (( 72.19/9.83 (singletoninpowunion) => 72.19/9.83 (( 72.19/9.83 (upairset2E) => 72.19/9.83 (( 72.19/9.83 (upairsubunion) => 72.19/9.83 (( 72.19/9.83 (upairinpowunion) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem1) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem2) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem3) => 72.19/9.83 (( 72.19/9.83 (cartprodpairin) => 72.19/9.83 (( 72.19/9.83 (cartprodmempair1) => 72.19/9.83 (( 72.19/9.83 (cartprodmempair) => 72.19/9.83 (( 72.19/9.83 (setunionE2) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton1) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton2) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton) => 72.19/9.83 (( 72.19/9.83 (singletonprop) => 72.19/9.83 (( 72.19/9.83 (ex1E1) => 72.19/9.83 (( 72.19/9.83 (ex1I) => 72.19/9.83 (( 72.19/9.83 (ex1I2) => 72.19/9.83 (( 72.19/9.83 (singletonsuniq) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL1) => 72.19/9.83 (( 72.19/9.83 (kfstsingleton) => 72.19/9.83 (( 72.19/9.83 (theprop) => 72.19/9.83 (( 72.19/9.83 (kfstpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodfstin) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL2) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR11) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR12) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR1) => 72.19/9.83 (( 72.19/9.83 (upairequniteq) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR2) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR) => 72.19/9.83 (( 72.19/9.83 (ksndsingleton) => 72.19/9.83 (( 72.19/9.83 (ksndpairEq) => 72.19/9.83 (( 72.19/9.83 (kpairsurjEq) => 72.19/9.83 (( 72.19/9.83 (cartprodsndin) => 72.19/9.83 (( 72.19/9.83 (cartprodpairmemEL) => 72.19/9.83 (( 72.19/9.83 (cartprodpairmemER) => 72.19/9.83 (( 72.19/9.83 (cartprodmempaircEq) => 72.19/9.83 (( 72.19/9.83 (cartprodfstpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodsndpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodpairsurjEq) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrI) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrSub) => 72.19/9.83 (( 72.19/9.83 (setOfPairsIsBReln) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrERa) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrEL1) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrEL2) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrER) => 72.19/9.83 (( 72.19/9.83 (funcImageSingleton) => 72.19/9.83 (( 72.19/9.83 (apProp) => 72.19/9.83 (( 72.19/9.83 (app) => 72.19/9.83 (( 72.19/9.83 (infuncsetfunc) => 72.19/9.83 (( 72.19/9.83 (ap2p) => 72.19/9.83 (( 72.19/9.83 (funcinfuncset) => 72.19/9.83 (( 72.19/9.83 (lamProp) => 72.19/9.83 (( 72.19/9.83 (lamp) => 72.19/9.83 (( 72.19/9.83 (lam2p) => 72.19/9.83 (( 72.19/9.83 (brelnall1) => 72.19/9.83 (( 72.19/9.83 (brelnall2) => 72.19/9.83 (( 72.19/9.83 (ex1E2) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp1) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp3) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp2) => 72.19/9.83 (( 72.19/9.83 (funcextLem) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp4) => 72.19/9.83 (( 72.19/9.83 (subbreln) => 72.19/9.83 (( 72.19/9.83 (eqbreln) => 72.19/9.83 (( 72.19/9.83 (funcext) => 72.19/9.83 (( 72.19/9.83 (funcext2) => 72.19/9.83 (( 72.19/9.83 (ap2apEq1) => 72.19/9.83 (( 72.19/9.83 (ap2apEq2) => 72.19/9.83 (( 72.19/9.83 (beta1) => 72.19/9.83 (( 72.19/9.83 (eta1) => 72.19/9.83 (( 72.19/9.83 (lam2lamEq) => 72.19/9.83 (( 72.19/9.83 (beta2) => 72.19/9.83 (( 72.19/9.83 (eta2) => 72.19/9.83 (( 72.19/9.83 (iffalseProp1) => 72.19/9.83 (( 72.19/9.83 (iffalseProp2) => 72.19/9.83 (( 72.19/9.83 (iftrueProp1) => 72.19/9.83 (( 72.19/9.83 (iftrueProp2) => 72.19/9.83 (( 72.19/9.83 (ifSingleton) => 72.19/9.83 (( 72.19/9.83 (ifp) => 72.19/9.83 (( 72.19/9.83 (theeq) => 72.19/9.83 (( 72.19/9.83 (iftrue) => 72.19/9.83 (( 72.19/9.83 (iffalse) => 72.19/9.83 (( 72.19/9.83 (iftrueorfalse) => 72.19/9.83 (( 72.19/9.83 (binintersectT_lem) => 72.19/9.83 (( 72.19/9.83 (binunionT_lem) => 72.19/9.83 (( 72.19/9.83 (powersetT_lem) => 72.19/9.83 (( 72.19/9.83 (setminusT_lem) => 72.19/9.83 (( 72.19/9.83 (complementT_lem) => 72.19/9.83 (( 72.19/9.83 (setextT) => 72.19/9.83 (( 72.19/9.83 (subsetTI) => 72.19/9.83 (( 72.19/9.83 (powersetTI1) => 72.19/9.83 (( 72.19/9.83 (powersetTE1) => 72.19/9.83 (( 72.19/9.83 (complementTI1) => 72.19/9.83 (( 72.19/9.83 (complementTE1) => 72.19/9.83 (( 72.19/9.83 (binintersectTELcontra) => 72.19/9.83 (( 72.19/9.83 (binintersectTERcontra) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT1) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT2) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT3) => 72.19/9.83 (( 72.19/9.83 (doubleComplementI1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementE1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementSub1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementSub2) => 72.19/9.83 (( 72.19/9.83 (doubleComplementEq) => 72.19/9.83 (( 72.19/9.83 (complementTnotintersectT) => 72.19/9.83 (( 72.19/9.83 (complementImpComplementIntersect) => 72.19/9.83 (( 72.19/9.83 (complementSubsetComplementIntersect) => 72.19/9.83 (( 72.19/9.83 (complementInPowersetComplementIntersect) => 72.19/9.83 (( 72.19/9.83 (contraSubsetComplement) => 72.19/9.83 (( 72.19/9.83 (complementTcontraSubset) => 72.19/9.83 (( 72.19/9.83 (binunionTILcontra) => 72.19/9.83 (( 72.19/9.83 (binunionTIRcontra) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInUnion) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInUnion2) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInIntersectUnions) => 72.19/9.83 (( 72.19/9.83 (intersectInPowersetIntersectUnions) => 72.19/9.83 (( 72.19/9.83 (inComplementUnionImpNotIn1) => 72.19/9.83 (( 72.19/9.83 (inComplementUnionImpInComplement1) => 72.19/9.83 (( 72.19/9.83 (binunionTE) => 72.19/9.83 (( 72.19/9.83 (binunionTEcontra) => 72.19/9.83 (( 72.19/9.83 (demorgan2a1) => 72.19/9.83 (( 72.19/9.83 (complementUnionInPowersetComplement) => 72.19/9.83 (( 72.19/9.83 (demorgan2a2) => 72.19/9.83 (( 72.19/9.83 (demorgan1a) => 72.19/9.83 (( 72.19/9.83 (demorgan1b) => 72.19/9.83 (( 72.19/9.83 (demorgan1) => 72.19/9.83 (( 72.19/9.83 (demorgan2a) => 72.19/9.83 (( 72.19/9.83 (demorgan2b2) => 72.19/9.83 (( 72.19/9.83 (demorgan2b) => 72.19/9.83 (( 72.19/9.83 (demorgan2) => 72.19/9.83 (( 72.19/9.83 (woz13rule0) => 72.19/9.83 (( 72.19/9.83 (woz13rule1) => 72.19/9.83 (( 72.19/9.83 (woz13rule2) => 72.19/9.83 (( 72.19/9.83 (woz13rule3) => 72.19/9.83 (( 72.19/9.83 (woz13rule4) => 72.19/9.83 (( 72.19/9.83 (woz1_1) => 72.19/9.83 (( 72.19/9.83 (woz1_2) => 72.19/9.83 (( 72.19/9.83 (woz1_3) => 72.19/9.83 (( 72.19/9.83 (woz1_4) => 72.19/9.83 (( 72.19/9.83 (woz1_5) => 72.19/9.83 (( 72.19/9.83 (breln1all2) => 72.19/9.83 (( 72.19/9.83 (breln1SetBreln1) => 72.19/9.83 (( 72.19/9.83 (choice2fnsingleton) => 72.19/9.83 (( 72.19/9.83 (setOfPairsIsBReln1) => 72.19/9.83 (( 72.19/9.83 (breln1all1) => 72.19/9.83 (( 72.19/9.83 (subbreln1) => 72.19/9.83 (( 72.19/9.83 (eqbreln1) => 72.19/9.83 (( 72.19/9.83 (breln1invprop) => 72.19/9.83 (( 72.19/9.83 (breln1invI) => 72.19/9.83 (( 72.19/9.83 (breln1invE) => 72.19/9.83 (( 72.19/9.83 (breln1compprop) => 72.19/9.83 (( 72.19/9.83 (breln1compI) => 72.19/9.83 (( 72.19/9.83 (breln1compE) => 72.19/9.83 (( 72.19/9.83 (breln1compEex) => 72.19/9.83 (( 72.19/9.83 (!!) @ ( 72.19/9.83 (('#B') @ ( 72.19/9.83 !!) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#S') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#S') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 =>))) @ 72.19/9.83 breln1)))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 !!))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#S') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#S') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 =>))) @ 72.19/9.83 breln1)))))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#C') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 breln1)))) @ 72.19/9.83 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.19/9.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])). 72.19/9.83 thf(zip_derived_cl1102, plain, 72.19/9.83 (~ (((upairset2IR) => 72.19/9.83 (((binunionIR) => 72.19/9.83 (((binunionEcases) => 72.19/9.83 (((binunionE) => 72.19/9.83 (((binunionLsub) => 72.19/9.83 (((binunionRsub) => 72.19/9.83 (((binintersectI) => 72.19/9.83 (((binintersectSubset5) => 72.19/9.83 (((binintersectEL) => 72.19/9.83 (((binintersectLsub) => 72.19/9.83 (((binintersectSubset2) => 72.19/9.83 (((binintersectSubset3) => 72.19/9.83 (((binintersectER) => 72.19/9.83 (((disjointsetsI1) => 72.19/9.83 (((binintersectRsub) => 72.19/9.83 (((binintersectSubset4) => 72.19/9.83 (((binintersectSubset1) => 72.19/9.83 (((bs114d) => 72.19/9.83 (((setminusI) => 72.19/9.83 (((setminusEL) => 72.19/9.83 (((setminusER) => 72.19/9.83 (((setminusSubset2) => 72.19/9.83 (((setminusERneg) => 72.19/9.83 (((setminusELneg) => 72.19/9.83 (((setminusILneg) => 72.19/9.83 (((setminusIRneg) => 72.19/9.83 (((setminusLsub) => 72.19/9.83 (((setminusSubset1) => 72.19/9.83 (((symdiffE) => 72.19/9.83 (((symdiffI1) => 72.19/9.83 (( 72.19/9.83 (symdiffI2) => 72.19/9.83 (( 72.19/9.83 (symdiffIneg1) => 72.19/9.83 (( 72.19/9.83 (symdiffIneg2) => 72.19/9.83 (( 72.19/9.83 (secondinupair) => 72.19/9.83 (( 72.19/9.83 (setukpairIL) => 72.19/9.83 (( 72.19/9.83 (setukpairIR) => 72.19/9.83 (( 72.19/9.83 (kpairiskpair) => 72.19/9.83 (( 72.19/9.83 (kpairp) => 72.19/9.83 (( 72.19/9.83 (singletonsubset) => 72.19/9.83 (( 72.19/9.83 (singletoninpowerset) => 72.19/9.83 (( 72.19/9.83 (singletoninpowunion) => 72.19/9.83 (( 72.19/9.83 (upairset2E) => 72.19/9.83 (( 72.19/9.83 (upairsubunion) => 72.19/9.83 (( 72.19/9.83 (upairinpowunion) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem1) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem2) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem3) => 72.19/9.83 (( 72.19/9.83 (cartprodpairin) => 72.19/9.83 (( 72.19/9.83 (cartprodmempair1) => 72.19/9.83 (( 72.19/9.83 (cartprodmempair) => 72.19/9.83 (( 72.19/9.83 (setunionE2) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton1) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton2) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton) => 72.19/9.83 (( 72.19/9.83 (singletonprop) => 72.19/9.83 (( 72.19/9.83 (ex1E1) => 72.19/9.83 (( 72.19/9.83 (ex1I) => 72.19/9.83 (( 72.19/9.83 (ex1I2) => 72.19/9.83 (( 72.19/9.83 (singletonsuniq) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL1) => 72.19/9.83 (( 72.19/9.83 (kfstsingleton) => 72.19/9.83 (( 72.19/9.83 (theprop) => 72.19/9.83 (( 72.19/9.83 (kfstpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodfstin) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL2) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR11) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR12) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR1) => 72.19/9.83 (( 72.19/9.83 (upairequniteq) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR2) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR) => 72.19/9.83 (( 72.19/9.83 (ksndsingleton) => 72.19/9.83 (( 72.19/9.83 (ksndpairEq) => 72.19/9.83 (( 72.19/9.83 (kpairsurjEq) => 72.19/9.83 (( 72.19/9.83 (cartprodsndin) => 72.19/9.83 (( 72.19/9.83 (cartprodpairmemEL) => 72.19/9.83 (( 72.19/9.83 (cartprodpairmemER) => 72.19/9.83 (( 72.19/9.83 (cartprodmempaircEq) => 72.19/9.83 (( 72.19/9.83 (cartprodfstpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodsndpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodpairsurjEq) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrI) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrSub) => 72.19/9.83 (( 72.19/9.83 (setOfPairsIsBReln) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrERa) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrEL1) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrEL2) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrER) => 72.19/9.83 (( 72.19/9.83 (funcImageSingleton) => 72.19/9.83 (( 72.19/9.83 (apProp) => 72.19/9.83 (( 72.19/9.83 (app) => 72.19/9.83 (( 72.19/9.83 (infuncsetfunc) => 72.19/9.83 (( 72.19/9.83 (ap2p) => 72.19/9.83 (( 72.19/9.83 (funcinfuncset) => 72.19/9.83 (( 72.19/9.83 (lamProp) => 72.19/9.83 (( 72.19/9.83 (lamp) => 72.19/9.83 (( 72.19/9.83 (lam2p) => 72.19/9.83 (( 72.19/9.83 (brelnall1) => 72.19/9.83 (( 72.19/9.83 (brelnall2) => 72.19/9.83 (( 72.19/9.83 (ex1E2) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp1) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp3) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp2) => 72.19/9.83 (( 72.19/9.83 (funcextLem) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp4) => 72.19/9.83 (( 72.19/9.83 (subbreln) => 72.19/9.83 (( 72.19/9.83 (eqbreln) => 72.19/9.83 (( 72.19/9.83 (funcext) => 72.19/9.83 (( 72.19/9.83 (funcext2) => 72.19/9.83 (( 72.19/9.83 (ap2apEq1) => 72.19/9.83 (( 72.19/9.83 (ap2apEq2) => 72.19/9.83 (( 72.19/9.83 (beta1) => 72.19/9.83 (( 72.19/9.83 (eta1) => 72.19/9.83 (( 72.19/9.83 (lam2lamEq) => 72.19/9.83 (( 72.19/9.83 (beta2) => 72.19/9.83 (( 72.19/9.83 (eta2) => 72.19/9.83 (( 72.19/9.83 (iffalseProp1) => 72.19/9.83 (( 72.19/9.83 (iffalseProp2) => 72.19/9.83 (( 72.19/9.83 (iftrueProp1) => 72.19/9.83 (( 72.19/9.83 (iftrueProp2) => 72.19/9.83 (( 72.19/9.83 (ifSingleton) => 72.19/9.83 (( 72.19/9.83 (ifp) => 72.19/9.83 (( 72.19/9.83 (theeq) => 72.19/9.83 (( 72.19/9.83 (iftrue) => 72.19/9.83 (( 72.19/9.83 (iffalse) => 72.19/9.83 (( 72.19/9.83 (iftrueorfalse) => 72.19/9.83 (( 72.19/9.83 (binintersectT_lem) => 72.19/9.83 (( 72.19/9.83 (binunionT_lem) => 72.19/9.83 (( 72.19/9.83 (powersetT_lem) => 72.19/9.83 (( 72.19/9.83 (setminusT_lem) => 72.19/9.83 (( 72.19/9.83 (complementT_lem) => 72.19/9.83 (( 72.19/9.83 (setextT) => 72.19/9.83 (( 72.19/9.83 (subsetTI) => 72.19/9.83 (( 72.19/9.83 (powersetTI1) => 72.19/9.83 (( 72.19/9.83 (powersetTE1) => 72.19/9.83 (( 72.19/9.83 (complementTI1) => 72.19/9.83 (( 72.19/9.83 (complementTE1) => 72.19/9.83 (( 72.19/9.83 (binintersectTELcontra) => 72.19/9.83 (( 72.19/9.83 (binintersectTERcontra) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT1) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT2) => 72.19/9.83 (( 72.19/9.83 (contrasubsetT3) => 72.19/9.83 (( 72.19/9.83 (doubleComplementI1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementE1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementSub1) => 72.19/9.83 (( 72.19/9.83 (doubleComplementSub2) => 72.19/9.83 (( 72.19/9.83 (doubleComplementEq) => 72.19/9.83 (( 72.19/9.83 (complementTnotintersectT) => 72.19/9.83 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72.19/9.83 ('#C') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 breln1)))) @ 72.19/9.83 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.19/9.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])). 72.19/9.83 thf(zip_derived_cl1109, plain, 72.19/9.83 (~ (((binunionIR) => 72.19/9.83 (((binunionEcases) => 72.19/9.83 (((binunionE) => 72.19/9.83 (((binunionLsub) => 72.19/9.83 (((binunionRsub) => 72.19/9.83 (((binintersectI) => 72.19/9.83 (((binintersectSubset5) => 72.19/9.83 (((binintersectEL) => 72.19/9.83 (((binintersectLsub) => 72.19/9.83 (((binintersectSubset2) => 72.19/9.83 (((binintersectSubset3) => 72.19/9.83 (((binintersectER) => 72.19/9.83 (((disjointsetsI1) => 72.19/9.83 (((binintersectRsub) => 72.19/9.83 (((binintersectSubset4) => 72.19/9.83 (((binintersectSubset1) => 72.19/9.83 (((bs114d) => 72.19/9.83 (((setminusI) => 72.19/9.83 (((setminusEL) => 72.19/9.83 (((setminusER) => 72.19/9.83 (((setminusSubset2) => 72.19/9.83 (((setminusERneg) => 72.19/9.83 (((setminusELneg) => 72.19/9.83 (((setminusILneg) => 72.19/9.83 (((setminusIRneg) => 72.19/9.83 (((setminusLsub) => 72.19/9.83 (((setminusSubset1) => 72.19/9.83 (((symdiffE) => 72.19/9.83 (((symdiffI1) => 72.19/9.83 (((symdiffI2) => 72.19/9.83 (( 72.19/9.83 (symdiffIneg1) => 72.19/9.83 (( 72.19/9.83 (symdiffIneg2) => 72.19/9.83 (( 72.19/9.83 (secondinupair) => 72.19/9.83 (( 72.19/9.83 (setukpairIL) => 72.19/9.83 (( 72.19/9.83 (setukpairIR) => 72.19/9.83 (( 72.19/9.83 (kpairiskpair) => 72.19/9.83 (( 72.19/9.83 (kpairp) => 72.19/9.83 (( 72.19/9.83 (singletonsubset) => 72.19/9.83 (( 72.19/9.83 (singletoninpowerset) => 72.19/9.83 (( 72.19/9.83 (singletoninpowunion) => 72.19/9.83 (( 72.19/9.83 (upairset2E) => 72.19/9.83 (( 72.19/9.83 (upairsubunion) => 72.19/9.83 (( 72.19/9.83 (upairinpowunion) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem1) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem2) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem3) => 72.19/9.83 (( 72.19/9.83 (cartprodpairin) => 72.19/9.83 (( 72.19/9.83 (cartprodmempair1) => 72.19/9.83 (( 72.19/9.83 (cartprodmempair) => 72.19/9.83 (( 72.19/9.83 (setunionE2) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton1) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton2) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton) => 72.19/9.83 (( 72.19/9.83 (singletonprop) => 72.19/9.83 (( 72.19/9.83 (ex1E1) => 72.19/9.83 (( 72.19/9.83 (ex1I) => 72.19/9.83 (( 72.19/9.83 (ex1I2) => 72.19/9.83 (( 72.19/9.83 (singletonsuniq) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL1) => 72.19/9.83 (( 72.19/9.83 (kfstsingleton) => 72.19/9.83 (( 72.19/9.83 (theprop) => 72.19/9.83 (( 72.19/9.83 (kfstpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodfstin) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL2) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR11) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR12) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR1) => 72.19/9.83 (( 72.19/9.83 (upairequniteq) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR2) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR) => 72.19/9.83 (( 72.19/9.83 (ksndsingleton) => 72.19/9.83 (( 72.19/9.83 (ksndpairEq) => 72.19/9.83 (( 72.19/9.83 (kpairsurjEq) => 72.19/9.83 (( 72.19/9.83 (cartprodsndin) => 72.19/9.83 (( 72.19/9.83 (cartprodpairmemEL) => 72.19/9.83 (( 72.19/9.83 (cartprodpairmemER) => 72.19/9.83 (( 72.19/9.83 (cartprodmempaircEq) => 72.19/9.83 (( 72.19/9.83 (cartprodfstpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodsndpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodpairsurjEq) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrI) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrSub) => 72.19/9.83 (( 72.19/9.83 (setOfPairsIsBReln) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrERa) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrEL1) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrEL2) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrER) => 72.19/9.83 (( 72.19/9.83 (funcImageSingleton) => 72.19/9.83 (( 72.19/9.83 (apProp) => 72.19/9.83 (( 72.19/9.83 (app) => 72.19/9.83 (( 72.19/9.83 (infuncsetfunc) => 72.19/9.83 (( 72.19/9.83 (ap2p) => 72.19/9.83 (( 72.19/9.83 (funcinfuncset) => 72.19/9.83 (( 72.19/9.83 (lamProp) => 72.19/9.83 (( 72.19/9.83 (lamp) => 72.19/9.83 (( 72.19/9.83 (lam2p) => 72.19/9.83 (( 72.19/9.83 (brelnall1) => 72.19/9.83 (( 72.19/9.83 (brelnall2) => 72.19/9.83 (( 72.19/9.83 (ex1E2) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp1) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp3) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp2) => 72.19/9.83 (( 72.19/9.83 (funcextLem) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp4) => 72.19/9.83 (( 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72.19/9.83 (( 72.19/9.83 (complementInPowersetComplementIntersect) => 72.19/9.83 (( 72.19/9.83 (contraSubsetComplement) => 72.19/9.83 (( 72.19/9.83 (complementTcontraSubset) => 72.19/9.83 (( 72.19/9.83 (binunionTILcontra) => 72.19/9.83 (( 72.19/9.83 (binunionTIRcontra) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInUnion) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInUnion2) => 72.19/9.83 (( 72.19/9.83 (inIntersectImpInIntersectUnions) => 72.19/9.83 (( 72.19/9.83 (intersectInPowersetIntersectUnions) => 72.19/9.83 (( 72.19/9.83 (inComplementUnionImpNotIn1) => 72.19/9.83 (( 72.19/9.83 (inComplementUnionImpInComplement1) => 72.19/9.83 (( 72.19/9.83 (binunionTE) => 72.19/9.83 (( 72.19/9.83 (binunionTEcontra) => 72.19/9.83 (( 72.19/9.83 (demorgan2a1) => 72.19/9.83 (( 72.19/9.83 (complementUnionInPowersetComplement) => 72.19/9.83 (( 72.19/9.83 (demorgan2a2) => 72.19/9.83 (( 72.19/9.83 (demorgan1a) => 72.19/9.83 (( 72.19/9.83 (demorgan1b) => 72.19/9.83 (( 72.19/9.83 (demorgan1) => 72.19/9.83 (( 72.19/9.83 (demorgan2a) => 72.19/9.83 (( 72.19/9.83 (demorgan2b2) => 72.19/9.83 (( 72.19/9.83 (demorgan2b) => 72.19/9.83 (( 72.19/9.83 (demorgan2) => 72.19/9.83 (( 72.19/9.83 (woz13rule0) => 72.19/9.83 (( 72.19/9.83 (woz13rule1) => 72.19/9.83 (( 72.19/9.83 (woz13rule2) => 72.19/9.83 (( 72.19/9.83 (woz13rule3) => 72.19/9.83 (( 72.19/9.83 (woz13rule4) => 72.19/9.83 (( 72.19/9.83 (woz1_1) => 72.19/9.83 (( 72.19/9.83 (woz1_2) => 72.19/9.83 (( 72.19/9.83 (woz1_3) => 72.19/9.83 (( 72.19/9.83 (woz1_4) => 72.19/9.83 (( 72.19/9.83 (woz1_5) => 72.19/9.83 (( 72.19/9.83 (breln1all2) => 72.19/9.83 (( 72.19/9.83 (breln1SetBreln1) => 72.19/9.83 (( 72.19/9.83 (choice2fnsingleton) => 72.19/9.83 (( 72.19/9.83 (setOfPairsIsBReln1) => 72.19/9.83 (( 72.19/9.83 (breln1all1) => 72.19/9.83 (( 72.19/9.83 (subbreln1) => 72.19/9.83 (( 72.19/9.83 (eqbreln1) => 72.19/9.83 (( 72.19/9.83 (breln1invprop) => 72.19/9.83 (( 72.19/9.83 (breln1invI) => 72.19/9.83 (( 72.19/9.83 (breln1invE) => 72.19/9.83 (( 72.19/9.83 (breln1compprop) => 72.19/9.83 (( 72.19/9.83 (breln1compI) => 72.19/9.83 (( 72.19/9.83 (breln1compE) => 72.19/9.83 (( 72.19/9.83 (breln1compEex) => 72.19/9.83 (( 72.19/9.83 (!!) @ ( 72.19/9.83 (('#B') @ ( 72.19/9.83 !!) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#S') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#S') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 =>))) @ 72.19/9.83 breln1)))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 !!))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#S') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#S') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 =>))) @ 72.19/9.83 breln1)))))) @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#C') @ ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 ( 72.19/9.83 ( 72.19/9.83 ('#B') @ ( 72.19/9.83 '#B') @ 72.19/9.83 breln1)))) @ 72.19/9.83 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.19/9.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1102])). 72.19/9.83 thf(zip_derived_cl1115, plain, 72.19/9.83 (~ (((binunionEcases) => 72.19/9.83 (((binunionE) => 72.19/9.83 (((binunionLsub) => 72.19/9.83 (((binunionRsub) => 72.19/9.83 (((binintersectI) => 72.19/9.83 (((binintersectSubset5) => 72.19/9.83 (((binintersectEL) => 72.19/9.83 (((binintersectLsub) => 72.19/9.83 (((binintersectSubset2) => 72.19/9.83 (((binintersectSubset3) => 72.19/9.83 (((binintersectER) => 72.19/9.83 (((disjointsetsI1) => 72.19/9.83 (((binintersectRsub) => 72.19/9.83 (((binintersectSubset4) => 72.19/9.83 (((binintersectSubset1) => 72.19/9.83 (((bs114d) => 72.19/9.83 (((setminusI) => 72.19/9.83 (((setminusEL) => 72.19/9.83 (((setminusER) => 72.19/9.83 (((setminusSubset2) => 72.19/9.83 (((setminusERneg) => 72.19/9.83 (((setminusELneg) => 72.19/9.83 (((setminusILneg) => 72.19/9.83 (((setminusIRneg) => 72.19/9.83 (((setminusLsub) => 72.19/9.83 (((setminusSubset1) => 72.19/9.83 (((symdiffE) => 72.19/9.83 (((symdiffI1) => 72.19/9.83 (((symdiffI2) => 72.19/9.83 (((symdiffIneg1) => 72.19/9.83 (( 72.19/9.83 (symdiffIneg2) => 72.19/9.83 (( 72.19/9.83 (secondinupair) => 72.19/9.83 (( 72.19/9.83 (setukpairIL) => 72.19/9.83 (( 72.19/9.83 (setukpairIR) => 72.19/9.83 (( 72.19/9.83 (kpairiskpair) => 72.19/9.83 (( 72.19/9.83 (kpairp) => 72.19/9.83 (( 72.19/9.83 (singletonsubset) => 72.19/9.83 (( 72.19/9.83 (singletoninpowerset) => 72.19/9.83 (( 72.19/9.83 (singletoninpowunion) => 72.19/9.83 (( 72.19/9.83 (upairset2E) => 72.19/9.83 (( 72.19/9.83 (upairsubunion) => 72.19/9.83 (( 72.19/9.83 (upairinpowunion) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem1) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem2) => 72.19/9.83 (( 72.19/9.83 (ubforcartprodlem3) => 72.19/9.83 (( 72.19/9.83 (cartprodpairin) => 72.19/9.83 (( 72.19/9.83 (cartprodmempair1) => 72.19/9.83 (( 72.19/9.83 (cartprodmempair) => 72.19/9.83 (( 72.19/9.83 (setunionE2) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton1) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton2) => 72.19/9.83 (( 72.19/9.83 (setunionsingleton) => 72.19/9.83 (( 72.19/9.83 (singletonprop) => 72.19/9.83 (( 72.19/9.83 (ex1E1) => 72.19/9.83 (( 72.19/9.83 (ex1I) => 72.19/9.83 (( 72.19/9.83 (ex1I2) => 72.19/9.83 (( 72.19/9.83 (singletonsuniq) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL1) => 72.19/9.83 (( 72.19/9.83 (kfstsingleton) => 72.19/9.83 (( 72.19/9.83 (theprop) => 72.19/9.83 (( 72.19/9.83 (kfstpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodfstin) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL2) => 72.19/9.83 (( 72.19/9.83 (setukpairinjL) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR11) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR12) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR1) => 72.19/9.83 (( 72.19/9.83 (upairequniteq) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR2) => 72.19/9.83 (( 72.19/9.83 (setukpairinjR) => 72.19/9.83 (( 72.19/9.83 (ksndsingleton) => 72.19/9.83 (( 72.19/9.83 (ksndpairEq) => 72.19/9.83 (( 72.19/9.83 (kpairsurjEq) => 72.19/9.83 (( 72.19/9.83 (cartprodsndin) => 72.19/9.83 (( 72.19/9.83 (cartprodpairmemEL) => 72.19/9.83 (( 72.19/9.83 (cartprodpairmemER) => 72.19/9.83 (( 72.19/9.83 (cartprodmempaircEq) => 72.19/9.83 (( 72.19/9.83 (cartprodfstpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodsndpairEq) => 72.19/9.83 (( 72.19/9.83 (cartprodpairsurjEq) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrI) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrSub) => 72.19/9.83 (( 72.19/9.83 (setOfPairsIsBReln) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrERa) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrEL1) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrEL2) => 72.19/9.83 (( 72.19/9.83 (dpsetconstrER) => 72.19/9.83 (( 72.19/9.83 (funcImageSingleton) => 72.19/9.83 (( 72.19/9.83 (apProp) => 72.19/9.83 (( 72.19/9.83 (app) => 72.19/9.83 (( 72.19/9.83 (infuncsetfunc) => 72.19/9.83 (( 72.19/9.83 (ap2p) => 72.19/9.83 (( 72.19/9.83 (funcinfuncset) => 72.19/9.83 (( 72.19/9.83 (lamProp) => 72.19/9.83 (( 72.19/9.83 (lamp) => 72.19/9.83 (( 72.19/9.83 (lam2p) => 72.19/9.83 (( 72.19/9.83 (brelnall1) => 72.19/9.83 (( 72.19/9.83 (brelnall2) => 72.19/9.83 (( 72.19/9.83 (ex1E2) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp1) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp3) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp2) => 72.19/9.83 (( 72.19/9.83 (funcextLem) => 72.19/9.83 (( 72.19/9.83 (funcGraphProp4) => 72.19/9.83 (( 72.19/9.83 (subbreln) => 72.19/9.83 (( 72.19/9.83 (eqbreln) => 72.19/9.83 (( 72.19/9.83 (funcext) => 72.19/9.83 (( 72.19/9.83 (funcext2) => 72.19/9.83 (( 72.19/9.83 (ap2apEq1) => 72.19/9.83 (( 72.19/9.83 (ap2apEq2) => 72.19/9.83 (( 72.19/9.83 (beta1) => 72.19/9.83 (( 72.19/9.83 (eta1) => 72.19/9.83 (( 72.19/9.83 (lam2lamEq) => 72.19/9.83 (( 72.19/9.83 (beta2) => 72.19/9.83 (( 72.19/9.83 (eta2) => 72.19/9.83 (( 72.19/9.83 (iffalseProp1) => 72.19/9.83 (( 72.19/9.83 (iffalseProp2) => 72.19/9.83 (( 72.19/9.83 (iftrueProp1) => 72.19/9.83 (( 72.19/9.83 (iftrueProp2) => 72.19/9.83 (( 72.19/9.83 (ifSingleton) => 72.19/9.83 (( 72.19/9.83 (ifp) => 72.19/9.83 (( 72.19/9.83 (theeq) => 72.19/9.84 (( 72.19/9.84 (iftrue) => 72.19/9.84 (( 72.19/9.84 (iffalse) => 72.19/9.84 (( 72.19/9.84 (iftrueorfalse) => 72.19/9.84 (( 72.19/9.84 (binintersectT_lem) => 72.19/9.84 (( 72.19/9.84 (binunionT_lem) => 72.19/9.84 (( 72.19/9.84 (powersetT_lem) => 72.19/9.84 (( 72.19/9.84 (setminusT_lem) => 72.19/9.84 (( 72.19/9.84 (complementT_lem) => 72.19/9.84 (( 72.19/9.84 (setextT) => 72.19/9.84 (( 72.19/9.84 (subsetTI) => 72.19/9.84 (( 72.19/9.84 (powersetTI1) => 72.19/9.84 (( 72.19/9.84 (powersetTE1) => 72.19/9.84 (( 72.19/9.84 (complementTI1) => 72.19/9.84 (( 72.19/9.84 (complementTE1) => 72.19/9.84 (( 72.19/9.84 (binintersectTELcontra) => 72.19/9.84 (( 72.19/9.84 (binintersectTERcontra) => 72.19/9.84 (( 72.19/9.84 (contrasubsetT) => 72.19/9.84 (( 72.19/9.84 (contrasubsetT1) => 72.19/9.84 (( 72.19/9.84 (contrasubsetT2) => 72.19/9.84 (( 72.19/9.84 (contrasubsetT3) => 72.19/9.84 (( 72.19/9.84 (doubleComplementI1) => 72.19/9.84 (( 72.19/9.84 (doubleComplementE1) => 72.19/9.84 (( 72.19/9.84 (doubleComplementSub1) => 72.19/9.84 (( 72.19/9.84 (doubleComplementSub2) => 72.19/9.84 (( 72.19/9.84 (doubleComplementEq) => 72.19/9.84 (( 72.19/9.84 (complementTnotintersectT) => 72.19/9.84 (( 72.19/9.84 (complementImpComplementIntersect) => 72.19/9.84 (( 72.19/9.84 (complementSubsetComplementIntersect) => 72.19/9.84 (( 72.19/9.84 (complementInPowersetComplementIntersect) => 72.19/9.84 (( 72.19/9.84 (contraSubsetComplement) => 72.19/9.84 (( 72.19/9.84 (complementTcontraSubset) => 72.19/9.84 (( 72.19/9.84 (binunionTILcontra) => 72.19/9.84 (( 72.19/9.84 (binunionTIRcontra) => 72.19/9.84 (( 72.19/9.84 (inIntersectImpInUnion) => 72.19/9.84 (( 72.19/9.84 (inIntersectImpInUnion2) => 72.19/9.84 (( 72.19/9.84 (inIntersectImpInIntersectUnions) => 72.19/9.84 (( 72.19/9.84 (intersectInPowersetIntersectUnions) => 72.19/9.84 (( 72.19/9.84 (inComplementUnionImpNotIn1) => 72.19/9.84 (( 72.19/9.84 (inComplementUnionImpInComplement1) => 72.19/9.84 (( 72.19/9.84 (binunionTE) => 72.19/9.84 (( 72.19/9.84 (binunionTEcontra) => 72.19/9.84 (( 72.19/9.84 (demorgan2a1) => 72.19/9.84 (( 72.19/9.84 (complementUnionInPowersetComplement) => 72.19/9.84 (( 72.19/9.84 (demorgan2a2) => 72.19/9.84 (( 72.19/9.84 (demorgan1a) => 72.19/9.84 (( 72.19/9.84 (demorgan1b) => 72.19/9.84 (( 72.19/9.84 (demorgan1) => 72.19/9.84 (( 72.19/9.84 (demorgan2a) => 72.19/9.84 (( 72.19/9.84 (demorgan2b2) => 72.19/9.84 (( 72.19/9.84 (demorgan2b) => 72.19/9.84 (( 72.19/9.84 (demorgan2) => 72.19/9.84 (( 72.19/9.84 (woz13rule0) => 72.19/9.84 (( 72.19/9.84 (woz13rule1) => 72.19/9.84 (( 72.19/9.84 (woz13rule2) => 72.19/9.84 (( 72.19/9.84 (woz13rule3) => 72.19/9.84 (( 72.19/9.84 (woz13rule4) => 72.19/9.84 (( 72.19/9.84 (woz1_1) => 72.19/9.84 (( 72.19/9.84 (woz1_2) => 72.19/9.84 (( 72.19/9.84 (woz1_3) => 72.19/9.84 (( 72.19/9.84 (woz1_4) => 72.19/9.84 (( 72.19/9.84 (woz1_5) => 72.19/9.84 (( 72.19/9.84 (breln1all2) => 72.19/9.84 (( 72.19/9.84 (breln1SetBreln1) => 72.19/9.84 (( 72.19/9.84 (choice2fnsingleton) => 72.19/9.84 (( 72.19/9.84 (setOfPairsIsBReln1) => 72.19/9.84 (( 72.19/9.84 (breln1all1) => 72.19/9.84 (( 72.19/9.84 (subbreln1) => 72.19/9.84 (( 72.19/9.84 (eqbreln1) => 72.19/9.84 (( 72.19/9.84 (breln1invprop) => 72.19/9.84 (( 72.19/9.84 (breln1invI) => 72.19/9.84 (( 72.19/9.84 (breln1invE) => 72.19/9.84 (( 72.19/9.84 (breln1compprop) => 72.19/9.84 (( 72.19/9.84 (breln1compI) => 72.19/9.84 (( 72.19/9.84 (breln1compE) => 72.19/9.84 (( 72.19/9.84 (breln1compEex) => 72.19/9.84 (( 72.19/9.84 (!!) @ ( 72.19/9.84 (('#B') @ ( 72.19/9.84 !!) @ 72.19/9.84 ( 72.19/9.84 ( 72.19/9.84 ('#S') @ ( 72.19/9.84 ( 72.19/9.84 ('#B') @ ( 72.19/9.84 '#S') @ 72.19/9.84 ( 72.19/9.84 ( 72.19/9.84 ('#B') @ ( 72.19/9.84 ( 72.19/9.84 ('#B') @ ( 72.19/9.84 =>))) @ 72.19/9.84 breln1)))) @ 72.19/9.84 ( 72.19/9.84 ( 72.19/9.84 ('#B') @ ( 72.19/9.84 ( 72.19/9.84 ('#B') @ ( 72.19/9.84 !!))) @ 72.19/9.84 ( 72.19/9.84 ( 72.19/9.84 ('#S') @ ( 72.19/9.84 ( 72.19/9.84 ('#B') @ ( 72.19/9.84 '#B') @ 72.19/9.84 ( 72.19/9.84 ( 72.19/9.84 ('#B') @ ( 72.19/9.84 '#S') @ 72.19/9.84 ( 72.19/9.84 ( 72.19/9.84 ('#B') @ ( 72.19/9.84 ( 72.19/9.84 ('#B') @ ( 72.19/9.84 =>))) @ 72.19/9.84 breln1)))))) @ 72.19/9.84 ( 72.19/9.84 ( 72.19/9.84 ('#C') @ ( 72.19/9.84 ( 72.19/9.84 ('#B') @ ( 72.19/9.84 '#B') @ 72.19/9.84 ( 72.19/9.84 ( 72.19/9.84 ('#B') @ ( 72.19/9.84 '#B') @ 72.19/9.84 breln1)))) @ 72.19/9.84 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.19/9.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1109])). 72.19/9.84 thf(zip_derived_cl1121, plain, 72.19/9.84 (~ (((binunionE) => 72.19/9.84 (((binunionLsub) => 72.19/9.84 (((binunionRsub) => 72.19/9.84 (((binintersectI) => 72.19/9.84 (((binintersectSubset5) => 72.19/9.84 (((binintersectEL) => 72.19/9.84 (((binintersectLsub) => 72.19/9.84 (((binintersectSubset2) => 72.19/9.84 (((binintersectSubset3) => 72.19/9.84 (((binintersectER) => 72.19/9.84 (((disjointsetsI1) => 72.19/9.84 (((binintersectRsub) => 72.19/9.84 (((binintersectSubset4) => 72.19/9.84 (((binintersectSubset1) => 72.19/9.84 (((bs114d) => 72.19/9.84 (((setminusI) => 72.19/9.84 (((setminusEL) => 72.19/9.84 (((setminusER) => 72.19/9.84 (((setminusSubset2) => 72.19/9.84 (((setminusERneg) => 72.19/9.84 (((setminusELneg) => 72.19/9.84 (((setminusILneg) => 72.19/9.84 (((setminusIRneg) => 72.19/9.84 (((setminusLsub) => 72.19/9.84 (((setminusSubset1) => 72.19/9.84 (((symdiffE) => 72.19/9.84 (((symdiffI1) => 72.19/9.84 (((symdiffI2) => 72.19/9.84 (((symdiffIneg1) => 72.19/9.84 (((symdiffIneg2) => 72.19/9.84 (( 72.19/9.84 (secondinupair) => 72.19/9.84 (( 72.19/9.84 (setukpairIL) => 72.19/9.84 (( 72.19/9.84 (setukpairIR) => 72.19/9.84 (( 72.19/9.84 (kpairiskpair) => 72.19/9.84 (( 72.19/9.84 (kpairp) => 72.19/9.84 (( 72.19/9.84 (singletonsubset) => 72.19/9.84 (( 72.19/9.84 (singletoninpowerset) => 72.19/9.84 (( 72.19/9.84 (singletoninpowunion) => 72.19/9.84 (( 72.19/9.84 (upairset2E) => 72.19/9.84 (( 72.19/9.84 (upairsubunion) => 72.19/9.84 (( 72.19/9.84 (upairinpowunion) => 72.19/9.84 (( 72.19/9.84 (ubforcartprodlem1) => 72.19/9.84 (( 72.19/9.84 (ubforcartprodlem2) => 72.19/9.84 (( 72.19/9.84 (ubforcartprodlem3) => 72.19/9.84 (( 72.19/9.84 (cartprodpairin) => 72.19/9.84 (( 72.19/9.84 (cartprodmempair1) => 72.19/9.84 (( 72.19/9.84 (cartprodmempair) => 72.19/9.84 (( 72.19/9.84 (setunionE2) => 72.19/9.84 (( 72.19/9.84 (setunionsingleton1) => 72.19/9.84 (( 72.19/9.84 (setunionsingleton2) => 72.19/9.84 (( 72.19/9.84 (setunionsingleton) => 72.19/9.84 (( 72.19/9.84 (singletonprop) => 72.19/9.84 (( 72.19/9.84 (ex1E1) => 72.19/9.84 (( 72.19/9.84 (ex1I) => 72.19/9.84 (( 72.19/9.84 (ex1I2) => 72.19/9.84 (( 72.19/9.84 (singletonsuniq) => 72.19/9.84 (( 72.19/9.84 (setukpairinjL1) => 72.19/9.84 (( 72.19/9.84 (kfstsingleton) => 72.19/9.84 (( 72.19/9.84 (theprop) => 72.19/9.84 (( 72.19/9.84 (kfstpairEq) => 72.19/9.84 (( 72.19/9.84 (cartprodfstin) => 72.19/9.84 (( 72.19/9.84 (setukpairinjL2) => 72.19/9.84 (( 72.19/9.84 (setukpairinjL) => 72.19/9.84 (( 72.19/9.84 (setukpairinjR11) => 72.19/9.84 (( 72.19/9.84 (setukpairinjR12) => 72.19/9.84 (( 72.19/9.84 (setukpairinjR1) => 72.19/9.84 (( 72.19/9.84 (upairequniteq) => 72.19/9.84 (( 72.19/9.84 (setukpairinjR2) => 72.19/9.84 (( 72.19/9.84 (setukpairinjR) => 72.19/9.84 (( 72.19/9.84 (ksndsingleton) => 72.19/9.84 (( 72.19/9.84 (ksndpairEq) => 72.19/9.84 (( 72.19/9.84 (kpairsurjEq) => 72.19/9.84 (( 72.19/9.84 (cartprodsndin) => 72.19/9.84 (( 72.19/9.84 (cartprodpairmemEL) => 72.19/9.84 (( 72.19/9.84 (cartprodpairmemER) => 72.19/9.84 (( 72.19/9.84 (cartprodmempaircEq) => 72.19/9.84 (( 72.19/9.84 (cartprodfstpairEq) => 72.19/9.84 (( 72.19/9.84 (cartprodsndpairEq) => 72.19/9.84 (( 72.19/9.84 (cartprodpairsurjEq) => 72.19/9.84 (( 72.19/9.84 (dpsetconstrI) => 72.19/9.84 (( 72.19/9.84 (dpsetconstrSub) => 72.19/9.84 (( 72.19/9.84 (setOfPairsIsBReln) => 72.19/9.84 (( 72.19/9.84 (dpsetconstrERa) => 72.19/9.84 (( 72.19/9.84 (dpsetconstrEL1) => 72.19/9.84 (( 72.19/9.84 (dpsetconstrEL2) => 72.19/9.84 (( 72.19/9.84 (dpsetconstrER) => 72.19/9.84 (( 72.19/9.84 (funcImageSingleton) => 72.19/9.84 (( 72.19/9.84 (apProp) => 72.19/9.84 (( 72.19/9.84 (app) => 72.19/9.84 (( 72.19/9.84 (infuncsetfunc) => 72.19/9.84 (( 72.19/9.84 (ap2p) => 72.19/9.84 (( 72.19/9.84 (funcinfuncset) => 72.19/9.84 (( 72.19/9.84 (lamProp) => 72.19/9.84 (( 72.19/9.84 (lamp) => 72.19/9.84 (( 72.19/9.84 (lam2p) => 72.19/9.84 (( 72.19/9.84 (brelnall1) => 72.19/9.84 (( 72.19/9.84 (brelnall2) => 72.19/9.84 (( 72.19/9.84 (ex1E2) => 72.19/9.84 (( 72.19/9.84 (funcGraphProp1) => 72.19/9.84 (( 72.19/9.84 (funcGraphProp3) => 72.19/9.84 (( 72.19/9.84 (funcGraphProp2) => 72.19/9.84 (( 72.19/9.84 (funcextLem) => 72.19/9.84 (( 72.19/9.84 (funcGraphProp4) => 72.19/9.84 (( 72.19/9.84 (subbreln) => 72.19/9.84 (( 72.19/9.84 (eqbreln) => 72.19/9.84 (( 72.19/9.84 (funcext) => 72.19/9.84 (( 72.19/9.84 (funcext2) => 72.19/9.84 (( 72.19/9.84 (ap2apEq1) => 72.19/9.84 (( 72.19/9.84 (ap2apEq2) => 72.19/9.84 (( 72.19/9.84 (beta1) => 72.19/9.84 (( 72.19/9.84 (eta1) => 72.19/9.84 (( 72.19/9.84 (lam2lamEq) => 72.19/9.84 (( 72.19/9.84 (beta2) => 72.19/9.84 (( 72.19/9.84 (eta2) => 72.19/9.84 (( 72.19/9.84 (iffalseProp1) => 72.19/9.84 (( 72.19/9.84 (iffalseProp2) => 72.19/9.84 (( 72.19/9.84 (iftrueProp1) => 72.19/9.84 (( 72.19/9.84 (iftrueProp2) => 72.19/9.84 (( 72.19/9.84 (ifSingleton) => 72.29/9.84 (( 72.29/9.84 (ifp) => 72.29/9.84 (( 72.29/9.84 (theeq) => 72.29/9.84 (( 72.29/9.84 (iftrue) => 72.29/9.84 (( 72.29/9.84 (iffalse) => 72.29/9.84 (( 72.29/9.84 (iftrueorfalse) => 72.29/9.84 (( 72.29/9.84 (binintersectT_lem) => 72.29/9.84 (( 72.29/9.84 (binunionT_lem) => 72.29/9.84 (( 72.29/9.84 (powersetT_lem) => 72.29/9.84 (( 72.29/9.84 (setminusT_lem) => 72.29/9.84 (( 72.29/9.84 (complementT_lem) => 72.29/9.84 (( 72.29/9.84 (setextT) => 72.29/9.84 (( 72.29/9.84 (subsetTI) => 72.29/9.84 (( 72.29/9.84 (powersetTI1) => 72.29/9.84 (( 72.29/9.84 (powersetTE1) => 72.29/9.84 (( 72.29/9.84 (complementTI1) => 72.29/9.84 (( 72.29/9.84 (complementTE1) => 72.29/9.84 (( 72.29/9.84 (binintersectTELcontra) => 72.29/9.84 (( 72.29/9.84 (binintersectTERcontra) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT1) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT2) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT3) => 72.29/9.84 (( 72.29/9.84 (doubleComplementI1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementE1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub2) => 72.29/9.84 (( 72.29/9.84 (doubleComplementEq) => 72.29/9.84 (( 72.29/9.84 (complementTnotintersectT) => 72.29/9.84 (( 72.29/9.84 (complementImpComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementSubsetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementInPowersetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (contraSubsetComplement) => 72.29/9.84 (( 72.29/9.84 (complementTcontraSubset) => 72.29/9.84 (( 72.29/9.84 (binunionTILcontra) => 72.29/9.84 (( 72.29/9.84 (binunionTIRcontra) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion2) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (intersectInPowersetIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpNotIn1) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpInComplement1) => 72.29/9.84 (( 72.29/9.84 (binunionTE) => 72.29/9.84 (( 72.29/9.84 (binunionTEcontra) => 72.29/9.84 (( 72.29/9.84 (demorgan2a1) => 72.29/9.84 (( 72.29/9.84 (complementUnionInPowersetComplement) => 72.29/9.84 (( 72.29/9.84 (demorgan2a2) => 72.29/9.84 (( 72.29/9.84 (demorgan1a) => 72.29/9.84 (( 72.29/9.84 (demorgan1b) => 72.29/9.84 (( 72.29/9.84 (demorgan1) => 72.29/9.84 (( 72.29/9.84 (demorgan2a) => 72.29/9.84 (( 72.29/9.84 (demorgan2b2) => 72.29/9.84 (( 72.29/9.84 (demorgan2b) => 72.29/9.84 (( 72.29/9.84 (demorgan2) => 72.29/9.84 (( 72.29/9.84 (woz13rule0) => 72.29/9.84 (( 72.29/9.84 (woz13rule1) => 72.29/9.84 (( 72.29/9.84 (woz13rule2) => 72.29/9.84 (( 72.29/9.84 (woz13rule3) => 72.29/9.84 (( 72.29/9.84 (woz13rule4) => 72.29/9.84 (( 72.29/9.84 (woz1_1) => 72.29/9.84 (( 72.29/9.84 (woz1_2) => 72.29/9.84 (( 72.29/9.84 (woz1_3) => 72.29/9.84 (( 72.29/9.84 (woz1_4) => 72.29/9.84 (( 72.29/9.84 (woz1_5) => 72.29/9.84 (( 72.29/9.84 (breln1all2) => 72.29/9.84 (( 72.29/9.84 (breln1SetBreln1) => 72.29/9.84 (( 72.29/9.84 (choice2fnsingleton) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln1) => 72.29/9.84 (( 72.29/9.84 (breln1all1) => 72.29/9.84 (( 72.29/9.84 (subbreln1) => 72.29/9.84 (( 72.29/9.84 (eqbreln1) => 72.29/9.84 (( 72.29/9.84 (breln1invprop) => 72.29/9.84 (( 72.29/9.84 (breln1invI) => 72.29/9.84 (( 72.29/9.84 (breln1invE) => 72.29/9.84 (( 72.29/9.84 (breln1compprop) => 72.29/9.84 (( 72.29/9.84 (breln1compI) => 72.29/9.84 (( 72.29/9.84 (breln1compE) => 72.29/9.84 (( 72.29/9.84 (breln1compEex) => 72.29/9.84 (( 72.29/9.84 (!!) @ ( 72.29/9.84 (('#B') @ ( 72.29/9.84 !!) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 !!))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#C') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 breln1)))) @ 72.29/9.84 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1115])). 72.29/9.84 thf(zip_derived_cl1128, plain, 72.29/9.84 (~ (((binunionLsub) => 72.29/9.84 (((binunionRsub) => 72.29/9.84 (((binintersectI) => 72.29/9.84 (((binintersectSubset5) => 72.29/9.84 (((binintersectEL) => 72.29/9.84 (((binintersectLsub) => 72.29/9.84 (((binintersectSubset2) => 72.29/9.84 (((binintersectSubset3) => 72.29/9.84 (((binintersectER) => 72.29/9.84 (((disjointsetsI1) => 72.29/9.84 (((binintersectRsub) => 72.29/9.84 (((binintersectSubset4) => 72.29/9.84 (((binintersectSubset1) => 72.29/9.84 (((bs114d) => 72.29/9.84 (((setminusI) => 72.29/9.84 (((setminusEL) => 72.29/9.84 (((setminusER) => 72.29/9.84 (((setminusSubset2) => 72.29/9.84 (((setminusERneg) => 72.29/9.84 (((setminusELneg) => 72.29/9.84 (((setminusILneg) => 72.29/9.84 (((setminusIRneg) => 72.29/9.84 (((setminusLsub) => 72.29/9.84 (((setminusSubset1) => 72.29/9.84 (((symdiffE) => 72.29/9.84 (((symdiffI1) => 72.29/9.84 (((symdiffI2) => 72.29/9.84 (((symdiffIneg1) => 72.29/9.84 (((symdiffIneg2) => 72.29/9.84 (((secondinupair) => 72.29/9.84 (( 72.29/9.84 (setukpairIL) => 72.29/9.84 (( 72.29/9.84 (setukpairIR) => 72.29/9.84 (( 72.29/9.84 (kpairiskpair) => 72.29/9.84 (( 72.29/9.84 (kpairp) => 72.29/9.84 (( 72.29/9.84 (singletonsubset) => 72.29/9.84 (( 72.29/9.84 (singletoninpowerset) => 72.29/9.84 (( 72.29/9.84 (singletoninpowunion) => 72.29/9.84 (( 72.29/9.84 (upairset2E) => 72.29/9.84 (( 72.29/9.84 (upairsubunion) => 72.29/9.84 (( 72.29/9.84 (upairinpowunion) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem1) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem2) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem3) => 72.29/9.84 (( 72.29/9.84 (cartprodpairin) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair1) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair) => 72.29/9.84 (( 72.29/9.84 (setunionE2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton1) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton) => 72.29/9.84 (( 72.29/9.84 (singletonprop) => 72.29/9.84 (( 72.29/9.84 (ex1E1) => 72.29/9.84 (( 72.29/9.84 (ex1I) => 72.29/9.84 (( 72.29/9.84 (ex1I2) => 72.29/9.84 (( 72.29/9.84 (singletonsuniq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL1) => 72.29/9.84 (( 72.29/9.84 (kfstsingleton) => 72.29/9.84 (( 72.29/9.84 (theprop) => 72.29/9.84 (( 72.29/9.84 (kfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstin) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR11) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR12) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR1) => 72.29/9.84 (( 72.29/9.84 (upairequniteq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR) => 72.29/9.84 (( 72.29/9.84 (ksndsingleton) => 72.29/9.84 (( 72.29/9.84 (ksndpairEq) => 72.29/9.84 (( 72.29/9.84 (kpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndin) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemEL) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemER) => 72.29/9.84 (( 72.29/9.84 (cartprodmempaircEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrI) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrSub) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrERa) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL1) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL2) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrER) => 72.29/9.84 (( 72.29/9.84 (funcImageSingleton) => 72.29/9.84 (( 72.29/9.84 (apProp) => 72.29/9.84 (( 72.29/9.84 (app) => 72.29/9.84 (( 72.29/9.84 (infuncsetfunc) => 72.29/9.84 (( 72.29/9.84 (ap2p) => 72.29/9.84 (( 72.29/9.84 (funcinfuncset) => 72.29/9.84 (( 72.29/9.84 (lamProp) => 72.29/9.84 (( 72.29/9.84 (lamp) => 72.29/9.84 (( 72.29/9.84 (lam2p) => 72.29/9.84 (( 72.29/9.84 (brelnall1) => 72.29/9.84 (( 72.29/9.84 (brelnall2) => 72.29/9.84 (( 72.29/9.84 (ex1E2) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp1) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp3) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp2) => 72.29/9.84 (( 72.29/9.84 (funcextLem) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp4) => 72.29/9.84 (( 72.29/9.84 (subbreln) => 72.29/9.84 (( 72.29/9.84 (eqbreln) => 72.29/9.84 (( 72.29/9.84 (funcext) => 72.29/9.84 (( 72.29/9.84 (funcext2) => 72.29/9.84 (( 72.29/9.84 (ap2apEq1) => 72.29/9.84 (( 72.29/9.84 (ap2apEq2) => 72.29/9.84 (( 72.29/9.84 (beta1) => 72.29/9.84 (( 72.29/9.84 (eta1) => 72.29/9.84 (( 72.29/9.84 (lam2lamEq) => 72.29/9.84 (( 72.29/9.84 (beta2) => 72.29/9.84 (( 72.29/9.84 (eta2) => 72.29/9.84 (( 72.29/9.84 (iffalseProp1) => 72.29/9.84 (( 72.29/9.84 (iffalseProp2) => 72.29/9.84 (( 72.29/9.84 (iftrueProp1) => 72.29/9.84 (( 72.29/9.84 (iftrueProp2) => 72.29/9.84 (( 72.29/9.84 (ifSingleton) => 72.29/9.84 (( 72.29/9.84 (ifp) => 72.29/9.84 (( 72.29/9.84 (theeq) => 72.29/9.84 (( 72.29/9.84 (iftrue) => 72.29/9.84 (( 72.29/9.84 (iffalse) => 72.29/9.84 (( 72.29/9.84 (iftrueorfalse) => 72.29/9.84 (( 72.29/9.84 (binintersectT_lem) => 72.29/9.84 (( 72.29/9.84 (binunionT_lem) => 72.29/9.84 (( 72.29/9.84 (powersetT_lem) => 72.29/9.84 (( 72.29/9.84 (setminusT_lem) => 72.29/9.84 (( 72.29/9.84 (complementT_lem) => 72.29/9.84 (( 72.29/9.84 (setextT) => 72.29/9.84 (( 72.29/9.84 (subsetTI) => 72.29/9.84 (( 72.29/9.84 (powersetTI1) => 72.29/9.84 (( 72.29/9.84 (powersetTE1) => 72.29/9.84 (( 72.29/9.84 (complementTI1) => 72.29/9.84 (( 72.29/9.84 (complementTE1) => 72.29/9.84 (( 72.29/9.84 (binintersectTELcontra) => 72.29/9.84 (( 72.29/9.84 (binintersectTERcontra) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT1) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT2) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT3) => 72.29/9.84 (( 72.29/9.84 (doubleComplementI1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementE1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub2) => 72.29/9.84 (( 72.29/9.84 (doubleComplementEq) => 72.29/9.84 (( 72.29/9.84 (complementTnotintersectT) => 72.29/9.84 (( 72.29/9.84 (complementImpComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementSubsetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementInPowersetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (contraSubsetComplement) => 72.29/9.84 (( 72.29/9.84 (complementTcontraSubset) => 72.29/9.84 (( 72.29/9.84 (binunionTILcontra) => 72.29/9.84 (( 72.29/9.84 (binunionTIRcontra) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion2) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (intersectInPowersetIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpNotIn1) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpInComplement1) => 72.29/9.84 (( 72.29/9.84 (binunionTE) => 72.29/9.84 (( 72.29/9.84 (binunionTEcontra) => 72.29/9.84 (( 72.29/9.84 (demorgan2a1) => 72.29/9.84 (( 72.29/9.84 (complementUnionInPowersetComplement) => 72.29/9.84 (( 72.29/9.84 (demorgan2a2) => 72.29/9.84 (( 72.29/9.84 (demorgan1a) => 72.29/9.84 (( 72.29/9.84 (demorgan1b) => 72.29/9.84 (( 72.29/9.84 (demorgan1) => 72.29/9.84 (( 72.29/9.84 (demorgan2a) => 72.29/9.84 (( 72.29/9.84 (demorgan2b2) => 72.29/9.84 (( 72.29/9.84 (demorgan2b) => 72.29/9.84 (( 72.29/9.84 (demorgan2) => 72.29/9.84 (( 72.29/9.84 (woz13rule0) => 72.29/9.84 (( 72.29/9.84 (woz13rule1) => 72.29/9.84 (( 72.29/9.84 (woz13rule2) => 72.29/9.84 (( 72.29/9.84 (woz13rule3) => 72.29/9.84 (( 72.29/9.84 (woz13rule4) => 72.29/9.84 (( 72.29/9.84 (woz1_1) => 72.29/9.84 (( 72.29/9.84 (woz1_2) => 72.29/9.84 (( 72.29/9.84 (woz1_3) => 72.29/9.84 (( 72.29/9.84 (woz1_4) => 72.29/9.84 (( 72.29/9.84 (woz1_5) => 72.29/9.84 (( 72.29/9.84 (breln1all2) => 72.29/9.84 (( 72.29/9.84 (breln1SetBreln1) => 72.29/9.84 (( 72.29/9.84 (choice2fnsingleton) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln1) => 72.29/9.84 (( 72.29/9.84 (breln1all1) => 72.29/9.84 (( 72.29/9.84 (subbreln1) => 72.29/9.84 (( 72.29/9.84 (eqbreln1) => 72.29/9.84 (( 72.29/9.84 (breln1invprop) => 72.29/9.84 (( 72.29/9.84 (breln1invI) => 72.29/9.84 (( 72.29/9.84 (breln1invE) => 72.29/9.84 (( 72.29/9.84 (breln1compprop) => 72.29/9.84 (( 72.29/9.84 (breln1compI) => 72.29/9.84 (( 72.29/9.84 (breln1compE) => 72.29/9.84 (( 72.29/9.84 (breln1compEex) => 72.29/9.84 (( 72.29/9.84 (!!) @ ( 72.29/9.84 (('#B') @ ( 72.29/9.84 !!) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 !!))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#C') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 breln1)))) @ 72.29/9.84 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1121])). 72.29/9.84 thf(zip_derived_cl1135, plain, 72.29/9.84 (~ (((binunionRsub) => 72.29/9.84 (((binintersectI) => 72.29/9.84 (((binintersectSubset5) => 72.29/9.84 (((binintersectEL) => 72.29/9.84 (((binintersectLsub) => 72.29/9.84 (((binintersectSubset2) => 72.29/9.84 (((binintersectSubset3) => 72.29/9.84 (((binintersectER) => 72.29/9.84 (((disjointsetsI1) => 72.29/9.84 (((binintersectRsub) => 72.29/9.84 (((binintersectSubset4) => 72.29/9.84 (((binintersectSubset1) => 72.29/9.84 (((bs114d) => 72.29/9.84 (((setminusI) => 72.29/9.84 (((setminusEL) => 72.29/9.84 (((setminusER) => 72.29/9.84 (((setminusSubset2) => 72.29/9.84 (((setminusERneg) => 72.29/9.84 (((setminusELneg) => 72.29/9.84 (((setminusILneg) => 72.29/9.84 (((setminusIRneg) => 72.29/9.84 (((setminusLsub) => 72.29/9.84 (((setminusSubset1) => 72.29/9.84 (((symdiffE) => 72.29/9.84 (((symdiffI1) => 72.29/9.84 (((symdiffI2) => 72.29/9.84 (((symdiffIneg1) => 72.29/9.84 (((symdiffIneg2) => 72.29/9.84 (((secondinupair) => 72.29/9.84 (((setukpairIL) => 72.29/9.84 (( 72.29/9.84 (setukpairIR) => 72.29/9.84 (( 72.29/9.84 (kpairiskpair) => 72.29/9.84 (( 72.29/9.84 (kpairp) => 72.29/9.84 (( 72.29/9.84 (singletonsubset) => 72.29/9.84 (( 72.29/9.84 (singletoninpowerset) => 72.29/9.84 (( 72.29/9.84 (singletoninpowunion) => 72.29/9.84 (( 72.29/9.84 (upairset2E) => 72.29/9.84 (( 72.29/9.84 (upairsubunion) => 72.29/9.84 (( 72.29/9.84 (upairinpowunion) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem1) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem2) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem3) => 72.29/9.84 (( 72.29/9.84 (cartprodpairin) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair1) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair) => 72.29/9.84 (( 72.29/9.84 (setunionE2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton1) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton) => 72.29/9.84 (( 72.29/9.84 (singletonprop) => 72.29/9.84 (( 72.29/9.84 (ex1E1) => 72.29/9.84 (( 72.29/9.84 (ex1I) => 72.29/9.84 (( 72.29/9.84 (ex1I2) => 72.29/9.84 (( 72.29/9.84 (singletonsuniq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL1) => 72.29/9.84 (( 72.29/9.84 (kfstsingleton) => 72.29/9.84 (( 72.29/9.84 (theprop) => 72.29/9.84 (( 72.29/9.84 (kfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstin) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR11) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR12) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR1) => 72.29/9.84 (( 72.29/9.84 (upairequniteq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR) => 72.29/9.84 (( 72.29/9.84 (ksndsingleton) => 72.29/9.84 (( 72.29/9.84 (ksndpairEq) => 72.29/9.84 (( 72.29/9.84 (kpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndin) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemEL) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemER) => 72.29/9.84 (( 72.29/9.84 (cartprodmempaircEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrI) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrSub) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrERa) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL1) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL2) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrER) => 72.29/9.84 (( 72.29/9.84 (funcImageSingleton) => 72.29/9.84 (( 72.29/9.84 (apProp) => 72.29/9.84 (( 72.29/9.84 (app) => 72.29/9.84 (( 72.29/9.84 (infuncsetfunc) => 72.29/9.84 (( 72.29/9.84 (ap2p) => 72.29/9.84 (( 72.29/9.84 (funcinfuncset) => 72.29/9.84 (( 72.29/9.84 (lamProp) => 72.29/9.84 (( 72.29/9.84 (lamp) => 72.29/9.84 (( 72.29/9.84 (lam2p) => 72.29/9.84 (( 72.29/9.84 (brelnall1) => 72.29/9.84 (( 72.29/9.84 (brelnall2) => 72.29/9.84 (( 72.29/9.84 (ex1E2) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp1) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp3) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp2) => 72.29/9.84 (( 72.29/9.84 (funcextLem) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp4) => 72.29/9.84 (( 72.29/9.84 (subbreln) => 72.29/9.84 (( 72.29/9.84 (eqbreln) => 72.29/9.84 (( 72.29/9.84 (funcext) => 72.29/9.84 (( 72.29/9.84 (funcext2) => 72.29/9.84 (( 72.29/9.84 (ap2apEq1) => 72.29/9.84 (( 72.29/9.84 (ap2apEq2) => 72.29/9.84 (( 72.29/9.84 (beta1) => 72.29/9.84 (( 72.29/9.84 (eta1) => 72.29/9.84 (( 72.29/9.84 (lam2lamEq) => 72.29/9.84 (( 72.29/9.84 (beta2) => 72.29/9.84 (( 72.29/9.84 (eta2) => 72.29/9.84 (( 72.29/9.84 (iffalseProp1) => 72.29/9.84 (( 72.29/9.84 (iffalseProp2) => 72.29/9.84 (( 72.29/9.84 (iftrueProp1) => 72.29/9.84 (( 72.29/9.84 (iftrueProp2) => 72.29/9.84 (( 72.29/9.84 (ifSingleton) => 72.29/9.84 (( 72.29/9.84 (ifp) => 72.29/9.84 (( 72.29/9.84 (theeq) => 72.29/9.84 (( 72.29/9.84 (iftrue) => 72.29/9.84 (( 72.29/9.84 (iffalse) => 72.29/9.84 (( 72.29/9.84 (iftrueorfalse) => 72.29/9.84 (( 72.29/9.84 (binintersectT_lem) => 72.29/9.84 (( 72.29/9.84 (binunionT_lem) => 72.29/9.84 (( 72.29/9.84 (powersetT_lem) => 72.29/9.84 (( 72.29/9.84 (setminusT_lem) => 72.29/9.84 (( 72.29/9.84 (complementT_lem) => 72.29/9.84 (( 72.29/9.84 (setextT) => 72.29/9.84 (( 72.29/9.84 (subsetTI) => 72.29/9.84 (( 72.29/9.84 (powersetTI1) => 72.29/9.84 (( 72.29/9.84 (powersetTE1) => 72.29/9.84 (( 72.29/9.84 (complementTI1) => 72.29/9.84 (( 72.29/9.84 (complementTE1) => 72.29/9.84 (( 72.29/9.84 (binintersectTELcontra) => 72.29/9.84 (( 72.29/9.84 (binintersectTERcontra) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT1) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT2) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT3) => 72.29/9.84 (( 72.29/9.84 (doubleComplementI1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementE1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub2) => 72.29/9.84 (( 72.29/9.84 (doubleComplementEq) => 72.29/9.84 (( 72.29/9.84 (complementTnotintersectT) => 72.29/9.84 (( 72.29/9.84 (complementImpComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementSubsetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementInPowersetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (contraSubsetComplement) => 72.29/9.84 (( 72.29/9.84 (complementTcontraSubset) => 72.29/9.84 (( 72.29/9.84 (binunionTILcontra) => 72.29/9.84 (( 72.29/9.84 (binunionTIRcontra) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion2) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (intersectInPowersetIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpNotIn1) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpInComplement1) => 72.29/9.84 (( 72.29/9.84 (binunionTE) => 72.29/9.84 (( 72.29/9.84 (binunionTEcontra) => 72.29/9.84 (( 72.29/9.84 (demorgan2a1) => 72.29/9.84 (( 72.29/9.84 (complementUnionInPowersetComplement) => 72.29/9.84 (( 72.29/9.84 (demorgan2a2) => 72.29/9.84 (( 72.29/9.84 (demorgan1a) => 72.29/9.84 (( 72.29/9.84 (demorgan1b) => 72.29/9.84 (( 72.29/9.84 (demorgan1) => 72.29/9.84 (( 72.29/9.84 (demorgan2a) => 72.29/9.84 (( 72.29/9.84 (demorgan2b2) => 72.29/9.84 (( 72.29/9.84 (demorgan2b) => 72.29/9.84 (( 72.29/9.84 (demorgan2) => 72.29/9.84 (( 72.29/9.84 (woz13rule0) => 72.29/9.84 (( 72.29/9.84 (woz13rule1) => 72.29/9.84 (( 72.29/9.84 (woz13rule2) => 72.29/9.84 (( 72.29/9.84 (woz13rule3) => 72.29/9.84 (( 72.29/9.84 (woz13rule4) => 72.29/9.84 (( 72.29/9.84 (woz1_1) => 72.29/9.84 (( 72.29/9.84 (woz1_2) => 72.29/9.84 (( 72.29/9.84 (woz1_3) => 72.29/9.84 (( 72.29/9.84 (woz1_4) => 72.29/9.84 (( 72.29/9.84 (woz1_5) => 72.29/9.84 (( 72.29/9.84 (breln1all2) => 72.29/9.84 (( 72.29/9.84 (breln1SetBreln1) => 72.29/9.84 (( 72.29/9.84 (choice2fnsingleton) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln1) => 72.29/9.84 (( 72.29/9.84 (breln1all1) => 72.29/9.84 (( 72.29/9.84 (subbreln1) => 72.29/9.84 (( 72.29/9.84 (eqbreln1) => 72.29/9.84 (( 72.29/9.84 (breln1invprop) => 72.29/9.84 (( 72.29/9.84 (breln1invI) => 72.29/9.84 (( 72.29/9.84 (breln1invE) => 72.29/9.84 (( 72.29/9.84 (breln1compprop) => 72.29/9.84 (( 72.29/9.84 (breln1compI) => 72.29/9.84 (( 72.29/9.84 (breln1compE) => 72.29/9.84 (( 72.29/9.84 (breln1compEex) => 72.29/9.84 (( 72.29/9.84 (!!) @ ( 72.29/9.84 (('#B') @ ( 72.29/9.84 !!) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 !!))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#C') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 breln1)))) @ 72.29/9.84 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1128])). 72.29/9.84 thf(zip_derived_cl1142, plain, 72.29/9.84 (~ (((binintersectI) => 72.29/9.84 (((binintersectSubset5) => 72.29/9.84 (((binintersectEL) => 72.29/9.84 (((binintersectLsub) => 72.29/9.84 (((binintersectSubset2) => 72.29/9.84 (((binintersectSubset3) => 72.29/9.84 (((binintersectER) => 72.29/9.84 (((disjointsetsI1) => 72.29/9.84 (((binintersectRsub) => 72.29/9.84 (((binintersectSubset4) => 72.29/9.84 (((binintersectSubset1) => 72.29/9.84 (((bs114d) => 72.29/9.84 (((setminusI) => 72.29/9.84 (((setminusEL) => 72.29/9.84 (((setminusER) => 72.29/9.84 (((setminusSubset2) => 72.29/9.84 (((setminusERneg) => 72.29/9.84 (((setminusELneg) => 72.29/9.84 (((setminusILneg) => 72.29/9.84 (((setminusIRneg) => 72.29/9.84 (((setminusLsub) => 72.29/9.84 (((setminusSubset1) => 72.29/9.84 (((symdiffE) => 72.29/9.84 (((symdiffI1) => 72.29/9.84 (((symdiffI2) => 72.29/9.84 (((symdiffIneg1) => 72.29/9.84 (((symdiffIneg2) => 72.29/9.84 (((secondinupair) => 72.29/9.84 (((setukpairIL) => 72.29/9.84 (((setukpairIR) => 72.29/9.84 (( 72.29/9.84 (kpairiskpair) => 72.29/9.84 (( 72.29/9.84 (kpairp) => 72.29/9.84 (( 72.29/9.84 (singletonsubset) => 72.29/9.84 (( 72.29/9.84 (singletoninpowerset) => 72.29/9.84 (( 72.29/9.84 (singletoninpowunion) => 72.29/9.84 (( 72.29/9.84 (upairset2E) => 72.29/9.84 (( 72.29/9.84 (upairsubunion) => 72.29/9.84 (( 72.29/9.84 (upairinpowunion) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem1) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem2) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem3) => 72.29/9.84 (( 72.29/9.84 (cartprodpairin) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair1) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair) => 72.29/9.84 (( 72.29/9.84 (setunionE2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton1) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton) => 72.29/9.84 (( 72.29/9.84 (singletonprop) => 72.29/9.84 (( 72.29/9.84 (ex1E1) => 72.29/9.84 (( 72.29/9.84 (ex1I) => 72.29/9.84 (( 72.29/9.84 (ex1I2) => 72.29/9.84 (( 72.29/9.84 (singletonsuniq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL1) => 72.29/9.84 (( 72.29/9.84 (kfstsingleton) => 72.29/9.84 (( 72.29/9.84 (theprop) => 72.29/9.84 (( 72.29/9.84 (kfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstin) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR11) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR12) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR1) => 72.29/9.84 (( 72.29/9.84 (upairequniteq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR) => 72.29/9.84 (( 72.29/9.84 (ksndsingleton) => 72.29/9.84 (( 72.29/9.84 (ksndpairEq) => 72.29/9.84 (( 72.29/9.84 (kpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndin) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemEL) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemER) => 72.29/9.84 (( 72.29/9.84 (cartprodmempaircEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrI) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrSub) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrERa) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL1) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL2) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrER) => 72.29/9.84 (( 72.29/9.84 (funcImageSingleton) => 72.29/9.84 (( 72.29/9.84 (apProp) => 72.29/9.84 (( 72.29/9.84 (app) => 72.29/9.84 (( 72.29/9.84 (infuncsetfunc) => 72.29/9.84 (( 72.29/9.84 (ap2p) => 72.29/9.84 (( 72.29/9.84 (funcinfuncset) => 72.29/9.84 (( 72.29/9.84 (lamProp) => 72.29/9.84 (( 72.29/9.84 (lamp) => 72.29/9.84 (( 72.29/9.84 (lam2p) => 72.29/9.84 (( 72.29/9.84 (brelnall1) => 72.29/9.84 (( 72.29/9.84 (brelnall2) => 72.29/9.84 (( 72.29/9.84 (ex1E2) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp1) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp3) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp2) => 72.29/9.84 (( 72.29/9.84 (funcextLem) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp4) => 72.29/9.84 (( 72.29/9.84 (subbreln) => 72.29/9.84 (( 72.29/9.84 (eqbreln) => 72.29/9.84 (( 72.29/9.84 (funcext) => 72.29/9.84 (( 72.29/9.84 (funcext2) => 72.29/9.84 (( 72.29/9.84 (ap2apEq1) => 72.29/9.84 (( 72.29/9.84 (ap2apEq2) => 72.29/9.84 (( 72.29/9.84 (beta1) => 72.29/9.84 (( 72.29/9.84 (eta1) => 72.29/9.84 (( 72.29/9.84 (lam2lamEq) => 72.29/9.84 (( 72.29/9.84 (beta2) => 72.29/9.84 (( 72.29/9.84 (eta2) => 72.29/9.84 (( 72.29/9.84 (iffalseProp1) => 72.29/9.84 (( 72.29/9.84 (iffalseProp2) => 72.29/9.84 (( 72.29/9.84 (iftrueProp1) => 72.29/9.84 (( 72.29/9.84 (iftrueProp2) => 72.29/9.84 (( 72.29/9.84 (ifSingleton) => 72.29/9.84 (( 72.29/9.84 (ifp) => 72.29/9.84 (( 72.29/9.84 (theeq) => 72.29/9.84 (( 72.29/9.84 (iftrue) => 72.29/9.84 (( 72.29/9.84 (iffalse) => 72.29/9.84 (( 72.29/9.84 (iftrueorfalse) => 72.29/9.84 (( 72.29/9.84 (binintersectT_lem) => 72.29/9.84 (( 72.29/9.84 (binunionT_lem) => 72.29/9.84 (( 72.29/9.84 (powersetT_lem) => 72.29/9.84 (( 72.29/9.84 (setminusT_lem) => 72.29/9.84 (( 72.29/9.84 (complementT_lem) => 72.29/9.84 (( 72.29/9.84 (setextT) => 72.29/9.84 (( 72.29/9.84 (subsetTI) => 72.29/9.84 (( 72.29/9.84 (powersetTI1) => 72.29/9.84 (( 72.29/9.84 (powersetTE1) => 72.29/9.84 (( 72.29/9.84 (complementTI1) => 72.29/9.84 (( 72.29/9.84 (complementTE1) => 72.29/9.84 (( 72.29/9.84 (binintersectTELcontra) => 72.29/9.84 (( 72.29/9.84 (binintersectTERcontra) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT1) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT2) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT3) => 72.29/9.84 (( 72.29/9.84 (doubleComplementI1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementE1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub2) => 72.29/9.84 (( 72.29/9.84 (doubleComplementEq) => 72.29/9.84 (( 72.29/9.84 (complementTnotintersectT) => 72.29/9.84 (( 72.29/9.84 (complementImpComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementSubsetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementInPowersetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (contraSubsetComplement) => 72.29/9.84 (( 72.29/9.84 (complementTcontraSubset) => 72.29/9.84 (( 72.29/9.84 (binunionTILcontra) => 72.29/9.84 (( 72.29/9.84 (binunionTIRcontra) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion2) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (intersectInPowersetIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpNotIn1) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpInComplement1) => 72.29/9.84 (( 72.29/9.84 (binunionTE) => 72.29/9.84 (( 72.29/9.84 (binunionTEcontra) => 72.29/9.84 (( 72.29/9.84 (demorgan2a1) => 72.29/9.84 (( 72.29/9.84 (complementUnionInPowersetComplement) => 72.29/9.84 (( 72.29/9.84 (demorgan2a2) => 72.29/9.84 (( 72.29/9.84 (demorgan1a) => 72.29/9.84 (( 72.29/9.84 (demorgan1b) => 72.29/9.84 (( 72.29/9.84 (demorgan1) => 72.29/9.84 (( 72.29/9.84 (demorgan2a) => 72.29/9.84 (( 72.29/9.84 (demorgan2b2) => 72.29/9.84 (( 72.29/9.84 (demorgan2b) => 72.29/9.84 (( 72.29/9.84 (demorgan2) => 72.29/9.84 (( 72.29/9.84 (woz13rule0) => 72.29/9.84 (( 72.29/9.84 (woz13rule1) => 72.29/9.84 (( 72.29/9.84 (woz13rule2) => 72.29/9.84 (( 72.29/9.84 (woz13rule3) => 72.29/9.84 (( 72.29/9.84 (woz13rule4) => 72.29/9.84 (( 72.29/9.84 (woz1_1) => 72.29/9.84 (( 72.29/9.84 (woz1_2) => 72.29/9.84 (( 72.29/9.84 (woz1_3) => 72.29/9.84 (( 72.29/9.84 (woz1_4) => 72.29/9.84 (( 72.29/9.84 (woz1_5) => 72.29/9.84 (( 72.29/9.84 (breln1all2) => 72.29/9.84 (( 72.29/9.84 (breln1SetBreln1) => 72.29/9.84 (( 72.29/9.84 (choice2fnsingleton) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln1) => 72.29/9.84 (( 72.29/9.84 (breln1all1) => 72.29/9.84 (( 72.29/9.84 (subbreln1) => 72.29/9.84 (( 72.29/9.84 (eqbreln1) => 72.29/9.84 (( 72.29/9.84 (breln1invprop) => 72.29/9.84 (( 72.29/9.84 (breln1invI) => 72.29/9.84 (( 72.29/9.84 (breln1invE) => 72.29/9.84 (( 72.29/9.84 (breln1compprop) => 72.29/9.84 (( 72.29/9.84 (breln1compI) => 72.29/9.84 (( 72.29/9.84 (breln1compE) => 72.29/9.84 (( 72.29/9.84 (breln1compEex) => 72.29/9.84 (( 72.29/9.84 (!!) @ ( 72.29/9.84 (('#B') @ ( 72.29/9.84 !!) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 !!))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#C') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 breln1)))) @ 72.29/9.84 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1135])). 72.29/9.84 thf(zip_derived_cl1150, plain, 72.29/9.84 (~ (((binintersectSubset5) => 72.29/9.84 (((binintersectEL) => 72.29/9.84 (((binintersectLsub) => 72.29/9.84 (((binintersectSubset2) => 72.29/9.84 (((binintersectSubset3) => 72.29/9.84 (((binintersectER) => 72.29/9.84 (((disjointsetsI1) => 72.29/9.84 (((binintersectRsub) => 72.29/9.84 (((binintersectSubset4) => 72.29/9.84 (((binintersectSubset1) => 72.29/9.84 (((bs114d) => 72.29/9.84 (((setminusI) => 72.29/9.84 (((setminusEL) => 72.29/9.84 (((setminusER) => 72.29/9.84 (((setminusSubset2) => 72.29/9.84 (((setminusERneg) => 72.29/9.84 (((setminusELneg) => 72.29/9.84 (((setminusILneg) => 72.29/9.84 (((setminusIRneg) => 72.29/9.84 (((setminusLsub) => 72.29/9.84 (((setminusSubset1) => 72.29/9.84 (((symdiffE) => 72.29/9.84 (((symdiffI1) => 72.29/9.84 (((symdiffI2) => 72.29/9.84 (((symdiffIneg1) => 72.29/9.84 (((symdiffIneg2) => 72.29/9.84 (((secondinupair) => 72.29/9.84 (((setukpairIL) => 72.29/9.84 (((setukpairIR) => 72.29/9.84 (((kpairiskpair) => 72.29/9.84 (( 72.29/9.84 (kpairp) => 72.29/9.84 (( 72.29/9.84 (singletonsubset) => 72.29/9.84 (( 72.29/9.84 (singletoninpowerset) => 72.29/9.84 (( 72.29/9.84 (singletoninpowunion) => 72.29/9.84 (( 72.29/9.84 (upairset2E) => 72.29/9.84 (( 72.29/9.84 (upairsubunion) => 72.29/9.84 (( 72.29/9.84 (upairinpowunion) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem1) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem2) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem3) => 72.29/9.84 (( 72.29/9.84 (cartprodpairin) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair1) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair) => 72.29/9.84 (( 72.29/9.84 (setunionE2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton1) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton) => 72.29/9.84 (( 72.29/9.84 (singletonprop) => 72.29/9.84 (( 72.29/9.84 (ex1E1) => 72.29/9.84 (( 72.29/9.84 (ex1I) => 72.29/9.84 (( 72.29/9.84 (ex1I2) => 72.29/9.84 (( 72.29/9.84 (singletonsuniq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL1) => 72.29/9.84 (( 72.29/9.84 (kfstsingleton) => 72.29/9.84 (( 72.29/9.84 (theprop) => 72.29/9.84 (( 72.29/9.84 (kfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstin) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR11) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR12) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR1) => 72.29/9.84 (( 72.29/9.84 (upairequniteq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR) => 72.29/9.84 (( 72.29/9.84 (ksndsingleton) => 72.29/9.84 (( 72.29/9.84 (ksndpairEq) => 72.29/9.84 (( 72.29/9.84 (kpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndin) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemEL) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemER) => 72.29/9.84 (( 72.29/9.84 (cartprodmempaircEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrI) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrSub) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrERa) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL1) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL2) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrER) => 72.29/9.84 (( 72.29/9.84 (funcImageSingleton) => 72.29/9.84 (( 72.29/9.84 (apProp) => 72.29/9.84 (( 72.29/9.84 (app) => 72.29/9.84 (( 72.29/9.84 (infuncsetfunc) => 72.29/9.84 (( 72.29/9.84 (ap2p) => 72.29/9.84 (( 72.29/9.84 (funcinfuncset) => 72.29/9.84 (( 72.29/9.84 (lamProp) => 72.29/9.84 (( 72.29/9.84 (lamp) => 72.29/9.84 (( 72.29/9.84 (lam2p) => 72.29/9.84 (( 72.29/9.84 (brelnall1) => 72.29/9.84 (( 72.29/9.84 (brelnall2) => 72.29/9.84 (( 72.29/9.84 (ex1E2) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp1) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp3) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp2) => 72.29/9.84 (( 72.29/9.84 (funcextLem) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp4) => 72.29/9.84 (( 72.29/9.84 (subbreln) => 72.29/9.84 (( 72.29/9.84 (eqbreln) => 72.29/9.84 (( 72.29/9.84 (funcext) => 72.29/9.84 (( 72.29/9.84 (funcext2) => 72.29/9.84 (( 72.29/9.84 (ap2apEq1) => 72.29/9.84 (( 72.29/9.84 (ap2apEq2) => 72.29/9.84 (( 72.29/9.84 (beta1) => 72.29/9.84 (( 72.29/9.84 (eta1) => 72.29/9.84 (( 72.29/9.84 (lam2lamEq) => 72.29/9.84 (( 72.29/9.84 (beta2) => 72.29/9.84 (( 72.29/9.84 (eta2) => 72.29/9.84 (( 72.29/9.84 (iffalseProp1) => 72.29/9.84 (( 72.29/9.84 (iffalseProp2) => 72.29/9.84 (( 72.29/9.84 (iftrueProp1) => 72.29/9.84 (( 72.29/9.84 (iftrueProp2) => 72.29/9.84 (( 72.29/9.84 (ifSingleton) => 72.29/9.84 (( 72.29/9.84 (ifp) => 72.29/9.84 (( 72.29/9.84 (theeq) => 72.29/9.84 (( 72.29/9.84 (iftrue) => 72.29/9.84 (( 72.29/9.84 (iffalse) => 72.29/9.84 (( 72.29/9.84 (iftrueorfalse) => 72.29/9.84 (( 72.29/9.84 (binintersectT_lem) => 72.29/9.84 (( 72.29/9.84 (binunionT_lem) => 72.29/9.84 (( 72.29/9.84 (powersetT_lem) => 72.29/9.84 (( 72.29/9.84 (setminusT_lem) => 72.29/9.84 (( 72.29/9.84 (complementT_lem) => 72.29/9.84 (( 72.29/9.84 (setextT) => 72.29/9.84 (( 72.29/9.84 (subsetTI) => 72.29/9.84 (( 72.29/9.84 (powersetTI1) => 72.29/9.84 (( 72.29/9.84 (powersetTE1) => 72.29/9.84 (( 72.29/9.84 (complementTI1) => 72.29/9.84 (( 72.29/9.84 (complementTE1) => 72.29/9.84 (( 72.29/9.84 (binintersectTELcontra) => 72.29/9.84 (( 72.29/9.84 (binintersectTERcontra) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT1) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT2) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT3) => 72.29/9.84 (( 72.29/9.84 (doubleComplementI1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementE1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub2) => 72.29/9.84 (( 72.29/9.84 (doubleComplementEq) => 72.29/9.84 (( 72.29/9.84 (complementTnotintersectT) => 72.29/9.84 (( 72.29/9.84 (complementImpComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementSubsetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementInPowersetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (contraSubsetComplement) => 72.29/9.84 (( 72.29/9.84 (complementTcontraSubset) => 72.29/9.84 (( 72.29/9.84 (binunionTILcontra) => 72.29/9.84 (( 72.29/9.84 (binunionTIRcontra) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion2) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (intersectInPowersetIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpNotIn1) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpInComplement1) => 72.29/9.84 (( 72.29/9.84 (binunionTE) => 72.29/9.84 (( 72.29/9.84 (binunionTEcontra) => 72.29/9.84 (( 72.29/9.84 (demorgan2a1) => 72.29/9.84 (( 72.29/9.84 (complementUnionInPowersetComplement) => 72.29/9.84 (( 72.29/9.84 (demorgan2a2) => 72.29/9.84 (( 72.29/9.84 (demorgan1a) => 72.29/9.84 (( 72.29/9.84 (demorgan1b) => 72.29/9.84 (( 72.29/9.84 (demorgan1) => 72.29/9.84 (( 72.29/9.84 (demorgan2a) => 72.29/9.84 (( 72.29/9.84 (demorgan2b2) => 72.29/9.84 (( 72.29/9.84 (demorgan2b) => 72.29/9.84 (( 72.29/9.84 (demorgan2) => 72.29/9.84 (( 72.29/9.84 (woz13rule0) => 72.29/9.84 (( 72.29/9.84 (woz13rule1) => 72.29/9.84 (( 72.29/9.84 (woz13rule2) => 72.29/9.84 (( 72.29/9.84 (woz13rule3) => 72.29/9.84 (( 72.29/9.84 (woz13rule4) => 72.29/9.84 (( 72.29/9.84 (woz1_1) => 72.29/9.84 (( 72.29/9.84 (woz1_2) => 72.29/9.84 (( 72.29/9.84 (woz1_3) => 72.29/9.84 (( 72.29/9.84 (woz1_4) => 72.29/9.84 (( 72.29/9.84 (woz1_5) => 72.29/9.84 (( 72.29/9.84 (breln1all2) => 72.29/9.84 (( 72.29/9.84 (breln1SetBreln1) => 72.29/9.84 (( 72.29/9.84 (choice2fnsingleton) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln1) => 72.29/9.84 (( 72.29/9.84 (breln1all1) => 72.29/9.84 (( 72.29/9.84 (subbreln1) => 72.29/9.84 (( 72.29/9.84 (eqbreln1) => 72.29/9.84 (( 72.29/9.84 (breln1invprop) => 72.29/9.84 (( 72.29/9.84 (breln1invI) => 72.29/9.84 (( 72.29/9.84 (breln1invE) => 72.29/9.84 (( 72.29/9.84 (breln1compprop) => 72.29/9.84 (( 72.29/9.84 (breln1compI) => 72.29/9.84 (( 72.29/9.84 (breln1compE) => 72.29/9.84 (( 72.29/9.84 (breln1compEex) => 72.29/9.84 (( 72.29/9.84 (!!) @ ( 72.29/9.84 (('#B') @ ( 72.29/9.84 !!) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 !!))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#C') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 breln1)))) @ 72.29/9.84 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1142])). 72.29/9.84 thf(zip_derived_cl1158, plain, 72.29/9.84 (~ (((binintersectEL) => 72.29/9.84 (((binintersectLsub) => 72.29/9.84 (((binintersectSubset2) => 72.29/9.84 (((binintersectSubset3) => 72.29/9.84 (((binintersectER) => 72.29/9.84 (((disjointsetsI1) => 72.29/9.84 (((binintersectRsub) => 72.29/9.84 (((binintersectSubset4) => 72.29/9.84 (((binintersectSubset1) => 72.29/9.84 (((bs114d) => 72.29/9.84 (((setminusI) => 72.29/9.84 (((setminusEL) => 72.29/9.84 (((setminusER) => 72.29/9.84 (((setminusSubset2) => 72.29/9.84 (((setminusERneg) => 72.29/9.84 (((setminusELneg) => 72.29/9.84 (((setminusILneg) => 72.29/9.84 (((setminusIRneg) => 72.29/9.84 (((setminusLsub) => 72.29/9.84 (((setminusSubset1) => 72.29/9.84 (((symdiffE) => 72.29/9.84 (((symdiffI1) => 72.29/9.84 (((symdiffI2) => 72.29/9.84 (((symdiffIneg1) => 72.29/9.84 (((symdiffIneg2) => 72.29/9.84 (((secondinupair) => 72.29/9.84 (((setukpairIL) => 72.29/9.84 (((setukpairIR) => 72.29/9.84 (((kpairiskpair) => 72.29/9.84 (((kpairp) => 72.29/9.84 (( 72.29/9.84 (singletonsubset) => 72.29/9.84 (( 72.29/9.84 (singletoninpowerset) => 72.29/9.84 (( 72.29/9.84 (singletoninpowunion) => 72.29/9.84 (( 72.29/9.84 (upairset2E) => 72.29/9.84 (( 72.29/9.84 (upairsubunion) => 72.29/9.84 (( 72.29/9.84 (upairinpowunion) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem1) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem2) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem3) => 72.29/9.84 (( 72.29/9.84 (cartprodpairin) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair1) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair) => 72.29/9.84 (( 72.29/9.84 (setunionE2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton1) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton) => 72.29/9.84 (( 72.29/9.84 (singletonprop) => 72.29/9.84 (( 72.29/9.84 (ex1E1) => 72.29/9.84 (( 72.29/9.84 (ex1I) => 72.29/9.84 (( 72.29/9.84 (ex1I2) => 72.29/9.84 (( 72.29/9.84 (singletonsuniq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL1) => 72.29/9.84 (( 72.29/9.84 (kfstsingleton) => 72.29/9.84 (( 72.29/9.84 (theprop) => 72.29/9.84 (( 72.29/9.84 (kfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstin) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR11) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR12) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR1) => 72.29/9.84 (( 72.29/9.84 (upairequniteq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR) => 72.29/9.84 (( 72.29/9.84 (ksndsingleton) => 72.29/9.84 (( 72.29/9.84 (ksndpairEq) => 72.29/9.84 (( 72.29/9.84 (kpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndin) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemEL) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemER) => 72.29/9.84 (( 72.29/9.84 (cartprodmempaircEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrI) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrSub) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrERa) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL1) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL2) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrER) => 72.29/9.84 (( 72.29/9.84 (funcImageSingleton) => 72.29/9.84 (( 72.29/9.84 (apProp) => 72.29/9.84 (( 72.29/9.84 (app) => 72.29/9.84 (( 72.29/9.84 (infuncsetfunc) => 72.29/9.84 (( 72.29/9.84 (ap2p) => 72.29/9.84 (( 72.29/9.84 (funcinfuncset) => 72.29/9.84 (( 72.29/9.84 (lamProp) => 72.29/9.84 (( 72.29/9.84 (lamp) => 72.29/9.84 (( 72.29/9.84 (lam2p) => 72.29/9.84 (( 72.29/9.84 (brelnall1) => 72.29/9.84 (( 72.29/9.84 (brelnall2) => 72.29/9.84 (( 72.29/9.84 (ex1E2) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp1) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp3) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp2) => 72.29/9.84 (( 72.29/9.84 (funcextLem) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp4) => 72.29/9.84 (( 72.29/9.84 (subbreln) => 72.29/9.84 (( 72.29/9.84 (eqbreln) => 72.29/9.84 (( 72.29/9.84 (funcext) => 72.29/9.84 (( 72.29/9.84 (funcext2) => 72.29/9.84 (( 72.29/9.84 (ap2apEq1) => 72.29/9.84 (( 72.29/9.84 (ap2apEq2) => 72.29/9.84 (( 72.29/9.84 (beta1) => 72.29/9.84 (( 72.29/9.84 (eta1) => 72.29/9.84 (( 72.29/9.84 (lam2lamEq) => 72.29/9.84 (( 72.29/9.84 (beta2) => 72.29/9.84 (( 72.29/9.84 (eta2) => 72.29/9.84 (( 72.29/9.84 (iffalseProp1) => 72.29/9.84 (( 72.29/9.84 (iffalseProp2) => 72.29/9.84 (( 72.29/9.84 (iftrueProp1) => 72.29/9.84 (( 72.29/9.84 (iftrueProp2) => 72.29/9.84 (( 72.29/9.84 (ifSingleton) => 72.29/9.84 (( 72.29/9.84 (ifp) => 72.29/9.84 (( 72.29/9.84 (theeq) => 72.29/9.84 (( 72.29/9.84 (iftrue) => 72.29/9.84 (( 72.29/9.84 (iffalse) => 72.29/9.84 (( 72.29/9.84 (iftrueorfalse) => 72.29/9.84 (( 72.29/9.84 (binintersectT_lem) => 72.29/9.84 (( 72.29/9.84 (binunionT_lem) => 72.29/9.84 (( 72.29/9.84 (powersetT_lem) => 72.29/9.84 (( 72.29/9.84 (setminusT_lem) => 72.29/9.84 (( 72.29/9.84 (complementT_lem) => 72.29/9.84 (( 72.29/9.84 (setextT) => 72.29/9.84 (( 72.29/9.84 (subsetTI) => 72.29/9.84 (( 72.29/9.84 (powersetTI1) => 72.29/9.84 (( 72.29/9.84 (powersetTE1) => 72.29/9.84 (( 72.29/9.84 (complementTI1) => 72.29/9.84 (( 72.29/9.84 (complementTE1) => 72.29/9.84 (( 72.29/9.84 (binintersectTELcontra) => 72.29/9.84 (( 72.29/9.84 (binintersectTERcontra) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT1) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT2) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT3) => 72.29/9.84 (( 72.29/9.84 (doubleComplementI1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementE1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub2) => 72.29/9.84 (( 72.29/9.84 (doubleComplementEq) => 72.29/9.84 (( 72.29/9.84 (complementTnotintersectT) => 72.29/9.84 (( 72.29/9.84 (complementImpComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementSubsetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementInPowersetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (contraSubsetComplement) => 72.29/9.84 (( 72.29/9.84 (complementTcontraSubset) => 72.29/9.84 (( 72.29/9.84 (binunionTILcontra) => 72.29/9.84 (( 72.29/9.84 (binunionTIRcontra) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion2) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (intersectInPowersetIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpNotIn1) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpInComplement1) => 72.29/9.84 (( 72.29/9.84 (binunionTE) => 72.29/9.84 (( 72.29/9.84 (binunionTEcontra) => 72.29/9.84 (( 72.29/9.84 (demorgan2a1) => 72.29/9.84 (( 72.29/9.84 (complementUnionInPowersetComplement) => 72.29/9.84 (( 72.29/9.84 (demorgan2a2) => 72.29/9.84 (( 72.29/9.84 (demorgan1a) => 72.29/9.84 (( 72.29/9.84 (demorgan1b) => 72.29/9.84 (( 72.29/9.84 (demorgan1) => 72.29/9.84 (( 72.29/9.84 (demorgan2a) => 72.29/9.84 (( 72.29/9.84 (demorgan2b2) => 72.29/9.84 (( 72.29/9.84 (demorgan2b) => 72.29/9.84 (( 72.29/9.84 (demorgan2) => 72.29/9.84 (( 72.29/9.84 (woz13rule0) => 72.29/9.84 (( 72.29/9.84 (woz13rule1) => 72.29/9.84 (( 72.29/9.84 (woz13rule2) => 72.29/9.84 (( 72.29/9.84 (woz13rule3) => 72.29/9.84 (( 72.29/9.84 (woz13rule4) => 72.29/9.84 (( 72.29/9.84 (woz1_1) => 72.29/9.84 (( 72.29/9.84 (woz1_2) => 72.29/9.84 (( 72.29/9.84 (woz1_3) => 72.29/9.84 (( 72.29/9.84 (woz1_4) => 72.29/9.84 (( 72.29/9.84 (woz1_5) => 72.29/9.84 (( 72.29/9.84 (breln1all2) => 72.29/9.84 (( 72.29/9.84 (breln1SetBreln1) => 72.29/9.84 (( 72.29/9.84 (choice2fnsingleton) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln1) => 72.29/9.84 (( 72.29/9.84 (breln1all1) => 72.29/9.84 (( 72.29/9.84 (subbreln1) => 72.29/9.84 (( 72.29/9.84 (eqbreln1) => 72.29/9.84 (( 72.29/9.84 (breln1invprop) => 72.29/9.84 (( 72.29/9.84 (breln1invI) => 72.29/9.84 (( 72.29/9.84 (breln1invE) => 72.29/9.84 (( 72.29/9.84 (breln1compprop) => 72.29/9.84 (( 72.29/9.84 (breln1compI) => 72.29/9.84 (( 72.29/9.84 (breln1compE) => 72.29/9.84 (( 72.29/9.84 (breln1compEex) => 72.29/9.84 (( 72.29/9.84 (!!) @ ( 72.29/9.84 (('#B') @ ( 72.29/9.84 !!) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 !!))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#C') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 breln1)))) @ 72.29/9.84 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1150])). 72.29/9.84 thf(zip_derived_cl1166, plain, 72.29/9.84 (~ (((binintersectLsub) => 72.29/9.84 (((binintersectSubset2) => 72.29/9.84 (((binintersectSubset3) => 72.29/9.84 (((binintersectER) => 72.29/9.84 (((disjointsetsI1) => 72.29/9.84 (((binintersectRsub) => 72.29/9.84 (((binintersectSubset4) => 72.29/9.84 (((binintersectSubset1) => 72.29/9.84 (((bs114d) => 72.29/9.84 (((setminusI) => 72.29/9.84 (((setminusEL) => 72.29/9.84 (((setminusER) => 72.29/9.84 (((setminusSubset2) => 72.29/9.84 (((setminusERneg) => 72.29/9.84 (((setminusELneg) => 72.29/9.84 (((setminusILneg) => 72.29/9.84 (((setminusIRneg) => 72.29/9.84 (((setminusLsub) => 72.29/9.84 (((setminusSubset1) => 72.29/9.84 (((symdiffE) => 72.29/9.84 (((symdiffI1) => 72.29/9.84 (((symdiffI2) => 72.29/9.84 (((symdiffIneg1) => 72.29/9.84 (((symdiffIneg2) => 72.29/9.84 (((secondinupair) => 72.29/9.84 (((setukpairIL) => 72.29/9.84 (((setukpairIR) => 72.29/9.84 (((kpairiskpair) => 72.29/9.84 (((kpairp) => 72.29/9.84 (((singletonsubset) => 72.29/9.84 (( 72.29/9.84 (singletoninpowerset) => 72.29/9.84 (( 72.29/9.84 (singletoninpowunion) => 72.29/9.84 (( 72.29/9.84 (upairset2E) => 72.29/9.84 (( 72.29/9.84 (upairsubunion) => 72.29/9.84 (( 72.29/9.84 (upairinpowunion) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem1) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem2) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem3) => 72.29/9.84 (( 72.29/9.84 (cartprodpairin) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair1) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair) => 72.29/9.84 (( 72.29/9.84 (setunionE2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton1) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton) => 72.29/9.84 (( 72.29/9.84 (singletonprop) => 72.29/9.84 (( 72.29/9.84 (ex1E1) => 72.29/9.84 (( 72.29/9.84 (ex1I) => 72.29/9.84 (( 72.29/9.84 (ex1I2) => 72.29/9.84 (( 72.29/9.84 (singletonsuniq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL1) => 72.29/9.84 (( 72.29/9.84 (kfstsingleton) => 72.29/9.84 (( 72.29/9.84 (theprop) => 72.29/9.84 (( 72.29/9.84 (kfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstin) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR11) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR12) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR1) => 72.29/9.84 (( 72.29/9.84 (upairequniteq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR) => 72.29/9.84 (( 72.29/9.84 (ksndsingleton) => 72.29/9.84 (( 72.29/9.84 (ksndpairEq) => 72.29/9.84 (( 72.29/9.84 (kpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndin) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemEL) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemER) => 72.29/9.84 (( 72.29/9.84 (cartprodmempaircEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrI) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrSub) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrERa) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL1) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL2) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrER) => 72.29/9.84 (( 72.29/9.84 (funcImageSingleton) => 72.29/9.84 (( 72.29/9.84 (apProp) => 72.29/9.84 (( 72.29/9.84 (app) => 72.29/9.84 (( 72.29/9.84 (infuncsetfunc) => 72.29/9.84 (( 72.29/9.84 (ap2p) => 72.29/9.84 (( 72.29/9.84 (funcinfuncset) => 72.29/9.84 (( 72.29/9.84 (lamProp) => 72.29/9.84 (( 72.29/9.84 (lamp) => 72.29/9.84 (( 72.29/9.84 (lam2p) => 72.29/9.84 (( 72.29/9.84 (brelnall1) => 72.29/9.84 (( 72.29/9.84 (brelnall2) => 72.29/9.84 (( 72.29/9.84 (ex1E2) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp1) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp3) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp2) => 72.29/9.84 (( 72.29/9.84 (funcextLem) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp4) => 72.29/9.84 (( 72.29/9.84 (subbreln) => 72.29/9.84 (( 72.29/9.84 (eqbreln) => 72.29/9.84 (( 72.29/9.84 (funcext) => 72.29/9.84 (( 72.29/9.84 (funcext2) => 72.29/9.84 (( 72.29/9.84 (ap2apEq1) => 72.29/9.84 (( 72.29/9.84 (ap2apEq2) => 72.29/9.84 (( 72.29/9.84 (beta1) => 72.29/9.84 (( 72.29/9.84 (eta1) => 72.29/9.84 (( 72.29/9.84 (lam2lamEq) => 72.29/9.84 (( 72.29/9.84 (beta2) => 72.29/9.84 (( 72.29/9.84 (eta2) => 72.29/9.84 (( 72.29/9.84 (iffalseProp1) => 72.29/9.84 (( 72.29/9.84 (iffalseProp2) => 72.29/9.84 (( 72.29/9.84 (iftrueProp1) => 72.29/9.84 (( 72.29/9.84 (iftrueProp2) => 72.29/9.84 (( 72.29/9.84 (ifSingleton) => 72.29/9.84 (( 72.29/9.84 (ifp) => 72.29/9.84 (( 72.29/9.84 (theeq) => 72.29/9.84 (( 72.29/9.84 (iftrue) => 72.29/9.84 (( 72.29/9.84 (iffalse) => 72.29/9.84 (( 72.29/9.84 (iftrueorfalse) => 72.29/9.84 (( 72.29/9.84 (binintersectT_lem) => 72.29/9.84 (( 72.29/9.84 (binunionT_lem) => 72.29/9.84 (( 72.29/9.84 (powersetT_lem) => 72.29/9.84 (( 72.29/9.84 (setminusT_lem) => 72.29/9.84 (( 72.29/9.84 (complementT_lem) => 72.29/9.84 (( 72.29/9.84 (setextT) => 72.29/9.84 (( 72.29/9.84 (subsetTI) => 72.29/9.84 (( 72.29/9.84 (powersetTI1) => 72.29/9.84 (( 72.29/9.84 (powersetTE1) => 72.29/9.84 (( 72.29/9.84 (complementTI1) => 72.29/9.84 (( 72.29/9.84 (complementTE1) => 72.29/9.84 (( 72.29/9.84 (binintersectTELcontra) => 72.29/9.84 (( 72.29/9.84 (binintersectTERcontra) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT1) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT2) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT3) => 72.29/9.84 (( 72.29/9.84 (doubleComplementI1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementE1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub2) => 72.29/9.84 (( 72.29/9.84 (doubleComplementEq) => 72.29/9.84 (( 72.29/9.84 (complementTnotintersectT) => 72.29/9.84 (( 72.29/9.84 (complementImpComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementSubsetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementInPowersetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (contraSubsetComplement) => 72.29/9.84 (( 72.29/9.84 (complementTcontraSubset) => 72.29/9.84 (( 72.29/9.84 (binunionTILcontra) => 72.29/9.84 (( 72.29/9.84 (binunionTIRcontra) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion2) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (intersectInPowersetIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpNotIn1) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpInComplement1) => 72.29/9.84 (( 72.29/9.84 (binunionTE) => 72.29/9.84 (( 72.29/9.84 (binunionTEcontra) => 72.29/9.84 (( 72.29/9.84 (demorgan2a1) => 72.29/9.84 (( 72.29/9.84 (complementUnionInPowersetComplement) => 72.29/9.84 (( 72.29/9.84 (demorgan2a2) => 72.29/9.84 (( 72.29/9.84 (demorgan1a) => 72.29/9.84 (( 72.29/9.84 (demorgan1b) => 72.29/9.84 (( 72.29/9.84 (demorgan1) => 72.29/9.84 (( 72.29/9.84 (demorgan2a) => 72.29/9.84 (( 72.29/9.84 (demorgan2b2) => 72.29/9.84 (( 72.29/9.84 (demorgan2b) => 72.29/9.84 (( 72.29/9.84 (demorgan2) => 72.29/9.84 (( 72.29/9.84 (woz13rule0) => 72.29/9.84 (( 72.29/9.84 (woz13rule1) => 72.29/9.84 (( 72.29/9.84 (woz13rule2) => 72.29/9.84 (( 72.29/9.84 (woz13rule3) => 72.29/9.84 (( 72.29/9.84 (woz13rule4) => 72.29/9.84 (( 72.29/9.84 (woz1_1) => 72.29/9.84 (( 72.29/9.84 (woz1_2) => 72.29/9.84 (( 72.29/9.84 (woz1_3) => 72.29/9.84 (( 72.29/9.84 (woz1_4) => 72.29/9.84 (( 72.29/9.84 (woz1_5) => 72.29/9.84 (( 72.29/9.84 (breln1all2) => 72.29/9.84 (( 72.29/9.84 (breln1SetBreln1) => 72.29/9.84 (( 72.29/9.84 (choice2fnsingleton) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln1) => 72.29/9.84 (( 72.29/9.84 (breln1all1) => 72.29/9.84 (( 72.29/9.84 (subbreln1) => 72.29/9.84 (( 72.29/9.84 (eqbreln1) => 72.29/9.84 (( 72.29/9.84 (breln1invprop) => 72.29/9.84 (( 72.29/9.84 (breln1invI) => 72.29/9.84 (( 72.29/9.84 (breln1invE) => 72.29/9.84 (( 72.29/9.84 (breln1compprop) => 72.29/9.84 (( 72.29/9.84 (breln1compI) => 72.29/9.84 (( 72.29/9.84 (breln1compE) => 72.29/9.84 (( 72.29/9.84 (breln1compEex) => 72.29/9.84 (( 72.29/9.84 (!!) @ ( 72.29/9.84 (('#B') @ ( 72.29/9.84 !!) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 !!))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#C') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 breln1)))) @ 72.29/9.84 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1158])). 72.29/9.84 thf(zip_derived_cl1174, plain, 72.29/9.84 (~ (((binintersectSubset2) => 72.29/9.84 (((binintersectSubset3) => 72.29/9.84 (((binintersectER) => 72.29/9.84 (((disjointsetsI1) => 72.29/9.84 (((binintersectRsub) => 72.29/9.84 (((binintersectSubset4) => 72.29/9.84 (((binintersectSubset1) => 72.29/9.84 (((bs114d) => 72.29/9.84 (((setminusI) => 72.29/9.84 (((setminusEL) => 72.29/9.84 (((setminusER) => 72.29/9.84 (((setminusSubset2) => 72.29/9.84 (((setminusERneg) => 72.29/9.84 (((setminusELneg) => 72.29/9.84 (((setminusILneg) => 72.29/9.84 (((setminusIRneg) => 72.29/9.84 (((setminusLsub) => 72.29/9.84 (((setminusSubset1) => 72.29/9.84 (((symdiffE) => 72.29/9.84 (((symdiffI1) => 72.29/9.84 (((symdiffI2) => 72.29/9.84 (((symdiffIneg1) => 72.29/9.84 (((symdiffIneg2) => 72.29/9.84 (((secondinupair) => 72.29/9.84 (((setukpairIL) => 72.29/9.84 (((setukpairIR) => 72.29/9.84 (((kpairiskpair) => 72.29/9.84 (((kpairp) => 72.29/9.84 (((singletonsubset) => 72.29/9.84 (((singletoninpowerset) => 72.29/9.84 (( 72.29/9.84 (singletoninpowunion) => 72.29/9.84 (( 72.29/9.84 (upairset2E) => 72.29/9.84 (( 72.29/9.84 (upairsubunion) => 72.29/9.84 (( 72.29/9.84 (upairinpowunion) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem1) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem2) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem3) => 72.29/9.84 (( 72.29/9.84 (cartprodpairin) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair1) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair) => 72.29/9.84 (( 72.29/9.84 (setunionE2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton1) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton) => 72.29/9.84 (( 72.29/9.84 (singletonprop) => 72.29/9.84 (( 72.29/9.84 (ex1E1) => 72.29/9.84 (( 72.29/9.84 (ex1I) => 72.29/9.84 (( 72.29/9.84 (ex1I2) => 72.29/9.84 (( 72.29/9.84 (singletonsuniq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL1) => 72.29/9.84 (( 72.29/9.84 (kfstsingleton) => 72.29/9.84 (( 72.29/9.84 (theprop) => 72.29/9.84 (( 72.29/9.84 (kfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstin) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR11) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR12) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR1) => 72.29/9.84 (( 72.29/9.84 (upairequniteq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR) => 72.29/9.84 (( 72.29/9.84 (ksndsingleton) => 72.29/9.84 (( 72.29/9.84 (ksndpairEq) => 72.29/9.84 (( 72.29/9.84 (kpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndin) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemEL) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemER) => 72.29/9.84 (( 72.29/9.84 (cartprodmempaircEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrI) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrSub) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrERa) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL1) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL2) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrER) => 72.29/9.84 (( 72.29/9.84 (funcImageSingleton) => 72.29/9.84 (( 72.29/9.84 (apProp) => 72.29/9.84 (( 72.29/9.84 (app) => 72.29/9.84 (( 72.29/9.84 (infuncsetfunc) => 72.29/9.84 (( 72.29/9.84 (ap2p) => 72.29/9.84 (( 72.29/9.84 (funcinfuncset) => 72.29/9.84 (( 72.29/9.84 (lamProp) => 72.29/9.84 (( 72.29/9.84 (lamp) => 72.29/9.84 (( 72.29/9.84 (lam2p) => 72.29/9.84 (( 72.29/9.84 (brelnall1) => 72.29/9.84 (( 72.29/9.84 (brelnall2) => 72.29/9.84 (( 72.29/9.84 (ex1E2) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp1) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp3) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp2) => 72.29/9.84 (( 72.29/9.84 (funcextLem) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp4) => 72.29/9.84 (( 72.29/9.84 (subbreln) => 72.29/9.84 (( 72.29/9.84 (eqbreln) => 72.29/9.84 (( 72.29/9.84 (funcext) => 72.29/9.84 (( 72.29/9.84 (funcext2) => 72.29/9.84 (( 72.29/9.84 (ap2apEq1) => 72.29/9.84 (( 72.29/9.84 (ap2apEq2) => 72.29/9.84 (( 72.29/9.84 (beta1) => 72.29/9.84 (( 72.29/9.84 (eta1) => 72.29/9.84 (( 72.29/9.84 (lam2lamEq) => 72.29/9.84 (( 72.29/9.84 (beta2) => 72.29/9.84 (( 72.29/9.84 (eta2) => 72.29/9.84 (( 72.29/9.84 (iffalseProp1) => 72.29/9.84 (( 72.29/9.84 (iffalseProp2) => 72.29/9.84 (( 72.29/9.84 (iftrueProp1) => 72.29/9.84 (( 72.29/9.84 (iftrueProp2) => 72.29/9.84 (( 72.29/9.84 (ifSingleton) => 72.29/9.84 (( 72.29/9.84 (ifp) => 72.29/9.84 (( 72.29/9.84 (theeq) => 72.29/9.84 (( 72.29/9.84 (iftrue) => 72.29/9.84 (( 72.29/9.84 (iffalse) => 72.29/9.84 (( 72.29/9.84 (iftrueorfalse) => 72.29/9.84 (( 72.29/9.84 (binintersectT_lem) => 72.29/9.84 (( 72.29/9.84 (binunionT_lem) => 72.29/9.84 (( 72.29/9.84 (powersetT_lem) => 72.29/9.84 (( 72.29/9.84 (setminusT_lem) => 72.29/9.84 (( 72.29/9.84 (complementT_lem) => 72.29/9.84 (( 72.29/9.84 (setextT) => 72.29/9.84 (( 72.29/9.84 (subsetTI) => 72.29/9.84 (( 72.29/9.84 (powersetTI1) => 72.29/9.84 (( 72.29/9.84 (powersetTE1) => 72.29/9.84 (( 72.29/9.84 (complementTI1) => 72.29/9.84 (( 72.29/9.84 (complementTE1) => 72.29/9.84 (( 72.29/9.84 (binintersectTELcontra) => 72.29/9.84 (( 72.29/9.84 (binintersectTERcontra) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT1) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT2) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT3) => 72.29/9.84 (( 72.29/9.84 (doubleComplementI1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementE1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub2) => 72.29/9.84 (( 72.29/9.84 (doubleComplementEq) => 72.29/9.84 (( 72.29/9.84 (complementTnotintersectT) => 72.29/9.84 (( 72.29/9.84 (complementImpComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementSubsetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementInPowersetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (contraSubsetComplement) => 72.29/9.84 (( 72.29/9.84 (complementTcontraSubset) => 72.29/9.84 (( 72.29/9.84 (binunionTILcontra) => 72.29/9.84 (( 72.29/9.84 (binunionTIRcontra) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion2) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (intersectInPowersetIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpNotIn1) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpInComplement1) => 72.29/9.84 (( 72.29/9.84 (binunionTE) => 72.29/9.84 (( 72.29/9.84 (binunionTEcontra) => 72.29/9.84 (( 72.29/9.84 (demorgan2a1) => 72.29/9.84 (( 72.29/9.84 (complementUnionInPowersetComplement) => 72.29/9.84 (( 72.29/9.84 (demorgan2a2) => 72.29/9.84 (( 72.29/9.84 (demorgan1a) => 72.29/9.84 (( 72.29/9.84 (demorgan1b) => 72.29/9.84 (( 72.29/9.84 (demorgan1) => 72.29/9.84 (( 72.29/9.84 (demorgan2a) => 72.29/9.84 (( 72.29/9.84 (demorgan2b2) => 72.29/9.84 (( 72.29/9.84 (demorgan2b) => 72.29/9.84 (( 72.29/9.84 (demorgan2) => 72.29/9.84 (( 72.29/9.84 (woz13rule0) => 72.29/9.84 (( 72.29/9.84 (woz13rule1) => 72.29/9.84 (( 72.29/9.84 (woz13rule2) => 72.29/9.84 (( 72.29/9.84 (woz13rule3) => 72.29/9.84 (( 72.29/9.84 (woz13rule4) => 72.29/9.84 (( 72.29/9.84 (woz1_1) => 72.29/9.84 (( 72.29/9.84 (woz1_2) => 72.29/9.84 (( 72.29/9.84 (woz1_3) => 72.29/9.84 (( 72.29/9.84 (woz1_4) => 72.29/9.84 (( 72.29/9.84 (woz1_5) => 72.29/9.84 (( 72.29/9.84 (breln1all2) => 72.29/9.84 (( 72.29/9.84 (breln1SetBreln1) => 72.29/9.84 (( 72.29/9.84 (choice2fnsingleton) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln1) => 72.29/9.84 (( 72.29/9.84 (breln1all1) => 72.29/9.84 (( 72.29/9.84 (subbreln1) => 72.29/9.84 (( 72.29/9.84 (eqbreln1) => 72.29/9.84 (( 72.29/9.84 (breln1invprop) => 72.29/9.84 (( 72.29/9.84 (breln1invI) => 72.29/9.84 (( 72.29/9.84 (breln1invE) => 72.29/9.84 (( 72.29/9.84 (breln1compprop) => 72.29/9.84 (( 72.29/9.84 (breln1compI) => 72.29/9.84 (( 72.29/9.84 (breln1compE) => 72.29/9.84 (( 72.29/9.84 (breln1compEex) => 72.29/9.84 (( 72.29/9.84 (!!) @ ( 72.29/9.84 (('#B') @ ( 72.29/9.84 !!) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 !!))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#S') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#S') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 =>))) @ 72.29/9.84 breln1)))))) @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#C') @ ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 ( 72.29/9.84 ( 72.29/9.84 ('#B') @ ( 72.29/9.84 '#B') @ 72.29/9.84 breln1)))) @ 72.29/9.84 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1166])). 72.29/9.84 thf(zip_derived_cl1183, plain, 72.29/9.84 (~ (((binintersectSubset3) => 72.29/9.84 (((binintersectER) => 72.29/9.84 (((disjointsetsI1) => 72.29/9.84 (((binintersectRsub) => 72.29/9.84 (((binintersectSubset4) => 72.29/9.84 (((binintersectSubset1) => 72.29/9.84 (((bs114d) => 72.29/9.84 (((setminusI) => 72.29/9.84 (((setminusEL) => 72.29/9.84 (((setminusER) => 72.29/9.84 (((setminusSubset2) => 72.29/9.84 (((setminusERneg) => 72.29/9.84 (((setminusELneg) => 72.29/9.84 (((setminusILneg) => 72.29/9.84 (((setminusIRneg) => 72.29/9.84 (((setminusLsub) => 72.29/9.84 (((setminusSubset1) => 72.29/9.84 (((symdiffE) => 72.29/9.84 (((symdiffI1) => 72.29/9.84 (((symdiffI2) => 72.29/9.84 (((symdiffIneg1) => 72.29/9.84 (((symdiffIneg2) => 72.29/9.84 (((secondinupair) => 72.29/9.84 (((setukpairIL) => 72.29/9.84 (((setukpairIR) => 72.29/9.84 (((kpairiskpair) => 72.29/9.84 (((kpairp) => 72.29/9.84 (((singletonsubset) => 72.29/9.84 (((singletoninpowerset) => 72.29/9.84 (((singletoninpowunion) => 72.29/9.84 (( 72.29/9.84 (upairset2E) => 72.29/9.84 (( 72.29/9.84 (upairsubunion) => 72.29/9.84 (( 72.29/9.84 (upairinpowunion) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem1) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem2) => 72.29/9.84 (( 72.29/9.84 (ubforcartprodlem3) => 72.29/9.84 (( 72.29/9.84 (cartprodpairin) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair1) => 72.29/9.84 (( 72.29/9.84 (cartprodmempair) => 72.29/9.84 (( 72.29/9.84 (setunionE2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton1) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton2) => 72.29/9.84 (( 72.29/9.84 (setunionsingleton) => 72.29/9.84 (( 72.29/9.84 (singletonprop) => 72.29/9.84 (( 72.29/9.84 (ex1E1) => 72.29/9.84 (( 72.29/9.84 (ex1I) => 72.29/9.84 (( 72.29/9.84 (ex1I2) => 72.29/9.84 (( 72.29/9.84 (singletonsuniq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL1) => 72.29/9.84 (( 72.29/9.84 (kfstsingleton) => 72.29/9.84 (( 72.29/9.84 (theprop) => 72.29/9.84 (( 72.29/9.84 (kfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstin) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjL) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR11) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR12) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR1) => 72.29/9.84 (( 72.29/9.84 (upairequniteq) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR2) => 72.29/9.84 (( 72.29/9.84 (setukpairinjR) => 72.29/9.84 (( 72.29/9.84 (ksndsingleton) => 72.29/9.84 (( 72.29/9.84 (ksndpairEq) => 72.29/9.84 (( 72.29/9.84 (kpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndin) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemEL) => 72.29/9.84 (( 72.29/9.84 (cartprodpairmemER) => 72.29/9.84 (( 72.29/9.84 (cartprodmempaircEq) => 72.29/9.84 (( 72.29/9.84 (cartprodfstpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodsndpairEq) => 72.29/9.84 (( 72.29/9.84 (cartprodpairsurjEq) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrI) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrSub) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrERa) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL1) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrEL2) => 72.29/9.84 (( 72.29/9.84 (dpsetconstrER) => 72.29/9.84 (( 72.29/9.84 (funcImageSingleton) => 72.29/9.84 (( 72.29/9.84 (apProp) => 72.29/9.84 (( 72.29/9.84 (app) => 72.29/9.84 (( 72.29/9.84 (infuncsetfunc) => 72.29/9.84 (( 72.29/9.84 (ap2p) => 72.29/9.84 (( 72.29/9.84 (funcinfuncset) => 72.29/9.84 (( 72.29/9.84 (lamProp) => 72.29/9.84 (( 72.29/9.84 (lamp) => 72.29/9.84 (( 72.29/9.84 (lam2p) => 72.29/9.84 (( 72.29/9.84 (brelnall1) => 72.29/9.84 (( 72.29/9.84 (brelnall2) => 72.29/9.84 (( 72.29/9.84 (ex1E2) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp1) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp3) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp2) => 72.29/9.84 (( 72.29/9.84 (funcextLem) => 72.29/9.84 (( 72.29/9.84 (funcGraphProp4) => 72.29/9.84 (( 72.29/9.84 (subbreln) => 72.29/9.84 (( 72.29/9.84 (eqbreln) => 72.29/9.84 (( 72.29/9.84 (funcext) => 72.29/9.84 (( 72.29/9.84 (funcext2) => 72.29/9.84 (( 72.29/9.84 (ap2apEq1) => 72.29/9.84 (( 72.29/9.84 (ap2apEq2) => 72.29/9.84 (( 72.29/9.84 (beta1) => 72.29/9.84 (( 72.29/9.84 (eta1) => 72.29/9.84 (( 72.29/9.84 (lam2lamEq) => 72.29/9.84 (( 72.29/9.84 (beta2) => 72.29/9.84 (( 72.29/9.84 (eta2) => 72.29/9.84 (( 72.29/9.84 (iffalseProp1) => 72.29/9.84 (( 72.29/9.84 (iffalseProp2) => 72.29/9.84 (( 72.29/9.84 (iftrueProp1) => 72.29/9.84 (( 72.29/9.84 (iftrueProp2) => 72.29/9.84 (( 72.29/9.84 (ifSingleton) => 72.29/9.84 (( 72.29/9.84 (ifp) => 72.29/9.84 (( 72.29/9.84 (theeq) => 72.29/9.84 (( 72.29/9.84 (iftrue) => 72.29/9.84 (( 72.29/9.84 (iffalse) => 72.29/9.84 (( 72.29/9.84 (iftrueorfalse) => 72.29/9.84 (( 72.29/9.84 (binintersectT_lem) => 72.29/9.84 (( 72.29/9.84 (binunionT_lem) => 72.29/9.84 (( 72.29/9.84 (powersetT_lem) => 72.29/9.84 (( 72.29/9.84 (setminusT_lem) => 72.29/9.84 (( 72.29/9.84 (complementT_lem) => 72.29/9.84 (( 72.29/9.84 (setextT) => 72.29/9.84 (( 72.29/9.84 (subsetTI) => 72.29/9.84 (( 72.29/9.84 (powersetTI1) => 72.29/9.84 (( 72.29/9.84 (powersetTE1) => 72.29/9.84 (( 72.29/9.84 (complementTI1) => 72.29/9.84 (( 72.29/9.84 (complementTE1) => 72.29/9.84 (( 72.29/9.84 (binintersectTELcontra) => 72.29/9.84 (( 72.29/9.84 (binintersectTERcontra) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT1) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT2) => 72.29/9.84 (( 72.29/9.84 (contrasubsetT3) => 72.29/9.84 (( 72.29/9.84 (doubleComplementI1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementE1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub1) => 72.29/9.84 (( 72.29/9.84 (doubleComplementSub2) => 72.29/9.84 (( 72.29/9.84 (doubleComplementEq) => 72.29/9.84 (( 72.29/9.84 (complementTnotintersectT) => 72.29/9.84 (( 72.29/9.84 (complementImpComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementSubsetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (complementInPowersetComplementIntersect) => 72.29/9.84 (( 72.29/9.84 (contraSubsetComplement) => 72.29/9.84 (( 72.29/9.84 (complementTcontraSubset) => 72.29/9.84 (( 72.29/9.84 (binunionTILcontra) => 72.29/9.84 (( 72.29/9.84 (binunionTIRcontra) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInUnion2) => 72.29/9.84 (( 72.29/9.84 (inIntersectImpInIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (intersectInPowersetIntersectUnions) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpNotIn1) => 72.29/9.84 (( 72.29/9.84 (inComplementUnionImpInComplement1) => 72.29/9.84 (( 72.29/9.84 (binunionTE) => 72.29/9.84 (( 72.29/9.84 (binunionTEcontra) => 72.29/9.84 (( 72.29/9.84 (demorgan2a1) => 72.29/9.84 (( 72.29/9.84 (complementUnionInPowersetComplement) => 72.29/9.84 (( 72.29/9.84 (demorgan2a2) => 72.29/9.84 (( 72.29/9.84 (demorgan1a) => 72.29/9.84 (( 72.29/9.84 (demorgan1b) => 72.29/9.84 (( 72.29/9.84 (demorgan1) => 72.29/9.84 (( 72.29/9.84 (demorgan2a) => 72.29/9.84 (( 72.29/9.84 (demorgan2b2) => 72.29/9.84 (( 72.29/9.84 (demorgan2b) => 72.29/9.84 (( 72.29/9.84 (demorgan2) => 72.29/9.84 (( 72.29/9.84 (woz13rule0) => 72.29/9.84 (( 72.29/9.84 (woz13rule1) => 72.29/9.84 (( 72.29/9.84 (woz13rule2) => 72.29/9.84 (( 72.29/9.84 (woz13rule3) => 72.29/9.84 (( 72.29/9.84 (woz13rule4) => 72.29/9.84 (( 72.29/9.84 (woz1_1) => 72.29/9.84 (( 72.29/9.84 (woz1_2) => 72.29/9.84 (( 72.29/9.84 (woz1_3) => 72.29/9.84 (( 72.29/9.84 (woz1_4) => 72.29/9.84 (( 72.29/9.84 (woz1_5) => 72.29/9.84 (( 72.29/9.84 (breln1all2) => 72.29/9.84 (( 72.29/9.84 (breln1SetBreln1) => 72.29/9.84 (( 72.29/9.84 (choice2fnsingleton) => 72.29/9.84 (( 72.29/9.84 (setOfPairsIsBReln1) => 72.29/9.84 (( 72.29/9.84 (breln1all1) => 72.29/9.84 (( 72.29/9.84 (subbreln1) => 72.29/9.84 (( 72.29/9.84 (eqbreln1) => 72.29/9.84 (( 72.29/9.84 (breln1invprop) => 72.29/9.84 (( 72.29/9.84 (breln1invI) => 72.29/9.84 (( 72.29/9.84 (breln1invE) => 72.29/9.84 (( 72.29/9.84 (breln1compprop) => 72.29/9.84 (( 72.29/9.84 (breln1compI) => 72.29/9.84 (( 72.29/9.84 (breln1compE) => 72.29/9.84 (( 72.29/9.84 (breln1compEex) => 72.29/9.84 (( 72.29/9.84 (!!) @ ( 72.29/9.84 (('#B') @ ( 72.29/9.84 !!) @ 72.29/9.84 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 !!))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#C') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 breln1)))) @ 72.29/9.85 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])). 72.29/9.85 thf(zip_derived_cl1193, plain, 72.29/9.85 (~ (((binintersectER) => 72.29/9.85 (((disjointsetsI1) => 72.29/9.85 (((binintersectRsub) => 72.29/9.85 (((binintersectSubset4) => 72.29/9.85 (((binintersectSubset1) => 72.29/9.85 (((bs114d) => 72.29/9.85 (((setminusI) => 72.29/9.85 (((setminusEL) => 72.29/9.85 (((setminusER) => 72.29/9.85 (((setminusSubset2) => 72.29/9.85 (((setminusERneg) => 72.29/9.85 (((setminusELneg) => 72.29/9.85 (((setminusILneg) => 72.29/9.85 (((setminusIRneg) => 72.29/9.85 (((setminusLsub) => 72.29/9.85 (((setminusSubset1) => 72.29/9.85 (((symdiffE) => 72.29/9.85 (((symdiffI1) => 72.29/9.85 (((symdiffI2) => 72.29/9.85 (((symdiffIneg1) => 72.29/9.85 (((symdiffIneg2) => 72.29/9.85 (((secondinupair) => 72.29/9.85 (((setukpairIL) => 72.29/9.85 (((setukpairIR) => 72.29/9.85 (((kpairiskpair) => 72.29/9.85 (((kpairp) => 72.29/9.85 (((singletonsubset) => 72.29/9.85 (((singletoninpowerset) => 72.29/9.85 (((singletoninpowunion) => 72.29/9.85 (((upairset2E) => 72.29/9.85 (( 72.29/9.85 (upairsubunion) => 72.29/9.85 (( 72.29/9.85 (upairinpowunion) => 72.29/9.85 (( 72.29/9.85 (ubforcartprodlem1) => 72.29/9.85 (( 72.29/9.85 (ubforcartprodlem2) => 72.29/9.85 (( 72.29/9.85 (ubforcartprodlem3) => 72.29/9.85 (( 72.29/9.85 (cartprodpairin) => 72.29/9.85 (( 72.29/9.85 (cartprodmempair1) => 72.29/9.85 (( 72.29/9.85 (cartprodmempair) => 72.29/9.85 (( 72.29/9.85 (setunionE2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton1) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton) => 72.29/9.85 (( 72.29/9.85 (singletonprop) => 72.29/9.85 (( 72.29/9.85 (ex1E1) => 72.29/9.85 (( 72.29/9.85 (ex1I) => 72.29/9.85 (( 72.29/9.85 (ex1I2) => 72.29/9.85 (( 72.29/9.85 (singletonsuniq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL1) => 72.29/9.85 (( 72.29/9.85 (kfstsingleton) => 72.29/9.85 (( 72.29/9.85 (theprop) => 72.29/9.85 (( 72.29/9.85 (kfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstin) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR11) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR12) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR1) => 72.29/9.85 (( 72.29/9.85 (upairequniteq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR) => 72.29/9.85 (( 72.29/9.85 (ksndsingleton) => 72.29/9.85 (( 72.29/9.85 (ksndpairEq) => 72.29/9.85 (( 72.29/9.85 (kpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndin) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemEL) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemER) => 72.29/9.85 (( 72.29/9.85 (cartprodmempaircEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrI) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrSub) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrERa) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL1) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL2) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrER) => 72.29/9.85 (( 72.29/9.85 (funcImageSingleton) => 72.29/9.85 (( 72.29/9.85 (apProp) => 72.29/9.85 (( 72.29/9.85 (app) => 72.29/9.85 (( 72.29/9.85 (infuncsetfunc) => 72.29/9.85 (( 72.29/9.85 (ap2p) => 72.29/9.85 (( 72.29/9.85 (funcinfuncset) => 72.29/9.85 (( 72.29/9.85 (lamProp) => 72.29/9.85 (( 72.29/9.85 (lamp) => 72.29/9.85 (( 72.29/9.85 (lam2p) => 72.29/9.85 (( 72.29/9.85 (brelnall1) => 72.29/9.85 (( 72.29/9.85 (brelnall2) => 72.29/9.85 (( 72.29/9.85 (ex1E2) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp1) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp3) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp2) => 72.29/9.85 (( 72.29/9.85 (funcextLem) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp4) => 72.29/9.85 (( 72.29/9.85 (subbreln) => 72.29/9.85 (( 72.29/9.85 (eqbreln) => 72.29/9.85 (( 72.29/9.85 (funcext) => 72.29/9.85 (( 72.29/9.85 (funcext2) => 72.29/9.85 (( 72.29/9.85 (ap2apEq1) => 72.29/9.85 (( 72.29/9.85 (ap2apEq2) => 72.29/9.85 (( 72.29/9.85 (beta1) => 72.29/9.85 (( 72.29/9.85 (eta1) => 72.29/9.85 (( 72.29/9.85 (lam2lamEq) => 72.29/9.85 (( 72.29/9.85 (beta2) => 72.29/9.85 (( 72.29/9.85 (eta2) => 72.29/9.85 (( 72.29/9.85 (iffalseProp1) => 72.29/9.85 (( 72.29/9.85 (iffalseProp2) => 72.29/9.85 (( 72.29/9.85 (iftrueProp1) => 72.29/9.85 (( 72.29/9.85 (iftrueProp2) => 72.29/9.85 (( 72.29/9.85 (ifSingleton) => 72.29/9.85 (( 72.29/9.85 (ifp) => 72.29/9.85 (( 72.29/9.85 (theeq) => 72.29/9.85 (( 72.29/9.85 (iftrue) => 72.29/9.85 (( 72.29/9.85 (iffalse) => 72.29/9.85 (( 72.29/9.85 (iftrueorfalse) => 72.29/9.85 (( 72.29/9.85 (binintersectT_lem) => 72.29/9.85 (( 72.29/9.85 (binunionT_lem) => 72.29/9.85 (( 72.29/9.85 (powersetT_lem) => 72.29/9.85 (( 72.29/9.85 (setminusT_lem) => 72.29/9.85 (( 72.29/9.85 (complementT_lem) => 72.29/9.85 (( 72.29/9.85 (setextT) => 72.29/9.85 (( 72.29/9.85 (subsetTI) => 72.29/9.85 (( 72.29/9.85 (powersetTI1) => 72.29/9.85 (( 72.29/9.85 (powersetTE1) => 72.29/9.85 (( 72.29/9.85 (complementTI1) => 72.29/9.85 (( 72.29/9.85 (complementTE1) => 72.29/9.85 (( 72.29/9.85 (binintersectTELcontra) => 72.29/9.85 (( 72.29/9.85 (binintersectTERcontra) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT1) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT2) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT3) => 72.29/9.85 (( 72.29/9.85 (doubleComplementI1) => 72.29/9.85 (( 72.29/9.85 (doubleComplementE1) => 72.29/9.85 (( 72.29/9.85 (doubleComplementSub1) => 72.29/9.85 (( 72.29/9.85 (doubleComplementSub2) => 72.29/9.85 (( 72.29/9.85 (doubleComplementEq) => 72.29/9.85 (( 72.29/9.85 (complementTnotintersectT) => 72.29/9.85 (( 72.29/9.85 (complementImpComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (complementSubsetComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (complementInPowersetComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (contraSubsetComplement) => 72.29/9.85 (( 72.29/9.85 (complementTcontraSubset) => 72.29/9.85 (( 72.29/9.85 (binunionTILcontra) => 72.29/9.85 (( 72.29/9.85 (binunionTIRcontra) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInUnion) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInUnion2) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInIntersectUnions) => 72.29/9.85 (( 72.29/9.85 (intersectInPowersetIntersectUnions) => 72.29/9.85 (( 72.29/9.85 (inComplementUnionImpNotIn1) => 72.29/9.85 (( 72.29/9.85 (inComplementUnionImpInComplement1) => 72.29/9.85 (( 72.29/9.85 (binunionTE) => 72.29/9.85 (( 72.29/9.85 (binunionTEcontra) => 72.29/9.85 (( 72.29/9.85 (demorgan2a1) => 72.29/9.85 (( 72.29/9.85 (complementUnionInPowersetComplement) => 72.29/9.85 (( 72.29/9.85 (demorgan2a2) => 72.29/9.85 (( 72.29/9.85 (demorgan1a) => 72.29/9.85 (( 72.29/9.85 (demorgan1b) => 72.29/9.85 (( 72.29/9.85 (demorgan1) => 72.29/9.85 (( 72.29/9.85 (demorgan2a) => 72.29/9.85 (( 72.29/9.85 (demorgan2b2) => 72.29/9.85 (( 72.29/9.85 (demorgan2b) => 72.29/9.85 (( 72.29/9.85 (demorgan2) => 72.29/9.85 (( 72.29/9.85 (woz13rule0) => 72.29/9.85 (( 72.29/9.85 (woz13rule1) => 72.29/9.85 (( 72.29/9.85 (woz13rule2) => 72.29/9.85 (( 72.29/9.85 (woz13rule3) => 72.29/9.85 (( 72.29/9.85 (woz13rule4) => 72.29/9.85 (( 72.29/9.85 (woz1_1) => 72.29/9.85 (( 72.29/9.85 (woz1_2) => 72.29/9.85 (( 72.29/9.85 (woz1_3) => 72.29/9.85 (( 72.29/9.85 (woz1_4) => 72.29/9.85 (( 72.29/9.85 (woz1_5) => 72.29/9.85 (( 72.29/9.85 (breln1all2) => 72.29/9.85 (( 72.29/9.85 (breln1SetBreln1) => 72.29/9.85 (( 72.29/9.85 (choice2fnsingleton) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln1) => 72.29/9.85 (( 72.29/9.85 (breln1all1) => 72.29/9.85 (( 72.29/9.85 (subbreln1) => 72.29/9.85 (( 72.29/9.85 (eqbreln1) => 72.29/9.85 (( 72.29/9.85 (breln1invprop) => 72.29/9.85 (( 72.29/9.85 (breln1invI) => 72.29/9.85 (( 72.29/9.85 (breln1invE) => 72.29/9.85 (( 72.29/9.85 (breln1compprop) => 72.29/9.85 (( 72.29/9.85 (breln1compI) => 72.29/9.85 (( 72.29/9.85 (breln1compE) => 72.29/9.85 (( 72.29/9.85 (breln1compEex) => 72.29/9.85 (( 72.29/9.85 (!!) @ ( 72.29/9.85 (('#B') @ ( 72.29/9.85 !!) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 !!))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#C') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 breln1)))) @ 72.29/9.85 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1183])). 72.29/9.85 thf(zip_derived_cl1206, plain, 72.29/9.85 (~ (((disjointsetsI1) => 72.29/9.85 (((binintersectRsub) => 72.29/9.85 (((binintersectSubset4) => 72.29/9.85 (((binintersectSubset1) => 72.29/9.85 (((bs114d) => 72.29/9.85 (((setminusI) => 72.29/9.85 (((setminusEL) => 72.29/9.85 (((setminusER) => 72.29/9.85 (((setminusSubset2) => 72.29/9.85 (((setminusERneg) => 72.29/9.85 (((setminusELneg) => 72.29/9.85 (((setminusILneg) => 72.29/9.85 (((setminusIRneg) => 72.29/9.85 (((setminusLsub) => 72.29/9.85 (((setminusSubset1) => 72.29/9.85 (((symdiffE) => 72.29/9.85 (((symdiffI1) => 72.29/9.85 (((symdiffI2) => 72.29/9.85 (((symdiffIneg1) => 72.29/9.85 (((symdiffIneg2) => 72.29/9.85 (((secondinupair) => 72.29/9.85 (((setukpairIL) => 72.29/9.85 (((setukpairIR) => 72.29/9.85 (((kpairiskpair) => 72.29/9.85 (((kpairp) => 72.29/9.85 (((singletonsubset) => 72.29/9.85 (((singletoninpowerset) => 72.29/9.85 (((singletoninpowunion) => 72.29/9.85 (((upairset2E) => 72.29/9.85 (((upairsubunion) => 72.29/9.85 (( 72.29/9.85 (upairinpowunion) => 72.29/9.85 (( 72.29/9.85 (ubforcartprodlem1) => 72.29/9.85 (( 72.29/9.85 (ubforcartprodlem2) => 72.29/9.85 (( 72.29/9.85 (ubforcartprodlem3) => 72.29/9.85 (( 72.29/9.85 (cartprodpairin) => 72.29/9.85 (( 72.29/9.85 (cartprodmempair1) => 72.29/9.85 (( 72.29/9.85 (cartprodmempair) => 72.29/9.85 (( 72.29/9.85 (setunionE2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton1) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton) => 72.29/9.85 (( 72.29/9.85 (singletonprop) => 72.29/9.85 (( 72.29/9.85 (ex1E1) => 72.29/9.85 (( 72.29/9.85 (ex1I) => 72.29/9.85 (( 72.29/9.85 (ex1I2) => 72.29/9.85 (( 72.29/9.85 (singletonsuniq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL1) => 72.29/9.85 (( 72.29/9.85 (kfstsingleton) => 72.29/9.85 (( 72.29/9.85 (theprop) => 72.29/9.85 (( 72.29/9.85 (kfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstin) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR11) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR12) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR1) => 72.29/9.85 (( 72.29/9.85 (upairequniteq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR) => 72.29/9.85 (( 72.29/9.85 (ksndsingleton) => 72.29/9.85 (( 72.29/9.85 (ksndpairEq) => 72.29/9.85 (( 72.29/9.85 (kpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndin) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemEL) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemER) => 72.29/9.85 (( 72.29/9.85 (cartprodmempaircEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrI) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrSub) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrERa) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL1) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL2) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrER) => 72.29/9.85 (( 72.29/9.85 (funcImageSingleton) => 72.29/9.85 (( 72.29/9.85 (apProp) => 72.29/9.85 (( 72.29/9.85 (app) => 72.29/9.85 (( 72.29/9.85 (infuncsetfunc) => 72.29/9.85 (( 72.29/9.85 (ap2p) => 72.29/9.85 (( 72.29/9.85 (funcinfuncset) => 72.29/9.85 (( 72.29/9.85 (lamProp) => 72.29/9.85 (( 72.29/9.85 (lamp) => 72.29/9.85 (( 72.29/9.85 (lam2p) => 72.29/9.85 (( 72.29/9.85 (brelnall1) => 72.29/9.85 (( 72.29/9.85 (brelnall2) => 72.29/9.85 (( 72.29/9.85 (ex1E2) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp1) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp3) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp2) => 72.29/9.85 (( 72.29/9.85 (funcextLem) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp4) => 72.29/9.85 (( 72.29/9.85 (subbreln) => 72.29/9.85 (( 72.29/9.85 (eqbreln) => 72.29/9.85 (( 72.29/9.85 (funcext) => 72.29/9.85 (( 72.29/9.85 (funcext2) => 72.29/9.85 (( 72.29/9.85 (ap2apEq1) => 72.29/9.85 (( 72.29/9.85 (ap2apEq2) => 72.29/9.85 (( 72.29/9.85 (beta1) => 72.29/9.85 (( 72.29/9.85 (eta1) => 72.29/9.85 (( 72.29/9.85 (lam2lamEq) => 72.29/9.85 (( 72.29/9.85 (beta2) => 72.29/9.85 (( 72.29/9.85 (eta2) => 72.29/9.85 (( 72.29/9.85 (iffalseProp1) => 72.29/9.85 (( 72.29/9.85 (iffalseProp2) => 72.29/9.85 (( 72.29/9.85 (iftrueProp1) => 72.29/9.85 (( 72.29/9.85 (iftrueProp2) => 72.29/9.85 (( 72.29/9.85 (ifSingleton) => 72.29/9.85 (( 72.29/9.85 (ifp) => 72.29/9.85 (( 72.29/9.85 (theeq) => 72.29/9.85 (( 72.29/9.85 (iftrue) => 72.29/9.85 (( 72.29/9.85 (iffalse) => 72.29/9.85 (( 72.29/9.85 (iftrueorfalse) => 72.29/9.85 (( 72.29/9.85 (binintersectT_lem) => 72.29/9.85 (( 72.29/9.85 (binunionT_lem) => 72.29/9.85 (( 72.29/9.85 (powersetT_lem) => 72.29/9.85 (( 72.29/9.85 (setminusT_lem) => 72.29/9.85 (( 72.29/9.85 (complementT_lem) => 72.29/9.85 (( 72.29/9.85 (setextT) => 72.29/9.85 (( 72.29/9.85 (subsetTI) => 72.29/9.85 (( 72.29/9.85 (powersetTI1) => 72.29/9.85 (( 72.29/9.85 (powersetTE1) => 72.29/9.85 (( 72.29/9.85 (complementTI1) => 72.29/9.85 (( 72.29/9.85 (complementTE1) => 72.29/9.85 (( 72.29/9.85 (binintersectTELcontra) => 72.29/9.85 (( 72.29/9.85 (binintersectTERcontra) => 72.29/9.85 (( 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(inIntersectImpInIntersectUnions) => 72.29/9.85 (( 72.29/9.85 (intersectInPowersetIntersectUnions) => 72.29/9.85 (( 72.29/9.85 (inComplementUnionImpNotIn1) => 72.29/9.85 (( 72.29/9.85 (inComplementUnionImpInComplement1) => 72.29/9.85 (( 72.29/9.85 (binunionTE) => 72.29/9.85 (( 72.29/9.85 (binunionTEcontra) => 72.29/9.85 (( 72.29/9.85 (demorgan2a1) => 72.29/9.85 (( 72.29/9.85 (complementUnionInPowersetComplement) => 72.29/9.85 (( 72.29/9.85 (demorgan2a2) => 72.29/9.85 (( 72.29/9.85 (demorgan1a) => 72.29/9.85 (( 72.29/9.85 (demorgan1b) => 72.29/9.85 (( 72.29/9.85 (demorgan1) => 72.29/9.85 (( 72.29/9.85 (demorgan2a) => 72.29/9.85 (( 72.29/9.85 (demorgan2b2) => 72.29/9.85 (( 72.29/9.85 (demorgan2b) => 72.29/9.85 (( 72.29/9.85 (demorgan2) => 72.29/9.85 (( 72.29/9.85 (woz13rule0) => 72.29/9.85 (( 72.29/9.85 (woz13rule1) => 72.29/9.85 (( 72.29/9.85 (woz13rule2) => 72.29/9.85 (( 72.29/9.85 (woz13rule3) => 72.29/9.85 (( 72.29/9.85 (woz13rule4) => 72.29/9.85 (( 72.29/9.85 (woz1_1) => 72.29/9.85 (( 72.29/9.85 (woz1_2) => 72.29/9.85 (( 72.29/9.85 (woz1_3) => 72.29/9.85 (( 72.29/9.85 (woz1_4) => 72.29/9.85 (( 72.29/9.85 (woz1_5) => 72.29/9.85 (( 72.29/9.85 (breln1all2) => 72.29/9.85 (( 72.29/9.85 (breln1SetBreln1) => 72.29/9.85 (( 72.29/9.85 (choice2fnsingleton) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln1) => 72.29/9.85 (( 72.29/9.85 (breln1all1) => 72.29/9.85 (( 72.29/9.85 (subbreln1) => 72.29/9.85 (( 72.29/9.85 (eqbreln1) => 72.29/9.85 (( 72.29/9.85 (breln1invprop) => 72.29/9.85 (( 72.29/9.85 (breln1invI) => 72.29/9.85 (( 72.29/9.85 (breln1invE) => 72.29/9.85 (( 72.29/9.85 (breln1compprop) => 72.29/9.85 (( 72.29/9.85 (breln1compI) => 72.29/9.85 (( 72.29/9.85 (breln1compE) => 72.29/9.85 (( 72.29/9.85 (breln1compEex) => 72.29/9.85 (( 72.29/9.85 (!!) @ ( 72.29/9.85 (('#B') @ ( 72.29/9.85 !!) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 !!))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#C') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 breln1)))) @ 72.29/9.85 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1193])). 72.29/9.85 thf(zip_derived_cl1216, plain, 72.29/9.85 (~ (((binintersectRsub) => 72.29/9.85 (((binintersectSubset4) => 72.29/9.85 (((binintersectSubset1) => 72.29/9.85 (((bs114d) => 72.29/9.85 (((setminusI) => 72.29/9.85 (((setminusEL) => 72.29/9.85 (((setminusER) => 72.29/9.85 (((setminusSubset2) => 72.29/9.85 (((setminusERneg) => 72.29/9.85 (((setminusELneg) => 72.29/9.85 (((setminusILneg) => 72.29/9.85 (((setminusIRneg) => 72.29/9.85 (((setminusLsub) => 72.29/9.85 (((setminusSubset1) => 72.29/9.85 (((symdiffE) => 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72.29/9.85 (ex1E1) => 72.29/9.85 (( 72.29/9.85 (ex1I) => 72.29/9.85 (( 72.29/9.85 (ex1I2) => 72.29/9.85 (( 72.29/9.85 (singletonsuniq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL1) => 72.29/9.85 (( 72.29/9.85 (kfstsingleton) => 72.29/9.85 (( 72.29/9.85 (theprop) => 72.29/9.85 (( 72.29/9.85 (kfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstin) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR11) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR12) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR1) => 72.29/9.85 (( 72.29/9.85 (upairequniteq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR) => 72.29/9.85 (( 72.29/9.85 (ksndsingleton) => 72.29/9.85 (( 72.29/9.85 (ksndpairEq) => 72.29/9.85 (( 72.29/9.85 (kpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndin) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemEL) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemER) => 72.29/9.85 (( 72.29/9.85 (cartprodmempaircEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrI) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrSub) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrERa) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL1) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL2) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrER) => 72.29/9.85 (( 72.29/9.85 (funcImageSingleton) => 72.29/9.85 (( 72.29/9.85 (apProp) => 72.29/9.85 (( 72.29/9.85 (app) => 72.29/9.85 (( 72.29/9.85 (infuncsetfunc) => 72.29/9.85 (( 72.29/9.85 (ap2p) => 72.29/9.85 (( 72.29/9.85 (funcinfuncset) => 72.29/9.85 (( 72.29/9.85 (lamProp) => 72.29/9.85 (( 72.29/9.85 (lamp) => 72.29/9.85 (( 72.29/9.85 (lam2p) => 72.29/9.85 (( 72.29/9.85 (brelnall1) => 72.29/9.85 (( 72.29/9.85 (brelnall2) => 72.29/9.85 (( 72.29/9.85 (ex1E2) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp1) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp3) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp2) => 72.29/9.85 (( 72.29/9.85 (funcextLem) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp4) => 72.29/9.85 (( 72.29/9.85 (subbreln) => 72.29/9.85 (( 72.29/9.85 (eqbreln) => 72.29/9.85 (( 72.29/9.85 (funcext) => 72.29/9.85 (( 72.29/9.85 (funcext2) => 72.29/9.85 (( 72.29/9.85 (ap2apEq1) => 72.29/9.85 (( 72.29/9.85 (ap2apEq2) => 72.29/9.85 (( 72.29/9.85 (beta1) => 72.29/9.85 (( 72.29/9.85 (eta1) => 72.29/9.85 (( 72.29/9.85 (lam2lamEq) => 72.29/9.85 (( 72.29/9.85 (beta2) => 72.29/9.85 (( 72.29/9.85 (eta2) => 72.29/9.85 (( 72.29/9.85 (iffalseProp1) => 72.29/9.85 (( 72.29/9.85 (iffalseProp2) => 72.29/9.85 (( 72.29/9.85 (iftrueProp1) => 72.29/9.85 (( 72.29/9.85 (iftrueProp2) => 72.29/9.85 (( 72.29/9.85 (ifSingleton) => 72.29/9.85 (( 72.29/9.85 (ifp) => 72.29/9.85 (( 72.29/9.85 (theeq) => 72.29/9.85 (( 72.29/9.85 (iftrue) => 72.29/9.85 (( 72.29/9.85 (iffalse) => 72.29/9.85 (( 72.29/9.85 (iftrueorfalse) => 72.29/9.85 (( 72.29/9.85 (binintersectT_lem) => 72.29/9.85 (( 72.29/9.85 (binunionT_lem) => 72.29/9.85 (( 72.29/9.85 (powersetT_lem) => 72.29/9.85 (( 72.29/9.85 (setminusT_lem) => 72.29/9.85 (( 72.29/9.85 (complementT_lem) => 72.29/9.85 (( 72.29/9.85 (setextT) => 72.29/9.85 (( 72.29/9.85 (subsetTI) => 72.29/9.85 (( 72.29/9.85 (powersetTI1) => 72.29/9.85 (( 72.29/9.85 (powersetTE1) => 72.29/9.85 (( 72.29/9.85 (complementTI1) => 72.29/9.85 (( 72.29/9.85 (complementTE1) => 72.29/9.85 (( 72.29/9.85 (binintersectTELcontra) => 72.29/9.85 (( 72.29/9.85 (binintersectTERcontra) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT1) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT2) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT3) => 72.29/9.85 (( 72.29/9.85 (doubleComplementI1) => 72.29/9.85 (( 72.29/9.85 (doubleComplementE1) => 72.29/9.85 (( 72.29/9.85 (doubleComplementSub1) => 72.29/9.85 (( 72.29/9.85 (doubleComplementSub2) => 72.29/9.85 (( 72.29/9.85 (doubleComplementEq) => 72.29/9.85 (( 72.29/9.85 (complementTnotintersectT) => 72.29/9.85 (( 72.29/9.85 (complementImpComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (complementSubsetComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (complementInPowersetComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (contraSubsetComplement) => 72.29/9.85 (( 72.29/9.85 (complementTcontraSubset) => 72.29/9.85 (( 72.29/9.85 (binunionTILcontra) => 72.29/9.85 (( 72.29/9.85 (binunionTIRcontra) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInUnion) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInUnion2) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInIntersectUnions) => 72.29/9.85 (( 72.29/9.85 (intersectInPowersetIntersectUnions) => 72.29/9.85 (( 72.29/9.85 (inComplementUnionImpNotIn1) => 72.29/9.85 (( 72.29/9.85 (inComplementUnionImpInComplement1) => 72.29/9.85 (( 72.29/9.85 (binunionTE) => 72.29/9.85 (( 72.29/9.85 (binunionTEcontra) => 72.29/9.85 (( 72.29/9.85 (demorgan2a1) => 72.29/9.85 (( 72.29/9.85 (complementUnionInPowersetComplement) => 72.29/9.85 (( 72.29/9.85 (demorgan2a2) => 72.29/9.85 (( 72.29/9.85 (demorgan1a) => 72.29/9.85 (( 72.29/9.85 (demorgan1b) => 72.29/9.85 (( 72.29/9.85 (demorgan1) => 72.29/9.85 (( 72.29/9.85 (demorgan2a) => 72.29/9.85 (( 72.29/9.85 (demorgan2b2) => 72.29/9.85 (( 72.29/9.85 (demorgan2b) => 72.29/9.85 (( 72.29/9.85 (demorgan2) => 72.29/9.85 (( 72.29/9.85 (woz13rule0) => 72.29/9.85 (( 72.29/9.85 (woz13rule1) => 72.29/9.85 (( 72.29/9.85 (woz13rule2) => 72.29/9.85 (( 72.29/9.85 (woz13rule3) => 72.29/9.85 (( 72.29/9.85 (woz13rule4) => 72.29/9.85 (( 72.29/9.85 (woz1_1) => 72.29/9.85 (( 72.29/9.85 (woz1_2) => 72.29/9.85 (( 72.29/9.85 (woz1_3) => 72.29/9.85 (( 72.29/9.85 (woz1_4) => 72.29/9.85 (( 72.29/9.85 (woz1_5) => 72.29/9.85 (( 72.29/9.85 (breln1all2) => 72.29/9.85 (( 72.29/9.85 (breln1SetBreln1) => 72.29/9.85 (( 72.29/9.85 (choice2fnsingleton) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln1) => 72.29/9.85 (( 72.29/9.85 (breln1all1) => 72.29/9.85 (( 72.29/9.85 (subbreln1) => 72.29/9.85 (( 72.29/9.85 (eqbreln1) => 72.29/9.85 (( 72.29/9.85 (breln1invprop) => 72.29/9.85 (( 72.29/9.85 (breln1invI) => 72.29/9.85 (( 72.29/9.85 (breln1invE) => 72.29/9.85 (( 72.29/9.85 (breln1compprop) => 72.29/9.85 (( 72.29/9.85 (breln1compI) => 72.29/9.85 (( 72.29/9.85 (breln1compE) => 72.29/9.85 (( 72.29/9.85 (breln1compEex) => 72.29/9.85 (( 72.29/9.85 (!!) @ ( 72.29/9.85 (('#B') @ ( 72.29/9.85 !!) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 !!))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#C') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 breln1)))) @ 72.29/9.85 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1206])). 72.29/9.85 thf(zip_derived_cl1223, plain, 72.29/9.85 (~ (((binintersectSubset4) => 72.29/9.85 (((binintersectSubset1) => 72.29/9.85 (((bs114d) => 72.29/9.85 (((setminusI) => 72.29/9.85 (((setminusEL) => 72.29/9.85 (((setminusER) => 72.29/9.85 (((setminusSubset2) => 72.29/9.85 (((setminusERneg) => 72.29/9.85 (((setminusELneg) => 72.29/9.85 (((setminusILneg) => 72.29/9.85 (((setminusIRneg) => 72.29/9.85 (((setminusLsub) => 72.29/9.85 (((setminusSubset1) => 72.29/9.85 (((symdiffE) => 72.29/9.85 (((symdiffI1) => 72.29/9.85 (((symdiffI2) => 72.29/9.85 (((symdiffIneg1) => 72.29/9.85 (((symdiffIneg2) => 72.29/9.85 (((secondinupair) => 72.29/9.85 (((setukpairIL) => 72.29/9.85 (((setukpairIR) => 72.29/9.85 (((kpairiskpair) => 72.29/9.85 (((kpairp) => 72.29/9.85 (((singletonsubset) => 72.29/9.85 (((singletoninpowerset) => 72.29/9.85 (((singletoninpowunion) => 72.29/9.85 (((upairset2E) => 72.29/9.85 (((upairsubunion) => 72.29/9.85 (((upairinpowunion) => 72.29/9.85 (((ubforcartprodlem1) => 72.29/9.85 (( 72.29/9.85 (ubforcartprodlem2) => 72.29/9.85 (( 72.29/9.85 (ubforcartprodlem3) => 72.29/9.85 (( 72.29/9.85 (cartprodpairin) => 72.29/9.85 (( 72.29/9.85 (cartprodmempair1) => 72.29/9.85 (( 72.29/9.85 (cartprodmempair) => 72.29/9.85 (( 72.29/9.85 (setunionE2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton1) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton) => 72.29/9.85 (( 72.29/9.85 (singletonprop) => 72.29/9.85 (( 72.29/9.85 (ex1E1) => 72.29/9.85 (( 72.29/9.85 (ex1I) => 72.29/9.85 (( 72.29/9.85 (ex1I2) => 72.29/9.85 (( 72.29/9.85 (singletonsuniq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL1) => 72.29/9.85 (( 72.29/9.85 (kfstsingleton) => 72.29/9.85 (( 72.29/9.85 (theprop) => 72.29/9.85 (( 72.29/9.85 (kfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstin) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR11) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR12) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR1) => 72.29/9.85 (( 72.29/9.85 (upairequniteq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR) => 72.29/9.85 (( 72.29/9.85 (ksndsingleton) => 72.29/9.85 (( 72.29/9.85 (ksndpairEq) => 72.29/9.85 (( 72.29/9.85 (kpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndin) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemEL) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemER) => 72.29/9.85 (( 72.29/9.85 (cartprodmempaircEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrI) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrSub) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrERa) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL1) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL2) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrER) => 72.29/9.85 (( 72.29/9.85 (funcImageSingleton) => 72.29/9.85 (( 72.29/9.85 (apProp) => 72.29/9.85 (( 72.29/9.85 (app) => 72.29/9.85 (( 72.29/9.85 (infuncsetfunc) => 72.29/9.85 (( 72.29/9.85 (ap2p) => 72.29/9.85 (( 72.29/9.85 (funcinfuncset) => 72.29/9.85 (( 72.29/9.85 (lamProp) => 72.29/9.85 (( 72.29/9.85 (lamp) => 72.29/9.85 (( 72.29/9.85 (lam2p) => 72.29/9.85 (( 72.29/9.85 (brelnall1) => 72.29/9.85 (( 72.29/9.85 (brelnall2) => 72.29/9.85 (( 72.29/9.85 (ex1E2) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp1) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp3) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp2) => 72.29/9.85 (( 72.29/9.85 (funcextLem) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp4) => 72.29/9.85 (( 72.29/9.85 (subbreln) => 72.29/9.85 (( 72.29/9.85 (eqbreln) => 72.29/9.85 (( 72.29/9.85 (funcext) => 72.29/9.85 (( 72.29/9.85 (funcext2) => 72.29/9.85 (( 72.29/9.85 (ap2apEq1) => 72.29/9.85 (( 72.29/9.85 (ap2apEq2) => 72.29/9.85 (( 72.29/9.85 (beta1) => 72.29/9.85 (( 72.29/9.85 (eta1) => 72.29/9.85 (( 72.29/9.85 (lam2lamEq) => 72.29/9.85 (( 72.29/9.85 (beta2) => 72.29/9.85 (( 72.29/9.85 (eta2) => 72.29/9.85 (( 72.29/9.85 (iffalseProp1) => 72.29/9.85 (( 72.29/9.85 (iffalseProp2) => 72.29/9.85 (( 72.29/9.85 (iftrueProp1) => 72.29/9.85 (( 72.29/9.85 (iftrueProp2) => 72.29/9.85 (( 72.29/9.85 (ifSingleton) => 72.29/9.85 (( 72.29/9.85 (ifp) => 72.29/9.85 (( 72.29/9.85 (theeq) => 72.29/9.85 (( 72.29/9.85 (iftrue) => 72.29/9.85 (( 72.29/9.85 (iffalse) => 72.29/9.85 (( 72.29/9.85 (iftrueorfalse) => 72.29/9.85 (( 72.29/9.85 (binintersectT_lem) => 72.29/9.85 (( 72.29/9.85 (binunionT_lem) => 72.29/9.85 (( 72.29/9.85 (powersetT_lem) => 72.29/9.85 (( 72.29/9.85 (setminusT_lem) => 72.29/9.85 (( 72.29/9.85 (complementT_lem) => 72.29/9.85 (( 72.29/9.85 (setextT) => 72.29/9.85 (( 72.29/9.85 (subsetTI) => 72.29/9.85 (( 72.29/9.85 (powersetTI1) => 72.29/9.85 (( 72.29/9.85 (powersetTE1) => 72.29/9.85 (( 72.29/9.85 (complementTI1) => 72.29/9.85 (( 72.29/9.85 (complementTE1) => 72.29/9.85 (( 72.29/9.85 (binintersectTELcontra) => 72.29/9.85 (( 72.29/9.85 (binintersectTERcontra) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT1) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT2) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT3) => 72.29/9.85 (( 72.29/9.85 (doubleComplementI1) => 72.29/9.85 (( 72.29/9.85 (doubleComplementE1) => 72.29/9.85 (( 72.29/9.85 (doubleComplementSub1) => 72.29/9.85 (( 72.29/9.85 (doubleComplementSub2) => 72.29/9.85 (( 72.29/9.85 (doubleComplementEq) => 72.29/9.85 (( 72.29/9.85 (complementTnotintersectT) => 72.29/9.85 (( 72.29/9.85 (complementImpComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (complementSubsetComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (complementInPowersetComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (contraSubsetComplement) => 72.29/9.85 (( 72.29/9.85 (complementTcontraSubset) => 72.29/9.85 (( 72.29/9.85 (binunionTILcontra) => 72.29/9.85 (( 72.29/9.85 (binunionTIRcontra) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInUnion) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInUnion2) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInIntersectUnions) => 72.29/9.85 (( 72.29/9.85 (intersectInPowersetIntersectUnions) => 72.29/9.85 (( 72.29/9.85 (inComplementUnionImpNotIn1) => 72.29/9.85 (( 72.29/9.85 (inComplementUnionImpInComplement1) => 72.29/9.85 (( 72.29/9.85 (binunionTE) => 72.29/9.85 (( 72.29/9.85 (binunionTEcontra) => 72.29/9.85 (( 72.29/9.85 (demorgan2a1) => 72.29/9.85 (( 72.29/9.85 (complementUnionInPowersetComplement) => 72.29/9.85 (( 72.29/9.85 (demorgan2a2) => 72.29/9.85 (( 72.29/9.85 (demorgan1a) => 72.29/9.85 (( 72.29/9.85 (demorgan1b) => 72.29/9.85 (( 72.29/9.85 (demorgan1) => 72.29/9.85 (( 72.29/9.85 (demorgan2a) => 72.29/9.85 (( 72.29/9.85 (demorgan2b2) => 72.29/9.85 (( 72.29/9.85 (demorgan2b) => 72.29/9.85 (( 72.29/9.85 (demorgan2) => 72.29/9.85 (( 72.29/9.85 (woz13rule0) => 72.29/9.85 (( 72.29/9.85 (woz13rule1) => 72.29/9.85 (( 72.29/9.85 (woz13rule2) => 72.29/9.85 (( 72.29/9.85 (woz13rule3) => 72.29/9.85 (( 72.29/9.85 (woz13rule4) => 72.29/9.85 (( 72.29/9.85 (woz1_1) => 72.29/9.85 (( 72.29/9.85 (woz1_2) => 72.29/9.85 (( 72.29/9.85 (woz1_3) => 72.29/9.85 (( 72.29/9.85 (woz1_4) => 72.29/9.85 (( 72.29/9.85 (woz1_5) => 72.29/9.85 (( 72.29/9.85 (breln1all2) => 72.29/9.85 (( 72.29/9.85 (breln1SetBreln1) => 72.29/9.85 (( 72.29/9.85 (choice2fnsingleton) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln1) => 72.29/9.85 (( 72.29/9.85 (breln1all1) => 72.29/9.85 (( 72.29/9.85 (subbreln1) => 72.29/9.85 (( 72.29/9.85 (eqbreln1) => 72.29/9.85 (( 72.29/9.85 (breln1invprop) => 72.29/9.85 (( 72.29/9.85 (breln1invI) => 72.29/9.85 (( 72.29/9.85 (breln1invE) => 72.29/9.85 (( 72.29/9.85 (breln1compprop) => 72.29/9.85 (( 72.29/9.85 (breln1compI) => 72.29/9.85 (( 72.29/9.85 (breln1compE) => 72.29/9.85 (( 72.29/9.85 (breln1compEex) => 72.29/9.85 (( 72.29/9.85 (!!) @ ( 72.29/9.85 (('#B') @ ( 72.29/9.85 !!) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 !!))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#C') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 breln1)))) @ 72.29/9.85 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])). 72.29/9.85 thf(zip_derived_cl1231, plain, 72.29/9.85 (~ (((binintersectSubset1) => 72.29/9.85 (((bs114d) => 72.29/9.85 (((setminusI) => 72.29/9.85 (((setminusEL) => 72.29/9.85 (((setminusER) => 72.29/9.85 (((setminusSubset2) => 72.29/9.85 (((setminusERneg) => 72.29/9.85 (((setminusELneg) => 72.29/9.85 (((setminusILneg) => 72.29/9.85 (((setminusIRneg) => 72.29/9.85 (((setminusLsub) => 72.29/9.85 (((setminusSubset1) => 72.29/9.85 (((symdiffE) => 72.29/9.85 (((symdiffI1) => 72.29/9.85 (((symdiffI2) => 72.29/9.85 (((symdiffIneg1) => 72.29/9.85 (((symdiffIneg2) => 72.29/9.85 (((secondinupair) => 72.29/9.85 (((setukpairIL) => 72.29/9.85 (((setukpairIR) => 72.29/9.85 (((kpairiskpair) => 72.29/9.85 (((kpairp) => 72.29/9.85 (((singletonsubset) => 72.29/9.85 (((singletoninpowerset) => 72.29/9.85 (((singletoninpowunion) => 72.29/9.85 (((upairset2E) => 72.29/9.85 (((upairsubunion) => 72.29/9.85 (((upairinpowunion) => 72.29/9.85 (((ubforcartprodlem1) => 72.29/9.85 (((ubforcartprodlem2) => 72.29/9.85 (( 72.29/9.85 (ubforcartprodlem3) => 72.29/9.85 (( 72.29/9.85 (cartprodpairin) => 72.29/9.85 (( 72.29/9.85 (cartprodmempair1) => 72.29/9.85 (( 72.29/9.85 (cartprodmempair) => 72.29/9.85 (( 72.29/9.85 (setunionE2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton1) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton) => 72.29/9.85 (( 72.29/9.85 (singletonprop) => 72.29/9.85 (( 72.29/9.85 (ex1E1) => 72.29/9.85 (( 72.29/9.85 (ex1I) => 72.29/9.85 (( 72.29/9.85 (ex1I2) => 72.29/9.85 (( 72.29/9.85 (singletonsuniq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL1) => 72.29/9.85 (( 72.29/9.85 (kfstsingleton) => 72.29/9.85 (( 72.29/9.85 (theprop) => 72.29/9.85 (( 72.29/9.85 (kfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstin) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR11) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR12) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR1) => 72.29/9.85 (( 72.29/9.85 (upairequniteq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR) => 72.29/9.85 (( 72.29/9.85 (ksndsingleton) => 72.29/9.85 (( 72.29/9.85 (ksndpairEq) => 72.29/9.85 (( 72.29/9.85 (kpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndin) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemEL) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemER) => 72.29/9.85 (( 72.29/9.85 (cartprodmempaircEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrI) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrSub) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrERa) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL1) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL2) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrER) => 72.29/9.85 (( 72.29/9.85 (funcImageSingleton) => 72.29/9.85 (( 72.29/9.85 (apProp) => 72.29/9.85 (( 72.29/9.85 (app) => 72.29/9.85 (( 72.29/9.85 (infuncsetfunc) => 72.29/9.85 (( 72.29/9.85 (ap2p) => 72.29/9.85 (( 72.29/9.85 (funcinfuncset) => 72.29/9.85 (( 72.29/9.85 (lamProp) => 72.29/9.85 (( 72.29/9.85 (lamp) => 72.29/9.85 (( 72.29/9.85 (lam2p) => 72.29/9.85 (( 72.29/9.85 (brelnall1) => 72.29/9.85 (( 72.29/9.85 (brelnall2) => 72.29/9.85 (( 72.29/9.85 (ex1E2) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp1) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp3) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp2) => 72.29/9.85 (( 72.29/9.85 (funcextLem) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp4) => 72.29/9.85 (( 72.29/9.85 (subbreln) => 72.29/9.85 (( 72.29/9.85 (eqbreln) => 72.29/9.85 (( 72.29/9.85 (funcext) => 72.29/9.85 (( 72.29/9.85 (funcext2) => 72.29/9.85 (( 72.29/9.85 (ap2apEq1) => 72.29/9.85 (( 72.29/9.85 (ap2apEq2) => 72.29/9.85 (( 72.29/9.85 (beta1) => 72.29/9.85 (( 72.29/9.85 (eta1) => 72.29/9.85 (( 72.29/9.85 (lam2lamEq) => 72.29/9.85 (( 72.29/9.85 (beta2) => 72.29/9.85 (( 72.29/9.85 (eta2) => 72.29/9.85 (( 72.29/9.85 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binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1223])). 72.29/9.85 thf(zip_derived_cl1239, plain, 72.29/9.85 (~ (((bs114d) => 72.29/9.85 (((setminusI) => 72.29/9.85 (((setminusEL) => 72.29/9.85 (((setminusER) => 72.29/9.85 (((setminusSubset2) => 72.29/9.85 (((setminusERneg) => 72.29/9.85 (((setminusELneg) => 72.29/9.85 (((setminusILneg) => 72.29/9.85 (((setminusIRneg) => 72.29/9.85 (((setminusLsub) => 72.29/9.85 (((setminusSubset1) => 72.29/9.85 (((symdiffE) => 72.29/9.85 (((symdiffI1) => 72.29/9.85 (((symdiffI2) => 72.29/9.85 (((symdiffIneg1) => 72.29/9.85 (((symdiffIneg2) => 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(breln1invE) => 72.29/9.85 (( 72.29/9.85 (breln1compprop) => 72.29/9.85 (( 72.29/9.85 (breln1compI) => 72.29/9.85 (( 72.29/9.85 (breln1compE) => 72.29/9.85 (( 72.29/9.85 (breln1compEex) => 72.29/9.85 (( 72.29/9.85 (!!) @ ( 72.29/9.85 (('#B') @ ( 72.29/9.85 !!) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 !!))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#C') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 breln1)))) @ 72.29/9.85 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1231])). 72.29/9.85 thf(zip_derived_cl1247, plain, 72.29/9.85 (~ (((setminusI) => 72.29/9.85 (((setminusEL) => 72.29/9.85 (((setminusER) => 72.29/9.85 (((setminusSubset2) => 72.29/9.85 (((setminusERneg) => 72.29/9.85 (((setminusELneg) => 72.29/9.85 (((setminusILneg) => 72.29/9.85 (((setminusIRneg) => 72.29/9.85 (((setminusLsub) => 72.29/9.85 (((setminusSubset1) => 72.29/9.85 (((symdiffE) => 72.29/9.85 (((symdiffI1) => 72.29/9.85 (((symdiffI2) => 72.29/9.85 (((symdiffIneg1) => 72.29/9.85 (((symdiffIneg2) => 72.29/9.85 (((secondinupair) => 72.29/9.85 (((setukpairIL) => 72.29/9.85 (((setukpairIR) => 72.29/9.85 (((kpairiskpair) => 72.29/9.85 (((kpairp) => 72.29/9.85 (((singletonsubset) => 72.29/9.85 (((singletoninpowerset) => 72.29/9.85 (((singletoninpowunion) => 72.29/9.85 (((upairset2E) => 72.29/9.85 (((upairsubunion) => 72.29/9.85 (((upairinpowunion) => 72.29/9.85 (((ubforcartprodlem1) => 72.29/9.85 (((ubforcartprodlem2) => 72.29/9.85 (((ubforcartprodlem3) => 72.29/9.85 (((cartprodpairin) => 72.29/9.85 (( 72.29/9.85 (cartprodmempair1) => 72.29/9.85 (( 72.29/9.85 (cartprodmempair) => 72.29/9.85 (( 72.29/9.85 (setunionE2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton1) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton) => 72.29/9.85 (( 72.29/9.85 (singletonprop) => 72.29/9.85 (( 72.29/9.85 (ex1E1) => 72.29/9.85 (( 72.29/9.85 (ex1I) => 72.29/9.85 (( 72.29/9.85 (ex1I2) => 72.29/9.85 (( 72.29/9.85 (singletonsuniq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL1) => 72.29/9.85 (( 72.29/9.85 (kfstsingleton) => 72.29/9.85 (( 72.29/9.85 (theprop) => 72.29/9.85 (( 72.29/9.85 (kfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstin) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR11) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR12) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR1) => 72.29/9.85 (( 72.29/9.85 (upairequniteq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR) => 72.29/9.85 (( 72.29/9.85 (ksndsingleton) => 72.29/9.85 (( 72.29/9.85 (ksndpairEq) => 72.29/9.85 (( 72.29/9.85 (kpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndin) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemEL) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemER) => 72.29/9.85 (( 72.29/9.85 (cartprodmempaircEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrI) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrSub) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrERa) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL1) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL2) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrER) => 72.29/9.85 (( 72.29/9.85 (funcImageSingleton) => 72.29/9.85 (( 72.29/9.85 (apProp) => 72.29/9.85 (( 72.29/9.85 (app) => 72.29/9.85 (( 72.29/9.85 (infuncsetfunc) => 72.29/9.85 (( 72.29/9.85 (ap2p) => 72.29/9.85 (( 72.29/9.85 (funcinfuncset) => 72.29/9.85 (( 72.29/9.85 (lamProp) => 72.29/9.85 (( 72.29/9.85 (lamp) => 72.29/9.85 (( 72.29/9.85 (lam2p) => 72.29/9.85 (( 72.29/9.85 (brelnall1) => 72.29/9.85 (( 72.29/9.85 (brelnall2) => 72.29/9.85 (( 72.29/9.85 (ex1E2) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp1) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp3) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp2) => 72.29/9.85 (( 72.29/9.85 (funcextLem) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp4) => 72.29/9.85 (( 72.29/9.85 (subbreln) => 72.29/9.85 (( 72.29/9.85 (eqbreln) => 72.29/9.85 (( 72.29/9.85 (funcext) => 72.29/9.85 (( 72.29/9.85 (funcext2) => 72.29/9.85 (( 72.29/9.85 (ap2apEq1) => 72.29/9.85 (( 72.29/9.85 (ap2apEq2) => 72.29/9.85 (( 72.29/9.85 (beta1) => 72.29/9.85 (( 72.29/9.85 (eta1) => 72.29/9.85 (( 72.29/9.85 (lam2lamEq) => 72.29/9.85 (( 72.29/9.85 (beta2) => 72.29/9.85 (( 72.29/9.85 (eta2) => 72.29/9.85 (( 72.29/9.85 (iffalseProp1) => 72.29/9.85 (( 72.29/9.85 (iffalseProp2) => 72.29/9.85 (( 72.29/9.85 (iftrueProp1) => 72.29/9.85 (( 72.29/9.85 (iftrueProp2) => 72.29/9.85 (( 72.29/9.85 (ifSingleton) => 72.29/9.85 (( 72.29/9.85 (ifp) => 72.29/9.85 (( 72.29/9.85 (theeq) => 72.29/9.85 (( 72.29/9.85 (iftrue) => 72.29/9.85 (( 72.29/9.85 (iffalse) => 72.29/9.85 (( 72.29/9.85 (iftrueorfalse) => 72.29/9.85 (( 72.29/9.85 (binintersectT_lem) => 72.29/9.85 (( 72.29/9.85 (binunionT_lem) => 72.29/9.85 (( 72.29/9.85 (powersetT_lem) => 72.29/9.85 (( 72.29/9.85 (setminusT_lem) => 72.29/9.85 (( 72.29/9.85 (complementT_lem) => 72.29/9.85 (( 72.29/9.85 (setextT) => 72.29/9.85 (( 72.29/9.85 (subsetTI) => 72.29/9.85 (( 72.29/9.85 (powersetTI1) => 72.29/9.85 (( 72.29/9.85 (powersetTE1) => 72.29/9.85 (( 72.29/9.85 (complementTI1) => 72.29/9.85 (( 72.29/9.85 (complementTE1) => 72.29/9.85 (( 72.29/9.85 (binintersectTELcontra) => 72.29/9.85 (( 72.29/9.85 (binintersectTERcontra) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT1) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT2) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT3) => 72.29/9.85 (( 72.29/9.85 (doubleComplementI1) => 72.29/9.85 (( 72.29/9.85 (doubleComplementE1) => 72.29/9.85 (( 72.29/9.85 (doubleComplementSub1) => 72.29/9.85 (( 72.29/9.85 (doubleComplementSub2) => 72.29/9.85 (( 72.29/9.85 (doubleComplementEq) => 72.29/9.85 (( 72.29/9.85 (complementTnotintersectT) => 72.29/9.85 (( 72.29/9.85 (complementImpComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (complementSubsetComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (complementInPowersetComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (contraSubsetComplement) => 72.29/9.85 (( 72.29/9.85 (complementTcontraSubset) => 72.29/9.85 (( 72.29/9.85 (binunionTILcontra) => 72.29/9.85 (( 72.29/9.85 (binunionTIRcontra) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInUnion) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInUnion2) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInIntersectUnions) => 72.29/9.85 (( 72.29/9.85 (intersectInPowersetIntersectUnions) => 72.29/9.85 (( 72.29/9.85 (inComplementUnionImpNotIn1) => 72.29/9.85 (( 72.29/9.85 (inComplementUnionImpInComplement1) => 72.29/9.85 (( 72.29/9.85 (binunionTE) => 72.29/9.85 (( 72.29/9.85 (binunionTEcontra) => 72.29/9.85 (( 72.29/9.85 (demorgan2a1) => 72.29/9.85 (( 72.29/9.85 (complementUnionInPowersetComplement) => 72.29/9.85 (( 72.29/9.85 (demorgan2a2) => 72.29/9.85 (( 72.29/9.85 (demorgan1a) => 72.29/9.85 (( 72.29/9.85 (demorgan1b) => 72.29/9.85 (( 72.29/9.85 (demorgan1) => 72.29/9.85 (( 72.29/9.85 (demorgan2a) => 72.29/9.85 (( 72.29/9.85 (demorgan2b2) => 72.29/9.85 (( 72.29/9.85 (demorgan2b) => 72.29/9.85 (( 72.29/9.85 (demorgan2) => 72.29/9.85 (( 72.29/9.85 (woz13rule0) => 72.29/9.85 (( 72.29/9.85 (woz13rule1) => 72.29/9.85 (( 72.29/9.85 (woz13rule2) => 72.29/9.85 (( 72.29/9.85 (woz13rule3) => 72.29/9.85 (( 72.29/9.85 (woz13rule4) => 72.29/9.85 (( 72.29/9.85 (woz1_1) => 72.29/9.85 (( 72.29/9.85 (woz1_2) => 72.29/9.85 (( 72.29/9.85 (woz1_3) => 72.29/9.85 (( 72.29/9.85 (woz1_4) => 72.29/9.85 (( 72.29/9.85 (woz1_5) => 72.29/9.85 (( 72.29/9.85 (breln1all2) => 72.29/9.85 (( 72.29/9.85 (breln1SetBreln1) => 72.29/9.85 (( 72.29/9.85 (choice2fnsingleton) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln1) => 72.29/9.85 (( 72.29/9.85 (breln1all1) => 72.29/9.85 (( 72.29/9.85 (subbreln1) => 72.29/9.85 (( 72.29/9.85 (eqbreln1) => 72.29/9.85 (( 72.29/9.85 (breln1invprop) => 72.29/9.85 (( 72.29/9.85 (breln1invI) => 72.29/9.85 (( 72.29/9.85 (breln1invE) => 72.29/9.85 (( 72.29/9.85 (breln1compprop) => 72.29/9.85 (( 72.29/9.85 (breln1compI) => 72.29/9.85 (( 72.29/9.85 (breln1compE) => 72.29/9.85 (( 72.29/9.85 (breln1compEex) => 72.29/9.85 (( 72.29/9.85 (!!) @ ( 72.29/9.85 (('#B') @ ( 72.29/9.85 !!) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 !!))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#C') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 breln1)))) @ 72.29/9.85 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1239])). 72.29/9.85 thf(zip_derived_cl1255, plain, 72.29/9.85 (~ (((setminusEL) => 72.29/9.85 (((setminusER) => 72.29/9.85 (((setminusSubset2) => 72.29/9.85 (((setminusERneg) => 72.29/9.85 (((setminusELneg) => 72.29/9.85 (((setminusILneg) => 72.29/9.85 (((setminusIRneg) => 72.29/9.85 (((setminusLsub) => 72.29/9.85 (((setminusSubset1) => 72.29/9.85 (((symdiffE) => 72.29/9.85 (((symdiffI1) => 72.29/9.85 (((symdiffI2) => 72.29/9.85 (((symdiffIneg1) => 72.29/9.85 (((symdiffIneg2) => 72.29/9.85 (((secondinupair) => 72.29/9.85 (((setukpairIL) => 72.29/9.85 (((setukpairIR) => 72.29/9.85 (((kpairiskpair) => 72.29/9.85 (((kpairp) => 72.29/9.85 (((singletonsubset) => 72.29/9.85 (((singletoninpowerset) => 72.29/9.85 (((singletoninpowunion) => 72.29/9.85 (((upairset2E) => 72.29/9.85 (((upairsubunion) => 72.29/9.85 (((upairinpowunion) => 72.29/9.85 (((ubforcartprodlem1) => 72.29/9.85 (((ubforcartprodlem2) => 72.29/9.85 (((ubforcartprodlem3) => 72.29/9.85 (((cartprodpairin) => 72.29/9.85 (((cartprodmempair1) => 72.29/9.85 (( 72.29/9.85 (cartprodmempair) => 72.29/9.85 (( 72.29/9.85 (setunionE2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton1) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton) => 72.29/9.85 (( 72.29/9.85 (singletonprop) => 72.29/9.85 (( 72.29/9.85 (ex1E1) => 72.29/9.85 (( 72.29/9.85 (ex1I) => 72.29/9.85 (( 72.29/9.85 (ex1I2) => 72.29/9.85 (( 72.29/9.85 (singletonsuniq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL1) => 72.29/9.85 (( 72.29/9.85 (kfstsingleton) => 72.29/9.85 (( 72.29/9.85 (theprop) => 72.29/9.85 (( 72.29/9.85 (kfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstin) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR11) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR12) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR1) => 72.29/9.85 (( 72.29/9.85 (upairequniteq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR) => 72.29/9.85 (( 72.29/9.85 (ksndsingleton) => 72.29/9.85 (( 72.29/9.85 (ksndpairEq) => 72.29/9.85 (( 72.29/9.85 (kpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndin) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemEL) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemER) => 72.29/9.85 (( 72.29/9.85 (cartprodmempaircEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrI) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrSub) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrERa) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL1) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL2) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrER) => 72.29/9.85 (( 72.29/9.85 (funcImageSingleton) => 72.29/9.85 (( 72.29/9.85 (apProp) => 72.29/9.85 (( 72.29/9.85 (app) => 72.29/9.85 (( 72.29/9.85 (infuncsetfunc) => 72.29/9.85 (( 72.29/9.85 (ap2p) => 72.29/9.85 (( 72.29/9.85 (funcinfuncset) => 72.29/9.85 (( 72.29/9.85 (lamProp) => 72.29/9.85 (( 72.29/9.85 (lamp) => 72.29/9.85 (( 72.29/9.85 (lam2p) => 72.29/9.85 (( 72.29/9.85 (brelnall1) => 72.29/9.85 (( 72.29/9.85 (brelnall2) => 72.29/9.85 (( 72.29/9.85 (ex1E2) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp1) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp3) => 72.29/9.85 (( 72.29/9.85 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72.29/9.85 (demorgan1a) => 72.29/9.85 (( 72.29/9.85 (demorgan1b) => 72.29/9.85 (( 72.29/9.85 (demorgan1) => 72.29/9.85 (( 72.29/9.85 (demorgan2a) => 72.29/9.85 (( 72.29/9.85 (demorgan2b2) => 72.29/9.85 (( 72.29/9.85 (demorgan2b) => 72.29/9.85 (( 72.29/9.85 (demorgan2) => 72.29/9.85 (( 72.29/9.85 (woz13rule0) => 72.29/9.85 (( 72.29/9.85 (woz13rule1) => 72.29/9.85 (( 72.29/9.85 (woz13rule2) => 72.29/9.85 (( 72.29/9.85 (woz13rule3) => 72.29/9.85 (( 72.29/9.85 (woz13rule4) => 72.29/9.85 (( 72.29/9.85 (woz1_1) => 72.29/9.85 (( 72.29/9.85 (woz1_2) => 72.29/9.85 (( 72.29/9.85 (woz1_3) => 72.29/9.85 (( 72.29/9.85 (woz1_4) => 72.29/9.85 (( 72.29/9.85 (woz1_5) => 72.29/9.85 (( 72.29/9.85 (breln1all2) => 72.29/9.85 (( 72.29/9.85 (breln1SetBreln1) => 72.29/9.85 (( 72.29/9.85 (choice2fnsingleton) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln1) => 72.29/9.85 (( 72.29/9.85 (breln1all1) => 72.29/9.85 (( 72.29/9.85 (subbreln1) => 72.29/9.85 (( 72.29/9.85 (eqbreln1) => 72.29/9.85 (( 72.29/9.85 (breln1invprop) => 72.29/9.85 (( 72.29/9.85 (breln1invI) => 72.29/9.85 (( 72.29/9.85 (breln1invE) => 72.29/9.85 (( 72.29/9.85 (breln1compprop) => 72.29/9.85 (( 72.29/9.85 (breln1compI) => 72.29/9.85 (( 72.29/9.85 (breln1compE) => 72.29/9.85 (( 72.29/9.85 (breln1compEex) => 72.29/9.85 (( 72.29/9.85 (!!) @ ( 72.29/9.85 (('#B') @ ( 72.29/9.85 !!) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 !!))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#C') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 breln1)))) @ 72.29/9.85 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1247])). 72.29/9.85 thf(zip_derived_cl1264, plain, 72.29/9.85 (~ (((setminusER) => 72.29/9.85 (((setminusSubset2) => 72.29/9.85 (((setminusERneg) => 72.29/9.85 (((setminusELneg) => 72.29/9.85 (((setminusILneg) => 72.29/9.85 (((setminusIRneg) => 72.29/9.85 (((setminusLsub) => 72.29/9.85 (((setminusSubset1) => 72.29/9.85 (((symdiffE) => 72.29/9.85 (((symdiffI1) => 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(complementImpComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (complementSubsetComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (complementInPowersetComplementIntersect) => 72.29/9.85 (( 72.29/9.85 (contraSubsetComplement) => 72.29/9.85 (( 72.29/9.85 (complementTcontraSubset) => 72.29/9.85 (( 72.29/9.85 (binunionTILcontra) => 72.29/9.85 (( 72.29/9.85 (binunionTIRcontra) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInUnion) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInUnion2) => 72.29/9.85 (( 72.29/9.85 (inIntersectImpInIntersectUnions) => 72.29/9.85 (( 72.29/9.85 (intersectInPowersetIntersectUnions) => 72.29/9.85 (( 72.29/9.85 (inComplementUnionImpNotIn1) => 72.29/9.85 (( 72.29/9.85 (inComplementUnionImpInComplement1) => 72.29/9.85 (( 72.29/9.85 (binunionTE) => 72.29/9.85 (( 72.29/9.85 (binunionTEcontra) => 72.29/9.85 (( 72.29/9.85 (demorgan2a1) => 72.29/9.85 (( 72.29/9.85 (complementUnionInPowersetComplement) => 72.29/9.85 (( 72.29/9.85 (demorgan2a2) => 72.29/9.85 (( 72.29/9.85 (demorgan1a) => 72.29/9.85 (( 72.29/9.85 (demorgan1b) => 72.29/9.85 (( 72.29/9.85 (demorgan1) => 72.29/9.85 (( 72.29/9.85 (demorgan2a) => 72.29/9.85 (( 72.29/9.85 (demorgan2b2) => 72.29/9.85 (( 72.29/9.85 (demorgan2b) => 72.29/9.85 (( 72.29/9.85 (demorgan2) => 72.29/9.85 (( 72.29/9.85 (woz13rule0) => 72.29/9.85 (( 72.29/9.85 (woz13rule1) => 72.29/9.85 (( 72.29/9.85 (woz13rule2) => 72.29/9.85 (( 72.29/9.85 (woz13rule3) => 72.29/9.85 (( 72.29/9.85 (woz13rule4) => 72.29/9.85 (( 72.29/9.85 (woz1_1) => 72.29/9.85 (( 72.29/9.85 (woz1_2) => 72.29/9.85 (( 72.29/9.85 (woz1_3) => 72.29/9.85 (( 72.29/9.85 (woz1_4) => 72.29/9.85 (( 72.29/9.85 (woz1_5) => 72.29/9.85 (( 72.29/9.85 (breln1all2) => 72.29/9.85 (( 72.29/9.85 (breln1SetBreln1) => 72.29/9.85 (( 72.29/9.85 (choice2fnsingleton) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln1) => 72.29/9.85 (( 72.29/9.85 (breln1all1) => 72.29/9.85 (( 72.29/9.85 (subbreln1) => 72.29/9.85 (( 72.29/9.85 (eqbreln1) => 72.29/9.85 (( 72.29/9.85 (breln1invprop) => 72.29/9.85 (( 72.29/9.85 (breln1invI) => 72.29/9.85 (( 72.29/9.85 (breln1invE) => 72.29/9.85 (( 72.29/9.85 (breln1compprop) => 72.29/9.85 (( 72.29/9.85 (breln1compI) => 72.29/9.85 (( 72.29/9.85 (breln1compE) => 72.29/9.85 (( 72.29/9.85 (breln1compEex) => 72.29/9.85 (( 72.29/9.85 (!!) @ ( 72.29/9.85 (('#B') @ ( 72.29/9.85 !!) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 !!))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#S') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#S') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 =>))) @ 72.29/9.85 breln1)))))) @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#C') @ ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 ( 72.29/9.85 ( 72.29/9.85 ('#B') @ ( 72.29/9.85 '#B') @ 72.29/9.85 breln1)))) @ 72.29/9.85 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1255])). 72.29/9.85 thf(zip_derived_cl1272, plain, 72.29/9.85 (~ (((setminusSubset2) => 72.29/9.85 (((setminusERneg) => 72.29/9.85 (((setminusELneg) => 72.29/9.85 (((setminusILneg) => 72.29/9.85 (((setminusIRneg) => 72.29/9.85 (((setminusLsub) => 72.29/9.85 (((setminusSubset1) => 72.29/9.85 (((symdiffE) => 72.29/9.85 (((symdiffI1) => 72.29/9.85 (((symdiffI2) => 72.29/9.85 (((symdiffIneg1) => 72.29/9.85 (((symdiffIneg2) => 72.29/9.85 (((secondinupair) => 72.29/9.85 (((setukpairIL) => 72.29/9.85 (((setukpairIR) => 72.29/9.85 (((kpairiskpair) => 72.29/9.85 (((kpairp) => 72.29/9.85 (((singletonsubset) => 72.29/9.85 (((singletoninpowerset) => 72.29/9.85 (((singletoninpowunion) => 72.29/9.85 (((upairset2E) => 72.29/9.85 (((upairsubunion) => 72.29/9.85 (((upairinpowunion) => 72.29/9.85 (((ubforcartprodlem1) => 72.29/9.85 (((ubforcartprodlem2) => 72.29/9.85 (((ubforcartprodlem3) => 72.29/9.85 (((cartprodpairin) => 72.29/9.85 (((cartprodmempair1) => 72.29/9.85 (((cartprodmempair) => 72.29/9.85 (((setunionE2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton1) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton2) => 72.29/9.85 (( 72.29/9.85 (setunionsingleton) => 72.29/9.85 (( 72.29/9.85 (singletonprop) => 72.29/9.85 (( 72.29/9.85 (ex1E1) => 72.29/9.85 (( 72.29/9.85 (ex1I) => 72.29/9.85 (( 72.29/9.85 (ex1I2) => 72.29/9.85 (( 72.29/9.85 (singletonsuniq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL1) => 72.29/9.85 (( 72.29/9.85 (kfstsingleton) => 72.29/9.85 (( 72.29/9.85 (theprop) => 72.29/9.85 (( 72.29/9.85 (kfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstin) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjL) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR11) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR12) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR1) => 72.29/9.85 (( 72.29/9.85 (upairequniteq) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR2) => 72.29/9.85 (( 72.29/9.85 (setukpairinjR) => 72.29/9.85 (( 72.29/9.85 (ksndsingleton) => 72.29/9.85 (( 72.29/9.85 (ksndpairEq) => 72.29/9.85 (( 72.29/9.85 (kpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndin) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemEL) => 72.29/9.85 (( 72.29/9.85 (cartprodpairmemER) => 72.29/9.85 (( 72.29/9.85 (cartprodmempaircEq) => 72.29/9.85 (( 72.29/9.85 (cartprodfstpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodsndpairEq) => 72.29/9.85 (( 72.29/9.85 (cartprodpairsurjEq) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrI) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrSub) => 72.29/9.85 (( 72.29/9.85 (setOfPairsIsBReln) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrERa) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL1) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrEL2) => 72.29/9.85 (( 72.29/9.85 (dpsetconstrER) => 72.29/9.85 (( 72.29/9.85 (funcImageSingleton) => 72.29/9.85 (( 72.29/9.85 (apProp) => 72.29/9.85 (( 72.29/9.85 (app) => 72.29/9.85 (( 72.29/9.85 (infuncsetfunc) => 72.29/9.85 (( 72.29/9.85 (ap2p) => 72.29/9.85 (( 72.29/9.85 (funcinfuncset) => 72.29/9.85 (( 72.29/9.85 (lamProp) => 72.29/9.85 (( 72.29/9.85 (lamp) => 72.29/9.85 (( 72.29/9.85 (lam2p) => 72.29/9.85 (( 72.29/9.85 (brelnall1) => 72.29/9.85 (( 72.29/9.85 (brelnall2) => 72.29/9.85 (( 72.29/9.85 (ex1E2) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp1) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp3) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp2) => 72.29/9.85 (( 72.29/9.85 (funcextLem) => 72.29/9.85 (( 72.29/9.85 (funcGraphProp4) => 72.29/9.85 (( 72.29/9.85 (subbreln) => 72.29/9.85 (( 72.29/9.85 (eqbreln) => 72.29/9.85 (( 72.29/9.85 (funcext) => 72.29/9.85 (( 72.29/9.85 (funcext2) => 72.29/9.85 (( 72.29/9.85 (ap2apEq1) => 72.29/9.85 (( 72.29/9.85 (ap2apEq2) => 72.29/9.85 (( 72.29/9.85 (beta1) => 72.29/9.85 (( 72.29/9.85 (eta1) => 72.29/9.85 (( 72.29/9.85 (lam2lamEq) => 72.29/9.85 (( 72.29/9.85 (beta2) => 72.29/9.85 (( 72.29/9.85 (eta2) => 72.29/9.85 (( 72.29/9.85 (iffalseProp1) => 72.29/9.85 (( 72.29/9.85 (iffalseProp2) => 72.29/9.85 (( 72.29/9.85 (iftrueProp1) => 72.29/9.85 (( 72.29/9.85 (iftrueProp2) => 72.29/9.85 (( 72.29/9.85 (ifSingleton) => 72.29/9.85 (( 72.29/9.85 (ifp) => 72.29/9.85 (( 72.29/9.85 (theeq) => 72.29/9.85 (( 72.29/9.85 (iftrue) => 72.29/9.85 (( 72.29/9.85 (iffalse) => 72.29/9.85 (( 72.29/9.85 (iftrueorfalse) => 72.29/9.85 (( 72.29/9.85 (binintersectT_lem) => 72.29/9.85 (( 72.29/9.85 (binunionT_lem) => 72.29/9.85 (( 72.29/9.85 (powersetT_lem) => 72.29/9.85 (( 72.29/9.85 (setminusT_lem) => 72.29/9.85 (( 72.29/9.85 (complementT_lem) => 72.29/9.85 (( 72.29/9.85 (setextT) => 72.29/9.85 (( 72.29/9.85 (subsetTI) => 72.29/9.85 (( 72.29/9.85 (powersetTI1) => 72.29/9.85 (( 72.29/9.85 (powersetTE1) => 72.29/9.85 (( 72.29/9.85 (complementTI1) => 72.29/9.85 (( 72.29/9.85 (complementTE1) => 72.29/9.85 (( 72.29/9.85 (binintersectTELcontra) => 72.29/9.85 (( 72.29/9.85 (binintersectTERcontra) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT1) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT2) => 72.29/9.85 (( 72.29/9.85 (contrasubsetT3) => 72.29/9.86 (( 72.29/9.86 (doubleComplementI1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementE1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub2) => 72.29/9.86 (( 72.29/9.86 (doubleComplementEq) => 72.29/9.86 (( 72.29/9.86 (complementTnotintersectT) => 72.29/9.86 (( 72.29/9.86 (complementImpComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementSubsetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementInPowersetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (contraSubsetComplement) => 72.29/9.86 (( 72.29/9.86 (complementTcontraSubset) => 72.29/9.86 (( 72.29/9.86 (binunionTILcontra) => 72.29/9.86 (( 72.29/9.86 (binunionTIRcontra) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion2) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (intersectInPowersetIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpNotIn1) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpInComplement1) => 72.29/9.86 (( 72.29/9.86 (binunionTE) => 72.29/9.86 (( 72.29/9.86 (binunionTEcontra) => 72.29/9.86 (( 72.29/9.86 (demorgan2a1) => 72.29/9.86 (( 72.29/9.86 (complementUnionInPowersetComplement) => 72.29/9.86 (( 72.29/9.86 (demorgan2a2) => 72.29/9.86 (( 72.29/9.86 (demorgan1a) => 72.29/9.86 (( 72.29/9.86 (demorgan1b) => 72.29/9.86 (( 72.29/9.86 (demorgan1) => 72.29/9.86 (( 72.29/9.86 (demorgan2a) => 72.29/9.86 (( 72.29/9.86 (demorgan2b2) => 72.29/9.86 (( 72.29/9.86 (demorgan2b) => 72.29/9.86 (( 72.29/9.86 (demorgan2) => 72.29/9.86 (( 72.29/9.86 (woz13rule0) => 72.29/9.86 (( 72.29/9.86 (woz13rule1) => 72.29/9.86 (( 72.29/9.86 (woz13rule2) => 72.29/9.86 (( 72.29/9.86 (woz13rule3) => 72.29/9.86 (( 72.29/9.86 (woz13rule4) => 72.29/9.86 (( 72.29/9.86 (woz1_1) => 72.29/9.86 (( 72.29/9.86 (woz1_2) => 72.29/9.86 (( 72.29/9.86 (woz1_3) => 72.29/9.86 (( 72.29/9.86 (woz1_4) => 72.29/9.86 (( 72.29/9.86 (woz1_5) => 72.29/9.86 (( 72.29/9.86 (breln1all2) => 72.29/9.86 (( 72.29/9.86 (breln1SetBreln1) => 72.29/9.86 (( 72.29/9.86 (choice2fnsingleton) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln1) => 72.29/9.86 (( 72.29/9.86 (breln1all1) => 72.29/9.86 (( 72.29/9.86 (subbreln1) => 72.29/9.86 (( 72.29/9.86 (eqbreln1) => 72.29/9.86 (( 72.29/9.86 (breln1invprop) => 72.29/9.86 (( 72.29/9.86 (breln1invI) => 72.29/9.86 (( 72.29/9.86 (breln1invE) => 72.29/9.86 (( 72.29/9.86 (breln1compprop) => 72.29/9.86 (( 72.29/9.86 (breln1compI) => 72.29/9.86 (( 72.29/9.86 (breln1compE) => 72.29/9.86 (( 72.29/9.86 (breln1compEex) => 72.29/9.86 (( 72.29/9.86 (!!) @ ( 72.29/9.86 (('#B') @ ( 72.29/9.86 !!) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 !!))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#C') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 breln1)))) @ 72.29/9.86 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1264])). 72.29/9.86 thf(zip_derived_cl1280, plain, 72.29/9.86 (~ (((setminusERneg) => 72.29/9.86 (((setminusELneg) => 72.29/9.86 (((setminusILneg) => 72.29/9.86 (((setminusIRneg) => 72.29/9.86 (((setminusLsub) => 72.29/9.86 (((setminusSubset1) => 72.29/9.86 (((symdiffE) => 72.29/9.86 (((symdiffI1) => 72.29/9.86 (((symdiffI2) => 72.29/9.86 (((symdiffIneg1) => 72.29/9.86 (((symdiffIneg2) => 72.29/9.86 (((secondinupair) => 72.29/9.86 (((setukpairIL) => 72.29/9.86 (((setukpairIR) => 72.29/9.86 (((kpairiskpair) => 72.29/9.86 (((kpairp) => 72.29/9.86 (((singletonsubset) => 72.29/9.86 (((singletoninpowerset) => 72.29/9.86 (((singletoninpowunion) => 72.29/9.86 (((upairset2E) => 72.29/9.86 (((upairsubunion) => 72.29/9.86 (((upairinpowunion) => 72.29/9.86 (((ubforcartprodlem1) => 72.29/9.86 (((ubforcartprodlem2) => 72.29/9.86 (((ubforcartprodlem3) => 72.29/9.86 (((cartprodpairin) => 72.29/9.86 (((cartprodmempair1) => 72.29/9.86 (((cartprodmempair) => 72.29/9.86 (((setunionE2) => 72.29/9.86 (((setunionsingleton1) => 72.29/9.86 (( 72.29/9.86 (setunionsingleton2) => 72.29/9.86 (( 72.29/9.86 (setunionsingleton) => 72.29/9.86 (( 72.29/9.86 (singletonprop) => 72.29/9.86 (( 72.29/9.86 (ex1E1) => 72.29/9.86 (( 72.29/9.86 (ex1I) => 72.29/9.86 (( 72.29/9.86 (ex1I2) => 72.29/9.86 (( 72.29/9.86 (singletonsuniq) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL1) => 72.29/9.86 (( 72.29/9.86 (kfstsingleton) => 72.29/9.86 (( 72.29/9.86 (theprop) => 72.29/9.86 (( 72.29/9.86 (kfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstin) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR11) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR12) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR1) => 72.29/9.86 (( 72.29/9.86 (upairequniteq) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR) => 72.29/9.86 (( 72.29/9.86 (ksndsingleton) => 72.29/9.86 (( 72.29/9.86 (ksndpairEq) => 72.29/9.86 (( 72.29/9.86 (kpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndin) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemEL) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemER) => 72.29/9.86 (( 72.29/9.86 (cartprodmempaircEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrI) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrSub) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrERa) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL1) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL2) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrER) => 72.29/9.86 (( 72.29/9.86 (funcImageSingleton) => 72.29/9.86 (( 72.29/9.86 (apProp) => 72.29/9.86 (( 72.29/9.86 (app) => 72.29/9.86 (( 72.29/9.86 (infuncsetfunc) => 72.29/9.86 (( 72.29/9.86 (ap2p) => 72.29/9.86 (( 72.29/9.86 (funcinfuncset) => 72.29/9.86 (( 72.29/9.86 (lamProp) => 72.29/9.86 (( 72.29/9.86 (lamp) => 72.29/9.86 (( 72.29/9.86 (lam2p) => 72.29/9.86 (( 72.29/9.86 (brelnall1) => 72.29/9.86 (( 72.29/9.86 (brelnall2) => 72.29/9.86 (( 72.29/9.86 (ex1E2) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp1) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp3) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp2) => 72.29/9.86 (( 72.29/9.86 (funcextLem) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp4) => 72.29/9.86 (( 72.29/9.86 (subbreln) => 72.29/9.86 (( 72.29/9.86 (eqbreln) => 72.29/9.86 (( 72.29/9.86 (funcext) => 72.29/9.86 (( 72.29/9.86 (funcext2) => 72.29/9.86 (( 72.29/9.86 (ap2apEq1) => 72.29/9.86 (( 72.29/9.86 (ap2apEq2) => 72.29/9.86 (( 72.29/9.86 (beta1) => 72.29/9.86 (( 72.29/9.86 (eta1) => 72.29/9.86 (( 72.29/9.86 (lam2lamEq) => 72.29/9.86 (( 72.29/9.86 (beta2) => 72.29/9.86 (( 72.29/9.86 (eta2) => 72.29/9.86 (( 72.29/9.86 (iffalseProp1) => 72.29/9.86 (( 72.29/9.86 (iffalseProp2) => 72.29/9.86 (( 72.29/9.86 (iftrueProp1) => 72.29/9.86 (( 72.29/9.86 (iftrueProp2) => 72.29/9.86 (( 72.29/9.86 (ifSingleton) => 72.29/9.86 (( 72.29/9.86 (ifp) => 72.29/9.86 (( 72.29/9.86 (theeq) => 72.29/9.86 (( 72.29/9.86 (iftrue) => 72.29/9.86 (( 72.29/9.86 (iffalse) => 72.29/9.86 (( 72.29/9.86 (iftrueorfalse) => 72.29/9.86 (( 72.29/9.86 (binintersectT_lem) => 72.29/9.86 (( 72.29/9.86 (binunionT_lem) => 72.29/9.86 (( 72.29/9.86 (powersetT_lem) => 72.29/9.86 (( 72.29/9.86 (setminusT_lem) => 72.29/9.86 (( 72.29/9.86 (complementT_lem) => 72.29/9.86 (( 72.29/9.86 (setextT) => 72.29/9.86 (( 72.29/9.86 (subsetTI) => 72.29/9.86 (( 72.29/9.86 (powersetTI1) => 72.29/9.86 (( 72.29/9.86 (powersetTE1) => 72.29/9.86 (( 72.29/9.86 (complementTI1) => 72.29/9.86 (( 72.29/9.86 (complementTE1) => 72.29/9.86 (( 72.29/9.86 (binintersectTELcontra) => 72.29/9.86 (( 72.29/9.86 (binintersectTERcontra) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT1) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT2) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT3) => 72.29/9.86 (( 72.29/9.86 (doubleComplementI1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementE1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub2) => 72.29/9.86 (( 72.29/9.86 (doubleComplementEq) => 72.29/9.86 (( 72.29/9.86 (complementTnotintersectT) => 72.29/9.86 (( 72.29/9.86 (complementImpComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementSubsetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementInPowersetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (contraSubsetComplement) => 72.29/9.86 (( 72.29/9.86 (complementTcontraSubset) => 72.29/9.86 (( 72.29/9.86 (binunionTILcontra) => 72.29/9.86 (( 72.29/9.86 (binunionTIRcontra) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion2) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (intersectInPowersetIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpNotIn1) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpInComplement1) => 72.29/9.86 (( 72.29/9.86 (binunionTE) => 72.29/9.86 (( 72.29/9.86 (binunionTEcontra) => 72.29/9.86 (( 72.29/9.86 (demorgan2a1) => 72.29/9.86 (( 72.29/9.86 (complementUnionInPowersetComplement) => 72.29/9.86 (( 72.29/9.86 (demorgan2a2) => 72.29/9.86 (( 72.29/9.86 (demorgan1a) => 72.29/9.86 (( 72.29/9.86 (demorgan1b) => 72.29/9.86 (( 72.29/9.86 (demorgan1) => 72.29/9.86 (( 72.29/9.86 (demorgan2a) => 72.29/9.86 (( 72.29/9.86 (demorgan2b2) => 72.29/9.86 (( 72.29/9.86 (demorgan2b) => 72.29/9.86 (( 72.29/9.86 (demorgan2) => 72.29/9.86 (( 72.29/9.86 (woz13rule0) => 72.29/9.86 (( 72.29/9.86 (woz13rule1) => 72.29/9.86 (( 72.29/9.86 (woz13rule2) => 72.29/9.86 (( 72.29/9.86 (woz13rule3) => 72.29/9.86 (( 72.29/9.86 (woz13rule4) => 72.29/9.86 (( 72.29/9.86 (woz1_1) => 72.29/9.86 (( 72.29/9.86 (woz1_2) => 72.29/9.86 (( 72.29/9.86 (woz1_3) => 72.29/9.86 (( 72.29/9.86 (woz1_4) => 72.29/9.86 (( 72.29/9.86 (woz1_5) => 72.29/9.86 (( 72.29/9.86 (breln1all2) => 72.29/9.86 (( 72.29/9.86 (breln1SetBreln1) => 72.29/9.86 (( 72.29/9.86 (choice2fnsingleton) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln1) => 72.29/9.86 (( 72.29/9.86 (breln1all1) => 72.29/9.86 (( 72.29/9.86 (subbreln1) => 72.29/9.86 (( 72.29/9.86 (eqbreln1) => 72.29/9.86 (( 72.29/9.86 (breln1invprop) => 72.29/9.86 (( 72.29/9.86 (breln1invI) => 72.29/9.86 (( 72.29/9.86 (breln1invE) => 72.29/9.86 (( 72.29/9.86 (breln1compprop) => 72.29/9.86 (( 72.29/9.86 (breln1compI) => 72.29/9.86 (( 72.29/9.86 (breln1compE) => 72.29/9.86 (( 72.29/9.86 (breln1compEex) => 72.29/9.86 (( 72.29/9.86 (!!) @ ( 72.29/9.86 (('#B') @ ( 72.29/9.86 !!) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 !!))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#C') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 breln1)))) @ 72.29/9.86 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1272])). 72.29/9.86 thf(zip_derived_cl1288, plain, 72.29/9.86 (~ (((setminusELneg) => 72.29/9.86 (((setminusILneg) => 72.29/9.86 (((setminusIRneg) => 72.29/9.86 (((setminusLsub) => 72.29/9.86 (((setminusSubset1) => 72.29/9.86 (((symdiffE) => 72.29/9.86 (((symdiffI1) => 72.29/9.86 (((symdiffI2) => 72.29/9.86 (((symdiffIneg1) => 72.29/9.86 (((symdiffIneg2) => 72.29/9.86 (((secondinupair) => 72.29/9.86 (((setukpairIL) => 72.29/9.86 (((setukpairIR) => 72.29/9.86 (((kpairiskpair) => 72.29/9.86 (((kpairp) => 72.29/9.86 (((singletonsubset) => 72.29/9.86 (((singletoninpowerset) => 72.29/9.86 (((singletoninpowunion) => 72.29/9.86 (((upairset2E) => 72.29/9.86 (((upairsubunion) => 72.29/9.86 (((upairinpowunion) => 72.29/9.86 (((ubforcartprodlem1) => 72.29/9.86 (((ubforcartprodlem2) => 72.29/9.86 (((ubforcartprodlem3) => 72.29/9.86 (((cartprodpairin) => 72.29/9.86 (((cartprodmempair1) => 72.29/9.86 (((cartprodmempair) => 72.29/9.86 (((setunionE2) => 72.29/9.86 (((setunionsingleton1) => 72.29/9.86 (((setunionsingleton2) => 72.29/9.86 (( 72.29/9.86 (setunionsingleton) => 72.29/9.86 (( 72.29/9.86 (singletonprop) => 72.29/9.86 (( 72.29/9.86 (ex1E1) => 72.29/9.86 (( 72.29/9.86 (ex1I) => 72.29/9.86 (( 72.29/9.86 (ex1I2) => 72.29/9.86 (( 72.29/9.86 (singletonsuniq) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL1) => 72.29/9.86 (( 72.29/9.86 (kfstsingleton) => 72.29/9.86 (( 72.29/9.86 (theprop) => 72.29/9.86 (( 72.29/9.86 (kfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstin) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR11) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR12) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR1) => 72.29/9.86 (( 72.29/9.86 (upairequniteq) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR) => 72.29/9.86 (( 72.29/9.86 (ksndsingleton) => 72.29/9.86 (( 72.29/9.86 (ksndpairEq) => 72.29/9.86 (( 72.29/9.86 (kpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndin) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemEL) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemER) => 72.29/9.86 (( 72.29/9.86 (cartprodmempaircEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrI) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrSub) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrERa) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL1) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL2) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrER) => 72.29/9.86 (( 72.29/9.86 (funcImageSingleton) => 72.29/9.86 (( 72.29/9.86 (apProp) => 72.29/9.86 (( 72.29/9.86 (app) => 72.29/9.86 (( 72.29/9.86 (infuncsetfunc) => 72.29/9.86 (( 72.29/9.86 (ap2p) => 72.29/9.86 (( 72.29/9.86 (funcinfuncset) => 72.29/9.86 (( 72.29/9.86 (lamProp) => 72.29/9.86 (( 72.29/9.86 (lamp) => 72.29/9.86 (( 72.29/9.86 (lam2p) => 72.29/9.86 (( 72.29/9.86 (brelnall1) => 72.29/9.86 (( 72.29/9.86 (brelnall2) => 72.29/9.86 (( 72.29/9.86 (ex1E2) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp1) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp3) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp2) => 72.29/9.86 (( 72.29/9.86 (funcextLem) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp4) => 72.29/9.86 (( 72.29/9.86 (subbreln) => 72.29/9.86 (( 72.29/9.86 (eqbreln) => 72.29/9.86 (( 72.29/9.86 (funcext) => 72.29/9.86 (( 72.29/9.86 (funcext2) => 72.29/9.86 (( 72.29/9.86 (ap2apEq1) => 72.29/9.86 (( 72.29/9.86 (ap2apEq2) => 72.29/9.86 (( 72.29/9.86 (beta1) => 72.29/9.86 (( 72.29/9.86 (eta1) => 72.29/9.86 (( 72.29/9.86 (lam2lamEq) => 72.29/9.86 (( 72.29/9.86 (beta2) => 72.29/9.86 (( 72.29/9.86 (eta2) => 72.29/9.86 (( 72.29/9.86 (iffalseProp1) => 72.29/9.86 (( 72.29/9.86 (iffalseProp2) => 72.29/9.86 (( 72.29/9.86 (iftrueProp1) => 72.29/9.86 (( 72.29/9.86 (iftrueProp2) => 72.29/9.86 (( 72.29/9.86 (ifSingleton) => 72.29/9.86 (( 72.29/9.86 (ifp) => 72.29/9.86 (( 72.29/9.86 (theeq) => 72.29/9.86 (( 72.29/9.86 (iftrue) => 72.29/9.86 (( 72.29/9.86 (iffalse) => 72.29/9.86 (( 72.29/9.86 (iftrueorfalse) => 72.29/9.86 (( 72.29/9.86 (binintersectT_lem) => 72.29/9.86 (( 72.29/9.86 (binunionT_lem) => 72.29/9.86 (( 72.29/9.86 (powersetT_lem) => 72.29/9.86 (( 72.29/9.86 (setminusT_lem) => 72.29/9.86 (( 72.29/9.86 (complementT_lem) => 72.29/9.86 (( 72.29/9.86 (setextT) => 72.29/9.86 (( 72.29/9.86 (subsetTI) => 72.29/9.86 (( 72.29/9.86 (powersetTI1) => 72.29/9.86 (( 72.29/9.86 (powersetTE1) => 72.29/9.86 (( 72.29/9.86 (complementTI1) => 72.29/9.86 (( 72.29/9.86 (complementTE1) => 72.29/9.86 (( 72.29/9.86 (binintersectTELcontra) => 72.29/9.86 (( 72.29/9.86 (binintersectTERcontra) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT1) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT2) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT3) => 72.29/9.86 (( 72.29/9.86 (doubleComplementI1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementE1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub2) => 72.29/9.86 (( 72.29/9.86 (doubleComplementEq) => 72.29/9.86 (( 72.29/9.86 (complementTnotintersectT) => 72.29/9.86 (( 72.29/9.86 (complementImpComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementSubsetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementInPowersetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (contraSubsetComplement) => 72.29/9.86 (( 72.29/9.86 (complementTcontraSubset) => 72.29/9.86 (( 72.29/9.86 (binunionTILcontra) => 72.29/9.86 (( 72.29/9.86 (binunionTIRcontra) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion2) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (intersectInPowersetIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpNotIn1) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpInComplement1) => 72.29/9.86 (( 72.29/9.86 (binunionTE) => 72.29/9.86 (( 72.29/9.86 (binunionTEcontra) => 72.29/9.86 (( 72.29/9.86 (demorgan2a1) => 72.29/9.86 (( 72.29/9.86 (complementUnionInPowersetComplement) => 72.29/9.86 (( 72.29/9.86 (demorgan2a2) => 72.29/9.86 (( 72.29/9.86 (demorgan1a) => 72.29/9.86 (( 72.29/9.86 (demorgan1b) => 72.29/9.86 (( 72.29/9.86 (demorgan1) => 72.29/9.86 (( 72.29/9.86 (demorgan2a) => 72.29/9.86 (( 72.29/9.86 (demorgan2b2) => 72.29/9.86 (( 72.29/9.86 (demorgan2b) => 72.29/9.86 (( 72.29/9.86 (demorgan2) => 72.29/9.86 (( 72.29/9.86 (woz13rule0) => 72.29/9.86 (( 72.29/9.86 (woz13rule1) => 72.29/9.86 (( 72.29/9.86 (woz13rule2) => 72.29/9.86 (( 72.29/9.86 (woz13rule3) => 72.29/9.86 (( 72.29/9.86 (woz13rule4) => 72.29/9.86 (( 72.29/9.86 (woz1_1) => 72.29/9.86 (( 72.29/9.86 (woz1_2) => 72.29/9.86 (( 72.29/9.86 (woz1_3) => 72.29/9.86 (( 72.29/9.86 (woz1_4) => 72.29/9.86 (( 72.29/9.86 (woz1_5) => 72.29/9.86 (( 72.29/9.86 (breln1all2) => 72.29/9.86 (( 72.29/9.86 (breln1SetBreln1) => 72.29/9.86 (( 72.29/9.86 (choice2fnsingleton) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln1) => 72.29/9.86 (( 72.29/9.86 (breln1all1) => 72.29/9.86 (( 72.29/9.86 (subbreln1) => 72.29/9.86 (( 72.29/9.86 (eqbreln1) => 72.29/9.86 (( 72.29/9.86 (breln1invprop) => 72.29/9.86 (( 72.29/9.86 (breln1invI) => 72.29/9.86 (( 72.29/9.86 (breln1invE) => 72.29/9.86 (( 72.29/9.86 (breln1compprop) => 72.29/9.86 (( 72.29/9.86 (breln1compI) => 72.29/9.86 (( 72.29/9.86 (breln1compE) => 72.29/9.86 (( 72.29/9.86 (breln1compEex) => 72.29/9.86 (( 72.29/9.86 (!!) @ ( 72.29/9.86 (('#B') @ ( 72.29/9.86 !!) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 !!))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#C') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 breln1)))) @ 72.29/9.86 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1280])). 72.29/9.86 thf(zip_derived_cl1296, plain, 72.29/9.86 (~ (((setminusILneg) => 72.29/9.86 (((setminusIRneg) => 72.29/9.86 (((setminusLsub) => 72.29/9.86 (((setminusSubset1) => 72.29/9.86 (((symdiffE) => 72.29/9.86 (((symdiffI1) => 72.29/9.86 (((symdiffI2) => 72.29/9.86 (((symdiffIneg1) => 72.29/9.86 (((symdiffIneg2) => 72.29/9.86 (((secondinupair) => 72.29/9.86 (((setukpairIL) => 72.29/9.86 (((setukpairIR) => 72.29/9.86 (((kpairiskpair) => 72.29/9.86 (((kpairp) => 72.29/9.86 (((singletonsubset) => 72.29/9.86 (((singletoninpowerset) => 72.29/9.86 (((singletoninpowunion) => 72.29/9.86 (((upairset2E) => 72.29/9.86 (((upairsubunion) => 72.29/9.86 (((upairinpowunion) => 72.29/9.86 (((ubforcartprodlem1) => 72.29/9.86 (((ubforcartprodlem2) => 72.29/9.86 (((ubforcartprodlem3) => 72.29/9.86 (((cartprodpairin) => 72.29/9.86 (((cartprodmempair1) => 72.29/9.86 (((cartprodmempair) => 72.29/9.86 (((setunionE2) => 72.29/9.86 (((setunionsingleton1) => 72.29/9.86 (((setunionsingleton2) => 72.29/9.86 (((setunionsingleton) => 72.29/9.86 (( 72.29/9.86 (singletonprop) => 72.29/9.86 (( 72.29/9.86 (ex1E1) => 72.29/9.86 (( 72.29/9.86 (ex1I) => 72.29/9.86 (( 72.29/9.86 (ex1I2) => 72.29/9.86 (( 72.29/9.86 (singletonsuniq) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL1) => 72.29/9.86 (( 72.29/9.86 (kfstsingleton) => 72.29/9.86 (( 72.29/9.86 (theprop) => 72.29/9.86 (( 72.29/9.86 (kfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstin) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR11) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR12) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR1) => 72.29/9.86 (( 72.29/9.86 (upairequniteq) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR) => 72.29/9.86 (( 72.29/9.86 (ksndsingleton) => 72.29/9.86 (( 72.29/9.86 (ksndpairEq) => 72.29/9.86 (( 72.29/9.86 (kpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndin) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemEL) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemER) => 72.29/9.86 (( 72.29/9.86 (cartprodmempaircEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrI) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrSub) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrERa) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL1) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL2) => 72.29/9.86 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72.29/9.86 (woz13rule2) => 72.29/9.86 (( 72.29/9.86 (woz13rule3) => 72.29/9.86 (( 72.29/9.86 (woz13rule4) => 72.29/9.86 (( 72.29/9.86 (woz1_1) => 72.29/9.86 (( 72.29/9.86 (woz1_2) => 72.29/9.86 (( 72.29/9.86 (woz1_3) => 72.29/9.86 (( 72.29/9.86 (woz1_4) => 72.29/9.86 (( 72.29/9.86 (woz1_5) => 72.29/9.86 (( 72.29/9.86 (breln1all2) => 72.29/9.86 (( 72.29/9.86 (breln1SetBreln1) => 72.29/9.86 (( 72.29/9.86 (choice2fnsingleton) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln1) => 72.29/9.86 (( 72.29/9.86 (breln1all1) => 72.29/9.86 (( 72.29/9.86 (subbreln1) => 72.29/9.86 (( 72.29/9.86 (eqbreln1) => 72.29/9.86 (( 72.29/9.86 (breln1invprop) => 72.29/9.86 (( 72.29/9.86 (breln1invI) => 72.29/9.86 (( 72.29/9.86 (breln1invE) => 72.29/9.86 (( 72.29/9.86 (breln1compprop) => 72.29/9.86 (( 72.29/9.86 (breln1compI) => 72.29/9.86 (( 72.29/9.86 (breln1compE) => 72.29/9.86 (( 72.29/9.86 (breln1compEex) => 72.29/9.86 (( 72.29/9.86 (!!) @ ( 72.29/9.86 (('#B') @ ( 72.29/9.86 !!) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 !!))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#C') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 breln1)))) @ 72.29/9.86 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])). 72.29/9.86 thf(zip_derived_cl1305, plain, 72.29/9.86 (~ (((setminusIRneg) => 72.29/9.86 (((setminusLsub) => 72.29/9.86 (((setminusSubset1) => 72.29/9.86 (((symdiffE) => 72.29/9.86 (((symdiffI1) => 72.29/9.86 (((symdiffI2) => 72.29/9.86 (((symdiffIneg1) => 72.29/9.86 (((symdiffIneg2) => 72.29/9.86 (((secondinupair) => 72.29/9.86 (((setukpairIL) => 72.29/9.86 (((setukpairIR) => 72.29/9.86 (((kpairiskpair) => 72.29/9.86 (((kpairp) => 72.29/9.86 (((singletonsubset) => 72.29/9.86 (((singletoninpowerset) => 72.29/9.86 (((singletoninpowunion) => 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(setukpairinjR12) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR1) => 72.29/9.86 (( 72.29/9.86 (upairequniteq) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR) => 72.29/9.86 (( 72.29/9.86 (ksndsingleton) => 72.29/9.86 (( 72.29/9.86 (ksndpairEq) => 72.29/9.86 (( 72.29/9.86 (kpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndin) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemEL) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemER) => 72.29/9.86 (( 72.29/9.86 (cartprodmempaircEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrI) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrSub) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrERa) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL1) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL2) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrER) => 72.29/9.86 (( 72.29/9.86 (funcImageSingleton) => 72.29/9.86 (( 72.29/9.86 (apProp) => 72.29/9.86 (( 72.29/9.86 (app) => 72.29/9.86 (( 72.29/9.86 (infuncsetfunc) => 72.29/9.86 (( 72.29/9.86 (ap2p) => 72.29/9.86 (( 72.29/9.86 (funcinfuncset) => 72.29/9.86 (( 72.29/9.86 (lamProp) => 72.29/9.86 (( 72.29/9.86 (lamp) => 72.29/9.86 (( 72.29/9.86 (lam2p) => 72.29/9.86 (( 72.29/9.86 (brelnall1) => 72.29/9.86 (( 72.29/9.86 (brelnall2) => 72.29/9.86 (( 72.29/9.86 (ex1E2) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp1) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp3) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp2) => 72.29/9.86 (( 72.29/9.86 (funcextLem) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp4) => 72.29/9.86 (( 72.29/9.86 (subbreln) => 72.29/9.86 (( 72.29/9.86 (eqbreln) => 72.29/9.86 (( 72.29/9.86 (funcext) => 72.29/9.86 (( 72.29/9.86 (funcext2) => 72.29/9.86 (( 72.29/9.86 (ap2apEq1) => 72.29/9.86 (( 72.29/9.86 (ap2apEq2) => 72.29/9.86 (( 72.29/9.86 (beta1) => 72.29/9.86 (( 72.29/9.86 (eta1) => 72.29/9.86 (( 72.29/9.86 (lam2lamEq) => 72.29/9.86 (( 72.29/9.86 (beta2) => 72.29/9.86 (( 72.29/9.86 (eta2) => 72.29/9.86 (( 72.29/9.86 (iffalseProp1) => 72.29/9.86 (( 72.29/9.86 (iffalseProp2) => 72.29/9.86 (( 72.29/9.86 (iftrueProp1) => 72.29/9.86 (( 72.29/9.86 (iftrueProp2) => 72.29/9.86 (( 72.29/9.86 (ifSingleton) => 72.29/9.86 (( 72.29/9.86 (ifp) => 72.29/9.86 (( 72.29/9.86 (theeq) => 72.29/9.86 (( 72.29/9.86 (iftrue) => 72.29/9.86 (( 72.29/9.86 (iffalse) => 72.29/9.86 (( 72.29/9.86 (iftrueorfalse) => 72.29/9.86 (( 72.29/9.86 (binintersectT_lem) => 72.29/9.86 (( 72.29/9.86 (binunionT_lem) => 72.29/9.86 (( 72.29/9.86 (powersetT_lem) => 72.29/9.86 (( 72.29/9.86 (setminusT_lem) => 72.29/9.86 (( 72.29/9.86 (complementT_lem) => 72.29/9.86 (( 72.29/9.86 (setextT) => 72.29/9.86 (( 72.29/9.86 (subsetTI) => 72.29/9.86 (( 72.29/9.86 (powersetTI1) => 72.29/9.86 (( 72.29/9.86 (powersetTE1) => 72.29/9.86 (( 72.29/9.86 (complementTI1) => 72.29/9.86 (( 72.29/9.86 (complementTE1) => 72.29/9.86 (( 72.29/9.86 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(inIntersectImpInUnion) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion2) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (intersectInPowersetIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpNotIn1) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpInComplement1) => 72.29/9.86 (( 72.29/9.86 (binunionTE) => 72.29/9.86 (( 72.29/9.86 (binunionTEcontra) => 72.29/9.86 (( 72.29/9.86 (demorgan2a1) => 72.29/9.86 (( 72.29/9.86 (complementUnionInPowersetComplement) => 72.29/9.86 (( 72.29/9.86 (demorgan2a2) => 72.29/9.86 (( 72.29/9.86 (demorgan1a) => 72.29/9.86 (( 72.29/9.86 (demorgan1b) => 72.29/9.86 (( 72.29/9.86 (demorgan1) => 72.29/9.86 (( 72.29/9.86 (demorgan2a) => 72.29/9.86 (( 72.29/9.86 (demorgan2b2) => 72.29/9.86 (( 72.29/9.86 (demorgan2b) => 72.29/9.86 (( 72.29/9.86 (demorgan2) => 72.29/9.86 (( 72.29/9.86 (woz13rule0) => 72.29/9.86 (( 72.29/9.86 (woz13rule1) => 72.29/9.86 (( 72.29/9.86 (woz13rule2) => 72.29/9.86 (( 72.29/9.86 (woz13rule3) => 72.29/9.86 (( 72.29/9.86 (woz13rule4) => 72.29/9.86 (( 72.29/9.86 (woz1_1) => 72.29/9.86 (( 72.29/9.86 (woz1_2) => 72.29/9.86 (( 72.29/9.86 (woz1_3) => 72.29/9.86 (( 72.29/9.86 (woz1_4) => 72.29/9.86 (( 72.29/9.86 (woz1_5) => 72.29/9.86 (( 72.29/9.86 (breln1all2) => 72.29/9.86 (( 72.29/9.86 (breln1SetBreln1) => 72.29/9.86 (( 72.29/9.86 (choice2fnsingleton) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln1) => 72.29/9.86 (( 72.29/9.86 (breln1all1) => 72.29/9.86 (( 72.29/9.86 (subbreln1) => 72.29/9.86 (( 72.29/9.86 (eqbreln1) => 72.29/9.86 (( 72.29/9.86 (breln1invprop) => 72.29/9.86 (( 72.29/9.86 (breln1invI) => 72.29/9.86 (( 72.29/9.86 (breln1invE) => 72.29/9.86 (( 72.29/9.86 (breln1compprop) => 72.29/9.86 (( 72.29/9.86 (breln1compI) => 72.29/9.86 (( 72.29/9.86 (breln1compE) => 72.29/9.86 (( 72.29/9.86 (breln1compEex) => 72.29/9.86 (( 72.29/9.86 (!!) @ ( 72.29/9.86 (('#B') @ ( 72.29/9.86 !!) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 !!))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#C') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 breln1)))) @ 72.29/9.86 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1296])). 72.29/9.86 thf(zip_derived_cl1313, plain, 72.29/9.86 (~ (((setminusLsub) => 72.29/9.86 (((setminusSubset1) => 72.29/9.86 (((symdiffE) => 72.29/9.86 (((symdiffI1) => 72.29/9.86 (((symdiffI2) => 72.29/9.86 (((symdiffIneg1) => 72.29/9.86 (((symdiffIneg2) => 72.29/9.86 (((secondinupair) => 72.29/9.86 (((setukpairIL) => 72.29/9.86 (((setukpairIR) => 72.29/9.86 (((kpairiskpair) => 72.29/9.86 (((kpairp) => 72.29/9.86 (((singletonsubset) => 72.29/9.86 (((singletoninpowerset) => 72.29/9.86 (((singletoninpowunion) => 72.29/9.86 (((upairset2E) => 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(( 72.29/9.86 (apProp) => 72.29/9.86 (( 72.29/9.86 (app) => 72.29/9.86 (( 72.29/9.86 (infuncsetfunc) => 72.29/9.86 (( 72.29/9.86 (ap2p) => 72.29/9.86 (( 72.29/9.86 (funcinfuncset) => 72.29/9.86 (( 72.29/9.86 (lamProp) => 72.29/9.86 (( 72.29/9.86 (lamp) => 72.29/9.86 (( 72.29/9.86 (lam2p) => 72.29/9.86 (( 72.29/9.86 (brelnall1) => 72.29/9.86 (( 72.29/9.86 (brelnall2) => 72.29/9.86 (( 72.29/9.86 (ex1E2) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp1) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp3) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp2) => 72.29/9.86 (( 72.29/9.86 (funcextLem) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp4) => 72.29/9.86 (( 72.29/9.86 (subbreln) => 72.29/9.86 (( 72.29/9.86 (eqbreln) => 72.29/9.86 (( 72.29/9.86 (funcext) => 72.29/9.86 (( 72.29/9.86 (funcext2) => 72.29/9.86 (( 72.29/9.86 (ap2apEq1) => 72.29/9.86 (( 72.29/9.86 (ap2apEq2) => 72.29/9.86 (( 72.29/9.86 (beta1) => 72.29/9.86 (( 72.29/9.86 (eta1) => 72.29/9.86 (( 72.29/9.86 (lam2lamEq) => 72.29/9.86 (( 72.29/9.86 (beta2) => 72.29/9.86 (( 72.29/9.86 (eta2) => 72.29/9.86 (( 72.29/9.86 (iffalseProp1) => 72.29/9.86 (( 72.29/9.86 (iffalseProp2) => 72.29/9.86 (( 72.29/9.86 (iftrueProp1) => 72.29/9.86 (( 72.29/9.86 (iftrueProp2) => 72.29/9.86 (( 72.29/9.86 (ifSingleton) => 72.29/9.86 (( 72.29/9.86 (ifp) => 72.29/9.86 (( 72.29/9.86 (theeq) => 72.29/9.86 (( 72.29/9.86 (iftrue) => 72.29/9.86 (( 72.29/9.86 (iffalse) => 72.29/9.86 (( 72.29/9.86 (iftrueorfalse) => 72.29/9.86 (( 72.29/9.86 (binintersectT_lem) => 72.29/9.86 (( 72.29/9.86 (binunionT_lem) => 72.29/9.86 (( 72.29/9.86 (powersetT_lem) => 72.29/9.86 (( 72.29/9.86 (setminusT_lem) => 72.29/9.86 (( 72.29/9.86 (complementT_lem) => 72.29/9.86 (( 72.29/9.86 (setextT) => 72.29/9.86 (( 72.29/9.86 (subsetTI) => 72.29/9.86 (( 72.29/9.86 (powersetTI1) => 72.29/9.86 (( 72.29/9.86 (powersetTE1) => 72.29/9.86 (( 72.29/9.86 (complementTI1) => 72.29/9.86 (( 72.29/9.86 (complementTE1) => 72.29/9.86 (( 72.29/9.86 (binintersectTELcontra) => 72.29/9.86 (( 72.29/9.86 (binintersectTERcontra) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT1) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT2) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT3) => 72.29/9.86 (( 72.29/9.86 (doubleComplementI1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementE1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub2) => 72.29/9.86 (( 72.29/9.86 (doubleComplementEq) => 72.29/9.86 (( 72.29/9.86 (complementTnotintersectT) => 72.29/9.86 (( 72.29/9.86 (complementImpComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementSubsetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementInPowersetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (contraSubsetComplement) => 72.29/9.86 (( 72.29/9.86 (complementTcontraSubset) => 72.29/9.86 (( 72.29/9.86 (binunionTILcontra) => 72.29/9.86 (( 72.29/9.86 (binunionTIRcontra) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion2) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (intersectInPowersetIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpNotIn1) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpInComplement1) => 72.29/9.86 (( 72.29/9.86 (binunionTE) => 72.29/9.86 (( 72.29/9.86 (binunionTEcontra) => 72.29/9.86 (( 72.29/9.86 (demorgan2a1) => 72.29/9.86 (( 72.29/9.86 (complementUnionInPowersetComplement) => 72.29/9.86 (( 72.29/9.86 (demorgan2a2) => 72.29/9.86 (( 72.29/9.86 (demorgan1a) => 72.29/9.86 (( 72.29/9.86 (demorgan1b) => 72.29/9.86 (( 72.29/9.86 (demorgan1) => 72.29/9.86 (( 72.29/9.86 (demorgan2a) => 72.29/9.86 (( 72.29/9.86 (demorgan2b2) => 72.29/9.86 (( 72.29/9.86 (demorgan2b) => 72.29/9.86 (( 72.29/9.86 (demorgan2) => 72.29/9.86 (( 72.29/9.86 (woz13rule0) => 72.29/9.86 (( 72.29/9.86 (woz13rule1) => 72.29/9.86 (( 72.29/9.86 (woz13rule2) => 72.29/9.86 (( 72.29/9.86 (woz13rule3) => 72.29/9.86 (( 72.29/9.86 (woz13rule4) => 72.29/9.86 (( 72.29/9.86 (woz1_1) => 72.29/9.86 (( 72.29/9.86 (woz1_2) => 72.29/9.86 (( 72.29/9.86 (woz1_3) => 72.29/9.86 (( 72.29/9.86 (woz1_4) => 72.29/9.86 (( 72.29/9.86 (woz1_5) => 72.29/9.86 (( 72.29/9.86 (breln1all2) => 72.29/9.86 (( 72.29/9.86 (breln1SetBreln1) => 72.29/9.86 (( 72.29/9.86 (choice2fnsingleton) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln1) => 72.29/9.86 (( 72.29/9.86 (breln1all1) => 72.29/9.86 (( 72.29/9.86 (subbreln1) => 72.29/9.86 (( 72.29/9.86 (eqbreln1) => 72.29/9.86 (( 72.29/9.86 (breln1invprop) => 72.29/9.86 (( 72.29/9.86 (breln1invI) => 72.29/9.86 (( 72.29/9.86 (breln1invE) => 72.29/9.86 (( 72.29/9.86 (breln1compprop) => 72.29/9.86 (( 72.29/9.86 (breln1compI) => 72.29/9.86 (( 72.29/9.86 (breln1compE) => 72.29/9.86 (( 72.29/9.86 (breln1compEex) => 72.29/9.86 (( 72.29/9.86 (!!) @ ( 72.29/9.86 (('#B') @ ( 72.29/9.86 !!) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 !!))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#C') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 breln1)))) @ 72.29/9.86 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])). 72.29/9.86 thf(zip_derived_cl1321, plain, 72.29/9.86 (~ (((setminusSubset1) => 72.29/9.86 (((symdiffE) => 72.29/9.86 (((symdiffI1) => 72.29/9.86 (((symdiffI2) => 72.29/9.86 (((symdiffIneg1) => 72.29/9.86 (((symdiffIneg2) => 72.29/9.86 (((secondinupair) => 72.29/9.86 (((setukpairIL) => 72.29/9.86 (((setukpairIR) => 72.29/9.86 (((kpairiskpair) => 72.29/9.86 (((kpairp) => 72.29/9.86 (((singletonsubset) => 72.29/9.86 (((singletoninpowerset) => 72.29/9.86 (((singletoninpowunion) => 72.29/9.86 (((upairset2E) => 72.29/9.86 (((upairsubunion) => 72.29/9.86 (((upairinpowunion) => 72.29/9.86 (((ubforcartprodlem1) => 72.29/9.86 (((ubforcartprodlem2) => 72.29/9.86 (((ubforcartprodlem3) => 72.29/9.86 (((cartprodpairin) => 72.29/9.86 (((cartprodmempair1) => 72.29/9.86 (((cartprodmempair) => 72.29/9.86 (((setunionE2) => 72.29/9.86 (((setunionsingleton1) => 72.29/9.86 (((setunionsingleton2) => 72.29/9.86 (((setunionsingleton) => 72.29/9.86 (((singletonprop) => 72.29/9.86 (((ex1E1) => 72.29/9.86 (((ex1I) => 72.29/9.86 (( 72.29/9.86 (ex1I2) => 72.29/9.86 (( 72.29/9.86 (singletonsuniq) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL1) => 72.29/9.86 (( 72.29/9.86 (kfstsingleton) => 72.29/9.86 (( 72.29/9.86 (theprop) => 72.29/9.86 (( 72.29/9.86 (kfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstin) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR11) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR12) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR1) => 72.29/9.86 (( 72.29/9.86 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(woz1_3) => 72.29/9.86 (( 72.29/9.86 (woz1_4) => 72.29/9.86 (( 72.29/9.86 (woz1_5) => 72.29/9.86 (( 72.29/9.86 (breln1all2) => 72.29/9.86 (( 72.29/9.86 (breln1SetBreln1) => 72.29/9.86 (( 72.29/9.86 (choice2fnsingleton) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln1) => 72.29/9.86 (( 72.29/9.86 (breln1all1) => 72.29/9.86 (( 72.29/9.86 (subbreln1) => 72.29/9.86 (( 72.29/9.86 (eqbreln1) => 72.29/9.86 (( 72.29/9.86 (breln1invprop) => 72.29/9.86 (( 72.29/9.86 (breln1invI) => 72.29/9.86 (( 72.29/9.86 (breln1invE) => 72.29/9.86 (( 72.29/9.86 (breln1compprop) => 72.29/9.86 (( 72.29/9.86 (breln1compI) => 72.29/9.86 (( 72.29/9.86 (breln1compE) => 72.29/9.86 (( 72.29/9.86 (breln1compEex) => 72.29/9.86 (( 72.29/9.86 (!!) @ ( 72.29/9.86 (('#B') @ ( 72.29/9.86 !!) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 !!))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#C') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 breln1)))) @ 72.29/9.86 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1321])). 72.29/9.86 thf(zip_derived_cl1338, plain, 72.29/9.86 (~ (((symdiffI1) => 72.29/9.86 (((symdiffI2) => 72.29/9.86 (((symdiffIneg1) => 72.29/9.86 (((symdiffIneg2) => 72.29/9.86 (((secondinupair) => 72.29/9.86 (((setukpairIL) => 72.29/9.86 (((setukpairIR) => 72.29/9.86 (((kpairiskpair) => 72.29/9.86 (((kpairp) => 72.29/9.86 (((singletonsubset) => 72.29/9.86 (((singletoninpowerset) => 72.29/9.86 (((singletoninpowunion) => 72.29/9.86 (((upairset2E) => 72.29/9.86 (((upairsubunion) => 72.29/9.86 (((upairinpowunion) => 72.29/9.86 (((ubforcartprodlem1) => 72.29/9.86 (((ubforcartprodlem2) => 72.29/9.86 (((ubforcartprodlem3) => 72.29/9.86 (((cartprodpairin) => 72.29/9.86 (((cartprodmempair1) => 72.29/9.86 (((cartprodmempair) => 72.29/9.86 (((setunionE2) => 72.29/9.86 (((setunionsingleton1) => 72.29/9.86 (((setunionsingleton2) => 72.29/9.86 (((setunionsingleton) => 72.29/9.86 (((singletonprop) => 72.29/9.86 (((ex1E1) => 72.29/9.86 (((ex1I) => 72.29/9.86 (((ex1I2) => 72.29/9.86 (((singletonsuniq) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL1) => 72.29/9.86 (( 72.29/9.86 (kfstsingleton) => 72.29/9.86 (( 72.29/9.86 (theprop) => 72.29/9.86 (( 72.29/9.86 (kfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstin) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR11) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR12) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR1) => 72.29/9.86 (( 72.29/9.86 (upairequniteq) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR) => 72.29/9.86 (( 72.29/9.86 (ksndsingleton) => 72.29/9.86 (( 72.29/9.86 (ksndpairEq) => 72.29/9.86 (( 72.29/9.86 (kpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndin) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemEL) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemER) => 72.29/9.86 (( 72.29/9.86 (cartprodmempaircEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrI) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrSub) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrERa) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL1) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL2) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrER) => 72.29/9.86 (( 72.29/9.86 (funcImageSingleton) => 72.29/9.86 (( 72.29/9.86 (apProp) => 72.29/9.86 (( 72.29/9.86 (app) => 72.29/9.86 (( 72.29/9.86 (infuncsetfunc) => 72.29/9.86 (( 72.29/9.86 (ap2p) => 72.29/9.86 (( 72.29/9.86 (funcinfuncset) => 72.29/9.86 (( 72.29/9.86 (lamProp) => 72.29/9.86 (( 72.29/9.86 (lamp) => 72.29/9.86 (( 72.29/9.86 (lam2p) => 72.29/9.86 (( 72.29/9.86 (brelnall1) => 72.29/9.86 (( 72.29/9.86 (brelnall2) => 72.29/9.86 (( 72.29/9.86 (ex1E2) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp1) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp3) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp2) => 72.29/9.86 (( 72.29/9.86 (funcextLem) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp4) => 72.29/9.86 (( 72.29/9.86 (subbreln) => 72.29/9.86 (( 72.29/9.86 (eqbreln) => 72.29/9.86 (( 72.29/9.86 (funcext) => 72.29/9.86 (( 72.29/9.86 (funcext2) => 72.29/9.86 (( 72.29/9.86 (ap2apEq1) => 72.29/9.86 (( 72.29/9.86 (ap2apEq2) => 72.29/9.86 (( 72.29/9.86 (beta1) => 72.29/9.86 (( 72.29/9.86 (eta1) => 72.29/9.86 (( 72.29/9.86 (lam2lamEq) => 72.29/9.86 (( 72.29/9.86 (beta2) => 72.29/9.86 (( 72.29/9.86 (eta2) => 72.29/9.86 (( 72.29/9.86 (iffalseProp1) => 72.29/9.86 (( 72.29/9.86 (iffalseProp2) => 72.29/9.86 (( 72.29/9.86 (iftrueProp1) => 72.29/9.86 (( 72.29/9.86 (iftrueProp2) => 72.29/9.86 (( 72.29/9.86 (ifSingleton) => 72.29/9.86 (( 72.29/9.86 (ifp) => 72.29/9.86 (( 72.29/9.86 (theeq) => 72.29/9.86 (( 72.29/9.86 (iftrue) => 72.29/9.86 (( 72.29/9.86 (iffalse) => 72.29/9.86 (( 72.29/9.86 (iftrueorfalse) => 72.29/9.86 (( 72.29/9.86 (binintersectT_lem) => 72.29/9.86 (( 72.29/9.86 (binunionT_lem) => 72.29/9.86 (( 72.29/9.86 (powersetT_lem) => 72.29/9.86 (( 72.29/9.86 (setminusT_lem) => 72.29/9.86 (( 72.29/9.86 (complementT_lem) => 72.29/9.86 (( 72.29/9.86 (setextT) => 72.29/9.86 (( 72.29/9.86 (subsetTI) => 72.29/9.86 (( 72.29/9.86 (powersetTI1) => 72.29/9.86 (( 72.29/9.86 (powersetTE1) => 72.29/9.86 (( 72.29/9.86 (complementTI1) => 72.29/9.86 (( 72.29/9.86 (complementTE1) => 72.29/9.86 (( 72.29/9.86 (binintersectTELcontra) => 72.29/9.86 (( 72.29/9.86 (binintersectTERcontra) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT1) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT2) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT3) => 72.29/9.86 (( 72.29/9.86 (doubleComplementI1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementE1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub2) => 72.29/9.86 (( 72.29/9.86 (doubleComplementEq) => 72.29/9.86 (( 72.29/9.86 (complementTnotintersectT) => 72.29/9.86 (( 72.29/9.86 (complementImpComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementSubsetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementInPowersetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (contraSubsetComplement) => 72.29/9.86 (( 72.29/9.86 (complementTcontraSubset) => 72.29/9.86 (( 72.29/9.86 (binunionTILcontra) => 72.29/9.86 (( 72.29/9.86 (binunionTIRcontra) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion2) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (intersectInPowersetIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpNotIn1) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpInComplement1) => 72.29/9.86 (( 72.29/9.86 (binunionTE) => 72.29/9.86 (( 72.29/9.86 (binunionTEcontra) => 72.29/9.86 (( 72.29/9.86 (demorgan2a1) => 72.29/9.86 (( 72.29/9.86 (complementUnionInPowersetComplement) => 72.29/9.86 (( 72.29/9.86 (demorgan2a2) => 72.29/9.86 (( 72.29/9.86 (demorgan1a) => 72.29/9.86 (( 72.29/9.86 (demorgan1b) => 72.29/9.86 (( 72.29/9.86 (demorgan1) => 72.29/9.86 (( 72.29/9.86 (demorgan2a) => 72.29/9.86 (( 72.29/9.86 (demorgan2b2) => 72.29/9.86 (( 72.29/9.86 (demorgan2b) => 72.29/9.86 (( 72.29/9.86 (demorgan2) => 72.29/9.86 (( 72.29/9.86 (woz13rule0) => 72.29/9.86 (( 72.29/9.86 (woz13rule1) => 72.29/9.86 (( 72.29/9.86 (woz13rule2) => 72.29/9.86 (( 72.29/9.86 (woz13rule3) => 72.29/9.86 (( 72.29/9.86 (woz13rule4) => 72.29/9.86 (( 72.29/9.86 (woz1_1) => 72.29/9.86 (( 72.29/9.86 (woz1_2) => 72.29/9.86 (( 72.29/9.86 (woz1_3) => 72.29/9.86 (( 72.29/9.86 (woz1_4) => 72.29/9.86 (( 72.29/9.86 (woz1_5) => 72.29/9.86 (( 72.29/9.86 (breln1all2) => 72.29/9.86 (( 72.29/9.86 (breln1SetBreln1) => 72.29/9.86 (( 72.29/9.86 (choice2fnsingleton) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln1) => 72.29/9.86 (( 72.29/9.86 (breln1all1) => 72.29/9.86 (( 72.29/9.86 (subbreln1) => 72.29/9.86 (( 72.29/9.86 (eqbreln1) => 72.29/9.86 (( 72.29/9.86 (breln1invprop) => 72.29/9.86 (( 72.29/9.86 (breln1invI) => 72.29/9.86 (( 72.29/9.86 (breln1invE) => 72.29/9.86 (( 72.29/9.86 (breln1compprop) => 72.29/9.86 (( 72.29/9.86 (breln1compI) => 72.29/9.86 (( 72.29/9.86 (breln1compE) => 72.29/9.86 (( 72.29/9.86 (breln1compEex) => 72.29/9.86 (( 72.29/9.86 (!!) @ ( 72.29/9.86 (('#B') @ ( 72.29/9.86 !!) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 !!))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#C') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 breln1)))) @ 72.29/9.86 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1329])). 72.29/9.86 thf(zip_derived_cl1347, plain, 72.29/9.86 (~ (((symdiffI2) => 72.29/9.86 (((symdiffIneg1) => 72.29/9.86 (((symdiffIneg2) => 72.29/9.86 (((secondinupair) => 72.29/9.86 (((setukpairIL) => 72.29/9.86 (((setukpairIR) => 72.29/9.86 (((kpairiskpair) => 72.29/9.86 (((kpairp) => 72.29/9.86 (((singletonsubset) => 72.29/9.86 (((singletoninpowerset) => 72.29/9.86 (((singletoninpowunion) => 72.29/9.86 (((upairset2E) => 72.29/9.86 (((upairsubunion) => 72.29/9.86 (((upairinpowunion) => 72.29/9.86 (((ubforcartprodlem1) => 72.29/9.86 (((ubforcartprodlem2) => 72.29/9.86 (((ubforcartprodlem3) => 72.29/9.86 (((cartprodpairin) => 72.29/9.86 (((cartprodmempair1) => 72.29/9.86 (((cartprodmempair) => 72.29/9.86 (((setunionE2) => 72.29/9.86 (((setunionsingleton1) => 72.29/9.86 (((setunionsingleton2) => 72.29/9.86 (((setunionsingleton) => 72.29/9.86 (((singletonprop) => 72.29/9.86 (((ex1E1) => 72.29/9.86 (((ex1I) => 72.29/9.86 (((ex1I2) => 72.29/9.86 (((singletonsuniq) => 72.29/9.86 (((setukpairinjL1) => 72.29/9.86 (( 72.29/9.86 (kfstsingleton) => 72.29/9.86 (( 72.29/9.86 (theprop) => 72.29/9.86 (( 72.29/9.86 (kfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstin) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR11) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR12) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR1) => 72.29/9.86 (( 72.29/9.86 (upairequniteq) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR) => 72.29/9.86 (( 72.29/9.86 (ksndsingleton) => 72.29/9.86 (( 72.29/9.86 (ksndpairEq) => 72.29/9.86 (( 72.29/9.86 (kpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndin) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemEL) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemER) => 72.29/9.86 (( 72.29/9.86 (cartprodmempaircEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrI) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrSub) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrERa) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL1) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL2) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrER) => 72.29/9.86 (( 72.29/9.86 (funcImageSingleton) => 72.29/9.86 (( 72.29/9.86 (apProp) => 72.29/9.86 (( 72.29/9.86 (app) => 72.29/9.86 (( 72.29/9.86 (infuncsetfunc) => 72.29/9.86 (( 72.29/9.86 (ap2p) => 72.29/9.86 (( 72.29/9.86 (funcinfuncset) => 72.29/9.86 (( 72.29/9.86 (lamProp) => 72.29/9.86 (( 72.29/9.86 (lamp) => 72.29/9.86 (( 72.29/9.86 (lam2p) => 72.29/9.86 (( 72.29/9.86 (brelnall1) => 72.29/9.86 (( 72.29/9.86 (brelnall2) => 72.29/9.86 (( 72.29/9.86 (ex1E2) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp1) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp3) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp2) => 72.29/9.86 (( 72.29/9.86 (funcextLem) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp4) => 72.29/9.86 (( 72.29/9.86 (subbreln) => 72.29/9.86 (( 72.29/9.86 (eqbreln) => 72.29/9.86 (( 72.29/9.86 (funcext) => 72.29/9.86 (( 72.29/9.86 (funcext2) => 72.29/9.86 (( 72.29/9.86 (ap2apEq1) => 72.29/9.86 (( 72.29/9.86 (ap2apEq2) => 72.29/9.86 (( 72.29/9.86 (beta1) => 72.29/9.86 (( 72.29/9.86 (eta1) => 72.29/9.86 (( 72.29/9.86 (lam2lamEq) => 72.29/9.86 (( 72.29/9.86 (beta2) => 72.29/9.86 (( 72.29/9.86 (eta2) => 72.29/9.86 (( 72.29/9.86 (iffalseProp1) => 72.29/9.86 (( 72.29/9.86 (iffalseProp2) => 72.29/9.86 (( 72.29/9.86 (iftrueProp1) => 72.29/9.86 (( 72.29/9.86 (iftrueProp2) => 72.29/9.86 (( 72.29/9.86 (ifSingleton) => 72.29/9.86 (( 72.29/9.86 (ifp) => 72.29/9.86 (( 72.29/9.86 (theeq) => 72.29/9.86 (( 72.29/9.86 (iftrue) => 72.29/9.86 (( 72.29/9.86 (iffalse) => 72.29/9.86 (( 72.29/9.86 (iftrueorfalse) => 72.29/9.86 (( 72.29/9.86 (binintersectT_lem) => 72.29/9.86 (( 72.29/9.86 (binunionT_lem) => 72.29/9.86 (( 72.29/9.86 (powersetT_lem) => 72.29/9.86 (( 72.29/9.86 (setminusT_lem) => 72.29/9.86 (( 72.29/9.86 (complementT_lem) => 72.29/9.86 (( 72.29/9.86 (setextT) => 72.29/9.86 (( 72.29/9.86 (subsetTI) => 72.29/9.86 (( 72.29/9.86 (powersetTI1) => 72.29/9.86 (( 72.29/9.86 (powersetTE1) => 72.29/9.86 (( 72.29/9.86 (complementTI1) => 72.29/9.86 (( 72.29/9.86 (complementTE1) => 72.29/9.86 (( 72.29/9.86 (binintersectTELcontra) => 72.29/9.86 (( 72.29/9.86 (binintersectTERcontra) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT1) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT2) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT3) => 72.29/9.86 (( 72.29/9.86 (doubleComplementI1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementE1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub2) => 72.29/9.86 (( 72.29/9.86 (doubleComplementEq) => 72.29/9.86 (( 72.29/9.86 (complementTnotintersectT) => 72.29/9.86 (( 72.29/9.86 (complementImpComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementSubsetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementInPowersetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (contraSubsetComplement) => 72.29/9.86 (( 72.29/9.86 (complementTcontraSubset) => 72.29/9.86 (( 72.29/9.86 (binunionTILcontra) => 72.29/9.86 (( 72.29/9.86 (binunionTIRcontra) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion2) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (intersectInPowersetIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpNotIn1) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpInComplement1) => 72.29/9.86 (( 72.29/9.86 (binunionTE) => 72.29/9.86 (( 72.29/9.86 (binunionTEcontra) => 72.29/9.86 (( 72.29/9.86 (demorgan2a1) => 72.29/9.86 (( 72.29/9.86 (complementUnionInPowersetComplement) => 72.29/9.86 (( 72.29/9.86 (demorgan2a2) => 72.29/9.86 (( 72.29/9.86 (demorgan1a) => 72.29/9.86 (( 72.29/9.86 (demorgan1b) => 72.29/9.86 (( 72.29/9.86 (demorgan1) => 72.29/9.86 (( 72.29/9.86 (demorgan2a) => 72.29/9.86 (( 72.29/9.86 (demorgan2b2) => 72.29/9.86 (( 72.29/9.86 (demorgan2b) => 72.29/9.86 (( 72.29/9.86 (demorgan2) => 72.29/9.86 (( 72.29/9.86 (woz13rule0) => 72.29/9.86 (( 72.29/9.86 (woz13rule1) => 72.29/9.86 (( 72.29/9.86 (woz13rule2) => 72.29/9.86 (( 72.29/9.86 (woz13rule3) => 72.29/9.86 (( 72.29/9.86 (woz13rule4) => 72.29/9.86 (( 72.29/9.86 (woz1_1) => 72.29/9.86 (( 72.29/9.86 (woz1_2) => 72.29/9.86 (( 72.29/9.86 (woz1_3) => 72.29/9.86 (( 72.29/9.86 (woz1_4) => 72.29/9.86 (( 72.29/9.86 (woz1_5) => 72.29/9.86 (( 72.29/9.86 (breln1all2) => 72.29/9.86 (( 72.29/9.86 (breln1SetBreln1) => 72.29/9.86 (( 72.29/9.86 (choice2fnsingleton) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln1) => 72.29/9.86 (( 72.29/9.86 (breln1all1) => 72.29/9.86 (( 72.29/9.86 (subbreln1) => 72.29/9.86 (( 72.29/9.86 (eqbreln1) => 72.29/9.86 (( 72.29/9.86 (breln1invprop) => 72.29/9.86 (( 72.29/9.86 (breln1invI) => 72.29/9.86 (( 72.29/9.86 (breln1invE) => 72.29/9.86 (( 72.29/9.86 (breln1compprop) => 72.29/9.86 (( 72.29/9.86 (breln1compI) => 72.29/9.86 (( 72.29/9.86 (breln1compE) => 72.29/9.86 (( 72.29/9.86 (breln1compEex) => 72.29/9.86 (( 72.29/9.86 (!!) @ ( 72.29/9.86 (('#B') @ ( 72.29/9.86 !!) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 !!))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#S') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#S') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 =>))) @ 72.29/9.86 breln1)))))) @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#C') @ ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 ( 72.29/9.86 ( 72.29/9.86 ('#B') @ ( 72.29/9.86 '#B') @ 72.29/9.86 breln1)))) @ 72.29/9.86 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1338])). 72.29/9.86 thf(zip_derived_cl1354, plain, 72.29/9.86 (~ (((symdiffIneg1) => 72.29/9.86 (((symdiffIneg2) => 72.29/9.86 (((secondinupair) => 72.29/9.86 (((setukpairIL) => 72.29/9.86 (((setukpairIR) => 72.29/9.86 (((kpairiskpair) => 72.29/9.86 (((kpairp) => 72.29/9.86 (((singletonsubset) => 72.29/9.86 (((singletoninpowerset) => 72.29/9.86 (((singletoninpowunion) => 72.29/9.86 (((upairset2E) => 72.29/9.86 (((upairsubunion) => 72.29/9.86 (((upairinpowunion) => 72.29/9.86 (((ubforcartprodlem1) => 72.29/9.86 (((ubforcartprodlem2) => 72.29/9.86 (((ubforcartprodlem3) => 72.29/9.86 (((cartprodpairin) => 72.29/9.86 (((cartprodmempair1) => 72.29/9.86 (((cartprodmempair) => 72.29/9.86 (((setunionE2) => 72.29/9.86 (((setunionsingleton1) => 72.29/9.86 (((setunionsingleton2) => 72.29/9.86 (((setunionsingleton) => 72.29/9.86 (((singletonprop) => 72.29/9.86 (((ex1E1) => 72.29/9.86 (((ex1I) => 72.29/9.86 (((ex1I2) => 72.29/9.86 (((singletonsuniq) => 72.29/9.86 (((setukpairinjL1) => 72.29/9.86 (((kfstsingleton) => 72.29/9.86 (( 72.29/9.86 (theprop) => 72.29/9.86 (( 72.29/9.86 (kfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstin) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjL) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR11) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR12) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR1) => 72.29/9.86 (( 72.29/9.86 (upairequniteq) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR2) => 72.29/9.86 (( 72.29/9.86 (setukpairinjR) => 72.29/9.86 (( 72.29/9.86 (ksndsingleton) => 72.29/9.86 (( 72.29/9.86 (ksndpairEq) => 72.29/9.86 (( 72.29/9.86 (kpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndin) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemEL) => 72.29/9.86 (( 72.29/9.86 (cartprodpairmemER) => 72.29/9.86 (( 72.29/9.86 (cartprodmempaircEq) => 72.29/9.86 (( 72.29/9.86 (cartprodfstpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodsndpairEq) => 72.29/9.86 (( 72.29/9.86 (cartprodpairsurjEq) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrI) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrSub) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrERa) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL1) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrEL2) => 72.29/9.86 (( 72.29/9.86 (dpsetconstrER) => 72.29/9.86 (( 72.29/9.86 (funcImageSingleton) => 72.29/9.86 (( 72.29/9.86 (apProp) => 72.29/9.86 (( 72.29/9.86 (app) => 72.29/9.86 (( 72.29/9.86 (infuncsetfunc) => 72.29/9.86 (( 72.29/9.86 (ap2p) => 72.29/9.86 (( 72.29/9.86 (funcinfuncset) => 72.29/9.86 (( 72.29/9.86 (lamProp) => 72.29/9.86 (( 72.29/9.86 (lamp) => 72.29/9.86 (( 72.29/9.86 (lam2p) => 72.29/9.86 (( 72.29/9.86 (brelnall1) => 72.29/9.86 (( 72.29/9.86 (brelnall2) => 72.29/9.86 (( 72.29/9.86 (ex1E2) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp1) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp3) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp2) => 72.29/9.86 (( 72.29/9.86 (funcextLem) => 72.29/9.86 (( 72.29/9.86 (funcGraphProp4) => 72.29/9.86 (( 72.29/9.86 (subbreln) => 72.29/9.86 (( 72.29/9.86 (eqbreln) => 72.29/9.86 (( 72.29/9.86 (funcext) => 72.29/9.86 (( 72.29/9.86 (funcext2) => 72.29/9.86 (( 72.29/9.86 (ap2apEq1) => 72.29/9.86 (( 72.29/9.86 (ap2apEq2) => 72.29/9.86 (( 72.29/9.86 (beta1) => 72.29/9.86 (( 72.29/9.86 (eta1) => 72.29/9.86 (( 72.29/9.86 (lam2lamEq) => 72.29/9.86 (( 72.29/9.86 (beta2) => 72.29/9.86 (( 72.29/9.86 (eta2) => 72.29/9.86 (( 72.29/9.86 (iffalseProp1) => 72.29/9.86 (( 72.29/9.86 (iffalseProp2) => 72.29/9.86 (( 72.29/9.86 (iftrueProp1) => 72.29/9.86 (( 72.29/9.86 (iftrueProp2) => 72.29/9.86 (( 72.29/9.86 (ifSingleton) => 72.29/9.86 (( 72.29/9.86 (ifp) => 72.29/9.86 (( 72.29/9.86 (theeq) => 72.29/9.86 (( 72.29/9.86 (iftrue) => 72.29/9.86 (( 72.29/9.86 (iffalse) => 72.29/9.86 (( 72.29/9.86 (iftrueorfalse) => 72.29/9.86 (( 72.29/9.86 (binintersectT_lem) => 72.29/9.86 (( 72.29/9.86 (binunionT_lem) => 72.29/9.86 (( 72.29/9.86 (powersetT_lem) => 72.29/9.86 (( 72.29/9.86 (setminusT_lem) => 72.29/9.86 (( 72.29/9.86 (complementT_lem) => 72.29/9.86 (( 72.29/9.86 (setextT) => 72.29/9.86 (( 72.29/9.86 (subsetTI) => 72.29/9.86 (( 72.29/9.86 (powersetTI1) => 72.29/9.86 (( 72.29/9.86 (powersetTE1) => 72.29/9.86 (( 72.29/9.86 (complementTI1) => 72.29/9.86 (( 72.29/9.86 (complementTE1) => 72.29/9.86 (( 72.29/9.86 (binintersectTELcontra) => 72.29/9.86 (( 72.29/9.86 (binintersectTERcontra) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT1) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT2) => 72.29/9.86 (( 72.29/9.86 (contrasubsetT3) => 72.29/9.86 (( 72.29/9.86 (doubleComplementI1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementE1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub1) => 72.29/9.86 (( 72.29/9.86 (doubleComplementSub2) => 72.29/9.86 (( 72.29/9.86 (doubleComplementEq) => 72.29/9.86 (( 72.29/9.86 (complementTnotintersectT) => 72.29/9.86 (( 72.29/9.86 (complementImpComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementSubsetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (complementInPowersetComplementIntersect) => 72.29/9.86 (( 72.29/9.86 (contraSubsetComplement) => 72.29/9.86 (( 72.29/9.86 (complementTcontraSubset) => 72.29/9.86 (( 72.29/9.86 (binunionTILcontra) => 72.29/9.86 (( 72.29/9.86 (binunionTIRcontra) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInUnion2) => 72.29/9.86 (( 72.29/9.86 (inIntersectImpInIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (intersectInPowersetIntersectUnions) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpNotIn1) => 72.29/9.86 (( 72.29/9.86 (inComplementUnionImpInComplement1) => 72.29/9.86 (( 72.29/9.86 (binunionTE) => 72.29/9.86 (( 72.29/9.86 (binunionTEcontra) => 72.29/9.86 (( 72.29/9.86 (demorgan2a1) => 72.29/9.86 (( 72.29/9.86 (complementUnionInPowersetComplement) => 72.29/9.86 (( 72.29/9.86 (demorgan2a2) => 72.29/9.86 (( 72.29/9.86 (demorgan1a) => 72.29/9.86 (( 72.29/9.86 (demorgan1b) => 72.29/9.86 (( 72.29/9.86 (demorgan1) => 72.29/9.86 (( 72.29/9.86 (demorgan2a) => 72.29/9.86 (( 72.29/9.86 (demorgan2b2) => 72.29/9.86 (( 72.29/9.86 (demorgan2b) => 72.29/9.86 (( 72.29/9.86 (demorgan2) => 72.29/9.86 (( 72.29/9.86 (woz13rule0) => 72.29/9.86 (( 72.29/9.86 (woz13rule1) => 72.29/9.86 (( 72.29/9.86 (woz13rule2) => 72.29/9.86 (( 72.29/9.86 (woz13rule3) => 72.29/9.86 (( 72.29/9.86 (woz13rule4) => 72.29/9.86 (( 72.29/9.86 (woz1_1) => 72.29/9.86 (( 72.29/9.86 (woz1_2) => 72.29/9.86 (( 72.29/9.86 (woz1_3) => 72.29/9.86 (( 72.29/9.86 (woz1_4) => 72.29/9.86 (( 72.29/9.86 (woz1_5) => 72.29/9.86 (( 72.29/9.86 (breln1all2) => 72.29/9.86 (( 72.29/9.86 (breln1SetBreln1) => 72.29/9.86 (( 72.29/9.86 (choice2fnsingleton) => 72.29/9.86 (( 72.29/9.86 (setOfPairsIsBReln1) => 72.29/9.86 (( 72.29/9.86 (breln1all1) => 72.29/9.86 (( 72.29/9.86 (subbreln1) => 72.29/9.86 (( 72.29/9.86 (eqbreln1) => 72.29/9.86 (( 72.29/9.87 (breln1invprop) => 72.29/9.87 (( 72.29/9.87 (breln1invI) => 72.29/9.87 (( 72.29/9.87 (breln1invE) => 72.29/9.87 (( 72.29/9.87 (breln1compprop) => 72.29/9.87 (( 72.29/9.87 (breln1compI) => 72.29/9.87 (( 72.29/9.87 (breln1compE) => 72.29/9.87 (( 72.29/9.87 (breln1compEex) => 72.29/9.87 (( 72.29/9.87 (!!) @ ( 72.29/9.87 (('#B') @ ( 72.29/9.87 !!) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 !!))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#C') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 breln1)))) @ 72.29/9.87 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1347])). 72.29/9.87 thf(zip_derived_cl1361, plain, 72.29/9.87 (~ (((symdiffIneg2) => 72.29/9.87 (((secondinupair) => 72.29/9.87 (((setukpairIL) => 72.29/9.87 (((setukpairIR) => 72.29/9.87 (((kpairiskpair) => 72.29/9.87 (((kpairp) => 72.29/9.87 (((singletonsubset) => 72.29/9.87 (((singletoninpowerset) => 72.29/9.87 (((singletoninpowunion) => 72.29/9.87 (((upairset2E) => 72.29/9.87 (((upairsubunion) => 72.29/9.87 (((upairinpowunion) => 72.29/9.87 (((ubforcartprodlem1) => 72.29/9.87 (((ubforcartprodlem2) => 72.29/9.87 (((ubforcartprodlem3) => 72.29/9.87 (((cartprodpairin) => 72.29/9.87 (((cartprodmempair1) => 72.29/9.87 (((cartprodmempair) => 72.29/9.87 (((setunionE2) => 72.29/9.87 (((setunionsingleton1) => 72.29/9.87 (((setunionsingleton2) => 72.29/9.87 (((setunionsingleton) => 72.29/9.87 (((singletonprop) => 72.29/9.87 (((ex1E1) => 72.29/9.87 (((ex1I) => 72.29/9.87 (((ex1I2) => 72.29/9.87 (((singletonsuniq) => 72.29/9.87 (((setukpairinjL1) => 72.29/9.87 (((kfstsingleton) => 72.29/9.87 (((theprop) => 72.29/9.87 (( 72.29/9.87 (kfstpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodfstin) => 72.29/9.87 (( 72.29/9.87 (setukpairinjL2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjL) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR11) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR12) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR1) => 72.29/9.87 (( 72.29/9.87 (upairequniteq) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR) => 72.29/9.87 (( 72.29/9.87 (ksndsingleton) => 72.29/9.87 (( 72.29/9.87 (ksndpairEq) => 72.29/9.87 (( 72.29/9.87 (kpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndin) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemEL) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemER) => 72.29/9.87 (( 72.29/9.87 (cartprodmempaircEq) => 72.29/9.87 (( 72.29/9.87 (cartprodfstpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrI) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrSub) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrERa) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL1) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL2) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrER) => 72.29/9.87 (( 72.29/9.87 (funcImageSingleton) => 72.29/9.87 (( 72.29/9.87 (apProp) => 72.29/9.87 (( 72.29/9.87 (app) => 72.29/9.87 (( 72.29/9.87 (infuncsetfunc) => 72.29/9.87 (( 72.29/9.87 (ap2p) => 72.29/9.87 (( 72.29/9.87 (funcinfuncset) => 72.29/9.87 (( 72.29/9.87 (lamProp) => 72.29/9.87 (( 72.29/9.87 (lamp) => 72.29/9.87 (( 72.29/9.87 (lam2p) => 72.29/9.87 (( 72.29/9.87 (brelnall1) => 72.29/9.87 (( 72.29/9.87 (brelnall2) => 72.29/9.87 (( 72.29/9.87 (ex1E2) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp1) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp3) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp2) => 72.29/9.87 (( 72.29/9.87 (funcextLem) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp4) => 72.29/9.87 (( 72.29/9.87 (subbreln) => 72.29/9.87 (( 72.29/9.87 (eqbreln) => 72.29/9.87 (( 72.29/9.87 (funcext) => 72.29/9.87 (( 72.29/9.87 (funcext2) => 72.29/9.87 (( 72.29/9.87 (ap2apEq1) => 72.29/9.87 (( 72.29/9.87 (ap2apEq2) => 72.29/9.87 (( 72.29/9.87 (beta1) => 72.29/9.87 (( 72.29/9.87 (eta1) => 72.29/9.87 (( 72.29/9.87 (lam2lamEq) => 72.29/9.87 (( 72.29/9.87 (beta2) => 72.29/9.87 (( 72.29/9.87 (eta2) => 72.29/9.87 (( 72.29/9.87 (iffalseProp1) => 72.29/9.87 (( 72.29/9.87 (iffalseProp2) => 72.29/9.87 (( 72.29/9.87 (iftrueProp1) => 72.29/9.87 (( 72.29/9.87 (iftrueProp2) => 72.29/9.87 (( 72.29/9.87 (ifSingleton) => 72.29/9.87 (( 72.29/9.87 (ifp) => 72.29/9.87 (( 72.29/9.87 (theeq) => 72.29/9.87 (( 72.29/9.87 (iftrue) => 72.29/9.87 (( 72.29/9.87 (iffalse) => 72.29/9.87 (( 72.29/9.87 (iftrueorfalse) => 72.29/9.87 (( 72.29/9.87 (binintersectT_lem) => 72.29/9.87 (( 72.29/9.87 (binunionT_lem) => 72.29/9.87 (( 72.29/9.87 (powersetT_lem) => 72.29/9.87 (( 72.29/9.87 (setminusT_lem) => 72.29/9.87 (( 72.29/9.87 (complementT_lem) => 72.29/9.87 (( 72.29/9.87 (setextT) => 72.29/9.87 (( 72.29/9.87 (subsetTI) => 72.29/9.87 (( 72.29/9.87 (powersetTI1) => 72.29/9.87 (( 72.29/9.87 (powersetTE1) => 72.29/9.87 (( 72.29/9.87 (complementTI1) => 72.29/9.87 (( 72.29/9.87 (complementTE1) => 72.29/9.87 (( 72.29/9.87 (binintersectTELcontra) => 72.29/9.87 (( 72.29/9.87 (binintersectTERcontra) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT1) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT2) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT3) => 72.29/9.87 (( 72.29/9.87 (doubleComplementI1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementE1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub2) => 72.29/9.87 (( 72.29/9.87 (doubleComplementEq) => 72.29/9.87 (( 72.29/9.87 (complementTnotintersectT) => 72.29/9.87 (( 72.29/9.87 (complementImpComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementSubsetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementInPowersetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (contraSubsetComplement) => 72.29/9.87 (( 72.29/9.87 (complementTcontraSubset) => 72.29/9.87 (( 72.29/9.87 (binunionTILcontra) => 72.29/9.87 (( 72.29/9.87 (binunionTIRcontra) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion2) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (intersectInPowersetIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpNotIn1) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpInComplement1) => 72.29/9.87 (( 72.29/9.87 (binunionTE) => 72.29/9.87 (( 72.29/9.87 (binunionTEcontra) => 72.29/9.87 (( 72.29/9.87 (demorgan2a1) => 72.29/9.87 (( 72.29/9.87 (complementUnionInPowersetComplement) => 72.29/9.87 (( 72.29/9.87 (demorgan2a2) => 72.29/9.87 (( 72.29/9.87 (demorgan1a) => 72.29/9.87 (( 72.29/9.87 (demorgan1b) => 72.29/9.87 (( 72.29/9.87 (demorgan1) => 72.29/9.87 (( 72.29/9.87 (demorgan2a) => 72.29/9.87 (( 72.29/9.87 (demorgan2b2) => 72.29/9.87 (( 72.29/9.87 (demorgan2b) => 72.29/9.87 (( 72.29/9.87 (demorgan2) => 72.29/9.87 (( 72.29/9.87 (woz13rule0) => 72.29/9.87 (( 72.29/9.87 (woz13rule1) => 72.29/9.87 (( 72.29/9.87 (woz13rule2) => 72.29/9.87 (( 72.29/9.87 (woz13rule3) => 72.29/9.87 (( 72.29/9.87 (woz13rule4) => 72.29/9.87 (( 72.29/9.87 (woz1_1) => 72.29/9.87 (( 72.29/9.87 (woz1_2) => 72.29/9.87 (( 72.29/9.87 (woz1_3) => 72.29/9.87 (( 72.29/9.87 (woz1_4) => 72.29/9.87 (( 72.29/9.87 (woz1_5) => 72.29/9.87 (( 72.29/9.87 (breln1all2) => 72.29/9.87 (( 72.29/9.87 (breln1SetBreln1) => 72.29/9.87 (( 72.29/9.87 (choice2fnsingleton) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln1) => 72.29/9.87 (( 72.29/9.87 (breln1all1) => 72.29/9.87 (( 72.29/9.87 (subbreln1) => 72.29/9.87 (( 72.29/9.87 (eqbreln1) => 72.29/9.87 (( 72.29/9.87 (breln1invprop) => 72.29/9.87 (( 72.29/9.87 (breln1invI) => 72.29/9.87 (( 72.29/9.87 (breln1invE) => 72.29/9.87 (( 72.29/9.87 (breln1compprop) => 72.29/9.87 (( 72.29/9.87 (breln1compI) => 72.29/9.87 (( 72.29/9.87 (breln1compE) => 72.29/9.87 (( 72.29/9.87 (breln1compEex) => 72.29/9.87 (( 72.29/9.87 (!!) @ ( 72.29/9.87 (('#B') @ ( 72.29/9.87 !!) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 !!))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#C') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 breln1)))) @ 72.29/9.87 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1354])). 72.29/9.87 thf(zip_derived_cl1369, plain, 72.29/9.87 (~ (((secondinupair) => 72.29/9.87 (((setukpairIL) => 72.29/9.87 (((setukpairIR) => 72.29/9.87 (((kpairiskpair) => 72.29/9.87 (((kpairp) => 72.29/9.87 (((singletonsubset) => 72.29/9.87 (((singletoninpowerset) => 72.29/9.87 (((singletoninpowunion) => 72.29/9.87 (((upairset2E) => 72.29/9.87 (((upairsubunion) => 72.29/9.87 (((upairinpowunion) => 72.29/9.87 (((ubforcartprodlem1) => 72.29/9.87 (((ubforcartprodlem2) => 72.29/9.87 (((ubforcartprodlem3) => 72.29/9.87 (((cartprodpairin) => 72.29/9.87 (((cartprodmempair1) => 72.29/9.87 (((cartprodmempair) => 72.29/9.87 (((setunionE2) => 72.29/9.87 (((setunionsingleton1) => 72.29/9.87 (((setunionsingleton2) => 72.29/9.87 (((setunionsingleton) => 72.29/9.87 (((singletonprop) => 72.29/9.87 (((ex1E1) => 72.29/9.87 (((ex1I) => 72.29/9.87 (((ex1I2) => 72.29/9.87 (((singletonsuniq) => 72.29/9.87 (((setukpairinjL1) => 72.29/9.87 (((kfstsingleton) => 72.29/9.87 (((theprop) => 72.29/9.87 (((kfstpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodfstin) => 72.29/9.87 (( 72.29/9.87 (setukpairinjL2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjL) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR11) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR12) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR1) => 72.29/9.87 (( 72.29/9.87 (upairequniteq) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR) => 72.29/9.87 (( 72.29/9.87 (ksndsingleton) => 72.29/9.87 (( 72.29/9.87 (ksndpairEq) => 72.29/9.87 (( 72.29/9.87 (kpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndin) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemEL) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemER) => 72.29/9.87 (( 72.29/9.87 (cartprodmempaircEq) => 72.29/9.87 (( 72.29/9.87 (cartprodfstpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrI) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrSub) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrERa) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL1) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL2) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrER) => 72.29/9.87 (( 72.29/9.87 (funcImageSingleton) => 72.29/9.87 (( 72.29/9.87 (apProp) => 72.29/9.87 (( 72.29/9.87 (app) => 72.29/9.87 (( 72.29/9.87 (infuncsetfunc) => 72.29/9.87 (( 72.29/9.87 (ap2p) => 72.29/9.87 (( 72.29/9.87 (funcinfuncset) => 72.29/9.87 (( 72.29/9.87 (lamProp) => 72.29/9.87 (( 72.29/9.87 (lamp) => 72.29/9.87 (( 72.29/9.87 (lam2p) => 72.29/9.87 (( 72.29/9.87 (brelnall1) => 72.29/9.87 (( 72.29/9.87 (brelnall2) => 72.29/9.87 (( 72.29/9.87 (ex1E2) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp1) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp3) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp2) => 72.29/9.87 (( 72.29/9.87 (funcextLem) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp4) => 72.29/9.87 (( 72.29/9.87 (subbreln) => 72.29/9.87 (( 72.29/9.87 (eqbreln) => 72.29/9.87 (( 72.29/9.87 (funcext) => 72.29/9.87 (( 72.29/9.87 (funcext2) => 72.29/9.87 (( 72.29/9.87 (ap2apEq1) => 72.29/9.87 (( 72.29/9.87 (ap2apEq2) => 72.29/9.87 (( 72.29/9.87 (beta1) => 72.29/9.87 (( 72.29/9.87 (eta1) => 72.29/9.87 (( 72.29/9.87 (lam2lamEq) => 72.29/9.87 (( 72.29/9.87 (beta2) => 72.29/9.87 (( 72.29/9.87 (eta2) => 72.29/9.87 (( 72.29/9.87 (iffalseProp1) => 72.29/9.87 (( 72.29/9.87 (iffalseProp2) => 72.29/9.87 (( 72.29/9.87 (iftrueProp1) => 72.29/9.87 (( 72.29/9.87 (iftrueProp2) => 72.29/9.87 (( 72.29/9.87 (ifSingleton) => 72.29/9.87 (( 72.29/9.87 (ifp) => 72.29/9.87 (( 72.29/9.87 (theeq) => 72.29/9.87 (( 72.29/9.87 (iftrue) => 72.29/9.87 (( 72.29/9.87 (iffalse) => 72.29/9.87 (( 72.29/9.87 (iftrueorfalse) => 72.29/9.87 (( 72.29/9.87 (binintersectT_lem) => 72.29/9.87 (( 72.29/9.87 (binunionT_lem) => 72.29/9.87 (( 72.29/9.87 (powersetT_lem) => 72.29/9.87 (( 72.29/9.87 (setminusT_lem) => 72.29/9.87 (( 72.29/9.87 (complementT_lem) => 72.29/9.87 (( 72.29/9.87 (setextT) => 72.29/9.87 (( 72.29/9.87 (subsetTI) => 72.29/9.87 (( 72.29/9.87 (powersetTI1) => 72.29/9.87 (( 72.29/9.87 (powersetTE1) => 72.29/9.87 (( 72.29/9.87 (complementTI1) => 72.29/9.87 (( 72.29/9.87 (complementTE1) => 72.29/9.87 (( 72.29/9.87 (binintersectTELcontra) => 72.29/9.87 (( 72.29/9.87 (binintersectTERcontra) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT1) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT2) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT3) => 72.29/9.87 (( 72.29/9.87 (doubleComplementI1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementE1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub2) => 72.29/9.87 (( 72.29/9.87 (doubleComplementEq) => 72.29/9.87 (( 72.29/9.87 (complementTnotintersectT) => 72.29/9.87 (( 72.29/9.87 (complementImpComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementSubsetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementInPowersetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (contraSubsetComplement) => 72.29/9.87 (( 72.29/9.87 (complementTcontraSubset) => 72.29/9.87 (( 72.29/9.87 (binunionTILcontra) => 72.29/9.87 (( 72.29/9.87 (binunionTIRcontra) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion2) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (intersectInPowersetIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpNotIn1) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpInComplement1) => 72.29/9.87 (( 72.29/9.87 (binunionTE) => 72.29/9.87 (( 72.29/9.87 (binunionTEcontra) => 72.29/9.87 (( 72.29/9.87 (demorgan2a1) => 72.29/9.87 (( 72.29/9.87 (complementUnionInPowersetComplement) => 72.29/9.87 (( 72.29/9.87 (demorgan2a2) => 72.29/9.87 (( 72.29/9.87 (demorgan1a) => 72.29/9.87 (( 72.29/9.87 (demorgan1b) => 72.29/9.87 (( 72.29/9.87 (demorgan1) => 72.29/9.87 (( 72.29/9.87 (demorgan2a) => 72.29/9.87 (( 72.29/9.87 (demorgan2b2) => 72.29/9.87 (( 72.29/9.87 (demorgan2b) => 72.29/9.87 (( 72.29/9.87 (demorgan2) => 72.29/9.87 (( 72.29/9.87 (woz13rule0) => 72.29/9.87 (( 72.29/9.87 (woz13rule1) => 72.29/9.87 (( 72.29/9.87 (woz13rule2) => 72.29/9.87 (( 72.29/9.87 (woz13rule3) => 72.29/9.87 (( 72.29/9.87 (woz13rule4) => 72.29/9.87 (( 72.29/9.87 (woz1_1) => 72.29/9.87 (( 72.29/9.87 (woz1_2) => 72.29/9.87 (( 72.29/9.87 (woz1_3) => 72.29/9.87 (( 72.29/9.87 (woz1_4) => 72.29/9.87 (( 72.29/9.87 (woz1_5) => 72.29/9.87 (( 72.29/9.87 (breln1all2) => 72.29/9.87 (( 72.29/9.87 (breln1SetBreln1) => 72.29/9.87 (( 72.29/9.87 (choice2fnsingleton) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln1) => 72.29/9.87 (( 72.29/9.87 (breln1all1) => 72.29/9.87 (( 72.29/9.87 (subbreln1) => 72.29/9.87 (( 72.29/9.87 (eqbreln1) => 72.29/9.87 (( 72.29/9.87 (breln1invprop) => 72.29/9.87 (( 72.29/9.87 (breln1invI) => 72.29/9.87 (( 72.29/9.87 (breln1invE) => 72.29/9.87 (( 72.29/9.87 (breln1compprop) => 72.29/9.87 (( 72.29/9.87 (breln1compI) => 72.29/9.87 (( 72.29/9.87 (breln1compE) => 72.29/9.87 (( 72.29/9.87 (breln1compEex) => 72.29/9.87 (( 72.29/9.87 (!!) @ ( 72.29/9.87 (('#B') @ ( 72.29/9.87 !!) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 !!))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#C') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 breln1)))) @ 72.29/9.87 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])). 72.29/9.87 thf(zip_derived_cl1377, plain, 72.29/9.87 (~ (((setukpairIL) => 72.29/9.87 (((setukpairIR) => 72.29/9.87 (((kpairiskpair) => 72.29/9.87 (((kpairp) => 72.29/9.87 (((singletonsubset) => 72.29/9.87 (((singletoninpowerset) => 72.29/9.87 (((singletoninpowunion) => 72.29/9.87 (((upairset2E) => 72.29/9.87 (((upairsubunion) => 72.29/9.87 (((upairinpowunion) => 72.29/9.87 (((ubforcartprodlem1) => 72.29/9.87 (((ubforcartprodlem2) => 72.29/9.87 (((ubforcartprodlem3) => 72.29/9.87 (((cartprodpairin) => 72.29/9.87 (((cartprodmempair1) => 72.29/9.87 (((cartprodmempair) => 72.29/9.87 (((setunionE2) => 72.29/9.87 (((setunionsingleton1) => 72.29/9.87 (((setunionsingleton2) => 72.29/9.87 (((setunionsingleton) => 72.29/9.87 (((singletonprop) => 72.29/9.87 (((ex1E1) => 72.29/9.87 (((ex1I) => 72.29/9.87 (((ex1I2) => 72.29/9.87 (((singletonsuniq) => 72.29/9.87 (((setukpairinjL1) => 72.29/9.87 (((kfstsingleton) => 72.29/9.87 (((theprop) => 72.29/9.87 (((kfstpairEq) => 72.29/9.87 (((cartprodfstin) => 72.29/9.87 (( 72.29/9.87 (setukpairinjL2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjL) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR11) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR12) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR1) => 72.29/9.87 (( 72.29/9.87 (upairequniteq) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR) => 72.29/9.87 (( 72.29/9.87 (ksndsingleton) => 72.29/9.87 (( 72.29/9.87 (ksndpairEq) => 72.29/9.87 (( 72.29/9.87 (kpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndin) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemEL) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemER) => 72.29/9.87 (( 72.29/9.87 (cartprodmempaircEq) => 72.29/9.87 (( 72.29/9.87 (cartprodfstpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrI) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrSub) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrERa) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL1) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL2) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrER) => 72.29/9.87 (( 72.29/9.87 (funcImageSingleton) => 72.29/9.87 (( 72.29/9.87 (apProp) => 72.29/9.87 (( 72.29/9.87 (app) => 72.29/9.87 (( 72.29/9.87 (infuncsetfunc) => 72.29/9.87 (( 72.29/9.87 (ap2p) => 72.29/9.87 (( 72.29/9.87 (funcinfuncset) => 72.29/9.87 (( 72.29/9.87 (lamProp) => 72.29/9.87 (( 72.29/9.87 (lamp) => 72.29/9.87 (( 72.29/9.87 (lam2p) => 72.29/9.87 (( 72.29/9.87 (brelnall1) => 72.29/9.87 (( 72.29/9.87 (brelnall2) => 72.29/9.87 (( 72.29/9.87 (ex1E2) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp1) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp3) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp2) => 72.29/9.87 (( 72.29/9.87 (funcextLem) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp4) => 72.29/9.87 (( 72.29/9.87 (subbreln) => 72.29/9.87 (( 72.29/9.87 (eqbreln) => 72.29/9.87 (( 72.29/9.87 (funcext) => 72.29/9.87 (( 72.29/9.87 (funcext2) => 72.29/9.87 (( 72.29/9.87 (ap2apEq1) => 72.29/9.87 (( 72.29/9.87 (ap2apEq2) => 72.29/9.87 (( 72.29/9.87 (beta1) => 72.29/9.87 (( 72.29/9.87 (eta1) => 72.29/9.87 (( 72.29/9.87 (lam2lamEq) => 72.29/9.87 (( 72.29/9.87 (beta2) => 72.29/9.87 (( 72.29/9.87 (eta2) => 72.29/9.87 (( 72.29/9.87 (iffalseProp1) => 72.29/9.87 (( 72.29/9.87 (iffalseProp2) => 72.29/9.87 (( 72.29/9.87 (iftrueProp1) => 72.29/9.87 (( 72.29/9.87 (iftrueProp2) => 72.29/9.87 (( 72.29/9.87 (ifSingleton) => 72.29/9.87 (( 72.29/9.87 (ifp) => 72.29/9.87 (( 72.29/9.87 (theeq) => 72.29/9.87 (( 72.29/9.87 (iftrue) => 72.29/9.87 (( 72.29/9.87 (iffalse) => 72.29/9.87 (( 72.29/9.87 (iftrueorfalse) => 72.29/9.87 (( 72.29/9.87 (binintersectT_lem) => 72.29/9.87 (( 72.29/9.87 (binunionT_lem) => 72.29/9.87 (( 72.29/9.87 (powersetT_lem) => 72.29/9.87 (( 72.29/9.87 (setminusT_lem) => 72.29/9.87 (( 72.29/9.87 (complementT_lem) => 72.29/9.87 (( 72.29/9.87 (setextT) => 72.29/9.87 (( 72.29/9.87 (subsetTI) => 72.29/9.87 (( 72.29/9.87 (powersetTI1) => 72.29/9.87 (( 72.29/9.87 (powersetTE1) => 72.29/9.87 (( 72.29/9.87 (complementTI1) => 72.29/9.87 (( 72.29/9.87 (complementTE1) => 72.29/9.87 (( 72.29/9.87 (binintersectTELcontra) => 72.29/9.87 (( 72.29/9.87 (binintersectTERcontra) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT1) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT2) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT3) => 72.29/9.87 (( 72.29/9.87 (doubleComplementI1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementE1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub2) => 72.29/9.87 (( 72.29/9.87 (doubleComplementEq) => 72.29/9.87 (( 72.29/9.87 (complementTnotintersectT) => 72.29/9.87 (( 72.29/9.87 (complementImpComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementSubsetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementInPowersetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (contraSubsetComplement) => 72.29/9.87 (( 72.29/9.87 (complementTcontraSubset) => 72.29/9.87 (( 72.29/9.87 (binunionTILcontra) => 72.29/9.87 (( 72.29/9.87 (binunionTIRcontra) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion2) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (intersectInPowersetIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpNotIn1) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpInComplement1) => 72.29/9.87 (( 72.29/9.87 (binunionTE) => 72.29/9.87 (( 72.29/9.87 (binunionTEcontra) => 72.29/9.87 (( 72.29/9.87 (demorgan2a1) => 72.29/9.87 (( 72.29/9.87 (complementUnionInPowersetComplement) => 72.29/9.87 (( 72.29/9.87 (demorgan2a2) => 72.29/9.87 (( 72.29/9.87 (demorgan1a) => 72.29/9.87 (( 72.29/9.87 (demorgan1b) => 72.29/9.87 (( 72.29/9.87 (demorgan1) => 72.29/9.87 (( 72.29/9.87 (demorgan2a) => 72.29/9.87 (( 72.29/9.87 (demorgan2b2) => 72.29/9.87 (( 72.29/9.87 (demorgan2b) => 72.29/9.87 (( 72.29/9.87 (demorgan2) => 72.29/9.87 (( 72.29/9.87 (woz13rule0) => 72.29/9.87 (( 72.29/9.87 (woz13rule1) => 72.29/9.87 (( 72.29/9.87 (woz13rule2) => 72.29/9.87 (( 72.29/9.87 (woz13rule3) => 72.29/9.87 (( 72.29/9.87 (woz13rule4) => 72.29/9.87 (( 72.29/9.87 (woz1_1) => 72.29/9.87 (( 72.29/9.87 (woz1_2) => 72.29/9.87 (( 72.29/9.87 (woz1_3) => 72.29/9.87 (( 72.29/9.87 (woz1_4) => 72.29/9.87 (( 72.29/9.87 (woz1_5) => 72.29/9.87 (( 72.29/9.87 (breln1all2) => 72.29/9.87 (( 72.29/9.87 (breln1SetBreln1) => 72.29/9.87 (( 72.29/9.87 (choice2fnsingleton) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln1) => 72.29/9.87 (( 72.29/9.87 (breln1all1) => 72.29/9.87 (( 72.29/9.87 (subbreln1) => 72.29/9.87 (( 72.29/9.87 (eqbreln1) => 72.29/9.87 (( 72.29/9.87 (breln1invprop) => 72.29/9.87 (( 72.29/9.87 (breln1invI) => 72.29/9.87 (( 72.29/9.87 (breln1invE) => 72.29/9.87 (( 72.29/9.87 (breln1compprop) => 72.29/9.87 (( 72.29/9.87 (breln1compI) => 72.29/9.87 (( 72.29/9.87 (breln1compE) => 72.29/9.87 (( 72.29/9.87 (breln1compEex) => 72.29/9.87 (( 72.29/9.87 (!!) @ ( 72.29/9.87 (('#B') @ ( 72.29/9.87 !!) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 !!))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#C') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 breln1)))) @ 72.29/9.87 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1369])). 72.29/9.87 thf(zip_derived_cl1386, plain, 72.29/9.87 (~ (((setukpairIR) => 72.29/9.87 (((kpairiskpair) => 72.29/9.87 (((kpairp) => 72.29/9.87 (((singletonsubset) => 72.29/9.87 (((singletoninpowerset) => 72.29/9.87 (((singletoninpowunion) => 72.29/9.87 (((upairset2E) => 72.29/9.87 (((upairsubunion) => 72.29/9.87 (((upairinpowunion) => 72.29/9.87 (((ubforcartprodlem1) => 72.29/9.87 (((ubforcartprodlem2) => 72.29/9.87 (((ubforcartprodlem3) => 72.29/9.87 (((cartprodpairin) => 72.29/9.87 (((cartprodmempair1) => 72.29/9.87 (((cartprodmempair) => 72.29/9.87 (((setunionE2) => 72.29/9.87 (((setunionsingleton1) => 72.29/9.87 (((setunionsingleton2) => 72.29/9.87 (((setunionsingleton) => 72.29/9.87 (((singletonprop) => 72.29/9.87 (((ex1E1) => 72.29/9.87 (((ex1I) => 72.29/9.87 (((ex1I2) => 72.29/9.87 (((singletonsuniq) => 72.29/9.87 (((setukpairinjL1) => 72.29/9.87 (((kfstsingleton) => 72.29/9.87 (((theprop) => 72.29/9.87 (((kfstpairEq) => 72.29/9.87 (((cartprodfstin) => 72.29/9.87 (((setukpairinjL2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjL) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR11) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR12) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR1) => 72.29/9.87 (( 72.29/9.87 (upairequniteq) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR) => 72.29/9.87 (( 72.29/9.87 (ksndsingleton) => 72.29/9.87 (( 72.29/9.87 (ksndpairEq) => 72.29/9.87 (( 72.29/9.87 (kpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndin) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemEL) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemER) => 72.29/9.87 (( 72.29/9.87 (cartprodmempaircEq) => 72.29/9.87 (( 72.29/9.87 (cartprodfstpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrI) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrSub) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrERa) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL1) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL2) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrER) => 72.29/9.87 (( 72.29/9.87 (funcImageSingleton) => 72.29/9.87 (( 72.29/9.87 (apProp) => 72.29/9.87 (( 72.29/9.87 (app) => 72.29/9.87 (( 72.29/9.87 (infuncsetfunc) => 72.29/9.87 (( 72.29/9.87 (ap2p) => 72.29/9.87 (( 72.29/9.87 (funcinfuncset) => 72.29/9.87 (( 72.29/9.87 (lamProp) => 72.29/9.87 (( 72.29/9.87 (lamp) => 72.29/9.87 (( 72.29/9.87 (lam2p) => 72.29/9.87 (( 72.29/9.87 (brelnall1) => 72.29/9.87 (( 72.29/9.87 (brelnall2) => 72.29/9.87 (( 72.29/9.87 (ex1E2) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp1) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp3) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp2) => 72.29/9.87 (( 72.29/9.87 (funcextLem) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp4) => 72.29/9.87 (( 72.29/9.87 (subbreln) => 72.29/9.87 (( 72.29/9.87 (eqbreln) => 72.29/9.87 (( 72.29/9.87 (funcext) => 72.29/9.87 (( 72.29/9.87 (funcext2) => 72.29/9.87 (( 72.29/9.87 (ap2apEq1) => 72.29/9.87 (( 72.29/9.87 (ap2apEq2) => 72.29/9.87 (( 72.29/9.87 (beta1) => 72.29/9.87 (( 72.29/9.87 (eta1) => 72.29/9.87 (( 72.29/9.87 (lam2lamEq) => 72.29/9.87 (( 72.29/9.87 (beta2) => 72.29/9.87 (( 72.29/9.87 (eta2) => 72.29/9.87 (( 72.29/9.87 (iffalseProp1) => 72.29/9.87 (( 72.29/9.87 (iffalseProp2) => 72.29/9.87 (( 72.29/9.87 (iftrueProp1) => 72.29/9.87 (( 72.29/9.87 (iftrueProp2) => 72.29/9.87 (( 72.29/9.87 (ifSingleton) => 72.29/9.87 (( 72.29/9.87 (ifp) => 72.29/9.87 (( 72.29/9.87 (theeq) => 72.29/9.87 (( 72.29/9.87 (iftrue) => 72.29/9.87 (( 72.29/9.87 (iffalse) => 72.29/9.87 (( 72.29/9.87 (iftrueorfalse) => 72.29/9.87 (( 72.29/9.87 (binintersectT_lem) => 72.29/9.87 (( 72.29/9.87 (binunionT_lem) => 72.29/9.87 (( 72.29/9.87 (powersetT_lem) => 72.29/9.87 (( 72.29/9.87 (setminusT_lem) => 72.29/9.87 (( 72.29/9.87 (complementT_lem) => 72.29/9.87 (( 72.29/9.87 (setextT) => 72.29/9.87 (( 72.29/9.87 (subsetTI) => 72.29/9.87 (( 72.29/9.87 (powersetTI1) => 72.29/9.87 (( 72.29/9.87 (powersetTE1) => 72.29/9.87 (( 72.29/9.87 (complementTI1) => 72.29/9.87 (( 72.29/9.87 (complementTE1) => 72.29/9.87 (( 72.29/9.87 (binintersectTELcontra) => 72.29/9.87 (( 72.29/9.87 (binintersectTERcontra) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT1) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT2) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT3) => 72.29/9.87 (( 72.29/9.87 (doubleComplementI1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementE1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub2) => 72.29/9.87 (( 72.29/9.87 (doubleComplementEq) => 72.29/9.87 (( 72.29/9.87 (complementTnotintersectT) => 72.29/9.87 (( 72.29/9.87 (complementImpComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementSubsetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementInPowersetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (contraSubsetComplement) => 72.29/9.87 (( 72.29/9.87 (complementTcontraSubset) => 72.29/9.87 (( 72.29/9.87 (binunionTILcontra) => 72.29/9.87 (( 72.29/9.87 (binunionTIRcontra) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion2) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (intersectInPowersetIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpNotIn1) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpInComplement1) => 72.29/9.87 (( 72.29/9.87 (binunionTE) => 72.29/9.87 (( 72.29/9.87 (binunionTEcontra) => 72.29/9.87 (( 72.29/9.87 (demorgan2a1) => 72.29/9.87 (( 72.29/9.87 (complementUnionInPowersetComplement) => 72.29/9.87 (( 72.29/9.87 (demorgan2a2) => 72.29/9.87 (( 72.29/9.87 (demorgan1a) => 72.29/9.87 (( 72.29/9.87 (demorgan1b) => 72.29/9.87 (( 72.29/9.87 (demorgan1) => 72.29/9.87 (( 72.29/9.87 (demorgan2a) => 72.29/9.87 (( 72.29/9.87 (demorgan2b2) => 72.29/9.87 (( 72.29/9.87 (demorgan2b) => 72.29/9.87 (( 72.29/9.87 (demorgan2) => 72.29/9.87 (( 72.29/9.87 (woz13rule0) => 72.29/9.87 (( 72.29/9.87 (woz13rule1) => 72.29/9.87 (( 72.29/9.87 (woz13rule2) => 72.29/9.87 (( 72.29/9.87 (woz13rule3) => 72.29/9.87 (( 72.29/9.87 (woz13rule4) => 72.29/9.87 (( 72.29/9.87 (woz1_1) => 72.29/9.87 (( 72.29/9.87 (woz1_2) => 72.29/9.87 (( 72.29/9.87 (woz1_3) => 72.29/9.87 (( 72.29/9.87 (woz1_4) => 72.29/9.87 (( 72.29/9.87 (woz1_5) => 72.29/9.87 (( 72.29/9.87 (breln1all2) => 72.29/9.87 (( 72.29/9.87 (breln1SetBreln1) => 72.29/9.87 (( 72.29/9.87 (choice2fnsingleton) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln1) => 72.29/9.87 (( 72.29/9.87 (breln1all1) => 72.29/9.87 (( 72.29/9.87 (subbreln1) => 72.29/9.87 (( 72.29/9.87 (eqbreln1) => 72.29/9.87 (( 72.29/9.87 (breln1invprop) => 72.29/9.87 (( 72.29/9.87 (breln1invI) => 72.29/9.87 (( 72.29/9.87 (breln1invE) => 72.29/9.87 (( 72.29/9.87 (breln1compprop) => 72.29/9.87 (( 72.29/9.87 (breln1compI) => 72.29/9.87 (( 72.29/9.87 (breln1compE) => 72.29/9.87 (( 72.29/9.87 (breln1compEex) => 72.29/9.87 (( 72.29/9.87 (!!) @ ( 72.29/9.87 (('#B') @ ( 72.29/9.87 !!) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 !!))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#C') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 breln1)))) @ 72.29/9.87 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])). 72.29/9.87 thf(zip_derived_cl1396, plain, 72.29/9.87 (~ (((kpairiskpair) => 72.29/9.87 (((kpairp) => 72.29/9.87 (((singletonsubset) => 72.29/9.87 (((singletoninpowerset) => 72.29/9.87 (((singletoninpowunion) => 72.29/9.87 (((upairset2E) => 72.29/9.87 (((upairsubunion) => 72.29/9.87 (((upairinpowunion) => 72.29/9.87 (((ubforcartprodlem1) => 72.29/9.87 (((ubforcartprodlem2) => 72.29/9.87 (((ubforcartprodlem3) => 72.29/9.87 (((cartprodpairin) => 72.29/9.87 (((cartprodmempair1) => 72.29/9.87 (((cartprodmempair) => 72.29/9.87 (((setunionE2) => 72.29/9.87 (((setunionsingleton1) => 72.29/9.87 (((setunionsingleton2) => 72.29/9.87 (((setunionsingleton) => 72.29/9.87 (((singletonprop) => 72.29/9.87 (((ex1E1) => 72.29/9.87 (((ex1I) => 72.29/9.87 (((ex1I2) => 72.29/9.87 (((singletonsuniq) => 72.29/9.87 (((setukpairinjL1) => 72.29/9.87 (((kfstsingleton) => 72.29/9.87 (((theprop) => 72.29/9.87 (((kfstpairEq) => 72.29/9.87 (((cartprodfstin) => 72.29/9.87 (((setukpairinjL2) => 72.29/9.87 (((setukpairinjL) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR11) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR12) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR1) => 72.29/9.87 (( 72.29/9.87 (upairequniteq) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR) => 72.29/9.87 (( 72.29/9.87 (ksndsingleton) => 72.29/9.87 (( 72.29/9.87 (ksndpairEq) => 72.29/9.87 (( 72.29/9.87 (kpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndin) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemEL) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemER) => 72.29/9.87 (( 72.29/9.87 (cartprodmempaircEq) => 72.29/9.87 (( 72.29/9.87 (cartprodfstpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrI) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrSub) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrERa) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL1) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL2) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrER) => 72.29/9.87 (( 72.29/9.87 (funcImageSingleton) => 72.29/9.87 (( 72.29/9.87 (apProp) => 72.29/9.87 (( 72.29/9.87 (app) => 72.29/9.87 (( 72.29/9.87 (infuncsetfunc) => 72.29/9.87 (( 72.29/9.87 (ap2p) => 72.29/9.87 (( 72.29/9.87 (funcinfuncset) => 72.29/9.87 (( 72.29/9.87 (lamProp) => 72.29/9.87 (( 72.29/9.87 (lamp) => 72.29/9.87 (( 72.29/9.87 (lam2p) => 72.29/9.87 (( 72.29/9.87 (brelnall1) => 72.29/9.87 (( 72.29/9.87 (brelnall2) => 72.29/9.87 (( 72.29/9.87 (ex1E2) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp1) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp3) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp2) => 72.29/9.87 (( 72.29/9.87 (funcextLem) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp4) => 72.29/9.87 (( 72.29/9.87 (subbreln) => 72.29/9.87 (( 72.29/9.87 (eqbreln) => 72.29/9.87 (( 72.29/9.87 (funcext) => 72.29/9.87 (( 72.29/9.87 (funcext2) => 72.29/9.87 (( 72.29/9.87 (ap2apEq1) => 72.29/9.87 (( 72.29/9.87 (ap2apEq2) => 72.29/9.87 (( 72.29/9.87 (beta1) => 72.29/9.87 (( 72.29/9.87 (eta1) => 72.29/9.87 (( 72.29/9.87 (lam2lamEq) => 72.29/9.87 (( 72.29/9.87 (beta2) => 72.29/9.87 (( 72.29/9.87 (eta2) => 72.29/9.87 (( 72.29/9.87 (iffalseProp1) => 72.29/9.87 (( 72.29/9.87 (iffalseProp2) => 72.29/9.87 (( 72.29/9.87 (iftrueProp1) => 72.29/9.87 (( 72.29/9.87 (iftrueProp2) => 72.29/9.87 (( 72.29/9.87 (ifSingleton) => 72.29/9.87 (( 72.29/9.87 (ifp) => 72.29/9.87 (( 72.29/9.87 (theeq) => 72.29/9.87 (( 72.29/9.87 (iftrue) => 72.29/9.87 (( 72.29/9.87 (iffalse) => 72.29/9.87 (( 72.29/9.87 (iftrueorfalse) => 72.29/9.87 (( 72.29/9.87 (binintersectT_lem) => 72.29/9.87 (( 72.29/9.87 (binunionT_lem) => 72.29/9.87 (( 72.29/9.87 (powersetT_lem) => 72.29/9.87 (( 72.29/9.87 (setminusT_lem) => 72.29/9.87 (( 72.29/9.87 (complementT_lem) => 72.29/9.87 (( 72.29/9.87 (setextT) => 72.29/9.87 (( 72.29/9.87 (subsetTI) => 72.29/9.87 (( 72.29/9.87 (powersetTI1) => 72.29/9.87 (( 72.29/9.87 (powersetTE1) => 72.29/9.87 (( 72.29/9.87 (complementTI1) => 72.29/9.87 (( 72.29/9.87 (complementTE1) => 72.29/9.87 (( 72.29/9.87 (binintersectTELcontra) => 72.29/9.87 (( 72.29/9.87 (binintersectTERcontra) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT1) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT2) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT3) => 72.29/9.87 (( 72.29/9.87 (doubleComplementI1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementE1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub2) => 72.29/9.87 (( 72.29/9.87 (doubleComplementEq) => 72.29/9.87 (( 72.29/9.87 (complementTnotintersectT) => 72.29/9.87 (( 72.29/9.87 (complementImpComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementSubsetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementInPowersetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (contraSubsetComplement) => 72.29/9.87 (( 72.29/9.87 (complementTcontraSubset) => 72.29/9.87 (( 72.29/9.87 (binunionTILcontra) => 72.29/9.87 (( 72.29/9.87 (binunionTIRcontra) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion2) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (intersectInPowersetIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpNotIn1) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpInComplement1) => 72.29/9.87 (( 72.29/9.87 (binunionTE) => 72.29/9.87 (( 72.29/9.87 (binunionTEcontra) => 72.29/9.87 (( 72.29/9.87 (demorgan2a1) => 72.29/9.87 (( 72.29/9.87 (complementUnionInPowersetComplement) => 72.29/9.87 (( 72.29/9.87 (demorgan2a2) => 72.29/9.87 (( 72.29/9.87 (demorgan1a) => 72.29/9.87 (( 72.29/9.87 (demorgan1b) => 72.29/9.87 (( 72.29/9.87 (demorgan1) => 72.29/9.87 (( 72.29/9.87 (demorgan2a) => 72.29/9.87 (( 72.29/9.87 (demorgan2b2) => 72.29/9.87 (( 72.29/9.87 (demorgan2b) => 72.29/9.87 (( 72.29/9.87 (demorgan2) => 72.29/9.87 (( 72.29/9.87 (woz13rule0) => 72.29/9.87 (( 72.29/9.87 (woz13rule1) => 72.29/9.87 (( 72.29/9.87 (woz13rule2) => 72.29/9.87 (( 72.29/9.87 (woz13rule3) => 72.29/9.87 (( 72.29/9.87 (woz13rule4) => 72.29/9.87 (( 72.29/9.87 (woz1_1) => 72.29/9.87 (( 72.29/9.87 (woz1_2) => 72.29/9.87 (( 72.29/9.87 (woz1_3) => 72.29/9.87 (( 72.29/9.87 (woz1_4) => 72.29/9.87 (( 72.29/9.87 (woz1_5) => 72.29/9.87 (( 72.29/9.87 (breln1all2) => 72.29/9.87 (( 72.29/9.87 (breln1SetBreln1) => 72.29/9.87 (( 72.29/9.87 (choice2fnsingleton) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln1) => 72.29/9.87 (( 72.29/9.87 (breln1all1) => 72.29/9.87 (( 72.29/9.87 (subbreln1) => 72.29/9.87 (( 72.29/9.87 (eqbreln1) => 72.29/9.87 (( 72.29/9.87 (breln1invprop) => 72.29/9.87 (( 72.29/9.87 (breln1invI) => 72.29/9.87 (( 72.29/9.87 (breln1invE) => 72.29/9.87 (( 72.29/9.87 (breln1compprop) => 72.29/9.87 (( 72.29/9.87 (breln1compI) => 72.29/9.87 (( 72.29/9.87 (breln1compE) => 72.29/9.87 (( 72.29/9.87 (breln1compEex) => 72.29/9.87 (( 72.29/9.87 (!!) @ ( 72.29/9.87 (('#B') @ ( 72.29/9.87 !!) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 !!))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#C') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 breln1)))) @ 72.29/9.87 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1386])). 72.29/9.87 thf(zip_derived_cl1407, plain, 72.29/9.87 (~ (((kpairp) => 72.29/9.87 (((singletonsubset) => 72.29/9.87 (((singletoninpowerset) => 72.29/9.87 (((singletoninpowunion) => 72.29/9.87 (((upairset2E) => 72.29/9.87 (((upairsubunion) => 72.29/9.87 (((upairinpowunion) => 72.29/9.87 (((ubforcartprodlem1) => 72.29/9.87 (((ubforcartprodlem2) => 72.29/9.87 (((ubforcartprodlem3) => 72.29/9.87 (((cartprodpairin) => 72.29/9.87 (((cartprodmempair1) => 72.29/9.87 (((cartprodmempair) => 72.29/9.87 (((setunionE2) => 72.29/9.87 (((setunionsingleton1) => 72.29/9.87 (((setunionsingleton2) => 72.29/9.87 (((setunionsingleton) => 72.29/9.87 (((singletonprop) => 72.29/9.87 (((ex1E1) => 72.29/9.87 (((ex1I) => 72.29/9.87 (((ex1I2) => 72.29/9.87 (((singletonsuniq) => 72.29/9.87 (((setukpairinjL1) => 72.29/9.87 (((kfstsingleton) => 72.29/9.87 (((theprop) => 72.29/9.87 (((kfstpairEq) => 72.29/9.87 (((cartprodfstin) => 72.29/9.87 (((setukpairinjL2) => 72.29/9.87 (((setukpairinjL) => 72.29/9.87 (((setukpairinjR11) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR12) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR1) => 72.29/9.87 (( 72.29/9.87 (upairequniteq) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR) => 72.29/9.87 (( 72.29/9.87 (ksndsingleton) => 72.29/9.87 (( 72.29/9.87 (ksndpairEq) => 72.29/9.87 (( 72.29/9.87 (kpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndin) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemEL) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemER) => 72.29/9.87 (( 72.29/9.87 (cartprodmempaircEq) => 72.29/9.87 (( 72.29/9.87 (cartprodfstpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrI) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrSub) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrERa) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL1) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL2) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrER) => 72.29/9.87 (( 72.29/9.87 (funcImageSingleton) => 72.29/9.87 (( 72.29/9.87 (apProp) => 72.29/9.87 (( 72.29/9.87 (app) => 72.29/9.87 (( 72.29/9.87 (infuncsetfunc) => 72.29/9.87 (( 72.29/9.87 (ap2p) => 72.29/9.87 (( 72.29/9.87 (funcinfuncset) => 72.29/9.87 (( 72.29/9.87 (lamProp) => 72.29/9.87 (( 72.29/9.87 (lamp) => 72.29/9.87 (( 72.29/9.87 (lam2p) => 72.29/9.87 (( 72.29/9.87 (brelnall1) => 72.29/9.87 (( 72.29/9.87 (brelnall2) => 72.29/9.87 (( 72.29/9.87 (ex1E2) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp1) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp3) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp2) => 72.29/9.87 (( 72.29/9.87 (funcextLem) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp4) => 72.29/9.87 (( 72.29/9.87 (subbreln) => 72.29/9.87 (( 72.29/9.87 (eqbreln) => 72.29/9.87 (( 72.29/9.87 (funcext) => 72.29/9.87 (( 72.29/9.87 (funcext2) => 72.29/9.87 (( 72.29/9.87 (ap2apEq1) => 72.29/9.87 (( 72.29/9.87 (ap2apEq2) => 72.29/9.87 (( 72.29/9.87 (beta1) => 72.29/9.87 (( 72.29/9.87 (eta1) => 72.29/9.87 (( 72.29/9.87 (lam2lamEq) => 72.29/9.87 (( 72.29/9.87 (beta2) => 72.29/9.87 (( 72.29/9.87 (eta2) => 72.29/9.87 (( 72.29/9.87 (iffalseProp1) => 72.29/9.87 (( 72.29/9.87 (iffalseProp2) => 72.29/9.87 (( 72.29/9.87 (iftrueProp1) => 72.29/9.87 (( 72.29/9.87 (iftrueProp2) => 72.29/9.87 (( 72.29/9.87 (ifSingleton) => 72.29/9.87 (( 72.29/9.87 (ifp) => 72.29/9.87 (( 72.29/9.87 (theeq) => 72.29/9.87 (( 72.29/9.87 (iftrue) => 72.29/9.87 (( 72.29/9.87 (iffalse) => 72.29/9.87 (( 72.29/9.87 (iftrueorfalse) => 72.29/9.87 (( 72.29/9.87 (binintersectT_lem) => 72.29/9.87 (( 72.29/9.87 (binunionT_lem) => 72.29/9.87 (( 72.29/9.87 (powersetT_lem) => 72.29/9.87 (( 72.29/9.87 (setminusT_lem) => 72.29/9.87 (( 72.29/9.87 (complementT_lem) => 72.29/9.87 (( 72.29/9.87 (setextT) => 72.29/9.87 (( 72.29/9.87 (subsetTI) => 72.29/9.87 (( 72.29/9.87 (powersetTI1) => 72.29/9.87 (( 72.29/9.87 (powersetTE1) => 72.29/9.87 (( 72.29/9.87 (complementTI1) => 72.29/9.87 (( 72.29/9.87 (complementTE1) => 72.29/9.87 (( 72.29/9.87 (binintersectTELcontra) => 72.29/9.87 (( 72.29/9.87 (binintersectTERcontra) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT1) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT2) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT3) => 72.29/9.87 (( 72.29/9.87 (doubleComplementI1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementE1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub2) => 72.29/9.87 (( 72.29/9.87 (doubleComplementEq) => 72.29/9.87 (( 72.29/9.87 (complementTnotintersectT) => 72.29/9.87 (( 72.29/9.87 (complementImpComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementSubsetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementInPowersetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (contraSubsetComplement) => 72.29/9.87 (( 72.29/9.87 (complementTcontraSubset) => 72.29/9.87 (( 72.29/9.87 (binunionTILcontra) => 72.29/9.87 (( 72.29/9.87 (binunionTIRcontra) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion2) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (intersectInPowersetIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpNotIn1) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpInComplement1) => 72.29/9.87 (( 72.29/9.87 (binunionTE) => 72.29/9.87 (( 72.29/9.87 (binunionTEcontra) => 72.29/9.87 (( 72.29/9.87 (demorgan2a1) => 72.29/9.87 (( 72.29/9.87 (complementUnionInPowersetComplement) => 72.29/9.87 (( 72.29/9.87 (demorgan2a2) => 72.29/9.87 (( 72.29/9.87 (demorgan1a) => 72.29/9.87 (( 72.29/9.87 (demorgan1b) => 72.29/9.87 (( 72.29/9.87 (demorgan1) => 72.29/9.87 (( 72.29/9.87 (demorgan2a) => 72.29/9.87 (( 72.29/9.87 (demorgan2b2) => 72.29/9.87 (( 72.29/9.87 (demorgan2b) => 72.29/9.87 (( 72.29/9.87 (demorgan2) => 72.29/9.87 (( 72.29/9.87 (woz13rule0) => 72.29/9.87 (( 72.29/9.87 (woz13rule1) => 72.29/9.87 (( 72.29/9.87 (woz13rule2) => 72.29/9.87 (( 72.29/9.87 (woz13rule3) => 72.29/9.87 (( 72.29/9.87 (woz13rule4) => 72.29/9.87 (( 72.29/9.87 (woz1_1) => 72.29/9.87 (( 72.29/9.87 (woz1_2) => 72.29/9.87 (( 72.29/9.87 (woz1_3) => 72.29/9.87 (( 72.29/9.87 (woz1_4) => 72.29/9.87 (( 72.29/9.87 (woz1_5) => 72.29/9.87 (( 72.29/9.87 (breln1all2) => 72.29/9.87 (( 72.29/9.87 (breln1SetBreln1) => 72.29/9.87 (( 72.29/9.87 (choice2fnsingleton) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln1) => 72.29/9.87 (( 72.29/9.87 (breln1all1) => 72.29/9.87 (( 72.29/9.87 (subbreln1) => 72.29/9.87 (( 72.29/9.87 (eqbreln1) => 72.29/9.87 (( 72.29/9.87 (breln1invprop) => 72.29/9.87 (( 72.29/9.87 (breln1invI) => 72.29/9.87 (( 72.29/9.87 (breln1invE) => 72.29/9.87 (( 72.29/9.87 (breln1compprop) => 72.29/9.87 (( 72.29/9.87 (breln1compI) => 72.29/9.87 (( 72.29/9.87 (breln1compE) => 72.29/9.87 (( 72.29/9.87 (breln1compEex) => 72.29/9.87 (( 72.29/9.87 (!!) @ ( 72.29/9.87 (('#B') @ ( 72.29/9.87 !!) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 !!))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#C') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 breln1)))) @ 72.29/9.87 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])). 72.29/9.87 thf(zip_derived_cl1420, plain, 72.29/9.87 (~ (((singletonsubset) => 72.29/9.87 (((singletoninpowerset) => 72.29/9.87 (((singletoninpowunion) => 72.29/9.87 (((upairset2E) => 72.29/9.87 (((upairsubunion) => 72.29/9.87 (((upairinpowunion) => 72.29/9.87 (((ubforcartprodlem1) => 72.29/9.87 (((ubforcartprodlem2) => 72.29/9.87 (((ubforcartprodlem3) => 72.29/9.87 (((cartprodpairin) => 72.29/9.87 (((cartprodmempair1) => 72.29/9.87 (((cartprodmempair) => 72.29/9.87 (((setunionE2) => 72.29/9.87 (((setunionsingleton1) => 72.29/9.87 (((setunionsingleton2) => 72.29/9.87 (((setunionsingleton) => 72.29/9.87 (((singletonprop) => 72.29/9.87 (((ex1E1) => 72.29/9.87 (((ex1I) => 72.29/9.87 (((ex1I2) => 72.29/9.87 (((singletonsuniq) => 72.29/9.87 (((setukpairinjL1) => 72.29/9.87 (((kfstsingleton) => 72.29/9.87 (((theprop) => 72.29/9.87 (((kfstpairEq) => 72.29/9.87 (((cartprodfstin) => 72.29/9.87 (((setukpairinjL2) => 72.29/9.87 (((setukpairinjL) => 72.29/9.87 (((setukpairinjR11) => 72.29/9.87 (((setukpairinjR12) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR1) => 72.29/9.87 (( 72.29/9.87 (upairequniteq) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR) => 72.29/9.87 (( 72.29/9.87 (ksndsingleton) => 72.29/9.87 (( 72.29/9.87 (ksndpairEq) => 72.29/9.87 (( 72.29/9.87 (kpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndin) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemEL) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemER) => 72.29/9.87 (( 72.29/9.87 (cartprodmempaircEq) => 72.29/9.87 (( 72.29/9.87 (cartprodfstpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrI) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrSub) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrERa) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL1) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL2) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrER) => 72.29/9.87 (( 72.29/9.87 (funcImageSingleton) => 72.29/9.87 (( 72.29/9.87 (apProp) => 72.29/9.87 (( 72.29/9.87 (app) => 72.29/9.87 (( 72.29/9.87 (infuncsetfunc) => 72.29/9.87 (( 72.29/9.87 (ap2p) => 72.29/9.87 (( 72.29/9.87 (funcinfuncset) => 72.29/9.87 (( 72.29/9.87 (lamProp) => 72.29/9.87 (( 72.29/9.87 (lamp) => 72.29/9.87 (( 72.29/9.87 (lam2p) => 72.29/9.87 (( 72.29/9.87 (brelnall1) => 72.29/9.87 (( 72.29/9.87 (brelnall2) => 72.29/9.87 (( 72.29/9.87 (ex1E2) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp1) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp3) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp2) => 72.29/9.87 (( 72.29/9.87 (funcextLem) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp4) => 72.29/9.87 (( 72.29/9.87 (subbreln) => 72.29/9.87 (( 72.29/9.87 (eqbreln) => 72.29/9.87 (( 72.29/9.87 (funcext) => 72.29/9.87 (( 72.29/9.87 (funcext2) => 72.29/9.87 (( 72.29/9.87 (ap2apEq1) => 72.29/9.87 (( 72.29/9.87 (ap2apEq2) => 72.29/9.87 (( 72.29/9.87 (beta1) => 72.29/9.87 (( 72.29/9.87 (eta1) => 72.29/9.87 (( 72.29/9.87 (lam2lamEq) => 72.29/9.87 (( 72.29/9.87 (beta2) => 72.29/9.87 (( 72.29/9.87 (eta2) => 72.29/9.87 (( 72.29/9.87 (iffalseProp1) => 72.29/9.87 (( 72.29/9.87 (iffalseProp2) => 72.29/9.87 (( 72.29/9.87 (iftrueProp1) => 72.29/9.87 (( 72.29/9.87 (iftrueProp2) => 72.29/9.87 (( 72.29/9.87 (ifSingleton) => 72.29/9.87 (( 72.29/9.87 (ifp) => 72.29/9.87 (( 72.29/9.87 (theeq) => 72.29/9.87 (( 72.29/9.87 (iftrue) => 72.29/9.87 (( 72.29/9.87 (iffalse) => 72.29/9.87 (( 72.29/9.87 (iftrueorfalse) => 72.29/9.87 (( 72.29/9.87 (binintersectT_lem) => 72.29/9.87 (( 72.29/9.87 (binunionT_lem) => 72.29/9.87 (( 72.29/9.87 (powersetT_lem) => 72.29/9.87 (( 72.29/9.87 (setminusT_lem) => 72.29/9.87 (( 72.29/9.87 (complementT_lem) => 72.29/9.87 (( 72.29/9.87 (setextT) => 72.29/9.87 (( 72.29/9.87 (subsetTI) => 72.29/9.87 (( 72.29/9.87 (powersetTI1) => 72.29/9.87 (( 72.29/9.87 (powersetTE1) => 72.29/9.87 (( 72.29/9.87 (complementTI1) => 72.29/9.87 (( 72.29/9.87 (complementTE1) => 72.29/9.87 (( 72.29/9.87 (binintersectTELcontra) => 72.29/9.87 (( 72.29/9.87 (binintersectTERcontra) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT1) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT2) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT3) => 72.29/9.87 (( 72.29/9.87 (doubleComplementI1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementE1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub2) => 72.29/9.87 (( 72.29/9.87 (doubleComplementEq) => 72.29/9.87 (( 72.29/9.87 (complementTnotintersectT) => 72.29/9.87 (( 72.29/9.87 (complementImpComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementSubsetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementInPowersetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (contraSubsetComplement) => 72.29/9.87 (( 72.29/9.87 (complementTcontraSubset) => 72.29/9.87 (( 72.29/9.87 (binunionTILcontra) => 72.29/9.87 (( 72.29/9.87 (binunionTIRcontra) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion2) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (intersectInPowersetIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpNotIn1) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpInComplement1) => 72.29/9.87 (( 72.29/9.87 (binunionTE) => 72.29/9.87 (( 72.29/9.87 (binunionTEcontra) => 72.29/9.87 (( 72.29/9.87 (demorgan2a1) => 72.29/9.87 (( 72.29/9.87 (complementUnionInPowersetComplement) => 72.29/9.87 (( 72.29/9.87 (demorgan2a2) => 72.29/9.87 (( 72.29/9.87 (demorgan1a) => 72.29/9.87 (( 72.29/9.87 (demorgan1b) => 72.29/9.87 (( 72.29/9.87 (demorgan1) => 72.29/9.87 (( 72.29/9.87 (demorgan2a) => 72.29/9.87 (( 72.29/9.87 (demorgan2b2) => 72.29/9.87 (( 72.29/9.87 (demorgan2b) => 72.29/9.87 (( 72.29/9.87 (demorgan2) => 72.29/9.87 (( 72.29/9.87 (woz13rule0) => 72.29/9.87 (( 72.29/9.87 (woz13rule1) => 72.29/9.87 (( 72.29/9.87 (woz13rule2) => 72.29/9.87 (( 72.29/9.87 (woz13rule3) => 72.29/9.87 (( 72.29/9.87 (woz13rule4) => 72.29/9.87 (( 72.29/9.87 (woz1_1) => 72.29/9.87 (( 72.29/9.87 (woz1_2) => 72.29/9.87 (( 72.29/9.87 (woz1_3) => 72.29/9.87 (( 72.29/9.87 (woz1_4) => 72.29/9.87 (( 72.29/9.87 (woz1_5) => 72.29/9.87 (( 72.29/9.87 (breln1all2) => 72.29/9.87 (( 72.29/9.87 (breln1SetBreln1) => 72.29/9.87 (( 72.29/9.87 (choice2fnsingleton) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln1) => 72.29/9.87 (( 72.29/9.87 (breln1all1) => 72.29/9.87 (( 72.29/9.87 (subbreln1) => 72.29/9.87 (( 72.29/9.87 (eqbreln1) => 72.29/9.87 (( 72.29/9.87 (breln1invprop) => 72.29/9.87 (( 72.29/9.87 (breln1invI) => 72.29/9.87 (( 72.29/9.87 (breln1invE) => 72.29/9.87 (( 72.29/9.87 (breln1compprop) => 72.29/9.87 (( 72.29/9.87 (breln1compI) => 72.29/9.87 (( 72.29/9.87 (breln1compE) => 72.29/9.87 (( 72.29/9.87 (breln1compEex) => 72.29/9.87 (( 72.29/9.87 (!!) @ ( 72.29/9.87 (('#B') @ ( 72.29/9.87 !!) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 !!))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#C') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 breln1)))) @ 72.29/9.87 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1407])). 72.29/9.87 thf(zip_derived_cl1433, plain, 72.29/9.87 (~ (((singletoninpowerset) => 72.29/9.87 (((singletoninpowunion) => 72.29/9.87 (((upairset2E) => 72.29/9.87 (((upairsubunion) => 72.29/9.87 (((upairinpowunion) => 72.29/9.87 (((ubforcartprodlem1) => 72.29/9.87 (((ubforcartprodlem2) => 72.29/9.87 (((ubforcartprodlem3) => 72.29/9.87 (((cartprodpairin) => 72.29/9.87 (((cartprodmempair1) => 72.29/9.87 (((cartprodmempair) => 72.29/9.87 (((setunionE2) => 72.29/9.87 (((setunionsingleton1) => 72.29/9.87 (((setunionsingleton2) => 72.29/9.87 (((setunionsingleton) => 72.29/9.87 (((singletonprop) => 72.29/9.87 (((ex1E1) => 72.29/9.87 (((ex1I) => 72.29/9.87 (((ex1I2) => 72.29/9.87 (((singletonsuniq) => 72.29/9.87 (((setukpairinjL1) => 72.29/9.87 (((kfstsingleton) => 72.29/9.87 (((theprop) => 72.29/9.87 (((kfstpairEq) => 72.29/9.87 (((cartprodfstin) => 72.29/9.87 (((setukpairinjL2) => 72.29/9.87 (((setukpairinjL) => 72.29/9.87 (((setukpairinjR11) => 72.29/9.87 (((setukpairinjR12) => 72.29/9.87 (((setukpairinjR1) => 72.29/9.87 (( 72.29/9.87 (upairequniteq) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR) => 72.29/9.87 (( 72.29/9.87 (ksndsingleton) => 72.29/9.87 (( 72.29/9.87 (ksndpairEq) => 72.29/9.87 (( 72.29/9.87 (kpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndin) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemEL) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemER) => 72.29/9.87 (( 72.29/9.87 (cartprodmempaircEq) => 72.29/9.87 (( 72.29/9.87 (cartprodfstpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrI) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrSub) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrERa) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL1) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL2) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrER) => 72.29/9.87 (( 72.29/9.87 (funcImageSingleton) => 72.29/9.87 (( 72.29/9.87 (apProp) => 72.29/9.87 (( 72.29/9.87 (app) => 72.29/9.87 (( 72.29/9.87 (infuncsetfunc) => 72.29/9.87 (( 72.29/9.87 (ap2p) => 72.29/9.87 (( 72.29/9.87 (funcinfuncset) => 72.29/9.87 (( 72.29/9.87 (lamProp) => 72.29/9.87 (( 72.29/9.87 (lamp) => 72.29/9.87 (( 72.29/9.87 (lam2p) => 72.29/9.87 (( 72.29/9.87 (brelnall1) => 72.29/9.87 (( 72.29/9.87 (brelnall2) => 72.29/9.87 (( 72.29/9.87 (ex1E2) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp1) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp3) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp2) => 72.29/9.87 (( 72.29/9.87 (funcextLem) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp4) => 72.29/9.87 (( 72.29/9.87 (subbreln) => 72.29/9.87 (( 72.29/9.87 (eqbreln) => 72.29/9.87 (( 72.29/9.87 (funcext) => 72.29/9.87 (( 72.29/9.87 (funcext2) => 72.29/9.87 (( 72.29/9.87 (ap2apEq1) => 72.29/9.87 (( 72.29/9.87 (ap2apEq2) => 72.29/9.87 (( 72.29/9.87 (beta1) => 72.29/9.87 (( 72.29/9.87 (eta1) => 72.29/9.87 (( 72.29/9.87 (lam2lamEq) => 72.29/9.87 (( 72.29/9.87 (beta2) => 72.29/9.87 (( 72.29/9.87 (eta2) => 72.29/9.87 (( 72.29/9.87 (iffalseProp1) => 72.29/9.87 (( 72.29/9.87 (iffalseProp2) => 72.29/9.87 (( 72.29/9.87 (iftrueProp1) => 72.29/9.87 (( 72.29/9.87 (iftrueProp2) => 72.29/9.87 (( 72.29/9.87 (ifSingleton) => 72.29/9.87 (( 72.29/9.87 (ifp) => 72.29/9.87 (( 72.29/9.87 (theeq) => 72.29/9.87 (( 72.29/9.87 (iftrue) => 72.29/9.87 (( 72.29/9.87 (iffalse) => 72.29/9.87 (( 72.29/9.87 (iftrueorfalse) => 72.29/9.87 (( 72.29/9.87 (binintersectT_lem) => 72.29/9.87 (( 72.29/9.87 (binunionT_lem) => 72.29/9.87 (( 72.29/9.87 (powersetT_lem) => 72.29/9.87 (( 72.29/9.87 (setminusT_lem) => 72.29/9.87 (( 72.29/9.87 (complementT_lem) => 72.29/9.87 (( 72.29/9.87 (setextT) => 72.29/9.87 (( 72.29/9.87 (subsetTI) => 72.29/9.87 (( 72.29/9.87 (powersetTI1) => 72.29/9.87 (( 72.29/9.87 (powersetTE1) => 72.29/9.87 (( 72.29/9.87 (complementTI1) => 72.29/9.87 (( 72.29/9.87 (complementTE1) => 72.29/9.87 (( 72.29/9.87 (binintersectTELcontra) => 72.29/9.87 (( 72.29/9.87 (binintersectTERcontra) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT1) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT2) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT3) => 72.29/9.87 (( 72.29/9.87 (doubleComplementI1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementE1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub2) => 72.29/9.87 (( 72.29/9.87 (doubleComplementEq) => 72.29/9.87 (( 72.29/9.87 (complementTnotintersectT) => 72.29/9.87 (( 72.29/9.87 (complementImpComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementSubsetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementInPowersetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (contraSubsetComplement) => 72.29/9.87 (( 72.29/9.87 (complementTcontraSubset) => 72.29/9.87 (( 72.29/9.87 (binunionTILcontra) => 72.29/9.87 (( 72.29/9.87 (binunionTIRcontra) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion2) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (intersectInPowersetIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpNotIn1) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpInComplement1) => 72.29/9.87 (( 72.29/9.87 (binunionTE) => 72.29/9.87 (( 72.29/9.87 (binunionTEcontra) => 72.29/9.87 (( 72.29/9.87 (demorgan2a1) => 72.29/9.87 (( 72.29/9.87 (complementUnionInPowersetComplement) => 72.29/9.87 (( 72.29/9.87 (demorgan2a2) => 72.29/9.87 (( 72.29/9.87 (demorgan1a) => 72.29/9.87 (( 72.29/9.87 (demorgan1b) => 72.29/9.87 (( 72.29/9.87 (demorgan1) => 72.29/9.87 (( 72.29/9.87 (demorgan2a) => 72.29/9.87 (( 72.29/9.87 (demorgan2b2) => 72.29/9.87 (( 72.29/9.87 (demorgan2b) => 72.29/9.87 (( 72.29/9.87 (demorgan2) => 72.29/9.87 (( 72.29/9.87 (woz13rule0) => 72.29/9.87 (( 72.29/9.87 (woz13rule1) => 72.29/9.87 (( 72.29/9.87 (woz13rule2) => 72.29/9.87 (( 72.29/9.87 (woz13rule3) => 72.29/9.87 (( 72.29/9.87 (woz13rule4) => 72.29/9.87 (( 72.29/9.87 (woz1_1) => 72.29/9.87 (( 72.29/9.87 (woz1_2) => 72.29/9.87 (( 72.29/9.87 (woz1_3) => 72.29/9.87 (( 72.29/9.87 (woz1_4) => 72.29/9.87 (( 72.29/9.87 (woz1_5) => 72.29/9.87 (( 72.29/9.87 (breln1all2) => 72.29/9.87 (( 72.29/9.87 (breln1SetBreln1) => 72.29/9.87 (( 72.29/9.87 (choice2fnsingleton) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln1) => 72.29/9.87 (( 72.29/9.87 (breln1all1) => 72.29/9.87 (( 72.29/9.87 (subbreln1) => 72.29/9.87 (( 72.29/9.87 (eqbreln1) => 72.29/9.87 (( 72.29/9.87 (breln1invprop) => 72.29/9.87 (( 72.29/9.87 (breln1invI) => 72.29/9.87 (( 72.29/9.87 (breln1invE) => 72.29/9.87 (( 72.29/9.87 (breln1compprop) => 72.29/9.87 (( 72.29/9.87 (breln1compI) => 72.29/9.87 (( 72.29/9.87 (breln1compE) => 72.29/9.87 (( 72.29/9.87 (breln1compEex) => 72.29/9.87 (( 72.29/9.87 (!!) @ ( 72.29/9.87 (('#B') @ ( 72.29/9.87 !!) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 !!))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#C') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 breln1)))) @ 72.29/9.87 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1420])). 72.29/9.87 thf(zip_derived_cl1444, plain, 72.29/9.87 (~ (((singletoninpowunion) => 72.29/9.87 (((upairset2E) => 72.29/9.87 (((upairsubunion) => 72.29/9.87 (((upairinpowunion) => 72.29/9.87 (((ubforcartprodlem1) => 72.29/9.87 (((ubforcartprodlem2) => 72.29/9.87 (((ubforcartprodlem3) => 72.29/9.87 (((cartprodpairin) => 72.29/9.87 (((cartprodmempair1) => 72.29/9.87 (((cartprodmempair) => 72.29/9.87 (((setunionE2) => 72.29/9.87 (((setunionsingleton1) => 72.29/9.87 (((setunionsingleton2) => 72.29/9.87 (((setunionsingleton) => 72.29/9.87 (((singletonprop) => 72.29/9.87 (((ex1E1) => 72.29/9.87 (((ex1I) => 72.29/9.87 (((ex1I2) => 72.29/9.87 (((singletonsuniq) => 72.29/9.87 (((setukpairinjL1) => 72.29/9.87 (((kfstsingleton) => 72.29/9.87 (((theprop) => 72.29/9.87 (((kfstpairEq) => 72.29/9.87 (((cartprodfstin) => 72.29/9.87 (((setukpairinjL2) => 72.29/9.87 (((setukpairinjL) => 72.29/9.87 (((setukpairinjR11) => 72.29/9.87 (((setukpairinjR12) => 72.29/9.87 (((setukpairinjR1) => 72.29/9.87 (((upairequniteq) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR) => 72.29/9.87 (( 72.29/9.87 (ksndsingleton) => 72.29/9.87 (( 72.29/9.87 (ksndpairEq) => 72.29/9.87 (( 72.29/9.87 (kpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndin) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemEL) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemER) => 72.29/9.87 (( 72.29/9.87 (cartprodmempaircEq) => 72.29/9.87 (( 72.29/9.87 (cartprodfstpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrI) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrSub) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrERa) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL1) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL2) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrER) => 72.29/9.87 (( 72.29/9.87 (funcImageSingleton) => 72.29/9.87 (( 72.29/9.87 (apProp) => 72.29/9.87 (( 72.29/9.87 (app) => 72.29/9.87 (( 72.29/9.87 (infuncsetfunc) => 72.29/9.87 (( 72.29/9.87 (ap2p) => 72.29/9.87 (( 72.29/9.87 (funcinfuncset) => 72.29/9.87 (( 72.29/9.87 (lamProp) => 72.29/9.87 (( 72.29/9.87 (lamp) => 72.29/9.87 (( 72.29/9.87 (lam2p) => 72.29/9.87 (( 72.29/9.87 (brelnall1) => 72.29/9.87 (( 72.29/9.87 (brelnall2) => 72.29/9.87 (( 72.29/9.87 (ex1E2) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp1) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp3) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp2) => 72.29/9.87 (( 72.29/9.87 (funcextLem) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp4) => 72.29/9.87 (( 72.29/9.87 (subbreln) => 72.29/9.87 (( 72.29/9.87 (eqbreln) => 72.29/9.87 (( 72.29/9.87 (funcext) => 72.29/9.87 (( 72.29/9.87 (funcext2) => 72.29/9.87 (( 72.29/9.87 (ap2apEq1) => 72.29/9.87 (( 72.29/9.87 (ap2apEq2) => 72.29/9.87 (( 72.29/9.87 (beta1) => 72.29/9.87 (( 72.29/9.87 (eta1) => 72.29/9.87 (( 72.29/9.87 (lam2lamEq) => 72.29/9.87 (( 72.29/9.87 (beta2) => 72.29/9.87 (( 72.29/9.87 (eta2) => 72.29/9.87 (( 72.29/9.87 (iffalseProp1) => 72.29/9.87 (( 72.29/9.87 (iffalseProp2) => 72.29/9.87 (( 72.29/9.87 (iftrueProp1) => 72.29/9.87 (( 72.29/9.87 (iftrueProp2) => 72.29/9.87 (( 72.29/9.87 (ifSingleton) => 72.29/9.87 (( 72.29/9.87 (ifp) => 72.29/9.87 (( 72.29/9.87 (theeq) => 72.29/9.87 (( 72.29/9.87 (iftrue) => 72.29/9.87 (( 72.29/9.87 (iffalse) => 72.29/9.87 (( 72.29/9.87 (iftrueorfalse) => 72.29/9.87 (( 72.29/9.87 (binintersectT_lem) => 72.29/9.87 (( 72.29/9.87 (binunionT_lem) => 72.29/9.87 (( 72.29/9.87 (powersetT_lem) => 72.29/9.87 (( 72.29/9.87 (setminusT_lem) => 72.29/9.87 (( 72.29/9.87 (complementT_lem) => 72.29/9.87 (( 72.29/9.87 (setextT) => 72.29/9.87 (( 72.29/9.87 (subsetTI) => 72.29/9.87 (( 72.29/9.87 (powersetTI1) => 72.29/9.87 (( 72.29/9.87 (powersetTE1) => 72.29/9.87 (( 72.29/9.87 (complementTI1) => 72.29/9.87 (( 72.29/9.87 (complementTE1) => 72.29/9.87 (( 72.29/9.87 (binintersectTELcontra) => 72.29/9.87 (( 72.29/9.87 (binintersectTERcontra) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT1) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT2) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT3) => 72.29/9.87 (( 72.29/9.87 (doubleComplementI1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementE1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub2) => 72.29/9.87 (( 72.29/9.87 (doubleComplementEq) => 72.29/9.87 (( 72.29/9.87 (complementTnotintersectT) => 72.29/9.87 (( 72.29/9.87 (complementImpComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementSubsetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementInPowersetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (contraSubsetComplement) => 72.29/9.87 (( 72.29/9.87 (complementTcontraSubset) => 72.29/9.87 (( 72.29/9.87 (binunionTILcontra) => 72.29/9.87 (( 72.29/9.87 (binunionTIRcontra) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion2) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (intersectInPowersetIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpNotIn1) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpInComplement1) => 72.29/9.87 (( 72.29/9.87 (binunionTE) => 72.29/9.87 (( 72.29/9.87 (binunionTEcontra) => 72.29/9.87 (( 72.29/9.87 (demorgan2a1) => 72.29/9.87 (( 72.29/9.87 (complementUnionInPowersetComplement) => 72.29/9.87 (( 72.29/9.87 (demorgan2a2) => 72.29/9.87 (( 72.29/9.87 (demorgan1a) => 72.29/9.87 (( 72.29/9.87 (demorgan1b) => 72.29/9.87 (( 72.29/9.87 (demorgan1) => 72.29/9.87 (( 72.29/9.87 (demorgan2a) => 72.29/9.87 (( 72.29/9.87 (demorgan2b2) => 72.29/9.87 (( 72.29/9.87 (demorgan2b) => 72.29/9.87 (( 72.29/9.87 (demorgan2) => 72.29/9.87 (( 72.29/9.87 (woz13rule0) => 72.29/9.87 (( 72.29/9.87 (woz13rule1) => 72.29/9.87 (( 72.29/9.87 (woz13rule2) => 72.29/9.87 (( 72.29/9.87 (woz13rule3) => 72.29/9.87 (( 72.29/9.87 (woz13rule4) => 72.29/9.87 (( 72.29/9.87 (woz1_1) => 72.29/9.87 (( 72.29/9.87 (woz1_2) => 72.29/9.87 (( 72.29/9.87 (woz1_3) => 72.29/9.87 (( 72.29/9.87 (woz1_4) => 72.29/9.87 (( 72.29/9.87 (woz1_5) => 72.29/9.87 (( 72.29/9.87 (breln1all2) => 72.29/9.87 (( 72.29/9.87 (breln1SetBreln1) => 72.29/9.87 (( 72.29/9.87 (choice2fnsingleton) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln1) => 72.29/9.87 (( 72.29/9.87 (breln1all1) => 72.29/9.87 (( 72.29/9.87 (subbreln1) => 72.29/9.87 (( 72.29/9.87 (eqbreln1) => 72.29/9.87 (( 72.29/9.87 (breln1invprop) => 72.29/9.87 (( 72.29/9.87 (breln1invI) => 72.29/9.87 (( 72.29/9.87 (breln1invE) => 72.29/9.87 (( 72.29/9.87 (breln1compprop) => 72.29/9.87 (( 72.29/9.87 (breln1compI) => 72.29/9.87 (( 72.29/9.87 (breln1compE) => 72.29/9.87 (( 72.29/9.87 (breln1compEex) => 72.29/9.87 (( 72.29/9.87 (!!) @ ( 72.29/9.87 (('#B') @ ( 72.29/9.87 !!) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 !!))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#C') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 breln1)))) @ 72.29/9.87 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1433])). 72.29/9.87 thf(zip_derived_cl1452, plain, 72.29/9.87 (~ (((upairset2E) => 72.29/9.87 (((upairsubunion) => 72.29/9.87 (((upairinpowunion) => 72.29/9.87 (((ubforcartprodlem1) => 72.29/9.87 (((ubforcartprodlem2) => 72.29/9.87 (((ubforcartprodlem3) => 72.29/9.87 (((cartprodpairin) => 72.29/9.87 (((cartprodmempair1) => 72.29/9.87 (((cartprodmempair) => 72.29/9.87 (((setunionE2) => 72.29/9.87 (((setunionsingleton1) => 72.29/9.87 (((setunionsingleton2) => 72.29/9.87 (((setunionsingleton) => 72.29/9.87 (((singletonprop) => 72.29/9.87 (((ex1E1) => 72.29/9.87 (((ex1I) => 72.29/9.87 (((ex1I2) => 72.29/9.87 (((singletonsuniq) => 72.29/9.87 (((setukpairinjL1) => 72.29/9.87 (((kfstsingleton) => 72.29/9.87 (((theprop) => 72.29/9.87 (((kfstpairEq) => 72.29/9.87 (((cartprodfstin) => 72.29/9.87 (((setukpairinjL2) => 72.29/9.87 (((setukpairinjL) => 72.29/9.87 (((setukpairinjR11) => 72.29/9.87 (((setukpairinjR12) => 72.29/9.87 (((setukpairinjR1) => 72.29/9.87 (((upairequniteq) => 72.29/9.87 (((setukpairinjR2) => 72.29/9.87 (( 72.29/9.87 (setukpairinjR) => 72.29/9.87 (( 72.29/9.87 (ksndsingleton) => 72.29/9.87 (( 72.29/9.87 (ksndpairEq) => 72.29/9.87 (( 72.29/9.87 (kpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndin) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemEL) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemER) => 72.29/9.87 (( 72.29/9.87 (cartprodmempaircEq) => 72.29/9.87 (( 72.29/9.87 (cartprodfstpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrI) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrSub) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrERa) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL1) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL2) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrER) => 72.29/9.87 (( 72.29/9.87 (funcImageSingleton) => 72.29/9.87 (( 72.29/9.87 (apProp) => 72.29/9.87 (( 72.29/9.87 (app) => 72.29/9.87 (( 72.29/9.87 (infuncsetfunc) => 72.29/9.87 (( 72.29/9.87 (ap2p) => 72.29/9.87 (( 72.29/9.87 (funcinfuncset) => 72.29/9.87 (( 72.29/9.87 (lamProp) => 72.29/9.87 (( 72.29/9.87 (lamp) => 72.29/9.87 (( 72.29/9.87 (lam2p) => 72.29/9.87 (( 72.29/9.87 (brelnall1) => 72.29/9.87 (( 72.29/9.87 (brelnall2) => 72.29/9.87 (( 72.29/9.87 (ex1E2) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp1) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp3) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp2) => 72.29/9.87 (( 72.29/9.87 (funcextLem) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp4) => 72.29/9.87 (( 72.29/9.87 (subbreln) => 72.29/9.87 (( 72.29/9.87 (eqbreln) => 72.29/9.87 (( 72.29/9.87 (funcext) => 72.29/9.87 (( 72.29/9.87 (funcext2) => 72.29/9.87 (( 72.29/9.87 (ap2apEq1) => 72.29/9.87 (( 72.29/9.87 (ap2apEq2) => 72.29/9.87 (( 72.29/9.87 (beta1) => 72.29/9.87 (( 72.29/9.87 (eta1) => 72.29/9.87 (( 72.29/9.87 (lam2lamEq) => 72.29/9.87 (( 72.29/9.87 (beta2) => 72.29/9.87 (( 72.29/9.87 (eta2) => 72.29/9.87 (( 72.29/9.87 (iffalseProp1) => 72.29/9.87 (( 72.29/9.87 (iffalseProp2) => 72.29/9.87 (( 72.29/9.87 (iftrueProp1) => 72.29/9.87 (( 72.29/9.87 (iftrueProp2) => 72.29/9.87 (( 72.29/9.87 (ifSingleton) => 72.29/9.87 (( 72.29/9.87 (ifp) => 72.29/9.87 (( 72.29/9.87 (theeq) => 72.29/9.87 (( 72.29/9.87 (iftrue) => 72.29/9.87 (( 72.29/9.87 (iffalse) => 72.29/9.87 (( 72.29/9.87 (iftrueorfalse) => 72.29/9.87 (( 72.29/9.87 (binintersectT_lem) => 72.29/9.87 (( 72.29/9.87 (binunionT_lem) => 72.29/9.87 (( 72.29/9.87 (powersetT_lem) => 72.29/9.87 (( 72.29/9.87 (setminusT_lem) => 72.29/9.87 (( 72.29/9.87 (complementT_lem) => 72.29/9.87 (( 72.29/9.87 (setextT) => 72.29/9.87 (( 72.29/9.87 (subsetTI) => 72.29/9.87 (( 72.29/9.87 (powersetTI1) => 72.29/9.87 (( 72.29/9.87 (powersetTE1) => 72.29/9.87 (( 72.29/9.87 (complementTI1) => 72.29/9.87 (( 72.29/9.87 (complementTE1) => 72.29/9.87 (( 72.29/9.87 (binintersectTELcontra) => 72.29/9.87 (( 72.29/9.87 (binintersectTERcontra) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT1) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT2) => 72.29/9.87 (( 72.29/9.87 (contrasubsetT3) => 72.29/9.87 (( 72.29/9.87 (doubleComplementI1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementE1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub1) => 72.29/9.87 (( 72.29/9.87 (doubleComplementSub2) => 72.29/9.87 (( 72.29/9.87 (doubleComplementEq) => 72.29/9.87 (( 72.29/9.87 (complementTnotintersectT) => 72.29/9.87 (( 72.29/9.87 (complementImpComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementSubsetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (complementInPowersetComplementIntersect) => 72.29/9.87 (( 72.29/9.87 (contraSubsetComplement) => 72.29/9.87 (( 72.29/9.87 (complementTcontraSubset) => 72.29/9.87 (( 72.29/9.87 (binunionTILcontra) => 72.29/9.87 (( 72.29/9.87 (binunionTIRcontra) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInUnion2) => 72.29/9.87 (( 72.29/9.87 (inIntersectImpInIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (intersectInPowersetIntersectUnions) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpNotIn1) => 72.29/9.87 (( 72.29/9.87 (inComplementUnionImpInComplement1) => 72.29/9.87 (( 72.29/9.87 (binunionTE) => 72.29/9.87 (( 72.29/9.87 (binunionTEcontra) => 72.29/9.87 (( 72.29/9.87 (demorgan2a1) => 72.29/9.87 (( 72.29/9.87 (complementUnionInPowersetComplement) => 72.29/9.87 (( 72.29/9.87 (demorgan2a2) => 72.29/9.87 (( 72.29/9.87 (demorgan1a) => 72.29/9.87 (( 72.29/9.87 (demorgan1b) => 72.29/9.87 (( 72.29/9.87 (demorgan1) => 72.29/9.87 (( 72.29/9.87 (demorgan2a) => 72.29/9.87 (( 72.29/9.87 (demorgan2b2) => 72.29/9.87 (( 72.29/9.87 (demorgan2b) => 72.29/9.87 (( 72.29/9.87 (demorgan2) => 72.29/9.87 (( 72.29/9.87 (woz13rule0) => 72.29/9.87 (( 72.29/9.87 (woz13rule1) => 72.29/9.87 (( 72.29/9.87 (woz13rule2) => 72.29/9.87 (( 72.29/9.87 (woz13rule3) => 72.29/9.87 (( 72.29/9.87 (woz13rule4) => 72.29/9.87 (( 72.29/9.87 (woz1_1) => 72.29/9.87 (( 72.29/9.87 (woz1_2) => 72.29/9.87 (( 72.29/9.87 (woz1_3) => 72.29/9.87 (( 72.29/9.87 (woz1_4) => 72.29/9.87 (( 72.29/9.87 (woz1_5) => 72.29/9.87 (( 72.29/9.87 (breln1all2) => 72.29/9.87 (( 72.29/9.87 (breln1SetBreln1) => 72.29/9.87 (( 72.29/9.87 (choice2fnsingleton) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln1) => 72.29/9.87 (( 72.29/9.87 (breln1all1) => 72.29/9.87 (( 72.29/9.87 (subbreln1) => 72.29/9.87 (( 72.29/9.87 (eqbreln1) => 72.29/9.87 (( 72.29/9.87 (breln1invprop) => 72.29/9.87 (( 72.29/9.87 (breln1invI) => 72.29/9.87 (( 72.29/9.87 (breln1invE) => 72.29/9.87 (( 72.29/9.87 (breln1compprop) => 72.29/9.87 (( 72.29/9.87 (breln1compI) => 72.29/9.87 (( 72.29/9.87 (breln1compE) => 72.29/9.87 (( 72.29/9.87 (breln1compEex) => 72.29/9.87 (( 72.29/9.87 (!!) @ ( 72.29/9.87 (('#B') @ ( 72.29/9.87 !!) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 !!))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#S') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#S') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 =>))) @ 72.29/9.87 breln1)))))) @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#C') @ ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 ( 72.29/9.87 ( 72.29/9.87 ('#B') @ ( 72.29/9.87 '#B') @ 72.29/9.87 breln1)))) @ 72.29/9.87 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1444])). 72.29/9.87 thf(zip_derived_cl1459, plain, 72.29/9.87 (~ (((upairsubunion) => 72.29/9.87 (((upairinpowunion) => 72.29/9.87 (((ubforcartprodlem1) => 72.29/9.87 (((ubforcartprodlem2) => 72.29/9.87 (((ubforcartprodlem3) => 72.29/9.87 (((cartprodpairin) => 72.29/9.87 (((cartprodmempair1) => 72.29/9.87 (((cartprodmempair) => 72.29/9.87 (((setunionE2) => 72.29/9.87 (((setunionsingleton1) => 72.29/9.87 (((setunionsingleton2) => 72.29/9.87 (((setunionsingleton) => 72.29/9.87 (((singletonprop) => 72.29/9.87 (((ex1E1) => 72.29/9.87 (((ex1I) => 72.29/9.87 (((ex1I2) => 72.29/9.87 (((singletonsuniq) => 72.29/9.87 (((setukpairinjL1) => 72.29/9.87 (((kfstsingleton) => 72.29/9.87 (((theprop) => 72.29/9.87 (((kfstpairEq) => 72.29/9.87 (((cartprodfstin) => 72.29/9.87 (((setukpairinjL2) => 72.29/9.87 (((setukpairinjL) => 72.29/9.87 (((setukpairinjR11) => 72.29/9.87 (((setukpairinjR12) => 72.29/9.87 (((setukpairinjR1) => 72.29/9.87 (((upairequniteq) => 72.29/9.87 (((setukpairinjR2) => 72.29/9.87 (((setukpairinjR) => 72.29/9.87 (( 72.29/9.87 (ksndsingleton) => 72.29/9.87 (( 72.29/9.87 (ksndpairEq) => 72.29/9.87 (( 72.29/9.87 (kpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndin) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemEL) => 72.29/9.87 (( 72.29/9.87 (cartprodpairmemER) => 72.29/9.87 (( 72.29/9.87 (cartprodmempaircEq) => 72.29/9.87 (( 72.29/9.87 (cartprodfstpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodsndpairEq) => 72.29/9.87 (( 72.29/9.87 (cartprodpairsurjEq) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrI) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrSub) => 72.29/9.87 (( 72.29/9.87 (setOfPairsIsBReln) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrERa) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL1) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrEL2) => 72.29/9.87 (( 72.29/9.87 (dpsetconstrER) => 72.29/9.87 (( 72.29/9.87 (funcImageSingleton) => 72.29/9.87 (( 72.29/9.87 (apProp) => 72.29/9.87 (( 72.29/9.87 (app) => 72.29/9.87 (( 72.29/9.87 (infuncsetfunc) => 72.29/9.87 (( 72.29/9.87 (ap2p) => 72.29/9.87 (( 72.29/9.87 (funcinfuncset) => 72.29/9.87 (( 72.29/9.87 (lamProp) => 72.29/9.87 (( 72.29/9.87 (lamp) => 72.29/9.87 (( 72.29/9.87 (lam2p) => 72.29/9.87 (( 72.29/9.87 (brelnall1) => 72.29/9.87 (( 72.29/9.87 (brelnall2) => 72.29/9.87 (( 72.29/9.87 (ex1E2) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp1) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp3) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp2) => 72.29/9.87 (( 72.29/9.87 (funcextLem) => 72.29/9.87 (( 72.29/9.87 (funcGraphProp4) => 72.29/9.87 (( 72.29/9.87 (subbreln) => 72.29/9.87 (( 72.29/9.87 (eqbreln) => 72.29/9.87 (( 72.29/9.87 (funcext) => 72.29/9.87 (( 72.29/9.87 (funcext2) => 72.29/9.87 (( 72.29/9.87 (ap2apEq1) => 72.29/9.87 (( 72.29/9.87 (ap2apEq2) => 72.29/9.87 (( 72.29/9.87 (beta1) => 72.29/9.87 (( 72.29/9.87 (eta1) => 72.29/9.87 (( 72.29/9.87 (lam2lamEq) => 72.29/9.87 (( 72.29/9.87 (beta2) => 72.29/9.87 (( 72.29/9.87 (eta2) => 72.29/9.87 (( 72.29/9.87 (iffalseProp1) => 72.29/9.87 (( 72.29/9.87 (iffalseProp2) => 72.29/9.87 (( 72.29/9.87 (iftrueProp1) => 72.29/9.87 (( 72.29/9.87 (iftrueProp2) => 72.29/9.87 (( 72.29/9.87 (ifSingleton) => 72.29/9.87 (( 72.29/9.87 (ifp) => 72.29/9.87 (( 72.29/9.87 (theeq) => 72.29/9.87 (( 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72.29/9.87 (binunionTEcontra) => 72.29/9.87 (( 72.29/9.87 (demorgan2a1) => 72.29/9.87 (( 72.29/9.87 (complementUnionInPowersetComplement) => 72.29/9.87 (( 72.29/9.87 (demorgan2a2) => 72.29/9.87 (( 72.29/9.87 (demorgan1a) => 72.29/9.87 (( 72.29/9.88 (demorgan1b) => 72.29/9.88 (( 72.29/9.88 (demorgan1) => 72.29/9.88 (( 72.29/9.88 (demorgan2a) => 72.29/9.88 (( 72.29/9.88 (demorgan2b2) => 72.29/9.88 (( 72.29/9.88 (demorgan2b) => 72.29/9.88 (( 72.29/9.88 (demorgan2) => 72.29/9.88 (( 72.29/9.88 (woz13rule0) => 72.29/9.88 (( 72.29/9.88 (woz13rule1) => 72.29/9.88 (( 72.29/9.88 (woz13rule2) => 72.29/9.88 (( 72.29/9.88 (woz13rule3) => 72.29/9.88 (( 72.29/9.88 (woz13rule4) => 72.29/9.88 (( 72.29/9.88 (woz1_1) => 72.29/9.88 (( 72.29/9.88 (woz1_2) => 72.29/9.88 (( 72.29/9.88 (woz1_3) => 72.29/9.88 (( 72.29/9.88 (woz1_4) => 72.29/9.88 (( 72.29/9.88 (woz1_5) => 72.29/9.88 (( 72.29/9.88 (breln1all2) => 72.29/9.88 (( 72.29/9.88 (breln1SetBreln1) => 72.29/9.88 (( 72.29/9.88 (choice2fnsingleton) => 72.29/9.88 (( 72.29/9.88 (setOfPairsIsBReln1) => 72.29/9.88 (( 72.29/9.88 (breln1all1) => 72.29/9.88 (( 72.29/9.88 (subbreln1) => 72.29/9.88 (( 72.29/9.88 (eqbreln1) => 72.29/9.88 (( 72.29/9.88 (breln1invprop) => 72.29/9.88 (( 72.29/9.88 (breln1invI) => 72.29/9.88 (( 72.29/9.88 (breln1invE) => 72.29/9.88 (( 72.29/9.88 (breln1compprop) => 72.29/9.88 (( 72.29/9.88 (breln1compI) => 72.29/9.88 (( 72.29/9.88 (breln1compE) => 72.29/9.88 (( 72.29/9.88 (breln1compEex) => 72.29/9.88 (( 72.29/9.88 (!!) @ ( 72.29/9.88 (('#B') @ ( 72.29/9.88 !!) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 !!))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#C') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 breln1)))) @ 72.29/9.88 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1452])). 72.29/9.88 thf(zip_derived_cl1466, plain, 72.29/9.88 (~ (((upairinpowunion) => 72.29/9.88 (((ubforcartprodlem1) => 72.29/9.88 (((ubforcartprodlem2) => 72.29/9.88 (((ubforcartprodlem3) => 72.29/9.88 (((cartprodpairin) => 72.29/9.88 (((cartprodmempair1) => 72.29/9.88 (((cartprodmempair) => 72.29/9.88 (((setunionE2) => 72.29/9.88 (((setunionsingleton1) => 72.29/9.88 (((setunionsingleton2) => 72.29/9.88 (((setunionsingleton) => 72.29/9.88 (((singletonprop) => 72.29/9.88 (((ex1E1) => 72.29/9.88 (((ex1I) => 72.29/9.88 (((ex1I2) => 72.29/9.88 (((singletonsuniq) => 72.29/9.88 (((setukpairinjL1) => 72.29/9.88 (((kfstsingleton) => 72.29/9.88 (((theprop) => 72.29/9.88 (((kfstpairEq) => 72.29/9.88 (((cartprodfstin) => 72.29/9.88 (((setukpairinjL2) => 72.29/9.88 (((setukpairinjL) => 72.29/9.88 (((setukpairinjR11) => 72.29/9.88 (((setukpairinjR12) => 72.29/9.88 (((setukpairinjR1) => 72.29/9.88 (((upairequniteq) => 72.29/9.88 (((setukpairinjR2) => 72.29/9.88 (((setukpairinjR) => 72.29/9.88 (((ksndsingleton) => 72.29/9.88 (( 72.29/9.88 (ksndpairEq) => 72.29/9.88 (( 72.29/9.88 (kpairsurjEq) => 72.29/9.88 (( 72.29/9.88 (cartprodsndin) => 72.29/9.88 (( 72.29/9.88 (cartprodpairmemEL) => 72.29/9.88 (( 72.29/9.88 (cartprodpairmemER) => 72.29/9.88 (( 72.29/9.88 (cartprodmempaircEq) => 72.29/9.88 (( 72.29/9.88 (cartprodfstpairEq) => 72.29/9.88 (( 72.29/9.88 (cartprodsndpairEq) => 72.29/9.88 (( 72.29/9.88 (cartprodpairsurjEq) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrI) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrSub) => 72.29/9.88 (( 72.29/9.88 (setOfPairsIsBReln) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrERa) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrEL1) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrEL2) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrER) => 72.29/9.88 (( 72.29/9.88 (funcImageSingleton) => 72.29/9.88 (( 72.29/9.88 (apProp) => 72.29/9.88 (( 72.29/9.88 (app) => 72.29/9.88 (( 72.29/9.88 (infuncsetfunc) => 72.29/9.88 (( 72.29/9.88 (ap2p) => 72.29/9.88 (( 72.29/9.88 (funcinfuncset) => 72.29/9.88 (( 72.29/9.88 (lamProp) => 72.29/9.88 (( 72.29/9.88 (lamp) => 72.29/9.88 (( 72.29/9.88 (lam2p) => 72.29/9.88 (( 72.29/9.88 (brelnall1) => 72.29/9.88 (( 72.29/9.88 (brelnall2) => 72.29/9.88 (( 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(iffalse) => 72.29/9.88 (( 72.29/9.88 (iftrueorfalse) => 72.29/9.88 (( 72.29/9.88 (binintersectT_lem) => 72.29/9.88 (( 72.29/9.88 (binunionT_lem) => 72.29/9.88 (( 72.29/9.88 (powersetT_lem) => 72.29/9.88 (( 72.29/9.88 (setminusT_lem) => 72.29/9.88 (( 72.29/9.88 (complementT_lem) => 72.29/9.88 (( 72.29/9.88 (setextT) => 72.29/9.88 (( 72.29/9.88 (subsetTI) => 72.29/9.88 (( 72.29/9.88 (powersetTI1) => 72.29/9.88 (( 72.29/9.88 (powersetTE1) => 72.29/9.88 (( 72.29/9.88 (complementTI1) => 72.29/9.88 (( 72.29/9.88 (complementTE1) => 72.29/9.88 (( 72.29/9.88 (binintersectTELcontra) => 72.29/9.88 (( 72.29/9.88 (binintersectTERcontra) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT1) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT2) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT3) => 72.29/9.88 (( 72.29/9.88 (doubleComplementI1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementE1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementSub1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementSub2) => 72.29/9.88 (( 72.29/9.88 (doubleComplementEq) => 72.29/9.88 (( 72.29/9.88 (complementTnotintersectT) => 72.29/9.88 (( 72.29/9.88 (complementImpComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (complementSubsetComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (complementInPowersetComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (contraSubsetComplement) => 72.29/9.88 (( 72.29/9.88 (complementTcontraSubset) => 72.29/9.88 (( 72.29/9.88 (binunionTILcontra) => 72.29/9.88 (( 72.29/9.88 (binunionTIRcontra) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInUnion) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInUnion2) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInIntersectUnions) => 72.29/9.88 (( 72.29/9.88 (intersectInPowersetIntersectUnions) => 72.29/9.88 (( 72.29/9.88 (inComplementUnionImpNotIn1) => 72.29/9.88 (( 72.29/9.88 (inComplementUnionImpInComplement1) => 72.29/9.88 (( 72.29/9.88 (binunionTE) => 72.29/9.88 (( 72.29/9.88 (binunionTEcontra) => 72.29/9.88 (( 72.29/9.88 (demorgan2a1) => 72.29/9.88 (( 72.29/9.88 (complementUnionInPowersetComplement) => 72.29/9.88 (( 72.29/9.88 (demorgan2a2) => 72.29/9.88 (( 72.29/9.88 (demorgan1a) => 72.29/9.88 (( 72.29/9.88 (demorgan1b) => 72.29/9.88 (( 72.29/9.88 (demorgan1) => 72.29/9.88 (( 72.29/9.88 (demorgan2a) => 72.29/9.88 (( 72.29/9.88 (demorgan2b2) => 72.29/9.88 (( 72.29/9.88 (demorgan2b) => 72.29/9.88 (( 72.29/9.88 (demorgan2) => 72.29/9.88 (( 72.29/9.88 (woz13rule0) => 72.29/9.88 (( 72.29/9.88 (woz13rule1) => 72.29/9.88 (( 72.29/9.88 (woz13rule2) => 72.29/9.88 (( 72.29/9.88 (woz13rule3) => 72.29/9.88 (( 72.29/9.88 (woz13rule4) => 72.29/9.88 (( 72.29/9.88 (woz1_1) => 72.29/9.88 (( 72.29/9.88 (woz1_2) => 72.29/9.88 (( 72.29/9.88 (woz1_3) => 72.29/9.88 (( 72.29/9.88 (woz1_4) => 72.29/9.88 (( 72.29/9.88 (woz1_5) => 72.29/9.88 (( 72.29/9.88 (breln1all2) => 72.29/9.88 (( 72.29/9.88 (breln1SetBreln1) => 72.29/9.88 (( 72.29/9.88 (choice2fnsingleton) => 72.29/9.88 (( 72.29/9.88 (setOfPairsIsBReln1) => 72.29/9.88 (( 72.29/9.88 (breln1all1) => 72.29/9.88 (( 72.29/9.88 (subbreln1) => 72.29/9.88 (( 72.29/9.88 (eqbreln1) => 72.29/9.88 (( 72.29/9.88 (breln1invprop) => 72.29/9.88 (( 72.29/9.88 (breln1invI) => 72.29/9.88 (( 72.29/9.88 (breln1invE) => 72.29/9.88 (( 72.29/9.88 (breln1compprop) => 72.29/9.88 (( 72.29/9.88 (breln1compI) => 72.29/9.88 (( 72.29/9.88 (breln1compE) => 72.29/9.88 (( 72.29/9.88 (breln1compEex) => 72.29/9.88 (( 72.29/9.88 (!!) @ ( 72.29/9.88 (('#B') @ ( 72.29/9.88 !!) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 !!))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#C') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 breln1)))) @ 72.29/9.88 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1459])). 72.29/9.88 thf(zip_derived_cl1473, plain, 72.29/9.88 (~ (((ubforcartprodlem1) => 72.29/9.88 (((ubforcartprodlem2) => 72.29/9.88 (((ubforcartprodlem3) => 72.29/9.88 (((cartprodpairin) => 72.29/9.88 (((cartprodmempair1) => 72.29/9.88 (((cartprodmempair) => 72.29/9.88 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breln1)))))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#C') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 breln1)))) @ 72.29/9.88 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1466])). 72.29/9.88 thf(zip_derived_cl1480, plain, 72.29/9.88 (~ (((ubforcartprodlem2) => 72.29/9.88 (((ubforcartprodlem3) => 72.29/9.88 (((cartprodpairin) => 72.29/9.88 (((cartprodmempair1) => 72.29/9.88 (((cartprodmempair) => 72.29/9.88 (((setunionE2) => 72.29/9.88 (((setunionsingleton1) => 72.29/9.88 (((setunionsingleton2) => 72.29/9.88 (((setunionsingleton) => 72.29/9.88 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72.29/9.88 (demorgan2a) => 72.29/9.88 (( 72.29/9.88 (demorgan2b2) => 72.29/9.88 (( 72.29/9.88 (demorgan2b) => 72.29/9.88 (( 72.29/9.88 (demorgan2) => 72.29/9.88 (( 72.29/9.88 (woz13rule0) => 72.29/9.88 (( 72.29/9.88 (woz13rule1) => 72.29/9.88 (( 72.29/9.88 (woz13rule2) => 72.29/9.88 (( 72.29/9.88 (woz13rule3) => 72.29/9.88 (( 72.29/9.88 (woz13rule4) => 72.29/9.88 (( 72.29/9.88 (woz1_1) => 72.29/9.88 (( 72.29/9.88 (woz1_2) => 72.29/9.88 (( 72.29/9.88 (woz1_3) => 72.29/9.88 (( 72.29/9.88 (woz1_4) => 72.29/9.88 (( 72.29/9.88 (woz1_5) => 72.29/9.88 (( 72.29/9.88 (breln1all2) => 72.29/9.88 (( 72.29/9.88 (breln1SetBreln1) => 72.29/9.88 (( 72.29/9.88 (choice2fnsingleton) => 72.29/9.88 (( 72.29/9.88 (setOfPairsIsBReln1) => 72.29/9.88 (( 72.29/9.88 (breln1all1) => 72.29/9.88 (( 72.29/9.88 (subbreln1) => 72.29/9.88 (( 72.29/9.88 (eqbreln1) => 72.29/9.88 (( 72.29/9.88 (breln1invprop) => 72.29/9.88 (( 72.29/9.88 (breln1invI) => 72.29/9.88 (( 72.29/9.88 (breln1invE) => 72.29/9.88 (( 72.29/9.88 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72.29/9.88 '#B') @ 72.29/9.88 breln1)))) @ 72.29/9.88 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1473])). 72.29/9.88 thf(zip_derived_cl1488, plain, 72.29/9.88 (~ (((ubforcartprodlem3) => 72.29/9.88 (((cartprodpairin) => 72.29/9.88 (((cartprodmempair1) => 72.29/9.88 (((cartprodmempair) => 72.29/9.88 (((setunionE2) => 72.29/9.88 (((setunionsingleton1) => 72.29/9.88 (((setunionsingleton2) => 72.29/9.88 (((setunionsingleton) => 72.29/9.88 (((singletonprop) => 72.29/9.88 (((ex1E1) => 72.29/9.88 (((ex1I) => 72.29/9.88 (((ex1I2) => 72.29/9.88 (((singletonsuniq) => 72.29/9.88 (((setukpairinjL1) => 72.29/9.88 (((kfstsingleton) => 72.29/9.88 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72.29/9.88 (dpsetconstrEL2) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrER) => 72.29/9.88 (( 72.29/9.88 (funcImageSingleton) => 72.29/9.88 (( 72.29/9.88 (apProp) => 72.29/9.88 (( 72.29/9.88 (app) => 72.29/9.88 (( 72.29/9.88 (infuncsetfunc) => 72.29/9.88 (( 72.29/9.88 (ap2p) => 72.29/9.88 (( 72.29/9.88 (funcinfuncset) => 72.29/9.88 (( 72.29/9.88 (lamProp) => 72.29/9.88 (( 72.29/9.88 (lamp) => 72.29/9.88 (( 72.29/9.88 (lam2p) => 72.29/9.88 (( 72.29/9.88 (brelnall1) => 72.29/9.88 (( 72.29/9.88 (brelnall2) => 72.29/9.88 (( 72.29/9.88 (ex1E2) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp1) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp3) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp2) => 72.29/9.88 (( 72.29/9.88 (funcextLem) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp4) => 72.29/9.88 (( 72.29/9.88 (subbreln) => 72.29/9.88 (( 72.29/9.88 (eqbreln) => 72.29/9.88 (( 72.29/9.88 (funcext) => 72.29/9.88 (( 72.29/9.88 (funcext2) => 72.29/9.88 (( 72.29/9.88 (ap2apEq1) => 72.29/9.88 (( 72.29/9.88 (ap2apEq2) => 72.29/9.88 (( 72.29/9.88 (beta1) => 72.29/9.88 (( 72.29/9.88 (eta1) => 72.29/9.88 (( 72.29/9.88 (lam2lamEq) => 72.29/9.88 (( 72.29/9.88 (beta2) => 72.29/9.88 (( 72.29/9.88 (eta2) => 72.29/9.88 (( 72.29/9.88 (iffalseProp1) => 72.29/9.88 (( 72.29/9.88 (iffalseProp2) => 72.29/9.88 (( 72.29/9.88 (iftrueProp1) => 72.29/9.88 (( 72.29/9.88 (iftrueProp2) => 72.29/9.88 (( 72.29/9.88 (ifSingleton) => 72.29/9.88 (( 72.29/9.88 (ifp) => 72.29/9.88 (( 72.29/9.88 (theeq) => 72.29/9.88 (( 72.29/9.88 (iftrue) => 72.29/9.88 (( 72.29/9.88 (iffalse) => 72.29/9.88 (( 72.29/9.88 (iftrueorfalse) => 72.29/9.88 (( 72.29/9.88 (binintersectT_lem) => 72.29/9.88 (( 72.29/9.88 (binunionT_lem) => 72.29/9.88 (( 72.29/9.88 (powersetT_lem) => 72.29/9.88 (( 72.29/9.88 (setminusT_lem) => 72.29/9.88 (( 72.29/9.88 (complementT_lem) => 72.29/9.88 (( 72.29/9.88 (setextT) => 72.29/9.88 (( 72.29/9.88 (subsetTI) => 72.29/9.88 (( 72.29/9.88 (powersetTI1) => 72.29/9.88 (( 72.29/9.88 (powersetTE1) => 72.29/9.88 (( 72.29/9.88 (complementTI1) => 72.29/9.88 (( 72.29/9.88 (complementTE1) => 72.29/9.88 (( 72.29/9.88 (binintersectTELcontra) => 72.29/9.88 (( 72.29/9.88 (binintersectTERcontra) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT1) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT2) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT3) => 72.29/9.88 (( 72.29/9.88 (doubleComplementI1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementE1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementSub1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementSub2) => 72.29/9.88 (( 72.29/9.88 (doubleComplementEq) => 72.29/9.88 (( 72.29/9.88 (complementTnotintersectT) => 72.29/9.88 (( 72.29/9.88 (complementImpComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (complementSubsetComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (complementInPowersetComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (contraSubsetComplement) => 72.29/9.88 (( 72.29/9.88 (complementTcontraSubset) => 72.29/9.88 (( 72.29/9.88 (binunionTILcontra) => 72.29/9.88 (( 72.29/9.88 (binunionTIRcontra) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInUnion) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInUnion2) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInIntersectUnions) => 72.29/9.88 (( 72.29/9.88 (intersectInPowersetIntersectUnions) => 72.29/9.88 (( 72.29/9.88 (inComplementUnionImpNotIn1) => 72.29/9.88 (( 72.29/9.88 (inComplementUnionImpInComplement1) => 72.29/9.88 (( 72.29/9.88 (binunionTE) => 72.29/9.88 (( 72.29/9.88 (binunionTEcontra) => 72.29/9.88 (( 72.29/9.88 (demorgan2a1) => 72.29/9.88 (( 72.29/9.88 (complementUnionInPowersetComplement) => 72.29/9.88 (( 72.29/9.88 (demorgan2a2) => 72.29/9.88 (( 72.29/9.88 (demorgan1a) => 72.29/9.88 (( 72.29/9.88 (demorgan1b) => 72.29/9.88 (( 72.29/9.88 (demorgan1) => 72.29/9.88 (( 72.29/9.88 (demorgan2a) => 72.29/9.88 (( 72.29/9.88 (demorgan2b2) => 72.29/9.88 (( 72.29/9.88 (demorgan2b) => 72.29/9.88 (( 72.29/9.88 (demorgan2) => 72.29/9.88 (( 72.29/9.88 (woz13rule0) => 72.29/9.88 (( 72.29/9.88 (woz13rule1) => 72.29/9.88 (( 72.29/9.88 (woz13rule2) => 72.29/9.88 (( 72.29/9.88 (woz13rule3) => 72.29/9.88 (( 72.29/9.88 (woz13rule4) => 72.29/9.88 (( 72.29/9.88 (woz1_1) => 72.29/9.88 (( 72.29/9.88 (woz1_2) => 72.29/9.88 (( 72.29/9.88 (woz1_3) => 72.29/9.88 (( 72.29/9.88 (woz1_4) => 72.29/9.88 (( 72.29/9.88 (woz1_5) => 72.29/9.88 (( 72.29/9.88 (breln1all2) => 72.29/9.88 (( 72.29/9.88 (breln1SetBreln1) => 72.29/9.88 (( 72.29/9.88 (choice2fnsingleton) => 72.29/9.88 (( 72.29/9.88 (setOfPairsIsBReln1) => 72.29/9.88 (( 72.29/9.88 (breln1all1) => 72.29/9.88 (( 72.29/9.88 (subbreln1) => 72.29/9.88 (( 72.29/9.88 (eqbreln1) => 72.29/9.88 (( 72.29/9.88 (breln1invprop) => 72.29/9.88 (( 72.29/9.88 (breln1invI) => 72.29/9.88 (( 72.29/9.88 (breln1invE) => 72.29/9.88 (( 72.29/9.88 (breln1compprop) => 72.29/9.88 (( 72.29/9.88 (breln1compI) => 72.29/9.88 (( 72.29/9.88 (breln1compE) => 72.29/9.88 (( 72.29/9.88 (breln1compEex) => 72.29/9.88 (( 72.29/9.88 (!!) @ ( 72.29/9.88 (('#B') @ ( 72.29/9.88 !!) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 !!))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#C') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 breln1)))) @ 72.29/9.88 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1480])). 72.29/9.88 thf(zip_derived_cl1496, plain, 72.29/9.88 (~ (((cartprodpairin) => 72.29/9.88 (((cartprodmempair1) => 72.29/9.88 (((cartprodmempair) => 72.29/9.88 (((setunionE2) => 72.29/9.88 (((setunionsingleton1) => 72.29/9.88 (((setunionsingleton2) => 72.29/9.88 (((setunionsingleton) => 72.29/9.88 (((singletonprop) => 72.29/9.88 (((ex1E1) => 72.29/9.88 (((ex1I) => 72.29/9.88 (((ex1I2) => 72.29/9.88 (((singletonsuniq) => 72.29/9.88 (((setukpairinjL1) => 72.29/9.88 (((kfstsingleton) => 72.29/9.88 (((theprop) => 72.29/9.88 (((kfstpairEq) => 72.29/9.88 (((cartprodfstin) => 72.29/9.88 (((setukpairinjL2) => 72.29/9.88 (((setukpairinjL) => 72.29/9.88 (((setukpairinjR11) => 72.29/9.88 (((setukpairinjR12) => 72.29/9.88 (((setukpairinjR1) => 72.29/9.88 (((upairequniteq) => 72.29/9.88 (((setukpairinjR2) => 72.29/9.88 (((setukpairinjR) => 72.29/9.88 (((ksndsingleton) => 72.29/9.88 (((ksndpairEq) => 72.29/9.88 (((kpairsurjEq) => 72.29/9.88 (((cartprodsndin) => 72.29/9.88 (((cartprodpairmemEL) => 72.29/9.88 (( 72.29/9.88 (cartprodpairmemER) => 72.29/9.88 (( 72.29/9.88 (cartprodmempaircEq) => 72.29/9.88 (( 72.29/9.88 (cartprodfstpairEq) => 72.29/9.88 (( 72.29/9.88 (cartprodsndpairEq) => 72.29/9.88 (( 72.29/9.88 (cartprodpairsurjEq) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrI) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrSub) => 72.29/9.88 (( 72.29/9.88 (setOfPairsIsBReln) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrERa) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrEL1) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrEL2) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrER) => 72.29/9.88 (( 72.29/9.88 (funcImageSingleton) => 72.29/9.88 (( 72.29/9.88 (apProp) => 72.29/9.88 (( 72.29/9.88 (app) => 72.29/9.88 (( 72.29/9.88 (infuncsetfunc) => 72.29/9.88 (( 72.29/9.88 (ap2p) => 72.29/9.88 (( 72.29/9.88 (funcinfuncset) => 72.29/9.88 (( 72.29/9.88 (lamProp) => 72.29/9.88 (( 72.29/9.88 (lamp) => 72.29/9.88 (( 72.29/9.88 (lam2p) => 72.29/9.88 (( 72.29/9.88 (brelnall1) => 72.29/9.88 (( 72.29/9.88 (brelnall2) => 72.29/9.88 (( 72.29/9.88 (ex1E2) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp1) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp3) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp2) => 72.29/9.88 (( 72.29/9.88 (funcextLem) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp4) => 72.29/9.88 (( 72.29/9.88 (subbreln) => 72.29/9.88 (( 72.29/9.88 (eqbreln) => 72.29/9.88 (( 72.29/9.88 (funcext) => 72.29/9.88 (( 72.29/9.88 (funcext2) => 72.29/9.88 (( 72.29/9.88 (ap2apEq1) => 72.29/9.88 (( 72.29/9.88 (ap2apEq2) => 72.29/9.88 (( 72.29/9.88 (beta1) => 72.29/9.88 (( 72.29/9.88 (eta1) => 72.29/9.88 (( 72.29/9.88 (lam2lamEq) => 72.29/9.88 (( 72.29/9.88 (beta2) => 72.29/9.88 (( 72.29/9.88 (eta2) => 72.29/9.88 (( 72.29/9.88 (iffalseProp1) => 72.29/9.88 (( 72.29/9.88 (iffalseProp2) => 72.29/9.88 (( 72.29/9.88 (iftrueProp1) => 72.29/9.88 (( 72.29/9.88 (iftrueProp2) => 72.29/9.88 (( 72.29/9.88 (ifSingleton) => 72.29/9.88 (( 72.29/9.88 (ifp) => 72.29/9.88 (( 72.29/9.88 (theeq) => 72.29/9.88 (( 72.29/9.88 (iftrue) => 72.29/9.88 (( 72.29/9.88 (iffalse) => 72.29/9.88 (( 72.29/9.88 (iftrueorfalse) => 72.29/9.88 (( 72.29/9.88 (binintersectT_lem) => 72.29/9.88 (( 72.29/9.88 (binunionT_lem) => 72.29/9.88 (( 72.29/9.88 (powersetT_lem) => 72.29/9.88 (( 72.29/9.88 (setminusT_lem) => 72.29/9.88 (( 72.29/9.88 (complementT_lem) => 72.29/9.88 (( 72.29/9.88 (setextT) => 72.29/9.88 (( 72.29/9.88 (subsetTI) => 72.29/9.88 (( 72.29/9.88 (powersetTI1) => 72.29/9.88 (( 72.29/9.88 (powersetTE1) => 72.29/9.88 (( 72.29/9.88 (complementTI1) => 72.29/9.88 (( 72.29/9.88 (complementTE1) => 72.29/9.88 (( 72.29/9.88 (binintersectTELcontra) => 72.29/9.88 (( 72.29/9.88 (binintersectTERcontra) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT1) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT2) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT3) => 72.29/9.88 (( 72.29/9.88 (doubleComplementI1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementE1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementSub1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementSub2) => 72.29/9.88 (( 72.29/9.88 (doubleComplementEq) => 72.29/9.88 (( 72.29/9.88 (complementTnotintersectT) => 72.29/9.88 (( 72.29/9.88 (complementImpComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (complementSubsetComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (complementInPowersetComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (contraSubsetComplement) => 72.29/9.88 (( 72.29/9.88 (complementTcontraSubset) => 72.29/9.88 (( 72.29/9.88 (binunionTILcontra) => 72.29/9.88 (( 72.29/9.88 (binunionTIRcontra) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInUnion) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInUnion2) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInIntersectUnions) => 72.29/9.88 (( 72.29/9.88 (intersectInPowersetIntersectUnions) => 72.29/9.88 (( 72.29/9.88 (inComplementUnionImpNotIn1) => 72.29/9.88 (( 72.29/9.88 (inComplementUnionImpInComplement1) => 72.29/9.88 (( 72.29/9.88 (binunionTE) => 72.29/9.88 (( 72.29/9.88 (binunionTEcontra) => 72.29/9.88 (( 72.29/9.88 (demorgan2a1) => 72.29/9.88 (( 72.29/9.88 (complementUnionInPowersetComplement) => 72.29/9.88 (( 72.29/9.88 (demorgan2a2) => 72.29/9.88 (( 72.29/9.88 (demorgan1a) => 72.29/9.88 (( 72.29/9.88 (demorgan1b) => 72.29/9.88 (( 72.29/9.88 (demorgan1) => 72.29/9.88 (( 72.29/9.88 (demorgan2a) => 72.29/9.88 (( 72.29/9.88 (demorgan2b2) => 72.29/9.88 (( 72.29/9.88 (demorgan2b) => 72.29/9.88 (( 72.29/9.88 (demorgan2) => 72.29/9.88 (( 72.29/9.88 (woz13rule0) => 72.29/9.88 (( 72.29/9.88 (woz13rule1) => 72.29/9.88 (( 72.29/9.88 (woz13rule2) => 72.29/9.88 (( 72.29/9.88 (woz13rule3) => 72.29/9.88 (( 72.29/9.88 (woz13rule4) => 72.29/9.88 (( 72.29/9.88 (woz1_1) => 72.29/9.88 (( 72.29/9.88 (woz1_2) => 72.29/9.88 (( 72.29/9.88 (woz1_3) => 72.29/9.88 (( 72.29/9.88 (woz1_4) => 72.29/9.88 (( 72.29/9.88 (woz1_5) => 72.29/9.88 (( 72.29/9.88 (breln1all2) => 72.29/9.88 (( 72.29/9.88 (breln1SetBreln1) => 72.29/9.88 (( 72.29/9.88 (choice2fnsingleton) => 72.29/9.88 (( 72.29/9.88 (setOfPairsIsBReln1) => 72.29/9.88 (( 72.29/9.88 (breln1all1) => 72.29/9.88 (( 72.29/9.88 (subbreln1) => 72.29/9.88 (( 72.29/9.88 (eqbreln1) => 72.29/9.88 (( 72.29/9.88 (breln1invprop) => 72.29/9.88 (( 72.29/9.88 (breln1invI) => 72.29/9.88 (( 72.29/9.88 (breln1invE) => 72.29/9.88 (( 72.29/9.88 (breln1compprop) => 72.29/9.88 (( 72.29/9.88 (breln1compI) => 72.29/9.88 (( 72.29/9.88 (breln1compE) => 72.29/9.88 (( 72.29/9.88 (breln1compEex) => 72.29/9.88 (( 72.29/9.88 (!!) @ ( 72.29/9.88 (('#B') @ ( 72.29/9.88 !!) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 !!))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#C') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 breln1)))) @ 72.29/9.88 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1488])). 72.29/9.88 thf(zip_derived_cl1505, plain, 72.29/9.88 (~ (((cartprodmempair1) => 72.29/9.88 (((cartprodmempair) => 72.29/9.88 (((setunionE2) => 72.29/9.88 (((setunionsingleton1) => 72.29/9.88 (((setunionsingleton2) => 72.29/9.88 (((setunionsingleton) => 72.29/9.88 (((singletonprop) => 72.29/9.88 (((ex1E1) => 72.29/9.88 (((ex1I) => 72.29/9.88 (((ex1I2) => 72.29/9.88 (((singletonsuniq) => 72.29/9.88 (((setukpairinjL1) => 72.29/9.88 (((kfstsingleton) => 72.29/9.88 (((theprop) => 72.29/9.88 (((kfstpairEq) => 72.29/9.88 (((cartprodfstin) => 72.29/9.88 (((setukpairinjL2) => 72.29/9.88 (((setukpairinjL) => 72.29/9.88 (((setukpairinjR11) => 72.29/9.88 (((setukpairinjR12) => 72.29/9.88 (((setukpairinjR1) => 72.29/9.88 (((upairequniteq) => 72.29/9.88 (((setukpairinjR2) => 72.29/9.88 (((setukpairinjR) => 72.29/9.88 (((ksndsingleton) => 72.29/9.88 (((ksndpairEq) => 72.29/9.88 (((kpairsurjEq) => 72.29/9.88 (((cartprodsndin) => 72.29/9.88 (((cartprodpairmemEL) => 72.29/9.88 (((cartprodpairmemER) => 72.29/9.88 (( 72.29/9.88 (cartprodmempaircEq) => 72.29/9.88 (( 72.29/9.88 (cartprodfstpairEq) => 72.29/9.88 (( 72.29/9.88 (cartprodsndpairEq) => 72.29/9.88 (( 72.29/9.88 (cartprodpairsurjEq) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrI) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrSub) => 72.29/9.88 (( 72.29/9.88 (setOfPairsIsBReln) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrERa) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrEL1) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrEL2) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrER) => 72.29/9.88 (( 72.29/9.88 (funcImageSingleton) => 72.29/9.88 (( 72.29/9.88 (apProp) => 72.29/9.88 (( 72.29/9.88 (app) => 72.29/9.88 (( 72.29/9.88 (infuncsetfunc) => 72.29/9.88 (( 72.29/9.88 (ap2p) => 72.29/9.88 (( 72.29/9.88 (funcinfuncset) => 72.29/9.88 (( 72.29/9.88 (lamProp) => 72.29/9.88 (( 72.29/9.88 (lamp) => 72.29/9.88 (( 72.29/9.88 (lam2p) => 72.29/9.88 (( 72.29/9.88 (brelnall1) => 72.29/9.88 (( 72.29/9.88 (brelnall2) => 72.29/9.88 (( 72.29/9.88 (ex1E2) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp1) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp3) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp2) => 72.29/9.88 (( 72.29/9.88 (funcextLem) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp4) => 72.29/9.88 (( 72.29/9.88 (subbreln) => 72.29/9.88 (( 72.29/9.88 (eqbreln) => 72.29/9.88 (( 72.29/9.88 (funcext) => 72.29/9.88 (( 72.29/9.88 (funcext2) => 72.29/9.88 (( 72.29/9.88 (ap2apEq1) => 72.29/9.88 (( 72.29/9.88 (ap2apEq2) => 72.29/9.88 (( 72.29/9.88 (beta1) => 72.29/9.88 (( 72.29/9.88 (eta1) => 72.29/9.88 (( 72.29/9.88 (lam2lamEq) => 72.29/9.88 (( 72.29/9.88 (beta2) => 72.29/9.88 (( 72.29/9.88 (eta2) => 72.29/9.88 (( 72.29/9.88 (iffalseProp1) => 72.29/9.88 (( 72.29/9.88 (iffalseProp2) => 72.29/9.88 (( 72.29/9.88 (iftrueProp1) => 72.29/9.88 (( 72.29/9.88 (iftrueProp2) => 72.29/9.88 (( 72.29/9.88 (ifSingleton) => 72.29/9.88 (( 72.29/9.88 (ifp) => 72.29/9.88 (( 72.29/9.88 (theeq) => 72.29/9.88 (( 72.29/9.88 (iftrue) => 72.29/9.88 (( 72.29/9.88 (iffalse) => 72.29/9.88 (( 72.29/9.88 (iftrueorfalse) => 72.29/9.88 (( 72.29/9.88 (binintersectT_lem) => 72.29/9.88 (( 72.29/9.88 (binunionT_lem) => 72.29/9.88 (( 72.29/9.88 (powersetT_lem) => 72.29/9.88 (( 72.29/9.88 (setminusT_lem) => 72.29/9.88 (( 72.29/9.88 (complementT_lem) => 72.29/9.88 (( 72.29/9.88 (setextT) => 72.29/9.88 (( 72.29/9.88 (subsetTI) => 72.29/9.88 (( 72.29/9.88 (powersetTI1) => 72.29/9.88 (( 72.29/9.88 (powersetTE1) => 72.29/9.88 (( 72.29/9.88 (complementTI1) => 72.29/9.88 (( 72.29/9.88 (complementTE1) => 72.29/9.88 (( 72.29/9.88 (binintersectTELcontra) => 72.29/9.88 (( 72.29/9.88 (binintersectTERcontra) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT1) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT2) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT3) => 72.29/9.88 (( 72.29/9.88 (doubleComplementI1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementE1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementSub1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementSub2) => 72.29/9.88 (( 72.29/9.88 (doubleComplementEq) => 72.29/9.88 (( 72.29/9.88 (complementTnotintersectT) => 72.29/9.88 (( 72.29/9.88 (complementImpComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (complementSubsetComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (complementInPowersetComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (contraSubsetComplement) => 72.29/9.88 (( 72.29/9.88 (complementTcontraSubset) => 72.29/9.88 (( 72.29/9.88 (binunionTILcontra) => 72.29/9.88 (( 72.29/9.88 (binunionTIRcontra) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInUnion) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInUnion2) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInIntersectUnions) => 72.29/9.88 (( 72.29/9.88 (intersectInPowersetIntersectUnions) => 72.29/9.88 (( 72.29/9.88 (inComplementUnionImpNotIn1) => 72.29/9.88 (( 72.29/9.88 (inComplementUnionImpInComplement1) => 72.29/9.88 (( 72.29/9.88 (binunionTE) => 72.29/9.88 (( 72.29/9.88 (binunionTEcontra) => 72.29/9.88 (( 72.29/9.88 (demorgan2a1) => 72.29/9.88 (( 72.29/9.88 (complementUnionInPowersetComplement) => 72.29/9.88 (( 72.29/9.88 (demorgan2a2) => 72.29/9.88 (( 72.29/9.88 (demorgan1a) => 72.29/9.88 (( 72.29/9.88 (demorgan1b) => 72.29/9.88 (( 72.29/9.88 (demorgan1) => 72.29/9.88 (( 72.29/9.88 (demorgan2a) => 72.29/9.88 (( 72.29/9.88 (demorgan2b2) => 72.29/9.88 (( 72.29/9.88 (demorgan2b) => 72.29/9.88 (( 72.29/9.88 (demorgan2) => 72.29/9.88 (( 72.29/9.88 (woz13rule0) => 72.29/9.88 (( 72.29/9.88 (woz13rule1) => 72.29/9.88 (( 72.29/9.88 (woz13rule2) => 72.29/9.88 (( 72.29/9.88 (woz13rule3) => 72.29/9.88 (( 72.29/9.88 (woz13rule4) => 72.29/9.88 (( 72.29/9.88 (woz1_1) => 72.29/9.88 (( 72.29/9.88 (woz1_2) => 72.29/9.88 (( 72.29/9.88 (woz1_3) => 72.29/9.88 (( 72.29/9.88 (woz1_4) => 72.29/9.88 (( 72.29/9.88 (woz1_5) => 72.29/9.88 (( 72.29/9.88 (breln1all2) => 72.29/9.88 (( 72.29/9.88 (breln1SetBreln1) => 72.29/9.88 (( 72.29/9.88 (choice2fnsingleton) => 72.29/9.88 (( 72.29/9.88 (setOfPairsIsBReln1) => 72.29/9.88 (( 72.29/9.88 (breln1all1) => 72.29/9.88 (( 72.29/9.88 (subbreln1) => 72.29/9.88 (( 72.29/9.88 (eqbreln1) => 72.29/9.88 (( 72.29/9.88 (breln1invprop) => 72.29/9.88 (( 72.29/9.88 (breln1invI) => 72.29/9.88 (( 72.29/9.88 (breln1invE) => 72.29/9.88 (( 72.29/9.88 (breln1compprop) => 72.29/9.88 (( 72.29/9.88 (breln1compI) => 72.29/9.88 (( 72.29/9.88 (breln1compE) => 72.29/9.88 (( 72.29/9.88 (breln1compEex) => 72.29/9.88 (( 72.29/9.88 (!!) @ ( 72.29/9.88 (('#B') @ ( 72.29/9.88 !!) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 !!))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#C') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 breln1)))) @ 72.29/9.88 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1496])). 72.29/9.88 thf(zip_derived_cl1515, plain, 72.29/9.88 (~ (((cartprodmempair) => 72.29/9.88 (((setunionE2) => 72.29/9.88 (((setunionsingleton1) => 72.29/9.88 (((setunionsingleton2) => 72.29/9.88 (((setunionsingleton) => 72.29/9.88 (((singletonprop) => 72.29/9.88 (((ex1E1) => 72.29/9.88 (((ex1I) => 72.29/9.88 (((ex1I2) => 72.29/9.88 (((singletonsuniq) => 72.29/9.88 (((setukpairinjL1) => 72.29/9.88 (((kfstsingleton) => 72.29/9.88 (((theprop) => 72.29/9.88 (((kfstpairEq) => 72.29/9.88 (((cartprodfstin) => 72.29/9.88 (((setukpairinjL2) => 72.29/9.88 (((setukpairinjL) => 72.29/9.88 (((setukpairinjR11) => 72.29/9.88 (((setukpairinjR12) => 72.29/9.88 (((setukpairinjR1) => 72.29/9.88 (((upairequniteq) => 72.29/9.88 (((setukpairinjR2) => 72.29/9.88 (((setukpairinjR) => 72.29/9.88 (((ksndsingleton) => 72.29/9.88 (((ksndpairEq) => 72.29/9.88 (((kpairsurjEq) => 72.29/9.88 (((cartprodsndin) => 72.29/9.88 (((cartprodpairmemEL) => 72.29/9.88 (((cartprodpairmemER) => 72.29/9.88 (((cartprodmempaircEq) => 72.29/9.88 (( 72.29/9.88 (cartprodfstpairEq) => 72.29/9.88 (( 72.29/9.88 (cartprodsndpairEq) => 72.29/9.88 (( 72.29/9.88 (cartprodpairsurjEq) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrI) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrSub) => 72.29/9.88 (( 72.29/9.88 (setOfPairsIsBReln) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrERa) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrEL1) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrEL2) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrER) => 72.29/9.88 (( 72.29/9.88 (funcImageSingleton) => 72.29/9.88 (( 72.29/9.88 (apProp) => 72.29/9.88 (( 72.29/9.88 (app) => 72.29/9.88 (( 72.29/9.88 (infuncsetfunc) => 72.29/9.88 (( 72.29/9.88 (ap2p) => 72.29/9.88 (( 72.29/9.88 (funcinfuncset) => 72.29/9.88 (( 72.29/9.88 (lamProp) => 72.29/9.88 (( 72.29/9.88 (lamp) => 72.29/9.88 (( 72.29/9.88 (lam2p) => 72.29/9.88 (( 72.29/9.88 (brelnall1) => 72.29/9.88 (( 72.29/9.88 (brelnall2) => 72.29/9.88 (( 72.29/9.88 (ex1E2) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp1) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp3) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp2) => 72.29/9.88 (( 72.29/9.88 (funcextLem) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp4) => 72.29/9.88 (( 72.29/9.88 (subbreln) => 72.29/9.88 (( 72.29/9.88 (eqbreln) => 72.29/9.88 (( 72.29/9.88 (funcext) => 72.29/9.88 (( 72.29/9.88 (funcext2) => 72.29/9.88 (( 72.29/9.88 (ap2apEq1) => 72.29/9.88 (( 72.29/9.88 (ap2apEq2) => 72.29/9.88 (( 72.29/9.88 (beta1) => 72.29/9.88 (( 72.29/9.88 (eta1) => 72.29/9.88 (( 72.29/9.88 (lam2lamEq) => 72.29/9.88 (( 72.29/9.88 (beta2) => 72.29/9.88 (( 72.29/9.88 (eta2) => 72.29/9.88 (( 72.29/9.88 (iffalseProp1) => 72.29/9.88 (( 72.29/9.88 (iffalseProp2) => 72.29/9.88 (( 72.29/9.88 (iftrueProp1) => 72.29/9.88 (( 72.29/9.88 (iftrueProp2) => 72.29/9.88 (( 72.29/9.88 (ifSingleton) => 72.29/9.88 (( 72.29/9.88 (ifp) => 72.29/9.88 (( 72.29/9.88 (theeq) => 72.29/9.88 (( 72.29/9.88 (iftrue) => 72.29/9.88 (( 72.29/9.88 (iffalse) => 72.29/9.88 (( 72.29/9.88 (iftrueorfalse) => 72.29/9.88 (( 72.29/9.88 (binintersectT_lem) => 72.29/9.88 (( 72.29/9.88 (binunionT_lem) => 72.29/9.88 (( 72.29/9.88 (powersetT_lem) => 72.29/9.88 (( 72.29/9.88 (setminusT_lem) => 72.29/9.88 (( 72.29/9.88 (complementT_lem) => 72.29/9.88 (( 72.29/9.88 (setextT) => 72.29/9.88 (( 72.29/9.88 (subsetTI) => 72.29/9.88 (( 72.29/9.88 (powersetTI1) => 72.29/9.88 (( 72.29/9.88 (powersetTE1) => 72.29/9.88 (( 72.29/9.88 (complementTI1) => 72.29/9.88 (( 72.29/9.88 (complementTE1) => 72.29/9.88 (( 72.29/9.88 (binintersectTELcontra) => 72.29/9.88 (( 72.29/9.88 (binintersectTERcontra) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT1) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT2) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT3) => 72.29/9.88 (( 72.29/9.88 (doubleComplementI1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementE1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementSub1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementSub2) => 72.29/9.88 (( 72.29/9.88 (doubleComplementEq) => 72.29/9.88 (( 72.29/9.88 (complementTnotintersectT) => 72.29/9.88 (( 72.29/9.88 (complementImpComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (complementSubsetComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (complementInPowersetComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (contraSubsetComplement) => 72.29/9.88 (( 72.29/9.88 (complementTcontraSubset) => 72.29/9.88 (( 72.29/9.88 (binunionTILcontra) => 72.29/9.88 (( 72.29/9.88 (binunionTIRcontra) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInUnion) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInUnion2) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInIntersectUnions) => 72.29/9.88 (( 72.29/9.88 (intersectInPowersetIntersectUnions) => 72.29/9.88 (( 72.29/9.88 (inComplementUnionImpNotIn1) => 72.29/9.88 (( 72.29/9.88 (inComplementUnionImpInComplement1) => 72.29/9.88 (( 72.29/9.88 (binunionTE) => 72.29/9.88 (( 72.29/9.88 (binunionTEcontra) => 72.29/9.88 (( 72.29/9.88 (demorgan2a1) => 72.29/9.88 (( 72.29/9.88 (complementUnionInPowersetComplement) => 72.29/9.88 (( 72.29/9.88 (demorgan2a2) => 72.29/9.88 (( 72.29/9.88 (demorgan1a) => 72.29/9.88 (( 72.29/9.88 (demorgan1b) => 72.29/9.88 (( 72.29/9.88 (demorgan1) => 72.29/9.88 (( 72.29/9.88 (demorgan2a) => 72.29/9.88 (( 72.29/9.88 (demorgan2b2) => 72.29/9.88 (( 72.29/9.88 (demorgan2b) => 72.29/9.88 (( 72.29/9.88 (demorgan2) => 72.29/9.88 (( 72.29/9.88 (woz13rule0) => 72.29/9.88 (( 72.29/9.88 (woz13rule1) => 72.29/9.88 (( 72.29/9.88 (woz13rule2) => 72.29/9.88 (( 72.29/9.88 (woz13rule3) => 72.29/9.88 (( 72.29/9.88 (woz13rule4) => 72.29/9.88 (( 72.29/9.88 (woz1_1) => 72.29/9.88 (( 72.29/9.88 (woz1_2) => 72.29/9.88 (( 72.29/9.88 (woz1_3) => 72.29/9.88 (( 72.29/9.88 (woz1_4) => 72.29/9.88 (( 72.29/9.88 (woz1_5) => 72.29/9.88 (( 72.29/9.88 (breln1all2) => 72.29/9.88 (( 72.29/9.88 (breln1SetBreln1) => 72.29/9.88 (( 72.29/9.88 (choice2fnsingleton) => 72.29/9.88 (( 72.29/9.88 (setOfPairsIsBReln1) => 72.29/9.88 (( 72.29/9.88 (breln1all1) => 72.29/9.88 (( 72.29/9.88 (subbreln1) => 72.29/9.88 (( 72.29/9.88 (eqbreln1) => 72.29/9.88 (( 72.29/9.88 (breln1invprop) => 72.29/9.88 (( 72.29/9.88 (breln1invI) => 72.29/9.88 (( 72.29/9.88 (breln1invE) => 72.29/9.88 (( 72.29/9.88 (breln1compprop) => 72.29/9.88 (( 72.29/9.88 (breln1compI) => 72.29/9.88 (( 72.29/9.88 (breln1compE) => 72.29/9.88 (( 72.29/9.88 (breln1compEex) => 72.29/9.88 (( 72.29/9.88 (!!) @ ( 72.29/9.88 (('#B') @ ( 72.29/9.88 !!) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 !!))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#C') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 breln1)))) @ 72.29/9.88 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1505])). 72.29/9.88 thf(zip_derived_cl1525, plain, 72.29/9.88 (~ (((setunionE2) => 72.29/9.88 (((setunionsingleton1) => 72.29/9.88 (((setunionsingleton2) => 72.29/9.88 (((setunionsingleton) => 72.29/9.88 (((singletonprop) => 72.29/9.88 (((ex1E1) => 72.29/9.88 (((ex1I) => 72.29/9.88 (((ex1I2) => 72.29/9.88 (((singletonsuniq) => 72.29/9.88 (((setukpairinjL1) => 72.29/9.88 (((kfstsingleton) => 72.29/9.88 (((theprop) => 72.29/9.88 (((kfstpairEq) => 72.29/9.88 (((cartprodfstin) => 72.29/9.88 (((setukpairinjL2) => 72.29/9.88 (((setukpairinjL) => 72.29/9.88 (((setukpairinjR11) => 72.29/9.88 (((setukpairinjR12) => 72.29/9.88 (((setukpairinjR1) => 72.29/9.88 (((upairequniteq) => 72.29/9.88 (((setukpairinjR2) => 72.29/9.88 (((setukpairinjR) => 72.29/9.88 (((ksndsingleton) => 72.29/9.88 (((ksndpairEq) => 72.29/9.88 (((kpairsurjEq) => 72.29/9.88 (((cartprodsndin) => 72.29/9.88 (((cartprodpairmemEL) => 72.29/9.88 (((cartprodpairmemER) => 72.29/9.88 (((cartprodmempaircEq) => 72.29/9.88 (((cartprodfstpairEq) => 72.29/9.88 (( 72.29/9.88 (cartprodsndpairEq) => 72.29/9.88 (( 72.29/9.88 (cartprodpairsurjEq) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrI) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrSub) => 72.29/9.88 (( 72.29/9.88 (setOfPairsIsBReln) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrERa) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrEL1) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrEL2) => 72.29/9.88 (( 72.29/9.88 (dpsetconstrER) => 72.29/9.88 (( 72.29/9.88 (funcImageSingleton) => 72.29/9.88 (( 72.29/9.88 (apProp) => 72.29/9.88 (( 72.29/9.88 (app) => 72.29/9.88 (( 72.29/9.88 (infuncsetfunc) => 72.29/9.88 (( 72.29/9.88 (ap2p) => 72.29/9.88 (( 72.29/9.88 (funcinfuncset) => 72.29/9.88 (( 72.29/9.88 (lamProp) => 72.29/9.88 (( 72.29/9.88 (lamp) => 72.29/9.88 (( 72.29/9.88 (lam2p) => 72.29/9.88 (( 72.29/9.88 (brelnall1) => 72.29/9.88 (( 72.29/9.88 (brelnall2) => 72.29/9.88 (( 72.29/9.88 (ex1E2) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp1) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp3) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp2) => 72.29/9.88 (( 72.29/9.88 (funcextLem) => 72.29/9.88 (( 72.29/9.88 (funcGraphProp4) => 72.29/9.88 (( 72.29/9.88 (subbreln) => 72.29/9.88 (( 72.29/9.88 (eqbreln) => 72.29/9.88 (( 72.29/9.88 (funcext) => 72.29/9.88 (( 72.29/9.88 (funcext2) => 72.29/9.88 (( 72.29/9.88 (ap2apEq1) => 72.29/9.88 (( 72.29/9.88 (ap2apEq2) => 72.29/9.88 (( 72.29/9.88 (beta1) => 72.29/9.88 (( 72.29/9.88 (eta1) => 72.29/9.88 (( 72.29/9.88 (lam2lamEq) => 72.29/9.88 (( 72.29/9.88 (beta2) => 72.29/9.88 (( 72.29/9.88 (eta2) => 72.29/9.88 (( 72.29/9.88 (iffalseProp1) => 72.29/9.88 (( 72.29/9.88 (iffalseProp2) => 72.29/9.88 (( 72.29/9.88 (iftrueProp1) => 72.29/9.88 (( 72.29/9.88 (iftrueProp2) => 72.29/9.88 (( 72.29/9.88 (ifSingleton) => 72.29/9.88 (( 72.29/9.88 (ifp) => 72.29/9.88 (( 72.29/9.88 (theeq) => 72.29/9.88 (( 72.29/9.88 (iftrue) => 72.29/9.88 (( 72.29/9.88 (iffalse) => 72.29/9.88 (( 72.29/9.88 (iftrueorfalse) => 72.29/9.88 (( 72.29/9.88 (binintersectT_lem) => 72.29/9.88 (( 72.29/9.88 (binunionT_lem) => 72.29/9.88 (( 72.29/9.88 (powersetT_lem) => 72.29/9.88 (( 72.29/9.88 (setminusT_lem) => 72.29/9.88 (( 72.29/9.88 (complementT_lem) => 72.29/9.88 (( 72.29/9.88 (setextT) => 72.29/9.88 (( 72.29/9.88 (subsetTI) => 72.29/9.88 (( 72.29/9.88 (powersetTI1) => 72.29/9.88 (( 72.29/9.88 (powersetTE1) => 72.29/9.88 (( 72.29/9.88 (complementTI1) => 72.29/9.88 (( 72.29/9.88 (complementTE1) => 72.29/9.88 (( 72.29/9.88 (binintersectTELcontra) => 72.29/9.88 (( 72.29/9.88 (binintersectTERcontra) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT1) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT2) => 72.29/9.88 (( 72.29/9.88 (contrasubsetT3) => 72.29/9.88 (( 72.29/9.88 (doubleComplementI1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementE1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementSub1) => 72.29/9.88 (( 72.29/9.88 (doubleComplementSub2) => 72.29/9.88 (( 72.29/9.88 (doubleComplementEq) => 72.29/9.88 (( 72.29/9.88 (complementTnotintersectT) => 72.29/9.88 (( 72.29/9.88 (complementImpComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (complementSubsetComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (complementInPowersetComplementIntersect) => 72.29/9.88 (( 72.29/9.88 (contraSubsetComplement) => 72.29/9.88 (( 72.29/9.88 (complementTcontraSubset) => 72.29/9.88 (( 72.29/9.88 (binunionTILcontra) => 72.29/9.88 (( 72.29/9.88 (binunionTIRcontra) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInUnion) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInUnion2) => 72.29/9.88 (( 72.29/9.88 (inIntersectImpInIntersectUnions) => 72.29/9.88 (( 72.29/9.88 (intersectInPowersetIntersectUnions) => 72.29/9.88 (( 72.29/9.88 (inComplementUnionImpNotIn1) => 72.29/9.88 (( 72.29/9.88 (inComplementUnionImpInComplement1) => 72.29/9.88 (( 72.29/9.88 (binunionTE) => 72.29/9.88 (( 72.29/9.88 (binunionTEcontra) => 72.29/9.88 (( 72.29/9.88 (demorgan2a1) => 72.29/9.88 (( 72.29/9.88 (complementUnionInPowersetComplement) => 72.29/9.88 (( 72.29/9.88 (demorgan2a2) => 72.29/9.88 (( 72.29/9.88 (demorgan1a) => 72.29/9.88 (( 72.29/9.88 (demorgan1b) => 72.29/9.88 (( 72.29/9.88 (demorgan1) => 72.29/9.88 (( 72.29/9.88 (demorgan2a) => 72.29/9.88 (( 72.29/9.88 (demorgan2b2) => 72.29/9.88 (( 72.29/9.88 (demorgan2b) => 72.29/9.88 (( 72.29/9.88 (demorgan2) => 72.29/9.88 (( 72.29/9.88 (woz13rule0) => 72.29/9.88 (( 72.29/9.88 (woz13rule1) => 72.29/9.88 (( 72.29/9.88 (woz13rule2) => 72.29/9.88 (( 72.29/9.88 (woz13rule3) => 72.29/9.88 (( 72.29/9.88 (woz13rule4) => 72.29/9.88 (( 72.29/9.88 (woz1_1) => 72.29/9.88 (( 72.29/9.88 (woz1_2) => 72.29/9.88 (( 72.29/9.88 (woz1_3) => 72.29/9.88 (( 72.29/9.88 (woz1_4) => 72.29/9.88 (( 72.29/9.88 (woz1_5) => 72.29/9.88 (( 72.29/9.88 (breln1all2) => 72.29/9.88 (( 72.29/9.88 (breln1SetBreln1) => 72.29/9.88 (( 72.29/9.88 (choice2fnsingleton) => 72.29/9.88 (( 72.29/9.88 (setOfPairsIsBReln1) => 72.29/9.88 (( 72.29/9.88 (breln1all1) => 72.29/9.88 (( 72.29/9.88 (subbreln1) => 72.29/9.88 (( 72.29/9.88 (eqbreln1) => 72.29/9.88 (( 72.29/9.88 (breln1invprop) => 72.29/9.88 (( 72.29/9.88 (breln1invI) => 72.29/9.88 (( 72.29/9.88 (breln1invE) => 72.29/9.88 (( 72.29/9.88 (breln1compprop) => 72.29/9.88 (( 72.29/9.88 (breln1compI) => 72.29/9.88 (( 72.29/9.88 (breln1compE) => 72.29/9.88 (( 72.29/9.88 (breln1compEex) => 72.29/9.88 (( 72.29/9.88 (!!) @ ( 72.29/9.88 (('#B') @ ( 72.29/9.88 !!) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 !!))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#S') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#S') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 =>))) @ 72.29/9.88 breln1)))))) @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#C') @ ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 ( 72.29/9.88 ( 72.29/9.88 ('#B') @ ( 72.29/9.88 '#B') @ 72.29/9.88 breln1)))) @ 72.29/9.88 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1515])). 72.29/9.88 thf(zip_derived_cl1535, plain, 72.29/9.88 (~ (((setunionsingleton1) => 72.29/9.88 (((setunionsingleton2) => 72.29/9.88 (((setunionsingleton) => 72.29/9.88 (((singletonprop) => 72.29/9.88 (((ex1E1) => 72.29/9.88 (((ex1I) => 72.29/9.88 (((ex1I2) => 72.29/9.88 (((singletonsuniq) => 72.29/9.88 (((setukpairinjL1) => 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72.29/9.89 (( 72.29/9.89 (setOfPairsIsBReln1) => 72.29/9.89 (( 72.29/9.89 (breln1all1) => 72.29/9.89 (( 72.29/9.89 (subbreln1) => 72.29/9.89 (( 72.29/9.89 (eqbreln1) => 72.29/9.89 (( 72.29/9.89 (breln1invprop) => 72.29/9.89 (( 72.29/9.89 (breln1invI) => 72.29/9.89 (( 72.29/9.89 (breln1invE) => 72.29/9.89 (( 72.29/9.89 (breln1compprop) => 72.29/9.89 (( 72.29/9.89 (breln1compI) => 72.29/9.89 (( 72.29/9.89 (breln1compE) => 72.29/9.89 (( 72.29/9.89 (breln1compEex) => 72.29/9.89 (( 72.29/9.89 (!!) @ ( 72.29/9.89 (('#B') @ ( 72.29/9.89 !!) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 !!))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 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=> 72.29/9.89 (((kfstpairEq) => 72.29/9.89 (((cartprodfstin) => 72.29/9.89 (((setukpairinjL2) => 72.29/9.89 (((setukpairinjL) => 72.29/9.89 (((setukpairinjR11) => 72.29/9.89 (((setukpairinjR12) => 72.29/9.89 (((setukpairinjR1) => 72.29/9.89 (((upairequniteq) => 72.29/9.89 (((setukpairinjR2) => 72.29/9.89 (((setukpairinjR) => 72.29/9.89 (((ksndsingleton) => 72.29/9.89 (((ksndpairEq) => 72.29/9.89 (((kpairsurjEq) => 72.29/9.89 (((cartprodsndin) => 72.29/9.89 (((cartprodpairmemEL) => 72.29/9.89 (((cartprodpairmemER) => 72.29/9.89 (((cartprodmempaircEq) => 72.29/9.89 (((cartprodfstpairEq) => 72.29/9.89 (((cartprodsndpairEq) => 72.29/9.89 (((cartprodpairsurjEq) => 72.29/9.89 (((dpsetconstrI) => 72.29/9.89 (((dpsetconstrSub) => 72.29/9.89 (((setOfPairsIsBReln) => 72.29/9.89 (( 72.29/9.89 (dpsetconstrERa) => 72.29/9.89 (( 72.29/9.89 (dpsetconstrEL1) => 72.29/9.89 (( 72.29/9.89 (dpsetconstrEL2) => 72.29/9.89 (( 72.29/9.89 (dpsetconstrER) => 72.29/9.89 (( 72.29/9.89 (funcImageSingleton) => 72.29/9.89 (( 72.29/9.89 (apProp) => 72.29/9.89 (( 72.29/9.89 (app) => 72.29/9.89 (( 72.29/9.89 (infuncsetfunc) => 72.29/9.89 (( 72.29/9.89 (ap2p) => 72.29/9.89 (( 72.29/9.89 (funcinfuncset) => 72.29/9.89 (( 72.29/9.89 (lamProp) => 72.29/9.89 (( 72.29/9.89 (lamp) => 72.29/9.89 (( 72.29/9.89 (lam2p) => 72.29/9.89 (( 72.29/9.89 (brelnall1) => 72.29/9.89 (( 72.29/9.89 (brelnall2) => 72.29/9.89 (( 72.29/9.89 (ex1E2) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp1) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp3) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp2) => 72.29/9.89 (( 72.29/9.89 (funcextLem) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp4) => 72.29/9.89 (( 72.29/9.89 (subbreln) => 72.29/9.89 (( 72.29/9.89 (eqbreln) => 72.29/9.89 (( 72.29/9.89 (funcext) => 72.29/9.89 (( 72.29/9.89 (funcext2) => 72.29/9.89 (( 72.29/9.89 (ap2apEq1) => 72.29/9.89 (( 72.29/9.89 (ap2apEq2) => 72.29/9.89 (( 72.29/9.89 (beta1) => 72.29/9.89 (( 72.29/9.89 (eta1) => 72.29/9.89 (( 72.29/9.89 (lam2lamEq) => 72.29/9.89 (( 72.29/9.89 (beta2) => 72.29/9.89 (( 72.29/9.89 (eta2) => 72.29/9.89 (( 72.29/9.89 (iffalseProp1) => 72.29/9.89 (( 72.29/9.89 (iffalseProp2) => 72.29/9.89 (( 72.29/9.89 (iftrueProp1) => 72.29/9.89 (( 72.29/9.89 (iftrueProp2) => 72.29/9.89 (( 72.29/9.89 (ifSingleton) => 72.29/9.89 (( 72.29/9.89 (ifp) => 72.29/9.89 (( 72.29/9.89 (theeq) => 72.29/9.89 (( 72.29/9.89 (iftrue) => 72.29/9.89 (( 72.29/9.89 (iffalse) => 72.29/9.89 (( 72.29/9.89 (iftrueorfalse) => 72.29/9.89 (( 72.29/9.89 (binintersectT_lem) => 72.29/9.89 (( 72.29/9.89 (binunionT_lem) => 72.29/9.89 (( 72.29/9.89 (powersetT_lem) => 72.29/9.89 (( 72.29/9.89 (setminusT_lem) => 72.29/9.89 (( 72.29/9.89 (complementT_lem) => 72.29/9.89 (( 72.29/9.89 (setextT) => 72.29/9.89 (( 72.29/9.89 (subsetTI) => 72.29/9.89 (( 72.29/9.89 (powersetTI1) => 72.29/9.89 (( 72.29/9.89 (powersetTE1) => 72.29/9.89 (( 72.29/9.89 (complementTI1) => 72.29/9.89 (( 72.29/9.89 (complementTE1) => 72.29/9.89 (( 72.29/9.89 (binintersectTELcontra) => 72.29/9.89 (( 72.29/9.89 (binintersectTERcontra) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT1) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT2) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT3) => 72.29/9.89 (( 72.29/9.89 (doubleComplementI1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementE1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub2) => 72.29/9.89 (( 72.29/9.89 (doubleComplementEq) => 72.29/9.89 (( 72.29/9.89 (complementTnotintersectT) => 72.29/9.89 (( 72.29/9.89 (complementImpComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementSubsetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementInPowersetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (contraSubsetComplement) => 72.29/9.89 (( 72.29/9.89 (complementTcontraSubset) => 72.29/9.89 (( 72.29/9.89 (binunionTILcontra) => 72.29/9.89 (( 72.29/9.89 (binunionTIRcontra) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion2) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (intersectInPowersetIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpNotIn1) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpInComplement1) => 72.29/9.89 (( 72.29/9.89 (binunionTE) => 72.29/9.89 (( 72.29/9.89 (binunionTEcontra) => 72.29/9.89 (( 72.29/9.89 (demorgan2a1) => 72.29/9.89 (( 72.29/9.89 (complementUnionInPowersetComplement) => 72.29/9.89 (( 72.29/9.89 (demorgan2a2) => 72.29/9.89 (( 72.29/9.89 (demorgan1a) => 72.29/9.89 (( 72.29/9.89 (demorgan1b) => 72.29/9.89 (( 72.29/9.89 (demorgan1) => 72.29/9.89 (( 72.29/9.89 (demorgan2a) => 72.29/9.89 (( 72.29/9.89 (demorgan2b2) => 72.29/9.89 (( 72.29/9.89 (demorgan2b) => 72.29/9.89 (( 72.29/9.89 (demorgan2) => 72.29/9.89 (( 72.29/9.89 (woz13rule0) => 72.29/9.89 (( 72.29/9.89 (woz13rule1) => 72.29/9.89 (( 72.29/9.89 (woz13rule2) => 72.29/9.89 (( 72.29/9.89 (woz13rule3) => 72.29/9.89 (( 72.29/9.89 (woz13rule4) => 72.29/9.89 (( 72.29/9.89 (woz1_1) => 72.29/9.89 (( 72.29/9.89 (woz1_2) => 72.29/9.89 (( 72.29/9.89 (woz1_3) => 72.29/9.89 (( 72.29/9.89 (woz1_4) => 72.29/9.89 (( 72.29/9.89 (woz1_5) => 72.29/9.89 (( 72.29/9.89 (breln1all2) => 72.29/9.89 (( 72.29/9.89 (breln1SetBreln1) => 72.29/9.89 (( 72.29/9.89 (choice2fnsingleton) => 72.29/9.89 (( 72.29/9.89 (setOfPairsIsBReln1) => 72.29/9.89 (( 72.29/9.89 (breln1all1) => 72.29/9.89 (( 72.29/9.89 (subbreln1) => 72.29/9.89 (( 72.29/9.89 (eqbreln1) => 72.29/9.89 (( 72.29/9.89 (breln1invprop) => 72.29/9.89 (( 72.29/9.89 (breln1invI) => 72.29/9.89 (( 72.29/9.89 (breln1invE) => 72.29/9.89 (( 72.29/9.89 (breln1compprop) => 72.29/9.89 (( 72.29/9.89 (breln1compI) => 72.29/9.89 (( 72.29/9.89 (breln1compE) => 72.29/9.89 (( 72.29/9.89 (breln1compEex) => 72.29/9.89 (( 72.29/9.89 (!!) @ ( 72.29/9.89 (('#B') @ ( 72.29/9.89 !!) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 !!))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#C') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 breln1)))) @ 72.29/9.89 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1565])). 72.29/9.89 thf(zip_derived_cl1582, plain, 72.29/9.89 (~ (((ex1I) => 72.29/9.89 (((ex1I2) => 72.29/9.89 (((singletonsuniq) => 72.29/9.89 (((setukpairinjL1) => 72.29/9.89 (((kfstsingleton) => 72.29/9.89 (((theprop) => 72.29/9.89 (((kfstpairEq) => 72.29/9.89 (((cartprodfstin) => 72.29/9.89 (((setukpairinjL2) => 72.29/9.89 (((setukpairinjL) => 72.29/9.89 (((setukpairinjR11) => 72.29/9.89 (((setukpairinjR12) => 72.29/9.89 (((setukpairinjR1) => 72.29/9.89 (((upairequniteq) => 72.29/9.89 (((setukpairinjR2) => 72.29/9.89 (((setukpairinjR) => 72.29/9.89 (((ksndsingleton) => 72.29/9.89 (((ksndpairEq) => 72.29/9.89 (((kpairsurjEq) => 72.29/9.89 (((cartprodsndin) => 72.29/9.89 (((cartprodpairmemEL) => 72.29/9.89 (((cartprodpairmemER) => 72.29/9.89 (((cartprodmempaircEq) => 72.29/9.89 (((cartprodfstpairEq) => 72.29/9.89 (((cartprodsndpairEq) => 72.29/9.89 (((cartprodpairsurjEq) => 72.29/9.89 (((dpsetconstrI) => 72.29/9.89 (((dpsetconstrSub) => 72.29/9.89 (((setOfPairsIsBReln) => 72.29/9.89 (((dpsetconstrERa) => 72.29/9.89 (( 72.29/9.89 (dpsetconstrEL1) => 72.29/9.89 (( 72.29/9.89 (dpsetconstrEL2) => 72.29/9.89 (( 72.29/9.89 (dpsetconstrER) => 72.29/9.89 (( 72.29/9.89 (funcImageSingleton) => 72.29/9.89 (( 72.29/9.89 (apProp) => 72.29/9.89 (( 72.29/9.89 (app) => 72.29/9.89 (( 72.29/9.89 (infuncsetfunc) => 72.29/9.89 (( 72.29/9.89 (ap2p) => 72.29/9.89 (( 72.29/9.89 (funcinfuncset) => 72.29/9.89 (( 72.29/9.89 (lamProp) => 72.29/9.89 (( 72.29/9.89 (lamp) => 72.29/9.89 (( 72.29/9.89 (lam2p) => 72.29/9.89 (( 72.29/9.89 (brelnall1) => 72.29/9.89 (( 72.29/9.89 (brelnall2) => 72.29/9.89 (( 72.29/9.89 (ex1E2) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp1) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp3) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp2) => 72.29/9.89 (( 72.29/9.89 (funcextLem) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp4) => 72.29/9.89 (( 72.29/9.89 (subbreln) => 72.29/9.89 (( 72.29/9.89 (eqbreln) => 72.29/9.89 (( 72.29/9.89 (funcext) => 72.29/9.89 (( 72.29/9.89 (funcext2) => 72.29/9.89 (( 72.29/9.89 (ap2apEq1) => 72.29/9.89 (( 72.29/9.89 (ap2apEq2) => 72.29/9.89 (( 72.29/9.89 (beta1) => 72.29/9.89 (( 72.29/9.89 (eta1) => 72.29/9.89 (( 72.29/9.89 (lam2lamEq) => 72.29/9.89 (( 72.29/9.89 (beta2) => 72.29/9.89 (( 72.29/9.89 (eta2) => 72.29/9.89 (( 72.29/9.89 (iffalseProp1) => 72.29/9.89 (( 72.29/9.89 (iffalseProp2) => 72.29/9.89 (( 72.29/9.89 (iftrueProp1) => 72.29/9.89 (( 72.29/9.89 (iftrueProp2) => 72.29/9.89 (( 72.29/9.89 (ifSingleton) => 72.29/9.89 (( 72.29/9.89 (ifp) => 72.29/9.89 (( 72.29/9.89 (theeq) => 72.29/9.89 (( 72.29/9.89 (iftrue) => 72.29/9.89 (( 72.29/9.89 (iffalse) => 72.29/9.89 (( 72.29/9.89 (iftrueorfalse) => 72.29/9.89 (( 72.29/9.89 (binintersectT_lem) => 72.29/9.89 (( 72.29/9.89 (binunionT_lem) => 72.29/9.89 (( 72.29/9.89 (powersetT_lem) => 72.29/9.89 (( 72.29/9.89 (setminusT_lem) => 72.29/9.89 (( 72.29/9.89 (complementT_lem) => 72.29/9.89 (( 72.29/9.89 (setextT) => 72.29/9.89 (( 72.29/9.89 (subsetTI) => 72.29/9.89 (( 72.29/9.89 (powersetTI1) => 72.29/9.89 (( 72.29/9.89 (powersetTE1) => 72.29/9.89 (( 72.29/9.89 (complementTI1) => 72.29/9.89 (( 72.29/9.89 (complementTE1) => 72.29/9.89 (( 72.29/9.89 (binintersectTELcontra) => 72.29/9.89 (( 72.29/9.89 (binintersectTERcontra) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT1) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT2) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT3) => 72.29/9.89 (( 72.29/9.89 (doubleComplementI1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementE1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub2) => 72.29/9.89 (( 72.29/9.89 (doubleComplementEq) => 72.29/9.89 (( 72.29/9.89 (complementTnotintersectT) => 72.29/9.89 (( 72.29/9.89 (complementImpComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementSubsetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementInPowersetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (contraSubsetComplement) => 72.29/9.89 (( 72.29/9.89 (complementTcontraSubset) => 72.29/9.89 (( 72.29/9.89 (binunionTILcontra) => 72.29/9.89 (( 72.29/9.89 (binunionTIRcontra) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion2) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (intersectInPowersetIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpNotIn1) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpInComplement1) => 72.29/9.89 (( 72.29/9.89 (binunionTE) => 72.29/9.89 (( 72.29/9.89 (binunionTEcontra) => 72.29/9.89 (( 72.29/9.89 (demorgan2a1) => 72.29/9.89 (( 72.29/9.89 (complementUnionInPowersetComplement) => 72.29/9.89 (( 72.29/9.89 (demorgan2a2) => 72.29/9.89 (( 72.29/9.89 (demorgan1a) => 72.29/9.89 (( 72.29/9.89 (demorgan1b) => 72.29/9.89 (( 72.29/9.89 (demorgan1) => 72.29/9.89 (( 72.29/9.89 (demorgan2a) => 72.29/9.89 (( 72.29/9.89 (demorgan2b2) => 72.29/9.89 (( 72.29/9.89 (demorgan2b) => 72.29/9.89 (( 72.29/9.89 (demorgan2) => 72.29/9.89 (( 72.29/9.89 (woz13rule0) => 72.29/9.89 (( 72.29/9.89 (woz13rule1) => 72.29/9.89 (( 72.29/9.89 (woz13rule2) => 72.29/9.89 (( 72.29/9.89 (woz13rule3) => 72.29/9.89 (( 72.29/9.89 (woz13rule4) => 72.29/9.89 (( 72.29/9.89 (woz1_1) => 72.29/9.89 (( 72.29/9.89 (woz1_2) => 72.29/9.89 (( 72.29/9.89 (woz1_3) => 72.29/9.89 (( 72.29/9.89 (woz1_4) => 72.29/9.89 (( 72.29/9.89 (woz1_5) => 72.29/9.89 (( 72.29/9.89 (breln1all2) => 72.29/9.89 (( 72.29/9.89 (breln1SetBreln1) => 72.29/9.89 (( 72.29/9.89 (choice2fnsingleton) => 72.29/9.89 (( 72.29/9.89 (setOfPairsIsBReln1) => 72.29/9.89 (( 72.29/9.89 (breln1all1) => 72.29/9.89 (( 72.29/9.89 (subbreln1) => 72.29/9.89 (( 72.29/9.89 (eqbreln1) => 72.29/9.89 (( 72.29/9.89 (breln1invprop) => 72.29/9.89 (( 72.29/9.89 (breln1invI) => 72.29/9.89 (( 72.29/9.89 (breln1invE) => 72.29/9.89 (( 72.29/9.89 (breln1compprop) => 72.29/9.89 (( 72.29/9.89 (breln1compI) => 72.29/9.89 (( 72.29/9.89 (breln1compE) => 72.29/9.89 (( 72.29/9.89 (breln1compEex) => 72.29/9.89 (( 72.29/9.89 (!!) @ ( 72.29/9.89 (('#B') @ ( 72.29/9.89 !!) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 !!))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#C') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 breln1)))) @ 72.29/9.89 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1574])). 72.29/9.89 thf(zip_derived_cl1591, plain, 72.29/9.89 (~ (((ex1I2) => 72.29/9.89 (((singletonsuniq) => 72.29/9.89 (((setukpairinjL1) => 72.29/9.89 (((kfstsingleton) => 72.29/9.89 (((theprop) => 72.29/9.89 (((kfstpairEq) => 72.29/9.89 (((cartprodfstin) => 72.29/9.89 (((setukpairinjL2) => 72.29/9.89 (((setukpairinjL) => 72.29/9.89 (((setukpairinjR11) => 72.29/9.89 (((setukpairinjR12) => 72.29/9.89 (((setukpairinjR1) => 72.29/9.89 (((upairequniteq) => 72.29/9.89 (((setukpairinjR2) => 72.29/9.89 (((setukpairinjR) => 72.29/9.89 (((ksndsingleton) => 72.29/9.89 (((ksndpairEq) => 72.29/9.89 (((kpairsurjEq) => 72.29/9.89 (((cartprodsndin) => 72.29/9.89 (((cartprodpairmemEL) => 72.29/9.89 (((cartprodpairmemER) => 72.29/9.89 (((cartprodmempaircEq) => 72.29/9.89 (((cartprodfstpairEq) => 72.29/9.89 (((cartprodsndpairEq) => 72.29/9.89 (((cartprodpairsurjEq) => 72.29/9.89 (((dpsetconstrI) => 72.29/9.89 (((dpsetconstrSub) => 72.29/9.89 (((setOfPairsIsBReln) => 72.29/9.89 (((dpsetconstrERa) => 72.29/9.89 (((dpsetconstrEL1) => 72.29/9.89 (( 72.29/9.89 (dpsetconstrEL2) => 72.29/9.89 (( 72.29/9.89 (dpsetconstrER) => 72.29/9.89 (( 72.29/9.89 (funcImageSingleton) => 72.29/9.89 (( 72.29/9.89 (apProp) => 72.29/9.89 (( 72.29/9.89 (app) => 72.29/9.89 (( 72.29/9.89 (infuncsetfunc) => 72.29/9.89 (( 72.29/9.89 (ap2p) => 72.29/9.89 (( 72.29/9.89 (funcinfuncset) => 72.29/9.89 (( 72.29/9.89 (lamProp) => 72.29/9.89 (( 72.29/9.89 (lamp) => 72.29/9.89 (( 72.29/9.89 (lam2p) => 72.29/9.89 (( 72.29/9.89 (brelnall1) => 72.29/9.89 (( 72.29/9.89 (brelnall2) => 72.29/9.89 (( 72.29/9.89 (ex1E2) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp1) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp3) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp2) => 72.29/9.89 (( 72.29/9.89 (funcextLem) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp4) => 72.29/9.89 (( 72.29/9.89 (subbreln) => 72.29/9.89 (( 72.29/9.89 (eqbreln) => 72.29/9.89 (( 72.29/9.89 (funcext) => 72.29/9.89 (( 72.29/9.89 (funcext2) => 72.29/9.89 (( 72.29/9.89 (ap2apEq1) => 72.29/9.89 (( 72.29/9.89 (ap2apEq2) => 72.29/9.89 (( 72.29/9.89 (beta1) => 72.29/9.89 (( 72.29/9.89 (eta1) => 72.29/9.89 (( 72.29/9.89 (lam2lamEq) => 72.29/9.89 (( 72.29/9.89 (beta2) => 72.29/9.89 (( 72.29/9.89 (eta2) => 72.29/9.89 (( 72.29/9.89 (iffalseProp1) => 72.29/9.89 (( 72.29/9.89 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(intersectInPowersetIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpNotIn1) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpInComplement1) => 72.29/9.89 (( 72.29/9.89 (binunionTE) => 72.29/9.89 (( 72.29/9.89 (binunionTEcontra) => 72.29/9.89 (( 72.29/9.89 (demorgan2a1) => 72.29/9.89 (( 72.29/9.89 (complementUnionInPowersetComplement) => 72.29/9.89 (( 72.29/9.89 (demorgan2a2) => 72.29/9.89 (( 72.29/9.89 (demorgan1a) => 72.29/9.89 (( 72.29/9.89 (demorgan1b) => 72.29/9.89 (( 72.29/9.89 (demorgan1) => 72.29/9.89 (( 72.29/9.89 (demorgan2a) => 72.29/9.89 (( 72.29/9.89 (demorgan2b2) => 72.29/9.89 (( 72.29/9.89 (demorgan2b) => 72.29/9.89 (( 72.29/9.89 (demorgan2) => 72.29/9.89 (( 72.29/9.89 (woz13rule0) => 72.29/9.89 (( 72.29/9.89 (woz13rule1) => 72.29/9.89 (( 72.29/9.89 (woz13rule2) => 72.29/9.89 (( 72.29/9.89 (woz13rule3) => 72.29/9.89 (( 72.29/9.89 (woz13rule4) => 72.29/9.89 (( 72.29/9.89 (woz1_1) => 72.29/9.89 (( 72.29/9.89 (woz1_2) => 72.29/9.89 (( 72.29/9.89 (woz1_3) => 72.29/9.89 (( 72.29/9.89 (woz1_4) => 72.29/9.89 (( 72.29/9.89 (woz1_5) => 72.29/9.89 (( 72.29/9.89 (breln1all2) => 72.29/9.89 (( 72.29/9.89 (breln1SetBreln1) => 72.29/9.89 (( 72.29/9.89 (choice2fnsingleton) => 72.29/9.89 (( 72.29/9.89 (setOfPairsIsBReln1) => 72.29/9.89 (( 72.29/9.89 (breln1all1) => 72.29/9.89 (( 72.29/9.89 (subbreln1) => 72.29/9.89 (( 72.29/9.89 (eqbreln1) => 72.29/9.89 (( 72.29/9.89 (breln1invprop) => 72.29/9.89 (( 72.29/9.89 (breln1invI) => 72.29/9.89 (( 72.29/9.89 (breln1invE) => 72.29/9.89 (( 72.29/9.89 (breln1compprop) => 72.29/9.89 (( 72.29/9.89 (breln1compI) => 72.29/9.89 (( 72.29/9.89 (breln1compE) => 72.29/9.89 (( 72.29/9.89 (breln1compEex) => 72.29/9.89 (( 72.29/9.89 (!!) @ ( 72.29/9.89 (('#B') @ ( 72.29/9.89 !!) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 !!))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#C') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 breln1)))) @ 72.29/9.89 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1582])). 72.29/9.89 thf(zip_derived_cl1599, plain, 72.29/9.89 (~ (((singletonsuniq) => 72.29/9.89 (((setukpairinjL1) => 72.29/9.89 (((kfstsingleton) => 72.29/9.89 (((theprop) => 72.29/9.89 (((kfstpairEq) => 72.29/9.89 (((cartprodfstin) => 72.29/9.89 (((setukpairinjL2) => 72.29/9.89 (((setukpairinjL) => 72.29/9.89 (((setukpairinjR11) => 72.29/9.89 (((setukpairinjR12) => 72.29/9.89 (((setukpairinjR1) => 72.29/9.89 (((upairequniteq) => 72.29/9.89 (((setukpairinjR2) => 72.29/9.89 (((setukpairinjR) => 72.29/9.89 (((ksndsingleton) => 72.29/9.89 (((ksndpairEq) => 72.29/9.89 (((kpairsurjEq) => 72.29/9.89 (((cartprodsndin) => 72.29/9.89 (((cartprodpairmemEL) => 72.29/9.89 (((cartprodpairmemER) => 72.29/9.89 (((cartprodmempaircEq) => 72.29/9.89 (((cartprodfstpairEq) => 72.29/9.89 (((cartprodsndpairEq) => 72.29/9.89 (((cartprodpairsurjEq) => 72.29/9.89 (((dpsetconstrI) => 72.29/9.89 (((dpsetconstrSub) => 72.29/9.89 (((setOfPairsIsBReln) => 72.29/9.89 (((dpsetconstrERa) => 72.29/9.89 (((dpsetconstrEL1) => 72.29/9.89 (((dpsetconstrEL2) => 72.29/9.89 (( 72.29/9.89 (dpsetconstrER) => 72.29/9.89 (( 72.29/9.89 (funcImageSingleton) => 72.29/9.89 (( 72.29/9.89 (apProp) => 72.29/9.89 (( 72.29/9.89 (app) => 72.29/9.89 (( 72.29/9.89 (infuncsetfunc) => 72.29/9.89 (( 72.29/9.89 (ap2p) => 72.29/9.89 (( 72.29/9.89 (funcinfuncset) => 72.29/9.89 (( 72.29/9.89 (lamProp) => 72.29/9.89 (( 72.29/9.89 (lamp) => 72.29/9.89 (( 72.29/9.89 (lam2p) => 72.29/9.89 (( 72.29/9.89 (brelnall1) => 72.29/9.89 (( 72.29/9.89 (brelnall2) => 72.29/9.89 (( 72.29/9.89 (ex1E2) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp1) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp3) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp2) => 72.29/9.89 (( 72.29/9.89 (funcextLem) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp4) => 72.29/9.89 (( 72.29/9.89 (subbreln) => 72.29/9.89 (( 72.29/9.89 (eqbreln) => 72.29/9.89 (( 72.29/9.89 (funcext) => 72.29/9.89 (( 72.29/9.89 (funcext2) => 72.29/9.89 (( 72.29/9.89 (ap2apEq1) => 72.29/9.89 (( 72.29/9.89 (ap2apEq2) => 72.29/9.89 (( 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72.29/9.89 (( 72.29/9.89 (complementTE1) => 72.29/9.89 (( 72.29/9.89 (binintersectTELcontra) => 72.29/9.89 (( 72.29/9.89 (binintersectTERcontra) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT1) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT2) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT3) => 72.29/9.89 (( 72.29/9.89 (doubleComplementI1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementE1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub2) => 72.29/9.89 (( 72.29/9.89 (doubleComplementEq) => 72.29/9.89 (( 72.29/9.89 (complementTnotintersectT) => 72.29/9.89 (( 72.29/9.89 (complementImpComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementSubsetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementInPowersetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (contraSubsetComplement) => 72.29/9.89 (( 72.29/9.89 (complementTcontraSubset) => 72.29/9.89 (( 72.29/9.89 (binunionTILcontra) => 72.29/9.89 (( 72.29/9.89 (binunionTIRcontra) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion2) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (intersectInPowersetIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpNotIn1) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpInComplement1) => 72.29/9.89 (( 72.29/9.89 (binunionTE) => 72.29/9.89 (( 72.29/9.89 (binunionTEcontra) => 72.29/9.89 (( 72.29/9.89 (demorgan2a1) => 72.29/9.89 (( 72.29/9.89 (complementUnionInPowersetComplement) => 72.29/9.89 (( 72.29/9.89 (demorgan2a2) => 72.29/9.89 (( 72.29/9.89 (demorgan1a) => 72.29/9.89 (( 72.29/9.89 (demorgan1b) => 72.29/9.89 (( 72.29/9.89 (demorgan1) => 72.29/9.89 (( 72.29/9.89 (demorgan2a) => 72.29/9.89 (( 72.29/9.89 (demorgan2b2) => 72.29/9.89 (( 72.29/9.89 (demorgan2b) => 72.29/9.89 (( 72.29/9.89 (demorgan2) => 72.29/9.89 (( 72.29/9.89 (woz13rule0) => 72.29/9.89 (( 72.29/9.89 (woz13rule1) => 72.29/9.89 (( 72.29/9.89 (woz13rule2) => 72.29/9.89 (( 72.29/9.89 (woz13rule3) => 72.29/9.89 (( 72.29/9.89 (woz13rule4) => 72.29/9.89 (( 72.29/9.89 (woz1_1) => 72.29/9.89 (( 72.29/9.89 (woz1_2) => 72.29/9.89 (( 72.29/9.89 (woz1_3) => 72.29/9.89 (( 72.29/9.89 (woz1_4) => 72.29/9.89 (( 72.29/9.89 (woz1_5) => 72.29/9.89 (( 72.29/9.89 (breln1all2) => 72.29/9.89 (( 72.29/9.89 (breln1SetBreln1) => 72.29/9.89 (( 72.29/9.89 (choice2fnsingleton) => 72.29/9.89 (( 72.29/9.89 (setOfPairsIsBReln1) => 72.29/9.89 (( 72.29/9.89 (breln1all1) => 72.29/9.89 (( 72.29/9.89 (subbreln1) => 72.29/9.89 (( 72.29/9.89 (eqbreln1) => 72.29/9.89 (( 72.29/9.89 (breln1invprop) => 72.29/9.89 (( 72.29/9.89 (breln1invI) => 72.29/9.89 (( 72.29/9.89 (breln1invE) => 72.29/9.89 (( 72.29/9.89 (breln1compprop) => 72.29/9.89 (( 72.29/9.89 (breln1compI) => 72.29/9.89 (( 72.29/9.89 (breln1compE) => 72.29/9.89 (( 72.29/9.89 (breln1compEex) => 72.29/9.89 (( 72.29/9.89 (!!) @ ( 72.29/9.89 (('#B') @ ( 72.29/9.89 !!) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 !!))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#C') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 breln1)))) @ 72.29/9.89 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1591])). 72.29/9.89 thf(zip_derived_cl1607, plain, 72.29/9.89 (~ (((setukpairinjL1) => 72.29/9.89 (((kfstsingleton) => 72.29/9.89 (((theprop) => 72.29/9.89 (((kfstpairEq) => 72.29/9.89 (((cartprodfstin) => 72.29/9.89 (((setukpairinjL2) => 72.29/9.89 (((setukpairinjL) => 72.29/9.89 (((setukpairinjR11) => 72.29/9.89 (((setukpairinjR12) => 72.29/9.89 (((setukpairinjR1) => 72.29/9.89 (((upairequniteq) => 72.29/9.89 (((setukpairinjR2) => 72.29/9.89 (((setukpairinjR) => 72.29/9.89 (((ksndsingleton) => 72.29/9.89 (((ksndpairEq) => 72.29/9.89 (((kpairsurjEq) => 72.29/9.89 (((cartprodsndin) => 72.29/9.89 (((cartprodpairmemEL) => 72.29/9.89 (((cartprodpairmemER) => 72.29/9.89 (((cartprodmempaircEq) => 72.29/9.89 (((cartprodfstpairEq) => 72.29/9.89 (((cartprodsndpairEq) => 72.29/9.89 (((cartprodpairsurjEq) => 72.29/9.89 (((dpsetconstrI) => 72.29/9.89 (((dpsetconstrSub) => 72.29/9.89 (((setOfPairsIsBReln) => 72.29/9.89 (((dpsetconstrERa) => 72.29/9.89 (((dpsetconstrEL1) => 72.29/9.89 (((dpsetconstrEL2) => 72.29/9.89 (((dpsetconstrER) => 72.29/9.89 (( 72.29/9.89 (funcImageSingleton) => 72.29/9.89 (( 72.29/9.89 (apProp) => 72.29/9.89 (( 72.29/9.89 (app) => 72.29/9.89 (( 72.29/9.89 (infuncsetfunc) => 72.29/9.89 (( 72.29/9.89 (ap2p) => 72.29/9.89 (( 72.29/9.89 (funcinfuncset) => 72.29/9.89 (( 72.29/9.89 (lamProp) => 72.29/9.89 (( 72.29/9.89 (lamp) => 72.29/9.89 (( 72.29/9.89 (lam2p) => 72.29/9.89 (( 72.29/9.89 (brelnall1) => 72.29/9.89 (( 72.29/9.89 (brelnall2) => 72.29/9.89 (( 72.29/9.89 (ex1E2) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp1) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp3) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp2) => 72.29/9.89 (( 72.29/9.89 (funcextLem) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp4) => 72.29/9.89 (( 72.29/9.89 (subbreln) => 72.29/9.89 (( 72.29/9.89 (eqbreln) => 72.29/9.89 (( 72.29/9.89 (funcext) => 72.29/9.89 (( 72.29/9.89 (funcext2) => 72.29/9.89 (( 72.29/9.89 (ap2apEq1) => 72.29/9.89 (( 72.29/9.89 (ap2apEq2) => 72.29/9.89 (( 72.29/9.89 (beta1) => 72.29/9.89 (( 72.29/9.89 (eta1) => 72.29/9.89 (( 72.29/9.89 (lam2lamEq) => 72.29/9.89 (( 72.29/9.89 (beta2) => 72.29/9.89 (( 72.29/9.89 (eta2) => 72.29/9.89 (( 72.29/9.89 (iffalseProp1) => 72.29/9.89 (( 72.29/9.89 (iffalseProp2) => 72.29/9.89 (( 72.29/9.89 (iftrueProp1) => 72.29/9.89 (( 72.29/9.89 (iftrueProp2) => 72.29/9.89 (( 72.29/9.89 (ifSingleton) => 72.29/9.89 (( 72.29/9.89 (ifp) => 72.29/9.89 (( 72.29/9.89 (theeq) => 72.29/9.89 (( 72.29/9.89 (iftrue) => 72.29/9.89 (( 72.29/9.89 (iffalse) => 72.29/9.89 (( 72.29/9.89 (iftrueorfalse) => 72.29/9.89 (( 72.29/9.89 (binintersectT_lem) => 72.29/9.89 (( 72.29/9.89 (binunionT_lem) => 72.29/9.89 (( 72.29/9.89 (powersetT_lem) => 72.29/9.89 (( 72.29/9.89 (setminusT_lem) => 72.29/9.89 (( 72.29/9.89 (complementT_lem) => 72.29/9.89 (( 72.29/9.89 (setextT) => 72.29/9.89 (( 72.29/9.89 (subsetTI) => 72.29/9.89 (( 72.29/9.89 (powersetTI1) => 72.29/9.89 (( 72.29/9.89 (powersetTE1) => 72.29/9.89 (( 72.29/9.89 (complementTI1) => 72.29/9.89 (( 72.29/9.89 (complementTE1) => 72.29/9.89 (( 72.29/9.89 (binintersectTELcontra) => 72.29/9.89 (( 72.29/9.89 (binintersectTERcontra) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT1) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT2) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT3) => 72.29/9.89 (( 72.29/9.89 (doubleComplementI1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementE1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub2) => 72.29/9.89 (( 72.29/9.89 (doubleComplementEq) => 72.29/9.89 (( 72.29/9.89 (complementTnotintersectT) => 72.29/9.89 (( 72.29/9.89 (complementImpComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementSubsetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementInPowersetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (contraSubsetComplement) => 72.29/9.89 (( 72.29/9.89 (complementTcontraSubset) => 72.29/9.89 (( 72.29/9.89 (binunionTILcontra) => 72.29/9.89 (( 72.29/9.89 (binunionTIRcontra) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion2) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (intersectInPowersetIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpNotIn1) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpInComplement1) => 72.29/9.89 (( 72.29/9.89 (binunionTE) => 72.29/9.89 (( 72.29/9.89 (binunionTEcontra) => 72.29/9.89 (( 72.29/9.89 (demorgan2a1) => 72.29/9.89 (( 72.29/9.89 (complementUnionInPowersetComplement) => 72.29/9.89 (( 72.29/9.89 (demorgan2a2) => 72.29/9.89 (( 72.29/9.89 (demorgan1a) => 72.29/9.89 (( 72.29/9.89 (demorgan1b) => 72.29/9.89 (( 72.29/9.89 (demorgan1) => 72.29/9.89 (( 72.29/9.89 (demorgan2a) => 72.29/9.89 (( 72.29/9.89 (demorgan2b2) => 72.29/9.89 (( 72.29/9.89 (demorgan2b) => 72.29/9.89 (( 72.29/9.89 (demorgan2) => 72.29/9.89 (( 72.29/9.89 (woz13rule0) => 72.29/9.89 (( 72.29/9.89 (woz13rule1) => 72.29/9.89 (( 72.29/9.89 (woz13rule2) => 72.29/9.89 (( 72.29/9.89 (woz13rule3) => 72.29/9.89 (( 72.29/9.89 (woz13rule4) => 72.29/9.89 (( 72.29/9.89 (woz1_1) => 72.29/9.89 (( 72.29/9.89 (woz1_2) => 72.29/9.89 (( 72.29/9.89 (woz1_3) => 72.29/9.89 (( 72.29/9.89 (woz1_4) => 72.29/9.89 (( 72.29/9.89 (woz1_5) => 72.29/9.89 (( 72.29/9.89 (breln1all2) => 72.29/9.89 (( 72.29/9.89 (breln1SetBreln1) => 72.29/9.89 (( 72.29/9.89 (choice2fnsingleton) => 72.29/9.89 (( 72.29/9.89 (setOfPairsIsBReln1) => 72.29/9.89 (( 72.29/9.89 (breln1all1) => 72.29/9.89 (( 72.29/9.89 (subbreln1) => 72.29/9.89 (( 72.29/9.89 (eqbreln1) => 72.29/9.89 (( 72.29/9.89 (breln1invprop) => 72.29/9.89 (( 72.29/9.89 (breln1invI) => 72.29/9.89 (( 72.29/9.89 (breln1invE) => 72.29/9.89 (( 72.29/9.89 (breln1compprop) => 72.29/9.89 (( 72.29/9.89 (breln1compI) => 72.29/9.89 (( 72.29/9.89 (breln1compE) => 72.29/9.89 (( 72.29/9.89 (breln1compEex) => 72.29/9.89 (( 72.29/9.89 (!!) @ ( 72.29/9.89 (('#B') @ ( 72.29/9.89 !!) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 !!))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#C') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 breln1)))) @ 72.29/9.89 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1599])). 72.29/9.89 thf(zip_derived_cl1615, plain, 72.29/9.89 (~ (((kfstsingleton) => 72.29/9.89 (((theprop) => 72.29/9.89 (((kfstpairEq) => 72.29/9.89 (((cartprodfstin) => 72.29/9.89 (((setukpairinjL2) => 72.29/9.89 (((setukpairinjL) => 72.29/9.89 (((setukpairinjR11) => 72.29/9.89 (((setukpairinjR12) => 72.29/9.89 (((setukpairinjR1) => 72.29/9.89 (((upairequniteq) => 72.29/9.89 (((setukpairinjR2) => 72.29/9.89 (((setukpairinjR) => 72.29/9.89 (((ksndsingleton) => 72.29/9.89 (((ksndpairEq) => 72.29/9.89 (((kpairsurjEq) => 72.29/9.89 (((cartprodsndin) => 72.29/9.89 (((cartprodpairmemEL) => 72.29/9.89 (((cartprodpairmemER) => 72.29/9.89 (((cartprodmempaircEq) => 72.29/9.89 (((cartprodfstpairEq) => 72.29/9.89 (((cartprodsndpairEq) => 72.29/9.89 (((cartprodpairsurjEq) => 72.29/9.89 (((dpsetconstrI) => 72.29/9.89 (((dpsetconstrSub) => 72.29/9.89 (((setOfPairsIsBReln) => 72.29/9.89 (((dpsetconstrERa) => 72.29/9.89 (((dpsetconstrEL1) => 72.29/9.89 (((dpsetconstrEL2) => 72.29/9.89 (((dpsetconstrER) => 72.29/9.89 (((funcImageSingleton) => 72.29/9.89 (( 72.29/9.89 (apProp) => 72.29/9.89 (( 72.29/9.89 (app) => 72.29/9.89 (( 72.29/9.89 (infuncsetfunc) => 72.29/9.89 (( 72.29/9.89 (ap2p) => 72.29/9.89 (( 72.29/9.89 (funcinfuncset) => 72.29/9.89 (( 72.29/9.89 (lamProp) => 72.29/9.89 (( 72.29/9.89 (lamp) => 72.29/9.89 (( 72.29/9.89 (lam2p) => 72.29/9.89 (( 72.29/9.89 (brelnall1) => 72.29/9.89 (( 72.29/9.89 (brelnall2) => 72.29/9.89 (( 72.29/9.89 (ex1E2) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp1) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp3) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp2) => 72.29/9.89 (( 72.29/9.89 (funcextLem) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp4) => 72.29/9.89 (( 72.29/9.89 (subbreln) => 72.29/9.89 (( 72.29/9.89 (eqbreln) => 72.29/9.89 (( 72.29/9.89 (funcext) => 72.29/9.89 (( 72.29/9.89 (funcext2) => 72.29/9.89 (( 72.29/9.89 (ap2apEq1) => 72.29/9.89 (( 72.29/9.89 (ap2apEq2) => 72.29/9.89 (( 72.29/9.89 (beta1) => 72.29/9.89 (( 72.29/9.89 (eta1) => 72.29/9.89 (( 72.29/9.89 (lam2lamEq) => 72.29/9.89 (( 72.29/9.89 (beta2) => 72.29/9.89 (( 72.29/9.89 (eta2) => 72.29/9.89 (( 72.29/9.89 (iffalseProp1) => 72.29/9.89 (( 72.29/9.89 (iffalseProp2) => 72.29/9.89 (( 72.29/9.89 (iftrueProp1) => 72.29/9.89 (( 72.29/9.89 (iftrueProp2) => 72.29/9.89 (( 72.29/9.89 (ifSingleton) => 72.29/9.89 (( 72.29/9.89 (ifp) => 72.29/9.89 (( 72.29/9.89 (theeq) => 72.29/9.89 (( 72.29/9.89 (iftrue) => 72.29/9.89 (( 72.29/9.89 (iffalse) => 72.29/9.89 (( 72.29/9.89 (iftrueorfalse) => 72.29/9.89 (( 72.29/9.89 (binintersectT_lem) => 72.29/9.89 (( 72.29/9.89 (binunionT_lem) => 72.29/9.89 (( 72.29/9.89 (powersetT_lem) => 72.29/9.89 (( 72.29/9.89 (setminusT_lem) => 72.29/9.89 (( 72.29/9.89 (complementT_lem) => 72.29/9.89 (( 72.29/9.89 (setextT) => 72.29/9.89 (( 72.29/9.89 (subsetTI) => 72.29/9.89 (( 72.29/9.89 (powersetTI1) => 72.29/9.89 (( 72.29/9.89 (powersetTE1) => 72.29/9.89 (( 72.29/9.89 (complementTI1) => 72.29/9.89 (( 72.29/9.89 (complementTE1) => 72.29/9.89 (( 72.29/9.89 (binintersectTELcontra) => 72.29/9.89 (( 72.29/9.89 (binintersectTERcontra) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT1) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT2) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT3) => 72.29/9.89 (( 72.29/9.89 (doubleComplementI1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementE1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub2) => 72.29/9.89 (( 72.29/9.89 (doubleComplementEq) => 72.29/9.89 (( 72.29/9.89 (complementTnotintersectT) => 72.29/9.89 (( 72.29/9.89 (complementImpComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementSubsetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementInPowersetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (contraSubsetComplement) => 72.29/9.89 (( 72.29/9.89 (complementTcontraSubset) => 72.29/9.89 (( 72.29/9.89 (binunionTILcontra) => 72.29/9.89 (( 72.29/9.89 (binunionTIRcontra) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion2) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (intersectInPowersetIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpNotIn1) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpInComplement1) => 72.29/9.89 (( 72.29/9.89 (binunionTE) => 72.29/9.89 (( 72.29/9.89 (binunionTEcontra) => 72.29/9.89 (( 72.29/9.89 (demorgan2a1) => 72.29/9.89 (( 72.29/9.89 (complementUnionInPowersetComplement) => 72.29/9.89 (( 72.29/9.89 (demorgan2a2) => 72.29/9.89 (( 72.29/9.89 (demorgan1a) => 72.29/9.89 (( 72.29/9.89 (demorgan1b) => 72.29/9.89 (( 72.29/9.89 (demorgan1) => 72.29/9.89 (( 72.29/9.89 (demorgan2a) => 72.29/9.89 (( 72.29/9.89 (demorgan2b2) => 72.29/9.89 (( 72.29/9.89 (demorgan2b) => 72.29/9.89 (( 72.29/9.89 (demorgan2) => 72.29/9.89 (( 72.29/9.89 (woz13rule0) => 72.29/9.89 (( 72.29/9.89 (woz13rule1) => 72.29/9.89 (( 72.29/9.89 (woz13rule2) => 72.29/9.89 (( 72.29/9.89 (woz13rule3) => 72.29/9.89 (( 72.29/9.89 (woz13rule4) => 72.29/9.89 (( 72.29/9.89 (woz1_1) => 72.29/9.89 (( 72.29/9.89 (woz1_2) => 72.29/9.89 (( 72.29/9.89 (woz1_3) => 72.29/9.89 (( 72.29/9.89 (woz1_4) => 72.29/9.89 (( 72.29/9.89 (woz1_5) => 72.29/9.89 (( 72.29/9.89 (breln1all2) => 72.29/9.89 (( 72.29/9.89 (breln1SetBreln1) => 72.29/9.89 (( 72.29/9.89 (choice2fnsingleton) => 72.29/9.89 (( 72.29/9.89 (setOfPairsIsBReln1) => 72.29/9.89 (( 72.29/9.89 (breln1all1) => 72.29/9.89 (( 72.29/9.89 (subbreln1) => 72.29/9.89 (( 72.29/9.89 (eqbreln1) => 72.29/9.89 (( 72.29/9.89 (breln1invprop) => 72.29/9.89 (( 72.29/9.89 (breln1invI) => 72.29/9.89 (( 72.29/9.89 (breln1invE) => 72.29/9.89 (( 72.29/9.89 (breln1compprop) => 72.29/9.89 (( 72.29/9.89 (breln1compI) => 72.29/9.89 (( 72.29/9.89 (breln1compE) => 72.29/9.89 (( 72.29/9.89 (breln1compEex) => 72.29/9.89 (( 72.29/9.89 (!!) @ ( 72.29/9.89 (('#B') @ ( 72.29/9.89 !!) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 !!))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#C') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 breln1)))) @ 72.29/9.89 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1607])). 72.29/9.89 thf(zip_derived_cl1625, plain, 72.29/9.89 (~ (((theprop) => 72.29/9.89 (((kfstpairEq) => 72.29/9.89 (((cartprodfstin) => 72.29/9.89 (((setukpairinjL2) => 72.29/9.89 (((setukpairinjL) => 72.29/9.89 (((setukpairinjR11) => 72.29/9.89 (((setukpairinjR12) => 72.29/9.89 (((setukpairinjR1) => 72.29/9.89 (((upairequniteq) => 72.29/9.89 (((setukpairinjR2) => 72.29/9.89 (((setukpairinjR) => 72.29/9.89 (((ksndsingleton) => 72.29/9.89 (((ksndpairEq) => 72.29/9.89 (((kpairsurjEq) => 72.29/9.89 (((cartprodsndin) => 72.29/9.89 (((cartprodpairmemEL) => 72.29/9.89 (((cartprodpairmemER) => 72.29/9.89 (((cartprodmempaircEq) => 72.29/9.89 (((cartprodfstpairEq) => 72.29/9.89 (((cartprodsndpairEq) => 72.29/9.89 (((cartprodpairsurjEq) => 72.29/9.89 (((dpsetconstrI) => 72.29/9.89 (((dpsetconstrSub) => 72.29/9.89 (((setOfPairsIsBReln) => 72.29/9.89 (((dpsetconstrERa) => 72.29/9.89 (((dpsetconstrEL1) => 72.29/9.89 (((dpsetconstrEL2) => 72.29/9.89 (((dpsetconstrER) => 72.29/9.89 (((funcImageSingleton) => 72.29/9.89 (((apProp) => 72.29/9.89 (( 72.29/9.89 (app) => 72.29/9.89 (( 72.29/9.89 (infuncsetfunc) => 72.29/9.89 (( 72.29/9.89 (ap2p) => 72.29/9.89 (( 72.29/9.89 (funcinfuncset) => 72.29/9.89 (( 72.29/9.89 (lamProp) => 72.29/9.89 (( 72.29/9.89 (lamp) => 72.29/9.89 (( 72.29/9.89 (lam2p) => 72.29/9.89 (( 72.29/9.89 (brelnall1) => 72.29/9.89 (( 72.29/9.89 (brelnall2) => 72.29/9.89 (( 72.29/9.89 (ex1E2) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp1) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp3) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp2) => 72.29/9.89 (( 72.29/9.89 (funcextLem) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp4) => 72.29/9.89 (( 72.29/9.89 (subbreln) => 72.29/9.89 (( 72.29/9.89 (eqbreln) => 72.29/9.89 (( 72.29/9.89 (funcext) => 72.29/9.89 (( 72.29/9.89 (funcext2) => 72.29/9.89 (( 72.29/9.89 (ap2apEq1) => 72.29/9.89 (( 72.29/9.89 (ap2apEq2) => 72.29/9.89 (( 72.29/9.89 (beta1) => 72.29/9.89 (( 72.29/9.89 (eta1) => 72.29/9.89 (( 72.29/9.89 (lam2lamEq) => 72.29/9.89 (( 72.29/9.89 (beta2) => 72.29/9.89 (( 72.29/9.89 (eta2) => 72.29/9.89 (( 72.29/9.89 (iffalseProp1) => 72.29/9.89 (( 72.29/9.89 (iffalseProp2) => 72.29/9.89 (( 72.29/9.89 (iftrueProp1) => 72.29/9.89 (( 72.29/9.89 (iftrueProp2) => 72.29/9.89 (( 72.29/9.89 (ifSingleton) => 72.29/9.89 (( 72.29/9.89 (ifp) => 72.29/9.89 (( 72.29/9.89 (theeq) => 72.29/9.89 (( 72.29/9.89 (iftrue) => 72.29/9.89 (( 72.29/9.89 (iffalse) => 72.29/9.89 (( 72.29/9.89 (iftrueorfalse) => 72.29/9.89 (( 72.29/9.89 (binintersectT_lem) => 72.29/9.89 (( 72.29/9.89 (binunionT_lem) => 72.29/9.89 (( 72.29/9.89 (powersetT_lem) => 72.29/9.89 (( 72.29/9.89 (setminusT_lem) => 72.29/9.89 (( 72.29/9.89 (complementT_lem) => 72.29/9.89 (( 72.29/9.89 (setextT) => 72.29/9.89 (( 72.29/9.89 (subsetTI) => 72.29/9.89 (( 72.29/9.89 (powersetTI1) => 72.29/9.89 (( 72.29/9.89 (powersetTE1) => 72.29/9.89 (( 72.29/9.89 (complementTI1) => 72.29/9.89 (( 72.29/9.89 (complementTE1) => 72.29/9.89 (( 72.29/9.89 (binintersectTELcontra) => 72.29/9.89 (( 72.29/9.89 (binintersectTERcontra) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT1) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT2) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT3) => 72.29/9.89 (( 72.29/9.89 (doubleComplementI1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementE1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub2) => 72.29/9.89 (( 72.29/9.89 (doubleComplementEq) => 72.29/9.89 (( 72.29/9.89 (complementTnotintersectT) => 72.29/9.89 (( 72.29/9.89 (complementImpComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementSubsetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementInPowersetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (contraSubsetComplement) => 72.29/9.89 (( 72.29/9.89 (complementTcontraSubset) => 72.29/9.89 (( 72.29/9.89 (binunionTILcontra) => 72.29/9.89 (( 72.29/9.89 (binunionTIRcontra) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion2) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (intersectInPowersetIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpNotIn1) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpInComplement1) => 72.29/9.89 (( 72.29/9.89 (binunionTE) => 72.29/9.89 (( 72.29/9.89 (binunionTEcontra) => 72.29/9.89 (( 72.29/9.89 (demorgan2a1) => 72.29/9.89 (( 72.29/9.89 (complementUnionInPowersetComplement) => 72.29/9.89 (( 72.29/9.89 (demorgan2a2) => 72.29/9.89 (( 72.29/9.89 (demorgan1a) => 72.29/9.89 (( 72.29/9.89 (demorgan1b) => 72.29/9.89 (( 72.29/9.89 (demorgan1) => 72.29/9.89 (( 72.29/9.89 (demorgan2a) => 72.29/9.89 (( 72.29/9.89 (demorgan2b2) => 72.29/9.89 (( 72.29/9.89 (demorgan2b) => 72.29/9.89 (( 72.29/9.89 (demorgan2) => 72.29/9.89 (( 72.29/9.89 (woz13rule0) => 72.29/9.89 (( 72.29/9.89 (woz13rule1) => 72.29/9.89 (( 72.29/9.89 (woz13rule2) => 72.29/9.89 (( 72.29/9.89 (woz13rule3) => 72.29/9.89 (( 72.29/9.89 (woz13rule4) => 72.29/9.89 (( 72.29/9.89 (woz1_1) => 72.29/9.89 (( 72.29/9.89 (woz1_2) => 72.29/9.89 (( 72.29/9.89 (woz1_3) => 72.29/9.89 (( 72.29/9.89 (woz1_4) => 72.29/9.89 (( 72.29/9.89 (woz1_5) => 72.29/9.89 (( 72.29/9.89 (breln1all2) => 72.29/9.89 (( 72.29/9.89 (breln1SetBreln1) => 72.29/9.89 (( 72.29/9.89 (choice2fnsingleton) => 72.29/9.89 (( 72.29/9.89 (setOfPairsIsBReln1) => 72.29/9.89 (( 72.29/9.89 (breln1all1) => 72.29/9.89 (( 72.29/9.89 (subbreln1) => 72.29/9.89 (( 72.29/9.89 (eqbreln1) => 72.29/9.89 (( 72.29/9.89 (breln1invprop) => 72.29/9.89 (( 72.29/9.89 (breln1invI) => 72.29/9.89 (( 72.29/9.89 (breln1invE) => 72.29/9.89 (( 72.29/9.89 (breln1compprop) => 72.29/9.89 (( 72.29/9.89 (breln1compI) => 72.29/9.89 (( 72.29/9.89 (breln1compE) => 72.29/9.89 (( 72.29/9.89 (breln1compEex) => 72.29/9.89 (( 72.29/9.89 (!!) @ ( 72.29/9.89 (('#B') @ ( 72.29/9.89 !!) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 !!))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#C') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 breln1)))) @ 72.29/9.89 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1615])). 72.29/9.89 thf(zip_derived_cl1637, plain, 72.29/9.89 (~ (((kfstpairEq) => 72.29/9.89 (((cartprodfstin) => 72.29/9.89 (((setukpairinjL2) => 72.29/9.89 (((setukpairinjL) => 72.29/9.89 (((setukpairinjR11) => 72.29/9.89 (((setukpairinjR12) => 72.29/9.89 (((setukpairinjR1) => 72.29/9.89 (((upairequniteq) => 72.29/9.89 (((setukpairinjR2) => 72.29/9.89 (((setukpairinjR) => 72.29/9.89 (((ksndsingleton) => 72.29/9.89 (((ksndpairEq) => 72.29/9.89 (((kpairsurjEq) => 72.29/9.89 (((cartprodsndin) => 72.29/9.89 (((cartprodpairmemEL) => 72.29/9.89 (((cartprodpairmemER) => 72.29/9.89 (((cartprodmempaircEq) => 72.29/9.89 (((cartprodfstpairEq) => 72.29/9.89 (((cartprodsndpairEq) => 72.29/9.89 (((cartprodpairsurjEq) => 72.29/9.89 (((dpsetconstrI) => 72.29/9.89 (((dpsetconstrSub) => 72.29/9.89 (((setOfPairsIsBReln) => 72.29/9.89 (((dpsetconstrERa) => 72.29/9.89 (((dpsetconstrEL1) => 72.29/9.89 (((dpsetconstrEL2) => 72.29/9.89 (((dpsetconstrER) => 72.29/9.89 (((funcImageSingleton) => 72.29/9.89 (((apProp) => 72.29/9.89 (((app) => 72.29/9.89 (( 72.29/9.89 (infuncsetfunc) => 72.29/9.89 (( 72.29/9.89 (ap2p) => 72.29/9.89 (( 72.29/9.89 (funcinfuncset) => 72.29/9.89 (( 72.29/9.89 (lamProp) => 72.29/9.89 (( 72.29/9.89 (lamp) => 72.29/9.89 (( 72.29/9.89 (lam2p) => 72.29/9.89 (( 72.29/9.89 (brelnall1) => 72.29/9.89 (( 72.29/9.89 (brelnall2) => 72.29/9.89 (( 72.29/9.89 (ex1E2) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp1) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp3) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp2) => 72.29/9.89 (( 72.29/9.89 (funcextLem) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp4) => 72.29/9.89 (( 72.29/9.89 (subbreln) => 72.29/9.89 (( 72.29/9.89 (eqbreln) => 72.29/9.89 (( 72.29/9.89 (funcext) => 72.29/9.89 (( 72.29/9.89 (funcext2) => 72.29/9.89 (( 72.29/9.89 (ap2apEq1) => 72.29/9.89 (( 72.29/9.89 (ap2apEq2) => 72.29/9.89 (( 72.29/9.89 (beta1) => 72.29/9.89 (( 72.29/9.89 (eta1) => 72.29/9.89 (( 72.29/9.89 (lam2lamEq) => 72.29/9.89 (( 72.29/9.89 (beta2) => 72.29/9.89 (( 72.29/9.89 (eta2) => 72.29/9.89 (( 72.29/9.89 (iffalseProp1) => 72.29/9.89 (( 72.29/9.89 (iffalseProp2) => 72.29/9.89 (( 72.29/9.89 (iftrueProp1) => 72.29/9.89 (( 72.29/9.89 (iftrueProp2) => 72.29/9.89 (( 72.29/9.89 (ifSingleton) => 72.29/9.89 (( 72.29/9.89 (ifp) => 72.29/9.89 (( 72.29/9.89 (theeq) => 72.29/9.89 (( 72.29/9.89 (iftrue) => 72.29/9.89 (( 72.29/9.89 (iffalse) => 72.29/9.89 (( 72.29/9.89 (iftrueorfalse) => 72.29/9.89 (( 72.29/9.89 (binintersectT_lem) => 72.29/9.89 (( 72.29/9.89 (binunionT_lem) => 72.29/9.89 (( 72.29/9.89 (powersetT_lem) => 72.29/9.89 (( 72.29/9.89 (setminusT_lem) => 72.29/9.89 (( 72.29/9.89 (complementT_lem) => 72.29/9.89 (( 72.29/9.89 (setextT) => 72.29/9.89 (( 72.29/9.89 (subsetTI) => 72.29/9.89 (( 72.29/9.89 (powersetTI1) => 72.29/9.89 (( 72.29/9.89 (powersetTE1) => 72.29/9.89 (( 72.29/9.89 (complementTI1) => 72.29/9.89 (( 72.29/9.89 (complementTE1) => 72.29/9.89 (( 72.29/9.89 (binintersectTELcontra) => 72.29/9.89 (( 72.29/9.89 (binintersectTERcontra) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT1) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT2) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT3) => 72.29/9.89 (( 72.29/9.89 (doubleComplementI1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementE1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub2) => 72.29/9.89 (( 72.29/9.89 (doubleComplementEq) => 72.29/9.89 (( 72.29/9.89 (complementTnotintersectT) => 72.29/9.89 (( 72.29/9.89 (complementImpComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementSubsetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementInPowersetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (contraSubsetComplement) => 72.29/9.89 (( 72.29/9.89 (complementTcontraSubset) => 72.29/9.89 (( 72.29/9.89 (binunionTILcontra) => 72.29/9.89 (( 72.29/9.89 (binunionTIRcontra) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion2) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (intersectInPowersetIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpNotIn1) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpInComplement1) => 72.29/9.89 (( 72.29/9.89 (binunionTE) => 72.29/9.89 (( 72.29/9.89 (binunionTEcontra) => 72.29/9.89 (( 72.29/9.89 (demorgan2a1) => 72.29/9.89 (( 72.29/9.89 (complementUnionInPowersetComplement) => 72.29/9.89 (( 72.29/9.89 (demorgan2a2) => 72.29/9.89 (( 72.29/9.89 (demorgan1a) => 72.29/9.89 (( 72.29/9.89 (demorgan1b) => 72.29/9.89 (( 72.29/9.89 (demorgan1) => 72.29/9.89 (( 72.29/9.89 (demorgan2a) => 72.29/9.89 (( 72.29/9.89 (demorgan2b2) => 72.29/9.89 (( 72.29/9.89 (demorgan2b) => 72.29/9.89 (( 72.29/9.89 (demorgan2) => 72.29/9.89 (( 72.29/9.89 (woz13rule0) => 72.29/9.89 (( 72.29/9.89 (woz13rule1) => 72.29/9.89 (( 72.29/9.89 (woz13rule2) => 72.29/9.89 (( 72.29/9.89 (woz13rule3) => 72.29/9.89 (( 72.29/9.89 (woz13rule4) => 72.29/9.89 (( 72.29/9.89 (woz1_1) => 72.29/9.89 (( 72.29/9.89 (woz1_2) => 72.29/9.89 (( 72.29/9.89 (woz1_3) => 72.29/9.89 (( 72.29/9.89 (woz1_4) => 72.29/9.89 (( 72.29/9.89 (woz1_5) => 72.29/9.89 (( 72.29/9.89 (breln1all2) => 72.29/9.89 (( 72.29/9.89 (breln1SetBreln1) => 72.29/9.89 (( 72.29/9.89 (choice2fnsingleton) => 72.29/9.89 (( 72.29/9.89 (setOfPairsIsBReln1) => 72.29/9.89 (( 72.29/9.89 (breln1all1) => 72.29/9.89 (( 72.29/9.89 (subbreln1) => 72.29/9.89 (( 72.29/9.89 (eqbreln1) => 72.29/9.89 (( 72.29/9.89 (breln1invprop) => 72.29/9.89 (( 72.29/9.89 (breln1invI) => 72.29/9.89 (( 72.29/9.89 (breln1invE) => 72.29/9.89 (( 72.29/9.89 (breln1compprop) => 72.29/9.89 (( 72.29/9.89 (breln1compI) => 72.29/9.89 (( 72.29/9.89 (breln1compE) => 72.29/9.89 (( 72.29/9.89 (breln1compEex) => 72.29/9.89 (( 72.29/9.89 (!!) @ ( 72.29/9.89 (('#B') @ ( 72.29/9.89 !!) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 !!))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#C') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 breln1)))) @ 72.29/9.89 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1625])). 72.29/9.89 thf(zip_derived_cl1649, plain, 72.29/9.89 (~ (((cartprodfstin) => 72.29/9.89 (((setukpairinjL2) => 72.29/9.89 (((setukpairinjL) => 72.29/9.89 (((setukpairinjR11) => 72.29/9.89 (((setukpairinjR12) => 72.29/9.89 (((setukpairinjR1) => 72.29/9.89 (((upairequniteq) => 72.29/9.89 (((setukpairinjR2) => 72.29/9.89 (((setukpairinjR) => 72.29/9.89 (((ksndsingleton) => 72.29/9.89 (((ksndpairEq) => 72.29/9.89 (((kpairsurjEq) => 72.29/9.89 (((cartprodsndin) => 72.29/9.89 (((cartprodpairmemEL) => 72.29/9.89 (((cartprodpairmemER) => 72.29/9.89 (((cartprodmempaircEq) => 72.29/9.89 (((cartprodfstpairEq) => 72.29/9.89 (((cartprodsndpairEq) => 72.29/9.89 (((cartprodpairsurjEq) => 72.29/9.89 (((dpsetconstrI) => 72.29/9.89 (((dpsetconstrSub) => 72.29/9.89 (((setOfPairsIsBReln) => 72.29/9.89 (((dpsetconstrERa) => 72.29/9.89 (((dpsetconstrEL1) => 72.29/9.89 (((dpsetconstrEL2) => 72.29/9.89 (((dpsetconstrER) => 72.29/9.89 (((funcImageSingleton) => 72.29/9.89 (((apProp) => 72.29/9.89 (((app) => 72.29/9.89 (((infuncsetfunc) => 72.29/9.89 (( 72.29/9.89 (ap2p) => 72.29/9.89 (( 72.29/9.89 (funcinfuncset) => 72.29/9.89 (( 72.29/9.89 (lamProp) => 72.29/9.89 (( 72.29/9.89 (lamp) => 72.29/9.89 (( 72.29/9.89 (lam2p) => 72.29/9.89 (( 72.29/9.89 (brelnall1) => 72.29/9.89 (( 72.29/9.89 (brelnall2) => 72.29/9.89 (( 72.29/9.89 (ex1E2) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp1) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp3) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp2) => 72.29/9.89 (( 72.29/9.89 (funcextLem) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp4) => 72.29/9.89 (( 72.29/9.89 (subbreln) => 72.29/9.89 (( 72.29/9.89 (eqbreln) => 72.29/9.89 (( 72.29/9.89 (funcext) => 72.29/9.89 (( 72.29/9.89 (funcext2) => 72.29/9.89 (( 72.29/9.89 (ap2apEq1) => 72.29/9.89 (( 72.29/9.89 (ap2apEq2) => 72.29/9.89 (( 72.29/9.89 (beta1) => 72.29/9.89 (( 72.29/9.89 (eta1) => 72.29/9.89 (( 72.29/9.89 (lam2lamEq) => 72.29/9.89 (( 72.29/9.89 (beta2) => 72.29/9.89 (( 72.29/9.89 (eta2) => 72.29/9.89 (( 72.29/9.89 (iffalseProp1) => 72.29/9.89 (( 72.29/9.89 (iffalseProp2) => 72.29/9.89 (( 72.29/9.89 (iftrueProp1) => 72.29/9.89 (( 72.29/9.89 (iftrueProp2) => 72.29/9.89 (( 72.29/9.89 (ifSingleton) => 72.29/9.89 (( 72.29/9.89 (ifp) => 72.29/9.89 (( 72.29/9.89 (theeq) => 72.29/9.89 (( 72.29/9.89 (iftrue) => 72.29/9.89 (( 72.29/9.89 (iffalse) => 72.29/9.89 (( 72.29/9.89 (iftrueorfalse) => 72.29/9.89 (( 72.29/9.89 (binintersectT_lem) => 72.29/9.89 (( 72.29/9.89 (binunionT_lem) => 72.29/9.89 (( 72.29/9.89 (powersetT_lem) => 72.29/9.89 (( 72.29/9.89 (setminusT_lem) => 72.29/9.89 (( 72.29/9.89 (complementT_lem) => 72.29/9.89 (( 72.29/9.89 (setextT) => 72.29/9.89 (( 72.29/9.89 (subsetTI) => 72.29/9.89 (( 72.29/9.89 (powersetTI1) => 72.29/9.89 (( 72.29/9.89 (powersetTE1) => 72.29/9.89 (( 72.29/9.89 (complementTI1) => 72.29/9.89 (( 72.29/9.89 (complementTE1) => 72.29/9.89 (( 72.29/9.89 (binintersectTELcontra) => 72.29/9.89 (( 72.29/9.89 (binintersectTERcontra) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT1) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT2) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT3) => 72.29/9.89 (( 72.29/9.89 (doubleComplementI1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementE1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub2) => 72.29/9.89 (( 72.29/9.89 (doubleComplementEq) => 72.29/9.89 (( 72.29/9.89 (complementTnotintersectT) => 72.29/9.89 (( 72.29/9.89 (complementImpComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementSubsetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementInPowersetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (contraSubsetComplement) => 72.29/9.89 (( 72.29/9.89 (complementTcontraSubset) => 72.29/9.89 (( 72.29/9.89 (binunionTILcontra) => 72.29/9.89 (( 72.29/9.89 (binunionTIRcontra) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion2) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (intersectInPowersetIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpNotIn1) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpInComplement1) => 72.29/9.89 (( 72.29/9.89 (binunionTE) => 72.29/9.89 (( 72.29/9.89 (binunionTEcontra) => 72.29/9.89 (( 72.29/9.89 (demorgan2a1) => 72.29/9.89 (( 72.29/9.89 (complementUnionInPowersetComplement) => 72.29/9.89 (( 72.29/9.89 (demorgan2a2) => 72.29/9.89 (( 72.29/9.89 (demorgan1a) => 72.29/9.89 (( 72.29/9.89 (demorgan1b) => 72.29/9.89 (( 72.29/9.89 (demorgan1) => 72.29/9.89 (( 72.29/9.89 (demorgan2a) => 72.29/9.89 (( 72.29/9.89 (demorgan2b2) => 72.29/9.89 (( 72.29/9.89 (demorgan2b) => 72.29/9.89 (( 72.29/9.89 (demorgan2) => 72.29/9.89 (( 72.29/9.89 (woz13rule0) => 72.29/9.89 (( 72.29/9.89 (woz13rule1) => 72.29/9.89 (( 72.29/9.89 (woz13rule2) => 72.29/9.89 (( 72.29/9.89 (woz13rule3) => 72.29/9.89 (( 72.29/9.89 (woz13rule4) => 72.29/9.89 (( 72.29/9.89 (woz1_1) => 72.29/9.89 (( 72.29/9.89 (woz1_2) => 72.29/9.89 (( 72.29/9.89 (woz1_3) => 72.29/9.89 (( 72.29/9.89 (woz1_4) => 72.29/9.89 (( 72.29/9.89 (woz1_5) => 72.29/9.89 (( 72.29/9.89 (breln1all2) => 72.29/9.89 (( 72.29/9.89 (breln1SetBreln1) => 72.29/9.89 (( 72.29/9.89 (choice2fnsingleton) => 72.29/9.89 (( 72.29/9.89 (setOfPairsIsBReln1) => 72.29/9.89 (( 72.29/9.89 (breln1all1) => 72.29/9.89 (( 72.29/9.89 (subbreln1) => 72.29/9.89 (( 72.29/9.89 (eqbreln1) => 72.29/9.89 (( 72.29/9.89 (breln1invprop) => 72.29/9.89 (( 72.29/9.89 (breln1invI) => 72.29/9.89 (( 72.29/9.89 (breln1invE) => 72.29/9.89 (( 72.29/9.89 (breln1compprop) => 72.29/9.89 (( 72.29/9.89 (breln1compI) => 72.29/9.89 (( 72.29/9.89 (breln1compE) => 72.29/9.89 (( 72.29/9.89 (breln1compEex) => 72.29/9.89 (( 72.29/9.89 (!!) @ ( 72.29/9.89 (('#B') @ ( 72.29/9.89 !!) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 !!))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#C') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 breln1)))) @ 72.29/9.89 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1637])). 72.29/9.89 thf(zip_derived_cl1664, plain, 72.29/9.89 (~ (((setukpairinjL2) => 72.29/9.89 (((setukpairinjL) => 72.29/9.89 (((setukpairinjR11) => 72.29/9.89 (((setukpairinjR12) => 72.29/9.89 (((setukpairinjR1) => 72.29/9.89 (((upairequniteq) => 72.29/9.89 (((setukpairinjR2) => 72.29/9.89 (((setukpairinjR) => 72.29/9.89 (((ksndsingleton) => 72.29/9.89 (((ksndpairEq) => 72.29/9.89 (((kpairsurjEq) => 72.29/9.89 (((cartprodsndin) => 72.29/9.89 (((cartprodpairmemEL) => 72.29/9.89 (((cartprodpairmemER) => 72.29/9.89 (((cartprodmempaircEq) => 72.29/9.89 (((cartprodfstpairEq) => 72.29/9.89 (((cartprodsndpairEq) => 72.29/9.89 (((cartprodpairsurjEq) => 72.29/9.89 (((dpsetconstrI) => 72.29/9.89 (((dpsetconstrSub) => 72.29/9.89 (((setOfPairsIsBReln) => 72.29/9.89 (((dpsetconstrERa) => 72.29/9.89 (((dpsetconstrEL1) => 72.29/9.89 (((dpsetconstrEL2) => 72.29/9.89 (((dpsetconstrER) => 72.29/9.89 (((funcImageSingleton) => 72.29/9.89 (((apProp) => 72.29/9.89 (((app) => 72.29/9.89 (((infuncsetfunc) => 72.29/9.89 (((ap2p) => 72.29/9.89 (( 72.29/9.89 (funcinfuncset) => 72.29/9.89 (( 72.29/9.89 (lamProp) => 72.29/9.89 (( 72.29/9.89 (lamp) => 72.29/9.89 (( 72.29/9.89 (lam2p) => 72.29/9.89 (( 72.29/9.89 (brelnall1) => 72.29/9.89 (( 72.29/9.89 (brelnall2) => 72.29/9.89 (( 72.29/9.89 (ex1E2) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp1) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp3) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp2) => 72.29/9.89 (( 72.29/9.89 (funcextLem) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp4) => 72.29/9.89 (( 72.29/9.89 (subbreln) => 72.29/9.89 (( 72.29/9.89 (eqbreln) => 72.29/9.89 (( 72.29/9.89 (funcext) => 72.29/9.89 (( 72.29/9.89 (funcext2) => 72.29/9.89 (( 72.29/9.89 (ap2apEq1) => 72.29/9.89 (( 72.29/9.89 (ap2apEq2) => 72.29/9.89 (( 72.29/9.89 (beta1) => 72.29/9.89 (( 72.29/9.89 (eta1) => 72.29/9.89 (( 72.29/9.89 (lam2lamEq) => 72.29/9.89 (( 72.29/9.89 (beta2) => 72.29/9.89 (( 72.29/9.89 (eta2) => 72.29/9.89 (( 72.29/9.89 (iffalseProp1) => 72.29/9.89 (( 72.29/9.89 (iffalseProp2) => 72.29/9.89 (( 72.29/9.89 (iftrueProp1) => 72.29/9.89 (( 72.29/9.89 (iftrueProp2) => 72.29/9.89 (( 72.29/9.89 (ifSingleton) => 72.29/9.89 (( 72.29/9.89 (ifp) => 72.29/9.89 (( 72.29/9.89 (theeq) => 72.29/9.89 (( 72.29/9.89 (iftrue) => 72.29/9.89 (( 72.29/9.89 (iffalse) => 72.29/9.89 (( 72.29/9.89 (iftrueorfalse) => 72.29/9.89 (( 72.29/9.89 (binintersectT_lem) => 72.29/9.89 (( 72.29/9.89 (binunionT_lem) => 72.29/9.89 (( 72.29/9.89 (powersetT_lem) => 72.29/9.89 (( 72.29/9.89 (setminusT_lem) => 72.29/9.89 (( 72.29/9.89 (complementT_lem) => 72.29/9.89 (( 72.29/9.89 (setextT) => 72.29/9.89 (( 72.29/9.89 (subsetTI) => 72.29/9.89 (( 72.29/9.89 (powersetTI1) => 72.29/9.89 (( 72.29/9.89 (powersetTE1) => 72.29/9.89 (( 72.29/9.89 (complementTI1) => 72.29/9.89 (( 72.29/9.89 (complementTE1) => 72.29/9.89 (( 72.29/9.89 (binintersectTELcontra) => 72.29/9.89 (( 72.29/9.89 (binintersectTERcontra) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT1) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT2) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT3) => 72.29/9.89 (( 72.29/9.89 (doubleComplementI1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementE1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub2) => 72.29/9.89 (( 72.29/9.89 (doubleComplementEq) => 72.29/9.89 (( 72.29/9.89 (complementTnotintersectT) => 72.29/9.89 (( 72.29/9.89 (complementImpComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementSubsetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementInPowersetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (contraSubsetComplement) => 72.29/9.89 (( 72.29/9.89 (complementTcontraSubset) => 72.29/9.89 (( 72.29/9.89 (binunionTILcontra) => 72.29/9.89 (( 72.29/9.89 (binunionTIRcontra) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion2) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (intersectInPowersetIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpNotIn1) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpInComplement1) => 72.29/9.89 (( 72.29/9.89 (binunionTE) => 72.29/9.89 (( 72.29/9.89 (binunionTEcontra) => 72.29/9.89 (( 72.29/9.89 (demorgan2a1) => 72.29/9.89 (( 72.29/9.89 (complementUnionInPowersetComplement) => 72.29/9.89 (( 72.29/9.89 (demorgan2a2) => 72.29/9.89 (( 72.29/9.89 (demorgan1a) => 72.29/9.89 (( 72.29/9.89 (demorgan1b) => 72.29/9.89 (( 72.29/9.89 (demorgan1) => 72.29/9.89 (( 72.29/9.89 (demorgan2a) => 72.29/9.89 (( 72.29/9.89 (demorgan2b2) => 72.29/9.89 (( 72.29/9.89 (demorgan2b) => 72.29/9.89 (( 72.29/9.89 (demorgan2) => 72.29/9.89 (( 72.29/9.89 (woz13rule0) => 72.29/9.89 (( 72.29/9.89 (woz13rule1) => 72.29/9.89 (( 72.29/9.89 (woz13rule2) => 72.29/9.89 (( 72.29/9.89 (woz13rule3) => 72.29/9.89 (( 72.29/9.89 (woz13rule4) => 72.29/9.89 (( 72.29/9.89 (woz1_1) => 72.29/9.89 (( 72.29/9.89 (woz1_2) => 72.29/9.89 (( 72.29/9.89 (woz1_3) => 72.29/9.89 (( 72.29/9.89 (woz1_4) => 72.29/9.89 (( 72.29/9.89 (woz1_5) => 72.29/9.89 (( 72.29/9.89 (breln1all2) => 72.29/9.89 (( 72.29/9.89 (breln1SetBreln1) => 72.29/9.89 (( 72.29/9.89 (choice2fnsingleton) => 72.29/9.89 (( 72.29/9.89 (setOfPairsIsBReln1) => 72.29/9.89 (( 72.29/9.89 (breln1all1) => 72.29/9.89 (( 72.29/9.89 (subbreln1) => 72.29/9.89 (( 72.29/9.89 (eqbreln1) => 72.29/9.89 (( 72.29/9.89 (breln1invprop) => 72.29/9.89 (( 72.29/9.89 (breln1invI) => 72.29/9.89 (( 72.29/9.89 (breln1invE) => 72.29/9.89 (( 72.29/9.89 (breln1compprop) => 72.29/9.89 (( 72.29/9.89 (breln1compI) => 72.29/9.89 (( 72.29/9.89 (breln1compE) => 72.29/9.89 (( 72.29/9.89 (breln1compEex) => 72.29/9.89 (( 72.29/9.89 (!!) @ ( 72.29/9.89 (('#B') @ ( 72.29/9.89 !!) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 !!))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#C') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 breln1)))) @ 72.29/9.89 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1649])). 72.29/9.89 thf(zip_derived_cl1678, plain, 72.29/9.89 (~ (((setukpairinjL) => 72.29/9.89 (((setukpairinjR11) => 72.29/9.89 (((setukpairinjR12) => 72.29/9.89 (((setukpairinjR1) => 72.29/9.89 (((upairequniteq) => 72.29/9.89 (((setukpairinjR2) => 72.29/9.89 (((setukpairinjR) => 72.29/9.89 (((ksndsingleton) => 72.29/9.89 (((ksndpairEq) => 72.29/9.89 (((kpairsurjEq) => 72.29/9.89 (((cartprodsndin) => 72.29/9.89 (((cartprodpairmemEL) => 72.29/9.89 (((cartprodpairmemER) => 72.29/9.89 (((cartprodmempaircEq) => 72.29/9.89 (((cartprodfstpairEq) => 72.29/9.89 (((cartprodsndpairEq) => 72.29/9.89 (((cartprodpairsurjEq) => 72.29/9.89 (((dpsetconstrI) => 72.29/9.89 (((dpsetconstrSub) => 72.29/9.89 (((setOfPairsIsBReln) => 72.29/9.89 (((dpsetconstrERa) => 72.29/9.89 (((dpsetconstrEL1) => 72.29/9.89 (((dpsetconstrEL2) => 72.29/9.89 (((dpsetconstrER) => 72.29/9.89 (((funcImageSingleton) => 72.29/9.89 (((apProp) => 72.29/9.89 (((app) => 72.29/9.89 (((infuncsetfunc) => 72.29/9.89 (((ap2p) => 72.29/9.89 (((funcinfuncset) => 72.29/9.89 (( 72.29/9.89 (lamProp) => 72.29/9.89 (( 72.29/9.89 (lamp) => 72.29/9.89 (( 72.29/9.89 (lam2p) => 72.29/9.89 (( 72.29/9.89 (brelnall1) => 72.29/9.89 (( 72.29/9.89 (brelnall2) => 72.29/9.89 (( 72.29/9.89 (ex1E2) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp1) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp3) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp2) => 72.29/9.89 (( 72.29/9.89 (funcextLem) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp4) => 72.29/9.89 (( 72.29/9.89 (subbreln) => 72.29/9.89 (( 72.29/9.89 (eqbreln) => 72.29/9.89 (( 72.29/9.89 (funcext) => 72.29/9.89 (( 72.29/9.89 (funcext2) => 72.29/9.89 (( 72.29/9.89 (ap2apEq1) => 72.29/9.89 (( 72.29/9.89 (ap2apEq2) => 72.29/9.89 (( 72.29/9.89 (beta1) => 72.29/9.89 (( 72.29/9.89 (eta1) => 72.29/9.89 (( 72.29/9.89 (lam2lamEq) => 72.29/9.89 (( 72.29/9.89 (beta2) => 72.29/9.89 (( 72.29/9.89 (eta2) => 72.29/9.89 (( 72.29/9.89 (iffalseProp1) => 72.29/9.89 (( 72.29/9.89 (iffalseProp2) => 72.29/9.89 (( 72.29/9.89 (iftrueProp1) => 72.29/9.89 (( 72.29/9.89 (iftrueProp2) => 72.29/9.89 (( 72.29/9.89 (ifSingleton) => 72.29/9.89 (( 72.29/9.89 (ifp) => 72.29/9.89 (( 72.29/9.89 (theeq) => 72.29/9.89 (( 72.29/9.89 (iftrue) => 72.29/9.89 (( 72.29/9.89 (iffalse) => 72.29/9.89 (( 72.29/9.89 (iftrueorfalse) => 72.29/9.89 (( 72.29/9.89 (binintersectT_lem) => 72.29/9.89 (( 72.29/9.89 (binunionT_lem) => 72.29/9.89 (( 72.29/9.89 (powersetT_lem) => 72.29/9.89 (( 72.29/9.89 (setminusT_lem) => 72.29/9.89 (( 72.29/9.89 (complementT_lem) => 72.29/9.89 (( 72.29/9.89 (setextT) => 72.29/9.89 (( 72.29/9.89 (subsetTI) => 72.29/9.89 (( 72.29/9.89 (powersetTI1) => 72.29/9.89 (( 72.29/9.89 (powersetTE1) => 72.29/9.89 (( 72.29/9.89 (complementTI1) => 72.29/9.89 (( 72.29/9.89 (complementTE1) => 72.29/9.89 (( 72.29/9.89 (binintersectTELcontra) => 72.29/9.89 (( 72.29/9.89 (binintersectTERcontra) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT1) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT2) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT3) => 72.29/9.89 (( 72.29/9.89 (doubleComplementI1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementE1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub2) => 72.29/9.89 (( 72.29/9.89 (doubleComplementEq) => 72.29/9.89 (( 72.29/9.89 (complementTnotintersectT) => 72.29/9.89 (( 72.29/9.89 (complementImpComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementSubsetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementInPowersetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (contraSubsetComplement) => 72.29/9.89 (( 72.29/9.89 (complementTcontraSubset) => 72.29/9.89 (( 72.29/9.89 (binunionTILcontra) => 72.29/9.89 (( 72.29/9.89 (binunionTIRcontra) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion2) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (intersectInPowersetIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpNotIn1) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpInComplement1) => 72.29/9.89 (( 72.29/9.89 (binunionTE) => 72.29/9.89 (( 72.29/9.89 (binunionTEcontra) => 72.29/9.89 (( 72.29/9.89 (demorgan2a1) => 72.29/9.89 (( 72.29/9.89 (complementUnionInPowersetComplement) => 72.29/9.89 (( 72.29/9.89 (demorgan2a2) => 72.29/9.89 (( 72.29/9.89 (demorgan1a) => 72.29/9.89 (( 72.29/9.89 (demorgan1b) => 72.29/9.89 (( 72.29/9.89 (demorgan1) => 72.29/9.89 (( 72.29/9.89 (demorgan2a) => 72.29/9.89 (( 72.29/9.89 (demorgan2b2) => 72.29/9.89 (( 72.29/9.89 (demorgan2b) => 72.29/9.89 (( 72.29/9.89 (demorgan2) => 72.29/9.89 (( 72.29/9.89 (woz13rule0) => 72.29/9.89 (( 72.29/9.89 (woz13rule1) => 72.29/9.89 (( 72.29/9.89 (woz13rule2) => 72.29/9.89 (( 72.29/9.89 (woz13rule3) => 72.29/9.89 (( 72.29/9.89 (woz13rule4) => 72.29/9.89 (( 72.29/9.89 (woz1_1) => 72.29/9.89 (( 72.29/9.89 (woz1_2) => 72.29/9.89 (( 72.29/9.89 (woz1_3) => 72.29/9.89 (( 72.29/9.89 (woz1_4) => 72.29/9.89 (( 72.29/9.89 (woz1_5) => 72.29/9.89 (( 72.29/9.89 (breln1all2) => 72.29/9.89 (( 72.29/9.89 (breln1SetBreln1) => 72.29/9.89 (( 72.29/9.89 (choice2fnsingleton) => 72.29/9.89 (( 72.29/9.89 (setOfPairsIsBReln1) => 72.29/9.89 (( 72.29/9.89 (breln1all1) => 72.29/9.89 (( 72.29/9.89 (subbreln1) => 72.29/9.89 (( 72.29/9.89 (eqbreln1) => 72.29/9.89 (( 72.29/9.89 (breln1invprop) => 72.29/9.89 (( 72.29/9.89 (breln1invI) => 72.29/9.89 (( 72.29/9.89 (breln1invE) => 72.29/9.89 (( 72.29/9.89 (breln1compprop) => 72.29/9.89 (( 72.29/9.89 (breln1compI) => 72.29/9.89 (( 72.29/9.89 (breln1compE) => 72.29/9.89 (( 72.29/9.89 (breln1compEex) => 72.29/9.89 (( 72.29/9.89 (!!) @ ( 72.29/9.89 (('#B') @ ( 72.29/9.89 !!) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 !!))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#C') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 breln1)))) @ 72.29/9.89 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1664])). 72.29/9.89 thf(zip_derived_cl1695, plain, 72.29/9.89 (~ (((setukpairinjR11) => 72.29/9.89 (((setukpairinjR12) => 72.29/9.89 (((setukpairinjR1) => 72.29/9.89 (((upairequniteq) => 72.29/9.89 (((setukpairinjR2) => 72.29/9.89 (((setukpairinjR) => 72.29/9.89 (((ksndsingleton) => 72.29/9.89 (((ksndpairEq) => 72.29/9.89 (((kpairsurjEq) => 72.29/9.89 (((cartprodsndin) => 72.29/9.89 (((cartprodpairmemEL) => 72.29/9.89 (((cartprodpairmemER) => 72.29/9.89 (((cartprodmempaircEq) => 72.29/9.89 (((cartprodfstpairEq) => 72.29/9.89 (((cartprodsndpairEq) => 72.29/9.89 (((cartprodpairsurjEq) => 72.29/9.89 (((dpsetconstrI) => 72.29/9.89 (((dpsetconstrSub) => 72.29/9.89 (((setOfPairsIsBReln) => 72.29/9.89 (((dpsetconstrERa) => 72.29/9.89 (((dpsetconstrEL1) => 72.29/9.89 (((dpsetconstrEL2) => 72.29/9.89 (((dpsetconstrER) => 72.29/9.89 (((funcImageSingleton) => 72.29/9.89 (((apProp) => 72.29/9.89 (((app) => 72.29/9.89 (((infuncsetfunc) => 72.29/9.89 (((ap2p) => 72.29/9.89 (((funcinfuncset) => 72.29/9.89 (((lamProp) => 72.29/9.89 (( 72.29/9.89 (lamp) => 72.29/9.89 (( 72.29/9.89 (lam2p) => 72.29/9.89 (( 72.29/9.89 (brelnall1) => 72.29/9.89 (( 72.29/9.89 (brelnall2) => 72.29/9.89 (( 72.29/9.89 (ex1E2) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp1) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp3) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp2) => 72.29/9.89 (( 72.29/9.89 (funcextLem) => 72.29/9.89 (( 72.29/9.89 (funcGraphProp4) => 72.29/9.89 (( 72.29/9.89 (subbreln) => 72.29/9.89 (( 72.29/9.89 (eqbreln) => 72.29/9.89 (( 72.29/9.89 (funcext) => 72.29/9.89 (( 72.29/9.89 (funcext2) => 72.29/9.89 (( 72.29/9.89 (ap2apEq1) => 72.29/9.89 (( 72.29/9.89 (ap2apEq2) => 72.29/9.89 (( 72.29/9.89 (beta1) => 72.29/9.89 (( 72.29/9.89 (eta1) => 72.29/9.89 (( 72.29/9.89 (lam2lamEq) => 72.29/9.89 (( 72.29/9.89 (beta2) => 72.29/9.89 (( 72.29/9.89 (eta2) => 72.29/9.89 (( 72.29/9.89 (iffalseProp1) => 72.29/9.89 (( 72.29/9.89 (iffalseProp2) => 72.29/9.89 (( 72.29/9.89 (iftrueProp1) => 72.29/9.89 (( 72.29/9.89 (iftrueProp2) => 72.29/9.89 (( 72.29/9.89 (ifSingleton) => 72.29/9.89 (( 72.29/9.89 (ifp) => 72.29/9.89 (( 72.29/9.89 (theeq) => 72.29/9.89 (( 72.29/9.89 (iftrue) => 72.29/9.89 (( 72.29/9.89 (iffalse) => 72.29/9.89 (( 72.29/9.89 (iftrueorfalse) => 72.29/9.89 (( 72.29/9.89 (binintersectT_lem) => 72.29/9.89 (( 72.29/9.89 (binunionT_lem) => 72.29/9.89 (( 72.29/9.89 (powersetT_lem) => 72.29/9.89 (( 72.29/9.89 (setminusT_lem) => 72.29/9.89 (( 72.29/9.89 (complementT_lem) => 72.29/9.89 (( 72.29/9.89 (setextT) => 72.29/9.89 (( 72.29/9.89 (subsetTI) => 72.29/9.89 (( 72.29/9.89 (powersetTI1) => 72.29/9.89 (( 72.29/9.89 (powersetTE1) => 72.29/9.89 (( 72.29/9.89 (complementTI1) => 72.29/9.89 (( 72.29/9.89 (complementTE1) => 72.29/9.89 (( 72.29/9.89 (binintersectTELcontra) => 72.29/9.89 (( 72.29/9.89 (binintersectTERcontra) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT1) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT2) => 72.29/9.89 (( 72.29/9.89 (contrasubsetT3) => 72.29/9.89 (( 72.29/9.89 (doubleComplementI1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementE1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub1) => 72.29/9.89 (( 72.29/9.89 (doubleComplementSub2) => 72.29/9.89 (( 72.29/9.89 (doubleComplementEq) => 72.29/9.89 (( 72.29/9.89 (complementTnotintersectT) => 72.29/9.89 (( 72.29/9.89 (complementImpComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementSubsetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (complementInPowersetComplementIntersect) => 72.29/9.89 (( 72.29/9.89 (contraSubsetComplement) => 72.29/9.89 (( 72.29/9.89 (complementTcontraSubset) => 72.29/9.89 (( 72.29/9.89 (binunionTILcontra) => 72.29/9.89 (( 72.29/9.89 (binunionTIRcontra) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInUnion2) => 72.29/9.89 (( 72.29/9.89 (inIntersectImpInIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (intersectInPowersetIntersectUnions) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpNotIn1) => 72.29/9.89 (( 72.29/9.89 (inComplementUnionImpInComplement1) => 72.29/9.89 (( 72.29/9.89 (binunionTE) => 72.29/9.89 (( 72.29/9.89 (binunionTEcontra) => 72.29/9.89 (( 72.29/9.89 (demorgan2a1) => 72.29/9.89 (( 72.29/9.89 (complementUnionInPowersetComplement) => 72.29/9.89 (( 72.29/9.89 (demorgan2a2) => 72.29/9.89 (( 72.29/9.89 (demorgan1a) => 72.29/9.89 (( 72.29/9.89 (demorgan1b) => 72.29/9.89 (( 72.29/9.89 (demorgan1) => 72.29/9.89 (( 72.29/9.89 (demorgan2a) => 72.29/9.89 (( 72.29/9.89 (demorgan2b2) => 72.29/9.89 (( 72.29/9.89 (demorgan2b) => 72.29/9.89 (( 72.29/9.89 (demorgan2) => 72.29/9.89 (( 72.29/9.89 (woz13rule0) => 72.29/9.89 (( 72.29/9.89 (woz13rule1) => 72.29/9.89 (( 72.29/9.89 (woz13rule2) => 72.29/9.89 (( 72.29/9.89 (woz13rule3) => 72.29/9.89 (( 72.29/9.89 (woz13rule4) => 72.29/9.89 (( 72.29/9.89 (woz1_1) => 72.29/9.89 (( 72.29/9.89 (woz1_2) => 72.29/9.89 (( 72.29/9.89 (woz1_3) => 72.29/9.89 (( 72.29/9.89 (woz1_4) => 72.29/9.89 (( 72.29/9.89 (woz1_5) => 72.29/9.89 (( 72.29/9.89 (breln1all2) => 72.29/9.89 (( 72.29/9.89 (breln1SetBreln1) => 72.29/9.89 (( 72.29/9.89 (choice2fnsingleton) => 72.29/9.89 (( 72.29/9.89 (setOfPairsIsBReln1) => 72.29/9.89 (( 72.29/9.89 (breln1all1) => 72.29/9.89 (( 72.29/9.89 (subbreln1) => 72.29/9.89 (( 72.29/9.89 (eqbreln1) => 72.29/9.89 (( 72.29/9.89 (breln1invprop) => 72.29/9.89 (( 72.29/9.89 (breln1invI) => 72.29/9.89 (( 72.29/9.89 (breln1invE) => 72.29/9.89 (( 72.29/9.89 (breln1compprop) => 72.29/9.89 (( 72.29/9.89 (breln1compI) => 72.29/9.89 (( 72.29/9.89 (breln1compE) => 72.29/9.89 (( 72.29/9.89 (breln1compEex) => 72.29/9.89 (( 72.29/9.89 (!!) @ ( 72.29/9.89 (('#B') @ ( 72.29/9.89 !!) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 =>))) @ 72.29/9.89 breln1)))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 !!))) @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#S') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#B') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 '#S') @ 72.29/9.89 ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.89 ( 72.29/9.89 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#C') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 breln1)))) @ 72.29/9.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1678])). 72.29/9.90 thf(zip_derived_cl1711, plain, 72.29/9.90 (~ (((setukpairinjR12) => 72.29/9.90 (((setukpairinjR1) => 72.29/9.90 (((upairequniteq) => 72.29/9.90 (((setukpairinjR2) => 72.29/9.90 (((setukpairinjR) => 72.29/9.90 (((ksndsingleton) => 72.29/9.90 (((ksndpairEq) => 72.29/9.90 (((kpairsurjEq) => 72.29/9.90 (((cartprodsndin) => 72.29/9.90 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72.29/9.90 (setminusT_lem) => 72.29/9.90 (( 72.29/9.90 (complementT_lem) => 72.29/9.90 (( 72.29/9.90 (setextT) => 72.29/9.90 (( 72.29/9.90 (subsetTI) => 72.29/9.90 (( 72.29/9.90 (powersetTI1) => 72.29/9.90 (( 72.29/9.90 (powersetTE1) => 72.29/9.90 (( 72.29/9.90 (complementTI1) => 72.29/9.90 (( 72.29/9.90 (complementTE1) => 72.29/9.90 (( 72.29/9.90 (binintersectTELcontra) => 72.29/9.90 (( 72.29/9.90 (binintersectTERcontra) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT1) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT2) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT3) => 72.29/9.90 (( 72.29/9.90 (doubleComplementI1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementE1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub2) => 72.29/9.90 (( 72.29/9.90 (doubleComplementEq) => 72.29/9.90 (( 72.29/9.90 (complementTnotintersectT) => 72.29/9.90 (( 72.29/9.90 (complementImpComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementSubsetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementInPowersetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (contraSubsetComplement) => 72.29/9.90 (( 72.29/9.90 (complementTcontraSubset) => 72.29/9.90 (( 72.29/9.90 (binunionTILcontra) => 72.29/9.90 (( 72.29/9.90 (binunionTIRcontra) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion2) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (intersectInPowersetIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpNotIn1) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpInComplement1) => 72.29/9.90 (( 72.29/9.90 (binunionTE) => 72.29/9.90 (( 72.29/9.90 (binunionTEcontra) => 72.29/9.90 (( 72.29/9.90 (demorgan2a1) => 72.29/9.90 (( 72.29/9.90 (complementUnionInPowersetComplement) => 72.29/9.90 (( 72.29/9.90 (demorgan2a2) => 72.29/9.90 (( 72.29/9.90 (demorgan1a) => 72.29/9.90 (( 72.29/9.90 (demorgan1b) => 72.29/9.90 (( 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(breln1invE) => 72.29/9.90 (( 72.29/9.90 (breln1compprop) => 72.29/9.90 (( 72.29/9.90 (breln1compI) => 72.29/9.90 (( 72.29/9.90 (breln1compE) => 72.29/9.90 (( 72.29/9.90 (breln1compEex) => 72.29/9.90 (( 72.29/9.90 (!!) @ ( 72.29/9.90 (('#B') @ ( 72.29/9.90 !!) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 !!))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#C') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 breln1)))) @ 72.29/9.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1695])). 72.29/9.90 thf(zip_derived_cl1725, plain, 72.29/9.90 (~ (((setukpairinjR1) => 72.29/9.90 (((upairequniteq) => 72.29/9.90 (((setukpairinjR2) => 72.29/9.90 (((setukpairinjR) => 72.29/9.90 (((ksndsingleton) => 72.29/9.90 (((ksndpairEq) => 72.29/9.90 (((kpairsurjEq) => 72.29/9.90 (((cartprodsndin) => 72.29/9.90 (((cartprodpairmemEL) => 72.29/9.90 (((cartprodpairmemER) => 72.29/9.90 (((cartprodmempaircEq) => 72.29/9.90 (((cartprodfstpairEq) => 72.29/9.90 (((cartprodsndpairEq) => 72.29/9.90 (((cartprodpairsurjEq) => 72.29/9.90 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(powersetTE1) => 72.29/9.90 (( 72.29/9.90 (complementTI1) => 72.29/9.90 (( 72.29/9.90 (complementTE1) => 72.29/9.90 (( 72.29/9.90 (binintersectTELcontra) => 72.29/9.90 (( 72.29/9.90 (binintersectTERcontra) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT1) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT2) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT3) => 72.29/9.90 (( 72.29/9.90 (doubleComplementI1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementE1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub2) => 72.29/9.90 (( 72.29/9.90 (doubleComplementEq) => 72.29/9.90 (( 72.29/9.90 (complementTnotintersectT) => 72.29/9.90 (( 72.29/9.90 (complementImpComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementSubsetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementInPowersetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (contraSubsetComplement) => 72.29/9.90 (( 72.29/9.90 (complementTcontraSubset) => 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(woz13rule0) => 72.29/9.90 (( 72.29/9.90 (woz13rule1) => 72.29/9.90 (( 72.29/9.90 (woz13rule2) => 72.29/9.90 (( 72.29/9.90 (woz13rule3) => 72.29/9.90 (( 72.29/9.90 (woz13rule4) => 72.29/9.90 (( 72.29/9.90 (woz1_1) => 72.29/9.90 (( 72.29/9.90 (woz1_2) => 72.29/9.90 (( 72.29/9.90 (woz1_3) => 72.29/9.90 (( 72.29/9.90 (woz1_4) => 72.29/9.90 (( 72.29/9.90 (woz1_5) => 72.29/9.90 (( 72.29/9.90 (breln1all2) => 72.29/9.90 (( 72.29/9.90 (breln1SetBreln1) => 72.29/9.90 (( 72.29/9.90 (choice2fnsingleton) => 72.29/9.90 (( 72.29/9.90 (setOfPairsIsBReln1) => 72.29/9.90 (( 72.29/9.90 (breln1all1) => 72.29/9.90 (( 72.29/9.90 (subbreln1) => 72.29/9.90 (( 72.29/9.90 (eqbreln1) => 72.29/9.90 (( 72.29/9.90 (breln1invprop) => 72.29/9.90 (( 72.29/9.90 (breln1invI) => 72.29/9.90 (( 72.29/9.90 (breln1invE) => 72.29/9.90 (( 72.29/9.90 (breln1compprop) => 72.29/9.90 (( 72.29/9.90 (breln1compI) => 72.29/9.90 (( 72.29/9.90 (breln1compE) => 72.29/9.90 (( 72.29/9.90 (breln1compEex) => 72.29/9.90 (( 72.29/9.90 (!!) @ ( 72.29/9.90 (('#B') @ ( 72.29/9.90 !!) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 !!))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#C') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 breln1)))) @ 72.29/9.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1711])). 72.29/9.90 thf(zip_derived_cl1738, plain, 72.29/9.90 (~ (((upairequniteq) => 72.29/9.90 (((setukpairinjR2) => 72.29/9.90 (((setukpairinjR) => 72.29/9.90 (((ksndsingleton) => 72.29/9.90 (((ksndpairEq) => 72.29/9.90 (((kpairsurjEq) => 72.29/9.90 (((cartprodsndin) => 72.29/9.90 (((cartprodpairmemEL) => 72.29/9.90 (((cartprodpairmemER) => 72.29/9.90 (((cartprodmempaircEq) => 72.29/9.90 (((cartprodfstpairEq) => 72.29/9.90 (((cartprodsndpairEq) => 72.29/9.90 (((cartprodpairsurjEq) => 72.29/9.90 (((dpsetconstrI) => 72.29/9.90 (((dpsetconstrSub) => 72.29/9.90 (((setOfPairsIsBReln) => 72.29/9.90 (((dpsetconstrERa) => 72.29/9.90 (((dpsetconstrEL1) => 72.29/9.90 (((dpsetconstrEL2) => 72.29/9.90 (((dpsetconstrER) => 72.29/9.90 (((funcImageSingleton) => 72.29/9.90 (((apProp) => 72.29/9.90 (((app) => 72.29/9.90 (((infuncsetfunc) => 72.29/9.90 (((ap2p) => 72.29/9.90 (((funcinfuncset) => 72.29/9.90 (((lamProp) => 72.29/9.90 (((lamp) => 72.29/9.90 (((lam2p) => 72.29/9.90 (((brelnall1) => 72.29/9.90 (( 72.29/9.90 (brelnall2) => 72.29/9.90 (( 72.29/9.90 (ex1E2) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp1) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp3) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp2) => 72.29/9.90 (( 72.29/9.90 (funcextLem) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp4) => 72.29/9.90 (( 72.29/9.90 (subbreln) => 72.29/9.90 (( 72.29/9.90 (eqbreln) => 72.29/9.90 (( 72.29/9.90 (funcext) => 72.29/9.90 (( 72.29/9.90 (funcext2) => 72.29/9.90 (( 72.29/9.90 (ap2apEq1) => 72.29/9.90 (( 72.29/9.90 (ap2apEq2) => 72.29/9.90 (( 72.29/9.90 (beta1) => 72.29/9.90 (( 72.29/9.90 (eta1) => 72.29/9.90 (( 72.29/9.90 (lam2lamEq) => 72.29/9.90 (( 72.29/9.90 (beta2) => 72.29/9.90 (( 72.29/9.90 (eta2) => 72.29/9.90 (( 72.29/9.90 (iffalseProp1) => 72.29/9.90 (( 72.29/9.90 (iffalseProp2) => 72.29/9.90 (( 72.29/9.90 (iftrueProp1) => 72.29/9.90 (( 72.29/9.90 (iftrueProp2) => 72.29/9.90 (( 72.29/9.90 (ifSingleton) => 72.29/9.90 (( 72.29/9.90 (ifp) => 72.29/9.90 (( 72.29/9.90 (theeq) => 72.29/9.90 (( 72.29/9.90 (iftrue) => 72.29/9.90 (( 72.29/9.90 (iffalse) => 72.29/9.90 (( 72.29/9.90 (iftrueorfalse) => 72.29/9.90 (( 72.29/9.90 (binintersectT_lem) => 72.29/9.90 (( 72.29/9.90 (binunionT_lem) => 72.29/9.90 (( 72.29/9.90 (powersetT_lem) => 72.29/9.90 (( 72.29/9.90 (setminusT_lem) => 72.29/9.90 (( 72.29/9.90 (complementT_lem) => 72.29/9.90 (( 72.29/9.90 (setextT) => 72.29/9.90 (( 72.29/9.90 (subsetTI) => 72.29/9.90 (( 72.29/9.90 (powersetTI1) => 72.29/9.90 (( 72.29/9.90 (powersetTE1) => 72.29/9.90 (( 72.29/9.90 (complementTI1) => 72.29/9.90 (( 72.29/9.90 (complementTE1) => 72.29/9.90 (( 72.29/9.90 (binintersectTELcontra) => 72.29/9.90 (( 72.29/9.90 (binintersectTERcontra) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT1) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT2) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT3) => 72.29/9.90 (( 72.29/9.90 (doubleComplementI1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementE1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub2) => 72.29/9.90 (( 72.29/9.90 (doubleComplementEq) => 72.29/9.90 (( 72.29/9.90 (complementTnotintersectT) => 72.29/9.90 (( 72.29/9.90 (complementImpComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementSubsetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementInPowersetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (contraSubsetComplement) => 72.29/9.90 (( 72.29/9.90 (complementTcontraSubset) => 72.29/9.90 (( 72.29/9.90 (binunionTILcontra) => 72.29/9.90 (( 72.29/9.90 (binunionTIRcontra) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion2) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (intersectInPowersetIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpNotIn1) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpInComplement1) => 72.29/9.90 (( 72.29/9.90 (binunionTE) => 72.29/9.90 (( 72.29/9.90 (binunionTEcontra) => 72.29/9.90 (( 72.29/9.90 (demorgan2a1) => 72.29/9.90 (( 72.29/9.90 (complementUnionInPowersetComplement) => 72.29/9.90 (( 72.29/9.90 (demorgan2a2) => 72.29/9.90 (( 72.29/9.90 (demorgan1a) => 72.29/9.90 (( 72.29/9.90 (demorgan1b) => 72.29/9.90 (( 72.29/9.90 (demorgan1) => 72.29/9.90 (( 72.29/9.90 (demorgan2a) => 72.29/9.90 (( 72.29/9.90 (demorgan2b2) => 72.29/9.90 (( 72.29/9.90 (demorgan2b) => 72.29/9.90 (( 72.29/9.90 (demorgan2) => 72.29/9.90 (( 72.29/9.90 (woz13rule0) => 72.29/9.90 (( 72.29/9.90 (woz13rule1) => 72.29/9.90 (( 72.29/9.90 (woz13rule2) => 72.29/9.90 (( 72.29/9.90 (woz13rule3) => 72.29/9.90 (( 72.29/9.90 (woz13rule4) => 72.29/9.90 (( 72.29/9.90 (woz1_1) => 72.29/9.90 (( 72.29/9.90 (woz1_2) => 72.29/9.90 (( 72.29/9.90 (woz1_3) => 72.29/9.90 (( 72.29/9.90 (woz1_4) => 72.29/9.90 (( 72.29/9.90 (woz1_5) => 72.29/9.90 (( 72.29/9.90 (breln1all2) => 72.29/9.90 (( 72.29/9.90 (breln1SetBreln1) => 72.29/9.90 (( 72.29/9.90 (choice2fnsingleton) => 72.29/9.90 (( 72.29/9.90 (setOfPairsIsBReln1) => 72.29/9.90 (( 72.29/9.90 (breln1all1) => 72.29/9.90 (( 72.29/9.90 (subbreln1) => 72.29/9.90 (( 72.29/9.90 (eqbreln1) => 72.29/9.90 (( 72.29/9.90 (breln1invprop) => 72.29/9.90 (( 72.29/9.90 (breln1invI) => 72.29/9.90 (( 72.29/9.90 (breln1invE) => 72.29/9.90 (( 72.29/9.90 (breln1compprop) => 72.29/9.90 (( 72.29/9.90 (breln1compI) => 72.29/9.90 (( 72.29/9.90 (breln1compE) => 72.29/9.90 (( 72.29/9.90 (breln1compEex) => 72.29/9.90 (( 72.29/9.90 (!!) @ ( 72.29/9.90 (('#B') @ ( 72.29/9.90 !!) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 !!))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#C') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 breln1)))) @ 72.29/9.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1725])). 72.29/9.90 thf(zip_derived_cl1749, plain, 72.29/9.90 (~ (((setukpairinjR2) => 72.29/9.90 (((setukpairinjR) => 72.29/9.90 (((ksndsingleton) => 72.29/9.90 (((ksndpairEq) => 72.29/9.90 (((kpairsurjEq) => 72.29/9.90 (((cartprodsndin) => 72.29/9.90 (((cartprodpairmemEL) => 72.29/9.90 (((cartprodpairmemER) => 72.29/9.90 (((cartprodmempaircEq) => 72.29/9.90 (((cartprodfstpairEq) => 72.29/9.90 (((cartprodsndpairEq) => 72.29/9.90 (((cartprodpairsurjEq) => 72.29/9.90 (((dpsetconstrI) => 72.29/9.90 (((dpsetconstrSub) => 72.29/9.90 (((setOfPairsIsBReln) => 72.29/9.90 (((dpsetconstrERa) => 72.29/9.90 (((dpsetconstrEL1) => 72.29/9.90 (((dpsetconstrEL2) => 72.29/9.90 (((dpsetconstrER) => 72.29/9.90 (((funcImageSingleton) => 72.29/9.90 (((apProp) => 72.29/9.90 (((app) => 72.29/9.90 (((infuncsetfunc) => 72.29/9.90 (((ap2p) => 72.29/9.90 (((funcinfuncset) => 72.29/9.90 (((lamProp) => 72.29/9.90 (((lamp) => 72.29/9.90 (((lam2p) => 72.29/9.90 (((brelnall1) => 72.29/9.90 (((brelnall2) => 72.29/9.90 (( 72.29/9.90 (ex1E2) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp1) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp3) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp2) => 72.29/9.90 (( 72.29/9.90 (funcextLem) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp4) => 72.29/9.90 (( 72.29/9.90 (subbreln) => 72.29/9.90 (( 72.29/9.90 (eqbreln) => 72.29/9.90 (( 72.29/9.90 (funcext) => 72.29/9.90 (( 72.29/9.90 (funcext2) => 72.29/9.90 (( 72.29/9.90 (ap2apEq1) => 72.29/9.90 (( 72.29/9.90 (ap2apEq2) => 72.29/9.90 (( 72.29/9.90 (beta1) => 72.29/9.90 (( 72.29/9.90 (eta1) => 72.29/9.90 (( 72.29/9.90 (lam2lamEq) => 72.29/9.90 (( 72.29/9.90 (beta2) => 72.29/9.90 (( 72.29/9.90 (eta2) => 72.29/9.90 (( 72.29/9.90 (iffalseProp1) => 72.29/9.90 (( 72.29/9.90 (iffalseProp2) => 72.29/9.90 (( 72.29/9.90 (iftrueProp1) => 72.29/9.90 (( 72.29/9.90 (iftrueProp2) => 72.29/9.90 (( 72.29/9.90 (ifSingleton) => 72.29/9.90 (( 72.29/9.90 (ifp) => 72.29/9.90 (( 72.29/9.90 (theeq) => 72.29/9.90 (( 72.29/9.90 (iftrue) => 72.29/9.90 (( 72.29/9.90 (iffalse) => 72.29/9.90 (( 72.29/9.90 (iftrueorfalse) => 72.29/9.90 (( 72.29/9.90 (binintersectT_lem) => 72.29/9.90 (( 72.29/9.90 (binunionT_lem) => 72.29/9.90 (( 72.29/9.90 (powersetT_lem) => 72.29/9.90 (( 72.29/9.90 (setminusT_lem) => 72.29/9.90 (( 72.29/9.90 (complementT_lem) => 72.29/9.90 (( 72.29/9.90 (setextT) => 72.29/9.90 (( 72.29/9.90 (subsetTI) => 72.29/9.90 (( 72.29/9.90 (powersetTI1) => 72.29/9.90 (( 72.29/9.90 (powersetTE1) => 72.29/9.90 (( 72.29/9.90 (complementTI1) => 72.29/9.90 (( 72.29/9.90 (complementTE1) => 72.29/9.90 (( 72.29/9.90 (binintersectTELcontra) => 72.29/9.90 (( 72.29/9.90 (binintersectTERcontra) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT1) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT2) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT3) => 72.29/9.90 (( 72.29/9.90 (doubleComplementI1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementE1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub2) => 72.29/9.90 (( 72.29/9.90 (doubleComplementEq) => 72.29/9.90 (( 72.29/9.90 (complementTnotintersectT) => 72.29/9.90 (( 72.29/9.90 (complementImpComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementSubsetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementInPowersetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (contraSubsetComplement) => 72.29/9.90 (( 72.29/9.90 (complementTcontraSubset) => 72.29/9.90 (( 72.29/9.90 (binunionTILcontra) => 72.29/9.90 (( 72.29/9.90 (binunionTIRcontra) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion2) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (intersectInPowersetIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpNotIn1) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpInComplement1) => 72.29/9.90 (( 72.29/9.90 (binunionTE) => 72.29/9.90 (( 72.29/9.90 (binunionTEcontra) => 72.29/9.90 (( 72.29/9.90 (demorgan2a1) => 72.29/9.90 (( 72.29/9.90 (complementUnionInPowersetComplement) => 72.29/9.90 (( 72.29/9.90 (demorgan2a2) => 72.29/9.90 (( 72.29/9.90 (demorgan1a) => 72.29/9.90 (( 72.29/9.90 (demorgan1b) => 72.29/9.90 (( 72.29/9.90 (demorgan1) => 72.29/9.90 (( 72.29/9.90 (demorgan2a) => 72.29/9.90 (( 72.29/9.90 (demorgan2b2) => 72.29/9.90 (( 72.29/9.90 (demorgan2b) => 72.29/9.90 (( 72.29/9.90 (demorgan2) => 72.29/9.90 (( 72.29/9.90 (woz13rule0) => 72.29/9.90 (( 72.29/9.90 (woz13rule1) => 72.29/9.90 (( 72.29/9.90 (woz13rule2) => 72.29/9.90 (( 72.29/9.90 (woz13rule3) => 72.29/9.90 (( 72.29/9.90 (woz13rule4) => 72.29/9.90 (( 72.29/9.90 (woz1_1) => 72.29/9.90 (( 72.29/9.90 (woz1_2) => 72.29/9.90 (( 72.29/9.90 (woz1_3) => 72.29/9.90 (( 72.29/9.90 (woz1_4) => 72.29/9.90 (( 72.29/9.90 (woz1_5) => 72.29/9.90 (( 72.29/9.90 (breln1all2) => 72.29/9.90 (( 72.29/9.90 (breln1SetBreln1) => 72.29/9.90 (( 72.29/9.90 (choice2fnsingleton) => 72.29/9.90 (( 72.29/9.90 (setOfPairsIsBReln1) => 72.29/9.90 (( 72.29/9.90 (breln1all1) => 72.29/9.90 (( 72.29/9.90 (subbreln1) => 72.29/9.90 (( 72.29/9.90 (eqbreln1) => 72.29/9.90 (( 72.29/9.90 (breln1invprop) => 72.29/9.90 (( 72.29/9.90 (breln1invI) => 72.29/9.90 (( 72.29/9.90 (breln1invE) => 72.29/9.90 (( 72.29/9.90 (breln1compprop) => 72.29/9.90 (( 72.29/9.90 (breln1compI) => 72.29/9.90 (( 72.29/9.90 (breln1compE) => 72.29/9.90 (( 72.29/9.90 (breln1compEex) => 72.29/9.90 (( 72.29/9.90 (!!) @ ( 72.29/9.90 (('#B') @ ( 72.29/9.90 !!) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 !!))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#C') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 breln1)))) @ 72.29/9.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1738])). 72.29/9.90 thf(zip_derived_cl1760, plain, 72.29/9.90 (~ (((setukpairinjR) => 72.29/9.90 (((ksndsingleton) => 72.29/9.90 (((ksndpairEq) => 72.29/9.90 (((kpairsurjEq) => 72.29/9.90 (((cartprodsndin) => 72.29/9.90 (((cartprodpairmemEL) => 72.29/9.90 (((cartprodpairmemER) => 72.29/9.90 (((cartprodmempaircEq) => 72.29/9.90 (((cartprodfstpairEq) => 72.29/9.90 (((cartprodsndpairEq) => 72.29/9.90 (((cartprodpairsurjEq) => 72.29/9.90 (((dpsetconstrI) => 72.29/9.90 (((dpsetconstrSub) => 72.29/9.90 (((setOfPairsIsBReln) => 72.29/9.90 (((dpsetconstrERa) => 72.29/9.90 (((dpsetconstrEL1) => 72.29/9.90 (((dpsetconstrEL2) => 72.29/9.90 (((dpsetconstrER) => 72.29/9.90 (((funcImageSingleton) => 72.29/9.90 (((apProp) => 72.29/9.90 (((app) => 72.29/9.90 (((infuncsetfunc) => 72.29/9.90 (((ap2p) => 72.29/9.90 (((funcinfuncset) => 72.29/9.90 (((lamProp) => 72.29/9.90 (((lamp) => 72.29/9.90 (((lam2p) => 72.29/9.90 (((brelnall1) => 72.29/9.90 (((brelnall2) => 72.29/9.90 (((ex1E2) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp1) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp3) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp2) => 72.29/9.90 (( 72.29/9.90 (funcextLem) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp4) => 72.29/9.90 (( 72.29/9.90 (subbreln) => 72.29/9.90 (( 72.29/9.90 (eqbreln) => 72.29/9.90 (( 72.29/9.90 (funcext) => 72.29/9.90 (( 72.29/9.90 (funcext2) => 72.29/9.90 (( 72.29/9.90 (ap2apEq1) => 72.29/9.90 (( 72.29/9.90 (ap2apEq2) => 72.29/9.90 (( 72.29/9.90 (beta1) => 72.29/9.90 (( 72.29/9.90 (eta1) => 72.29/9.90 (( 72.29/9.90 (lam2lamEq) => 72.29/9.90 (( 72.29/9.90 (beta2) => 72.29/9.90 (( 72.29/9.90 (eta2) => 72.29/9.90 (( 72.29/9.90 (iffalseProp1) => 72.29/9.90 (( 72.29/9.90 (iffalseProp2) => 72.29/9.90 (( 72.29/9.90 (iftrueProp1) => 72.29/9.90 (( 72.29/9.90 (iftrueProp2) => 72.29/9.90 (( 72.29/9.90 (ifSingleton) => 72.29/9.90 (( 72.29/9.90 (ifp) => 72.29/9.90 (( 72.29/9.90 (theeq) => 72.29/9.90 (( 72.29/9.90 (iftrue) => 72.29/9.90 (( 72.29/9.90 (iffalse) => 72.29/9.90 (( 72.29/9.90 (iftrueorfalse) => 72.29/9.90 (( 72.29/9.90 (binintersectT_lem) => 72.29/9.90 (( 72.29/9.90 (binunionT_lem) => 72.29/9.90 (( 72.29/9.90 (powersetT_lem) => 72.29/9.90 (( 72.29/9.90 (setminusT_lem) => 72.29/9.90 (( 72.29/9.90 (complementT_lem) => 72.29/9.90 (( 72.29/9.90 (setextT) => 72.29/9.90 (( 72.29/9.90 (subsetTI) => 72.29/9.90 (( 72.29/9.90 (powersetTI1) => 72.29/9.90 (( 72.29/9.90 (powersetTE1) => 72.29/9.90 (( 72.29/9.90 (complementTI1) => 72.29/9.90 (( 72.29/9.90 (complementTE1) => 72.29/9.90 (( 72.29/9.90 (binintersectTELcontra) => 72.29/9.90 (( 72.29/9.90 (binintersectTERcontra) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT1) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT2) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT3) => 72.29/9.90 (( 72.29/9.90 (doubleComplementI1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementE1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub2) => 72.29/9.90 (( 72.29/9.90 (doubleComplementEq) => 72.29/9.90 (( 72.29/9.90 (complementTnotintersectT) => 72.29/9.90 (( 72.29/9.90 (complementImpComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementSubsetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementInPowersetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (contraSubsetComplement) => 72.29/9.90 (( 72.29/9.90 (complementTcontraSubset) => 72.29/9.90 (( 72.29/9.90 (binunionTILcontra) => 72.29/9.90 (( 72.29/9.90 (binunionTIRcontra) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion2) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (intersectInPowersetIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpNotIn1) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpInComplement1) => 72.29/9.90 (( 72.29/9.90 (binunionTE) => 72.29/9.90 (( 72.29/9.90 (binunionTEcontra) => 72.29/9.90 (( 72.29/9.90 (demorgan2a1) => 72.29/9.90 (( 72.29/9.90 (complementUnionInPowersetComplement) => 72.29/9.90 (( 72.29/9.90 (demorgan2a2) => 72.29/9.90 (( 72.29/9.90 (demorgan1a) => 72.29/9.90 (( 72.29/9.90 (demorgan1b) => 72.29/9.90 (( 72.29/9.90 (demorgan1) => 72.29/9.90 (( 72.29/9.90 (demorgan2a) => 72.29/9.90 (( 72.29/9.90 (demorgan2b2) => 72.29/9.90 (( 72.29/9.90 (demorgan2b) => 72.29/9.90 (( 72.29/9.90 (demorgan2) => 72.29/9.90 (( 72.29/9.90 (woz13rule0) => 72.29/9.90 (( 72.29/9.90 (woz13rule1) => 72.29/9.90 (( 72.29/9.90 (woz13rule2) => 72.29/9.90 (( 72.29/9.90 (woz13rule3) => 72.29/9.90 (( 72.29/9.90 (woz13rule4) => 72.29/9.90 (( 72.29/9.90 (woz1_1) => 72.29/9.90 (( 72.29/9.90 (woz1_2) => 72.29/9.90 (( 72.29/9.90 (woz1_3) => 72.29/9.90 (( 72.29/9.90 (woz1_4) => 72.29/9.90 (( 72.29/9.90 (woz1_5) => 72.29/9.90 (( 72.29/9.90 (breln1all2) => 72.29/9.90 (( 72.29/9.90 (breln1SetBreln1) => 72.29/9.90 (( 72.29/9.90 (choice2fnsingleton) => 72.29/9.90 (( 72.29/9.90 (setOfPairsIsBReln1) => 72.29/9.90 (( 72.29/9.90 (breln1all1) => 72.29/9.90 (( 72.29/9.90 (subbreln1) => 72.29/9.90 (( 72.29/9.90 (eqbreln1) => 72.29/9.90 (( 72.29/9.90 (breln1invprop) => 72.29/9.90 (( 72.29/9.90 (breln1invI) => 72.29/9.90 (( 72.29/9.90 (breln1invE) => 72.29/9.90 (( 72.29/9.90 (breln1compprop) => 72.29/9.90 (( 72.29/9.90 (breln1compI) => 72.29/9.90 (( 72.29/9.90 (breln1compE) => 72.29/9.90 (( 72.29/9.90 (breln1compEex) => 72.29/9.90 (( 72.29/9.90 (!!) @ ( 72.29/9.90 (('#B') @ ( 72.29/9.90 !!) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 !!))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#C') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 breln1)))) @ 72.29/9.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1749])). 72.29/9.90 thf(zip_derived_cl1770, plain, 72.29/9.90 (~ (((ksndsingleton) => 72.29/9.90 (((ksndpairEq) => 72.29/9.90 (((kpairsurjEq) => 72.29/9.90 (((cartprodsndin) => 72.29/9.90 (((cartprodpairmemEL) => 72.29/9.90 (((cartprodpairmemER) => 72.29/9.90 (((cartprodmempaircEq) => 72.29/9.90 (((cartprodfstpairEq) => 72.29/9.90 (((cartprodsndpairEq) => 72.29/9.90 (((cartprodpairsurjEq) => 72.29/9.90 (((dpsetconstrI) => 72.29/9.90 (((dpsetconstrSub) => 72.29/9.90 (((setOfPairsIsBReln) => 72.29/9.90 (((dpsetconstrERa) => 72.29/9.90 (((dpsetconstrEL1) => 72.29/9.90 (((dpsetconstrEL2) => 72.29/9.90 (((dpsetconstrER) => 72.29/9.90 (((funcImageSingleton) => 72.29/9.90 (((apProp) => 72.29/9.90 (((app) => 72.29/9.90 (((infuncsetfunc) => 72.29/9.90 (((ap2p) => 72.29/9.90 (((funcinfuncset) => 72.29/9.90 (((lamProp) => 72.29/9.90 (((lamp) => 72.29/9.90 (((lam2p) => 72.29/9.90 (((brelnall1) => 72.29/9.90 (((brelnall2) => 72.29/9.90 (((ex1E2) => 72.29/9.90 (((funcGraphProp1) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp3) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp2) => 72.29/9.90 (( 72.29/9.90 (funcextLem) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp4) => 72.29/9.90 (( 72.29/9.90 (subbreln) => 72.29/9.90 (( 72.29/9.90 (eqbreln) => 72.29/9.90 (( 72.29/9.90 (funcext) => 72.29/9.90 (( 72.29/9.90 (funcext2) => 72.29/9.90 (( 72.29/9.90 (ap2apEq1) => 72.29/9.90 (( 72.29/9.90 (ap2apEq2) => 72.29/9.90 (( 72.29/9.90 (beta1) => 72.29/9.90 (( 72.29/9.90 (eta1) => 72.29/9.90 (( 72.29/9.90 (lam2lamEq) => 72.29/9.90 (( 72.29/9.90 (beta2) => 72.29/9.90 (( 72.29/9.90 (eta2) => 72.29/9.90 (( 72.29/9.90 (iffalseProp1) => 72.29/9.90 (( 72.29/9.90 (iffalseProp2) => 72.29/9.90 (( 72.29/9.90 (iftrueProp1) => 72.29/9.90 (( 72.29/9.90 (iftrueProp2) => 72.29/9.90 (( 72.29/9.90 (ifSingleton) => 72.29/9.90 (( 72.29/9.90 (ifp) => 72.29/9.90 (( 72.29/9.90 (theeq) => 72.29/9.90 (( 72.29/9.90 (iftrue) => 72.29/9.90 (( 72.29/9.90 (iffalse) => 72.29/9.90 (( 72.29/9.90 (iftrueorfalse) => 72.29/9.90 (( 72.29/9.90 (binintersectT_lem) => 72.29/9.90 (( 72.29/9.90 (binunionT_lem) => 72.29/9.90 (( 72.29/9.90 (powersetT_lem) => 72.29/9.90 (( 72.29/9.90 (setminusT_lem) => 72.29/9.90 (( 72.29/9.90 (complementT_lem) => 72.29/9.90 (( 72.29/9.90 (setextT) => 72.29/9.90 (( 72.29/9.90 (subsetTI) => 72.29/9.90 (( 72.29/9.90 (powersetTI1) => 72.29/9.90 (( 72.29/9.90 (powersetTE1) => 72.29/9.90 (( 72.29/9.90 (complementTI1) => 72.29/9.90 (( 72.29/9.90 (complementTE1) => 72.29/9.90 (( 72.29/9.90 (binintersectTELcontra) => 72.29/9.90 (( 72.29/9.90 (binintersectTERcontra) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT1) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT2) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT3) => 72.29/9.90 (( 72.29/9.90 (doubleComplementI1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementE1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub2) => 72.29/9.90 (( 72.29/9.90 (doubleComplementEq) => 72.29/9.90 (( 72.29/9.90 (complementTnotintersectT) => 72.29/9.90 (( 72.29/9.90 (complementImpComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementSubsetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementInPowersetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (contraSubsetComplement) => 72.29/9.90 (( 72.29/9.90 (complementTcontraSubset) => 72.29/9.90 (( 72.29/9.90 (binunionTILcontra) => 72.29/9.90 (( 72.29/9.90 (binunionTIRcontra) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion2) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (intersectInPowersetIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpNotIn1) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpInComplement1) => 72.29/9.90 (( 72.29/9.90 (binunionTE) => 72.29/9.90 (( 72.29/9.90 (binunionTEcontra) => 72.29/9.90 (( 72.29/9.90 (demorgan2a1) => 72.29/9.90 (( 72.29/9.90 (complementUnionInPowersetComplement) => 72.29/9.90 (( 72.29/9.90 (demorgan2a2) => 72.29/9.90 (( 72.29/9.90 (demorgan1a) => 72.29/9.90 (( 72.29/9.90 (demorgan1b) => 72.29/9.90 (( 72.29/9.90 (demorgan1) => 72.29/9.90 (( 72.29/9.90 (demorgan2a) => 72.29/9.90 (( 72.29/9.90 (demorgan2b2) => 72.29/9.90 (( 72.29/9.90 (demorgan2b) => 72.29/9.90 (( 72.29/9.90 (demorgan2) => 72.29/9.90 (( 72.29/9.90 (woz13rule0) => 72.29/9.90 (( 72.29/9.90 (woz13rule1) => 72.29/9.90 (( 72.29/9.90 (woz13rule2) => 72.29/9.90 (( 72.29/9.90 (woz13rule3) => 72.29/9.90 (( 72.29/9.90 (woz13rule4) => 72.29/9.90 (( 72.29/9.90 (woz1_1) => 72.29/9.90 (( 72.29/9.90 (woz1_2) => 72.29/9.90 (( 72.29/9.90 (woz1_3) => 72.29/9.90 (( 72.29/9.90 (woz1_4) => 72.29/9.90 (( 72.29/9.90 (woz1_5) => 72.29/9.90 (( 72.29/9.90 (breln1all2) => 72.29/9.90 (( 72.29/9.90 (breln1SetBreln1) => 72.29/9.90 (( 72.29/9.90 (choice2fnsingleton) => 72.29/9.90 (( 72.29/9.90 (setOfPairsIsBReln1) => 72.29/9.90 (( 72.29/9.90 (breln1all1) => 72.29/9.90 (( 72.29/9.90 (subbreln1) => 72.29/9.90 (( 72.29/9.90 (eqbreln1) => 72.29/9.90 (( 72.29/9.90 (breln1invprop) => 72.29/9.90 (( 72.29/9.90 (breln1invI) => 72.29/9.90 (( 72.29/9.90 (breln1invE) => 72.29/9.90 (( 72.29/9.90 (breln1compprop) => 72.29/9.90 (( 72.29/9.90 (breln1compI) => 72.29/9.90 (( 72.29/9.90 (breln1compE) => 72.29/9.90 (( 72.29/9.90 (breln1compEex) => 72.29/9.90 (( 72.29/9.90 (!!) @ ( 72.29/9.90 (('#B') @ ( 72.29/9.90 !!) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 !!))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#C') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 breln1)))) @ 72.29/9.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1760])). 72.29/9.90 thf(zip_derived_cl1779, plain, 72.29/9.90 (~ (((ksndpairEq) => 72.29/9.90 (((kpairsurjEq) => 72.29/9.90 (((cartprodsndin) => 72.29/9.90 (((cartprodpairmemEL) => 72.29/9.90 (((cartprodpairmemER) => 72.29/9.90 (((cartprodmempaircEq) => 72.29/9.90 (((cartprodfstpairEq) => 72.29/9.90 (((cartprodsndpairEq) => 72.29/9.90 (((cartprodpairsurjEq) => 72.29/9.90 (((dpsetconstrI) => 72.29/9.90 (((dpsetconstrSub) => 72.29/9.90 (((setOfPairsIsBReln) => 72.29/9.90 (((dpsetconstrERa) => 72.29/9.90 (((dpsetconstrEL1) => 72.29/9.90 (((dpsetconstrEL2) => 72.29/9.90 (((dpsetconstrER) => 72.29/9.90 (((funcImageSingleton) => 72.29/9.90 (((apProp) => 72.29/9.90 (((app) => 72.29/9.90 (((infuncsetfunc) => 72.29/9.90 (((ap2p) => 72.29/9.90 (((funcinfuncset) => 72.29/9.90 (((lamProp) => 72.29/9.90 (((lamp) => 72.29/9.90 (((lam2p) => 72.29/9.90 (((brelnall1) => 72.29/9.90 (((brelnall2) => 72.29/9.90 (((ex1E2) => 72.29/9.90 (((funcGraphProp1) => 72.29/9.90 (((funcGraphProp3) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp2) => 72.29/9.90 (( 72.29/9.90 (funcextLem) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp4) => 72.29/9.90 (( 72.29/9.90 (subbreln) => 72.29/9.90 (( 72.29/9.90 (eqbreln) => 72.29/9.90 (( 72.29/9.90 (funcext) => 72.29/9.90 (( 72.29/9.90 (funcext2) => 72.29/9.90 (( 72.29/9.90 (ap2apEq1) => 72.29/9.90 (( 72.29/9.90 (ap2apEq2) => 72.29/9.90 (( 72.29/9.90 (beta1) => 72.29/9.90 (( 72.29/9.90 (eta1) => 72.29/9.90 (( 72.29/9.90 (lam2lamEq) => 72.29/9.90 (( 72.29/9.90 (beta2) => 72.29/9.90 (( 72.29/9.90 (eta2) => 72.29/9.90 (( 72.29/9.90 (iffalseProp1) => 72.29/9.90 (( 72.29/9.90 (iffalseProp2) => 72.29/9.90 (( 72.29/9.90 (iftrueProp1) => 72.29/9.90 (( 72.29/9.90 (iftrueProp2) => 72.29/9.90 (( 72.29/9.90 (ifSingleton) => 72.29/9.90 (( 72.29/9.90 (ifp) => 72.29/9.90 (( 72.29/9.90 (theeq) => 72.29/9.90 (( 72.29/9.90 (iftrue) => 72.29/9.90 (( 72.29/9.90 (iffalse) => 72.29/9.90 (( 72.29/9.90 (iftrueorfalse) => 72.29/9.90 (( 72.29/9.90 (binintersectT_lem) => 72.29/9.90 (( 72.29/9.90 (binunionT_lem) => 72.29/9.90 (( 72.29/9.90 (powersetT_lem) => 72.29/9.90 (( 72.29/9.90 (setminusT_lem) => 72.29/9.90 (( 72.29/9.90 (complementT_lem) => 72.29/9.90 (( 72.29/9.90 (setextT) => 72.29/9.90 (( 72.29/9.90 (subsetTI) => 72.29/9.90 (( 72.29/9.90 (powersetTI1) => 72.29/9.90 (( 72.29/9.90 (powersetTE1) => 72.29/9.90 (( 72.29/9.90 (complementTI1) => 72.29/9.90 (( 72.29/9.90 (complementTE1) => 72.29/9.90 (( 72.29/9.90 (binintersectTELcontra) => 72.29/9.90 (( 72.29/9.90 (binintersectTERcontra) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT1) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT2) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT3) => 72.29/9.90 (( 72.29/9.90 (doubleComplementI1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementE1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub2) => 72.29/9.90 (( 72.29/9.90 (doubleComplementEq) => 72.29/9.90 (( 72.29/9.90 (complementTnotintersectT) => 72.29/9.90 (( 72.29/9.90 (complementImpComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementSubsetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementInPowersetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (contraSubsetComplement) => 72.29/9.90 (( 72.29/9.90 (complementTcontraSubset) => 72.29/9.90 (( 72.29/9.90 (binunionTILcontra) => 72.29/9.90 (( 72.29/9.90 (binunionTIRcontra) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion2) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (intersectInPowersetIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpNotIn1) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpInComplement1) => 72.29/9.90 (( 72.29/9.90 (binunionTE) => 72.29/9.90 (( 72.29/9.90 (binunionTEcontra) => 72.29/9.90 (( 72.29/9.90 (demorgan2a1) => 72.29/9.90 (( 72.29/9.90 (complementUnionInPowersetComplement) => 72.29/9.90 (( 72.29/9.90 (demorgan2a2) => 72.29/9.90 (( 72.29/9.90 (demorgan1a) => 72.29/9.90 (( 72.29/9.90 (demorgan1b) => 72.29/9.90 (( 72.29/9.90 (demorgan1) => 72.29/9.90 (( 72.29/9.90 (demorgan2a) => 72.29/9.90 (( 72.29/9.90 (demorgan2b2) => 72.29/9.90 (( 72.29/9.90 (demorgan2b) => 72.29/9.90 (( 72.29/9.90 (demorgan2) => 72.29/9.90 (( 72.29/9.90 (woz13rule0) => 72.29/9.90 (( 72.29/9.90 (woz13rule1) => 72.29/9.90 (( 72.29/9.90 (woz13rule2) => 72.29/9.90 (( 72.29/9.90 (woz13rule3) => 72.29/9.90 (( 72.29/9.90 (woz13rule4) => 72.29/9.90 (( 72.29/9.90 (woz1_1) => 72.29/9.90 (( 72.29/9.90 (woz1_2) => 72.29/9.90 (( 72.29/9.90 (woz1_3) => 72.29/9.90 (( 72.29/9.90 (woz1_4) => 72.29/9.90 (( 72.29/9.90 (woz1_5) => 72.29/9.90 (( 72.29/9.90 (breln1all2) => 72.29/9.90 (( 72.29/9.90 (breln1SetBreln1) => 72.29/9.90 (( 72.29/9.90 (choice2fnsingleton) => 72.29/9.90 (( 72.29/9.90 (setOfPairsIsBReln1) => 72.29/9.90 (( 72.29/9.90 (breln1all1) => 72.29/9.90 (( 72.29/9.90 (subbreln1) => 72.29/9.90 (( 72.29/9.90 (eqbreln1) => 72.29/9.90 (( 72.29/9.90 (breln1invprop) => 72.29/9.90 (( 72.29/9.90 (breln1invI) => 72.29/9.90 (( 72.29/9.90 (breln1invE) => 72.29/9.90 (( 72.29/9.90 (breln1compprop) => 72.29/9.90 (( 72.29/9.90 (breln1compI) => 72.29/9.90 (( 72.29/9.90 (breln1compE) => 72.29/9.90 (( 72.29/9.90 (breln1compEex) => 72.29/9.90 (( 72.29/9.90 (!!) @ ( 72.29/9.90 (('#B') @ ( 72.29/9.90 !!) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 !!))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#C') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 breln1)))) @ 72.29/9.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1770])). 72.29/9.90 thf(zip_derived_cl1787, plain, 72.29/9.90 (~ (((kpairsurjEq) => 72.29/9.90 (((cartprodsndin) => 72.29/9.90 (((cartprodpairmemEL) => 72.29/9.90 (((cartprodpairmemER) => 72.29/9.90 (((cartprodmempaircEq) => 72.29/9.90 (((cartprodfstpairEq) => 72.29/9.90 (((cartprodsndpairEq) => 72.29/9.90 (((cartprodpairsurjEq) => 72.29/9.90 (((dpsetconstrI) => 72.29/9.90 (((dpsetconstrSub) => 72.29/9.90 (((setOfPairsIsBReln) => 72.29/9.90 (((dpsetconstrERa) => 72.29/9.90 (((dpsetconstrEL1) => 72.29/9.90 (((dpsetconstrEL2) => 72.29/9.90 (((dpsetconstrER) => 72.29/9.90 (((funcImageSingleton) => 72.29/9.90 (((apProp) => 72.29/9.90 (((app) => 72.29/9.90 (((infuncsetfunc) => 72.29/9.90 (((ap2p) => 72.29/9.90 (((funcinfuncset) => 72.29/9.90 (((lamProp) => 72.29/9.90 (((lamp) => 72.29/9.90 (((lam2p) => 72.29/9.90 (((brelnall1) => 72.29/9.90 (((brelnall2) => 72.29/9.90 (((ex1E2) => 72.29/9.90 (((funcGraphProp1) => 72.29/9.90 (((funcGraphProp3) => 72.29/9.90 (((funcGraphProp2) => 72.29/9.90 (( 72.29/9.90 (funcextLem) => 72.29/9.90 (( 72.29/9.90 (funcGraphProp4) => 72.29/9.90 (( 72.29/9.90 (subbreln) => 72.29/9.90 (( 72.29/9.90 (eqbreln) => 72.29/9.90 (( 72.29/9.90 (funcext) => 72.29/9.90 (( 72.29/9.90 (funcext2) => 72.29/9.90 (( 72.29/9.90 (ap2apEq1) => 72.29/9.90 (( 72.29/9.90 (ap2apEq2) => 72.29/9.90 (( 72.29/9.90 (beta1) => 72.29/9.90 (( 72.29/9.90 (eta1) => 72.29/9.90 (( 72.29/9.90 (lam2lamEq) => 72.29/9.90 (( 72.29/9.90 (beta2) => 72.29/9.90 (( 72.29/9.90 (eta2) => 72.29/9.90 (( 72.29/9.90 (iffalseProp1) => 72.29/9.90 (( 72.29/9.90 (iffalseProp2) => 72.29/9.90 (( 72.29/9.90 (iftrueProp1) => 72.29/9.90 (( 72.29/9.90 (iftrueProp2) => 72.29/9.90 (( 72.29/9.90 (ifSingleton) => 72.29/9.90 (( 72.29/9.90 (ifp) => 72.29/9.90 (( 72.29/9.90 (theeq) => 72.29/9.90 (( 72.29/9.90 (iftrue) => 72.29/9.90 (( 72.29/9.90 (iffalse) => 72.29/9.90 (( 72.29/9.90 (iftrueorfalse) => 72.29/9.90 (( 72.29/9.90 (binintersectT_lem) => 72.29/9.90 (( 72.29/9.90 (binunionT_lem) => 72.29/9.90 (( 72.29/9.90 (powersetT_lem) => 72.29/9.90 (( 72.29/9.90 (setminusT_lem) => 72.29/9.90 (( 72.29/9.90 (complementT_lem) => 72.29/9.90 (( 72.29/9.90 (setextT) => 72.29/9.90 (( 72.29/9.90 (subsetTI) => 72.29/9.90 (( 72.29/9.90 (powersetTI1) => 72.29/9.90 (( 72.29/9.90 (powersetTE1) => 72.29/9.90 (( 72.29/9.90 (complementTI1) => 72.29/9.90 (( 72.29/9.90 (complementTE1) => 72.29/9.90 (( 72.29/9.90 (binintersectTELcontra) => 72.29/9.90 (( 72.29/9.90 (binintersectTERcontra) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT1) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT2) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT3) => 72.29/9.90 (( 72.29/9.90 (doubleComplementI1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementE1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub2) => 72.29/9.90 (( 72.29/9.90 (doubleComplementEq) => 72.29/9.90 (( 72.29/9.90 (complementTnotintersectT) => 72.29/9.90 (( 72.29/9.90 (complementImpComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementSubsetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementInPowersetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (contraSubsetComplement) => 72.29/9.90 (( 72.29/9.90 (complementTcontraSubset) => 72.29/9.90 (( 72.29/9.90 (binunionTILcontra) => 72.29/9.90 (( 72.29/9.90 (binunionTIRcontra) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion2) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (intersectInPowersetIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpNotIn1) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpInComplement1) => 72.29/9.90 (( 72.29/9.90 (binunionTE) => 72.29/9.90 (( 72.29/9.90 (binunionTEcontra) => 72.29/9.90 (( 72.29/9.90 (demorgan2a1) => 72.29/9.90 (( 72.29/9.90 (complementUnionInPowersetComplement) => 72.29/9.90 (( 72.29/9.90 (demorgan2a2) => 72.29/9.90 (( 72.29/9.90 (demorgan1a) => 72.29/9.90 (( 72.29/9.90 (demorgan1b) => 72.29/9.90 (( 72.29/9.90 (demorgan1) => 72.29/9.90 (( 72.29/9.90 (demorgan2a) => 72.29/9.90 (( 72.29/9.90 (demorgan2b2) => 72.29/9.90 (( 72.29/9.90 (demorgan2b) => 72.29/9.90 (( 72.29/9.90 (demorgan2) => 72.29/9.90 (( 72.29/9.90 (woz13rule0) => 72.29/9.90 (( 72.29/9.90 (woz13rule1) => 72.29/9.90 (( 72.29/9.90 (woz13rule2) => 72.29/9.90 (( 72.29/9.90 (woz13rule3) => 72.29/9.90 (( 72.29/9.90 (woz13rule4) => 72.29/9.90 (( 72.29/9.90 (woz1_1) => 72.29/9.90 (( 72.29/9.90 (woz1_2) => 72.29/9.90 (( 72.29/9.90 (woz1_3) => 72.29/9.90 (( 72.29/9.90 (woz1_4) => 72.29/9.90 (( 72.29/9.90 (woz1_5) => 72.29/9.90 (( 72.29/9.90 (breln1all2) => 72.29/9.90 (( 72.29/9.90 (breln1SetBreln1) => 72.29/9.90 (( 72.29/9.90 (choice2fnsingleton) => 72.29/9.90 (( 72.29/9.90 (setOfPairsIsBReln1) => 72.29/9.90 (( 72.29/9.90 (breln1all1) => 72.29/9.90 (( 72.29/9.90 (subbreln1) => 72.29/9.90 (( 72.29/9.90 (eqbreln1) => 72.29/9.90 (( 72.29/9.90 (breln1invprop) => 72.29/9.90 (( 72.29/9.90 (breln1invI) => 72.29/9.90 (( 72.29/9.90 (breln1invE) => 72.29/9.90 (( 72.29/9.90 (breln1compprop) => 72.29/9.90 (( 72.29/9.90 (breln1compI) => 72.29/9.90 (( 72.29/9.90 (breln1compE) => 72.29/9.90 (( 72.29/9.90 (breln1compEex) => 72.29/9.90 (( 72.29/9.90 (!!) @ ( 72.29/9.90 (('#B') @ ( 72.29/9.90 !!) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 !!))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#C') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 breln1)))) @ 72.29/9.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1779])). 72.29/9.90 thf(zip_derived_cl1796, plain, 72.29/9.90 (~ (((cartprodsndin) => 72.29/9.90 (((cartprodpairmemEL) => 72.29/9.90 (((cartprodpairmemER) => 72.29/9.90 (((cartprodmempaircEq) => 72.29/9.90 (((cartprodfstpairEq) => 72.29/9.90 (((cartprodsndpairEq) => 72.29/9.90 (((cartprodpairsurjEq) => 72.29/9.90 (((dpsetconstrI) => 72.29/9.90 (((dpsetconstrSub) => 72.29/9.90 (((setOfPairsIsBReln) => 72.29/9.90 (((dpsetconstrERa) => 72.29/9.90 (((dpsetconstrEL1) => 72.29/9.90 (((dpsetconstrEL2) => 72.29/9.90 (((dpsetconstrER) => 72.29/9.90 (((funcImageSingleton) => 72.29/9.90 (((apProp) => 72.29/9.90 (((app) => 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72.29/9.90 (( 72.29/9.90 (ifSingleton) => 72.29/9.90 (( 72.29/9.90 (ifp) => 72.29/9.90 (( 72.29/9.90 (theeq) => 72.29/9.90 (( 72.29/9.90 (iftrue) => 72.29/9.90 (( 72.29/9.90 (iffalse) => 72.29/9.90 (( 72.29/9.90 (iftrueorfalse) => 72.29/9.90 (( 72.29/9.90 (binintersectT_lem) => 72.29/9.90 (( 72.29/9.90 (binunionT_lem) => 72.29/9.90 (( 72.29/9.90 (powersetT_lem) => 72.29/9.90 (( 72.29/9.90 (setminusT_lem) => 72.29/9.90 (( 72.29/9.90 (complementT_lem) => 72.29/9.90 (( 72.29/9.90 (setextT) => 72.29/9.90 (( 72.29/9.90 (subsetTI) => 72.29/9.90 (( 72.29/9.90 (powersetTI1) => 72.29/9.90 (( 72.29/9.90 (powersetTE1) => 72.29/9.90 (( 72.29/9.90 (complementTI1) => 72.29/9.90 (( 72.29/9.90 (complementTE1) => 72.29/9.90 (( 72.29/9.90 (binintersectTELcontra) => 72.29/9.90 (( 72.29/9.90 (binintersectTERcontra) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT1) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT2) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT3) => 72.29/9.90 (( 72.29/9.90 (doubleComplementI1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementE1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub2) => 72.29/9.90 (( 72.29/9.90 (doubleComplementEq) => 72.29/9.90 (( 72.29/9.90 (complementTnotintersectT) => 72.29/9.90 (( 72.29/9.90 (complementImpComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementSubsetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementInPowersetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (contraSubsetComplement) => 72.29/9.90 (( 72.29/9.90 (complementTcontraSubset) => 72.29/9.90 (( 72.29/9.90 (binunionTILcontra) => 72.29/9.90 (( 72.29/9.90 (binunionTIRcontra) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion2) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (intersectInPowersetIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpNotIn1) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpInComplement1) => 72.29/9.90 (( 72.29/9.90 (binunionTE) => 72.29/9.90 (( 72.29/9.90 (binunionTEcontra) => 72.29/9.90 (( 72.29/9.90 (demorgan2a1) => 72.29/9.90 (( 72.29/9.90 (complementUnionInPowersetComplement) => 72.29/9.90 (( 72.29/9.90 (demorgan2a2) => 72.29/9.90 (( 72.29/9.90 (demorgan1a) => 72.29/9.90 (( 72.29/9.90 (demorgan1b) => 72.29/9.90 (( 72.29/9.90 (demorgan1) => 72.29/9.90 (( 72.29/9.90 (demorgan2a) => 72.29/9.90 (( 72.29/9.90 (demorgan2b2) => 72.29/9.90 (( 72.29/9.90 (demorgan2b) => 72.29/9.90 (( 72.29/9.90 (demorgan2) => 72.29/9.90 (( 72.29/9.90 (woz13rule0) => 72.29/9.90 (( 72.29/9.90 (woz13rule1) => 72.29/9.90 (( 72.29/9.90 (woz13rule2) => 72.29/9.90 (( 72.29/9.90 (woz13rule3) => 72.29/9.90 (( 72.29/9.90 (woz13rule4) => 72.29/9.90 (( 72.29/9.90 (woz1_1) => 72.29/9.90 (( 72.29/9.90 (woz1_2) => 72.29/9.90 (( 72.29/9.90 (woz1_3) => 72.29/9.90 (( 72.29/9.90 (woz1_4) => 72.29/9.90 (( 72.29/9.90 (woz1_5) => 72.29/9.90 (( 72.29/9.90 (breln1all2) => 72.29/9.90 (( 72.29/9.90 (breln1SetBreln1) => 72.29/9.90 (( 72.29/9.90 (choice2fnsingleton) => 72.29/9.90 (( 72.29/9.90 (setOfPairsIsBReln1) => 72.29/9.90 (( 72.29/9.90 (breln1all1) => 72.29/9.90 (( 72.29/9.90 (subbreln1) => 72.29/9.90 (( 72.29/9.90 (eqbreln1) => 72.29/9.90 (( 72.29/9.90 (breln1invprop) => 72.29/9.90 (( 72.29/9.90 (breln1invI) => 72.29/9.90 (( 72.29/9.90 (breln1invE) => 72.29/9.90 (( 72.29/9.90 (breln1compprop) => 72.29/9.90 (( 72.29/9.90 (breln1compI) => 72.29/9.90 (( 72.29/9.90 (breln1compE) => 72.29/9.90 (( 72.29/9.90 (breln1compEex) => 72.29/9.90 (( 72.29/9.90 (!!) @ ( 72.29/9.90 (('#B') @ ( 72.29/9.90 !!) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 !!))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#C') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 breln1)))) @ 72.29/9.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1787])). 72.29/9.90 thf(zip_derived_cl1807, plain, 72.29/9.90 (~ (((cartprodpairmemEL) => 72.29/9.90 (((cartprodpairmemER) => 72.29/9.90 (((cartprodmempaircEq) => 72.29/9.90 (((cartprodfstpairEq) => 72.29/9.90 (((cartprodsndpairEq) => 72.29/9.90 (((cartprodpairsurjEq) => 72.29/9.90 (((dpsetconstrI) => 72.29/9.90 (((dpsetconstrSub) => 72.29/9.90 (((setOfPairsIsBReln) => 72.29/9.90 (((dpsetconstrERa) => 72.29/9.90 (((dpsetconstrEL1) => 72.29/9.90 (((dpsetconstrEL2) => 72.29/9.90 (((dpsetconstrER) => 72.29/9.90 (((funcImageSingleton) => 72.29/9.90 (((apProp) => 72.29/9.90 (((app) => 72.29/9.90 (((infuncsetfunc) => 72.29/9.90 (((ap2p) => 72.29/9.90 (((funcinfuncset) => 72.29/9.90 (((lamProp) => 72.29/9.90 (((lamp) => 72.29/9.90 (((lam2p) => 72.29/9.90 (((brelnall1) => 72.29/9.90 (((brelnall2) => 72.29/9.90 (((ex1E2) => 72.29/9.90 (((funcGraphProp1) => 72.29/9.90 (((funcGraphProp3) => 72.29/9.90 (((funcGraphProp2) => 72.29/9.90 (((funcextLem) => 72.29/9.90 (((funcGraphProp4) => 72.29/9.90 (( 72.29/9.90 (subbreln) => 72.29/9.90 (( 72.29/9.90 (eqbreln) => 72.29/9.90 (( 72.29/9.90 (funcext) => 72.29/9.90 (( 72.29/9.90 (funcext2) => 72.29/9.90 (( 72.29/9.90 (ap2apEq1) => 72.29/9.90 (( 72.29/9.90 (ap2apEq2) => 72.29/9.90 (( 72.29/9.90 (beta1) => 72.29/9.90 (( 72.29/9.90 (eta1) => 72.29/9.90 (( 72.29/9.90 (lam2lamEq) => 72.29/9.90 (( 72.29/9.90 (beta2) => 72.29/9.90 (( 72.29/9.90 (eta2) => 72.29/9.90 (( 72.29/9.90 (iffalseProp1) => 72.29/9.90 (( 72.29/9.90 (iffalseProp2) => 72.29/9.90 (( 72.29/9.90 (iftrueProp1) => 72.29/9.90 (( 72.29/9.90 (iftrueProp2) => 72.29/9.90 (( 72.29/9.90 (ifSingleton) => 72.29/9.90 (( 72.29/9.90 (ifp) => 72.29/9.90 (( 72.29/9.90 (theeq) => 72.29/9.90 (( 72.29/9.90 (iftrue) => 72.29/9.90 (( 72.29/9.90 (iffalse) => 72.29/9.90 (( 72.29/9.90 (iftrueorfalse) => 72.29/9.90 (( 72.29/9.90 (binintersectT_lem) => 72.29/9.90 (( 72.29/9.90 (binunionT_lem) => 72.29/9.90 (( 72.29/9.90 (powersetT_lem) => 72.29/9.90 (( 72.29/9.90 (setminusT_lem) => 72.29/9.90 (( 72.29/9.90 (complementT_lem) => 72.29/9.90 (( 72.29/9.90 (setextT) => 72.29/9.90 (( 72.29/9.90 (subsetTI) => 72.29/9.90 (( 72.29/9.90 (powersetTI1) => 72.29/9.90 (( 72.29/9.90 (powersetTE1) => 72.29/9.90 (( 72.29/9.90 (complementTI1) => 72.29/9.90 (( 72.29/9.90 (complementTE1) => 72.29/9.90 (( 72.29/9.90 (binintersectTELcontra) => 72.29/9.90 (( 72.29/9.90 (binintersectTERcontra) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT1) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT2) => 72.29/9.90 (( 72.29/9.90 (contrasubsetT3) => 72.29/9.90 (( 72.29/9.90 (doubleComplementI1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementE1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub1) => 72.29/9.90 (( 72.29/9.90 (doubleComplementSub2) => 72.29/9.90 (( 72.29/9.90 (doubleComplementEq) => 72.29/9.90 (( 72.29/9.90 (complementTnotintersectT) => 72.29/9.90 (( 72.29/9.90 (complementImpComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementSubsetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementInPowersetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (contraSubsetComplement) => 72.29/9.90 (( 72.29/9.90 (complementTcontraSubset) => 72.29/9.90 (( 72.29/9.90 (binunionTILcontra) => 72.29/9.90 (( 72.29/9.90 (binunionTIRcontra) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion2) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (intersectInPowersetIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpNotIn1) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpInComplement1) => 72.29/9.90 (( 72.29/9.90 (binunionTE) => 72.29/9.90 (( 72.29/9.90 (binunionTEcontra) => 72.29/9.90 (( 72.29/9.90 (demorgan2a1) => 72.29/9.90 (( 72.29/9.90 (complementUnionInPowersetComplement) => 72.29/9.90 (( 72.29/9.90 (demorgan2a2) => 72.29/9.90 (( 72.29/9.90 (demorgan1a) => 72.29/9.90 (( 72.29/9.90 (demorgan1b) => 72.29/9.90 (( 72.29/9.90 (demorgan1) => 72.29/9.90 (( 72.29/9.90 (demorgan2a) => 72.29/9.90 (( 72.29/9.90 (demorgan2b2) => 72.29/9.90 (( 72.29/9.90 (demorgan2b) => 72.29/9.90 (( 72.29/9.90 (demorgan2) => 72.29/9.90 (( 72.29/9.90 (woz13rule0) => 72.29/9.90 (( 72.29/9.90 (woz13rule1) => 72.29/9.90 (( 72.29/9.90 (woz13rule2) => 72.29/9.90 (( 72.29/9.90 (woz13rule3) => 72.29/9.90 (( 72.29/9.90 (woz13rule4) => 72.29/9.90 (( 72.29/9.90 (woz1_1) => 72.29/9.90 (( 72.29/9.90 (woz1_2) => 72.29/9.90 (( 72.29/9.90 (woz1_3) => 72.29/9.90 (( 72.29/9.90 (woz1_4) => 72.29/9.90 (( 72.29/9.90 (woz1_5) => 72.29/9.90 (( 72.29/9.90 (breln1all2) => 72.29/9.90 (( 72.29/9.90 (breln1SetBreln1) => 72.29/9.90 (( 72.29/9.90 (choice2fnsingleton) => 72.29/9.90 (( 72.29/9.90 (setOfPairsIsBReln1) => 72.29/9.90 (( 72.29/9.90 (breln1all1) => 72.29/9.90 (( 72.29/9.90 (subbreln1) => 72.29/9.90 (( 72.29/9.90 (eqbreln1) => 72.29/9.90 (( 72.29/9.90 (breln1invprop) => 72.29/9.90 (( 72.29/9.90 (breln1invI) => 72.29/9.90 (( 72.29/9.90 (breln1invE) => 72.29/9.90 (( 72.29/9.90 (breln1compprop) => 72.29/9.90 (( 72.29/9.90 (breln1compI) => 72.29/9.90 (( 72.29/9.90 (breln1compE) => 72.29/9.90 (( 72.29/9.90 (breln1compEex) => 72.29/9.90 (( 72.29/9.90 (!!) @ ( 72.29/9.90 (('#B') @ ( 72.29/9.90 !!) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 !!))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#C') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 breln1)))) @ 72.29/9.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1796])). 72.29/9.90 thf(zip_derived_cl1816, plain, 72.29/9.90 (~ (((cartprodpairmemER) => 72.29/9.90 (((cartprodmempaircEq) => 72.29/9.90 (((cartprodfstpairEq) => 72.29/9.90 (((cartprodsndpairEq) => 72.29/9.90 (((cartprodpairsurjEq) => 72.29/9.90 (((dpsetconstrI) => 72.29/9.90 (((dpsetconstrSub) => 72.29/9.90 (((setOfPairsIsBReln) => 72.29/9.90 (((dpsetconstrERa) => 72.29/9.90 (((dpsetconstrEL1) => 72.29/9.90 (((dpsetconstrEL2) => 72.29/9.90 (((dpsetconstrER) => 72.29/9.90 (((funcImageSingleton) => 72.29/9.90 (((apProp) => 72.29/9.90 (((app) => 72.29/9.90 (((infuncsetfunc) => 72.29/9.90 (((ap2p) => 72.29/9.90 (((funcinfuncset) => 72.29/9.90 (((lamProp) => 72.29/9.90 (((lamp) => 72.29/9.90 (((lam2p) => 72.29/9.90 (((brelnall1) => 72.29/9.90 (((brelnall2) => 72.29/9.90 (((ex1E2) => 72.29/9.90 (((funcGraphProp1) => 72.29/9.90 (((funcGraphProp3) => 72.29/9.90 (((funcGraphProp2) => 72.29/9.90 (((funcextLem) => 72.29/9.90 (((funcGraphProp4) => 72.29/9.90 (((subbreln) => 72.29/9.90 (( 72.29/9.90 (eqbreln) => 72.29/9.90 (( 72.29/9.90 (funcext) => 72.29/9.90 (( 72.29/9.90 (funcext2) => 72.29/9.90 (( 72.29/9.90 (ap2apEq1) => 72.29/9.90 (( 72.29/9.90 (ap2apEq2) => 72.29/9.90 (( 72.29/9.90 (beta1) => 72.29/9.90 (( 72.29/9.90 (eta1) => 72.29/9.90 (( 72.29/9.90 (lam2lamEq) => 72.29/9.90 (( 72.29/9.90 (beta2) => 72.29/9.90 (( 72.29/9.90 (eta2) => 72.29/9.90 (( 72.29/9.90 (iffalseProp1) => 72.29/9.90 (( 72.29/9.90 (iffalseProp2) => 72.29/9.90 (( 72.29/9.90 (iftrueProp1) => 72.29/9.90 (( 72.29/9.90 (iftrueProp2) => 72.29/9.90 (( 72.29/9.90 (ifSingleton) => 72.29/9.90 (( 72.29/9.90 (ifp) => 72.29/9.90 (( 72.29/9.90 (theeq) => 72.29/9.90 (( 72.29/9.90 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72.29/9.90 (( 72.29/9.90 (doubleComplementSub2) => 72.29/9.90 (( 72.29/9.90 (doubleComplementEq) => 72.29/9.90 (( 72.29/9.90 (complementTnotintersectT) => 72.29/9.90 (( 72.29/9.90 (complementImpComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementSubsetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (complementInPowersetComplementIntersect) => 72.29/9.90 (( 72.29/9.90 (contraSubsetComplement) => 72.29/9.90 (( 72.29/9.90 (complementTcontraSubset) => 72.29/9.90 (( 72.29/9.90 (binunionTILcontra) => 72.29/9.90 (( 72.29/9.90 (binunionTIRcontra) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInUnion2) => 72.29/9.90 (( 72.29/9.90 (inIntersectImpInIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (intersectInPowersetIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpNotIn1) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpInComplement1) => 72.29/9.90 (( 72.29/9.90 (binunionTE) => 72.29/9.90 (( 72.29/9.90 (binunionTEcontra) => 72.29/9.90 (( 72.29/9.90 (demorgan2a1) => 72.29/9.90 (( 72.29/9.90 (complementUnionInPowersetComplement) => 72.29/9.90 (( 72.29/9.90 (demorgan2a2) => 72.29/9.90 (( 72.29/9.90 (demorgan1a) => 72.29/9.90 (( 72.29/9.90 (demorgan1b) => 72.29/9.90 (( 72.29/9.90 (demorgan1) => 72.29/9.90 (( 72.29/9.90 (demorgan2a) => 72.29/9.90 (( 72.29/9.90 (demorgan2b2) => 72.29/9.90 (( 72.29/9.90 (demorgan2b) => 72.29/9.90 (( 72.29/9.90 (demorgan2) => 72.29/9.90 (( 72.29/9.90 (woz13rule0) => 72.29/9.90 (( 72.29/9.90 (woz13rule1) => 72.29/9.90 (( 72.29/9.90 (woz13rule2) => 72.29/9.90 (( 72.29/9.90 (woz13rule3) => 72.29/9.90 (( 72.29/9.90 (woz13rule4) => 72.29/9.90 (( 72.29/9.90 (woz1_1) => 72.29/9.90 (( 72.29/9.90 (woz1_2) => 72.29/9.90 (( 72.29/9.90 (woz1_3) => 72.29/9.90 (( 72.29/9.90 (woz1_4) => 72.29/9.90 (( 72.29/9.90 (woz1_5) => 72.29/9.90 (( 72.29/9.90 (breln1all2) => 72.29/9.90 (( 72.29/9.90 (breln1SetBreln1) => 72.29/9.90 (( 72.29/9.90 (choice2fnsingleton) => 72.29/9.90 (( 72.29/9.90 (setOfPairsIsBReln1) => 72.29/9.90 (( 72.29/9.90 (breln1all1) => 72.29/9.90 (( 72.29/9.90 (subbreln1) => 72.29/9.90 (( 72.29/9.90 (eqbreln1) => 72.29/9.90 (( 72.29/9.90 (breln1invprop) => 72.29/9.90 (( 72.29/9.90 (breln1invI) => 72.29/9.90 (( 72.29/9.90 (breln1invE) => 72.29/9.90 (( 72.29/9.90 (breln1compprop) => 72.29/9.90 (( 72.29/9.90 (breln1compI) => 72.29/9.90 (( 72.29/9.90 (breln1compE) => 72.29/9.90 (( 72.29/9.90 (breln1compEex) => 72.29/9.90 (( 72.29/9.90 (!!) @ ( 72.29/9.90 (('#B') @ ( 72.29/9.90 !!) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 !!))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 =>))) @ 72.29/9.90 breln1)))))) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#C') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#B') @ 72.29/9.90 breln1)))) @ 72.29/9.90 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1807])). 72.29/9.90 thf(zip_derived_cl1825, plain, 72.29/9.90 (~ (((cartprodmempaircEq) => 72.29/9.90 (((cartprodfstpairEq) => 72.29/9.90 (((cartprodsndpairEq) => 72.29/9.90 (((cartprodpairsurjEq) => 72.29/9.90 (((dpsetconstrI) => 72.29/9.90 (((dpsetconstrSub) => 72.29/9.90 (((setOfPairsIsBReln) => 72.29/9.90 (((dpsetconstrERa) => 72.29/9.90 (((dpsetconstrEL1) => 72.29/9.90 (((dpsetconstrEL2) => 72.29/9.90 (((dpsetconstrER) => 72.29/9.90 (((funcImageSingleton) => 72.29/9.90 (((apProp) => 72.29/9.90 (((app) => 72.29/9.90 (((infuncsetfunc) => 72.29/9.90 (((ap2p) => 72.29/9.90 (((funcinfuncset) => 72.29/9.90 (((lamProp) => 72.29/9.90 (((lamp) => 72.29/9.90 (((lam2p) => 72.29/9.90 (((brelnall1) => 72.29/9.90 (((brelnall2) => 72.29/9.90 (((ex1E2) => 72.29/9.90 (((funcGraphProp1) => 72.29/9.90 (((funcGraphProp3) => 72.29/9.90 (((funcGraphProp2) => 72.29/9.90 (((funcextLem) => 72.29/9.90 (((funcGraphProp4) => 72.29/9.90 (((subbreln) => 72.29/9.90 (((eqbreln) => 72.29/9.90 (( 72.29/9.90 (funcext) => 72.29/9.90 (( 72.29/9.90 (funcext2) => 72.29/9.90 (( 72.29/9.90 (ap2apEq1) => 72.29/9.90 (( 72.29/9.90 (ap2apEq2) => 72.29/9.90 (( 72.29/9.90 (beta1) => 72.29/9.90 (( 72.29/9.90 (eta1) => 72.29/9.90 (( 72.29/9.90 (lam2lamEq) => 72.29/9.90 (( 72.29/9.90 (beta2) => 72.29/9.90 (( 72.29/9.90 (eta2) => 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(inIntersectImpInIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (intersectInPowersetIntersectUnions) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpNotIn1) => 72.29/9.90 (( 72.29/9.90 (inComplementUnionImpInComplement1) => 72.29/9.90 (( 72.29/9.90 (binunionTE) => 72.29/9.90 (( 72.29/9.90 (binunionTEcontra) => 72.29/9.90 (( 72.29/9.90 (demorgan2a1) => 72.29/9.90 (( 72.29/9.90 (complementUnionInPowersetComplement) => 72.29/9.90 (( 72.29/9.90 (demorgan2a2) => 72.29/9.90 (( 72.29/9.90 (demorgan1a) => 72.29/9.90 (( 72.29/9.90 (demorgan1b) => 72.29/9.90 (( 72.29/9.90 (demorgan1) => 72.29/9.90 (( 72.29/9.90 (demorgan2a) => 72.29/9.90 (( 72.29/9.90 (demorgan2b2) => 72.29/9.90 (( 72.29/9.90 (demorgan2b) => 72.29/9.90 (( 72.29/9.90 (demorgan2) => 72.29/9.90 (( 72.29/9.90 (woz13rule0) => 72.29/9.90 (( 72.29/9.90 (woz13rule1) => 72.29/9.90 (( 72.29/9.90 (woz13rule2) => 72.29/9.90 (( 72.29/9.90 (woz13rule3) => 72.29/9.90 (( 72.29/9.90 (woz13rule4) => 72.29/9.90 (( 72.29/9.90 (woz1_1) => 72.29/9.90 (( 72.29/9.90 (woz1_2) => 72.29/9.90 (( 72.29/9.90 (woz1_3) => 72.29/9.90 (( 72.29/9.90 (woz1_4) => 72.29/9.90 (( 72.29/9.90 (woz1_5) => 72.29/9.90 (( 72.29/9.90 (breln1all2) => 72.29/9.90 (( 72.29/9.90 (breln1SetBreln1) => 72.29/9.90 (( 72.29/9.90 (choice2fnsingleton) => 72.29/9.90 (( 72.29/9.90 (setOfPairsIsBReln1) => 72.29/9.90 (( 72.29/9.90 (breln1all1) => 72.29/9.90 (( 72.29/9.90 (subbreln1) => 72.29/9.90 (( 72.29/9.90 (eqbreln1) => 72.29/9.90 (( 72.29/9.90 (breln1invprop) => 72.29/9.90 (( 72.29/9.90 (breln1invI) => 72.29/9.90 (( 72.29/9.90 (breln1invE) => 72.29/9.90 (( 72.29/9.90 (breln1compprop) => 72.29/9.90 (( 72.29/9.90 (breln1compI) => 72.29/9.90 (( 72.29/9.90 (breln1compE) => 72.29/9.90 (( 72.29/9.90 (breln1compEex) => 72.29/9.90 (( 72.29/9.90 (!!) @ ( 72.29/9.90 (('#B') @ ( 72.29/9.90 !!) @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#S') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 '#S') @ 72.29/9.90 ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 72.29/9.90 ( 72.29/9.90 ('#B') @ ( 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binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1825])). 72.29/9.90 thf(zip_derived_cl1840, plain, 72.29/9.90 (~ (((cartprodsndpairEq) => 72.29/9.90 (((cartprodpairsurjEq) => 72.29/9.90 (((dpsetconstrI) => 72.29/9.90 (((dpsetconstrSub) => 72.29/9.90 (((setOfPairsIsBReln) => 72.29/9.90 (((dpsetconstrERa) => 72.29/9.90 (((dpsetconstrEL1) => 72.29/9.90 (((dpsetconstrEL2) => 72.29/9.90 (((dpsetconstrER) => 72.29/9.90 (((funcImageSingleton) => 72.29/9.90 (((apProp) => 72.29/9.90 (((app) => 72.29/9.90 (((infuncsetfunc) => 72.29/9.90 (((ap2p) => 72.29/9.90 (((funcinfuncset) => 72.29/9.90 (((lamProp) => 72.29/9.90 (((lamp) => 72.29/9.90 (((lam2p) => 72.29/9.90 (((brelnall1) => 72.29/9.90 (((brelnall2) => 72.29/9.90 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72.29/9.91 !!))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#S') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#S') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 =>))) @ 72.29/9.91 breln1)))))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#C') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 breln1)))) @ 72.29/9.91 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1856])). 72.29/9.91 thf(zip_derived_cl1874, plain, 72.29/9.91 (~ (((setOfPairsIsBReln) => 72.29/9.91 (((dpsetconstrERa) => 72.29/9.91 (((dpsetconstrEL1) => 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72.29/9.91 !!))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#S') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#S') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 =>))) @ 72.29/9.91 breln1)))))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#C') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 breln1)))) @ 72.29/9.91 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1865])). 72.29/9.91 thf(zip_derived_cl1883, plain, 72.29/9.91 (~ (((dpsetconstrERa) => 72.29/9.91 (((dpsetconstrEL1) => 72.29/9.91 (((dpsetconstrEL2) => 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72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#S') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 =>))) @ 72.29/9.91 breln1)))))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#C') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 breln1)))) @ 72.29/9.91 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1932])). 72.29/9.91 thf(zip_derived_cl1951, plain, 72.29/9.91 (~ (((infuncsetfunc) => 72.29/9.91 (((ap2p) => 72.29/9.91 (((funcinfuncset) => 72.29/9.91 (((lamProp) => 72.29/9.91 (((lamp) => 72.29/9.91 (((lam2p) => 72.29/9.91 (((brelnall1) => 72.29/9.91 (((brelnall2) => 72.29/9.91 (((ex1E2) => 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( 72.29/9.91 '#S') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 =>))) @ 72.29/9.91 breln1)))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 !!))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#S') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#S') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 =>))) @ 72.29/9.91 breln1)))))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#C') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 breln1)))) @ 72.29/9.91 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1972])). 72.29/9.91 thf(zip_derived_cl1993, plain, 72.29/9.91 (~ (((lamp) => 72.29/9.91 (((lam2p) => 72.29/9.91 (((brelnall1) => 72.29/9.91 (((brelnall2) => 72.29/9.91 (((ex1E2) => 72.29/9.91 (((funcGraphProp1) => 72.29/9.91 (((funcGraphProp3) => 72.29/9.91 (((funcGraphProp2) => 72.29/9.91 (((funcextLem) => 72.29/9.91 (((funcGraphProp4) => 72.29/9.91 (((subbreln) => 72.29/9.91 (((eqbreln) => 72.29/9.91 (((funcext) => 72.29/9.91 (((funcext2) => 72.29/9.91 (((ap2apEq1) => 72.29/9.91 (((ap2apEq2) => 72.29/9.91 (((beta1) => 72.29/9.91 (((eta1) => 72.29/9.91 (((lam2lamEq) => 72.29/9.91 (((beta2) => 72.29/9.91 (((eta2) => 72.29/9.91 (((iffalseProp1) => 72.29/9.91 (((iffalseProp2) => 72.29/9.91 (((iftrueProp1) => 72.29/9.91 (((iftrueProp2) => 72.29/9.91 (((ifSingleton) => 72.29/9.91 (((ifp) => 72.29/9.91 (((theeq) => 72.29/9.91 (((iftrue) => 72.29/9.91 (((iffalse) => 72.29/9.91 (( 72.29/9.91 (iftrueorfalse) => 72.29/9.91 (( 72.29/9.91 (binintersectT_lem) => 72.29/9.91 (( 72.29/9.91 (binunionT_lem) => 72.29/9.91 (( 72.29/9.91 (powersetT_lem) => 72.29/9.91 (( 72.29/9.91 (setminusT_lem) => 72.29/9.91 (( 72.29/9.91 (complementT_lem) => 72.29/9.91 (( 72.29/9.91 (setextT) => 72.29/9.91 (( 72.29/9.91 (subsetTI) => 72.29/9.91 (( 72.29/9.91 (powersetTI1) => 72.29/9.91 (( 72.29/9.91 (powersetTE1) => 72.29/9.91 (( 72.29/9.91 (complementTI1) => 72.29/9.91 (( 72.29/9.91 (complementTE1) => 72.29/9.91 (( 72.29/9.91 (binintersectTELcontra) => 72.29/9.91 (( 72.29/9.91 (binintersectTERcontra) => 72.29/9.91 (( 72.29/9.91 (contrasubsetT) => 72.29/9.91 (( 72.29/9.91 (contrasubsetT1) => 72.29/9.91 (( 72.29/9.91 (contrasubsetT2) => 72.29/9.91 (( 72.29/9.91 (contrasubsetT3) => 72.29/9.91 (( 72.29/9.91 (doubleComplementI1) => 72.29/9.91 (( 72.29/9.91 (doubleComplementE1) => 72.29/9.91 (( 72.29/9.91 (doubleComplementSub1) => 72.29/9.91 (( 72.29/9.91 (doubleComplementSub2) => 72.29/9.91 (( 72.29/9.91 (doubleComplementEq) => 72.29/9.91 (( 72.29/9.91 (complementTnotintersectT) => 72.29/9.91 (( 72.29/9.91 (complementImpComplementIntersect) => 72.29/9.91 (( 72.29/9.91 (complementSubsetComplementIntersect) => 72.29/9.91 (( 72.29/9.91 (complementInPowersetComplementIntersect) => 72.29/9.91 (( 72.29/9.91 (contraSubsetComplement) => 72.29/9.91 (( 72.29/9.91 (complementTcontraSubset) => 72.29/9.91 (( 72.29/9.91 (binunionTILcontra) => 72.29/9.91 (( 72.29/9.91 (binunionTIRcontra) => 72.29/9.91 (( 72.29/9.91 (inIntersectImpInUnion) => 72.29/9.91 (( 72.29/9.91 (inIntersectImpInUnion2) => 72.29/9.91 (( 72.29/9.91 (inIntersectImpInIntersectUnions) => 72.29/9.91 (( 72.29/9.91 (intersectInPowersetIntersectUnions) => 72.29/9.91 (( 72.29/9.91 (inComplementUnionImpNotIn1) => 72.29/9.91 (( 72.29/9.91 (inComplementUnionImpInComplement1) => 72.29/9.91 (( 72.29/9.91 (binunionTE) => 72.29/9.91 (( 72.29/9.91 (binunionTEcontra) => 72.29/9.91 (( 72.29/9.91 (demorgan2a1) => 72.29/9.91 (( 72.29/9.91 (complementUnionInPowersetComplement) => 72.29/9.91 (( 72.29/9.91 (demorgan2a2) => 72.29/9.91 (( 72.29/9.91 (demorgan1a) => 72.29/9.91 (( 72.29/9.91 (demorgan1b) => 72.29/9.91 (( 72.29/9.91 (demorgan1) => 72.29/9.91 (( 72.29/9.91 (demorgan2a) => 72.29/9.91 (( 72.29/9.91 (demorgan2b2) => 72.29/9.91 (( 72.29/9.91 (demorgan2b) => 72.29/9.91 (( 72.29/9.91 (demorgan2) => 72.29/9.91 (( 72.29/9.91 (woz13rule0) => 72.29/9.91 (( 72.29/9.91 (woz13rule1) => 72.29/9.91 (( 72.29/9.91 (woz13rule2) => 72.29/9.91 (( 72.29/9.91 (woz13rule3) => 72.29/9.91 (( 72.29/9.91 (woz13rule4) => 72.29/9.91 (( 72.29/9.91 (woz1_1) => 72.29/9.91 (( 72.29/9.91 (woz1_2) => 72.29/9.91 (( 72.29/9.91 (woz1_3) => 72.29/9.91 (( 72.29/9.91 (woz1_4) => 72.29/9.91 (( 72.29/9.91 (woz1_5) => 72.29/9.91 (( 72.29/9.91 (breln1all2) => 72.29/9.91 (( 72.29/9.91 (breln1SetBreln1) => 72.29/9.91 (( 72.29/9.91 (choice2fnsingleton) => 72.29/9.91 (( 72.29/9.91 (setOfPairsIsBReln1) => 72.29/9.91 (( 72.29/9.91 (breln1all1) => 72.29/9.91 (( 72.29/9.91 (subbreln1) => 72.29/9.91 (( 72.29/9.91 (eqbreln1) => 72.29/9.91 (( 72.29/9.91 (breln1invprop) => 72.29/9.91 (( 72.29/9.91 (breln1invI) => 72.29/9.91 (( 72.29/9.91 (breln1invE) => 72.29/9.91 (( 72.29/9.91 (breln1compprop) => 72.29/9.91 (( 72.29/9.91 (breln1compI) => 72.29/9.91 (( 72.29/9.91 (breln1compE) => 72.29/9.91 (( 72.29/9.91 (breln1compEex) => 72.29/9.91 (( 72.29/9.91 (!!) @ ( 72.29/9.91 (('#B') @ ( 72.29/9.91 !!) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#S') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#S') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 =>))) @ 72.29/9.91 breln1)))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 !!))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#S') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#S') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 =>))) @ 72.29/9.91 breln1)))))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#C') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 breln1)))) @ 72.29/9.91 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1983])). 72.29/9.91 thf(zip_derived_cl2003, plain, 72.29/9.91 (~ (((lam2p) => 72.29/9.91 (((brelnall1) => 72.29/9.91 (((brelnall2) => 72.29/9.91 (((ex1E2) => 72.29/9.91 (((funcGraphProp1) => 72.29/9.91 (((funcGraphProp3) => 72.29/9.91 (((funcGraphProp2) => 72.29/9.91 (((funcextLem) => 72.29/9.91 (((funcGraphProp4) => 72.29/9.91 (((subbreln) => 72.29/9.91 (((eqbreln) => 72.29/9.91 (((funcext) => 72.29/9.91 (((funcext2) => 72.29/9.91 (((ap2apEq1) => 72.29/9.91 (((ap2apEq2) => 72.29/9.91 (((beta1) => 72.29/9.91 (((eta1) => 72.29/9.91 (((lam2lamEq) => 72.29/9.91 (((beta2) => 72.29/9.91 (((eta2) => 72.29/9.91 (((iffalseProp1) => 72.29/9.91 (((iffalseProp2) => 72.29/9.91 (((iftrueProp1) => 72.29/9.91 (((iftrueProp2) => 72.29/9.91 (((ifSingleton) => 72.29/9.91 (((ifp) => 72.29/9.91 (((theeq) => 72.29/9.91 (((iftrue) => 72.29/9.91 (((iffalse) => 72.29/9.91 (((iftrueorfalse) => 72.29/9.91 (( 72.29/9.91 (binintersectT_lem) => 72.29/9.91 (( 72.29/9.91 (binunionT_lem) => 72.29/9.91 (( 72.29/9.91 (powersetT_lem) => 72.29/9.91 (( 72.29/9.91 (setminusT_lem) => 72.29/9.91 (( 72.29/9.91 (complementT_lem) => 72.29/9.91 (( 72.29/9.91 (setextT) => 72.29/9.91 (( 72.29/9.91 (subsetTI) => 72.29/9.91 (( 72.29/9.91 (powersetTI1) => 72.29/9.91 (( 72.29/9.91 (powersetTE1) => 72.29/9.91 (( 72.29/9.91 (complementTI1) => 72.29/9.91 (( 72.29/9.91 (complementTE1) => 72.29/9.91 (( 72.29/9.91 (binintersectTELcontra) => 72.29/9.91 (( 72.29/9.91 (binintersectTERcontra) => 72.29/9.91 (( 72.29/9.91 (contrasubsetT) => 72.29/9.91 (( 72.29/9.91 (contrasubsetT1) => 72.29/9.91 (( 72.29/9.91 (contrasubsetT2) => 72.29/9.91 (( 72.29/9.91 (contrasubsetT3) => 72.29/9.91 (( 72.29/9.91 (doubleComplementI1) => 72.29/9.91 (( 72.29/9.91 (doubleComplementE1) => 72.29/9.91 (( 72.29/9.91 (doubleComplementSub1) => 72.29/9.91 (( 72.29/9.91 (doubleComplementSub2) => 72.29/9.91 (( 72.29/9.91 (doubleComplementEq) => 72.29/9.91 (( 72.29/9.91 (complementTnotintersectT) => 72.29/9.91 (( 72.29/9.91 (complementImpComplementIntersect) => 72.29/9.91 (( 72.29/9.91 (complementSubsetComplementIntersect) => 72.29/9.91 (( 72.29/9.91 (complementInPowersetComplementIntersect) => 72.29/9.91 (( 72.29/9.91 (contraSubsetComplement) => 72.29/9.91 (( 72.29/9.91 (complementTcontraSubset) => 72.29/9.91 (( 72.29/9.91 (binunionTILcontra) => 72.29/9.91 (( 72.29/9.91 (binunionTIRcontra) => 72.29/9.91 (( 72.29/9.91 (inIntersectImpInUnion) => 72.29/9.91 (( 72.29/9.91 (inIntersectImpInUnion2) => 72.29/9.91 (( 72.29/9.91 (inIntersectImpInIntersectUnions) => 72.29/9.91 (( 72.29/9.91 (intersectInPowersetIntersectUnions) => 72.29/9.91 (( 72.29/9.91 (inComplementUnionImpNotIn1) => 72.29/9.91 (( 72.29/9.91 (inComplementUnionImpInComplement1) => 72.29/9.91 (( 72.29/9.91 (binunionTE) => 72.29/9.91 (( 72.29/9.91 (binunionTEcontra) => 72.29/9.91 (( 72.29/9.91 (demorgan2a1) => 72.29/9.91 (( 72.29/9.91 (complementUnionInPowersetComplement) => 72.29/9.91 (( 72.29/9.91 (demorgan2a2) => 72.29/9.91 (( 72.29/9.91 (demorgan1a) => 72.29/9.91 (( 72.29/9.91 (demorgan1b) => 72.29/9.91 (( 72.29/9.91 (demorgan1) => 72.29/9.91 (( 72.29/9.91 (demorgan2a) => 72.29/9.91 (( 72.29/9.91 (demorgan2b2) => 72.29/9.91 (( 72.29/9.91 (demorgan2b) => 72.29/9.91 (( 72.29/9.91 (demorgan2) => 72.29/9.91 (( 72.29/9.91 (woz13rule0) => 72.29/9.91 (( 72.29/9.91 (woz13rule1) => 72.29/9.91 (( 72.29/9.91 (woz13rule2) => 72.29/9.91 (( 72.29/9.91 (woz13rule3) => 72.29/9.91 (( 72.29/9.91 (woz13rule4) => 72.29/9.91 (( 72.29/9.91 (woz1_1) => 72.29/9.91 (( 72.29/9.91 (woz1_2) => 72.29/9.91 (( 72.29/9.91 (woz1_3) => 72.29/9.91 (( 72.29/9.91 (woz1_4) => 72.29/9.91 (( 72.29/9.91 (woz1_5) => 72.29/9.91 (( 72.29/9.91 (breln1all2) => 72.29/9.91 (( 72.29/9.91 (breln1SetBreln1) => 72.29/9.91 (( 72.29/9.91 (choice2fnsingleton) => 72.29/9.91 (( 72.29/9.91 (setOfPairsIsBReln1) => 72.29/9.91 (( 72.29/9.91 (breln1all1) => 72.29/9.91 (( 72.29/9.91 (subbreln1) => 72.29/9.91 (( 72.29/9.91 (eqbreln1) => 72.29/9.91 (( 72.29/9.91 (breln1invprop) => 72.29/9.91 (( 72.29/9.91 (breln1invI) => 72.29/9.91 (( 72.29/9.91 (breln1invE) => 72.29/9.91 (( 72.29/9.91 (breln1compprop) => 72.29/9.91 (( 72.29/9.91 (breln1compI) => 72.29/9.91 (( 72.29/9.91 (breln1compE) => 72.29/9.91 (( 72.29/9.91 (breln1compEex) => 72.29/9.91 (( 72.29/9.91 (!!) @ ( 72.29/9.91 (('#B') @ ( 72.29/9.91 !!) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#S') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#S') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 =>))) @ 72.29/9.91 breln1)))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 !!))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#S') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#S') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 =>))) @ 72.29/9.91 breln1)))))) @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#C') @ ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 ( 72.29/9.91 ( 72.29/9.91 ('#B') @ ( 72.29/9.91 '#B') @ 72.29/9.91 breln1)))) @ 72.29/9.91 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1993])). 72.29/9.91 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72.29/9.92 (((powersetT_lem) => 72.29/9.92 (((setminusT_lem) => 72.29/9.92 (((complementT_lem) => 72.29/9.92 (((setextT) => 72.29/9.92 (((subsetTI) => 72.29/9.92 (((powersetTI1) => 72.29/9.92 (((powersetTE1) => 72.29/9.92 (((complementTI1) => 72.29/9.92 (((complementTE1) => 72.29/9.92 (((binintersectTELcontra) => 72.29/9.92 (( 72.29/9.92 (binintersectTERcontra) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT1) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT2) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT3) => 72.29/9.92 (( 72.29/9.92 (doubleComplementI1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementE1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementSub1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementSub2) => 72.29/9.92 (( 72.29/9.92 (doubleComplementEq) => 72.29/9.92 (( 72.29/9.92 (complementTnotintersectT) => 72.29/9.92 (( 72.29/9.92 (complementImpComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (complementSubsetComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (complementInPowersetComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (contraSubsetComplement) => 72.29/9.92 (( 72.29/9.92 (complementTcontraSubset) => 72.29/9.92 (( 72.29/9.92 (binunionTILcontra) => 72.29/9.92 (( 72.29/9.92 (binunionTIRcontra) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion2) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (intersectInPowersetIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpNotIn1) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpInComplement1) => 72.29/9.92 (( 72.29/9.92 (binunionTE) => 72.29/9.92 (( 72.29/9.92 (binunionTEcontra) => 72.29/9.92 (( 72.29/9.92 (demorgan2a1) => 72.29/9.92 (( 72.29/9.92 (complementUnionInPowersetComplement) => 72.29/9.92 (( 72.29/9.92 (demorgan2a2) => 72.29/9.92 (( 72.29/9.92 (demorgan1a) => 72.29/9.92 (( 72.29/9.92 (demorgan1b) => 72.29/9.92 (( 72.29/9.92 (demorgan1) => 72.29/9.92 (( 72.29/9.92 (demorgan2a) => 72.29/9.92 (( 72.29/9.92 (demorgan2b2) => 72.29/9.92 (( 72.29/9.92 (demorgan2b) => 72.29/9.92 (( 72.29/9.92 (demorgan2) => 72.29/9.92 (( 72.29/9.92 (woz13rule0) => 72.29/9.92 (( 72.29/9.92 (woz13rule1) => 72.29/9.92 (( 72.29/9.92 (woz13rule2) => 72.29/9.92 (( 72.29/9.92 (woz13rule3) => 72.29/9.92 (( 72.29/9.92 (woz13rule4) => 72.29/9.92 (( 72.29/9.92 (woz1_1) => 72.29/9.92 (( 72.29/9.92 (woz1_2) => 72.29/9.92 (( 72.29/9.92 (woz1_3) => 72.29/9.92 (( 72.29/9.92 (woz1_4) => 72.29/9.92 (( 72.29/9.92 (woz1_5) => 72.29/9.92 (( 72.29/9.92 (breln1all2) => 72.29/9.92 (( 72.29/9.92 (breln1SetBreln1) => 72.29/9.92 (( 72.29/9.92 (choice2fnsingleton) => 72.29/9.92 (( 72.29/9.92 (setOfPairsIsBReln1) => 72.29/9.92 (( 72.29/9.92 (breln1all1) => 72.29/9.92 (( 72.29/9.92 (subbreln1) => 72.29/9.92 (( 72.29/9.92 (eqbreln1) => 72.29/9.92 (( 72.29/9.92 (breln1invprop) => 72.29/9.92 (( 72.29/9.92 (breln1invI) => 72.29/9.92 (( 72.29/9.92 (breln1invE) => 72.29/9.92 (( 72.29/9.92 (breln1compprop) => 72.29/9.92 (( 72.29/9.92 (breln1compI) => 72.29/9.92 (( 72.29/9.92 (breln1compE) => 72.29/9.92 (( 72.29/9.92 (breln1compEex) => 72.29/9.92 (( 72.29/9.92 (!!) @ ( 72.29/9.92 (('#B') @ ( 72.29/9.92 !!) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 !!))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#C') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 breln1)))) @ 72.29/9.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2118])). 72.29/9.92 thf(zip_derived_cl2149, plain, 72.29/9.92 (~ (((ap2apEq1) => 72.29/9.92 (((ap2apEq2) => 72.29/9.92 (((beta1) => 72.29/9.92 (((eta1) => 72.29/9.92 (((lam2lamEq) => 72.29/9.92 (((beta2) => 72.29/9.92 (((eta2) => 72.29/9.92 (((iffalseProp1) => 72.29/9.92 (((iffalseProp2) => 72.29/9.92 (((iftrueProp1) => 72.29/9.92 (((iftrueProp2) => 72.29/9.92 (((ifSingleton) => 72.29/9.92 (((ifp) => 72.29/9.92 (((theeq) => 72.29/9.92 (((iftrue) => 72.29/9.92 (((iffalse) => 72.29/9.92 (((iftrueorfalse) => 72.29/9.92 (((binintersectT_lem) => 72.29/9.92 (((binunionT_lem) => 72.29/9.92 (((powersetT_lem) => 72.29/9.92 (((setminusT_lem) => 72.29/9.92 (((complementT_lem) => 72.29/9.92 (((setextT) => 72.29/9.92 (((subsetTI) => 72.29/9.92 (((powersetTI1) => 72.29/9.92 (((powersetTE1) => 72.29/9.92 (((complementTI1) => 72.29/9.92 (((complementTE1) => 72.29/9.92 (((binintersectTELcontra) => 72.29/9.92 (((binintersectTERcontra) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT1) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT2) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT3) => 72.29/9.92 (( 72.29/9.92 (doubleComplementI1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementE1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementSub1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementSub2) => 72.29/9.92 (( 72.29/9.92 (doubleComplementEq) => 72.29/9.92 (( 72.29/9.92 (complementTnotintersectT) => 72.29/9.92 (( 72.29/9.92 (complementImpComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (complementSubsetComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (complementInPowersetComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (contraSubsetComplement) => 72.29/9.92 (( 72.29/9.92 (complementTcontraSubset) => 72.29/9.92 (( 72.29/9.92 (binunionTILcontra) => 72.29/9.92 (( 72.29/9.92 (binunionTIRcontra) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion2) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (intersectInPowersetIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpNotIn1) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpInComplement1) => 72.29/9.92 (( 72.29/9.92 (binunionTE) => 72.29/9.92 (( 72.29/9.92 (binunionTEcontra) => 72.29/9.92 (( 72.29/9.92 (demorgan2a1) => 72.29/9.92 (( 72.29/9.92 (complementUnionInPowersetComplement) => 72.29/9.92 (( 72.29/9.92 (demorgan2a2) => 72.29/9.92 (( 72.29/9.92 (demorgan1a) => 72.29/9.92 (( 72.29/9.92 (demorgan1b) => 72.29/9.92 (( 72.29/9.92 (demorgan1) => 72.29/9.92 (( 72.29/9.92 (demorgan2a) => 72.29/9.92 (( 72.29/9.92 (demorgan2b2) => 72.29/9.92 (( 72.29/9.92 (demorgan2b) => 72.29/9.92 (( 72.29/9.92 (demorgan2) => 72.29/9.92 (( 72.29/9.92 (woz13rule0) => 72.29/9.92 (( 72.29/9.92 (woz13rule1) => 72.29/9.92 (( 72.29/9.92 (woz13rule2) => 72.29/9.92 (( 72.29/9.92 (woz13rule3) => 72.29/9.92 (( 72.29/9.92 (woz13rule4) => 72.29/9.92 (( 72.29/9.92 (woz1_1) => 72.29/9.92 (( 72.29/9.92 (woz1_2) => 72.29/9.92 (( 72.29/9.92 (woz1_3) => 72.29/9.92 (( 72.29/9.92 (woz1_4) => 72.29/9.92 (( 72.29/9.92 (woz1_5) => 72.29/9.92 (( 72.29/9.92 (breln1all2) => 72.29/9.92 (( 72.29/9.92 (breln1SetBreln1) => 72.29/9.92 (( 72.29/9.92 (choice2fnsingleton) => 72.29/9.92 (( 72.29/9.92 (setOfPairsIsBReln1) => 72.29/9.92 (( 72.29/9.92 (breln1all1) => 72.29/9.92 (( 72.29/9.92 (subbreln1) => 72.29/9.92 (( 72.29/9.92 (eqbreln1) => 72.29/9.92 (( 72.29/9.92 (breln1invprop) => 72.29/9.92 (( 72.29/9.92 (breln1invI) => 72.29/9.92 (( 72.29/9.92 (breln1invE) => 72.29/9.92 (( 72.29/9.92 (breln1compprop) => 72.29/9.92 (( 72.29/9.92 (breln1compI) => 72.29/9.92 (( 72.29/9.92 (breln1compE) => 72.29/9.92 (( 72.29/9.92 (breln1compEex) => 72.29/9.92 (( 72.29/9.92 (!!) @ ( 72.29/9.92 (('#B') @ ( 72.29/9.92 !!) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 !!))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#C') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 breln1)))) @ 72.29/9.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2133])). 72.29/9.92 thf(zip_derived_cl2166, plain, 72.29/9.92 (~ (((ap2apEq2) => 72.29/9.92 (((beta1) => 72.29/9.92 (((eta1) => 72.29/9.92 (((lam2lamEq) => 72.29/9.92 (((beta2) => 72.29/9.92 (((eta2) => 72.29/9.92 (((iffalseProp1) => 72.29/9.92 (((iffalseProp2) => 72.29/9.92 (((iftrueProp1) => 72.29/9.92 (((iftrueProp2) => 72.29/9.92 (((ifSingleton) => 72.29/9.92 (((ifp) => 72.29/9.92 (((theeq) => 72.29/9.92 (((iftrue) => 72.29/9.92 (((iffalse) => 72.29/9.92 (((iftrueorfalse) => 72.29/9.92 (((binintersectT_lem) => 72.29/9.92 (((binunionT_lem) => 72.29/9.92 (((powersetT_lem) => 72.29/9.92 (((setminusT_lem) => 72.29/9.92 (((complementT_lem) => 72.29/9.92 (((setextT) => 72.29/9.92 (((subsetTI) => 72.29/9.92 (((powersetTI1) => 72.29/9.92 (((powersetTE1) => 72.29/9.92 (((complementTI1) => 72.29/9.92 (((complementTE1) => 72.29/9.92 (((binintersectTELcontra) => 72.29/9.92 (((binintersectTERcontra) => 72.29/9.92 (((contrasubsetT) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT1) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT2) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT3) => 72.29/9.92 (( 72.29/9.92 (doubleComplementI1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementE1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementSub1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementSub2) => 72.29/9.92 (( 72.29/9.92 (doubleComplementEq) => 72.29/9.92 (( 72.29/9.92 (complementTnotintersectT) => 72.29/9.92 (( 72.29/9.92 (complementImpComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (complementSubsetComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (complementInPowersetComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (contraSubsetComplement) => 72.29/9.92 (( 72.29/9.92 (complementTcontraSubset) => 72.29/9.92 (( 72.29/9.92 (binunionTILcontra) => 72.29/9.92 (( 72.29/9.92 (binunionTIRcontra) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion2) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (intersectInPowersetIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpNotIn1) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpInComplement1) => 72.29/9.92 (( 72.29/9.92 (binunionTE) => 72.29/9.92 (( 72.29/9.92 (binunionTEcontra) => 72.29/9.92 (( 72.29/9.92 (demorgan2a1) => 72.29/9.92 (( 72.29/9.92 (complementUnionInPowersetComplement) => 72.29/9.92 (( 72.29/9.92 (demorgan2a2) => 72.29/9.92 (( 72.29/9.92 (demorgan1a) => 72.29/9.92 (( 72.29/9.92 (demorgan1b) => 72.29/9.92 (( 72.29/9.92 (demorgan1) => 72.29/9.92 (( 72.29/9.92 (demorgan2a) => 72.29/9.92 (( 72.29/9.92 (demorgan2b2) => 72.29/9.92 (( 72.29/9.92 (demorgan2b) => 72.29/9.92 (( 72.29/9.92 (demorgan2) => 72.29/9.92 (( 72.29/9.92 (woz13rule0) => 72.29/9.92 (( 72.29/9.92 (woz13rule1) => 72.29/9.92 (( 72.29/9.92 (woz13rule2) => 72.29/9.92 (( 72.29/9.92 (woz13rule3) => 72.29/9.92 (( 72.29/9.92 (woz13rule4) => 72.29/9.92 (( 72.29/9.92 (woz1_1) => 72.29/9.92 (( 72.29/9.92 (woz1_2) => 72.29/9.92 (( 72.29/9.92 (woz1_3) => 72.29/9.92 (( 72.29/9.92 (woz1_4) => 72.29/9.92 (( 72.29/9.92 (woz1_5) => 72.29/9.92 (( 72.29/9.92 (breln1all2) => 72.29/9.92 (( 72.29/9.92 (breln1SetBreln1) => 72.29/9.92 (( 72.29/9.92 (choice2fnsingleton) => 72.29/9.92 (( 72.29/9.92 (setOfPairsIsBReln1) => 72.29/9.92 (( 72.29/9.92 (breln1all1) => 72.29/9.92 (( 72.29/9.92 (subbreln1) => 72.29/9.92 (( 72.29/9.92 (eqbreln1) => 72.29/9.92 (( 72.29/9.92 (breln1invprop) => 72.29/9.92 (( 72.29/9.92 (breln1invI) => 72.29/9.92 (( 72.29/9.92 (breln1invE) => 72.29/9.92 (( 72.29/9.92 (breln1compprop) => 72.29/9.92 (( 72.29/9.92 (breln1compI) => 72.29/9.92 (( 72.29/9.92 (breln1compE) => 72.29/9.92 (( 72.29/9.92 (breln1compEex) => 72.29/9.92 (( 72.29/9.92 (!!) @ ( 72.29/9.92 (('#B') @ ( 72.29/9.92 !!) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 !!))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#C') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 breln1)))) @ 72.29/9.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2149])). 72.29/9.92 thf(zip_derived_cl2185, plain, 72.29/9.92 (~ (((beta1) => 72.29/9.92 (((eta1) => 72.29/9.92 (((lam2lamEq) => 72.29/9.92 (((beta2) => 72.29/9.92 (((eta2) => 72.29/9.92 (((iffalseProp1) => 72.29/9.92 (((iffalseProp2) => 72.29/9.92 (((iftrueProp1) => 72.29/9.92 (((iftrueProp2) => 72.29/9.92 (((ifSingleton) => 72.29/9.92 (((ifp) => 72.29/9.92 (((theeq) => 72.29/9.92 (((iftrue) => 72.29/9.92 (((iffalse) => 72.29/9.92 (((iftrueorfalse) => 72.29/9.92 (((binintersectT_lem) => 72.29/9.92 (((binunionT_lem) => 72.29/9.92 (((powersetT_lem) => 72.29/9.92 (((setminusT_lem) => 72.29/9.92 (((complementT_lem) => 72.29/9.92 (((setextT) => 72.29/9.92 (((subsetTI) => 72.29/9.92 (((powersetTI1) => 72.29/9.92 (((powersetTE1) => 72.29/9.92 (((complementTI1) => 72.29/9.92 (((complementTE1) => 72.29/9.92 (((binintersectTELcontra) => 72.29/9.92 (((binintersectTERcontra) => 72.29/9.92 (((contrasubsetT) => 72.29/9.92 (((contrasubsetT1) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT2) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT3) => 72.29/9.92 (( 72.29/9.92 (doubleComplementI1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementE1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementSub1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementSub2) => 72.29/9.92 (( 72.29/9.92 (doubleComplementEq) => 72.29/9.92 (( 72.29/9.92 (complementTnotintersectT) => 72.29/9.92 (( 72.29/9.92 (complementImpComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (complementSubsetComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (complementInPowersetComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (contraSubsetComplement) => 72.29/9.92 (( 72.29/9.92 (complementTcontraSubset) => 72.29/9.92 (( 72.29/9.92 (binunionTILcontra) => 72.29/9.92 (( 72.29/9.92 (binunionTIRcontra) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion2) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (intersectInPowersetIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpNotIn1) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpInComplement1) => 72.29/9.92 (( 72.29/9.92 (binunionTE) => 72.29/9.92 (( 72.29/9.92 (binunionTEcontra) => 72.29/9.92 (( 72.29/9.92 (demorgan2a1) => 72.29/9.92 (( 72.29/9.92 (complementUnionInPowersetComplement) => 72.29/9.92 (( 72.29/9.92 (demorgan2a2) => 72.29/9.92 (( 72.29/9.92 (demorgan1a) => 72.29/9.92 (( 72.29/9.92 (demorgan1b) => 72.29/9.92 (( 72.29/9.92 (demorgan1) => 72.29/9.92 (( 72.29/9.92 (demorgan2a) => 72.29/9.92 (( 72.29/9.92 (demorgan2b2) => 72.29/9.92 (( 72.29/9.92 (demorgan2b) => 72.29/9.92 (( 72.29/9.92 (demorgan2) => 72.29/9.92 (( 72.29/9.92 (woz13rule0) => 72.29/9.92 (( 72.29/9.92 (woz13rule1) => 72.29/9.92 (( 72.29/9.92 (woz13rule2) => 72.29/9.92 (( 72.29/9.92 (woz13rule3) => 72.29/9.92 (( 72.29/9.92 (woz13rule4) => 72.29/9.92 (( 72.29/9.92 (woz1_1) => 72.29/9.92 (( 72.29/9.92 (woz1_2) => 72.29/9.92 (( 72.29/9.92 (woz1_3) => 72.29/9.92 (( 72.29/9.92 (woz1_4) => 72.29/9.92 (( 72.29/9.92 (woz1_5) => 72.29/9.92 (( 72.29/9.92 (breln1all2) => 72.29/9.92 (( 72.29/9.92 (breln1SetBreln1) => 72.29/9.92 (( 72.29/9.92 (choice2fnsingleton) => 72.29/9.92 (( 72.29/9.92 (setOfPairsIsBReln1) => 72.29/9.92 (( 72.29/9.92 (breln1all1) => 72.29/9.92 (( 72.29/9.92 (subbreln1) => 72.29/9.92 (( 72.29/9.92 (eqbreln1) => 72.29/9.92 (( 72.29/9.92 (breln1invprop) => 72.29/9.92 (( 72.29/9.92 (breln1invI) => 72.29/9.92 (( 72.29/9.92 (breln1invE) => 72.29/9.92 (( 72.29/9.92 (breln1compprop) => 72.29/9.92 (( 72.29/9.92 (breln1compI) => 72.29/9.92 (( 72.29/9.92 (breln1compE) => 72.29/9.92 (( 72.29/9.92 (breln1compEex) => 72.29/9.92 (( 72.29/9.92 (!!) @ ( 72.29/9.92 (('#B') @ ( 72.29/9.92 !!) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 !!))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#C') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 breln1)))) @ 72.29/9.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2166])). 72.29/9.92 thf(zip_derived_cl2203, plain, 72.29/9.92 (~ (((eta1) => 72.29/9.92 (((lam2lamEq) => 72.29/9.92 (((beta2) => 72.29/9.92 (((eta2) => 72.29/9.92 (((iffalseProp1) => 72.29/9.92 (((iffalseProp2) => 72.29/9.92 (((iftrueProp1) => 72.29/9.92 (((iftrueProp2) => 72.29/9.92 (((ifSingleton) => 72.29/9.92 (((ifp) => 72.29/9.92 (((theeq) => 72.29/9.92 (((iftrue) => 72.29/9.92 (((iffalse) => 72.29/9.92 (((iftrueorfalse) => 72.29/9.92 (((binintersectT_lem) => 72.29/9.92 (((binunionT_lem) => 72.29/9.92 (((powersetT_lem) => 72.29/9.92 (((setminusT_lem) => 72.29/9.92 (((complementT_lem) => 72.29/9.92 (((setextT) => 72.29/9.92 (((subsetTI) => 72.29/9.92 (((powersetTI1) => 72.29/9.92 (((powersetTE1) => 72.29/9.92 (((complementTI1) => 72.29/9.92 (((complementTE1) => 72.29/9.92 (((binintersectTELcontra) => 72.29/9.92 (((binintersectTERcontra) => 72.29/9.92 (((contrasubsetT) => 72.29/9.92 (((contrasubsetT1) => 72.29/9.92 (((contrasubsetT2) => 72.29/9.92 (( 72.29/9.92 (contrasubsetT3) => 72.29/9.92 (( 72.29/9.92 (doubleComplementI1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementE1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementSub1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementSub2) => 72.29/9.92 (( 72.29/9.92 (doubleComplementEq) => 72.29/9.92 (( 72.29/9.92 (complementTnotintersectT) => 72.29/9.92 (( 72.29/9.92 (complementImpComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (complementSubsetComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (complementInPowersetComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (contraSubsetComplement) => 72.29/9.92 (( 72.29/9.92 (complementTcontraSubset) => 72.29/9.92 (( 72.29/9.92 (binunionTILcontra) => 72.29/9.92 (( 72.29/9.92 (binunionTIRcontra) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion2) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (intersectInPowersetIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpNotIn1) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpInComplement1) => 72.29/9.92 (( 72.29/9.92 (binunionTE) => 72.29/9.92 (( 72.29/9.92 (binunionTEcontra) => 72.29/9.92 (( 72.29/9.92 (demorgan2a1) => 72.29/9.92 (( 72.29/9.92 (complementUnionInPowersetComplement) => 72.29/9.92 (( 72.29/9.92 (demorgan2a2) => 72.29/9.92 (( 72.29/9.92 (demorgan1a) => 72.29/9.92 (( 72.29/9.92 (demorgan1b) => 72.29/9.92 (( 72.29/9.92 (demorgan1) => 72.29/9.92 (( 72.29/9.92 (demorgan2a) => 72.29/9.92 (( 72.29/9.92 (demorgan2b2) => 72.29/9.92 (( 72.29/9.92 (demorgan2b) => 72.29/9.92 (( 72.29/9.92 (demorgan2) => 72.29/9.92 (( 72.29/9.92 (woz13rule0) => 72.29/9.92 (( 72.29/9.92 (woz13rule1) => 72.29/9.92 (( 72.29/9.92 (woz13rule2) => 72.29/9.92 (( 72.29/9.92 (woz13rule3) => 72.29/9.92 (( 72.29/9.92 (woz13rule4) => 72.29/9.92 (( 72.29/9.92 (woz1_1) => 72.29/9.92 (( 72.29/9.92 (woz1_2) => 72.29/9.92 (( 72.29/9.92 (woz1_3) => 72.29/9.92 (( 72.29/9.92 (woz1_4) => 72.29/9.92 (( 72.29/9.92 (woz1_5) => 72.29/9.92 (( 72.29/9.92 (breln1all2) => 72.29/9.92 (( 72.29/9.92 (breln1SetBreln1) => 72.29/9.92 (( 72.29/9.92 (choice2fnsingleton) => 72.29/9.92 (( 72.29/9.92 (setOfPairsIsBReln1) => 72.29/9.92 (( 72.29/9.92 (breln1all1) => 72.29/9.92 (( 72.29/9.92 (subbreln1) => 72.29/9.92 (( 72.29/9.92 (eqbreln1) => 72.29/9.92 (( 72.29/9.92 (breln1invprop) => 72.29/9.92 (( 72.29/9.92 (breln1invI) => 72.29/9.92 (( 72.29/9.92 (breln1invE) => 72.29/9.92 (( 72.29/9.92 (breln1compprop) => 72.29/9.92 (( 72.29/9.92 (breln1compI) => 72.29/9.92 (( 72.29/9.92 (breln1compE) => 72.29/9.92 (( 72.29/9.92 (breln1compEex) => 72.29/9.92 (( 72.29/9.92 (!!) @ ( 72.29/9.92 (('#B') @ ( 72.29/9.92 !!) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 !!))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#C') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 breln1)))) @ 72.29/9.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2185])). 72.29/9.92 thf(zip_derived_cl2219, plain, 72.29/9.92 (~ (((lam2lamEq) => 72.29/9.92 (((beta2) => 72.29/9.92 (((eta2) => 72.29/9.92 (((iffalseProp1) => 72.29/9.92 (((iffalseProp2) => 72.29/9.92 (((iftrueProp1) => 72.29/9.92 (((iftrueProp2) => 72.29/9.92 (((ifSingleton) => 72.29/9.92 (((ifp) => 72.29/9.92 (((theeq) => 72.29/9.92 (((iftrue) => 72.29/9.92 (((iffalse) => 72.29/9.92 (((iftrueorfalse) => 72.29/9.92 (((binintersectT_lem) => 72.29/9.92 (((binunionT_lem) => 72.29/9.92 (((powersetT_lem) => 72.29/9.92 (((setminusT_lem) => 72.29/9.92 (((complementT_lem) => 72.29/9.92 (((setextT) => 72.29/9.92 (((subsetTI) => 72.29/9.92 (((powersetTI1) => 72.29/9.92 (((powersetTE1) => 72.29/9.92 (((complementTI1) => 72.29/9.92 (((complementTE1) => 72.29/9.92 (((binintersectTELcontra) => 72.29/9.92 (((binintersectTERcontra) => 72.29/9.92 (((contrasubsetT) => 72.29/9.92 (((contrasubsetT1) => 72.29/9.92 (((contrasubsetT2) => 72.29/9.92 (((contrasubsetT3) => 72.29/9.92 (( 72.29/9.92 (doubleComplementI1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementE1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementSub1) => 72.29/9.92 (( 72.29/9.92 (doubleComplementSub2) => 72.29/9.92 (( 72.29/9.92 (doubleComplementEq) => 72.29/9.92 (( 72.29/9.92 (complementTnotintersectT) => 72.29/9.92 (( 72.29/9.92 (complementImpComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (complementSubsetComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (complementInPowersetComplementIntersect) => 72.29/9.92 (( 72.29/9.92 (contraSubsetComplement) => 72.29/9.92 (( 72.29/9.92 (complementTcontraSubset) => 72.29/9.92 (( 72.29/9.92 (binunionTILcontra) => 72.29/9.92 (( 72.29/9.92 (binunionTIRcontra) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion2) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (intersectInPowersetIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpNotIn1) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpInComplement1) => 72.29/9.92 (( 72.29/9.92 (binunionTE) => 72.29/9.92 (( 72.29/9.92 (binunionTEcontra) => 72.29/9.92 (( 72.29/9.92 (demorgan2a1) => 72.29/9.92 (( 72.29/9.92 (complementUnionInPowersetComplement) => 72.29/9.92 (( 72.29/9.92 (demorgan2a2) => 72.29/9.92 (( 72.29/9.92 (demorgan1a) => 72.29/9.92 (( 72.29/9.92 (demorgan1b) => 72.29/9.92 (( 72.29/9.92 (demorgan1) => 72.29/9.92 (( 72.29/9.92 (demorgan2a) => 72.29/9.92 (( 72.29/9.92 (demorgan2b2) => 72.29/9.92 (( 72.29/9.92 (demorgan2b) => 72.29/9.92 (( 72.29/9.92 (demorgan2) => 72.29/9.92 (( 72.29/9.92 (woz13rule0) => 72.29/9.92 (( 72.29/9.92 (woz13rule1) => 72.29/9.92 (( 72.29/9.92 (woz13rule2) => 72.29/9.92 (( 72.29/9.92 (woz13rule3) => 72.29/9.92 (( 72.29/9.92 (woz13rule4) => 72.29/9.92 (( 72.29/9.92 (woz1_1) => 72.29/9.92 (( 72.29/9.92 (woz1_2) => 72.29/9.92 (( 72.29/9.92 (woz1_3) => 72.29/9.92 (( 72.29/9.92 (woz1_4) => 72.29/9.92 (( 72.29/9.92 (woz1_5) => 72.29/9.92 (( 72.29/9.92 (breln1all2) => 72.29/9.92 (( 72.29/9.92 (breln1SetBreln1) => 72.29/9.92 (( 72.29/9.92 (choice2fnsingleton) => 72.29/9.92 (( 72.29/9.92 (setOfPairsIsBReln1) => 72.29/9.92 (( 72.29/9.92 (breln1all1) => 72.29/9.92 (( 72.29/9.92 (subbreln1) => 72.29/9.92 (( 72.29/9.92 (eqbreln1) => 72.29/9.92 (( 72.29/9.92 (breln1invprop) => 72.29/9.92 (( 72.29/9.92 (breln1invI) => 72.29/9.92 (( 72.29/9.92 (breln1invE) => 72.29/9.92 (( 72.29/9.92 (breln1compprop) => 72.29/9.92 (( 72.29/9.92 (breln1compI) => 72.29/9.92 (( 72.29/9.92 (breln1compE) => 72.29/9.92 (( 72.29/9.92 (breln1compEex) => 72.29/9.92 (( 72.29/9.92 (!!) @ ( 72.29/9.92 (('#B') @ ( 72.29/9.92 !!) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 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breln1)))))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#C') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 breln1)))) @ 72.29/9.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2306])). 72.29/9.92 thf(zip_derived_cl2344, plain, 72.29/9.92 (~ (((ifSingleton) => 72.29/9.92 (((ifp) => 72.29/9.92 (((theeq) => 72.29/9.92 (((iftrue) => 72.29/9.92 (((iffalse) => 72.29/9.92 (((iftrueorfalse) => 72.29/9.92 (((binintersectT_lem) => 72.29/9.92 (((binunionT_lem) => 72.29/9.92 (((powersetT_lem) => 72.29/9.92 (((setminusT_lem) => 72.29/9.92 (((complementT_lem) => 72.29/9.92 (((setextT) => 72.29/9.92 (((subsetTI) => 72.29/9.92 (((powersetTI1) => 72.29/9.92 (((powersetTE1) => 72.29/9.92 (((complementTI1) => 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72.29/9.92 =>))) @ 72.29/9.92 breln1)))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 !!))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#C') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 breln1)))) @ 72.29/9.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2328])). 72.29/9.92 thf(zip_derived_cl2360, plain, 72.29/9.92 (~ (((ifp) => 72.29/9.92 (((theeq) => 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=> 72.29/9.92 (( 72.29/9.92 (demorgan2b2) => 72.29/9.92 (( 72.29/9.92 (demorgan2b) => 72.29/9.92 (( 72.29/9.92 (demorgan2) => 72.29/9.92 (( 72.29/9.92 (woz13rule0) => 72.29/9.92 (( 72.29/9.92 (woz13rule1) => 72.29/9.92 (( 72.29/9.92 (woz13rule2) => 72.29/9.92 (( 72.29/9.92 (woz13rule3) => 72.29/9.92 (( 72.29/9.92 (woz13rule4) => 72.29/9.92 (( 72.29/9.92 (woz1_1) => 72.29/9.92 (( 72.29/9.92 (woz1_2) => 72.29/9.92 (( 72.29/9.92 (woz1_3) => 72.29/9.92 (( 72.29/9.92 (woz1_4) => 72.29/9.92 (( 72.29/9.92 (woz1_5) => 72.29/9.92 (( 72.29/9.92 (breln1all2) => 72.29/9.92 (( 72.29/9.92 (breln1SetBreln1) => 72.29/9.92 (( 72.29/9.92 (choice2fnsingleton) => 72.29/9.92 (( 72.29/9.92 (setOfPairsIsBReln1) => 72.29/9.92 (( 72.29/9.92 (breln1all1) => 72.29/9.92 (( 72.29/9.92 (subbreln1) => 72.29/9.92 (( 72.29/9.92 (eqbreln1) => 72.29/9.92 (( 72.29/9.92 (breln1invprop) => 72.29/9.92 (( 72.29/9.92 (breln1invI) => 72.29/9.92 (( 72.29/9.92 (breln1invE) => 72.29/9.92 (( 72.29/9.92 (breln1compprop) => 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72.29/9.92 breln1)))) @ 72.29/9.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2344])). 72.29/9.92 thf(zip_derived_cl2381, plain, 72.29/9.92 (~ (((theeq) => 72.29/9.92 (((iftrue) => 72.29/9.92 (((iffalse) => 72.29/9.92 (((iftrueorfalse) => 72.29/9.92 (((binintersectT_lem) => 72.29/9.92 (((binunionT_lem) => 72.29/9.92 (((powersetT_lem) => 72.29/9.92 (((setminusT_lem) => 72.29/9.92 (((complementT_lem) => 72.29/9.92 (((setextT) => 72.29/9.92 (((subsetTI) => 72.29/9.92 (((powersetTI1) => 72.29/9.92 (((powersetTE1) => 72.29/9.92 (((complementTI1) => 72.29/9.92 (((complementTE1) => 72.29/9.92 (((binintersectTELcontra) => 72.29/9.92 (((binintersectTERcontra) => 72.29/9.92 (((contrasubsetT) => 72.29/9.92 (((contrasubsetT1) => 72.29/9.92 (((contrasubsetT2) => 72.29/9.92 (((contrasubsetT3) => 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(choice2fnsingleton) => 72.29/9.92 (( 72.29/9.92 (setOfPairsIsBReln1) => 72.29/9.92 (( 72.29/9.92 (breln1all1) => 72.29/9.92 (( 72.29/9.92 (subbreln1) => 72.29/9.92 (( 72.29/9.92 (eqbreln1) => 72.29/9.92 (( 72.29/9.92 (breln1invprop) => 72.29/9.92 (( 72.29/9.92 (breln1invI) => 72.29/9.92 (( 72.29/9.92 (breln1invE) => 72.29/9.92 (( 72.29/9.92 (breln1compprop) => 72.29/9.92 (( 72.29/9.92 (breln1compI) => 72.29/9.92 (( 72.29/9.92 (breln1compE) => 72.29/9.92 (( 72.29/9.92 (breln1compEex) => 72.29/9.92 (( 72.29/9.92 (!!) @ ( 72.29/9.92 (('#B') @ ( 72.29/9.92 !!) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 !!))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#C') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 breln1)))) @ 72.29/9.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2360])). 72.29/9.92 thf(zip_derived_cl2399, plain, 72.29/9.92 (~ (((iftrue) => 72.29/9.92 (((iffalse) => 72.29/9.92 (((iftrueorfalse) => 72.29/9.92 (((binintersectT_lem) => 72.29/9.92 (((binunionT_lem) => 72.29/9.92 (((powersetT_lem) => 72.29/9.92 (((setminusT_lem) => 72.29/9.92 (((complementT_lem) => 72.29/9.92 (((setextT) => 72.29/9.92 (((subsetTI) => 72.29/9.92 (((powersetTI1) => 72.29/9.92 (((powersetTE1) => 72.29/9.92 (((complementTI1) => 72.29/9.92 (((complementTE1) => 72.29/9.92 (((binintersectTELcontra) => 72.29/9.92 (((binintersectTERcontra) => 72.29/9.92 (((contrasubsetT) => 72.29/9.92 (((contrasubsetT1) => 72.29/9.92 (((contrasubsetT2) => 72.29/9.92 (((contrasubsetT3) => 72.29/9.92 (((doubleComplementI1) => 72.29/9.92 (((doubleComplementE1) => 72.29/9.92 (((doubleComplementSub1) => 72.29/9.92 (((doubleComplementSub2) => 72.29/9.92 (((doubleComplementEq) => 72.29/9.92 (((complementTnotintersectT) => 72.29/9.92 (((complementImpComplementIntersect) => 72.29/9.92 (((complementSubsetComplementIntersect) => 72.29/9.92 (((complementInPowersetComplementIntersect) => 72.29/9.92 (((contraSubsetComplement) => 72.29/9.92 (( 72.29/9.92 (complementTcontraSubset) => 72.29/9.92 (( 72.29/9.92 (binunionTILcontra) => 72.29/9.92 (( 72.29/9.92 (binunionTIRcontra) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion2) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (intersectInPowersetIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpNotIn1) => 72.29/9.92 (( 72.29/9.92 (inComplementUnionImpInComplement1) => 72.29/9.92 (( 72.29/9.92 (binunionTE) => 72.29/9.92 (( 72.29/9.92 (binunionTEcontra) => 72.29/9.92 (( 72.29/9.92 (demorgan2a1) => 72.29/9.92 (( 72.29/9.92 (complementUnionInPowersetComplement) => 72.29/9.92 (( 72.29/9.92 (demorgan2a2) => 72.29/9.92 (( 72.29/9.92 (demorgan1a) => 72.29/9.92 (( 72.29/9.92 (demorgan1b) => 72.29/9.92 (( 72.29/9.92 (demorgan1) => 72.29/9.92 (( 72.29/9.92 (demorgan2a) => 72.29/9.92 (( 72.29/9.92 (demorgan2b2) => 72.29/9.92 (( 72.29/9.92 (demorgan2b) => 72.29/9.92 (( 72.29/9.92 (demorgan2) => 72.29/9.92 (( 72.29/9.92 (woz13rule0) => 72.29/9.92 (( 72.29/9.92 (woz13rule1) => 72.29/9.92 (( 72.29/9.92 (woz13rule2) => 72.29/9.92 (( 72.29/9.92 (woz13rule3) => 72.29/9.92 (( 72.29/9.92 (woz13rule4) => 72.29/9.92 (( 72.29/9.92 (woz1_1) => 72.29/9.92 (( 72.29/9.92 (woz1_2) => 72.29/9.92 (( 72.29/9.92 (woz1_3) => 72.29/9.92 (( 72.29/9.92 (woz1_4) => 72.29/9.92 (( 72.29/9.92 (woz1_5) => 72.29/9.92 (( 72.29/9.92 (breln1all2) => 72.29/9.92 (( 72.29/9.92 (breln1SetBreln1) => 72.29/9.92 (( 72.29/9.92 (choice2fnsingleton) => 72.29/9.92 (( 72.29/9.92 (setOfPairsIsBReln1) => 72.29/9.92 (( 72.29/9.92 (breln1all1) => 72.29/9.92 (( 72.29/9.92 (subbreln1) => 72.29/9.92 (( 72.29/9.92 (eqbreln1) => 72.29/9.92 (( 72.29/9.92 (breln1invprop) => 72.29/9.92 (( 72.29/9.92 (breln1invI) => 72.29/9.92 (( 72.29/9.92 (breln1invE) => 72.29/9.92 (( 72.29/9.92 (breln1compprop) => 72.29/9.92 (( 72.29/9.92 (breln1compI) => 72.29/9.92 (( 72.29/9.92 (breln1compE) => 72.29/9.92 (( 72.29/9.92 (breln1compEex) => 72.29/9.92 (( 72.29/9.92 (!!) @ ( 72.29/9.92 (('#B') @ ( 72.29/9.92 !!) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 !!))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#S') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#S') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 =>))) @ 72.29/9.92 breln1)))))) @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#C') @ ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 ( 72.29/9.92 ( 72.29/9.92 ('#B') @ ( 72.29/9.92 '#B') @ 72.29/9.92 breln1)))) @ 72.29/9.92 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2381])). 72.29/9.92 thf(zip_derived_cl2415, plain, 72.29/9.92 (~ (((iffalse) => 72.29/9.92 (((iftrueorfalse) => 72.29/9.92 (((binintersectT_lem) => 72.29/9.92 (((binunionT_lem) => 72.29/9.92 (((powersetT_lem) => 72.29/9.92 (((setminusT_lem) => 72.29/9.92 (((complementT_lem) => 72.29/9.92 (((setextT) => 72.29/9.92 (((subsetTI) => 72.29/9.92 (((powersetTI1) => 72.29/9.92 (((powersetTE1) => 72.29/9.92 (((complementTI1) => 72.29/9.92 (((complementTE1) => 72.29/9.92 (((binintersectTELcontra) => 72.29/9.92 (((binintersectTERcontra) => 72.29/9.92 (((contrasubsetT) => 72.29/9.92 (((contrasubsetT1) => 72.29/9.92 (((contrasubsetT2) => 72.29/9.92 (((contrasubsetT3) => 72.29/9.92 (((doubleComplementI1) => 72.29/9.92 (((doubleComplementE1) => 72.29/9.92 (((doubleComplementSub1) => 72.29/9.92 (((doubleComplementSub2) => 72.29/9.92 (((doubleComplementEq) => 72.29/9.92 (((complementTnotintersectT) => 72.29/9.92 (((complementImpComplementIntersect) => 72.29/9.92 (((complementSubsetComplementIntersect) => 72.29/9.92 (((complementInPowersetComplementIntersect) => 72.29/9.92 (((contraSubsetComplement) => 72.29/9.92 (((complementTcontraSubset) => 72.29/9.92 (( 72.29/9.92 (binunionTILcontra) => 72.29/9.92 (( 72.29/9.92 (binunionTIRcontra) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInUnion2) => 72.29/9.92 (( 72.29/9.92 (inIntersectImpInIntersectUnions) => 72.29/9.92 (( 72.29/9.92 (intersectInPowersetIntersectUnions) => 72.29/9.92 (( 72.29/9.93 (inComplementUnionImpNotIn1) => 72.29/9.93 (( 72.29/9.93 (inComplementUnionImpInComplement1) => 72.29/9.93 (( 72.29/9.93 (binunionTE) => 72.29/9.93 (( 72.29/9.93 (binunionTEcontra) => 72.29/9.93 (( 72.29/9.93 (demorgan2a1) => 72.29/9.93 (( 72.29/9.93 (complementUnionInPowersetComplement) => 72.29/9.93 (( 72.29/9.93 (demorgan2a2) => 72.29/9.93 (( 72.29/9.93 (demorgan1a) => 72.29/9.93 (( 72.29/9.93 (demorgan1b) => 72.29/9.93 (( 72.29/9.93 (demorgan1) => 72.29/9.93 (( 72.29/9.93 (demorgan2a) => 72.29/9.93 (( 72.29/9.93 (demorgan2b2) => 72.29/9.93 (( 72.29/9.93 (demorgan2b) => 72.29/9.93 (( 72.29/9.93 (demorgan2) => 72.29/9.93 (( 72.29/9.93 (woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2399])). 72.29/9.93 thf(zip_derived_cl2434, plain, 72.29/9.93 (~ (((iftrueorfalse) => 72.29/9.93 (((binintersectT_lem) => 72.29/9.93 (((binunionT_lem) => 72.29/9.93 (((powersetT_lem) => 72.29/9.93 (((setminusT_lem) => 72.29/9.93 (((complementT_lem) => 72.29/9.93 (((setextT) => 72.29/9.93 (((subsetTI) => 72.29/9.93 (((powersetTI1) => 72.29/9.93 (((powersetTE1) => 72.29/9.93 (((complementTI1) => 72.29/9.93 (((complementTE1) => 72.29/9.93 (((binintersectTELcontra) => 72.29/9.93 (((binintersectTERcontra) => 72.29/9.93 (((contrasubsetT) => 72.29/9.93 (((contrasubsetT1) => 72.29/9.93 (((contrasubsetT2) => 72.29/9.93 (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (( 72.29/9.93 (binunionTIRcontra) => 72.29/9.93 (( 72.29/9.93 (inIntersectImpInUnion) => 72.29/9.93 (( 72.29/9.93 (inIntersectImpInUnion2) => 72.29/9.93 (( 72.29/9.93 (inIntersectImpInIntersectUnions) => 72.29/9.93 (( 72.29/9.93 (intersectInPowersetIntersectUnions) => 72.29/9.93 (( 72.29/9.93 (inComplementUnionImpNotIn1) => 72.29/9.93 (( 72.29/9.93 (inComplementUnionImpInComplement1) => 72.29/9.93 (( 72.29/9.93 (binunionTE) => 72.29/9.93 (( 72.29/9.93 (binunionTEcontra) => 72.29/9.93 (( 72.29/9.93 (demorgan2a1) => 72.29/9.93 (( 72.29/9.93 (complementUnionInPowersetComplement) => 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72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2415])). 72.29/9.93 thf(zip_derived_cl2449, plain, 72.29/9.93 (~ (((binintersectT_lem) => 72.29/9.93 (((binunionT_lem) => 72.29/9.93 (((powersetT_lem) => 72.29/9.93 (((setminusT_lem) => 72.29/9.93 (((complementT_lem) => 72.29/9.93 (((setextT) => 72.29/9.93 (((subsetTI) => 72.29/9.93 (((powersetTI1) => 72.29/9.93 (((powersetTE1) => 72.29/9.93 (((complementTI1) => 72.29/9.93 (((complementTE1) => 72.29/9.93 (((binintersectTELcontra) => 72.29/9.93 (((binintersectTERcontra) => 72.29/9.93 (((contrasubsetT) => 72.29/9.93 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(((complementT_lem) => 72.29/9.93 (((setextT) => 72.29/9.93 (((subsetTI) => 72.29/9.93 (((powersetTI1) => 72.29/9.93 (((powersetTE1) => 72.29/9.93 (((complementTI1) => 72.29/9.93 (((complementTE1) => 72.29/9.93 (((binintersectTELcontra) => 72.29/9.93 (((binintersectTERcontra) => 72.29/9.93 (((contrasubsetT) => 72.29/9.93 (((contrasubsetT1) => 72.29/9.93 (((contrasubsetT2) => 72.29/9.93 (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 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72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2483])). 72.29/9.93 thf(zip_derived_cl2502, plain, 72.29/9.93 (~ (((setextT) => 72.29/9.93 (((subsetTI) => 72.29/9.93 (((powersetTI1) => 72.29/9.93 (((powersetTE1) => 72.29/9.93 (((complementTI1) => 72.29/9.93 (((complementTE1) => 72.29/9.93 (((binintersectTELcontra) => 72.29/9.93 (((binintersectTERcontra) => 72.29/9.93 (((contrasubsetT) => 72.29/9.93 (((contrasubsetT1) => 72.29/9.93 (((contrasubsetT2) => 72.29/9.93 (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (( 72.29/9.93 (inComplementUnionImpInComplement1) => 72.29/9.93 (( 72.29/9.93 (binunionTE) => 72.29/9.93 (( 72.29/9.93 (binunionTEcontra) => 72.29/9.93 (( 72.29/9.93 (demorgan2a1) => 72.29/9.93 (( 72.29/9.93 (complementUnionInPowersetComplement) => 72.29/9.93 (( 72.29/9.93 (demorgan2a2) => 72.29/9.93 (( 72.29/9.93 (demorgan1a) => 72.29/9.93 (( 72.29/9.93 (demorgan1b) => 72.29/9.93 (( 72.29/9.93 (demorgan1) => 72.29/9.93 (( 72.29/9.93 (demorgan2a) => 72.29/9.93 (( 72.29/9.93 (demorgan2b2) => 72.29/9.93 (( 72.29/9.93 (demorgan2b) => 72.29/9.93 (( 72.29/9.93 (demorgan2) => 72.29/9.93 (( 72.29/9.93 (woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 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72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2492])). 72.29/9.93 thf(zip_derived_cl2513, plain, 72.29/9.93 (~ (((subsetTI) => 72.29/9.93 (((powersetTI1) => 72.29/9.93 (((powersetTE1) => 72.29/9.93 (((complementTI1) => 72.29/9.93 (((complementTE1) => 72.29/9.93 (((binintersectTELcontra) => 72.29/9.93 (((binintersectTERcontra) => 72.29/9.93 (((contrasubsetT) => 72.29/9.93 (((contrasubsetT1) => 72.29/9.93 (((contrasubsetT2) => 72.29/9.93 (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (( 72.29/9.93 (binunionTE) => 72.29/9.93 (( 72.29/9.93 (binunionTEcontra) => 72.29/9.93 (( 72.29/9.93 (demorgan2a1) => 72.29/9.93 (( 72.29/9.93 (complementUnionInPowersetComplement) => 72.29/9.93 (( 72.29/9.93 (demorgan2a2) => 72.29/9.93 (( 72.29/9.93 (demorgan1a) => 72.29/9.93 (( 72.29/9.93 (demorgan1b) => 72.29/9.93 (( 72.29/9.93 (demorgan1) => 72.29/9.93 (( 72.29/9.93 (demorgan2a) => 72.29/9.93 (( 72.29/9.93 (demorgan2b2) => 72.29/9.93 (( 72.29/9.93 (demorgan2b) => 72.29/9.93 (( 72.29/9.93 (demorgan2) => 72.29/9.93 (( 72.29/9.93 (woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 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72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2502])). 72.29/9.93 thf(zip_derived_cl2525, plain, 72.29/9.93 (~ (((powersetTI1) => 72.29/9.93 (((powersetTE1) => 72.29/9.93 (((complementTI1) => 72.29/9.93 (((complementTE1) => 72.29/9.93 (((binintersectTELcontra) => 72.29/9.93 (((binintersectTERcontra) => 72.29/9.93 (((contrasubsetT) => 72.29/9.93 (((contrasubsetT1) => 72.29/9.93 (((contrasubsetT2) => 72.29/9.93 (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (( 72.29/9.93 (binunionTEcontra) => 72.29/9.93 (( 72.29/9.93 (demorgan2a1) => 72.29/9.93 (( 72.29/9.93 (complementUnionInPowersetComplement) => 72.29/9.93 (( 72.29/9.93 (demorgan2a2) => 72.29/9.93 (( 72.29/9.93 (demorgan1a) => 72.29/9.93 (( 72.29/9.93 (demorgan1b) => 72.29/9.93 (( 72.29/9.93 (demorgan1) => 72.29/9.93 (( 72.29/9.93 (demorgan2a) => 72.29/9.93 (( 72.29/9.93 (demorgan2b2) => 72.29/9.93 (( 72.29/9.93 (demorgan2b) => 72.29/9.93 (( 72.29/9.93 (demorgan2) => 72.29/9.93 (( 72.29/9.93 (woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2513])). 72.29/9.93 thf(zip_derived_cl2534, plain, 72.29/9.93 (~ (((powersetTE1) => 72.29/9.93 (((complementTI1) => 72.29/9.93 (((complementTE1) => 72.29/9.93 (((binintersectTELcontra) => 72.29/9.93 (((binintersectTERcontra) => 72.29/9.93 (((contrasubsetT) => 72.29/9.93 (((contrasubsetT1) => 72.29/9.93 (((contrasubsetT2) => 72.29/9.93 (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (( 72.29/9.93 (demorgan2a1) => 72.29/9.93 (( 72.29/9.93 (complementUnionInPowersetComplement) => 72.29/9.93 (( 72.29/9.93 (demorgan2a2) => 72.29/9.93 (( 72.29/9.93 (demorgan1a) => 72.29/9.93 (( 72.29/9.93 (demorgan1b) => 72.29/9.93 (( 72.29/9.93 (demorgan1) => 72.29/9.93 (( 72.29/9.93 (demorgan2a) => 72.29/9.93 (( 72.29/9.93 (demorgan2b2) => 72.29/9.93 (( 72.29/9.93 (demorgan2b) => 72.29/9.93 (( 72.29/9.93 (demorgan2) => 72.29/9.93 (( 72.29/9.93 (woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2525])). 72.29/9.93 thf(zip_derived_cl2542, plain, 72.29/9.93 (~ (((complementTI1) => 72.29/9.93 (((complementTE1) => 72.29/9.93 (((binintersectTELcontra) => 72.29/9.93 (((binintersectTERcontra) => 72.29/9.93 (((contrasubsetT) => 72.29/9.93 (((contrasubsetT1) => 72.29/9.93 (((contrasubsetT2) => 72.29/9.93 (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (( 72.29/9.93 (complementUnionInPowersetComplement) => 72.29/9.93 (( 72.29/9.93 (demorgan2a2) => 72.29/9.93 (( 72.29/9.93 (demorgan1a) => 72.29/9.93 (( 72.29/9.93 (demorgan1b) => 72.29/9.93 (( 72.29/9.93 (demorgan1) => 72.29/9.93 (( 72.29/9.93 (demorgan2a) => 72.29/9.93 (( 72.29/9.93 (demorgan2b2) => 72.29/9.93 (( 72.29/9.93 (demorgan2b) => 72.29/9.93 (( 72.29/9.93 (demorgan2) => 72.29/9.93 (( 72.29/9.93 (woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2534])). 72.29/9.93 thf(zip_derived_cl2550, plain, 72.29/9.93 (~ (((complementTE1) => 72.29/9.93 (((binintersectTELcontra) => 72.29/9.93 (((binintersectTERcontra) => 72.29/9.93 (((contrasubsetT) => 72.29/9.93 (((contrasubsetT1) => 72.29/9.93 (((contrasubsetT2) => 72.29/9.93 (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (( 72.29/9.93 (demorgan2a2) => 72.29/9.93 (( 72.29/9.93 (demorgan1a) => 72.29/9.93 (( 72.29/9.93 (demorgan1b) => 72.29/9.93 (( 72.29/9.93 (demorgan1) => 72.29/9.93 (( 72.29/9.93 (demorgan2a) => 72.29/9.93 (( 72.29/9.93 (demorgan2b2) => 72.29/9.93 (( 72.29/9.93 (demorgan2b) => 72.29/9.93 (( 72.29/9.93 (demorgan2) => 72.29/9.93 (( 72.29/9.93 (woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2542])). 72.29/9.93 thf(zip_derived_cl2558, plain, 72.29/9.93 (~ (((binintersectTELcontra) => 72.29/9.93 (((binintersectTERcontra) => 72.29/9.93 (((contrasubsetT) => 72.29/9.93 (((contrasubsetT1) => 72.29/9.93 (((contrasubsetT2) => 72.29/9.93 (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 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72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2550])). 72.29/9.93 thf(zip_derived_cl2567, plain, 72.29/9.93 (~ (((binintersectTERcontra) => 72.29/9.93 (((contrasubsetT) => 72.29/9.93 (((contrasubsetT1) => 72.29/9.93 (((contrasubsetT2) => 72.29/9.93 (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 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72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2558])). 72.29/9.93 thf(zip_derived_cl2577, plain, 72.29/9.93 (~ (((contrasubsetT) => 72.29/9.93 (((contrasubsetT1) => 72.29/9.93 (((contrasubsetT2) => 72.29/9.93 (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 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(( 72.29/9.93 (woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2567])). 72.29/9.93 thf(zip_derived_cl2588, plain, 72.29/9.93 (~ (((contrasubsetT1) => 72.29/9.93 (((contrasubsetT2) => 72.29/9.93 (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (( 72.29/9.93 (demorgan2a) => 72.29/9.93 (( 72.29/9.93 (demorgan2b2) => 72.29/9.93 (( 72.29/9.93 (demorgan2b) => 72.29/9.93 (( 72.29/9.93 (demorgan2) => 72.29/9.93 (( 72.29/9.93 (woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2577])). 72.29/9.93 thf(zip_derived_cl2601, plain, 72.29/9.93 (~ (((contrasubsetT2) => 72.29/9.93 (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (( 72.29/9.93 (demorgan2b2) => 72.29/9.93 (( 72.29/9.93 (demorgan2b) => 72.29/9.93 (( 72.29/9.93 (demorgan2) => 72.29/9.93 (( 72.29/9.93 (woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2588])). 72.29/9.93 thf(zip_derived_cl2617, plain, 72.29/9.93 (~ (((contrasubsetT3) => 72.29/9.93 (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (( 72.29/9.93 (demorgan2b) => 72.29/9.93 (( 72.29/9.93 (demorgan2) => 72.29/9.93 (( 72.29/9.93 (woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2601])). 72.29/9.93 thf(zip_derived_cl2636, plain, 72.29/9.93 (~ (((doubleComplementI1) => 72.29/9.93 (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (( 72.29/9.93 (demorgan2) => 72.29/9.93 (( 72.29/9.93 (woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2617])). 72.29/9.93 thf(zip_derived_cl2655, plain, 72.29/9.93 (~ (((doubleComplementE1) => 72.29/9.93 (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (((demorgan2) => 72.29/9.93 (( 72.29/9.93 (woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2636])). 72.29/9.93 thf(zip_derived_cl2672, plain, 72.29/9.93 (~ (((doubleComplementSub1) => 72.29/9.93 (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (((demorgan2) => 72.29/9.93 (((woz13rule0) => 72.29/9.93 (( 72.29/9.93 (woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2655])). 72.29/9.93 thf(zip_derived_cl2687, plain, 72.29/9.93 (~ (((doubleComplementSub2) => 72.29/9.93 (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (((demorgan2) => 72.29/9.93 (((woz13rule0) => 72.29/9.93 (((woz13rule1) => 72.29/9.93 (( 72.29/9.93 (woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2672])). 72.29/9.93 thf(zip_derived_cl2699, plain, 72.29/9.93 (~ (((doubleComplementEq) => 72.29/9.93 (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (((demorgan2) => 72.29/9.93 (((woz13rule0) => 72.29/9.93 (((woz13rule1) => 72.29/9.93 (((woz13rule2) => 72.29/9.93 (( 72.29/9.93 (woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2687])). 72.29/9.93 thf(zip_derived_cl2711, plain, 72.29/9.93 (~ (((complementTnotintersectT) => 72.29/9.93 (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (((demorgan2) => 72.29/9.93 (((woz13rule0) => 72.29/9.93 (((woz13rule1) => 72.29/9.93 (((woz13rule2) => 72.29/9.93 (((woz13rule3) => 72.29/9.93 (( 72.29/9.93 (woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2699])). 72.29/9.93 thf(zip_derived_cl2723, plain, 72.29/9.93 (~ (((complementImpComplementIntersect) => 72.29/9.93 (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (((demorgan2) => 72.29/9.93 (((woz13rule0) => 72.29/9.93 (((woz13rule1) => 72.29/9.93 (((woz13rule2) => 72.29/9.93 (((woz13rule3) => 72.29/9.93 (((woz13rule4) => 72.29/9.93 (( 72.29/9.93 (woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2711])). 72.29/9.93 thf(zip_derived_cl2735, plain, 72.29/9.93 (~ (((complementSubsetComplementIntersect) => 72.29/9.93 (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (((demorgan2) => 72.29/9.93 (((woz13rule0) => 72.29/9.93 (((woz13rule1) => 72.29/9.93 (((woz13rule2) => 72.29/9.93 (((woz13rule3) => 72.29/9.93 (((woz13rule4) => 72.29/9.93 (((woz1_1) => 72.29/9.93 (( 72.29/9.93 (woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2723])). 72.29/9.93 thf(zip_derived_cl2745, plain, 72.29/9.93 (~ (((complementInPowersetComplementIntersect) => 72.29/9.93 (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (((demorgan2) => 72.29/9.93 (((woz13rule0) => 72.29/9.93 (((woz13rule1) => 72.29/9.93 (((woz13rule2) => 72.29/9.93 (((woz13rule3) => 72.29/9.93 (((woz13rule4) => 72.29/9.93 (((woz1_1) => 72.29/9.93 (((woz1_2) => 72.29/9.93 (( 72.29/9.93 (woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2735])). 72.29/9.93 thf(zip_derived_cl2753, plain, 72.29/9.93 (~ (((contraSubsetComplement) => 72.29/9.93 (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (((demorgan2) => 72.29/9.93 (((woz13rule0) => 72.29/9.93 (((woz13rule1) => 72.29/9.93 (((woz13rule2) => 72.29/9.93 (((woz13rule3) => 72.29/9.93 (((woz13rule4) => 72.29/9.93 (((woz1_1) => 72.29/9.93 (((woz1_2) => 72.29/9.93 (((woz1_3) => 72.29/9.93 (( 72.29/9.93 (woz1_4) => 72.29/9.93 (( 72.29/9.93 (woz1_5) => 72.29/9.93 (( 72.29/9.93 (breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 (breln1all1) => 72.29/9.93 (( 72.29/9.93 (subbreln1) => 72.29/9.93 (( 72.29/9.93 (eqbreln1) => 72.29/9.93 (( 72.29/9.93 (breln1invprop) => 72.29/9.93 (( 72.29/9.93 (breln1invI) => 72.29/9.93 (( 72.29/9.93 (breln1invE) => 72.29/9.93 (( 72.29/9.93 (breln1compprop) => 72.29/9.93 (( 72.29/9.93 (breln1compI) => 72.29/9.93 (( 72.29/9.93 (breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2745])). 72.29/9.93 thf(zip_derived_cl2761, plain, 72.29/9.93 (~ (((complementTcontraSubset) => 72.29/9.93 (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 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[status(thm)], [zip_derived_cl2753])). 72.29/9.93 thf(zip_derived_cl2769, plain, 72.29/9.93 (~ (((binunionTILcontra) => 72.29/9.93 (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (((demorgan2) => 72.29/9.93 (((woz13rule0) => 72.29/9.93 (((woz13rule1) => 72.29/9.93 (((woz13rule2) => 72.29/9.93 (((woz13rule3) => 72.29/9.93 (((woz13rule4) => 72.29/9.93 (((woz1_1) => 72.29/9.93 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72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2761])). 72.29/9.93 thf(zip_derived_cl2778, plain, 72.29/9.93 (~ (((binunionTIRcontra) => 72.29/9.93 (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (((demorgan2) => 72.29/9.93 (((woz13rule0) => 72.29/9.93 (((woz13rule1) => 72.29/9.93 (((woz13rule2) => 72.29/9.93 (((woz13rule3) => 72.29/9.93 (((woz13rule4) => 72.29/9.93 (((woz1_1) => 72.29/9.93 (((woz1_2) => 72.29/9.93 (((woz1_3) => 72.29/9.93 (((woz1_4) => 72.29/9.93 (((woz1_5) => 72.29/9.93 (((breln1all2) => 72.29/9.93 (( 72.29/9.93 (breln1SetBreln1) => 72.29/9.93 (( 72.29/9.93 (choice2fnsingleton) => 72.29/9.93 (( 72.29/9.93 (setOfPairsIsBReln1) => 72.29/9.93 (( 72.29/9.93 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72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2769])). 72.29/9.93 thf(zip_derived_cl2788, plain, 72.29/9.93 (~ (((inIntersectImpInUnion) => 72.29/9.93 (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 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(breln1compE) => 72.29/9.93 (( 72.29/9.93 (breln1compEex) => 72.29/9.93 (( 72.29/9.93 (!!) @ ( 72.29/9.93 (('#B') @ ( 72.29/9.93 !!) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2778])). 72.29/9.93 thf(zip_derived_cl2799, plain, 72.29/9.93 (~ (((inIntersectImpInUnion2) => 72.29/9.93 (((inIntersectImpInIntersectUnions) => 72.29/9.93 (((intersectInPowersetIntersectUnions) => 72.29/9.93 (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (((demorgan2) => 72.29/9.93 (((woz13rule0) => 72.29/9.93 (((woz13rule1) => 72.29/9.93 (((woz13rule2) => 72.29/9.93 (((woz13rule3) => 72.29/9.93 (((woz13rule4) => 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=>))) @ 72.29/9.93 breln1)))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 !!))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#S') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#S') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 =>))) @ 72.29/9.93 breln1)))))) @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#C') @ ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 ( 72.29/9.93 ( 72.29/9.93 ('#B') @ ( 72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2810])). 72.29/9.93 thf(zip_derived_cl2830, plain, 72.29/9.93 (~ (((inComplementUnionImpNotIn1) => 72.29/9.93 (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 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72.29/9.93 '#B') @ 72.29/9.93 breln1)))) @ 72.29/9.93 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2820])). 72.29/9.93 thf(zip_derived_cl2841, plain, 72.29/9.93 (~ (((inComplementUnionImpInComplement1) => 72.29/9.93 (((binunionTE) => 72.29/9.93 (((binunionTEcontra) => 72.29/9.93 (((demorgan2a1) => 72.29/9.93 (((complementUnionInPowersetComplement) => 72.29/9.93 (((demorgan2a2) => 72.29/9.93 (((demorgan1a) => 72.29/9.93 (((demorgan1b) => 72.29/9.93 (((demorgan1) => 72.29/9.93 (((demorgan2a) => 72.29/9.93 (((demorgan2b2) => 72.29/9.93 (((demorgan2b) => 72.29/9.93 (((demorgan2) => 72.29/9.93 (((woz13rule0) => 72.29/9.93 (((woz13rule1) => 72.29/9.93 (((woz13rule2) => 72.29/9.93 (((woz13rule3) => 72.29/9.93 (((woz13rule4) => 72.29/9.93 (((woz1_1) => 72.29/9.93 (((woz1_2) => 72.29/9.93 (((woz1_3) => 72.29/9.93 (((woz1_4) => 72.29/9.93 (((woz1_5) => 72.29/9.93 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[status(thm)], [zip_derived_cl2965])). 72.29/9.94 thf(zip_derived_cl2989, plain, 72.29/9.94 (~ (((demorgan2) => 72.29/9.94 (((woz13rule0) => 72.29/9.94 (((woz13rule1) => 72.29/9.94 (((woz13rule2) => 72.29/9.94 (((woz13rule3) => 72.29/9.94 (((woz13rule4) => 72.29/9.94 (((woz1_1) => 72.29/9.94 (((woz1_2) => 72.29/9.94 (((woz1_3) => 72.29/9.94 (((woz1_4) => 72.29/9.94 (((woz1_5) => 72.29/9.94 (((breln1all2) => 72.29/9.94 (((breln1SetBreln1) => 72.29/9.94 (((choice2fnsingleton) => 72.29/9.94 (((setOfPairsIsBReln1) => 72.29/9.94 (((breln1all1) => 72.29/9.94 (((subbreln1) => 72.29/9.94 (((eqbreln1) => 72.29/9.94 (((breln1invprop) => 72.29/9.94 (((breln1invI) => 72.29/9.94 (((breln1invE) => 72.29/9.94 (((breln1compprop) => 72.29/9.94 (((breln1compI) => 72.29/9.94 (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ ( 72.29/9.94 !!) @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#S') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#S') @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 =>))) @ 72.29/9.94 breln1)))) @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 !!))) @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#S') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#B') @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#S') @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 =>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#C') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#B') @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#B') @ 72.29/9.94 breln1)))) @ 72.29/9.94 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2977])). 72.29/9.94 thf(zip_derived_cl3002, plain, 72.29/9.94 (~ (((woz13rule0) => 72.29/9.94 (((woz13rule1) => 72.29/9.94 (((woz13rule2) => 72.29/9.94 (((woz13rule3) => 72.29/9.94 (((woz13rule4) => 72.29/9.94 (((woz1_1) => 72.29/9.94 (((woz1_2) => 72.29/9.94 (((woz1_3) => 72.29/9.94 (((woz1_4) => 72.29/9.94 (((woz1_5) => 72.29/9.94 (((breln1all2) => 72.29/9.94 (((breln1SetBreln1) => 72.29/9.94 (((choice2fnsingleton) => 72.29/9.94 (((setOfPairsIsBReln1) => 72.29/9.94 (((breln1all1) => 72.29/9.94 (((subbreln1) => 72.29/9.94 (((eqbreln1) => 72.29/9.94 (((breln1invprop) => 72.29/9.94 (((breln1invI) => 72.29/9.94 (((breln1invE) => 72.29/9.94 (((breln1compprop) => 72.29/9.94 (((breln1compI) => 72.29/9.94 (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ ( 72.29/9.94 !!) @ 72.29/9.94 ((('#S') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#S') @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 =>))) @ 72.29/9.94 breln1)))) @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 !!))) @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#S') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#B') @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#S') @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 =>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#C') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#B') @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#B') @ 72.29/9.94 breln1)))) @ 72.29/9.94 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2989])). 72.29/9.94 thf(zip_derived_cl3015, plain, 72.29/9.94 (~ (((woz13rule1) => 72.29/9.94 (((woz13rule2) => 72.29/9.94 (((woz13rule3) => 72.29/9.94 (((woz13rule4) => 72.29/9.94 (((woz1_1) => 72.29/9.94 (((woz1_2) => 72.29/9.94 (((woz1_3) => 72.29/9.94 (((woz1_4) => 72.29/9.94 (((woz1_5) => 72.29/9.94 (((breln1all2) => 72.29/9.94 (((breln1SetBreln1) => 72.29/9.94 (((choice2fnsingleton) => 72.29/9.94 (((setOfPairsIsBReln1) => 72.29/9.94 (((breln1all1) => 72.29/9.94 (((subbreln1) => 72.29/9.94 (((eqbreln1) => 72.29/9.94 (((breln1invprop) => 72.29/9.94 (((breln1invI) => 72.29/9.94 (((breln1invE) => 72.29/9.94 (((breln1compprop) => 72.29/9.94 (((breln1compI) => 72.29/9.94 (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ ( 72.29/9.94 !!) @ 72.29/9.94 ((('#S') @ ( 72.29/9.94 (('#B') @ ( 72.29/9.94 '#S') @ 72.29/9.94 (( 72.29/9.94 ('#B') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 =>))) @ 72.29/9.94 breln1)))) @ 72.29/9.94 ((('#B') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 !!))) @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#S') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#B') @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#S') @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 =>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#C') @ ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#B') @ 72.29/9.94 ( 72.29/9.94 ( 72.29/9.94 ('#B') @ ( 72.29/9.94 '#B') @ 72.29/9.94 breln1)))) @ 72.29/9.94 binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3002])). 72.29/9.94 thf(zip_derived_cl3029, plain, 72.29/9.94 (~ (((woz13rule2) => 72.29/9.94 (((woz13rule3) => 72.29/9.94 (((woz13rule4) => 72.29/9.94 (((woz1_1) => 72.29/9.94 (((woz1_2) => 72.29/9.94 (((woz1_3) => 72.29/9.94 (((woz1_4) => 72.29/9.94 (((woz1_5) => 72.29/9.94 (((breln1all2) => 72.29/9.94 (((breln1SetBreln1) => 72.29/9.94 (((choice2fnsingleton) => 72.29/9.94 (((setOfPairsIsBReln1) => 72.29/9.94 (((breln1all1) => 72.29/9.94 (((subbreln1) => 72.29/9.94 (((eqbreln1) => 72.29/9.94 (((breln1invprop) => 72.29/9.94 (((breln1invI) => 72.29/9.94 (((breln1invE) => 72.29/9.94 (((breln1compprop) => 72.29/9.94 (((breln1compI) => 72.29/9.94 (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 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(((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ ( 72.29/9.94 =>))) @ 72.29/9.94 breln1)))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ( 72.29/9.94 '#B') @ 72.29/9.94 ((('#B') @ ( 72.29/9.94 '#S') @ 72.29/9.94 ((('#B') @ ( 72.29/9.94 (('#B') @ (=>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ( 72.29/9.94 '#B') @ 72.29/9.94 ((('#B') @ ( 72.29/9.94 '#B') @ breln1)))) @ 72.29/9.94 binunion))))))))))))))))))))))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3139])). 72.29/9.94 thf(zip_derived_cl3162, plain, 72.29/9.94 (~ (((setOfPairsIsBReln1) => 72.29/9.94 (((breln1all1) => 72.29/9.94 (((subbreln1) => 72.29/9.94 (((eqbreln1) => 72.29/9.94 (((breln1invprop) => 72.29/9.94 (((breln1invI) => 72.29/9.94 (((breln1invE) => 72.29/9.94 (((breln1compprop) => 72.29/9.94 (((breln1compI) => 72.29/9.94 (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ ( 72.29/9.94 =>))) @ 72.29/9.94 breln1)))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ( 72.29/9.94 '#S') @ 72.29/9.94 ((('#B') @ ( 72.29/9.94 (('#B') @ (=>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ( 72.29/9.94 '#B') @ 72.29/9.94 ((('#B') @ ( 72.29/9.94 '#B') @ breln1)))) @ 72.29/9.94 binunion))))))))))))))))))))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3151])). 72.29/9.94 thf(zip_derived_cl3174, plain, 72.29/9.94 (~ (((breln1all1) => 72.29/9.94 (((subbreln1) => 72.29/9.94 (((eqbreln1) => 72.29/9.94 (((breln1invprop) => 72.29/9.94 (((breln1invI) => 72.29/9.94 (((breln1invE) => 72.29/9.94 (((breln1compprop) => 72.29/9.94 (((breln1compI) => 72.29/9.94 (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 breln1)))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ( 72.29/9.94 (('#B') @ (=>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ( 72.29/9.94 '#B') @ breln1)))) @ 72.29/9.94 binunion))))))))))))))))))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3162])). 72.29/9.94 thf(zip_derived_cl3187, plain, 72.29/9.94 (~ (((subbreln1) => 72.29/9.94 (((eqbreln1) => 72.29/9.94 (((breln1invprop) => 72.29/9.94 (((breln1invI) => 72.29/9.94 (((breln1invE) => 72.29/9.94 (((breln1compprop) => 72.29/9.94 (((breln1compI) => 72.29/9.94 (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 breln1)))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ ( 72.29/9.94 =>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#B') @ 72.29/9.94 breln1)))) @ 72.29/9.94 binunion))))))))))))))))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3174])). 72.29/9.94 thf(zip_derived_cl3201, plain, 72.29/9.94 (~ (((eqbreln1) => 72.29/9.94 (((breln1invprop) => 72.29/9.94 (((breln1invI) => 72.29/9.94 (((breln1invE) => 72.29/9.94 (((breln1compprop) => 72.29/9.94 (((breln1compI) => 72.29/9.94 (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 breln1)))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ ( 72.29/9.94 =>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#B') @ 72.29/9.94 breln1)))) @ 72.29/9.94 binunion))))))))))))))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3187])). 72.29/9.94 thf(zip_derived_cl3211, plain, 72.29/9.94 (~ (((breln1invprop) => 72.29/9.94 (((breln1invI) => 72.29/9.94 (((breln1invE) => 72.29/9.94 (((breln1compprop) => 72.29/9.94 (((breln1compI) => 72.29/9.94 (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 breln1)))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#B') @ breln1)))) @ 72.29/9.94 binunion))))))))))))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3201])). 72.29/9.94 thf(zip_derived_cl3221, plain, 72.29/9.94 (~ (((breln1invI) => 72.29/9.94 (((breln1invE) => 72.29/9.94 (((breln1compprop) => 72.29/9.94 (((breln1compI) => 72.29/9.94 (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 breln1)))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#B') @ breln1)))) @ 72.29/9.94 binunion))))))))))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3211])). 72.29/9.94 thf(zip_derived_cl3232, plain, 72.29/9.94 (~ (((breln1invE) => 72.29/9.94 (((breln1compprop) => 72.29/9.94 (((breln1compI) => 72.29/9.94 (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 breln1)))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#B') @ breln1)))) @ 72.29/9.94 binunion))))))))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3221])). 72.29/9.94 thf(zip_derived_cl3245, plain, 72.29/9.94 (~ (((breln1compprop) => 72.29/9.94 (((breln1compI) => 72.29/9.94 (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#B') @ breln1)))) @ 72.29/9.94 binunion))))))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3232])). 72.29/9.94 thf(zip_derived_cl3260, plain, 72.29/9.94 (~ (((breln1compI) => 72.29/9.94 (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#B') @ breln1)))) @ 72.29/9.94 binunion))))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3245])). 72.29/9.94 thf(zip_derived_cl3277, plain, 72.29/9.94 (~ (((breln1compE) => 72.29/9.94 (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 breln1)))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#B') @ breln1)))) @ 72.29/9.94 binunion))))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3260])). 72.29/9.94 thf(zip_derived_cl3295, plain, 72.29/9.94 (~ (((breln1compEex) => 72.29/9.94 (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ breln1)))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#B') @ breln1)))) @ 72.29/9.94 binunion))))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3277])). 72.29/9.94 thf(zip_derived_cl3312, plain, 72.29/9.94 (~ (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ breln1)))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ breln1)))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#B') @ breln1)))) @ 72.29/9.94 binunion))))))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3295])). 72.29/9.94 thf(zip_derived_cl3329, plain, 72.29/9.94 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (breln1 @ '#sk43'))) @ 72.29/9.94 ((('#B') @ (!!) @ 72.29/9.94 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 72.29/9.94 (breln1 @ '#sk43'))))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (breln1 @ '#sk43'))) @ binunion))))))))))), 72.29/9.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3312])). 72.29/9.94 thf(zip_derived_cl3345, plain, 72.29/9.94 (~ (((breln1 @ '#sk43' @ '#sk44') => 72.29/9.94 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (breln1 @ '#sk43'))) @ 72.29/9.94 ((('#B') @ (breln1 @ '#sk43') @ (binunion @ '#sk44')))))))))), 72.29/9.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3329])). 72.29/9.94 thf(breln, axiom,(( breln @ (X1)@ (X2)@ (X0)) = 72.29/9.94 ((subset @ X0 @ (cartprod @ X1 @ X2))))). 72.29/9.94 thf('4', plain, 72.29/9.94 (![X2:$i,X1:$i,X0:$i]: 72.29/9.94 ( ( breln @ X1 @ X2 @ X0 ) = ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) )), 72.29/9.94 define([status(thm)])). 72.29/9.94 thf(breln1, axiom,(( breln1 @ (X0)@ (X1)) = ((breln @ X0 @ X0 @ X1)))). 72.29/9.94 thf('5', plain, 72.29/9.94 (![X1:$i,X0:$i]: ( ( breln1 @ X0 @ X1 ) = ( breln @ X0 @ X0 @ X1 ) )), 72.29/9.94 define([status(thm)])). 72.29/9.94 thf(zip_derived_cl3362, plain, 72.29/9.94 (~ (((subset @ '#sk44' @ (cartprod @ '#sk43' @ '#sk43')) => 72.29/9.94 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (breln1 @ '#sk43'))) @ 72.29/9.94 ((('#B') @ (breln1 @ '#sk43') @ (binunion @ '#sk44')))))))))), 72.29/9.94 inference('rw', [status(thm)], [zip_derived_cl3345, '4', '5'])). 72.29/9.94 thf(zip_derived_cl3364, plain, 72.29/9.94 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (breln1 @ '#sk43'))) @ 72.29/9.94 ((('#B') @ (breln1 @ '#sk43') @ (binunion @ '#sk44')))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3362])). 72.29/9.94 thf(zip_derived_cl3380, plain, 72.29/9.94 (~ (((breln1 @ '#sk43' @ '#sk45') => (breln1 @ '#sk43' @ 72.29/9.94 (binunion @ '#sk44' @ '#sk45'))))), 72.29/9.94 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3364])). 72.29/9.94 thf(zip_derived_cl3391, plain, 72.29/9.94 (~ (((subset @ '#sk45' @ (cartprod @ '#sk43' @ '#sk43')) => (subset @ 72.29/9.94 (binunion @ '#sk44' @ '#sk45') @ (cartprod @ '#sk43' @ '#sk43'))))), 72.29/9.94 inference('rw', [status(thm)], [zip_derived_cl3380, '4', '4', '5', '5'])). 72.29/9.94 thf(zip_derived_cl3392, plain, 72.29/9.94 ( (subset @ '#sk45' @ (cartprod @ '#sk43' @ '#sk43'))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3391])). 72.29/9.94 thf(zip_derived_cl3363, plain, 72.29/9.94 ( (subset @ '#sk44' @ (cartprod @ '#sk43' @ '#sk43'))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3362])). 72.29/9.94 thf(zip_derived_cl2471, plain, ( (binunionT_lem)), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2461])). 72.29/9.94 thf(binunionT_lem, axiom, (binunionT_lem) => 72.29/9.94 ((((!!) @ (^[Y0 : $i]: 72.29/9.94 (((!!) @ (^[Y1 : $i]: 72.29/9.94 (((in @ Y1 @ (powerset @ Y0)) => 72.29/9.94 (((!!) @ (^[Y2 : $i]: 72.29/9.94 (((in @ Y2 @ (powerset @ Y0)) => 72.29/9.94 (in @ (binunion @ Y1 @ Y2) @ 72.29/9.94 (powerset @ Y0))))))))))))))) 72.29/9.94 = ($true))). 72.29/9.94 thf('6', plain, 72.29/9.94 (( binunionT_lem ) <=> 72.29/9.94 ( ![X5:$i,X7:$i]: 72.29/9.94 ( ( in @ X7 @ ( powerset @ X5 ) ) => 72.29/9.94 ( ![X9:$i]: 72.29/9.94 ( ( in @ X9 @ ( powerset @ X5 ) ) => 72.29/9.94 ( in @ ( binunion @ X7 @ X9 ) @ ( powerset @ X5 ) ) ) ) ) )), 72.29/9.94 inference('rw.lit', [status(esa)], [binunionT_lem])). 72.29/9.94 thf(zip_derived_cl2481, plain, 72.29/9.94 ( (((!!) @ (^[Y0 : $i]: 72.29/9.94 (((!!) @ (^[Y1 : $i]: 72.29/9.94 (((in @ Y1 @ (powerset @ Y0)) => 72.29/9.94 (((!!) @ (^[Y2 : $i]: 72.29/9.94 (((in @ Y2 @ (powerset @ Y0)) => 72.29/9.94 (in @ (binunion @ Y1 @ Y2) @ 72.29/9.94 (powerset @ Y0)))))))))))))))), 72.29/9.94 inference('rw_clause', [status(thm)], [zip_derived_cl2471, '6'])). 72.29/9.94 thf(zip_derived_cl2488, plain, 72.29/9.94 ( (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 72.29/9.94 ((('#B') @ ((('#B') @ (!!))) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#B') @ 72.29/9.94 ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 ((('#B') @ ((('#C') @ in)) @ powerset)))))))) @ 72.29/9.94 ((('#B') @ ((('#C') @ ((('#B') @ ('#C') @ 72.29/9.94 ((('#B') @ ((('#B') @ in)) @ 72.29/9.94 binunion)))))) @ 72.29/9.94 powerset))))))))))))), 72.29/9.94 inference('comb-normalize', [status(thm)], [zip_derived_cl2481])). 72.29/9.94 thf(zip_derived_cl2489, plain, 72.29/9.94 (![X2 : $i]: 72.29/9.94 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 72.29/9.94 ((('#C') @ in @ (powerset @ X2))))) @ 72.29/9.94 ((('#B') @ (!!) @ 72.29/9.94 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 72.29/9.94 ((('#C') @ in @ (powerset @ X2))))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ('#C') @ 72.29/9.94 ((('#B') @ ((('#B') @ in)) @ binunion)))) @ 72.29/9.94 (powerset @ X2)))))))))))), 72.29/9.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2488])). 72.29/9.94 thf(zip_derived_cl2497, plain, 72.29/9.94 (![X2 : $i, X4 : $i]: 72.29/9.94 (((in @ X4 @ (powerset @ X2)) => 72.29/9.94 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 72.29/9.94 ((('#C') @ in @ (powerset @ X2))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ in @ (binunion @ X4))) @ 72.29/9.94 (powerset @ X2)))))))))), 72.29/9.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2489])). 72.29/9.94 thf(zip_derived_cl2507, plain, 72.29/9.94 (![X2 : $i, X4 : $i]: 72.29/9.94 (~ (in @ X4 @ (powerset @ X2)) 72.29/9.94 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 72.29/9.94 ((('#C') @ in @ (powerset @ X2))))) @ 72.29/9.94 ((('#C') @ ((('#B') @ in @ (binunion @ X4))) @ 72.29/9.94 (powerset @ X2))))))))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2497])). 72.29/9.94 thf(zip_derived_cl2518, plain, 72.29/9.94 (![X2 : $i, X4 : $i, X6 : $i]: 72.29/9.94 ( (((in @ X6 @ (powerset @ X2)) => (in @ (binunion @ X4 @ X6) @ 72.29/9.94 (powerset @ X2)))) 72.29/9.94 | ~ (in @ X4 @ (powerset @ X2)))), 72.29/9.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2507])). 72.29/9.94 thf(zip_derived_cl2527, plain, 72.29/9.94 (![X2 : $i, X4 : $i, X6 : $i]: 72.29/9.94 (~ (in @ X6 @ (powerset @ X2)) 72.29/9.94 | (in @ (binunion @ X4 @ X6) @ (powerset @ X2)) 72.29/9.94 | ~ (in @ X4 @ (powerset @ X2)))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2518])). 72.29/9.94 thf(zip_derived_cl3393, plain, 72.29/9.94 (~ (subset @ (binunion @ '#sk44' @ '#sk45') @ 72.29/9.94 (cartprod @ '#sk43' @ '#sk43'))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3391])). 72.29/9.94 thf(zip_derived_cl1014, plain, ( (subset2powerset)), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])). 72.29/9.94 thf(subset2powerset, axiom, (subset2powerset) => 72.29/9.94 ((((!!) @ (^[Y0 : $i]: 72.29/9.94 (((!!) @ (^[Y1 : $i]: 72.29/9.94 (((subset @ Y0 @ Y1) => (in @ Y0 @ 72.29/9.94 (powerset @ Y1)))))))))) 72.29/9.94 = ($true))). 72.29/9.94 thf('7', plain, 72.29/9.94 (( subset2powerset ) <=> 72.29/9.94 ( ![X5:$i,X7:$i]: 72.29/9.94 ( ( subset @ X5 @ X7 ) => ( in @ X5 @ ( powerset @ X7 ) ) ) )), 72.29/9.94 inference('rw.lit', [status(esa)], [subset2powerset])). 72.29/9.94 thf(zip_derived_cl1025, plain, 72.29/9.94 ( (((!!) @ (^[Y0 : $i]: 72.29/9.94 (((!!) @ (^[Y1 : $i]: 72.29/9.94 (((subset @ Y0 @ Y1) => (in @ Y0 @ 72.29/9.94 (powerset @ Y1))))))))))), 72.29/9.94 inference('rw_clause', [status(thm)], [zip_derived_cl1014, '7'])). 72.29/9.94 thf(zip_derived_cl1035, plain, 72.29/9.94 ( (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ subset)))) @ 72.29/9.94 ((('#C') @ ((('#B') @ ('#B') @ in)) @ powerset))))))))), 72.29/9.94 inference('comb-normalize', [status(thm)], [zip_derived_cl1025])). 72.29/9.94 thf(zip_derived_cl1036, plain, 72.29/9.94 (![X2 : $i]: 72.29/9.94 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (subset @ X2))) @ 72.29/9.94 ((('#B') @ (in @ X2) @ powerset))))))), 72.29/9.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1035])). 72.29/9.94 thf(zip_derived_cl1050, plain, 72.29/9.94 (![X2 : $i, X4 : $i]: 72.29/9.94 (((subset @ X2 @ X4) => (in @ X2 @ (powerset @ X4))))), 72.29/9.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1036])). 72.29/9.94 thf(zip_derived_cl1061, plain, 72.29/9.94 (![X2 : $i, X4 : $i]: 72.29/9.94 (~ (subset @ X2 @ X4) | (in @ X2 @ (powerset @ X4)))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1050])). 72.29/9.94 thf(zip_derived_cl1066, plain, ( (powersetE1)), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1055])). 72.29/9.94 thf(powersetE1, axiom, (powersetE1) => 72.29/9.94 ((((!!) @ (^[Y0 : $i]: 72.29/9.94 (((!!) @ (^[Y1 : $i]: 72.29/9.94 (((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ 72.29/9.94 Y0))))))))) 72.29/9.94 = ($true))). 72.29/9.94 thf('8', plain, 72.29/9.94 (( powersetE1 ) <=> 72.29/9.94 ( ![X5:$i,X7:$i]: 72.29/9.94 ( ( in @ X7 @ ( powerset @ X5 ) ) => ( subset @ X7 @ X5 ) ) )), 72.29/9.94 inference('rw.lit', [status(esa)], [powersetE1])). 72.29/9.94 thf(zip_derived_cl1072, plain, 72.29/9.94 ( (((!!) @ (^[Y0 : $i]: 72.29/9.94 (((!!) @ (^[Y1 : $i]: 72.29/9.94 (((in @ Y1 @ (powerset @ Y0)) => (subset @ 72.29/9.94 Y1 @ Y0)))))))))), 72.29/9.94 inference('rw_clause', [status(thm)], [zip_derived_cl1066, '8'])). 72.29/9.94 thf(zip_derived_cl1078, plain, 72.29/9.94 ( (((!!) @ ((('#B') @ (!!) @ 72.29/9.94 ((('#S') @ ((('#B') @ ('#S') @ 72.29/9.94 ((('#B') @ ((('#B') @ (=>))) @ 72.29/9.94 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @ 72.29/9.94 ((('#C') @ subset))))))))), 72.29/9.94 inference('comb-normalize', [status(thm)], [zip_derived_cl1072])). 72.29/9.94 thf(zip_derived_cl1079, plain, 72.29/9.94 (![X2 : $i]: 72.29/9.94 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 72.29/9.94 ((('#C') @ in @ (powerset @ X2))))) @ 72.29/9.94 ((('#C') @ subset @ X2))))))), 72.29/9.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1078])). 72.29/9.94 thf(zip_derived_cl1085, plain, 72.29/9.94 (![X2 : $i, X4 : $i]: 72.29/9.94 (((in @ X4 @ (powerset @ X2)) => (subset @ X4 @ X2)))), 72.29/9.94 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1079])). 72.29/9.94 thf(zip_derived_cl1091, plain, 72.29/9.94 (![X2 : $i, X4 : $i]: 72.29/9.94 (~ (in @ X4 @ (powerset @ X2)) | (subset @ X4 @ X2))), 72.29/9.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1085])). 72.29/9.94 thf(zip_derived_cl3526, plain, ($false), 72.29/9.94 inference('eprover', [status(thm)], 72.29/9.94 [zip_derived_cl3392, zip_derived_cl3363, zip_derived_cl2527, 72.29/9.94 zip_derived_cl3393, zip_derived_cl1061, zip_derived_cl1091])). 72.29/9.94 72.29/9.94 % SZS output end Refutation 72.29/9.94 72.29/9.94 72.29/9.94 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 53s 72.29/9.94 % Terminating... 73.04/10.07 % Runner terminated. 73.04/10.10 % Zipperpin 1.5 exiting 73.04/10.12 EOF