0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.MVqHeD4RUu true 0.14/0.34 % Computer : n007.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 960 0.14/0.34 % WCLimit : 120 0.14/0.34 % DateTime : Tue Aug 9 04:44:27 EDT 2022 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 960 s 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.35 % Python version: Python 3.6.8 0.14/0.35 % Running in HO mode 0.50/0.64 % Total configuration time : 828 0.50/0.64 % Estimated wc time : 1656 0.50/0.64 % Estimated cpu time (8 cpus) : 207.0 0.50/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.51/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.51/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.51/0.72 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.51/0.72 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.51/0.72 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.51/0.72 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.51/0.73 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.53/0.97 % Solved by lams/40_c_ic.sh. 0.53/0.97 % done 223 iterations in 0.188s 0.53/0.97 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 0.53/0.97 % SZS output start Refutation 0.53/0.97 thf(setadjoinAx_type, type, setadjoinAx: $o). 0.53/0.97 thf(notdexE_type, type, notdexE: $o). 0.53/0.97 thf(kfstpairEq_type, type, kfstpairEq: $o). 0.53/0.97 thf(setunionAx_type, type, setunionAx: $o). 0.53/0.97 thf(setminusELneg_type, type, setminusELneg: $o). 0.53/0.97 thf(sk__53_type, type, sk__53: $i). 0.53/0.97 thf(powersetE_type, type, powersetE: $o). 0.53/0.97 thf(omegaSAx_type, type, omegaSAx: $o). 0.53/0.97 thf(exuI1_type, type, exuI1: $o). 0.53/0.97 thf(exuI2_type, type, exuI2: $o). 0.53/0.97 thf(notequalI2_type, type, notequalI2: $o). 0.53/0.97 thf(setukpairIR_type, type, setukpairIR: $o). 0.53/0.97 thf(powerset__Cong_type, type, powerset__Cong: $o). 0.53/0.97 thf(setminusILneg_type, type, setminusILneg: $o). 0.53/0.97 thf(wellorderingAx_type, type, wellorderingAx: $o). 0.53/0.97 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 0.53/0.97 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 0.53/0.97 thf(upairsubunion_type, type, upairsubunion: $o). 0.53/0.97 thf(setoftrueEq_type, type, setoftrueEq: $o). 0.53/0.97 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 0.53/0.97 thf(sepInPowerset_type, type, sepInPowerset: $o). 0.53/0.97 thf(setukpairIL_type, type, setukpairIL: $o). 0.53/0.97 thf(kpairiskpair_type, type, kpairiskpair: $o). 0.53/0.97 thf(binunionE_type, type, binunionE: $o). 0.53/0.97 thf(setext_type, type, setext: $o). 0.53/0.97 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 0.53/0.97 thf(upairinpowunion_type, type, upairinpowunion: $o). 0.53/0.97 thf(descr__Cong_type, type, descr__Cong: $o). 0.53/0.97 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 0.53/0.97 thf(in_type, type, in: $i > $i > $o). 0.53/0.97 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 0.53/0.97 thf(theprop_type, type, theprop: $o). 0.53/0.97 thf(upairset2E_type, type, upairset2E: $o). 0.53/0.97 thf(setadjoinIR_type, type, setadjoinIR: $o). 0.53/0.97 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 0.53/0.97 thf(symdiffI2_type, type, symdiffI2: $o). 0.53/0.97 thf(upairset2IR_type, type, upairset2IR: $o). 0.53/0.97 thf(subsetE_type, type, subsetE: $o). 0.53/0.97 thf(prop2set2propI_type, type, prop2set2propI: $o). 0.53/0.97 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 0.53/0.97 thf(setbeta_type, type, setbeta: $o). 0.53/0.97 thf(eqinunit_type, type, eqinunit: $o). 0.53/0.97 thf(upairsetIL_type, type, upairsetIL: $o). 0.53/0.97 thf(powersetI1_type, type, powersetI1: $o). 0.53/0.97 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 0.53/0.97 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 0.53/0.97 thf(setminusIRneg_type, type, setminusIRneg: $o). 0.53/0.97 thf(kfstsingleton_type, type, kfstsingleton: $o). 0.53/0.97 thf(powersetAx_type, type, powersetAx: $o). 0.53/0.97 thf(setunionsingleton_type, type, setunionsingleton: $o). 0.53/0.97 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 0.53/0.97 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 0.53/0.97 thf(powersetI_type, type, powersetI: $o). 0.53/0.97 thf(upairsetIR_type, type, upairsetIR: $o). 0.53/0.97 thf(inCongP_type, type, inCongP: $o). 0.53/0.97 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 0.53/0.97 thf(setadjoinSub_type, type, setadjoinSub: $o). 0.53/0.97 thf(exuE3e_type, type, exuE3e: $o). 0.53/0.97 thf(emptysetE_type, type, emptysetE: $o). 0.53/0.97 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 0.53/0.97 thf(setunionI_type, type, setunionI: $o). 0.53/0.97 thf(setunion__Cong_type, type, setunion__Cong: $o). 0.53/0.97 thf(prop2setI_type, type, prop2setI: $o). 0.53/0.97 thf(ex1I2_type, type, ex1I2: $o). 0.53/0.97 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 0.53/0.97 thf(setminusER_type, type, setminusER: $o). 0.53/0.97 thf(exuE2_type, type, exuE2: $o). 0.53/0.97 thf(emptyset_type, type, emptyset: $i). 0.53/0.97 thf(singletonsuniq_type, type, singletonsuniq: $o). 0.53/0.97 thf(powersetsubset_type, type, powersetsubset: $o). 0.53/0.97 thf(subPowSU_type, type, subPowSU: $o). 0.53/0.97 thf(notequalI1_type, type, notequalI1: $o). 0.53/0.97 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 0.53/0.97 thf(notinemptyset_type, type, notinemptyset: $o). 0.53/0.97 thf(nonemptyI1_type, type, nonemptyI1: $o). 0.53/0.97 thf(subsetTrans_type, type, subsetTrans: $o). 0.53/0.97 thf(setminusI_type, type, setminusI: $o). 0.53/0.97 thf(binunionIL_type, type, binunionIL: $o). 0.53/0.97 thf(subsetE2_type, type, subsetE2: $o). 0.53/0.97 thf(singletonsswitch_type, type, singletonsswitch: $o). 0.53/0.97 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 0.53/0.97 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 0.53/0.97 thf(setextsub_type, type, setextsub: $o). 0.53/0.97 thf(binunionLsub_type, type, binunionLsub: $o). 0.53/0.97 thf(emptysetsubset_type, type, emptysetsubset: $o). 0.53/0.97 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 0.53/0.97 thf(setunionE_type, type, setunionE: $o). 0.53/0.97 thf(setminusSubset1_type, type, setminusSubset1: $o). 0.53/0.97 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 0.53/0.97 thf(binunionIR_type, type, binunionIR: $o). 0.53/0.97 thf(setadjoinE_type, type, setadjoinE: $o). 0.53/0.97 thf(singletonprop_type, type, singletonprop: $o). 0.53/0.97 thf(setadjoinIL_type, type, setadjoinIL: $o). 0.53/0.97 thf(exuE1_type, type, exuE1: $o). 0.53/0.97 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 0.53/0.97 thf(binintersectRsub_type, type, binintersectRsub: $o). 0.53/0.97 thf(setminusLsub_type, type, setminusLsub: $o). 0.53/0.97 thf(notinsingleton_type, type, notinsingleton: $o). 0.53/0.97 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 0.53/0.97 thf(exuEu_type, type, exuEu: $o). 0.53/0.97 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 0.53/0.97 thf(upairsetE_type, type, upairsetE: $o). 0.53/0.97 thf(omega0Ax_type, type, omega0Ax: $o). 0.53/0.97 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o). 0.53/0.97 thf(notsubsetI_type, type, notsubsetI: $o). 0.53/0.97 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 0.53/0.97 thf(setextAx_type, type, setextAx: $o). 0.53/0.97 thf(powersetE1_type, type, powersetE1: $o). 0.53/0.97 thf(bs114d_type, type, bs114d: $o). 0.53/0.97 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 0.53/0.97 thf(binintersectLsub_type, type, binintersectLsub: $o). 0.53/0.97 thf(subsetI1_type, type, subsetI1: $o). 0.53/0.97 thf(symdiffE_type, type, symdiffE: $o). 0.53/0.97 thf(descrp_type, type, descrp: $o). 0.53/0.97 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 0.53/0.97 thf(foundationAx_type, type, foundationAx: $o). 0.53/0.97 thf(emptysetAx_type, type, emptysetAx: $o). 0.53/0.97 thf(emptyI_type, type, emptyI: $o). 0.53/0.97 thf(setadjoinOr_type, type, setadjoinOr: $o). 0.53/0.97 thf(binintersectEL_type, type, binintersectEL: $o). 0.53/0.97 thf(emptyE1_type, type, emptyE1: $o). 0.53/0.97 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 0.53/0.97 thf(vacuousDall_type, type, vacuousDall: $o). 0.53/0.97 thf(dsetconstrER_type, type, dsetconstrER: $o). 0.53/0.97 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 0.53/0.97 thf(binintersectI_type, type, binintersectI: $o). 0.53/0.97 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 0.53/0.97 thf(ex1E1_type, type, ex1E1: $o). 0.53/0.97 thf(cartprodpairin_type, type, cartprodpairin: $o). 0.53/0.97 thf(setukpairinjL_type, type, setukpairinjL: $o). 0.53/0.97 thf(symdiffI1_type, type, symdiffI1: $o). 0.53/0.97 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 0.53/0.97 thf(subsetI2_type, type, subsetI2: $o). 0.53/0.97 thf(cartprodfstin_type, type, cartprodfstin: $o). 0.53/0.97 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 0.53/0.97 thf(setminusERneg_type, type, setminusERneg: $o). 0.53/0.97 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 0.53/0.97 thf(omega__Cong_type, type, omega__Cong: $o). 0.53/0.97 thf(subsetRefl_type, type, subsetRefl: $o). 0.53/0.97 thf(uniqinunit_type, type, uniqinunit: $o). 0.53/0.97 thf(setminusSubset2_type, type, setminusSubset2: $o). 0.53/0.97 thf(prop2setE_type, type, prop2setE: $o). 0.53/0.97 thf(binunionEcases_type, type, binunionEcases: $o). 0.53/0.97 thf(nonemptyI_type, type, nonemptyI: $o). 0.53/0.97 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 0.53/0.97 thf(exuE3u_type, type, exuE3u: $o). 0.53/0.97 thf(setminusEL_type, type, setminusEL: $o). 0.53/0.97 thf(singletonsubset_type, type, singletonsubset: $o). 0.53/0.97 thf(sepSubset_type, type, sepSubset: $o). 0.53/0.97 thf(setunionE2_type, type, setunionE2: $o). 0.53/0.97 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 0.53/0.97 thf(ex1I_type, type, ex1I: $o). 0.53/0.97 thf(exuI3_type, type, exuI3: $o). 0.53/0.97 thf(notdallE_type, type, notdallE: $o). 0.53/0.97 thf(binintersectER_type, type, binintersectER: $o). 0.53/0.97 thf(kpairp_type, type, kpairp: $o). 0.53/0.97 thf(dsetconstrI_type, type, dsetconstrI: $o). 0.53/0.97 thf(sk__52_type, type, sk__52: $i). 0.53/0.97 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 0.53/0.97 thf(exu__Cong_type, type, exu__Cong: $o). 0.53/0.97 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 0.53/0.97 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 0.53/0.97 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 0.53/0.97 thf(replAx_type, type, replAx: $o). 0.53/0.97 thf(nonemptyE1_type, type, nonemptyE1: $o). 0.53/0.97 thf(omegaIndAx_type, type, omegaIndAx: $o). 0.53/0.97 thf(secondinupair_type, type, secondinupair: $o). 0.53/0.97 thf(inPowerset_type, type, inPowerset: $o). 0.53/0.97 thf(cartprodmempair_type, type, cartprodmempair: $o). 0.53/0.97 thf(in__Cong_type, type, in__Cong: $o). 0.53/0.97 thf(binunionRsub_type, type, binunionRsub: $o). 0.53/0.97 thf(subset2powerset_type, type, subset2powerset: $o). 0.53/0.97 thf(setukpairinjR11, axiom, setukpairinjR11 = 0.53/0.97 (![Xx:$i,Xy:$i]: 0.53/0.97 ( ( ( Xx ) = ( Xy ) ) => 0.53/0.97 ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) = 0.53/0.97 ( setadjoin @ Xx @ emptyset ) ) ))). 0.53/0.97 thf('0', plain, 0.53/0.97 (( setukpairinjR11 ) = 0.53/0.97 ( ![X4:$i,X6:$i]: 0.53/0.97 ( ( ( X4 ) = ( X6 ) ) => 0.53/0.97 ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) = 0.53/0.97 ( setadjoin @ X4 @ emptyset ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(setukpairinjL2, axiom, setukpairinjL2 = 0.53/0.97 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]: 0.53/0.97 ( ( ( setadjoin @ 0.53/0.97 ( setadjoin @ Xx @ emptyset ) @ 0.53/0.97 ( setadjoin @ 0.53/0.97 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) = 0.53/0.97 ( setadjoin @ 0.53/0.97 ( setadjoin @ Xz @ emptyset ) @ 0.53/0.97 ( setadjoin @ 0.53/0.97 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) => 0.53/0.97 ( ( Xx ) = ( Xz ) ) ))). 0.53/0.97 thf('1', plain, 0.53/0.97 (( setukpairinjL2 ) = 0.53/0.97 ( ![X4:$i,X6:$i,X8:$i,X10:$i]: 0.53/0.97 ( ( ( setadjoin @ 0.53/0.97 ( setadjoin @ X4 @ emptyset ) @ 0.53/0.97 ( setadjoin @ 0.53/0.97 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) = 0.53/0.97 ( setadjoin @ 0.53/0.97 ( setadjoin @ X8 @ emptyset ) @ 0.53/0.97 ( setadjoin @ 0.53/0.97 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) => 0.53/0.97 ( ( X4 ) = ( X8 ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(setukpairinjL1, axiom, setukpairinjL1 = 0.53/0.97 (![Xx:$i,Xy:$i,Xz:$i]: 0.53/0.97 ( ( in @ 0.53/0.97 ( setadjoin @ Xz @ emptyset ) @ 0.53/0.97 ( setadjoin @ 0.53/0.97 ( setadjoin @ Xx @ emptyset ) @ 0.53/0.97 ( setadjoin @ 0.53/0.97 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) => 0.53/0.97 ( ( Xx ) = ( Xz ) ) ))). 0.53/0.97 thf('2', plain, 0.53/0.97 (( setukpairinjL1 ) = 0.53/0.97 ( ![X4:$i,X6:$i,X8:$i]: 0.53/0.97 ( ( in @ 0.53/0.97 ( setadjoin @ X8 @ emptyset ) @ 0.53/0.97 ( setadjoin @ 0.53/0.97 ( setadjoin @ X4 @ emptyset ) @ 0.53/0.97 ( setadjoin @ 0.53/0.97 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) => 0.53/0.97 ( ( X4 ) = ( X8 ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(singletonsuniq, axiom, singletonsuniq = 0.53/0.97 (![Xx:$i,Xy:$i]: 0.53/0.97 ( ( ( setadjoin @ Xx @ emptyset ) = ( setadjoin @ Xy @ emptyset ) ) => 0.53/0.97 ( ( Xx ) = ( Xy ) ) ))). 0.53/0.97 thf('3', plain, 0.53/0.97 (( singletonsuniq ) = 0.53/0.97 ( ![X4:$i,X6:$i]: 0.53/0.97 ( ( ( setadjoin @ X4 @ emptyset ) = ( setadjoin @ X6 @ emptyset ) ) => 0.53/0.97 ( ( X4 ) = ( X6 ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(upairset2E, axiom, upairset2E = 0.53/0.97 (![Xx:$i,Xy:$i,Xz:$i]: 0.53/0.97 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) => 0.53/0.97 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))). 0.53/0.97 thf('4', plain, 0.53/0.97 (( upairset2E ) = 0.53/0.97 ( ![X4:$i,X6:$i,X8:$i]: 0.53/0.97 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) => 0.53/0.97 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(secondinupair, axiom, secondinupair = 0.53/0.97 (![Xx:$i,Xy:$i]: 0.53/0.97 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 0.53/0.97 thf('5', plain, 0.53/0.97 (( secondinupair ) = 0.53/0.97 ( ![X4:$i,X6:$i]: 0.53/0.97 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(upairset2IR, axiom, upairset2IR = 0.53/0.97 (![Xx:$i,Xy:$i]: 0.53/0.97 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 0.53/0.97 thf('6', plain, 0.53/0.97 (( upairset2IR ) = 0.53/0.97 ( ![X4:$i,X6:$i]: 0.53/0.97 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(setadjoin__Cong, axiom, setadjoin__Cong = 0.53/0.97 (![Xx:$i,Xy:$i]: 0.53/0.97 ( ( ( Xx ) = ( Xy ) ) => 0.53/0.97 ( ![Xz:$i,Xu:$i]: 0.53/0.97 ( ( ( Xz ) = ( Xu ) ) => 0.53/0.97 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))). 0.53/0.97 thf('7', plain, 0.53/0.97 (( setadjoin__Cong ) = 0.53/0.97 ( ![X4:$i,X6:$i]: 0.53/0.97 ( ( ( X4 ) = ( X6 ) ) => 0.53/0.97 ( ![X8:$i,X10:$i]: 0.53/0.97 ( ( ( X8 ) = ( X10 ) ) => 0.53/0.97 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(upairsetIR, axiom, upairsetIR = 0.53/0.97 (![Xx:$i,Xy:$i]: 0.53/0.97 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 0.53/0.97 thf('8', plain, 0.53/0.97 (( upairsetIR ) = 0.53/0.97 ( ![X4:$i,X6:$i]: 0.53/0.97 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(upairsetIL, axiom, upairsetIL = 0.53/0.97 (![Xx:$i,Xy:$i]: 0.53/0.97 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 0.53/0.97 thf('9', plain, 0.53/0.97 (( upairsetIL ) = 0.53/0.97 ( ![X4:$i,X6:$i]: 0.53/0.97 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(upairsetE, axiom, upairsetE = 0.53/0.97 (![Xx:$i,Xy:$i,Xz:$i]: 0.53/0.97 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) => 0.53/0.97 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))). 0.53/0.97 thf('10', plain, 0.53/0.97 (( upairsetE ) = 0.53/0.97 ( ![X4:$i,X6:$i,X8:$i]: 0.53/0.97 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) => 0.53/0.97 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(singletonsswitch, axiom, singletonsswitch = 0.53/0.97 (![Xx:$i,Xy:$i]: 0.53/0.97 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => 0.53/0.97 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))). 0.53/0.97 thf('11', plain, 0.53/0.97 (( singletonsswitch ) = 0.53/0.97 ( ![X4:$i,X6:$i]: 0.53/0.97 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => 0.53/0.97 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(eqinunit, axiom, eqinunit = 0.53/0.97 (![Xx:$i,Xy:$i]: 0.53/0.97 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 0.53/0.97 thf('12', plain, 0.53/0.97 (( eqinunit ) = 0.53/0.97 ( ![X4:$i,X6:$i]: 0.53/0.97 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(notinsingleton, axiom, notinsingleton = 0.53/0.97 (![Xx:$i,Xy:$i]: 0.53/0.97 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))). 0.53/0.97 thf('13', plain, 0.53/0.97 (( notinsingleton ) = 0.53/0.97 ( ![X4:$i,X6:$i]: 0.53/0.97 ( ( ( X4 ) != ( X6 ) ) => 0.53/0.97 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(uniqinunit, axiom, uniqinunit = 0.53/0.97 (![Xx:$i,Xy:$i]: 0.53/0.97 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))). 0.53/0.97 thf('14', plain, 0.53/0.97 (( uniqinunit ) = 0.53/0.97 ( ![X4:$i,X6:$i]: 0.53/0.97 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(setadjoinOr, axiom, setadjoinOr = 0.53/0.97 (![Xx:$i,A:$i,Xy:$i]: 0.53/0.97 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) => 0.53/0.97 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))). 0.53/0.97 thf('15', plain, 0.53/0.97 (( setadjoinOr ) = 0.53/0.97 ( ![X4:$i,X6:$i,X8:$i]: 0.53/0.97 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) => 0.53/0.97 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(setadjoinE, axiom, setadjoinE = 0.53/0.97 (![Xx:$i,A:$i,Xy:$i]: 0.53/0.97 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) => 0.53/0.97 ( ![Xphi:$o]: 0.53/0.97 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) => 0.53/0.97 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))). 0.53/0.97 thf('16', plain, 0.53/0.97 (( setadjoinE ) = 0.53/0.97 ( ![X4:$i,X6:$i,X8:$i]: 0.53/0.97 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) => 0.53/0.97 ( ![X10:$o]: 0.53/0.97 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) => 0.53/0.97 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(setadjoinIR, axiom, setadjoinIR = 0.53/0.97 (![Xx:$i,A:$i,Xy:$i]: 0.53/0.97 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))). 0.53/0.97 thf('17', plain, 0.53/0.97 (( setadjoinIR ) = 0.53/0.97 ( ![X4:$i,X6:$i,X8:$i]: 0.53/0.97 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(emptyinunitempty, axiom,(( emptyinunitempty ) = 0.53/0.97 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))). 0.53/0.97 thf('18', plain, 0.53/0.97 (( emptyinunitempty ) = 0.53/0.97 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )), 0.53/0.97 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])). 0.53/0.97 thf('19', plain, 0.53/0.97 (( emptyinunitempty ) = 0.53/0.97 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(setadjoinIL, axiom, setadjoinIL = 0.53/0.97 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))). 0.53/0.97 thf('20', plain, 0.53/0.97 (( setadjoinIL ) = 0.53/0.97 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(setadjoinAx, axiom, setadjoinAx = 0.53/0.97 (![Xx:$i,A:$i,Xy:$i]: 0.53/0.97 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=> 0.53/0.97 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))). 0.53/0.97 thf('21', plain, 0.53/0.97 (( setadjoinAx ) = 0.53/0.97 ( ![X4:$i,X6:$i,X8:$i]: 0.53/0.97 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 0.53/0.97 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )), 0.53/0.97 define([status(thm)])). 0.53/0.97 thf(setukpairinjR12, conjecture, 0.53/0.97 (( setextAx ) => 0.53/0.97 ( ( emptysetAx ) => 0.53/0.97 ( ( setadjoinAx ) => 0.53/0.97 ( ( powersetAx ) => 0.53/0.97 ( ( setunionAx ) => 0.53/0.97 ( ( omega0Ax ) => 0.53/0.97 ( ( omegaSAx ) => 0.53/0.97 ( ( omegaIndAx ) => 0.53/0.97 ( ( replAx ) => 0.53/0.97 ( ( foundationAx ) => 0.53/0.97 ( ( wellorderingAx ) => 0.53/0.97 ( ( descrp ) => 0.53/0.97 ( ( dsetconstrI ) => 0.53/0.97 ( ( dsetconstrEL ) => 0.53/0.97 ( ( dsetconstrER ) => 0.53/0.97 ( ( exuE1 ) => 0.53/0.97 ( ( prop2setE ) => 0.53/0.97 ( ( emptysetE ) => 0.53/0.97 ( ( emptysetimpfalse ) => 0.53/0.97 ( ( notinemptyset ) => 0.53/0.97 ( ( exuE3e ) => 0.53/0.97 ( ( setext ) => 0.53/0.97 ( ( emptyI ) => 0.53/0.97 ( ( noeltsimpempty ) => 0.53/0.97 ( ( setbeta ) => 0.53/0.97 ( ( nonemptyE1 ) => 0.53/0.97 ( ( nonemptyI ) => 0.53/0.97 ( ( nonemptyI1 ) => 0.53/0.97 ( ( setadjoinIL ) => 0.53/0.97 ( ( emptyinunitempty ) => 0.53/0.97 ( ( setadjoinIR ) => 0.53/0.97 ( ( setadjoinE ) => 0.53/0.97 ( ( 0.53/0.97 setadjoinOr ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setoftrueEq ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 powersetI ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 emptyinPowerset ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 emptyInPowerset ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 powersetE ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setunionI ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setunionE ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 subPowSU ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 exuE2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 nonemptyImpWitness ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 uniqinunit ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 notinsingleton ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 eqinunit ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 singletonsswitch ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 upairsetE ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 upairsetIL ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 upairsetIR ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 emptyE1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 vacuousDall ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 quantDeMorgan1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 quantDeMorgan2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 quantDeMorgan3 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 quantDeMorgan4 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 prop2setI ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 prop2set2propI ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 notdexE ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 notdallE ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 exuI1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 exuI3 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 exuI2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 inCongP ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 in__Cong ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 exuE3u ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 exu__Cong ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 emptyset__Cong ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setadjoin__Cong ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 powerset__Cong ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setunion__Cong ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 omega__Cong ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 exuEu ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 descr__Cong ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 dsetconstr__Cong ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 subsetI1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 eqimpsubset2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 eqimpsubset1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 subsetI2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 emptysetsubset ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 subsetE ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 subsetE2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 notsubsetI ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 notequalI1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 notequalI2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 subsetRefl ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 subsetTrans ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setadjoinSub ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setadjoinSub2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 subset2powerset ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setextsub ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 subsetemptysetimpeq ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 powersetI1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 powersetE1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 inPowerset ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 powersetsubset ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 sepInPowerset ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 sepSubset ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binunionIL ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 upairset2IR ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binunionIR ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binunionEcases ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binunionE ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binunionLsub ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binunionRsub ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binintersectI ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binintersectSubset5 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binintersectEL ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binintersectLsub ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binintersectSubset2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binintersectSubset3 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binintersectER ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 disjointsetsI1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binintersectRsub ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binintersectSubset4 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 binintersectSubset1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 bs114d ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setminusI ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setminusEL ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setminusER ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setminusSubset2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setminusERneg ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setminusELneg ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setminusILneg ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setminusIRneg ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setminusLsub ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setminusSubset1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 symdiffE ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 symdiffI1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 symdiffI2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 symdiffIneg1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 symdiffIneg2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 secondinupair ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setukpairIL ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setukpairIR ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 kpairiskpair ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 kpairp ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 singletonsubset ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 singletoninpowerset ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 singletoninpowunion ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 upairset2E ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 upairsubunion ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 upairinpowunion ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 ubforcartprodlem1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 ubforcartprodlem2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 ubforcartprodlem3 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 cartprodpairin ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 cartprodmempair1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 cartprodmempair ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setunionE2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setunionsingleton1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setunionsingleton2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setunionsingleton ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 singletonprop ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 ex1E1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 ex1I ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 ex1I2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 singletonsuniq ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setukpairinjL1 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 kfstsingleton ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 theprop ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 kfstpairEq ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 cartprodfstin ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setukpairinjL2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setukpairinjL ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setukpairinjR11 ) => 0.53/0.97 ( 0.53/0.97 ![ 0.53/0.97 Xx:$i, 0.53/0.97 Xy:$i]: 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 Xx ) = 0.53/0.97 ( 0.53/0.97 Xy ) ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setadjoin 0.53/0.97 @ 0.53/0.97 ( 0.53/0.97 setadjoin 0.53/0.97 @ 0.53/0.97 Xx @ 0.53/0.97 emptyset ) @ 0.53/0.97 ( 0.53/0.97 setadjoin 0.53/0.97 @ 0.53/0.97 ( 0.53/0.97 setadjoin 0.53/0.97 @ 0.53/0.97 Xx @ 0.53/0.97 ( 0.53/0.97 setadjoin 0.53/0.97 @ 0.53/0.97 Xy @ 0.53/0.97 emptyset ) ) @ 0.53/0.97 emptyset ) ) = 0.53/0.97 ( 0.53/0.97 setadjoin 0.53/0.97 @ 0.53/0.97 ( 0.53/0.97 setadjoin 0.53/0.97 @ 0.53/0.97 Xx @ 0.53/0.97 emptyset ) @ 0.53/0.97 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 0.53/0.97 thf(zf_stmt_0, conjecture, 0.53/0.97 (( setextAx ) => 0.53/0.97 ( ( emptysetAx ) => 0.53/0.97 ( ( ![X4:$i,X6:$i,X8:$i]: 0.53/0.97 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 0.53/0.97 ( ( in @ X8 @ X6 ) | ( ( X8 ) = ( X4 ) ) ) ) ) => 0.53/0.97 ( ( powersetAx ) => 0.53/0.97 ( ( setunionAx ) => 0.53/0.97 ( ( omega0Ax ) => 0.53/0.97 ( ( omegaSAx ) => 0.53/0.97 ( ( omegaIndAx ) => 0.53/0.97 ( ( replAx ) => 0.53/0.97 ( ( foundationAx ) => 0.53/0.97 ( ( wellorderingAx ) => 0.53/0.97 ( ( descrp ) => 0.53/0.97 ( ( dsetconstrI ) => 0.53/0.97 ( ( dsetconstrEL ) => 0.53/0.97 ( ( dsetconstrER ) => 0.53/0.97 ( ( exuE1 ) => 0.53/0.97 ( ( prop2setE ) => 0.53/0.97 ( ( emptysetE ) => 0.53/0.97 ( ( emptysetimpfalse ) => 0.53/0.97 ( ( notinemptyset ) => 0.53/0.97 ( ( exuE3e ) => 0.53/0.97 ( ( setext ) => 0.53/0.97 ( ( emptyI ) => 0.53/0.97 ( ( noeltsimpempty ) => 0.53/0.97 ( ( setbeta ) => 0.53/0.97 ( ( nonemptyE1 ) => 0.53/0.97 ( ( nonemptyI ) => 0.53/0.97 ( ( nonemptyI1 ) => 0.53/0.97 ( ( ![X10:$i,X12:$i]: 0.53/0.97 ( in @ 0.53/0.97 X10 @ 0.53/0.97 ( setadjoin @ 0.53/0.97 X10 @ X12 ) ) ) => 0.53/0.97 ( ( in @ 0.53/0.97 emptyset @ 0.53/0.97 ( setadjoin @ 0.53/0.97 emptyset @ 0.53/0.97 emptyset ) ) => 0.53/0.97 ( ( ![X14:$i, 0.53/0.97 X16:$i, 0.53/0.97 X18:$i]: 0.53/0.97 ( ( 0.53/0.97 in @ 0.53/0.97 X18 @ X16 ) => 0.53/0.97 ( 0.53/0.97 in @ 0.53/0.97 X18 @ 0.53/0.97 ( 0.53/0.97 setadjoin 0.53/0.97 @ 0.53/0.97 X14 @ X16 ) ) ) ) => 0.53/0.97 ( ( ![ 0.53/0.97 X20:$i, 0.53/0.97 X22:$i, 0.53/0.97 X24:$i]: 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 in @ 0.53/0.97 X24 @ 0.53/0.97 ( 0.53/0.97 setadjoin 0.53/0.97 @ 0.53/0.97 X20 @ X22 ) ) => 0.53/0.97 ( 0.53/0.97 ![ 0.53/0.97 X26:$o]: 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 X24 ) = 0.53/0.97 ( 0.53/0.97 X20 ) ) => 0.53/0.97 ( 0.53/0.97 X26 ) ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 in @ 0.53/0.97 X24 @ X22 ) => 0.53/0.97 ( 0.53/0.97 X26 ) ) => 0.53/0.97 ( 0.53/0.97 X26 ) ) ) ) ) ) => 0.53/0.97 ( ( 0.53/0.97 ![ 0.53/0.97 X28:$i, 0.53/0.97 X30:$i, 0.53/0.97 X32:$i]: 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 in @ 0.53/0.97 X32 @ 0.53/0.97 ( 0.53/0.97 setadjoin 0.53/0.97 @ 0.53/0.97 X28 @ X30 ) ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 in @ 0.53/0.97 X32 @ X30 ) | 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 X32 ) = 0.53/0.97 ( 0.53/0.97 X28 ) ) ) ) ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setoftrueEq ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 powersetI ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 emptyinPowerset ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 emptyInPowerset ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 powersetE ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setunionI ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 setunionE ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 subPowSU ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 exuE2 ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 nonemptyImpWitness ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 ![ 0.53/0.97 X34:$i, 0.53/0.97 X36:$i]: 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 in @ 0.53/0.97 X34 @ 0.53/0.97 ( 0.53/0.97 setadjoin 0.53/0.97 @ 0.53/0.97 X36 @ 0.53/0.97 emptyset ) ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 X34 ) = 0.53/0.97 ( 0.53/0.97 X36 ) ) ) ) => 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 ![ 0.53/0.97 X38:$i, 0.53/0.97 X40:$i]: 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 ( 0.53/0.97 X38 ) != 0.53/0.97 ( 0.53/0.97 X40 ) ) => 0.53/0.97 ( 0.53/0.98 ~( 0.53/0.98 in @ 0.53/0.98 X40 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X38 @ 0.53/0.98 emptyset ) ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X42:$i, 0.53/0.98 X44:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X42 ) = 0.53/0.98 ( 0.53/0.98 X44 ) ) => 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X42 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X44 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X46:$i, 0.53/0.98 X48:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X46 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X48 @ 0.53/0.98 emptyset ) ) => 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X48 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X46 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X50:$i, 0.53/0.98 X52:$i, 0.53/0.98 X54:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X54 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X50 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X52 @ 0.53/0.98 emptyset ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X54 ) = 0.53/0.98 ( 0.53/0.98 X52 ) ) | 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X54 ) = 0.53/0.98 ( 0.53/0.98 X50 ) ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X56:$i, 0.53/0.98 X58:$i]: 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X56 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X56 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X58 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X60:$i, 0.53/0.98 X62:$i]: 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X62 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X60 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X62 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 emptyE1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 vacuousDall ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 quantDeMorgan1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 quantDeMorgan2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 quantDeMorgan3 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 quantDeMorgan4 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 prop2setI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 prop2set2propI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notdexE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notdallE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuI3 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuI2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 inCongP ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuE3u ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exu__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 emptyset__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X64:$i, 0.53/0.98 X66:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X64 ) = 0.53/0.98 ( 0.53/0.98 X66 ) ) => 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X68:$i, 0.53/0.98 X70:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X68 ) = 0.53/0.98 ( 0.53/0.98 X70 ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X64 @ X68 ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X66 @ X70 ) ) ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powerset__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunion__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 omega__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuEu ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 descr__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 dsetconstr__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 eqimpsubset2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 eqimpsubset1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetI2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 emptysetsubset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetE2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notsubsetI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notequalI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notequalI2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetRefl ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetTrans ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoinSub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoinSub2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subset2powerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setextsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetemptysetimpeq ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powersetI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powersetE1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 inPowerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powersetsubset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 sepInPowerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 sepSubset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionIL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X72:$i, 0.53/0.98 X74:$i]: 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X74 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X72 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X74 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionIR ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionEcases ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionLsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionRsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset5 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectEL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectLsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset3 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectER ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 disjointsetsI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectRsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset4 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 bs114d ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusEL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusER ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusSubset2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusERneg ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusELneg ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusILneg ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusIRneg ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusLsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusSubset1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffI2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffIneg1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffIneg2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X76:$i, 0.53/0.98 X78:$i]: 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X78 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X76 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X78 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setukpairIL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setukpairIR ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 kpairiskpair ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 kpairp ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 singletonsubset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 singletoninpowerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 singletoninpowunion ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X80:$i, 0.53/0.98 X82:$i, 0.53/0.98 X84:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X84 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X80 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X82 @ 0.53/0.98 emptyset ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X84 ) = 0.53/0.98 ( 0.53/0.98 X82 ) ) | 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X84 ) = 0.53/0.98 ( 0.53/0.98 X80 ) ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 upairsubunion ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 upairinpowunion ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ubforcartprodlem1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ubforcartprodlem2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ubforcartprodlem3 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 cartprodpairin ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 cartprodmempair1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 cartprodmempair ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionE2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionsingleton1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionsingleton2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionsingleton ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 singletonprop ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ex1E1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ex1I ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ex1I2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X86:$i, 0.53/0.98 X88:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X86 @ 0.53/0.98 emptyset ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X88 @ 0.53/0.98 emptyset ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X86 ) = 0.53/0.98 ( 0.53/0.98 X88 ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X90:$i, 0.53/0.98 X92:$i, 0.53/0.98 X94:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X94 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X90 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X90 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X92 @ 0.53/0.98 emptyset ) ) @ 0.53/0.98 emptyset ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X90 ) = 0.53/0.98 ( 0.53/0.98 X94 ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 kfstsingleton ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 theprop ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 kfstpairEq ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 cartprodfstin ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X96:$i, 0.53/0.98 X98:$i, 0.53/0.98 X100:$i, 0.53/0.98 X102:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X96 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X96 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X98 @ 0.53/0.98 emptyset ) ) @ 0.53/0.98 emptyset ) ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X100 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X100 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X102 @ 0.53/0.98 emptyset ) ) @ 0.53/0.98 emptyset ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X96 ) = 0.53/0.98 ( 0.53/0.98 X100 ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setukpairinjL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X104:$i, 0.53/0.98 X106:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X104 ) = 0.53/0.98 ( 0.53/0.98 X106 ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X104 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X106 @ 0.53/0.98 emptyset ) ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X104 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X108:$i, 0.53/0.98 X110:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X108 ) = 0.53/0.98 ( 0.53/0.98 X110 ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X108 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X108 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X110 @ 0.53/0.98 emptyset ) ) @ 0.53/0.98 emptyset ) ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X108 @ 0.53/0.98 emptyset ) @ 0.53/0.98 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 0.53/0.98 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o). 0.53/0.98 thf(zf_stmt_2, axiom, 0.53/0.98 (![X8:$i,X6:$i,X4:$i]: 0.53/0.98 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=> 0.53/0.98 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ))). 0.53/0.98 thf(zf_stmt_3, conjecture, 0.53/0.98 (( setextAx ) => 0.53/0.98 ( ( emptysetAx ) => 0.53/0.98 ( ( ![X4:$i,X6:$i,X8:$i]: 0.53/0.98 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 0.53/0.98 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) => 0.53/0.98 ( ( powersetAx ) => 0.53/0.98 ( ( setunionAx ) => 0.53/0.98 ( ( omega0Ax ) => 0.53/0.98 ( ( omegaSAx ) => 0.53/0.98 ( ( omegaIndAx ) => 0.53/0.98 ( ( replAx ) => 0.53/0.98 ( ( foundationAx ) => 0.53/0.98 ( ( wellorderingAx ) => 0.53/0.98 ( ( descrp ) => 0.53/0.98 ( ( dsetconstrI ) => 0.53/0.98 ( ( dsetconstrEL ) => 0.53/0.98 ( ( dsetconstrER ) => 0.53/0.98 ( ( exuE1 ) => 0.53/0.98 ( ( prop2setE ) => 0.53/0.98 ( ( emptysetE ) => 0.53/0.98 ( ( emptysetimpfalse ) => 0.53/0.98 ( ( notinemptyset ) => 0.53/0.98 ( ( exuE3e ) => 0.53/0.98 ( ( setext ) => 0.53/0.98 ( ( emptyI ) => 0.53/0.98 ( ( noeltsimpempty ) => 0.53/0.98 ( ( setbeta ) => 0.53/0.98 ( ( nonemptyE1 ) => 0.53/0.98 ( ( nonemptyI ) => 0.53/0.98 ( ( nonemptyI1 ) => 0.53/0.98 ( ( ![X10:$i,X12:$i]: 0.53/0.98 ( in @ 0.53/0.98 X10 @ 0.53/0.98 ( setadjoin @ 0.53/0.98 X10 @ X12 ) ) ) => 0.53/0.98 ( ( in @ 0.53/0.98 emptyset @ 0.53/0.98 ( setadjoin @ 0.53/0.98 emptyset @ 0.53/0.98 emptyset ) ) => 0.53/0.98 ( ( ![X14:$i, 0.53/0.98 X16:$i, 0.53/0.98 X18:$i]: 0.53/0.98 ( ( 0.53/0.98 in @ 0.53/0.98 X18 @ X16 ) => 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X18 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X14 @ X16 ) ) ) ) => 0.53/0.98 ( ( ![ 0.53/0.98 X20:$i, 0.53/0.98 X22:$i, 0.53/0.98 X24:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X24 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X20 @ X22 ) ) => 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X26:$o]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X24 ) = 0.53/0.98 ( 0.53/0.98 X20 ) ) => 0.53/0.98 ( 0.53/0.98 X26 ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X24 @ X22 ) => 0.53/0.98 ( 0.53/0.98 X26 ) ) => 0.53/0.98 ( 0.53/0.98 X26 ) ) ) ) ) ) => 0.53/0.98 ( ( 0.53/0.98 ![ 0.53/0.98 X28:$i, 0.53/0.98 X30:$i, 0.53/0.98 X32:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X32 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X28 @ X30 ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X32 ) = 0.53/0.98 ( 0.53/0.98 X28 ) ) | 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X32 @ X30 ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setoftrueEq ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powersetI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 emptyinPowerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 emptyInPowerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powersetE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subPowSU ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuE2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 nonemptyImpWitness ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X34:$i, 0.53/0.98 X36:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X34 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X36 @ 0.53/0.98 emptyset ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X34 ) = 0.53/0.98 ( 0.53/0.98 X36 ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X38:$i, 0.53/0.98 X40:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X38 ) != 0.53/0.98 ( 0.53/0.98 X40 ) ) => 0.53/0.98 ( 0.53/0.98 ~( 0.53/0.98 in @ 0.53/0.98 X40 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X38 @ 0.53/0.98 emptyset ) ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X42:$i, 0.53/0.98 X44:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X42 ) = 0.53/0.98 ( 0.53/0.98 X44 ) ) => 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X42 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X44 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X46:$i, 0.53/0.98 X48:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X46 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X48 @ 0.53/0.98 emptyset ) ) => 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X48 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X46 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X50:$i, 0.53/0.98 X52:$i, 0.53/0.98 X54:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X54 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X50 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X52 @ 0.53/0.98 emptyset ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X54 ) = 0.53/0.98 ( 0.53/0.98 X50 ) ) | 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X54 ) = 0.53/0.98 ( 0.53/0.98 X52 ) ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X56:$i, 0.53/0.98 X58:$i]: 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X56 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X56 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X58 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X60:$i, 0.53/0.98 X62:$i]: 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X62 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X60 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X62 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 emptyE1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 vacuousDall ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 quantDeMorgan1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 quantDeMorgan2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 quantDeMorgan3 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 quantDeMorgan4 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 prop2setI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 prop2set2propI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notdexE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notdallE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuI3 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuI2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 inCongP ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuE3u ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exu__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 emptyset__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X64:$i, 0.53/0.98 X66:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X64 ) = 0.53/0.98 ( 0.53/0.98 X66 ) ) => 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X68:$i, 0.53/0.98 X70:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X68 ) = 0.53/0.98 ( 0.53/0.98 X70 ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X64 @ X68 ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X66 @ X70 ) ) ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powerset__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunion__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 omega__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuEu ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 descr__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 dsetconstr__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 eqimpsubset2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 eqimpsubset1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetI2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 emptysetsubset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetE2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notsubsetI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notequalI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notequalI2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetRefl ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetTrans ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoinSub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoinSub2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subset2powerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setextsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetemptysetimpeq ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powersetI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powersetE1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 inPowerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powersetsubset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 sepInPowerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 sepSubset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionIL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X72:$i, 0.53/0.98 X74:$i]: 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X74 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X72 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X74 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionIR ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionEcases ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionLsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionRsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset5 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectEL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectLsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset3 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectER ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 disjointsetsI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectRsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset4 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 bs114d ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusEL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusER ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusSubset2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusERneg ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusELneg ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusILneg ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusIRneg ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusLsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusSubset1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffI2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffIneg1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffIneg2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X76:$i, 0.53/0.98 X78:$i]: 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X78 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X76 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X78 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setukpairIL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setukpairIR ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 kpairiskpair ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 kpairp ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 singletonsubset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 singletoninpowerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 singletoninpowunion ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X80:$i, 0.53/0.98 X82:$i, 0.53/0.98 X84:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X84 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X80 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X82 @ 0.53/0.98 emptyset ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X84 ) = 0.53/0.98 ( 0.53/0.98 X80 ) ) | 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X84 ) = 0.53/0.98 ( 0.53/0.98 X82 ) ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 upairsubunion ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 upairinpowunion ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ubforcartprodlem1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ubforcartprodlem2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ubforcartprodlem3 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 cartprodpairin ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 cartprodmempair1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 cartprodmempair ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionE2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionsingleton1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionsingleton2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionsingleton ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 singletonprop ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ex1E1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ex1I ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ex1I2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X86:$i, 0.53/0.98 X88:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X86 @ 0.53/0.98 emptyset ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X88 @ 0.53/0.98 emptyset ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X86 ) = 0.53/0.98 ( 0.53/0.98 X88 ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X90:$i, 0.53/0.98 X92:$i, 0.53/0.98 X94:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X94 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X90 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X90 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X92 @ 0.53/0.98 emptyset ) ) @ 0.53/0.98 emptyset ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X90 ) = 0.53/0.98 ( 0.53/0.98 X94 ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 kfstsingleton ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 theprop ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 kfstpairEq ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 cartprodfstin ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X96:$i, 0.53/0.98 X98:$i, 0.53/0.98 X100:$i, 0.53/0.98 X102:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X96 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X96 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X98 @ 0.53/0.98 emptyset ) ) @ 0.53/0.98 emptyset ) ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X100 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X100 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X102 @ 0.53/0.98 emptyset ) ) @ 0.53/0.98 emptyset ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X96 ) = 0.53/0.98 ( 0.53/0.98 X100 ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setukpairinjL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X104:$i, 0.53/0.98 X106:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X104 ) = 0.53/0.98 ( 0.53/0.98 X106 ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X104 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X106 @ 0.53/0.98 emptyset ) ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X104 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X108:$i, 0.53/0.98 X110:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X108 ) = 0.53/0.98 ( 0.53/0.98 X110 ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X108 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X108 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X110 @ 0.53/0.98 emptyset ) ) @ 0.53/0.98 emptyset ) ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X108 @ 0.53/0.98 emptyset ) @ 0.53/0.98 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 0.53/0.98 thf(zf_stmt_4, negated_conjecture, 0.53/0.98 (~( ( setextAx ) => 0.53/0.98 ( ( emptysetAx ) => 0.53/0.98 ( ( ![X4:$i,X6:$i,X8:$i]: 0.53/0.98 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 0.53/0.98 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) => 0.53/0.98 ( ( powersetAx ) => 0.53/0.98 ( ( setunionAx ) => 0.53/0.98 ( ( omega0Ax ) => 0.53/0.98 ( ( omegaSAx ) => 0.53/0.98 ( ( omegaIndAx ) => 0.53/0.98 ( ( replAx ) => 0.53/0.98 ( ( foundationAx ) => 0.53/0.98 ( ( wellorderingAx ) => 0.53/0.98 ( ( descrp ) => 0.53/0.98 ( ( dsetconstrI ) => 0.53/0.98 ( ( dsetconstrEL ) => 0.53/0.98 ( ( dsetconstrER ) => 0.53/0.98 ( ( exuE1 ) => 0.53/0.98 ( ( prop2setE ) => 0.53/0.98 ( ( emptysetE ) => 0.53/0.98 ( ( emptysetimpfalse ) => 0.53/0.98 ( ( notinemptyset ) => 0.53/0.98 ( ( exuE3e ) => 0.53/0.98 ( ( setext ) => 0.53/0.98 ( ( emptyI ) => 0.53/0.98 ( ( noeltsimpempty ) => 0.53/0.98 ( ( setbeta ) => 0.53/0.98 ( ( nonemptyE1 ) => 0.53/0.98 ( ( nonemptyI ) => 0.53/0.98 ( ( nonemptyI1 ) => 0.53/0.98 ( ( ![X10:$i, 0.53/0.98 X12:$i]: 0.53/0.98 ( in @ 0.53/0.98 X10 @ 0.53/0.98 ( setadjoin 0.53/0.98 @ 0.53/0.98 X10 @ X12 ) ) ) => 0.53/0.98 ( ( in @ 0.53/0.98 emptyset @ 0.53/0.98 ( setadjoin 0.53/0.98 @ 0.53/0.98 emptyset @ 0.53/0.98 emptyset ) ) => 0.53/0.98 ( ( ![ 0.53/0.98 X14:$i, 0.53/0.98 X16:$i, 0.53/0.98 X18:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X18 @ X16 ) => 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X18 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X14 @ X16 ) ) ) ) => 0.53/0.98 ( ( 0.53/0.98 ![ 0.53/0.98 X20:$i, 0.53/0.98 X22:$i, 0.53/0.98 X24:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X24 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X20 @ X22 ) ) => 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X26:$o]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X24 ) = 0.53/0.98 ( 0.53/0.98 X20 ) ) => 0.53/0.98 ( 0.53/0.98 X26 ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X24 @ X22 ) => 0.53/0.98 ( 0.53/0.98 X26 ) ) => 0.53/0.98 ( 0.53/0.98 X26 ) ) ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X28:$i, 0.53/0.98 X30:$i, 0.53/0.98 X32:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X32 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X28 @ X30 ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X32 ) = 0.53/0.98 ( 0.53/0.98 X28 ) ) | 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X32 @ X30 ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setoftrueEq ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powersetI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 emptyinPowerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 emptyInPowerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powersetE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subPowSU ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuE2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 nonemptyImpWitness ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X34:$i, 0.53/0.98 X36:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X34 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X36 @ 0.53/0.98 emptyset ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X34 ) = 0.53/0.98 ( 0.53/0.98 X36 ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X38:$i, 0.53/0.98 X40:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X38 ) != 0.53/0.98 ( 0.53/0.98 X40 ) ) => 0.53/0.98 ( 0.53/0.98 ~ 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X40 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X38 @ 0.53/0.98 emptyset ) ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X42:$i, 0.53/0.98 X44:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X42 ) = 0.53/0.98 ( 0.53/0.98 X44 ) ) => 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X42 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X44 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X46:$i, 0.53/0.98 X48:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X46 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X48 @ 0.53/0.98 emptyset ) ) => 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X48 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X46 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X50:$i, 0.53/0.98 X52:$i, 0.53/0.98 X54:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X54 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X50 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X52 @ 0.53/0.98 emptyset ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X54 ) = 0.53/0.98 ( 0.53/0.98 X50 ) ) | 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X54 ) = 0.53/0.98 ( 0.53/0.98 X52 ) ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X56:$i, 0.53/0.98 X58:$i]: 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X56 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X56 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X58 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X60:$i, 0.53/0.98 X62:$i]: 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X62 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X60 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X62 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 emptyE1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 vacuousDall ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 quantDeMorgan1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 quantDeMorgan2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 quantDeMorgan3 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 quantDeMorgan4 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 prop2setI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 prop2set2propI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notdexE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notdallE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuI3 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuI2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 inCongP ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuE3u ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exu__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 emptyset__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X64:$i, 0.53/0.98 X66:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X64 ) = 0.53/0.98 ( 0.53/0.98 X66 ) ) => 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X68:$i, 0.53/0.98 X70:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X68 ) = 0.53/0.98 ( 0.53/0.98 X70 ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X64 @ X68 ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X66 @ X70 ) ) ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powerset__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunion__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 omega__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 exuEu ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 descr__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 dsetconstr__Cong ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 eqimpsubset2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 eqimpsubset1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetI2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 emptysetsubset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetE2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notsubsetI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notequalI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 notequalI2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetRefl ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetTrans ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoinSub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoinSub2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subset2powerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setextsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 subsetemptysetimpeq ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powersetI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powersetE1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 inPowerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 powersetsubset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 sepInPowerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 sepSubset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionIL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X72:$i, 0.53/0.98 X74:$i]: 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X74 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X72 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X74 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionIR ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionEcases ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionLsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binunionRsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset5 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectEL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectLsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset3 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectER ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 disjointsetsI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectRsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset4 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 binintersectSubset1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 bs114d ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusI ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusEL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusER ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusSubset2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusERneg ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusELneg ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusILneg ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusIRneg ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusLsub ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setminusSubset1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffE ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffI1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffI2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffIneg1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 symdiffIneg2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X76:$i, 0.53/0.98 X78:$i]: 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X78 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X76 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X78 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setukpairIL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setukpairIR ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 kpairiskpair ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 kpairp ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 singletonsubset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 singletoninpowerset ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 singletoninpowunion ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X80:$i, 0.53/0.98 X82:$i, 0.53/0.98 X84:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 X84 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X80 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X82 @ 0.53/0.98 emptyset ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X84 ) = 0.53/0.98 ( 0.53/0.98 X80 ) ) | 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X84 ) = 0.53/0.98 ( 0.53/0.98 X82 ) ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 upairsubunion ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 upairinpowunion ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ubforcartprodlem1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ubforcartprodlem2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ubforcartprodlem3 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 cartprodpairin ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 cartprodmempair1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 cartprodmempair ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionE2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionsingleton1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionsingleton2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setunionsingleton ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 singletonprop ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ex1E1 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ex1I ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ex1I2 ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X86:$i, 0.53/0.98 X88:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X86 @ 0.53/0.98 emptyset ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X88 @ 0.53/0.98 emptyset ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X86 ) = 0.53/0.98 ( 0.53/0.98 X88 ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X90:$i, 0.53/0.98 X92:$i, 0.53/0.98 X94:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 in @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X94 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X90 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X90 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X92 @ 0.53/0.98 emptyset ) ) @ 0.53/0.98 emptyset ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X90 ) = 0.53/0.98 ( 0.53/0.98 X94 ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 kfstsingleton ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 theprop ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 kfstpairEq ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 cartprodfstin ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X96:$i, 0.53/0.98 X98:$i, 0.53/0.98 X100:$i, 0.53/0.98 X102:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X96 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X96 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X98 @ 0.53/0.98 emptyset ) ) @ 0.53/0.98 emptyset ) ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X100 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X100 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X102 @ 0.53/0.98 emptyset ) ) @ 0.53/0.98 emptyset ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X96 ) = 0.53/0.98 ( 0.53/0.98 X100 ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setukpairinjL ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X104:$i, 0.53/0.98 X106:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X104 ) = 0.53/0.98 ( 0.53/0.98 X106 ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X104 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X106 @ 0.53/0.98 emptyset ) ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X104 @ 0.53/0.98 emptyset ) ) ) ) => 0.53/0.98 ( 0.53/0.98 ![ 0.53/0.98 X108:$i, 0.53/0.98 X110:$i]: 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 X108 ) = 0.53/0.98 ( 0.53/0.98 X110 ) ) => 0.53/0.98 ( 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X108 @ 0.53/0.98 emptyset ) @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X108 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X110 @ 0.53/0.98 emptyset ) ) @ 0.53/0.98 emptyset ) ) = 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 ( 0.53/0.98 setadjoin 0.53/0.98 @ 0.53/0.98 X108 @ 0.53/0.98 emptyset ) @ 0.53/0.98 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 0.53/0.98 inference('cnf.neg', [status(esa)], [zf_stmt_3])). 0.53/0.98 thf(zip_derived_cl87, plain, 0.53/0.98 (((setadjoin @ (setadjoin @ sk__52 @ emptyset) @ 0.53/0.98 (setadjoin @ (setadjoin @ sk__52 @ (setadjoin @ sk__53 @ emptyset)) @ 0.53/0.98 emptyset)) 0.53/0.98 != (setadjoin @ (setadjoin @ sk__52 @ emptyset) @ emptyset))), 0.53/0.98 inference('cnf', [status(esa)], [zf_stmt_4])). 0.53/0.98 thf(zip_derived_cl88, plain, (((sk__52) = (sk__53))), 0.53/0.98 inference('cnf', [status(esa)], [zf_stmt_4])). 0.53/0.98 thf(zip_derived_cl89, plain, 0.53/0.98 (![X30 : $i, X31 : $i]: 0.53/0.98 (((setadjoin @ X30 @ (setadjoin @ X31 @ emptyset)) 0.53/0.98 = (setadjoin @ X30 @ emptyset)) 0.53/0.98 | ((X30) != (X31)))), 0.53/0.98 inference('cnf', [status(esa)], [zf_stmt_4])). 0.53/0.98 thf(zip_derived_cl326, plain, 0.53/0.98 (![X31 : $i]: 0.53/0.98 ((setadjoin @ X31 @ (setadjoin @ X31 @ emptyset)) 0.53/0.98 = (setadjoin @ X31 @ emptyset))), 0.53/0.98 inference('simplify', [status(thm)], [zip_derived_cl89])). 0.53/0.98 thf(zip_derived_cl326, plain, 0.53/0.98 (![X31 : $i]: 0.53/0.98 ((setadjoin @ X31 @ (setadjoin @ X31 @ emptyset)) 0.53/0.98 = (setadjoin @ X31 @ emptyset))), 0.53/0.98 inference('simplify', [status(thm)], [zip_derived_cl89])). 0.53/0.98 thf(zip_derived_cl399, plain, 0.53/0.98 (((setadjoin @ (setadjoin @ sk__52 @ emptyset) @ emptyset) 0.53/0.98 != (setadjoin @ (setadjoin @ sk__52 @ emptyset) @ emptyset))), 0.53/0.98 inference('demod', [status(thm)], 0.53/0.98 [zip_derived_cl87, zip_derived_cl88, zip_derived_cl326, 0.53/0.98 zip_derived_cl326])). 0.53/0.98 thf(zip_derived_cl400, plain, ($false), 0.53/0.98 inference('simplify', [status(thm)], [zip_derived_cl399])). 0.53/0.98 0.53/0.98 % SZS output end Refutation 0.53/0.98 0.53/0.98 0.53/0.98 % Terminating... 0.54/1.05 % Runner terminated. 1.79/1.07 % Zipperpin 1.5 exiting 1.79/1.07 EOF