0.09/0.19 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.21 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.SB9FjFyOlp true 0.12/0.44 % Computer : n001.cluster.edu 0.12/0.44 % Model : x86_64 x86_64 0.12/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.44 % Memory : 8042.1875MB 0.12/0.44 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.44 % CPULimit : 1440 0.12/0.44 % WCLimit : 180 0.12/0.44 % DateTime : Thu Jul 4 08:28:09 EDT 2024 0.12/0.44 % CPUTime : 0.12/0.44 % Running portfolio for 1440 s 0.12/0.44 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.12/0.44 % Number of cores: 8 0.12/0.44 % Python version: Python 3.6.8 0.12/0.45 % Running in HO mode 0.29/0.75 % Total configuration time : 828 0.29/0.75 % Estimated wc time : 1656 0.29/0.75 % Estimated cpu time (8 cpus) : 207.0 0.31/0.96 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.31/0.97 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.31/0.97 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.31/0.97 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.31/0.97 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.31/0.97 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.31/0.97 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.31/0.98 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 10.84/3.29 % Solved by lams/40_c_ic.sh. 10.84/3.29 % done 222 iterations in 2.169s 10.84/3.29 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 10.84/3.29 % SZS output start Refutation 10.84/3.29 thf(setadjoinAx_type, type, setadjoinAx: $o). 10.84/3.29 thf(notdexE_type, type, notdexE: $o). 10.84/3.29 thf(upairequniteq_type, type, upairequniteq: $o). 10.84/3.29 thf(kfstpairEq_type, type, kfstpairEq: $o). 10.84/3.29 thf(setunionAx_type, type, setunionAx: $o). 10.84/3.29 thf(setminusELneg_type, type, setminusELneg: $o). 10.84/3.29 thf(powersetE_type, type, powersetE: $o). 10.84/3.29 thf(omegaSAx_type, type, omegaSAx: $o). 10.84/3.29 thf(exuI1_type, type, exuI1: $o). 10.84/3.29 thf(exuI2_type, type, exuI2: $o). 10.84/3.29 thf(notequalI2_type, type, notequalI2: $o). 10.84/3.29 thf(setukpairIR_type, type, setukpairIR: $o). 10.84/3.29 thf(powerset__Cong_type, type, powerset__Cong: $o). 10.84/3.29 thf(setminusILneg_type, type, setminusILneg: $o). 10.84/3.29 thf(wellorderingAx_type, type, wellorderingAx: $o). 10.84/3.29 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 10.84/3.29 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 10.84/3.29 thf(upairsubunion_type, type, upairsubunion: $o). 10.84/3.29 thf(setoftrueEq_type, type, setoftrueEq: $o). 10.84/3.29 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 10.84/3.29 thf(sepInPowerset_type, type, sepInPowerset: $o). 10.84/3.29 thf(setukpairIL_type, type, setukpairIL: $o). 10.84/3.29 thf(kpairiskpair_type, type, kpairiskpair: $o). 10.84/3.29 thf(binunionE_type, type, binunionE: $o). 10.84/3.29 thf(setext_type, type, setext: $o). 10.84/3.29 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 10.84/3.29 thf(upairinpowunion_type, type, upairinpowunion: $o). 10.84/3.29 thf(descr__Cong_type, type, descr__Cong: $o). 10.84/3.29 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 10.84/3.29 thf(in_type, type, in: $i > $i > $o). 10.84/3.29 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 10.84/3.29 thf(theprop_type, type, theprop: $o). 10.84/3.29 thf(binunion_type, type, binunion: $i > $i > $i). 10.84/3.29 thf(upairset2E_type, type, upairset2E: $o). 10.84/3.29 thf(ksndsingleton_type, type, ksndsingleton: $o). 10.84/3.29 thf(setadjoinIR_type, type, setadjoinIR: $o). 10.84/3.29 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 10.84/3.29 thf(symdiffI2_type, type, symdiffI2: $o). 10.84/3.29 thf(upairset2IR_type, type, upairset2IR: $o). 10.84/3.29 thf(subsetE_type, type, subsetE: $o). 10.84/3.29 thf(prop2set2propI_type, type, prop2set2propI: $o). 10.84/3.29 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 10.84/3.29 thf(setbeta_type, type, setbeta: $o). 10.84/3.29 thf(eqinunit_type, type, eqinunit: $o). 10.84/3.29 thf(upairsetIL_type, type, upairsetIL: $o). 10.84/3.29 thf(powersetI1_type, type, powersetI1: $o). 10.84/3.29 thf(sk__29_type, type, sk__29: $i). 10.84/3.29 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 10.84/3.29 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 10.84/3.29 thf(setukpairinjR2_type, type, setukpairinjR2: $o). 10.84/3.29 thf(setminusIRneg_type, type, setminusIRneg: $o). 10.84/3.29 thf(kfstsingleton_type, type, kfstsingleton: $o). 10.84/3.29 thf(powersetAx_type, type, powersetAx: $o). 10.84/3.29 thf(setunionsingleton_type, type, setunionsingleton: $o). 10.84/3.29 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 10.84/3.29 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 10.84/3.29 thf(powersetI_type, type, powersetI: $o). 10.84/3.29 thf(upairsetIR_type, type, upairsetIR: $o). 10.84/3.29 thf(ksnd_type, type, ksnd: $i > $i). 10.84/3.29 thf(inCongP_type, type, inCongP: $o). 10.84/3.29 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 10.84/3.29 thf(setadjoinSub_type, type, setadjoinSub: $o). 10.84/3.29 thf(exuE3e_type, type, exuE3e: $o). 10.84/3.29 thf(emptysetE_type, type, emptysetE: $o). 10.84/3.29 thf(setukpairinjR1_type, type, setukpairinjR1: $o). 10.84/3.29 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 10.84/3.29 thf(setunionI_type, type, setunionI: $o). 10.84/3.29 thf(setunion__Cong_type, type, setunion__Cong: $o). 10.84/3.29 thf(prop2setI_type, type, prop2setI: $o). 10.84/3.29 thf(ex1I2_type, type, ex1I2: $o). 10.84/3.29 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 10.84/3.29 thf(setminusER_type, type, setminusER: $o). 10.84/3.29 thf(exuE2_type, type, exuE2: $o). 10.84/3.29 thf(emptyset_type, type, emptyset: $i). 10.84/3.29 thf(singletonsuniq_type, type, singletonsuniq: $o). 10.84/3.29 thf(powersetsubset_type, type, powersetsubset: $o). 10.84/3.29 thf(subPowSU_type, type, subPowSU: $o). 10.84/3.29 thf(notequalI1_type, type, notequalI1: $o). 10.84/3.29 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 10.84/3.29 thf(notinemptyset_type, type, notinemptyset: $o). 10.84/3.29 thf(nonemptyI1_type, type, nonemptyI1: $o). 10.84/3.29 thf(subsetTrans_type, type, subsetTrans: $o). 10.84/3.29 thf(setminusI_type, type, setminusI: $o). 10.84/3.29 thf(binunionIL_type, type, binunionIL: $o). 10.84/3.29 thf(subsetE2_type, type, subsetE2: $o). 10.84/3.29 thf(singletonsswitch_type, type, singletonsswitch: $o). 10.84/3.29 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 10.84/3.29 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 10.84/3.29 thf(setextsub_type, type, setextsub: $o). 10.84/3.29 thf(binunionLsub_type, type, binunionLsub: $o). 10.84/3.29 thf(emptysetsubset_type, type, emptysetsubset: $o). 10.84/3.29 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 10.84/3.29 thf(setunionE_type, type, setunionE: $o). 10.84/3.29 thf(setminusSubset1_type, type, setminusSubset1: $o). 10.84/3.29 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 10.84/3.29 thf(binunionIR_type, type, binunionIR: $o). 10.84/3.29 thf(setadjoinE_type, type, setadjoinE: $o). 10.84/3.29 thf(singletonprop_type, type, singletonprop: $o). 10.84/3.29 thf(kfst_type, type, kfst: $i > $i). 10.84/3.29 thf(setadjoinIL_type, type, setadjoinIL: $o). 10.84/3.29 thf(exuE1_type, type, exuE1: $o). 10.84/3.29 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 10.84/3.29 thf(binintersectRsub_type, type, binintersectRsub: $o). 10.84/3.29 thf(setminusLsub_type, type, setminusLsub: $o). 10.84/3.29 thf(notinsingleton_type, type, notinsingleton: $o). 10.84/3.29 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 10.84/3.29 thf(exuEu_type, type, exuEu: $o). 10.84/3.29 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 10.84/3.29 thf(upairsetE_type, type, upairsetE: $o). 10.84/3.29 thf(omega0Ax_type, type, omega0Ax: $o). 10.84/3.29 thf(notsubsetI_type, type, notsubsetI: $o). 10.84/3.29 thf(singleton_type, type, singleton: $i > $o). 10.84/3.29 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 10.84/3.29 thf(setextAx_type, type, setextAx: $o). 10.84/3.29 thf(kpair_type, type, kpair: $i > $i > $i). 10.84/3.29 thf(cartprod_type, type, cartprod: $i > $i > $i). 10.84/3.29 thf(powersetE1_type, type, powersetE1: $o). 10.84/3.29 thf(bs114d_type, type, bs114d: $o). 10.84/3.29 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 10.84/3.29 thf(setunion_type, type, setunion: $i > $i). 10.84/3.29 thf(iskpair_type, type, iskpair: $i > $o). 10.84/3.29 thf(binintersectLsub_type, type, binintersectLsub: $o). 10.84/3.29 thf(subsetI1_type, type, subsetI1: $o). 10.84/3.29 thf(symdiffE_type, type, symdiffE: $o). 10.84/3.29 thf(descrp_type, type, descrp: $o). 10.84/3.29 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 10.84/3.29 thf(foundationAx_type, type, foundationAx: $o). 10.84/3.29 thf(emptysetAx_type, type, emptysetAx: $o). 10.84/3.29 thf(emptyI_type, type, emptyI: $o). 10.84/3.29 thf(setadjoinOr_type, type, setadjoinOr: $o). 10.84/3.29 thf(binintersectEL_type, type, binintersectEL: $o). 10.84/3.29 thf(emptyE1_type, type, emptyE1: $o). 10.84/3.29 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 10.84/3.29 thf(vacuousDall_type, type, vacuousDall: $o). 10.84/3.29 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 10.84/3.29 thf(dsetconstrER_type, type, dsetconstrER: $o). 10.84/3.29 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 10.84/3.29 thf(binintersectI_type, type, binintersectI: $o). 10.84/3.29 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 10.84/3.29 thf(ex1E1_type, type, ex1E1: $o). 10.84/3.29 thf(cartprodpairin_type, type, cartprodpairin: $o). 10.84/3.29 thf(ksndpairEq_type, type, ksndpairEq: $o). 10.84/3.29 thf(setukpairinjL_type, type, setukpairinjL: $o). 10.84/3.29 thf(symdiffI1_type, type, symdiffI1: $o). 10.84/3.29 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 10.84/3.29 thf(subsetI2_type, type, subsetI2: $o). 10.84/3.29 thf(cartprodfstin_type, type, cartprodfstin: $o). 10.84/3.29 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 10.84/3.29 thf(setminusERneg_type, type, setminusERneg: $o). 10.84/3.29 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 10.84/3.29 thf(omega__Cong_type, type, omega__Cong: $o). 10.84/3.29 thf(subsetRefl_type, type, subsetRefl: $o). 10.84/3.29 thf(uniqinunit_type, type, uniqinunit: $o). 10.84/3.29 thf(setukpairinjR12_type, type, setukpairinjR12: $o). 10.84/3.29 thf(setminusSubset2_type, type, setminusSubset2: $o). 10.84/3.29 thf(prop2setE_type, type, prop2setE: $o). 10.84/3.29 thf(binunionEcases_type, type, binunionEcases: $o). 10.84/3.29 thf(nonemptyI_type, type, nonemptyI: $o). 10.84/3.29 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 10.84/3.29 thf(exuE3u_type, type, exuE3u: $o). 10.84/3.29 thf(setminusEL_type, type, setminusEL: $o). 10.84/3.29 thf(singletonsubset_type, type, singletonsubset: $o). 10.84/3.29 thf(sepSubset_type, type, sepSubset: $o). 10.84/3.29 thf(setunionE2_type, type, setunionE2: $o). 10.84/3.29 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 10.84/3.29 thf(ex1I_type, type, ex1I: $o). 10.84/3.29 thf(exuI3_type, type, exuI3: $o). 10.84/3.29 thf(notdallE_type, type, notdallE: $o). 10.84/3.29 thf(binintersectER_type, type, binintersectER: $o). 10.84/3.29 thf(setukpairinjR_type, type, setukpairinjR: $o). 10.84/3.29 thf(powerset_type, type, powerset: $i > $i). 10.84/3.29 thf(kpairp_type, type, kpairp: $o). 10.84/3.29 thf(dsetconstrI_type, type, dsetconstrI: $o). 10.84/3.29 thf(sk__31_type, type, sk__31: $i). 10.84/3.29 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 10.84/3.29 thf(exu__Cong_type, type, exu__Cong: $o). 10.84/3.29 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 10.84/3.29 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 10.84/3.29 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 10.84/3.29 thf(replAx_type, type, replAx: $o). 10.84/3.29 thf(nonemptyE1_type, type, nonemptyE1: $o). 10.84/3.29 thf(omegaIndAx_type, type, omegaIndAx: $o). 10.84/3.29 thf(secondinupair_type, type, secondinupair: $o). 10.84/3.29 thf(inPowerset_type, type, inPowerset: $o). 10.84/3.29 thf(sk__30_type, type, sk__30: $i). 10.84/3.29 thf(cartprodmempair_type, type, cartprodmempair: $o). 10.84/3.29 thf(in__Cong_type, type, in__Cong: $o). 10.84/3.29 thf(binunionRsub_type, type, binunionRsub: $o). 10.84/3.29 thf(subset2powerset_type, type, subset2powerset: $o). 10.84/3.29 thf(ksndpairEq, axiom, ksndpairEq = 10.84/3.29 (![Xx:$i,Xy:$i]: ( ( ksnd @ ( kpair @ Xx @ Xy ) ) = ( Xy ) ))). 10.84/3.29 thf('0', plain, 10.84/3.29 (( ksndpairEq ) = 10.84/3.29 ( ![X4:$i,X6:$i]: ( ( ksnd @ ( kpair @ X4 @ X6 ) ) = ( X6 ) ) )), 10.84/3.29 define([status(thm)])). 10.84/3.29 thf(ksndsingleton, axiom, ksndsingleton = 10.84/3.29 (![Xu:$i]: 10.84/3.29 ( ( iskpair @ Xu ) => 10.84/3.29 ( singleton @ 10.84/3.29 ( dsetconstr @ 10.84/3.29 ( setunion @ Xu ) @ 10.84/3.29 ( ^[Xx:$i]: ( ( Xu ) = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ))). 10.84/3.29 thf('1', plain, 10.84/3.29 (( ksndsingleton ) = 10.84/3.29 ( ![X4:$i]: 10.84/3.29 ( ( iskpair @ X4 ) => 10.84/3.29 ( singleton @ 10.84/3.29 ( dsetconstr @ 10.84/3.29 ( setunion @ X4 ) @ 10.84/3.29 ( ^[V_1:$i]: ( ( X4 ) = ( kpair @ ( kfst @ X4 ) @ V_1 ) ) ) ) ) ) )), 10.84/3.29 define([status(thm)])). 10.84/3.29 thf(setukpairinjR, axiom, setukpairinjR = 10.84/3.29 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]: 10.84/3.29 ( ( ( kpair @ Xx @ Xy ) = ( kpair @ Xz @ Xu ) ) => ( ( Xy ) = ( Xu ) ) ))). 10.84/3.29 thf('2', plain, 10.84/3.29 (( setukpairinjR ) = 10.84/3.29 ( ![X4:$i,X6:$i,X8:$i,X10:$i]: 10.84/3.29 ( ( ( kpair @ X4 @ X6 ) = ( kpair @ X8 @ X10 ) ) => 10.84/3.29 ( ( X6 ) = ( X10 ) ) ) )), 10.84/3.29 define([status(thm)])). 10.84/3.29 thf(setukpairinjL, axiom, setukpairinjL = 10.84/3.29 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]: 10.84/3.29 ( ( ( kpair @ Xx @ Xy ) = ( kpair @ Xz @ Xu ) ) => ( ( Xx ) = ( Xz ) ) ))). 10.84/3.29 thf('3', plain, 10.84/3.29 (( setukpairinjL ) = 10.84/3.29 ( ![X4:$i,X6:$i,X8:$i,X10:$i]: 10.84/3.29 ( ( ( kpair @ X4 @ X6 ) = ( kpair @ X8 @ X10 ) ) => 10.84/3.29 ( ( X4 ) = ( X8 ) ) ) )), 10.84/3.29 define([status(thm)])). 10.84/3.29 thf(cartprodfstin, axiom, cartprodfstin = 10.84/3.29 (![A:$i,B:$i,Xu:$i]: 10.84/3.29 ( ( in @ Xu @ ( cartprod @ A @ B ) ) => ( in @ ( kfst @ Xu ) @ A ) ))). 10.84/3.29 thf('4', plain, 10.84/3.29 (( cartprodfstin ) = 10.84/3.29 ( ![X4:$i,X6:$i,X8:$i]: 10.84/3.29 ( ( in @ X8 @ ( cartprod @ X4 @ X6 ) ) => ( in @ ( kfst @ X8 ) @ X4 ) ) )), 10.84/3.29 define([status(thm)])). 10.84/3.29 thf(kfstpairEq, axiom, kfstpairEq = 10.84/3.29 (![Xx:$i,Xy:$i]: ( ( kfst @ ( kpair @ Xx @ Xy ) ) = ( Xx ) ))). 10.84/3.29 thf('5', plain, 10.84/3.29 (( kfstpairEq ) = 10.84/3.29 ( ![X4:$i,X6:$i]: ( ( kfst @ ( kpair @ X4 @ X6 ) ) = ( X4 ) ) )), 10.84/3.29 define([status(thm)])). 10.84/3.29 thf(kfstsingleton, axiom, kfstsingleton = 10.84/3.29 (![Xu:$i]: 10.84/3.29 ( ( iskpair @ Xu ) => 10.84/3.29 ( singleton @ 10.84/3.29 ( dsetconstr @ 10.84/3.29 ( setunion @ Xu ) @ 10.84/3.29 ( ^[Xx:$i]: ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ))). 10.84/3.29 thf('6', plain, 10.84/3.29 (( kfstsingleton ) = 10.84/3.29 ( ![X4:$i]: 10.84/3.29 ( ( iskpair @ X4 ) => 10.84/3.29 ( singleton @ 10.84/3.29 ( dsetconstr @ 10.84/3.29 ( setunion @ X4 ) @ 10.84/3.29 ( ^[V_1:$i]: ( in @ ( setadjoin @ V_1 @ emptyset ) @ X4 ) ) ) ) ) )), 10.84/3.29 define([status(thm)])). 10.84/3.29 thf(ubforcartprodlem3, axiom, ubforcartprodlem3 = 10.84/3.29 (![A:$i,B:$i,Xx:$i]: 10.84/3.29 ( ( in @ Xx @ A ) => 10.84/3.29 ( ![Xy:$i]: 10.84/3.29 ( ( in @ Xy @ B ) => 10.84/3.29 ( in @ 10.84/3.29 ( kpair @ Xx @ Xy ) @ 10.84/3.29 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))). 10.84/3.29 thf('7', plain, 10.84/3.29 (( ubforcartprodlem3 ) = 10.84/3.29 ( ![X4:$i,X6:$i,X8:$i]: 10.84/3.29 ( ( in @ X8 @ X4 ) => 10.84/3.29 ( ![X10:$i]: 10.84/3.29 ( ( in @ X10 @ X6 ) => 10.84/3.29 ( in @ 10.84/3.29 ( kpair @ X8 @ X10 ) @ 10.84/3.29 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )), 10.84/3.29 define([status(thm)])). 10.84/3.29 thf(kpairp, axiom, kpairp = 10.84/3.29 (![Xx:$i,Xy:$i]: ( iskpair @ ( kpair @ Xx @ Xy ) ))). 10.84/3.29 thf('8', plain, 10.84/3.29 (( kpairp ) = ( ![X4:$i,X6:$i]: ( iskpair @ ( kpair @ X4 @ X6 ) ) )), 10.84/3.29 define([status(thm)])). 10.84/3.29 thf(kpair, axiom,(( kpair ) = 10.84/3.29 (^[Xx:$i,Xy:$i]: 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ Xx @ emptyset ) @ 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )))). 10.84/3.29 thf('9', plain, 10.84/3.29 (( kpair ) = 10.84/3.29 ( ^[Xx:$i,Xy:$i]: 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ Xx @ emptyset ) @ 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )), 10.84/3.29 inference('simplify_rw_rule', [status(thm)], [kpair])). 10.84/3.29 thf('10', plain, 10.84/3.29 (( kpair ) = 10.84/3.29 ( ^[V_1:$i,V_2:$i]: 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ V_1 @ emptyset ) @ 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ V_1 @ ( setadjoin @ V_2 @ emptyset ) ) @ emptyset ) ) )), 10.84/3.29 define([status(thm)])). 10.84/3.29 thf(kpairiskpair, axiom, kpairiskpair = 10.84/3.29 (![Xx:$i,Xy:$i]: 10.84/3.29 ( iskpair @ 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ Xx @ emptyset ) @ 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ))). 10.84/3.29 thf('11', plain, 10.84/3.29 (( kpairiskpair ) = 10.84/3.29 ( ![X4:$i,X6:$i]: 10.84/3.29 ( iskpair @ 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ X4 @ emptyset ) @ 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) )), 10.84/3.29 define([status(thm)])). 10.84/3.29 thf(iskpair, axiom,(( iskpair ) = 10.84/3.29 (^[A:$i]: 10.84/3.29 ( ?[Xx:$i]: 10.84/3.29 ( ( ?[Xy:$i]: 10.84/3.29 ( ( ( A ) = 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ Xx @ emptyset ) @ 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ 10.84/3.29 emptyset ) ) ) & 10.84/3.29 ( in @ Xy @ ( setunion @ A ) ) ) ) & 10.84/3.29 ( in @ Xx @ ( setunion @ A ) ) ) )))). 10.84/3.29 thf('12', plain, 10.84/3.29 (( iskpair ) = 10.84/3.29 ( ^[A:$i]: 10.84/3.29 ( ?[Xx:$i]: 10.84/3.29 ( ( ?[Xy:$i]: 10.84/3.29 ( ( ( A ) = 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ Xx @ emptyset ) @ 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ 10.84/3.29 emptyset ) ) ) & 10.84/3.29 ( in @ Xy @ ( setunion @ A ) ) ) ) & 10.84/3.29 ( in @ Xx @ ( setunion @ A ) ) ) ) )), 10.84/3.29 inference('simplify_rw_rule', [status(thm)], [iskpair])). 10.84/3.29 thf('13', plain, 10.84/3.29 (( iskpair ) = 10.84/3.29 ( ^[V_1:$i]: 10.84/3.29 ( ?[X4:$i]: 10.84/3.29 ( ( ?[X6:$i]: 10.84/3.29 ( ( ( V_1 ) = 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ X4 @ emptyset ) @ 10.84/3.29 ( setadjoin @ 10.84/3.29 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ 10.84/3.29 emptyset ) ) ) & 10.84/3.29 ( in @ X6 @ ( setunion @ V_1 ) ) ) ) & 10.84/3.29 ( in @ X4 @ ( setunion @ V_1 ) ) ) ) )), 10.84/3.29 define([status(thm)])). 10.84/3.29 thf(kpairsurjEq, conjecture, 10.84/3.29 (( setextAx ) => 10.84/3.29 ( ( emptysetAx ) => 10.84/3.29 ( ( setadjoinAx ) => 10.84/3.29 ( ( powersetAx ) => 10.84/3.29 ( ( setunionAx ) => 10.84/3.29 ( ( omega0Ax ) => 10.84/3.29 ( ( omegaSAx ) => 10.84/3.29 ( ( omegaIndAx ) => 10.84/3.29 ( ( replAx ) => 10.84/3.29 ( ( foundationAx ) => 10.84/3.29 ( ( wellorderingAx ) => 10.84/3.29 ( ( descrp ) => 10.84/3.29 ( ( dsetconstrI ) => 10.84/3.29 ( ( dsetconstrEL ) => 10.84/3.29 ( ( dsetconstrER ) => 10.84/3.29 ( ( exuE1 ) => 10.84/3.29 ( ( prop2setE ) => 10.84/3.29 ( ( emptysetE ) => 10.84/3.29 ( ( emptysetimpfalse ) => 10.84/3.29 ( ( notinemptyset ) => 10.84/3.29 ( ( exuE3e ) => 10.84/3.29 ( ( setext ) => 10.84/3.29 ( ( emptyI ) => 10.84/3.29 ( ( noeltsimpempty ) => 10.84/3.29 ( ( setbeta ) => 10.84/3.29 ( ( nonemptyE1 ) => 10.84/3.29 ( ( nonemptyI ) => 10.84/3.29 ( ( nonemptyI1 ) => 10.84/3.29 ( ( setadjoinIL ) => 10.84/3.29 ( ( emptyinunitempty ) => 10.84/3.29 ( ( setadjoinIR ) => 10.84/3.29 ( ( setadjoinE ) => 10.84/3.29 ( ( 10.84/3.29 setadjoinOr ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setoftrueEq ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptyinPowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptyInPowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subPowSU ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuE2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 nonemptyImpWitness ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 uniqinunit ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notinsingleton ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 eqinunit ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletonsswitch ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairsetE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairsetIL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairsetIR ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptyE1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 vacuousDall ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 quantDeMorgan1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 quantDeMorgan2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 quantDeMorgan3 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 quantDeMorgan4 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 prop2setI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 prop2set2propI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notdexE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notdallE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuI3 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuI2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 inCongP ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 in__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuE3u ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exu__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptyset__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoin__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powerset__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunion__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 omega__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuEu ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 descr__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 dsetconstr__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 eqimpsubset2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 eqimpsubset1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetI2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptysetsubset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetE2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notsubsetI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notequalI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notequalI2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetRefl ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetTrans ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoinSub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoinSub2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subset2powerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setextsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetemptysetimpeq ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetE1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 inPowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetsubset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 sepInPowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 sepSubset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionIL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairset2IR ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionIR ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionEcases ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionLsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionRsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset5 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectEL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectLsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset3 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectER ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 disjointsetsI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectRsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset4 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 bs114d ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusEL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusER ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusSubset2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusERneg ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusELneg ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusILneg ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusIRneg ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusLsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusSubset1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffI2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffIneg1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffIneg2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 secondinupair ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairIL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairIR ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 kpairiskpair ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 kpairp ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletonsubset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletoninpowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletoninpowunion ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairset2E ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairsubunion ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairinpowunion ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ubforcartprodlem1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ubforcartprodlem2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ubforcartprodlem3 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 cartprodpairin ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 cartprodmempair1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 cartprodmempair ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionE2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionsingleton1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionsingleton2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionsingleton ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletonprop ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ex1E1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ex1I ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ex1I2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletonsuniq ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjL1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 kfstsingleton ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 theprop ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 kfstpairEq ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 cartprodfstin ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjL2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjR11 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjR12 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjR1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairequniteq ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjR2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjR ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ksndsingleton ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ksndpairEq ) => 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 Xu:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 iskpair @ 10.84/3.29 Xu ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 kpair @ 10.84/3.29 ( 10.84/3.29 kfst @ Xu ) @ 10.84/3.29 ( 10.84/3.29 ksnd @ Xu ) ) = 10.84/3.29 ( 10.84/3.29 Xu ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 10.84/3.29 thf(zf_stmt_0, conjecture, 10.84/3.29 (( setextAx ) => 10.84/3.29 ( ( emptysetAx ) => 10.84/3.29 ( ( setadjoinAx ) => 10.84/3.29 ( ( powersetAx ) => 10.84/3.29 ( ( setunionAx ) => 10.84/3.29 ( ( omega0Ax ) => 10.84/3.29 ( ( omegaSAx ) => 10.84/3.29 ( ( omegaIndAx ) => 10.84/3.29 ( ( replAx ) => 10.84/3.29 ( ( foundationAx ) => 10.84/3.29 ( ( wellorderingAx ) => 10.84/3.29 ( ( descrp ) => 10.84/3.29 ( ( dsetconstrI ) => 10.84/3.29 ( ( dsetconstrEL ) => 10.84/3.29 ( ( dsetconstrER ) => 10.84/3.29 ( ( exuE1 ) => 10.84/3.29 ( ( prop2setE ) => 10.84/3.29 ( ( emptysetE ) => 10.84/3.29 ( ( emptysetimpfalse ) => 10.84/3.29 ( ( notinemptyset ) => 10.84/3.29 ( ( exuE3e ) => 10.84/3.29 ( ( setext ) => 10.84/3.29 ( ( emptyI ) => 10.84/3.29 ( ( noeltsimpempty ) => 10.84/3.29 ( ( setbeta ) => 10.84/3.29 ( ( nonemptyE1 ) => 10.84/3.29 ( ( nonemptyI ) => 10.84/3.29 ( ( nonemptyI1 ) => 10.84/3.29 ( ( setadjoinIL ) => 10.84/3.29 ( ( emptyinunitempty ) => 10.84/3.29 ( ( setadjoinIR ) => 10.84/3.29 ( ( setadjoinE ) => 10.84/3.29 ( ( 10.84/3.29 setadjoinOr ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setoftrueEq ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptyinPowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptyInPowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subPowSU ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuE2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 nonemptyImpWitness ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 uniqinunit ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notinsingleton ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 eqinunit ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletonsswitch ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairsetE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairsetIL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairsetIR ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptyE1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 vacuousDall ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 quantDeMorgan1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 quantDeMorgan2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 quantDeMorgan3 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 quantDeMorgan4 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 prop2setI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 prop2set2propI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notdexE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notdallE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuI3 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuI2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 inCongP ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 in__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuE3u ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exu__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptyset__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoin__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powerset__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunion__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 omega__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuEu ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 descr__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 dsetconstr__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 eqimpsubset2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 eqimpsubset1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetI2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptysetsubset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetE2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notsubsetI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notequalI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notequalI2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetRefl ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetTrans ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoinSub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoinSub2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subset2powerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setextsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetemptysetimpeq ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetE1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 inPowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetsubset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 sepInPowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 sepSubset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionIL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairset2IR ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionIR ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionEcases ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionLsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionRsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset5 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectEL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectLsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset3 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectER ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 disjointsetsI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectRsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset4 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 bs114d ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusEL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusER ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusSubset2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusERneg ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusELneg ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusILneg ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusIRneg ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusLsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusSubset1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffI2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffIneg1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffIneg2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 secondinupair ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairIL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairIR ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X4:$i, 10.84/3.29 X6:$i]: 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X8:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X10:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X4 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X4 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X6 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) = 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X8 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X8 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X10 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X10 @ 10.84/3.29 ( 10.84/3.29 setunion @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X4 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X4 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X6 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X8 @ 10.84/3.29 ( 10.84/3.29 setunion @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X4 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X4 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X6 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) ) ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X12:$i, 10.84/3.29 X14:$i]: 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X16:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X18:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X12 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X12 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X14 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) = 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X16 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X16 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X18 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X18 @ 10.84/3.29 ( 10.84/3.29 setunion @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X12 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X12 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X14 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X16 @ 10.84/3.29 ( 10.84/3.29 setunion @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X12 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X12 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X14 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) ) ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletonsubset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletoninpowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletoninpowunion ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairset2E ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairsubunion ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairinpowunion ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ubforcartprodlem1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ubforcartprodlem2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X20:$i, 10.84/3.29 X22:$i, 10.84/3.29 X24:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X24 @ X20 ) => 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X26:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X26 @ X22 ) => 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X24 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X24 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X26 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 ( 10.84/3.29 powerset @ 10.84/3.29 ( 10.84/3.29 powerset @ 10.84/3.29 ( 10.84/3.29 binunion @ 10.84/3.29 X20 @ X22 ) ) ) ) ) ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 cartprodpairin ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 cartprodmempair1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 cartprodmempair ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionE2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionsingleton1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionsingleton2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionsingleton ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletonprop ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ex1E1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ex1I ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ex1I2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletonsuniq ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjL1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X28:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X30:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X32:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 X28 ) = 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X30 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X30 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X32 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X32 @ 10.84/3.29 ( 10.84/3.29 setunion @ 10.84/3.29 X28 ) ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X30 @ 10.84/3.29 ( 10.84/3.29 setunion @ 10.84/3.29 X28 ) ) ) ) => 10.84/3.29 ( 10.84/3.29 singleton 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 dsetconstr 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setunion @ 10.84/3.29 X28 ) @ 10.84/3.29 ( 10.84/3.29 ^[ 10.84/3.29 V_1:$i]: 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 V_1 @ 10.84/3.29 emptyset ) @ 10.84/3.29 X28 ) ) ) ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 theprop ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X34:$i, 10.84/3.29 X36:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 kfst @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X34 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X34 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X36 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) = 10.84/3.29 ( 10.84/3.29 X34 ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X38:$i, 10.84/3.29 X40:$i, 10.84/3.29 X42:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X42 @ 10.84/3.29 ( 10.84/3.29 cartprod @ 10.84/3.29 X38 @ X40 ) ) => 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 ( 10.84/3.29 kfst @ X42 ) @ 10.84/3.29 X38 ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjL2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X44:$i, 10.84/3.29 X46:$i, 10.84/3.29 X48:$i, 10.84/3.29 X50:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X44 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X44 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X46 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) = 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X48 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X48 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X50 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 X44 ) = 10.84/3.29 ( 10.84/3.29 X48 ) ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjR11 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjR12 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjR1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairequniteq ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjR2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X52:$i, 10.84/3.29 X54:$i, 10.84/3.29 X56:$i, 10.84/3.29 X58:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X52 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X52 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X54 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) = 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X56 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X56 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X58 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 X54 ) = 10.84/3.29 ( 10.84/3.29 X58 ) ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X60:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X62:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X64:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 X60 ) = 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X62 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X62 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X64 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X64 @ 10.84/3.29 ( 10.84/3.29 setunion @ 10.84/3.29 X60 ) ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X62 @ 10.84/3.29 ( 10.84/3.29 setunion @ 10.84/3.29 X60 ) ) ) ) => 10.84/3.29 ( 10.84/3.29 singleton 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 dsetconstr 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setunion @ 10.84/3.29 X60 ) @ 10.84/3.29 ( 10.84/3.29 ^[ 10.84/3.29 V_2:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 X60 ) = 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 kfst @ X60 ) @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 kfst @ X60 ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 V_2 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) ) ) ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X66:$i, 10.84/3.29 X68:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ksnd @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X66 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X66 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X68 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) = 10.84/3.29 ( 10.84/3.29 X68 ) ) ) => 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X70:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X72:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X74:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 X70 ) = 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X72 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X72 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X74 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X74 @ 10.84/3.29 ( 10.84/3.29 setunion @ 10.84/3.29 X70 ) ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X72 @ 10.84/3.29 ( 10.84/3.29 setunion @ 10.84/3.29 X70 ) ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 kfst @ X70 ) @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 kfst @ X70 ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 ksnd @ X70 ) @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) = 10.84/3.29 ( 10.84/3.29 X70 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 10.84/3.29 thf(zf_stmt_1, negated_conjecture, 10.84/3.29 (~( ( setextAx ) => 10.84/3.29 ( ( emptysetAx ) => 10.84/3.29 ( ( setadjoinAx ) => 10.84/3.29 ( ( powersetAx ) => 10.84/3.29 ( ( setunionAx ) => 10.84/3.29 ( ( omega0Ax ) => 10.84/3.29 ( ( omegaSAx ) => 10.84/3.29 ( ( omegaIndAx ) => 10.84/3.29 ( ( replAx ) => 10.84/3.29 ( ( foundationAx ) => 10.84/3.29 ( ( wellorderingAx ) => 10.84/3.29 ( ( descrp ) => 10.84/3.29 ( ( dsetconstrI ) => 10.84/3.29 ( ( dsetconstrEL ) => 10.84/3.29 ( ( dsetconstrER ) => 10.84/3.29 ( ( exuE1 ) => 10.84/3.29 ( ( prop2setE ) => 10.84/3.29 ( ( emptysetE ) => 10.84/3.29 ( ( emptysetimpfalse ) => 10.84/3.29 ( ( notinemptyset ) => 10.84/3.29 ( ( exuE3e ) => 10.84/3.29 ( ( setext ) => 10.84/3.29 ( ( emptyI ) => 10.84/3.29 ( ( noeltsimpempty ) => 10.84/3.29 ( ( setbeta ) => 10.84/3.29 ( ( nonemptyE1 ) => 10.84/3.29 ( ( nonemptyI ) => 10.84/3.29 ( ( nonemptyI1 ) => 10.84/3.29 ( ( setadjoinIL ) => 10.84/3.29 ( ( emptyinunitempty ) => 10.84/3.29 ( ( setadjoinIR ) => 10.84/3.29 ( ( 10.84/3.29 setadjoinE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoinOr ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setoftrueEq ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptyinPowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptyInPowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subPowSU ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuE2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 nonemptyImpWitness ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 uniqinunit ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notinsingleton ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 eqinunit ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletonsswitch ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairsetE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairsetIL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairsetIR ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptyE1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 vacuousDall ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 quantDeMorgan1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 quantDeMorgan2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 quantDeMorgan3 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 quantDeMorgan4 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 prop2setI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 prop2set2propI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notdexE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notdallE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuI3 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuI2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 inCongP ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 in__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuE3u ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exu__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptyset__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoin__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powerset__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunion__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 omega__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 exuEu ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 descr__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 dsetconstr__Cong ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 eqimpsubset2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 eqimpsubset1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetI2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 emptysetsubset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetE2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notsubsetI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notequalI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 notequalI2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetRefl ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetTrans ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoinSub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoinSub2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subset2powerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setextsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 subsetemptysetimpeq ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetE1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 inPowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 powersetsubset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 sepInPowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 sepSubset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionIL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairset2IR ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionIR ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionEcases ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionLsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binunionRsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset5 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectEL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectLsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset3 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectER ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 disjointsetsI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectRsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset4 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 binintersectSubset1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 bs114d ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusI ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusEL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusER ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusSubset2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusERneg ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusELneg ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusILneg ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusIRneg ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusLsub ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setminusSubset1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffE ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffI1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffI2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffIneg1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 symdiffIneg2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 secondinupair ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairIL ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairIR ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X4:$i, 10.84/3.29 X6:$i]: 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X8:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X10:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X4 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X4 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X6 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) = 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X8 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X8 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X10 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X10 @ 10.84/3.29 ( 10.84/3.29 setunion 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X4 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X4 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X6 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X8 @ 10.84/3.29 ( 10.84/3.29 setunion 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X4 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X4 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X6 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) ) ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X12:$i, 10.84/3.29 X14:$i]: 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X16:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X18:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X12 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X12 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X14 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) = 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X16 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X16 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X18 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X18 @ 10.84/3.29 ( 10.84/3.29 setunion 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X12 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X12 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X14 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X16 @ 10.84/3.29 ( 10.84/3.29 setunion 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X12 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X12 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X14 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) ) ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletonsubset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletoninpowerset ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletoninpowunion ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairset2E ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairsubunion ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairinpowunion ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ubforcartprodlem1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ubforcartprodlem2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X20:$i, 10.84/3.29 X22:$i, 10.84/3.29 X24:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X24 @ X20 ) => 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X26:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X26 @ X22 ) => 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X24 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X24 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X26 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 ( 10.84/3.29 powerset 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 powerset 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 binunion 10.84/3.29 @ 10.84/3.29 X20 @ X22 ) ) ) ) ) ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 cartprodpairin ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 cartprodmempair1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 cartprodmempair ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionE2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionsingleton1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionsingleton2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setunionsingleton ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletonprop ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ex1E1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ex1I ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ex1I2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 singletonsuniq ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjL1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X28:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X30:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ?[ 10.84/3.29 X32:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 X28 ) = 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X30 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X30 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X32 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X32 @ 10.84/3.29 ( 10.84/3.29 setunion 10.84/3.29 @ 10.84/3.29 X28 ) ) ) ) & 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X30 @ 10.84/3.29 ( 10.84/3.29 setunion 10.84/3.29 @ 10.84/3.29 X28 ) ) ) ) => 10.84/3.29 ( 10.84/3.29 singleton 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 dsetconstr 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setunion 10.84/3.29 @ 10.84/3.29 X28 ) @ 10.84/3.29 ( 10.84/3.29 ^[ 10.84/3.29 V_1:$i]: 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 V_1 @ 10.84/3.29 emptyset ) @ 10.84/3.29 X28 ) ) ) ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 theprop ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X34:$i, 10.84/3.29 X36:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 kfst @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X34 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X34 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X36 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) = 10.84/3.29 ( 10.84/3.29 X34 ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X38:$i, 10.84/3.29 X40:$i, 10.84/3.29 X42:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 X42 @ 10.84/3.29 ( 10.84/3.29 cartprod 10.84/3.29 @ 10.84/3.29 X38 @ X40 ) ) => 10.84/3.29 ( 10.84/3.29 in @ 10.84/3.29 ( 10.84/3.29 kfst @ 10.84/3.29 X42 ) @ 10.84/3.29 X38 ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjL2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X44:$i, 10.84/3.29 X46:$i, 10.84/3.29 X48:$i, 10.84/3.29 X50:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X44 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X44 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X46 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) = 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X48 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X48 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X50 @ 10.84/3.29 emptyset ) ) @ 10.84/3.29 emptyset ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 X44 ) = 10.84/3.29 ( 10.84/3.29 X48 ) ) ) ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjR11 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjR12 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjR1 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 upairequniteq ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setukpairinjR2 ) => 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ![ 10.84/3.29 X52:$i, 10.84/3.29 X54:$i, 10.84/3.29 X56:$i, 10.84/3.29 X58:$i]: 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X52 @ 10.84/3.29 emptyset ) @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.29 @ 10.84/3.29 X52 @ 10.84/3.29 ( 10.84/3.29 setadjoin 10.84/3.30 @ 10.84/3.30 X54 @ 10.84/3.30 emptyset ) ) @ 10.84/3.30 emptyset ) ) = 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 X56 @ 10.84/3.30 emptyset ) @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 X56 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 X58 @ 10.84/3.30 emptyset ) ) @ 10.84/3.30 emptyset ) ) ) => 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 X54 ) = 10.84/3.30 ( 10.84/3.30 X58 ) ) ) ) => 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 ![ 10.84/3.30 X60:$i]: 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 ?[ 10.84/3.30 X62:$i]: 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 ?[ 10.84/3.30 X64:$i]: 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 X60 ) = 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 X62 @ 10.84/3.30 emptyset ) @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 X62 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 X64 @ 10.84/3.30 emptyset ) ) @ 10.84/3.30 emptyset ) ) ) & 10.84/3.30 ( 10.84/3.30 in @ 10.84/3.30 X64 @ 10.84/3.30 ( 10.84/3.30 setunion 10.84/3.30 @ 10.84/3.30 X60 ) ) ) ) & 10.84/3.30 ( 10.84/3.30 in @ 10.84/3.30 X62 @ 10.84/3.30 ( 10.84/3.30 setunion 10.84/3.30 @ 10.84/3.30 X60 ) ) ) ) => 10.84/3.30 ( 10.84/3.30 singleton 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 dsetconstr 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 setunion 10.84/3.30 @ 10.84/3.30 X60 ) @ 10.84/3.30 ( 10.84/3.30 ^[ 10.84/3.30 V_2:$i]: 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 X60 ) = 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 kfst @ 10.84/3.30 X60 ) @ 10.84/3.30 emptyset ) @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 kfst @ 10.84/3.30 X60 ) @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 V_2 @ 10.84/3.30 emptyset ) ) @ 10.84/3.30 emptyset ) ) ) ) ) ) ) ) => 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 ![ 10.84/3.30 X66:$i, 10.84/3.30 X68:$i]: 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 ksnd @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 X66 @ 10.84/3.30 emptyset ) @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 X66 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 X68 @ 10.84/3.30 emptyset ) ) @ 10.84/3.30 emptyset ) ) ) = 10.84/3.30 ( 10.84/3.30 X68 ) ) ) => 10.84/3.30 ( 10.84/3.30 ![ 10.84/3.30 X70:$i]: 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 ?[ 10.84/3.30 X72:$i]: 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 ?[ 10.84/3.30 X74:$i]: 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 X70 ) = 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 X72 @ 10.84/3.30 emptyset ) @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 X72 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 X74 @ 10.84/3.30 emptyset ) ) @ 10.84/3.30 emptyset ) ) ) & 10.84/3.30 ( 10.84/3.30 in @ 10.84/3.30 X74 @ 10.84/3.30 ( 10.84/3.30 setunion 10.84/3.30 @ 10.84/3.30 X70 ) ) ) ) & 10.84/3.30 ( 10.84/3.30 in @ 10.84/3.30 X72 @ 10.84/3.30 ( 10.84/3.30 setunion 10.84/3.30 @ 10.84/3.30 X70 ) ) ) ) => 10.84/3.30 ( 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 kfst @ 10.84/3.30 X70 ) @ 10.84/3.30 emptyset ) @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 kfst @ 10.84/3.30 X70 ) @ 10.84/3.30 ( 10.84/3.30 setadjoin 10.84/3.30 @ 10.84/3.30 ( 10.84/3.30 ksnd @ 10.84/3.30 X70 ) @ 10.84/3.30 emptyset ) ) @ 10.84/3.30 emptyset ) ) = 10.84/3.30 ( 10.84/3.30 X70 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 10.84/3.30 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 10.84/3.30 thf(zip_derived_cl89, plain, 10.84/3.30 (((setadjoin @ (setadjoin @ (kfst @ sk__29) @ emptyset) @ 10.84/3.30 (setadjoin @ 10.84/3.30 (setadjoin @ (kfst @ sk__29) @ 10.84/3.30 (setadjoin @ (ksnd @ sk__29) @ emptyset)) @ 10.84/3.30 emptyset)) 10.84/3.30 != (sk__29))), 10.84/3.30 inference('cnf', [status(esa)], [zf_stmt_1])). 10.84/3.30 thf(zip_derived_cl91, plain, 10.84/3.30 (((sk__29) 10.84/3.30 = (setadjoin @ (setadjoin @ sk__30 @ emptyset) @ 10.84/3.30 (setadjoin @ 10.84/3.30 (setadjoin @ sk__30 @ (setadjoin @ sk__31 @ emptyset)) @ emptyset)))), 10.84/3.30 inference('cnf', [status(esa)], [zf_stmt_1])). 10.84/3.30 thf(zip_derived_cl88, plain, 10.84/3.30 (![X13 : $i, X14 : $i]: 10.84/3.30 ((ksnd @ 10.84/3.30 (setadjoin @ (setadjoin @ X14 @ emptyset) @ 10.84/3.30 (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X13 @ emptyset)) @ 10.84/3.30 emptyset))) 10.84/3.30 = (X13))), 10.84/3.30 inference('cnf', [status(esa)], [zf_stmt_1])). 10.84/3.30 thf(zip_derived_cl1246, plain, (((ksnd @ sk__29) = (sk__31))), 10.84/3.30 inference('sup+', [status(thm)], [zip_derived_cl91, zip_derived_cl88])). 10.84/3.30 thf(zip_derived_cl1376, plain, 10.84/3.30 (((setadjoin @ (setadjoin @ (kfst @ sk__29) @ emptyset) @ 10.84/3.30 (setadjoin @ 10.84/3.30 (setadjoin @ (kfst @ sk__29) @ (setadjoin @ sk__31 @ emptyset)) @ 10.84/3.30 emptyset)) 10.84/3.30 != (sk__29))), 10.84/3.30 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl1246])). 10.84/3.30 thf(zip_derived_cl91, plain, 10.84/3.30 (((sk__29) 10.84/3.30 = (setadjoin @ (setadjoin @ sk__30 @ emptyset) @ 10.84/3.30 (setadjoin @ 10.84/3.30 (setadjoin @ sk__30 @ (setadjoin @ sk__31 @ emptyset)) @ emptyset)))), 10.84/3.30 inference('cnf', [status(esa)], [zf_stmt_1])). 10.84/3.30 thf(zip_derived_cl98, plain, 10.84/3.30 (![X18 : $i, X19 : $i]: 10.84/3.30 ((kfst @ 10.84/3.30 (setadjoin @ (setadjoin @ X18 @ emptyset) @ 10.84/3.30 (setadjoin @ (setadjoin @ X18 @ (setadjoin @ X19 @ emptyset)) @ 10.84/3.30 emptyset))) 10.84/3.30 = (X18))), 10.84/3.30 inference('cnf', [status(esa)], [zf_stmt_1])). 10.84/3.30 thf(zip_derived_cl1369, plain, (((kfst @ sk__29) = (sk__30))), 10.84/3.30 inference('sup+', [status(thm)], [zip_derived_cl91, zip_derived_cl98])). 10.84/3.30 thf(zip_derived_cl1369, plain, (((kfst @ sk__29) = (sk__30))), 10.84/3.30 inference('sup+', [status(thm)], [zip_derived_cl91, zip_derived_cl98])). 10.84/3.30 thf(zip_derived_cl91, plain, 10.84/3.30 (((sk__29) 10.84/3.30 = (setadjoin @ (setadjoin @ sk__30 @ emptyset) @ 10.84/3.30 (setadjoin @ 10.84/3.30 (setadjoin @ sk__30 @ (setadjoin @ sk__31 @ emptyset)) @ emptyset)))), 10.84/3.30 inference('cnf', [status(esa)], [zf_stmt_1])). 10.84/3.30 thf(zip_derived_cl1402, plain, (((sk__29) != (sk__29))), 10.84/3.30 inference('demod', [status(thm)], 10.84/3.30 [zip_derived_cl1376, zip_derived_cl1369, zip_derived_cl1369, 10.84/3.30 zip_derived_cl91])). 10.84/3.30 thf(zip_derived_cl1403, plain, ($false), 10.84/3.30 inference('simplify', [status(thm)], [zip_derived_cl1402])). 10.84/3.30 10.84/3.30 % SZS output end Refutation 10.84/3.30 10.84/3.30 10.84/3.30 % Terminating... 11.21/3.46 % Runner terminated. 11.25/3.49 % Zipperpin 1.5 exiting 11.25/3.51 EOF