0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.8TTXTktj4e true 0.12/0.33 % Computer : n032.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1440 0.12/0.33 % WCLimit : 180 0.12/0.33 % DateTime : Thu Jul 4 04:34:09 EDT 2024 0.12/0.33 % CPUTime : 0.12/0.33 % Running portfolio for 1440 s 0.12/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.12/0.33 % Number of cores: 8 0.12/0.33 % Python version: Python 3.6.8 0.12/0.33 % Running in HO mode 0.18/0.58 % Total configuration time : 828 0.18/0.58 % Estimated wc time : 1656 0.18/0.58 % Estimated cpu time (8 cpus) : 207.0 0.18/0.63 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.18/0.64 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.18/0.65 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.18/0.66 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.18/0.66 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.18/0.66 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.18/0.67 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.18/0.67 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 1.62/0.79 % Solved by lams/40_c_ic.sh. 1.62/0.79 % done 134 iterations in 0.081s 1.62/0.79 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 1.62/0.79 % SZS output start Refutation 1.62/0.79 thf(setadjoinAx_type, type, setadjoinAx: $o). 1.62/0.79 thf(notdexE_type, type, notdexE: $o). 1.62/0.79 thf(setunionAx_type, type, setunionAx: $o). 1.62/0.79 thf(setminusELneg_type, type, setminusELneg: $o). 1.62/0.79 thf(powersetE_type, type, powersetE: $o). 1.62/0.79 thf(omegaSAx_type, type, omegaSAx: $o). 1.62/0.79 thf(exuI1_type, type, exuI1: $o). 1.62/0.79 thf(exuI2_type, type, exuI2: $o). 1.62/0.79 thf(notequalI2_type, type, notequalI2: $o). 1.62/0.79 thf(powerset__Cong_type, type, powerset__Cong: $o). 1.62/0.79 thf(setminusILneg_type, type, setminusILneg: $o). 1.62/0.79 thf(wellorderingAx_type, type, wellorderingAx: $o). 1.62/0.79 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 1.62/0.79 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 1.62/0.79 thf(setoftrueEq_type, type, setoftrueEq: $o). 1.62/0.79 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 1.62/0.79 thf(sepInPowerset_type, type, sepInPowerset: $o). 1.62/0.79 thf(binunionE_type, type, binunionE: $o). 1.62/0.79 thf(setext_type, type, setext: $o). 1.62/0.79 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 1.62/0.79 thf(descr__Cong_type, type, descr__Cong: $o). 1.62/0.79 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 1.62/0.79 thf(in_type, type, in: $i > $i > $o). 1.62/0.79 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 1.62/0.79 thf(setadjoinIR_type, type, setadjoinIR: $o). 1.62/0.79 thf(sk__55_type, type, sk__55: $i). 1.62/0.79 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 1.62/0.79 thf(symdiffI2_type, type, symdiffI2: $o). 1.62/0.79 thf(upairset2IR_type, type, upairset2IR: $o). 1.62/0.79 thf(subsetE_type, type, subsetE: $o). 1.62/0.79 thf(prop2set2propI_type, type, prop2set2propI: $o). 1.62/0.79 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 1.62/0.79 thf(setbeta_type, type, setbeta: $o). 1.62/0.79 thf(eqinunit_type, type, eqinunit: $o). 1.62/0.79 thf(upairsetIL_type, type, upairsetIL: $o). 1.62/0.79 thf(powersetI1_type, type, powersetI1: $o). 1.62/0.79 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 1.62/0.79 thf(setminusIRneg_type, type, setminusIRneg: $o). 1.62/0.79 thf(powersetAx_type, type, powersetAx: $o). 1.62/0.79 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 1.62/0.79 thf(powersetI_type, type, powersetI: $o). 1.62/0.79 thf(upairsetIR_type, type, upairsetIR: $o). 1.62/0.79 thf(inCongP_type, type, inCongP: $o). 1.62/0.79 thf(setadjoinSub_type, type, setadjoinSub: $o). 1.62/0.79 thf(exuE3e_type, type, exuE3e: $o). 1.62/0.79 thf(emptysetE_type, type, emptysetE: $o). 1.62/0.79 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 1.62/0.79 thf(setunionI_type, type, setunionI: $o). 1.62/0.79 thf(setunion__Cong_type, type, setunion__Cong: $o). 1.62/0.79 thf(prop2setI_type, type, prop2setI: $o). 1.62/0.79 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 1.62/0.79 thf(setminusER_type, type, setminusER: $o). 1.62/0.79 thf(exuE2_type, type, exuE2: $o). 1.62/0.79 thf(emptyset_type, type, emptyset: $i). 1.62/0.79 thf(powersetsubset_type, type, powersetsubset: $o). 1.62/0.79 thf(subPowSU_type, type, subPowSU: $o). 1.62/0.79 thf(notequalI1_type, type, notequalI1: $o). 1.62/0.79 thf(notinemptyset_type, type, notinemptyset: $o). 1.62/0.79 thf(nonemptyI1_type, type, nonemptyI1: $o). 1.62/0.79 thf(subsetTrans_type, type, subsetTrans: $o). 1.62/0.79 thf(setminusI_type, type, setminusI: $o). 1.62/0.79 thf(binunionIL_type, type, binunionIL: $o). 1.62/0.79 thf(subsetE2_type, type, subsetE2: $o). 1.62/0.79 thf(singletonsswitch_type, type, singletonsswitch: $o). 1.62/0.79 thf(setextsub_type, type, setextsub: $o). 1.62/0.79 thf(binunionLsub_type, type, binunionLsub: $o). 1.62/0.79 thf(emptysetsubset_type, type, emptysetsubset: $o). 1.62/0.79 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 1.62/0.79 thf(setunionE_type, type, setunionE: $o). 1.62/0.79 thf(setminusSubset1_type, type, setminusSubset1: $o). 1.62/0.79 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 1.62/0.79 thf(binunionIR_type, type, binunionIR: $o). 1.62/0.79 thf(setadjoinE_type, type, setadjoinE: $o). 1.62/0.79 thf(setadjoinIL_type, type, setadjoinIL: $o). 1.62/0.79 thf(sk__56_type, type, sk__56: $i). 1.62/0.79 thf(exuE1_type, type, exuE1: $o). 1.62/0.79 thf(binintersectRsub_type, type, binintersectRsub: $o). 1.62/0.79 thf(setminusLsub_type, type, setminusLsub: $o). 1.62/0.79 thf(notinsingleton_type, type, notinsingleton: $o). 1.62/0.79 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 1.62/0.79 thf(exuEu_type, type, exuEu: $o). 1.62/0.79 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 1.62/0.79 thf(upairsetE_type, type, upairsetE: $o). 1.62/0.79 thf(omega0Ax_type, type, omega0Ax: $o). 1.62/0.79 thf(notsubsetI_type, type, notsubsetI: $o). 1.62/0.79 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 1.62/0.79 thf(setextAx_type, type, setextAx: $o). 1.62/0.79 thf(powersetE1_type, type, powersetE1: $o). 1.62/0.79 thf(bs114d_type, type, bs114d: $o). 1.62/0.79 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 1.62/0.79 thf(binintersectLsub_type, type, binintersectLsub: $o). 1.62/0.79 thf(subsetI1_type, type, subsetI1: $o). 1.62/0.79 thf(symdiffE_type, type, symdiffE: $o). 1.62/0.79 thf(descrp_type, type, descrp: $o). 1.62/0.79 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 1.62/0.79 thf(foundationAx_type, type, foundationAx: $o). 1.62/0.79 thf(emptysetAx_type, type, emptysetAx: $o). 1.62/0.79 thf(emptyI_type, type, emptyI: $o). 1.62/0.79 thf(setadjoinOr_type, type, setadjoinOr: $o). 1.62/0.79 thf(binintersectEL_type, type, binintersectEL: $o). 1.62/0.79 thf(emptyE1_type, type, emptyE1: $o). 1.62/0.79 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 1.62/0.79 thf(vacuousDall_type, type, vacuousDall: $o). 1.62/0.79 thf(dsetconstrER_type, type, dsetconstrER: $o). 1.62/0.79 thf(binintersectI_type, type, binintersectI: $o). 1.62/0.79 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o). 1.62/0.79 thf(symdiffI1_type, type, symdiffI1: $o). 1.62/0.79 thf(subsetI2_type, type, subsetI2: $o). 1.62/0.79 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 1.62/0.79 thf(setminusERneg_type, type, setminusERneg: $o). 1.62/0.79 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 1.62/0.79 thf(omega__Cong_type, type, omega__Cong: $o). 1.62/0.79 thf(subsetRefl_type, type, subsetRefl: $o). 1.62/0.79 thf(uniqinunit_type, type, uniqinunit: $o). 1.62/0.79 thf(setminusSubset2_type, type, setminusSubset2: $o). 1.62/0.79 thf(prop2setE_type, type, prop2setE: $o). 1.62/0.79 thf(binunionEcases_type, type, binunionEcases: $o). 1.62/0.79 thf(nonemptyI_type, type, nonemptyI: $o). 1.62/0.79 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 1.62/0.79 thf(exuE3u_type, type, exuE3u: $o). 1.62/0.79 thf(setminusEL_type, type, setminusEL: $o). 1.62/0.79 thf(sepSubset_type, type, sepSubset: $o). 1.62/0.79 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 1.62/0.79 thf(exuI3_type, type, exuI3: $o). 1.62/0.79 thf(notdallE_type, type, notdallE: $o). 1.62/0.79 thf(binintersectER_type, type, binintersectER: $o). 1.62/0.79 thf(dsetconstrI_type, type, dsetconstrI: $o). 1.62/0.79 thf(setadjoin_type, type, setadjoin: $i > $i > $i). 1.62/0.79 thf(exu__Cong_type, type, exu__Cong: $o). 1.62/0.79 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 1.62/0.79 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 1.62/0.79 thf(replAx_type, type, replAx: $o). 1.62/0.79 thf(nonemptyE1_type, type, nonemptyE1: $o). 1.62/0.79 thf(omegaIndAx_type, type, omegaIndAx: $o). 1.62/0.79 thf(inPowerset_type, type, inPowerset: $o). 1.62/0.79 thf(subset_type, type, subset: $i > $i > $o). 1.62/0.79 thf(in__Cong_type, type, in__Cong: $o). 1.62/0.79 thf(binunionRsub_type, type, binunionRsub: $o). 1.62/0.79 thf(subset2powerset_type, type, subset2powerset: $o). 1.62/0.79 thf(upairset2IR, axiom, upairset2IR = 1.62/0.79 (![Xx:$i,Xy:$i]: 1.62/0.79 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 1.62/0.79 thf('0', plain, 1.62/0.79 (( upairset2IR ) = 1.62/0.79 ( ![X4:$i,X6:$i]: 1.62/0.79 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq = 1.62/0.79 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))). 1.62/0.79 thf('1', plain, 1.62/0.79 (( subsetemptysetimpeq ) = 1.62/0.79 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(setadjoinSub2, axiom, setadjoinSub2 = 1.62/0.79 (![A:$i,Xx:$i,B:$i]: 1.62/0.79 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))). 1.62/0.79 thf('2', plain, 1.62/0.79 (( setadjoinSub2 ) = 1.62/0.79 ( ![X4:$i,X6:$i,X8:$i]: 1.62/0.79 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(setadjoinSub, axiom, setadjoinSub = 1.62/0.79 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))). 1.62/0.79 thf('3', plain, 1.62/0.79 (( setadjoinSub ) = 1.62/0.79 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(emptysetsubset, axiom, emptysetsubset = 1.62/0.79 (![A:$i]: ( subset @ emptyset @ A ))). 1.62/0.79 thf('4', plain, 1.62/0.79 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(setadjoin__Cong, axiom, setadjoin__Cong = 1.62/0.79 (![Xx:$i,Xy:$i]: 1.62/0.79 ( ( ( Xx ) = ( Xy ) ) => 1.62/0.79 ( ![Xz:$i,Xu:$i]: 1.62/0.79 ( ( ( Xz ) = ( Xu ) ) => 1.62/0.79 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))). 1.62/0.79 thf('5', plain, 1.62/0.79 (( setadjoin__Cong ) = 1.62/0.79 ( ![X4:$i,X6:$i]: 1.62/0.79 ( ( ( X4 ) = ( X6 ) ) => 1.62/0.79 ( ![X8:$i,X10:$i]: 1.62/0.79 ( ( ( X8 ) = ( X10 ) ) => 1.62/0.79 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(emptyset__Cong, axiom, emptyset__Cong = (( emptyset ) = ( emptyset ))). 1.62/0.79 thf('6', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(vacuousDall, axiom, vacuousDall = 1.62/0.79 (![Xphi:( $i > $o ),Xx:$i]: ( ( in @ Xx @ emptyset ) => ( Xphi @ Xx ) ))). 1.62/0.79 thf('7', plain, 1.62/0.79 (( vacuousDall ) = 1.62/0.79 ( ![X4:( $i > $o ),X6:$i]: ( ( in @ X6 @ emptyset ) => ( X4 @ X6 ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(upairsetIR, axiom, upairsetIR = 1.62/0.79 (![Xx:$i,Xy:$i]: 1.62/0.79 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 1.62/0.79 thf('8', plain, 1.62/0.79 (( upairsetIR ) = 1.62/0.79 ( ![X4:$i,X6:$i]: 1.62/0.79 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(upairsetIL, axiom, upairsetIL = 1.62/0.79 (![Xx:$i,Xy:$i]: 1.62/0.79 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 1.62/0.79 thf('9', plain, 1.62/0.79 (( upairsetIL ) = 1.62/0.79 ( ![X4:$i,X6:$i]: 1.62/0.79 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(upairsetE, axiom, upairsetE = 1.62/0.79 (![Xx:$i,Xy:$i,Xz:$i]: 1.62/0.79 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) => 1.62/0.79 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))). 1.62/0.79 thf('10', plain, 1.62/0.79 (( upairsetE ) = 1.62/0.79 ( ![X4:$i,X6:$i,X8:$i]: 1.62/0.79 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) => 1.62/0.79 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(singletonsswitch, axiom, singletonsswitch = 1.62/0.79 (![Xx:$i,Xy:$i]: 1.62/0.79 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => 1.62/0.79 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))). 1.62/0.79 thf('11', plain, 1.62/0.79 (( singletonsswitch ) = 1.62/0.79 ( ![X4:$i,X6:$i]: 1.62/0.79 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => 1.62/0.79 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(eqinunit, axiom, eqinunit = 1.62/0.79 (![Xx:$i,Xy:$i]: 1.62/0.79 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))). 1.62/0.79 thf('12', plain, 1.62/0.79 (( eqinunit ) = 1.62/0.79 ( ![X4:$i,X6:$i]: 1.62/0.79 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(notinsingleton, axiom, notinsingleton = 1.62/0.79 (![Xx:$i,Xy:$i]: 1.62/0.79 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))). 1.62/0.79 thf('13', plain, 1.62/0.79 (( notinsingleton ) = 1.62/0.79 ( ![X4:$i,X6:$i]: 1.62/0.79 ( ( ( X4 ) != ( X6 ) ) => 1.62/0.79 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(uniqinunit, axiom, uniqinunit = 1.62/0.79 (![Xx:$i,Xy:$i]: 1.62/0.79 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))). 1.62/0.79 thf('14', plain, 1.62/0.79 (( uniqinunit ) = 1.62/0.79 ( ![X4:$i,X6:$i]: 1.62/0.79 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(setadjoinOr, axiom, setadjoinOr = 1.62/0.79 (![Xx:$i,A:$i,Xy:$i]: 1.62/0.79 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) => 1.62/0.79 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))). 1.62/0.79 thf('15', plain, 1.62/0.79 (( setadjoinOr ) = 1.62/0.79 ( ![X4:$i,X6:$i,X8:$i]: 1.62/0.79 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) => 1.62/0.79 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(setadjoinE, axiom, setadjoinE = 1.62/0.79 (![Xx:$i,A:$i,Xy:$i]: 1.62/0.79 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) => 1.62/0.79 ( ![Xphi:$o]: 1.62/0.79 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) => 1.62/0.79 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))). 1.62/0.79 thf('16', plain, 1.62/0.79 (( setadjoinE ) = 1.62/0.79 ( ![X4:$i,X6:$i,X8:$i]: 1.62/0.79 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) => 1.62/0.79 ( ![X10:$o]: 1.62/0.79 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) => 1.62/0.79 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(setadjoinIR, axiom, setadjoinIR = 1.62/0.79 (![Xx:$i,A:$i,Xy:$i]: 1.62/0.79 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))). 1.62/0.79 thf('17', plain, 1.62/0.79 (( setadjoinIR ) = 1.62/0.79 ( ![X4:$i,X6:$i,X8:$i]: 1.62/0.79 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(emptyinunitempty, axiom,(( emptyinunitempty ) = 1.62/0.79 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))). 1.62/0.79 thf('18', plain, 1.62/0.79 (( emptyinunitempty ) = 1.62/0.79 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )), 1.62/0.79 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])). 1.62/0.79 thf('19', plain, 1.62/0.79 (( emptyinunitempty ) = 1.62/0.79 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(setadjoinIL, axiom, setadjoinIL = 1.62/0.79 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))). 1.62/0.79 thf('20', plain, 1.62/0.79 (( setadjoinIL ) = 1.62/0.79 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(noeltsimpempty, axiom, noeltsimpempty = 1.62/0.79 (![A:$i]: 1.62/0.79 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))). 1.62/0.79 thf('21', plain, 1.62/0.79 (( noeltsimpempty ) = 1.62/0.79 ( ![X4:$i]: 1.62/0.79 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(emptyI, axiom, emptyI = 1.62/0.79 (![A:$i]: 1.62/0.79 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))). 1.62/0.79 thf('22', plain, 1.62/0.79 (( emptyI ) = 1.62/0.79 ( ![X4:$i]: 1.62/0.79 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(notinemptyset, axiom, notinemptyset = 1.62/0.79 (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))). 1.62/0.79 thf('23', plain, 1.62/0.79 (( notinemptyset ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(emptysetimpfalse, axiom, emptysetimpfalse = 1.62/0.79 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( $false ) ))). 1.62/0.79 thf('24', plain, 1.62/0.79 (( emptysetimpfalse ) = 1.62/0.79 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( $false ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(emptysetE, axiom, emptysetE = 1.62/0.79 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( ![Xphi:$o]: ( Xphi ) ) ))). 1.62/0.79 thf('25', plain, 1.62/0.79 (( emptysetE ) = 1.62/0.79 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( ![X6:$o]: ( X6 ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(setadjoinAx, axiom, setadjoinAx = 1.62/0.79 (![Xx:$i,A:$i,Xy:$i]: 1.62/0.79 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=> 1.62/0.79 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))). 1.62/0.79 thf('26', plain, 1.62/0.79 (( setadjoinAx ) = 1.62/0.79 ( ![X4:$i,X6:$i,X8:$i]: 1.62/0.79 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=> 1.62/0.79 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))). 1.62/0.79 thf('27', plain, 1.62/0.79 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )), 1.62/0.79 define([status(thm)])). 1.62/0.79 thf(secondinupair, conjecture, 1.62/0.79 (( setextAx ) => 1.62/0.79 ( ( emptysetAx ) => 1.62/0.79 ( ( setadjoinAx ) => 1.62/0.79 ( ( powersetAx ) => 1.62/0.79 ( ( setunionAx ) => 1.62/0.79 ( ( omega0Ax ) => 1.62/0.79 ( ( omegaSAx ) => 1.62/0.79 ( ( omegaIndAx ) => 1.62/0.79 ( ( replAx ) => 1.62/0.79 ( ( foundationAx ) => 1.62/0.79 ( ( wellorderingAx ) => 1.62/0.79 ( ( descrp ) => 1.62/0.79 ( ( dsetconstrI ) => 1.62/0.79 ( ( dsetconstrEL ) => 1.62/0.79 ( ( dsetconstrER ) => 1.62/0.79 ( ( exuE1 ) => 1.62/0.79 ( ( prop2setE ) => 1.62/0.79 ( ( emptysetE ) => 1.62/0.79 ( ( emptysetimpfalse ) => 1.62/0.79 ( ( notinemptyset ) => 1.62/0.79 ( ( exuE3e ) => 1.62/0.79 ( ( setext ) => 1.62/0.79 ( ( emptyI ) => 1.62/0.79 ( ( noeltsimpempty ) => 1.62/0.79 ( ( setbeta ) => 1.62/0.79 ( ( nonemptyE1 ) => 1.62/0.79 ( ( nonemptyI ) => 1.62/0.79 ( ( nonemptyI1 ) => 1.62/0.79 ( ( setadjoinIL ) => 1.62/0.79 ( ( emptyinunitempty ) => 1.62/0.79 ( ( setadjoinIR ) => 1.62/0.79 ( ( setadjoinE ) => 1.62/0.79 ( ( 1.62/0.79 setadjoinOr ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setoftrueEq ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyinPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyInPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setunionI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setunionE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subPowSU ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuE2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 nonemptyImpWitness ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 uniqinunit ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notinsingleton ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 eqinunit ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 singletonsswitch ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 upairsetE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 upairsetIL ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 upairsetIR ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyE1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 vacuousDall ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan3 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan4 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 prop2setI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 prop2set2propI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notdexE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notdallE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuI3 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 inCongP ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuE3u ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exu__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyset__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setadjoin__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powerset__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setunion__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 omega__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuEu ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 descr__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 dsetconstr__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 eqimpsubset2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 eqimpsubset1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptysetsubset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetE2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notsubsetI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notequalI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notequalI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetRefl ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetTrans ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setadjoinSub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setadjoinSub2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subset2powerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setextsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetemptysetimpeq ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetE1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 inPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetsubset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 sepInPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 sepSubset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionIL ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 upairset2IR ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionIR ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionEcases ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionLsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionRsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset5 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectEL ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectLsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset3 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectER ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 disjointsetsI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectRsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset4 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 bs114d ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusEL ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusER ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusSubset2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusERneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusELneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusILneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusIRneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusLsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusSubset1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffIneg1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffIneg2 ) => 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 Xx:$i, 1.62/0.79 Xy:$i]: 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 Xy @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 Xx @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 Xy @ 1.62/0.79 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 1.62/0.79 thf(zf_stmt_0, conjecture, 1.62/0.79 (( setextAx ) => 1.62/0.79 ( ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) ) => 1.62/0.79 ( ( ![X6:$i,X8:$i,X10:$i]: 1.62/0.79 ( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) ) <=> 1.62/0.79 ( ( in @ X10 @ X8 ) | ( ( X10 ) = ( X6 ) ) ) ) ) => 1.62/0.79 ( ( powersetAx ) => 1.62/0.79 ( ( setunionAx ) => 1.62/0.79 ( ( omega0Ax ) => 1.62/0.79 ( ( omegaSAx ) => 1.62/0.79 ( ( omegaIndAx ) => 1.62/0.79 ( ( replAx ) => 1.62/0.79 ( ( foundationAx ) => 1.62/0.79 ( ( wellorderingAx ) => 1.62/0.79 ( ( descrp ) => 1.62/0.79 ( ( dsetconstrI ) => 1.62/0.79 ( ( dsetconstrEL ) => 1.62/0.79 ( ( dsetconstrER ) => 1.62/0.79 ( ( exuE1 ) => 1.62/0.79 ( ( prop2setE ) => 1.62/0.79 ( ( ![X12:$i]: 1.62/0.79 ( ( in @ X12 @ emptyset ) => 1.62/0.79 ( ![X14:$o]: ( X14 ) ) ) ) => 1.62/0.79 ( ( ![X16:$i]: 1.62/0.79 ( ( in @ X16 @ emptyset ) => 1.62/0.79 ( $false ) ) ) => 1.62/0.79 ( ( ![X18:$i]: 1.62/0.79 ( ~( in @ X18 @ emptyset ) ) ) => 1.62/0.79 ( ( exuE3e ) => 1.62/0.79 ( ( setext ) => 1.62/0.79 ( ( ![X20:$i]: 1.62/0.79 ( ( ![X22:$i]: 1.62/0.79 ( ~( in @ X22 @ X20 ) ) ) => 1.62/0.79 ( ( X20 ) = ( emptyset ) ) ) ) => 1.62/0.79 ( ( ![X24:$i]: 1.62/0.79 ( ( ![X26:$i]: 1.62/0.79 ( ~( in @ X26 @ X24 ) ) ) => 1.62/0.79 ( ( X24 ) = ( emptyset ) ) ) ) => 1.62/0.79 ( ( setbeta ) => 1.62/0.79 ( ( nonemptyE1 ) => 1.62/0.79 ( ( nonemptyI ) => 1.62/0.79 ( ( nonemptyI1 ) => 1.62/0.79 ( ( ![X28:$i,X30:$i]: 1.62/0.79 ( in @ 1.62/0.79 X28 @ 1.62/0.79 ( setadjoin @ 1.62/0.79 X28 @ X30 ) ) ) => 1.62/0.79 ( ( in @ 1.62/0.79 emptyset @ 1.62/0.79 ( setadjoin @ 1.62/0.79 emptyset @ 1.62/0.79 emptyset ) ) => 1.62/0.79 ( ( ![X32:$i, 1.62/0.79 X34:$i, 1.62/0.79 X36:$i]: 1.62/0.79 ( ( 1.62/0.79 in @ 1.62/0.79 X36 @ X34 ) => 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X36 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X32 @ X34 ) ) ) ) => 1.62/0.79 ( ( ![ 1.62/0.79 X38:$i, 1.62/0.79 X40:$i, 1.62/0.79 X42:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X42 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X38 @ X40 ) ) => 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X44:$o]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X42 ) = 1.62/0.79 ( 1.62/0.79 X38 ) ) => 1.62/0.79 ( 1.62/0.79 X44 ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X42 @ X40 ) => 1.62/0.79 ( 1.62/0.79 X44 ) ) => 1.62/0.79 ( 1.62/0.79 X44 ) ) ) ) ) ) => 1.62/0.79 ( ( 1.62/0.79 ![ 1.62/0.79 X46:$i, 1.62/0.79 X48:$i, 1.62/0.79 X50:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X50 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X46 @ X48 ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X50 @ X48 ) | 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X50 ) = 1.62/0.79 ( 1.62/0.79 X46 ) ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setoftrueEq ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyinPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyInPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setunionI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setunionE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subPowSU ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuE2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 nonemptyImpWitness ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X52:$i, 1.62/0.79 X54:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X52 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X54 @ 1.62/0.79 emptyset ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X52 ) = 1.62/0.79 ( 1.62/0.79 X54 ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X56:$i, 1.62/0.79 X58:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X56 ) != 1.62/0.79 ( 1.62/0.79 X58 ) ) => 1.62/0.79 ( 1.62/0.79 ~( 1.62/0.79 in @ 1.62/0.79 X58 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X56 @ 1.62/0.79 emptyset ) ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X60:$i, 1.62/0.79 X62:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X60 ) = 1.62/0.79 ( 1.62/0.79 X62 ) ) => 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X60 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X62 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X64:$i, 1.62/0.79 X66:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X64 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X66 @ 1.62/0.79 emptyset ) ) => 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X66 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X64 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X68:$i, 1.62/0.79 X70:$i, 1.62/0.79 X72:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X72 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X68 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X70 @ 1.62/0.79 emptyset ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X72 ) = 1.62/0.79 ( 1.62/0.79 X70 ) ) | 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X72 ) = 1.62/0.79 ( 1.62/0.79 X68 ) ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X74:$i, 1.62/0.79 X76:$i]: 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X74 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X74 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X76 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X78:$i, 1.62/0.79 X80:$i]: 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X80 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X78 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X80 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyE1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X82:( 1.62/0.79 $i > $o ), 1.62/0.79 X84:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X84 @ 1.62/0.79 emptyset ) => 1.62/0.79 ( 1.62/0.79 X82 @ X84 ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan3 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan4 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 prop2setI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 prop2set2propI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notdexE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notdallE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuI3 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 inCongP ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuE3u ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exu__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyset ) = 1.62/0.79 ( 1.62/0.79 emptyset ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X86:$i, 1.62/0.79 X88:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X86 ) = 1.62/0.79 ( 1.62/0.79 X88 ) ) => 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X90:$i, 1.62/0.79 X92:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X90 ) = 1.62/0.79 ( 1.62/0.79 X92 ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X86 @ X90 ) = 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X88 @ X92 ) ) ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powerset__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setunion__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 omega__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuEu ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 descr__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 dsetconstr__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 eqimpsubset2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 eqimpsubset1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X94:$i]: 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 emptyset @ 1.62/0.79 X94 ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetE2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notsubsetI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notequalI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notequalI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetRefl ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetTrans ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X96:$i, 1.62/0.79 X98:$i]: 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 X98 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X96 @ X98 ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X100:$i, 1.62/0.79 X102:$i, 1.62/0.79 X104:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 X100 @ 1.62/0.79 X104 ) => 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 X100 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X102 @ 1.62/0.79 X104 ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subset2powerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setextsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X106:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 X106 @ 1.62/0.79 emptyset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X106 ) = 1.62/0.79 ( 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetE1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 inPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetsubset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 sepInPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 sepSubset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionIL ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X108:$i, 1.62/0.79 X110:$i]: 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X110 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X108 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X110 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionIR ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionEcases ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionLsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionRsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset5 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectEL ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectLsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset3 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectER ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 disjointsetsI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectRsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset4 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 bs114d ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusEL ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusER ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusSubset2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusERneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusELneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusILneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusIRneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusLsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusSubset1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffIneg1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffIneg2 ) => 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X112:$i, 1.62/0.79 X114:$i]: 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X114 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X112 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X114 @ 1.62/0.79 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 1.62/0.79 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o). 1.62/0.79 thf(zf_stmt_2, axiom, 1.62/0.79 (![X10:$i,X8:$i,X6:$i]: 1.62/0.79 ( ( zip_tseitin_0 @ X10 @ X8 @ X6 ) <=> 1.62/0.79 ( ( ( X10 ) = ( X6 ) ) | ( in @ X10 @ X8 ) ) ))). 1.62/0.79 thf(zf_stmt_3, conjecture, 1.62/0.79 (( setextAx ) => 1.62/0.79 ( ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) ) => 1.62/0.79 ( ( ![X6:$i,X8:$i,X10:$i]: 1.62/0.79 ( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) ) <=> 1.62/0.79 ( zip_tseitin_0 @ X10 @ X8 @ X6 ) ) ) => 1.62/0.79 ( ( powersetAx ) => 1.62/0.79 ( ( setunionAx ) => 1.62/0.79 ( ( omega0Ax ) => 1.62/0.79 ( ( omegaSAx ) => 1.62/0.79 ( ( omegaIndAx ) => 1.62/0.79 ( ( replAx ) => 1.62/0.79 ( ( foundationAx ) => 1.62/0.79 ( ( wellorderingAx ) => 1.62/0.79 ( ( descrp ) => 1.62/0.79 ( ( dsetconstrI ) => 1.62/0.79 ( ( dsetconstrEL ) => 1.62/0.79 ( ( dsetconstrER ) => 1.62/0.79 ( ( exuE1 ) => 1.62/0.79 ( ( prop2setE ) => 1.62/0.79 ( ( ![X12:$i]: 1.62/0.79 ( ( in @ X12 @ emptyset ) => 1.62/0.79 ( ![X14:$o]: ( X14 ) ) ) ) => 1.62/0.79 ( ( ![X16:$i]: 1.62/0.79 ( ~( in @ X16 @ emptyset ) ) ) => 1.62/0.79 ( ( ![X18:$i]: 1.62/0.79 ( ~( in @ X18 @ emptyset ) ) ) => 1.62/0.79 ( ( exuE3e ) => 1.62/0.79 ( ( setext ) => 1.62/0.79 ( ( ![X20:$i]: 1.62/0.79 ( ( ![X22:$i]: 1.62/0.79 ( ~( in @ X22 @ X20 ) ) ) => 1.62/0.79 ( ( X20 ) = ( emptyset ) ) ) ) => 1.62/0.79 ( ( ![X24:$i]: 1.62/0.79 ( ( ![X26:$i]: 1.62/0.79 ( ~( in @ X26 @ X24 ) ) ) => 1.62/0.79 ( ( X24 ) = ( emptyset ) ) ) ) => 1.62/0.79 ( ( setbeta ) => 1.62/0.79 ( ( nonemptyE1 ) => 1.62/0.79 ( ( nonemptyI ) => 1.62/0.79 ( ( nonemptyI1 ) => 1.62/0.79 ( ( ![X28:$i,X30:$i]: 1.62/0.79 ( in @ 1.62/0.79 X28 @ 1.62/0.79 ( setadjoin @ 1.62/0.79 X28 @ X30 ) ) ) => 1.62/0.79 ( ( in @ 1.62/0.79 emptyset @ 1.62/0.79 ( setadjoin @ 1.62/0.79 emptyset @ 1.62/0.79 emptyset ) ) => 1.62/0.79 ( ( ![X32:$i, 1.62/0.79 X34:$i, 1.62/0.79 X36:$i]: 1.62/0.79 ( ( 1.62/0.79 in @ 1.62/0.79 X36 @ X34 ) => 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X36 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X32 @ X34 ) ) ) ) => 1.62/0.79 ( ( ![ 1.62/0.79 X38:$i, 1.62/0.79 X40:$i, 1.62/0.79 X42:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X42 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X38 @ X40 ) ) => 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X44:$o]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X42 ) = 1.62/0.79 ( 1.62/0.79 X38 ) ) => 1.62/0.79 ( 1.62/0.79 X44 ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X42 @ X40 ) => 1.62/0.79 ( 1.62/0.79 X44 ) ) => 1.62/0.79 ( 1.62/0.79 X44 ) ) ) ) ) ) => 1.62/0.79 ( ( 1.62/0.79 ![ 1.62/0.79 X46:$i, 1.62/0.79 X48:$i, 1.62/0.79 X50:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X50 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X46 @ X48 ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X50 ) = 1.62/0.79 ( 1.62/0.79 X46 ) ) | 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X50 @ X48 ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setoftrueEq ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyinPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyInPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setunionI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setunionE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subPowSU ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuE2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 nonemptyImpWitness ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X52:$i, 1.62/0.79 X54:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X52 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X54 @ 1.62/0.79 emptyset ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X52 ) = 1.62/0.79 ( 1.62/0.79 X54 ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X56:$i, 1.62/0.79 X58:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X56 ) != 1.62/0.79 ( 1.62/0.79 X58 ) ) => 1.62/0.79 ( 1.62/0.79 ~( 1.62/0.79 in @ 1.62/0.79 X58 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X56 @ 1.62/0.79 emptyset ) ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X60:$i, 1.62/0.79 X62:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X60 ) = 1.62/0.79 ( 1.62/0.79 X62 ) ) => 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X60 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X62 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X64:$i, 1.62/0.79 X66:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X64 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X66 @ 1.62/0.79 emptyset ) ) => 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X66 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X64 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X68:$i, 1.62/0.79 X70:$i, 1.62/0.79 X72:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X72 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X68 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X70 @ 1.62/0.79 emptyset ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X72 ) = 1.62/0.79 ( 1.62/0.79 X68 ) ) | 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X72 ) = 1.62/0.79 ( 1.62/0.79 X70 ) ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X74:$i, 1.62/0.79 X76:$i]: 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X74 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X74 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X76 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X78:$i, 1.62/0.79 X80:$i]: 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X80 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X78 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X80 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyE1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X82:( 1.62/0.79 $i > $o ), 1.62/0.79 X84:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X84 @ 1.62/0.79 emptyset ) => 1.62/0.79 ( 1.62/0.79 X82 @ X84 ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan3 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan4 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 prop2setI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 prop2set2propI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notdexE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notdallE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuI3 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 inCongP ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuE3u ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exu__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyset ) = 1.62/0.79 ( 1.62/0.79 emptyset ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X86:$i, 1.62/0.79 X88:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X86 ) = 1.62/0.79 ( 1.62/0.79 X88 ) ) => 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X90:$i, 1.62/0.79 X92:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X90 ) = 1.62/0.79 ( 1.62/0.79 X92 ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X86 @ X90 ) = 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X88 @ X92 ) ) ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powerset__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setunion__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 omega__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuEu ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 descr__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 dsetconstr__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 eqimpsubset2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 eqimpsubset1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X94:$i]: 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 emptyset @ 1.62/0.79 X94 ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetE2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notsubsetI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notequalI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notequalI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetRefl ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetTrans ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X96:$i, 1.62/0.79 X98:$i]: 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 X98 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X96 @ X98 ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X100:$i, 1.62/0.79 X102:$i, 1.62/0.79 X104:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 X100 @ 1.62/0.79 X104 ) => 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 X100 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X102 @ 1.62/0.79 X104 ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subset2powerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setextsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X106:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 X106 @ 1.62/0.79 emptyset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X106 ) = 1.62/0.79 ( 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetE1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 inPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetsubset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 sepInPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 sepSubset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionIL ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X108:$i, 1.62/0.79 X110:$i]: 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X110 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X108 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X110 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionIR ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionEcases ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionLsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionRsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset5 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectEL ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectLsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset3 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectER ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 disjointsetsI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectRsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset4 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 bs114d ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusEL ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusER ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusSubset2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusERneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusELneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusILneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusIRneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusLsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusSubset1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffIneg1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffIneg2 ) => 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X112:$i, 1.62/0.79 X114:$i]: 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X114 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X112 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X114 @ 1.62/0.79 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 1.62/0.79 thf(zf_stmt_4, negated_conjecture, 1.62/0.79 (~( ( setextAx ) => 1.62/0.79 ( ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) ) => 1.62/0.79 ( ( ![X6:$i,X8:$i,X10:$i]: 1.62/0.79 ( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) ) <=> 1.62/0.79 ( zip_tseitin_0 @ X10 @ X8 @ X6 ) ) ) => 1.62/0.79 ( ( powersetAx ) => 1.62/0.79 ( ( setunionAx ) => 1.62/0.79 ( ( omega0Ax ) => 1.62/0.79 ( ( omegaSAx ) => 1.62/0.79 ( ( omegaIndAx ) => 1.62/0.79 ( ( replAx ) => 1.62/0.79 ( ( foundationAx ) => 1.62/0.79 ( ( wellorderingAx ) => 1.62/0.79 ( ( descrp ) => 1.62/0.79 ( ( dsetconstrI ) => 1.62/0.79 ( ( dsetconstrEL ) => 1.62/0.79 ( ( dsetconstrER ) => 1.62/0.79 ( ( exuE1 ) => 1.62/0.79 ( ( prop2setE ) => 1.62/0.79 ( ( ![X12:$i]: 1.62/0.79 ( ( in @ X12 @ emptyset ) => 1.62/0.79 ( ![X14:$o]: ( X14 ) ) ) ) => 1.62/0.79 ( ( ![X16:$i]: 1.62/0.79 ( ~( in @ X16 @ emptyset ) ) ) => 1.62/0.79 ( ( ![X18:$i]: 1.62/0.79 ( ~( in @ X18 @ emptyset ) ) ) => 1.62/0.79 ( ( exuE3e ) => 1.62/0.79 ( ( setext ) => 1.62/0.79 ( ( ![X20:$i]: 1.62/0.79 ( ( ![X22:$i]: 1.62/0.79 ( ~( in @ X22 @ X20 ) ) ) => 1.62/0.79 ( ( X20 ) = 1.62/0.79 ( emptyset ) ) ) ) => 1.62/0.79 ( ( ![X24:$i]: 1.62/0.79 ( ( ![X26:$i]: 1.62/0.79 ( ~( in @ X26 @ X24 ) ) ) => 1.62/0.79 ( ( X24 ) = 1.62/0.79 ( emptyset ) ) ) ) => 1.62/0.79 ( ( setbeta ) => 1.62/0.79 ( ( nonemptyE1 ) => 1.62/0.79 ( ( nonemptyI ) => 1.62/0.79 ( ( nonemptyI1 ) => 1.62/0.79 ( ( ![X28:$i, 1.62/0.79 X30:$i]: 1.62/0.79 ( in @ 1.62/0.79 X28 @ 1.62/0.79 ( setadjoin 1.62/0.79 @ 1.62/0.79 X28 @ X30 ) ) ) => 1.62/0.79 ( ( in @ 1.62/0.79 emptyset @ 1.62/0.79 ( setadjoin 1.62/0.79 @ 1.62/0.79 emptyset @ 1.62/0.79 emptyset ) ) => 1.62/0.79 ( ( ![ 1.62/0.79 X32:$i, 1.62/0.79 X34:$i, 1.62/0.79 X36:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X36 @ X34 ) => 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X36 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X32 @ X34 ) ) ) ) => 1.62/0.79 ( ( 1.62/0.79 ![ 1.62/0.79 X38:$i, 1.62/0.79 X40:$i, 1.62/0.79 X42:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X42 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X38 @ X40 ) ) => 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X44:$o]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X42 ) = 1.62/0.79 ( 1.62/0.79 X38 ) ) => 1.62/0.79 ( 1.62/0.79 X44 ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X42 @ X40 ) => 1.62/0.79 ( 1.62/0.79 X44 ) ) => 1.62/0.79 ( 1.62/0.79 X44 ) ) ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X46:$i, 1.62/0.79 X48:$i, 1.62/0.79 X50:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X50 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X46 @ X48 ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X50 ) = 1.62/0.79 ( 1.62/0.79 X46 ) ) | 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X50 @ X48 ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setoftrueEq ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyinPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyInPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setunionI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setunionE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subPowSU ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuE2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 nonemptyImpWitness ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X52:$i, 1.62/0.79 X54:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X52 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X54 @ 1.62/0.79 emptyset ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X52 ) = 1.62/0.79 ( 1.62/0.79 X54 ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X56:$i, 1.62/0.79 X58:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X56 ) != 1.62/0.79 ( 1.62/0.79 X58 ) ) => 1.62/0.79 ( 1.62/0.79 ~ 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X58 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X56 @ 1.62/0.79 emptyset ) ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X60:$i, 1.62/0.79 X62:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X60 ) = 1.62/0.79 ( 1.62/0.79 X62 ) ) => 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X60 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X62 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X64:$i, 1.62/0.79 X66:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X64 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X66 @ 1.62/0.79 emptyset ) ) => 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X66 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X64 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X68:$i, 1.62/0.79 X70:$i, 1.62/0.79 X72:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X72 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X68 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X70 @ 1.62/0.79 emptyset ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X72 ) = 1.62/0.79 ( 1.62/0.79 X68 ) ) | 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X72 ) = 1.62/0.79 ( 1.62/0.79 X70 ) ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X74:$i, 1.62/0.79 X76:$i]: 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X74 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X74 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X76 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X78:$i, 1.62/0.79 X80:$i]: 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X80 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X78 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X80 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyE1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X82:( 1.62/0.79 $i > $o ), 1.62/0.79 X84:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X84 @ 1.62/0.79 emptyset ) => 1.62/0.79 ( 1.62/0.79 X82 @ X84 ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan3 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 quantDeMorgan4 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 prop2setI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 prop2set2propI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notdexE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notdallE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuI3 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 inCongP ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 in__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuE3u ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exu__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 emptyset ) = 1.62/0.79 ( 1.62/0.79 emptyset ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X86:$i, 1.62/0.79 X88:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X86 ) = 1.62/0.79 ( 1.62/0.79 X88 ) ) => 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X90:$i, 1.62/0.79 X92:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X90 ) = 1.62/0.79 ( 1.62/0.79 X92 ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X86 @ X90 ) = 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X88 @ X92 ) ) ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powerset__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setunion__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 omega__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 exuEu ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 descr__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 dsetconstr__Cong ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 eqimpsubset2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 eqimpsubset1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X94:$i]: 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 emptyset @ 1.62/0.79 X94 ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetE2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notsubsetI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notequalI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 notequalI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetRefl ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subsetTrans ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X96:$i, 1.62/0.79 X98:$i]: 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 X98 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X96 @ X98 ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X100:$i, 1.62/0.79 X102:$i, 1.62/0.79 X104:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 X100 @ 1.62/0.79 X104 ) => 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 X100 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X102 @ 1.62/0.79 X104 ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subset2powerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setextsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X106:$i]: 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 subset @ 1.62/0.79 X106 @ 1.62/0.79 emptyset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 X106 ) = 1.62/0.79 ( 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetE1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 inPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 powersetsubset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 sepInPowerset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 sepSubset ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionIL ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X108:$i, 1.62/0.79 X110:$i]: 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X110 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X108 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X110 @ 1.62/0.79 emptyset ) ) ) ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionIR ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionEcases ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionLsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binunionRsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset5 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectEL ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectLsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset3 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectER ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 disjointsetsI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectRsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset4 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 binintersectSubset1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 bs114d ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusI ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusEL ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusER ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusSubset2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusERneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusELneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusILneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusIRneg ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusLsub ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 setminusSubset1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffE ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffI1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffI2 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffIneg1 ) => 1.62/0.79 ( 1.62/0.79 ( 1.62/0.79 symdiffIneg2 ) => 1.62/0.79 ( 1.62/0.79 ![ 1.62/0.79 X112:$i, 1.62/0.79 X114:$i]: 1.62/0.79 ( 1.62/0.79 in @ 1.62/0.79 X114 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X112 @ 1.62/0.79 ( 1.62/0.79 setadjoin 1.62/0.79 @ 1.62/0.79 X114 @ 1.62/0.79 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 1.62/0.79 inference('cnf.neg', [status(esa)], [zf_stmt_3])). 1.62/0.79 thf(zip_derived_cl70, plain, 1.62/0.79 (~ (in @ sk__56 @ (setadjoin @ sk__55 @ (setadjoin @ sk__56 @ emptyset)))), 1.62/0.79 inference('cnf', [status(esa)], [zf_stmt_4])). 1.62/0.79 thf(zip_derived_cl87, plain, 1.62/0.79 (![X27 : $i, X28 : $i]: 1.62/0.79 (in @ X27 @ (setadjoin @ X28 @ (setadjoin @ X27 @ emptyset)))), 1.62/0.79 inference('cnf', [status(esa)], [zf_stmt_4])). 1.62/0.79 thf(zip_derived_cl188, plain, ($false), 1.62/0.79 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl87])). 1.62/0.79 1.62/0.79 % SZS output end Refutation 1.62/0.79 1.62/0.79 1.62/0.79 % Terminating... 2.38/0.92 % Runner terminated. 2.38/0.93 % Zipperpin 1.5 exiting 2.38/0.93 EOF