%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU616^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Hne00PZxpV true
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:55:23 PM UTC 2025
% Result : Theorem 0.54s 0.86s
% Output : Refutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU616^1 : TPTP v9.2.0. Released v3.7.0.
% 0.06/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Hne00PZxpV true
% 0.11/0.32 % Computer : n012.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Oct 1 16:06:38 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Running portfolio for 300 s
% 0.11/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.32 % Number of cores: 8
% 0.11/0.33 % Python version: Python 3.6.8
% 0.11/0.33 % Running in HO mode
% 0.51/0.63 % Total configuration time : 828
% 0.51/0.63 % Estimated wc time : 1656
% 0.51/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.52/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.52/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.52/0.72 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.54/0.86 % Solved by lams/40_c_ic.sh.
% 0.54/0.86 % done 134 iterations in 0.090s
% 0.54/0.86 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.54/0.86 % SZS output start Refutation
% 0.54/0.86 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 0.54/0.86 thf(notdexE_type, type, notdexE: $o).
% 0.54/0.86 thf(setunionAx_type, type, setunionAx: $o).
% 0.54/0.86 thf(setminusELneg_type, type, setminusELneg: $o).
% 0.54/0.86 thf(powersetE_type, type, powersetE: $o).
% 0.54/0.86 thf(omegaSAx_type, type, omegaSAx: $o).
% 0.54/0.86 thf(exuI1_type, type, exuI1: $o).
% 0.54/0.86 thf(exuI2_type, type, exuI2: $o).
% 0.54/0.86 thf(notequalI2_type, type, notequalI2: $o).
% 0.54/0.86 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 0.54/0.86 thf(setminusILneg_type, type, setminusILneg: $o).
% 0.54/0.86 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 0.54/0.86 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 0.54/0.86 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 0.54/0.86 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 0.54/0.86 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 0.54/0.86 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 0.54/0.86 thf(binunionE_type, type, binunionE: $o).
% 0.54/0.86 thf(setext_type, type, setext: $o).
% 0.54/0.86 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 0.54/0.86 thf(descr__Cong_type, type, descr__Cong: $o).
% 0.54/0.86 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 0.54/0.86 thf(in_type, type, in: $i > $i > $o).
% 0.54/0.86 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 0.54/0.86 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 0.54/0.86 thf(sk__55_type, type, sk__55: $i).
% 0.54/0.86 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 0.54/0.86 thf(symdiffI2_type, type, symdiffI2: $o).
% 0.54/0.86 thf(upairset2IR_type, type, upairset2IR: $o).
% 0.54/0.86 thf(subsetE_type, type, subsetE: $o).
% 0.54/0.86 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 0.54/0.86 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 0.54/0.86 thf(setbeta_type, type, setbeta: $o).
% 0.54/0.86 thf(eqinunit_type, type, eqinunit: $o).
% 0.54/0.86 thf(upairsetIL_type, type, upairsetIL: $o).
% 0.54/0.86 thf(powersetI1_type, type, powersetI1: $o).
% 0.54/0.86 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 0.54/0.86 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 0.54/0.86 thf(powersetAx_type, type, powersetAx: $o).
% 0.54/0.86 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 0.54/0.86 thf(powersetI_type, type, powersetI: $o).
% 0.54/0.86 thf(upairsetIR_type, type, upairsetIR: $o).
% 0.54/0.86 thf(inCongP_type, type, inCongP: $o).
% 0.54/0.86 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 0.54/0.86 thf(exuE3e_type, type, exuE3e: $o).
% 0.54/0.86 thf(emptysetE_type, type, emptysetE: $o).
% 0.54/0.86 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 0.54/0.86 thf(setunionI_type, type, setunionI: $o).
% 0.54/0.86 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 0.54/0.86 thf(prop2setI_type, type, prop2setI: $o).
% 0.54/0.86 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 0.54/0.86 thf(setminusER_type, type, setminusER: $o).
% 0.54/0.86 thf(exuE2_type, type, exuE2: $o).
% 0.54/0.86 thf(emptyset_type, type, emptyset: $i).
% 0.54/0.86 thf(powersetsubset_type, type, powersetsubset: $o).
% 0.54/0.86 thf(subPowSU_type, type, subPowSU: $o).
% 0.54/0.86 thf(notequalI1_type, type, notequalI1: $o).
% 0.54/0.86 thf(notinemptyset_type, type, notinemptyset: $o).
% 0.54/0.86 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 0.54/0.86 thf(subsetTrans_type, type, subsetTrans: $o).
% 0.54/0.86 thf(setminusI_type, type, setminusI: $o).
% 0.54/0.86 thf(binunionIL_type, type, binunionIL: $o).
% 0.54/0.86 thf(subsetE2_type, type, subsetE2: $o).
% 0.54/0.86 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 0.54/0.86 thf(setextsub_type, type, setextsub: $o).
% 0.54/0.86 thf(binunionLsub_type, type, binunionLsub: $o).
% 0.54/0.86 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 0.54/0.86 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 0.54/0.86 thf(setunionE_type, type, setunionE: $o).
% 0.54/0.86 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 0.54/0.86 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 0.54/0.86 thf(binunionIR_type, type, binunionIR: $o).
% 0.54/0.86 thf(setadjoinE_type, type, setadjoinE: $o).
% 0.54/0.86 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 0.54/0.86 thf(sk__56_type, type, sk__56: $i).
% 0.54/0.86 thf(exuE1_type, type, exuE1: $o).
% 0.54/0.86 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 0.54/0.86 thf(setminusLsub_type, type, setminusLsub: $o).
% 0.54/0.86 thf(notinsingleton_type, type, notinsingleton: $o).
% 0.54/0.86 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 0.54/0.86 thf(exuEu_type, type, exuEu: $o).
% 0.54/0.86 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 0.54/0.86 thf(upairsetE_type, type, upairsetE: $o).
% 0.54/0.86 thf(omega0Ax_type, type, omega0Ax: $o).
% 0.54/0.86 thf(notsubsetI_type, type, notsubsetI: $o).
% 0.54/0.86 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 0.54/0.86 thf(setextAx_type, type, setextAx: $o).
% 0.54/0.86 thf(powersetE1_type, type, powersetE1: $o).
% 0.54/0.86 thf(bs114d_type, type, bs114d: $o).
% 0.54/0.86 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 0.54/0.86 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 0.54/0.86 thf(subsetI1_type, type, subsetI1: $o).
% 0.54/0.86 thf(symdiffE_type, type, symdiffE: $o).
% 0.54/0.86 thf(descrp_type, type, descrp: $o).
% 0.54/0.86 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 0.54/0.86 thf(foundationAx_type, type, foundationAx: $o).
% 0.54/0.86 thf(emptysetAx_type, type, emptysetAx: $o).
% 0.54/0.86 thf(emptyI_type, type, emptyI: $o).
% 0.54/0.86 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 0.54/0.86 thf(binintersectEL_type, type, binintersectEL: $o).
% 0.54/0.86 thf(emptyE1_type, type, emptyE1: $o).
% 0.54/0.86 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 0.54/0.86 thf(vacuousDall_type, type, vacuousDall: $o).
% 0.54/0.86 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 0.54/0.86 thf(binintersectI_type, type, binintersectI: $o).
% 0.54/0.86 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 0.54/0.86 thf(symdiffI1_type, type, symdiffI1: $o).
% 0.54/0.86 thf(subsetI2_type, type, subsetI2: $o).
% 0.54/0.86 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 0.54/0.86 thf(setminusERneg_type, type, setminusERneg: $o).
% 0.54/0.86 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 0.54/0.86 thf(omega__Cong_type, type, omega__Cong: $o).
% 0.54/0.86 thf(subsetRefl_type, type, subsetRefl: $o).
% 0.54/0.86 thf(uniqinunit_type, type, uniqinunit: $o).
% 0.54/0.86 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 0.54/0.86 thf(prop2setE_type, type, prop2setE: $o).
% 0.54/0.86 thf(binunionEcases_type, type, binunionEcases: $o).
% 0.54/0.86 thf(nonemptyI_type, type, nonemptyI: $o).
% 0.54/0.86 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 0.54/0.86 thf(exuE3u_type, type, exuE3u: $o).
% 0.54/0.86 thf(setminusEL_type, type, setminusEL: $o).
% 0.54/0.86 thf(sepSubset_type, type, sepSubset: $o).
% 0.54/0.86 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 0.54/0.86 thf(exuI3_type, type, exuI3: $o).
% 0.54/0.86 thf(notdallE_type, type, notdallE: $o).
% 0.54/0.86 thf(binintersectER_type, type, binintersectER: $o).
% 0.54/0.86 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 0.54/0.86 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 0.54/0.86 thf(exu__Cong_type, type, exu__Cong: $o).
% 0.54/0.86 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 0.54/0.86 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 0.54/0.86 thf(replAx_type, type, replAx: $o).
% 0.54/0.86 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 0.54/0.86 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 0.54/0.86 thf(inPowerset_type, type, inPowerset: $o).
% 0.54/0.86 thf(subset_type, type, subset: $i > $i > $o).
% 0.54/0.86 thf(in__Cong_type, type, in__Cong: $o).
% 0.54/0.86 thf(binunionRsub_type, type, binunionRsub: $o).
% 0.54/0.86 thf(subset2powerset_type, type, subset2powerset: $o).
% 0.54/0.86 thf(upairset2IR, axiom, upairset2IR =
% 0.54/0.86 (![Xx:$i,Xy:$i]:
% 0.54/0.86 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.54/0.86 thf('0', plain,
% 0.54/0.86 (( upairset2IR ) =
% 0.54/0.86 ( ![X4:$i,X6:$i]:
% 0.54/0.86 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 0.54/0.86 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 0.54/0.86 thf('1', plain,
% 0.54/0.86 (( subsetemptysetimpeq ) =
% 0.54/0.86 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 0.54/0.86 (![A:$i,Xx:$i,B:$i]:
% 0.54/0.86 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 0.54/0.86 thf('2', plain,
% 0.54/0.86 (( setadjoinSub2 ) =
% 0.54/0.86 ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/0.86 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(setadjoinSub, axiom, setadjoinSub =
% 0.54/0.86 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 0.54/0.86 thf('3', plain,
% 0.54/0.86 (( setadjoinSub ) =
% 0.54/0.86 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(emptysetsubset, axiom, emptysetsubset =
% 0.54/0.86 (![A:$i]: ( subset @ emptyset @ A ))).
% 0.54/0.86 thf('4', plain,
% 0.54/0.86 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 0.54/0.86 (![Xx:$i,Xy:$i]:
% 0.54/0.86 ( ( ( Xx ) = ( Xy ) ) =>
% 0.54/0.86 ( ![Xz:$i,Xu:$i]:
% 0.54/0.86 ( ( ( Xz ) = ( Xu ) ) =>
% 0.54/0.86 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 0.54/0.86 thf('5', plain,
% 0.54/0.86 (( setadjoin__Cong ) =
% 0.54/0.86 ( ![X4:$i,X6:$i]:
% 0.54/0.86 ( ( ( X4 ) = ( X6 ) ) =>
% 0.54/0.86 ( ![X8:$i,X10:$i]:
% 0.54/0.86 ( ( ( X8 ) = ( X10 ) ) =>
% 0.54/0.86 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(emptyset__Cong, axiom, emptyset__Cong = (( emptyset ) = ( emptyset ))).
% 0.54/0.86 thf('6', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(vacuousDall, axiom, vacuousDall =
% 0.54/0.86 (![Xphi:( $i > $o ),Xx:$i]: ( ( in @ Xx @ emptyset ) => ( Xphi @ Xx ) ))).
% 0.54/0.86 thf('7', plain,
% 0.54/0.86 (( vacuousDall ) =
% 0.54/0.86 ( ![X4:( $i > $o ),X6:$i]: ( ( in @ X6 @ emptyset ) => ( X4 @ X6 ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(upairsetIR, axiom, upairsetIR =
% 0.54/0.86 (![Xx:$i,Xy:$i]:
% 0.54/0.86 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.54/0.86 thf('8', plain,
% 0.54/0.86 (( upairsetIR ) =
% 0.54/0.86 ( ![X4:$i,X6:$i]:
% 0.54/0.86 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(upairsetIL, axiom, upairsetIL =
% 0.54/0.86 (![Xx:$i,Xy:$i]:
% 0.54/0.86 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.54/0.86 thf('9', plain,
% 0.54/0.86 (( upairsetIL ) =
% 0.54/0.86 ( ![X4:$i,X6:$i]:
% 0.54/0.86 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(upairsetE, axiom, upairsetE =
% 0.54/0.86 (![Xx:$i,Xy:$i,Xz:$i]:
% 0.54/0.86 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 0.54/0.86 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 0.54/0.86 thf('10', plain,
% 0.54/0.86 (( upairsetE ) =
% 0.54/0.86 ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/0.86 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 0.54/0.86 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(singletonsswitch, axiom, singletonsswitch =
% 0.54/0.86 (![Xx:$i,Xy:$i]:
% 0.54/0.86 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 0.54/0.86 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 0.54/0.86 thf('11', plain,
% 0.54/0.86 (( singletonsswitch ) =
% 0.54/0.86 ( ![X4:$i,X6:$i]:
% 0.54/0.86 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 0.54/0.86 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(eqinunit, axiom, eqinunit =
% 0.54/0.86 (![Xx:$i,Xy:$i]:
% 0.54/0.86 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.54/0.86 thf('12', plain,
% 0.54/0.86 (( eqinunit ) =
% 0.54/0.86 ( ![X4:$i,X6:$i]:
% 0.54/0.86 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(notinsingleton, axiom, notinsingleton =
% 0.54/0.86 (![Xx:$i,Xy:$i]:
% 0.54/0.86 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 0.54/0.86 thf('13', plain,
% 0.54/0.86 (( notinsingleton ) =
% 0.54/0.86 ( ![X4:$i,X6:$i]:
% 0.54/0.86 ( ( ( X4 ) != ( X6 ) ) =>
% 0.54/0.86 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(uniqinunit, axiom, uniqinunit =
% 0.54/0.86 (![Xx:$i,Xy:$i]:
% 0.54/0.86 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 0.54/0.86 thf('14', plain,
% 0.54/0.86 (( uniqinunit ) =
% 0.54/0.86 ( ![X4:$i,X6:$i]:
% 0.54/0.86 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(setadjoinOr, axiom, setadjoinOr =
% 0.54/0.86 (![Xx:$i,A:$i,Xy:$i]:
% 0.54/0.86 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 0.54/0.86 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 0.54/0.86 thf('15', plain,
% 0.54/0.86 (( setadjoinOr ) =
% 0.54/0.86 ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/0.86 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 0.54/0.86 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(setadjoinE, axiom, setadjoinE =
% 0.54/0.86 (![Xx:$i,A:$i,Xy:$i]:
% 0.54/0.86 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 0.54/0.86 ( ![Xphi:$o]:
% 0.54/0.86 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 0.54/0.86 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 0.54/0.86 thf('16', plain,
% 0.54/0.86 (( setadjoinE ) =
% 0.54/0.86 ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/0.86 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 0.54/0.86 ( ![X10:$o]:
% 0.54/0.86 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 0.54/0.86 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(setadjoinIR, axiom, setadjoinIR =
% 0.54/0.86 (![Xx:$i,A:$i,Xy:$i]:
% 0.54/0.86 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 0.54/0.86 thf('17', plain,
% 0.54/0.86 (( setadjoinIR ) =
% 0.54/0.86 ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/0.86 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 0.54/0.86 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 0.54/0.86 thf('18', plain,
% 0.54/0.86 (( emptyinunitempty ) =
% 0.54/0.86 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 0.54/0.86 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 0.54/0.86 thf('19', plain,
% 0.54/0.86 (( emptyinunitempty ) =
% 0.54/0.86 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(setadjoinIL, axiom, setadjoinIL =
% 0.54/0.86 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 0.54/0.86 thf('20', plain,
% 0.54/0.86 (( setadjoinIL ) =
% 0.54/0.86 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(noeltsimpempty, axiom, noeltsimpempty =
% 0.54/0.86 (![A:$i]:
% 0.54/0.86 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 0.54/0.86 thf('21', plain,
% 0.54/0.86 (( noeltsimpempty ) =
% 0.54/0.86 ( ![X4:$i]:
% 0.54/0.86 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(emptyI, axiom, emptyI =
% 0.54/0.86 (![A:$i]:
% 0.54/0.86 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 0.54/0.86 thf('22', plain,
% 0.54/0.86 (( emptyI ) =
% 0.54/0.86 ( ![X4:$i]:
% 0.54/0.86 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(notinemptyset, axiom, notinemptyset =
% 0.54/0.86 (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 0.54/0.86 thf('23', plain,
% 0.54/0.86 (( notinemptyset ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(emptysetimpfalse, axiom, emptysetimpfalse =
% 0.54/0.86 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( $false ) ))).
% 0.54/0.86 thf('24', plain,
% 0.54/0.86 (( emptysetimpfalse ) =
% 0.54/0.86 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( $false ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(emptysetE, axiom, emptysetE =
% 0.54/0.86 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( ![Xphi:$o]: ( Xphi ) ) ))).
% 0.54/0.86 thf('25', plain,
% 0.54/0.86 (( emptysetE ) =
% 0.54/0.86 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( ![X6:$o]: ( X6 ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(setadjoinAx, axiom, setadjoinAx =
% 0.54/0.86 (![Xx:$i,A:$i,Xy:$i]:
% 0.54/0.86 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 0.54/0.86 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 0.54/0.86 thf('26', plain,
% 0.54/0.86 (( setadjoinAx ) =
% 0.54/0.86 ( ![X4:$i,X6:$i,X8:$i]:
% 0.54/0.86 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.54/0.86 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 0.54/0.86 thf('27', plain,
% 0.54/0.86 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 0.54/0.86 define([status(thm)])).
% 0.54/0.86 thf(secondinupair, conjecture,
% 0.54/0.86 (( setextAx ) =>
% 0.54/0.86 ( ( emptysetAx ) =>
% 0.54/0.86 ( ( setadjoinAx ) =>
% 0.54/0.86 ( ( powersetAx ) =>
% 0.54/0.86 ( ( setunionAx ) =>
% 0.54/0.86 ( ( omega0Ax ) =>
% 0.54/0.86 ( ( omegaSAx ) =>
% 0.54/0.86 ( ( omegaIndAx ) =>
% 0.54/0.86 ( ( replAx ) =>
% 0.54/0.86 ( ( foundationAx ) =>
% 0.54/0.86 ( ( wellorderingAx ) =>
% 0.54/0.86 ( ( descrp ) =>
% 0.54/0.86 ( ( dsetconstrI ) =>
% 0.54/0.86 ( ( dsetconstrEL ) =>
% 0.54/0.86 ( ( dsetconstrER ) =>
% 0.54/0.86 ( ( exuE1 ) =>
% 0.54/0.86 ( ( prop2setE ) =>
% 0.54/0.86 ( ( emptysetE ) =>
% 0.54/0.86 ( ( emptysetimpfalse ) =>
% 0.54/0.86 ( ( notinemptyset ) =>
% 0.54/0.86 ( ( exuE3e ) =>
% 0.54/0.86 ( ( setext ) =>
% 0.54/0.86 ( ( emptyI ) =>
% 0.54/0.86 ( ( noeltsimpempty ) =>
% 0.54/0.86 ( ( setbeta ) =>
% 0.54/0.86 ( ( nonemptyE1 ) =>
% 0.54/0.86 ( ( nonemptyI ) =>
% 0.54/0.86 ( ( nonemptyI1 ) =>
% 0.54/0.86 ( ( setadjoinIL ) =>
% 0.54/0.86 ( ( emptyinunitempty ) =>
% 0.54/0.86 ( ( setadjoinIR ) =>
% 0.54/0.86 ( ( setadjoinE ) =>
% 0.54/0.86 ( (
% 0.54/0.86 setadjoinOr ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setoftrueEq ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyinPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyInPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setunionI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setunionE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subPowSU ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuE2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 nonemptyImpWitness ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 uniqinunit ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notinsingleton ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 eqinunit ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 singletonsswitch ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 upairsetE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 upairsetIL ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 upairsetIR ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyE1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 vacuousDall ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan3 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan4 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 prop2setI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 prop2set2propI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notdexE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notdallE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuI3 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 inCongP ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuE3u ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exu__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyset__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setadjoin__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powerset__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setunion__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 omega__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuEu ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 descr__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 dsetconstr__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 eqimpsubset2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 eqimpsubset1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptysetsubset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetE2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notsubsetI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notequalI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notequalI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetRefl ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetTrans ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setadjoinSub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setadjoinSub2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subset2powerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setextsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetemptysetimpeq ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetE1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 inPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetsubset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 sepInPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 sepSubset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionIL ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 upairset2IR ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionIR ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionEcases ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionLsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionRsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset5 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectEL ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectLsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset3 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectER ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 disjointsetsI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectRsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset4 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 bs114d ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusEL ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusER ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusSubset2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusERneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusELneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusILneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusIRneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusLsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusSubset1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffIneg1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffIneg2 ) =>
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 Xx:$i,
% 0.54/0.86 Xy:$i]:
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 Xy @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 Xx @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 Xy @
% 0.54/0.86 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.54/0.86 thf(zf_stmt_0, conjecture,
% 0.54/0.86 (( setextAx ) =>
% 0.54/0.86 ( ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) ) =>
% 0.54/0.86 ( ( ![X6:$i,X8:$i,X10:$i]:
% 0.54/0.86 ( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) ) <=>
% 0.54/0.86 ( ( in @ X10 @ X8 ) | ( ( X10 ) = ( X6 ) ) ) ) ) =>
% 0.54/0.86 ( ( powersetAx ) =>
% 0.54/0.86 ( ( setunionAx ) =>
% 0.54/0.86 ( ( omega0Ax ) =>
% 0.54/0.86 ( ( omegaSAx ) =>
% 0.54/0.86 ( ( omegaIndAx ) =>
% 0.54/0.86 ( ( replAx ) =>
% 0.54/0.86 ( ( foundationAx ) =>
% 0.54/0.86 ( ( wellorderingAx ) =>
% 0.54/0.86 ( ( descrp ) =>
% 0.54/0.86 ( ( dsetconstrI ) =>
% 0.54/0.86 ( ( dsetconstrEL ) =>
% 0.54/0.86 ( ( dsetconstrER ) =>
% 0.54/0.86 ( ( exuE1 ) =>
% 0.54/0.86 ( ( prop2setE ) =>
% 0.54/0.86 ( ( ![X12:$i]:
% 0.54/0.86 ( ( in @ X12 @ emptyset ) =>
% 0.54/0.86 ( ![X14:$o]: ( X14 ) ) ) ) =>
% 0.54/0.86 ( ( ![X16:$i]:
% 0.54/0.86 ( ( in @ X16 @ emptyset ) =>
% 0.54/0.86 ( $false ) ) ) =>
% 0.54/0.86 ( ( ![X18:$i]:
% 0.54/0.86 ( ~( in @ X18 @ emptyset ) ) ) =>
% 0.54/0.86 ( ( exuE3e ) =>
% 0.54/0.86 ( ( setext ) =>
% 0.54/0.86 ( ( ![X20:$i]:
% 0.54/0.86 ( ( ![X22:$i]:
% 0.54/0.86 ( ~( in @ X22 @ X20 ) ) ) =>
% 0.54/0.86 ( ( X20 ) = ( emptyset ) ) ) ) =>
% 0.54/0.86 ( ( ![X24:$i]:
% 0.54/0.86 ( ( ![X26:$i]:
% 0.54/0.86 ( ~( in @ X26 @ X24 ) ) ) =>
% 0.54/0.86 ( ( X24 ) = ( emptyset ) ) ) ) =>
% 0.54/0.86 ( ( setbeta ) =>
% 0.54/0.86 ( ( nonemptyE1 ) =>
% 0.54/0.86 ( ( nonemptyI ) =>
% 0.54/0.86 ( ( nonemptyI1 ) =>
% 0.54/0.86 ( ( ![X28:$i,X30:$i]:
% 0.54/0.86 ( in @
% 0.54/0.86 X28 @
% 0.54/0.86 ( setadjoin @
% 0.54/0.86 X28 @ X30 ) ) ) =>
% 0.54/0.86 ( ( in @
% 0.54/0.86 emptyset @
% 0.54/0.86 ( setadjoin @
% 0.54/0.86 emptyset @
% 0.54/0.86 emptyset ) ) =>
% 0.54/0.86 ( ( ![X32:$i,
% 0.54/0.86 X34:$i,
% 0.54/0.86 X36:$i]:
% 0.54/0.86 ( (
% 0.54/0.86 in @
% 0.54/0.86 X36 @ X34 ) =>
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X36 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X32 @ X34 ) ) ) ) =>
% 0.54/0.86 ( ( ![
% 0.54/0.86 X38:$i,
% 0.54/0.86 X40:$i,
% 0.54/0.86 X42:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X42 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X38 @ X40 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X44:$o]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X42 ) =
% 0.54/0.86 (
% 0.54/0.86 X38 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 X44 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X42 @ X40 ) =>
% 0.54/0.86 (
% 0.54/0.86 X44 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 X44 ) ) ) ) ) ) =>
% 0.54/0.86 ( (
% 0.54/0.86 ![
% 0.54/0.86 X46:$i,
% 0.54/0.86 X48:$i,
% 0.54/0.86 X50:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X50 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X46 @ X48 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X50 @ X48 ) |
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X50 ) =
% 0.54/0.86 (
% 0.54/0.86 X46 ) ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setoftrueEq ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyinPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyInPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setunionI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setunionE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subPowSU ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuE2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 nonemptyImpWitness ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X52:$i,
% 0.54/0.86 X54:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X52 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X54 @
% 0.54/0.86 emptyset ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X52 ) =
% 0.54/0.86 (
% 0.54/0.86 X54 ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X56:$i,
% 0.54/0.86 X58:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X56 ) !=
% 0.54/0.86 (
% 0.54/0.86 X58 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 ~(
% 0.54/0.86 in @
% 0.54/0.86 X58 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X56 @
% 0.54/0.86 emptyset ) ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X60:$i,
% 0.54/0.86 X62:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X60 ) =
% 0.54/0.86 (
% 0.54/0.86 X62 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X60 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X62 @
% 0.54/0.86 emptyset ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X64:$i,
% 0.54/0.86 X66:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X64 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X66 @
% 0.54/0.86 emptyset ) ) =>
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X66 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X64 @
% 0.54/0.86 emptyset ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X68:$i,
% 0.54/0.86 X70:$i,
% 0.54/0.86 X72:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X72 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X68 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X70 @
% 0.54/0.86 emptyset ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X72 ) =
% 0.54/0.86 (
% 0.54/0.86 X70 ) ) |
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X72 ) =
% 0.54/0.86 (
% 0.54/0.86 X68 ) ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X74:$i,
% 0.54/0.86 X76:$i]:
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X74 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X74 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X76 @
% 0.54/0.86 emptyset ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X78:$i,
% 0.54/0.86 X80:$i]:
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X80 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X78 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X80 @
% 0.54/0.86 emptyset ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyE1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X82:(
% 0.54/0.86 $i > $o ),
% 0.54/0.86 X84:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X84 @
% 0.54/0.86 emptyset ) =>
% 0.54/0.86 (
% 0.54/0.86 X82 @ X84 ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan3 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan4 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 prop2setI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 prop2set2propI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notdexE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notdallE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuI3 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 inCongP ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuE3u ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exu__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyset ) =
% 0.54/0.86 (
% 0.54/0.86 emptyset ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X86:$i,
% 0.54/0.86 X88:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X86 ) =
% 0.54/0.86 (
% 0.54/0.86 X88 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X90:$i,
% 0.54/0.86 X92:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X90 ) =
% 0.54/0.86 (
% 0.54/0.86 X92 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X86 @ X90 ) =
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X88 @ X92 ) ) ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powerset__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setunion__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 omega__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuEu ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 descr__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 dsetconstr__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 eqimpsubset2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 eqimpsubset1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X94:$i]:
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 emptyset @
% 0.54/0.86 X94 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetE2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notsubsetI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notequalI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notequalI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetRefl ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetTrans ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X96:$i,
% 0.54/0.86 X98:$i]:
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 X98 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X96 @ X98 ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X100:$i,
% 0.54/0.86 X102:$i,
% 0.54/0.86 X104:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 X100 @
% 0.54/0.86 X104 ) =>
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 X100 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X102 @
% 0.54/0.86 X104 ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subset2powerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setextsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X106:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 X106 @
% 0.54/0.86 emptyset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X106 ) =
% 0.54/0.86 (
% 0.54/0.86 emptyset ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetE1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 inPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetsubset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 sepInPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 sepSubset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionIL ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X108:$i,
% 0.54/0.86 X110:$i]:
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X110 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X108 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X110 @
% 0.54/0.86 emptyset ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionIR ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionEcases ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionLsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionRsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset5 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectEL ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectLsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset3 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectER ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 disjointsetsI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectRsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset4 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 bs114d ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusEL ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusER ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusSubset2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusERneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusELneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusILneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusIRneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusLsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusSubset1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffIneg1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffIneg2 ) =>
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X112:$i,
% 0.54/0.86 X114:$i]:
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X114 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X112 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X114 @
% 0.54/0.86 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.54/0.86 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 0.54/0.86 thf(zf_stmt_2, axiom,
% 0.54/0.86 (![X10:$i,X8:$i,X6:$i]:
% 0.54/0.86 ( ( zip_tseitin_0 @ X10 @ X8 @ X6 ) <=>
% 0.54/0.86 ( ( ( X10 ) = ( X6 ) ) | ( in @ X10 @ X8 ) ) ))).
% 0.54/0.86 thf(zf_stmt_3, conjecture,
% 0.54/0.86 (( setextAx ) =>
% 0.54/0.86 ( ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) ) =>
% 0.54/0.86 ( ( ![X6:$i,X8:$i,X10:$i]:
% 0.54/0.86 ( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) ) <=>
% 0.54/0.86 ( zip_tseitin_0 @ X10 @ X8 @ X6 ) ) ) =>
% 0.54/0.86 ( ( powersetAx ) =>
% 0.54/0.86 ( ( setunionAx ) =>
% 0.54/0.86 ( ( omega0Ax ) =>
% 0.54/0.86 ( ( omegaSAx ) =>
% 0.54/0.86 ( ( omegaIndAx ) =>
% 0.54/0.86 ( ( replAx ) =>
% 0.54/0.86 ( ( foundationAx ) =>
% 0.54/0.86 ( ( wellorderingAx ) =>
% 0.54/0.86 ( ( descrp ) =>
% 0.54/0.86 ( ( dsetconstrI ) =>
% 0.54/0.86 ( ( dsetconstrEL ) =>
% 0.54/0.86 ( ( dsetconstrER ) =>
% 0.54/0.86 ( ( exuE1 ) =>
% 0.54/0.86 ( ( prop2setE ) =>
% 0.54/0.86 ( ( ![X12:$i]:
% 0.54/0.86 ( ( in @ X12 @ emptyset ) =>
% 0.54/0.86 ( ![X14:$o]: ( X14 ) ) ) ) =>
% 0.54/0.86 ( ( ![X16:$i]:
% 0.54/0.86 ( ~( in @ X16 @ emptyset ) ) ) =>
% 0.54/0.86 ( ( ![X18:$i]:
% 0.54/0.86 ( ~( in @ X18 @ emptyset ) ) ) =>
% 0.54/0.86 ( ( exuE3e ) =>
% 0.54/0.86 ( ( setext ) =>
% 0.54/0.86 ( ( ![X20:$i]:
% 0.54/0.86 ( ( ![X22:$i]:
% 0.54/0.86 ( ~( in @ X22 @ X20 ) ) ) =>
% 0.54/0.86 ( ( X20 ) = ( emptyset ) ) ) ) =>
% 0.54/0.86 ( ( ![X24:$i]:
% 0.54/0.86 ( ( ![X26:$i]:
% 0.54/0.86 ( ~( in @ X26 @ X24 ) ) ) =>
% 0.54/0.86 ( ( X24 ) = ( emptyset ) ) ) ) =>
% 0.54/0.86 ( ( setbeta ) =>
% 0.54/0.86 ( ( nonemptyE1 ) =>
% 0.54/0.86 ( ( nonemptyI ) =>
% 0.54/0.86 ( ( nonemptyI1 ) =>
% 0.54/0.86 ( ( ![X28:$i,X30:$i]:
% 0.54/0.86 ( in @
% 0.54/0.86 X28 @
% 0.54/0.86 ( setadjoin @
% 0.54/0.86 X28 @ X30 ) ) ) =>
% 0.54/0.86 ( ( in @
% 0.54/0.86 emptyset @
% 0.54/0.86 ( setadjoin @
% 0.54/0.86 emptyset @
% 0.54/0.86 emptyset ) ) =>
% 0.54/0.86 ( ( ![X32:$i,
% 0.54/0.86 X34:$i,
% 0.54/0.86 X36:$i]:
% 0.54/0.86 ( (
% 0.54/0.86 in @
% 0.54/0.86 X36 @ X34 ) =>
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X36 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
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% 0.54/0.86 ( ( ![
% 0.54/0.86 X38:$i,
% 0.54/0.86 X40:$i,
% 0.54/0.86 X42:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X42 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X38 @ X40 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X44:$o]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X42 ) =
% 0.54/0.86 (
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% 0.54/0.86 (
% 0.54/0.86 X44 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
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% 0.54/0.86 ( (
% 0.54/0.86 ![
% 0.54/0.86 X46:$i,
% 0.54/0.86 X48:$i,
% 0.54/0.86 X50:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X50 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X46 @ X48 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X50 ) =
% 0.54/0.86 (
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% 0.54/0.86 (
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% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setoftrueEq ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyinPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyInPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setunionI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setunionE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subPowSU ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuE2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 nonemptyImpWitness ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X52:$i,
% 0.54/0.86 X54:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X52 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
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% 0.54/0.86 X54 @
% 0.54/0.86 emptyset ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
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% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X56:$i,
% 0.54/0.86 X58:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X56 ) !=
% 0.54/0.86 (
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% 0.54/0.86 (
% 0.54/0.86 ~(
% 0.54/0.86 in @
% 0.54/0.86 X58 @
% 0.54/0.86 (
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% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X60:$i,
% 0.54/0.86 X62:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X60 ) =
% 0.54/0.86 (
% 0.54/0.86 X62 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X60 @
% 0.54/0.86 (
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% 0.54/0.86 X62 @
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% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X64:$i,
% 0.54/0.86 X66:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X64 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
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% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X66 @
% 0.54/0.86 (
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% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X68:$i,
% 0.54/0.86 X70:$i,
% 0.54/0.86 X72:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X72 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X68 @
% 0.54/0.86 (
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% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
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% 0.54/0.86 (
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% 0.54/0.86 (
% 0.54/0.86 (
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% 0.54/0.86 (
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% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X74:$i,
% 0.54/0.86 X76:$i]:
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X74 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X74 @
% 0.54/0.86 (
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% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X78:$i,
% 0.54/0.86 X80:$i]:
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X80 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X78 @
% 0.54/0.86 (
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% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyE1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X82:(
% 0.54/0.86 $i > $o ),
% 0.54/0.86 X84:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
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% 0.54/0.86 X84 @
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% 0.54/0.86 (
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% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan3 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan4 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 prop2setI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 prop2set2propI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notdexE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notdallE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuI3 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 inCongP ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuE3u ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exu__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyset ) =
% 0.54/0.86 (
% 0.54/0.86 emptyset ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X86:$i,
% 0.54/0.86 X88:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X86 ) =
% 0.54/0.86 (
% 0.54/0.86 X88 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X90:$i,
% 0.54/0.86 X92:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X90 ) =
% 0.54/0.86 (
% 0.54/0.86 X92 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X86 @ X90 ) =
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X88 @ X92 ) ) ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powerset__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setunion__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 omega__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuEu ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 descr__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 dsetconstr__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 eqimpsubset2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 eqimpsubset1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X94:$i]:
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 emptyset @
% 0.54/0.86 X94 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetE2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notsubsetI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notequalI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notequalI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetRefl ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetTrans ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X96:$i,
% 0.54/0.86 X98:$i]:
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 X98 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X96 @ X98 ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X100:$i,
% 0.54/0.86 X102:$i,
% 0.54/0.86 X104:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 X100 @
% 0.54/0.86 X104 ) =>
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 X100 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
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% 0.54/0.86 X102 @
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% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subset2powerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setextsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X106:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 X106 @
% 0.54/0.86 emptyset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X106 ) =
% 0.54/0.86 (
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% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetE1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 inPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetsubset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 sepInPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 sepSubset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionIL ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X108:$i,
% 0.54/0.86 X110:$i]:
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X110 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X108 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
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% 0.54/0.86 X110 @
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% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionIR ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionEcases ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionLsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionRsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset5 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectEL ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectLsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset3 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectER ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 disjointsetsI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectRsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset4 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 bs114d ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusEL ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusER ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusSubset2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusERneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusELneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusILneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusIRneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusLsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusSubset1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffIneg1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffIneg2 ) =>
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X112:$i,
% 0.54/0.86 X114:$i]:
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X114 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X112 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X114 @
% 0.54/0.86 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.54/0.86 thf(zf_stmt_4, negated_conjecture,
% 0.54/0.86 (~( ( setextAx ) =>
% 0.54/0.86 ( ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) ) =>
% 0.54/0.86 ( ( ![X6:$i,X8:$i,X10:$i]:
% 0.54/0.86 ( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) ) <=>
% 0.54/0.86 ( zip_tseitin_0 @ X10 @ X8 @ X6 ) ) ) =>
% 0.54/0.86 ( ( powersetAx ) =>
% 0.54/0.86 ( ( setunionAx ) =>
% 0.54/0.86 ( ( omega0Ax ) =>
% 0.54/0.86 ( ( omegaSAx ) =>
% 0.54/0.86 ( ( omegaIndAx ) =>
% 0.54/0.86 ( ( replAx ) =>
% 0.54/0.86 ( ( foundationAx ) =>
% 0.54/0.86 ( ( wellorderingAx ) =>
% 0.54/0.86 ( ( descrp ) =>
% 0.54/0.86 ( ( dsetconstrI ) =>
% 0.54/0.86 ( ( dsetconstrEL ) =>
% 0.54/0.86 ( ( dsetconstrER ) =>
% 0.54/0.86 ( ( exuE1 ) =>
% 0.54/0.86 ( ( prop2setE ) =>
% 0.54/0.86 ( ( ![X12:$i]:
% 0.54/0.86 ( ( in @ X12 @ emptyset ) =>
% 0.54/0.86 ( ![X14:$o]: ( X14 ) ) ) ) =>
% 0.54/0.86 ( ( ![X16:$i]:
% 0.54/0.86 ( ~( in @ X16 @ emptyset ) ) ) =>
% 0.54/0.86 ( ( ![X18:$i]:
% 0.54/0.86 ( ~( in @ X18 @ emptyset ) ) ) =>
% 0.54/0.86 ( ( exuE3e ) =>
% 0.54/0.86 ( ( setext ) =>
% 0.54/0.86 ( ( ![X20:$i]:
% 0.54/0.86 ( ( ![X22:$i]:
% 0.54/0.86 ( ~( in @ X22 @ X20 ) ) ) =>
% 0.54/0.86 ( ( X20 ) =
% 0.54/0.86 ( emptyset ) ) ) ) =>
% 0.54/0.86 ( ( ![X24:$i]:
% 0.54/0.86 ( ( ![X26:$i]:
% 0.54/0.86 ( ~( in @ X26 @ X24 ) ) ) =>
% 0.54/0.86 ( ( X24 ) =
% 0.54/0.86 ( emptyset ) ) ) ) =>
% 0.54/0.86 ( ( setbeta ) =>
% 0.54/0.86 ( ( nonemptyE1 ) =>
% 0.54/0.86 ( ( nonemptyI ) =>
% 0.54/0.86 ( ( nonemptyI1 ) =>
% 0.54/0.86 ( ( ![X28:$i,
% 0.54/0.86 X30:$i]:
% 0.54/0.86 ( in @
% 0.54/0.86 X28 @
% 0.54/0.86 ( setadjoin
% 0.54/0.86 @
% 0.54/0.86 X28 @ X30 ) ) ) =>
% 0.54/0.86 ( ( in @
% 0.54/0.86 emptyset @
% 0.54/0.86 ( setadjoin
% 0.54/0.86 @
% 0.54/0.86 emptyset @
% 0.54/0.86 emptyset ) ) =>
% 0.54/0.86 ( ( ![
% 0.54/0.86 X32:$i,
% 0.54/0.86 X34:$i,
% 0.54/0.86 X36:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X36 @ X34 ) =>
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X36 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X32 @ X34 ) ) ) ) =>
% 0.54/0.86 ( (
% 0.54/0.86 ![
% 0.54/0.86 X38:$i,
% 0.54/0.86 X40:$i,
% 0.54/0.86 X42:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X42 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X38 @ X40 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X44:$o]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X42 ) =
% 0.54/0.86 (
% 0.54/0.86 X38 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 X44 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X42 @ X40 ) =>
% 0.54/0.86 (
% 0.54/0.86 X44 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 X44 ) ) ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X46:$i,
% 0.54/0.86 X48:$i,
% 0.54/0.86 X50:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X50 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X46 @ X48 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X50 ) =
% 0.54/0.86 (
% 0.54/0.86 X46 ) ) |
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X50 @ X48 ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setoftrueEq ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyinPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyInPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setunionI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setunionE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subPowSU ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuE2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 nonemptyImpWitness ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X52:$i,
% 0.54/0.86 X54:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X52 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X54 @
% 0.54/0.86 emptyset ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X52 ) =
% 0.54/0.86 (
% 0.54/0.86 X54 ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X56:$i,
% 0.54/0.86 X58:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X56 ) !=
% 0.54/0.86 (
% 0.54/0.86 X58 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 ~
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X58 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X56 @
% 0.54/0.86 emptyset ) ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X60:$i,
% 0.54/0.86 X62:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X60 ) =
% 0.54/0.86 (
% 0.54/0.86 X62 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X60 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X62 @
% 0.54/0.86 emptyset ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X64:$i,
% 0.54/0.86 X66:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X64 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X66 @
% 0.54/0.86 emptyset ) ) =>
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X66 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X64 @
% 0.54/0.86 emptyset ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X68:$i,
% 0.54/0.86 X70:$i,
% 0.54/0.86 X72:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X72 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X68 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X70 @
% 0.54/0.86 emptyset ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X72 ) =
% 0.54/0.86 (
% 0.54/0.86 X68 ) ) |
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X72 ) =
% 0.54/0.86 (
% 0.54/0.86 X70 ) ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X74:$i,
% 0.54/0.86 X76:$i]:
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X74 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X74 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X76 @
% 0.54/0.86 emptyset ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X78:$i,
% 0.54/0.86 X80:$i]:
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X80 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X78 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X80 @
% 0.54/0.86 emptyset ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyE1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X82:(
% 0.54/0.86 $i > $o ),
% 0.54/0.86 X84:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X84 @
% 0.54/0.86 emptyset ) =>
% 0.54/0.86 (
% 0.54/0.86 X82 @ X84 ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan3 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 quantDeMorgan4 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 prop2setI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 prop2set2propI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notdexE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notdallE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuI3 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 inCongP ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 in__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuE3u ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exu__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 emptyset ) =
% 0.54/0.86 (
% 0.54/0.86 emptyset ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X86:$i,
% 0.54/0.86 X88:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X86 ) =
% 0.54/0.86 (
% 0.54/0.86 X88 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X90:$i,
% 0.54/0.86 X92:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X90 ) =
% 0.54/0.86 (
% 0.54/0.86 X92 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X86 @ X90 ) =
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X88 @ X92 ) ) ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powerset__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setunion__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 omega__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 exuEu ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 descr__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 dsetconstr__Cong ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 eqimpsubset2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 eqimpsubset1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X94:$i]:
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 emptyset @
% 0.54/0.86 X94 ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetE2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notsubsetI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notequalI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 notequalI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetRefl ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subsetTrans ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X96:$i,
% 0.54/0.86 X98:$i]:
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 X98 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X96 @ X98 ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X100:$i,
% 0.54/0.86 X102:$i,
% 0.54/0.86 X104:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 X100 @
% 0.54/0.86 X104 ) =>
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 X100 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X102 @
% 0.54/0.86 X104 ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subset2powerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setextsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X106:$i]:
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 subset @
% 0.54/0.86 X106 @
% 0.54/0.86 emptyset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 X106 ) =
% 0.54/0.86 (
% 0.54/0.86 emptyset ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetE1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 inPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 powersetsubset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 sepInPowerset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 sepSubset ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionIL ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.86 X108:$i,
% 0.54/0.86 X110:$i]:
% 0.54/0.86 (
% 0.54/0.86 in @
% 0.54/0.86 X110 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X108 @
% 0.54/0.86 (
% 0.54/0.86 setadjoin
% 0.54/0.86 @
% 0.54/0.86 X110 @
% 0.54/0.86 emptyset ) ) ) ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionIR ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionEcases ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionLsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binunionRsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset5 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectEL ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectLsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset3 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectER ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 disjointsetsI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectRsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset4 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 binintersectSubset1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 bs114d ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusI ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusEL ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusER ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusSubset2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusERneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusELneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusILneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusIRneg ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusLsub ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 setminusSubset1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffE ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffI1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffI2 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffIneg1 ) =>
% 0.54/0.86 (
% 0.54/0.86 (
% 0.54/0.86 symdiffIneg2 ) =>
% 0.54/0.86 (
% 0.54/0.86 ![
% 0.54/0.87 X112:$i,
% 0.54/0.87 X114:$i]:
% 0.54/0.87 (
% 0.54/0.87 in @
% 0.54/0.87 X114 @
% 0.54/0.87 (
% 0.54/0.87 setadjoin
% 0.54/0.87 @
% 0.54/0.87 X112 @
% 0.54/0.87 (
% 0.54/0.87 setadjoin
% 0.54/0.87 @
% 0.54/0.87 X114 @
% 0.54/0.87 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 0.54/0.87 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 0.54/0.87 thf(zip_derived_cl70, plain,
% 0.54/0.87 (~ (in @ sk__56 @ (setadjoin @ sk__55 @ (setadjoin @ sk__56 @ emptyset)))),
% 0.54/0.87 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.54/0.87 thf(zip_derived_cl87, plain,
% 0.54/0.87 (![X27 : $i, X28 : $i]:
% 0.54/0.87 (in @ X27 @ (setadjoin @ X28 @ (setadjoin @ X27 @ emptyset)))),
% 0.54/0.87 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.54/0.87 thf(zip_derived_cl188, plain, ($false),
% 0.54/0.87 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl87])).
% 0.54/0.87
% 0.54/0.87 % SZS output end Refutation
% 0.54/0.87
% 0.54/0.87
% 0.54/0.87 % Terminating...
% 0.59/0.96 % Runner terminated.
% 1.78/0.98 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------