%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU579^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.DoxadAp53r true
% Computer : n021.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 04:55:10 PM UTC 2025
% Result : Theorem 4.33s 1.31s
% Output : Refutation 4.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU579^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.DoxadAp53r true
% 0.12/0.33 % Computer : n021.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 : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 1 16:13:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in HO mode
% 0.43/0.63 % Total configuration time : 828
% 0.43/0.63 % Estimated wc time : 1656
% 0.43/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.53/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.53/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.53/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.53/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.53/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.53/0.75 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.55/0.83 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.55/0.85 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 4.33/1.31 % Solved by lams/40_c_ic.sh.
% 4.33/1.31 % done 436 iterations in 0.471s
% 4.33/1.31 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 4.33/1.31 % SZS output start Refutation
% 4.33/1.31 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 4.33/1.31 thf(notdexE_type, type, notdexE: $o).
% 4.33/1.31 thf(setunionAx_type, type, setunionAx: $o).
% 4.33/1.31 thf(powersetE_type, type, powersetE: $o).
% 4.33/1.31 thf(omegaSAx_type, type, omegaSAx: $o).
% 4.33/1.31 thf(exuI1_type, type, exuI1: $o).
% 4.33/1.31 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 4.33/1.31 thf(exuI2_type, type, exuI2: $o).
% 4.33/1.31 thf(notequalI2_type, type, notequalI2: $o).
% 4.33/1.31 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 4.33/1.31 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 4.33/1.31 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 4.33/1.31 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 4.33/1.31 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 4.33/1.31 thf(setext_type, type, setext: $o).
% 4.33/1.31 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 4.33/1.31 thf(descr__Cong_type, type, descr__Cong: $o).
% 4.33/1.31 thf(in_type, type, in: $i > $i > $o).
% 4.33/1.31 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 4.33/1.31 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 4.33/1.31 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 4.33/1.31 thf(subsetE_type, type, subsetE: $o).
% 4.33/1.31 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 4.33/1.31 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 4.33/1.31 thf(setbeta_type, type, setbeta: $o).
% 4.33/1.31 thf(eqinunit_type, type, eqinunit: $o).
% 4.33/1.31 thf(upairsetIL_type, type, upairsetIL: $o).
% 4.33/1.31 thf(powersetI1_type, type, powersetI1: $o).
% 4.33/1.31 thf(powersetAx_type, type, powersetAx: $o).
% 4.33/1.31 thf(powersetI_type, type, powersetI: $o).
% 4.33/1.31 thf(upairsetIR_type, type, upairsetIR: $o).
% 4.33/1.31 thf(inCongP_type, type, inCongP: $o).
% 4.33/1.31 thf(sk__58_type, type, sk__58: $i).
% 4.33/1.31 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 4.33/1.31 thf(exuE3e_type, type, exuE3e: $o).
% 4.33/1.31 thf(emptysetE_type, type, emptysetE: $o).
% 4.33/1.31 thf(setunionI_type, type, setunionI: $o).
% 4.33/1.31 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 4.33/1.31 thf(prop2setI_type, type, prop2setI: $o).
% 4.33/1.31 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 4.33/1.31 thf(exuE2_type, type, exuE2: $o).
% 4.33/1.31 thf(emptyset_type, type, emptyset: $i).
% 4.33/1.31 thf(subPowSU_type, type, subPowSU: $o).
% 4.33/1.31 thf(notequalI1_type, type, notequalI1: $o).
% 4.33/1.31 thf(notinemptyset_type, type, notinemptyset: $o).
% 4.33/1.31 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 4.33/1.31 thf(subsetTrans_type, type, subsetTrans: $o).
% 4.33/1.31 thf(subsetE2_type, type, subsetE2: $o).
% 4.33/1.31 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 4.33/1.31 thf(setextsub_type, type, setextsub: $o).
% 4.33/1.31 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 4.33/1.31 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 4.33/1.31 thf(setunionE_type, type, setunionE: $o).
% 4.33/1.31 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 4.33/1.31 thf(setadjoinE_type, type, setadjoinE: $o).
% 4.33/1.31 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 4.33/1.31 thf(exuE1_type, type, exuE1: $o).
% 4.33/1.31 thf(notinsingleton_type, type, notinsingleton: $o).
% 4.33/1.31 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 4.33/1.31 thf(exuEu_type, type, exuEu: $o).
% 4.33/1.31 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 4.33/1.31 thf(upairsetE_type, type, upairsetE: $o).
% 4.33/1.31 thf(omega0Ax_type, type, omega0Ax: $o).
% 4.33/1.31 thf(notsubsetI_type, type, notsubsetI: $o).
% 4.33/1.31 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 4.33/1.31 thf(setextAx_type, type, setextAx: $o).
% 4.33/1.31 thf(powersetE1_type, type, powersetE1: $o).
% 4.33/1.31 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 4.33/1.31 thf(subsetI1_type, type, subsetI1: $o).
% 4.33/1.31 thf(descrp_type, type, descrp: $o).
% 4.33/1.31 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 4.33/1.31 thf(foundationAx_type, type, foundationAx: $o).
% 4.33/1.31 thf(emptysetAx_type, type, emptysetAx: $o).
% 4.33/1.31 thf(emptyI_type, type, emptyI: $o).
% 4.33/1.31 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 4.33/1.31 thf(emptyE1_type, type, emptyE1: $o).
% 4.33/1.31 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 4.33/1.31 thf(vacuousDall_type, type, vacuousDall: $o).
% 4.33/1.31 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 4.33/1.31 thf(sk__57_type, type, sk__57: $i).
% 4.33/1.31 thf(subsetI2_type, type, subsetI2: $o).
% 4.33/1.31 thf(omega__Cong_type, type, omega__Cong: $o).
% 4.33/1.31 thf(subsetRefl_type, type, subsetRefl: $o).
% 4.33/1.31 thf(uniqinunit_type, type, uniqinunit: $o).
% 4.33/1.31 thf(prop2setE_type, type, prop2setE: $o).
% 4.33/1.31 thf(nonemptyI_type, type, nonemptyI: $o).
% 4.33/1.31 thf(exuE3u_type, type, exuE3u: $o).
% 4.33/1.31 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 4.33/1.31 thf(exuI3_type, type, exuI3: $o).
% 4.33/1.31 thf(notdallE_type, type, notdallE: $o).
% 4.33/1.31 thf(powerset_type, type, powerset: $i > $i).
% 4.33/1.31 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 4.33/1.31 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 4.33/1.31 thf(exu__Cong_type, type, exu__Cong: $o).
% 4.33/1.31 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 4.33/1.31 thf(sk__59_type, type, sk__59: $i > $i > $i).
% 4.33/1.31 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 4.33/1.31 thf(replAx_type, type, replAx: $o).
% 4.33/1.31 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 4.33/1.31 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 4.33/1.31 thf(inPowerset_type, type, inPowerset: $o).
% 4.33/1.31 thf(subset_type, type, subset: $i > $i > $o).
% 4.33/1.31 thf(in__Cong_type, type, in__Cong: $o).
% 4.33/1.31 thf(subset2powerset_type, type, subset2powerset: $o).
% 4.33/1.31 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 4.33/1.31 thf('0', plain,
% 4.33/1.31 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(powersetE1, axiom, powersetE1 =
% 4.33/1.31 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 4.33/1.31 thf('1', plain,
% 4.33/1.31 (( powersetE1 ) =
% 4.33/1.31 ( ![X4:$i,X6:$i]:
% 4.33/1.31 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(powersetI1, axiom, powersetI1 =
% 4.33/1.31 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 4.33/1.31 thf('2', plain,
% 4.33/1.31 (( powersetI1 ) =
% 4.33/1.31 ( ![X4:$i,X6:$i]:
% 4.33/1.31 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 4.33/1.31 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 4.33/1.31 thf('3', plain,
% 4.33/1.31 (( subsetemptysetimpeq ) =
% 4.33/1.31 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(setextsub, axiom, setextsub =
% 4.33/1.31 (![A:$i,B:$i]:
% 4.33/1.31 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 4.33/1.31 thf('4', plain,
% 4.33/1.31 (( setextsub ) =
% 4.33/1.31 ( ![X4:$i,X6:$i]:
% 4.33/1.31 ( ( subset @ X4 @ X6 ) =>
% 4.33/1.31 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(subset2powerset, axiom, subset2powerset =
% 4.33/1.31 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 4.33/1.31 thf('5', plain,
% 4.33/1.31 (( subset2powerset ) =
% 4.33/1.31 ( ![X4:$i,X6:$i]:
% 4.33/1.31 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 4.33/1.31 (![A:$i,Xx:$i,B:$i]:
% 4.33/1.31 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 4.33/1.31 thf('6', plain,
% 4.33/1.31 (( setadjoinSub2 ) =
% 4.33/1.31 ( ![X4:$i,X6:$i,X8:$i]:
% 4.33/1.31 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(setadjoinSub, axiom, setadjoinSub =
% 4.33/1.31 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 4.33/1.31 thf('7', plain,
% 4.33/1.31 (( setadjoinSub ) =
% 4.33/1.31 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(subsetTrans, axiom, subsetTrans =
% 4.33/1.31 (![A:$i,B:$i,C:$i]:
% 4.33/1.31 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 4.33/1.31 thf('8', plain,
% 4.33/1.31 (( subsetTrans ) =
% 4.33/1.31 ( ![X4:$i,X6:$i,X8:$i]:
% 4.33/1.31 ( ( subset @ X4 @ X6 ) =>
% 4.33/1.31 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 4.33/1.31 thf('9', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(notequalI1, axiom, notequalI1 =
% 4.33/1.31 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 4.33/1.31 thf('10', plain,
% 4.33/1.31 (( notequalI1 ) =
% 4.33/1.31 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(notsubsetI, axiom, notsubsetI =
% 4.33/1.31 (![A:$i,B:$i,Xx:$i]:
% 4.33/1.31 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 4.33/1.31 thf('11', plain,
% 4.33/1.31 (( notsubsetI ) =
% 4.33/1.31 ( ![X4:$i,X6:$i,X8:$i]:
% 4.33/1.31 ( ( in @ X8 @ X4 ) =>
% 4.33/1.31 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(subsetE2, axiom, subsetE2 =
% 4.33/1.31 (![A:$i,B:$i,Xx:$i]:
% 4.33/1.31 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 4.33/1.31 thf('12', plain,
% 4.33/1.31 (( subsetE2 ) =
% 4.33/1.31 ( ![X4:$i,X6:$i,X8:$i]:
% 4.33/1.31 ( ( subset @ X4 @ X6 ) =>
% 4.33/1.31 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(subsetE, axiom, subsetE =
% 4.33/1.31 (![A:$i,B:$i,Xx:$i]:
% 4.33/1.31 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 4.33/1.31 thf('13', plain,
% 4.33/1.31 (( subsetE ) =
% 4.33/1.31 ( ![X4:$i,X6:$i,X8:$i]:
% 4.33/1.31 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(emptysetsubset, axiom, emptysetsubset =
% 4.33/1.31 (![A:$i]: ( subset @ emptyset @ A ))).
% 4.33/1.31 thf('14', plain,
% 4.33/1.31 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(subsetI2, axiom, subsetI2 =
% 4.33/1.31 (![A:$i,B:$i]:
% 4.33/1.31 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 4.33/1.31 ( subset @ A @ B ) ))).
% 4.33/1.31 thf('15', plain,
% 4.33/1.31 (( subsetI2 ) =
% 4.33/1.31 ( ![X4:$i,X6:$i]:
% 4.33/1.31 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 4.33/1.31 ( subset @ X4 @ X6 ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 4.33/1.31 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 4.33/1.31 thf('16', plain,
% 4.33/1.31 (( eqimpsubset1 ) =
% 4.33/1.31 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 4.33/1.31 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 4.33/1.31 thf('17', plain,
% 4.33/1.31 (( eqimpsubset2 ) =
% 4.33/1.31 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(subsetI1, axiom, subsetI1 =
% 4.33/1.31 (![A:$i,B:$i]:
% 4.33/1.31 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 4.33/1.31 ( subset @ A @ B ) ))).
% 4.33/1.31 thf('18', plain,
% 4.33/1.31 (( subsetI1 ) =
% 4.33/1.31 ( ![X4:$i,X6:$i]:
% 4.33/1.31 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 4.33/1.31 ( subset @ X4 @ X6 ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(powerset__Cong, axiom, powerset__Cong =
% 4.33/1.31 (![A:$i,B:$i]:
% 4.33/1.31 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 4.33/1.31 thf('19', plain,
% 4.33/1.31 (( powerset__Cong ) =
% 4.33/1.31 ( ![X4:$i,X6:$i]:
% 4.33/1.31 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(powersetE, axiom, powersetE =
% 4.33/1.31 (![A:$i,B:$i,Xx:$i]:
% 4.33/1.31 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 4.33/1.31 thf('20', plain,
% 4.33/1.31 (( powersetE ) =
% 4.33/1.31 ( ![X4:$i,X6:$i,X8:$i]:
% 4.33/1.31 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 4.33/1.31 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(emptyInPowerset, axiom, emptyInPowerset =
% 4.33/1.31 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 4.33/1.31 thf('21', plain,
% 4.33/1.31 (( emptyInPowerset ) =
% 4.33/1.31 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(emptyinPowerset, axiom, emptyinPowerset =
% 4.33/1.31 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 4.33/1.31 thf('22', plain,
% 4.33/1.31 (( emptyinPowerset ) =
% 4.33/1.31 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(powersetI, axiom, powersetI =
% 4.33/1.31 (![A:$i,B:$i]:
% 4.33/1.31 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 4.33/1.31 ( in @ B @ ( powerset @ A ) ) ))).
% 4.33/1.31 thf('23', plain,
% 4.33/1.31 (( powersetI ) =
% 4.33/1.31 ( ![X4:$i,X6:$i]:
% 4.33/1.31 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 4.33/1.31 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(powersetAx, axiom, powersetAx =
% 4.33/1.31 (![A:$i,B:$i]:
% 4.33/1.31 ( ( in @ B @ ( powerset @ A ) ) <=>
% 4.33/1.31 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 4.33/1.31 thf('24', plain,
% 4.33/1.31 (( powersetAx ) =
% 4.33/1.31 ( ![X4:$i,X6:$i]:
% 4.33/1.31 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 4.33/1.31 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 4.33/1.31 define([status(thm)])).
% 4.33/1.31 thf(powersetsubset, conjecture,
% 4.33/1.31 (( setextAx ) =>
% 4.33/1.31 ( ( emptysetAx ) =>
% 4.33/1.31 ( ( setadjoinAx ) =>
% 4.33/1.31 ( ( powersetAx ) =>
% 4.33/1.31 ( ( setunionAx ) =>
% 4.33/1.31 ( ( omega0Ax ) =>
% 4.33/1.31 ( ( omegaSAx ) =>
% 4.33/1.31 ( ( omegaIndAx ) =>
% 4.33/1.31 ( ( replAx ) =>
% 4.33/1.31 ( ( foundationAx ) =>
% 4.33/1.31 ( ( wellorderingAx ) =>
% 4.33/1.31 ( ( descrp ) =>
% 4.33/1.31 ( ( dsetconstrI ) =>
% 4.33/1.31 ( ( dsetconstrEL ) =>
% 4.33/1.31 ( ( dsetconstrER ) =>
% 4.33/1.31 ( ( exuE1 ) =>
% 4.33/1.31 ( ( prop2setE ) =>
% 4.33/1.31 ( ( emptysetE ) =>
% 4.33/1.31 ( ( emptysetimpfalse ) =>
% 4.33/1.31 ( ( notinemptyset ) =>
% 4.33/1.31 ( ( exuE3e ) =>
% 4.33/1.31 ( ( setext ) =>
% 4.33/1.31 ( ( emptyI ) =>
% 4.33/1.31 ( ( noeltsimpempty ) =>
% 4.33/1.31 ( ( setbeta ) =>
% 4.33/1.31 ( ( nonemptyE1 ) =>
% 4.33/1.31 ( ( nonemptyI ) =>
% 4.33/1.31 ( ( nonemptyI1 ) =>
% 4.33/1.31 ( ( setadjoinIL ) =>
% 4.33/1.31 ( ( emptyinunitempty ) =>
% 4.33/1.31 ( ( setadjoinIR ) =>
% 4.33/1.31 ( ( setadjoinE ) =>
% 4.33/1.31 ( (
% 4.33/1.31 setadjoinOr ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setoftrueEq ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 powersetI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 emptyinPowerset ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 emptyInPowerset ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 powersetE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setunionI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setunionE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subPowSU ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuE2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 nonemptyImpWitness ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 uniqinunit ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notinsingleton ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 eqinunit ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 singletonsswitch ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 upairsetE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 upairsetIL ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 upairsetIR ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 emptyE1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 vacuousDall ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan3 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan4 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 prop2setI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 prop2set2propI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notdexE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notdallE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuI1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuI3 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuI2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 inCongP ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuE3u ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exu__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 emptyset__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setadjoin__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 powerset__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setunion__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 omega__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuEu ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 descr__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 dsetconstr__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subsetI1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 eqimpsubset2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 eqimpsubset1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subsetI2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 emptysetsubset ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subsetE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subsetE2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notsubsetI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notequalI1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notequalI2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subsetRefl ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subsetTrans ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setadjoinSub ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setadjoinSub2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset2powerset ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setextsub ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subsetemptysetimpeq ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 powersetI1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 powersetE1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 inPowerset ) =>
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 A:$i,B:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 A @ B ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 A ) @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 4.33/1.31 thf(zf_stmt_0, conjecture,
% 4.33/1.31 (( setextAx ) =>
% 4.33/1.31 ( ( emptysetAx ) =>
% 4.33/1.31 ( ( setadjoinAx ) =>
% 4.33/1.31 ( ( ![X4:$i,X6:$i]:
% 4.33/1.31 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 4.33/1.31 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 4.33/1.31 ( ( setunionAx ) =>
% 4.33/1.31 ( ( omega0Ax ) =>
% 4.33/1.31 ( ( omegaSAx ) =>
% 4.33/1.31 ( ( omegaIndAx ) =>
% 4.33/1.31 ( ( replAx ) =>
% 4.33/1.31 ( ( foundationAx ) =>
% 4.33/1.31 ( ( wellorderingAx ) =>
% 4.33/1.31 ( ( descrp ) =>
% 4.33/1.31 ( ( dsetconstrI ) =>
% 4.33/1.31 ( ( dsetconstrEL ) =>
% 4.33/1.31 ( ( dsetconstrER ) =>
% 4.33/1.31 ( ( exuE1 ) =>
% 4.33/1.31 ( ( prop2setE ) =>
% 4.33/1.31 ( ( emptysetE ) =>
% 4.33/1.31 ( ( emptysetimpfalse ) =>
% 4.33/1.31 ( ( notinemptyset ) =>
% 4.33/1.31 ( ( exuE3e ) =>
% 4.33/1.31 ( ( setext ) =>
% 4.33/1.31 ( ( emptyI ) =>
% 4.33/1.31 ( ( noeltsimpempty ) =>
% 4.33/1.31 ( ( setbeta ) =>
% 4.33/1.31 ( ( nonemptyE1 ) =>
% 4.33/1.31 ( ( nonemptyI ) =>
% 4.33/1.31 ( ( nonemptyI1 ) =>
% 4.33/1.31 ( ( setadjoinIL ) =>
% 4.33/1.31 ( ( emptyinunitempty ) =>
% 4.33/1.31 ( ( setadjoinIR ) =>
% 4.33/1.31 ( ( setadjoinE ) =>
% 4.33/1.31 ( (
% 4.33/1.31 setadjoinOr ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setoftrueEq ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X10:$i,
% 4.33/1.31 X12:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X14:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X14 @ X12 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X14 @ X10 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X12 @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X10 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X16:$i]:
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 emptyset @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X16 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X18:$i]:
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 emptyset @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X18 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X20:$i,
% 4.33/1.31 X22:$i,
% 4.33/1.31 X24:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X22 @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X20 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X24 @ X22 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X24 @ X20 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setunionI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setunionE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subPowSU ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuE2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 nonemptyImpWitness ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 uniqinunit ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notinsingleton ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 eqinunit ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 singletonsswitch ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 upairsetE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 upairsetIL ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 upairsetIR ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 emptyE1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 vacuousDall ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan3 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan4 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 prop2setI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 prop2set2propI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notdexE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notdallE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuI1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuI3 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuI2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 inCongP ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuE3u ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exu__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 emptyset__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setadjoin__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X26:$i,
% 4.33/1.31 X28:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X26 ) =
% 4.33/1.31 (
% 4.33/1.31 X28 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X26 ) =
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X28 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setunion__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 omega__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuEu ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 descr__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 dsetconstr__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X30:$i,
% 4.33/1.31 X32:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X34:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X34 @ X30 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X34 @ X32 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X30 @ X32 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X36:$i,
% 4.33/1.31 X38:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X36 ) =
% 4.33/1.31 (
% 4.33/1.31 X38 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X38 @ X36 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X40:$i,
% 4.33/1.31 X42:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X40 ) =
% 4.33/1.31 (
% 4.33/1.31 X42 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X40 @ X42 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X44:$i,
% 4.33/1.31 X46:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X48:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X48 @ X44 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X48 @ X46 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X44 @ X46 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X50:$i]:
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 emptyset @
% 4.33/1.31 X50 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X52:$i,
% 4.33/1.31 X54:$i,
% 4.33/1.31 X56:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X52 @ X54 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X56 @ X52 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X56 @ X54 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X58:$i,
% 4.33/1.31 X60:$i,
% 4.33/1.31 X62:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X58 @ X60 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ~(
% 4.33/1.31 in @
% 4.33/1.31 X62 @ X60 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 ~(
% 4.33/1.31 in @
% 4.33/1.31 X62 @ X58 ) ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X64:$i,
% 4.33/1.31 X66:$i,
% 4.33/1.31 X68:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X68 @ X64 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ~(
% 4.33/1.31 in @
% 4.33/1.31 X68 @ X66 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 ~(
% 4.33/1.31 subset @
% 4.33/1.31 X64 @ X66 ) ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X70:$i,
% 4.33/1.31 X72:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ~(
% 4.33/1.31 subset @
% 4.33/1.31 X70 @ X72 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X70 ) !=
% 4.33/1.31 (
% 4.33/1.31 X72 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notequalI2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X74:$i]:
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X74 @ X74 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X76:$i,
% 4.33/1.31 X78:$i,
% 4.33/1.31 X80:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X76 @ X78 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X78 @ X80 ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X76 @ X80 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X82:$i,
% 4.33/1.31 X84:$i]:
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X84 @
% 4.33/1.31 (
% 4.33/1.31 setadjoin
% 4.33/1.31 @
% 4.33/1.31 X82 @ X84 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X86:$i,
% 4.33/1.31 X88:$i,
% 4.33/1.31 X90:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X86 @ X90 ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X86 @
% 4.33/1.31 (
% 4.33/1.31 setadjoin
% 4.33/1.31 @
% 4.33/1.31 X88 @ X90 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X92:$i,
% 4.33/1.31 X94:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X92 @ X94 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X92 @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X94 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X96:$i,
% 4.33/1.31 X98:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X96 @ X98 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X98 @ X96 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X96 ) =
% 4.33/1.31 (
% 4.33/1.31 X98 ) ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X100:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X100 @
% 4.33/1.31 emptyset ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X100 ) =
% 4.33/1.31 (
% 4.33/1.31 emptyset ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X102:$i,
% 4.33/1.31 X104:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X104 @
% 4.33/1.31 X102 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X104 @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X102 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X106:$i,
% 4.33/1.31 X108:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X108 @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X106 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X108 @
% 4.33/1.31 X106 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X110:$i]:
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X110 @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X110 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X112:$i,
% 4.33/1.31 X114:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X112 @
% 4.33/1.31 X114 ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X112 ) @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X114 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 4.33/1.31 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 4.33/1.31 thf(zf_stmt_2, axiom,
% 4.33/1.31 (![X8:$i,X6:$i,X4:$i]:
% 4.33/1.31 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 4.33/1.31 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 4.33/1.31 thf(zf_stmt_3, conjecture,
% 4.33/1.31 (( setextAx ) =>
% 4.33/1.31 ( ( emptysetAx ) =>
% 4.33/1.31 ( ( setadjoinAx ) =>
% 4.33/1.31 ( ( ![X4:$i,X6:$i]:
% 4.33/1.31 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 4.33/1.31 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 4.33/1.31 ( ( setunionAx ) =>
% 4.33/1.31 ( ( omega0Ax ) =>
% 4.33/1.31 ( ( omegaSAx ) =>
% 4.33/1.31 ( ( omegaIndAx ) =>
% 4.33/1.31 ( ( replAx ) =>
% 4.33/1.31 ( ( foundationAx ) =>
% 4.33/1.31 ( ( wellorderingAx ) =>
% 4.33/1.31 ( ( descrp ) =>
% 4.33/1.31 ( ( dsetconstrI ) =>
% 4.33/1.31 ( ( dsetconstrEL ) =>
% 4.33/1.31 ( ( dsetconstrER ) =>
% 4.33/1.31 ( ( exuE1 ) =>
% 4.33/1.31 ( ( prop2setE ) =>
% 4.33/1.31 ( ( emptysetE ) =>
% 4.33/1.31 ( ( emptysetimpfalse ) =>
% 4.33/1.31 ( ( notinemptyset ) =>
% 4.33/1.31 ( ( exuE3e ) =>
% 4.33/1.31 ( ( setext ) =>
% 4.33/1.31 ( ( emptyI ) =>
% 4.33/1.31 ( ( noeltsimpempty ) =>
% 4.33/1.31 ( ( setbeta ) =>
% 4.33/1.31 ( ( nonemptyE1 ) =>
% 4.33/1.31 ( ( nonemptyI ) =>
% 4.33/1.31 ( ( nonemptyI1 ) =>
% 4.33/1.31 ( ( setadjoinIL ) =>
% 4.33/1.31 ( ( emptyinunitempty ) =>
% 4.33/1.31 ( ( setadjoinIR ) =>
% 4.33/1.31 ( ( setadjoinE ) =>
% 4.33/1.31 ( (
% 4.33/1.31 setadjoinOr ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setoftrueEq ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X10:$i,
% 4.33/1.31 X12:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X14:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X14 @ X12 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X14 @ X10 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X12 @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X10 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X16:$i]:
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 emptyset @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X16 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X18:$i]:
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 emptyset @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X18 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X20:$i,
% 4.33/1.31 X22:$i,
% 4.33/1.31 X24:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X22 @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X20 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X24 @ X22 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X24 @ X20 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setunionI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setunionE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subPowSU ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuE2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 nonemptyImpWitness ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 uniqinunit ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notinsingleton ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 eqinunit ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 singletonsswitch ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 upairsetE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 upairsetIL ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 upairsetIR ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 emptyE1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 vacuousDall ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan3 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan4 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 prop2setI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 prop2set2propI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notdexE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notdallE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuI1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuI3 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuI2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 inCongP ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuE3u ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exu__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 emptyset__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setadjoin__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X26:$i,
% 4.33/1.31 X28:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X26 ) =
% 4.33/1.31 (
% 4.33/1.31 X28 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X26 ) =
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X28 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setunion__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 omega__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuEu ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 descr__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 dsetconstr__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X30:$i,
% 4.33/1.31 X32:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X34:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X34 @ X30 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X34 @ X32 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X30 @ X32 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X36:$i,
% 4.33/1.31 X38:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X36 ) =
% 4.33/1.31 (
% 4.33/1.31 X38 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X38 @ X36 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X40:$i,
% 4.33/1.31 X42:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X40 ) =
% 4.33/1.31 (
% 4.33/1.31 X42 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X40 @ X42 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X44:$i,
% 4.33/1.31 X46:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X48:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X48 @ X44 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X48 @ X46 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X44 @ X46 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X50:$i]:
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 emptyset @
% 4.33/1.31 X50 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X52:$i,
% 4.33/1.31 X54:$i,
% 4.33/1.31 X56:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X52 @ X54 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X56 @ X52 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X56 @ X54 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X58:$i,
% 4.33/1.31 X60:$i,
% 4.33/1.31 X62:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X58 @ X60 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ~(
% 4.33/1.31 in @
% 4.33/1.31 X62 @ X60 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 ~(
% 4.33/1.31 in @
% 4.33/1.31 X62 @ X58 ) ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X64:$i,
% 4.33/1.31 X66:$i,
% 4.33/1.31 X68:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X68 @ X64 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ~(
% 4.33/1.31 in @
% 4.33/1.31 X68 @ X66 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 ~(
% 4.33/1.31 subset @
% 4.33/1.31 X64 @ X66 ) ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X70:$i,
% 4.33/1.31 X72:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ~(
% 4.33/1.31 subset @
% 4.33/1.31 X70 @ X72 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X70 ) !=
% 4.33/1.31 (
% 4.33/1.31 X72 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notequalI2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X74:$i]:
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X74 @ X74 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X76:$i,
% 4.33/1.31 X78:$i,
% 4.33/1.31 X80:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X76 @ X78 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X78 @ X80 ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X76 @ X80 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X82:$i,
% 4.33/1.31 X84:$i]:
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X84 @
% 4.33/1.31 (
% 4.33/1.31 setadjoin
% 4.33/1.31 @
% 4.33/1.31 X82 @ X84 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X86:$i,
% 4.33/1.31 X88:$i,
% 4.33/1.31 X90:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X86 @ X90 ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X86 @
% 4.33/1.31 (
% 4.33/1.31 setadjoin
% 4.33/1.31 @
% 4.33/1.31 X88 @ X90 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X92:$i,
% 4.33/1.31 X94:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X92 @ X94 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X92 @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X94 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X96:$i,
% 4.33/1.31 X98:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X96 @ X98 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X98 @ X96 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X96 ) =
% 4.33/1.31 (
% 4.33/1.31 X98 ) ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X100:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X100 @
% 4.33/1.31 emptyset ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X100 ) =
% 4.33/1.31 (
% 4.33/1.31 emptyset ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X102:$i,
% 4.33/1.31 X104:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X104 @
% 4.33/1.31 X102 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X104 @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X102 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X106:$i,
% 4.33/1.31 X108:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X108 @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X106 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X108 @
% 4.33/1.31 X106 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X110:$i]:
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X110 @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X110 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X112:$i,
% 4.33/1.31 X114:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X112 @
% 4.33/1.31 X114 ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X112 ) @
% 4.33/1.31 (
% 4.33/1.31 powerset @
% 4.33/1.31 X114 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 4.33/1.31 thf(zf_stmt_4, negated_conjecture,
% 4.33/1.31 (~( ( setextAx ) =>
% 4.33/1.31 ( ( emptysetAx ) =>
% 4.33/1.31 ( ( setadjoinAx ) =>
% 4.33/1.31 ( ( ![X4:$i,X6:$i]:
% 4.33/1.31 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 4.33/1.31 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 4.33/1.31 ( ( setunionAx ) =>
% 4.33/1.31 ( ( omega0Ax ) =>
% 4.33/1.31 ( ( omegaSAx ) =>
% 4.33/1.31 ( ( omegaIndAx ) =>
% 4.33/1.31 ( ( replAx ) =>
% 4.33/1.31 ( ( foundationAx ) =>
% 4.33/1.31 ( ( wellorderingAx ) =>
% 4.33/1.31 ( ( descrp ) =>
% 4.33/1.31 ( ( dsetconstrI ) =>
% 4.33/1.31 ( ( dsetconstrEL ) =>
% 4.33/1.31 ( ( dsetconstrER ) =>
% 4.33/1.31 ( ( exuE1 ) =>
% 4.33/1.31 ( ( prop2setE ) =>
% 4.33/1.31 ( ( emptysetE ) =>
% 4.33/1.31 ( ( emptysetimpfalse ) =>
% 4.33/1.31 ( ( notinemptyset ) =>
% 4.33/1.31 ( ( exuE3e ) =>
% 4.33/1.31 ( ( setext ) =>
% 4.33/1.31 ( ( emptyI ) =>
% 4.33/1.31 ( ( noeltsimpempty ) =>
% 4.33/1.31 ( ( setbeta ) =>
% 4.33/1.31 ( ( nonemptyE1 ) =>
% 4.33/1.31 ( ( nonemptyI ) =>
% 4.33/1.31 ( ( nonemptyI1 ) =>
% 4.33/1.31 ( ( setadjoinIL ) =>
% 4.33/1.31 ( ( emptyinunitempty ) =>
% 4.33/1.31 ( ( setadjoinIR ) =>
% 4.33/1.31 ( (
% 4.33/1.31 setadjoinE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setadjoinOr ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setoftrueEq ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X10:$i,
% 4.33/1.31 X12:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X14:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X14 @ X12 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X14 @ X10 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X12 @
% 4.33/1.31 (
% 4.33/1.31 powerset
% 4.33/1.31 @
% 4.33/1.31 X10 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X16:$i]:
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 emptyset @
% 4.33/1.31 (
% 4.33/1.31 powerset
% 4.33/1.31 @
% 4.33/1.31 X16 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X18:$i]:
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 emptyset @
% 4.33/1.31 (
% 4.33/1.31 powerset
% 4.33/1.31 @
% 4.33/1.31 X18 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X20:$i,
% 4.33/1.31 X22:$i,
% 4.33/1.31 X24:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X22 @
% 4.33/1.31 (
% 4.33/1.31 powerset
% 4.33/1.31 @
% 4.33/1.31 X20 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X24 @ X22 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X24 @ X20 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setunionI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setunionE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subPowSU ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuE2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 nonemptyImpWitness ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 uniqinunit ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notinsingleton ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 eqinunit ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 singletonsswitch ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 upairsetE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 upairsetIL ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 upairsetIR ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 emptyE1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 vacuousDall ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan3 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 quantDeMorgan4 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 prop2setI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 prop2set2propI ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notdexE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notdallE ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuI1 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuI3 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuI2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 inCongP ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuE3u ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exu__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 emptyset__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setadjoin__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X26:$i,
% 4.33/1.31 X28:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X26 ) =
% 4.33/1.31 (
% 4.33/1.31 X28 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 powerset
% 4.33/1.31 @
% 4.33/1.31 X26 ) =
% 4.33/1.31 (
% 4.33/1.31 powerset
% 4.33/1.31 @
% 4.33/1.31 X28 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 setunion__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 omega__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 exuEu ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 descr__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 dsetconstr__Cong ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X30:$i,
% 4.33/1.31 X32:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X34:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X34 @ X30 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X34 @ X32 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X30 @ X32 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X36:$i,
% 4.33/1.31 X38:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X36 ) =
% 4.33/1.31 (
% 4.33/1.31 X38 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X38 @ X36 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X40:$i,
% 4.33/1.31 X42:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X40 ) =
% 4.33/1.31 (
% 4.33/1.31 X42 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X40 @ X42 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X44:$i,
% 4.33/1.31 X46:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X48:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X48 @ X44 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X48 @ X46 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X44 @ X46 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X50:$i]:
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 emptyset @
% 4.33/1.31 X50 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X52:$i,
% 4.33/1.31 X54:$i,
% 4.33/1.31 X56:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X52 @ X54 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X56 @ X52 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X56 @ X54 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X58:$i,
% 4.33/1.31 X60:$i,
% 4.33/1.31 X62:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X58 @ X60 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ~
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X62 @ X60 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 ~
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X62 @ X58 ) ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X64:$i,
% 4.33/1.31 X66:$i,
% 4.33/1.31 X68:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X68 @ X64 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ~
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X68 @ X66 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 ~
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X64 @ X66 ) ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X70:$i,
% 4.33/1.31 X72:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ~
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X70 @ X72 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X70 ) !=
% 4.33/1.31 (
% 4.33/1.31 X72 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 notequalI2 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X74:$i]:
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X74 @ X74 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X76:$i,
% 4.33/1.31 X78:$i,
% 4.33/1.31 X80:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X76 @ X78 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X78 @ X80 ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X76 @ X80 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X82:$i,
% 4.33/1.31 X84:$i]:
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X84 @
% 4.33/1.31 (
% 4.33/1.31 setadjoin
% 4.33/1.31 @
% 4.33/1.31 X82 @ X84 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X86:$i,
% 4.33/1.31 X88:$i,
% 4.33/1.31 X90:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X86 @ X90 ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X86 @
% 4.33/1.31 (
% 4.33/1.31 setadjoin
% 4.33/1.31 @
% 4.33/1.31 X88 @ X90 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X92:$i,
% 4.33/1.31 X94:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X92 @ X94 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X92 @
% 4.33/1.31 (
% 4.33/1.31 powerset
% 4.33/1.31 @
% 4.33/1.31 X94 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X96:$i,
% 4.33/1.31 X98:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X96 @ X98 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X98 @ X96 ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X96 ) =
% 4.33/1.31 (
% 4.33/1.31 X98 ) ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X100:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X100 @
% 4.33/1.31 emptyset ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 X100 ) =
% 4.33/1.31 (
% 4.33/1.31 emptyset ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X102:$i,
% 4.33/1.31 X104:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X104 @
% 4.33/1.31 X102 ) =>
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X104 @
% 4.33/1.31 (
% 4.33/1.31 powerset
% 4.33/1.31 @
% 4.33/1.31 X102 ) ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X106:$i,
% 4.33/1.31 X108:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X108 @
% 4.33/1.31 (
% 4.33/1.31 powerset
% 4.33/1.31 @
% 4.33/1.31 X106 ) ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X108 @
% 4.33/1.31 X106 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X110:$i]:
% 4.33/1.31 (
% 4.33/1.31 in @
% 4.33/1.31 X110 @
% 4.33/1.31 (
% 4.33/1.31 powerset
% 4.33/1.31 @
% 4.33/1.31 X110 ) ) ) =>
% 4.33/1.31 (
% 4.33/1.31 ![
% 4.33/1.31 X112:$i,
% 4.33/1.31 X114:$i]:
% 4.33/1.31 (
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 X112 @
% 4.33/1.31 X114 ) =>
% 4.33/1.31 (
% 4.33/1.31 subset @
% 4.33/1.31 (
% 4.33/1.31 powerset
% 4.33/1.31 @
% 4.33/1.31 X112 ) @
% 4.33/1.31 (
% 4.33/1.31 powerset
% 4.33/1.31 @
% 4.33/1.31 X114 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 4.33/1.31 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 4.33/1.31 thf(zip_derived_cl53, plain,
% 4.33/1.31 (~ (subset @ (powerset @ sk__57) @ (powerset @ sk__58))),
% 4.33/1.31 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.33/1.31 thf(zip_derived_cl51, plain,
% 4.33/1.31 (![X21 : $i, X22 : $i]:
% 4.33/1.31 ( (in @ X21 @ (powerset @ X22)) | ~ (subset @ X21 @ X22))),
% 4.33/1.31 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.33/1.31 thf(zip_derived_cl43, plain,
% 4.33/1.31 (![X5 : $i, X6 : $i]:
% 4.33/1.31 ( (subset @ X5 @ X6) | ~ (in @ (sk__59 @ X6 @ X5) @ X6))),
% 4.33/1.31 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.33/1.31 thf(zip_derived_cl167, plain,
% 4.33/1.31 (![X0 : $i, X1 : $i]:
% 4.33/1.31 (~ (subset @ (sk__59 @ (powerset @ X0) @ X1) @ X0)
% 4.33/1.31 | (subset @ X1 @ (powerset @ X0)))),
% 4.33/1.31 inference('sup-', [status(thm)], [zip_derived_cl51, zip_derived_cl43])).
% 4.33/1.31 thf(zip_derived_cl54, plain, ( (subset @ sk__57 @ sk__58)),
% 4.33/1.31 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.33/1.31 thf(zip_derived_cl44, plain,
% 4.33/1.31 (![X5 : $i, X6 : $i]:
% 4.33/1.31 ( (subset @ X5 @ X6) | (in @ (sk__59 @ X6 @ X5) @ X5))),
% 4.33/1.31 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.33/1.31 thf(zip_derived_cl55, plain,
% 4.33/1.31 (![X24 : $i, X25 : $i]:
% 4.33/1.31 ( (subset @ X24 @ X25) | ~ (in @ X24 @ (powerset @ X25)))),
% 4.33/1.31 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.33/1.31 thf(zip_derived_cl209, plain,
% 4.33/1.31 (![X0 : $i, X1 : $i]:
% 4.33/1.31 ( (subset @ (powerset @ X0) @ X1)
% 4.33/1.31 | (subset @ (sk__59 @ X1 @ (powerset @ X0)) @ X0))),
% 4.33/1.31 inference('sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl55])).
% 4.33/1.31 thf(zip_derived_cl48, plain,
% 4.33/1.31 (![X13 : $i, X14 : $i, X15 : $i]:
% 4.33/1.31 (~ (subset @ X13 @ X14)
% 4.33/1.31 | (subset @ X13 @ X15)
% 4.33/1.31 | ~ (subset @ X14 @ X15))),
% 4.33/1.31 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.33/1.31 thf(zip_derived_cl227, plain,
% 4.33/1.31 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.33/1.31 ( (subset @ (powerset @ X0) @ X1)
% 4.33/1.31 | ~ (subset @ X0 @ X2)
% 4.33/1.31 | (subset @ (sk__59 @ X1 @ (powerset @ X0)) @ X2))),
% 4.33/1.31 inference('sup-', [status(thm)], [zip_derived_cl209, zip_derived_cl48])).
% 4.33/1.31 thf(zip_derived_cl1106, plain,
% 4.33/1.31 (![X0 : $i]:
% 4.33/1.31 ( (subset @ (sk__59 @ X0 @ (powerset @ sk__57)) @ sk__58)
% 4.33/1.31 | (subset @ (powerset @ sk__57) @ X0))),
% 4.33/1.31 inference('sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl227])).
% 4.33/1.31 thf(zip_derived_cl1161, plain,
% 4.33/1.31 (( (subset @ (powerset @ sk__57) @ (powerset @ sk__58))
% 4.33/1.31 | (subset @ (powerset @ sk__57) @ (powerset @ sk__58)))),
% 4.33/1.31 inference('sup+', [status(thm)], [zip_derived_cl167, zip_derived_cl1106])).
% 4.33/1.31 thf(zip_derived_cl1176, plain,
% 4.33/1.31 ( (subset @ (powerset @ sk__57) @ (powerset @ sk__58))),
% 4.33/1.31 inference('simplify', [status(thm)], [zip_derived_cl1161])).
% 4.33/1.31 thf(zip_derived_cl1180, plain, ($false),
% 4.33/1.31 inference('demod', [status(thm)], [zip_derived_cl53, zip_derived_cl1176])).
% 4.33/1.31
% 4.33/1.31 % SZS output end Refutation
% 4.33/1.31
% 4.33/1.31
% 4.33/1.31 % Terminating...
% 4.91/1.48 % Runner terminated.
% 4.91/1.51 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------