%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU571^1 : 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.80UpyS6pqW true
% Computer : n016.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 04:55:07 PM UTC 2025
% Result : Theorem 0.48s 1.03s
% Output : Refutation 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU571^1 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.80UpyS6pqW true
% 0.13/0.36 % Computer : n016.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Oct 1 16:15:08 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Running portfolio for 300 s
% 0.13/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.37 % Python version: Python 3.6.8
% 0.13/0.37 % Running in HO mode
% 0.45/0.63 % Total configuration time : 828
% 0.45/0.63 % Estimated wc time : 1656
% 0.45/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.47/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.47/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.47/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.47/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.47/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.47/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.47/0.74 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.48/0.81 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.48/1.03 % Solved by lams/40_c_ic.sh.
% 0.48/1.03 % done 229 iterations in 0.253s
% 0.48/1.03 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.48/1.03 % SZS output start Refutation
% 0.48/1.03 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 0.48/1.03 thf(notdexE_type, type, notdexE: $o).
% 0.48/1.03 thf(setunionAx_type, type, setunionAx: $o).
% 0.48/1.03 thf(powersetE_type, type, powersetE: $o).
% 0.48/1.03 thf(omegaSAx_type, type, omegaSAx: $o).
% 0.48/1.03 thf(exuI1_type, type, exuI1: $o).
% 0.48/1.03 thf(exuI2_type, type, exuI2: $o).
% 0.48/1.03 thf(notequalI2_type, type, notequalI2: $o).
% 0.48/1.03 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 0.48/1.03 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 0.48/1.03 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 0.48/1.03 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 0.48/1.03 thf(sk__61_type, type, sk__61: $i).
% 0.48/1.03 thf(setext_type, type, setext: $o).
% 0.48/1.03 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 0.48/1.03 thf(descr__Cong_type, type, descr__Cong: $o).
% 0.48/1.03 thf(in_type, type, in: $i > $i > $o).
% 0.48/1.03 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 0.48/1.03 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 0.48/1.03 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 0.48/1.03 thf(subsetE_type, type, subsetE: $o).
% 0.48/1.03 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 0.48/1.03 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 0.48/1.03 thf(setbeta_type, type, setbeta: $o).
% 0.48/1.03 thf(eqinunit_type, type, eqinunit: $o).
% 0.48/1.03 thf(upairsetIL_type, type, upairsetIL: $o).
% 0.48/1.03 thf(powersetAx_type, type, powersetAx: $o).
% 0.48/1.03 thf(powersetI_type, type, powersetI: $o).
% 0.48/1.03 thf(upairsetIR_type, type, upairsetIR: $o).
% 0.48/1.03 thf(inCongP_type, type, inCongP: $o).
% 0.48/1.03 thf(sk__63_type, type, sk__63: $i > $i > $i).
% 0.48/1.03 thf(exuE3e_type, type, exuE3e: $o).
% 0.48/1.03 thf(emptysetE_type, type, emptysetE: $o).
% 0.48/1.03 thf(setunionI_type, type, setunionI: $o).
% 0.48/1.03 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 0.48/1.03 thf(prop2setI_type, type, prop2setI: $o).
% 0.48/1.03 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 0.48/1.03 thf(exuE2_type, type, exuE2: $o).
% 0.48/1.03 thf(emptyset_type, type, emptyset: $i).
% 0.48/1.03 thf(subPowSU_type, type, subPowSU: $o).
% 0.48/1.03 thf(notequalI1_type, type, notequalI1: $o).
% 0.48/1.03 thf(notinemptyset_type, type, notinemptyset: $o).
% 0.48/1.03 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 0.48/1.03 thf(subsetTrans_type, type, subsetTrans: $o).
% 0.48/1.03 thf(subsetE2_type, type, subsetE2: $o).
% 0.48/1.03 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 0.48/1.03 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 0.48/1.03 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 0.48/1.03 thf(setunionE_type, type, setunionE: $o).
% 0.48/1.03 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 0.48/1.03 thf(setadjoinE_type, type, setadjoinE: $o).
% 0.48/1.03 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 0.48/1.03 thf(exuE1_type, type, exuE1: $o).
% 0.48/1.03 thf(notinsingleton_type, type, notinsingleton: $o).
% 0.48/1.03 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 0.48/1.03 thf(exuEu_type, type, exuEu: $o).
% 0.48/1.03 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 0.48/1.03 thf(upairsetE_type, type, upairsetE: $o).
% 0.48/1.03 thf(omega0Ax_type, type, omega0Ax: $o).
% 0.48/1.03 thf(notsubsetI_type, type, notsubsetI: $o).
% 0.48/1.03 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 0.48/1.03 thf(setextAx_type, type, setextAx: $o).
% 0.48/1.03 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 0.48/1.03 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 0.48/1.03 thf(subsetI1_type, type, subsetI1: $o).
% 0.48/1.03 thf(descrp_type, type, descrp: $o).
% 0.48/1.03 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 0.48/1.03 thf(foundationAx_type, type, foundationAx: $o).
% 0.48/1.03 thf(emptysetAx_type, type, emptysetAx: $o).
% 0.48/1.03 thf(emptyI_type, type, emptyI: $o).
% 0.48/1.03 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 0.48/1.03 thf(emptyE1_type, type, emptyE1: $o).
% 0.48/1.03 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 0.48/1.03 thf(vacuousDall_type, type, vacuousDall: $o).
% 0.48/1.03 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 0.48/1.03 thf(sk__62_type, type, sk__62: $i).
% 0.48/1.03 thf(subsetI2_type, type, subsetI2: $o).
% 0.48/1.03 thf(omega__Cong_type, type, omega__Cong: $o).
% 0.48/1.03 thf(subsetRefl_type, type, subsetRefl: $o).
% 0.48/1.03 thf(uniqinunit_type, type, uniqinunit: $o).
% 0.48/1.03 thf(prop2setE_type, type, prop2setE: $o).
% 0.48/1.03 thf(nonemptyI_type, type, nonemptyI: $o).
% 0.48/1.03 thf(exuE3u_type, type, exuE3u: $o).
% 0.48/1.03 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 0.48/1.03 thf(exuI3_type, type, exuI3: $o).
% 0.48/1.03 thf(notdallE_type, type, notdallE: $o).
% 0.48/1.03 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 0.48/1.03 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 0.48/1.03 thf(exu__Cong_type, type, exu__Cong: $o).
% 0.48/1.03 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 0.48/1.03 thf(replAx_type, type, replAx: $o).
% 0.48/1.03 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 0.48/1.03 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 0.48/1.03 thf(subset_type, type, subset: $i > $i > $o).
% 0.48/1.03 thf(in__Cong_type, type, in__Cong: $o).
% 0.48/1.03 thf(subsetTrans, axiom, subsetTrans =
% 0.48/1.03 (![A:$i,B:$i,C:$i]:
% 0.48/1.03 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 0.48/1.03 thf('0', plain,
% 0.48/1.03 (( subsetTrans ) =
% 0.48/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.48/1.03 ( ( subset @ X4 @ X6 ) =>
% 0.48/1.03 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 0.48/1.03 thf('1', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(notequalI1, axiom, notequalI1 =
% 0.48/1.03 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 0.48/1.03 thf('2', plain,
% 0.48/1.03 (( notequalI1 ) =
% 0.48/1.03 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(notsubsetI, axiom, notsubsetI =
% 0.48/1.03 (![A:$i,B:$i,Xx:$i]:
% 0.48/1.03 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 0.48/1.03 thf('3', plain,
% 0.48/1.03 (( notsubsetI ) =
% 0.48/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.48/1.03 ( ( in @ X8 @ X4 ) =>
% 0.48/1.03 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(subsetE2, axiom, subsetE2 =
% 0.48/1.03 (![A:$i,B:$i,Xx:$i]:
% 0.48/1.03 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 0.48/1.03 thf('4', plain,
% 0.48/1.03 (( subsetE2 ) =
% 0.48/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.48/1.03 ( ( subset @ X4 @ X6 ) =>
% 0.48/1.03 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(subsetE, axiom, subsetE =
% 0.48/1.03 (![A:$i,B:$i,Xx:$i]:
% 0.48/1.03 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 0.48/1.03 thf('5', plain,
% 0.48/1.03 (( subsetE ) =
% 0.48/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.48/1.03 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(emptysetsubset, axiom, emptysetsubset =
% 0.48/1.03 (![A:$i]: ( subset @ emptyset @ A ))).
% 0.48/1.03 thf('6', plain,
% 0.48/1.03 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(subsetI2, axiom, subsetI2 =
% 0.48/1.03 (![A:$i,B:$i]:
% 0.48/1.03 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 0.48/1.03 ( subset @ A @ B ) ))).
% 0.48/1.03 thf('7', plain,
% 0.48/1.03 (( subsetI2 ) =
% 0.48/1.03 ( ![X4:$i,X6:$i]:
% 0.48/1.03 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 0.48/1.03 ( subset @ X4 @ X6 ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 0.48/1.03 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 0.48/1.03 thf('8', plain,
% 0.48/1.03 (( eqimpsubset1 ) =
% 0.48/1.03 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 0.48/1.03 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 0.48/1.03 thf('9', plain,
% 0.48/1.03 (( eqimpsubset2 ) =
% 0.48/1.03 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(subsetI1, axiom, subsetI1 =
% 0.48/1.03 (![A:$i,B:$i]:
% 0.48/1.03 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 0.48/1.03 ( subset @ A @ B ) ))).
% 0.48/1.03 thf('10', plain,
% 0.48/1.03 (( subsetI1 ) =
% 0.48/1.03 ( ![X4:$i,X6:$i]:
% 0.48/1.03 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 0.48/1.03 ( subset @ X4 @ X6 ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 0.48/1.03 (![Xx:$i,Xy:$i]:
% 0.48/1.03 ( ( ( Xx ) = ( Xy ) ) =>
% 0.48/1.03 ( ![Xz:$i,Xu:$i]:
% 0.48/1.03 ( ( ( Xz ) = ( Xu ) ) =>
% 0.48/1.03 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 0.48/1.03 thf('11', plain,
% 0.48/1.03 (( setadjoin__Cong ) =
% 0.48/1.03 ( ![X4:$i,X6:$i]:
% 0.48/1.03 ( ( ( X4 ) = ( X6 ) ) =>
% 0.48/1.03 ( ![X8:$i,X10:$i]:
% 0.48/1.03 ( ( ( X8 ) = ( X10 ) ) =>
% 0.48/1.03 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(upairsetIR, axiom, upairsetIR =
% 0.48/1.03 (![Xx:$i,Xy:$i]:
% 0.48/1.03 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.48/1.03 thf('12', plain,
% 0.48/1.03 (( upairsetIR ) =
% 0.48/1.03 ( ![X4:$i,X6:$i]:
% 0.48/1.03 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(upairsetIL, axiom, upairsetIL =
% 0.48/1.03 (![Xx:$i,Xy:$i]:
% 0.48/1.03 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.48/1.03 thf('13', plain,
% 0.48/1.03 (( upairsetIL ) =
% 0.48/1.03 ( ![X4:$i,X6:$i]:
% 0.48/1.03 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(upairsetE, axiom, upairsetE =
% 0.48/1.03 (![Xx:$i,Xy:$i,Xz:$i]:
% 0.48/1.03 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 0.48/1.03 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 0.48/1.03 thf('14', plain,
% 0.48/1.03 (( upairsetE ) =
% 0.48/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.48/1.03 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 0.48/1.03 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(singletonsswitch, axiom, singletonsswitch =
% 0.48/1.03 (![Xx:$i,Xy:$i]:
% 0.48/1.03 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 0.48/1.03 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 0.48/1.03 thf('15', plain,
% 0.48/1.03 (( singletonsswitch ) =
% 0.48/1.03 ( ![X4:$i,X6:$i]:
% 0.48/1.03 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 0.48/1.03 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(eqinunit, axiom, eqinunit =
% 0.48/1.03 (![Xx:$i,Xy:$i]:
% 0.48/1.03 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.48/1.03 thf('16', plain,
% 0.48/1.03 (( eqinunit ) =
% 0.48/1.03 ( ![X4:$i,X6:$i]:
% 0.48/1.03 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(notinsingleton, axiom, notinsingleton =
% 0.48/1.03 (![Xx:$i,Xy:$i]:
% 0.48/1.03 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 0.48/1.03 thf('17', plain,
% 0.48/1.03 (( notinsingleton ) =
% 0.48/1.03 ( ![X4:$i,X6:$i]:
% 0.48/1.03 ( ( ( X4 ) != ( X6 ) ) =>
% 0.48/1.03 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(uniqinunit, axiom, uniqinunit =
% 0.48/1.03 (![Xx:$i,Xy:$i]:
% 0.48/1.03 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 0.48/1.03 thf('18', plain,
% 0.48/1.03 (( uniqinunit ) =
% 0.48/1.03 ( ![X4:$i,X6:$i]:
% 0.48/1.03 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(setadjoinOr, axiom, setadjoinOr =
% 0.48/1.03 (![Xx:$i,A:$i,Xy:$i]:
% 0.48/1.03 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 0.48/1.03 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 0.48/1.03 thf('19', plain,
% 0.48/1.03 (( setadjoinOr ) =
% 0.48/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.48/1.03 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 0.48/1.03 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(setadjoinE, axiom, setadjoinE =
% 0.48/1.03 (![Xx:$i,A:$i,Xy:$i]:
% 0.48/1.03 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 0.48/1.03 ( ![Xphi:$o]:
% 0.48/1.03 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 0.48/1.03 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 0.48/1.03 thf('20', plain,
% 0.48/1.03 (( setadjoinE ) =
% 0.48/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.48/1.03 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 0.48/1.03 ( ![X10:$o]:
% 0.48/1.03 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 0.48/1.03 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(setadjoinIR, axiom, setadjoinIR =
% 0.48/1.03 (![Xx:$i,A:$i,Xy:$i]:
% 0.48/1.03 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 0.48/1.03 thf('21', plain,
% 0.48/1.03 (( setadjoinIR ) =
% 0.48/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.48/1.03 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 0.48/1.03 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 0.48/1.03 thf('22', plain,
% 0.48/1.03 (( emptyinunitempty ) =
% 0.48/1.03 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 0.48/1.03 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 0.48/1.03 thf('23', plain,
% 0.48/1.03 (( emptyinunitempty ) =
% 0.48/1.03 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(setadjoinIL, axiom, setadjoinIL =
% 0.48/1.03 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 0.48/1.03 thf('24', plain,
% 0.48/1.03 (( setadjoinIL ) =
% 0.48/1.03 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(setadjoinAx, axiom, setadjoinAx =
% 0.48/1.03 (![Xx:$i,A:$i,Xy:$i]:
% 0.48/1.03 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 0.48/1.03 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 0.48/1.03 thf('25', plain,
% 0.48/1.03 (( setadjoinAx ) =
% 0.48/1.03 ( ![X4:$i,X6:$i,X8:$i]:
% 0.48/1.03 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.48/1.03 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 0.48/1.03 define([status(thm)])).
% 0.48/1.03 thf(setadjoinSub, conjecture,
% 0.48/1.03 (( setextAx ) =>
% 0.48/1.03 ( ( emptysetAx ) =>
% 0.48/1.03 ( ( setadjoinAx ) =>
% 0.48/1.03 ( ( powersetAx ) =>
% 0.48/1.03 ( ( setunionAx ) =>
% 0.48/1.03 ( ( omega0Ax ) =>
% 0.48/1.03 ( ( omegaSAx ) =>
% 0.48/1.03 ( ( omegaIndAx ) =>
% 0.48/1.03 ( ( replAx ) =>
% 0.48/1.03 ( ( foundationAx ) =>
% 0.48/1.03 ( ( wellorderingAx ) =>
% 0.48/1.03 ( ( descrp ) =>
% 0.48/1.03 ( ( dsetconstrI ) =>
% 0.48/1.03 ( ( dsetconstrEL ) =>
% 0.48/1.03 ( ( dsetconstrER ) =>
% 0.48/1.03 ( ( exuE1 ) =>
% 0.48/1.03 ( ( prop2setE ) =>
% 0.48/1.03 ( ( emptysetE ) =>
% 0.48/1.03 ( ( emptysetimpfalse ) =>
% 0.48/1.03 ( ( notinemptyset ) =>
% 0.48/1.03 ( ( exuE3e ) =>
% 0.48/1.03 ( ( setext ) =>
% 0.48/1.03 ( ( emptyI ) =>
% 0.48/1.03 ( ( noeltsimpempty ) =>
% 0.48/1.03 ( ( setbeta ) =>
% 0.48/1.03 ( ( nonemptyE1 ) =>
% 0.48/1.03 ( ( nonemptyI ) =>
% 0.48/1.03 ( ( nonemptyI1 ) =>
% 0.48/1.03 ( ( setadjoinIL ) =>
% 0.48/1.03 ( ( emptyinunitempty ) =>
% 0.48/1.03 ( ( setadjoinIR ) =>
% 0.48/1.03 ( ( setadjoinE ) =>
% 0.48/1.03 ( (
% 0.48/1.03 setadjoinOr ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 setoftrueEq ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 powersetI ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 emptyinPowerset ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 emptyInPowerset ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 powersetE ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 setunionI ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 setunionE ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 subPowSU ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 exuE2 ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 nonemptyImpWitness ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 uniqinunit ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 notinsingleton ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 eqinunit ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 singletonsswitch ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 upairsetE ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 upairsetIL ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 upairsetIR ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.03 emptyE1 ) =>
% 0.48/1.03 (
% 0.48/1.03 (
% 0.48/1.04 vacuousDall ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan3 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan4 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 prop2setI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 prop2set2propI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notdexE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notdallE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuI1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuI3 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuI2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 inCongP ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuE3u ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exu__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptyset__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setadjoin__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 powerset__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setunion__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 omega__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuEu ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 descr__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 dsetconstr__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subsetI1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 eqimpsubset2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 eqimpsubset1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subsetI2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptysetsubset ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subsetE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subsetE2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notsubsetI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notequalI1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notequalI2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subsetRefl ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subsetTrans ) =>
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 Xx:$i,A:$i]:
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 A @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.48/1.04 thf(zf_stmt_0, conjecture,
% 0.48/1.04 (( setextAx ) =>
% 0.48/1.04 ( ( emptysetAx ) =>
% 0.48/1.04 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.48/1.04 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.48/1.04 ( ( in @ X8 @ X6 ) | ( ( X8 ) = ( X4 ) ) ) ) ) =>
% 0.48/1.04 ( ( powersetAx ) =>
% 0.48/1.04 ( ( setunionAx ) =>
% 0.48/1.04 ( ( omega0Ax ) =>
% 0.48/1.04 ( ( omegaSAx ) =>
% 0.48/1.04 ( ( omegaIndAx ) =>
% 0.48/1.04 ( ( replAx ) =>
% 0.48/1.04 ( ( foundationAx ) =>
% 0.48/1.04 ( ( wellorderingAx ) =>
% 0.48/1.04 ( ( descrp ) =>
% 0.48/1.04 ( ( dsetconstrI ) =>
% 0.48/1.04 ( ( dsetconstrEL ) =>
% 0.48/1.04 ( ( dsetconstrER ) =>
% 0.48/1.04 ( ( exuE1 ) =>
% 0.48/1.04 ( ( prop2setE ) =>
% 0.48/1.04 ( ( emptysetE ) =>
% 0.48/1.04 ( ( emptysetimpfalse ) =>
% 0.48/1.04 ( ( notinemptyset ) =>
% 0.48/1.04 ( ( exuE3e ) =>
% 0.48/1.04 ( ( setext ) =>
% 0.48/1.04 ( ( emptyI ) =>
% 0.48/1.04 ( ( noeltsimpempty ) =>
% 0.48/1.04 ( ( setbeta ) =>
% 0.48/1.04 ( ( nonemptyE1 ) =>
% 0.48/1.04 ( ( nonemptyI ) =>
% 0.48/1.04 ( ( nonemptyI1 ) =>
% 0.48/1.04 ( ( ![X10:$i,X12:$i]:
% 0.48/1.04 ( in @
% 0.48/1.04 X10 @
% 0.48/1.04 ( setadjoin @
% 0.48/1.04 X10 @ X12 ) ) ) =>
% 0.48/1.04 ( ( in @
% 0.48/1.04 emptyset @
% 0.48/1.04 ( setadjoin @
% 0.48/1.04 emptyset @
% 0.48/1.04 emptyset ) ) =>
% 0.48/1.04 ( ( ![X14:$i,
% 0.48/1.04 X16:$i,
% 0.48/1.04 X18:$i]:
% 0.48/1.04 ( (
% 0.48/1.04 in @
% 0.48/1.04 X18 @ X16 ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X18 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X14 @ X16 ) ) ) ) =>
% 0.48/1.04 ( ( ![
% 0.48/1.04 X20:$i,
% 0.48/1.04 X22:$i,
% 0.48/1.04 X24:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X24 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X20 @ X22 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X26:$o]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X24 ) =
% 0.48/1.04 (
% 0.48/1.04 X20 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 X26 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X24 @ X22 ) =>
% 0.48/1.04 (
% 0.48/1.04 X26 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 X26 ) ) ) ) ) ) =>
% 0.48/1.04 ( (
% 0.48/1.04 ![
% 0.48/1.04 X28:$i,
% 0.48/1.04 X30:$i,
% 0.48/1.04 X32:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X32 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X28 @ X30 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X32 @ X30 ) |
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X32 ) =
% 0.48/1.04 (
% 0.48/1.04 X28 ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setoftrueEq ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 powersetI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptyinPowerset ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptyInPowerset ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 powersetE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setunionI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setunionE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subPowSU ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuE2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 nonemptyImpWitness ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X34:$i,
% 0.48/1.04 X36:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X34 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X36 @
% 0.48/1.04 emptyset ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X34 ) =
% 0.48/1.04 (
% 0.48/1.04 X36 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X38:$i,
% 0.48/1.04 X40:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X38 ) !=
% 0.48/1.04 (
% 0.48/1.04 X40 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ~(
% 0.48/1.04 in @
% 0.48/1.04 X40 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X38 @
% 0.48/1.04 emptyset ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X42:$i,
% 0.48/1.04 X44:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X42 ) =
% 0.48/1.04 (
% 0.48/1.04 X44 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X42 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X44 @
% 0.48/1.04 emptyset ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X46:$i,
% 0.48/1.04 X48:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X46 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X48 @
% 0.48/1.04 emptyset ) ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X48 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X46 @
% 0.48/1.04 emptyset ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X50:$i,
% 0.48/1.04 X52:$i,
% 0.48/1.04 X54:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X54 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X50 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X52 @
% 0.48/1.04 emptyset ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X54 ) =
% 0.48/1.04 (
% 0.48/1.04 X52 ) ) |
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X54 ) =
% 0.48/1.04 (
% 0.48/1.04 X50 ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X56:$i,
% 0.48/1.04 X58:$i]:
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X56 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X56 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X58 @
% 0.48/1.04 emptyset ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X60:$i,
% 0.48/1.04 X62:$i]:
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X62 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X60 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X62 @
% 0.48/1.04 emptyset ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptyE1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 vacuousDall ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan3 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan4 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 prop2setI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 prop2set2propI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notdexE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notdallE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuI1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuI3 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuI2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 inCongP ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuE3u ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exu__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptyset__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X64:$i,
% 0.48/1.04 X66:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X64 ) =
% 0.48/1.04 (
% 0.48/1.04 X66 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X68:$i,
% 0.48/1.04 X70:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X68 ) =
% 0.48/1.04 (
% 0.48/1.04 X70 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X64 @ X68 ) =
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X66 @ X70 ) ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 powerset__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setunion__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 omega__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuEu ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 descr__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 dsetconstr__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X72:$i,
% 0.48/1.04 X74:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X76:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X76 @ X72 ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X76 @ X74 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X72 @ X74 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X78:$i,
% 0.48/1.04 X80:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X78 ) =
% 0.48/1.04 (
% 0.48/1.04 X80 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X80 @ X78 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X82:$i,
% 0.48/1.04 X84:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X82 ) =
% 0.48/1.04 (
% 0.48/1.04 X84 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X82 @ X84 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X86:$i,
% 0.48/1.04 X88:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X90:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X90 @ X86 ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X90 @ X88 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X86 @ X88 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X92:$i]:
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 emptyset @
% 0.48/1.04 X92 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X94:$i,
% 0.48/1.04 X96:$i,
% 0.48/1.04 X98:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X94 @ X96 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X98 @ X94 ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X98 @ X96 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X100:$i,
% 0.48/1.04 X102:$i,
% 0.48/1.04 X104:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X100 @
% 0.48/1.04 X102 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ~(
% 0.48/1.04 in @
% 0.48/1.04 X104 @
% 0.48/1.04 X102 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ~(
% 0.48/1.04 in @
% 0.48/1.04 X104 @
% 0.48/1.04 X100 ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X106:$i,
% 0.48/1.04 X108:$i,
% 0.48/1.04 X110:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X110 @
% 0.48/1.04 X106 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ~(
% 0.48/1.04 in @
% 0.48/1.04 X110 @
% 0.48/1.04 X108 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ~(
% 0.48/1.04 subset @
% 0.48/1.04 X106 @
% 0.48/1.04 X108 ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X112:$i,
% 0.48/1.04 X114:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ~(
% 0.48/1.04 subset @
% 0.48/1.04 X112 @
% 0.48/1.04 X114 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X112 ) !=
% 0.48/1.04 (
% 0.48/1.04 X114 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notequalI2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X116:$i]:
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X116 @
% 0.48/1.04 X116 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X118:$i,
% 0.48/1.04 X120:$i,
% 0.48/1.04 X122:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X118 @
% 0.48/1.04 X120 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X120 @
% 0.48/1.04 X122 ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X118 @
% 0.48/1.04 X122 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X124:$i,
% 0.48/1.04 X126:$i]:
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X126 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X124 @
% 0.48/1.04 X126 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.48/1.04 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 0.48/1.04 thf(zf_stmt_2, axiom,
% 0.48/1.04 (![X8:$i,X6:$i,X4:$i]:
% 0.48/1.04 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 0.48/1.04 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ))).
% 0.48/1.04 thf(zf_stmt_3, conjecture,
% 0.48/1.04 (( setextAx ) =>
% 0.48/1.04 ( ( emptysetAx ) =>
% 0.48/1.04 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.48/1.04 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.48/1.04 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 0.48/1.04 ( ( powersetAx ) =>
% 0.48/1.04 ( ( setunionAx ) =>
% 0.48/1.04 ( ( omega0Ax ) =>
% 0.48/1.04 ( ( omegaSAx ) =>
% 0.48/1.04 ( ( omegaIndAx ) =>
% 0.48/1.04 ( ( replAx ) =>
% 0.48/1.04 ( ( foundationAx ) =>
% 0.48/1.04 ( ( wellorderingAx ) =>
% 0.48/1.04 ( ( descrp ) =>
% 0.48/1.04 ( ( dsetconstrI ) =>
% 0.48/1.04 ( ( dsetconstrEL ) =>
% 0.48/1.04 ( ( dsetconstrER ) =>
% 0.48/1.04 ( ( exuE1 ) =>
% 0.48/1.04 ( ( prop2setE ) =>
% 0.48/1.04 ( ( emptysetE ) =>
% 0.48/1.04 ( ( emptysetimpfalse ) =>
% 0.48/1.04 ( ( notinemptyset ) =>
% 0.48/1.04 ( ( exuE3e ) =>
% 0.48/1.04 ( ( setext ) =>
% 0.48/1.04 ( ( emptyI ) =>
% 0.48/1.04 ( ( noeltsimpempty ) =>
% 0.48/1.04 ( ( setbeta ) =>
% 0.48/1.04 ( ( nonemptyE1 ) =>
% 0.48/1.04 ( ( nonemptyI ) =>
% 0.48/1.04 ( ( nonemptyI1 ) =>
% 0.48/1.04 ( ( ![X10:$i,X12:$i]:
% 0.48/1.04 ( in @
% 0.48/1.04 X10 @
% 0.48/1.04 ( setadjoin @
% 0.48/1.04 X10 @ X12 ) ) ) =>
% 0.48/1.04 ( ( in @
% 0.48/1.04 emptyset @
% 0.48/1.04 ( setadjoin @
% 0.48/1.04 emptyset @
% 0.48/1.04 emptyset ) ) =>
% 0.48/1.04 ( ( ![X14:$i,
% 0.48/1.04 X16:$i,
% 0.48/1.04 X18:$i]:
% 0.48/1.04 ( (
% 0.48/1.04 in @
% 0.48/1.04 X18 @ X16 ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X18 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X14 @ X16 ) ) ) ) =>
% 0.48/1.04 ( ( ![
% 0.48/1.04 X20:$i,
% 0.48/1.04 X22:$i,
% 0.48/1.04 X24:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X24 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X20 @ X22 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X26:$o]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X24 ) =
% 0.48/1.04 (
% 0.48/1.04 X20 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 X26 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X24 @ X22 ) =>
% 0.48/1.04 (
% 0.48/1.04 X26 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 X26 ) ) ) ) ) ) =>
% 0.48/1.04 ( (
% 0.48/1.04 ![
% 0.48/1.04 X28:$i,
% 0.48/1.04 X30:$i,
% 0.48/1.04 X32:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X32 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X28 @ X30 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X32 ) =
% 0.48/1.04 (
% 0.48/1.04 X28 ) ) |
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X32 @ X30 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setoftrueEq ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 powersetI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptyinPowerset ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptyInPowerset ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 powersetE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setunionI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setunionE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subPowSU ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuE2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 nonemptyImpWitness ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X34:$i,
% 0.48/1.04 X36:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X34 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X36 @
% 0.48/1.04 emptyset ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X34 ) =
% 0.48/1.04 (
% 0.48/1.04 X36 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X38:$i,
% 0.48/1.04 X40:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X38 ) !=
% 0.48/1.04 (
% 0.48/1.04 X40 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ~(
% 0.48/1.04 in @
% 0.48/1.04 X40 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X38 @
% 0.48/1.04 emptyset ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X42:$i,
% 0.48/1.04 X44:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X42 ) =
% 0.48/1.04 (
% 0.48/1.04 X44 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X42 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X44 @
% 0.48/1.04 emptyset ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X46:$i,
% 0.48/1.04 X48:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X46 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X48 @
% 0.48/1.04 emptyset ) ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X48 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X46 @
% 0.48/1.04 emptyset ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X50:$i,
% 0.48/1.04 X52:$i,
% 0.48/1.04 X54:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X54 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X50 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X52 @
% 0.48/1.04 emptyset ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X54 ) =
% 0.48/1.04 (
% 0.48/1.04 X50 ) ) |
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X54 ) =
% 0.48/1.04 (
% 0.48/1.04 X52 ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X56:$i,
% 0.48/1.04 X58:$i]:
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X56 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X56 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X58 @
% 0.48/1.04 emptyset ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X60:$i,
% 0.48/1.04 X62:$i]:
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X62 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X60 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X62 @
% 0.48/1.04 emptyset ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptyE1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 vacuousDall ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan3 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan4 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 prop2setI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 prop2set2propI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notdexE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notdallE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuI1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuI3 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuI2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 inCongP ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuE3u ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exu__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptyset__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X64:$i,
% 0.48/1.04 X66:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X64 ) =
% 0.48/1.04 (
% 0.48/1.04 X66 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X68:$i,
% 0.48/1.04 X70:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X68 ) =
% 0.48/1.04 (
% 0.48/1.04 X70 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X64 @ X68 ) =
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X66 @ X70 ) ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 powerset__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setunion__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 omega__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuEu ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 descr__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 dsetconstr__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X72:$i,
% 0.48/1.04 X74:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X76:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X76 @ X72 ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X76 @ X74 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X72 @ X74 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X78:$i,
% 0.48/1.04 X80:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X78 ) =
% 0.48/1.04 (
% 0.48/1.04 X80 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X80 @ X78 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X82:$i,
% 0.48/1.04 X84:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X82 ) =
% 0.48/1.04 (
% 0.48/1.04 X84 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X82 @ X84 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X86:$i,
% 0.48/1.04 X88:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X90:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X90 @ X86 ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X90 @ X88 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X86 @ X88 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X92:$i]:
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 emptyset @
% 0.48/1.04 X92 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X94:$i,
% 0.48/1.04 X96:$i,
% 0.48/1.04 X98:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X94 @ X96 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X98 @ X94 ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X98 @ X96 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X100:$i,
% 0.48/1.04 X102:$i,
% 0.48/1.04 X104:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X100 @
% 0.48/1.04 X102 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ~(
% 0.48/1.04 in @
% 0.48/1.04 X104 @
% 0.48/1.04 X102 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ~(
% 0.48/1.04 in @
% 0.48/1.04 X104 @
% 0.48/1.04 X100 ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X106:$i,
% 0.48/1.04 X108:$i,
% 0.48/1.04 X110:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X110 @
% 0.48/1.04 X106 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ~(
% 0.48/1.04 in @
% 0.48/1.04 X110 @
% 0.48/1.04 X108 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ~(
% 0.48/1.04 subset @
% 0.48/1.04 X106 @
% 0.48/1.04 X108 ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X112:$i,
% 0.48/1.04 X114:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ~(
% 0.48/1.04 subset @
% 0.48/1.04 X112 @
% 0.48/1.04 X114 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X112 ) !=
% 0.48/1.04 (
% 0.48/1.04 X114 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notequalI2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X116:$i]:
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X116 @
% 0.48/1.04 X116 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X118:$i,
% 0.48/1.04 X120:$i,
% 0.48/1.04 X122:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X118 @
% 0.48/1.04 X120 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X120 @
% 0.48/1.04 X122 ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X118 @
% 0.48/1.04 X122 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X124:$i,
% 0.48/1.04 X126:$i]:
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X126 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X124 @
% 0.48/1.04 X126 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.48/1.04 thf(zf_stmt_4, negated_conjecture,
% 0.48/1.04 (~( ( setextAx ) =>
% 0.48/1.04 ( ( emptysetAx ) =>
% 0.48/1.04 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.48/1.04 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.48/1.04 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 0.48/1.04 ( ( powersetAx ) =>
% 0.48/1.04 ( ( setunionAx ) =>
% 0.48/1.04 ( ( omega0Ax ) =>
% 0.48/1.04 ( ( omegaSAx ) =>
% 0.48/1.04 ( ( omegaIndAx ) =>
% 0.48/1.04 ( ( replAx ) =>
% 0.48/1.04 ( ( foundationAx ) =>
% 0.48/1.04 ( ( wellorderingAx ) =>
% 0.48/1.04 ( ( descrp ) =>
% 0.48/1.04 ( ( dsetconstrI ) =>
% 0.48/1.04 ( ( dsetconstrEL ) =>
% 0.48/1.04 ( ( dsetconstrER ) =>
% 0.48/1.04 ( ( exuE1 ) =>
% 0.48/1.04 ( ( prop2setE ) =>
% 0.48/1.04 ( ( emptysetE ) =>
% 0.48/1.04 ( ( emptysetimpfalse ) =>
% 0.48/1.04 ( ( notinemptyset ) =>
% 0.48/1.04 ( ( exuE3e ) =>
% 0.48/1.04 ( ( setext ) =>
% 0.48/1.04 ( ( emptyI ) =>
% 0.48/1.04 ( ( noeltsimpempty ) =>
% 0.48/1.04 ( ( setbeta ) =>
% 0.48/1.04 ( ( nonemptyE1 ) =>
% 0.48/1.04 ( ( nonemptyI ) =>
% 0.48/1.04 ( ( nonemptyI1 ) =>
% 0.48/1.04 ( ( ![X10:$i,
% 0.48/1.04 X12:$i]:
% 0.48/1.04 ( in @
% 0.48/1.04 X10 @
% 0.48/1.04 ( setadjoin
% 0.48/1.04 @
% 0.48/1.04 X10 @ X12 ) ) ) =>
% 0.48/1.04 ( ( in @
% 0.48/1.04 emptyset @
% 0.48/1.04 ( setadjoin
% 0.48/1.04 @
% 0.48/1.04 emptyset @
% 0.48/1.04 emptyset ) ) =>
% 0.48/1.04 ( ( ![
% 0.48/1.04 X14:$i,
% 0.48/1.04 X16:$i,
% 0.48/1.04 X18:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X18 @ X16 ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X18 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X14 @ X16 ) ) ) ) =>
% 0.48/1.04 ( (
% 0.48/1.04 ![
% 0.48/1.04 X20:$i,
% 0.48/1.04 X22:$i,
% 0.48/1.04 X24:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X24 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X20 @ X22 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X26:$o]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X24 ) =
% 0.48/1.04 (
% 0.48/1.04 X20 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 X26 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X24 @ X22 ) =>
% 0.48/1.04 (
% 0.48/1.04 X26 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 X26 ) ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X28:$i,
% 0.48/1.04 X30:$i,
% 0.48/1.04 X32:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X32 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X28 @ X30 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X32 ) =
% 0.48/1.04 (
% 0.48/1.04 X28 ) ) |
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X32 @ X30 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setoftrueEq ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 powersetI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptyinPowerset ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptyInPowerset ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 powersetE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setunionI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setunionE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subPowSU ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuE2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 nonemptyImpWitness ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X34:$i,
% 0.48/1.04 X36:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X34 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X36 @
% 0.48/1.04 emptyset ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X34 ) =
% 0.48/1.04 (
% 0.48/1.04 X36 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X38:$i,
% 0.48/1.04 X40:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X38 ) !=
% 0.48/1.04 (
% 0.48/1.04 X40 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ~
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X40 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X38 @
% 0.48/1.04 emptyset ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X42:$i,
% 0.48/1.04 X44:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X42 ) =
% 0.48/1.04 (
% 0.48/1.04 X44 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X42 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X44 @
% 0.48/1.04 emptyset ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X46:$i,
% 0.48/1.04 X48:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X46 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X48 @
% 0.48/1.04 emptyset ) ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X48 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X46 @
% 0.48/1.04 emptyset ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X50:$i,
% 0.48/1.04 X52:$i,
% 0.48/1.04 X54:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X54 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X50 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X52 @
% 0.48/1.04 emptyset ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X54 ) =
% 0.48/1.04 (
% 0.48/1.04 X50 ) ) |
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X54 ) =
% 0.48/1.04 (
% 0.48/1.04 X52 ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X56:$i,
% 0.48/1.04 X58:$i]:
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X56 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X56 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X58 @
% 0.48/1.04 emptyset ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X60:$i,
% 0.48/1.04 X62:$i]:
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X62 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X60 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X62 @
% 0.48/1.04 emptyset ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptyE1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 vacuousDall ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan3 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 quantDeMorgan4 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 prop2setI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 prop2set2propI ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notdexE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notdallE ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuI1 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuI3 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuI2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 inCongP ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuE3u ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exu__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 emptyset__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X64:$i,
% 0.48/1.04 X66:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X64 ) =
% 0.48/1.04 (
% 0.48/1.04 X66 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X68:$i,
% 0.48/1.04 X70:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X68 ) =
% 0.48/1.04 (
% 0.48/1.04 X70 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X64 @ X68 ) =
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X66 @ X70 ) ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 powerset__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 setunion__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 omega__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 exuEu ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 descr__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 dsetconstr__Cong ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X72:$i,
% 0.48/1.04 X74:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X76:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X76 @ X72 ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X76 @ X74 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X72 @ X74 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X78:$i,
% 0.48/1.04 X80:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X78 ) =
% 0.48/1.04 (
% 0.48/1.04 X80 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X80 @ X78 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X82:$i,
% 0.48/1.04 X84:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X82 ) =
% 0.48/1.04 (
% 0.48/1.04 X84 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X82 @ X84 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X86:$i,
% 0.48/1.04 X88:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X90:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X90 @ X86 ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X90 @ X88 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X86 @ X88 ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X92:$i]:
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 emptyset @
% 0.48/1.04 X92 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X94:$i,
% 0.48/1.04 X96:$i,
% 0.48/1.04 X98:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X94 @ X96 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X98 @ X94 ) =>
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X98 @ X96 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X100:$i,
% 0.48/1.04 X102:$i,
% 0.48/1.04 X104:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X100 @
% 0.48/1.04 X102 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ~
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X104 @
% 0.48/1.04 X102 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ~
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X104 @
% 0.48/1.04 X100 ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X106:$i,
% 0.48/1.04 X108:$i,
% 0.48/1.04 X110:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X110 @
% 0.48/1.04 X106 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ~
% 0.48/1.04 (
% 0.48/1.04 in @
% 0.48/1.04 X110 @
% 0.48/1.04 X108 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ~
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X106 @
% 0.48/1.04 X108 ) ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X112:$i,
% 0.48/1.04 X114:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ~
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X112 @
% 0.48/1.04 X114 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 X112 ) !=
% 0.48/1.04 (
% 0.48/1.04 X114 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 notequalI2 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X116:$i]:
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X116 @
% 0.48/1.04 X116 ) ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X118:$i,
% 0.48/1.04 X120:$i,
% 0.48/1.04 X122:$i]:
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X118 @
% 0.48/1.04 X120 ) =>
% 0.48/1.04 (
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X120 @
% 0.48/1.04 X122 ) =>
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X118 @
% 0.48/1.04 X122 ) ) ) ) =>
% 0.48/1.04 (
% 0.48/1.04 ![
% 0.48/1.04 X124:$i,
% 0.48/1.04 X126:$i]:
% 0.48/1.04 (
% 0.48/1.04 subset @
% 0.48/1.04 X126 @
% 0.48/1.04 (
% 0.48/1.04 setadjoin
% 0.48/1.04 @
% 0.48/1.04 X124 @
% 0.48/1.04 X126 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 0.48/1.04 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 0.48/1.04 thf(zip_derived_cl49, plain,
% 0.48/1.04 (~ (subset @ sk__62 @ (setadjoin @ sk__61 @ sk__62))),
% 0.48/1.04 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.48/1.04 thf(zip_derived_cl44, plain,
% 0.48/1.04 (![X24 : $i, X25 : $i]:
% 0.48/1.04 ( (subset @ X24 @ X25) | (in @ (sk__63 @ X25 @ X24) @ X24))),
% 0.48/1.04 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.48/1.04 thf(zip_derived_cl19, plain,
% 0.48/1.04 (![X6 : $i, X7 : $i, X8 : $i]:
% 0.48/1.04 ( (in @ X6 @ (setadjoin @ X7 @ X8)) | ~ (in @ X6 @ X8))),
% 0.48/1.04 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.48/1.04 thf(zip_derived_cl43, plain,
% 0.48/1.04 (![X24 : $i, X25 : $i]:
% 0.48/1.04 ( (subset @ X24 @ X25) | ~ (in @ (sk__63 @ X25 @ X24) @ X25))),
% 0.48/1.04 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.48/1.04 thf(zip_derived_cl235, plain,
% 0.48/1.04 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.48/1.04 (~ (in @ (sk__63 @ (setadjoin @ X1 @ X0) @ X2) @ X0)
% 0.48/1.04 | (subset @ X2 @ (setadjoin @ X1 @ X0)))),
% 0.48/1.04 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl43])).
% 0.48/1.04 thf(zip_derived_cl535, plain,
% 0.48/1.04 (![X0 : $i, X1 : $i]:
% 0.48/1.04 ( (subset @ X0 @ (setadjoin @ X1 @ X0))
% 0.48/1.04 | (subset @ X0 @ (setadjoin @ X1 @ X0)))),
% 0.48/1.04 inference('sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl235])).
% 0.48/1.04 thf(zip_derived_cl554, plain,
% 0.48/1.04 (![X0 : $i, X1 : $i]: (subset @ X0 @ (setadjoin @ X1 @ X0))),
% 0.48/1.04 inference('simplify', [status(thm)], [zip_derived_cl535])).
% 0.48/1.04 thf(zip_derived_cl559, plain, ($false),
% 0.48/1.04 inference('demod', [status(thm)], [zip_derived_cl49, zip_derived_cl554])).
% 0.48/1.04
% 0.48/1.04 % SZS output end Refutation
% 0.48/1.04
% 0.48/1.04
% 0.48/1.04 % Terminating...
% 3.71/1.15 % Runner terminated.
% 3.71/1.17 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------