%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU533^1 : 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.ywKSgQMC1u true
% Computer : n011.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 04:54:57 PM UTC 2025
% Result : Theorem 0.58s 0.84s
% Output : Refutation 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU533^1 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ywKSgQMC1u true
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Oct 1 16:11:38 EDT 2025
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.35 % Number of cores: 8
% 0.15/0.35 % Python version: Python 3.6.8
% 0.15/0.36 % Running in HO mode
% 0.58/0.66 % Total configuration time : 828
% 0.58/0.66 % Estimated wc time : 1656
% 0.58/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.58/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.58/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.58/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.58/0.79 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.58/0.79 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.58/0.81 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.58/0.81 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.58/0.84 % Solved by lams/40_c_ic.sh.
% 0.58/0.84 % done 54 iterations in 0.044s
% 0.58/0.84 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.58/0.84 % SZS output start Refutation
% 0.58/0.84 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 0.58/0.84 thf(setunionAx_type, type, setunionAx: $o).
% 0.58/0.84 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 0.58/0.84 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 0.58/0.84 thf(omegaSAx_type, type, omegaSAx: $o).
% 0.58/0.84 thf(eqinunit_type, type, eqinunit: $o).
% 0.58/0.84 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 0.58/0.84 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 0.58/0.84 thf(emptysetE_type, type, emptysetE: $o).
% 0.58/0.84 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 0.58/0.84 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 0.58/0.84 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 0.58/0.84 thf(in_type, type, in: $i > $i > $o).
% 0.58/0.84 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 0.58/0.84 thf(emptyI_type, type, emptyI: $o).
% 0.58/0.84 thf(upairsetE_type, type, upairsetE: $o).
% 0.58/0.84 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 0.58/0.84 thf(sk__29_type, type, sk__29: $i).
% 0.58/0.84 thf(exuE2_type, type, exuE2: $o).
% 0.58/0.84 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 0.58/0.84 thf(notinsingleton_type, type, notinsingleton: $o).
% 0.58/0.84 thf(powersetAx_type, type, powersetAx: $o).
% 0.58/0.84 thf(subPowSU_type, type, subPowSU: $o).
% 0.58/0.84 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 0.58/0.84 thf(notinemptyset_type, type, notinemptyset: $o).
% 0.58/0.84 thf(emptyset_type, type, emptyset: $i).
% 0.58/0.84 thf(setext_type, type, setext: $o).
% 0.58/0.84 thf(setbeta_type, type, setbeta: $o).
% 0.58/0.84 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 0.58/0.84 thf(uniqinunit_type, type, uniqinunit: $o).
% 0.58/0.84 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 0.58/0.84 thf(exuE1_type, type, exuE1: $o).
% 0.58/0.84 thf(nonemptyI_type, type, nonemptyI: $o).
% 0.58/0.84 thf(omega0Ax_type, type, omega0Ax: $o).
% 0.58/0.84 thf(powersetI_type, type, powersetI: $o).
% 0.58/0.84 thf(upairsetIL_type, type, upairsetIL: $o).
% 0.58/0.84 thf(prop2setE_type, type, prop2setE: $o).
% 0.58/0.84 thf(setextAx_type, type, setextAx: $o).
% 0.58/0.84 thf(descrp_type, type, descrp: $o).
% 0.58/0.84 thf(foundationAx_type, type, foundationAx: $o).
% 0.58/0.84 thf(emptysetAx_type, type, emptysetAx: $o).
% 0.58/0.84 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 0.58/0.84 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 0.58/0.84 thf(powersetE_type, type, powersetE: $o).
% 0.58/0.84 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 0.58/0.84 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 0.58/0.84 thf(setunionI_type, type, setunionI: $o).
% 0.58/0.84 thf(exuE3e_type, type, exuE3e: $o).
% 0.58/0.84 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 0.58/0.84 thf(setadjoinE_type, type, setadjoinE: $o).
% 0.58/0.84 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 0.58/0.84 thf(sk__28_type, type, sk__28: $i).
% 0.58/0.84 thf(replAx_type, type, replAx: $o).
% 0.58/0.84 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 0.58/0.84 thf(setunionE_type, type, setunionE: $o).
% 0.58/0.84 thf(upairsetIL, axiom, upairsetIL =
% 0.58/0.84 (![Xx:$i,Xy:$i]:
% 0.58/0.84 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.58/0.84 thf('0', plain,
% 0.58/0.84 (( upairsetIL ) =
% 0.58/0.84 ( ![X4:$i,X6:$i]:
% 0.58/0.84 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.58/0.84 define([status(thm)])).
% 0.58/0.84 thf(upairsetE, axiom, upairsetE =
% 0.58/0.84 (![Xx:$i,Xy:$i,Xz:$i]:
% 0.58/0.84 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 0.58/0.84 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 0.58/0.84 thf('1', plain,
% 0.58/0.84 (( upairsetE ) =
% 0.58/0.84 ( ![X4:$i,X6:$i,X8:$i]:
% 0.58/0.84 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 0.58/0.84 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 0.58/0.84 define([status(thm)])).
% 0.58/0.84 thf(singletonsswitch, axiom, singletonsswitch =
% 0.58/0.84 (![Xx:$i,Xy:$i]:
% 0.58/0.84 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 0.58/0.84 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 0.58/0.84 thf('2', plain,
% 0.58/0.84 (( singletonsswitch ) =
% 0.58/0.84 ( ![X4:$i,X6:$i]:
% 0.58/0.84 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 0.58/0.84 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 0.58/0.84 define([status(thm)])).
% 0.58/0.84 thf(eqinunit, axiom, eqinunit =
% 0.58/0.84 (![Xx:$i,Xy:$i]:
% 0.58/0.84 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 0.58/0.84 thf('3', plain,
% 0.58/0.84 (( eqinunit ) =
% 0.58/0.84 ( ![X4:$i,X6:$i]:
% 0.58/0.84 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 0.58/0.84 define([status(thm)])).
% 0.58/0.84 thf(notinsingleton, axiom, notinsingleton =
% 0.58/0.84 (![Xx:$i,Xy:$i]:
% 0.58/0.84 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 0.58/0.84 thf('4', plain,
% 0.58/0.84 (( notinsingleton ) =
% 0.58/0.84 ( ![X4:$i,X6:$i]:
% 0.58/0.84 ( ( ( X4 ) != ( X6 ) ) =>
% 0.58/0.84 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 0.58/0.84 define([status(thm)])).
% 0.58/0.84 thf(uniqinunit, axiom, uniqinunit =
% 0.58/0.84 (![Xx:$i,Xy:$i]:
% 0.58/0.84 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 0.58/0.84 thf('5', plain,
% 0.58/0.84 (( uniqinunit ) =
% 0.58/0.84 ( ![X4:$i,X6:$i]:
% 0.58/0.84 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 0.58/0.84 define([status(thm)])).
% 0.58/0.84 thf(setadjoinOr, axiom, setadjoinOr =
% 0.58/0.84 (![Xx:$i,A:$i,Xy:$i]:
% 0.58/0.84 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 0.58/0.84 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 0.58/0.84 thf('6', plain,
% 0.58/0.84 (( setadjoinOr ) =
% 0.58/0.84 ( ![X4:$i,X6:$i,X8:$i]:
% 0.58/0.84 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 0.58/0.84 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 0.58/0.84 define([status(thm)])).
% 0.58/0.84 thf(setadjoinE, axiom, setadjoinE =
% 0.58/0.84 (![Xx:$i,A:$i,Xy:$i]:
% 0.58/0.84 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 0.58/0.84 ( ![Xphi:$o]:
% 0.58/0.84 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 0.58/0.84 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 0.58/0.84 thf('7', plain,
% 0.58/0.84 (( setadjoinE ) =
% 0.58/0.84 ( ![X4:$i,X6:$i,X8:$i]:
% 0.58/0.84 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 0.58/0.84 ( ![X10:$o]:
% 0.58/0.84 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 0.58/0.84 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 0.58/0.84 define([status(thm)])).
% 0.58/0.84 thf(setadjoinIR, axiom, setadjoinIR =
% 0.58/0.84 (![Xx:$i,A:$i,Xy:$i]:
% 0.58/0.84 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 0.58/0.84 thf('8', plain,
% 0.58/0.84 (( setadjoinIR ) =
% 0.58/0.84 ( ![X4:$i,X6:$i,X8:$i]:
% 0.58/0.84 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 0.58/0.84 define([status(thm)])).
% 0.58/0.84 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 0.58/0.84 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 0.58/0.84 thf('9', plain,
% 0.58/0.84 (( emptyinunitempty ) =
% 0.58/0.84 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 0.58/0.84 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 0.58/0.84 thf('10', plain,
% 0.58/0.84 (( emptyinunitempty ) =
% 0.58/0.84 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 0.58/0.84 define([status(thm)])).
% 0.58/0.84 thf(setadjoinIL, axiom, setadjoinIL =
% 0.58/0.84 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 0.58/0.84 thf('11', plain,
% 0.58/0.84 (( setadjoinIL ) =
% 0.58/0.84 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 0.58/0.84 define([status(thm)])).
% 0.58/0.84 thf(setadjoinAx, axiom, setadjoinAx =
% 0.58/0.84 (![Xx:$i,A:$i,Xy:$i]:
% 0.58/0.84 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 0.58/0.84 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 0.58/0.84 thf('12', plain,
% 0.58/0.84 (( setadjoinAx ) =
% 0.58/0.84 ( ![X4:$i,X6:$i,X8:$i]:
% 0.58/0.84 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.58/0.84 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 0.58/0.84 define([status(thm)])).
% 0.58/0.84 thf(upairsetIR, conjecture,
% 0.58/0.84 (( setextAx ) =>
% 0.58/0.84 ( ( emptysetAx ) =>
% 0.58/0.84 ( ( setadjoinAx ) =>
% 0.58/0.84 ( ( powersetAx ) =>
% 0.58/0.84 ( ( setunionAx ) =>
% 0.58/0.84 ( ( omega0Ax ) =>
% 0.58/0.84 ( ( omegaSAx ) =>
% 0.58/0.84 ( ( omegaIndAx ) =>
% 0.58/0.84 ( ( replAx ) =>
% 0.58/0.84 ( ( foundationAx ) =>
% 0.58/0.84 ( ( wellorderingAx ) =>
% 0.58/0.84 ( ( descrp ) =>
% 0.58/0.84 ( ( dsetconstrI ) =>
% 0.58/0.84 ( ( dsetconstrEL ) =>
% 0.58/0.84 ( ( dsetconstrER ) =>
% 0.58/0.84 ( ( exuE1 ) =>
% 0.58/0.84 ( ( prop2setE ) =>
% 0.58/0.84 ( ( emptysetE ) =>
% 0.58/0.84 ( ( emptysetimpfalse ) =>
% 0.58/0.84 ( ( notinemptyset ) =>
% 0.58/0.84 ( ( exuE3e ) =>
% 0.58/0.84 ( ( setext ) =>
% 0.58/0.84 ( ( emptyI ) =>
% 0.58/0.84 ( ( noeltsimpempty ) =>
% 0.58/0.84 ( ( setbeta ) =>
% 0.58/0.84 ( ( nonemptyE1 ) =>
% 0.58/0.84 ( ( nonemptyI ) =>
% 0.58/0.84 ( ( nonemptyI1 ) =>
% 0.58/0.84 ( ( setadjoinIL ) =>
% 0.58/0.84 ( ( emptyinunitempty ) =>
% 0.58/0.84 ( ( setadjoinIR ) =>
% 0.58/0.84 ( ( setadjoinE ) =>
% 0.58/0.84 ( (
% 0.58/0.84 setadjoinOr ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 setoftrueEq ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 powersetI ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 emptyinPowerset ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 emptyInPowerset ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 powersetE ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 setunionI ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 setunionE ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 subPowSU ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 exuE2 ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 nonemptyImpWitness ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 uniqinunit ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 notinsingleton ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 eqinunit ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 singletonsswitch ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 upairsetE ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 upairsetIL ) =>
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 Xx:$i,
% 0.58/0.84 Xy:$i]:
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 Xy @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 Xx @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 Xy @
% 0.58/0.84 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.58/0.84 thf(zf_stmt_0, conjecture,
% 0.58/0.84 (( setextAx ) =>
% 0.58/0.84 ( ( emptysetAx ) =>
% 0.58/0.84 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.58/0.84 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.58/0.84 ( ( in @ X8 @ X6 ) | ( ( X8 ) = ( X4 ) ) ) ) ) =>
% 0.58/0.84 ( ( powersetAx ) =>
% 0.58/0.84 ( ( setunionAx ) =>
% 0.58/0.84 ( ( omega0Ax ) =>
% 0.58/0.84 ( ( omegaSAx ) =>
% 0.58/0.84 ( ( omegaIndAx ) =>
% 0.58/0.84 ( ( replAx ) =>
% 0.58/0.84 ( ( foundationAx ) =>
% 0.58/0.84 ( ( wellorderingAx ) =>
% 0.58/0.84 ( ( descrp ) =>
% 0.58/0.84 ( ( dsetconstrI ) =>
% 0.58/0.84 ( ( dsetconstrEL ) =>
% 0.58/0.84 ( ( dsetconstrER ) =>
% 0.58/0.84 ( ( exuE1 ) =>
% 0.58/0.84 ( ( prop2setE ) =>
% 0.58/0.84 ( ( emptysetE ) =>
% 0.58/0.84 ( ( emptysetimpfalse ) =>
% 0.58/0.84 ( ( notinemptyset ) =>
% 0.58/0.84 ( ( exuE3e ) =>
% 0.58/0.84 ( ( setext ) =>
% 0.58/0.84 ( ( emptyI ) =>
% 0.58/0.84 ( ( noeltsimpempty ) =>
% 0.58/0.84 ( ( setbeta ) =>
% 0.58/0.84 ( ( nonemptyE1 ) =>
% 0.58/0.84 ( ( nonemptyI ) =>
% 0.58/0.84 ( ( nonemptyI1 ) =>
% 0.58/0.84 ( ( ![X10:$i,X12:$i]:
% 0.58/0.84 ( in @
% 0.58/0.84 X10 @
% 0.58/0.84 ( setadjoin @
% 0.58/0.84 X10 @ X12 ) ) ) =>
% 0.58/0.84 ( ( in @
% 0.58/0.84 emptyset @
% 0.58/0.84 ( setadjoin @
% 0.58/0.84 emptyset @
% 0.58/0.84 emptyset ) ) =>
% 0.58/0.84 ( ( ![X14:$i,
% 0.58/0.84 X16:$i,
% 0.58/0.84 X18:$i]:
% 0.58/0.84 ( (
% 0.58/0.84 in @
% 0.58/0.84 X18 @ X16 ) =>
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X18 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X14 @ X16 ) ) ) ) =>
% 0.58/0.84 ( ( ![
% 0.58/0.84 X20:$i,
% 0.58/0.84 X22:$i,
% 0.58/0.84 X24:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X24 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X20 @ X22 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X26:$o]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X24 ) =
% 0.58/0.84 (
% 0.58/0.84 X20 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 X26 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X24 @ X22 ) =>
% 0.58/0.84 (
% 0.58/0.84 X26 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 X26 ) ) ) ) ) ) =>
% 0.58/0.84 ( (
% 0.58/0.84 ![
% 0.58/0.84 X28:$i,
% 0.58/0.84 X30:$i,
% 0.58/0.84 X32:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X32 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X28 @ X30 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X32 @ X30 ) |
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X32 ) =
% 0.58/0.84 (
% 0.58/0.84 X28 ) ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 setoftrueEq ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 powersetI ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 emptyinPowerset ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 emptyInPowerset ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 powersetE ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 setunionI ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 setunionE ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 subPowSU ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 exuE2 ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 nonemptyImpWitness ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X34:$i,
% 0.58/0.84 X36:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X34 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X36 @
% 0.58/0.84 emptyset ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X34 ) =
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% 0.58/0.84 X36 ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X38:$i,
% 0.58/0.84 X40:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X38 ) !=
% 0.58/0.84 (
% 0.58/0.84 X40 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 ~(
% 0.58/0.84 in @
% 0.58/0.84 X40 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X38 @
% 0.58/0.84 emptyset ) ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X42:$i,
% 0.58/0.84 X44:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X42 ) =
% 0.58/0.84 (
% 0.58/0.84 X44 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X42 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X44 @
% 0.58/0.84 emptyset ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X46:$i,
% 0.58/0.84 X48:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X46 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X48 @
% 0.58/0.84 emptyset ) ) =>
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X48 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X46 @
% 0.58/0.84 emptyset ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X50:$i,
% 0.58/0.84 X52:$i,
% 0.58/0.84 X54:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X54 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X50 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X52 @
% 0.58/0.84 emptyset ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X54 ) =
% 0.58/0.84 (
% 0.58/0.84 X52 ) ) |
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X54 ) =
% 0.58/0.84 (
% 0.58/0.84 X50 ) ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X56:$i,
% 0.58/0.84 X58:$i]:
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X56 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X56 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X58 @
% 0.58/0.84 emptyset ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X60:$i,
% 0.58/0.84 X62:$i]:
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X62 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X60 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X62 @
% 0.58/0.84 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.58/0.84 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 0.58/0.84 thf(zf_stmt_2, axiom,
% 0.58/0.84 (![X8:$i,X6:$i,X4:$i]:
% 0.58/0.84 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 0.58/0.84 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ))).
% 0.58/0.84 thf(zf_stmt_3, conjecture,
% 0.58/0.84 (( setextAx ) =>
% 0.58/0.84 ( ( emptysetAx ) =>
% 0.58/0.84 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.58/0.84 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.58/0.84 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 0.58/0.84 ( ( powersetAx ) =>
% 0.58/0.84 ( ( setunionAx ) =>
% 0.58/0.84 ( ( omega0Ax ) =>
% 0.58/0.84 ( ( omegaSAx ) =>
% 0.58/0.84 ( ( omegaIndAx ) =>
% 0.58/0.84 ( ( replAx ) =>
% 0.58/0.84 ( ( foundationAx ) =>
% 0.58/0.84 ( ( wellorderingAx ) =>
% 0.58/0.84 ( ( descrp ) =>
% 0.58/0.84 ( ( dsetconstrI ) =>
% 0.58/0.84 ( ( dsetconstrEL ) =>
% 0.58/0.84 ( ( dsetconstrER ) =>
% 0.58/0.84 ( ( exuE1 ) =>
% 0.58/0.84 ( ( prop2setE ) =>
% 0.58/0.84 ( ( emptysetE ) =>
% 0.58/0.84 ( ( emptysetimpfalse ) =>
% 0.58/0.84 ( ( notinemptyset ) =>
% 0.58/0.84 ( ( exuE3e ) =>
% 0.58/0.84 ( ( setext ) =>
% 0.58/0.84 ( ( emptyI ) =>
% 0.58/0.84 ( ( noeltsimpempty ) =>
% 0.58/0.84 ( ( setbeta ) =>
% 0.58/0.84 ( ( nonemptyE1 ) =>
% 0.58/0.84 ( ( nonemptyI ) =>
% 0.58/0.84 ( ( nonemptyI1 ) =>
% 0.58/0.84 ( ( ![X10:$i,X12:$i]:
% 0.58/0.84 ( in @
% 0.58/0.84 X10 @
% 0.58/0.84 ( setadjoin @
% 0.58/0.84 X10 @ X12 ) ) ) =>
% 0.58/0.84 ( ( in @
% 0.58/0.84 emptyset @
% 0.58/0.84 ( setadjoin @
% 0.58/0.84 emptyset @
% 0.58/0.84 emptyset ) ) =>
% 0.58/0.84 ( ( ![X14:$i,
% 0.58/0.84 X16:$i,
% 0.58/0.84 X18:$i]:
% 0.58/0.84 ( (
% 0.58/0.84 in @
% 0.58/0.84 X18 @ X16 ) =>
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X18 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X14 @ X16 ) ) ) ) =>
% 0.58/0.84 ( ( ![
% 0.58/0.84 X20:$i,
% 0.58/0.84 X22:$i,
% 0.58/0.84 X24:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X24 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X20 @ X22 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X26:$o]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X24 ) =
% 0.58/0.84 (
% 0.58/0.84 X20 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 X26 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X24 @ X22 ) =>
% 0.58/0.84 (
% 0.58/0.84 X26 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 X26 ) ) ) ) ) ) =>
% 0.58/0.84 ( (
% 0.58/0.84 ![
% 0.58/0.84 X28:$i,
% 0.58/0.84 X30:$i,
% 0.58/0.84 X32:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X32 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X28 @ X30 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X32 ) =
% 0.58/0.84 (
% 0.58/0.84 X28 ) ) |
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X32 @ X30 ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 setoftrueEq ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 powersetI ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 emptyinPowerset ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 emptyInPowerset ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 powersetE ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 setunionI ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 setunionE ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 subPowSU ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 exuE2 ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 nonemptyImpWitness ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X34:$i,
% 0.58/0.84 X36:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X34 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X36 @
% 0.58/0.84 emptyset ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X34 ) =
% 0.58/0.84 (
% 0.58/0.84 X36 ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X38:$i,
% 0.58/0.84 X40:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X38 ) !=
% 0.58/0.84 (
% 0.58/0.84 X40 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 ~(
% 0.58/0.84 in @
% 0.58/0.84 X40 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X38 @
% 0.58/0.84 emptyset ) ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X42:$i,
% 0.58/0.84 X44:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X42 ) =
% 0.58/0.84 (
% 0.58/0.84 X44 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X42 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X44 @
% 0.58/0.84 emptyset ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X46:$i,
% 0.58/0.84 X48:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X46 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X48 @
% 0.58/0.84 emptyset ) ) =>
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X48 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X46 @
% 0.58/0.84 emptyset ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X50:$i,
% 0.58/0.84 X52:$i,
% 0.58/0.84 X54:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X54 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X50 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X52 @
% 0.58/0.84 emptyset ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X54 ) =
% 0.58/0.84 (
% 0.58/0.84 X50 ) ) |
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X54 ) =
% 0.58/0.84 (
% 0.58/0.84 X52 ) ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X56:$i,
% 0.58/0.84 X58:$i]:
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X56 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X56 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X58 @
% 0.58/0.84 emptyset ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X60:$i,
% 0.58/0.84 X62:$i]:
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X62 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X60 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X62 @
% 0.58/0.84 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 0.58/0.84 thf(zf_stmt_4, negated_conjecture,
% 0.58/0.84 (~( ( setextAx ) =>
% 0.58/0.84 ( ( emptysetAx ) =>
% 0.58/0.84 ( ( ![X4:$i,X6:$i,X8:$i]:
% 0.58/0.84 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 0.58/0.84 ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) =>
% 0.58/0.84 ( ( powersetAx ) =>
% 0.58/0.84 ( ( setunionAx ) =>
% 0.58/0.84 ( ( omega0Ax ) =>
% 0.58/0.84 ( ( omegaSAx ) =>
% 0.58/0.84 ( ( omegaIndAx ) =>
% 0.58/0.84 ( ( replAx ) =>
% 0.58/0.84 ( ( foundationAx ) =>
% 0.58/0.84 ( ( wellorderingAx ) =>
% 0.58/0.84 ( ( descrp ) =>
% 0.58/0.84 ( ( dsetconstrI ) =>
% 0.58/0.84 ( ( dsetconstrEL ) =>
% 0.58/0.84 ( ( dsetconstrER ) =>
% 0.58/0.84 ( ( exuE1 ) =>
% 0.58/0.84 ( ( prop2setE ) =>
% 0.58/0.84 ( ( emptysetE ) =>
% 0.58/0.84 ( ( emptysetimpfalse ) =>
% 0.58/0.84 ( ( notinemptyset ) =>
% 0.58/0.84 ( ( exuE3e ) =>
% 0.58/0.84 ( ( setext ) =>
% 0.58/0.84 ( ( emptyI ) =>
% 0.58/0.84 ( ( noeltsimpempty ) =>
% 0.58/0.84 ( ( setbeta ) =>
% 0.58/0.84 ( ( nonemptyE1 ) =>
% 0.58/0.84 ( ( nonemptyI ) =>
% 0.58/0.84 ( ( nonemptyI1 ) =>
% 0.58/0.84 ( ( ![X10:$i,
% 0.58/0.84 X12:$i]:
% 0.58/0.84 ( in @
% 0.58/0.84 X10 @
% 0.58/0.84 ( setadjoin
% 0.58/0.84 @
% 0.58/0.84 X10 @ X12 ) ) ) =>
% 0.58/0.84 ( ( in @
% 0.58/0.84 emptyset @
% 0.58/0.84 ( setadjoin
% 0.58/0.84 @
% 0.58/0.84 emptyset @
% 0.58/0.84 emptyset ) ) =>
% 0.58/0.84 ( ( ![
% 0.58/0.84 X14:$i,
% 0.58/0.84 X16:$i,
% 0.58/0.84 X18:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X18 @ X16 ) =>
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X18 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X14 @ X16 ) ) ) ) =>
% 0.58/0.84 ( (
% 0.58/0.84 ![
% 0.58/0.84 X20:$i,
% 0.58/0.84 X22:$i,
% 0.58/0.84 X24:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X24 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X20 @ X22 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X26:$o]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X24 ) =
% 0.58/0.84 (
% 0.58/0.84 X20 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 X26 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X24 @ X22 ) =>
% 0.58/0.84 (
% 0.58/0.84 X26 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 X26 ) ) ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X28:$i,
% 0.58/0.84 X30:$i,
% 0.58/0.84 X32:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X32 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X28 @ X30 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X32 ) =
% 0.58/0.84 (
% 0.58/0.84 X28 ) ) |
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X32 @ X30 ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 setoftrueEq ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 powersetI ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 emptyinPowerset ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 emptyInPowerset ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 powersetE ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 setunionI ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 setunionE ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 subPowSU ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 exuE2 ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 nonemptyImpWitness ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X34:$i,
% 0.58/0.84 X36:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X34 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X36 @
% 0.58/0.84 emptyset ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X34 ) =
% 0.58/0.84 (
% 0.58/0.84 X36 ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X38:$i,
% 0.58/0.84 X40:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X38 ) !=
% 0.58/0.84 (
% 0.58/0.84 X40 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 ~
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X40 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X38 @
% 0.58/0.84 emptyset ) ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X42:$i,
% 0.58/0.84 X44:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X42 ) =
% 0.58/0.84 (
% 0.58/0.84 X44 ) ) =>
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X42 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X44 @
% 0.58/0.84 emptyset ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X46:$i,
% 0.58/0.84 X48:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X46 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X48 @
% 0.58/0.84 emptyset ) ) =>
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X48 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X46 @
% 0.58/0.84 emptyset ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X50:$i,
% 0.58/0.84 X52:$i,
% 0.58/0.84 X54:$i]:
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X54 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X50 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X52 @
% 0.58/0.84 emptyset ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X54 ) =
% 0.58/0.84 (
% 0.58/0.84 X50 ) ) |
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 X54 ) =
% 0.58/0.84 (
% 0.58/0.84 X52 ) ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X56:$i,
% 0.58/0.84 X58:$i]:
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X56 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X56 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X58 @
% 0.58/0.84 emptyset ) ) ) ) =>
% 0.58/0.84 (
% 0.58/0.84 ![
% 0.58/0.84 X60:$i,
% 0.58/0.84 X62:$i]:
% 0.58/0.84 (
% 0.58/0.84 in @
% 0.58/0.84 X62 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X60 @
% 0.58/0.84 (
% 0.58/0.84 setadjoin
% 0.58/0.84 @
% 0.58/0.84 X62 @
% 0.58/0.84 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 0.58/0.84 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 0.58/0.84 thf(zip_derived_cl19, plain,
% 0.58/0.84 (![X6 : $i, X7 : $i, X8 : $i]:
% 0.58/0.84 ( (in @ X6 @ (setadjoin @ X7 @ X8)) | ~ (in @ X6 @ X8))),
% 0.58/0.84 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.58/0.84 thf(zip_derived_cl29, plain,
% 0.58/0.84 (~ (in @ sk__29 @ (setadjoin @ sk__28 @ (setadjoin @ sk__29 @ emptyset)))),
% 0.58/0.84 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.58/0.84 thf(zip_derived_cl76, plain,
% 0.58/0.84 (~ (in @ sk__29 @ (setadjoin @ sk__29 @ emptyset))),
% 0.58/0.84 inference('sup-', [status(thm)], [zip_derived_cl19, zip_derived_cl29])).
% 0.58/0.84 thf(zip_derived_cl18, plain,
% 0.58/0.84 (![X4 : $i, X5 : $i]: (in @ X4 @ (setadjoin @ X4 @ X5))),
% 0.58/0.84 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.58/0.84 thf(zip_derived_cl82, plain, ($false),
% 0.58/0.84 inference('demod', [status(thm)], [zip_derived_cl76, zip_derived_cl18])).
% 0.58/0.84
% 0.58/0.84 % SZS output end Refutation
% 0.58/0.84
% 0.58/0.84
% 0.58/0.84 % Terminating...
% 1.86/1.02 % Runner terminated.
% 1.86/1.03 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------