%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU545^1 : 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.vfpcj0wIg0 true
% Computer : n024.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 04:55:00 PM UTC 2025
% Result : Theorem 1.10s 1.51s
% Output : Refutation 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.58 % Problem : SEU545^1 : TPTP v9.2.0. Released v3.7.0.
% 0.08/0.58 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.vfpcj0wIg0 true
% 0.10/0.85 % Computer : n024.cluster.edu
% 0.10/0.85 % Model : x86_64 x86_64
% 0.10/0.85 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.85 % Memory : 8042.1875MB
% 0.10/0.85 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.85 % CPULimit : 300
% 0.10/0.85 % WCLimit : 300
% 0.10/0.85 % DateTime : Wed Oct 1 16:04:38 EDT 2025
% 0.10/0.85 % CPUTime :
% 0.10/0.85 % Running portfolio for 300 s
% 0.10/0.85 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.86 % Number of cores: 8
% 0.10/0.86 % Python version: Python 3.6.8
% 0.10/0.87 % Running in HO mode
% 0.41/1.16 % Total configuration time : 828
% 0.41/1.16 % Estimated wc time : 1656
% 0.41/1.16 % Estimated cpu time (8 cpus) : 207.0
% 0.78/1.28 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.92/1.44 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.92/1.44 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.95/1.45 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.95/1.45 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.95/1.45 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.10/1.48 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.10/1.51 % Solved by lams/40_c.s.sh.
% 1.10/1.51 % done 46 iterations in 0.106s
% 1.10/1.51 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.10/1.51 % SZS output start Refutation
% 1.10/1.51 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 1.10/1.51 thf(notdexE_type, type, notdexE: $o).
% 1.10/1.51 thf(setunionAx_type, type, setunionAx: $o).
% 1.10/1.51 thf(powersetE_type, type, powersetE: $o).
% 1.10/1.51 thf(omegaSAx_type, type, omegaSAx: $o).
% 1.10/1.51 thf(exuI1_type, type, exuI1: $o).
% 1.10/1.51 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 1.10/1.51 thf(sk__190_type, type, sk__190: $i > $o).
% 1.10/1.51 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 1.10/1.51 thf(zip_tseitin_2_type, type, zip_tseitin_2: $i > $i > $i > $o).
% 1.10/1.51 thf(setext_type, type, setext: $o).
% 1.10/1.51 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 1.10/1.51 thf(in_type, type, in: $i > $i > $o).
% 1.10/1.51 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 1.10/1.51 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 1.10/1.51 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 1.10/1.51 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 1.10/1.51 thf(setbeta_type, type, setbeta: $o).
% 1.10/1.51 thf(eqinunit_type, type, eqinunit: $o).
% 1.10/1.51 thf(upairsetIL_type, type, upairsetIL: $o).
% 1.10/1.51 thf(sk__192_type, type, sk__192: $i).
% 1.10/1.51 thf(powersetAx_type, type, powersetAx: $o).
% 1.10/1.51 thf(zip_tseitin_3_type, type, zip_tseitin_3: $i > $i > $i > ($i > $i > $o) > $o).
% 1.10/1.51 thf(powersetI_type, type, powersetI: $o).
% 1.10/1.51 thf(upairsetIR_type, type, upairsetIR: $o).
% 1.10/1.51 thf(exuE3e_type, type, exuE3e: $o).
% 1.10/1.51 thf(emptysetE_type, type, emptysetE: $o).
% 1.10/1.51 thf(setunionI_type, type, setunionI: $o).
% 1.10/1.51 thf(prop2setI_type, type, prop2setI: $o).
% 1.10/1.51 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 1.10/1.51 thf(exuE2_type, type, exuE2: $o).
% 1.10/1.51 thf(emptyset_type, type, emptyset: $i).
% 1.10/1.51 thf(subPowSU_type, type, subPowSU: $o).
% 1.10/1.51 thf(notinemptyset_type, type, notinemptyset: $o).
% 1.10/1.51 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 1.10/1.51 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 1.10/1.51 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 1.10/1.51 thf(sk__191_type, type, sk__191: $i > $i).
% 1.10/1.51 thf(setunionE_type, type, setunionE: $o).
% 1.10/1.51 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 1.10/1.51 thf(setadjoinE_type, type, setadjoinE: $o).
% 1.10/1.51 thf(descr_type, type, descr: ($i > $o) > $i).
% 1.10/1.51 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 1.10/1.51 thf(exuE1_type, type, exuE1: $o).
% 1.10/1.51 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 1.10/1.51 thf(prop2set_type, type, prop2set: $o > $i).
% 1.10/1.51 thf(notinsingleton_type, type, notinsingleton: $o).
% 1.10/1.51 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 1.10/1.51 thf(upairsetE_type, type, upairsetE: $o).
% 1.10/1.51 thf(omega0Ax_type, type, omega0Ax: $o).
% 1.10/1.51 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 1.10/1.51 thf(setextAx_type, type, setextAx: $o).
% 1.10/1.51 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 1.10/1.51 thf(setunion_type, type, setunion: $i > $i).
% 1.10/1.51 thf(descrp_type, type, descrp: $o).
% 1.10/1.51 thf(foundationAx_type, type, foundationAx: $o).
% 1.10/1.51 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 1.10/1.51 thf(emptysetAx_type, type, emptysetAx: $o).
% 1.10/1.51 thf(emptyI_type, type, emptyI: $o).
% 1.10/1.51 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 1.10/1.51 thf(emptyE1_type, type, emptyE1: $o).
% 1.10/1.51 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 1.10/1.51 thf(vacuousDall_type, type, vacuousDall: $o).
% 1.10/1.51 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 1.10/1.51 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 1.10/1.51 thf(exu_type, type, exu: ($i > $o) > $o).
% 1.10/1.51 thf(uniqinunit_type, type, uniqinunit: $o).
% 1.10/1.51 thf(prop2setE_type, type, prop2setE: $o).
% 1.10/1.51 thf(omega_type, type, omega: $i).
% 1.10/1.51 thf(nonemptyI_type, type, nonemptyI: $o).
% 1.10/1.51 thf(notdallE_type, type, notdallE: $o).
% 1.10/1.51 thf(powerset_type, type, powerset: $i > $i).
% 1.10/1.51 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 1.10/1.51 thf(nonempty_type, type, nonempty: $i > $o).
% 1.10/1.51 thf(set2prop_type, type, set2prop: $i > $o).
% 1.10/1.51 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 1.10/1.51 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 1.10/1.51 thf(replAx_type, type, replAx: $o).
% 1.10/1.51 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 1.10/1.51 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 1.10/1.51 thf(exuI1, axiom, exuI1 =
% 1.10/1.51 (![Xphi:( $i > $o )]:
% 1.10/1.51 ( ( ?[Xx:$i]:
% 1.10/1.51 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 1.10/1.51 ( Xphi @ Xx ) ) ) =>
% 1.10/1.51 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ))).
% 1.10/1.51 thf('0', plain,
% 1.10/1.51 (( exuI1 ) =
% 1.10/1.51 ( ![X4:( $i > $o )]:
% 1.10/1.51 ( ( ?[X6:$i]:
% 1.10/1.51 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 1.10/1.51 ( X4 @ X6 ) ) ) =>
% 1.10/1.51 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(notdallE, axiom, notdallE =
% 1.10/1.51 (![A:$i,Xphi:( $i > $o )]:
% 1.10/1.51 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) =>
% 1.10/1.51 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))).
% 1.10/1.51 thf('1', plain,
% 1.10/1.51 (( notdallE ) =
% 1.10/1.51 ( ![X4:$i,X6:( $i > $o )]:
% 1.10/1.51 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) =>
% 1.10/1.51 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(notdexE, axiom, notdexE =
% 1.10/1.51 (![A:$i,Xphi:( $i > $o )]:
% 1.10/1.51 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) =>
% 1.10/1.51 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))).
% 1.10/1.51 thf('2', plain,
% 1.10/1.51 (( notdexE ) =
% 1.10/1.51 ( ![X4:$i,X6:( $i > $o )]:
% 1.10/1.51 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 1.10/1.51 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(prop2set2propI, axiom, prop2set2propI =
% 1.10/1.51 (![Xphi:$o]: ( ( Xphi ) => ( set2prop @ ( prop2set @ Xphi ) ) ))).
% 1.10/1.51 thf('3', plain,
% 1.10/1.51 (( prop2set2propI ) =
% 1.10/1.51 ( ![X4:$o]: ( ( X4 ) => ( set2prop @ ( prop2set @ X4 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(prop2setI, axiom, prop2setI =
% 1.10/1.51 (![Xphi:$o]: ( ( Xphi ) => ( in @ emptyset @ ( prop2set @ Xphi ) ) ))).
% 1.10/1.51 thf('4', plain,
% 1.10/1.51 (( prop2setI ) =
% 1.10/1.51 ( ![X4:$o]: ( ( X4 ) => ( in @ emptyset @ ( prop2set @ X4 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(quantDeMorgan4, axiom, quantDeMorgan4 =
% 1.10/1.51 (![A:$i,Xphi:( $i > $o )]:
% 1.10/1.51 ( ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) =>
% 1.10/1.51 ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) ))).
% 1.10/1.51 thf('5', plain,
% 1.10/1.51 (( quantDeMorgan4 ) =
% 1.10/1.51 ( ![X4:$i,X6:( $i > $o )]:
% 1.10/1.51 ( ( ?[X8:$i]: ( ( ~( X6 @ X8 ) ) & ( in @ X8 @ X4 ) ) ) =>
% 1.10/1.51 ( ~( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( X6 @ X10 ) ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(quantDeMorgan3, axiom, quantDeMorgan3 =
% 1.10/1.51 (![A:$i,Xphi:( $i > $o )]:
% 1.10/1.51 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) =>
% 1.10/1.51 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))).
% 1.10/1.51 thf('6', plain,
% 1.10/1.51 (( quantDeMorgan3 ) =
% 1.10/1.51 ( ![X4:$i,X6:( $i > $o )]:
% 1.10/1.51 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 1.10/1.51 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(quantDeMorgan2, axiom, quantDeMorgan2 =
% 1.10/1.51 (![A:$i,Xphi:( $i > $o )]:
% 1.10/1.51 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) =>
% 1.10/1.51 ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) ))).
% 1.10/1.51 thf('7', plain,
% 1.10/1.51 (( quantDeMorgan2 ) =
% 1.10/1.51 ( ![X4:$i,X6:( $i > $o )]:
% 1.10/1.51 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( ~( X6 @ X8 ) ) ) ) =>
% 1.10/1.51 ( ~( ?[X10:$i]: ( ( X6 @ X10 ) & ( in @ X10 @ X4 ) ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(quantDeMorgan1, axiom, quantDeMorgan1 =
% 1.10/1.51 (![A:$i,Xphi:( $i > $o )]:
% 1.10/1.51 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) =>
% 1.10/1.51 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))).
% 1.10/1.51 thf('8', plain,
% 1.10/1.51 (( quantDeMorgan1 ) =
% 1.10/1.51 ( ![X4:$i,X6:( $i > $o )]:
% 1.10/1.51 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) =>
% 1.10/1.51 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(vacuousDall, axiom, vacuousDall =
% 1.10/1.51 (![Xphi:( $i > $o ),Xx:$i]: ( ( in @ Xx @ emptyset ) => ( Xphi @ Xx ) ))).
% 1.10/1.51 thf('9', plain,
% 1.10/1.51 (( vacuousDall ) =
% 1.10/1.51 ( ![X4:( $i > $o ),X6:$i]: ( ( in @ X6 @ emptyset ) => ( X4 @ X6 ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(emptyE1, axiom, emptyE1 =
% 1.10/1.51 (![A:$i,Xphi:( $i > $o )]:
% 1.10/1.51 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) =>
% 1.10/1.51 ( ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) = ( emptyset ) ) =>
% 1.10/1.51 ( $false ) ) ))).
% 1.10/1.51 thf('10', plain,
% 1.10/1.51 (( emptyE1 ) =
% 1.10/1.51 ( ![X4:$i,X6:( $i > $o )]:
% 1.10/1.51 ( ( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) =>
% 1.10/1.51 ( ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = ( emptyset ) ) =>
% 1.10/1.51 ( $false ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(upairsetIR, axiom, upairsetIR =
% 1.10/1.51 (![Xx:$i,Xy:$i]:
% 1.10/1.51 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 1.10/1.51 thf('11', plain,
% 1.10/1.51 (( upairsetIR ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(upairsetIL, axiom, upairsetIL =
% 1.10/1.51 (![Xx:$i,Xy:$i]:
% 1.10/1.51 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 1.10/1.51 thf('12', plain,
% 1.10/1.51 (( upairsetIL ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(upairsetE, axiom, upairsetE =
% 1.10/1.51 (![Xx:$i,Xy:$i,Xz:$i]:
% 1.10/1.51 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 1.10/1.51 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 1.10/1.51 thf('13', plain,
% 1.10/1.51 (( upairsetE ) =
% 1.10/1.51 ( ![X4:$i,X6:$i,X8:$i]:
% 1.10/1.51 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 1.10/1.51 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(singletonsswitch, axiom, singletonsswitch =
% 1.10/1.51 (![Xx:$i,Xy:$i]:
% 1.10/1.51 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 1.10/1.51 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 1.10/1.51 thf('14', plain,
% 1.10/1.51 (( singletonsswitch ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 1.10/1.51 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(eqinunit, axiom, eqinunit =
% 1.10/1.51 (![Xx:$i,Xy:$i]:
% 1.10/1.51 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 1.10/1.51 thf('15', plain,
% 1.10/1.51 (( eqinunit ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(notinsingleton, axiom, notinsingleton =
% 1.10/1.51 (![Xx:$i,Xy:$i]:
% 1.10/1.51 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 1.10/1.51 thf('16', plain,
% 1.10/1.51 (( notinsingleton ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( ( X4 ) != ( X6 ) ) =>
% 1.10/1.51 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(uniqinunit, axiom, uniqinunit =
% 1.10/1.51 (![Xx:$i,Xy:$i]:
% 1.10/1.51 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 1.10/1.51 thf('17', plain,
% 1.10/1.51 (( uniqinunit ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(nonemptyImpWitness, axiom, nonemptyImpWitness =
% 1.10/1.51 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 1.10/1.51 thf('18', plain,
% 1.10/1.51 (( nonemptyImpWitness ) =
% 1.10/1.51 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(exuE2, axiom, exuE2 =
% 1.10/1.51 (![Xphi:( $i > $o )]:
% 1.10/1.51 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 1.10/1.51 ( ?[Xx:$i]: ( ![Xy:$i]: ( ( Xphi @ Xy ) <=> ( ( Xy ) = ( Xx ) ) ) ) ) ))).
% 1.10/1.51 thf('19', plain,
% 1.10/1.51 (( exuE2 ) =
% 1.10/1.51 ( ![X4:( $i > $o )]:
% 1.10/1.51 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 1.10/1.51 ( ?[X6:$i]: ( ![X8:$i]: ( ( X4 @ X8 ) <=> ( ( X8 ) = ( X6 ) ) ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(subPowSU, axiom, subPowSU =
% 1.10/1.51 (![A:$i,Xx:$i]:
% 1.10/1.51 ( ( in @ Xx @ A ) => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ))).
% 1.10/1.51 thf('20', plain,
% 1.10/1.51 (( subPowSU ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( in @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ ( setunion @ X4 ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(setunionE, axiom, setunionE =
% 1.10/1.51 (![A:$i,Xx:$i]:
% 1.10/1.51 ( ( in @ Xx @ ( setunion @ A ) ) =>
% 1.10/1.51 ( ![Xphi:$o]:
% 1.10/1.51 ( ( ![B:$i]: ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( Xphi ) ) ) ) =>
% 1.10/1.51 ( Xphi ) ) ) ))).
% 1.10/1.51 thf('21', plain,
% 1.10/1.51 (( setunionE ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( in @ X6 @ ( setunion @ X4 ) ) =>
% 1.10/1.51 ( ![X8:$o]:
% 1.10/1.51 ( ( ![X10:$i]:
% 1.10/1.51 ( ( in @ X6 @ X10 ) => ( ( in @ X10 @ X4 ) => ( X8 ) ) ) ) =>
% 1.10/1.51 ( X8 ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(setunionI, axiom, setunionI =
% 1.10/1.51 (![A:$i,Xx:$i,B:$i]:
% 1.10/1.51 ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( in @ Xx @ ( setunion @ A ) ) ) ))).
% 1.10/1.51 thf('22', plain,
% 1.10/1.51 (( setunionI ) =
% 1.10/1.51 ( ![X4:$i,X6:$i,X8:$i]:
% 1.10/1.51 ( ( in @ X6 @ X8 ) =>
% 1.10/1.51 ( ( in @ X8 @ X4 ) => ( in @ X6 @ ( setunion @ X4 ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(powersetE, axiom, powersetE =
% 1.10/1.51 (![A:$i,B:$i,Xx:$i]:
% 1.10/1.51 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 1.10/1.51 thf('23', plain,
% 1.10/1.51 (( powersetE ) =
% 1.10/1.51 ( ![X4:$i,X6:$i,X8:$i]:
% 1.10/1.51 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.10/1.51 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(emptyInPowerset, axiom, emptyInPowerset =
% 1.10/1.51 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 1.10/1.51 thf('24', plain,
% 1.10/1.51 (( emptyInPowerset ) =
% 1.10/1.51 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(emptyinPowerset, axiom, emptyinPowerset =
% 1.10/1.51 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 1.10/1.51 thf('25', plain,
% 1.10/1.51 (( emptyinPowerset ) =
% 1.10/1.51 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(powersetI, axiom, powersetI =
% 1.10/1.51 (![A:$i,B:$i]:
% 1.10/1.51 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 1.10/1.51 ( in @ B @ ( powerset @ A ) ) ))).
% 1.10/1.51 thf('26', plain,
% 1.10/1.51 (( powersetI ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 1.10/1.51 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(setoftrueEq, axiom, setoftrueEq =
% 1.10/1.51 (![A:$i]: ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( $true ) ) ) = ( A ) ))).
% 1.10/1.51 thf('27', plain,
% 1.10/1.51 (( setoftrueEq ) =
% 1.10/1.51 ( ![X4:$i]: ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( $true ) ) ) = ( X4 ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(setadjoinOr, axiom, setadjoinOr =
% 1.10/1.51 (![Xx:$i,A:$i,Xy:$i]:
% 1.10/1.51 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 1.10/1.51 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 1.10/1.51 thf('28', plain,
% 1.10/1.51 (( setadjoinOr ) =
% 1.10/1.51 ( ![X4:$i,X6:$i,X8:$i]:
% 1.10/1.51 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 1.10/1.51 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(setadjoinE, axiom, setadjoinE =
% 1.10/1.51 (![Xx:$i,A:$i,Xy:$i]:
% 1.10/1.51 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 1.10/1.51 ( ![Xphi:$o]:
% 1.10/1.51 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 1.10/1.51 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 1.10/1.51 thf('29', plain,
% 1.10/1.51 (( setadjoinE ) =
% 1.10/1.51 ( ![X4:$i,X6:$i,X8:$i]:
% 1.10/1.51 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 1.10/1.51 ( ![X10:$o]:
% 1.10/1.51 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 1.10/1.51 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(setadjoinIR, axiom, setadjoinIR =
% 1.10/1.51 (![Xx:$i,A:$i,Xy:$i]:
% 1.10/1.51 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 1.10/1.51 thf('30', plain,
% 1.10/1.51 (( setadjoinIR ) =
% 1.10/1.51 ( ![X4:$i,X6:$i,X8:$i]:
% 1.10/1.51 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 1.10/1.51 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 1.10/1.51 thf('31', plain,
% 1.10/1.51 (( emptyinunitempty ) =
% 1.10/1.51 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 1.10/1.51 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 1.10/1.51 thf('32', plain,
% 1.10/1.51 (( emptyinunitempty ) =
% 1.10/1.51 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(setadjoinIL, axiom, setadjoinIL =
% 1.10/1.51 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 1.10/1.51 thf('33', plain,
% 1.10/1.51 (( setadjoinIL ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(nonemptyI1, axiom, nonemptyI1 =
% 1.10/1.51 (![A:$i]: ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) => ( nonempty @ A ) ))).
% 1.10/1.51 thf('34', plain,
% 1.10/1.51 (( nonemptyI1 ) =
% 1.10/1.51 ( ![X4:$i]: ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) => ( nonempty @ X4 ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(nonemptyI, axiom, nonemptyI =
% 1.10/1.51 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 1.10/1.51 ( ( in @ Xx @ A ) =>
% 1.10/1.51 ( ( Xphi @ Xx ) =>
% 1.10/1.51 ( nonempty @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 1.10/1.51 thf('35', plain,
% 1.10/1.51 (( nonemptyI ) =
% 1.10/1.51 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 1.10/1.51 ( ( in @ X8 @ X4 ) =>
% 1.10/1.51 ( ( X6 @ X8 ) =>
% 1.10/1.51 ( nonempty @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(nonemptyE1, axiom, nonemptyE1 =
% 1.10/1.51 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 1.10/1.51 thf('36', plain,
% 1.10/1.51 (( nonemptyE1 ) =
% 1.10/1.51 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(nonempty, axiom,(( nonempty ) = (^[Xx:$i]: ( ( Xx ) != ( emptyset ) )))).
% 1.10/1.51 thf('37', plain, (( nonempty ) = ( ^[Xx:$i]: ( ( Xx ) != ( emptyset ) ) )),
% 1.10/1.51 inference('simplify_rw_rule', [status(thm)], [nonempty])).
% 1.10/1.51 thf('38', plain, (( nonempty ) = ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(setbeta, axiom, setbeta =
% 1.10/1.51 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 1.10/1.51 ( ( in @ Xx @ A ) =>
% 1.10/1.51 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) <=>
% 1.10/1.51 ( Xphi @ Xx ) ) ))).
% 1.10/1.51 thf('39', plain,
% 1.10/1.51 (( setbeta ) =
% 1.10/1.51 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 1.10/1.51 ( ( in @ X8 @ X4 ) =>
% 1.10/1.51 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=>
% 1.10/1.51 ( X6 @ X8 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(noeltsimpempty, axiom, noeltsimpempty =
% 1.10/1.51 (![A:$i]:
% 1.10/1.51 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 1.10/1.51 thf('40', plain,
% 1.10/1.51 (( noeltsimpempty ) =
% 1.10/1.51 ( ![X4:$i]:
% 1.10/1.51 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(emptyI, axiom, emptyI =
% 1.10/1.51 (![A:$i]:
% 1.10/1.51 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 1.10/1.51 thf('41', plain,
% 1.10/1.51 (( emptyI ) =
% 1.10/1.51 ( ![X4:$i]:
% 1.10/1.51 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(setext, axiom, setext =
% 1.10/1.51 (![A:$i,B:$i]:
% 1.10/1.51 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 1.10/1.51 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 1.10/1.51 ( ( A ) = ( B ) ) ) ))).
% 1.10/1.51 thf('42', plain,
% 1.10/1.51 (( setext ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 1.10/1.51 ( ( ![X10:$i]: ( ( in @ X10 @ X6 ) => ( in @ X10 @ X4 ) ) ) =>
% 1.10/1.51 ( ( X4 ) = ( X6 ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(exuE3e, axiom, exuE3e =
% 1.10/1.51 (![Xphi:( $i > $o )]:
% 1.10/1.51 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) => ( ?[Xx:$i]: ( Xphi @ Xx ) ) ))).
% 1.10/1.51 thf('43', plain,
% 1.10/1.51 (( exuE3e ) =
% 1.10/1.51 ( ![X4:( $i > $o )]:
% 1.10/1.51 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) => ( ?[X6:$i]: ( X4 @ X6 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(notinemptyset, axiom, notinemptyset =
% 1.10/1.51 (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 1.10/1.51 thf('44', plain,
% 1.10/1.51 (( notinemptyset ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(emptysetimpfalse, axiom, emptysetimpfalse =
% 1.10/1.51 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( $false ) ))).
% 1.10/1.51 thf('45', plain,
% 1.10/1.51 (( emptysetimpfalse ) =
% 1.10/1.51 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( $false ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(emptysetE, axiom, emptysetE =
% 1.10/1.51 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( ![Xphi:$o]: ( Xphi ) ) ))).
% 1.10/1.51 thf('46', plain,
% 1.10/1.51 (( emptysetE ) =
% 1.10/1.51 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( ![X6:$o]: ( X6 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(prop2setE, axiom, prop2setE =
% 1.10/1.51 (![Xphi:$o,Xx:$i]: ( ( in @ Xx @ ( prop2set @ Xphi ) ) => ( Xphi ) ))).
% 1.10/1.51 thf('47', plain,
% 1.10/1.51 (( prop2setE ) =
% 1.10/1.51 ( ![X4:$o,X6:$i]: ( ( in @ X6 @ ( prop2set @ X4 ) ) => ( X4 ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(exuE1, axiom, exuE1 =
% 1.10/1.51 (![Xphi:( $i > $o )]:
% 1.10/1.51 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 1.10/1.51 ( ?[Xx:$i]:
% 1.10/1.51 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 1.10/1.51 ( Xphi @ Xx ) ) ) ))).
% 1.10/1.51 thf('48', plain,
% 1.10/1.51 (( exuE1 ) =
% 1.10/1.51 ( ![X4:( $i > $o )]:
% 1.10/1.51 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 1.10/1.51 ( ?[X6:$i]:
% 1.10/1.51 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 1.10/1.51 ( X4 @ X6 ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(dsetconstrER, axiom, dsetconstrER =
% 1.10/1.51 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 1.10/1.51 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 1.10/1.51 ( Xphi @ Xx ) ))).
% 1.10/1.51 thf('49', plain,
% 1.10/1.51 (( dsetconstrER ) =
% 1.10/1.51 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 1.10/1.51 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 1.10/1.51 ( X6 @ X8 ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(dsetconstrEL, axiom, dsetconstrEL =
% 1.10/1.51 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 1.10/1.51 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 1.10/1.51 ( in @ Xx @ A ) ))).
% 1.10/1.51 thf('50', plain,
% 1.10/1.51 (( dsetconstrEL ) =
% 1.10/1.51 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 1.10/1.51 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 1.10/1.51 ( in @ X8 @ X4 ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(dsetconstrI, axiom, dsetconstrI =
% 1.10/1.51 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 1.10/1.51 ( ( in @ Xx @ A ) =>
% 1.10/1.51 ( ( Xphi @ Xx ) =>
% 1.10/1.51 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 1.10/1.51 thf('51', plain,
% 1.10/1.51 (( dsetconstrI ) =
% 1.10/1.51 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 1.10/1.51 ( ( in @ X8 @ X4 ) =>
% 1.10/1.51 ( ( X6 @ X8 ) =>
% 1.10/1.51 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(descrp, axiom, descrp =
% 1.10/1.51 (![Xphi:( $i > $o )]:
% 1.10/1.51 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 1.10/1.51 ( Xphi @ ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 1.10/1.51 thf('52', plain,
% 1.10/1.51 (( descrp ) =
% 1.10/1.51 ( ![X4:( $i > $o )]:
% 1.10/1.51 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 1.10/1.51 ( X4 @ ( descr @ ( ^[V_2:$i]: ( X4 @ V_2 ) ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(wellorderingAx, axiom, wellorderingAx =
% 1.10/1.51 (![A:$i]:
% 1.10/1.51 ( ?[B:$i]:
% 1.10/1.51 ( ( ![C:$i]:
% 1.10/1.51 ( ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) &
% 1.10/1.51 ( ?[Xx:$i]: ( in @ Xx @ C ) ) ) =>
% 1.10/1.51 ( ?[D:$i,Xx:$i]:
% 1.10/1.51 ( ( ![E:$i]:
% 1.10/1.51 ( ( in @ E @ B ) =>
% 1.10/1.51 ( ( ![Xy:$i]: ( ( in @ Xy @ E ) => ( in @ Xy @ D ) ) ) |
% 1.10/1.51 ( in @ Xx @ E ) ) ) ) &
% 1.10/1.51 ( ~( ?[Xy:$i]: ( ( in @ Xy @ C ) & ( in @ Xy @ D ) ) ) ) &
% 1.10/1.51 ( in @ Xx @ C ) & ( in @ D @ B ) ) ) ) ) &
% 1.10/1.51 ( ![C:$i,D:$i]:
% 1.10/1.51 ( ( ( in @ C @ B ) & ( in @ D @ B ) ) =>
% 1.10/1.51 ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ D ) ) ) |
% 1.10/1.51 ( ![Xx:$i]: ( ( in @ Xx @ D ) => ( in @ Xx @ C ) ) ) ) ) ) &
% 1.10/1.51 ( ![Xx:$i,Xy:$i]:
% 1.10/1.51 ( ( ( in @ Xx @ A ) & ( in @ Xy @ A ) ) =>
% 1.10/1.51 ( ( ![C:$i]:
% 1.10/1.51 ( ( in @ C @ B ) => ( ( in @ Xx @ C ) <=> ( in @ Xy @ C ) ) ) ) =>
% 1.10/1.51 ( ( Xx ) = ( Xy ) ) ) ) ) &
% 1.10/1.51 ( ![C:$i]:
% 1.10/1.51 ( ( in @ C @ B ) =>
% 1.10/1.51 ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) ) ) ) ))).
% 1.10/1.51 thf('53', plain,
% 1.10/1.51 (( wellorderingAx ) =
% 1.10/1.51 ( ![X4:$i]:
% 1.10/1.51 ( ?[X6:$i]:
% 1.10/1.51 ( ( ![X8:$i]:
% 1.10/1.51 ( ( ( ![X10:$i]: ( ( in @ X10 @ X8 ) => ( in @ X10 @ X4 ) ) ) &
% 1.10/1.51 ( ?[X12:$i]: ( in @ X12 @ X8 ) ) ) =>
% 1.10/1.51 ( ?[X14:$i,X16:$i]:
% 1.10/1.51 ( ( ![X18:$i]:
% 1.10/1.51 ( ( in @ X18 @ X6 ) =>
% 1.10/1.51 ( ( ![X20:$i]:
% 1.10/1.51 ( ( in @ X20 @ X18 ) => ( in @ X20 @ X14 ) ) ) |
% 1.10/1.51 ( in @ X16 @ X18 ) ) ) ) &
% 1.10/1.51 ( ~( ?[X22:$i]: ( ( in @ X22 @ X8 ) & ( in @ X22 @ X14 ) ) ) ) &
% 1.10/1.51 ( in @ X16 @ X8 ) & ( in @ X14 @ X6 ) ) ) ) ) &
% 1.10/1.51 ( ![X24:$i,X26:$i]:
% 1.10/1.51 ( ( ( in @ X24 @ X6 ) & ( in @ X26 @ X6 ) ) =>
% 1.10/1.51 ( ( ![X28:$i]: ( ( in @ X28 @ X24 ) => ( in @ X28 @ X26 ) ) ) |
% 1.10/1.51 ( ![X30:$i]: ( ( in @ X30 @ X26 ) => ( in @ X30 @ X24 ) ) ) ) ) ) &
% 1.10/1.51 ( ![X32:$i,X34:$i]:
% 1.10/1.51 ( ( ( in @ X32 @ X4 ) & ( in @ X34 @ X4 ) ) =>
% 1.10/1.51 ( ( ![X36:$i]:
% 1.10/1.51 ( ( in @ X36 @ X6 ) =>
% 1.10/1.51 ( ( in @ X32 @ X36 ) <=> ( in @ X34 @ X36 ) ) ) ) =>
% 1.10/1.51 ( ( X32 ) = ( X34 ) ) ) ) ) &
% 1.10/1.51 ( ![X38:$i]:
% 1.10/1.51 ( ( in @ X38 @ X6 ) =>
% 1.10/1.51 ( ![X40:$i]: ( ( in @ X40 @ X38 ) => ( in @ X40 @ X4 ) ) ) ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(foundationAx, axiom, foundationAx =
% 1.10/1.51 (![A:$i]:
% 1.10/1.51 ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) =>
% 1.10/1.51 ( ?[B:$i]:
% 1.10/1.51 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ A ) & ( in @ Xx @ B ) ) ) ) &
% 1.10/1.51 ( in @ B @ A ) ) ) ))).
% 1.10/1.51 thf('54', plain,
% 1.10/1.51 (( foundationAx ) =
% 1.10/1.51 ( ![X4:$i]:
% 1.10/1.51 ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) =>
% 1.10/1.51 ( ?[X8:$i]:
% 1.10/1.51 ( ( ~( ?[X10:$i]: ( ( in @ X10 @ X4 ) & ( in @ X10 @ X8 ) ) ) ) &
% 1.10/1.51 ( in @ X8 @ X4 ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(replAx, axiom, replAx =
% 1.10/1.51 (![Xphi:( $i > $i > $o ),A:$i]:
% 1.10/1.51 ( ( ![Xx:$i]:
% 1.10/1.51 ( ( in @ Xx @ A ) => ( exu @ ( ^[Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ) ) =>
% 1.10/1.51 ( ?[B:$i]:
% 1.10/1.51 ( ![Xx:$i]:
% 1.10/1.51 ( ( in @ Xx @ B ) <=>
% 1.10/1.51 ( ?[Xy:$i]: ( ( Xphi @ Xy @ Xx ) & ( in @ Xy @ A ) ) ) ) ) ) ))).
% 1.10/1.51 thf('55', plain,
% 1.10/1.51 (( replAx ) =
% 1.10/1.51 ( ![X4:( $i > $i > $o ),X6:$i]:
% 1.10/1.51 ( ( ![X8:$i]:
% 1.10/1.51 ( ( in @ X8 @ X6 ) => ( exu @ ( ^[V_1:$i]: ( X4 @ X8 @ V_1 ) ) ) ) ) =>
% 1.10/1.51 ( ?[X10:$i]:
% 1.10/1.51 ( ![X12:$i]:
% 1.10/1.51 ( ( in @ X12 @ X10 ) <=>
% 1.10/1.51 ( ?[X14:$i]: ( ( X4 @ X14 @ X12 ) & ( in @ X14 @ X6 ) ) ) ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(omegaIndAx, axiom, omegaIndAx =
% 1.10/1.51 (![A:$i]:
% 1.10/1.51 ( ( ( in @ emptyset @ A ) &
% 1.10/1.51 ( ![Xx:$i]:
% 1.10/1.51 ( ( ( in @ Xx @ omega ) & ( in @ Xx @ A ) ) =>
% 1.10/1.51 ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) ) =>
% 1.10/1.51 ( ![Xx:$i]: ( ( in @ Xx @ omega ) => ( in @ Xx @ A ) ) ) ))).
% 1.10/1.51 thf('56', plain,
% 1.10/1.51 (( omegaIndAx ) =
% 1.10/1.51 ( ![X4:$i]:
% 1.10/1.51 ( ( ( in @ emptyset @ X4 ) &
% 1.10/1.51 ( ![X6:$i]:
% 1.10/1.51 ( ( ( in @ X6 @ omega ) & ( in @ X6 @ X4 ) ) =>
% 1.10/1.51 ( in @ ( setadjoin @ X6 @ X6 ) @ X4 ) ) ) ) =>
% 1.10/1.51 ( ![X8:$i]: ( ( in @ X8 @ omega ) => ( in @ X8 @ X4 ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(omegaSAx, axiom, omegaSAx =
% 1.10/1.51 (![Xx:$i]:
% 1.10/1.51 ( ( in @ Xx @ omega ) => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ))).
% 1.10/1.51 thf('57', plain,
% 1.10/1.51 (( omegaSAx ) =
% 1.10/1.51 ( ![X4:$i]:
% 1.10/1.51 ( ( in @ X4 @ omega ) => ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(omega0Ax, axiom,(( omega0Ax ) = (in @ emptyset @ omega))).
% 1.10/1.51 thf('58', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 1.10/1.51 inference('simplify_rw_rule', [status(thm)], [omega0Ax])).
% 1.10/1.51 thf('59', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(setunionAx, axiom, setunionAx =
% 1.10/1.51 (![A:$i,Xx:$i]:
% 1.10/1.51 ( ( in @ Xx @ ( setunion @ A ) ) <=>
% 1.10/1.51 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))).
% 1.10/1.51 thf('60', plain,
% 1.10/1.51 (( setunionAx ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( in @ X6 @ ( setunion @ X4 ) ) <=>
% 1.10/1.51 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(powersetAx, axiom, powersetAx =
% 1.10/1.51 (![A:$i,B:$i]:
% 1.10/1.51 ( ( in @ B @ ( powerset @ A ) ) <=>
% 1.10/1.51 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 1.10/1.51 thf('61', plain,
% 1.10/1.51 (( powersetAx ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 1.10/1.51 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(setadjoinAx, axiom, setadjoinAx =
% 1.10/1.51 (![Xx:$i,A:$i,Xy:$i]:
% 1.10/1.51 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 1.10/1.51 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 1.10/1.51 thf('62', plain,
% 1.10/1.51 (( setadjoinAx ) =
% 1.10/1.51 ( ![X4:$i,X6:$i,X8:$i]:
% 1.10/1.51 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 1.10/1.51 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 1.10/1.51 thf('63', plain,
% 1.10/1.51 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(setextAx, axiom, setextAx =
% 1.10/1.51 (![A:$i,B:$i]:
% 1.10/1.51 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) <=> ( in @ Xx @ B ) ) ) =>
% 1.10/1.51 ( ( A ) = ( B ) ) ))).
% 1.10/1.51 thf('64', plain,
% 1.10/1.51 (( setextAx ) =
% 1.10/1.51 ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 1.10/1.51 ( ( X4 ) = ( X6 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(exu, axiom,(( exu ) =
% 1.10/1.51 (^[Xphi:( $i > $o )]:
% 1.10/1.51 ( ?[Xx:$i]:
% 1.10/1.51 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & ( Xphi @ Xx ) ) )))).
% 1.10/1.51 thf('65', plain,
% 1.10/1.51 (( exu ) =
% 1.10/1.51 ( ^[Xphi:( $i > $o )]:
% 1.10/1.51 ( ?[Xx:$i]:
% 1.10/1.51 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 1.10/1.51 ( Xphi @ Xx ) ) ) )),
% 1.10/1.51 inference('simplify_rw_rule', [status(thm)], [exu])).
% 1.10/1.51 thf('66', plain,
% 1.10/1.51 (( exu ) =
% 1.10/1.51 ( ^[V_1:( $i > $o )]:
% 1.10/1.51 ( ?[X4:$i]:
% 1.10/1.51 ( ( ![X6:$i]: ( ( V_1 @ X6 ) => ( ( X4 ) = ( X6 ) ) ) ) &
% 1.10/1.51 ( V_1 @ X4 ) ) ) )),
% 1.10/1.51 define([status(thm)])).
% 1.10/1.51 thf(exuI3, conjecture,
% 1.10/1.51 (( setextAx ) =>
% 1.10/1.51 ( ( emptysetAx ) =>
% 1.10/1.51 ( ( setadjoinAx ) =>
% 1.10/1.51 ( ( powersetAx ) =>
% 1.10/1.51 ( ( setunionAx ) =>
% 1.10/1.51 ( ( omega0Ax ) =>
% 1.10/1.51 ( ( omegaSAx ) =>
% 1.10/1.51 ( ( omegaIndAx ) =>
% 1.10/1.51 ( ( replAx ) =>
% 1.10/1.51 ( ( foundationAx ) =>
% 1.10/1.51 ( ( wellorderingAx ) =>
% 1.10/1.51 ( ( descrp ) =>
% 1.10/1.51 ( ( dsetconstrI ) =>
% 1.10/1.51 ( ( dsetconstrEL ) =>
% 1.10/1.51 ( ( dsetconstrER ) =>
% 1.10/1.51 ( ( exuE1 ) =>
% 1.10/1.51 ( ( prop2setE ) =>
% 1.10/1.51 ( ( emptysetE ) =>
% 1.10/1.51 ( ( emptysetimpfalse ) =>
% 1.10/1.51 ( ( notinemptyset ) =>
% 1.10/1.51 ( ( exuE3e ) =>
% 1.10/1.51 ( ( setext ) =>
% 1.10/1.51 ( ( emptyI ) =>
% 1.10/1.51 ( ( noeltsimpempty ) =>
% 1.10/1.51 ( ( setbeta ) =>
% 1.10/1.51 ( ( nonemptyE1 ) =>
% 1.10/1.51 ( ( nonemptyI ) =>
% 1.10/1.51 ( ( nonemptyI1 ) =>
% 1.10/1.51 ( ( setadjoinIL ) =>
% 1.10/1.51 ( ( emptyinunitempty ) =>
% 1.10/1.51 ( ( setadjoinIR ) =>
% 1.10/1.51 ( ( setadjoinE ) =>
% 1.10/1.51 ( (
% 1.10/1.51 setadjoinOr ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 setoftrueEq ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 powersetI ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 emptyinPowerset ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 emptyInPowerset ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 powersetE ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 setunionI ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 setunionE ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 subPowSU ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 exuE2 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 nonemptyImpWitness ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 uniqinunit ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 notinsingleton ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 eqinunit ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 singletonsswitch ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 upairsetE ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 upairsetIL ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 upairsetIR ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 emptyE1 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 vacuousDall ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 quantDeMorgan1 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 quantDeMorgan2 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 quantDeMorgan3 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 quantDeMorgan4 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 prop2setI ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 prop2set2propI ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 notdexE ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 notdallE ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 exuI1 ) =>
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 Xphi:(
% 1.10/1.51 $i > $o )]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 Xx:$i]:
% 1.10/1.51 (
% 1.10/1.51 Xphi @ Xx ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 Xx:$i,
% 1.10/1.51 Xy:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 Xphi @ Xx ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 Xphi @ Xy ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 Xx ) =
% 1.10/1.51 (
% 1.10/1.51 Xy ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 exu @
% 1.10/1.51 (
% 1.10/1.51 ^[
% 1.10/1.51 Xx:$i]:
% 1.10/1.51 (
% 1.10/1.51 Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.10/1.51 thf(zf_stmt_0, conjecture,
% 1.10/1.51 (( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 1.10/1.51 ( ( X4 ) = ( X6 ) ) ) ) =>
% 1.10/1.51 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 1.10/1.51 ( ( ![X12:$i,X14:$i,X16:$i]:
% 1.10/1.51 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 1.10/1.51 ( ( in @ X16 @ X14 ) | ( ( X16 ) = ( X12 ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X18:$i,X20:$i]:
% 1.10/1.51 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 1.10/1.51 ( ![X22:$i]: ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X24:$i,X26:$i]:
% 1.10/1.51 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 1.10/1.51 ( ?[X28:$i]: ( ( in @ X26 @ X28 ) & ( in @ X28 @ X24 ) ) ) ) ) =>
% 1.10/1.51 ( ( in @ emptyset @ omega ) =>
% 1.10/1.51 ( ( ![X30:$i]:
% 1.10/1.51 ( ( in @ X30 @ omega ) =>
% 1.10/1.51 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 1.10/1.51 ( ( ![X32:$i]:
% 1.10/1.51 ( ( ( ![X34:$i]:
% 1.10/1.51 ( ( ( in @ X34 @ X32 ) & ( in @ X34 @ omega ) ) =>
% 1.10/1.51 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) &
% 1.10/1.51 ( in @ emptyset @ X32 ) ) =>
% 1.10/1.51 ( ![X36:$i]:
% 1.10/1.51 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 1.10/1.51 ( ( ![X42:$i]:
% 1.10/1.51 ( ( in @ X42 @ X40 ) =>
% 1.10/1.51 ( ?[X44:$i]:
% 1.10/1.51 ( ( X38 @ X42 @ X44 ) &
% 1.10/1.51 ( ![X46:$i]:
% 1.10/1.51 ( ( X38 @ X42 @ X46 ) =>
% 1.10/1.51 ( ( X44 ) = ( X46 ) ) ) ) ) ) ) ) =>
% 1.10/1.51 ( ?[X48:$i]:
% 1.10/1.51 ( ![X50:$i]:
% 1.10/1.51 ( ( in @ X50 @ X48 ) <=>
% 1.10/1.51 ( ?[X52:$i]:
% 1.10/1.51 ( ( in @ X52 @ X40 ) & ( X38 @ X52 @ X50 ) ) ) ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X54:$i]:
% 1.10/1.51 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 1.10/1.51 ( ?[X58:$i]:
% 1.10/1.51 ( ( in @ X58 @ X54 ) &
% 1.10/1.51 ( ~( ?[X60:$i]:
% 1.10/1.51 ( ( in @ X60 @ X58 ) & ( in @ X60 @ X54 ) ) ) ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X62:$i]:
% 1.10/1.51 ( ?[X64:$i]:
% 1.10/1.51 ( ( ![X96:$i]:
% 1.10/1.51 ( ( in @ X96 @ X64 ) =>
% 1.10/1.51 ( ![X98:$i]:
% 1.10/1.51 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) &
% 1.10/1.51 ( ![X90:$i,X92:$i]:
% 1.10/1.51 ( ( ( in @ X92 @ X62 ) & ( in @ X90 @ X62 ) ) =>
% 1.10/1.51 ( ( ![X94:$i]:
% 1.10/1.51 ( ( in @ X94 @ X64 ) =>
% 1.10/1.51 ( ( in @ X90 @ X94 ) <=>
% 1.10/1.51 ( in @ X92 @ X94 ) ) ) ) =>
% 1.10/1.51 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 1.10/1.51 ( ![X82:$i,X84:$i]:
% 1.10/1.51 ( ( ( in @ X84 @ X64 ) & ( in @ X82 @ X64 ) ) =>
% 1.10/1.51 ( ( ![X88:$i]:
% 1.10/1.51 ( ( in @ X88 @ X84 ) =>
% 1.10/1.51 ( in @ X88 @ X82 ) ) ) |
% 1.10/1.51 ( ![X86:$i]:
% 1.10/1.51 ( ( in @ X86 @ X82 ) =>
% 1.10/1.51 ( in @ X86 @ X84 ) ) ) ) ) ) &
% 1.10/1.51 ( ![X66:$i]:
% 1.10/1.51 ( ( ( ?[X70:$i]: ( in @ X70 @ X66 ) ) &
% 1.10/1.51 ( ![X68:$i]:
% 1.10/1.51 ( ( in @ X68 @ X66 ) =>
% 1.10/1.51 ( in @ X68 @ X62 ) ) ) ) =>
% 1.10/1.51 ( ?[X72:$i,X74:$i]:
% 1.10/1.51 ( ( in @ X72 @ X64 ) &
% 1.10/1.51 ( in @ X74 @ X66 ) &
% 1.10/1.51 ( ~( ?[X80:$i]:
% 1.10/1.51 ( ( in @ X80 @ X72 ) &
% 1.10/1.51 ( in @ X80 @ X66 ) ) ) ) &
% 1.10/1.51 ( ![X76:$i]:
% 1.10/1.51 ( ( in @ X76 @ X64 ) =>
% 1.10/1.51 ( ( in @ X74 @ X76 ) |
% 1.10/1.51 ( ![X78:$i]:
% 1.10/1.51 ( ( in @ X78 @ X76 ) =>
% 1.10/1.51 ( in @ X78 @ X72 ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X100:( $i > $o )]:
% 1.10/1.51 ( ( ?[X102:$i]:
% 1.10/1.51 ( ( X100 @ X102 ) &
% 1.10/1.51 ( ![X104:$i]:
% 1.10/1.51 ( ( X100 @ X104 ) =>
% 1.10/1.51 ( ( X102 ) = ( X104 ) ) ) ) ) ) =>
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% 1.10/1.51 emptyset ) =>
% 1.10/1.51 (
% 1.10/1.51 X300 @
% 1.10/1.51 X302 ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X304:$i,
% 1.10/1.51 X306:(
% 1.10/1.51 $i > $o )]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 ![
% 1.10/1.51 X308:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X308 @
% 1.10/1.51 X304 ) =>
% 1.10/1.51 (
% 1.10/1.51 X306 @
% 1.10/1.51 X308 ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X310:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X310 @
% 1.10/1.51 X304 ) &
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 X306 @
% 1.10/1.51 X310 ) ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X312:$i,
% 1.10/1.51 X314:(
% 1.10/1.51 $i > $o )]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X316:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X316 @
% 1.10/1.51 X312 ) =>
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 X314 @
% 1.10/1.51 X316 ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 ?[
% 1.10/1.51 X318:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X318 @
% 1.10/1.51 X312 ) &
% 1.10/1.51 (
% 1.10/1.51 X314 @
% 1.10/1.51 X318 ) ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X320:$i,
% 1.10/1.51 X322:(
% 1.10/1.51 $i > $o )]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 ?[
% 1.10/1.51 X324:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X324 @
% 1.10/1.51 X320 ) &
% 1.10/1.51 (
% 1.10/1.51 X322 @
% 1.10/1.51 X324 ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X326:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X326 @
% 1.10/1.51 X320 ) =>
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 X322 @
% 1.10/1.51 X326 ) ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X328:$i,
% 1.10/1.51 X330:(
% 1.10/1.51 $i > $o )]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X332:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X332 @
% 1.10/1.51 X328 ) &
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 X330 @
% 1.10/1.51 X332 ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 ![
% 1.10/1.51 X334:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X334 @
% 1.10/1.51 X328 ) =>
% 1.10/1.51 (
% 1.10/1.51 X330 @
% 1.10/1.51 X334 ) ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X336:$o]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X336 ) =>
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 emptyset @
% 1.10/1.51 (
% 1.10/1.51 prop2set @
% 1.10/1.51 X336 ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X338:$o]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X338 ) =>
% 1.10/1.51 (
% 1.10/1.51 set2prop @
% 1.10/1.51 (
% 1.10/1.51 prop2set @
% 1.10/1.51 X338 ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X340:$i,
% 1.10/1.51 X342:(
% 1.10/1.51 $i > $o )]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 ?[
% 1.10/1.51 X344:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X344 @
% 1.10/1.51 X340 ) &
% 1.10/1.51 (
% 1.10/1.51 X342 @
% 1.10/1.51 X344 ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X346:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X346 @
% 1.10/1.51 X340 ) =>
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 X342 @
% 1.10/1.51 X346 ) ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X348:$i,
% 1.10/1.51 X350:(
% 1.10/1.51 $i > $o )]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 ![
% 1.10/1.51 X352:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X352 @
% 1.10/1.51 X348 ) =>
% 1.10/1.51 (
% 1.10/1.51 X350 @
% 1.10/1.51 X352 ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X354:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X354 @
% 1.10/1.51 X348 ) &
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 X350 @
% 1.10/1.51 X354 ) ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X356:(
% 1.10/1.51 $i > $o )]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X358:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X356 @
% 1.10/1.51 X358 ) &
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X360:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X356 @
% 1.10/1.51 X360 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X358 ) =
% 1.10/1.51 (
% 1.10/1.51 X360 ) ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X362:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X356 @
% 1.10/1.51 X362 ) &
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X364:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X356 @
% 1.10/1.51 X364 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X362 ) =
% 1.10/1.51 (
% 1.10/1.51 X364 ) ) ) ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X366:(
% 1.10/1.51 $i > $o )]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X368:$i]:
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X368 ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X370:$i,
% 1.10/1.51 X372:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X370 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X372 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X370 ) =
% 1.10/1.51 (
% 1.10/1.51 X372 ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X374:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X374 ) &
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X376:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X376 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X374 ) =
% 1.10/1.51 (
% 1.10/1.51 X376 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.10/1.51 thf(zf_stmt_1, type, zip_tseitin_3 : $i > $i > $i > ( $i > $i > $o ) > $o).
% 1.10/1.51 thf(zf_stmt_2, axiom,
% 1.10/1.51 (![X52:$i,X50:$i,X40:$i,X38:( $i > $i > $o )]:
% 1.10/1.51 ( ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) <=>
% 1.10/1.51 ( ( X38 @ X52 @ X50 ) & ( in @ X52 @ X40 ) ) ))).
% 1.10/1.51 thf(zf_stmt_3, type, zip_tseitin_2 : $i > $i > $i > $o).
% 1.10/1.51 thf(zf_stmt_4, axiom,
% 1.10/1.51 (![X28:$i,X26:$i,X24:$i]:
% 1.10/1.51 ( ( zip_tseitin_2 @ X28 @ X26 @ X24 ) <=>
% 1.10/1.51 ( ( in @ X28 @ X24 ) & ( in @ X26 @ X28 ) ) ))).
% 1.10/1.51 thf(zf_stmt_5, type, zip_tseitin_1 : $i > $i > $i > $o).
% 1.10/1.51 thf(zf_stmt_6, axiom,
% 1.10/1.51 (![X22:$i,X20:$i,X18:$i]:
% 1.10/1.51 ( ( zip_tseitin_1 @ X22 @ X20 @ X18 ) <=>
% 1.10/1.51 ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ))).
% 1.10/1.51 thf(zf_stmt_7, type, zip_tseitin_0 : $i > $i > $i > $o).
% 1.10/1.51 thf(zf_stmt_8, axiom,
% 1.10/1.51 (![X16:$i,X14:$i,X12:$i]:
% 1.10/1.51 ( ( zip_tseitin_0 @ X16 @ X14 @ X12 ) <=>
% 1.10/1.51 ( ( ( X16 ) = ( X12 ) ) | ( in @ X16 @ X14 ) ) ))).
% 1.10/1.51 thf(zf_stmt_9, conjecture,
% 1.10/1.51 (( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 1.10/1.51 ( ( X4 ) = ( X6 ) ) ) ) =>
% 1.10/1.51 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 1.10/1.51 ( ( ![X12:$i,X14:$i,X16:$i]:
% 1.10/1.51 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 1.10/1.51 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 1.10/1.51 ( ( ![X18:$i,X20:$i]:
% 1.10/1.51 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 1.10/1.51 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 1.10/1.51 ( ( ![X24:$i,X26:$i]:
% 1.10/1.51 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 1.10/1.51 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 1.10/1.51 ( ( in @ emptyset @ omega ) =>
% 1.10/1.51 ( ( ![X30:$i]:
% 1.10/1.51 ( ( in @ X30 @ omega ) =>
% 1.10/1.51 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 1.10/1.51 ( ( ![X32:$i]:
% 1.10/1.51 ( ( ( in @ emptyset @ X32 ) &
% 1.10/1.51 ( ![X34:$i]:
% 1.10/1.51 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 1.10/1.51 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 1.10/1.51 ( ![X36:$i]:
% 1.10/1.51 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 1.10/1.51 ( ( ![X42:$i]:
% 1.10/1.51 ( ( in @ X42 @ X40 ) =>
% 1.10/1.51 ( ?[X44:$i]:
% 1.10/1.51 ( ( ![X46:$i]:
% 1.10/1.51 ( ( X38 @ X42 @ X46 ) =>
% 1.10/1.51 ( ( X44 ) = ( X46 ) ) ) ) &
% 1.10/1.51 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 1.10/1.51 ( ?[X48:$i]:
% 1.10/1.51 ( ![X50:$i]:
% 1.10/1.51 ( ( in @ X50 @ X48 ) <=>
% 1.10/1.51 ( ?[X52:$i]:
% 1.10/1.51 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X54:$i]:
% 1.10/1.51 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 1.10/1.51 ( ?[X58:$i]:
% 1.10/1.51 ( ( ~( ?[X60:$i]:
% 1.10/1.51 ( ( in @ X60 @ X54 ) & ( in @ X60 @ X58 ) ) ) ) &
% 1.10/1.51 ( in @ X58 @ X54 ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X62:$i]:
% 1.10/1.51 ( ?[X64:$i]:
% 1.10/1.51 ( ( ![X66:$i]:
% 1.10/1.51 ( ( ( ![X68:$i]:
% 1.10/1.51 ( ( in @ X68 @ X66 ) =>
% 1.10/1.51 ( in @ X68 @ X62 ) ) ) &
% 1.10/1.51 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 1.10/1.51 ( ?[X72:$i,X74:$i]:
% 1.10/1.51 ( ( ![X76:$i]:
% 1.10/1.51 ( ( in @ X76 @ X64 ) =>
% 1.10/1.51 ( ( ![X78:$i]:
% 1.10/1.51 ( ( in @ X78 @ X76 ) =>
% 1.10/1.51 ( in @ X78 @ X72 ) ) ) |
% 1.10/1.51 ( in @ X74 @ X76 ) ) ) ) &
% 1.10/1.51 ( ~( ?[X80:$i]:
% 1.10/1.51 ( ( in @ X80 @ X66 ) &
% 1.10/1.51 ( in @ X80 @ X72 ) ) ) ) &
% 1.10/1.51 ( in @ X74 @ X66 ) & ( in @ X72 @ X64 ) ) ) ) ) &
% 1.10/1.51 ( ![X82:$i,X84:$i]:
% 1.10/1.51 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 1.10/1.51 ( ( ![X86:$i]:
% 1.10/1.51 ( ( in @ X86 @ X82 ) =>
% 1.10/1.51 ( in @ X86 @ X84 ) ) ) |
% 1.10/1.51 ( ![X88:$i]:
% 1.10/1.51 ( ( in @ X88 @ X84 ) =>
% 1.10/1.51 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 1.10/1.51 ( ![X90:$i,X92:$i]:
% 1.10/1.51 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 1.10/1.51 ( ( ![X94:$i]:
% 1.10/1.51 ( ( in @ X94 @ X64 ) =>
% 1.10/1.51 ( ( in @ X90 @ X94 ) <=>
% 1.10/1.51 ( in @ X92 @ X94 ) ) ) ) =>
% 1.10/1.51 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 1.10/1.51 ( ![X96:$i]:
% 1.10/1.51 ( ( in @ X96 @ X64 ) =>
% 1.10/1.51 ( ![X98:$i]:
% 1.10/1.51 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X100:( $i > $o )]:
% 1.10/1.51 ( ( ?[X102:$i]:
% 1.10/1.51 ( ( ![X104:$i]:
% 1.10/1.51 ( ( X100 @ X104 ) =>
% 1.10/1.51 ( ( X102 ) = ( X104 ) ) ) ) &
% 1.10/1.51 ( X100 @ X102 ) ) ) =>
% 1.10/1.51 ( X100 @
% 1.10/1.51 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 1.10/1.51 ( ( in @ X110 @ X106 ) =>
% 1.10/1.51 ( ( X108 @ X110 ) =>
% 1.10/1.51 ( in @
% 1.10/1.51 X110 @
% 1.10/1.51 ( dsetconstr @
% 1.10/1.51 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 1.10/1.51 ( ( in @
% 1.10/1.51 X116 @
% 1.10/1.51 ( dsetconstr @
% 1.10/1.51 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 1.10/1.51 ( in @ X116 @ X112 ) ) ) =>
% 1.10/1.51 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 1.10/1.51 ( ( in @
% 1.10/1.51 X122 @
% 1.10/1.51 ( dsetconstr @
% 1.10/1.51 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 1.10/1.51 ( X120 @ X122 ) ) ) =>
% 1.10/1.51 ( ( ![X124:( $i > $o )]:
% 1.10/1.51 ( ( ?[X126:$i]:
% 1.10/1.51 ( ( ![X128:$i]:
% 1.10/1.51 ( ( X124 @ X128 ) =>
% 1.10/1.51 ( ( X126 ) = ( X128 ) ) ) ) &
% 1.10/1.51 ( X124 @ X126 ) ) ) =>
% 1.10/1.51 ( ?[X130:$i]:
% 1.10/1.51 ( ( ![X132:$i]:
% 1.10/1.51 ( ( X124 @ X132 ) =>
% 1.10/1.51 ( ( X130 ) = ( X132 ) ) ) ) &
% 1.10/1.51 ( X124 @ X130 ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X134:$o,X136:$i]:
% 1.10/1.51 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 1.10/1.51 ( X134 ) ) ) =>
% 1.10/1.51 ( ( ![X138:$i]:
% 1.10/1.51 ( ( in @ X138 @ emptyset ) =>
% 1.10/1.51 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 1.10/1.51 ( ( ![X142:$i]:
% 1.10/1.51 ( ~( in @ X142 @ emptyset ) ) ) =>
% 1.10/1.51 ( ( ![X144:$i]:
% 1.10/1.51 ( ~( in @ X144 @ emptyset ) ) ) =>
% 1.10/1.51 ( ( ![X146:( $i > $o )]:
% 1.10/1.51 ( ( ?[X148:$i]:
% 1.10/1.51 ( ( ![X150:$i]:
% 1.10/1.51 ( ( X146 @ X150 ) =>
% 1.10/1.51 ( ( X148 ) = ( X150 ) ) ) ) &
% 1.10/1.51 ( X146 @ X148 ) ) ) =>
% 1.10/1.51 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 1.10/1.51 ( ( ![X154:$i,X156:$i]:
% 1.10/1.51 ( ( ![X158:$i]:
% 1.10/1.51 ( ( in @ X158 @ X154 ) =>
% 1.10/1.51 ( in @ X158 @ X156 ) ) ) =>
% 1.10/1.51 ( ( ![X160:$i]:
% 1.10/1.51 ( ( in @ X160 @ X156 ) =>
% 1.10/1.51 ( in @ X160 @ X154 ) ) ) =>
% 1.10/1.51 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X162:$i]:
% 1.10/1.51 ( ( ![X164:$i]:
% 1.10/1.51 ( ~( in @ X164 @ X162 ) ) ) =>
% 1.10/1.51 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 1.10/1.51 ( ( ![X166:$i]:
% 1.10/1.51 ( ( ![X168:$i]:
% 1.10/1.51 ( ~( in @ X168 @ X166 ) ) ) =>
% 1.10/1.51 ( ( X166 ) =
% 1.10/1.51 ( emptyset ) ) ) ) =>
% 1.10/1.51 ( ( ![X170:$i,
% 1.10/1.51 X172:( $i > $o ),
% 1.10/1.51 X174:$i]:
% 1.10/1.51 ( ( in @ X174 @ X170 ) =>
% 1.10/1.51 ( ( in @
% 1.10/1.51 X174 @
% 1.10/1.51 ( dsetconstr @
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% 1.10/1.51 (
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% 1.10/1.51 X334 ) ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X336:$o]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X336 ) =>
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 emptyset @
% 1.10/1.51 (
% 1.10/1.51 prop2set @
% 1.10/1.51 X336 ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X338:$o]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X338 ) =>
% 1.10/1.51 (
% 1.10/1.51 set2prop @
% 1.10/1.51 (
% 1.10/1.51 prop2set @
% 1.10/1.51 X338 ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X340:$i,
% 1.10/1.51 X342:(
% 1.10/1.51 $i > $o )]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 ?[
% 1.10/1.51 X344:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X342 @
% 1.10/1.51 X344 ) &
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X344 @
% 1.10/1.51 X340 ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X346:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X346 @
% 1.10/1.51 X340 ) =>
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 X342 @
% 1.10/1.51 X346 ) ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X348:$i,
% 1.10/1.51 X350:(
% 1.10/1.51 $i > $o )]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 ![
% 1.10/1.51 X352:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X352 @
% 1.10/1.51 X348 ) =>
% 1.10/1.51 (
% 1.10/1.51 X350 @
% 1.10/1.51 X352 ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X354:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ~(
% 1.10/1.51 X350 @
% 1.10/1.51 X354 ) ) &
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X354 @
% 1.10/1.51 X348 ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X356:(
% 1.10/1.51 $i > $o )]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X358:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X360:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X356 @
% 1.10/1.51 X360 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X358 ) =
% 1.10/1.51 (
% 1.10/1.51 X360 ) ) ) ) &
% 1.10/1.51 (
% 1.10/1.51 X356 @
% 1.10/1.51 X358 ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X362:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X364:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X356 @
% 1.10/1.51 X364 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X362 ) =
% 1.10/1.51 (
% 1.10/1.51 X364 ) ) ) ) &
% 1.10/1.51 (
% 1.10/1.51 X356 @
% 1.10/1.51 X362 ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X366:(
% 1.10/1.51 $i > $o )]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X368:$i]:
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X368 ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X370:$i,
% 1.10/1.51 X372:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X370 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X372 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X370 ) =
% 1.10/1.51 (
% 1.10/1.51 X372 ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X374:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X376:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X376 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X374 ) =
% 1.10/1.51 (
% 1.10/1.51 X376 ) ) ) ) &
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X374 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.10/1.51 thf(zf_stmt_10, negated_conjecture,
% 1.10/1.51 (~( ( ![X4:$i,X6:$i]:
% 1.10/1.51 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 1.10/1.51 ( ( X4 ) = ( X6 ) ) ) ) =>
% 1.10/1.51 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 1.10/1.51 ( ( ![X12:$i,X14:$i,X16:$i]:
% 1.10/1.51 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 1.10/1.51 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 1.10/1.51 ( ( ![X18:$i,X20:$i]:
% 1.10/1.51 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 1.10/1.51 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 1.10/1.51 ( ( ![X24:$i,X26:$i]:
% 1.10/1.51 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 1.10/1.51 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 1.10/1.51 ( ( in @ emptyset @ omega ) =>
% 1.10/1.51 ( ( ![X30:$i]:
% 1.10/1.51 ( ( in @ X30 @ omega ) =>
% 1.10/1.51 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 1.10/1.51 ( ( ![X32:$i]:
% 1.10/1.51 ( ( ( in @ emptyset @ X32 ) &
% 1.10/1.51 ( ![X34:$i]:
% 1.10/1.51 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 1.10/1.51 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 1.10/1.51 ( ![X36:$i]:
% 1.10/1.51 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 1.10/1.51 ( ( ![X42:$i]:
% 1.10/1.51 ( ( in @ X42 @ X40 ) =>
% 1.10/1.51 ( ?[X44:$i]:
% 1.10/1.51 ( ( ![X46:$i]:
% 1.10/1.51 ( ( X38 @ X42 @ X46 ) =>
% 1.10/1.51 ( ( X44 ) = ( X46 ) ) ) ) &
% 1.10/1.51 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 1.10/1.51 ( ?[X48:$i]:
% 1.10/1.51 ( ![X50:$i]:
% 1.10/1.51 ( ( in @ X50 @ X48 ) <=>
% 1.10/1.51 ( ?[X52:$i]:
% 1.10/1.51 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X54:$i]:
% 1.10/1.51 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 1.10/1.51 ( ?[X58:$i]:
% 1.10/1.51 ( ( ~( ?[X60:$i]:
% 1.10/1.51 ( ( in @ X60 @ X54 ) &
% 1.10/1.51 ( in @ X60 @ X58 ) ) ) ) &
% 1.10/1.51 ( in @ X58 @ X54 ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X62:$i]:
% 1.10/1.51 ( ?[X64:$i]:
% 1.10/1.51 ( ( ![X66:$i]:
% 1.10/1.51 ( ( ( ![X68:$i]:
% 1.10/1.51 ( ( in @ X68 @ X66 ) =>
% 1.10/1.51 ( in @ X68 @ X62 ) ) ) &
% 1.10/1.51 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 1.10/1.51 ( ?[X72:$i,X74:$i]:
% 1.10/1.51 ( ( ![X76:$i]:
% 1.10/1.51 ( ( in @ X76 @ X64 ) =>
% 1.10/1.51 ( ( ![X78:$i]:
% 1.10/1.51 ( ( in @ X78 @ X76 ) =>
% 1.10/1.51 ( in @ X78 @ X72 ) ) ) |
% 1.10/1.51 ( in @ X74 @ X76 ) ) ) ) &
% 1.10/1.51 ( ~( ?[X80:$i]:
% 1.10/1.51 ( ( in @ X80 @ X66 ) &
% 1.10/1.51 ( in @ X80 @ X72 ) ) ) ) &
% 1.10/1.51 ( in @ X74 @ X66 ) &
% 1.10/1.51 ( in @ X72 @ X64 ) ) ) ) ) &
% 1.10/1.51 ( ![X82:$i,X84:$i]:
% 1.10/1.51 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 1.10/1.51 ( ( ![X86:$i]:
% 1.10/1.51 ( ( in @ X86 @ X82 ) =>
% 1.10/1.51 ( in @ X86 @ X84 ) ) ) |
% 1.10/1.51 ( ![X88:$i]:
% 1.10/1.51 ( ( in @ X88 @ X84 ) =>
% 1.10/1.51 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 1.10/1.51 ( ![X90:$i,X92:$i]:
% 1.10/1.51 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 1.10/1.51 ( ( ![X94:$i]:
% 1.10/1.51 ( ( in @ X94 @ X64 ) =>
% 1.10/1.51 ( ( in @ X90 @ X94 ) <=>
% 1.10/1.51 ( in @ X92 @ X94 ) ) ) ) =>
% 1.10/1.51 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 1.10/1.51 ( ![X96:$i]:
% 1.10/1.51 ( ( in @ X96 @ X64 ) =>
% 1.10/1.51 ( ![X98:$i]:
% 1.10/1.51 ( ( in @ X98 @ X96 ) =>
% 1.10/1.51 ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X100:( $i > $o )]:
% 1.10/1.51 ( ( ?[X102:$i]:
% 1.10/1.51 ( ( ![X104:$i]:
% 1.10/1.51 ( ( X100 @ X104 ) =>
% 1.10/1.51 ( ( X102 ) = ( X104 ) ) ) ) &
% 1.10/1.51 ( X100 @ X102 ) ) ) =>
% 1.10/1.51 ( X100 @
% 1.10/1.51 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 1.10/1.51 ( ( in @ X110 @ X106 ) =>
% 1.10/1.51 ( ( X108 @ X110 ) =>
% 1.10/1.51 ( in @
% 1.10/1.51 X110 @
% 1.10/1.51 ( dsetconstr @
% 1.10/1.51 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 1.10/1.51 ( ( in @
% 1.10/1.51 X116 @
% 1.10/1.51 ( dsetconstr @
% 1.10/1.51 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 1.10/1.51 ( in @ X116 @ X112 ) ) ) =>
% 1.10/1.51 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 1.10/1.51 ( ( in @
% 1.10/1.51 X122 @
% 1.10/1.51 ( dsetconstr @
% 1.10/1.51 X118 @
% 1.10/1.51 ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 1.10/1.51 ( X120 @ X122 ) ) ) =>
% 1.10/1.51 ( ( ![X124:( $i > $o )]:
% 1.10/1.51 ( ( ?[X126:$i]:
% 1.10/1.51 ( ( ![X128:$i]:
% 1.10/1.51 ( ( X124 @ X128 ) =>
% 1.10/1.51 ( ( X126 ) = ( X128 ) ) ) ) &
% 1.10/1.51 ( X124 @ X126 ) ) ) =>
% 1.10/1.51 ( ?[X130:$i]:
% 1.10/1.51 ( ( ![X132:$i]:
% 1.10/1.51 ( ( X124 @ X132 ) =>
% 1.10/1.51 ( ( X130 ) = ( X132 ) ) ) ) &
% 1.10/1.51 ( X124 @ X130 ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X134:$o,X136:$i]:
% 1.10/1.51 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 1.10/1.51 ( X134 ) ) ) =>
% 1.10/1.51 ( ( ![X138:$i]:
% 1.10/1.51 ( ( in @ X138 @ emptyset ) =>
% 1.10/1.51 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 1.10/1.51 ( ( ![X142:$i]:
% 1.10/1.51 ( ~( in @ X142 @ emptyset ) ) ) =>
% 1.10/1.51 ( ( ![X144:$i]:
% 1.10/1.51 ( ~( in @ X144 @ emptyset ) ) ) =>
% 1.10/1.51 ( ( ![X146:( $i > $o )]:
% 1.10/1.51 ( ( ?[X148:$i]:
% 1.10/1.51 ( ( ![X150:$i]:
% 1.10/1.51 ( ( X146 @ X150 ) =>
% 1.10/1.51 ( ( X148 ) =
% 1.10/1.51 ( X150 ) ) ) ) &
% 1.10/1.51 ( X146 @ X148 ) ) ) =>
% 1.10/1.51 ( ?[X152:$i]:
% 1.10/1.51 ( X146 @ X152 ) ) ) ) =>
% 1.10/1.51 ( ( ![X154:$i,X156:$i]:
% 1.10/1.51 ( ( ![X158:$i]:
% 1.10/1.51 ( ( in @ X158 @ X154 ) =>
% 1.10/1.51 ( in @ X158 @ X156 ) ) ) =>
% 1.10/1.51 ( ( ![X160:$i]:
% 1.10/1.51 ( ( in @ X160 @ X156 ) =>
% 1.10/1.51 ( in @ X160 @ X154 ) ) ) =>
% 1.10/1.51 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X162:$i]:
% 1.10/1.51 ( ( ![X164:$i]:
% 1.10/1.51 ( ~( in @ X164 @ X162 ) ) ) =>
% 1.10/1.51 ( ( X162 ) =
% 1.10/1.51 ( emptyset ) ) ) ) =>
% 1.10/1.51 ( ( ![X166:$i]:
% 1.10/1.51 ( ( ![X168:$i]:
% 1.10/1.51 ( ~( in @
% 1.10/1.51 X168 @ X166 ) ) ) =>
% 1.10/1.51 ( ( X166 ) =
% 1.10/1.51 ( emptyset ) ) ) ) =>
% 1.10/1.51 ( ( ![X170:$i,
% 1.10/1.51 X172:( $i > $o ),
% 1.10/1.51 X174:$i]:
% 1.10/1.51 ( ( in @ X174 @ X170 ) =>
% 1.10/1.51 ( ( in @
% 1.10/1.51 X174 @
% 1.10/1.51 ( dsetconstr @
% 1.10/1.51 X170 @
% 1.10/1.51 ( ^[V_5:$i]:
% 1.10/1.51 ( X172 @
% 1.10/1.51 V_5 ) ) ) ) <=>
% 1.10/1.51 ( X172 @ X174 ) ) ) ) =>
% 1.10/1.51 ( ( ![X176:$i]:
% 1.10/1.51 ( ( ( X176 ) !=
% 1.10/1.51 ( emptyset ) ) =>
% 1.10/1.51 ( ?[X178:$i]:
% 1.10/1.51 ( in @
% 1.10/1.51 X178 @ X176 ) ) ) ) =>
% 1.10/1.51 ( ( ![X180:$i,
% 1.10/1.51 X182:(
% 1.10/1.51 $i > $o ),
% 1.10/1.51 X184:$i]:
% 1.10/1.51 ( ( in @
% 1.10/1.51 X184 @ X180 ) =>
% 1.10/1.51 ( ( X182 @ X184 ) =>
% 1.10/1.51 ( ( dsetconstr
% 1.10/1.51 @
% 1.10/1.51 X180 @
% 1.10/1.51 (
% 1.10/1.51 ^[
% 1.10/1.51 V_6:$i]:
% 1.10/1.51 (
% 1.10/1.51 X182 @
% 1.10/1.51 V_6 ) ) ) !=
% 1.10/1.51 ( emptyset ) ) ) ) ) =>
% 1.10/1.51 ( ( ![X186:$i]:
% 1.10/1.51 ( ( ?[X188:$i]:
% 1.10/1.51 ( in @
% 1.10/1.51 X188 @
% 1.10/1.51 X186 ) ) =>
% 1.10/1.51 ( ( X186 ) !=
% 1.10/1.51 ( emptyset ) ) ) ) =>
% 1.10/1.51 ( ( ![X190:$i,
% 1.10/1.51 X192:$i]:
% 1.10/1.51 ( in @
% 1.10/1.51 X190 @
% 1.10/1.51 ( setadjoin
% 1.10/1.51 @
% 1.10/1.51 X190 @
% 1.10/1.51 X192 ) ) ) =>
% 1.10/1.51 ( ( in @
% 1.10/1.51 emptyset @
% 1.10/1.51 ( setadjoin
% 1.10/1.51 @
% 1.10/1.51 emptyset @
% 1.10/1.51 emptyset ) ) =>
% 1.10/1.51 ( ( ![
% 1.10/1.51 X194:$i,
% 1.10/1.51 X196:$i,
% 1.10/1.51 X198:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X198 @
% 1.10/1.51 X196 ) =>
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X198 @
% 1.10/1.51 (
% 1.10/1.51 setadjoin
% 1.10/1.51 @
% 1.10/1.51 X194 @
% 1.10/1.51 X196 ) ) ) ) =>
% 1.10/1.51 ( (
% 1.10/1.51 ![
% 1.10/1.51 X200:$i,
% 1.10/1.51 X202:$i,
% 1.10/1.51 X204:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X204 @
% 1.10/1.51 (
% 1.10/1.51 setadjoin
% 1.10/1.51 @
% 1.10/1.51 X200 @
% 1.10/1.51 X202 ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X206:$o]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X204 ) =
% 1.10/1.51 (
% 1.10/1.51 X200 ) ) =>
% 1.10/1.51 (
% 1.10/1.51 X206 ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X204 @
% 1.10/1.51 X202 ) =>
% 1.10/1.51 (
% 1.10/1.51 X206 ) ) =>
% 1.10/1.51 (
% 1.10/1.51 X206 ) ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X208:$i,
% 1.10/1.51 X210:$i,
% 1.10/1.51 X212:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X212 @
% 1.10/1.51 (
% 1.10/1.51 setadjoin
% 1.10/1.51 @
% 1.10/1.51 X208 @
% 1.10/1.51 X210 ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X212 ) =
% 1.10/1.51 (
% 1.10/1.51 X208 ) ) |
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X212 @
% 1.10/1.51 X210 ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X214:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 dsetconstr
% 1.10/1.51 @
% 1.10/1.51 X214 @
% 1.10/1.51 (
% 1.10/1.51 ^[
% 1.10/1.51 V_7:$i]:
% 1.10/1.51 (
% 1.10/1.51 $true ) ) ) =
% 1.10/1.51 (
% 1.10/1.51 X214 ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X216:$i,
% 1.10/1.51 X218:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X220:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X220 @
% 1.10/1.51 X218 ) =>
% 1.10/1.51 (
% 1.10/1.51 in @
% 1.10/1.51 X220 @
% 1.10/1.51 X216 ) ) ) =>
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% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X368:$i]:
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X368 ) ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X370:$i,
% 1.10/1.51 X372:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X370 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X372 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X370 ) =
% 1.10/1.51 (
% 1.10/1.51 X372 ) ) ) ) ) =>
% 1.10/1.51 (
% 1.10/1.51 ?[
% 1.10/1.51 X374:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 ![
% 1.10/1.51 X376:$i]:
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X376 ) =>
% 1.10/1.51 (
% 1.10/1.51 (
% 1.10/1.51 X374 ) =
% 1.10/1.51 (
% 1.10/1.51 X376 ) ) ) ) &
% 1.10/1.51 (
% 1.10/1.51 X366 @
% 1.10/1.51 X374 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 1.10/1.51 inference('cnf.neg', [status(esa)], [zf_stmt_9])).
% 1.10/1.51 thf(zip_derived_cl72, plain,
% 1.10/1.51 (![X88 : $i, X89 : $i]:
% 1.10/1.51 (~ (sk__190 @ X88) | ((X88) = (X89)) | ~ (sk__190 @ X89))),
% 1.10/1.51 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.10/1.51 thf(zip_derived_cl75, plain, ( (sk__190 @ sk__192)),
% 1.10/1.51 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.10/1.51 thf(zip_derived_cl221, plain,
% 1.10/1.51 (![X0 : $i]: (((X0) = (sk__192)) | ~ (sk__190 @ X0))),
% 1.10/1.51 inference('sup+', [status(thm)], [zip_derived_cl72, zip_derived_cl75])).
% 1.10/1.51 thf(zip_derived_cl74, plain,
% 1.10/1.51 (![X90 : $i]: ( (sk__190 @ (sk__191 @ X90)) | ~ (sk__190 @ X90))),
% 1.10/1.51 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.10/1.51 thf(zip_derived_cl273, plain,
% 1.10/1.51 (![X0 : $i]: (((sk__191 @ X0) = (sk__192)) | ~ (sk__190 @ X0))),
% 1.10/1.51 inference('sup+', [status(thm)], [zip_derived_cl221, zip_derived_cl74])).
% 1.10/1.51 thf(zip_derived_cl73, plain,
% 1.10/1.51 (![X90 : $i]: (((X90) != (sk__191 @ X90)) | ~ (sk__190 @ X90))),
% 1.10/1.51 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.10/1.51 thf(zip_derived_cl308, plain,
% 1.10/1.51 (![X0 : $i]: (((X0) != (sk__192)) | ~ (sk__190 @ X0) | ~ (sk__190 @ X0))),
% 1.10/1.51 inference('sup-', [status(thm)], [zip_derived_cl273, zip_derived_cl73])).
% 1.10/1.51 thf(zip_derived_cl316, plain, (~ (sk__190 @ sk__192)),
% 1.10/1.51 inference('simplify', [status(thm)], [zip_derived_cl308])).
% 1.10/1.51 thf(zip_derived_cl75, plain, ( (sk__190 @ sk__192)),
% 1.10/1.51 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.10/1.51 thf(zip_derived_cl317, plain, ($false),
% 1.10/1.51 inference('simplify_reflect+', [status(thm)],
% 1.10/1.51 [zip_derived_cl316, zip_derived_cl75])).
% 1.10/1.51
% 1.10/1.51 % SZS output end Refutation
% 1.10/1.51
% 1.10/1.51
% 1.10/1.51 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.10/1.51 % Terminating...
% 1.17/1.67 % Runner terminated.
% 1.17/1.68 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------