%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU527^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fSQYHPM9ay true
% Computer : n001.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 04:54:55 PM UTC 2025
% Result : Theorem 7.28s 2.78s
% Output : Refutation 7.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 7
% Syntax : Number of formulae : 73 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 1342 ( 67 equ; 2 cnn)
% Maximal formula atoms : 47 ( 18 avg)
% Number of connectives : 1842 ( 54 ~; 10 |; 0 &; 542 @)
% ( 8 <=>;1126 =>; 0 <=; 0 <~>)
% Maximal formula depth : 53 ( 23 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 49 usr; 50 con; 0-2 aty)
% ( 102 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 127 ( 109 ^; 18 !; 0 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
thf(setadjoinAx_type,type,
setadjoinAx: $o ).
thf(setunionAx_type,type,
setunionAx: $o ).
thf(emptyinunitempty_type,type,
emptyinunitempty: $o ).
thf(emptyInPowerset_type,type,
emptyInPowerset: $o ).
thf(omegaSAx_type,type,
omegaSAx: $o ).
thf('#sk96_type',type,
'#sk96': ( $i > $o ) > $i > $i ).
thf(nonemptyI1_type,type,
nonemptyI1: $o ).
thf(wellorderingAx_type,type,
wellorderingAx: $o ).
thf(emptysetE_type,type,
emptysetE: $o ).
thf(nonemptyE1_type,type,
nonemptyE1: $o ).
thf(setadjoinIR_type,type,
setadjoinIR: $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(setoftrueEq_type,type,
setoftrueEq: $o ).
thf(emptyI_type,type,
emptyI: $o ).
thf(exuE2_type,type,
exuE2: $o ).
thf(dsetconstrEL_type,type,
dsetconstrEL: $o ).
thf(powersetAx_type,type,
powersetAx: $o ).
thf(subPowSU_type,type,
subPowSU: $o ).
thf(setadjoinOr_type,type,
setadjoinOr: $o ).
thf(notinemptyset_type,type,
notinemptyset: $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setext_type,type,
setext: $o ).
thf(setbeta_type,type,
setbeta: $o ).
thf(emptysetimpfalse_type,type,
emptysetimpfalse: $o ).
thf(setadjoinIL_type,type,
setadjoinIL: $o ).
thf(exuE1_type,type,
exuE1: $o ).
thf(nonemptyI_type,type,
nonemptyI: $o ).
thf(omega0Ax_type,type,
omega0Ax: $o ).
thf(powersetI_type,type,
powersetI: $o ).
thf(prop2setE_type,type,
prop2setE: $o ).
thf(setextAx_type,type,
setextAx: $o ).
thf(descrp_type,type,
descrp: $o ).
thf(foundationAx_type,type,
foundationAx: $o ).
thf(emptysetAx_type,type,
emptysetAx: $o ).
thf(emptyinPowerset_type,type,
emptyinPowerset: $o ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(powersetE_type,type,
powersetE: $o ).
thf(nonemptyImpWitness_type,type,
nonemptyImpWitness: $o ).
thf('#sk252_type',type,
'#sk252': $i ).
thf(noeltsimpempty_type,type,
noeltsimpempty: $o ).
thf(omega_type,type,
omega: $i ).
thf(setunionI_type,type,
setunionI: $o ).
thf(exuE3e_type,type,
exuE3e: $o ).
thf(dsetconstrI_type,type,
dsetconstrI: $o ).
thf(setadjoinE_type,type,
setadjoinE: $o ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(replAx_type,type,
replAx: $o ).
thf(omegaIndAx_type,type,
omegaIndAx: $o ).
thf(setunionE_type,type,
setunionE: $o ).
thf(uniqinunit,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[uniqinunit]) ).
thf(zip_derived_cl0,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(omega0Ax,axiom,
( omega0Ax
= ( in @ emptyset @ omega ) ) ).
thf('0',plain,
( omega0Ax
= ( in @ emptyset @ omega ) ),
define([status(thm)]) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
thf('1',plain,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl1,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( ( in @ emptyset @ omega )
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rw,[status(thm)],[zip_derived_cl0,'0','1']) ).
thf(zip_derived_cl3,plain,
~ ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( ( in @ emptyset @ omega )
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
~ ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( ( in @ emptyset @ omega )
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl10,plain,
~ ( powersetAx
=> ( setunionAx
=> ( ( in @ emptyset @ omega )
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl15,plain,
~ ( setunionAx
=> ( ( in @ emptyset @ omega )
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl20,plain,
~ ( ( in @ emptyset @ omega )
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl27,plain,
~ ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl33,plain,
~ ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl39,plain,
~ ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl44,plain,
~ ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl49,plain,
~ ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl55,plain,
~ ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl61,plain,
~ ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl68,plain,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl78,plain,
~ ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl94,plain,
~ ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl114,plain,
~ ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl132,plain,
~ ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl148,plain,
~ ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl132]) ).
thf(zip_derived_cl163,plain,
~ ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl148]) ).
thf(zip_derived_cl177,plain,
~ ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl163]) ).
thf(zip_derived_cl191,plain,
~ ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl177]) ).
thf(zip_derived_cl205,plain,
~ ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl191]) ).
thf(zip_derived_cl219,plain,
~ ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl205]) ).
thf(zip_derived_cl231,plain,
~ ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl219]) ).
thf(zip_derived_cl244,plain,
~ ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl231]) ).
thf(zip_derived_cl258,plain,
~ ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl244]) ).
thf(zip_derived_cl274,plain,
~ ( nonemptyI1
=> ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl258]) ).
thf(zip_derived_cl285,plain,
~ ( setadjoinIL
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl274]) ).
thf(zip_derived_cl297,plain,
~ ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl285]) ).
thf(zip_derived_cl305,plain,
~ ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl297]) ).
thf(zip_derived_cl312,plain,
~ ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl305]) ).
thf(zip_derived_cl318,plain,
~ ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl312]) ).
thf(zip_derived_cl325,plain,
~ ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl318]) ).
thf(zip_derived_cl331,plain,
~ ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl325]) ).
thf(zip_derived_cl337,plain,
~ ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl331]) ).
thf(zip_derived_cl343,plain,
~ ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl337]) ).
thf(zip_derived_cl350,plain,
~ ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl343]) ).
thf(zip_derived_cl357,plain,
~ ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl350]) ).
thf(zip_derived_cl364,plain,
~ ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl357]) ).
thf(zip_derived_cl372,plain,
~ ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl364]) ).
thf(zip_derived_cl382,plain,
~ ( exuE2
=> ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl372]) ).
thf(zip_derived_cl390,plain,
~ ( nonemptyImpWitness
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl382]) ).
thf(zip_derived_cl397,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ emptyset ) )
=> ( Y0 = Y1 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl390]) ).
thf(zip_derived_cl405,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ '#sk252' @ ( setadjoin @ Y0 @ emptyset ) )
=> ( '#sk252' = Y0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl397]) ).
thf(zip_derived_cl410,plain,
~ ( ( in @ '#sk252'
@ ( setadjoin
@ ( '#sk96'
@ ^ [Y0: $i] : ( in @ '#sk252' @ ( setadjoin @ Y0 @ emptyset ) )
@ '#sk252' )
@ emptyset ) )
=> ( '#sk252'
= ( '#sk96'
@ ^ [Y0: $i] : ( in @ '#sk252' @ ( setadjoin @ Y0 @ emptyset ) )
@ '#sk252' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl405]) ).
thf(zip_derived_cl414,plain,
( in @ '#sk252'
@ ( setadjoin
@ ( '#sk96'
@ ^ [Y0: $i] : ( in @ '#sk252' @ ( setadjoin @ Y0 @ emptyset ) )
@ '#sk252' )
@ emptyset ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl410]) ).
thf(zip_derived_cl9,plain,
setadjoinAx,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(setadjoinAx,axiom,
( setadjoinAx
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
<=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
= $true ) ) ).
thf('2',plain,
( setadjoinAx
<=> ! [X5: $i,X7: $i,X9: $i] :
( ( in @ X9 @ ( setadjoin @ X5 @ X7 ) )
<=> ( ( in @ X9 @ X7 )
| ( X9 = X5 ) ) ) ),
inference('rw.lit',[status(esa)],[setadjoinAx]) ).
thf(zip_derived_cl13,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
<=> ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) ),
inference(rw_clause,[status(thm)],[zip_derived_cl9,'2']) ).
thf(zip_derived_cl17,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ X2 @ Y0 ) )
<=> ( ( in @ Y1 @ Y0 )
| ( Y1 = X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl23,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( in @ Y0 @ X4 )
| ( Y0 = X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl29,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ X6 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( in @ X6 @ X4 )
| ( X6 = X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl34,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ X6 @ ( setadjoin @ X2 @ X4 ) )
= ( ( in @ X6 @ X4 )
| ( X6 = X2 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl870,plain,
( ( in @ '#sk252' @ emptyset )
| ( '#sk252'
= ( '#sk96'
@ ^ [Y0: $i] : ( in @ '#sk252' @ ( setadjoin @ Y0 @ emptyset ) )
@ '#sk252' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl414,zip_derived_cl34]) ).
thf(zip_derived_cl5,plain,
emptysetAx,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(emptysetAx,axiom,
( emptysetAx
=> ( ( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) )
= $true ) ) ).
thf('3',plain,
( emptysetAx
<=> ! [X5: $i] :
~ ( in @ X5 @ emptyset ) ),
inference('rw.lit',[status(esa)],[emptysetAx]) ).
thf(zip_derived_cl8,plain,
( !!
@ ^ [Y0: $i] : ( (~) @ ( in @ Y0 @ emptyset ) ) ),
inference(rw_clause,[status(thm)],[zip_derived_cl5,'3']) ).
thf(zip_derived_cl12,plain,
! [X2: $i] :
~ ( in @ X2 @ emptyset ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl901,plain,
( $false
| ( '#sk252'
= ( '#sk96'
@ ^ [Y0: $i] : ( in @ '#sk252' @ ( setadjoin @ Y0 @ emptyset ) )
@ '#sk252' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl870,zip_derived_cl12]) ).
thf(zip_derived_cl415,plain,
( '#sk252'
!= ( '#sk96'
@ ^ [Y0: $i] : ( in @ '#sk252' @ ( setadjoin @ Y0 @ emptyset ) )
@ '#sk252' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl410]) ).
thf(zip_derived_cl419,plain,
( '#sk252'
!= ( '#sk96'
@ ^ [Y0: $i] : ( in @ '#sk252' @ ( setadjoin @ Y0 @ emptyset ) )
@ '#sk252' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl415]) ).
thf(zip_derived_cl902,plain,
( $false
| $false ),
inference(inner_simplify_reflect,[status(thm)],[zip_derived_cl901,zip_derived_cl419]) ).
thf(zip_derived_cl903,plain,
$false,
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl902]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.24 % Problem : SEU527^1 : TPTP v9.2.0. Released v3.7.0.
% 0.00/0.25 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fSQYHPM9ay true
% 0.08/0.44 % Computer : n001.cluster.edu
% 0.08/0.44 % Model : x86_64 x86_64
% 0.08/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.44 % Memory : 8042.1875MB
% 0.08/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.44 % CPULimit : 300
% 0.08/0.44 % WCLimit : 300
% 0.08/0.44 % DateTime : Wed Oct 1 16:01:53 EDT 2025
% 0.08/0.46 % CPUTime :
% 0.08/0.46 % Running portfolio for 300 s
% 0.08/0.46 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.47 % Number of cores: 8
% 0.13/0.48 % Python version: Python 3.6.8
% 0.13/0.49 % Running in HO mode
% 0.28/0.89 % Total configuration time : 828
% 0.28/0.89 % Estimated wc time : 1656
% 0.28/0.89 % Estimated cpu time (8 cpus) : 207.0
% 0.28/1.07 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.28/1.10 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.28/1.16 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.33/1.22 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.37/1.23 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.37/1.26 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.37/1.28 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.37/1.30 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.66/1.44 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 7.28/2.78 % Solved by lams/30_b.l.sh.
% 7.28/2.78 % done 23 iterations in 1.196s
% 7.28/2.78 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 7.28/2.78 % SZS output start Refutation
% See solution above
% 7.69/2.79
% 7.69/2.79
% 7.69/2.79 % Terminating...
% 8.30/3.02 % Runner terminated.
% 8.30/3.05 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------