%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU704^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.y062ZnN9uD true
% Computer : n018.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 Aug 31 19:16:22 EDT 2023
% Result : Theorem 71.37s 9.74s
% Output : Refutation 71.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 273
% Syntax : Number of formulae : 286 ( 41 unt; 234 typ; 0 def)
% Number of atoms : 999 ( 149 equ; 10 cnn)
% Maximal formula atoms : 257 ( 19 avg)
% Number of connectives : 1643 ( 60 ~; 50 |; 81 &; 648 @)
% ( 8 <=>; 796 =>; 0 <=; 0 <~>)
% Maximal formula depth : 236 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 238 ( 234 usr; 228 con; 0-4 aty)
% Number of variables : 345 ( 77 ^; 249 !; 19 ?; 345 :)
% Comments :
%------------------------------------------------------------------------------
thf(setadjoinAx_type,type,
setadjoinAx: $o ).
thf(cartprodmempaircEq_type,type,
cartprodmempaircEq: $o ).
thf(notdexE_type,type,
notdexE: $o ).
thf('#l_lift30160_type',type,
'#l_lift30160': $i > $o > $i > $i > $o ).
thf(setunionAx_type,type,
setunionAx: $o ).
thf(setminusELneg_type,type,
setminusELneg: $o ).
thf(kpairsurjEq_type,type,
kpairsurjEq: $o ).
thf(ap2apEq2_type,type,
ap2apEq2: $o ).
thf(powersetE_type,type,
powersetE: $o ).
thf(omegaSAx_type,type,
omegaSAx: $o ).
thf(exuI1_type,type,
exuI1: $o ).
thf(exuI2_type,type,
exuI2: $o ).
thf(notequalI2_type,type,
notequalI2: $o ).
thf(kpairiskpair_type,type,
kpairiskpair: $o ).
thf(upairsubunion_type,type,
upairsubunion: $o ).
thf(powerset__Cong_type,type,
powerset__Cong: $o ).
thf(iftrueProp1_type,type,
iftrueProp1: $o ).
thf(setminusILneg_type,type,
setminusILneg: $o ).
thf(lam2lamEq_type,type,
lam2lamEq: $o ).
thf(ap2p_type,type,
ap2p: $o ).
thf(wellorderingAx_type,type,
wellorderingAx: $o ).
thf(setadjoinSub2_type,type,
setadjoinSub2: $o ).
thf(binintersectSubset5_type,type,
binintersectSubset5: $o ).
thf(upairinpowunion_type,type,
upairinpowunion: $o ).
thf(setoftrueEq_type,type,
setoftrueEq: $o ).
thf(func_type,type,
func: $i > $i > $i > $o ).
thf(emptyset__Cong_type,type,
emptyset__Cong: $o ).
thf(cartprodpairmemER_type,type,
cartprodpairmemER: $o ).
thf(dpsetconstrI_type,type,
dpsetconstrI: $o ).
thf(dpsetconstrER_type,type,
dpsetconstrER: $o ).
thf(sepInPowerset_type,type,
sepInPowerset: $o ).
thf(setukpairIR_type,type,
setukpairIR: $o ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(binunionE_type,type,
binunionE: $o ).
thf(setext_type,type,
setext: $o ).
thf(emptyinPowerset_type,type,
emptyinPowerset: $o ).
thf(ubforcartprodlem1_type,type,
ubforcartprodlem1: $o ).
thf(setukpairinjR12_type,type,
setukpairinjR12: $o ).
thf(descr__Cong_type,type,
descr__Cong: $o ).
thf(iffalseProp1_type,type,
iffalseProp1: $o ).
thf(binintersectSubset1_type,type,
binintersectSubset1: $o ).
thf(app_type,type,
app: $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(dpsetconstrSub_type,type,
dpsetconstrSub: $o ).
thf(cartprodfstpairEq_type,type,
cartprodfstpairEq: $o ).
thf(quantDeMorgan1_type,type,
quantDeMorgan1: $o ).
thf(funcGraphProp2_type,type,
funcGraphProp2: $o ).
thf(setadjoinIR_type,type,
setadjoinIR: $o ).
thf(funcGraphProp1_type,type,
funcGraphProp1: $o ).
thf(setadjoin__Cong_type,type,
setadjoin__Cong: $o ).
thf(symdiffI2_type,type,
symdiffI2: $o ).
thf(upairset2IR_type,type,
upairset2IR: $o ).
thf(sk__55_type,type,
sk__55: $o ).
thf(subsetE_type,type,
subsetE: $o ).
thf(prop2set2propI_type,type,
prop2set2propI: $o ).
thf(dsetconstrEL_type,type,
dsetconstrEL: $o ).
thf(setbeta_type,type,
setbeta: $o ).
thf(eqinunit_type,type,
eqinunit: $o ).
thf(upairsetIL_type,type,
upairsetIL: $o ).
thf(powersetI1_type,type,
powersetI1: $o ).
thf(lamProp_type,type,
lamProp: $o ).
thf(binintersectSubset3_type,type,
binintersectSubset3: $o ).
thf(setukpairinjR_type,type,
setukpairinjR: $o ).
thf(cartprodfstin_type,type,
cartprodfstin: $o ).
thf(setminusIRneg_type,type,
setminusIRneg: $o ).
thf(powersetAx_type,type,
powersetAx: $o ).
thf(singletonprop_type,type,
singletonprop: $o ).
thf(binintersectSubset4_type,type,
binintersectSubset4: $o ).
thf(singletoninpowunion_type,type,
singletoninpowunion: $o ).
thf(powersetI_type,type,
powersetI: $o ).
thf(iffalseProp2_type,type,
iffalseProp2: $o ).
thf(cartprodmempair_type,type,
cartprodmempair: $o ).
thf(upairsetIR_type,type,
upairsetIR: $o ).
thf(cartprodsndpairEq_type,type,
cartprodsndpairEq: $o ).
thf(inCongP_type,type,
inCongP: $o ).
thf(setukpairinjL_type,type,
setukpairinjL: $o ).
thf(setadjoinSub_type,type,
setadjoinSub: $o ).
thf(exuE3e_type,type,
exuE3e: $o ).
thf(emptysetE_type,type,
emptysetE: $o ).
thf(upairequniteq_type,type,
upairequniteq: $o ).
thf(binintersectSubset2_type,type,
binintersectSubset2: $o ).
thf(setunionI_type,type,
setunionI: $o ).
thf(setunion__Cong_type,type,
setunion__Cong: $o ).
thf(prop2setI_type,type,
prop2setI: $o ).
thf(nonemptyImpWitness_type,type,
nonemptyImpWitness: $o ).
thf(funcinfuncset_type,type,
funcinfuncset: $o ).
thf(setminusER_type,type,
setminusER: $o ).
thf(exuE2_type,type,
exuE2: $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(powersetsubset_type,type,
powersetsubset: $o ).
thf(setukpairinjR1_type,type,
setukpairinjR1: $o ).
thf(dpsetconstrERa_type,type,
dpsetconstrERa: $o ).
thf(subPowSU_type,type,
subPowSU: $o ).
thf(notequalI1_type,type,
notequalI1: $o ).
thf(notinemptyset_type,type,
notinemptyset: $o ).
thf(nonemptyI1_type,type,
nonemptyI1: $o ).
thf(subsetTrans_type,type,
subsetTrans: $o ).
thf(setukpairinjR2_type,type,
setukpairinjR2: $o ).
thf(kpairp_type,type,
kpairp: $o ).
thf(setminusI_type,type,
setminusI: $o ).
thf(binunionIL_type,type,
binunionIL: $o ).
thf(setunionsingleton_type,type,
setunionsingleton: $o ).
thf(subsetE2_type,type,
subsetE2: $o ).
thf(singletonsswitch_type,type,
singletonsswitch: $o ).
thf(kfstpairEq_type,type,
kfstpairEq: $o ).
thf(ubforcartprodlem3_type,type,
ubforcartprodlem3: $o ).
thf(setextsub_type,type,
setextsub: $o ).
thf(binunionLsub_type,type,
binunionLsub: $o ).
thf(setunionsingleton1_type,type,
setunionsingleton1: $o ).
thf(emptysetsubset_type,type,
emptysetsubset: $o ).
thf(quantDeMorgan3_type,type,
quantDeMorgan3: $o ).
thf(setunionE_type,type,
setunionE: $o ).
thf(setminusSubset1_type,type,
setminusSubset1: $o ).
thf(sk__57_type,type,
sk__57: $i ).
thf(emptyinunitempty_type,type,
emptyinunitempty: $o ).
thf(binunionIR_type,type,
binunionIR: $o ).
thf(setadjoinE_type,type,
setadjoinE: $o ).
thf(cartprodpairmemEL_type,type,
cartprodpairmemEL: $o ).
thf(subbreln_type,type,
subbreln: $o ).
thf(singletonsuniq_type,type,
singletonsuniq: $o ).
thf(dpsetconstrEL2_type,type,
dpsetconstrEL2: $o ).
thf(setadjoinIL_type,type,
setadjoinIL: $o ).
thf(exuE1_type,type,
exuE1: $o ).
thf(ubforcartprodlem2_type,type,
ubforcartprodlem2: $o ).
thf(binintersectRsub_type,type,
binintersectRsub: $o ).
thf(setminusLsub_type,type,
setminusLsub: $o ).
thf(notinsingleton_type,type,
notinsingleton: $o ).
thf(dpsetconstrEL1_type,type,
dpsetconstrEL1: $o ).
thf(funcext_type,type,
funcext: $o ).
thf(infuncsetfunc_type,type,
infuncsetfunc: $o ).
thf(eqimpsubset2_type,type,
eqimpsubset2: $o ).
thf(exuEu_type,type,
exuEu: $o ).
thf(emptysetimpfalse_type,type,
emptysetimpfalse: $o ).
thf(ex1I2_type,type,
ex1I2: $o ).
thf(upairsetE_type,type,
upairsetE: $o ).
thf(omega0Ax_type,type,
omega0Ax: $o ).
thf(funcext2_type,type,
funcext2: $o ).
thf(notsubsetI_type,type,
notsubsetI: $o ).
thf(quantDeMorgan4_type,type,
quantDeMorgan4: $o ).
thf(setextAx_type,type,
setextAx: $o ).
thf(powersetE1_type,type,
powersetE1: $o ).
thf(bs114d_type,type,
bs114d: $o ).
thf(sk__54_type,type,
sk__54: $i ).
thf(noeltsimpempty_type,type,
noeltsimpempty: $o ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(eqbreln_type,type,
eqbreln: $o ).
thf(binintersectLsub_type,type,
binintersectLsub: $o ).
thf(subsetI1_type,type,
subsetI1: $o ).
thf(symdiffE_type,type,
symdiffE: $o ).
thf(sk__56_type,type,
sk__56: $i ).
thf(descrp_type,type,
descrp: $o ).
thf(dsetconstr__Cong_type,type,
dsetconstr__Cong: $o ).
thf(foundationAx_type,type,
foundationAx: $o ).
thf(brelnall1_type,type,
brelnall1: $o ).
thf(emptysetAx_type,type,
emptysetAx: $o ).
thf(emptyI_type,type,
emptyI: $o ).
thf(setadjoinOr_type,type,
setadjoinOr: $o ).
thf(binintersectEL_type,type,
binintersectEL: $o ).
thf(emptyE1_type,type,
emptyE1: $o ).
thf(ex1E2_type,type,
ex1E2: $o ).
thf(emptyInPowerset_type,type,
emptyInPowerset: $o ).
thf(funcImageSingleton_type,type,
funcImageSingleton: $o ).
thf(vacuousDall_type,type,
vacuousDall: $o ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(funcGraphProp3_type,type,
funcGraphProp3: $o ).
thf(binintersectI_type,type,
binintersectI: $o ).
thf(funcGraphProp4_type,type,
funcGraphProp4: $o ).
thf(lamp_type,type,
lamp: $o ).
thf(cartprodpairin_type,type,
cartprodpairin: $o ).
thf(eta1_type,type,
eta1: $o ).
thf(ex1I_type,type,
ex1I: $o ).
thf(cartprodmempair1_type,type,
cartprodmempair1: $o ).
thf(eta2_type,type,
eta2: $o ).
thf(cartprodsndin_type,type,
cartprodsndin: $o ).
thf(setukpairinjR11_type,type,
setukpairinjR11: $o ).
thf(singleton_type,type,
singleton: $i > $o ).
thf(symdiffI1_type,type,
symdiffI1: $o ).
thf(subsetI2_type,type,
subsetI2: $o ).
thf(setOfPairsIsBReln_type,type,
setOfPairsIsBReln: $o ).
thf(symdiffIneg1_type,type,
symdiffIneg1: $o ).
thf(theprop_type,type,
theprop: $o ).
thf(setminusERneg_type,type,
setminusERneg: $o ).
thf(symdiffIneg2_type,type,
symdiffIneg2: $o ).
thf(omega__Cong_type,type,
omega__Cong: $o ).
thf(subsetRefl_type,type,
subsetRefl: $o ).
thf(uniqinunit_type,type,
uniqinunit: $o ).
thf(lam2p_type,type,
lam2p: $o ).
thf(beta1_type,type,
beta1: $o ).
thf(setminusSubset2_type,type,
setminusSubset2: $o ).
thf(prop2setE_type,type,
prop2setE: $o ).
thf(binunionEcases_type,type,
binunionEcases: $o ).
thf(nonemptyI_type,type,
nonemptyI: $o ).
thf(disjointsetsI1_type,type,
disjointsetsI1: $o ).
thf(exuE3u_type,type,
exuE3u: $o ).
thf(setminusEL_type,type,
setminusEL: $o ).
thf(funcextLem_type,type,
funcextLem: $o ).
thf(setunionsingleton2_type,type,
setunionsingleton2: $o ).
thf(sepSubset_type,type,
sepSubset: $o ).
thf(upairset2E_type,type,
upairset2E: $o ).
thf(eqimpsubset1_type,type,
eqimpsubset1: $o ).
thf(exuI3_type,type,
exuI3: $o ).
thf(notdallE_type,type,
notdallE: $o ).
thf(binintersectER_type,type,
binintersectER: $o ).
thf(ksndsingleton_type,type,
ksndsingleton: $o ).
thf(ap2apEq1_type,type,
ap2apEq1: $o ).
thf(beta2_type,type,
beta2: $o ).
thf(kfstsingleton_type,type,
kfstsingleton: $o ).
thf(dsetconstrI_type,type,
dsetconstrI: $o ).
thf(cartprodpairsurjEq_type,type,
cartprodpairsurjEq: $o ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(exu__Cong_type,type,
exu__Cong: $o ).
thf(ksndpairEq_type,type,
ksndpairEq: $o ).
thf(quantDeMorgan2_type,type,
quantDeMorgan2: $o ).
thf(iftrueProp2_type,type,
iftrueProp2: $o ).
thf(ex1E1_type,type,
ex1E1: $o ).
thf(secondinupair_type,type,
secondinupair: $o ).
thf(singletonsubset_type,type,
singletonsubset: $o ).
thf(singletoninpowerset_type,type,
singletoninpowerset: $o ).
thf(subsetemptysetimpeq_type,type,
subsetemptysetimpeq: $o ).
thf(brelnall2_type,type,
brelnall2: $o ).
thf(replAx_type,type,
replAx: $o ).
thf(nonemptyE1_type,type,
nonemptyE1: $o ).
thf(omegaIndAx_type,type,
omegaIndAx: $o ).
thf(setukpairIL_type,type,
setukpairIL: $o ).
thf(setunionE2_type,type,
setunionE2: $o ).
thf(inPowerset_type,type,
inPowerset: $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(apProp_type,type,
apProp: $o ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(setukpairinjL2_type,type,
setukpairinjL2: $o ).
thf(binunionRsub_type,type,
binunionRsub: $o ).
thf(subset2powerset_type,type,
subset2powerset: $o ).
thf(setukpairinjL1_type,type,
setukpairinjL1: $o ).
thf(iftrueProp2,axiom,
( iftrueProp2
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
thf('0',plain,
( iftrueProp2
= ( ! [X4: $i,X6: $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( X6
=> ( ( dsetconstr @ X4
@ ^ [V_1: $i] :
( ( X6
& ( V_1 = X8 ) )
| ( ~ X6
& ( V_1 = X10 ) ) ) )
= ( setadjoin @ X8 @ emptyset ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(iftrueProp1,axiom,
( iftrueProp1
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
thf('1',plain,
( iftrueProp1
= ( ! [X4: $i,X6: $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( X6
=> ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] :
( ( X6
& ( V_1 = X8 ) )
| ( ~ X6
& ( V_1 = X10 ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(iffalseProp2,axiom,
( iffalseProp2
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
thf('2',plain,
( iffalseProp2
= ( ! [X4: $i,X6: $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ~ X6
=> ( ( dsetconstr @ X4
@ ^ [V_1: $i] :
( ( X6
& ( V_1 = X8 ) )
| ( ~ X6
& ( V_1 = X10 ) ) ) )
= ( setadjoin @ X10 @ emptyset ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(iffalseProp1,axiom,
( iffalseProp1
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( in @ Xy
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
thf('3',plain,
( iffalseProp1
= ( ! [X4: $i,X6: $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ~ X6
=> ( in @ X10
@ ( dsetconstr @ X4
@ ^ [V_1: $i] :
( ( X6
& ( V_1 = X8 ) )
| ( ~ X6
& ( V_1 = X10 ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
thf('4',plain,
( funcImageSingleton
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( func @ X4 @ X6 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( singleton
@ ( dsetconstr @ X6
@ ^ [V_1: $i] : ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(theprop,axiom,
( theprop
= ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ) ).
thf('5',plain,
( theprop
= ( ! [X4: $i] :
( ( singleton @ X4 )
=> ( in @ ( setunion @ X4 ) @ X4 ) ) ) ),
define([status(thm)]) ).
thf(singletonprop,axiom,
( singletonprop
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( Xphi @ Xx )
& ( in @ Xx @ A ) )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
thf('6',plain,
( singletonprop
= ( ! [X4: $i,X6: $i > $o] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( X6 @ X8 )
=> ( ( X6 @ X10 )
=> ( X8 = X10 ) ) ) ) )
=> ( ? [X12: $i] :
( ( X6 @ X12 )
& ( in @ X12 @ X4 ) )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(singleton,axiom,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ) ).
thf('7',plain,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[singleton]) ).
thf('8',plain,
( singleton
= ( ^ [V_1: $i] :
? [X4: $i] :
( ( V_1
= ( setadjoin @ X4 @ emptyset ) )
& ( in @ X4 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(sepSubset,axiom,
( sepSubset
= ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ) ).
thf('9',plain,
( sepSubset
= ( ! [X4: $i,X6: $i > $o] :
( subset
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) )
@ X4 ) ) ),
define([status(thm)]) ).
thf(dsetconstr__Cong,axiom,
( dsetconstr__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
thf('10',plain,
( dsetconstr__Cong
= ( ! [X4: $i,X6: $i] :
( ( X4 = X6 )
=> ! [X8: $i > $o,X10: $i > $o] :
( ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ! [X14: $i] :
( ( in @ X14 @ X6 )
=> ( ( X12 = X14 )
=> ( ( X8 @ X12 )
<=> ( X10 @ X14 ) ) ) ) )
=> ( ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X8 @ V_1 ) )
= ( dsetconstr @ X6
@ ^ [V_2: $i] : ( X10 @ V_2 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(emptyE1,axiom,
( emptyE1
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( Xphi @ Xx )
& ( in @ Xx @ A ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) ) ) ).
thf('11',plain,
( emptyE1
= ( ! [X4: $i,X6: $i > $o] :
( ? [X8: $i] :
( ( X6 @ X8 )
& ( in @ X8 @ X4 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) )
= emptyset )
=> $false ) ) ) ),
define([status(thm)]) ).
thf(setoftrueEq,axiom,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ) ).
thf('12',plain,
( setoftrueEq
= ( ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [V_1: $i] : $true )
= X4 ) ) ),
define([status(thm)]) ).
thf(setbeta,axiom,
( setbeta
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) ) ) ).
thf('13',plain,
( setbeta
= ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
<=> ( X6 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(dsetconstrER,axiom,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ) ).
thf('14',plain,
( dsetconstrER
= ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( X6 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ) ).
thf('15',plain,
( dsetconstrEL
= ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( in @ X8 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(dsetconstrI,axiom,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
thf('16',plain,
( dsetconstrI
= ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( X6 @ X8 )
=> ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(ifSingleton,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
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( X6 @ X8 )
=> ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) ) ) )
=> ( ! [X10: $i,X12: $i > $o,X14: $i] :
( ( in @ X14
@ ( dsetconstr @ X10
@ ^ [V_2: $i] : ( X12 @ V_2 ) ) )
=> ( in @ X14 @ X10 ) )
=> ( ! [X16: $i,X18: $i > $o,X20: $i] :
( ( in @ X20
@ ( dsetconstr @ X16
@ ^ [V_3: $i] : ( X18 @ V_3 ) ) )
=> ( X18 @ X20 ) )
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( ! [X22: $i,X24: $i > $o,X26: $i] :
( ( in @ X26 @ X22 )
=> ( ( in @ X26
@ ( dsetconstr @ X22
@ ^ [V_4: $i] : ( X24 @ V_4 ) ) )
<=> ( X24 @ X26 ) ) )
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( ! [X28: $i] :
( ( dsetconstr @ X28
@ ^ [V_5: $i] : $true )
= X28 )
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( ! [X30: $i,X32: $i > $o] :
( ? [X34: $i] :
( ( X32 @ X34 )
& ( in @ X34 @ X30 ) )
=> ( ( dsetconstr @ X30
@ ^ [V_6: $i] : ( X32 @ V_6 ) )
!= emptyset ) )
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( ! [X36: $i,X38: $i] :
( ( X36 = X38 )
=> ! [X40: $i > $o,X42: $i > $o] :
( ! [X44: $i] :
( ( in @ X44 @ X36 )
=> ! [X46: $i] :
( ( in @ X46 @ X38 )
=> ( ( X44 = X46 )
=> ( ( X40 @ X44 )
<=> ( X42 @ X46 ) ) ) ) )
=> ( ( dsetconstr @ X36
@ ^ [V_7: $i] : ( X40 @ V_7 ) )
= ( dsetconstr @ X38
@ ^ [V_8: $i] : ( X42 @ V_8 ) ) ) ) )
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( ! [X48: $i,X50: $i > $o] :
( subset
@ ( dsetconstr @ X48
@ ^ [V_9: $i] : ( X50 @ V_9 ) )
@ X48 )
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( ! [X52: $i,X54: $i > $o] :
( ! [X56: $i] :
( ( in @ X56 @ X52 )
=> ! [X58: $i] :
( ( in @ X58 @ X52 )
=> ( ( X54 @ X56 )
=> ( ( X54 @ X58 )
=> ( X56 = X58 ) ) ) ) )
=> ( ? [X60: $i] :
( ( X54 @ X60 )
& ( in @ X60 @ X52 ) )
=> ? [X62: $i] :
( ( ( dsetconstr @ X52
@ ^ [V_10: $i] : ( X54 @ V_10 ) )
= ( setadjoin @ X62 @ emptyset ) )
& ( in @ X62
@ ( dsetconstr @ X52
@ ^ [V_11: $i] : ( X54 @ V_11 ) ) ) ) ) )
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( ! [X64: $i] :
( ? [X66: $i] :
( ( X64
= ( setadjoin @ X66 @ emptyset ) )
& ( in @ X66 @ X64 ) )
=> ( in @ ( setunion @ X64 ) @ X64 ) )
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( ! [X68: $i,X70: $i,X72: $i] :
( ( func @ X68 @ X70 @ X72 )
=> ! [X74: $i] :
( ( in @ X74 @ X68 )
=> ? [X76: $i] :
( ( ( dsetconstr @ X70
@ ^ [V_12: $i] : ( in @ ( kpair @ X74 @ V_12 ) @ X72 ) )
= ( setadjoin @ X76 @ emptyset ) )
& ( in @ X76
@ ( dsetconstr @ X70
@ ^ [V_13: $i] : ( in @ ( kpair @ X74 @ V_13 ) @ X72 ) ) ) ) ) )
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( ! [X78: $i,X80: $o,X82: $i] :
( ( in @ X82 @ X78 )
=> ! [X84: $i] :
( ( in @ X84 @ X78 )
=> ( ~ X80
=> ( in @ X84
@ ( dsetconstr @ X78
@ ^ [V_14: $i] :
( ( ( V_14 = X84 )
& ~ X80 )
| ( ( V_14 = X82 )
& X80 ) ) ) ) ) ) )
=> ( ! [X86: $i,X88: $o,X90: $i] :
( ( in @ X90 @ X86 )
=> ! [X92: $i] :
( ( in @ X92 @ X86 )
=> ( ~ X88
=> ( ( dsetconstr @ X86
@ ^ [V_15: $i] :
( ( ( V_15 = X92 )
& ~ X88 )
| ( ( V_15 = X90 )
& X88 ) ) )
= ( setadjoin @ X92 @ emptyset ) ) ) ) )
=> ( ! [X94: $i,X96: $o,X98: $i] :
( ( in @ X98 @ X94 )
=> ! [X100: $i] :
( ( in @ X100 @ X94 )
=> ( X96
=> ( in @ X98
@ ( dsetconstr @ X94
@ ^ [V_16: $i] :
( ( ( V_16 = X100 )
& ~ X96 )
| ( ( V_16 = X98 )
& X96 ) ) ) ) ) ) )
=> ( ! [X102: $i,X104: $o,X106: $i] :
( ( in @ X106 @ X102 )
=> ! [X108: $i] :
( ( in @ X108 @ X102 )
=> ( X104
=> ( ( dsetconstr @ X102
@ ^ [V_17: $i] :
( ( ( V_17 = X108 )
& ~ X104 )
| ( ( V_17 = X106 )
& X104 ) ) )
= ( setadjoin @ X106 @ emptyset ) ) ) ) )
=> ! [X110: $i,X112: $o,X114: $i] :
( ( in @ X114 @ X110 )
=> ! [X116: $i] :
( ( in @ X116 @ X110 )
=> ? [X118: $i] :
( ( ( dsetconstr @ X110
@ ^ [V_18: $i] :
( ( ( V_18 = X116 )
& ~ X112 )
| ( ( V_18 = X114 )
& X112 ) ) )
= ( setadjoin @ X118 @ emptyset ) )
& ( in @ X118
@ ( dsetconstr @ X110
@ ^ [V_19: $i] :
( ( ( V_19 = X116 )
& ~ X112 )
| ( ( V_19 = X114 )
& X112 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( X6 @ X8 )
=> ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) ) ) )
=> ( ! [X10: $i,X12: $i > $o,X14: $i] :
( ( in @ X14
@ ( dsetconstr @ X10
@ ^ [V_2: $i] : ( X12 @ V_2 ) ) )
=> ( in @ X14 @ X10 ) )
=> ( ! [X16: $i,X18: $i > $o,X20: $i] :
( ( in @ X20
@ ( dsetconstr @ X16
@ ^ [V_3: $i] : ( X18 @ V_3 ) ) )
=> ( X18 @ X20 ) )
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( ! [X22: $i,X24: $i > $o,X26: $i] :
( ( in @ X26 @ X22 )
=> ( ( in @ X26
@ ( dsetconstr @ X22
@ ^ [V_4: $i] : ( X24 @ V_4 ) ) )
<=> ( X24 @ X26 ) ) )
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( ! [X28: $i] :
( ( dsetconstr @ X28
@ ^ [V_5: $i] : $true )
= X28 )
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( ! [X30: $i,X32: $i > $o] :
( ? [X34: $i] :
( ( X32 @ X34 )
& ( in @ X34 @ X30 ) )
=> ( ( dsetconstr @ X30
@ ^ [V_6: $i] : ( X32 @ V_6 ) )
!= emptyset ) )
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( ! [X36: $i,X38: $i] :
( ( X36 = X38 )
=> ! [X40: $i > $o,X42: $i > $o] :
( ! [X44: $i] :
( ( in @ X44 @ X36 )
=> ! [X46: $i] :
( ( in @ X46 @ X38 )
=> ( ( X44 = X46 )
=> ( ( X40 @ X44 )
<=> ( X42 @ X46 ) ) ) ) )
=> ( ( dsetconstr @ X36
@ ^ [V_7: $i] : ( X40 @ V_7 ) )
= ( dsetconstr @ X38
@ ^ [V_8: $i] : ( X42 @ V_8 ) ) ) ) )
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( ! [X48: $i,X50: $i > $o] :
( subset
@ ( dsetconstr @ X48
@ ^ [V_9: $i] : ( X50 @ V_9 ) )
@ X48 )
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( ! [X52: $i,X54: $i > $o] :
( ! [X56: $i] :
( ( in @ X56 @ X52 )
=> ! [X58: $i] :
( ( in @ X58 @ X52 )
=> ( ( X54 @ X56 )
=> ( ( X54 @ X58 )
=> ( X56 = X58 ) ) ) ) )
=> ( ? [X60: $i] :
( ( X54 @ X60 )
& ( in @ X60 @ X52 ) )
=> ? [X62: $i] :
( ( ( dsetconstr @ X52
@ ^ [V_10: $i] : ( X54 @ V_10 ) )
= ( setadjoin @ X62 @ emptyset ) )
& ( in @ X62
@ ( dsetconstr @ X52
@ ^ [V_11: $i] : ( X54 @ V_11 ) ) ) ) ) )
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( ! [X64: $i] :
( ? [X66: $i] :
( ( X64
= ( setadjoin @ X66 @ emptyset ) )
& ( in @ X66 @ X64 ) )
=> ( in @ ( setunion @ X64 ) @ X64 ) )
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( ! [X68: $i,X70: $i,X72: $i] :
( ( func @ X68 @ X70 @ X72 )
=> ! [X74: $i] :
( ( in @ X74 @ X68 )
=> ? [X76: $i] :
( ( ( dsetconstr @ X70
@ ^ [V_12: $i] : ( in @ ( kpair @ X74 @ V_12 ) @ X72 ) )
= ( setadjoin @ X76 @ emptyset ) )
& ( in @ X76
@ ( dsetconstr @ X70
@ ^ [V_13: $i] : ( in @ ( kpair @ X74 @ V_13 ) @ X72 ) ) ) ) ) )
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( ! [X78: $i,X80: $o,X82: $i] :
( ( in @ X82 @ X78 )
=> ! [X84: $i] :
( ( in @ X84 @ X78 )
=> ( ~ X80
=> ( in @ X84
@ ( dsetconstr @ X78
@ ^ [V_14: $i] :
( ( ( V_14 = X84 )
& ~ X80 )
| ( ( V_14 = X82 )
& X80 ) ) ) ) ) ) )
=> ( ! [X86: $i,X88: $o,X90: $i] :
( ( in @ X90 @ X86 )
=> ! [X92: $i] :
( ( in @ X92 @ X86 )
=> ( ~ X88
=> ( ( dsetconstr @ X86
@ ^ [V_15: $i] :
( ( ( V_15 = X92 )
& ~ X88 )
| ( ( V_15 = X90 )
& X88 ) ) )
= ( setadjoin @ X92 @ emptyset ) ) ) ) )
=> ( ! [X94: $i,X96: $o,X98: $i] :
( ( in @ X98 @ X94 )
=> ! [X100: $i] :
( ( in @ X100 @ X94 )
=> ( X96
=> ( in @ X98
@ ( dsetconstr @ X94
@ ^ [V_16: $i] :
( ( ( V_16 = X100 )
& ~ X96 )
| ( ( V_16 = X98 )
& X96 ) ) ) ) ) ) )
=> ( ! [X102: $i,X104: $o,X106: $i] :
( ( in @ X106 @ X102 )
=> ! [X108: $i] :
( ( in @ X108 @ X102 )
=> ( X104
=> ( ( dsetconstr @ X102
@ ^ [V_17: $i] :
( ( ( V_17 = X108 )
& ~ X104 )
| ( ( V_17 = X106 )
& X104 ) ) )
= ( setadjoin @ X106 @ emptyset ) ) ) ) )
=> ! [X110: $i,X112: $o,X114: $i] :
( ( in @ X114 @ X110 )
=> ! [X116: $i] :
( ( in @ X116 @ X110 )
=> ? [X118: $i] :
( ( ( dsetconstr @ X110
@ ^ [V_18: $i] :
( ( ( V_18 = X116 )
& ~ X112 )
| ( ( V_18 = X114 )
& X112 ) ) )
= ( setadjoin @ X118 @ emptyset ) )
& ( in @ X118
@ ( dsetconstr @ X110
@ ^ [V_19: $i] :
( ( ( V_19 = X116 )
& ~ X112 )
| ( ( V_19 = X114 )
& X112 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl116,plain,
in @ sk__57 @ sk__54,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl118,plain,
in @ sk__56 @ sk__54,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl120,plain,
! [X35: $i,X36: $i,X37: $o,X38: $i] :
( ~ ( in @ X35 @ X36 )
| ( ( dsetconstr @ X36
@ ^ [Y0: $i] :
( ( ( Y0 = X35 )
& ( (~) @ X37 ) )
| ( ( Y0 = X38 )
& X37 ) ) )
= ( setadjoin @ X35 @ emptyset ) )
| X37
| ~ ( in @ X38 @ X36 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl114,plain,
! [X22: $i,X23: $i,X24: $o,X25: $i] :
( ~ ( in @ X22 @ X23 )
| ( in @ X22
@ ( dsetconstr @ X23
@ ^ [Y0: $i] :
( ( ( Y0 = X22 )
& ( (~) @ X24 ) )
| ( ( Y0 = X25 )
& X24 ) ) ) )
| X24
| ~ ( in @ X25 @ X23 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl13414,plain,
! [X22: $i,X24: $o,X25: $i,X26: $i] :
( ( '#l_lift30160' @ X22 @ X24 @ X25 @ X26 )
= ( ( ( X26 = X22 )
& ( (~) @ X24 ) )
| ( ( X26 = X25 )
& X24 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl13419,plain,
! [X35: $i,X36: $i,X37: $o,X38: $i] :
( ~ ( in @ X35 @ X36 )
| ( ( dsetconstr @ X36 @ ( '#l_lift30160' @ X35 @ X37 @ X38 ) )
= ( setadjoin @ X35 @ emptyset ) )
| X37
| ~ ( in @ X38 @ X36 ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl120,zip_derived_cl13414]) ).
thf(zip_derived_cl119,plain,
! [X31: $i,X32: $i,X33: $i,X34: $o] :
( ~ ( in @ X31 @ X32 )
| ( ( dsetconstr @ X32
@ ^ [Y0: $i] :
( ( ( Y0 = X31 )
& ( (~) @ X34 ) )
| ( ( Y0 = X33 )
& X34 ) ) )
= ( setadjoin @ X33 @ emptyset ) )
| ~ X34
| ~ ( in @ X33 @ X32 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl13414_001,plain,
! [X22: $i,X24: $o,X25: $i,X26: $i] :
( ( '#l_lift30160' @ X22 @ X24 @ X25 @ X26 )
= ( ( ( X26 = X22 )
& ( (~) @ X24 ) )
| ( ( X26 = X25 )
& X24 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl13418,plain,
! [X31: $i,X32: $i,X33: $i,X34: $o] :
( ~ ( in @ X31 @ X32 )
| ( ( dsetconstr @ X32 @ ( '#l_lift30160' @ X31 @ X34 @ X33 ) )
= ( setadjoin @ X33 @ emptyset ) )
| ~ X34
| ~ ( in @ X33 @ X32 ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl119,zip_derived_cl13414]) ).
thf(zip_derived_cl13414_002,plain,
! [X22: $i,X24: $o,X25: $i,X26: $i] :
( ( '#l_lift30160' @ X22 @ X24 @ X25 @ X26 )
= ( ( ( X26 = X22 )
& ( (~) @ X24 ) )
| ( ( X26 = X25 )
& X24 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl13403,plain,
! [X6: $i > $o,X7: $i,X8: $i] :
( ~ ( X6 @ X7 )
| ( in @ X7 @ ( dsetconstr @ X8 @ X6 ) )
| ~ ( in @ X7 @ X8 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl117,plain,
! [X30: $i] :
( ( ( dsetconstr @ sk__54
@ ^ [Y0: $i] :
( ( ( Y0 = sk__57 )
& ( (~) @ sk__55 ) )
| ( ( Y0 = sk__56 )
& sk__55 ) ) )
!= ( setadjoin @ X30 @ emptyset ) )
| ~ ( in @ X30
@ ( dsetconstr @ sk__54
@ ^ [Y0: $i] :
( ( ( Y0 = sk__57 )
& ( (~) @ sk__55 ) )
| ( ( Y0 = sk__56 )
& sk__55 ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl13414_003,plain,
! [X22: $i,X24: $o,X25: $i,X26: $i] :
( ( '#l_lift30160' @ X22 @ X24 @ X25 @ X26 )
= ( ( ( X26 = X22 )
& ( (~) @ X24 ) )
| ( ( X26 = X25 )
& X24 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl13414_004,plain,
! [X22: $i,X24: $o,X25: $i,X26: $i] :
( ( '#l_lift30160' @ X22 @ X24 @ X25 @ X26 )
= ( ( ( X26 = X22 )
& ( (~) @ X24 ) )
| ( ( X26 = X25 )
& X24 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl13417,plain,
! [X30: $i] :
( ( ( dsetconstr @ sk__54 @ ( '#l_lift30160' @ sk__57 @ sk__55 @ sk__56 ) )
!= ( setadjoin @ X30 @ emptyset ) )
| ~ ( in @ X30 @ ( dsetconstr @ sk__54 @ ( '#l_lift30160' @ sk__57 @ sk__55 @ sk__56 ) ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl117,zip_derived_cl13414,zip_derived_cl13414]) ).
thf(zip_derived_cl13443,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl116,zip_derived_cl118,zip_derived_cl13419,zip_derived_cl13418,zip_derived_cl13414,zip_derived_cl13403,zip_derived_cl13417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU704^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.y062ZnN9uD true
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 18:01:27 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.19/0.66 % Total configuration time : 828
% 0.19/0.66 % Estimated wc time : 1656
% 0.19/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.19/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.19/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.19/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.19/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.19/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.19/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.19/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.19/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 71.37/9.74 % Solved by lams/40_c_ic.sh.
% 71.37/9.74 % done 1566 iterations in 8.946s
% 71.37/9.74 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 71.37/9.74 % SZS output start Refutation
% See solution above
% 71.37/9.74
% 71.37/9.74
% 71.37/9.74 % Terminating...
% 71.52/9.83 % Runner terminated.
% 71.52/9.84 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------