0.11/0.19	% Problem    : Vampire---4.8_11437 : TPTP v0.0.0. Released v0.0.0.
0.11/0.20	% Command    : do_cvc5 %s %d
0.20/0.41	% Computer : n022.cluster.edu
0.20/0.41	% Model    : x86_64 x86_64
0.20/0.41	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.20/0.41	% Memory   : 8042.1875MB
0.20/0.41	% OS       : Linux 3.10.0-693.el7.x86_64
0.20/0.41	% CPULimit   : 1440
0.20/0.41	% WCLimit    : 180
0.20/0.41	% DateTime   : Mon Jul  3 12:48:59 EDT 2023
0.20/0.41	% CPUTime    : 
0.51/0.74	%----Proving TH0
0.51/0.75	thf(in_type,type,
0.51/0.75	    in: $i > $i > $o ).
0.51/0.75	
0.51/0.75	thf(exu_type,type,
0.51/0.75	    exu: ( $i > $o ) > $o ).
0.51/0.75	
0.51/0.75	thf(exu,definition,
0.51/0.75	    ( exu
0.51/0.75	    = ( ^ [Xphi: $i > $o] :
0.51/0.75	        ? [Xx: $i] :
0.51/0.75	          ( ( Xphi @ Xx )
0.51/0.75	          & ! [Xy: $i] :
0.51/0.75	              ( ( Xphi @ Xy )
0.51/0.75	             => ( Xx = Xy ) ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(setextAx_type,type,
0.51/0.75	    setextAx: $o ).
0.51/0.75	
0.51/0.75	thf(setextAx,definition,
0.51/0.75	    ( setextAx
0.51/0.75	    = ( ! [A: $i,B: $i] :
0.51/0.75	          ( ! [Xx: $i] :
0.51/0.75	              ( ( in @ Xx @ A )
0.51/0.75	            <=> ( in @ Xx @ B ) )
0.51/0.75	         => ( A = B ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(emptyset_type,type,
0.51/0.75	    emptyset: $i ).
0.51/0.75	
0.51/0.75	thf(emptysetAx_type,type,
0.51/0.75	    emptysetAx: $o ).
0.51/0.75	
0.51/0.75	thf(emptysetAx,definition,
0.51/0.75	    ( emptysetAx
0.51/0.75	    = ( ! [Xx: $i] :
0.51/0.75	          ~ ( in @ Xx @ emptyset ) ) ) ).
0.51/0.75	
0.51/0.75	thf(setadjoin_type,type,
0.51/0.75	    setadjoin: $i > $i > $i ).
0.51/0.75	
0.51/0.75	thf(setadjoinAx_type,type,
0.51/0.75	    setadjoinAx: $o ).
0.51/0.75	
0.51/0.75	thf(setadjoinAx,definition,
0.51/0.75	    ( setadjoinAx
0.51/0.75	    = ( ! [Xx: $i,A: $i,Xy: $i] :
0.51/0.75	          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
0.51/0.75	        <=> ( ( Xy = Xx )
0.51/0.75	            | ( in @ Xy @ A ) ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(powerset_type,type,
0.51/0.75	    powerset: $i > $i ).
0.51/0.75	
0.51/0.75	thf(powersetAx_type,type,
0.51/0.75	    powersetAx: $o ).
0.51/0.75	
0.51/0.75	thf(powersetAx,definition,
0.51/0.75	    ( powersetAx
0.51/0.75	    = ( ! [A: $i,B: $i] :
0.51/0.75	          ( ( in @ B @ ( powerset @ A ) )
0.51/0.75	        <=> ! [Xx: $i] :
0.51/0.75	              ( ( in @ Xx @ B )
0.51/0.75	             => ( in @ Xx @ A ) ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(setunion_type,type,
0.51/0.75	    setunion: $i > $i ).
0.51/0.75	
0.51/0.75	thf(setunionAx_type,type,
0.51/0.75	    setunionAx: $o ).
0.51/0.75	
0.51/0.75	thf(setunionAx,definition,
0.51/0.75	    ( setunionAx
0.51/0.75	    = ( ! [A: $i,Xx: $i] :
0.51/0.75	          ( ( in @ Xx @ ( setunion @ A ) )
0.51/0.75	        <=> ? [B: $i] :
0.51/0.75	              ( ( in @ Xx @ B )
0.51/0.75	              & ( in @ B @ A ) ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(omega_type,type,
0.51/0.75	    omega: $i ).
0.51/0.75	
0.51/0.75	thf(omega0Ax_type,type,
0.51/0.75	    omega0Ax: $o ).
0.51/0.75	
0.51/0.75	thf(omega0Ax,definition,
0.51/0.75	    ( omega0Ax
0.51/0.75	    = ( in @ emptyset @ omega ) ) ).
0.51/0.75	
0.51/0.75	thf(omegaSAx_type,type,
0.51/0.75	    omegaSAx: $o ).
0.51/0.75	
0.51/0.75	thf(omegaSAx,definition,
0.51/0.75	    ( omegaSAx
0.51/0.75	    = ( ! [Xx: $i] :
0.51/0.75	          ( ( in @ Xx @ omega )
0.51/0.75	         => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(omegaIndAx_type,type,
0.51/0.75	    omegaIndAx: $o ).
0.51/0.75	
0.51/0.75	thf(omegaIndAx,definition,
0.51/0.75	    ( omegaIndAx
0.51/0.75	    = ( ! [A: $i] :
0.51/0.75	          ( ( ( in @ emptyset @ A )
0.51/0.75	            & ! [Xx: $i] :
0.51/0.75	                ( ( ( in @ Xx @ omega )
0.51/0.75	                  & ( in @ Xx @ A ) )
0.51/0.75	               => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
0.51/0.75	         => ! [Xx: $i] :
0.51/0.75	              ( ( in @ Xx @ omega )
0.51/0.75	             => ( in @ Xx @ A ) ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(replAx_type,type,
0.51/0.75	    replAx: $o ).
0.51/0.75	
0.51/0.75	thf(replAx,definition,
0.51/0.75	    ( replAx
0.51/0.75	    = ( ! [Xphi: $i > $i > $o,A: $i] :
0.51/0.75	          ( ! [Xx: $i] :
0.51/0.75	              ( ( in @ Xx @ A )
0.51/0.75	             => ( exu
0.51/0.75	                @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
0.51/0.75	         => ? [B: $i] :
0.51/0.75	            ! [Xx: $i] :
0.51/0.75	              ( ( in @ Xx @ B )
0.51/0.75	            <=> ? [Xy: $i] :
0.51/0.75	                  ( ( in @ Xy @ A )
0.51/0.75	                  & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(foundationAx_type,type,
0.51/0.75	    foundationAx: $o ).
0.51/0.75	
0.51/0.75	thf(foundationAx,definition,
0.51/0.75	    ( foundationAx
0.51/0.75	    = ( ! [A: $i] :
0.51/0.75	          ( ? [Xx: $i] : ( in @ Xx @ A )
0.51/0.75	         => ? [B: $i] :
0.51/0.75	              ( ( in @ B @ A )
0.51/0.75	              & ~ ? [Xx: $i] :
0.51/0.75	                    ( ( in @ Xx @ B )
0.51/0.75	                    & ( in @ Xx @ A ) ) ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(wellorderingAx_type,type,
0.51/0.75	    wellorderingAx: $o ).
0.51/0.75	
0.51/0.75	thf(wellorderingAx,definition,
0.51/0.75	    ( wellorderingAx
0.51/0.75	    = ( ! [A: $i] :
0.51/0.75	        ? [B: $i] :
0.51/0.75	          ( ! [C: $i] :
0.51/0.75	              ( ( in @ C @ B )
0.51/0.75	             => ! [Xx: $i] :
0.51/0.75	                  ( ( in @ Xx @ C )
0.51/0.75	                 => ( in @ Xx @ A ) ) )
0.51/0.75	          & ! [Xx: $i,Xy: $i] :
0.51/0.75	              ( ( ( in @ Xx @ A )
0.51/0.75	                & ( in @ Xy @ A ) )
0.51/0.75	             => ( ! [C: $i] :
0.51/0.75	                    ( ( in @ C @ B )
0.51/0.75	                   => ( ( in @ Xx @ C )
0.51/0.75	                    <=> ( in @ Xy @ C ) ) )
0.51/0.75	               => ( Xx = Xy ) ) )
0.51/0.75	          & ! [C: $i,D: $i] :
0.51/0.75	              ( ( ( in @ C @ B )
0.51/0.75	                & ( in @ D @ B ) )
0.51/0.75	             => ( ! [Xx: $i] :
0.51/0.75	                    ( ( in @ Xx @ C )
0.51/0.75	                   => ( in @ Xx @ D ) )
0.51/0.75	                | ! [Xx: $i] :
0.51/0.75	                    ( ( in @ Xx @ D )
0.51/0.75	                   => ( in @ Xx @ C ) ) ) )
0.51/0.75	          & ! [C: $i] :
0.51/0.75	              ( ( ! [Xx: $i] :
0.51/0.75	                    ( ( in @ Xx @ C )
0.51/0.75	                   => ( in @ Xx @ A ) )
0.51/0.75	                & ? [Xx: $i] : ( in @ Xx @ C ) )
0.51/0.75	             => ? [D: $i,Xx: $i] :
0.51/0.75	                  ( ( in @ D @ B )
0.51/0.75	                  & ( in @ Xx @ C )
0.51/0.75	                  & ~ ? [Xy: $i] :
0.51/0.75	                        ( ( in @ Xy @ D )
0.51/0.75	                        & ( in @ Xy @ C ) )
0.51/0.75	                  & ! [E: $i] :
0.51/0.75	                      ( ( in @ E @ B )
0.51/0.75	                     => ( ! [Xy: $i] :
0.51/0.75	                            ( ( in @ Xy @ E )
0.51/0.75	                           => ( in @ Xy @ D ) )
0.51/0.75	                        | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(descr_type,type,
0.51/0.75	    descr: ( $i > $o ) > $i ).
0.51/0.75	
0.51/0.75	thf(descrp_type,type,
0.51/0.75	    descrp: $o ).
0.51/0.75	
0.51/0.75	thf(descrp,definition,
0.51/0.75	    ( descrp
0.51/0.75	    = ( ! [Xphi: $i > $o] :
0.51/0.75	          ( ( exu
0.51/0.75	            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.51/0.75	         => ( Xphi
0.51/0.75	            @ ( descr
0.51/0.75	              @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(dsetconstr_type,type,
0.51/0.75	    dsetconstr: $i > ( $i > $o ) > $i ).
0.51/0.75	
0.51/0.75	thf(dsetconstrI_type,type,
0.51/0.75	    dsetconstrI: $o ).
0.51/0.75	
0.51/0.75	thf(dsetconstrI,definition,
0.51/0.75	    ( dsetconstrI
0.51/0.75	    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
0.51/0.75	          ( ( in @ Xx @ A )
0.51/0.75	         => ( ( Xphi @ Xx )
0.51/0.75	           => ( in @ Xx
0.51/0.75	              @ ( dsetconstr @ A
0.51/0.75	                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(dsetconstrEL_type,type,
0.51/0.75	    dsetconstrEL: $o ).
0.51/0.75	
0.51/0.75	thf(dsetconstrEL,definition,
0.51/0.75	    ( dsetconstrEL
0.51/0.75	    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
0.51/0.75	          ( ( in @ Xx
0.51/0.75	            @ ( dsetconstr @ A
0.51/0.75	              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
0.51/0.75	         => ( in @ Xx @ A ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(dsetconstrER_type,type,
0.51/0.75	    dsetconstrER: $o ).
0.51/0.75	
0.51/0.75	thf(dsetconstrER,definition,
0.51/0.75	    ( dsetconstrER
0.51/0.75	    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
0.51/0.75	          ( ( in @ Xx
0.51/0.75	            @ ( dsetconstr @ A
0.51/0.75	              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
0.51/0.75	         => ( Xphi @ Xx ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(exuE1_type,type,
0.51/0.75	    exuE1: $o ).
0.51/0.75	
0.51/0.75	thf(exuE1,definition,
0.51/0.75	    ( exuE1
0.51/0.75	    = ( ! [Xphi: $i > $o] :
0.51/0.75	          ( ( exu
0.51/0.75	            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.51/0.75	         => ? [Xx: $i] :
0.51/0.75	              ( ( Xphi @ Xx )
0.51/0.75	              & ! [Xy: $i] :
0.51/0.75	                  ( ( Xphi @ Xy )
0.51/0.75	                 => ( Xx = Xy ) ) ) ) ) ) ).
0.51/0.75	
0.51/0.75	thf(prop2set_type,type,
0.51/0.75	    prop2set: $o > $i ).
0.51/0.75	
0.51/0.75	thf(prop2setE_type,type,
0.51/0.75	    prop2setE: $o ).
0.51/0.75	
0.51/0.75	thf(prop2setE,definition,
0.51/0.75	    ( prop2setE
0.51/0.75	    = ( ! [Xphi: $o,Xx: $i] :
0.51/0.75	          ( ( in @ Xx @ ( prop2set @ Xphi ) )
0.51/0.75	         => Xphi ) ) ) ).
0.51/0.75	
0.51/0.75	thf(emptysetE_type,type,
0.51/0.75	    emptysetE: $o ).
0.51/0.75	
0.51/0.75	thf(emptysetE,definition,
0.51/0.75	    ( emptysetE
0.51/0.75	    = ( ! [Xx: $i] :
0.51/0.75	          ( ( in @ Xx @ emptyset )
0.51/0.75	         => ! [Xphi: $o] : Xphi ) ) ) ).
0.51/0.75	
0.51/0.75	thf(emptysetimpfalse_type,type,
0.51/0.75	    emptysetimpfalse: $o ).
0.51/0.75	
0.51/0.75	thf(emptysetimpfalse,definition,
0.51/0.75	    ( emptysetimpfalse
0.51/0.75	    = ( ! [Xx: $i] :
0.51/0.75	          ( ( in @ Xx @ emptyset )
0.51/0.75	         => $false ) ) ) ).
0.51/0.75	
0.51/0.75	thf(notinemptyset_type,type,
0.51/0.75	    notinemptyset: $o ).
0.51/0.75	
0.51/0.75	thf(notinemptyset,definition,
0.51/0.75	    ( notinemptyset
0.51/0.75	    = ( ! [Xx: $i] :
0.51/0.75	          ~ ( in @ Xx @ emptyset ) ) ) ).
0.59/0.75	
0.59/0.75	thf(exuE3e_type,type,
0.59/0.75	    exuE3e: $o ).
0.59/0.75	
0.59/0.75	thf(exuE3e,definition,
0.59/0.75	    ( exuE3e
0.59/0.75	    = ( ! [Xphi: $i > $o] :
0.59/0.75	          ( ( exu
0.59/0.75	            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.59/0.75	         => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setext_type,type,
0.59/0.75	    setext: $o ).
0.59/0.75	
0.59/0.75	thf(setext,definition,
0.59/0.75	    ( setext
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ! [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	             => ( in @ Xx @ B ) )
0.59/0.75	         => ( ! [Xx: $i] :
0.59/0.75	                ( ( in @ Xx @ B )
0.59/0.75	               => ( in @ Xx @ A ) )
0.59/0.75	           => ( A = B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(emptyI_type,type,
0.59/0.75	    emptyI: $o ).
0.59/0.75	
0.59/0.75	thf(emptyI,definition,
0.59/0.75	    ( emptyI
0.59/0.75	    = ( ! [A: $i] :
0.59/0.75	          ( ! [Xx: $i] :
0.59/0.75	              ~ ( in @ Xx @ A )
0.59/0.75	         => ( A = emptyset ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(noeltsimpempty_type,type,
0.59/0.75	    noeltsimpempty: $o ).
0.59/0.75	
0.59/0.75	thf(noeltsimpempty,definition,
0.59/0.75	    ( noeltsimpempty
0.59/0.75	    = ( ! [A: $i] :
0.59/0.75	          ( ! [Xx: $i] :
0.59/0.75	              ~ ( in @ Xx @ A )
0.59/0.75	         => ( A = emptyset ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setbeta_type,type,
0.59/0.75	    setbeta: $o ).
0.59/0.75	
0.59/0.75	thf(setbeta,definition,
0.59/0.75	    ( setbeta
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( ( in @ Xx
0.59/0.75	              @ ( dsetconstr @ A
0.59/0.75	                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
0.59/0.75	          <=> ( Xphi @ Xx ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(nonempty_type,type,
0.59/0.75	    nonempty: $i > $o ).
0.59/0.75	
0.59/0.75	thf(nonempty,definition,
0.59/0.75	    ( nonempty
0.59/0.75	    = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
0.59/0.75	
0.59/0.75	thf(nonemptyE1_type,type,
0.59/0.75	    nonemptyE1: $o ).
0.59/0.75	
0.59/0.75	thf(nonemptyE1,definition,
0.59/0.75	    ( nonemptyE1
0.59/0.75	    = ( ! [A: $i] :
0.59/0.75	          ( ( nonempty @ A )
0.59/0.75	         => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(nonemptyI_type,type,
0.59/0.75	    nonemptyI: $o ).
0.59/0.75	
0.59/0.75	thf(nonemptyI,definition,
0.59/0.75	    ( nonemptyI
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( ( Xphi @ Xx )
0.59/0.75	           => ( nonempty
0.59/0.75	              @ ( dsetconstr @ A
0.59/0.75	                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(nonemptyI1_type,type,
0.59/0.75	    nonemptyI1: $o ).
0.59/0.75	
0.59/0.75	thf(nonemptyI1,definition,
0.59/0.75	    ( nonemptyI1
0.59/0.75	    = ( ! [A: $i] :
0.59/0.75	          ( ? [Xx: $i] : ( in @ Xx @ A )
0.59/0.75	         => ( nonempty @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setadjoinIL_type,type,
0.59/0.75	    setadjoinIL: $o ).
0.59/0.75	
0.59/0.75	thf(setadjoinIL,definition,
0.59/0.75	    ( setadjoinIL
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(emptyinunitempty_type,type,
0.59/0.75	    emptyinunitempty: $o ).
0.59/0.75	
0.59/0.75	thf(emptyinunitempty,definition,
0.59/0.75	    ( emptyinunitempty
0.59/0.75	    = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setadjoinIR_type,type,
0.59/0.75	    setadjoinIR: $o ).
0.59/0.75	
0.59/0.75	thf(setadjoinIR,definition,
0.59/0.75	    ( setadjoinIR
0.59/0.75	    = ( ! [Xx: $i,A: $i,Xy: $i] :
0.59/0.75	          ( ( in @ Xy @ A )
0.59/0.75	         => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setadjoinE_type,type,
0.59/0.75	    setadjoinE: $o ).
0.59/0.75	
0.59/0.75	thf(setadjoinE,definition,
0.59/0.75	    ( setadjoinE
0.59/0.75	    = ( ! [Xx: $i,A: $i,Xy: $i] :
0.59/0.75	          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
0.59/0.75	         => ! [Xphi: $o] :
0.59/0.75	              ( ( ( Xy = Xx )
0.59/0.75	               => Xphi )
0.59/0.75	             => ( ( ( in @ Xy @ A )
0.59/0.75	                 => Xphi )
0.59/0.75	               => Xphi ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setadjoinOr_type,type,
0.59/0.75	    setadjoinOr: $o ).
0.59/0.75	
0.59/0.75	thf(setadjoinOr,definition,
0.59/0.75	    ( setadjoinOr
0.59/0.75	    = ( ! [Xx: $i,A: $i,Xy: $i] :
0.59/0.75	          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
0.59/0.75	         => ( ( Xy = Xx )
0.59/0.75	            | ( in @ Xy @ A ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setoftrueEq_type,type,
0.59/0.75	    setoftrueEq: $o ).
0.59/0.75	
0.59/0.75	thf(setoftrueEq,definition,
0.59/0.75	    ( setoftrueEq
0.59/0.75	    = ( ! [A: $i] :
0.59/0.75	          ( ( dsetconstr @ A
0.59/0.75	            @ ^ [Xx: $i] : $true )
0.59/0.75	          = A ) ) ) ).
0.59/0.75	
0.59/0.75	thf(powersetI_type,type,
0.59/0.75	    powersetI: $o ).
0.59/0.75	
0.59/0.75	thf(powersetI,definition,
0.59/0.75	    ( powersetI
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ! [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ B )
0.59/0.75	             => ( in @ Xx @ A ) )
0.59/0.75	         => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(emptyinPowerset_type,type,
0.59/0.75	    emptyinPowerset: $o ).
0.59/0.75	
0.59/0.75	thf(emptyinPowerset,definition,
0.59/0.75	    ( emptyinPowerset
0.59/0.75	    = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(emptyInPowerset_type,type,
0.59/0.75	    emptyInPowerset: $o ).
0.59/0.75	
0.59/0.75	thf(emptyInPowerset,definition,
0.59/0.75	    ( emptyInPowerset
0.59/0.75	    = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(powersetE_type,type,
0.59/0.75	    powersetE: $o ).
0.59/0.75	
0.59/0.75	thf(powersetE,definition,
0.59/0.75	    ( powersetE
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ B @ ( powerset @ A ) )
0.59/0.75	         => ( ( in @ Xx @ B )
0.59/0.75	           => ( in @ Xx @ A ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setunionI_type,type,
0.59/0.75	    setunionI: $o ).
0.59/0.75	
0.59/0.75	thf(setunionI,definition,
0.59/0.75	    ( setunionI
0.59/0.75	    = ( ! [A: $i,Xx: $i,B: $i] :
0.59/0.75	          ( ( in @ Xx @ B )
0.59/0.75	         => ( ( in @ B @ A )
0.59/0.75	           => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setunionE_type,type,
0.59/0.75	    setunionE: $o ).
0.59/0.75	
0.59/0.75	thf(setunionE,definition,
0.59/0.75	    ( setunionE
0.59/0.75	    = ( ! [A: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ ( setunion @ A ) )
0.59/0.75	         => ! [Xphi: $o] :
0.59/0.75	              ( ! [B: $i] :
0.59/0.75	                  ( ( in @ Xx @ B )
0.59/0.75	                 => ( ( in @ B @ A )
0.59/0.75	                   => Xphi ) )
0.59/0.75	             => Xphi ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(subPowSU_type,type,
0.59/0.75	    subPowSU: $o ).
0.59/0.75	
0.59/0.75	thf(subPowSU,definition,
0.59/0.75	    ( subPowSU
0.59/0.75	    = ( ! [A: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(exuE2_type,type,
0.59/0.75	    exuE2: $o ).
0.59/0.75	
0.59/0.75	thf(exuE2,definition,
0.59/0.75	    ( exuE2
0.59/0.75	    = ( ! [Xphi: $i > $o] :
0.59/0.75	          ( ( exu
0.59/0.75	            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.59/0.75	         => ? [Xx: $i] :
0.59/0.75	            ! [Xy: $i] :
0.59/0.75	              ( ( Xphi @ Xy )
0.59/0.75	            <=> ( Xy = Xx ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(nonemptyImpWitness_type,type,
0.59/0.75	    nonemptyImpWitness: $o ).
0.59/0.75	
0.59/0.75	thf(nonemptyImpWitness,definition,
0.59/0.75	    ( nonemptyImpWitness
0.59/0.75	    = ( ! [A: $i] :
0.59/0.75	          ( ( nonempty @ A )
0.59/0.75	         => ? [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	              & $true ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(uniqinunit_type,type,
0.59/0.75	    uniqinunit: $o ).
0.59/0.75	
0.59/0.75	thf(uniqinunit,definition,
0.59/0.75	    ( uniqinunit
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] :
0.59/0.75	          ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
0.59/0.75	         => ( Xx = Xy ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(notinsingleton_type,type,
0.59/0.75	    notinsingleton: $o ).
0.59/0.75	
0.59/0.75	thf(notinsingleton,definition,
0.59/0.75	    ( notinsingleton
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] :
0.59/0.75	          ( ( Xx != Xy )
0.59/0.75	         => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(eqinunit_type,type,
0.59/0.75	    eqinunit: $o ).
0.59/0.75	
0.59/0.75	thf(eqinunit,definition,
0.59/0.75	    ( eqinunit
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] :
0.59/0.75	          ( ( Xx = Xy )
0.59/0.75	         => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(singletonsswitch_type,type,
0.59/0.75	    singletonsswitch: $o ).
0.59/0.75	
0.59/0.75	thf(singletonsswitch,definition,
0.59/0.75	    ( singletonsswitch
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] :
0.59/0.75	          ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
0.59/0.75	         => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(upairsetE_type,type,
0.59/0.75	    upairsetE: $o ).
0.59/0.75	
0.59/0.75	thf(upairsetE,definition,
0.59/0.75	    ( upairsetE
0.59/0.75	    = ( ! [Xx: $i,Xy: $i,Xz: $i] :
0.59/0.75	          ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
0.59/0.75	         => ( ( Xz = Xx )
0.59/0.75	            | ( Xz = Xy ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(upairsetIL_type,type,
0.59/0.75	    upairsetIL: $o ).
0.59/0.75	
0.59/0.75	thf(upairsetIL,definition,
0.59/0.75	    ( upairsetIL
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(upairsetIR_type,type,
0.59/0.75	    upairsetIR: $o ).
0.59/0.75	
0.59/0.75	thf(upairsetIR,definition,
0.59/0.75	    ( upairsetIR
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(emptyE1_type,type,
0.59/0.75	    emptyE1: $o ).
0.59/0.75	
0.59/0.75	thf(emptyE1,definition,
0.59/0.75	    ( emptyE1
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o] :
0.59/0.75	          ( ? [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	              & ( Xphi @ Xx ) )
0.59/0.75	         => ( ( ( dsetconstr @ A
0.59/0.75	                @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.59/0.75	              = emptyset )
0.59/0.75	           => $false ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(vacuousDall_type,type,
0.59/0.75	    vacuousDall: $o ).
0.59/0.75	
0.59/0.75	thf(vacuousDall,definition,
0.59/0.75	    ( vacuousDall
0.59/0.75	    = ( ! [Xphi: $i > $o,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ emptyset )
0.59/0.75	         => ( Xphi @ Xx ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(quantDeMorgan1_type,type,
0.59/0.75	    quantDeMorgan1: $o ).
0.59/0.75	
0.59/0.75	thf(quantDeMorgan1,definition,
0.59/0.75	    ( quantDeMorgan1
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o] :
0.59/0.75	          ( ~ ! [Xx: $i] :
0.59/0.75	                ( ( in @ Xx @ A )
0.59/0.75	               => ( Xphi @ Xx ) )
0.59/0.75	         => ? [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	              & ~ ( Xphi @ Xx ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(quantDeMorgan2_type,type,
0.59/0.75	    quantDeMorgan2: $o ).
0.59/0.75	
0.59/0.75	thf(quantDeMorgan2,definition,
0.59/0.75	    ( quantDeMorgan2
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o] :
0.59/0.75	          ( ! [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	             => ~ ( Xphi @ Xx ) )
0.59/0.75	         => ~ ? [Xx: $i] :
0.59/0.75	                ( ( in @ Xx @ A )
0.59/0.75	                & ( Xphi @ Xx ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(quantDeMorgan3_type,type,
0.59/0.75	    quantDeMorgan3: $o ).
0.59/0.75	
0.59/0.75	thf(quantDeMorgan3,definition,
0.59/0.75	    ( quantDeMorgan3
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o] :
0.59/0.75	          ( ~ ? [Xx: $i] :
0.59/0.75	                ( ( in @ Xx @ A )
0.59/0.75	                & ( Xphi @ Xx ) )
0.59/0.75	         => ! [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	             => ~ ( Xphi @ Xx ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(quantDeMorgan4_type,type,
0.59/0.75	    quantDeMorgan4: $o ).
0.59/0.75	
0.59/0.75	thf(quantDeMorgan4,definition,
0.59/0.75	    ( quantDeMorgan4
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o] :
0.59/0.75	          ( ? [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	              & ~ ( Xphi @ Xx ) )
0.59/0.75	         => ~ ! [Xx: $i] :
0.59/0.75	                ( ( in @ Xx @ A )
0.59/0.75	               => ( Xphi @ Xx ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(prop2setI_type,type,
0.59/0.75	    prop2setI: $o ).
0.59/0.75	
0.59/0.75	thf(prop2setI,definition,
0.59/0.75	    ( prop2setI
0.59/0.75	    = ( ! [Xphi: $o] :
0.59/0.75	          ( Xphi
0.59/0.75	         => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(set2prop_type,type,
0.59/0.75	    set2prop: $i > $o ).
0.59/0.75	
0.59/0.75	thf(prop2set2propI_type,type,
0.59/0.75	    prop2set2propI: $o ).
0.59/0.75	
0.59/0.75	thf(prop2set2propI,definition,
0.59/0.75	    ( prop2set2propI
0.59/0.75	    = ( ! [Xphi: $o] :
0.59/0.75	          ( Xphi
0.59/0.75	         => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(notdexE_type,type,
0.59/0.75	    notdexE: $o ).
0.59/0.75	
0.59/0.75	thf(notdexE,definition,
0.59/0.75	    ( notdexE
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o] :
0.59/0.75	          ( ~ ? [Xx: $i] :
0.59/0.75	                ( ( in @ Xx @ A )
0.59/0.75	                & ( Xphi @ Xx ) )
0.59/0.75	         => ! [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	             => ~ ( Xphi @ Xx ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(notdallE_type,type,
0.59/0.75	    notdallE: $o ).
0.59/0.75	
0.59/0.75	thf(notdallE,definition,
0.59/0.75	    ( notdallE
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o] :
0.59/0.75	          ( ~ ! [Xx: $i] :
0.59/0.75	                ( ( in @ Xx @ A )
0.59/0.75	               => ( Xphi @ Xx ) )
0.59/0.75	         => ? [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	              & ~ ( Xphi @ Xx ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(exuI1_type,type,
0.59/0.75	    exuI1: $o ).
0.59/0.75	
0.59/0.75	thf(exuI1,definition,
0.59/0.75	    ( exuI1
0.59/0.75	    = ( ! [Xphi: $i > $o] :
0.59/0.75	          ( ? [Xx: $i] :
0.59/0.75	              ( ( Xphi @ Xx )
0.59/0.75	              & ! [Xy: $i] :
0.59/0.75	                  ( ( Xphi @ Xy )
0.59/0.75	                 => ( Xx = Xy ) ) )
0.59/0.75	         => ( exu
0.59/0.75	            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(exuI3_type,type,
0.59/0.75	    exuI3: $o ).
0.59/0.75	
0.59/0.75	thf(exuI3,definition,
0.59/0.75	    ( exuI3
0.59/0.75	    = ( ! [Xphi: $i > $o] :
0.59/0.75	          ( ? [Xx: $i] : ( Xphi @ Xx )
0.59/0.75	         => ( ! [Xx: $i,Xy: $i] :
0.59/0.75	                ( ( Xphi @ Xx )
0.59/0.75	               => ( ( Xphi @ Xy )
0.59/0.75	                 => ( Xx = Xy ) ) )
0.59/0.75	           => ( exu
0.59/0.75	              @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(exuI2_type,type,
0.59/0.75	    exuI2: $o ).
0.59/0.75	
0.59/0.75	thf(exuI2,definition,
0.59/0.75	    ( exuI2
0.59/0.75	    = ( ! [Xphi: $i > $o] :
0.59/0.75	          ( ? [Xx: $i] :
0.59/0.75	            ! [Xy: $i] :
0.59/0.75	              ( ( Xphi @ Xy )
0.59/0.75	            <=> ( Xy = Xx ) )
0.59/0.75	         => ( exu
0.59/0.75	            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(inCongP_type,type,
0.59/0.75	    inCongP: $o ).
0.59/0.75	
0.59/0.75	thf(inCongP,definition,
0.59/0.75	    ( inCongP
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( A = B )
0.59/0.75	         => ! [Xx: $i,Xy: $i] :
0.59/0.75	              ( ( Xx = Xy )
0.59/0.75	             => ( ( in @ Xx @ A )
0.59/0.75	               => ( in @ Xy @ B ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(in__Cong_type,type,
0.59/0.75	    in__Cong: $o ).
0.59/0.75	
0.59/0.75	thf(in__Cong,definition,
0.59/0.75	    ( in__Cong
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( A = B )
0.59/0.75	         => ! [Xx: $i,Xy: $i] :
0.59/0.75	              ( ( Xx = Xy )
0.59/0.75	             => ( ( in @ Xx @ A )
0.59/0.75	              <=> ( in @ Xy @ B ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(exuE3u_type,type,
0.59/0.75	    exuE3u: $o ).
0.59/0.75	
0.59/0.75	thf(exuE3u,definition,
0.59/0.75	    ( exuE3u
0.59/0.75	    = ( ! [Xphi: $i > $o] :
0.59/0.75	          ( ( exu
0.59/0.75	            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.59/0.75	         => ! [Xx: $i,Xy: $i] :
0.59/0.75	              ( ( Xphi @ Xx )
0.59/0.75	             => ( ( Xphi @ Xy )
0.59/0.75	               => ( Xx = Xy ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(exu__Cong_type,type,
0.59/0.75	    exu__Cong: $o ).
0.59/0.75	
0.59/0.75	thf(exu__Cong,definition,
0.59/0.75	    ( exu__Cong
0.59/0.75	    = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
0.59/0.75	          ( ! [Xx: $i,Xy: $i] :
0.59/0.75	              ( ( Xx = Xy )
0.59/0.75	             => ( ( Xphi @ Xx )
0.59/0.75	              <=> ( Xpsi @ Xy ) ) )
0.59/0.75	         => ( ( exu
0.59/0.75	              @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.59/0.75	          <=> ( exu
0.59/0.75	              @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(emptyset__Cong_type,type,
0.59/0.75	    emptyset__Cong: $o ).
0.59/0.75	
0.59/0.75	thf(emptyset__Cong,definition,
0.59/0.75	    ( emptyset__Cong
0.59/0.75	    = ( emptyset = emptyset ) ) ).
0.59/0.75	
0.59/0.75	thf(setadjoin__Cong_type,type,
0.59/0.75	    setadjoin__Cong: $o ).
0.59/0.75	
0.59/0.75	thf(setadjoin__Cong,definition,
0.59/0.75	    ( setadjoin__Cong
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] :
0.59/0.75	          ( ( Xx = Xy )
0.59/0.75	         => ! [Xz: $i,Xu: $i] :
0.59/0.75	              ( ( Xz = Xu )
0.59/0.75	             => ( ( setadjoin @ Xx @ Xz )
0.59/0.75	                = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(powerset__Cong_type,type,
0.59/0.75	    powerset__Cong: $o ).
0.59/0.75	
0.59/0.75	thf(powerset__Cong,definition,
0.59/0.75	    ( powerset__Cong
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( A = B )
0.59/0.75	         => ( ( powerset @ A )
0.59/0.75	            = ( powerset @ B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setunion__Cong_type,type,
0.59/0.75	    setunion__Cong: $o ).
0.59/0.75	
0.59/0.75	thf(setunion__Cong,definition,
0.59/0.75	    ( setunion__Cong
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( A = B )
0.59/0.75	         => ( ( setunion @ A )
0.59/0.75	            = ( setunion @ B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(omega__Cong_type,type,
0.59/0.75	    omega__Cong: $o ).
0.59/0.75	
0.59/0.75	thf(omega__Cong,definition,
0.59/0.75	    ( omega__Cong
0.59/0.75	    = ( omega = omega ) ) ).
0.59/0.75	
0.59/0.75	thf(exuEu_type,type,
0.59/0.75	    exuEu: $o ).
0.59/0.75	
0.59/0.75	thf(exuEu,definition,
0.59/0.75	    ( exuEu
0.59/0.75	    = ( ! [Xphi: $i > $o] :
0.59/0.75	          ( ( exu
0.59/0.75	            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.59/0.75	         => ! [Xx: $i,Xy: $i] :
0.59/0.75	              ( ( Xphi @ Xx )
0.59/0.75	             => ( ( Xphi @ Xy )
0.59/0.75	               => ( Xx = Xy ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(descr__Cong_type,type,
0.59/0.75	    descr__Cong: $o ).
0.59/0.75	
0.59/0.75	thf(descr__Cong,definition,
0.59/0.75	    ( descr__Cong
0.59/0.75	    = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
0.59/0.75	          ( ! [Xx: $i,Xy: $i] :
0.59/0.75	              ( ( Xx = Xy )
0.59/0.75	             => ( ( Xphi @ Xx )
0.59/0.75	              <=> ( Xpsi @ Xy ) ) )
0.59/0.75	         => ( ( exu
0.59/0.75	              @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.59/0.75	           => ( ( exu
0.59/0.75	                @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
0.59/0.75	             => ( ( descr
0.59/0.75	                  @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.59/0.75	                = ( descr
0.59/0.75	                  @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(dsetconstr__Cong_type,type,
0.59/0.75	    dsetconstr__Cong: $o ).
0.59/0.75	
0.59/0.75	thf(dsetconstr__Cong,definition,
0.59/0.75	    ( dsetconstr__Cong
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( A = B )
0.59/0.75	         => ! [Xphi: $i > $o,Xpsi: $i > $o] :
0.59/0.75	              ( ! [Xx: $i] :
0.59/0.75	                  ( ( in @ Xx @ A )
0.59/0.75	                 => ! [Xy: $i] :
0.59/0.75	                      ( ( in @ Xy @ B )
0.59/0.75	                     => ( ( Xx = Xy )
0.59/0.75	                       => ( ( Xphi @ Xx )
0.59/0.75	                        <=> ( Xpsi @ Xy ) ) ) ) )
0.59/0.75	             => ( ( dsetconstr @ A
0.59/0.75	                  @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.59/0.75	                = ( dsetconstr @ B
0.59/0.75	                  @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(subset_type,type,
0.59/0.75	    subset: $i > $i > $o ).
0.59/0.75	
0.59/0.75	thf(disjoint_type,type,
0.59/0.75	    disjoint: $i > $i > $o ).
0.59/0.75	
0.59/0.75	thf(setsmeet_type,type,
0.59/0.75	    setsmeet: $i > $i > $o ).
0.59/0.75	
0.59/0.75	thf(subsetI1_type,type,
0.59/0.75	    subsetI1: $o ).
0.59/0.75	
0.59/0.75	thf(subsetI1,definition,
0.59/0.75	    ( subsetI1
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ! [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	             => ( in @ Xx @ B ) )
0.59/0.75	         => ( subset @ A @ B ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(eqimpsubset2_type,type,
0.59/0.75	    eqimpsubset2: $o ).
0.59/0.75	
0.59/0.75	thf(eqimpsubset2,definition,
0.59/0.75	    ( eqimpsubset2
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( A = B )
0.59/0.75	         => ( subset @ B @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(eqimpsubset1_type,type,
0.59/0.75	    eqimpsubset1: $o ).
0.59/0.75	
0.59/0.75	thf(eqimpsubset1,definition,
0.59/0.75	    ( eqimpsubset1
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( A = B )
0.59/0.75	         => ( subset @ A @ B ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(subsetI2_type,type,
0.59/0.75	    subsetI2: $o ).
0.59/0.75	
0.59/0.75	thf(subsetI2,definition,
0.59/0.75	    ( subsetI2
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ! [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	             => ( in @ Xx @ B ) )
0.59/0.75	         => ( subset @ A @ B ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(emptysetsubset_type,type,
0.59/0.75	    emptysetsubset: $o ).
0.59/0.75	
0.59/0.75	thf(emptysetsubset,definition,
0.59/0.75	    ( emptysetsubset
0.59/0.75	    = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
0.59/0.75	
0.59/0.75	thf(subsetE_type,type,
0.59/0.75	    subsetE: $o ).
0.59/0.75	
0.59/0.75	thf(subsetE,definition,
0.59/0.75	    ( subsetE
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( subset @ A @ B )
0.59/0.75	         => ( ( in @ Xx @ A )
0.59/0.75	           => ( in @ Xx @ B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(subsetE2_type,type,
0.59/0.75	    subsetE2: $o ).
0.59/0.75	
0.59/0.75	thf(subsetE2,definition,
0.59/0.75	    ( subsetE2
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( subset @ A @ B )
0.59/0.75	         => ( ~ ( in @ Xx @ B )
0.59/0.75	           => ~ ( in @ Xx @ A ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(notsubsetI_type,type,
0.59/0.75	    notsubsetI: $o ).
0.59/0.75	
0.59/0.75	thf(notsubsetI,definition,
0.59/0.75	    ( notsubsetI
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( ~ ( in @ Xx @ B )
0.59/0.75	           => ~ ( subset @ A @ B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(notequalI1_type,type,
0.59/0.75	    notequalI1: $o ).
0.59/0.75	
0.59/0.75	thf(notequalI1,definition,
0.59/0.75	    ( notequalI1
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ~ ( subset @ A @ B )
0.59/0.75	         => ( A != B ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(notequalI2_type,type,
0.59/0.75	    notequalI2: $o ).
0.59/0.75	
0.59/0.75	thf(notequalI2,definition,
0.59/0.75	    ( notequalI2
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( ~ ( in @ Xx @ B )
0.59/0.75	           => ( A != B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(subsetRefl_type,type,
0.59/0.75	    subsetRefl: $o ).
0.59/0.75	
0.59/0.75	thf(subsetRefl,definition,
0.59/0.75	    ( subsetRefl
0.59/0.75	    = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
0.59/0.75	
0.59/0.75	thf(subsetTrans_type,type,
0.59/0.75	    subsetTrans: $o ).
0.59/0.75	
0.59/0.75	thf(subsetTrans,definition,
0.59/0.75	    ( subsetTrans
0.59/0.75	    = ( ! [A: $i,B: $i,C: $i] :
0.59/0.75	          ( ( subset @ A @ B )
0.59/0.75	         => ( ( subset @ B @ C )
0.59/0.75	           => ( subset @ A @ C ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setadjoinSub_type,type,
0.59/0.75	    setadjoinSub: $o ).
0.59/0.75	
0.59/0.75	thf(setadjoinSub,definition,
0.59/0.75	    ( setadjoinSub
0.59/0.75	    = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setadjoinSub2_type,type,
0.59/0.75	    setadjoinSub2: $o ).
0.59/0.75	
0.59/0.75	thf(setadjoinSub2,definition,
0.59/0.75	    ( setadjoinSub2
0.59/0.75	    = ( ! [A: $i,Xx: $i,B: $i] :
0.59/0.75	          ( ( subset @ A @ B )
0.59/0.75	         => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(subset2powerset_type,type,
0.59/0.75	    subset2powerset: $o ).
0.59/0.75	
0.59/0.75	thf(subset2powerset,definition,
0.59/0.75	    ( subset2powerset
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( subset @ A @ B )
0.59/0.75	         => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setextsub_type,type,
0.59/0.75	    setextsub: $o ).
0.59/0.75	
0.59/0.75	thf(setextsub,definition,
0.59/0.75	    ( setextsub
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( subset @ A @ B )
0.59/0.75	         => ( ( subset @ B @ A )
0.59/0.75	           => ( A = B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(subsetemptysetimpeq_type,type,
0.59/0.75	    subsetemptysetimpeq: $o ).
0.59/0.75	
0.59/0.75	thf(subsetemptysetimpeq,definition,
0.59/0.75	    ( subsetemptysetimpeq
0.59/0.75	    = ( ! [A: $i] :
0.59/0.75	          ( ( subset @ A @ emptyset )
0.59/0.75	         => ( A = emptyset ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(powersetI1_type,type,
0.59/0.75	    powersetI1: $o ).
0.59/0.75	
0.59/0.75	thf(powersetI1,definition,
0.59/0.75	    ( powersetI1
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( subset @ B @ A )
0.59/0.75	         => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(powersetE1_type,type,
0.59/0.75	    powersetE1: $o ).
0.59/0.75	
0.59/0.75	thf(powersetE1,definition,
0.59/0.75	    ( powersetE1
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( in @ B @ ( powerset @ A ) )
0.59/0.75	         => ( subset @ B @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(inPowerset_type,type,
0.59/0.75	    inPowerset: $o ).
0.59/0.75	
0.59/0.75	thf(inPowerset,definition,
0.59/0.75	    ( inPowerset
0.59/0.75	    = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(powersetsubset_type,type,
0.59/0.75	    powersetsubset: $o ).
0.59/0.75	
0.59/0.75	thf(powersetsubset,definition,
0.59/0.75	    ( powersetsubset
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( subset @ A @ B )
0.59/0.75	         => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(sepInPowerset_type,type,
0.59/0.75	    sepInPowerset: $o ).
0.59/0.75	
0.59/0.75	thf(sepInPowerset,definition,
0.59/0.75	    ( sepInPowerset
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o] :
0.59/0.75	          ( in
0.59/0.75	          @ ( dsetconstr @ A
0.59/0.75	            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.59/0.75	          @ ( powerset @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(sepSubset_type,type,
0.59/0.75	    sepSubset: $o ).
0.59/0.75	
0.59/0.75	thf(sepSubset,definition,
0.59/0.75	    ( sepSubset
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o] :
0.59/0.75	          ( subset
0.59/0.75	          @ ( dsetconstr @ A
0.59/0.75	            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.59/0.75	          @ A ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binunion_type,type,
0.59/0.75	    binunion: $i > $i > $i ).
0.59/0.75	
0.59/0.75	thf(binunionIL_type,type,
0.59/0.75	    binunionIL: $o ).
0.59/0.75	
0.59/0.75	thf(binunionIL,definition,
0.59/0.75	    ( binunionIL
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(upairset2IR_type,type,
0.59/0.75	    upairset2IR: $o ).
0.59/0.75	
0.59/0.75	thf(upairset2IR,definition,
0.59/0.75	    ( upairset2IR
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binunionIR_type,type,
0.59/0.75	    binunionIR: $o ).
0.59/0.75	
0.59/0.75	thf(binunionIR,definition,
0.59/0.75	    ( binunionIR
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ B )
0.59/0.75	         => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binunionEcases_type,type,
0.59/0.75	    binunionEcases: $o ).
0.59/0.75	
0.59/0.75	thf(binunionEcases,definition,
0.59/0.75	    ( binunionEcases
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
0.59/0.75	          ( ( in @ Xx @ ( binunion @ A @ B ) )
0.59/0.75	         => ( ( ( in @ Xx @ A )
0.59/0.75	             => Xphi )
0.59/0.75	           => ( ( ( in @ Xx @ B )
0.59/0.75	               => Xphi )
0.59/0.75	             => Xphi ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binunionE_type,type,
0.59/0.75	    binunionE: $o ).
0.59/0.75	
0.59/0.75	thf(binunionE,definition,
0.59/0.75	    ( binunionE
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ ( binunion @ A @ B ) )
0.59/0.75	         => ( ( in @ Xx @ A )
0.59/0.75	            | ( in @ Xx @ B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binunionLsub_type,type,
0.59/0.75	    binunionLsub: $o ).
0.59/0.75	
0.59/0.75	thf(binunionLsub,definition,
0.59/0.75	    ( binunionLsub
0.59/0.75	    = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binunionRsub_type,type,
0.59/0.75	    binunionRsub: $o ).
0.59/0.75	
0.59/0.75	thf(binunionRsub,definition,
0.59/0.75	    ( binunionRsub
0.59/0.75	    = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binintersect_type,type,
0.59/0.75	    binintersect: $i > $i > $i ).
0.59/0.75	
0.59/0.75	thf(binintersectI_type,type,
0.59/0.75	    binintersectI: $o ).
0.59/0.75	
0.59/0.75	thf(binintersectI,definition,
0.59/0.75	    ( binintersectI
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( ( in @ Xx @ B )
0.59/0.75	           => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binintersectSubset5_type,type,
0.59/0.75	    binintersectSubset5: $o ).
0.59/0.75	
0.59/0.75	thf(binintersectSubset5,definition,
0.59/0.75	    ( binintersectSubset5
0.59/0.75	    = ( ! [A: $i,B: $i,C: $i] :
0.59/0.75	          ( ( subset @ C @ A )
0.59/0.75	         => ( ( subset @ C @ B )
0.59/0.75	           => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binintersectEL_type,type,
0.59/0.75	    binintersectEL: $o ).
0.59/0.75	
0.59/0.75	thf(binintersectEL,definition,
0.59/0.75	    ( binintersectEL
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ ( binintersect @ A @ B ) )
0.59/0.75	         => ( in @ Xx @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binintersectLsub_type,type,
0.59/0.75	    binintersectLsub: $o ).
0.59/0.75	
0.59/0.75	thf(binintersectLsub,definition,
0.59/0.75	    ( binintersectLsub
0.59/0.75	    = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binintersectSubset2_type,type,
0.59/0.75	    binintersectSubset2: $o ).
0.59/0.75	
0.59/0.75	thf(binintersectSubset2,definition,
0.59/0.75	    ( binintersectSubset2
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( subset @ A @ B )
0.59/0.75	         => ( ( binintersect @ A @ B )
0.59/0.75	            = A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binintersectSubset3_type,type,
0.59/0.75	    binintersectSubset3: $o ).
0.59/0.75	
0.59/0.75	thf(binintersectSubset3,definition,
0.59/0.75	    ( binintersectSubset3
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( ( binintersect @ A @ B )
0.59/0.75	            = B )
0.59/0.75	         => ( subset @ B @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binintersectER_type,type,
0.59/0.75	    binintersectER: $o ).
0.59/0.75	
0.59/0.75	thf(binintersectER,definition,
0.59/0.75	    ( binintersectER
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ ( binintersect @ A @ B ) )
0.59/0.75	         => ( in @ Xx @ B ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(disjointsetsI1_type,type,
0.59/0.75	    disjointsetsI1: $o ).
0.59/0.75	
0.59/0.75	thf(disjointsetsI1,definition,
0.59/0.75	    ( disjointsetsI1
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ~ ? [Xx: $i] :
0.59/0.75	                ( ( in @ Xx @ A )
0.59/0.75	                & ( in @ Xx @ B ) )
0.59/0.75	         => ( ( binintersect @ A @ B )
0.59/0.75	            = emptyset ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binintersectRsub_type,type,
0.59/0.75	    binintersectRsub: $o ).
0.59/0.75	
0.59/0.75	thf(binintersectRsub,definition,
0.59/0.75	    ( binintersectRsub
0.59/0.75	    = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binintersectSubset4_type,type,
0.59/0.75	    binintersectSubset4: $o ).
0.59/0.75	
0.59/0.75	thf(binintersectSubset4,definition,
0.59/0.75	    ( binintersectSubset4
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( subset @ B @ A )
0.59/0.75	         => ( ( binintersect @ A @ B )
0.59/0.75	            = B ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(binintersectSubset1_type,type,
0.59/0.75	    binintersectSubset1: $o ).
0.59/0.75	
0.59/0.75	thf(binintersectSubset1,definition,
0.59/0.75	    ( binintersectSubset1
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( ( binintersect @ A @ B )
0.59/0.75	            = A )
0.59/0.75	         => ( subset @ A @ B ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(bs114d_type,type,
0.59/0.75	    bs114d: $o ).
0.59/0.75	
0.59/0.75	thf(bs114d,definition,
0.59/0.75	    ( bs114d
0.59/0.75	    = ( ! [A: $i,B: $i,C: $i] :
0.59/0.75	          ( ( binintersect @ A @ ( binunion @ B @ C ) )
0.59/0.75	          = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(regular_type,type,
0.59/0.75	    regular: $i > $o ).
0.59/0.75	
0.59/0.75	thf(setminus_type,type,
0.59/0.75	    setminus: $i > $i > $i ).
0.59/0.75	
0.59/0.75	thf(setminusI_type,type,
0.59/0.75	    setminusI: $o ).
0.59/0.75	
0.59/0.75	thf(setminusI,definition,
0.59/0.75	    ( setminusI
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( ~ ( in @ Xx @ B )
0.59/0.75	           => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setminusEL_type,type,
0.59/0.75	    setminusEL: $o ).
0.59/0.75	
0.59/0.75	thf(setminusEL,definition,
0.59/0.75	    ( setminusEL
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ ( setminus @ A @ B ) )
0.59/0.75	         => ( in @ Xx @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setminusER_type,type,
0.59/0.75	    setminusER: $o ).
0.59/0.75	
0.59/0.75	thf(setminusER,definition,
0.59/0.75	    ( setminusER
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ ( setminus @ A @ B ) )
0.59/0.75	         => ~ ( in @ Xx @ B ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setminusSubset2_type,type,
0.59/0.75	    setminusSubset2: $o ).
0.59/0.75	
0.59/0.75	thf(setminusSubset2,definition,
0.59/0.75	    ( setminusSubset2
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( subset @ A @ B )
0.59/0.75	         => ( ( setminus @ A @ B )
0.59/0.75	            = emptyset ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setminusERneg_type,type,
0.59/0.75	    setminusERneg: $o ).
0.59/0.75	
0.59/0.75	thf(setminusERneg,definition,
0.59/0.75	    ( setminusERneg
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
0.59/0.75	         => ( ( in @ Xx @ A )
0.59/0.75	           => ( in @ Xx @ B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setminusELneg_type,type,
0.59/0.75	    setminusELneg: $o ).
0.59/0.75	
0.59/0.75	thf(setminusELneg,definition,
0.59/0.75	    ( setminusELneg
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
0.59/0.75	         => ( ~ ( in @ Xx @ B )
0.59/0.75	           => ~ ( in @ Xx @ A ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setminusILneg_type,type,
0.59/0.75	    setminusILneg: $o ).
0.59/0.75	
0.59/0.75	thf(setminusILneg,definition,
0.59/0.75	    ( setminusILneg
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ~ ( in @ Xx @ A )
0.59/0.75	         => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setminusIRneg_type,type,
0.59/0.75	    setminusIRneg: $o ).
0.59/0.75	
0.59/0.75	thf(setminusIRneg,definition,
0.59/0.75	    ( setminusIRneg
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ B )
0.59/0.75	         => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setminusLsub_type,type,
0.59/0.75	    setminusLsub: $o ).
0.59/0.75	
0.59/0.75	thf(setminusLsub,definition,
0.59/0.75	    ( setminusLsub
0.59/0.75	    = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setminusSubset1_type,type,
0.59/0.75	    setminusSubset1: $o ).
0.59/0.75	
0.59/0.75	thf(setminusSubset1,definition,
0.59/0.75	    ( setminusSubset1
0.59/0.75	    = ( ! [A: $i,B: $i] :
0.59/0.75	          ( ( ( setminus @ A @ B )
0.59/0.75	            = emptyset )
0.59/0.75	         => ( subset @ A @ B ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(symdiff_type,type,
0.59/0.75	    symdiff: $i > $i > $i ).
0.59/0.75	
0.59/0.75	thf(symdiffE_type,type,
0.59/0.75	    symdiffE: $o ).
0.59/0.75	
0.59/0.75	thf(symdiffE,definition,
0.59/0.75	    ( symdiffE
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ ( symdiff @ A @ B ) )
0.59/0.75	         => ! [Xphi: $o] :
0.59/0.75	              ( ( ( in @ Xx @ A )
0.59/0.75	               => ( ~ ( in @ Xx @ B )
0.59/0.75	                 => Xphi ) )
0.59/0.75	             => ( ( ~ ( in @ Xx @ A )
0.59/0.75	                 => ( ( in @ Xx @ B )
0.59/0.75	                   => Xphi ) )
0.59/0.75	               => Xphi ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(symdiffI1_type,type,
0.59/0.75	    symdiffI1: $o ).
0.59/0.75	
0.59/0.75	thf(symdiffI1,definition,
0.59/0.75	    ( symdiffI1
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( ~ ( in @ Xx @ B )
0.59/0.75	           => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(symdiffI2_type,type,
0.59/0.75	    symdiffI2: $o ).
0.59/0.75	
0.59/0.75	thf(symdiffI2,definition,
0.59/0.75	    ( symdiffI2
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ~ ( in @ Xx @ A )
0.59/0.75	         => ( ( in @ Xx @ B )
0.59/0.75	           => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(symdiffIneg1_type,type,
0.59/0.75	    symdiffIneg1: $o ).
0.59/0.75	
0.59/0.75	thf(symdiffIneg1,definition,
0.59/0.75	    ( symdiffIneg1
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( ( in @ Xx @ B )
0.59/0.75	           => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(symdiffIneg2_type,type,
0.59/0.75	    symdiffIneg2: $o ).
0.59/0.75	
0.59/0.75	thf(symdiffIneg2,definition,
0.59/0.75	    ( symdiffIneg2
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ~ ( in @ Xx @ A )
0.59/0.75	         => ( ~ ( in @ Xx @ B )
0.59/0.75	           => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(iskpair_type,type,
0.59/0.75	    iskpair: $i > $o ).
0.59/0.75	
0.59/0.75	thf(secondinupair_type,type,
0.59/0.75	    secondinupair: $o ).
0.59/0.75	
0.59/0.75	thf(secondinupair,definition,
0.59/0.75	    ( secondinupair
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setukpairIL_type,type,
0.59/0.75	    setukpairIL: $o ).
0.59/0.75	
0.59/0.75	thf(setukpairIL,definition,
0.59/0.75	    ( setukpairIL
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setukpairIR_type,type,
0.59/0.75	    setukpairIR: $o ).
0.59/0.75	
0.59/0.75	thf(setukpairIR,definition,
0.59/0.75	    ( setukpairIR
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(kpairiskpair_type,type,
0.59/0.75	    kpairiskpair: $o ).
0.59/0.75	
0.59/0.75	thf(kpairiskpair,definition,
0.59/0.75	    ( kpairiskpair
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(kpair_type,type,
0.59/0.75	    kpair: $i > $i > $i ).
0.59/0.75	
0.59/0.75	thf(kpairp_type,type,
0.59/0.75	    kpairp: $o ).
0.59/0.75	
0.59/0.75	thf(kpairp,definition,
0.59/0.75	    ( kpairp
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(cartprod_type,type,
0.59/0.75	    cartprod: $i > $i > $i ).
0.59/0.75	
0.59/0.75	thf(singletonsubset_type,type,
0.59/0.75	    singletonsubset: $o ).
0.59/0.75	
0.59/0.75	thf(singletonsubset,definition,
0.59/0.75	    ( singletonsubset
0.59/0.75	    = ( ! [A: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(singletoninpowerset_type,type,
0.59/0.75	    singletoninpowerset: $o ).
0.59/0.75	
0.59/0.75	thf(singletoninpowerset,definition,
0.59/0.75	    ( singletoninpowerset
0.59/0.75	    = ( ! [A: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(singletoninpowunion_type,type,
0.59/0.75	    singletoninpowunion: $o ).
0.59/0.75	
0.59/0.75	thf(singletoninpowunion,definition,
0.59/0.75	    ( singletoninpowunion
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(upairset2E_type,type,
0.59/0.75	    upairset2E: $o ).
0.59/0.75	
0.59/0.75	thf(upairset2E,definition,
0.59/0.75	    ( upairset2E
0.59/0.75	    = ( ! [Xx: $i,Xy: $i,Xz: $i] :
0.59/0.75	          ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
0.59/0.75	         => ( ( Xz = Xx )
0.59/0.75	            | ( Xz = Xy ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(upairsubunion_type,type,
0.59/0.75	    upairsubunion: $o ).
0.59/0.75	
0.59/0.75	thf(upairsubunion,definition,
0.59/0.75	    ( upairsubunion
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ! [Xy: $i] :
0.59/0.75	              ( ( in @ Xy @ B )
0.59/0.75	             => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(upairinpowunion_type,type,
0.59/0.75	    upairinpowunion: $o ).
0.59/0.75	
0.59/0.75	thf(upairinpowunion,definition,
0.59/0.75	    ( upairinpowunion
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ! [Xy: $i] :
0.59/0.75	              ( ( in @ Xy @ B )
0.59/0.75	             => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(ubforcartprodlem1_type,type,
0.59/0.75	    ubforcartprodlem1: $o ).
0.59/0.75	
0.59/0.75	thf(ubforcartprodlem1,definition,
0.59/0.75	    ( ubforcartprodlem1
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ! [Xy: $i] :
0.59/0.75	              ( ( in @ Xy @ B )
0.59/0.75	             => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(ubforcartprodlem2_type,type,
0.59/0.75	    ubforcartprodlem2: $o ).
0.59/0.75	
0.59/0.75	thf(ubforcartprodlem2,definition,
0.59/0.75	    ( ubforcartprodlem2
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ! [Xy: $i] :
0.59/0.75	              ( ( in @ Xy @ B )
0.59/0.75	             => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(ubforcartprodlem3_type,type,
0.59/0.75	    ubforcartprodlem3: $o ).
0.59/0.75	
0.59/0.75	thf(ubforcartprodlem3,definition,
0.59/0.75	    ( ubforcartprodlem3
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ! [Xy: $i] :
0.59/0.75	              ( ( in @ Xy @ B )
0.59/0.75	             => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(cartprodpairin_type,type,
0.59/0.75	    cartprodpairin: $o ).
0.59/0.75	
0.59/0.75	thf(cartprodpairin,definition,
0.59/0.75	    ( cartprodpairin
0.59/0.75	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ! [Xy: $i] :
0.59/0.75	              ( ( in @ Xy @ B )
0.59/0.75	             => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(cartprodmempair1_type,type,
0.59/0.75	    cartprodmempair1: $o ).
0.59/0.75	
0.59/0.75	thf(cartprodmempair1,definition,
0.59/0.75	    ( cartprodmempair1
0.59/0.75	    = ( ! [A: $i,B: $i,Xu: $i] :
0.59/0.75	          ( ( in @ Xu @ ( cartprod @ A @ B ) )
0.59/0.75	         => ? [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	              & ? [Xy: $i] :
0.59/0.75	                  ( ( in @ Xy @ B )
0.59/0.75	                  & ( Xu
0.59/0.75	                    = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(cartprodmempair_type,type,
0.59/0.75	    cartprodmempair: $o ).
0.59/0.75	
0.59/0.75	thf(cartprodmempair,definition,
0.59/0.75	    ( cartprodmempair
0.59/0.75	    = ( ! [A: $i,B: $i,Xu: $i] :
0.59/0.75	          ( ( in @ Xu @ ( cartprod @ A @ B ) )
0.59/0.75	         => ( iskpair @ Xu ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setunionE2_type,type,
0.59/0.75	    setunionE2: $o ).
0.59/0.75	
0.59/0.75	thf(setunionE2,definition,
0.59/0.75	    ( setunionE2
0.59/0.75	    = ( ! [A: $i,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ ( setunion @ A ) )
0.59/0.75	         => ? [X: $i] :
0.59/0.75	              ( ( in @ X @ A )
0.59/0.75	              & ( in @ Xx @ X ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setunionsingleton1_type,type,
0.59/0.75	    setunionsingleton1: $o ).
0.59/0.75	
0.59/0.75	thf(setunionsingleton1,definition,
0.59/0.75	    ( setunionsingleton1
0.59/0.75	    = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setunionsingleton2_type,type,
0.59/0.75	    setunionsingleton2: $o ).
0.59/0.75	
0.59/0.75	thf(setunionsingleton2,definition,
0.59/0.75	    ( setunionsingleton2
0.59/0.75	    = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setunionsingleton_type,type,
0.59/0.75	    setunionsingleton: $o ).
0.59/0.75	
0.59/0.75	thf(setunionsingleton,definition,
0.59/0.75	    ( setunionsingleton
0.59/0.75	    = ( ! [Xx: $i] :
0.59/0.75	          ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
0.59/0.75	          = Xx ) ) ) ).
0.59/0.75	
0.59/0.75	thf(singleton_type,type,
0.59/0.75	    singleton: $i > $o ).
0.59/0.75	
0.59/0.75	thf(singletonprop_type,type,
0.59/0.75	    singletonprop: $o ).
0.59/0.75	
0.59/0.75	thf(singletonprop,definition,
0.59/0.75	    ( singletonprop
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o] :
0.59/0.75	          ( ! [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	             => ! [Xy: $i] :
0.59/0.75	                  ( ( in @ Xy @ A )
0.59/0.75	                 => ( ( Xphi @ Xx )
0.59/0.75	                   => ( ( Xphi @ Xy )
0.59/0.75	                     => ( Xx = Xy ) ) ) ) )
0.59/0.75	         => ( ? [Xx: $i] :
0.59/0.75	                ( ( in @ Xx @ A )
0.59/0.75	                & ( Xphi @ Xx ) )
0.59/0.75	           => ( singleton
0.59/0.75	              @ ( dsetconstr @ A
0.59/0.75	                @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(ex1_type,type,
0.59/0.75	    ex1: $i > ( $i > $o ) > $o ).
0.59/0.75	
0.59/0.75	thf(ex1E1_type,type,
0.59/0.75	    ex1E1: $o ).
0.59/0.75	
0.59/0.75	thf(ex1E1,definition,
0.59/0.75	    ( ex1E1
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o] :
0.59/0.75	          ( ( ex1 @ A
0.59/0.75	            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.59/0.75	         => ? [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	              & ( Xphi @ Xx ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(ex1I_type,type,
0.59/0.75	    ex1I: $o ).
0.59/0.75	
0.59/0.75	thf(ex1I,definition,
0.59/0.75	    ( ex1I
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
0.59/0.75	          ( ( in @ Xx @ A )
0.59/0.75	         => ( ( Xphi @ Xx )
0.59/0.75	           => ( ! [Xy: $i] :
0.59/0.75	                  ( ( in @ Xy @ A )
0.59/0.75	                 => ( ( Xphi @ Xy )
0.59/0.75	                   => ( Xy = Xx ) ) )
0.59/0.75	             => ( ex1 @ A
0.59/0.75	                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(ex1I2_type,type,
0.59/0.75	    ex1I2: $o ).
0.59/0.75	
0.59/0.75	thf(ex1I2,definition,
0.59/0.75	    ( ex1I2
0.59/0.75	    = ( ! [A: $i,Xphi: $i > $o] :
0.59/0.75	          ( ! [Xx: $i] :
0.59/0.75	              ( ( in @ Xx @ A )
0.59/0.75	             => ! [Xy: $i] :
0.59/0.75	                  ( ( in @ Xy @ A )
0.59/0.75	                 => ( ( Xphi @ Xx )
0.59/0.75	                   => ( ( Xphi @ Xy )
0.59/0.75	                     => ( Xx = Xy ) ) ) ) )
0.59/0.75	         => ( ? [Xx: $i] :
0.59/0.75	                ( ( in @ Xx @ A )
0.59/0.75	                & ( Xphi @ Xx ) )
0.59/0.75	           => ( ex1 @ A
0.59/0.75	              @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(singletonsuniq_type,type,
0.59/0.75	    singletonsuniq: $o ).
0.59/0.75	
0.59/0.75	thf(singletonsuniq,definition,
0.59/0.75	    ( singletonsuniq
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] :
0.59/0.75	          ( ( ( setadjoin @ Xx @ emptyset )
0.59/0.75	            = ( setadjoin @ Xy @ emptyset ) )
0.59/0.75	         => ( Xx = Xy ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(atmost1p_type,type,
0.59/0.75	    atmost1p: $i > $o ).
0.59/0.75	
0.59/0.75	thf(atleast2p_type,type,
0.59/0.75	    atleast2p: $i > $o ).
0.59/0.75	
0.59/0.75	thf(atmost2p_type,type,
0.59/0.75	    atmost2p: $i > $o ).
0.59/0.75	
0.59/0.75	thf(upairsetp_type,type,
0.59/0.75	    upairsetp: $i > $o ).
0.59/0.75	
0.59/0.75	thf(setukpairinjL1_type,type,
0.59/0.75	    setukpairinjL1: $o ).
0.59/0.75	
0.59/0.75	thf(setukpairinjL1,definition,
0.59/0.75	    ( setukpairinjL1
0.59/0.75	    = ( ! [Xx: $i,Xy: $i,Xz: $i] :
0.59/0.75	          ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
0.59/0.75	         => ( Xx = Xz ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(kfstsingleton_type,type,
0.59/0.75	    kfstsingleton: $o ).
0.59/0.75	
0.59/0.75	thf(kfstsingleton,definition,
0.59/0.75	    ( kfstsingleton
0.59/0.75	    = ( ! [Xu: $i] :
0.59/0.75	          ( ( iskpair @ Xu )
0.59/0.75	         => ( singleton
0.59/0.75	            @ ( dsetconstr @ ( setunion @ Xu )
0.59/0.75	              @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(theprop_type,type,
0.59/0.75	    theprop: $o ).
0.59/0.75	
0.59/0.75	thf(theprop,definition,
0.59/0.75	    ( theprop
0.59/0.75	    = ( ! [X: $i] :
0.59/0.75	          ( ( singleton @ X )
0.59/0.75	         => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(kfst_type,type,
0.59/0.75	    kfst: $i > $i ).
0.59/0.75	
0.59/0.75	thf(kfstpairEq_type,type,
0.59/0.75	    kfstpairEq: $o ).
0.59/0.75	
0.59/0.75	thf(kfstpairEq,definition,
0.59/0.75	    ( kfstpairEq
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] :
0.59/0.75	          ( ( kfst @ ( kpair @ Xx @ Xy ) )
0.59/0.75	          = Xx ) ) ) ).
0.59/0.75	
0.59/0.75	thf(cartprodfstin_type,type,
0.59/0.75	    cartprodfstin: $o ).
0.59/0.75	
0.59/0.75	thf(cartprodfstin,definition,
0.59/0.75	    ( cartprodfstin
0.59/0.75	    = ( ! [A: $i,B: $i,Xu: $i] :
0.59/0.75	          ( ( in @ Xu @ ( cartprod @ A @ B ) )
0.59/0.75	         => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setukpairinjL2_type,type,
0.59/0.75	    setukpairinjL2: $o ).
0.59/0.75	
0.59/0.75	thf(setukpairinjL2,definition,
0.59/0.75	    ( setukpairinjL2
0.59/0.75	    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
0.59/0.75	          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
0.59/0.75	            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
0.59/0.75	         => ( Xx = Xz ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setukpairinjL_type,type,
0.59/0.75	    setukpairinjL: $o ).
0.59/0.75	
0.59/0.75	thf(setukpairinjL,definition,
0.59/0.75	    ( setukpairinjL
0.59/0.75	    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
0.59/0.75	          ( ( ( kpair @ Xx @ Xy )
0.59/0.75	            = ( kpair @ Xz @ Xu ) )
0.59/0.75	         => ( Xx = Xz ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setukpairinjR11_type,type,
0.59/0.75	    setukpairinjR11: $o ).
0.59/0.75	
0.59/0.75	thf(setukpairinjR11,definition,
0.59/0.75	    ( setukpairinjR11
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] :
0.59/0.75	          ( ( Xx = Xy )
0.59/0.75	         => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
0.59/0.75	            = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setukpairinjR12_type,type,
0.59/0.75	    setukpairinjR12: $o ).
0.59/0.75	
0.59/0.75	thf(setukpairinjR12,definition,
0.59/0.75	    ( setukpairinjR12
0.59/0.75	    = ( ! [Xx: $i,Xy: $i] :
0.59/0.75	          ( ( Xx = Xy )
0.59/0.75	         => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
0.59/0.75	            = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setukpairinjR1_type,type,
0.59/0.75	    setukpairinjR1: $o ).
0.59/0.75	
0.59/0.75	thf(setukpairinjR1,definition,
0.59/0.75	    ( setukpairinjR1
0.59/0.75	    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
0.59/0.75	          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
0.59/0.75	            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
0.59/0.75	         => ( ( Xz = Xu )
0.59/0.75	           => ( Xy = Xu ) ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(upairequniteq_type,type,
0.59/0.75	    upairequniteq: $o ).
0.59/0.75	
0.59/0.75	thf(upairequniteq,definition,
0.59/0.75	    ( upairequniteq
0.59/0.75	    = ( ! [Xx: $i,Xy: $i,Xz: $i] :
0.59/0.75	          ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
0.59/0.75	            = ( setadjoin @ Xz @ emptyset ) )
0.59/0.75	         => ( Xx = Xy ) ) ) ) ).
0.59/0.75	
0.59/0.75	thf(setukpairinjR2_type,type,
0.59/0.75	    setukpairinjR2: $o ).
0.59/0.75	
0.59/0.75	thf(setukpairinjR2,definition,
0.59/0.75	    ( setukpairinjR2
0.59/0.75	    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
0.59/0.75	          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
0.59/0.75	            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
0.59/0.76	         => ( Xy = Xu ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(setukpairinjR_type,type,
0.59/0.76	    setukpairinjR: $o ).
0.59/0.76	
0.59/0.76	thf(setukpairinjR,definition,
0.59/0.76	    ( setukpairinjR
0.59/0.76	    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
0.59/0.76	          ( ( ( kpair @ Xx @ Xy )
0.59/0.76	            = ( kpair @ Xz @ Xu ) )
0.59/0.76	         => ( Xy = Xu ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(ksndsingleton_type,type,
0.59/0.76	    ksndsingleton: $o ).
0.59/0.76	
0.59/0.76	thf(ksndsingleton,definition,
0.59/0.76	    ( ksndsingleton
0.59/0.76	    = ( ! [Xu: $i] :
0.59/0.76	          ( ( iskpair @ Xu )
0.59/0.76	         => ( singleton
0.59/0.76	            @ ( dsetconstr @ ( setunion @ Xu )
0.59/0.76	              @ ^ [Xx: $i] :
0.59/0.76	                  ( Xu
0.59/0.76	                  = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(ksnd_type,type,
0.59/0.76	    ksnd: $i > $i ).
0.59/0.76	
0.59/0.76	thf(ksndpairEq_type,type,
0.59/0.76	    ksndpairEq: $o ).
0.59/0.76	
0.59/0.76	thf(ksndpairEq,definition,
0.59/0.76	    ( ksndpairEq
0.59/0.76	    = ( ! [Xx: $i,Xy: $i] :
0.59/0.76	          ( ( ksnd @ ( kpair @ Xx @ Xy ) )
0.59/0.76	          = Xy ) ) ) ).
0.59/0.76	
0.59/0.76	thf(kpairsurjEq_type,type,
0.59/0.76	    kpairsurjEq: $o ).
0.59/0.76	
0.59/0.76	thf(kpairsurjEq,definition,
0.59/0.76	    ( kpairsurjEq
0.59/0.76	    = ( ! [Xu: $i] :
0.59/0.76	          ( ( iskpair @ Xu )
0.59/0.76	         => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
0.59/0.76	            = Xu ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(cartprodsndin_type,type,
0.59/0.76	    cartprodsndin: $o ).
0.59/0.76	
0.59/0.76	thf(cartprodsndin,definition,
0.59/0.76	    ( cartprodsndin
0.59/0.76	    = ( ! [A: $i,B: $i,Xu: $i] :
0.59/0.76	          ( ( in @ Xu @ ( cartprod @ A @ B ) )
0.59/0.76	         => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(cartprodpairmemEL_type,type,
0.59/0.76	    cartprodpairmemEL: $o ).
0.59/0.76	
0.59/0.76	thf(cartprodpairmemEL,definition,
0.59/0.76	    ( cartprodpairmemEL
0.59/0.76	    = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
0.59/0.76	          ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
0.59/0.76	         => ( in @ Xx @ A ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(cartprodpairmemER_type,type,
0.59/0.76	    cartprodpairmemER: $o ).
0.59/0.76	
0.59/0.76	thf(cartprodpairmemER,definition,
0.59/0.76	    ( cartprodpairmemER
0.59/0.76	    = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
0.59/0.76	          ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
0.59/0.76	         => ( in @ Xy @ B ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(cartprodmempaircEq_type,type,
0.59/0.76	    cartprodmempaircEq: $o ).
0.59/0.76	
0.59/0.76	thf(cartprodmempaircEq,definition,
0.59/0.76	    ( cartprodmempaircEq
0.59/0.76	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ B )
0.59/0.76	             => ( ( kpair @ Xx @ Xy )
0.59/0.76	                = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(cartprodfstpairEq_type,type,
0.59/0.76	    cartprodfstpairEq: $o ).
0.59/0.76	
0.59/0.76	thf(cartprodfstpairEq,definition,
0.59/0.76	    ( cartprodfstpairEq
0.59/0.76	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ B )
0.59/0.76	             => ( ( kfst @ ( kpair @ Xx @ Xy ) )
0.59/0.76	                = Xx ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(cartprodsndpairEq_type,type,
0.59/0.76	    cartprodsndpairEq: $o ).
0.59/0.76	
0.59/0.76	thf(cartprodsndpairEq,definition,
0.59/0.76	    ( cartprodsndpairEq
0.59/0.76	    = ( ! [A: $i,B: $i,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ B )
0.59/0.76	             => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
0.59/0.76	                = Xy ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(cartprodpairsurjEq_type,type,
0.59/0.76	    cartprodpairsurjEq: $o ).
0.59/0.76	
0.59/0.76	thf(cartprodpairsurjEq,definition,
0.59/0.76	    ( cartprodpairsurjEq
0.59/0.76	    = ( ! [A: $i,B: $i,Xu: $i] :
0.59/0.76	          ( ( in @ Xu @ ( cartprod @ A @ B ) )
0.59/0.76	         => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
0.59/0.76	            = Xu ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln_type,type,
0.59/0.76	    breln: $i > $i > $i > $o ).
0.59/0.76	
0.59/0.76	thf(dpsetconstr_type,type,
0.59/0.76	    dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
0.59/0.76	
0.59/0.76	thf(dpsetconstrI_type,type,
0.59/0.76	    dpsetconstrI: $o ).
0.59/0.76	
0.59/0.76	thf(dpsetconstrI,definition,
0.59/0.76	    ( dpsetconstrI
0.59/0.76	    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ B )
0.59/0.76	             => ( ( Xphi @ Xx @ Xy )
0.59/0.76	               => ( in @ ( kpair @ Xx @ Xy )
0.59/0.76	                  @ ( dpsetconstr @ A @ B
0.59/0.76	                    @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(dpsetconstrSub_type,type,
0.59/0.76	    dpsetconstrSub: $o ).
0.59/0.76	
0.59/0.76	thf(dpsetconstrSub,definition,
0.59/0.76	    ( dpsetconstrSub
0.59/0.76	    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
0.59/0.76	          ( subset
0.59/0.76	          @ ( dpsetconstr @ A @ B
0.59/0.76	            @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
0.59/0.76	          @ ( cartprod @ A @ B ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(setOfPairsIsBReln_type,type,
0.59/0.76	    setOfPairsIsBReln: $o ).
0.59/0.76	
0.59/0.76	thf(setOfPairsIsBReln,definition,
0.59/0.76	    ( setOfPairsIsBReln
0.59/0.76	    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
0.59/0.76	          ( breln @ A @ B
0.59/0.76	          @ ( dpsetconstr @ A @ B
0.59/0.76	            @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(dpsetconstrERa_type,type,
0.59/0.76	    dpsetconstrERa: $o ).
0.59/0.76	
0.59/0.76	thf(dpsetconstrERa,definition,
0.59/0.76	    ( dpsetconstrERa
0.59/0.76	    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ B )
0.59/0.76	             => ( ( in @ ( kpair @ Xx @ Xy )
0.59/0.76	                  @ ( dpsetconstr @ A @ B
0.59/0.76	                    @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
0.59/0.76	               => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(dpsetconstrEL1_type,type,
0.59/0.76	    dpsetconstrEL1: $o ).
0.59/0.76	
0.59/0.76	thf(dpsetconstrEL1,definition,
0.59/0.76	    ( dpsetconstrEL1
0.59/0.76	    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
0.59/0.76	          ( ( in @ ( kpair @ Xx @ Xy )
0.59/0.76	            @ ( dpsetconstr @ A @ B
0.59/0.76	              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
0.59/0.76	         => ( in @ Xx @ A ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(dpsetconstrEL2_type,type,
0.59/0.76	    dpsetconstrEL2: $o ).
0.59/0.76	
0.59/0.76	thf(dpsetconstrEL2,definition,
0.59/0.76	    ( dpsetconstrEL2
0.59/0.76	    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
0.59/0.76	          ( ( in @ ( kpair @ Xx @ Xy )
0.59/0.76	            @ ( dpsetconstr @ A @ B
0.59/0.76	              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
0.59/0.76	         => ( in @ Xy @ B ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(dpsetconstrER_type,type,
0.59/0.76	    dpsetconstrER: $o ).
0.59/0.76	
0.59/0.76	thf(dpsetconstrER,definition,
0.59/0.76	    ( dpsetconstrER
0.59/0.76	    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
0.59/0.76	          ( ( in @ ( kpair @ Xx @ Xy )
0.59/0.76	            @ ( dpsetconstr @ A @ B
0.59/0.76	              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
0.59/0.76	         => ( Xphi @ Xx @ Xy ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(func_type,type,
0.59/0.76	    func: $i > $i > $i > $o ).
0.59/0.76	
0.59/0.76	thf(funcSet_type,type,
0.59/0.76	    funcSet: $i > $i > $i ).
0.59/0.76	
0.59/0.76	thf(funcImageSingleton_type,type,
0.59/0.76	    funcImageSingleton: $o ).
0.59/0.76	
0.59/0.76	thf(funcImageSingleton,definition,
0.59/0.76	    ( funcImageSingleton
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( func @ A @ B @ Xf )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( singleton
0.59/0.76	                @ ( dsetconstr @ B
0.59/0.76	                  @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(apProp_type,type,
0.59/0.76	    apProp: $o ).
0.59/0.76	
0.59/0.76	thf(apProp,definition,
0.59/0.76	    ( apProp
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( func @ A @ B @ Xf )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( in
0.59/0.76	                @ ( setunion
0.59/0.76	                  @ ( dsetconstr @ B
0.59/0.76	                    @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
0.59/0.76	                @ B ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(ap_type,type,
0.59/0.76	    ap: $i > $i > $i > $i > $i ).
0.59/0.76	
0.59/0.76	thf(app_type,type,
0.59/0.76	    app: $o ).
0.59/0.76	
0.59/0.76	thf(app,definition,
0.59/0.76	    ( app
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( func @ A @ B @ Xf )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(infuncsetfunc_type,type,
0.59/0.76	    infuncsetfunc: $o ).
0.59/0.76	
0.59/0.76	thf(infuncsetfunc,definition,
0.59/0.76	    ( infuncsetfunc
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( in @ Xf @ ( funcSet @ A @ B ) )
0.59/0.76	         => ( func @ A @ B @ Xf ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(ap2p_type,type,
0.59/0.76	    ap2p: $o ).
0.59/0.76	
0.59/0.76	thf(ap2p,definition,
0.59/0.76	    ( ap2p
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( in @ Xf @ ( funcSet @ A @ B ) )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(funcinfuncset_type,type,
0.59/0.76	    funcinfuncset: $o ).
0.59/0.76	
0.59/0.76	thf(funcinfuncset,definition,
0.59/0.76	    ( funcinfuncset
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( func @ A @ B @ Xf )
0.59/0.76	         => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(lamProp_type,type,
0.59/0.76	    lamProp: $o ).
0.59/0.76	
0.59/0.76	thf(lamProp,definition,
0.59/0.76	    ( lamProp
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i > $i] :
0.59/0.76	          ( ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( in @ ( Xf @ Xx ) @ B ) )
0.59/0.76	         => ( func @ A @ B
0.59/0.76	            @ ( dpsetconstr @ A @ B
0.59/0.76	              @ ^ [Xx: $i,Xy: $i] :
0.59/0.76	                  ( ( Xf @ Xx )
0.59/0.76	                  = Xy ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(lam_type,type,
0.59/0.76	    lam: $i > $i > ( $i > $i ) > $i ).
0.59/0.76	
0.59/0.76	thf(lamp_type,type,
0.59/0.76	    lamp: $o ).
0.59/0.76	
0.59/0.76	thf(lamp,definition,
0.59/0.76	    ( lamp
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i > $i] :
0.59/0.76	          ( ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( in @ ( Xf @ Xx ) @ B ) )
0.59/0.76	         => ( func @ A @ B
0.59/0.76	            @ ( lam @ A @ B
0.59/0.76	              @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(lam2p_type,type,
0.59/0.76	    lam2p: $o ).
0.59/0.76	
0.59/0.76	thf(lam2p,definition,
0.59/0.76	    ( lam2p
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i > $i] :
0.59/0.76	          ( ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( in @ ( Xf @ Xx ) @ B ) )
0.59/0.76	         => ( in
0.59/0.76	            @ ( lam @ A @ B
0.59/0.76	              @ ^ [Xx: $i] : ( Xf @ Xx ) )
0.59/0.76	            @ ( funcSet @ A @ B ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(brelnall1_type,type,
0.59/0.76	    brelnall1: $o ).
0.59/0.76	
0.59/0.76	thf(brelnall1,definition,
0.59/0.76	    ( brelnall1
0.59/0.76	    = ( ! [A: $i,B: $i,R: $i] :
0.59/0.76	          ( ( breln @ A @ B @ R )
0.59/0.76	         => ! [Xphi: $i > $o] :
0.59/0.76	              ( ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ! [Xy: $i] :
0.59/0.76	                      ( ( in @ Xy @ B )
0.59/0.76	                     => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
0.59/0.76	                       => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ R )
0.59/0.76	                 => ( Xphi @ Xx ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(brelnall2_type,type,
0.59/0.76	    brelnall2: $o ).
0.59/0.76	
0.59/0.76	thf(brelnall2,definition,
0.59/0.76	    ( brelnall2
0.59/0.76	    = ( ! [A: $i,B: $i,R: $i] :
0.59/0.76	          ( ( breln @ A @ B @ R )
0.59/0.76	         => ! [Xphi: $i > $o] :
0.59/0.76	              ( ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ! [Xy: $i] :
0.59/0.76	                      ( ( in @ Xy @ B )
0.59/0.76	                     => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
0.59/0.76	                       => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ R )
0.59/0.76	                 => ( Xphi @ Xx ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(ex1E2_type,type,
0.59/0.76	    ex1E2: $o ).
0.59/0.76	
0.59/0.76	thf(ex1E2,definition,
0.59/0.76	    ( ex1E2
0.59/0.76	    = ( ! [A: $i,Xphi: $i > $o] :
0.59/0.76	          ( ( ex1 @ A
0.59/0.76	            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ! [Xy: $i] :
0.59/0.76	                  ( ( in @ Xy @ A )
0.59/0.76	                 => ( ( Xphi @ Xx )
0.59/0.76	                   => ( ( Xphi @ Xy )
0.59/0.76	                     => ( Xx = Xy ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(funcGraphProp1_type,type,
0.59/0.76	    funcGraphProp1: $o ).
0.59/0.76	
0.59/0.76	thf(funcGraphProp1,definition,
0.59/0.76	    ( funcGraphProp1
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( func @ A @ B @ Xf )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(funcGraphProp3_type,type,
0.59/0.76	    funcGraphProp3: $o ).
0.59/0.76	
0.59/0.76	thf(funcGraphProp3,definition,
0.59/0.76	    ( funcGraphProp3
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( in @ Xf @ ( funcSet @ A @ B ) )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(funcGraphProp2_type,type,
0.59/0.76	    funcGraphProp2: $o ).
0.59/0.76	
0.59/0.76	thf(funcGraphProp2,definition,
0.59/0.76	    ( funcGraphProp2
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( func @ A @ B @ Xf )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ! [Xy: $i] :
0.59/0.76	                  ( ( in @ Xy @ B )
0.59/0.76	                 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
0.59/0.76	                   => ( ( ap @ A @ B @ Xf @ Xx )
0.59/0.76	                      = Xy ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(funcextLem_type,type,
0.59/0.76	    funcextLem: $o ).
0.59/0.76	
0.59/0.76	thf(funcextLem,definition,
0.59/0.76	    ( funcextLem
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( func @ A @ B @ Xf )
0.59/0.76	         => ! [Xg: $i] :
0.59/0.76	              ( ( func @ A @ B @ Xg )
0.59/0.76	             => ( ! [Xx: $i] :
0.59/0.76	                    ( ( in @ Xx @ A )
0.59/0.76	                   => ( ( ap @ A @ B @ Xf @ Xx )
0.59/0.76	                      = ( ap @ A @ B @ Xg @ Xx ) ) )
0.59/0.76	               => ! [Xx: $i] :
0.59/0.76	                    ( ( in @ Xx @ A )
0.59/0.76	                   => ! [Xy: $i] :
0.59/0.76	                        ( ( in @ Xy @ B )
0.59/0.76	                       => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
0.59/0.76	                         => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(funcGraphProp4_type,type,
0.59/0.76	    funcGraphProp4: $o ).
0.59/0.76	
0.59/0.76	thf(funcGraphProp4,definition,
0.59/0.76	    ( funcGraphProp4
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( in @ Xf @ ( funcSet @ A @ B ) )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ! [Xy: $i] :
0.59/0.76	                  ( ( in @ Xy @ B )
0.59/0.76	                 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
0.59/0.76	                   => ( ( ap @ A @ B @ Xf @ Xx )
0.59/0.76	                      = Xy ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(subbreln_type,type,
0.59/0.76	    subbreln: $o ).
0.59/0.76	
0.59/0.76	thf(subbreln,definition,
0.59/0.76	    ( subbreln
0.59/0.76	    = ( ! [A: $i,B: $i,R: $i] :
0.59/0.76	          ( ( breln @ A @ B @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln @ A @ B @ S )
0.59/0.76	             => ( ! [Xx: $i] :
0.59/0.76	                    ( ( in @ Xx @ A )
0.59/0.76	                   => ! [Xy: $i] :
0.59/0.76	                        ( ( in @ Xy @ B )
0.59/0.76	                       => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
0.59/0.76	                         => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
0.59/0.76	               => ( subset @ R @ S ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(eqbreln_type,type,
0.59/0.76	    eqbreln: $o ).
0.59/0.76	
0.59/0.76	thf(eqbreln,definition,
0.59/0.76	    ( eqbreln
0.59/0.76	    = ( ! [A: $i,B: $i,R: $i] :
0.59/0.76	          ( ( breln @ A @ B @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln @ A @ B @ S )
0.59/0.76	             => ( ! [Xx: $i] :
0.59/0.76	                    ( ( in @ Xx @ A )
0.59/0.76	                   => ! [Xy: $i] :
0.59/0.76	                        ( ( in @ Xy @ B )
0.59/0.76	                       => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
0.59/0.76	                         => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
0.59/0.76	               => ( ! [Xx: $i] :
0.59/0.76	                      ( ( in @ Xx @ A )
0.59/0.76	                     => ! [Xy: $i] :
0.59/0.76	                          ( ( in @ Xy @ B )
0.59/0.76	                         => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
0.59/0.76	                           => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
0.59/0.76	                 => ( R = S ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(funcext_type,type,
0.59/0.76	    funcext: $o ).
0.59/0.76	
0.59/0.76	thf(funcext,definition,
0.59/0.76	    ( funcext
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( func @ A @ B @ Xf )
0.59/0.76	         => ! [Xg: $i] :
0.59/0.76	              ( ( func @ A @ B @ Xg )
0.59/0.76	             => ( ! [Xx: $i] :
0.59/0.76	                    ( ( in @ Xx @ A )
0.59/0.76	                   => ( ( ap @ A @ B @ Xf @ Xx )
0.59/0.76	                      = ( ap @ A @ B @ Xg @ Xx ) ) )
0.59/0.76	               => ( Xf = Xg ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(funcext2_type,type,
0.59/0.76	    funcext2: $o ).
0.59/0.76	
0.59/0.76	thf(funcext2,definition,
0.59/0.76	    ( funcext2
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( in @ Xf @ ( funcSet @ A @ B ) )
0.59/0.76	         => ! [Xg: $i] :
0.59/0.76	              ( ( in @ Xg @ ( funcSet @ A @ B ) )
0.59/0.76	             => ( ! [Xx: $i] :
0.59/0.76	                    ( ( in @ Xx @ A )
0.59/0.76	                   => ( ( ap @ A @ B @ Xf @ Xx )
0.59/0.76	                      = ( ap @ A @ B @ Xg @ Xx ) ) )
0.59/0.76	               => ( Xf = Xg ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(ap2apEq1_type,type,
0.59/0.76	    ap2apEq1: $o ).
0.59/0.76	
0.59/0.76	thf(ap2apEq1,definition,
0.59/0.76	    ( ap2apEq1
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( in @ Xf @ ( funcSet @ A @ B ) )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( ( ap @ A @ B @ Xf @ Xx )
0.59/0.76	                = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(ap2apEq2_type,type,
0.59/0.76	    ap2apEq2: $o ).
0.59/0.76	
0.59/0.76	thf(ap2apEq2,definition,
0.59/0.76	    ( ap2apEq2
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( func @ A @ B @ Xf )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( ( ap @ A @ B @ Xf @ Xx )
0.59/0.76	                = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(beta1_type,type,
0.59/0.76	    beta1: $o ).
0.59/0.76	
0.59/0.76	thf(beta1,definition,
0.59/0.76	    ( beta1
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i > $i] :
0.59/0.76	          ( ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( in @ ( Xf @ Xx ) @ B ) )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( ( ap @ A @ B
0.59/0.76	                  @ ( lam @ A @ B
0.59/0.76	                    @ ^ [Xy: $i] : ( Xf @ Xy ) )
0.59/0.76	                  @ Xx )
0.59/0.76	                = ( Xf @ Xx ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(eta1_type,type,
0.59/0.76	    eta1: $o ).
0.59/0.76	
0.59/0.76	thf(eta1,definition,
0.59/0.76	    ( eta1
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( func @ A @ B @ Xf )
0.59/0.76	         => ( ( lam @ A @ B
0.59/0.76	              @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
0.59/0.76	            = Xf ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(lam2lamEq_type,type,
0.59/0.76	    lam2lamEq: $o ).
0.59/0.76	
0.59/0.76	thf(lam2lamEq,definition,
0.59/0.76	    ( lam2lamEq
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i > $i] :
0.59/0.76	          ( ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( in @ ( Xf @ Xx ) @ B ) )
0.59/0.76	         => ( ( lam @ A @ B
0.59/0.76	              @ ^ [Xx: $i] : ( Xf @ Xx ) )
0.59/0.76	            = ( lam @ A @ B
0.59/0.76	              @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(beta2_type,type,
0.59/0.76	    beta2: $o ).
0.59/0.76	
0.59/0.76	thf(beta2,definition,
0.59/0.76	    ( beta2
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i > $i] :
0.59/0.76	          ( ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( in @ ( Xf @ Xx ) @ B ) )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( ( ap @ A @ B
0.59/0.76	                  @ ( lam @ A @ B
0.59/0.76	                    @ ^ [Xy: $i] : ( Xf @ Xy ) )
0.59/0.76	                  @ Xx )
0.59/0.76	                = ( Xf @ Xx ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(eta2_type,type,
0.59/0.76	    eta2: $o ).
0.59/0.76	
0.59/0.76	thf(eta2,definition,
0.59/0.76	    ( eta2
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( in @ Xf @ ( funcSet @ A @ B ) )
0.59/0.76	         => ( ( lam @ A @ B
0.59/0.76	              @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
0.59/0.76	            = Xf ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(iffalseProp1_type,type,
0.59/0.76	    iffalseProp1: $o ).
0.59/0.76	
0.59/0.76	thf(iffalseProp1,definition,
0.59/0.76	    ( iffalseProp1
0.59/0.76	    = ( ! [A: $i,Xphi: $o,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	             => ( ~ Xphi
0.59/0.76	               => ( in @ Xy
0.59/0.76	                  @ ( dsetconstr @ A
0.59/0.76	                    @ ^ [Xz: $i] :
0.59/0.76	                        ( ( Xphi
0.59/0.76	                          & ( Xz = Xx ) )
0.59/0.76	                        | ( ~ Xphi
0.59/0.76	                          & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(iffalseProp2_type,type,
0.59/0.76	    iffalseProp2: $o ).
0.59/0.76	
0.59/0.76	thf(iffalseProp2,definition,
0.59/0.76	    ( iffalseProp2
0.59/0.76	    = ( ! [A: $i,Xphi: $o,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	             => ( ~ Xphi
0.59/0.76	               => ( ( dsetconstr @ A
0.59/0.76	                    @ ^ [Xz: $i] :
0.59/0.76	                        ( ( Xphi
0.59/0.76	                          & ( Xz = Xx ) )
0.59/0.76	                        | ( ~ Xphi
0.59/0.76	                          & ( Xz = Xy ) ) ) )
0.59/0.76	                  = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(iftrueProp1_type,type,
0.59/0.76	    iftrueProp1: $o ).
0.59/0.76	
0.59/0.76	thf(iftrueProp1,definition,
0.59/0.76	    ( iftrueProp1
0.59/0.76	    = ( ! [A: $i,Xphi: $o,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	             => ( Xphi
0.59/0.76	               => ( in @ Xx
0.59/0.76	                  @ ( dsetconstr @ A
0.59/0.76	                    @ ^ [Xz: $i] :
0.59/0.76	                        ( ( Xphi
0.59/0.76	                          & ( Xz = Xx ) )
0.59/0.76	                        | ( ~ Xphi
0.59/0.76	                          & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(iftrueProp2_type,type,
0.59/0.76	    iftrueProp2: $o ).
0.59/0.76	
0.59/0.76	thf(iftrueProp2,definition,
0.59/0.76	    ( iftrueProp2
0.59/0.76	    = ( ! [A: $i,Xphi: $o,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	             => ( Xphi
0.59/0.76	               => ( ( dsetconstr @ A
0.59/0.76	                    @ ^ [Xz: $i] :
0.59/0.76	                        ( ( Xphi
0.59/0.76	                          & ( Xz = Xx ) )
0.59/0.76	                        | ( ~ Xphi
0.59/0.76	                          & ( Xz = Xy ) ) ) )
0.59/0.76	                  = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(ifSingleton_type,type,
0.59/0.76	    ifSingleton: $o ).
0.59/0.76	
0.59/0.76	thf(ifSingleton,definition,
0.59/0.76	    ( ifSingleton
0.59/0.76	    = ( ! [A: $i,Xphi: $o,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	             => ( singleton
0.59/0.76	                @ ( dsetconstr @ A
0.59/0.76	                  @ ^ [Xz: $i] :
0.59/0.76	                      ( ( Xphi
0.59/0.76	                        & ( Xz = Xx ) )
0.59/0.76	                      | ( ~ Xphi
0.59/0.76	                        & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(if_type,type,
0.59/0.76	    if: $i > $o > $i > $i > $i ).
0.59/0.76	
0.59/0.76	thf(ifp_type,type,
0.59/0.76	    ifp: $o ).
0.59/0.76	
0.59/0.76	thf(ifp,definition,
0.59/0.76	    ( ifp
0.59/0.76	    = ( ! [A: $i,Xphi: $o,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	             => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(theeq_type,type,
0.59/0.76	    theeq: $o ).
0.59/0.76	
0.59/0.76	thf(theeq,definition,
0.59/0.76	    ( theeq
0.59/0.76	    = ( ! [X: $i] :
0.59/0.76	          ( ( singleton @ X )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ X )
0.59/0.76	             => ( ( setunion @ X )
0.59/0.76	                = Xx ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(iftrue_type,type,
0.59/0.76	    iftrue: $o ).
0.59/0.76	
0.59/0.76	thf(iftrue,definition,
0.59/0.76	    ( iftrue
0.59/0.76	    = ( ! [A: $i,Xphi: $o,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	             => ( Xphi
0.59/0.76	               => ( ( if @ A @ Xphi @ Xx @ Xy )
0.59/0.76	                  = Xx ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(iffalse_type,type,
0.59/0.76	    iffalse: $o ).
0.59/0.76	
0.59/0.76	thf(iffalse,definition,
0.59/0.76	    ( iffalse
0.59/0.76	    = ( ! [A: $i,Xphi: $o,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	             => ( ~ Xphi
0.59/0.76	               => ( ( if @ A @ Xphi @ Xx @ Xy )
0.59/0.76	                  = Xy ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(iftrueorfalse_type,type,
0.59/0.76	    iftrueorfalse: $o ).
0.59/0.76	
0.59/0.76	thf(iftrueorfalse,definition,
0.59/0.76	    ( iftrueorfalse
0.59/0.76	    = ( ! [A: $i,Xphi: $o,Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ A )
0.59/0.76	         => ! [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	             => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(binintersectT_lem_type,type,
0.59/0.76	    binintersectT_lem: $o ).
0.59/0.76	
0.59/0.76	thf(binintersectT_lem,definition,
0.59/0.76	    ( binintersectT_lem
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(binunionT_lem_type,type,
0.59/0.76	    binunionT_lem: $o ).
0.59/0.76	
0.59/0.76	thf(binunionT_lem,definition,
0.59/0.76	    ( binunionT_lem
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(powersetT_lem_type,type,
0.59/0.76	    powersetT_lem: $o ).
0.59/0.76	
0.59/0.76	thf(powersetT_lem,definition,
0.59/0.76	    ( powersetT_lem
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(setminusT_lem_type,type,
0.59/0.76	    setminusT_lem: $o ).
0.59/0.76	
0.59/0.76	thf(setminusT_lem,definition,
0.59/0.76	    ( setminusT_lem
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(complementT_lem_type,type,
0.59/0.76	    complementT_lem: $o ).
0.59/0.76	
0.59/0.76	thf(complementT_lem,definition,
0.59/0.76	    ( complementT_lem
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(setextT_type,type,
0.59/0.76	    setextT: $o ).
0.59/0.76	
0.59/0.76	thf(setextT,definition,
0.59/0.76	    ( setextT
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( ! [Xx: $i] :
0.59/0.76	                    ( ( in @ Xx @ A )
0.59/0.76	                   => ( ( in @ Xx @ X )
0.59/0.76	                     => ( in @ Xx @ Y ) ) )
0.59/0.76	               => ( ! [Xx: $i] :
0.59/0.76	                      ( ( in @ Xx @ A )
0.59/0.76	                     => ( ( in @ Xx @ Y )
0.59/0.76	                       => ( in @ Xx @ X ) ) )
0.59/0.76	                 => ( X = Y ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(subsetTI_type,type,
0.59/0.76	    subsetTI: $o ).
0.59/0.76	
0.59/0.76	thf(subsetTI,definition,
0.59/0.76	    ( subsetTI
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( ! [Xx: $i] :
0.59/0.76	                    ( ( in @ Xx @ A )
0.59/0.76	                   => ( ( in @ Xx @ X )
0.59/0.76	                     => ( in @ Xx @ Y ) ) )
0.59/0.76	               => ( subset @ X @ Y ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(powersetTI1_type,type,
0.59/0.76	    powersetTI1: $o ).
0.59/0.76	
0.59/0.76	thf(powersetTI1,definition,
0.59/0.76	    ( powersetTI1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( ! [Xx: $i] :
0.59/0.76	                    ( ( in @ Xx @ A )
0.59/0.76	                   => ( ( in @ Xx @ X )
0.59/0.76	                     => ( in @ Xx @ Y ) ) )
0.59/0.76	               => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(powersetTE1_type,type,
0.59/0.76	    powersetTE1: $o ).
0.59/0.76	
0.59/0.76	thf(powersetTE1,definition,
0.59/0.76	    ( powersetTE1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( in @ X @ ( powerset @ Y ) )
0.59/0.76	                   => ( ( in @ Xx @ X )
0.59/0.76	                     => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(complementTI1_type,type,
0.59/0.76	    complementTI1: $o ).
0.59/0.76	
0.59/0.76	thf(complementTI1,definition,
0.59/0.76	    ( complementTI1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( ( in @ Xx @ X )
0.59/0.76	               => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(complementTE1_type,type,
0.59/0.76	    complementTE1: $o ).
0.59/0.76	
0.59/0.76	thf(complementTE1,definition,
0.59/0.76	    ( complementTE1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
0.59/0.76	               => ( in @ Xx @ X ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(binintersectTELcontra_type,type,
0.59/0.76	    binintersectTELcontra: $o ).
0.59/0.76	
0.59/0.76	thf(binintersectTELcontra,definition,
0.59/0.76	    ( binintersectTELcontra
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ~ ( in @ Xx @ X )
0.59/0.76	                   => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(binintersectTERcontra_type,type,
0.59/0.76	    binintersectTERcontra: $o ).
0.59/0.76	
0.59/0.76	thf(binintersectTERcontra,definition,
0.59/0.76	    ( binintersectTERcontra
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ~ ( in @ Xx @ Y )
0.59/0.76	                   => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(contrasubsetT_type,type,
0.59/0.76	    contrasubsetT: $o ).
0.59/0.76	
0.59/0.76	thf(contrasubsetT,definition,
0.59/0.76	    ( contrasubsetT
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( subset @ X @ ( setminus @ A @ Y ) )
0.59/0.76	                   => ( ( in @ Xx @ Y )
0.59/0.76	                     => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(contrasubsetT1_type,type,
0.59/0.76	    contrasubsetT1: $o ).
0.59/0.76	
0.59/0.76	thf(contrasubsetT1,definition,
0.59/0.76	    ( contrasubsetT1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( subset @ X @ Y )
0.59/0.76	                   => ( ~ ( in @ Xx @ Y )
0.59/0.76	                     => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(contrasubsetT2_type,type,
0.59/0.76	    contrasubsetT2: $o ).
0.59/0.76	
0.59/0.76	thf(contrasubsetT2,definition,
0.59/0.76	    ( contrasubsetT2
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( ( subset @ X @ Y )
0.59/0.76	               => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(contrasubsetT3_type,type,
0.59/0.76	    contrasubsetT3: $o ).
0.59/0.76	
0.59/0.76	thf(contrasubsetT3,definition,
0.59/0.76	    ( contrasubsetT3
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
0.59/0.76	               => ( subset @ X @ Y ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(doubleComplementI1_type,type,
0.59/0.76	    doubleComplementI1: $o ).
0.59/0.76	
0.59/0.76	thf(doubleComplementI1,definition,
0.59/0.76	    ( doubleComplementI1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( ( in @ Xx @ X )
0.59/0.76	               => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(doubleComplementE1_type,type,
0.59/0.76	    doubleComplementE1: $o ).
0.59/0.76	
0.59/0.76	thf(doubleComplementE1,definition,
0.59/0.76	    ( doubleComplementE1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
0.59/0.76	               => ( in @ Xx @ X ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(doubleComplementSub1_type,type,
0.59/0.76	    doubleComplementSub1: $o ).
0.59/0.76	
0.59/0.76	thf(doubleComplementSub1,definition,
0.59/0.76	    ( doubleComplementSub1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(doubleComplementSub2_type,type,
0.59/0.76	    doubleComplementSub2: $o ).
0.59/0.76	
0.59/0.76	thf(doubleComplementSub2,definition,
0.59/0.76	    ( doubleComplementSub2
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(doubleComplementEq_type,type,
0.59/0.76	    doubleComplementEq: $o ).
0.59/0.76	
0.59/0.76	thf(doubleComplementEq,definition,
0.59/0.76	    ( doubleComplementEq
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ( X
0.59/0.76	            = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(complementTnotintersectT_type,type,
0.59/0.76	    complementTnotintersectT: $o ).
0.59/0.76	
0.59/0.76	thf(complementTnotintersectT,definition,
0.59/0.76	    ( complementTnotintersectT
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( in @ Xx @ ( setminus @ A @ X ) )
0.59/0.76	                   => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(complementImpComplementIntersect_type,type,
0.59/0.76	    complementImpComplementIntersect: $o ).
0.59/0.76	
0.59/0.76	thf(complementImpComplementIntersect,definition,
0.59/0.76	    ( complementImpComplementIntersect
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( in @ Xx @ ( setminus @ A @ X ) )
0.59/0.76	                   => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(complementSubsetComplementIntersect_type,type,
0.59/0.76	    complementSubsetComplementIntersect: $o ).
0.59/0.76	
0.59/0.76	thf(complementSubsetComplementIntersect,definition,
0.59/0.76	    ( complementSubsetComplementIntersect
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(complementInPowersetComplementIntersect_type,type,
0.59/0.76	    complementInPowersetComplementIntersect: $o ).
0.59/0.76	
0.59/0.76	thf(complementInPowersetComplementIntersect,definition,
0.59/0.76	    ( complementInPowersetComplementIntersect
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(contraSubsetComplement_type,type,
0.59/0.76	    contraSubsetComplement: $o ).
0.59/0.76	
0.59/0.76	thf(contraSubsetComplement,definition,
0.59/0.76	    ( contraSubsetComplement
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( ( subset @ X @ ( setminus @ A @ Y ) )
0.59/0.76	               => ! [Xx: $i] :
0.59/0.76	                    ( ( in @ Xx @ A )
0.59/0.76	                   => ( ( in @ Xx @ Y )
0.59/0.76	                     => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(complementTcontraSubset_type,type,
0.59/0.76	    complementTcontraSubset: $o ).
0.59/0.76	
0.59/0.76	thf(complementTcontraSubset,definition,
0.59/0.76	    ( complementTcontraSubset
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( ( subset @ X @ ( setminus @ A @ Y ) )
0.59/0.76	               => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(binunionTILcontra_type,type,
0.59/0.76	    binunionTILcontra: $o ).
0.59/0.76	
0.59/0.76	thf(binunionTILcontra,definition,
0.59/0.76	    ( binunionTILcontra
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
0.59/0.76	                   => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(binunionTIRcontra_type,type,
0.59/0.76	    binunionTIRcontra: $o ).
0.59/0.76	
0.59/0.76	thf(binunionTIRcontra,definition,
0.59/0.76	    ( binunionTIRcontra
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
0.59/0.76	                   => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(inIntersectImpInUnion_type,type,
0.59/0.76	    inIntersectImpInUnion: $o ).
0.59/0.76	
0.59/0.76	thf(inIntersectImpInUnion,definition,
0.59/0.76	    ( inIntersectImpInUnion
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Z: $i] :
0.59/0.76	                  ( ( in @ Z @ ( powerset @ A ) )
0.59/0.76	                 => ! [Xx: $i] :
0.59/0.76	                      ( ( in @ Xx @ A )
0.59/0.76	                     => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
0.59/0.76	                       => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(inIntersectImpInUnion2_type,type,
0.59/0.76	    inIntersectImpInUnion2: $o ).
0.59/0.76	
0.59/0.76	thf(inIntersectImpInUnion2,definition,
0.59/0.76	    ( inIntersectImpInUnion2
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Z: $i] :
0.59/0.76	                  ( ( in @ Z @ ( powerset @ A ) )
0.59/0.76	                 => ! [Xx: $i] :
0.59/0.76	                      ( ( in @ Xx @ A )
0.59/0.76	                     => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
0.59/0.76	                       => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(inIntersectImpInIntersectUnions_type,type,
0.59/0.76	    inIntersectImpInIntersectUnions: $o ).
0.59/0.76	
0.59/0.76	thf(inIntersectImpInIntersectUnions,definition,
0.59/0.76	    ( inIntersectImpInIntersectUnions
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Z: $i] :
0.59/0.76	                  ( ( in @ Z @ ( powerset @ A ) )
0.59/0.76	                 => ! [Xx: $i] :
0.59/0.76	                      ( ( in @ Xx @ A )
0.59/0.76	                     => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
0.59/0.76	                       => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(intersectInPowersetIntersectUnions_type,type,
0.59/0.76	    intersectInPowersetIntersectUnions: $o ).
0.59/0.76	
0.59/0.76	thf(intersectInPowersetIntersectUnions,definition,
0.59/0.76	    ( intersectInPowersetIntersectUnions
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Z: $i] :
0.59/0.76	                  ( ( in @ Z @ ( powerset @ A ) )
0.59/0.76	                 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(inComplementUnionImpNotIn1_type,type,
0.59/0.76	    inComplementUnionImpNotIn1: $o ).
0.59/0.76	
0.59/0.76	thf(inComplementUnionImpNotIn1,definition,
0.59/0.76	    ( inComplementUnionImpNotIn1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
0.59/0.76	                   => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(inComplementUnionImpInComplement1_type,type,
0.59/0.76	    inComplementUnionImpInComplement1: $o ).
0.59/0.76	
0.59/0.76	thf(inComplementUnionImpInComplement1,definition,
0.59/0.76	    ( inComplementUnionImpInComplement1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
0.59/0.76	                   => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(binunionTE_type,type,
0.59/0.76	    binunionTE: $o ).
0.59/0.76	
0.59/0.76	thf(binunionTE,definition,
0.59/0.76	    ( binunionTE
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xphi: $o,Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
0.59/0.76	                   => ( ( ( in @ Xx @ X )
0.59/0.76	                       => Xphi )
0.59/0.76	                     => ( ( ( in @ Xx @ Y )
0.59/0.76	                         => Xphi )
0.59/0.76	                       => Xphi ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(binunionTEcontra_type,type,
0.59/0.76	    binunionTEcontra: $o ).
0.59/0.76	
0.59/0.76	thf(binunionTEcontra,definition,
0.59/0.76	    ( binunionTEcontra
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ~ ( in @ Xx @ X )
0.59/0.76	                   => ( ~ ( in @ Xx @ Y )
0.59/0.76	                     => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(demorgan2a1_type,type,
0.59/0.76	    demorgan2a1: $o ).
0.59/0.76	
0.59/0.76	thf(demorgan2a1,definition,
0.59/0.76	    ( demorgan2a1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
0.59/0.76	                   => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(complementUnionInPowersetComplement_type,type,
0.59/0.76	    complementUnionInPowersetComplement: $o ).
0.59/0.76	
0.59/0.76	thf(complementUnionInPowersetComplement,definition,
0.59/0.76	    ( complementUnionInPowersetComplement
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(demorgan2a2_type,type,
0.59/0.76	    demorgan2a2: $o ).
0.59/0.76	
0.59/0.76	thf(demorgan2a2,definition,
0.59/0.76	    ( demorgan2a2
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
0.59/0.76	                   => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(demorgan1a_type,type,
0.59/0.76	    demorgan1a: $o ).
0.59/0.76	
0.59/0.76	thf(demorgan1a,definition,
0.59/0.76	    ( demorgan1a
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
0.59/0.76	                   => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(demorgan1b_type,type,
0.59/0.76	    demorgan1b: $o ).
0.59/0.76	
0.59/0.76	thf(demorgan1b,definition,
0.59/0.76	    ( demorgan1b
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
0.59/0.76	                   => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(demorgan1_type,type,
0.59/0.76	    demorgan1: $o ).
0.59/0.76	
0.59/0.76	thf(demorgan1,definition,
0.59/0.76	    ( demorgan1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
0.59/0.76	                = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(demorgan2a_type,type,
0.59/0.76	    demorgan2a: $o ).
0.59/0.76	
0.59/0.76	thf(demorgan2a,definition,
0.59/0.76	    ( demorgan2a
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
0.59/0.76	                   => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(demorgan2b2_type,type,
0.59/0.76	    demorgan2b2: $o ).
0.59/0.76	
0.59/0.76	thf(demorgan2b2,definition,
0.59/0.76	    ( demorgan2b2
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( in @ Xx @ ( setminus @ A @ X ) )
0.59/0.76	                   => ( ( in @ Xx @ ( setminus @ A @ Y ) )
0.59/0.76	                     => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(demorgan2b_type,type,
0.59/0.76	    demorgan2b: $o ).
0.59/0.76	
0.59/0.76	thf(demorgan2b,definition,
0.59/0.76	    ( demorgan2b
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
0.59/0.76	                   => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(demorgan2_type,type,
0.59/0.76	    demorgan2: $o ).
0.59/0.76	
0.59/0.76	thf(demorgan2,definition,
0.59/0.76	    ( demorgan2
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( ( setminus @ A @ ( binunion @ X @ Y ) )
0.59/0.76	                = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz13rule0_type,type,
0.59/0.76	    woz13rule0: $o ).
0.59/0.76	
0.59/0.76	thf(woz13rule0,definition,
0.59/0.76	    ( woz13rule0
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ ( binintersect @ X @ Y ) )
0.59/0.76	                 => ( in @ Xx @ A ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz13rule1_type,type,
0.59/0.76	    woz13rule1: $o ).
0.59/0.76	
0.59/0.76	thf(woz13rule1,definition,
0.59/0.76	    ( woz13rule1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Z: $i] :
0.59/0.76	                  ( ( in @ Z @ ( powerset @ A ) )
0.59/0.76	                 => ( ( subset @ X @ Z )
0.59/0.76	                   => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz13rule2_type,type,
0.59/0.76	    woz13rule2: $o ).
0.59/0.76	
0.59/0.76	thf(woz13rule2,definition,
0.59/0.76	    ( woz13rule2
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Z: $i] :
0.59/0.76	                  ( ( in @ Z @ ( powerset @ A ) )
0.59/0.76	                 => ( ( subset @ Y @ Z )
0.59/0.76	                   => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz13rule3_type,type,
0.59/0.76	    woz13rule3: $o ).
0.59/0.76	
0.59/0.76	thf(woz13rule3,definition,
0.59/0.76	    ( woz13rule3
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Z: $i] :
0.59/0.76	                  ( ( in @ Z @ ( powerset @ A ) )
0.59/0.76	                 => ( ( subset @ X @ Y )
0.59/0.76	                   => ( ( subset @ X @ Z )
0.59/0.76	                     => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz13rule4_type,type,
0.59/0.76	    woz13rule4: $o ).
0.59/0.76	
0.59/0.76	thf(woz13rule4,definition,
0.59/0.76	    ( woz13rule4
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Z: $i] :
0.59/0.76	                  ( ( in @ Z @ ( powerset @ A ) )
0.59/0.76	                 => ! [W: $i] :
0.59/0.76	                      ( ( in @ W @ ( powerset @ A ) )
0.59/0.76	                     => ( ( subset @ X @ Z )
0.59/0.76	                       => ( ( subset @ Y @ W )
0.59/0.76	                         => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz1_1_type,type,
0.59/0.76	    woz1_1: $o ).
0.59/0.76	
0.59/0.76	thf(woz1_1,definition,
0.59/0.76	    ( woz1_1
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz1_2_type,type,
0.59/0.76	    woz1_2: $o ).
0.59/0.76	
0.59/0.76	thf(woz1_2,definition,
0.59/0.76	    ( woz1_2
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Z: $i] :
0.59/0.76	                  ( ( in @ Z @ ( powerset @ A ) )
0.59/0.76	                 => ! [W: $i] :
0.59/0.76	                      ( ( in @ W @ ( powerset @ A ) )
0.59/0.76	                     => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
0.59/0.76	                        = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz1_3_type,type,
0.59/0.76	    woz1_3: $o ).
0.59/0.76	
0.59/0.76	thf(woz1_3,definition,
0.59/0.76	    ( woz1_3
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ! [Z: $i] :
0.59/0.76	                  ( ( in @ Z @ ( powerset @ A ) )
0.59/0.76	                 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz1_4_type,type,
0.59/0.76	    woz1_4: $o ).
0.59/0.76	
0.59/0.76	thf(woz1_4,definition,
0.59/0.76	    ( woz1_4
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( ( subset @ X @ ( setminus @ A @ Y ) )
0.59/0.76	               => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz1_5_type,type,
0.59/0.76	    woz1_5: $o ).
0.59/0.76	
0.59/0.76	thf(woz1_5,definition,
0.59/0.76	    ( woz1_5
0.59/0.76	    = ( ! [A: $i,X: $i] :
0.59/0.76	          ( ( in @ X @ ( powerset @ A ) )
0.59/0.76	         => ! [Y: $i] :
0.59/0.76	              ( ( in @ Y @ ( powerset @ A ) )
0.59/0.76	             => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1_type,type,
0.59/0.76	    breln1: $i > $i > $o ).
0.59/0.76	
0.59/0.76	thf(breln1all2_type,type,
0.59/0.76	    breln1all2: $o ).
0.59/0.76	
0.59/0.76	thf(breln1all2,definition,
0.59/0.76	    ( breln1all2
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [Xphi: $i > $o] :
0.59/0.76	              ( ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ! [Xy: $i] :
0.59/0.76	                      ( ( in @ Xy @ A )
0.59/0.76	                     => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
0.59/0.76	                       => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ R )
0.59/0.76	                 => ( Xphi @ Xx ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1Set_type,type,
0.59/0.76	    breln1Set: $i > $i ).
0.59/0.76	
0.59/0.76	thf(breln1SetBreln1_type,type,
0.59/0.76	    breln1SetBreln1: $o ).
0.59/0.76	
0.59/0.76	thf(breln1SetBreln1,definition,
0.59/0.76	    ( breln1SetBreln1
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( in @ R @ ( breln1Set @ A ) )
0.59/0.76	         => ( breln1 @ A @ R ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(transitive_type,type,
0.59/0.76	    transitive: $i > $i > $o ).
0.59/0.76	
0.59/0.76	thf(antisymmetric_type,type,
0.59/0.76	    antisymmetric: $i > $i > $o ).
0.59/0.76	
0.59/0.76	thf(reflexive_type,type,
0.59/0.76	    reflexive: $i > $i > $o ).
0.59/0.76	
0.59/0.76	thf(refltransitive_type,type,
0.59/0.76	    refltransitive: $i > $i > $o ).
0.59/0.76	
0.59/0.76	thf(refllinearorder_type,type,
0.59/0.76	    refllinearorder: $i > $i > $o ).
0.59/0.76	
0.59/0.76	thf(reflwellordering_type,type,
0.59/0.76	    reflwellordering: $i > $i > $o ).
0.59/0.76	
0.59/0.76	thf(choice2fnsingleton_type,type,
0.59/0.76	    choice2fnsingleton: $o ).
0.59/0.76	
0.59/0.76	thf(choice2fnsingleton,definition,
0.59/0.76	    ( choice2fnsingleton
0.59/0.76	    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
0.59/0.76	          ( ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ? [Xy: $i] :
0.59/0.76	                  ( ( in @ Xy @ B )
0.59/0.76	                  & ( Xphi @ Xx @ Xy ) ) )
0.59/0.76	         => ! [R: $i] :
0.59/0.76	              ( ( in @ R @ ( breln1Set @ B ) )
0.59/0.76	             => ( ( reflwellordering @ B @ R )
0.59/0.76	               => ! [Xx: $i] :
0.59/0.76	                    ( ( in @ Xx @ A )
0.59/0.76	                   => ( singleton
0.59/0.76	                      @ ( dsetconstr @ B
0.59/0.76	                        @ ^ [Xy: $i] :
0.59/0.76	                            ( ( Xphi @ Xx @ Xy )
0.59/0.76	                            & ! [Xz: $i] :
0.59/0.76	                                ( ( in @ Xz @ B )
0.59/0.76	                               => ( ( Xphi @ Xx @ Xz )
0.59/0.76	                                 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(setOfPairsIsBReln1_type,type,
0.59/0.76	    setOfPairsIsBReln1: $o ).
0.59/0.76	
0.59/0.76	thf(setOfPairsIsBReln1,definition,
0.59/0.76	    ( setOfPairsIsBReln1
0.59/0.76	    = ( ! [A: $i,Xphi: $i > $i > $o] :
0.59/0.76	          ( breln1 @ A
0.59/0.76	          @ ( dpsetconstr @ A @ A
0.59/0.76	            @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1all1_type,type,
0.59/0.76	    breln1all1: $o ).
0.59/0.76	
0.59/0.76	thf(breln1all1,definition,
0.59/0.76	    ( breln1all1
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [Xphi: $i > $o] :
0.59/0.76	              ( ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ! [Xy: $i] :
0.59/0.76	                      ( ( in @ Xy @ A )
0.59/0.76	                     => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
0.59/0.76	                       => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ R )
0.59/0.76	                 => ( Xphi @ Xx ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(subbreln1_type,type,
0.59/0.76	    subbreln1: $o ).
0.59/0.76	
0.59/0.76	thf(subbreln1,definition,
0.59/0.76	    ( subbreln1
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ( ! [Xx: $i] :
0.59/0.76	                    ( ( in @ Xx @ A )
0.59/0.76	                   => ! [Xy: $i] :
0.59/0.76	                        ( ( in @ Xy @ A )
0.59/0.76	                       => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
0.59/0.76	                         => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
0.59/0.76	               => ( subset @ R @ S ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(eqbreln1_type,type,
0.59/0.76	    eqbreln1: $o ).
0.59/0.76	
0.59/0.76	thf(eqbreln1,definition,
0.59/0.76	    ( eqbreln1
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ( ! [Xx: $i] :
0.59/0.76	                    ( ( in @ Xx @ A )
0.59/0.76	                   => ! [Xy: $i] :
0.59/0.76	                        ( ( in @ Xy @ A )
0.59/0.76	                       => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
0.59/0.76	                         => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
0.59/0.76	               => ( ! [Xx: $i] :
0.59/0.76	                      ( ( in @ Xx @ A )
0.59/0.76	                     => ! [Xy: $i] :
0.59/0.76	                          ( ( in @ Xy @ A )
0.59/0.76	                         => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
0.59/0.76	                           => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
0.59/0.76	                 => ( R = S ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1invset_type,type,
0.59/0.76	    breln1invset: $i > $i > $i ).
0.59/0.76	
0.59/0.76	thf(breln1invprop_type,type,
0.59/0.76	    breln1invprop: $o ).
0.59/0.76	
0.59/0.76	thf(breln1invprop,definition,
0.59/0.76	    ( breln1invprop
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1invI_type,type,
0.59/0.76	    breln1invI: $o ).
0.59/0.76	
0.59/0.76	thf(breln1invI,definition,
0.59/0.76	    ( breln1invI
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ! [Xy: $i] :
0.59/0.76	                  ( ( in @ Xy @ A )
0.59/0.76	                 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
0.59/0.76	                   => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1invE_type,type,
0.59/0.76	    breln1invE: $o ).
0.59/0.76	
0.59/0.76	thf(breln1invE,definition,
0.59/0.76	    ( breln1invE
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ A )
0.59/0.76	             => ! [Xy: $i] :
0.59/0.76	                  ( ( in @ Xy @ A )
0.59/0.76	                 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
0.59/0.76	                   => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1compset_type,type,
0.59/0.76	    breln1compset: $i > $i > $i > $i ).
0.59/0.76	
0.59/0.76	thf(breln1compprop_type,type,
0.59/0.76	    breln1compprop: $o ).
0.59/0.76	
0.59/0.76	thf(breln1compprop,definition,
0.59/0.76	    ( breln1compprop
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1compI_type,type,
0.59/0.76	    breln1compI: $o ).
0.59/0.76	
0.59/0.76	thf(breln1compI,definition,
0.59/0.76	    ( breln1compI
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ! [Xy: $i] :
0.59/0.76	                      ( ( in @ Xy @ A )
0.59/0.76	                     => ! [Xz: $i] :
0.59/0.76	                          ( ( in @ Xz @ A )
0.59/0.76	                         => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
0.59/0.76	                           => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
0.59/0.76	                             => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1compE_type,type,
0.59/0.76	    breln1compE: $o ).
0.59/0.76	
0.59/0.76	thf(breln1compE,definition,
0.59/0.76	    ( breln1compE
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ! [Xy: $i] :
0.59/0.76	                      ( ( in @ Xy @ A )
0.59/0.76	                     => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
0.59/0.76	                       => ? [Xz: $i] :
0.59/0.76	                            ( ( in @ Xz @ A )
0.59/0.76	                            & ( in @ ( kpair @ Xx @ Xz ) @ R )
0.59/0.76	                            & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1compEex_type,type,
0.59/0.76	    breln1compEex: $o ).
0.59/0.76	
0.59/0.76	thf(breln1compEex,definition,
0.59/0.76	    ( breln1compEex
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ! [Xy: $i] :
0.59/0.76	                      ( ( in @ Xy @ A )
0.59/0.76	                     => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
0.59/0.76	                       => ! [Xphi: $o] :
0.59/0.76	                            ( ! [Xz: $i] :
0.59/0.76	                                ( ( in @ Xz @ A )
0.59/0.76	                               => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
0.59/0.76	                                 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
0.59/0.76	                                   => Xphi ) ) )
0.59/0.76	                           => Xphi ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1unionprop_type,type,
0.59/0.76	    breln1unionprop: $o ).
0.59/0.76	
0.59/0.76	thf(breln1unionprop,definition,
0.59/0.76	    ( breln1unionprop
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1unionIL_type,type,
0.59/0.76	    breln1unionIL: $o ).
0.59/0.76	
0.59/0.76	thf(breln1unionIL,definition,
0.59/0.76	    ( breln1unionIL
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ! [Xy: $i] :
0.59/0.76	                      ( ( in @ Xy @ A )
0.59/0.76	                     => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
0.59/0.76	                       => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1unionIR_type,type,
0.59/0.76	    breln1unionIR: $o ).
0.59/0.76	
0.59/0.76	thf(breln1unionIR,definition,
0.59/0.76	    ( breln1unionIR
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ! [Xy: $i] :
0.59/0.76	                      ( ( in @ Xy @ A )
0.59/0.76	                     => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
0.59/0.76	                       => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1unionI_type,type,
0.59/0.76	    breln1unionI: $o ).
0.59/0.76	
0.59/0.76	thf(breln1unionI,definition,
0.59/0.76	    ( breln1unionI
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ! [Xy: $i] :
0.59/0.76	                      ( ( in @ Xy @ A )
0.59/0.76	                     => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
0.59/0.76	                          | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
0.59/0.76	                       => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1unionE_type,type,
0.59/0.76	    breln1unionE: $o ).
0.59/0.76	
0.59/0.76	thf(breln1unionE,definition,
0.59/0.76	    ( breln1unionE
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ! [Xy: $i] :
0.59/0.76	                      ( ( in @ Xy @ A )
0.59/0.76	                     => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
0.59/0.76	                       => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
0.59/0.76	                          | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1unionEcases_type,type,
0.59/0.76	    breln1unionEcases: $o ).
0.59/0.76	
0.59/0.76	thf(breln1unionEcases,definition,
0.59/0.76	    ( breln1unionEcases
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ! [Xx: $i] :
0.59/0.76	                  ( ( in @ Xx @ A )
0.59/0.76	                 => ! [Xy: $i] :
0.59/0.76	                      ( ( in @ Xy @ A )
0.59/0.76	                     => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
0.59/0.76	                       => ! [Xphi: $o] :
0.59/0.76	                            ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
0.59/0.76	                             => Xphi )
0.59/0.76	                           => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
0.59/0.76	                               => Xphi )
0.59/0.76	                             => Xphi ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(breln1unionCommutes_type,type,
0.59/0.76	    breln1unionCommutes: $o ).
0.59/0.76	
0.59/0.76	thf(breln1unionCommutes,definition,
0.59/0.76	    ( breln1unionCommutes
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ( ( binunion @ R @ S )
0.59/0.76	                = ( binunion @ S @ R ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz2Ex_type,type,
0.59/0.76	    woz2Ex: $o ).
0.59/0.76	
0.59/0.76	thf(woz2Ex,definition,
0.59/0.76	    ( woz2Ex
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ( R
0.59/0.76	            = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz2W_type,type,
0.59/0.76	    woz2W: $o ).
0.59/0.76	
0.59/0.76	thf(woz2W,definition,
0.59/0.76	    ( woz2W
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
0.59/0.76	                = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz2A_type,type,
0.59/0.76	    woz2A: $o ).
0.59/0.76	
0.59/0.76	thf(woz2A,definition,
0.59/0.76	    ( woz2A
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ! [T: $i] :
0.59/0.76	                  ( ( breln1 @ A @ T )
0.59/0.76	                 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
0.59/0.76	                    = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(woz2B_type,type,
0.59/0.76	    woz2B: $o ).
0.59/0.76	
0.59/0.76	thf(woz2B,definition,
0.59/0.76	    ( woz2B
0.59/0.76	    = ( ! [A: $i,R: $i] :
0.59/0.76	          ( ( breln1 @ A @ R )
0.59/0.76	         => ! [S: $i] :
0.59/0.76	              ( ( breln1 @ A @ S )
0.59/0.76	             => ! [T: $i] :
0.59/0.76	                  ( ( breln1 @ A @ T )
0.59/0.76	                 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
0.59/0.76	                    = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(image1Ex_type,type,
0.59/0.76	    image1Ex: $o ).
0.59/0.76	
0.59/0.76	thf(image1Ex,definition,
0.59/0.76	    ( image1Ex
0.59/0.76	    = ( ! [A: $i,Xf: $i > $i] :
0.59/0.76	        ? [B: $i] :
0.59/0.76	        ! [Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ B )
0.59/0.76	        <=> ? [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	              & ( Xx
0.59/0.76	                = ( Xf @ Xy ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(image1Ex1_type,type,
0.59/0.76	    image1Ex1: $o ).
0.59/0.76	
0.59/0.76	thf(image1Ex1,definition,
0.59/0.76	    ( image1Ex1
0.59/0.76	    = ( ! [A: $i,Xf: $i > $i] :
0.59/0.76	          ( exu
0.59/0.76	          @ ^ [B: $i] :
0.59/0.76	            ! [Xx: $i] :
0.59/0.76	              ( ( in @ Xx @ B )
0.59/0.76	            <=> ? [Xy: $i] :
0.59/0.76	                  ( ( in @ Xy @ A )
0.59/0.76	                  & ( Xx
0.59/0.76	                    = ( Xf @ Xy ) ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(image1_type,type,
0.59/0.76	    image1: $i > ( $i > $i ) > $i ).
0.59/0.76	
0.59/0.76	thf(image1Equiv_type,type,
0.59/0.76	    image1Equiv: $o ).
0.59/0.76	
0.59/0.76	thf(image1Equiv,definition,
0.59/0.76	    ( image1Equiv
0.59/0.76	    = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
0.59/0.76	          ( ( in @ Xx
0.59/0.76	            @ ( image1 @ A
0.59/0.76	              @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
0.59/0.76	        <=> ? [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	              & ( Xx
0.59/0.76	                = ( Xf @ Xy ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(image1E_type,type,
0.59/0.76	    image1E: $o ).
0.59/0.76	
0.59/0.76	thf(image1E,definition,
0.59/0.76	    ( image1E
0.59/0.76	    = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
0.59/0.76	          ( ( in @ Xx
0.59/0.76	            @ ( image1 @ A
0.59/0.76	              @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
0.59/0.76	         => ? [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	              & ( Xx
0.59/0.76	                = ( Xf @ Xy ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(image1I_type,type,
0.59/0.76	    image1I: $o ).
0.59/0.76	
0.59/0.76	thf(image1I,definition,
0.59/0.76	    ( image1I
0.59/0.76	    = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
0.59/0.76	          ( ? [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	              & ( Xx
0.59/0.76	                = ( Xf @ Xy ) ) )
0.59/0.76	         => ( in @ Xx
0.59/0.76	            @ ( image1 @ A
0.59/0.76	              @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(injective_type,type,
0.59/0.76	    injective: $i > $i > $i > $o ).
0.59/0.76	
0.59/0.76	thf(injFuncSet_type,type,
0.59/0.76	    injFuncSet: $i > $i > $i ).
0.59/0.76	
0.59/0.76	thf(injFuncInInjFuncSet_type,type,
0.59/0.76	    injFuncInInjFuncSet: $o ).
0.59/0.76	
0.59/0.76	thf(injFuncInInjFuncSet,definition,
0.59/0.76	    ( injFuncInInjFuncSet
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( in @ Xf @ ( funcSet @ A @ B ) )
0.59/0.76	         => ( ( injective @ A @ B @ Xf )
0.59/0.76	           => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(injFuncSetFuncIn_type,type,
0.59/0.76	    injFuncSetFuncIn: $o ).
0.59/0.76	
0.59/0.76	thf(injFuncSetFuncIn,definition,
0.59/0.76	    ( injFuncSetFuncIn
0.59/0.76	    = ( ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	          ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
0.59/0.76	         => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(injFuncSetFuncInj_type,type,
0.59/0.76	    injFuncSetFuncInj: $o ).
0.59/0.76	
0.59/0.76	thf(injFuncSetFuncInj,definition,
0.59/0.76	    ( injFuncSetFuncInj
0.59/0.76	    = ( ! [Xx: $i,Xy: $i,Xf: $i] :
0.59/0.76	          ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
0.59/0.76	         => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(surjective_type,type,
0.59/0.76	    surjective: $i > $i > $i > $o ).
0.59/0.76	
0.59/0.76	thf(surjective,definition,
0.59/0.76	    ( surjective
0.59/0.76	    = ( ^ [A: $i,B: $i,Xf: $i] :
0.59/0.76	        ! [Xx: $i] :
0.59/0.76	          ( ( in @ Xx @ B )
0.59/0.76	         => ? [Xy: $i] :
0.59/0.76	              ( ( in @ Xy @ A )
0.59/0.76	              & ( ( ap @ A @ B @ Xf @ Xy )
0.59/0.76	                = Xx ) ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(surjFuncSet_type,type,
0.59/0.76	    surjFuncSet: $i > $i > $i ).
0.59/0.76	
0.59/0.76	thf(surjFuncSet,definition,
0.59/0.76	    ( surjFuncSet
0.59/0.76	    = ( ^ [A: $i,B: $i] :
0.59/0.76	          ( dsetconstr @ ( funcSet @ A @ B )
0.59/0.76	          @ ^ [Xf: $i] : ( surjective @ A @ B @ Xf ) ) ) ) ).
0.59/0.76	
0.59/0.76	thf(surjFuncSetFuncIn,conjecture,
0.59/0.76	    ( setextAx
0.59/0.76	   => ( ( setadjoinAx
0.59/0.76	       => ( powersetAx
0.59/0.76	         => ( ( omega0Ax
0.59/0.76	             => ( omegaSAx
0.59/0.76	               => ( omegaIndAx
0.59/0.76	                 => ( ( foundationAx
0.59/0.76	                     => ( ( ( ( dsetconstrEL
0.59/0.76	                             => ( ( ( ( emptysetE
0.59/0.76	                                     => ( emptysetimpfalse
0.59/0.76	                                       => ( ( ( setext
0.59/0.76	                                             => ( emptyI
0.59/0.76	                                               => ( noeltsimpempty
0.59/0.76	                                                 => ( setbeta
0.59/0.76	                                                   => ( ( ( ( setadjoinIL
0.59/0.76	                                                           => ( emptyinunitempty
0.59/0.76	                                                             => ( setadjoinIR
0.59/0.76	                                                               => ( setadjoinE
0.59/0.76	                                                                 => ( setadjoinOr
0.59/0.76	                                                                   => ( setoftrueEq
0.59/0.76	                                                                     => ( powersetI
0.59/0.76	                                                                       => ( ( ( powersetE
0.59/0.76	                                                                             => ( ( ( subPowSU
0.59/0.76	                                                                                   => ( exuE2
0.59/0.76	                                                                                     => ( nonemptyImpWitness
0.59/0.76	                                                                                       => ( uniqinunit
0.59/0.76	                                                                                         => ( ( ( ( upairsetE
0.59/0.76	                                                                                                 => ( upairsetIL
0.59/0.76	                                                                                                   => ( ( ( ( quantDeMorgan1
0.59/0.76	                                                                                                           => ( ( ( ( ( ( ( notdallE
0.59/0.76	                                                                                                                         => ( exuI1
0.59/0.76	                                                                                                                           => ( exuI3
0.59/0.76	                                                                                                                             => ( ( ( in__Cong
0.59/0.76	                                                                                                                                   => ( exuE3u
0.59/0.76	                                                                                                                                     => ( exu__Cong
0.59/0.76	                                                                                                                                       => ( emptyset__Cong
0.59/0.76	                                                                                                                                         => ( ( powerset__Cong
0.59/0.76	                                                                                                                                             => ( ( omega__Cong
0.59/0.76	                                                                                                                                                 => ( ( ( dsetconstr__Cong
0.59/0.76	                                                                                                                                                       => ( ( eqimpsubset2
0.59/0.76	                                                                                                                                                           => ( eqimpsubset1
0.59/0.76	                                                                                                                                                             => ( ( ( ( subsetE2
0.59/0.76	                                                                                                                                                                     => ( notsubsetI
0.59/0.76	                                                                                                                                                                       => ( ( notequalI2
0.59/0.76	                                                                                                                                                                           => ( subsetRefl
0.59/0.76	                                                                                                                                                                             => ( subsetTrans
0.59/0.76	                                                                                                                                                                               => ( setadjoinSub
0.59/0.76	                                                                                                                                                                                 => ( ( subset2powerset
0.59/0.76	                                                                                                                                                                                     => ( ( subsetemptysetimpeq
0.59/0.76	                                                                                                                                                                                         => ( powersetI1
0.59/0.76	                                                                                                                                                                                           => ( ( ( powersetsubset
0.59/0.76	                                                                                                                                                                                                 => ( ( ( ( ( ( ( binunionE
0.59/0.76	                                                                                                                                                                                                               => ( binunionLsub
0.59/0.76	                                                                                                                                                                                                                 => ( ( binintersectI
0.59/0.76	                                                                                                                                                                                                                     => ( binintersectSubset5
0.59/0.76	                                                                                                                                                                                                                       => ( ( binintersectLsub
0.59/0.76	                                                                                                                                                                                                                           => ( ( ( binintersectER
0.59/0.76	                                                                                                                                                                                                                                 => ( disjointsetsI1
0.59/0.76	                                                                                                                                                                                                                                   => ( binintersectRsub
0.59/0.76	                                                                                                                                                                                                                                     => ( ( ( ( ( ( setminusER
0.59/0.76	                                                                                                                                                                                                                                                 => ( setminusSubset2
0.59/0.76	                                                                                                                                                                                                                                                   => ( setminusERneg
0.59/0.76	                                                                                                                                                                                                                                                     => ( ( ( setminusIRneg
0.59/0.76	                                                                                                                                                                                                                                                           => ( setminusLsub
0.59/0.76	                                                                                                                                                                                                                                                             => ( ( symdiffE
0.59/0.76	                                                                                                                                                                                                                                                                 => ( symdiffI1
0.59/0.76	                                                                                                                                                                                                                                                                   => ( ( ( symdiffIneg2
0.59/0.76	                                                                                                                                                                                                                                                                         => ( secondinupair
0.59/0.76	                                                                                                                                                                                                                                                                           => ( ( setukpairIR
0.59/0.76	                                                                                                                                                                                                                                                                               => ( kpairiskpair
0.59/0.76	                                                                                                                                                                                                                                                                                 => ( kpairp
0.59/0.76	                                                                                                                                                                                                                                                                                   => ( ( ( singletoninpowunion
0.59/0.76	                                                                                                                                                                                                                                                                                         => ( ( ( ( ubforcartprodlem1
0.59/0.76	                                                                                                                                                                                                                                                                                                 => ( ( ( cartprodpairin
0.59/0.76	                                                                                                                                                                                                                                                                                                       => ( cartprodmempair1
0.59/0.76	                                                                                                                                                                                                                                                                                                         => ( ( ( ( ( setunionsingleton
0.59/0.76	                                                                                                                                                                                                                                                                                                                   => ( ( ex1E1
0.59/0.76	                                                                                                                                                                                                                                                                                                                       => ( ex1I
0.59/0.76	                                                                                                                                                                                                                                                                                                                         => ( ( singletonsuniq
0.59/0.76	                                                                                                                                                                                                                                                                                                                             => ( ( kfstsingleton
0.59/0.76	                                                                                                                                                                                                                                                                                                                                 => ( ( ( cartprodfstin
0.59/0.76	                                                                                                                                                                                                                                                                                                                                       => ( setukpairinjL2
0.59/0.76	                                                                                                                                                                                                                                                                                                                                         => ( ( ( setukpairinjR12
0.59/0.76	                                                                                                                                                                                                                                                                                                                                               => ( setukpairinjR1
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                 => ( upairequniteq
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                   => ( setukpairinjR2
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                     => ( setukpairinjR
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                       => ( ksndsingleton
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                         => ( ksndpairEq
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                           => ( kpairsurjEq
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                             => ( cartprodsndin
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                               => ( cartprodpairmemEL
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                 => ( cartprodpairmemER
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                   => ( cartprodmempaircEq
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                     => ( ( cartprodsndpairEq
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                         => ( ( dpsetconstrI
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                             => ( ( setOfPairsIsBReln
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                 => ( ( dpsetconstrEL1
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                     => ( ( ( ( ( app
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                               => ( infuncsetfunc
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                 => ( ap2p
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                   => ( funcinfuncset
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                     => ( lamProp
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( ( brelnall1
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( ( ( funcGraphProp3
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                     => ( funcGraphProp2
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                       => ( funcextLem
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( subbreln
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( funcext
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ap2apEq1
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( ( ( ( ( eta2
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ( ( iftrueProp2
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( ( theeq
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( iftrue
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ( binintersectT_lem
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( binunionT_lem
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( ( ( ( ( powersetTI1
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( powersetTE1
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( ( ( ( ( ( contrasubsetT2
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( contrasubsetT3
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( doubleComplementE1
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( doubleComplementSub2
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( doubleComplementEq
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( complementTnotintersectT
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( complementImpComplementIntersect
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( complementSubsetComplementIntersect
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( contraSubsetComplement
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( binunionTILcontra
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( inIntersectImpInUnion
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( inIntersectImpInIntersectUnions
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( inComplementUnionImpNotIn1
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( ( binunionTEcontra
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ( ( ( ( ( ( demorgan2b2
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( demorgan2b
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( woz13rule0
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( ( woz13rule3
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( woz13rule4
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( ( ( woz1_4
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( breln1all2
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( choice2fnsingleton
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( ( ( eqbreln1
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( breln1invprop
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( breln1invI
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( breln1compprop
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( breln1compE
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( breln1compEex
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( breln1unionprop
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( ( breln1unionI
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( breln1unionE
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( breln1unionEcases
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( woz2Ex
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( woz2A
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( ( image1Ex1
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( image1Equiv
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( image1E
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ( ( injFuncSetFuncInj
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [A: $i,B: $i,Xf: $i] :
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xf @ ( funcSet @ A @ B ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               <= ( in @ Xf @ ( surjFuncSet @ A @ B ) ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         <= injFuncSetFuncIn )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       <= injFuncInInjFuncSet )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     <= image1I ) ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             <= image1Ex )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           <= woz2B ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       <= woz2W ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   <= breln1unionCommutes ) ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           <= breln1unionIR )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         <= breln1unionIL ) ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 <= breln1compI ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             <= breln1invE ) ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     <= subbreln1 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   <= breln1all1 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 <= setOfPairsIsBReln1 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             <= breln1SetBreln1 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         <= woz1_5 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     <= woz1_3 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   <= woz1_2 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 <= woz1_1 ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           <= woz13rule2 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         <= woz13rule1 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     <= demorgan2 ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               <= demorgan2a )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             <= demorgan1 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           <= demorgan1b )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         <= demorgan1a )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       <= demorgan2a2 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     <= complementUnionInPowersetComplement )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   <= demorgan2a1 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               <= binunionTE )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             <= inComplementUnionImpInComplement1 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         <= intersectInPowersetIntersectUnions ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     <= inIntersectImpInUnion2 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 <= binunionTIRcontra ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             <= complementTcontraSubset ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         <= complementInPowersetComplementIntersect ) ) ) ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             <= doubleComplementSub1 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         <= doubleComplementI1 ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   <= contrasubsetT1 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 <= contrasubsetT )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               <= binintersectTERcontra )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             <= binintersectTELcontra )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           <= complementTE1 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         <= complementTI1 ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   <= subsetTI )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 <= setextT )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                               <= complementT_lem )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                             <= setminusT_lem )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                           <= powersetT_lem ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                     <= iftrueorfalse )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                                   <= iffalse ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                             <= ifp )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                           <= ifSingleton ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                       <= iftrueProp1 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                     <= iffalseProp2 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                                   <= iffalseProp1 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                               <= beta2 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                             <= lam2lamEq )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                           <= eta1 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                         <= beta1 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                       <= ap2apEq2 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                                   <= funcext2 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                               <= eqbreln ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                           <= funcGraphProp4 ) ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                   <= funcGraphProp1 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                                 <= ex1E2 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                               <= brelnall2 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                           <= lam2p )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                                         <= lamp ) ) ) ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                             <= apProp )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                           <= funcImageSingleton )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                         <= dpsetconstrER )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                       <= dpsetconstrEL2 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                                   <= dpsetconstrERa ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                               <= dpsetconstrSub ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                           <= cartprodpairsurjEq ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                                                       <= cartprodfstpairEq ) ) ) ) ) ) ) ) ) ) ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                             <= setukpairinjR11 )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                           <= setukpairinjL ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                     <= kfstpairEq )
0.59/0.76	                                                                                                                                                                                                                                                                                                                                   <= theprop ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                               <= setukpairinjL1 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                           <= ex1I2 ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                     <= singletonprop ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                                 <= setunionsingleton2 )
0.59/0.76	                                                                                                                                                                                                                                                                                                               <= setunionsingleton1 )
0.59/0.76	                                                                                                                                                                                                                                                                                                             <= setunionE2 )
0.59/0.76	                                                                                                                                                                                                                                                                                                           <= cartprodmempair ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                                                     <= ubforcartprodlem3 )
0.59/0.76	                                                                                                                                                                                                                                                                                                   <= ubforcartprodlem2 ) )
0.59/0.76	                                                                                                                                                                                                                                                                                               <= upairinpowunion )
0.59/0.76	                                                                                                                                                                                                                                                                                             <= upairsubunion )
0.59/0.76	                                                                                                                                                                                                                                                                                           <= upairset2E ) )
0.59/0.76	                                                                                                                                                                                                                                                                                       <= singletoninpowerset )
0.59/0.76	                                                                                                                                                                                                                                                                                     <= singletonsubset ) ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                             <= setukpairIL ) ) )
0.59/0.76	                                                                                                                                                                                                                                                                       <= symdiffIneg1 )
0.59/0.76	                                                                                                                                                                                                                                                                     <= symdiffI2 ) ) )
0.59/0.76	                                                                                                                                                                                                                                                               <= setminusSubset1 ) ) )
0.59/0.76	                                                                                                                                                                                                                                                         <= setminusILneg )
0.59/0.76	                                                                                                                                                                                                                                                       <= setminusELneg ) ) ) )
0.59/0.76	                                                                                                                                                                                                                                               <= setminusEL )
0.59/0.76	                                                                                                                                                                                                                                             <= setminusI )
0.59/0.76	                                                                                                                                                                                                                                           <= bs114d )
0.59/0.76	                                                                                                                                                                                                                                         <= binintersectSubset1 )
0.59/0.76	                                                                                                                                                                                                                                       <= binintersectSubset4 ) ) ) )
0.59/0.76	                                                                                                                                                                                                                               <= binintersectSubset3 )
0.59/0.76	                                                                                                                                                                                                                             <= binintersectSubset2 ) )
0.59/0.76	                                                                                                                                                                                                                         <= binintersectEL ) ) )
0.59/0.76	                                                                                                                                                                                                                   <= binunionRsub ) ) )
0.59/0.76	                                                                                                                                                                                                             <= binunionEcases )
0.59/0.76	                                                                                                                                                                                                           <= binunionIR )
0.59/0.76	                                                                                                                                                                                                         <= upairset2IR )
0.59/0.76	                                                                                                                                                                                                       <= binunionIL )
0.59/0.76	                                                                                                                                                                                                     <= sepSubset )
0.59/0.76	                                                                                                                                                                                                   <= sepInPowerset ) )
0.59/0.76	                                                                                                                                                                                               <= inPowerset )
0.59/0.76	                                                                                                                                                                                             <= powersetE1 ) ) )
0.59/0.76	                                                                                                                                                                                       <= setextsub ) )
0.59/0.76	                                                                                                                                                                                   <= setadjoinSub2 ) ) ) ) )
0.59/0.76	                                                                                                                                                                         <= notequalI1 ) ) )
0.59/0.76	                                                                                                                                                                   <= subsetE )
0.59/0.76	                                                                                                                                                                 <= emptysetsubset )
0.59/0.76	                                                                                                                                                               <= subsetI2 ) ) )
0.59/0.76	                                                                                                                                                         <= subsetI1 ) )
0.59/0.76	                                                                                                                                                     <= descr__Cong )
0.59/0.76	                                                                                                                                                   <= exuEu ) )
0.59/0.85	                                                                                                                                               <= setunion__Cong ) )
0.59/0.85	                                                                                                                                           <= setadjoin__Cong ) ) ) ) )
0.59/0.85	                                                                                                                                 <= inCongP )
0.59/0.85	                                                                                                                               <= exuI2 ) ) ) )
0.59/0.85	                                                                                                                       <= notdexE )
0.59/0.85	                                                                                                                     <= prop2set2propI )
0.59/0.85	                                                                                                                   <= prop2setI )
0.59/0.85	                                                                                                                 <= quantDeMorgan4 )
0.59/0.85	                                                                                                               <= quantDeMorgan3 )
0.59/0.85	                                                                                                             <= quantDeMorgan2 ) )
0.59/0.85	                                                                                                         <= vacuousDall )
0.59/0.85	                                                                                                       <= emptyE1 )
0.59/0.85	                                                                                                     <= upairsetIR ) ) )
0.59/0.85	                                                                                               <= singletonsswitch )
0.59/0.85	                                                                                             <= eqinunit )
0.59/0.85	                                                                                           <= notinsingleton ) ) ) ) )
0.59/0.85	                                                                                 <= setunionE )
0.59/0.85	                                                                               <= setunionI ) )
0.59/0.85	                                                                           <= emptyInPowerset )
0.59/0.85	                                                                         <= emptyinPowerset ) ) ) ) ) ) ) )
0.59/0.85	                                                         <= nonemptyI1 )
0.59/0.85	                                                       <= nonemptyI )
0.59/0.85	                                                     <= nonemptyE1 ) ) ) ) )
0.59/0.85	                                           <= exuE3e )
0.59/0.85	                                         <= notinemptyset ) ) )
0.59/0.85	                                   <= prop2setE )
0.59/0.85	                                 <= exuE1 )
0.59/0.85	                               <= dsetconstrER ) )
0.59/0.85	                           <= dsetconstrI )
0.59/0.85	                         <= descrp )
0.59/0.85	                       <= wellorderingAx ) )
0.59/0.85	                   <= replAx ) ) ) )
0.59/0.85	           <= setunionAx ) ) )
0.59/0.85	     <= emptysetAx ) ) ).
0.59/0.85	
0.59/0.85	------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.9gfzsmwfsH/cvc5---1.0.5_11637.p...
0.59/0.85	(declare-sort $$unsorted 0)
0.59/0.85	(declare-fun tptp.in ($$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.exu ((-> $$unsorted Bool)) Bool)
0.59/0.85	(assert (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))))))
0.59/0.85	(declare-fun tptp.setextAx () Bool)
0.59/0.85	(assert (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B)))))
0.59/0.85	(declare-fun tptp.emptyset () $$unsorted)
0.59/0.85	(declare-fun tptp.emptysetAx () Bool)
0.59/0.85	(assert (= tptp.emptysetAx (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset)))))
0.59/0.85	(declare-fun tptp.setadjoin ($$unsorted $$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.setadjoinAx () Bool)
0.59/0.85	(assert (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A)))))))
0.59/0.85	(declare-fun tptp.powerset ($$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.powersetAx () Bool)
0.59/0.85	(assert (= tptp.powersetAx (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A))))))))
0.59/0.85	(declare-fun tptp.setunion ($$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.setunionAx () Bool)
0.59/0.85	(assert (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A)))))))
0.59/0.85	(declare-fun tptp.omega () $$unsorted)
0.59/0.85	(declare-fun tptp.omega0Ax () Bool)
0.59/0.85	(assert (= tptp.omega0Ax (@ (@ tptp.in tptp.emptyset) tptp.omega)))
0.59/0.85	(declare-fun tptp.omegaSAx () Bool)
0.59/0.85	(assert (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega)))))
0.59/0.85	(declare-fun tptp.omegaIndAx () Bool)
0.59/0.85	(assert (= tptp.omegaIndAx (forall ((A $$unsorted)) (=> (and (@ (@ tptp.in tptp.emptyset) A) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (and (@ _let_1 tptp.omega) (@ _let_1 A)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) A))))) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 tptp.omega) (@ _let_1 A))))))))
0.59/0.85	(declare-fun tptp.replAx () Bool)
0.59/0.85	(assert (= tptp.replAx (forall ((Xphi (-> $$unsorted $$unsorted Bool)) (A $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ tptp.exu (lambda ((Xy $$unsorted)) (@ (@ Xphi Xx) Xy))))) (exists ((B $$unsorted)) (forall ((Xx $$unsorted)) (= (@ (@ tptp.in Xx) B) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) A) (@ (@ Xphi Xy) Xx))))))))))
0.59/0.85	(declare-fun tptp.foundationAx () Bool)
0.59/0.85	(assert (= tptp.foundationAx (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in B) A) (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 B) (@ _let_1 A)))))))))))
0.59/0.85	(declare-fun tptp.wellorderingAx () Bool)
0.59/0.85	(assert (= tptp.wellorderingAx (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (forall ((C $$unsorted)) (=> (@ (@ tptp.in C) B) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 C) (@ _let_1 A)))))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (and (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) A)) (=> (forall ((C $$unsorted)) (=> (@ (@ tptp.in C) B) (= (@ (@ tptp.in Xx) C) (@ (@ tptp.in Xy) C)))) (= Xx Xy)))) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (@ (@ tptp.in C) B) (@ (@ tptp.in D) B)) (or (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 C) (@ _let_1 D)))) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 D) (@ _let_1 C))))))) (forall ((C $$unsorted)) (=> (and (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 C) (@ _let_1 A)))) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) C))) (exists ((D $$unsorted) (Xx $$unsorted)) (and (@ (@ tptp.in D) B) (@ (@ tptp.in Xx) C) (not (exists ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (and (@ _let_1 D) (@ _let_1 C))))) (forall ((E $$unsorted)) (=> (@ (@ tptp.in E) B) (or (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 E) (@ _let_1 D)))) (@ (@ tptp.in Xx) E)))))))))))))
0.59/0.85	(declare-fun tptp.descr ((-> $$unsorted Bool)) $$unsorted)
0.59/0.85	(declare-fun tptp.descrp () Bool)
0.59/0.85	(assert (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))
0.59/0.85	(declare-fun tptp.dsetconstr ($$unsorted (-> $$unsorted Bool)) $$unsorted)
0.59/0.85	(declare-fun tptp.dsetconstrI () Bool)
0.59/0.85	(assert (= tptp.dsetconstrI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ Xphi Xx) (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))))))
0.59/0.85	(declare-fun tptp.dsetconstrEL () Bool)
0.59/0.85	(assert (= tptp.dsetconstrEL (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ _let_1 A))))))
0.59/0.85	(declare-fun tptp.dsetconstrER () Bool)
0.59/0.85	(assert (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx)))))
0.59/0.85	(declare-fun tptp.exuE1 () Bool)
0.59/0.85	(assert (= tptp.exuE1 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy)))))))))
0.59/0.85	(declare-fun tptp.prop2set (Bool) $$unsorted)
0.59/0.85	(declare-fun tptp.prop2setE () Bool)
0.59/0.85	(assert (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi))))
0.59/0.85	(declare-fun tptp.emptysetE () Bool)
0.59/0.85	(assert (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi)))))
0.59/0.85	(declare-fun tptp.emptysetimpfalse () Bool)
0.59/0.85	(assert (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false))))
0.59/0.85	(declare-fun tptp.notinemptyset () Bool)
0.59/0.85	(assert (= tptp.notinemptyset (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset)))))
0.59/0.85	(declare-fun tptp.exuE3e () Bool)
0.59/0.85	(assert (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx))))))
0.59/0.85	(declare-fun tptp.setext () Bool)
0.59/0.85	(assert (= tptp.setext (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (= A B))))))
0.59/0.85	(declare-fun tptp.emptyI () Bool)
0.59/0.85	(assert (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))
0.59/0.85	(declare-fun tptp.noeltsimpempty () Bool)
0.59/0.85	(assert (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))
0.59/0.85	(declare-fun tptp.setbeta () Bool)
0.59/0.85	(assert (= tptp.setbeta (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (= (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx)))))))
0.59/0.85	(declare-fun tptp.nonempty ($$unsorted) Bool)
0.59/0.85	(assert (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset)))))
0.59/0.85	(declare-fun tptp.nonemptyE1 () Bool)
0.59/0.85	(assert (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A))))))
0.59/0.85	(declare-fun tptp.nonemptyI () Bool)
0.59/0.85	(assert (= tptp.nonemptyI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (@ tptp.nonempty (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))))))))
0.59/0.85	(declare-fun tptp.nonemptyI1 () Bool)
0.59/0.85	(assert (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A)))))
0.59/0.85	(declare-fun tptp.setadjoinIL () Bool)
0.59/0.85	(assert (= tptp.setadjoinIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy)))))
0.59/0.85	(declare-fun tptp.emptyinunitempty () Bool)
0.59/0.85	(assert (= tptp.emptyinunitempty (@ (@ tptp.in tptp.emptyset) (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset))))
0.59/0.85	(declare-fun tptp.setadjoinIR () Bool)
0.59/0.85	(assert (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A)))))))
0.59/0.85	(declare-fun tptp.setadjoinE () Bool)
0.59/0.85	(assert (= tptp.setadjoinE (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (forall ((Xphi Bool)) (=> (=> (= Xy Xx) Xphi) (=> (=> (@ (@ tptp.in Xy) A) Xphi) Xphi)))))))
0.59/0.85	(declare-fun tptp.setadjoinOr () Bool)
0.59/0.85	(assert (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A)))))))
0.59/0.85	(declare-fun tptp.setoftrueEq () Bool)
0.59/0.85	(assert (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A))))
0.59/0.85	(declare-fun tptp.powersetI () Bool)
0.59/0.85	(assert (= tptp.powersetI (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (@ (@ tptp.in B) (@ tptp.powerset A))))))
0.59/0.85	(declare-fun tptp.emptyinPowerset () Bool)
0.59/0.85	(assert (= tptp.emptyinPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A)))))
0.59/0.85	(declare-fun tptp.emptyInPowerset () Bool)
0.59/0.85	(assert (= tptp.emptyInPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A)))))
0.59/0.85	(declare-fun tptp.powersetE () Bool)
0.59/0.85	(assert (= tptp.powersetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (=> (@ _let_1 B) (@ _let_1 A)))))))
0.59/0.85	(declare-fun tptp.setunionI () Bool)
0.59/0.85	(assert (= tptp.setunionI (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (=> (@ (@ tptp.in B) A) (@ _let_1 (@ tptp.setunion A))))))))
0.59/0.85	(declare-fun tptp.setunionE () Bool)
0.59/0.85	(assert (= tptp.setunionE (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (forall ((Xphi Bool)) (=> (forall ((B $$unsorted)) (=> (@ (@ tptp.in Xx) B) (=> (@ (@ tptp.in B) A) Xphi))) Xphi))))))
0.59/0.85	(declare-fun tptp.subPowSU () Bool)
0.59/0.85	(assert (= tptp.subPowSU (forall ((A $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.powerset (@ tptp.setunion A))))))))
0.59/0.85	(declare-fun tptp.exuE2 () Bool)
0.59/0.85	(assert (= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx))))))))
0.59/0.85	(declare-fun tptp.nonemptyImpWitness () Bool)
0.59/0.85	(assert (= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) true))))))
0.59/0.85	(declare-fun tptp.uniqinunit () Bool)
0.59/0.85	(assert (= tptp.uniqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy)))))
0.59/0.85	(declare-fun tptp.notinsingleton () Bool)
0.59/0.85	(assert (= tptp.notinsingleton (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (not (= Xx Xy)) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))
0.59/0.85	(declare-fun tptp.eqinunit () Bool)
0.59/0.85	(assert (= tptp.eqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))
0.59/0.85	(declare-fun tptp.singletonsswitch () Bool)
0.59/0.85	(assert (= tptp.singletonsswitch (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))
0.59/0.85	(declare-fun tptp.upairsetE () Bool)
0.59/0.85	(assert (= tptp.upairsetE (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy))))))
0.59/0.85	(declare-fun tptp.upairsetIL () Bool)
0.59/0.85	(assert (= tptp.upairsetIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))
0.59/0.85	(declare-fun tptp.upairsetIR () Bool)
0.59/0.85	(assert (= tptp.upairsetIR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))
0.59/0.85	(declare-fun tptp.emptyE1 () Bool)
0.59/0.85	(assert (= tptp.emptyE1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (=> (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) tptp.emptyset) false)))))
0.59/0.85	(declare-fun tptp.vacuousDall () Bool)
0.59/0.85	(assert (= tptp.vacuousDall (forall ((Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (@ Xphi Xx)))))
0.59/0.85	(declare-fun tptp.quantDeMorgan1 () Bool)
0.59/0.85	(assert (= tptp.quantDeMorgan1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))
0.59/0.85	(declare-fun tptp.quantDeMorgan2 () Bool)
0.59/0.85	(assert (= tptp.quantDeMorgan2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))) (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))))))))
0.59/0.85	(declare-fun tptp.quantDeMorgan3 () Bool)
0.59/0.85	(assert (= tptp.quantDeMorgan3 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))
0.59/0.85	(declare-fun tptp.quantDeMorgan4 () Bool)
0.59/0.85	(assert (= tptp.quantDeMorgan4 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx))))))))
0.59/0.85	(declare-fun tptp.prop2setI () Bool)
0.59/0.85	(assert (= tptp.prop2setI (forall ((Xphi Bool)) (=> Xphi (@ (@ tptp.in tptp.emptyset) (@ tptp.prop2set Xphi))))))
0.59/0.85	(declare-fun tptp.set2prop ($$unsorted) Bool)
0.59/0.85	(declare-fun tptp.prop2set2propI () Bool)
0.59/0.85	(assert (= tptp.prop2set2propI (forall ((Xphi Bool)) (=> Xphi (@ tptp.set2prop (@ tptp.prop2set Xphi))))))
0.59/0.85	(declare-fun tptp.notdexE () Bool)
0.59/0.85	(assert (= tptp.notdexE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))
0.59/0.85	(declare-fun tptp.notdallE () Bool)
0.59/0.85	(assert (= tptp.notdallE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))
0.59/0.85	(declare-fun tptp.exuI1 () Bool)
0.59/0.85	(assert (= tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))
0.59/0.85	(declare-fun tptp.exuI3 () Bool)
0.59/0.85	(assert (= tptp.exuI3 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (@ Xphi Xx)) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))
0.59/0.85	(declare-fun tptp.exuI2 () Bool)
0.59/0.85	(assert (= tptp.exuI2 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))
0.59/0.85	(declare-fun tptp.inCongP () Bool)
0.59/0.85	(assert (= tptp.inCongP (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) B))))))))
0.59/0.85	(declare-fun tptp.in__Cong () Bool)
0.59/0.85	(assert (= tptp.in__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) B))))))))
0.59/0.85	(declare-fun tptp.exuE3u () Bool)
0.59/0.85	(assert (= tptp.exuE3u (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))))
0.59/0.85	(declare-fun tptp.exu__Cong () Bool)
0.59/0.85	(assert (= tptp.exu__Cong (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ Xphi Xx) (@ Xpsi Xy)))) (= (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xpsi Xx))))))))
0.59/0.85	(declare-fun tptp.emptyset__Cong () Bool)
0.59/0.85	(assert (= tptp.emptyset__Cong (= tptp.emptyset tptp.emptyset)))
0.59/0.85	(declare-fun tptp.setadjoin__Cong () Bool)
0.59/0.85	(assert (= tptp.setadjoin__Cong (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (forall ((Xz $$unsorted) (Xu $$unsorted)) (=> (= Xz Xu) (= (@ (@ tptp.setadjoin Xx) Xz) (@ (@ tptp.setadjoin Xy) Xu))))))))
0.59/0.85	(declare-fun tptp.powerset__Cong () Bool)
0.59/0.85	(assert (= tptp.powerset__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.powerset A) (@ tptp.powerset B))))))
0.59/0.85	(declare-fun tptp.setunion__Cong () Bool)
0.59/0.85	(assert (= tptp.setunion__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.setunion A) (@ tptp.setunion B))))))
0.59/0.85	(declare-fun tptp.omega__Cong () Bool)
0.59/0.85	(assert (= tptp.omega__Cong (= tptp.omega tptp.omega)))
0.59/0.85	(declare-fun tptp.exuEu () Bool)
0.59/0.85	(assert (= tptp.exuEu (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))))
0.59/0.85	(declare-fun tptp.descr__Cong () Bool)
0.59/0.85	(assert (= tptp.descr__Cong (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ Xphi Xx) (@ Xpsi Xy)))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xpsi Xx))) (= (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xpsi Xx))))))))))
0.59/0.85	(declare-fun tptp.dsetconstr__Cong () Bool)
0.59/0.85	(assert (= tptp.dsetconstr__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (= Xx Xy) (= (@ Xphi Xx) (@ Xpsi Xy))))))) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xpsi Xx))))))))))
0.59/0.85	(declare-fun tptp.subset ($$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.disjoint ($$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.setsmeet ($$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.subsetI1 () Bool)
0.59/0.85	(assert (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B)))))
0.59/0.85	(declare-fun tptp.eqimpsubset2 () Bool)
0.59/0.85	(assert (= tptp.eqimpsubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset B) A)))))
0.59/0.85	(declare-fun tptp.eqimpsubset1 () Bool)
0.59/0.85	(assert (= tptp.eqimpsubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B)))))
0.59/0.85	(declare-fun tptp.subsetI2 () Bool)
0.59/0.85	(assert (= tptp.subsetI2 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B)))))
0.59/0.85	(declare-fun tptp.emptysetsubset () Bool)
0.59/0.85	(assert (= tptp.emptysetsubset (forall ((A $$unsorted)) (@ (@ tptp.subset tptp.emptyset) A))))
0.59/0.85	(declare-fun tptp.subsetE () Bool)
0.59/0.85	(assert (= tptp.subsetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (@ _let_1 A) (@ _let_1 B)))))))
0.59/0.85	(declare-fun tptp.subsetE2 () Bool)
0.59/0.85	(assert (= tptp.subsetE2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (not (@ _let_1 B)) (not (@ _let_1 A))))))))
0.59/0.85	(declare-fun tptp.notsubsetI () Bool)
0.59/0.85	(assert (= tptp.notsubsetI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (@ (@ tptp.subset A) B))))))))
0.59/0.85	(declare-fun tptp.notequalI1 () Bool)
0.59/0.85	(assert (= tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (@ (@ tptp.subset A) B)) (not (= A B))))))
0.59/0.85	(declare-fun tptp.notequalI2 () Bool)
0.59/0.85	(assert (= tptp.notequalI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (= A B))))))))
0.59/0.85	(declare-fun tptp.subsetRefl () Bool)
0.59/0.85	(assert (= tptp.subsetRefl (forall ((A $$unsorted)) (@ (@ tptp.subset A) A))))
0.59/0.85	(declare-fun tptp.subsetTrans () Bool)
0.59/0.85	(assert (= tptp.subsetTrans (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (=> (@ (@ tptp.subset B) C) (@ _let_1 C)))))))
0.59/0.85	(declare-fun tptp.setadjoinSub () Bool)
0.59/0.85	(assert (= tptp.setadjoinSub (forall ((Xx $$unsorted) (A $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.setadjoin Xx) A)))))
0.59/0.85	(declare-fun tptp.setadjoinSub2 () Bool)
0.59/0.85	(assert (= tptp.setadjoinSub2 (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.setadjoin Xx) B)))))))
0.59/0.85	(declare-fun tptp.subset2powerset () Bool)
0.59/0.85	(assert (= tptp.subset2powerset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.in A) (@ tptp.powerset B))))))
0.59/0.85	(declare-fun tptp.setextsub () Bool)
0.59/0.85	(assert (= tptp.setextsub (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (=> (@ (@ tptp.subset B) A) (= A B))))))
0.59/0.85	(declare-fun tptp.subsetemptysetimpeq () Bool)
0.59/0.85	(assert (= tptp.subsetemptysetimpeq (forall ((A $$unsorted)) (=> (@ (@ tptp.subset A) tptp.emptyset) (= A tptp.emptyset)))))
0.59/0.85	(declare-fun tptp.powersetI1 () Bool)
0.59/0.85	(assert (= tptp.powersetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (@ (@ tptp.in B) (@ tptp.powerset A))))))
0.59/0.85	(declare-fun tptp.powersetE1 () Bool)
0.59/0.85	(assert (= tptp.powersetE1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (@ (@ tptp.subset B) A)))))
0.59/0.85	(declare-fun tptp.inPowerset () Bool)
0.59/0.85	(assert (= tptp.inPowerset (forall ((A $$unsorted)) (@ (@ tptp.in A) (@ tptp.powerset A)))))
0.59/0.85	(declare-fun tptp.powersetsubset () Bool)
0.59/0.85	(assert (= tptp.powersetsubset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.subset (@ tptp.powerset A)) (@ tptp.powerset B))))))
0.59/0.85	(declare-fun tptp.sepInPowerset () Bool)
0.59/0.85	(assert (= tptp.sepInPowerset (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.in (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ tptp.powerset A)))))
0.59/0.85	(declare-fun tptp.sepSubset () Bool)
0.59/0.85	(assert (= tptp.sepSubset (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.subset (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) A))))
0.59/0.85	(declare-fun tptp.binunion ($$unsorted $$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.binunionIL () Bool)
0.59/0.85	(assert (= tptp.binunionIL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.binunion A) B)))))))
0.59/0.85	(declare-fun tptp.upairset2IR () Bool)
0.59/0.85	(assert (= tptp.upairset2IR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))
0.59/0.85	(declare-fun tptp.binunionIR () Bool)
0.59/0.85	(assert (= tptp.binunionIR (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binunion A) B)))))))
0.59/0.85	(declare-fun tptp.binunionEcases () Bool)
0.59/0.85	(assert (= tptp.binunionEcases (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xphi Bool)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binunion A) B)) (=> (=> (@ _let_1 A) Xphi) (=> (=> (@ _let_1 B) Xphi) Xphi)))))))
0.59/0.85	(declare-fun tptp.binunionE () Bool)
0.59/0.85	(assert (= tptp.binunionE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binunion A) B)) (or (@ _let_1 A) (@ _let_1 B)))))))
0.59/0.85	(declare-fun tptp.binunionLsub () Bool)
0.59/0.85	(assert (= tptp.binunionLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.binunion A) B)))))
0.59/0.85	(declare-fun tptp.binunionRsub () Bool)
0.59/0.85	(assert (= tptp.binunionRsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset B) (@ (@ tptp.binunion A) B)))))
0.59/0.85	(declare-fun tptp.binintersect ($$unsorted $$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.binintersectI () Bool)
0.59/0.85	(assert (= tptp.binintersectI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B))))))))
0.59/0.85	(declare-fun tptp.binintersectSubset5 () Bool)
0.59/0.85	(assert (= tptp.binintersectSubset5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B))))))))
0.59/0.85	(declare-fun tptp.binintersectEL () Bool)
0.59/0.85	(assert (= tptp.binintersectEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect A) B)) (@ _let_1 A))))))
0.59/0.85	(declare-fun tptp.binintersectLsub () Bool)
0.59/0.85	(assert (= tptp.binintersectLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) A))))
0.59/0.85	(declare-fun tptp.binintersectSubset2 () Bool)
0.59/0.85	(assert (= tptp.binintersectSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.binintersect A) B) A)))))
0.59/0.85	(declare-fun tptp.binintersectSubset3 () Bool)
0.59/0.85	(assert (= tptp.binintersectSubset3 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) B) (@ (@ tptp.subset B) A)))))
0.59/0.85	(declare-fun tptp.binintersectER () Bool)
0.59/0.85	(assert (= tptp.binintersectER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect A) B)) (@ _let_1 B))))))
0.59/0.85	(declare-fun tptp.disjointsetsI1 () Bool)
0.59/0.85	(assert (= tptp.disjointsetsI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 A) (@ _let_1 B))))) (= (@ (@ tptp.binintersect A) B) tptp.emptyset)))))
0.59/0.85	(declare-fun tptp.binintersectRsub () Bool)
0.59/0.85	(assert (= tptp.binintersectRsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) B))))
0.59/0.85	(declare-fun tptp.binintersectSubset4 () Bool)
0.59/0.85	(assert (= tptp.binintersectSubset4 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (= (@ (@ tptp.binintersect A) B) B)))))
0.59/0.85	(declare-fun tptp.binintersectSubset1 () Bool)
0.59/0.85	(assert (= tptp.binintersectSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) A) (@ (@ tptp.subset A) B)))))
0.59/0.85	(declare-fun tptp.bs114d () Bool)
0.59/0.85	(assert (= tptp.bs114d (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.binintersect A))) (= (@ _let_1 (@ (@ tptp.binunion B) C)) (@ (@ tptp.binunion (@ _let_1 B)) (@ _let_1 C)))))))
0.59/0.85	(declare-fun tptp.regular ($$unsorted) Bool)
0.59/0.85	(declare-fun tptp.setminus ($$unsorted $$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.setminusI () Bool)
0.59/0.85	(assert (= tptp.setminusI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.setminus A) B))))))))
0.59/0.85	(declare-fun tptp.setminusEL () Bool)
0.59/0.85	(assert (= tptp.setminusEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.setminus A) B)) (@ _let_1 A))))))
0.59/0.85	(declare-fun tptp.setminusER () Bool)
0.59/0.85	(assert (= tptp.setminusER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.setminus A) B)) (not (@ _let_1 B)))))))
0.59/0.85	(declare-fun tptp.setminusSubset2 () Bool)
0.59/0.85	(assert (= tptp.setminusSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.setminus A) B) tptp.emptyset)))))
0.59/0.85	(declare-fun tptp.setminusERneg () Bool)
0.59/0.85	(assert (= tptp.setminusERneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 (@ (@ tptp.setminus A) B))) (=> (@ _let_1 A) (@ _let_1 B)))))))
0.59/0.85	(declare-fun tptp.setminusELneg () Bool)
0.59/0.85	(assert (= tptp.setminusELneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 (@ (@ tptp.setminus A) B))) (=> (not (@ _let_1 B)) (not (@ _let_1 A))))))))
0.59/0.85	(declare-fun tptp.setminusILneg () Bool)
0.59/0.85	(assert (= tptp.setminusILneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (not (@ _let_1 (@ (@ tptp.setminus A) B))))))))
0.59/0.85	(declare-fun tptp.setminusIRneg () Bool)
0.59/0.85	(assert (= tptp.setminusIRneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (not (@ _let_1 (@ (@ tptp.setminus A) B))))))))
0.59/0.85	(declare-fun tptp.setminusLsub () Bool)
0.59/0.85	(assert (= tptp.setminusLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.setminus A) B)) A))))
0.59/0.85	(declare-fun tptp.setminusSubset1 () Bool)
0.59/0.85	(assert (= tptp.setminusSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.setminus A) B) tptp.emptyset) (@ (@ tptp.subset A) B)))))
0.59/0.85	(declare-fun tptp.symdiff ($$unsorted $$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.symdiffE () Bool)
0.59/0.85	(assert (= tptp.symdiffE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.symdiff A) B)) (forall ((Xphi Bool)) (let ((_let_1 (@ tptp.in Xx))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ _let_1 A))) (=> (=> _let_3 (=> (not _let_2) Xphi)) (=> (=> (not _let_3) (=> _let_2 Xphi)) Xphi))))))))))
0.59/0.85	(declare-fun tptp.symdiffI1 () Bool)
0.59/0.85	(assert (= tptp.symdiffI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.symdiff A) B))))))))
0.59/0.85	(declare-fun tptp.symdiffI2 () Bool)
0.59/0.85	(assert (= tptp.symdiffI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.symdiff A) B))))))))
0.59/0.85	(declare-fun tptp.symdiffIneg1 () Bool)
0.59/0.85	(assert (= tptp.symdiffIneg1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 B) (not (@ _let_1 (@ (@ tptp.symdiff A) B)))))))))
0.59/0.85	(declare-fun tptp.symdiffIneg2 () Bool)
0.59/0.85	(assert (= tptp.symdiffIneg2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (not (@ _let_1 (@ (@ tptp.symdiff A) B)))))))))
0.59/0.85	(declare-fun tptp.iskpair ($$unsorted) Bool)
0.59/0.85	(declare-fun tptp.secondinupair () Bool)
0.59/0.85	(assert (= tptp.secondinupair (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))
0.59/0.85	(declare-fun tptp.setukpairIL () Bool)
0.59/0.85	(assert (= tptp.setukpairIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ (@ tptp.in Xx) (@ tptp.setunion (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))))))))
0.59/0.85	(declare-fun tptp.setukpairIR () Bool)
0.59/0.85	(assert (= tptp.setukpairIR (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ (@ tptp.in Xy) (@ tptp.setunion (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))))))))
0.59/0.85	(declare-fun tptp.kpairiskpair () Bool)
0.59/0.85	(assert (= tptp.kpairiskpair (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ tptp.iskpair (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)))))))
0.59/0.85	(declare-fun tptp.kpair ($$unsorted $$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.kpairp () Bool)
0.59/0.85	(assert (= tptp.kpairp (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ tptp.iskpair (@ (@ tptp.kpair Xx) Xy)))))
0.59/0.85	(declare-fun tptp.cartprod ($$unsorted $$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.singletonsubset () Bool)
0.59/0.85	(assert (= tptp.singletonsubset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) tptp.emptyset)) A)))))
0.59/0.85	(declare-fun tptp.singletoninpowerset () Bool)
0.59/0.85	(assert (= tptp.singletoninpowerset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset A))))))
0.59/0.85	(declare-fun tptp.singletoninpowunion () Bool)
0.59/0.85	(assert (= tptp.singletoninpowunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))
0.59/0.85	(declare-fun tptp.upairset2E () Bool)
0.59/0.85	(assert (= tptp.upairset2E (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy))))))
0.59/0.85	(declare-fun tptp.upairsubunion () Bool)
0.59/0.85	(assert (= tptp.upairsubunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (@ (@ tptp.binunion A) B))))))))
0.59/0.85	(declare-fun tptp.upairinpowunion () Bool)
0.59/0.85	(assert (= tptp.upairinpowunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))))
0.59/0.85	(declare-fun tptp.ubforcartprodlem1 () Bool)
0.59/0.85	(assert (= tptp.ubforcartprodlem1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.subset (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (@ tptp.powerset (@ (@ tptp.binunion A) B))))))))))
0.59/0.85	(declare-fun tptp.ubforcartprodlem2 () Bool)
0.59/0.85	(assert (= tptp.ubforcartprodlem2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (@ tptp.powerset (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))))))
0.59/0.85	(declare-fun tptp.ubforcartprodlem3 () Bool)
0.59/0.85	(assert (= tptp.ubforcartprodlem3 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ tptp.powerset (@ tptp.powerset (@ (@ tptp.binunion A) B))))))))))
0.59/0.85	(declare-fun tptp.cartprodpairin () Bool)
0.59/0.85	(assert (= tptp.cartprodpairin (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B))))))))
0.59/0.85	(declare-fun tptp.cartprodmempair1 () Bool)
0.59/0.85	(assert (= tptp.cartprodmempair1 (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) B) (= Xu (@ (@ tptp.kpair Xx) Xy))))))))))
0.59/0.85	(declare-fun tptp.cartprodmempair () Bool)
0.59/0.85	(assert (= tptp.cartprodmempair (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ tptp.iskpair Xu)))))
0.59/0.85	(declare-fun tptp.setunionE2 () Bool)
0.59/0.85	(assert (= tptp.setunionE2 (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((X $$unsorted)) (and (@ (@ tptp.in X) A) (@ (@ tptp.in Xx) X)))))))
0.59/0.85	(declare-fun tptp.setunionsingleton1 () Bool)
0.59/0.85	(assert (= tptp.setunionsingleton1 (forall ((A $$unsorted)) (@ (@ tptp.subset (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset))) A))))
0.59/0.85	(declare-fun tptp.setunionsingleton2 () Bool)
0.59/0.85	(assert (= tptp.setunionsingleton2 (forall ((A $$unsorted)) (@ (@ tptp.subset A) (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset))))))
0.59/0.85	(declare-fun tptp.setunionsingleton () Bool)
0.59/0.85	(assert (= tptp.setunionsingleton (forall ((Xx $$unsorted)) (= (@ tptp.setunion (@ (@ tptp.setadjoin Xx) tptp.emptyset)) Xx))))
0.59/0.85	(declare-fun tptp.singleton ($$unsorted) Bool)
0.59/0.85	(declare-fun tptp.singletonprop () Bool)
0.59/0.85	(assert (= tptp.singletonprop (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))
0.59/0.85	(declare-fun tptp.ex1 ($$unsorted (-> $$unsorted Bool)) Bool)
0.59/0.85	(declare-fun tptp.ex1E1 () Bool)
0.59/0.85	(assert (= tptp.ex1E1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))))))
0.59/0.85	(declare-fun tptp.ex1I () Bool)
0.59/0.85	(assert (= tptp.ex1I (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (=> (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xy) (= Xy Xx)))) (@ (@ tptp.ex1 A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))))))))
0.59/0.85	(declare-fun tptp.ex1I2 () Bool)
0.59/0.85	(assert (= tptp.ex1I2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))
0.59/0.85	(declare-fun tptp.singletonsuniq () Bool)
0.59/0.85	(assert (= tptp.singletonsuniq (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy)))))
0.59/0.85	(declare-fun tptp.atmost1p ($$unsorted) Bool)
0.59/0.85	(declare-fun tptp.atleast2p ($$unsorted) Bool)
0.59/0.85	(declare-fun tptp.atmost2p ($$unsorted) Bool)
0.59/0.85	(declare-fun tptp.upairsetp ($$unsorted) Bool)
0.59/0.85	(declare-fun tptp.setukpairinjL1 () Bool)
0.59/0.85	(assert (= tptp.setukpairinjL1 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (@ (@ tptp.in (@ (@ tptp.setadjoin Xz) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (= Xx Xz))))))
0.59/0.85	(declare-fun tptp.kfstsingleton () Bool)
0.59/0.85	(assert (= tptp.kfstsingleton (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (@ tptp.singleton (@ (@ tptp.dsetconstr (@ tptp.setunion Xu)) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) Xu))))))))
0.59/0.85	(declare-fun tptp.theprop () Bool)
0.59/0.85	(assert (= tptp.theprop (forall ((X $$unsorted)) (=> (@ tptp.singleton X) (@ (@ tptp.in (@ tptp.setunion X)) X)))))
0.59/0.85	(declare-fun tptp.kfst ($$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.kfstpairEq () Bool)
0.59/0.85	(assert (= tptp.kfstpairEq (forall ((Xx $$unsorted) (Xy $$unsorted)) (= (@ tptp.kfst (@ (@ tptp.kpair Xx) Xy)) Xx))))
0.59/0.85	(declare-fun tptp.cartprodfstin () Bool)
0.59/0.85	(assert (= tptp.cartprodfstin (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in (@ tptp.kfst Xu)) A)))))
0.59/0.85	(declare-fun tptp.setukpairinjL2 () Bool)
0.59/0.85	(assert (= tptp.setukpairinjL2 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xz))) (let ((_let_2 (@ tptp.setadjoin Xx))) (=> (= (@ (@ tptp.setadjoin (@ _let_2 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_2 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset))) (= Xx Xz)))))))
0.59/0.85	(declare-fun tptp.setukpairinjL () Bool)
0.59/0.85	(assert (= tptp.setukpairinjL (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xx Xz)))))
0.59/0.85	(declare-fun tptp.setukpairinjR11 () Bool)
0.59/0.85	(assert (= tptp.setukpairinjR11 (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (= Xx Xy) (= (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ _let_1 tptp.emptyset)))))))
0.59/0.85	(declare-fun tptp.setukpairinjR12 () Bool)
0.59/0.85	(assert (= tptp.setukpairinjR12 (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (let ((_let_2 (@ tptp.setadjoin (@ _let_1 tptp.emptyset)))) (=> (= Xx Xy) (= (@ _let_2 (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ _let_2 tptp.emptyset))))))))
0.59/0.85	(declare-fun tptp.setukpairinjR1 () Bool)
0.59/0.85	(assert (= tptp.setukpairinjR1 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xz))) (let ((_let_2 (@ tptp.setadjoin Xx))) (=> (= (@ (@ tptp.setadjoin (@ _let_2 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_2 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset))) (=> (= Xz Xu) (= Xy Xu))))))))
0.59/0.85	(declare-fun tptp.upairequniteq () Bool)
0.59/0.85	(assert (= tptp.upairequniteq (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (= (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.setadjoin Xz) tptp.emptyset)) (= Xx Xy)))))
0.59/0.85	(declare-fun tptp.setukpairinjR2 () Bool)
0.59/0.85	(assert (= tptp.setukpairinjR2 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xz))) (let ((_let_2 (@ tptp.setadjoin Xx))) (=> (= (@ (@ tptp.setadjoin (@ _let_2 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_2 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset))) (= Xy Xu)))))))
0.59/0.85	(declare-fun tptp.setukpairinjR () Bool)
0.59/0.85	(assert (= tptp.setukpairinjR (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xy Xu)))))
0.59/0.85	(declare-fun tptp.ksndsingleton () Bool)
0.59/0.85	(assert (= tptp.ksndsingleton (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (@ tptp.singleton (@ (@ tptp.dsetconstr (@ tptp.setunion Xu)) (lambda ((Xx $$unsorted)) (= Xu (@ (@ tptp.kpair (@ tptp.kfst Xu)) Xx)))))))))
0.59/0.85	(declare-fun tptp.ksnd ($$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.ksndpairEq () Bool)
0.59/0.85	(assert (= tptp.ksndpairEq (forall ((Xx $$unsorted) (Xy $$unsorted)) (= (@ tptp.ksnd (@ (@ tptp.kpair Xx) Xy)) Xy))))
0.59/0.85	(declare-fun tptp.kpairsurjEq () Bool)
0.59/0.85	(assert (= tptp.kpairsurjEq (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (= (@ (@ tptp.kpair (@ tptp.kfst Xu)) (@ tptp.ksnd Xu)) Xu)))))
0.59/0.85	(declare-fun tptp.cartprodsndin () Bool)
0.59/0.85	(assert (= tptp.cartprodsndin (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in (@ tptp.ksnd Xu)) B)))))
0.59/0.85	(declare-fun tptp.cartprodpairmemEL () Bool)
0.59/0.85	(assert (= tptp.cartprodpairmemEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in Xx) A)))))
0.59/0.85	(declare-fun tptp.cartprodpairmemER () Bool)
0.59/0.85	(assert (= tptp.cartprodpairmemER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in Xy) B)))))
0.59/0.85	(declare-fun tptp.cartprodmempaircEq () Bool)
0.59/0.85	(assert (= tptp.cartprodmempaircEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) Xy))) (=> (@ (@ tptp.in Xy) B) (= _let_1 _let_1))))))))
0.59/0.85	(declare-fun tptp.cartprodfstpairEq () Bool)
0.59/0.85	(assert (= tptp.cartprodfstpairEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (= (@ tptp.kfst (@ (@ tptp.kpair Xx) Xy)) Xx)))))))
0.59/0.85	(declare-fun tptp.cartprodsndpairEq () Bool)
0.59/0.85	(assert (= tptp.cartprodsndpairEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (= (@ tptp.ksnd (@ (@ tptp.kpair Xx) Xy)) Xy)))))))
0.59/0.85	(declare-fun tptp.cartprodpairsurjEq () Bool)
0.59/0.85	(assert (= tptp.cartprodpairsurjEq (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (= (@ (@ tptp.kpair (@ tptp.kfst Xu)) (@ tptp.ksnd Xu)) Xu)))))
0.59/0.85	(declare-fun tptp.breln ($$unsorted $$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.dpsetconstr ($$unsorted $$unsorted (-> $$unsorted $$unsorted Bool)) $$unsorted)
0.59/0.85	(declare-fun tptp.dpsetconstrI () Bool)
0.59/0.85	(assert (= tptp.dpsetconstrI (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ Xphi Xx) Xy) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))))))))))
0.59/0.85	(declare-fun tptp.dpsetconstrSub () Bool)
0.59/0.85	(assert (= tptp.dpsetconstrSub (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.subset (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ Xphi Xx) Xy)))) (@ (@ tptp.cartprod A) B)))))
0.59/0.85	(declare-fun tptp.setOfPairsIsBReln () Bool)
0.59/0.85	(assert (= tptp.setOfPairsIsBReln (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ (@ tptp.breln A) B) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ Xphi Xx) Xy)))))))
0.59/0.85	(declare-fun tptp.dpsetconstrERa () Bool)
0.59/0.85	(assert (= tptp.dpsetconstrERa (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ Xphi Xx) Xy))))))))
0.59/0.85	(declare-fun tptp.dpsetconstrEL1 () Bool)
0.59/0.85	(assert (= tptp.dpsetconstrEL1 (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ tptp.in Xx) A)))))
0.59/0.85	(declare-fun tptp.dpsetconstrEL2 () Bool)
0.59/0.85	(assert (= tptp.dpsetconstrEL2 (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ tptp.in Xy) B)))))
0.59/0.85	(declare-fun tptp.dpsetconstrER () Bool)
0.59/0.85	(assert (= tptp.dpsetconstrER (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ Xphi Xx) Xy)))))
0.59/0.85	(declare-fun tptp.func ($$unsorted $$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.funcSet ($$unsorted $$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.funcImageSingleton () Bool)
0.59/0.85	(assert (= tptp.funcImageSingleton (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ tptp.singleton (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))))))))
0.59/0.85	(declare-fun tptp.apProp () Bool)
0.59/0.85	(assert (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B)))))))
0.59/0.85	(declare-fun tptp.ap ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.app () Bool)
0.59/0.85	(assert (= tptp.app (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B)))))))
0.59/0.85	(declare-fun tptp.infuncsetfunc () Bool)
0.59/0.85	(assert (= tptp.infuncsetfunc (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (@ (@ (@ tptp.func A) B) Xf)))))
0.59/0.85	(declare-fun tptp.ap2p () Bool)
0.59/0.85	(assert (= tptp.ap2p (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B)))))))
0.59/0.85	(declare-fun tptp.funcinfuncset () Bool)
0.59/0.85	(assert (= tptp.funcinfuncset (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B))))))
0.59/0.85	(declare-fun tptp.lamProp () Bool)
0.59/0.85	(assert (= tptp.lamProp (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (@ (@ (@ tptp.func A) B) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (= (@ Xf Xx) Xy))))))))
0.59/0.85	(declare-fun tptp.lam ($$unsorted $$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
0.59/0.85	(declare-fun tptp.lamp () Bool)
0.59/0.85	(assert (= tptp.lamp (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (@ (@ (@ tptp.func A) B) (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ Xf Xx))))))))
0.59/0.85	(declare-fun tptp.lam2p () Bool)
0.59/0.85	(assert (= tptp.lam2p (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (@ (@ tptp.in (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ Xf Xx)))) (@ (@ tptp.funcSet A) B))))))
0.59/0.85	(declare-fun tptp.brelnall1 () Bool)
0.59/0.85	(assert (= tptp.brelnall1 (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) Xy))) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in _let_1) R) (@ Xphi _let_1))))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) R) (@ Xphi Xx)))))))))
0.59/0.85	(declare-fun tptp.brelnall2 () Bool)
0.59/0.85	(assert (= tptp.brelnall2 (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) Xy))) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in _let_1) R) (@ Xphi _let_1))))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) R) (@ Xphi Xx)))))))))
0.59/0.85	(declare-fun tptp.ex1E2 () Bool)
0.59/0.85	(assert (= tptp.ex1E2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy)))))))))))
0.59/0.85	(declare-fun tptp.funcGraphProp1 () Bool)
0.59/0.85	(assert (= tptp.funcGraphProp1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.kpair Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf)))))))
0.59/0.85	(declare-fun tptp.funcGraphProp3 () Bool)
0.59/0.85	(assert (= tptp.funcGraphProp3 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.kpair Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf)))))))
0.59/0.85	(declare-fun tptp.funcGraphProp2 () Bool)
0.59/0.85	(assert (= tptp.funcGraphProp2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) Xy))))))))))
0.59/0.85	(declare-fun tptp.funcextLem () Bool)
0.59/0.85	(assert (= tptp.funcextLem (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xg $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xg) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (=> (@ (@ tptp.in Xx) A) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 Xg) Xx))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 Xg) (@ _let_1 Xf))))))))))))))
0.59/0.85	(declare-fun tptp.funcGraphProp4 () Bool)
0.59/0.85	(assert (= tptp.funcGraphProp4 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) Xy))))))))))
0.59/0.85	(declare-fun tptp.subbreln () Bool)
0.59/0.85	(assert (= tptp.subbreln (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((S $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) S) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 R) (@ _let_1 S))))))) (@ (@ tptp.subset R) S))))))))
0.59/0.85	(declare-fun tptp.eqbreln () Bool)
0.59/0.85	(assert (= tptp.eqbreln (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((S $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) S) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 R) (@ _let_1 S))))))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 S) (@ _let_1 R))))))) (= R S)))))))))
0.59/0.85	(declare-fun tptp.funcext () Bool)
0.59/0.85	(assert (= tptp.funcext (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xg $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xg) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (=> (@ (@ tptp.in Xx) A) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 Xg) Xx))))) (= Xf Xg))))))))
0.59/0.85	(declare-fun tptp.funcext2 () Bool)
0.59/0.85	(assert (= tptp.funcext2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xg $$unsorted)) (=> (@ (@ tptp.in Xg) (@ (@ tptp.funcSet A) B)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (=> (@ (@ tptp.in Xx) A) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 Xg) Xx))))) (= Xf Xg))))))))
0.59/0.85	(declare-fun tptp.ap2apEq1 () Bool)
0.59/0.85	(assert (= tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) (=> (@ (@ tptp.in Xx) A) (= _let_1 _let_1))))))))
0.59/0.85	(declare-fun tptp.ap2apEq2 () Bool)
0.59/0.85	(assert (= tptp.ap2apEq2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) (=> (@ (@ tptp.in Xx) A) (= _let_1 _let_1))))))))
0.59/0.85	(declare-fun tptp.beta1 () Bool)
0.59/0.85	(assert (= tptp.beta1 (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) (@ (@ (@ tptp.lam A) B) (lambda ((Xy $$unsorted)) (@ Xf Xy)))) Xx) (@ Xf Xx))))))))
0.59/0.85	(declare-fun tptp.eta1 () Bool)
0.59/0.85	(assert (= tptp.eta1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (= (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf)))))
0.59/0.85	(declare-fun tptp.lam2lamEq () Bool)
0.59/0.85	(assert (= tptp.lam2lamEq (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (let ((_let_1 (@ (@ tptp.lam A) B))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (= (@ _let_1 (lambda ((Xx $$unsorted)) (@ Xf Xx))) (@ _let_1 (lambda ((Xx $$unsorted)) (@ Xf Xx)))))))))
0.59/0.85	(declare-fun tptp.beta2 () Bool)
0.59/0.85	(assert (= tptp.beta2 (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) (@ (@ (@ tptp.lam A) B) (lambda ((Xy $$unsorted)) (@ Xf Xy)))) Xx) (@ Xf Xx))))))))
0.59/0.85	(declare-fun tptp.eta2 () Bool)
0.59/0.85	(assert (= tptp.eta2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (= (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf)))))
0.59/0.85	(declare-fun tptp.iffalseProp1 () Bool)
0.59/0.85	(assert (= tptp.iffalseProp1 (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (=> (not Xphi) (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy))))))))))))))
0.59/0.85	(declare-fun tptp.iffalseProp2 () Bool)
0.59/0.85	(assert (= tptp.iffalseProp2 (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (not Xphi) (= (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy))))) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))))))
0.59/0.85	(declare-fun tptp.iftrueProp1 () Bool)
0.59/0.85	(assert (= tptp.iftrueProp1 (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> Xphi (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy)))))))))))))
0.59/0.85	(declare-fun tptp.iftrueProp2 () Bool)
0.59/0.85	(assert (= tptp.iftrueProp2 (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> Xphi (= (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy))))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))
0.59/0.85	(declare-fun tptp.ifSingleton () Bool)
0.59/0.85	(assert (= tptp.ifSingleton (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy))))))))))))
0.59/0.85	(declare-fun tptp.if ($$unsorted Bool $$unsorted $$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.ifp () Bool)
0.59/0.85	(assert (= tptp.ifp (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.if A) Xphi) Xx) Xy)) A)))))))
0.59/0.85	(declare-fun tptp.theeq () Bool)
0.59/0.85	(assert (= tptp.theeq (forall ((X $$unsorted)) (=> (@ tptp.singleton X) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) X) (= (@ tptp.setunion X) Xx)))))))
0.59/0.85	(declare-fun tptp.iftrue () Bool)
0.59/0.85	(assert (= tptp.iftrue (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> Xphi (= (@ (@ (@ (@ tptp.if A) Xphi) Xx) Xy) Xx))))))))
0.59/0.85	(declare-fun tptp.iffalse () Bool)
0.59/0.85	(assert (= tptp.iffalse (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (not Xphi) (= (@ (@ (@ (@ tptp.if A) Xphi) Xx) Xy) Xy))))))))
0.59/0.85	(declare-fun tptp.iftrueorfalse () Bool)
0.59/0.85	(assert (= tptp.iftrueorfalse (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.if A) Xphi) Xx) Xy)) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))))))
0.59/0.85	(declare-fun tptp.binintersectT_lem () Bool)
0.59/0.85	(assert (= tptp.binintersectT_lem (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.powerset A))) (=> (@ (@ tptp.in Y) _let_1) (@ (@ tptp.in (@ (@ tptp.binintersect X) Y)) _let_1))))))))
0.59/0.85	(declare-fun tptp.binunionT_lem () Bool)
0.59/0.85	(assert (= tptp.binunionT_lem (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.powerset A))) (=> (@ (@ tptp.in Y) _let_1) (@ (@ tptp.in (@ (@ tptp.binunion X) Y)) _let_1))))))))
0.59/0.85	(declare-fun tptp.powersetT_lem () Bool)
0.59/0.85	(assert (= tptp.powersetT_lem (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (@ tptp.powerset A))) (=> (@ (@ tptp.in X) _let_1) (@ (@ tptp.in (@ tptp.powerset X)) (@ tptp.powerset _let_1)))))))
0.59/0.85	(declare-fun tptp.setminusT_lem () Bool)
0.59/0.85	(assert (= tptp.setminusT_lem (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.powerset A))) (=> (@ (@ tptp.in Y) _let_1) (@ (@ tptp.in (@ (@ tptp.setminus X) Y)) _let_1))))))))
0.59/0.85	(declare-fun tptp.complementT_lem () Bool)
0.59/0.85	(assert (= tptp.complementT_lem (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (@ tptp.powerset A))) (=> (@ (@ tptp.in X) _let_1) (@ (@ tptp.in (@ (@ tptp.setminus A) X)) _let_1))))))
0.59/0.85	(declare-fun tptp.setextT () Bool)
0.59/0.85	(assert (= tptp.setextT (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 X) (@ _let_1 Y))))) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 Y) (@ _let_1 X))))) (= X Y)))))))))
0.59/0.85	(declare-fun tptp.subsetTI () Bool)
0.59/0.85	(assert (= tptp.subsetTI (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 X) (@ _let_1 Y))))) (@ (@ tptp.subset X) Y))))))))
0.59/0.85	(declare-fun tptp.powersetTI1 () Bool)
0.59/0.85	(assert (= tptp.powersetTI1 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 X) (@ _let_1 Y))))) (@ (@ tptp.in X) (@ tptp.powerset Y)))))))))
0.59/0.85	(declare-fun tptp.powersetTE1 () Bool)
0.59/0.85	(assert (= tptp.powersetTE1 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ (@ tptp.in X) (@ tptp.powerset Y)) (=> (@ _let_1 X) (@ _let_1 Y))))))))))))
0.59/0.85	(declare-fun tptp.complementTI1 () Bool)
0.59/0.85	(assert (= tptp.complementTI1 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 X) (not (@ _let_1 (@ (@ tptp.setminus A) X)))))))))))
0.59/0.85	(declare-fun tptp.complementTE1 () Bool)
0.59/0.85	(assert (= tptp.complementTE1 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 (@ (@ tptp.setminus A) X))) (@ _let_1 X)))))))))
0.59/0.85	(declare-fun tptp.binintersectTELcontra () Bool)
0.59/0.85	(assert (= tptp.binintersectTELcontra (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 X)) (not (@ _let_1 (@ (@ tptp.binintersect X) Y)))))))))))))
0.59/0.85	(declare-fun tptp.binintersectTERcontra () Bool)
0.59/0.85	(assert (= tptp.binintersectTERcontra (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 Y)) (not (@ _let_1 (@ (@ tptp.binintersect X) Y)))))))))))))
0.59/0.85	(declare-fun tptp.contrasubsetT () Bool)
0.59/0.85	(assert (= tptp.contrasubsetT (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ (@ tptp.subset X) (@ (@ tptp.setminus A) Y)) (=> (@ _let_1 Y) (not (@ _let_1 X)))))))))))))
0.59/0.85	(declare-fun tptp.contrasubsetT1 () Bool)
0.59/0.85	(assert (= tptp.contrasubsetT1 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ (@ tptp.subset X) Y) (=> (not (@ _let_1 Y)) (not (@ _let_1 X)))))))))))))
0.59/0.85	(declare-fun tptp.contrasubsetT2 () Bool)
0.59/0.85	(assert (= tptp.contrasubsetT2 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (=> (@ (@ tptp.subset X) Y) (@ (@ tptp.subset (@ _let_1 Y)) (@ _let_1 X))))))))))
0.59/0.85	(declare-fun tptp.contrasubsetT3 () Bool)
0.59/0.85	(assert (= tptp.contrasubsetT3 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (=> (@ (@ tptp.subset (@ _let_1 Y)) (@ _let_1 X)) (@ (@ tptp.subset X) Y)))))))))
0.59/0.85	(declare-fun tptp.doubleComplementI1 () Bool)
0.59/0.85	(assert (= tptp.doubleComplementI1 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (let ((_let_2 (@ tptp.in Xx))) (=> (@ _let_2 A) (=> (@ _let_2 X) (@ _let_2 (@ _let_1 (@ _let_1 X))))))))))))
0.59/0.85	(declare-fun tptp.doubleComplementE1 () Bool)
0.59/0.85	(assert (= tptp.doubleComplementE1 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (let ((_let_2 (@ tptp.setminus A))) (=> (@ _let_1 A) (=> (@ _let_1 (@ _let_2 (@ _let_2 X))) (@ _let_1 X))))))))))
0.59/0.85	(declare-fun tptp.doubleComplementSub1 () Bool)
0.59/0.85	(assert (= tptp.doubleComplementSub1 (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (@ (@ tptp.subset X) (@ _let_1 (@ _let_1 X))))))))
0.59/0.85	(declare-fun tptp.doubleComplementSub2 () Bool)
0.59/0.85	(assert (= tptp.doubleComplementSub2 (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (@ (@ tptp.subset (@ _let_1 (@ _let_1 X))) X))))))
0.59/0.85	(declare-fun tptp.doubleComplementEq () Bool)
0.59/0.85	(assert (= tptp.doubleComplementEq (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (= X (@ _let_1 (@ _let_1 X))))))))
0.59/0.85	(declare-fun tptp.complementTnotintersectT () Bool)
0.59/0.85	(assert (= tptp.complementTnotintersectT (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 (@ (@ tptp.setminus A) X)) (not (@ _let_1 (@ (@ tptp.binintersect X) Y)))))))))))))
0.59/0.85	(declare-fun tptp.complementImpComplementIntersect () Bool)
0.59/0.85	(assert (= tptp.complementImpComplementIntersect (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (let ((_let_2 (@ tptp.in Xx))) (=> (@ _let_2 A) (=> (@ _let_2 (@ _let_1 X)) (@ _let_2 (@ _let_1 (@ (@ tptp.binintersect X) Y))))))))))))))
0.59/0.85	(declare-fun tptp.complementSubsetComplementIntersect () Bool)
0.59/0.85	(assert (= tptp.complementSubsetComplementIntersect (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (@ (@ tptp.subset (@ _let_1 X)) (@ _let_1 (@ (@ tptp.binintersect X) Y))))))))))
0.59/0.85	(declare-fun tptp.complementInPowersetComplementIntersect () Bool)
0.59/0.85	(assert (= tptp.complementInPowersetComplementIntersect (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (@ (@ tptp.in (@ _let_1 X)) (@ tptp.powerset (@ _let_1 (@ (@ tptp.binintersect X) Y)))))))))))
0.59/0.85	(declare-fun tptp.contraSubsetComplement () Bool)
0.59/0.85	(assert (= tptp.contraSubsetComplement (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (=> (@ (@ tptp.subset X) (@ (@ tptp.setminus A) Y)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.setminus A) X)))))))))))))
0.59/0.85	(declare-fun tptp.complementTcontraSubset () Bool)
0.59/0.85	(assert (= tptp.complementTcontraSubset (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (=> (@ (@ tptp.subset X) (@ _let_1 Y)) (@ (@ tptp.subset Y) (@ _let_1 X))))))))))
0.59/0.85	(declare-fun tptp.binunionTILcontra () Bool)
0.59/0.85	(assert (= tptp.binunionTILcontra (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 (@ (@ tptp.binunion X) Y))) (not (@ _let_1 X))))))))))))
0.59/0.85	(declare-fun tptp.binunionTIRcontra () Bool)
0.59/0.85	(assert (= tptp.binunionTIRcontra (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 (@ (@ tptp.binunion X) Y))) (not (@ _let_1 Y))))))))))))
0.59/0.85	(declare-fun tptp.inIntersectImpInUnion () Bool)
0.59/0.85	(assert (= tptp.inIntersectImpInUnion (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Z $$unsorted)) (=> (@ (@ tptp.in Z) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 (@ (@ tptp.binintersect X) Y)) (@ _let_1 (@ (@ tptp.binunion X) Z))))))))))))))
0.59/0.85	(declare-fun tptp.inIntersectImpInUnion2 () Bool)
0.59/0.85	(assert (= tptp.inIntersectImpInUnion2 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Z $$unsorted)) (=> (@ (@ tptp.in Z) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 (@ (@ tptp.binintersect X) Y)) (@ _let_1 (@ (@ tptp.binunion Y) Z))))))))))))))
0.59/0.85	(declare-fun tptp.inIntersectImpInIntersectUnions () Bool)
0.59/0.85	(assert (= tptp.inIntersectImpInIntersectUnions (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Z $$unsorted)) (=> (@ (@ tptp.in Z) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 (@ (@ tptp.binintersect X) Y)) (@ _let_1 (@ (@ tptp.binintersect (@ (@ tptp.binunion X) Z)) (@ (@ tptp.binunion Y) Z)))))))))))))))
0.59/0.85	(declare-fun tptp.intersectInPowersetIntersectUnions () Bool)
0.59/0.85	(assert (= tptp.intersectInPowersetIntersectUnions (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Z $$unsorted)) (=> (@ (@ tptp.in Z) (@ tptp.powerset A)) (@ (@ tptp.in (@ (@ tptp.binintersect X) Y)) (@ tptp.powerset (@ (@ tptp.binintersect (@ (@ tptp.binunion X) Z)) (@ (@ tptp.binunion Y) Z))))))))))))
0.59/0.85	(declare-fun tptp.inComplementUnionImpNotIn1 () Bool)
0.59/0.85	(assert (= tptp.inComplementUnionImpNotIn1 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 (@ (@ tptp.setminus A) (@ (@ tptp.binunion X) Y))) (not (@ _let_1 X))))))))))))
0.59/0.85	(declare-fun tptp.inComplementUnionImpInComplement1 () Bool)
0.59/0.85	(assert (= tptp.inComplementUnionImpInComplement1 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (let ((_let_2 (@ tptp.in Xx))) (=> (@ _let_2 A) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.binunion X) Y))) (@ _let_2 (@ _let_1 X)))))))))))))
0.59/0.85	(declare-fun tptp.binunionTE () Bool)
0.59/0.85	(assert (= tptp.binunionTE (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xphi Bool) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 (@ (@ tptp.binunion X) Y)) (=> (=> (@ _let_1 X) Xphi) (=> (=> (@ _let_1 Y) Xphi) Xphi))))))))))))
0.59/0.85	(declare-fun tptp.binunionTEcontra () Bool)
0.59/0.85	(assert (= tptp.binunionTEcontra (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 X)) (=> (not (@ _let_1 Y)) (not (@ _let_1 (@ (@ tptp.binunion X) Y))))))))))))))
0.59/0.85	(declare-fun tptp.demorgan2a1 () Bool)
0.59/0.85	(assert (= tptp.demorgan2a1 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (let ((_let_2 (@ tptp.in Xx))) (=> (@ _let_2 A) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.binunion X) Y))) (@ _let_2 (@ _let_1 X)))))))))))))
0.59/0.85	(declare-fun tptp.complementUnionInPowersetComplement () Bool)
0.59/0.85	(assert (= tptp.complementUnionInPowersetComplement (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (@ (@ tptp.in (@ _let_1 (@ (@ tptp.binunion X) Y))) (@ tptp.powerset (@ _let_1 X))))))))))
0.59/0.85	(declare-fun tptp.demorgan2a2 () Bool)
0.59/0.85	(assert (= tptp.demorgan2a2 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (let ((_let_2 (@ tptp.in Xx))) (=> (@ _let_2 A) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.binunion X) Y))) (@ _let_2 (@ _let_1 Y)))))))))))))
0.59/0.85	(declare-fun tptp.demorgan1a () Bool)
0.59/0.85	(assert (= tptp.demorgan1a (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (let ((_let_2 (@ tptp.in Xx))) (=> (@ _let_2 A) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.binintersect X) Y))) (@ _let_2 (@ (@ tptp.binunion (@ _let_1 X)) (@ _let_1 Y))))))))))))))
0.59/0.85	(declare-fun tptp.demorgan1b () Bool)
0.59/0.85	(assert (= tptp.demorgan1b (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (let ((_let_2 (@ tptp.in Xx))) (=> (@ _let_2 A) (=> (@ _let_2 (@ (@ tptp.binunion (@ _let_1 X)) (@ _let_1 Y))) (@ _let_2 (@ _let_1 (@ (@ tptp.binintersect X) Y))))))))))))))
0.59/0.85	(declare-fun tptp.demorgan1 () Bool)
0.59/0.85	(assert (= tptp.demorgan1 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (= (@ _let_1 (@ (@ tptp.binintersect X) Y)) (@ (@ tptp.binunion (@ _let_1 X)) (@ _let_1 Y))))))))))
0.59/0.85	(declare-fun tptp.demorgan2a () Bool)
0.59/0.85	(assert (= tptp.demorgan2a (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (let ((_let_2 (@ tptp.in Xx))) (=> (@ _let_2 A) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.binunion X) Y))) (@ _let_2 (@ (@ tptp.binintersect (@ _let_1 X)) (@ _let_1 Y))))))))))))))
0.59/0.85	(declare-fun tptp.demorgan2b2 () Bool)
0.59/0.85	(assert (= tptp.demorgan2b2 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (let ((_let_2 (@ tptp.in Xx))) (=> (@ _let_2 A) (=> (@ _let_2 (@ _let_1 X)) (=> (@ _let_2 (@ _let_1 Y)) (@ _let_2 (@ _let_1 (@ (@ tptp.binunion X) Y)))))))))))))))
0.59/0.85	(declare-fun tptp.demorgan2b () Bool)
0.59/0.85	(assert (= tptp.demorgan2b (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (let ((_let_2 (@ tptp.in Xx))) (=> (@ _let_2 A) (=> (@ _let_2 (@ (@ tptp.binintersect (@ _let_1 X)) (@ _let_1 Y))) (@ _let_2 (@ _let_1 (@ (@ tptp.binunion X) Y))))))))))))))
0.59/0.85	(declare-fun tptp.demorgan2 () Bool)
0.59/0.85	(assert (= tptp.demorgan2 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (= (@ _let_1 (@ (@ tptp.binunion X) Y)) (@ (@ tptp.binintersect (@ _let_1 X)) (@ _let_1 Y))))))))))
0.59/0.85	(declare-fun tptp.woz13rule0 () Bool)
0.59/0.85	(assert (= tptp.woz13rule0 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect X) Y)) (@ _let_1 A))))))))))
0.59/0.85	(declare-fun tptp.woz13rule1 () Bool)
0.59/0.85	(assert (= tptp.woz13rule1 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Z $$unsorted)) (=> (@ (@ tptp.in Z) (@ tptp.powerset A)) (=> (@ (@ tptp.subset X) Z) (@ (@ tptp.subset (@ (@ tptp.binintersect X) Y)) Z))))))))))
0.59/0.85	(declare-fun tptp.woz13rule2 () Bool)
0.59/0.85	(assert (= tptp.woz13rule2 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Z $$unsorted)) (=> (@ (@ tptp.in Z) (@ tptp.powerset A)) (=> (@ (@ tptp.subset Y) Z) (@ (@ tptp.subset (@ (@ tptp.binintersect X) Y)) Z))))))))))
0.59/0.85	(declare-fun tptp.woz13rule3 () Bool)
0.59/0.85	(assert (= tptp.woz13rule3 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Z $$unsorted)) (let ((_let_1 (@ tptp.subset X))) (=> (@ (@ tptp.in Z) (@ tptp.powerset A)) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.binintersect Y) Z)))))))))))))
0.59/0.85	(declare-fun tptp.woz13rule4 () Bool)
0.59/0.85	(assert (= tptp.woz13rule4 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Z $$unsorted)) (=> (@ (@ tptp.in Z) (@ tptp.powerset A)) (forall ((W $$unsorted)) (=> (@ (@ tptp.in W) (@ tptp.powerset A)) (=> (@ (@ tptp.subset X) Z) (=> (@ (@ tptp.subset Y) W) (@ (@ tptp.subset (@ (@ tptp.binintersect X) Y)) (@ (@ tptp.binintersect Z) W))))))))))))))
0.59/0.85	(declare-fun tptp.woz1_1 () Bool)
0.59/0.85	(assert (= tptp.woz1_1 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (@ (@ tptp.in (@ _let_1 X)) (@ tptp.powerset (@ _let_1 (@ (@ tptp.binintersect X) Y)))))))))))
0.59/0.85	(declare-fun tptp.woz1_2 () Bool)
0.59/0.85	(assert (= tptp.woz1_2 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Z $$unsorted)) (=> (@ (@ tptp.in Z) (@ tptp.powerset A)) (forall ((W $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in W) (@ tptp.powerset A)) (= (@ _let_1 (@ (@ tptp.binintersect (@ (@ tptp.binunion X) Y)) (@ (@ tptp.binunion Z) W))) (@ (@ tptp.binunion (@ (@ tptp.binintersect (@ _let_1 X)) (@ _let_1 Y))) (@ (@ tptp.binintersect (@ _let_1 Z)) (@ _let_1 W)))))))))))))))
0.59/0.85	(declare-fun tptp.woz1_3 () Bool)
0.59/0.85	(assert (= tptp.woz1_3 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (forall ((Z $$unsorted)) (=> (@ (@ tptp.in Z) (@ tptp.powerset A)) (@ (@ tptp.in (@ (@ tptp.binintersect X) Y)) (@ tptp.powerset (@ (@ tptp.binintersect (@ (@ tptp.binunion X) Z)) (@ (@ tptp.binunion Y) Z))))))))))))
0.59/0.85	(declare-fun tptp.woz1_4 () Bool)
0.59/0.85	(assert (= tptp.woz1_4 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (=> (@ (@ tptp.subset X) (@ _let_1 Y)) (@ (@ tptp.subset Y) (@ _let_1 X))))))))))
0.59/0.85	(declare-fun tptp.woz1_5 () Bool)
0.59/0.85	(assert (= tptp.woz1_5 (forall ((A $$unsorted) (X $$unsorted)) (=> (@ (@ tptp.in X) (@ tptp.powerset A)) (forall ((Y $$unsorted)) (let ((_let_1 (@ tptp.setminus A))) (=> (@ (@ tptp.in Y) (@ tptp.powerset A)) (@ (@ tptp.in (@ _let_1 (@ (@ tptp.binunion X) Y))) (@ tptp.powerset (@ _let_1 X))))))))))
0.59/0.85	(declare-fun tptp.breln1 ($$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.breln1all2 () Bool)
0.59/0.85	(assert (= tptp.breln1all2 (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) Xy))) (=> (@ (@ tptp.in Xy) A) (=> (@ (@ tptp.in _let_1) R) (@ Xphi _let_1))))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) R) (@ Xphi Xx)))))))))
0.59/0.85	(declare-fun tptp.breln1Set ($$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.breln1SetBreln1 () Bool)
0.59/0.85	(assert (= tptp.breln1SetBreln1 (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.in R) (@ tptp.breln1Set A)) (@ (@ tptp.breln1 A) R)))))
0.59/0.85	(declare-fun tptp.transitive ($$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.antisymmetric ($$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.reflexive ($$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.refltransitive ($$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.refllinearorder ($$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.reflwellordering ($$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.choice2fnsingleton () Bool)
0.59/0.85	(assert (= tptp.choice2fnsingleton (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) B) (@ (@ Xphi Xx) Xy))))) (forall ((R $$unsorted)) (=> (@ (@ tptp.in R) (@ tptp.breln1Set B)) (=> (@ (@ tptp.reflwellordering B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ tptp.singleton (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (and (@ (@ Xphi Xx) Xy) (forall ((Xz $$unsorted)) (=> (@ (@ tptp.in Xz) B) (=> (@ (@ Xphi Xx) Xz) (@ (@ tptp.in (@ (@ tptp.kpair Xy) Xz)) R)))))))))))))))))
0.59/0.85	(declare-fun tptp.setOfPairsIsBReln1 () Bool)
0.59/0.85	(assert (= tptp.setOfPairsIsBReln1 (forall ((A $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.breln1 A) (@ (@ (@ tptp.dpsetconstr A) A) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ Xphi Xx) Xy)))))))
0.59/0.85	(declare-fun tptp.breln1all1 () Bool)
0.59/0.85	(assert (= tptp.breln1all1 (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) Xy))) (=> (@ (@ tptp.in Xy) A) (=> (@ (@ tptp.in _let_1) R) (@ Xphi _let_1))))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) R) (@ Xphi Xx)))))))))
0.59/0.85	(declare-fun tptp.subbreln1 () Bool)
0.59/0.85	(assert (= tptp.subbreln1 (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (=> (@ (@ tptp.breln1 A) S) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) A) (=> (@ _let_1 R) (@ _let_1 S))))))) (@ (@ tptp.subset R) S))))))))
0.59/0.85	(declare-fun tptp.eqbreln1 () Bool)
0.59/0.85	(assert (= tptp.eqbreln1 (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (=> (@ (@ tptp.breln1 A) S) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) A) (=> (@ _let_1 R) (@ _let_1 S))))))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) A) (=> (@ _let_1 S) (@ _let_1 R))))))) (= R S)))))))))
0.59/0.85	(declare-fun tptp.breln1invset ($$unsorted $$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.breln1invprop () Bool)
0.59/0.85	(assert (= tptp.breln1invprop (forall ((A $$unsorted) (R $$unsorted)) (let ((_let_1 (@ tptp.breln1 A))) (=> (@ _let_1 R) (@ _let_1 (@ (@ tptp.breln1invset A) R)))))))
0.59/0.85	(declare-fun tptp.breln1invI () Bool)
0.59/0.85	(assert (= tptp.breln1invI (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R) (@ (@ tptp.in (@ (@ tptp.kpair Xy) Xx)) (@ (@ tptp.breln1invset A) R)))))))))))
0.59/0.85	(declare-fun tptp.breln1invE () Bool)
0.59/0.85	(assert (= tptp.breln1invE (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xy) Xx)) (@ (@ tptp.breln1invset A) R)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))))
0.59/0.85	(declare-fun tptp.breln1compset ($$unsorted $$unsorted $$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.breln1compprop () Bool)
0.59/0.85	(assert (= tptp.breln1compprop (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (let ((_let_1 (@ tptp.breln1 A))) (=> (@ _let_1 S) (@ _let_1 (@ (@ (@ tptp.breln1compset A) R) S)))))))))
0.59/0.85	(declare-fun tptp.breln1compI () Bool)
0.59/0.85	(assert (= tptp.breln1compI (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (=> (@ (@ tptp.breln1 A) S) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (forall ((Xz $$unsorted)) (let ((_let_1 (@ tptp.kpair Xx))) (=> (@ (@ tptp.in Xz) A) (=> (@ (@ tptp.in (@ _let_1 Xz)) R) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xz) Xy)) S) (@ (@ tptp.in (@ _let_1 Xy)) (@ (@ (@ tptp.breln1compset A) R) S)))))))))))))))))
0.59/0.85	(declare-fun tptp.breln1compE () Bool)
0.59/0.85	(assert (= tptp.breln1compE (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (=> (@ (@ tptp.breln1 A) S) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.breln1compset A) R) S)) (exists ((Xz $$unsorted)) (and (@ (@ tptp.in Xz) A) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xz)) R) (@ (@ tptp.in (@ (@ tptp.kpair Xz) Xy)) S))))))))))))))
0.59/0.85	(declare-fun tptp.breln1compEex () Bool)
0.59/0.85	(assert (= tptp.breln1compEex (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (=> (@ (@ tptp.breln1 A) S) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.breln1compset A) R) S)) (forall ((Xphi Bool)) (=> (forall ((Xz $$unsorted)) (=> (@ (@ tptp.in Xz) A) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xz)) R) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xz) Xy)) S) Xphi)))) Xphi)))))))))))))
0.59/0.85	(declare-fun tptp.breln1unionprop () Bool)
0.59/0.85	(assert (= tptp.breln1unionprop (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (let ((_let_1 (@ tptp.breln1 A))) (=> (@ _let_1 S) (@ _let_1 (@ (@ tptp.binunion R) S)))))))))
0.59/0.85	(declare-fun tptp.breln1unionIL () Bool)
0.59/0.85	(assert (= tptp.breln1unionIL (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (=> (@ (@ tptp.breln1 A) S) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) A) (=> (@ _let_1 R) (@ _let_1 (@ (@ tptp.binunion R) S))))))))))))))
0.59/0.85	(declare-fun tptp.breln1unionIR () Bool)
0.59/0.85	(assert (= tptp.breln1unionIR (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (=> (@ (@ tptp.breln1 A) S) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) A) (=> (@ _let_1 S) (@ _let_1 (@ (@ tptp.binunion R) S))))))))))))))
0.59/0.85	(declare-fun tptp.breln1unionI () Bool)
0.59/0.85	(assert (= tptp.breln1unionI (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (=> (@ (@ tptp.breln1 A) S) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) A) (=> (or (@ _let_1 R) (@ _let_1 S)) (@ _let_1 (@ (@ tptp.binunion R) S))))))))))))))
0.59/0.85	(declare-fun tptp.breln1unionE () Bool)
0.59/0.85	(assert (= tptp.breln1unionE (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (=> (@ (@ tptp.breln1 A) S) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) A) (=> (@ _let_1 (@ (@ tptp.binunion R) S)) (or (@ _let_1 R) (@ _let_1 S))))))))))))))
0.59/0.85	(declare-fun tptp.breln1unionEcases () Bool)
0.59/0.85	(assert (= tptp.breln1unionEcases (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (=> (@ (@ tptp.breln1 A) S) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.binunion R) S)) (forall ((Xphi Bool)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (=> (@ _let_1 R) Xphi) (=> (=> (@ _let_1 S) Xphi) Xphi)))))))))))))))
0.59/0.85	(declare-fun tptp.breln1unionCommutes () Bool)
0.59/0.85	(assert (= tptp.breln1unionCommutes (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (=> (@ (@ tptp.breln1 A) S) (= (@ (@ tptp.binunion R) S) (@ (@ tptp.binunion S) R))))))))
0.59/0.85	(declare-fun tptp.woz2Ex () Bool)
0.59/0.85	(assert (= tptp.woz2Ex (forall ((A $$unsorted) (R $$unsorted)) (let ((_let_1 (@ tptp.breln1invset A))) (=> (@ (@ tptp.breln1 A) R) (= R (@ _let_1 (@ _let_1 R))))))))
0.59/0.85	(declare-fun tptp.woz2W () Bool)
0.59/0.85	(assert (= tptp.woz2W (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (let ((_let_1 (@ tptp.breln1invset A))) (let ((_let_2 (@ tptp.breln1compset A))) (=> (@ (@ tptp.breln1 A) S) (= (@ _let_1 (@ (@ _let_2 R) S)) (@ (@ _let_2 (@ _let_1 S)) (@ _let_1 R)))))))))))
0.59/0.85	(declare-fun tptp.woz2A () Bool)
0.59/0.85	(assert (= tptp.woz2A (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (=> (@ (@ tptp.breln1 A) S) (forall ((T $$unsorted)) (let ((_let_1 (@ tptp.breln1compset A))) (=> (@ (@ tptp.breln1 A) T) (= (@ (@ _let_1 (@ (@ tptp.binunion R) S)) T) (@ (@ tptp.binunion (@ (@ _let_1 R) T)) (@ (@ _let_1 S) T))))))))))))
0.59/0.85	(declare-fun tptp.woz2B () Bool)
0.59/0.85	(assert (= tptp.woz2B (forall ((A $$unsorted) (R $$unsorted)) (=> (@ (@ tptp.breln1 A) R) (forall ((S $$unsorted)) (=> (@ (@ tptp.breln1 A) S) (forall ((T $$unsorted)) (let ((_let_1 (@ tptp.breln1invset A))) (let ((_let_2 (@ tptp.breln1compset A))) (let ((_let_3 (@ _let_2 (@ _let_1 T)))) (=> (@ (@ tptp.breln1 A) T) (= (@ (@ _let_2 (@ (@ tptp.binunion R) S)) T) (@ (@ tptp.binunion (@ _let_1 (@ _let_3 (@ _let_1 S)))) (@ _let_1 (@ _let_3 (@ _let_1 R))))))))))))))))
0.59/0.85	(declare-fun tptp.image1Ex () Bool)
0.59/0.85	(assert (= tptp.image1Ex (forall ((A $$unsorted) (Xf (-> $$unsorted $$unsorted))) (exists ((B $$unsorted)) (forall ((Xx $$unsorted)) (= (@ (@ tptp.in Xx) B) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) A) (= Xx (@ Xf Xy))))))))))
0.59/0.85	(declare-fun tptp.image1Ex1 () Bool)
0.59/0.85	(assert (= tptp.image1Ex1 (forall ((A $$unsorted) (Xf (-> $$unsorted $$unsorted))) (@ tptp.exu (lambda ((B $$unsorted)) (forall ((Xx $$unsorted)) (= (@ (@ tptp.in Xx) B) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) A) (= Xx (@ Xf Xy)))))))))))
0.59/0.85	(declare-fun tptp.image1 ($$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
0.59/0.85	(declare-fun tptp.image1Equiv () Bool)
0.59/0.85	(assert (= tptp.image1Equiv (forall ((A $$unsorted) (Xf (-> $$unsorted $$unsorted)) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ (@ tptp.image1 A) (lambda ((Xy $$unsorted)) (@ Xf Xy)))) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) A) (= Xx (@ Xf Xy))))))))
0.59/0.85	(declare-fun tptp.image1E () Bool)
0.59/0.85	(assert (= tptp.image1E (forall ((A $$unsorted) (Xf (-> $$unsorted $$unsorted)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.image1 A) (lambda ((Xy $$unsorted)) (@ Xf Xy)))) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) A) (= Xx (@ Xf Xy))))))))
0.59/0.85	(declare-fun tptp.image1I () Bool)
0.59/0.85	(assert (= tptp.image1I (forall ((A $$unsorted) (Xf (-> $$unsorted $$unsorted)) (Xx $$unsorted)) (=> (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) A) (= Xx (@ Xf Xy)))) (@ (@ tptp.in Xx) (@ (@ tptp.image1 A) (lambda ((Xy $$unsorted)) (@ Xf Xy))))))))
0.59/0.85	(declare-fun tptp.injective ($$unsorted $$unsorted $$unsorted) Bool)
0.59/0.85	(declare-fun tptp.injFuncSet ($$unsorted $$unsorted) $$unsorted)
0.59/0.85	(declare-fun tptp.injFuncInInjFuncSet () Bool)
0.59/0.85	(assert (= tptp.injFuncInInjFuncSet (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (let ((_let_1 (@ tptp.in Xf))) (=> (@ _let_1 (@ (@ tptp.funcSet A) B)) (=> (@ (@ (@ tptp.injective A) B) Xf) (@ _let_1 (@ (@ tptp.injFuncSet A) B))))))))
0.59/0.85	(declare-fun tptp.injFuncSetFuncIn () Bool)
0.59/0.85	(assert (= tptp.injFuncSetFuncIn (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (let ((_let_1 (@ tptp.in Xf))) (=> (@ _let_1 (@ (@ tptp.injFuncSet A) B)) (@ _let_1 (@ (@ tptp.funcSet A) B)))))))
0.59/0.85	(declare-fun tptp.injFuncSetFuncInj () Bool)
0.59/0.85	(assert (= tptp.injFuncSetFuncInj (forall ((Xx $$unsorted) (Xy $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.injFuncSet Xx) Xy)) (@ (@ (@ tptp.injective Xx) Xy) Xf)))))
0.59/0.85	(declare-fun tptp.surjective ($$unsorted $$unsorted $$unsorted) Bool)
0.59/0.85	(assert (= tptp.surjective (lambda ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) B) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) A) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xy) Xx))))))))
0.59/0.85	(declare-fun tptp.surjFuncSet ($$unsorted $$unsorted) $$unsorted)
0.59/0.85	(assert (= tptp.surjFuncSet (lambda ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.dsetconstr (@ (@ tptp.funcSet A) B)) (lambda ((Xf $$unsorted)) (@ (@ (@ tptp.surjective A) B) Xf))))))
0.59/0.85	(assert (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (=> tptp.ap2apEq2 (=> tptp.beta1 (=> tptp.eta1 (=> tptp.lam2lamEq (=> tptp.beta2 (=> tptp.eta2 (=> tptp.iffalseProp1 (=> tptp.iffalseProp2 (=> tptp.iftrueProp1 (=> tptp.iftrueProp2 (=> tptp.ifSingleton (=> tptp.ifp (=> tptp.theeq (=> tptp.iftrue (=> tptp.iffalse (=> tptp.iftrueorfalse (=> tptp.binintersectT_lem (=> tptp.binunionT_lem (=> tptp.powersetT_lem (=> tptp.setminusT_lem (=> tptp.complementT_lem (=> tptp.setextT (=> tptp.subsetTI (=> tptp.powersetTI1 (=> tptp.powersetTE1 (=> tptp.complementTI1 (=> tptp.complementTE1 (=> tptp.binintersectTELcontra (=> tptp.binintersectTERcontra (=> tptp.contrasubsetT (=> tptp.contrasubsetT1 (=> tptp.contrasubsetT2 (=> tptp.contrasubsetT3 (=> tptp.doubleComplementI1 (=> tptp.doubleComplementE1 (=> tptp.doubleComplementSub1 (=> tptp.doubleComplementSub2 (=> tptp.doubleComplementEq (=> tptp.complementTnotintersectT (=> tptp.complementImpComplementIntersect (=> tptp.complementSubsetComplementIntersect (=> tptp.complementInPowersetComplementIntersect (=> tptp.contraSubsetComplement (=> tptp.complementTcontraSubset (=> tptp.binunionTILcontra (=> tptp.binunionTIRcontra (=> tptp.inIntersectImpInUnion (=> tptp.inIntersectImpInUnion2 (=> tptp.inIntersectImpInIntersectUnions (=> tptp.intersectInPowersetIntersectUnions (=> tptp.inComplementUnionImpNotIn1 (=> tptp.inComplementUnionImpInComplement1 (=> tptp.binunionTE (=> tptp.binunionTEcontra (=> tptp.demorgan2a1 (=> tptp.complementUnionInPowersetComplement (=> tptp.demorgan2a2 (=> tptp.demorgan1a (=> tptp.demorgan1b (=> tptp.demorgan1 (=> tptp.demorgan2a (=> tptp.demorgan2b2 (=> tptp.demorgan2b (=> tptp.demorgan2 (=> tptp.woz13rule0 (=> tptp.woz13rule1 (=> tptp.woz13rule2 (=> tptp.woz13rule3 (=> tptp.woz13rule4 (=> tptp.woz1_1 (=> tptp.woz1_2 (=> tptp.woz1_3 (=> tptp.w/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 12477 Alarm clock             ( read result; case "$result" in 
179.72/180.03	    unsat)
179.72/180.03	        echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
179.72/180.03	    ;;
179.72/180.03	    sat)
179.72/180.03	        echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
179.72/180.03	    ;;
179.72/180.03	esac; exit 1 )
179.72/180.04	oz1_4 (=> tptp.woz1_5 (=> tptp.breln1all2 (=> tptp.breln1SetBreln1 (=> tptp.choice2fnsingleton (=> tptp.setOfPairsIsBReln1 (=> tptp.breln1all1 (=> tptp.subbreln1 (=> tptp.eqbreln1 (=> tptp.breln1invprop (=> tptp.breln1invI (=> tptp.breln1invE (=> tptp.breln1compprop (=> tptp.breln1compI (=> tptp.breln1compE (=> tptp.breln1compEex (=> tptp.breln1unionprop (=> tptp.breln1unionIL (=> tptp.breln1unionIR (=> tptp.breln1unionI (=> tptp.breln1unionE (=> tptp.breln1unionEcases (=> tptp.breln1unionCommutes (=> tptp.woz2Ex (=> tptp.woz2W (=> tptp.woz2A (=> tptp.woz2B (=> tptp.image1Ex (=> tptp.image1Ex1 (=> tptp.image1Equiv (=> tptp.image1E (=> tptp.image1I (=> tptp.injFuncInInjFuncSet (=> tptp.injFuncSetFuncIn (=> tptp.injFuncSetFuncInj (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (let ((_let_1 (@ tptp.in Xf))) (=> (@ _let_1 (@ (@ tptp.surjFuncSet A) B)) (@ _let_1 (@ (@ tptp.funcSet A) B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
179.72/180.04	(set-info :filename cvc5---1.0.5_11637)
179.72/180.04	(check-sat-assuming ( true ))
179.72/180.04	------- get file name : TPTP file name is 
179.72/180.04	------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11637.smt2...
179.72/180.04	--- Run --ho-elim --full-saturate-quant at 10...
179.72/180.04	--- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
179.72/180.04	--- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
179.72/180.04	--- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
179.72/180.04	--- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
179.72/180.04	--- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
179.72/180.04	--- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
179.72/180.04	--- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
179.72/180.04	--- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
179.72/180.04	--- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
179.72/180.04	% cvc5---1.0.5 exiting
179.72/180.04	% cvc5---1.0.5 exiting
179.72/180.04	EOF