0.04/0.12 % Problem : Vampire---4.8_22437 : TPTP v0.0.0. Released v0.0.0. 0.04/0.13 % Command : do_cvc5 %s %d 0.13/0.33 % Computer : n009.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 1440 0.13/0.33 % WCLimit : 180 0.13/0.33 % DateTime : Mon Jul 3 13:01:41 EDT 2023 0.13/0.33 % CPUTime : 0.18/0.47 %----Proving TH0 0.18/0.48 thf(in_type,type, 0.18/0.48 in: $i > $i > $o ). 0.18/0.48 0.18/0.48 thf(exu_type,type, 0.18/0.48 exu: ( $i > $o ) > $o ). 0.18/0.48 0.18/0.48 thf(exu,definition, 0.18/0.48 ( exu 0.18/0.48 = ( ^ [Xphi: $i > $o] : 0.18/0.48 ? [Xx: $i] : 0.18/0.48 ( ( Xphi @ Xx ) 0.18/0.48 & ! [Xy: $i] : 0.18/0.48 ( ( Xphi @ Xy ) 0.18/0.48 => ( Xx = Xy ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setextAx_type,type, 0.18/0.48 setextAx: $o ). 0.18/0.48 0.18/0.48 thf(setextAx,definition, 0.18/0.48 ( setextAx 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 <=> ( in @ Xx @ B ) ) 0.18/0.48 => ( A = B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(emptyset_type,type, 0.18/0.48 emptyset: $i ). 0.18/0.48 0.18/0.48 thf(emptysetAx_type,type, 0.18/0.48 emptysetAx: $o ). 0.18/0.48 0.18/0.48 thf(emptysetAx,definition, 0.18/0.48 ( emptysetAx 0.18/0.48 = ( ! [Xx: $i] : 0.18/0.48 ~ ( in @ Xx @ emptyset ) ) ) ). 0.18/0.48 0.18/0.48 thf(setadjoin_type,type, 0.18/0.48 setadjoin: $i > $i > $i ). 0.18/0.48 0.18/0.48 thf(setadjoinAx_type,type, 0.18/0.48 setadjoinAx: $o ). 0.18/0.48 0.18/0.48 thf(setadjoinAx,definition, 0.18/0.48 ( setadjoinAx 0.18/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.18/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.18/0.48 <=> ( ( Xy = Xx ) 0.18/0.48 | ( in @ Xy @ A ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(powerset_type,type, 0.18/0.48 powerset: $i > $i ). 0.18/0.48 0.18/0.48 thf(powersetAx_type,type, 0.18/0.48 powersetAx: $o ). 0.18/0.48 0.18/0.48 thf(powersetAx,definition, 0.18/0.48 ( powersetAx 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( in @ B @ ( powerset @ A ) ) 0.18/0.48 <=> ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ B ) 0.18/0.48 => ( in @ Xx @ A ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setunion_type,type, 0.18/0.48 setunion: $i > $i ). 0.18/0.48 0.18/0.48 thf(setunionAx_type,type, 0.18/0.48 setunionAx: $o ). 0.18/0.48 0.18/0.48 thf(setunionAx,definition, 0.18/0.48 ( setunionAx 0.18/0.48 = ( ! [A: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ ( setunion @ A ) ) 0.18/0.48 <=> ? [B: $i] : 0.18/0.48 ( ( in @ Xx @ B ) 0.18/0.48 & ( in @ B @ A ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(omega_type,type, 0.18/0.48 omega: $i ). 0.18/0.48 0.18/0.48 thf(omega0Ax_type,type, 0.18/0.48 omega0Ax: $o ). 0.18/0.48 0.18/0.48 thf(omega0Ax,definition, 0.18/0.48 ( omega0Ax 0.18/0.48 = ( in @ emptyset @ omega ) ) ). 0.18/0.48 0.18/0.48 thf(omegaSAx_type,type, 0.18/0.48 omegaSAx: $o ). 0.18/0.48 0.18/0.48 thf(omegaSAx,definition, 0.18/0.48 ( omegaSAx 0.18/0.48 = ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ omega ) 0.18/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(omegaIndAx_type,type, 0.18/0.48 omegaIndAx: $o ). 0.18/0.48 0.18/0.48 thf(omegaIndAx,definition, 0.18/0.48 ( omegaIndAx 0.18/0.48 = ( ! [A: $i] : 0.18/0.48 ( ( ( in @ emptyset @ A ) 0.18/0.48 & ! [Xx: $i] : 0.18/0.48 ( ( ( in @ Xx @ omega ) 0.18/0.48 & ( in @ Xx @ A ) ) 0.18/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ omega ) 0.18/0.48 => ( in @ Xx @ A ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(replAx_type,type, 0.18/0.48 replAx: $o ). 0.18/0.48 0.18/0.48 thf(replAx,definition, 0.18/0.48 ( replAx 0.18/0.48 = ( ! [Xphi: $i > $i > $o,A: $i] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( exu 0.18/0.48 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) 0.18/0.48 => ? [B: $i] : 0.18/0.48 ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ B ) 0.18/0.48 <=> ? [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ A ) 0.18/0.48 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(foundationAx_type,type, 0.18/0.48 foundationAx: $o ). 0.18/0.48 0.18/0.48 thf(foundationAx,definition, 0.18/0.48 ( foundationAx 0.18/0.48 = ( ! [A: $i] : 0.18/0.48 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.18/0.48 => ? [B: $i] : 0.18/0.48 ( ( in @ B @ A ) 0.18/0.48 & ~ ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ B ) 0.18/0.48 & ( in @ Xx @ A ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(wellorderingAx_type,type, 0.18/0.48 wellorderingAx: $o ). 0.18/0.48 0.18/0.48 thf(wellorderingAx,definition, 0.18/0.48 ( wellorderingAx 0.18/0.48 = ( ! [A: $i] : 0.18/0.48 ? [B: $i] : 0.18/0.48 ( ! [C: $i] : 0.18/0.48 ( ( in @ C @ B ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ C ) 0.18/0.48 => ( in @ Xx @ A ) ) ) 0.18/0.48 & ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( ( in @ Xx @ A ) 0.18/0.48 & ( in @ Xy @ A ) ) 0.18/0.48 => ( ! [C: $i] : 0.18/0.48 ( ( in @ C @ B ) 0.18/0.48 => ( ( in @ Xx @ C ) 0.18/0.48 <=> ( in @ Xy @ C ) ) ) 0.18/0.48 => ( Xx = Xy ) ) ) 0.18/0.48 & ! [C: $i,D: $i] : 0.18/0.48 ( ( ( in @ C @ B ) 0.18/0.48 & ( in @ D @ B ) ) 0.18/0.48 => ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ C ) 0.18/0.48 => ( in @ Xx @ D ) ) 0.18/0.48 | ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ D ) 0.18/0.48 => ( in @ Xx @ C ) ) ) ) 0.18/0.48 & ! [C: $i] : 0.18/0.48 ( ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ C ) 0.18/0.48 => ( in @ Xx @ A ) ) 0.18/0.48 & ? [Xx: $i] : ( in @ Xx @ C ) ) 0.18/0.48 => ? [D: $i,Xx: $i] : 0.18/0.48 ( ( in @ D @ B ) 0.18/0.48 & ( in @ Xx @ C ) 0.18/0.48 & ~ ? [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ D ) 0.18/0.48 & ( in @ Xy @ C ) ) 0.18/0.48 & ! [E: $i] : 0.18/0.48 ( ( in @ E @ B ) 0.18/0.48 => ( ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ E ) 0.18/0.48 => ( in @ Xy @ D ) ) 0.18/0.48 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(descr_type,type, 0.18/0.48 descr: ( $i > $o ) > $i ). 0.18/0.48 0.18/0.48 thf(descrp_type,type, 0.18/0.48 descrp: $o ). 0.18/0.48 0.18/0.48 thf(descrp,definition, 0.18/0.48 ( descrp 0.18/0.48 = ( ! [Xphi: $i > $o] : 0.18/0.48 ( ( exu 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 => ( Xphi 0.18/0.48 @ ( descr 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(dsetconstr_type,type, 0.18/0.48 dsetconstr: $i > ( $i > $o ) > $i ). 0.18/0.48 0.18/0.48 thf(dsetconstrI_type,type, 0.18/0.48 dsetconstrI: $o ). 0.18/0.48 0.18/0.48 thf(dsetconstrI,definition, 0.18/0.48 ( dsetconstrI 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( ( Xphi @ Xx ) 0.18/0.48 => ( in @ Xx 0.18/0.48 @ ( dsetconstr @ A 0.18/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(dsetconstrEL_type,type, 0.18/0.48 dsetconstrEL: $o ). 0.18/0.48 0.18/0.48 thf(dsetconstrEL,definition, 0.18/0.48 ( dsetconstrEL 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.18/0.48 ( ( in @ Xx 0.18/0.48 @ ( dsetconstr @ A 0.18/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.18/0.48 => ( in @ Xx @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(dsetconstrER_type,type, 0.18/0.48 dsetconstrER: $o ). 0.18/0.48 0.18/0.48 thf(dsetconstrER,definition, 0.18/0.48 ( dsetconstrER 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.18/0.48 ( ( in @ Xx 0.18/0.48 @ ( dsetconstr @ A 0.18/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.18/0.48 => ( Xphi @ Xx ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(exuE1_type,type, 0.18/0.48 exuE1: $o ). 0.18/0.48 0.18/0.48 thf(exuE1,definition, 0.18/0.48 ( exuE1 0.18/0.48 = ( ! [Xphi: $i > $o] : 0.18/0.48 ( ( exu 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 => ? [Xx: $i] : 0.18/0.48 ( ( Xphi @ Xx ) 0.18/0.48 & ! [Xy: $i] : 0.18/0.48 ( ( Xphi @ Xy ) 0.18/0.48 => ( Xx = Xy ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(prop2set_type,type, 0.18/0.48 prop2set: $o > $i ). 0.18/0.48 0.18/0.48 thf(prop2setE_type,type, 0.18/0.48 prop2setE: $o ). 0.18/0.48 0.18/0.48 thf(prop2setE,definition, 0.18/0.48 ( prop2setE 0.18/0.48 = ( ! [Xphi: $o,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ ( prop2set @ Xphi ) ) 0.18/0.48 => Xphi ) ) ) ). 0.18/0.48 0.18/0.48 thf(emptysetE_type,type, 0.18/0.48 emptysetE: $o ). 0.18/0.48 0.18/0.48 thf(emptysetE,definition, 0.18/0.48 ( emptysetE 0.18/0.48 = ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ emptyset ) 0.18/0.48 => ! [Xphi: $o] : Xphi ) ) ) ). 0.18/0.48 0.18/0.48 thf(emptysetimpfalse_type,type, 0.18/0.48 emptysetimpfalse: $o ). 0.18/0.48 0.18/0.48 thf(emptysetimpfalse,definition, 0.18/0.48 ( emptysetimpfalse 0.18/0.48 = ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ emptyset ) 0.18/0.48 => $false ) ) ) ). 0.18/0.48 0.18/0.48 thf(notinemptyset_type,type, 0.18/0.48 notinemptyset: $o ). 0.18/0.48 0.18/0.48 thf(notinemptyset,definition, 0.18/0.48 ( notinemptyset 0.18/0.48 = ( ! [Xx: $i] : 0.18/0.48 ~ ( in @ Xx @ emptyset ) ) ) ). 0.18/0.48 0.18/0.48 thf(exuE3e_type,type, 0.18/0.48 exuE3e: $o ). 0.18/0.48 0.18/0.48 thf(exuE3e,definition, 0.18/0.48 ( exuE3e 0.18/0.48 = ( ! [Xphi: $i > $o] : 0.18/0.48 ( ( exu 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setext_type,type, 0.18/0.48 setext: $o ). 0.18/0.48 0.18/0.48 thf(setext,definition, 0.18/0.48 ( setext 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ Xx @ B ) ) 0.18/0.48 => ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ B ) 0.18/0.48 => ( in @ Xx @ A ) ) 0.18/0.48 => ( A = B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(emptyI_type,type, 0.18/0.48 emptyI: $o ). 0.18/0.48 0.18/0.48 thf(emptyI,definition, 0.18/0.48 ( emptyI 0.18/0.48 = ( ! [A: $i] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ~ ( in @ Xx @ A ) 0.18/0.48 => ( A = emptyset ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(noeltsimpempty_type,type, 0.18/0.48 noeltsimpempty: $o ). 0.18/0.48 0.18/0.48 thf(noeltsimpempty,definition, 0.18/0.48 ( noeltsimpempty 0.18/0.48 = ( ! [A: $i] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ~ ( in @ Xx @ A ) 0.18/0.48 => ( A = emptyset ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setbeta_type,type, 0.18/0.48 setbeta: $o ). 0.18/0.48 0.18/0.48 thf(setbeta,definition, 0.18/0.48 ( setbeta 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( ( in @ Xx 0.18/0.48 @ ( dsetconstr @ A 0.18/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.18/0.48 <=> ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(nonempty_type,type, 0.18/0.48 nonempty: $i > $o ). 0.18/0.48 0.18/0.48 thf(nonempty,definition, 0.18/0.48 ( nonempty 0.18/0.48 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ). 0.18/0.48 0.18/0.48 thf(nonemptyE1_type,type, 0.18/0.48 nonemptyE1: $o ). 0.18/0.48 0.18/0.48 thf(nonemptyE1,definition, 0.18/0.48 ( nonemptyE1 0.18/0.48 = ( ! [A: $i] : 0.18/0.48 ( ( nonempty @ A ) 0.18/0.48 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(nonemptyI_type,type, 0.18/0.48 nonemptyI: $o ). 0.18/0.48 0.18/0.48 thf(nonemptyI,definition, 0.18/0.48 ( nonemptyI 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( ( Xphi @ Xx ) 0.18/0.48 => ( nonempty 0.18/0.48 @ ( dsetconstr @ A 0.18/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(nonemptyI1_type,type, 0.18/0.48 nonemptyI1: $o ). 0.18/0.48 0.18/0.48 thf(nonemptyI1,definition, 0.18/0.48 ( nonemptyI1 0.18/0.48 = ( ! [A: $i] : 0.18/0.48 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.18/0.48 => ( nonempty @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setadjoinIL_type,type, 0.18/0.48 setadjoinIL: $o ). 0.18/0.48 0.18/0.48 thf(setadjoinIL,definition, 0.18/0.48 ( setadjoinIL 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(emptyinunitempty_type,type, 0.18/0.48 emptyinunitempty: $o ). 0.18/0.48 0.18/0.48 thf(emptyinunitempty,definition, 0.18/0.48 ( emptyinunitempty 0.18/0.48 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ). 0.18/0.48 0.18/0.48 thf(setadjoinIR_type,type, 0.18/0.48 setadjoinIR: $o ). 0.18/0.48 0.18/0.48 thf(setadjoinIR,definition, 0.18/0.48 ( setadjoinIR 0.18/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.18/0.48 ( ( in @ Xy @ A ) 0.18/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setadjoinE_type,type, 0.18/0.48 setadjoinE: $o ). 0.18/0.48 0.18/0.48 thf(setadjoinE,definition, 0.18/0.48 ( setadjoinE 0.18/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.18/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.18/0.48 => ! [Xphi: $o] : 0.18/0.48 ( ( ( Xy = Xx ) 0.18/0.48 => Xphi ) 0.18/0.48 => ( ( ( in @ Xy @ A ) 0.18/0.48 => Xphi ) 0.18/0.48 => Xphi ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setadjoinOr_type,type, 0.18/0.48 setadjoinOr: $o ). 0.18/0.48 0.18/0.48 thf(setadjoinOr,definition, 0.18/0.48 ( setadjoinOr 0.18/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.18/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.18/0.48 => ( ( Xy = Xx ) 0.18/0.48 | ( in @ Xy @ A ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setoftrueEq_type,type, 0.18/0.48 setoftrueEq: $o ). 0.18/0.48 0.18/0.48 thf(setoftrueEq,definition, 0.18/0.48 ( setoftrueEq 0.18/0.48 = ( ! [A: $i] : 0.18/0.48 ( ( dsetconstr @ A 0.18/0.48 @ ^ [Xx: $i] : $true ) 0.18/0.48 = A ) ) ) ). 0.18/0.48 0.18/0.48 thf(powersetI_type,type, 0.18/0.48 powersetI: $o ). 0.18/0.48 0.18/0.48 thf(powersetI,definition, 0.18/0.48 ( powersetI 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ B ) 0.18/0.48 => ( in @ Xx @ A ) ) 0.18/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(emptyinPowerset_type,type, 0.18/0.48 emptyinPowerset: $o ). 0.18/0.48 0.18/0.48 thf(emptyinPowerset,definition, 0.18/0.48 ( emptyinPowerset 0.18/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(emptyInPowerset_type,type, 0.18/0.48 emptyInPowerset: $o ). 0.18/0.48 0.18/0.48 thf(emptyInPowerset,definition, 0.18/0.48 ( emptyInPowerset 0.18/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(powersetE_type,type, 0.18/0.48 powersetE: $o ). 0.18/0.48 0.18/0.48 thf(powersetE,definition, 0.18/0.48 ( powersetE 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ B @ ( powerset @ A ) ) 0.18/0.48 => ( ( in @ Xx @ B ) 0.18/0.48 => ( in @ Xx @ A ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setunionI_type,type, 0.18/0.48 setunionI: $o ). 0.18/0.48 0.18/0.48 thf(setunionI,definition, 0.18/0.48 ( setunionI 0.18/0.48 = ( ! [A: $i,Xx: $i,B: $i] : 0.18/0.48 ( ( in @ Xx @ B ) 0.18/0.48 => ( ( in @ B @ A ) 0.18/0.48 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setunionE_type,type, 0.18/0.48 setunionE: $o ). 0.18/0.48 0.18/0.48 thf(setunionE,definition, 0.18/0.48 ( setunionE 0.18/0.48 = ( ! [A: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ ( setunion @ A ) ) 0.18/0.48 => ! [Xphi: $o] : 0.18/0.48 ( ! [B: $i] : 0.18/0.48 ( ( in @ Xx @ B ) 0.18/0.48 => ( ( in @ B @ A ) 0.18/0.48 => Xphi ) ) 0.18/0.48 => Xphi ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(subPowSU_type,type, 0.18/0.48 subPowSU: $o ). 0.18/0.48 0.18/0.48 thf(subPowSU,definition, 0.18/0.48 ( subPowSU 0.18/0.48 = ( ! [A: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(exuE2_type,type, 0.18/0.48 exuE2: $o ). 0.18/0.48 0.18/0.48 thf(exuE2,definition, 0.18/0.48 ( exuE2 0.18/0.48 = ( ! [Xphi: $i > $o] : 0.18/0.48 ( ( exu 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 => ? [Xx: $i] : 0.18/0.48 ! [Xy: $i] : 0.18/0.48 ( ( Xphi @ Xy ) 0.18/0.48 <=> ( Xy = Xx ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(nonemptyImpWitness_type,type, 0.18/0.48 nonemptyImpWitness: $o ). 0.18/0.48 0.18/0.48 thf(nonemptyImpWitness,definition, 0.18/0.48 ( nonemptyImpWitness 0.18/0.48 = ( ! [A: $i] : 0.18/0.48 ( ( nonempty @ A ) 0.18/0.48 => ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & $true ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(uniqinunit_type,type, 0.18/0.48 uniqinunit: $o ). 0.18/0.48 0.18/0.48 thf(uniqinunit,definition, 0.18/0.48 ( uniqinunit 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.18/0.48 => ( Xx = Xy ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(notinsingleton_type,type, 0.18/0.48 notinsingleton: $o ). 0.18/0.48 0.18/0.48 thf(notinsingleton,definition, 0.18/0.48 ( notinsingleton 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xx != Xy ) 0.18/0.48 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(eqinunit_type,type, 0.18/0.48 eqinunit: $o ). 0.18/0.48 0.18/0.48 thf(eqinunit,definition, 0.18/0.48 ( eqinunit 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xx = Xy ) 0.18/0.48 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(singletonsswitch_type,type, 0.18/0.48 singletonsswitch: $o ). 0.18/0.48 0.18/0.48 thf(singletonsswitch,definition, 0.18/0.48 ( singletonsswitch 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.18/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(upairsetE_type,type, 0.18/0.48 upairsetE: $o ). 0.18/0.48 0.18/0.48 thf(upairsetE,definition, 0.18/0.48 ( upairsetE 0.18/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] : 0.18/0.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) 0.18/0.48 => ( ( Xz = Xx ) 0.18/0.48 | ( Xz = Xy ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(upairsetIL_type,type, 0.18/0.48 upairsetIL: $o ). 0.18/0.48 0.18/0.48 thf(upairsetIL,definition, 0.18/0.48 ( upairsetIL 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(upairsetIR_type,type, 0.18/0.48 upairsetIR: $o ). 0.18/0.48 0.18/0.48 thf(upairsetIR,definition, 0.18/0.48 ( upairsetIR 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(emptyE1_type,type, 0.18/0.48 emptyE1: $o ). 0.18/0.48 0.18/0.48 thf(emptyE1,definition, 0.18/0.48 ( emptyE1 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.48 ( ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & ( Xphi @ Xx ) ) 0.18/0.48 => ( ( ( dsetconstr @ A 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 = emptyset ) 0.18/0.48 => $false ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(vacuousDall_type,type, 0.18/0.48 vacuousDall: $o ). 0.18/0.48 0.18/0.48 thf(vacuousDall,definition, 0.18/0.48 ( vacuousDall 0.18/0.48 = ( ! [Xphi: $i > $o,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ emptyset ) 0.18/0.48 => ( Xphi @ Xx ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(quantDeMorgan1_type,type, 0.18/0.48 quantDeMorgan1: $o ). 0.18/0.48 0.18/0.48 thf(quantDeMorgan1,definition, 0.18/0.48 ( quantDeMorgan1 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.48 ( ~ ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( Xphi @ Xx ) ) 0.18/0.48 => ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(quantDeMorgan2_type,type, 0.18/0.48 quantDeMorgan2: $o ). 0.18/0.48 0.18/0.48 thf(quantDeMorgan2,definition, 0.18/0.48 ( quantDeMorgan2 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ~ ( Xphi @ Xx ) ) 0.18/0.48 => ~ ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(quantDeMorgan3_type,type, 0.18/0.48 quantDeMorgan3: $o ). 0.18/0.48 0.18/0.48 thf(quantDeMorgan3,definition, 0.18/0.48 ( quantDeMorgan3 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.48 ( ~ ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & ( Xphi @ Xx ) ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(quantDeMorgan4_type,type, 0.18/0.48 quantDeMorgan4: $o ). 0.18/0.48 0.18/0.48 thf(quantDeMorgan4,definition, 0.18/0.48 ( quantDeMorgan4 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.48 ( ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & ~ ( Xphi @ Xx ) ) 0.18/0.48 => ~ ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(prop2setI_type,type, 0.18/0.48 prop2setI: $o ). 0.18/0.48 0.18/0.48 thf(prop2setI,definition, 0.18/0.48 ( prop2setI 0.18/0.48 = ( ! [Xphi: $o] : 0.18/0.48 ( Xphi 0.18/0.48 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(set2prop_type,type, 0.18/0.48 set2prop: $i > $o ). 0.18/0.48 0.18/0.48 thf(prop2set2propI_type,type, 0.18/0.48 prop2set2propI: $o ). 0.18/0.48 0.18/0.48 thf(prop2set2propI,definition, 0.18/0.48 ( prop2set2propI 0.18/0.48 = ( ! [Xphi: $o] : 0.18/0.48 ( Xphi 0.18/0.48 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(notdexE_type,type, 0.18/0.48 notdexE: $o ). 0.18/0.48 0.18/0.48 thf(notdexE,definition, 0.18/0.48 ( notdexE 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.48 ( ~ ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & ( Xphi @ Xx ) ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(notdallE_type,type, 0.18/0.48 notdallE: $o ). 0.18/0.48 0.18/0.48 thf(notdallE,definition, 0.18/0.48 ( notdallE 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.48 ( ~ ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( Xphi @ Xx ) ) 0.18/0.48 => ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(exuI1_type,type, 0.18/0.48 exuI1: $o ). 0.18/0.48 0.18/0.48 thf(exuI1,definition, 0.18/0.48 ( exuI1 0.18/0.48 = ( ! [Xphi: $i > $o] : 0.18/0.48 ( ? [Xx: $i] : 0.18/0.48 ( ( Xphi @ Xx ) 0.18/0.48 & ! [Xy: $i] : 0.18/0.48 ( ( Xphi @ Xy ) 0.18/0.48 => ( Xx = Xy ) ) ) 0.18/0.48 => ( exu 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(exuI3_type,type, 0.18/0.48 exuI3: $o ). 0.18/0.48 0.18/0.48 thf(exuI3,definition, 0.18/0.48 ( exuI3 0.18/0.48 = ( ! [Xphi: $i > $o] : 0.18/0.48 ( ? [Xx: $i] : ( Xphi @ Xx ) 0.18/0.48 => ( ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xphi @ Xx ) 0.18/0.48 => ( ( Xphi @ Xy ) 0.18/0.48 => ( Xx = Xy ) ) ) 0.18/0.48 => ( exu 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(exuI2_type,type, 0.18/0.48 exuI2: $o ). 0.18/0.48 0.18/0.48 thf(exuI2,definition, 0.18/0.48 ( exuI2 0.18/0.48 = ( ! [Xphi: $i > $o] : 0.18/0.48 ( ? [Xx: $i] : 0.18/0.48 ! [Xy: $i] : 0.18/0.48 ( ( Xphi @ Xy ) 0.18/0.48 <=> ( Xy = Xx ) ) 0.18/0.48 => ( exu 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(inCongP_type,type, 0.18/0.48 inCongP: $o ). 0.18/0.48 0.18/0.48 thf(inCongP,definition, 0.18/0.48 ( inCongP 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( A = B ) 0.18/0.48 => ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xx = Xy ) 0.18/0.48 => ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ Xy @ B ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(in__Cong_type,type, 0.18/0.48 in__Cong: $o ). 0.18/0.48 0.18/0.48 thf(in__Cong,definition, 0.18/0.48 ( in__Cong 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( A = B ) 0.18/0.48 => ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xx = Xy ) 0.18/0.48 => ( ( in @ Xx @ A ) 0.18/0.48 <=> ( in @ Xy @ B ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(exuE3u_type,type, 0.18/0.48 exuE3u: $o ). 0.18/0.48 0.18/0.48 thf(exuE3u,definition, 0.18/0.48 ( exuE3u 0.18/0.48 = ( ! [Xphi: $i > $o] : 0.18/0.48 ( ( exu 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 => ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xphi @ Xx ) 0.18/0.48 => ( ( Xphi @ Xy ) 0.18/0.48 => ( Xx = Xy ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(exu__Cong_type,type, 0.18/0.48 exu__Cong: $o ). 0.18/0.48 0.18/0.48 thf(exu__Cong,definition, 0.18/0.48 ( exu__Cong 0.18/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] : 0.18/0.48 ( ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xx = Xy ) 0.18/0.48 => ( ( Xphi @ Xx ) 0.18/0.48 <=> ( Xpsi @ Xy ) ) ) 0.18/0.48 => ( ( exu 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 <=> ( exu 0.18/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(emptyset__Cong_type,type, 0.18/0.48 emptyset__Cong: $o ). 0.18/0.48 0.18/0.48 thf(emptyset__Cong,definition, 0.18/0.48 ( emptyset__Cong 0.18/0.48 = ( emptyset = emptyset ) ) ). 0.18/0.48 0.18/0.48 thf(setadjoin__Cong_type,type, 0.18/0.48 setadjoin__Cong: $o ). 0.18/0.48 0.18/0.48 thf(setadjoin__Cong,definition, 0.18/0.48 ( setadjoin__Cong 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xx = Xy ) 0.18/0.48 => ! [Xz: $i,Xu: $i] : 0.18/0.48 ( ( Xz = Xu ) 0.18/0.48 => ( ( setadjoin @ Xx @ Xz ) 0.18/0.48 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(powerset__Cong_type,type, 0.18/0.48 powerset__Cong: $o ). 0.18/0.48 0.18/0.48 thf(powerset__Cong,definition, 0.18/0.48 ( powerset__Cong 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( A = B ) 0.18/0.48 => ( ( powerset @ A ) 0.18/0.48 = ( powerset @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setunion__Cong_type,type, 0.18/0.48 setunion__Cong: $o ). 0.18/0.48 0.18/0.48 thf(setunion__Cong,definition, 0.18/0.48 ( setunion__Cong 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( A = B ) 0.18/0.48 => ( ( setunion @ A ) 0.18/0.48 = ( setunion @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(omega__Cong_type,type, 0.18/0.48 omega__Cong: $o ). 0.18/0.48 0.18/0.48 thf(omega__Cong,definition, 0.18/0.48 ( omega__Cong 0.18/0.48 = ( omega = omega ) ) ). 0.18/0.48 0.18/0.48 thf(exuEu_type,type, 0.18/0.48 exuEu: $o ). 0.18/0.48 0.18/0.48 thf(exuEu,definition, 0.18/0.48 ( exuEu 0.18/0.48 = ( ! [Xphi: $i > $o] : 0.18/0.48 ( ( exu 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 => ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xphi @ Xx ) 0.18/0.48 => ( ( Xphi @ Xy ) 0.18/0.48 => ( Xx = Xy ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(descr__Cong_type,type, 0.18/0.48 descr__Cong: $o ). 0.18/0.48 0.18/0.48 thf(descr__Cong,definition, 0.18/0.48 ( descr__Cong 0.18/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] : 0.18/0.48 ( ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xx = Xy ) 0.18/0.48 => ( ( Xphi @ Xx ) 0.18/0.48 <=> ( Xpsi @ Xy ) ) ) 0.18/0.48 => ( ( exu 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 => ( ( exu 0.18/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) 0.18/0.48 => ( ( descr 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 = ( descr 0.18/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(dsetconstr__Cong_type,type, 0.18/0.48 dsetconstr__Cong: $o ). 0.18/0.48 0.18/0.48 thf(dsetconstr__Cong,definition, 0.18/0.48 ( dsetconstr__Cong 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( A = B ) 0.18/0.48 => ! [Xphi: $i > $o,Xpsi: $i > $o] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( ( Xx = Xy ) 0.18/0.48 => ( ( Xphi @ Xx ) 0.18/0.48 <=> ( Xpsi @ Xy ) ) ) ) ) 0.18/0.48 => ( ( dsetconstr @ A 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 = ( dsetconstr @ B 0.18/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(subset_type,type, 0.18/0.48 subset: $i > $i > $o ). 0.18/0.48 0.18/0.48 thf(disjoint_type,type, 0.18/0.48 disjoint: $i > $i > $o ). 0.18/0.48 0.18/0.48 thf(setsmeet_type,type, 0.18/0.48 setsmeet: $i > $i > $o ). 0.18/0.48 0.18/0.48 thf(subsetI1_type,type, 0.18/0.48 subsetI1: $o ). 0.18/0.48 0.18/0.48 thf(subsetI1,definition, 0.18/0.48 ( subsetI1 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ Xx @ B ) ) 0.18/0.48 => ( subset @ A @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(eqimpsubset2_type,type, 0.18/0.48 eqimpsubset2: $o ). 0.18/0.48 0.18/0.48 thf(eqimpsubset2,definition, 0.18/0.48 ( eqimpsubset2 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( A = B ) 0.18/0.48 => ( subset @ B @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(eqimpsubset1_type,type, 0.18/0.48 eqimpsubset1: $o ). 0.18/0.48 0.18/0.48 thf(eqimpsubset1,definition, 0.18/0.48 ( eqimpsubset1 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( A = B ) 0.18/0.48 => ( subset @ A @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(subsetI2_type,type, 0.18/0.48 subsetI2: $o ). 0.18/0.48 0.18/0.48 thf(subsetI2,definition, 0.18/0.48 ( subsetI2 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ Xx @ B ) ) 0.18/0.48 => ( subset @ A @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(emptysetsubset_type,type, 0.18/0.48 emptysetsubset: $o ). 0.18/0.48 0.18/0.48 thf(emptysetsubset,definition, 0.18/0.48 ( emptysetsubset 0.18/0.48 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ). 0.18/0.48 0.18/0.48 thf(subsetE_type,type, 0.18/0.48 subsetE: $o ). 0.18/0.48 0.18/0.48 thf(subsetE,definition, 0.18/0.48 ( subsetE 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( subset @ A @ B ) 0.18/0.48 => ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ Xx @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(subsetE2_type,type, 0.18/0.48 subsetE2: $o ). 0.18/0.48 0.18/0.48 thf(subsetE2,definition, 0.18/0.48 ( subsetE2 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( subset @ A @ B ) 0.18/0.48 => ( ~ ( in @ Xx @ B ) 0.18/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(notsubsetI_type,type, 0.18/0.48 notsubsetI: $o ). 0.18/0.48 0.18/0.48 thf(notsubsetI,definition, 0.18/0.48 ( notsubsetI 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( ~ ( in @ Xx @ B ) 0.18/0.48 => ~ ( subset @ A @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(notequalI1_type,type, 0.18/0.48 notequalI1: $o ). 0.18/0.48 0.18/0.48 thf(notequalI1,definition, 0.18/0.48 ( notequalI1 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ~ ( subset @ A @ B ) 0.18/0.48 => ( A != B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(notequalI2_type,type, 0.18/0.48 notequalI2: $o ). 0.18/0.48 0.18/0.48 thf(notequalI2,definition, 0.18/0.48 ( notequalI2 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( ~ ( in @ Xx @ B ) 0.18/0.48 => ( A != B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(subsetRefl_type,type, 0.18/0.48 subsetRefl: $o ). 0.18/0.48 0.18/0.48 thf(subsetRefl,definition, 0.18/0.48 ( subsetRefl 0.18/0.48 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ). 0.18/0.48 0.18/0.48 thf(subsetTrans_type,type, 0.18/0.48 subsetTrans: $o ). 0.18/0.48 0.18/0.48 thf(subsetTrans,definition, 0.18/0.48 ( subsetTrans 0.18/0.48 = ( ! [A: $i,B: $i,C: $i] : 0.18/0.48 ( ( subset @ A @ B ) 0.18/0.48 => ( ( subset @ B @ C ) 0.18/0.48 => ( subset @ A @ C ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setadjoinSub_type,type, 0.18/0.48 setadjoinSub: $o ). 0.18/0.48 0.18/0.48 thf(setadjoinSub,definition, 0.18/0.48 ( setadjoinSub 0.18/0.48 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setadjoinSub2_type,type, 0.18/0.48 setadjoinSub2: $o ). 0.18/0.48 0.18/0.48 thf(setadjoinSub2,definition, 0.18/0.48 ( setadjoinSub2 0.18/0.48 = ( ! [A: $i,Xx: $i,B: $i] : 0.18/0.48 ( ( subset @ A @ B ) 0.18/0.48 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(subset2powerset_type,type, 0.18/0.48 subset2powerset: $o ). 0.18/0.48 0.18/0.48 thf(subset2powerset,definition, 0.18/0.48 ( subset2powerset 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( subset @ A @ B ) 0.18/0.48 => ( in @ A @ ( powerset @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setextsub_type,type, 0.18/0.48 setextsub: $o ). 0.18/0.48 0.18/0.48 thf(setextsub,definition, 0.18/0.48 ( setextsub 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( subset @ A @ B ) 0.18/0.48 => ( ( subset @ B @ A ) 0.18/0.48 => ( A = B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(subsetemptysetimpeq_type,type, 0.18/0.48 subsetemptysetimpeq: $o ). 0.18/0.48 0.18/0.48 thf(subsetemptysetimpeq,definition, 0.18/0.48 ( subsetemptysetimpeq 0.18/0.48 = ( ! [A: $i] : 0.18/0.48 ( ( subset @ A @ emptyset ) 0.18/0.48 => ( A = emptyset ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(powersetI1_type,type, 0.18/0.48 powersetI1: $o ). 0.18/0.48 0.18/0.48 thf(powersetI1,definition, 0.18/0.48 ( powersetI1 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( subset @ B @ A ) 0.18/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(powersetE1_type,type, 0.18/0.48 powersetE1: $o ). 0.18/0.48 0.18/0.48 thf(powersetE1,definition, 0.18/0.48 ( powersetE1 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( in @ B @ ( powerset @ A ) ) 0.18/0.48 => ( subset @ B @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(inPowerset_type,type, 0.18/0.48 inPowerset: $o ). 0.18/0.48 0.18/0.48 thf(inPowerset,definition, 0.18/0.48 ( inPowerset 0.18/0.48 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(powersetsubset_type,type, 0.18/0.48 powersetsubset: $o ). 0.18/0.48 0.18/0.48 thf(powersetsubset,definition, 0.18/0.48 ( powersetsubset 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( subset @ A @ B ) 0.18/0.48 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(sepInPowerset_type,type, 0.18/0.48 sepInPowerset: $o ). 0.18/0.48 0.18/0.48 thf(sepInPowerset,definition, 0.18/0.48 ( sepInPowerset 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.48 ( in 0.18/0.48 @ ( dsetconstr @ A 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 @ ( powerset @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(sepSubset_type,type, 0.18/0.48 sepSubset: $o ). 0.18/0.48 0.18/0.48 thf(sepSubset,definition, 0.18/0.48 ( sepSubset 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.48 ( subset 0.18/0.48 @ ( dsetconstr @ A 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 @ A ) ) ) ). 0.18/0.48 0.18/0.48 thf(binunion_type,type, 0.18/0.48 binunion: $i > $i > $i ). 0.18/0.48 0.18/0.48 thf(binunionIL_type,type, 0.18/0.48 binunionIL: $o ). 0.18/0.48 0.18/0.48 thf(binunionIL,definition, 0.18/0.48 ( binunionIL 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(upairset2IR_type,type, 0.18/0.48 upairset2IR: $o ). 0.18/0.48 0.18/0.48 thf(upairset2IR,definition, 0.18/0.48 ( upairset2IR 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(binunionIR_type,type, 0.18/0.48 binunionIR: $o ). 0.18/0.48 0.18/0.48 thf(binunionIR,definition, 0.18/0.48 ( binunionIR 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ B ) 0.18/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(binunionEcases_type,type, 0.18/0.48 binunionEcases: $o ). 0.18/0.48 0.18/0.48 thf(binunionEcases,definition, 0.18/0.48 ( binunionEcases 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] : 0.18/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) ) 0.18/0.48 => ( ( ( in @ Xx @ A ) 0.18/0.48 => Xphi ) 0.18/0.48 => ( ( ( in @ Xx @ B ) 0.18/0.48 => Xphi ) 0.18/0.48 => Xphi ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(binunionE_type,type, 0.18/0.48 binunionE: $o ). 0.18/0.48 0.18/0.48 thf(binunionE,definition, 0.18/0.48 ( binunionE 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) ) 0.18/0.48 => ( ( in @ Xx @ A ) 0.18/0.48 | ( in @ Xx @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(binunionLsub_type,type, 0.18/0.48 binunionLsub: $o ). 0.18/0.48 0.18/0.48 thf(binunionLsub,definition, 0.18/0.48 ( binunionLsub 0.18/0.48 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(binunionRsub_type,type, 0.18/0.48 binunionRsub: $o ). 0.18/0.48 0.18/0.48 thf(binunionRsub,definition, 0.18/0.48 ( binunionRsub 0.18/0.48 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(binintersect_type,type, 0.18/0.48 binintersect: $i > $i > $i ). 0.18/0.48 0.18/0.48 thf(binintersectI_type,type, 0.18/0.48 binintersectI: $o ). 0.18/0.48 0.18/0.48 thf(binintersectI,definition, 0.18/0.48 ( binintersectI 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( ( in @ Xx @ B ) 0.18/0.48 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(binintersectSubset5_type,type, 0.18/0.48 binintersectSubset5: $o ). 0.18/0.48 0.18/0.48 thf(binintersectSubset5,definition, 0.18/0.48 ( binintersectSubset5 0.18/0.48 = ( ! [A: $i,B: $i,C: $i] : 0.18/0.48 ( ( subset @ C @ A ) 0.18/0.48 => ( ( subset @ C @ B ) 0.18/0.48 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(binintersectEL_type,type, 0.18/0.48 binintersectEL: $o ). 0.18/0.48 0.18/0.48 thf(binintersectEL,definition, 0.18/0.48 ( binintersectEL 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) ) 0.18/0.48 => ( in @ Xx @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(binintersectLsub_type,type, 0.18/0.48 binintersectLsub: $o ). 0.18/0.48 0.18/0.48 thf(binintersectLsub,definition, 0.18/0.48 ( binintersectLsub 0.18/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ). 0.18/0.48 0.18/0.48 thf(binintersectSubset2_type,type, 0.18/0.48 binintersectSubset2: $o ). 0.18/0.48 0.18/0.48 thf(binintersectSubset2,definition, 0.18/0.48 ( binintersectSubset2 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( subset @ A @ B ) 0.18/0.48 => ( ( binintersect @ A @ B ) 0.18/0.48 = A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(binintersectSubset3_type,type, 0.18/0.48 binintersectSubset3: $o ). 0.18/0.48 0.18/0.48 thf(binintersectSubset3,definition, 0.18/0.48 ( binintersectSubset3 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( ( binintersect @ A @ B ) 0.18/0.48 = B ) 0.18/0.48 => ( subset @ B @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(binintersectER_type,type, 0.18/0.48 binintersectER: $o ). 0.18/0.48 0.18/0.48 thf(binintersectER,definition, 0.18/0.48 ( binintersectER 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) ) 0.18/0.48 => ( in @ Xx @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(disjointsetsI1_type,type, 0.18/0.48 disjointsetsI1: $o ). 0.18/0.48 0.18/0.48 thf(disjointsetsI1,definition, 0.18/0.48 ( disjointsetsI1 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ~ ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & ( in @ Xx @ B ) ) 0.18/0.48 => ( ( binintersect @ A @ B ) 0.18/0.48 = emptyset ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(binintersectRsub_type,type, 0.18/0.48 binintersectRsub: $o ). 0.18/0.48 0.18/0.48 thf(binintersectRsub,definition, 0.18/0.48 ( binintersectRsub 0.18/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ). 0.18/0.48 0.18/0.48 thf(binintersectSubset4_type,type, 0.18/0.48 binintersectSubset4: $o ). 0.18/0.48 0.18/0.48 thf(binintersectSubset4,definition, 0.18/0.48 ( binintersectSubset4 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( subset @ B @ A ) 0.18/0.48 => ( ( binintersect @ A @ B ) 0.18/0.48 = B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(binintersectSubset1_type,type, 0.18/0.48 binintersectSubset1: $o ). 0.18/0.48 0.18/0.48 thf(binintersectSubset1,definition, 0.18/0.48 ( binintersectSubset1 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( ( binintersect @ A @ B ) 0.18/0.48 = A ) 0.18/0.48 => ( subset @ A @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(bs114d_type,type, 0.18/0.48 bs114d: $o ). 0.18/0.48 0.18/0.48 thf(bs114d,definition, 0.18/0.48 ( bs114d 0.18/0.48 = ( ! [A: $i,B: $i,C: $i] : 0.18/0.48 ( ( binintersect @ A @ ( binunion @ B @ C ) ) 0.18/0.48 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(regular_type,type, 0.18/0.48 regular: $i > $o ). 0.18/0.48 0.18/0.48 thf(setminus_type,type, 0.18/0.48 setminus: $i > $i > $i ). 0.18/0.48 0.18/0.48 thf(setminusI_type,type, 0.18/0.48 setminusI: $o ). 0.18/0.48 0.18/0.48 thf(setminusI,definition, 0.18/0.48 ( setminusI 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( ~ ( in @ Xx @ B ) 0.18/0.48 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setminusEL_type,type, 0.18/0.48 setminusEL: $o ). 0.18/0.48 0.18/0.48 thf(setminusEL,definition, 0.18/0.48 ( setminusEL 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) ) 0.18/0.48 => ( in @ Xx @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setminusER_type,type, 0.18/0.48 setminusER: $o ). 0.18/0.48 0.18/0.48 thf(setminusER,definition, 0.18/0.48 ( setminusER 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) ) 0.18/0.48 => ~ ( in @ Xx @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setminusSubset2_type,type, 0.18/0.48 setminusSubset2: $o ). 0.18/0.48 0.18/0.48 thf(setminusSubset2,definition, 0.18/0.48 ( setminusSubset2 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( subset @ A @ B ) 0.18/0.48 => ( ( setminus @ A @ B ) 0.18/0.48 = emptyset ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setminusERneg_type,type, 0.18/0.48 setminusERneg: $o ). 0.18/0.48 0.18/0.48 thf(setminusERneg,definition, 0.18/0.48 ( setminusERneg 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) ) 0.18/0.48 => ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ Xx @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setminusELneg_type,type, 0.18/0.48 setminusELneg: $o ). 0.18/0.48 0.18/0.48 thf(setminusELneg,definition, 0.18/0.48 ( setminusELneg 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) ) 0.18/0.48 => ( ~ ( in @ Xx @ B ) 0.18/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setminusILneg_type,type, 0.18/0.48 setminusILneg: $o ). 0.18/0.48 0.18/0.48 thf(setminusILneg,definition, 0.18/0.48 ( setminusILneg 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ~ ( in @ Xx @ A ) 0.18/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setminusIRneg_type,type, 0.18/0.48 setminusIRneg: $o ). 0.18/0.48 0.18/0.48 thf(setminusIRneg,definition, 0.18/0.48 ( setminusIRneg 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ B ) 0.18/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setminusLsub_type,type, 0.18/0.48 setminusLsub: $o ). 0.18/0.48 0.18/0.48 thf(setminusLsub,definition, 0.18/0.48 ( setminusLsub 0.18/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ). 0.18/0.48 0.18/0.48 thf(setminusSubset1_type,type, 0.18/0.48 setminusSubset1: $o ). 0.18/0.48 0.18/0.48 thf(setminusSubset1,definition, 0.18/0.48 ( setminusSubset1 0.18/0.48 = ( ! [A: $i,B: $i] : 0.18/0.48 ( ( ( setminus @ A @ B ) 0.18/0.48 = emptyset ) 0.18/0.48 => ( subset @ A @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(symdiff_type,type, 0.18/0.48 symdiff: $i > $i > $i ). 0.18/0.48 0.18/0.48 thf(symdiffE_type,type, 0.18/0.48 symdiffE: $o ). 0.18/0.48 0.18/0.48 thf(symdiffE,definition, 0.18/0.48 ( symdiffE 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ ( symdiff @ A @ B ) ) 0.18/0.48 => ! [Xphi: $o] : 0.18/0.48 ( ( ( in @ Xx @ A ) 0.18/0.48 => ( ~ ( in @ Xx @ B ) 0.18/0.48 => Xphi ) ) 0.18/0.48 => ( ( ~ ( in @ Xx @ A ) 0.18/0.48 => ( ( in @ Xx @ B ) 0.18/0.48 => Xphi ) ) 0.18/0.48 => Xphi ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(symdiffI1_type,type, 0.18/0.48 symdiffI1: $o ). 0.18/0.48 0.18/0.48 thf(symdiffI1,definition, 0.18/0.48 ( symdiffI1 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( ~ ( in @ Xx @ B ) 0.18/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(symdiffI2_type,type, 0.18/0.48 symdiffI2: $o ). 0.18/0.48 0.18/0.48 thf(symdiffI2,definition, 0.18/0.48 ( symdiffI2 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ~ ( in @ Xx @ A ) 0.18/0.48 => ( ( in @ Xx @ B ) 0.18/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(symdiffIneg1_type,type, 0.18/0.48 symdiffIneg1: $o ). 0.18/0.48 0.18/0.48 thf(symdiffIneg1,definition, 0.18/0.48 ( symdiffIneg1 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( ( in @ Xx @ B ) 0.18/0.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(symdiffIneg2_type,type, 0.18/0.48 symdiffIneg2: $o ). 0.18/0.48 0.18/0.48 thf(symdiffIneg2,definition, 0.18/0.48 ( symdiffIneg2 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ~ ( in @ Xx @ A ) 0.18/0.48 => ( ~ ( in @ Xx @ B ) 0.18/0.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(iskpair_type,type, 0.18/0.48 iskpair: $i > $o ). 0.18/0.48 0.18/0.48 thf(secondinupair_type,type, 0.18/0.48 secondinupair: $o ). 0.18/0.48 0.18/0.48 thf(secondinupair,definition, 0.18/0.48 ( secondinupair 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setukpairIL_type,type, 0.18/0.48 setukpairIL: $o ). 0.18/0.48 0.18/0.48 thf(setukpairIL,definition, 0.18/0.48 ( setukpairIL 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setukpairIR_type,type, 0.18/0.48 setukpairIR: $o ). 0.18/0.48 0.18/0.48 thf(setukpairIR,definition, 0.18/0.48 ( setukpairIR 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(kpairiskpair_type,type, 0.18/0.48 kpairiskpair: $o ). 0.18/0.48 0.18/0.48 thf(kpairiskpair,definition, 0.18/0.48 ( kpairiskpair 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(kpair_type,type, 0.18/0.48 kpair: $i > $i > $i ). 0.18/0.48 0.18/0.48 thf(kpairp_type,type, 0.18/0.48 kpairp: $o ). 0.18/0.48 0.18/0.48 thf(kpairp,definition, 0.18/0.48 ( kpairp 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(cartprod_type,type, 0.18/0.48 cartprod: $i > $i > $i ). 0.18/0.48 0.18/0.48 thf(singletonsubset_type,type, 0.18/0.48 singletonsubset: $o ). 0.18/0.48 0.18/0.48 thf(singletonsubset,definition, 0.18/0.48 ( singletonsubset 0.18/0.48 = ( ! [A: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(singletoninpowerset_type,type, 0.18/0.48 singletoninpowerset: $o ). 0.18/0.48 0.18/0.48 thf(singletoninpowerset,definition, 0.18/0.48 ( singletoninpowerset 0.18/0.48 = ( ! [A: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(singletoninpowunion_type,type, 0.18/0.48 singletoninpowunion: $o ). 0.18/0.48 0.18/0.48 thf(singletoninpowunion,definition, 0.18/0.48 ( singletoninpowunion 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(upairset2E_type,type, 0.18/0.48 upairset2E: $o ). 0.18/0.48 0.18/0.48 thf(upairset2E,definition, 0.18/0.48 ( upairset2E 0.18/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] : 0.18/0.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) 0.18/0.48 => ( ( Xz = Xx ) 0.18/0.48 | ( Xz = Xy ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(upairsubunion_type,type, 0.18/0.48 upairsubunion: $o ). 0.18/0.48 0.18/0.48 thf(upairsubunion,definition, 0.18/0.48 ( upairsubunion 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(upairinpowunion_type,type, 0.18/0.48 upairinpowunion: $o ). 0.18/0.48 0.18/0.48 thf(upairinpowunion,definition, 0.18/0.48 ( upairinpowunion 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(ubforcartprodlem1_type,type, 0.18/0.48 ubforcartprodlem1: $o ). 0.18/0.48 0.18/0.48 thf(ubforcartprodlem1,definition, 0.18/0.48 ( ubforcartprodlem1 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(ubforcartprodlem2_type,type, 0.18/0.48 ubforcartprodlem2: $o ). 0.18/0.48 0.18/0.48 thf(ubforcartprodlem2,definition, 0.18/0.48 ( ubforcartprodlem2 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(ubforcartprodlem3_type,type, 0.18/0.48 ubforcartprodlem3: $o ). 0.18/0.48 0.18/0.48 thf(ubforcartprodlem3,definition, 0.18/0.48 ( ubforcartprodlem3 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(cartprodpairin_type,type, 0.18/0.48 cartprodpairin: $o ). 0.18/0.48 0.18/0.48 thf(cartprodpairin,definition, 0.18/0.48 ( cartprodpairin 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(cartprodmempair1_type,type, 0.18/0.48 cartprodmempair1: $o ). 0.18/0.48 0.18/0.48 thf(cartprodmempair1,definition, 0.18/0.48 ( cartprodmempair1 0.18/0.48 = ( ! [A: $i,B: $i,Xu: $i] : 0.18/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) ) 0.18/0.48 => ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & ? [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 & ( Xu 0.18/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(cartprodmempair_type,type, 0.18/0.48 cartprodmempair: $o ). 0.18/0.48 0.18/0.48 thf(cartprodmempair,definition, 0.18/0.48 ( cartprodmempair 0.18/0.48 = ( ! [A: $i,B: $i,Xu: $i] : 0.18/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) ) 0.18/0.48 => ( iskpair @ Xu ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setunionE2_type,type, 0.18/0.48 setunionE2: $o ). 0.18/0.48 0.18/0.48 thf(setunionE2,definition, 0.18/0.48 ( setunionE2 0.18/0.48 = ( ! [A: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ ( setunion @ A ) ) 0.18/0.48 => ? [X: $i] : 0.18/0.48 ( ( in @ X @ A ) 0.18/0.48 & ( in @ Xx @ X ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setunionsingleton1_type,type, 0.18/0.48 setunionsingleton1: $o ). 0.18/0.48 0.18/0.48 thf(setunionsingleton1,definition, 0.18/0.48 ( setunionsingleton1 0.18/0.48 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ). 0.18/0.48 0.18/0.48 thf(setunionsingleton2_type,type, 0.18/0.48 setunionsingleton2: $o ). 0.18/0.48 0.18/0.48 thf(setunionsingleton2,definition, 0.18/0.48 ( setunionsingleton2 0.18/0.48 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setunionsingleton_type,type, 0.18/0.48 setunionsingleton: $o ). 0.18/0.48 0.18/0.48 thf(setunionsingleton,definition, 0.18/0.48 ( setunionsingleton 0.18/0.48 = ( ! [Xx: $i] : 0.18/0.48 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) ) 0.18/0.48 = Xx ) ) ) ). 0.18/0.48 0.18/0.48 thf(singleton_type,type, 0.18/0.48 singleton: $i > $o ). 0.18/0.48 0.18/0.48 thf(singleton,definition, 0.18/0.48 ( singleton 0.18/0.48 = ( ^ [A: $i] : 0.18/0.48 ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & ( A 0.18/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(singletonprop_type,type, 0.18/0.48 singletonprop: $o ). 0.18/0.48 0.18/0.48 thf(singletonprop,definition, 0.18/0.48 ( singletonprop 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ A ) 0.18/0.48 => ( ( Xphi @ Xx ) 0.18/0.48 => ( ( Xphi @ Xy ) 0.18/0.48 => ( Xx = Xy ) ) ) ) ) 0.18/0.48 => ( ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & ( Xphi @ Xx ) ) 0.18/0.48 => ( singleton 0.18/0.48 @ ( dsetconstr @ A 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(ex1_type,type, 0.18/0.48 ex1: $i > ( $i > $o ) > $o ). 0.18/0.48 0.18/0.48 thf(ex1,definition, 0.18/0.48 ( ex1 0.18/0.48 = ( ^ [A: $i,Xphi: $i > $o] : 0.18/0.48 ( singleton 0.18/0.48 @ ( dsetconstr @ A 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(ex1E1_type,type, 0.18/0.48 ex1E1: $o ). 0.18/0.48 0.18/0.48 thf(ex1E1,definition, 0.18/0.48 ( ex1E1 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.48 ( ( ex1 @ A 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 => ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(ex1I_type,type, 0.18/0.48 ex1I: $o ). 0.18/0.48 0.18/0.48 thf(ex1I,definition, 0.18/0.48 ( ex1I 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( ( Xphi @ Xx ) 0.18/0.48 => ( ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ A ) 0.18/0.48 => ( ( Xphi @ Xy ) 0.18/0.48 => ( Xy = Xx ) ) ) 0.18/0.48 => ( ex1 @ A 0.18/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(ex1I2_type,type, 0.18/0.48 ex1I2: $o ). 0.18/0.48 0.18/0.48 thf(ex1I2,definition, 0.18/0.48 ( ex1I2 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ A ) 0.18/0.48 => ( ( Xphi @ Xx ) 0.18/0.48 => ( ( Xphi @ Xy ) 0.18/0.48 => ( Xx = Xy ) ) ) ) ) 0.18/0.48 => ( ? [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 & ( Xphi @ Xx ) ) 0.18/0.48 => ( ex1 @ A 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(singletonsuniq_type,type, 0.18/0.48 singletonsuniq: $o ). 0.18/0.48 0.18/0.48 thf(singletonsuniq,definition, 0.18/0.48 ( singletonsuniq 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( ( setadjoin @ Xx @ emptyset ) 0.18/0.48 = ( setadjoin @ Xy @ emptyset ) ) 0.18/0.48 => ( Xx = Xy ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(atmost1p_type,type, 0.18/0.48 atmost1p: $i > $o ). 0.18/0.48 0.18/0.48 thf(atleast2p_type,type, 0.18/0.48 atleast2p: $i > $o ). 0.18/0.48 0.18/0.48 thf(atmost2p_type,type, 0.18/0.48 atmost2p: $i > $o ). 0.18/0.48 0.18/0.48 thf(upairsetp_type,type, 0.18/0.48 upairsetp: $i > $o ). 0.18/0.48 0.18/0.48 thf(setukpairinjL1_type,type, 0.18/0.48 setukpairinjL1: $o ). 0.18/0.48 0.18/0.48 thf(setukpairinjL1,definition, 0.18/0.48 ( setukpairinjL1 0.18/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] : 0.18/0.48 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) 0.18/0.48 => ( Xx = Xz ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(kfstsingleton_type,type, 0.18/0.48 kfstsingleton: $o ). 0.18/0.48 0.18/0.48 thf(kfstsingleton,definition, 0.18/0.48 ( kfstsingleton 0.18/0.48 = ( ! [Xu: $i] : 0.18/0.48 ( ( iskpair @ Xu ) 0.18/0.48 => ( singleton 0.18/0.48 @ ( dsetconstr @ ( setunion @ Xu ) 0.18/0.48 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(theprop_type,type, 0.18/0.48 theprop: $o ). 0.18/0.48 0.18/0.48 thf(theprop,definition, 0.18/0.48 ( theprop 0.18/0.48 = ( ! [X: $i] : 0.18/0.48 ( ( singleton @ X ) 0.18/0.48 => ( in @ ( setunion @ X ) @ X ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(kfst_type,type, 0.18/0.48 kfst: $i > $i ). 0.18/0.48 0.18/0.48 thf(kfstpairEq_type,type, 0.18/0.48 kfstpairEq: $o ). 0.18/0.48 0.18/0.48 thf(kfstpairEq,definition, 0.18/0.48 ( kfstpairEq 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( kfst @ ( kpair @ Xx @ Xy ) ) 0.18/0.48 = Xx ) ) ) ). 0.18/0.48 0.18/0.48 thf(cartprodfstin_type,type, 0.18/0.48 cartprodfstin: $o ). 0.18/0.48 0.18/0.48 thf(cartprodfstin,definition, 0.18/0.48 ( cartprodfstin 0.18/0.48 = ( ! [A: $i,B: $i,Xu: $i] : 0.18/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) ) 0.18/0.48 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setukpairinjL2_type,type, 0.18/0.48 setukpairinjL2: $o ). 0.18/0.48 0.18/0.48 thf(setukpairinjL2,definition, 0.18/0.48 ( setukpairinjL2 0.18/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] : 0.18/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) 0.18/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) 0.18/0.48 => ( Xx = Xz ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setukpairinjL_type,type, 0.18/0.48 setukpairinjL: $o ). 0.18/0.48 0.18/0.48 thf(setukpairinjL,definition, 0.18/0.48 ( setukpairinjL 0.18/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] : 0.18/0.48 ( ( ( kpair @ Xx @ Xy ) 0.18/0.48 = ( kpair @ Xz @ Xu ) ) 0.18/0.48 => ( Xx = Xz ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setukpairinjR11_type,type, 0.18/0.48 setukpairinjR11: $o ). 0.18/0.48 0.18/0.48 thf(setukpairinjR11,definition, 0.18/0.48 ( setukpairinjR11 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xx = Xy ) 0.18/0.48 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.18/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setukpairinjR12_type,type, 0.18/0.48 setukpairinjR12: $o ). 0.18/0.48 0.18/0.48 thf(setukpairinjR12,definition, 0.18/0.48 ( setukpairinjR12 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xx = Xy ) 0.18/0.48 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) 0.18/0.48 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setukpairinjR1_type,type, 0.18/0.48 setukpairinjR1: $o ). 0.18/0.48 0.18/0.48 thf(setukpairinjR1,definition, 0.18/0.48 ( setukpairinjR1 0.18/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] : 0.18/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) 0.18/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) 0.18/0.48 => ( ( Xz = Xu ) 0.18/0.48 => ( Xy = Xu ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(upairequniteq_type,type, 0.18/0.48 upairequniteq: $o ). 0.18/0.48 0.18/0.48 thf(upairequniteq,definition, 0.18/0.48 ( upairequniteq 0.18/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] : 0.18/0.48 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.18/0.48 = ( setadjoin @ Xz @ emptyset ) ) 0.18/0.48 => ( Xx = Xy ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setukpairinjR2_type,type, 0.18/0.48 setukpairinjR2: $o ). 0.18/0.48 0.18/0.48 thf(setukpairinjR2,definition, 0.18/0.48 ( setukpairinjR2 0.18/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] : 0.18/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) 0.18/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) 0.18/0.48 => ( Xy = Xu ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setukpairinjR_type,type, 0.18/0.48 setukpairinjR: $o ). 0.18/0.48 0.18/0.48 thf(setukpairinjR,definition, 0.18/0.48 ( setukpairinjR 0.18/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] : 0.18/0.48 ( ( ( kpair @ Xx @ Xy ) 0.18/0.48 = ( kpair @ Xz @ Xu ) ) 0.18/0.48 => ( Xy = Xu ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(ksndsingleton_type,type, 0.18/0.48 ksndsingleton: $o ). 0.18/0.48 0.18/0.48 thf(ksndsingleton,definition, 0.18/0.48 ( ksndsingleton 0.18/0.48 = ( ! [Xu: $i] : 0.18/0.48 ( ( iskpair @ Xu ) 0.18/0.48 => ( singleton 0.18/0.48 @ ( dsetconstr @ ( setunion @ Xu ) 0.18/0.48 @ ^ [Xx: $i] : 0.18/0.48 ( Xu 0.18/0.48 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(ksnd_type,type, 0.18/0.48 ksnd: $i > $i ). 0.18/0.48 0.18/0.48 thf(ksndpairEq_type,type, 0.18/0.48 ksndpairEq: $o ). 0.18/0.48 0.18/0.48 thf(ksndpairEq,definition, 0.18/0.48 ( ksndpairEq 0.18/0.48 = ( ! [Xx: $i,Xy: $i] : 0.18/0.48 ( ( ksnd @ ( kpair @ Xx @ Xy ) ) 0.18/0.48 = Xy ) ) ) ). 0.18/0.48 0.18/0.48 thf(kpairsurjEq_type,type, 0.18/0.48 kpairsurjEq: $o ). 0.18/0.48 0.18/0.48 thf(kpairsurjEq,definition, 0.18/0.48 ( kpairsurjEq 0.18/0.48 = ( ! [Xu: $i] : 0.18/0.48 ( ( iskpair @ Xu ) 0.18/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) ) 0.18/0.48 = Xu ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(cartprodsndin_type,type, 0.18/0.48 cartprodsndin: $o ). 0.18/0.48 0.18/0.48 thf(cartprodsndin,definition, 0.18/0.48 ( cartprodsndin 0.18/0.48 = ( ! [A: $i,B: $i,Xu: $i] : 0.18/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) ) 0.18/0.48 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(cartprodpairmemEL_type,type, 0.18/0.48 cartprodpairmemEL: $o ). 0.18/0.48 0.18/0.48 thf(cartprodpairmemEL,definition, 0.18/0.48 ( cartprodpairmemEL 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] : 0.18/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) 0.18/0.48 => ( in @ Xx @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(cartprodpairmemER_type,type, 0.18/0.48 cartprodpairmemER: $o ). 0.18/0.48 0.18/0.48 thf(cartprodpairmemER,definition, 0.18/0.48 ( cartprodpairmemER 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] : 0.18/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) 0.18/0.48 => ( in @ Xy @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(cartprodmempaircEq_type,type, 0.18/0.48 cartprodmempaircEq: $o ). 0.18/0.48 0.18/0.48 thf(cartprodmempaircEq,definition, 0.18/0.48 ( cartprodmempaircEq 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( ( kpair @ Xx @ Xy ) 0.18/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(cartprodfstpairEq_type,type, 0.18/0.48 cartprodfstpairEq: $o ). 0.18/0.48 0.18/0.48 thf(cartprodfstpairEq,definition, 0.18/0.48 ( cartprodfstpairEq 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( ( kfst @ ( kpair @ Xx @ Xy ) ) 0.18/0.48 = Xx ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(cartprodsndpairEq_type,type, 0.18/0.48 cartprodsndpairEq: $o ). 0.18/0.48 0.18/0.48 thf(cartprodsndpairEq,definition, 0.18/0.48 ( cartprodsndpairEq 0.18/0.48 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( ( ksnd @ ( kpair @ Xx @ Xy ) ) 0.18/0.48 = Xy ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(cartprodpairsurjEq_type,type, 0.18/0.48 cartprodpairsurjEq: $o ). 0.18/0.48 0.18/0.48 thf(cartprodpairsurjEq,definition, 0.18/0.48 ( cartprodpairsurjEq 0.18/0.48 = ( ! [A: $i,B: $i,Xu: $i] : 0.18/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) ) 0.18/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) ) 0.18/0.48 = Xu ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(breln_type,type, 0.18/0.48 breln: $i > $i > $i > $o ). 0.18/0.48 0.18/0.48 thf(breln,definition, 0.18/0.48 ( breln 0.18/0.48 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(dpsetconstr_type,type, 0.18/0.48 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ). 0.18/0.48 0.18/0.48 thf(dpsetconstrI_type,type, 0.18/0.48 dpsetconstrI: $o ). 0.18/0.48 0.18/0.48 thf(dpsetconstrI,definition, 0.18/0.48 ( dpsetconstrI 0.18/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( ( Xphi @ Xx @ Xy ) 0.18/0.48 => ( in @ ( kpair @ Xx @ Xy ) 0.18/0.48 @ ( dpsetconstr @ A @ B 0.18/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(dpsetconstrSub_type,type, 0.18/0.48 dpsetconstrSub: $o ). 0.18/0.48 0.18/0.48 thf(dpsetconstrSub,definition, 0.18/0.48 ( dpsetconstrSub 0.18/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] : 0.18/0.48 ( subset 0.18/0.48 @ ( dpsetconstr @ A @ B 0.18/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) 0.18/0.48 @ ( cartprod @ A @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(setOfPairsIsBReln_type,type, 0.18/0.48 setOfPairsIsBReln: $o ). 0.18/0.48 0.18/0.48 thf(setOfPairsIsBReln,definition, 0.18/0.48 ( setOfPairsIsBReln 0.18/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] : 0.18/0.48 ( breln @ A @ B 0.18/0.48 @ ( dpsetconstr @ A @ B 0.18/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(dpsetconstrERa_type,type, 0.18/0.48 dpsetconstrERa: $o ). 0.18/0.48 0.18/0.48 thf(dpsetconstrERa,definition, 0.18/0.48 ( dpsetconstrERa 0.18/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) 0.18/0.48 @ ( dpsetconstr @ A @ B 0.18/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) 0.18/0.48 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(dpsetconstrEL1_type,type, 0.18/0.48 dpsetconstrEL1: $o ). 0.18/0.48 0.18/0.48 thf(dpsetconstrEL1,definition, 0.18/0.48 ( dpsetconstrEL1 0.18/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] : 0.18/0.48 ( ( in @ ( kpair @ Xx @ Xy ) 0.18/0.48 @ ( dpsetconstr @ A @ B 0.18/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) 0.18/0.48 => ( in @ Xx @ A ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(dpsetconstrEL2_type,type, 0.18/0.48 dpsetconstrEL2: $o ). 0.18/0.48 0.18/0.48 thf(dpsetconstrEL2,definition, 0.18/0.48 ( dpsetconstrEL2 0.18/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] : 0.18/0.48 ( ( in @ ( kpair @ Xx @ Xy ) 0.18/0.48 @ ( dpsetconstr @ A @ B 0.18/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) 0.18/0.48 => ( in @ Xy @ B ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(dpsetconstrER_type,type, 0.18/0.48 dpsetconstrER: $o ). 0.18/0.48 0.18/0.48 thf(dpsetconstrER,definition, 0.18/0.48 ( dpsetconstrER 0.18/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] : 0.18/0.48 ( ( in @ ( kpair @ Xx @ Xy ) 0.18/0.48 @ ( dpsetconstr @ A @ B 0.18/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) 0.18/0.48 => ( Xphi @ Xx @ Xy ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(func_type,type, 0.18/0.48 func: $i > $i > $i > $o ). 0.18/0.48 0.18/0.48 thf(func,definition, 0.18/0.48 ( func 0.18/0.48 = ( ^ [A: $i,B: $i,R: $i] : 0.18/0.48 ( ( breln @ A @ B @ R ) 0.18/0.48 & ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( ex1 @ B 0.18/0.48 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(funcSet_type,type, 0.18/0.48 funcSet: $i > $i > $i ). 0.18/0.48 0.18/0.48 thf(funcImageSingleton_type,type, 0.18/0.48 funcImageSingleton: $o ). 0.18/0.48 0.18/0.48 thf(funcImageSingleton,definition, 0.18/0.48 ( funcImageSingleton 0.18/0.48 = ( ! [A: $i,B: $i,Xf: $i] : 0.18/0.48 ( ( func @ A @ B @ Xf ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( singleton 0.18/0.48 @ ( dsetconstr @ B 0.18/0.48 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(apProp_type,type, 0.18/0.48 apProp: $o ). 0.18/0.48 0.18/0.48 thf(apProp,definition, 0.18/0.48 ( apProp 0.18/0.48 = ( ! [A: $i,B: $i,Xf: $i] : 0.18/0.48 ( ( func @ A @ B @ Xf ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in 0.18/0.48 @ ( setunion 0.18/0.48 @ ( dsetconstr @ B 0.18/0.48 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) 0.18/0.48 @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(ap_type,type, 0.18/0.48 ap: $i > $i > $i > $i > $i ). 0.18/0.48 0.18/0.48 thf(app_type,type, 0.18/0.48 app: $o ). 0.18/0.48 0.18/0.48 thf(app,definition, 0.18/0.48 ( app 0.18/0.48 = ( ! [A: $i,B: $i,Xf: $i] : 0.18/0.48 ( ( func @ A @ B @ Xf ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(infuncsetfunc_type,type, 0.18/0.48 infuncsetfunc: $o ). 0.18/0.48 0.18/0.48 thf(infuncsetfunc,definition, 0.18/0.48 ( infuncsetfunc 0.18/0.48 = ( ! [A: $i,B: $i,Xf: $i] : 0.18/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) ) 0.18/0.48 => ( func @ A @ B @ Xf ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(ap2p_type,type, 0.18/0.48 ap2p: $o ). 0.18/0.48 0.18/0.48 thf(ap2p,definition, 0.18/0.48 ( ap2p 0.18/0.48 = ( ! [A: $i,B: $i,Xf: $i] : 0.18/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(funcinfuncset_type,type, 0.18/0.48 funcinfuncset: $o ). 0.18/0.48 0.18/0.48 thf(funcinfuncset,definition, 0.18/0.48 ( funcinfuncset 0.18/0.48 = ( ! [A: $i,B: $i,Xf: $i] : 0.18/0.48 ( ( func @ A @ B @ Xf ) 0.18/0.48 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(lamProp_type,type, 0.18/0.48 lamProp: $o ). 0.18/0.48 0.18/0.48 thf(lamProp,definition, 0.18/0.48 ( lamProp 0.18/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ ( Xf @ Xx ) @ B ) ) 0.18/0.48 => ( func @ A @ B 0.18/0.48 @ ( dpsetconstr @ A @ B 0.18/0.48 @ ^ [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xf @ Xx ) 0.18/0.48 = Xy ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(lam_type,type, 0.18/0.48 lam: $i > $i > ( $i > $i ) > $i ). 0.18/0.48 0.18/0.48 thf(lam,definition, 0.18/0.48 ( lam 0.18/0.48 = ( ^ [A: $i,B: $i,Xf: $i > $i] : 0.18/0.48 ( dpsetconstr @ A @ B 0.18/0.48 @ ^ [Xx: $i,Xy: $i] : 0.18/0.48 ( ( Xf @ Xx ) 0.18/0.48 = Xy ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(lamp_type,type, 0.18/0.48 lamp: $o ). 0.18/0.48 0.18/0.48 thf(lamp,definition, 0.18/0.48 ( lamp 0.18/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ ( Xf @ Xx ) @ B ) ) 0.18/0.48 => ( func @ A @ B 0.18/0.48 @ ( lam @ A @ B 0.18/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(lam2p_type,type, 0.18/0.48 lam2p: $o ). 0.18/0.48 0.18/0.48 thf(lam2p,definition, 0.18/0.48 ( lam2p 0.18/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ ( Xf @ Xx ) @ B ) ) 0.18/0.48 => ( in 0.18/0.48 @ ( lam @ A @ B 0.18/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) ) 0.18/0.48 @ ( funcSet @ A @ B ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(brelnall1_type,type, 0.18/0.48 brelnall1: $o ). 0.18/0.48 0.18/0.48 thf(brelnall1,definition, 0.18/0.48 ( brelnall1 0.18/0.48 = ( ! [A: $i,B: $i,R: $i] : 0.18/0.48 ( ( breln @ A @ B @ R ) 0.18/0.48 => ! [Xphi: $i > $o] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R ) 0.18/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ R ) 0.18/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(brelnall2_type,type, 0.18/0.48 brelnall2: $o ). 0.18/0.48 0.18/0.48 thf(brelnall2,definition, 0.18/0.48 ( brelnall2 0.18/0.48 = ( ! [A: $i,B: $i,R: $i] : 0.18/0.48 ( ( breln @ A @ B @ R ) 0.18/0.48 => ! [Xphi: $i > $o] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R ) 0.18/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ R ) 0.18/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(ex1E2_type,type, 0.18/0.48 ex1E2: $o ). 0.18/0.48 0.18/0.48 thf(ex1E2,definition, 0.18/0.48 ( ex1E2 0.18/0.48 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.48 ( ( ex1 @ A 0.18/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ A ) 0.18/0.48 => ( ( Xphi @ Xx ) 0.18/0.48 => ( ( Xphi @ Xy ) 0.18/0.48 => ( Xx = Xy ) ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(funcGraphProp1_type,type, 0.18/0.48 funcGraphProp1: $o ). 0.18/0.48 0.18/0.48 thf(funcGraphProp1,definition, 0.18/0.48 ( funcGraphProp1 0.18/0.48 = ( ! [A: $i,B: $i,Xf: $i] : 0.18/0.48 ( ( func @ A @ B @ Xf ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(funcGraphProp3_type,type, 0.18/0.48 funcGraphProp3: $o ). 0.18/0.48 0.18/0.48 thf(funcGraphProp3,definition, 0.18/0.48 ( funcGraphProp3 0.18/0.48 = ( ! [A: $i,B: $i,Xf: $i] : 0.18/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(funcGraphProp2_type,type, 0.18/0.48 funcGraphProp2: $o ). 0.18/0.48 0.18/0.48 thf(funcGraphProp2,definition, 0.18/0.48 ( funcGraphProp2 0.18/0.48 = ( ! [A: $i,B: $i,Xf: $i] : 0.18/0.48 ( ( func @ A @ B @ Xf ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf ) 0.18/0.48 => ( ( ap @ A @ B @ Xf @ Xx ) 0.18/0.48 = Xy ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(funcextLem_type,type, 0.18/0.48 funcextLem: $o ). 0.18/0.48 0.18/0.48 thf(funcextLem,definition, 0.18/0.48 ( funcextLem 0.18/0.48 = ( ! [A: $i,B: $i,Xf: $i] : 0.18/0.48 ( ( func @ A @ B @ Xf ) 0.18/0.48 => ! [Xg: $i] : 0.18/0.48 ( ( func @ A @ B @ Xg ) 0.18/0.48 => ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ( ( ap @ A @ B @ Xf @ Xx ) 0.18/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) ) 0.18/0.48 => ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( in @ Xy @ B ) 0.18/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg ) 0.18/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ). 0.18/0.48 0.18/0.48 thf(funcGraphProp4,conjecture, 0.18/0.48 ( ( emptysetAx 0.18/0.48 => ( ( ( setunionAx 0.18/0.48 => ( ( ( ( ( ( ( descrp 0.18/0.48 => ( dsetconstrI 0.18/0.48 => ( ( ( exuE1 0.18/0.48 => ( ( emptysetE 0.18/0.48 => ( emptysetimpfalse 0.18/0.48 => ( ( ( ( emptyI 0.18/0.48 => ( ( setbeta 0.18/0.48 => ( ( nonemptyI 0.18/0.48 => ( nonemptyI1 0.18/0.48 => ( ( emptyinunitempty 0.18/0.48 => ( setadjoinIR 0.18/0.48 => ( setadjoinE 0.18/0.48 => ( setadjoinOr 0.18/0.48 => ( setoftrueEq 0.18/0.48 => ( powersetI 0.18/0.48 => ( ( emptyInPowerset 0.18/0.48 => ( powersetE 0.18/0.48 => ( setunionI 0.18/0.48 => ( setunionE 0.18/0.48 => ( ( exuE2 0.18/0.48 => ( ( ( notinsingleton 0.18/0.48 => ( eqinunit 0.18/0.48 => ( singletonsswitch 0.18/0.48 => ( ( ( upairsetIR 0.18/0.48 => ( ( ( ( ( ( ( ( prop2set2propI 0.18/0.48 => ( notdexE 0.18/0.48 => ( ( exuI1 0.18/0.48 => ( exuI3 0.18/0.48 => ( exuI2 0.18/0.48 => ( ( ( exuE3u 0.18/0.48 => ( ( emptyset__Cong 0.18/0.48 => ( ( ( ( ( exuEu 0.18/0.48 => ( ( ( subsetI1 0.18/0.48 => ( ( eqimpsubset1 0.18/0.48 => ( subsetI2 0.18/0.48 => ( emptysetsubset 0.18/0.48 => ( ( subsetE2 0.18/0.48 => ( notsubsetI 0.18/0.48 => ( notequalI1 0.18/0.48 => ( ( subsetRefl 0.18/0.48 => ( ( setadjoinSub 0.18/0.48 => ( setadjoinSub2 0.18/0.48 => ( subset2powerset 0.18/0.48 => ( ( ( powersetI1 0.18/0.48 => ( powersetE1 0.18/0.48 => ( inPowerset 0.18/0.48 => ( ( ( ( ( ( ( binunionEcases 0.18/0.48 => ( binunionE 0.18/0.48 => ( binunionLsub 0.18/0.48 => ( binunionRsub 0.18/0.48 => ( ( binintersectSubset5 0.18/0.48 => ( ( ( ( ( ( ( binintersectRsub 0.18/0.48 => ( ( ( bs114d 0.18/0.48 => ( setminusI 0.18/0.48 => ( setminusEL 0.18/0.48 => ( ( setminusSubset2 0.18/0.48 => ( ( ( ( ( setminusLsub 0.18/0.48 => ( setminusSubset1 0.18/0.48 => ( ( symdiffI1 0.18/0.48 => ( ( ( ( secondinupair 0.18/0.48 => ( ( ( ( kpairp 0.18/0.48 => ( ( ( singletoninpowunion 0.18/0.48 => ( upairset2E 0.18/0.48 => ( ( upairinpowunion 0.18/0.48 => ( ( ubforcartprodlem2 0.18/0.48 => ( ubforcartprodlem3 0.18/0.48 => ( ( cartprodmempair1 0.18/0.48 => ( cartprodmempair 0.18/0.48 => ( ( setunionsingleton1 0.18/0.48 => ( ( setunionsingleton 0.18/0.48 => ( singletonprop 0.18/0.48 => ( ex1E1 0.18/0.48 => ( ( ex1I2 0.18/0.48 => ( ( setukpairinjL1 0.18/0.48 => ( ( ( ( ( ( ( setukpairinjR11 0.18/0.48 => ( ( setukpairinjR1 0.18/0.48 => ( upairequniteq 0.18/0.48 => ( setukpairinjR2 0.18/0.48 => ( setukpairinjR 0.18/0.48 => ( ( ( ( cartprodsndin 0.18/0.48 => ( ( cartprodpairmemER 0.18/0.48 => ( cartprodmempaircEq 0.18/0.48 => ( cartprodfstpairEq 0.18/0.48 => ( ( cartprodpairsurjEq 0.18/0.48 => ( dpsetconstrI 0.18/0.48 => ( dpsetconstrSub 0.18/0.48 => ( ( dpsetconstrERa 0.18/0.48 => ( ( ( dpsetconstrER 0.18/0.48 => ( funcImageSingleton 0.18/0.48 => ( ( app 0.18/0.48 => ( infuncsetfunc 0.18/0.48 => ( ap2p 0.18/0.48 => ( ( ( ( lam2p 0.18/0.48 => ( ( brelnall2 0.18/0.48 => ( ( funcGraphProp1 0.18/0.48 => ( funcGraphProp3 0.18/0.48 => ( funcGraphProp2 0.18/0.48 => ( funcextLem 0.18/0.48 => ! [A: $i,B: $i,Xf: $i] : 0.18/0.48 ( ! [Xx: $i] : 0.18/0.48 ( ( in @ Xx @ A ) 0.18/0.48 => ! [Xy: $i] : 0.18/0.48 ( ( ( in @ ( kpair @ Xx @ Xy ) @ Xf ) 0.18/0.48 => ( ( ap @ A @ B @ Xf @ Xx ) 0.18/0.48 = Xy ) ) 0.18/0.48 <= ( in @ Xy @ B ) ) ) 0.18/0.48 <= ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ) ) 0.18/0.48 <= ex1E2 ) ) 0.18/0.48 <= brelnall1 ) ) 0.18/0.48 <= lamp ) 0.18/0.48 <= lamProp ) 0.18/0.48 <= funcinfuncset ) ) ) ) 0.18/0.48 <= apProp ) ) ) 0.18/0.48 <= dpsetconstrEL2 ) 0.18/0.48 <= dpsetconstrEL1 ) ) 0.18/0.48 <= setOfPairsIsBReln ) ) ) ) 0.18/0.48 <= cartprodsndpairEq ) ) ) ) 0.18/0.48 <= cartprodpairmemEL ) ) 0.18/0.48 <= kpairsurjEq ) 0.18/0.48 <= ksndpairEq ) 0.18/0.48 <= ksndsingleton ) ) ) ) ) 0.18/0.48 <= setukpairinjR12 ) ) 0.18/0.48 <= setukpairinjL ) 0.18/0.48 <= setukpairinjL2 ) 0.18/0.48 <= cartprodfstin ) 0.18/0.48 <= kfstpairEq ) 0.18/0.48 <= theprop ) 0.18/0.48 <= kfstsingleton ) ) 0.18/0.48 <= singletonsuniq ) ) 0.18/0.48 <= ex1I ) ) ) ) 0.18/0.48 <= setunionsingleton2 ) ) 0.18/0.48 <= setunionE2 ) ) ) 0.18/0.48 <= cartprodpairin ) ) ) 0.18/0.48 <= ubforcartprodlem1 ) ) 0.18/0.48 <= upairsubunion ) ) ) 0.18/0.48 <= singletoninpowerset ) 0.18/0.48 <= singletonsubset ) ) 0.18/0.48 <= kpairiskpair ) 0.18/0.48 <= setukpairIR ) 0.18/0.48 <= setukpairIL ) ) 0.18/0.48 <= symdiffIneg2 ) 0.18/0.48 <= symdiffIneg1 ) 0.18/0.48 <= symdiffI2 ) ) 0.18/0.48 <= symdiffE ) ) ) 0.18/0.48 <= setminusIRneg ) 0.18/0.48 <= setminusILneg ) 0.18/0.48 <= setminusELneg ) 0.18/0.48 <= setminusERneg ) ) 0.18/0.48 <= setminusER ) ) ) ) 0.18/0.48 <= binintersectSubset1 ) 0.18/0.48 <= binintersectSubset4 ) ) 0.18/0.48 <= disjointsetsI1 ) 0.18/0.48 <= binintersectER ) 0.18/0.48 <= binintersectSubset3 ) 0.18/0.48 <= binintersectSubset2 ) 0.18/0.48 <= binintersectLsub ) 0.18/0.48 <= binintersectEL ) ) 0.18/0.48 <= binintersectI ) ) ) ) ) 0.18/0.48 <= binunionIR ) 0.18/0.48 <= upairset2IR ) 0.18/0.48 <= binunionIL ) 0.18/0.48 <= sepSubset ) 0.18/0.48 <= sepInPowerset ) 0.18/0.48 <= powersetsubset ) ) ) ) 0.18/0.48 <= subsetemptysetimpeq ) 0.18/0.48 <= setextsub ) ) ) ) 0.18/0.48 <= subsetTrans ) ) 0.18/0.48 <= notequalI2 ) ) ) ) 0.18/0.48 <= subsetE ) ) ) ) 0.18/0.48 <= eqimpsubset2 ) ) 0.18/0.48 <= dsetconstr__Cong ) 0.18/0.48 <= descr__Cong ) ) 0.18/0.48 <= omega__Cong ) 0.18/0.48 <= setunion__Cong ) 0.18/0.48 <= powerset__Cong ) 0.18/0.48 <= setadjoin__Cong ) ) 0.18/0.48 <= exu__Cong ) ) 0.18/0.48 <= in__Cong ) 0.18/0.48 <= inCongP ) ) ) ) 0.18/0.48 <= notdallE ) ) ) 0.18/0.48 <= prop2setI ) 0.18/0.48 <= quantDeMorgan4 ) 0.18/0.48 <= quantDeMorgan3 ) 0.18/0.48 <= quantDeMorgan2 ) 0.18/0.48 <= quantDeMorgan1 ) 0.18/0.48 <= vacuousDall ) 0.18/0.48 <= emptyE1 ) ) 0.18/0.48 <= upairsetIL ) 0.18/0.48 <= upairsetE ) ) ) ) 0.18/0.48 <= uniqinunit ) 0.18/0.48 <= nonemptyImpWitness ) ) 0.18/0.48 <= subPowSU ) ) ) ) ) 0.18/0.48 <= emptyinPowerset ) ) ) ) ) ) ) 0.18/0.48 <= setadjoinIL ) ) ) 0.18/0.48 <= nonemptyE1 ) ) 0.18/0.48 <= noeltsimpempty ) ) 0.18/0.48 <= setext ) 0.18/0.48 <= exuE3e ) 0.18/0.48 <= notinemptyset ) ) ) 0.18/0.48 <= prop2setE ) ) 0.18/0.48 <= dsetconstrER ) 0.18/0.48 <= dsetconstrEL ) ) ) 0.18/0.51 <= wellorderingAx ) 0.18/0.51 <= foundationAx ) 0.18/0.51 <= replAx ) 0.18/0.51 <= omegaIndAx ) 0.18/0.51 <= omegaSAx ) 0.18/0.51 <= omega0Ax ) ) 0.18/0.51 <= powersetAx ) 0.18/0.51 <= setadjoinAx ) ) 0.18/0.51 <= setextAx ) ). 0.18/0.51 0.18/0.51 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.qmNgA0jd3D/cvc5---1.0.5_22540.p... 0.18/0.51 (declare-sort $$unsorted 0) 0.18/0.51 (declare-fun tptp.in ($$unsorted $$unsorted) Bool) 0.18/0.51 (declare-fun tptp.exu ((-> $$unsorted Bool)) Bool) 0.18/0.51 (assert (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy)))))))) 0.18/0.51 (declare-fun tptp.setextAx () Bool) 0.18/0.51 (assert (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B))))) 0.18/0.51 (declare-fun tptp.emptyset () $$unsorted) 0.18/0.51 (declare-fun tptp.emptysetAx () Bool) 0.18/0.51 (assert (= tptp.emptysetAx (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.18/0.51 (declare-fun tptp.setadjoin ($$unsorted $$unsorted) $$unsorted) 0.18/0.51 (declare-fun tptp.setadjoinAx () Bool) 0.18/0.51 (assert (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.18/0.51 (declare-fun tptp.powerset ($$unsorted) $$unsorted) 0.18/0.51 (declare-fun tptp.powersetAx () Bool) 0.18/0.51 (assert (= tptp.powersetAx (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))))))) 0.18/0.51 (declare-fun tptp.setunion ($$unsorted) $$unsorted) 0.18/0.51 (declare-fun tptp.setunionAx () Bool) 0.18/0.51 (assert (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A))))))) 0.18/0.51 (declare-fun tptp.omega () $$unsorted) 0.18/0.51 (declare-fun tptp.omega0Ax () Bool) 0.18/0.51 (assert (= tptp.omega0Ax (@ (@ tptp.in tptp.emptyset) tptp.omega))) 0.18/0.51 (declare-fun tptp.omegaSAx () Bool) 0.18/0.51 (assert (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega))))) 0.18/0.51 (declare-fun tptp.omegaIndAx () Bool) 0.18/0.51 (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 $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 tptp.omega) (@ _let_1 A)))))))) 0.18/0.51 (declare-fun tptp.replAx () Bool) 0.18/0.51 (assert (= tptp.replAx (forall ((Xphi (-> $$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 $$unsorted)) (and (@ (@ tptp.in Xy) A) (@ (@ Xphi Xy) Xx)))))))))) 0.18/0.51 (declare-fun tptp.foundationAx () Bool) 0.18/0.51 (assert (= tptp.foundationAx (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in B) A) (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 B) (@ _let_1 A))))))))))) 0.18/0.51 (declare-fun tptp.wellorderingAx () Bool) 0.18/0.51 (assert (= tptp.wellorderingAx (forall ((A $$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))))))))))))) 0.18/0.51 (declare-fun tptp.descr ((-> $$unsorted Bool)) $$unsorted) 0.18/0.51 (declare-fun tptp.descrp () Bool) 0.18/0.51 (assert (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) 0.18/0.51 (declare-fun tptp.dsetconstr ($$unsorted (-> $$unsorted Bool)) $$unsorted) 0.18/0.51 (declare-fun tptp.dsetconstrI () Bool) 0.18/0.51 (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)))))))))) 0.18/0.51 (declare-fun tptp.dsetconstrEL () Bool) 0.18/0.51 (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)))))) 0.18/0.51 (declare-fun tptp.dsetconstrER () Bool) 0.18/0.51 (assert (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))) 0.18/0.51 (declare-fun tptp.exuE1 () Bool) 0.18/0.51 (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))))))))) 0.18/0.51 (declare-fun tptp.prop2set (Bool) $$unsorted) 0.18/0.51 (declare-fun tptp.prop2setE () Bool) 0.18/0.51 (assert (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi)))) 0.18/0.51 (declare-fun tptp.emptysetE () Bool) 0.18/0.51 (assert (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi))))) 0.18/0.51 (declare-fun tptp.emptysetimpfalse () Bool) 0.18/0.51 (assert (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false)))) 0.18/0.51 (declare-fun tptp.notinemptyset () Bool) 0.18/0.51 (assert (= tptp.notinemptyset (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.18/0.51 (declare-fun tptp.exuE3e () Bool) 0.18/0.51 (assert (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx)))))) 0.18/0.51 (declare-fun tptp.setext () Bool) 0.18/0.51 (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)))))) 0.18/0.51 (declare-fun tptp.emptyI () Bool) 0.18/0.51 (assert (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.18/0.51 (declare-fun tptp.noeltsimpempty () Bool) 0.18/0.51 (assert (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.18/0.51 (declare-fun tptp.setbeta () Bool) 0.18/0.51 (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))))))) 0.18/0.51 (declare-fun tptp.nonempty ($$unsorted) Bool) 0.18/0.51 (assert (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset))))) 0.18/0.51 (declare-fun tptp.nonemptyE1 () Bool) 0.18/0.51 (assert (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)))))) 0.18/0.51 (declare-fun tptp.nonemptyI () Bool) 0.18/0.51 (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))))))))) 0.18/0.51 (declare-fun tptp.nonemptyI1 () Bool) 0.18/0.51 (assert (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A))))) 0.18/0.51 (declare-fun tptp.setadjoinIL () Bool) 0.18/0.51 (assert (= tptp.setadjoinIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) 0.18/0.51 (declare-fun tptp.emptyinunitempty () Bool) 0.18/0.51 (assert (= tptp.emptyinunitempty (@ (@ tptp.in tptp.emptyset) (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) 0.18/0.51 (declare-fun tptp.setadjoinIR () Bool) 0.18/0.51 (assert (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A))))))) 0.18/0.51 (declare-fun tptp.setadjoinE () Bool) 0.18/0.51 (assert (= tptp.setadjoinE (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (forall ((Xphi Bool)) (=> (=> (= Xy Xx) Xphi) (=> (=> (@ (@ tptp.in Xy) A) Xphi) Xphi))))))) 0.18/0.51 (declare-fun tptp.setadjoinOr () Bool) 0.18/0.51 (assert (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.18/0.51 (declare-fun tptp.setoftrueEq () Bool) 0.18/0.51 (assert (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A)))) 0.18/0.51 (declare-fun tptp.powersetI () Bool) 0.18/0.51 (assert (= tptp.powersetI (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (@ (@ tptp.in B) (@ tptp.powerset A)))))) 0.18/0.51 (declare-fun tptp.emptyinPowerset () Bool) 0.18/0.51 (assert (= tptp.emptyinPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) 0.18/0.51 (declare-fun tptp.emptyInPowerset () Bool) 0.18/0.51 (assert (= tptp.emptyInPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) 0.18/0.51 (declare-fun tptp.powersetE () Bool) 0.18/0.51 (assert (= tptp.powersetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (=> (@ _let_1 B) (@ _let_1 A))))))) 0.18/0.51 (declare-fun tptp.setunionI () Bool) 0.18/0.51 (assert (= tptp.setunionI (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (=> (@ (@ tptp.in B) A) (@ _let_1 (@ tptp.setunion A)))))))) 0.18/0.51 (declare-fun tptp.setunionE () Bool) 0.18/0.51 (assert (= tptp.setunionE (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (forall ((Xphi Bool)) (=> (forall ((B $$unsorted)) (=> (@ (@ tptp.in Xx) B) (=> (@ (@ tptp.in B) A) Xphi))) Xphi)))))) 0.18/0.51 (declare-fun tptp.subPowSU () Bool) 0.18/0.51 (assert (= tptp.subPowSU (forall ((A $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.powerset (@ tptp.setunion A)))))))) 0.18/0.51 (declare-fun tptp.exuE2 () Bool) 0.18/0.51 (assert (= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))))))) 0.18/0.51 (declare-fun tptp.nonemptyImpWitness () Bool) 0.18/0.51 (assert (= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) true)))))) 0.18/0.51 (declare-fun tptp.uniqinunit () Bool) 0.18/0.51 (assert (= tptp.uniqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy))))) 0.18/0.51 (declare-fun tptp.notinsingleton () Bool) 0.18/0.51 (assert (= tptp.notinsingleton (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (not (= Xx Xy)) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) 0.18/0.51 (declare-fun tptp.eqinunit () Bool) 0.18/0.51 (assert (= tptp.eqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.18/0.51 (declare-fun tptp.singletonsswitch () Bool) 0.18/0.51 (assert (= tptp.singletonsswitch (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) 0.18/0.51 (declare-fun tptp.upairsetE () Bool) 0.18/0.51 (assert (= tptp.upairsetE (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy)))))) 0.18/0.51 (declare-fun tptp.upairsetIL () Bool) 0.18/0.51 (assert (= tptp.upairsetIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.18/0.51 (declare-fun tptp.upairsetIR () Bool) 0.18/0.51 (assert (= tptp.upairsetIR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.18/0.51 (declare-fun tptp.emptyE1 () Bool) 0.18/0.51 (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))))) 0.18/0.51 (declare-fun tptp.vacuousDall () Bool) 0.18/0.51 (assert (= tptp.vacuousDall (forall ((Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (@ Xphi Xx))))) 0.18/0.51 (declare-fun tptp.quantDeMorgan1 () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.quantDeMorgan2 () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.quantDeMorgan3 () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.quantDeMorgan4 () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.prop2setI () Bool) 0.18/0.51 (assert (= tptp.prop2setI (forall ((Xphi Bool)) (=> Xphi (@ (@ tptp.in tptp.emptyset) (@ tptp.prop2set Xphi)))))) 0.18/0.51 (declare-fun tptp.set2prop ($$unsorted) Bool) 0.18/0.51 (declare-fun tptp.prop2set2propI () Bool) 0.18/0.51 (assert (= tptp.prop2set2propI (forall ((Xphi Bool)) (=> Xphi (@ tptp.set2prop (@ tptp.prop2set Xphi)))))) 0.18/0.51 (declare-fun tptp.notdexE () Bool) 0.18/0.51 (assert (= tptp.notdexE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.18/0.51 (declare-fun tptp.notdallE () Bool) 0.18/0.51 (assert (= tptp.notdallE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.18/0.51 (declare-fun tptp.exuI1 () Bool) 0.18/0.51 (assert (= tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) 0.18/0.51 (declare-fun tptp.exuI3 () Bool) 0.18/0.51 (assert (= tptp.exuI3 (forall ((Xphi (-> $$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)))))))) 0.18/0.51 (declare-fun tptp.exuI2 () Bool) 0.18/0.51 (assert (= tptp.exuI2 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) 0.18/0.51 (declare-fun tptp.inCongP () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.in__Cong () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.exuE3u () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.exu__Cong () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.emptyset__Cong () Bool) 0.18/0.51 (assert (= tptp.emptyset__Cong (= tptp.emptyset tptp.emptyset))) 0.18/0.51 (declare-fun tptp.setadjoin__Cong () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.powerset__Cong () Bool) 0.18/0.51 (assert (= tptp.powerset__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.powerset A) (@ tptp.powerset B)))))) 0.18/0.51 (declare-fun tptp.setunion__Cong () Bool) 0.18/0.51 (assert (= tptp.setunion__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.setunion A) (@ tptp.setunion B)))))) 0.18/0.51 (declare-fun tptp.omega__Cong () Bool) 0.18/0.51 (assert (= tptp.omega__Cong (= tptp.omega tptp.omega))) 0.18/0.51 (declare-fun tptp.exuEu () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.descr__Cong () Bool) 0.18/0.51 (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)))))))))) 0.18/0.51 (declare-fun tptp.dsetconstr__Cong () Bool) 0.18/0.51 (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)))))))))) 0.18/0.51 (declare-fun tptp.subset ($$unsorted $$unsorted) Bool) 0.18/0.51 (declare-fun tptp.disjoint ($$unsorted $$unsorted) Bool) 0.18/0.51 (declare-fun tptp.setsmeet ($$unsorted $$unsorted) Bool) 0.18/0.51 (declare-fun tptp.subsetI1 () Bool) 0.18/0.51 (assert (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B))))) 0.18/0.51 (declare-fun tptp.eqimpsubset2 () Bool) 0.18/0.51 (assert (= tptp.eqimpsubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset B) A))))) 0.18/0.51 (declare-fun tptp.eqimpsubset1 () Bool) 0.18/0.51 (assert (= tptp.eqimpsubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B))))) 0.18/0.51 (declare-fun tptp.subsetI2 () Bool) 0.18/0.51 (assert (= tptp.subsetI2 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B))))) 0.18/0.51 (declare-fun tptp.emptysetsubset () Bool) 0.18/0.51 (assert (= tptp.emptysetsubset (forall ((A $$unsorted)) (@ (@ tptp.subset tptp.emptyset) A)))) 0.18/0.51 (declare-fun tptp.subsetE () Bool) 0.18/0.51 (assert (= tptp.subsetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (@ _let_1 A) (@ _let_1 B))))))) 0.18/0.51 (declare-fun tptp.subsetE2 () Bool) 0.18/0.51 (assert (= tptp.subsetE2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (not (@ _let_1 B)) (not (@ _let_1 A)))))))) 0.18/0.51 (declare-fun tptp.notsubsetI () Bool) 0.18/0.51 (assert (= tptp.notsubsetI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (@ (@ tptp.subset A) B)))))))) 0.18/0.51 (declare-fun tptp.notequalI1 () Bool) 0.18/0.51 (assert (= tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (@ (@ tptp.subset A) B)) (not (= A B)))))) 0.18/0.51 (declare-fun tptp.notequalI2 () Bool) 0.18/0.51 (assert (= tptp.notequalI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (= A B)))))))) 0.18/0.51 (declare-fun tptp.subsetRefl () Bool) 0.18/0.51 (assert (= tptp.subsetRefl (forall ((A $$unsorted)) (@ (@ tptp.subset A) A)))) 0.18/0.51 (declare-fun tptp.subsetTrans () Bool) 0.18/0.51 (assert (= tptp.subsetTrans (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (=> (@ (@ tptp.subset B) C) (@ _let_1 C))))))) 0.18/0.51 (declare-fun tptp.setadjoinSub () Bool) 0.18/0.51 (assert (= tptp.setadjoinSub (forall ((Xx $$unsorted) (A $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.setadjoin Xx) A))))) 0.18/0.51 (declare-fun tptp.setadjoinSub2 () Bool) 0.18/0.51 (assert (= tptp.setadjoinSub2 (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.setadjoin Xx) B))))))) 0.18/0.51 (declare-fun tptp.subset2powerset () Bool) 0.18/0.51 (assert (= tptp.subset2powerset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.in A) (@ tptp.powerset B)))))) 0.18/0.51 (declare-fun tptp.setextsub () Bool) 0.18/0.51 (assert (= tptp.setextsub (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (=> (@ (@ tptp.subset B) A) (= A B)))))) 0.18/0.51 (declare-fun tptp.subsetemptysetimpeq () Bool) 0.18/0.51 (assert (= tptp.subsetemptysetimpeq (forall ((A $$unsorted)) (=> (@ (@ tptp.subset A) tptp.emptyset) (= A tptp.emptyset))))) 0.18/0.51 (declare-fun tptp.powersetI1 () Bool) 0.18/0.51 (assert (= tptp.powersetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (@ (@ tptp.in B) (@ tptp.powerset A)))))) 0.18/0.51 (declare-fun tptp.powersetE1 () Bool) 0.18/0.51 (assert (= tptp.powersetE1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (@ (@ tptp.subset B) A))))) 0.18/0.51 (declare-fun tptp.inPowerset () Bool) 0.18/0.51 (assert (= tptp.inPowerset (forall ((A $$unsorted)) (@ (@ tptp.in A) (@ tptp.powerset A))))) 0.18/0.51 (declare-fun tptp.powersetsubset () Bool) 0.18/0.51 (assert (= tptp.powersetsubset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.subset (@ tptp.powerset A)) (@ tptp.powerset B)))))) 0.18/0.51 (declare-fun tptp.sepInPowerset () Bool) 0.18/0.51 (assert (= tptp.sepInPowerset (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.in (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ tptp.powerset A))))) 0.18/0.51 (declare-fun tptp.sepSubset () Bool) 0.18/0.51 (assert (= tptp.sepSubset (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.subset (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) A)))) 0.18/0.51 (declare-fun tptp.binunion ($$unsorted $$unsorted) $$unsorted) 0.18/0.51 (declare-fun tptp.binunionIL () Bool) 0.18/0.51 (assert (= tptp.binunionIL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.binunion A) B))))))) 0.18/0.51 (declare-fun tptp.upairset2IR () Bool) 0.18/0.51 (assert (= tptp.upairset2IR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.18/0.51 (declare-fun tptp.binunionIR () Bool) 0.18/0.51 (assert (= tptp.binunionIR (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binunion A) B))))))) 0.18/0.51 (declare-fun tptp.binunionEcases () Bool) 0.18/0.51 (assert (= tptp.binunionEcases (forall ((A $$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))))))) 0.18/0.51 (declare-fun tptp.binunionE () Bool) 0.18/0.51 (assert (= tptp.binunionE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binunion A) B)) (or (@ _let_1 A) (@ _let_1 B))))))) 0.18/0.51 (declare-fun tptp.binunionLsub () Bool) 0.18/0.51 (assert (= tptp.binunionLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.binunion A) B))))) 0.18/0.51 (declare-fun tptp.binunionRsub () Bool) 0.18/0.51 (assert (= tptp.binunionRsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset B) (@ (@ tptp.binunion A) B))))) 0.18/0.51 (declare-fun tptp.binintersect ($$unsorted $$unsorted) $$unsorted) 0.18/0.51 (declare-fun tptp.binintersectI () Bool) 0.18/0.51 (assert (= tptp.binintersectI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B)))))))) 0.18/0.51 (declare-fun tptp.binintersectSubset5 () Bool) 0.18/0.51 (assert (= tptp.binintersectSubset5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B)))))))) 0.18/0.51 (declare-fun tptp.binintersectEL () Bool) 0.18/0.51 (assert (= tptp.binintersectEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect A) B)) (@ _let_1 A)))))) 0.18/0.51 (declare-fun tptp.binintersectLsub () Bool) 0.18/0.51 (assert (= tptp.binintersectLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) A)))) 0.18/0.51 (declare-fun tptp.binintersectSubset2 () Bool) 0.18/0.51 (assert (= tptp.binintersectSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.binintersect A) B) A))))) 0.18/0.51 (declare-fun tptp.binintersectSubset3 () Bool) 0.18/0.51 (assert (= tptp.binintersectSubset3 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) B) (@ (@ tptp.subset B) A))))) 0.18/0.51 (declare-fun tptp.binintersectER () Bool) 0.18/0.51 (assert (= tptp.binintersectER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect A) B)) (@ _let_1 B)))))) 0.18/0.51 (declare-fun tptp.disjointsetsI1 () Bool) 0.18/0.51 (assert (= tptp.disjointsetsI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 A) (@ _let_1 B))))) (= (@ (@ tptp.binintersect A) B) tptp.emptyset))))) 0.18/0.51 (declare-fun tptp.binintersectRsub () Bool) 0.18/0.51 (assert (= tptp.binintersectRsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) B)))) 0.18/0.51 (declare-fun tptp.binintersectSubset4 () Bool) 0.18/0.51 (assert (= tptp.binintersectSubset4 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (= (@ (@ tptp.binintersect A) B) B))))) 0.18/0.51 (declare-fun tptp.binintersectSubset1 () Bool) 0.18/0.51 (assert (= tptp.binintersectSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) A) (@ (@ tptp.subset A) B))))) 0.18/0.51 (declare-fun tptp.bs114d () Bool) 0.18/0.51 (assert (= tptp.bs114d (forall ((A $$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))))))) 0.18/0.51 (declare-fun tptp.regular ($$unsorted) Bool) 0.18/0.51 (declare-fun tptp.setminus ($$unsorted $$unsorted) $$unsorted) 0.18/0.51 (declare-fun tptp.setminusI () Bool) 0.18/0.51 (assert (= tptp.setminusI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.setminus A) B)))))))) 0.18/0.51 (declare-fun tptp.setminusEL () Bool) 0.18/0.51 (assert (= tptp.setminusEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.setminus A) B)) (@ _let_1 A)))))) 0.18/0.51 (declare-fun tptp.setminusER () Bool) 0.18/0.51 (assert (= tptp.setminusER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.setminus A) B)) (not (@ _let_1 B))))))) 0.18/0.51 (declare-fun tptp.setminusSubset2 () Bool) 0.18/0.51 (assert (= tptp.setminusSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.setminus A) B) tptp.emptyset))))) 0.18/0.51 (declare-fun tptp.setminusERneg () Bool) 0.18/0.51 (assert (= tptp.setminusERneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 (@ (@ tptp.setminus A) B))) (=> (@ _let_1 A) (@ _let_1 B))))))) 0.18/0.51 (declare-fun tptp.setminusELneg () Bool) 0.18/0.51 (assert (= tptp.setminusELneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 (@ (@ tptp.setminus A) B))) (=> (not (@ _let_1 B)) (not (@ _let_1 A)))))))) 0.18/0.51 (declare-fun tptp.setminusILneg () Bool) 0.18/0.51 (assert (= tptp.setminusILneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (not (@ _let_1 (@ (@ tptp.setminus A) B)))))))) 0.18/0.51 (declare-fun tptp.setminusIRneg () Bool) 0.18/0.51 (assert (= tptp.setminusIRneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (not (@ _let_1 (@ (@ tptp.setminus A) B)))))))) 0.18/0.51 (declare-fun tptp.setminusLsub () Bool) 0.18/0.51 (assert (= tptp.setminusLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.setminus A) B)) A)))) 0.18/0.51 (declare-fun tptp.setminusSubset1 () Bool) 0.18/0.51 (assert (= tptp.setminusSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.setminus A) B) tptp.emptyset) (@ (@ tptp.subset A) B))))) 0.18/0.51 (declare-fun tptp.symdiff ($$unsorted $$unsorted) $$unsorted) 0.18/0.51 (declare-fun tptp.symdiffE () Bool) 0.18/0.51 (assert (= tptp.symdiffE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.symdiff A) B)) (forall ((Xphi Bool)) (let ((_let_1 (@ tptp.in Xx))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ _let_1 A))) (=> (=> _let_3 (=> (not _let_2) Xphi)) (=> (=> (not _let_3) (=> _let_2 Xphi)) Xphi)))))))))) 0.18/0.51 (declare-fun tptp.symdiffI1 () Bool) 0.18/0.51 (assert (= tptp.symdiffI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.symdiff A) B)))))))) 0.18/0.51 (declare-fun tptp.symdiffI2 () Bool) 0.18/0.51 (assert (= tptp.symdiffI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.symdiff A) B)))))))) 0.18/0.51 (declare-fun tptp.symdiffIneg1 () Bool) 0.18/0.51 (assert (= tptp.symdiffIneg1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 B) (not (@ _let_1 (@ (@ tptp.symdiff A) B))))))))) 0.18/0.51 (declare-fun tptp.symdiffIneg2 () Bool) 0.18/0.51 (assert (= tptp.symdiffIneg2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (not (@ _let_1 (@ (@ tptp.symdiff A) B))))))))) 0.18/0.51 (declare-fun tptp.iskpair ($$unsorted) Bool) 0.18/0.51 (declare-fun tptp.secondinupair () Bool) 0.18/0.51 (assert (= tptp.secondinupair (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.18/0.51 (declare-fun tptp.setukpairIL () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.setukpairIR () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.kpairiskpair () Bool) 0.18/0.51 (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))))))) 0.18/0.51 (declare-fun tptp.kpair ($$unsorted $$unsorted) $$unsorted) 0.18/0.51 (declare-fun tptp.kpairp () Bool) 0.18/0.51 (assert (= tptp.kpairp (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ tptp.iskpair (@ (@ tptp.kpair Xx) Xy))))) 0.18/0.51 (declare-fun tptp.cartprod ($$unsorted $$unsorted) $$unsorted) 0.18/0.51 (declare-fun tptp.singletonsubset () Bool) 0.18/0.51 (assert (= tptp.singletonsubset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) tptp.emptyset)) A))))) 0.18/0.51 (declare-fun tptp.singletoninpowerset () Bool) 0.18/0.51 (assert (= tptp.singletoninpowerset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset A)))))) 0.18/0.51 (declare-fun tptp.singletoninpowunion () Bool) 0.18/0.51 (assert (= tptp.singletoninpowunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset (@ (@ tptp.binunion A) B))))))) 0.18/0.51 (declare-fun tptp.upairset2E () Bool) 0.18/0.51 (assert (= tptp.upairset2E (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy)))))) 0.18/0.51 (declare-fun tptp.upairsubunion () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.upairinpowunion () Bool) 0.18/0.51 (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))))))))) 0.18/0.51 (declare-fun tptp.ubforcartprodlem1 () Bool) 0.18/0.51 (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)))))))))) 0.18/0.51 (declare-fun tptp.ubforcartprodlem2 () Bool) 0.18/0.51 (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))))))))))) 0.18/0.51 (declare-fun tptp.ubforcartprodlem3 () Bool) 0.18/0.51 (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)))))))))) 0.18/0.51 (declare-fun tptp.cartprodpairin () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.cartprodmempair1 () Bool) 0.18/0.51 (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 $$unsorted)) (and (@ (@ tptp.in Xy) B) (= Xu (@ (@ tptp.kpair Xx) Xy)))))))))) 0.18/0.51 (declare-fun tptp.cartprodmempair () Bool) 0.18/0.51 (assert (= tptp.cartprodmempair (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ tptp.iskpair Xu))))) 0.18/0.51 (declare-fun tptp.setunionE2 () Bool) 0.18/0.51 (assert (= tptp.setunionE2 (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((X $$unsorted)) (and (@ (@ tptp.in X) A) (@ (@ tptp.in Xx) X))))))) 0.18/0.51 (declare-fun tptp.setunionsingleton1 () Bool) 0.18/0.51 (assert (= tptp.setunionsingleton1 (forall ((A $$unsorted)) (@ (@ tptp.subset (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset))) A)))) 0.18/0.51 (declare-fun tptp.setunionsingleton2 () Bool) 0.18/0.51 (assert (= tptp.setunionsingleton2 (forall ((A $$unsorted)) (@ (@ tptp.subset A) (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset)))))) 0.18/0.51 (declare-fun tptp.setunionsingleton () Bool) 0.18/0.51 (assert (= tptp.setunionsingleton (forall ((Xx $$unsorted)) (= (@ tptp.setunion (@ (@ tptp.setadjoin Xx) tptp.emptyset)) Xx)))) 0.18/0.51 (declare-fun tptp.singleton ($$unsorted) Bool) 0.18/0.51 (assert (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) 0.18/0.51 (declare-fun tptp.singletonprop () Bool) 0.18/0.51 (assert (= tptp.singletonprop (forall ((A $$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 $$unsorted)) (@ Xphi Xx))))))))) 0.18/0.51 (declare-fun tptp.ex1 ($$unsorted (-> $$unsorted Bool)) Bool) 0.18/0.51 (assert (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) 0.18/0.51 (declare-fun tptp.ex1E1 () Bool) 0.18/0.51 (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))))))) 0.18/0.51 (declare-fun tptp.ex1I () Bool) 0.18/0.51 (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 $$unsorted)) (@ Xphi Xy))))))))) 0.18/0.51 (declare-fun tptp.ex1I2 () Bool) 0.18/0.51 (assert (= tptp.ex1I2 (forall ((A $$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 $$unsorted)) (@ Xphi Xx)))))))) 0.18/0.51 (declare-fun tptp.singletonsuniq () Bool) 0.18/0.51 (assert (= tptp.singletonsuniq (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy))))) 0.18/0.51 (declare-fun tptp.atmost1p ($$unsorted) Bool) 0.18/0.51 (declare-fun tptp.atleast2p ($$unsorted) Bool) 0.18/0.51 (declare-fun tptp.atmost2p ($$unsorted) Bool) 0.18/0.51 (declare-fun tptp.upairsetp ($$unsorted) Bool) 0.18/0.51 (declare-fun tptp.setukpairinjL1 () Bool) 0.18/0.51 (assert (= tptp.setukpairinjL1 (forall ((Xx $$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)))))) 0.18/0.51 (declare-fun tptp.kfstsingleton () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.theprop () Bool) 0.18/0.51 (assert (= tptp.theprop (forall ((X $$unsorted)) (=> (@ tptp.singleton X) (@ (@ tptp.in (@ tptp.setunion X)) X))))) 0.18/0.51 (declare-fun tptp.kfst ($$unsorted) $$unsorted) 0.18/0.51 (declare-fun tptp.kfstpairEq () Bool) 0.18/0.51 (assert (= tptp.kfstpairEq (forall ((Xx $$unsorted) (Xy $$unsorted)) (= (@ tptp.kfst (@ (@ tptp.kpair Xx) Xy)) Xx)))) 0.18/0.51 (declare-fun tptp.cartprodfstin () Bool) 0.18/0.51 (assert (= tptp.cartprodfstin (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in (@ tptp.kfst Xu)) A))))) 0.18/0.51 (declare-fun tptp.setukpairinjL2 () Bool) 0.18/0.51 (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))))))) 0.18/0.51 (declare-fun tptp.setukpairinjL () Bool) 0.18/0.51 (assert (= tptp.setukpairinjL (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xx Xz))))) 0.18/0.51 (declare-fun tptp.setukpairinjR11 () Bool) 0.18/0.51 (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))))))) 0.18/0.51 (declare-fun tptp.setukpairinjR12 () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.setukpairinjR1 () Bool) 0.18/0.51 (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)))))))) 0.18/0.51 (declare-fun tptp.upairequniteq () Bool) 0.18/0.51 (assert (= tptp.upairequniteq (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (= (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.setadjoin Xz) tptp.emptyset)) (= Xx Xy))))) 0.18/0.51 (declare-fun tptp.setukpairinjR2 () Bool) 0.18/0.51 (assert (= tptp.setukpairinjR2 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xz))) (let ((_let_2 (@ tptp.setadjoin Xx))) (=> (= (@ (@ tptp.setadjoin (@ _let_2 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_2 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset))) (= Xy Xu))))))) 0.18/0.51 (declare-fun tptp.setukpairinjR () Bool) 0.18/0.51 (assert (= tptp.setukpairinjR (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xy Xu))))) 0.18/0.51 (declare-fun tptp.ksndsingleton () Bool) 0.18/0.51 (assert (= tptp.ksndsingleton (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (@ tptp.singleton (@ (@ tptp.dsetconstr (@ tptp.setunion Xu)) (lambda ((Xx $$unsorted)) (= Xu (@ (@ tptp.kpair (@ tptp.kfst Xu)) Xx))))))))) 0.18/0.51 (declare-fun tptp.ksnd ($$unsorted) $$unsorted) 0.18/0.51 (declare-fun tptp.ksndpairEq () Bool) 0.18/0.51 (assert (= tptp.ksndpairEq (forall ((Xx $$unsorted) (Xy $$unsorted)) (= (@ tptp.ksnd (@ (@ tptp.kpair Xx) Xy)) Xy)))) 0.18/0.51 (declare-fun tptp.kpairsurjEq () Bool) 0.18/0.51 (assert (= tptp.kpairsurjEq (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (= (@ (@ tptp.kpair (@ tptp.kfst Xu)) (@ tptp.ksnd Xu)) Xu))))) 0.18/0.51 (declare-fun tptp.cartprodsndin () Bool) 0.18/0.51 (assert (= tptp.cartprodsndin (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in (@ tptp.ksnd Xu)) B))))) 0.18/0.51 (declare-fun tptp.cartprodpairmemEL () Bool) 0.18/0.51 (assert (= tptp.cartprodpairmemEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in Xx) A))))) 0.18/0.51 (declare-fun tptp.cartprodpairmemER () Bool) 0.18/0.51 (assert (= tptp.cartprodpairmemER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in Xy) B))))) 0.18/0.51 (declare-fun tptp.cartprodmempaircEq () Bool) 0.18/0.51 (assert (= tptp.cartprodmempaircEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) Xy))) (=> (@ (@ tptp.in Xy) B) (= _let_1 _let_1)))))))) 0.18/0.51 (declare-fun tptp.cartprodfstpairEq () Bool) 0.18/0.51 (assert (= tptp.cartprodfstpairEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (= (@ tptp.kfst (@ (@ tptp.kpair Xx) Xy)) Xx))))))) 0.18/0.51 (declare-fun tptp.cartprodsndpairEq () Bool) 0.18/0.51 (assert (= tptp.cartprodsndpairEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (= (@ tptp.ksnd (@ (@ tptp.kpair Xx) Xy)) Xy))))))) 0.18/0.51 (declare-fun tptp.cartprodpairsurjEq () Bool) 0.18/0.51 (assert (= tptp.cartprodpairsurjEq (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (= (@ (@ tptp.kpair (@ tptp.kfst Xu)) (@ tptp.ksnd Xu)) Xu))))) 0.18/0.51 (declare-fun tptp.breln ($$unsorted $$unsorted $$unsorted) Bool) 0.18/0.51 (assert (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) 0.18/0.51 (declare-fun tptp.dpsetconstr ($$unsorted $$unsorted (-> $$unsorted $$unsorted Bool)) $$unsorted) 0.18/0.51 (declare-fun tptp.dpsetconstrI () Bool) 0.18/0.51 (assert (= tptp.dpsetconstrI (forall ((A $$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 $$unsorted)) (@ (@ Xphi Xz) Xu))))))))))) 0.18/0.51 (declare-fun tptp.dpsetconstrSub () Bool) 0.18/0.51 (assert (= tptp.dpsetconstrSub (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.subset (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ Xphi Xx) Xy)))) (@ (@ tptp.cartprod A) B))))) 0.18/0.51 (declare-fun tptp.setOfPairsIsBReln () Bool) 0.18/0.51 (assert (= tptp.setOfPairsIsBReln (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ (@ tptp.breln A) B) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ Xphi Xx) Xy))))))) 0.18/0.51 (declare-fun tptp.dpsetconstrERa () Bool) 0.18/0.51 (assert (= tptp.dpsetconstrERa (forall ((A $$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 $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ Xphi Xx) Xy)))))))) 0.18/0.51 (declare-fun tptp.dpsetconstrEL1 () Bool) 0.18/0.51 (assert (= tptp.dpsetconstrEL1 (forall ((A $$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 $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ tptp.in Xx) A))))) 0.18/0.51 (declare-fun tptp.dpsetconstrEL2 () Bool) 0.18/0.51 (assert (= tptp.dpsetconstrEL2 (forall ((A $$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 $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ tptp.in Xy) B))))) 0.18/0.51 (declare-fun tptp.dpsetconstrER () Bool) 0.18/0.51 (assert (= tptp.dpsetconstrER (forall ((A $$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 $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ Xphi Xx) Xy))))) 0.18/0.51 (declare-fun tptp.func ($$unsorted $$unsorted $$unsorted) Bool) 0.18/0.51 (assert (= tptp.func (lambda ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (and (@ (@ (@ tptp.breln A) B) R) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.ex1 B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) R))))))))) 0.18/0.51 (declare-fun tptp.funcSet ($$unsorted $$unsorted) $$unsorted) 0.18/0.51 (declare-fun tptp.funcImageSingleton () Bool) 0.18/0.51 (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 $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf)))))))))) 0.18/0.51 (declare-fun tptp.apProp () Bool) 0.18/0.51 (assert (= tptp.apProp (forall ((A $$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))))))) 0.18/0.51 (declare-fun tptp.ap ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted) 0.18/0.51 (declare-fun tptp.app () Bool) 0.18/0.51 (assert (= tptp.app (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))))) 0.18/0.51 (declare-fun tptp.infuncsetfunc () Bool) 0.18/0.51 (assert (= tptp.infuncsetfunc (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (@ (@ (@ tptp.func A) B) Xf))))) 0.18/0.51 (declare-fun tptp.ap2p () Bool) 0.18/0.51 (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))))))) 0.18/0.51 (declare-fun tptp.funcinfuncset () Bool) 0.18/0.51 (assert (= tptp.funcinfuncset (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)))))) 0.18/0.51 (declare-fun tptp.lamProp () Bool) 0.18/0.51 (assert (= tptp.lamProp (forall ((A $$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)))))))) 0.18/0.51 (declare-fun tptp.lam ($$unsorted $$unsorted (-> $$unsorted $$unsorted)) $$unsorted) 0.18/0.51 (assert (= tptp.lam (lambda ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (= (@ Xf Xx) Xy)))))) 0.18/0.51 (declare-fun tptp.lamp () Bool) 0.18/0.51 (assert (= tptp.lamp (forall ((A $$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 $$unsorted)) (@ Xf Xx)))))))) 0.18/0.51 (declare-fun tptp.lam2p () Bool) 0.18/0.51 (assert (= tptp.lam2p (forall ((A $$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 $$unsorted)) (@ Xf Xx)))) (@ (@ tptp.funcSet A) B)))))) 0.18/0.51 (declare-fun tptp.brelnall1 () Bool) 0.18/0.51 (assert (= tptp.brelnall1 (forall ((A $$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))))))))) 0.18/0.51 (declare-fun tptp.brelnall2 () Bool) 0.18/0.51 (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 $$unsorted)) (=> (@ (@ tptp.in Xx) R) (@ Xphi Xx))))))))) 0.18/0.51 (declare-fun tptp.ex1E2 () Bool) 0.18/0.51 (assert (= tptp.ex1E2 (forall ((A $$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))))))))))) 0.18/0.51 (declare-fun tptp.funcGraphProp1 () Bool) 0.18/0.51 (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))))))) 0.18/0.51 (declare-fun tptp.funcGraphProp3 () Bool) 0.18/0.51 (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))))))) 0.18/0.51 (declare-fun tptp.funcGraphProp2 () Bool) 0.18/0.51 (assert (= tptp.funcGraphProp2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) Xy)))))))))) 0.18/0.51 (declare-fun tptp.funcextLem () Bool) 0.18/0.51 (assert (= tptp.funcextLem (forall ((A $$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)))))))))))))) 0.18/0.51 (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 (=> /export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 25900 Alarm clock ( read result; case "$result" in 179.70/180.05 unsat) 179.70/180.05 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0 179.70/180.05 ;; 179.70/180.05 sat) 179.70/180.05 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0 179.70/180.05 ;; 179.70/180.05 esac; exit 1 ) 179.70/180.05 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 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 179.70/180.05 (set-info :filename cvc5---1.0.5_22540) 179.70/180.05 (check-sat-assuming ( true )) 179.70/180.05 ------- get file name : TPTP file name is 179.70/180.05 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22540.smt2... 179.70/180.05 --- Run --ho-elim --full-saturate-quant at 10... 179.70/180.05 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 179.70/180.05 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10... 179.70/180.05 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5... 179.70/180.05 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5... 179.70/180.05 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10... 179.70/180.05 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10... 179.70/180.05 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10... 179.70/180.05 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10... 179.70/180.05 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant... 179.70/180.05 % cvc5---1.0.5 exiting 179.70/180.05 % cvc5---1.0.5 exiting 179.70/180.05 EOF