0.04/0.15 % Problem : Vampire---4.8_20343 : TPTP v0.0.0. Released v0.0.0. 0.15/0.16 % Command : do_cvc5 %s %d 0.15/0.37 % Computer : n012.cluster.edu 0.15/0.37 % Model : x86_64 x86_64 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.37 % Memory : 8042.1875MB 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.37 % CPULimit : 1440 0.15/0.37 % WCLimit : 180 0.15/0.37 % DateTime : Mon Jul 3 12:46:37 EDT 2023 0.15/0.37 % CPUTime : 0.40/0.56 %----Proving TH0 0.40/0.57 thf(in_type,type, 0.40/0.57 in: $i > $i > $o ). 0.40/0.57 0.40/0.57 thf(exu_type,type, 0.40/0.57 exu: ( $i > $o ) > $o ). 0.40/0.57 0.40/0.57 thf(exu,definition, 0.40/0.57 ( exu 0.40/0.57 = ( ^ [Xphi: $i > $o] : 0.40/0.57 ? [Xx: $i] : 0.40/0.57 ( ( Xphi @ Xx ) 0.40/0.57 & ! [Xy: $i] : 0.40/0.57 ( ( Xphi @ Xy ) 0.40/0.57 => ( Xx = Xy ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setextAx_type,type, 0.40/0.57 setextAx: $o ). 0.40/0.57 0.40/0.57 thf(setextAx,definition, 0.40/0.57 ( setextAx 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 <=> ( in @ Xx @ B ) ) 0.40/0.57 => ( A = B ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(emptyset_type,type, 0.40/0.57 emptyset: $i ). 0.40/0.57 0.40/0.57 thf(emptysetAx_type,type, 0.40/0.57 emptysetAx: $o ). 0.40/0.57 0.40/0.57 thf(emptysetAx,definition, 0.40/0.57 ( emptysetAx 0.40/0.57 = ( ! [Xx: $i] : 0.40/0.57 ~ ( in @ Xx @ emptyset ) ) ) ). 0.40/0.57 0.40/0.57 thf(setadjoin_type,type, 0.40/0.57 setadjoin: $i > $i > $i ). 0.40/0.57 0.40/0.57 thf(setadjoinAx_type,type, 0.40/0.57 setadjoinAx: $o ). 0.40/0.57 0.40/0.57 thf(setadjoinAx,definition, 0.40/0.57 ( setadjoinAx 0.40/0.57 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.40/0.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.40/0.57 <=> ( ( Xy = Xx ) 0.40/0.57 | ( in @ Xy @ A ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(powerset_type,type, 0.40/0.57 powerset: $i > $i ). 0.40/0.57 0.40/0.57 thf(powersetAx_type,type, 0.40/0.57 powersetAx: $o ). 0.40/0.57 0.40/0.57 thf(powersetAx,definition, 0.40/0.57 ( powersetAx 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( in @ B @ ( powerset @ A ) ) 0.40/0.57 <=> ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ B ) 0.40/0.57 => ( in @ Xx @ A ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setunion_type,type, 0.40/0.57 setunion: $i > $i ). 0.40/0.57 0.40/0.57 thf(setunionAx_type,type, 0.40/0.57 setunionAx: $o ). 0.40/0.57 0.40/0.57 thf(setunionAx,definition, 0.40/0.57 ( setunionAx 0.40/0.57 = ( ! [A: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ ( setunion @ A ) ) 0.40/0.57 <=> ? [B: $i] : 0.40/0.57 ( ( in @ Xx @ B ) 0.40/0.57 & ( in @ B @ A ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(omega_type,type, 0.40/0.57 omega: $i ). 0.40/0.57 0.40/0.57 thf(omega0Ax_type,type, 0.40/0.57 omega0Ax: $o ). 0.40/0.57 0.40/0.57 thf(omega0Ax,definition, 0.40/0.57 ( omega0Ax 0.40/0.57 = ( in @ emptyset @ omega ) ) ). 0.40/0.57 0.40/0.57 thf(omegaSAx_type,type, 0.40/0.57 omegaSAx: $o ). 0.40/0.57 0.40/0.57 thf(omegaSAx,definition, 0.40/0.57 ( omegaSAx 0.40/0.57 = ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ omega ) 0.40/0.57 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(omegaIndAx_type,type, 0.40/0.57 omegaIndAx: $o ). 0.40/0.57 0.40/0.57 thf(omegaIndAx,definition, 0.40/0.57 ( omegaIndAx 0.40/0.57 = ( ! [A: $i] : 0.40/0.57 ( ( ( in @ emptyset @ A ) 0.40/0.57 & ! [Xx: $i] : 0.40/0.57 ( ( ( in @ Xx @ omega ) 0.40/0.57 & ( in @ Xx @ A ) ) 0.40/0.57 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) 0.40/0.57 => ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ omega ) 0.40/0.57 => ( in @ Xx @ A ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(replAx_type,type, 0.40/0.57 replAx: $o ). 0.40/0.57 0.40/0.57 thf(replAx,definition, 0.40/0.57 ( replAx 0.40/0.57 = ( ! [Xphi: $i > $i > $o,A: $i] : 0.40/0.57 ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( exu 0.40/0.57 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) 0.40/0.57 => ? [B: $i] : 0.40/0.57 ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ B ) 0.40/0.57 <=> ? [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ A ) 0.40/0.57 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(foundationAx_type,type, 0.40/0.57 foundationAx: $o ). 0.40/0.57 0.40/0.57 thf(foundationAx,definition, 0.40/0.57 ( foundationAx 0.40/0.57 = ( ! [A: $i] : 0.40/0.57 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.40/0.57 => ? [B: $i] : 0.40/0.57 ( ( in @ B @ A ) 0.40/0.57 & ~ ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ B ) 0.40/0.57 & ( in @ Xx @ A ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(wellorderingAx_type,type, 0.40/0.57 wellorderingAx: $o ). 0.40/0.57 0.40/0.57 thf(wellorderingAx,definition, 0.40/0.57 ( wellorderingAx 0.40/0.57 = ( ! [A: $i] : 0.40/0.57 ? [B: $i] : 0.40/0.57 ( ! [C: $i] : 0.40/0.57 ( ( in @ C @ B ) 0.40/0.57 => ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ C ) 0.40/0.57 => ( in @ Xx @ A ) ) ) 0.40/0.57 & ! [Xx: $i,Xy: $i] : 0.40/0.57 ( ( ( in @ Xx @ A ) 0.40/0.57 & ( in @ Xy @ A ) ) 0.40/0.57 => ( ! [C: $i] : 0.40/0.57 ( ( in @ C @ B ) 0.40/0.57 => ( ( in @ Xx @ C ) 0.40/0.57 <=> ( in @ Xy @ C ) ) ) 0.40/0.57 => ( Xx = Xy ) ) ) 0.40/0.57 & ! [C: $i,D: $i] : 0.40/0.57 ( ( ( in @ C @ B ) 0.40/0.57 & ( in @ D @ B ) ) 0.40/0.57 => ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ C ) 0.40/0.57 => ( in @ Xx @ D ) ) 0.40/0.57 | ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ D ) 0.40/0.57 => ( in @ Xx @ C ) ) ) ) 0.40/0.57 & ! [C: $i] : 0.40/0.57 ( ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ C ) 0.40/0.57 => ( in @ Xx @ A ) ) 0.40/0.57 & ? [Xx: $i] : ( in @ Xx @ C ) ) 0.40/0.57 => ? [D: $i,Xx: $i] : 0.40/0.57 ( ( in @ D @ B ) 0.40/0.57 & ( in @ Xx @ C ) 0.40/0.57 & ~ ? [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ D ) 0.40/0.57 & ( in @ Xy @ C ) ) 0.40/0.57 & ! [E: $i] : 0.40/0.57 ( ( in @ E @ B ) 0.40/0.57 => ( ! [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ E ) 0.40/0.57 => ( in @ Xy @ D ) ) 0.40/0.57 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(descr_type,type, 0.40/0.57 descr: ( $i > $o ) > $i ). 0.40/0.57 0.40/0.57 thf(descrp_type,type, 0.40/0.57 descrp: $o ). 0.40/0.57 0.40/0.57 thf(descrp,definition, 0.40/0.57 ( descrp 0.40/0.57 = ( ! [Xphi: $i > $o] : 0.40/0.57 ( ( exu 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 => ( Xphi 0.40/0.57 @ ( descr 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(dsetconstr_type,type, 0.40/0.57 dsetconstr: $i > ( $i > $o ) > $i ). 0.40/0.57 0.40/0.57 thf(dsetconstrI_type,type, 0.40/0.57 dsetconstrI: $o ). 0.40/0.57 0.40/0.57 thf(dsetconstrI,definition, 0.40/0.57 ( dsetconstrI 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( ( Xphi @ Xx ) 0.40/0.57 => ( in @ Xx 0.40/0.57 @ ( dsetconstr @ A 0.40/0.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(dsetconstrEL_type,type, 0.40/0.57 dsetconstrEL: $o ). 0.40/0.57 0.40/0.57 thf(dsetconstrEL,definition, 0.40/0.57 ( dsetconstrEL 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.40/0.57 ( ( in @ Xx 0.40/0.57 @ ( dsetconstr @ A 0.40/0.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.40/0.57 => ( in @ Xx @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(dsetconstrER_type,type, 0.40/0.57 dsetconstrER: $o ). 0.40/0.57 0.40/0.57 thf(dsetconstrER,definition, 0.40/0.57 ( dsetconstrER 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.40/0.57 ( ( in @ Xx 0.40/0.57 @ ( dsetconstr @ A 0.40/0.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.40/0.57 => ( Xphi @ Xx ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(exuE1_type,type, 0.40/0.57 exuE1: $o ). 0.40/0.57 0.40/0.57 thf(exuE1,definition, 0.40/0.57 ( exuE1 0.40/0.57 = ( ! [Xphi: $i > $o] : 0.40/0.57 ( ( exu 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 => ? [Xx: $i] : 0.40/0.57 ( ( Xphi @ Xx ) 0.40/0.57 & ! [Xy: $i] : 0.40/0.57 ( ( Xphi @ Xy ) 0.40/0.57 => ( Xx = Xy ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(prop2set_type,type, 0.40/0.57 prop2set: $o > $i ). 0.40/0.57 0.40/0.57 thf(prop2setE_type,type, 0.40/0.57 prop2setE: $o ). 0.40/0.57 0.40/0.57 thf(prop2setE,definition, 0.40/0.57 ( prop2setE 0.40/0.57 = ( ! [Xphi: $o,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ ( prop2set @ Xphi ) ) 0.40/0.57 => Xphi ) ) ) ). 0.40/0.57 0.40/0.57 thf(emptysetE_type,type, 0.40/0.57 emptysetE: $o ). 0.40/0.57 0.40/0.57 thf(emptysetE,definition, 0.40/0.57 ( emptysetE 0.40/0.57 = ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ emptyset ) 0.40/0.57 => ! [Xphi: $o] : Xphi ) ) ) ). 0.40/0.57 0.40/0.57 thf(emptysetimpfalse_type,type, 0.40/0.57 emptysetimpfalse: $o ). 0.40/0.57 0.40/0.57 thf(emptysetimpfalse,definition, 0.40/0.57 ( emptysetimpfalse 0.40/0.57 = ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ emptyset ) 0.40/0.57 => $false ) ) ) ). 0.40/0.57 0.40/0.57 thf(notinemptyset_type,type, 0.40/0.57 notinemptyset: $o ). 0.40/0.57 0.40/0.57 thf(notinemptyset,definition, 0.40/0.57 ( notinemptyset 0.40/0.57 = ( ! [Xx: $i] : 0.40/0.57 ~ ( in @ Xx @ emptyset ) ) ) ). 0.40/0.57 0.40/0.57 thf(exuE3e_type,type, 0.40/0.57 exuE3e: $o ). 0.40/0.57 0.40/0.57 thf(exuE3e,definition, 0.40/0.57 ( exuE3e 0.40/0.57 = ( ! [Xphi: $i > $o] : 0.40/0.57 ( ( exu 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setext_type,type, 0.40/0.57 setext: $o ). 0.40/0.57 0.40/0.57 thf(setext,definition, 0.40/0.57 ( setext 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( in @ Xx @ B ) ) 0.40/0.57 => ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ B ) 0.40/0.57 => ( in @ Xx @ A ) ) 0.40/0.57 => ( A = B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(emptyI_type,type, 0.40/0.57 emptyI: $o ). 0.40/0.57 0.40/0.57 thf(emptyI,definition, 0.40/0.57 ( emptyI 0.40/0.57 = ( ! [A: $i] : 0.40/0.57 ( ! [Xx: $i] : 0.40/0.57 ~ ( in @ Xx @ A ) 0.40/0.57 => ( A = emptyset ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(noeltsimpempty_type,type, 0.40/0.57 noeltsimpempty: $o ). 0.40/0.57 0.40/0.57 thf(noeltsimpempty,definition, 0.40/0.57 ( noeltsimpempty 0.40/0.57 = ( ! [A: $i] : 0.40/0.57 ( ! [Xx: $i] : 0.40/0.57 ~ ( in @ Xx @ A ) 0.40/0.57 => ( A = emptyset ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setbeta_type,type, 0.40/0.57 setbeta: $o ). 0.40/0.57 0.40/0.57 thf(setbeta,definition, 0.40/0.57 ( setbeta 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( ( in @ Xx 0.40/0.57 @ ( dsetconstr @ A 0.40/0.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.40/0.57 <=> ( Xphi @ Xx ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(nonempty_type,type, 0.40/0.57 nonempty: $i > $o ). 0.40/0.57 0.40/0.57 thf(nonempty,definition, 0.40/0.57 ( nonempty 0.40/0.57 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ). 0.40/0.57 0.40/0.57 thf(nonemptyE1_type,type, 0.40/0.57 nonemptyE1: $o ). 0.40/0.57 0.40/0.57 thf(nonemptyE1,definition, 0.40/0.57 ( nonemptyE1 0.40/0.57 = ( ! [A: $i] : 0.40/0.57 ( ( nonempty @ A ) 0.40/0.57 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(nonemptyI_type,type, 0.40/0.57 nonemptyI: $o ). 0.40/0.57 0.40/0.57 thf(nonemptyI,definition, 0.40/0.57 ( nonemptyI 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( ( Xphi @ Xx ) 0.40/0.57 => ( nonempty 0.40/0.57 @ ( dsetconstr @ A 0.40/0.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(nonemptyI1_type,type, 0.40/0.57 nonemptyI1: $o ). 0.40/0.57 0.40/0.57 thf(nonemptyI1,definition, 0.40/0.57 ( nonemptyI1 0.40/0.57 = ( ! [A: $i] : 0.40/0.57 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.40/0.57 => ( nonempty @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setadjoinIL_type,type, 0.40/0.57 setadjoinIL: $o ). 0.40/0.57 0.40/0.57 thf(setadjoinIL,definition, 0.40/0.57 ( setadjoinIL 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(emptyinunitempty_type,type, 0.40/0.57 emptyinunitempty: $o ). 0.40/0.57 0.40/0.57 thf(emptyinunitempty,definition, 0.40/0.57 ( emptyinunitempty 0.40/0.57 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ). 0.40/0.57 0.40/0.57 thf(setadjoinIR_type,type, 0.40/0.57 setadjoinIR: $o ). 0.40/0.57 0.40/0.57 thf(setadjoinIR,definition, 0.40/0.57 ( setadjoinIR 0.40/0.57 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.40/0.57 ( ( in @ Xy @ A ) 0.40/0.57 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setadjoinE_type,type, 0.40/0.57 setadjoinE: $o ). 0.40/0.57 0.40/0.57 thf(setadjoinE,definition, 0.40/0.57 ( setadjoinE 0.40/0.57 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.40/0.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.40/0.57 => ! [Xphi: $o] : 0.40/0.57 ( ( ( Xy = Xx ) 0.40/0.57 => Xphi ) 0.40/0.57 => ( ( ( in @ Xy @ A ) 0.40/0.57 => Xphi ) 0.40/0.57 => Xphi ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setadjoinOr_type,type, 0.40/0.57 setadjoinOr: $o ). 0.40/0.57 0.40/0.57 thf(setadjoinOr,definition, 0.40/0.57 ( setadjoinOr 0.40/0.57 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.40/0.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.40/0.57 => ( ( Xy = Xx ) 0.40/0.57 | ( in @ Xy @ A ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setoftrueEq_type,type, 0.40/0.57 setoftrueEq: $o ). 0.40/0.57 0.40/0.57 thf(setoftrueEq,definition, 0.40/0.57 ( setoftrueEq 0.40/0.57 = ( ! [A: $i] : 0.40/0.57 ( ( dsetconstr @ A 0.40/0.57 @ ^ [Xx: $i] : $true ) 0.40/0.57 = A ) ) ) ). 0.40/0.57 0.40/0.57 thf(powersetI_type,type, 0.40/0.57 powersetI: $o ). 0.40/0.57 0.40/0.57 thf(powersetI,definition, 0.40/0.57 ( powersetI 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ B ) 0.40/0.57 => ( in @ Xx @ A ) ) 0.40/0.57 => ( in @ B @ ( powerset @ A ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(emptyinPowerset_type,type, 0.40/0.57 emptyinPowerset: $o ). 0.40/0.57 0.40/0.57 thf(emptyinPowerset,definition, 0.40/0.57 ( emptyinPowerset 0.40/0.57 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(emptyInPowerset_type,type, 0.40/0.57 emptyInPowerset: $o ). 0.40/0.57 0.40/0.57 thf(emptyInPowerset,definition, 0.40/0.57 ( emptyInPowerset 0.40/0.57 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(powersetE_type,type, 0.40/0.57 powersetE: $o ). 0.40/0.57 0.40/0.57 thf(powersetE,definition, 0.40/0.57 ( powersetE 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ B @ ( powerset @ A ) ) 0.40/0.57 => ( ( in @ Xx @ B ) 0.40/0.57 => ( in @ Xx @ A ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setunionI_type,type, 0.40/0.57 setunionI: $o ). 0.40/0.57 0.40/0.57 thf(setunionI,definition, 0.40/0.57 ( setunionI 0.40/0.57 = ( ! [A: $i,Xx: $i,B: $i] : 0.40/0.57 ( ( in @ Xx @ B ) 0.40/0.57 => ( ( in @ B @ A ) 0.40/0.57 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setunionE_type,type, 0.40/0.57 setunionE: $o ). 0.40/0.57 0.40/0.57 thf(setunionE,definition, 0.40/0.57 ( setunionE 0.40/0.57 = ( ! [A: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ ( setunion @ A ) ) 0.40/0.57 => ! [Xphi: $o] : 0.40/0.57 ( ! [B: $i] : 0.40/0.57 ( ( in @ Xx @ B ) 0.40/0.57 => ( ( in @ B @ A ) 0.40/0.57 => Xphi ) ) 0.40/0.57 => Xphi ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(subPowSU_type,type, 0.40/0.57 subPowSU: $o ). 0.40/0.57 0.40/0.57 thf(subPowSU,definition, 0.40/0.57 ( subPowSU 0.40/0.57 = ( ! [A: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(exuE2_type,type, 0.40/0.57 exuE2: $o ). 0.40/0.57 0.40/0.57 thf(exuE2,definition, 0.40/0.57 ( exuE2 0.40/0.57 = ( ! [Xphi: $i > $o] : 0.40/0.57 ( ( exu 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 => ? [Xx: $i] : 0.40/0.57 ! [Xy: $i] : 0.40/0.57 ( ( Xphi @ Xy ) 0.40/0.57 <=> ( Xy = Xx ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(nonemptyImpWitness_type,type, 0.40/0.57 nonemptyImpWitness: $o ). 0.40/0.57 0.40/0.57 thf(nonemptyImpWitness,definition, 0.40/0.57 ( nonemptyImpWitness 0.40/0.57 = ( ! [A: $i] : 0.40/0.57 ( ( nonempty @ A ) 0.40/0.57 => ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & $true ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(uniqinunit_type,type, 0.40/0.57 uniqinunit: $o ). 0.40/0.57 0.40/0.57 thf(uniqinunit,definition, 0.40/0.57 ( uniqinunit 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : 0.40/0.57 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.40/0.57 => ( Xx = Xy ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(notinsingleton_type,type, 0.40/0.57 notinsingleton: $o ). 0.40/0.57 0.40/0.57 thf(notinsingleton,definition, 0.40/0.57 ( notinsingleton 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : 0.40/0.57 ( ( Xx != Xy ) 0.40/0.57 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(eqinunit_type,type, 0.40/0.57 eqinunit: $o ). 0.40/0.57 0.40/0.57 thf(eqinunit,definition, 0.40/0.57 ( eqinunit 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : 0.40/0.57 ( ( Xx = Xy ) 0.40/0.57 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(singletonsswitch_type,type, 0.40/0.57 singletonsswitch: $o ). 0.40/0.57 0.40/0.57 thf(singletonsswitch,definition, 0.40/0.57 ( singletonsswitch 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : 0.40/0.57 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.40/0.57 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(upairsetE_type,type, 0.40/0.57 upairsetE: $o ). 0.40/0.57 0.40/0.57 thf(upairsetE,definition, 0.40/0.57 ( upairsetE 0.40/0.57 = ( ! [Xx: $i,Xy: $i,Xz: $i] : 0.40/0.57 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) 0.40/0.57 => ( ( Xz = Xx ) 0.40/0.57 | ( Xz = Xy ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(upairsetIL_type,type, 0.40/0.57 upairsetIL: $o ). 0.40/0.57 0.40/0.57 thf(upairsetIL,definition, 0.40/0.57 ( upairsetIL 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(upairsetIR_type,type, 0.40/0.57 upairsetIR: $o ). 0.40/0.57 0.40/0.57 thf(upairsetIR,definition, 0.40/0.57 ( upairsetIR 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(emptyE1_type,type, 0.40/0.57 emptyE1: $o ). 0.40/0.57 0.40/0.57 thf(emptyE1,definition, 0.40/0.57 ( emptyE1 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o] : 0.40/0.57 ( ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & ( Xphi @ Xx ) ) 0.40/0.57 => ( ( ( dsetconstr @ A 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 = emptyset ) 0.40/0.57 => $false ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(vacuousDall_type,type, 0.40/0.57 vacuousDall: $o ). 0.40/0.57 0.40/0.57 thf(vacuousDall,definition, 0.40/0.57 ( vacuousDall 0.40/0.57 = ( ! [Xphi: $i > $o,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ emptyset ) 0.40/0.57 => ( Xphi @ Xx ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(quantDeMorgan1_type,type, 0.40/0.57 quantDeMorgan1: $o ). 0.40/0.57 0.40/0.57 thf(quantDeMorgan1,definition, 0.40/0.57 ( quantDeMorgan1 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o] : 0.40/0.57 ( ~ ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( Xphi @ Xx ) ) 0.40/0.57 => ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & ~ ( Xphi @ Xx ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(quantDeMorgan2_type,type, 0.40/0.57 quantDeMorgan2: $o ). 0.40/0.57 0.40/0.57 thf(quantDeMorgan2,definition, 0.40/0.57 ( quantDeMorgan2 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o] : 0.40/0.57 ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ~ ( Xphi @ Xx ) ) 0.40/0.57 => ~ ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & ( Xphi @ Xx ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(quantDeMorgan3_type,type, 0.40/0.57 quantDeMorgan3: $o ). 0.40/0.57 0.40/0.57 thf(quantDeMorgan3,definition, 0.40/0.57 ( quantDeMorgan3 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o] : 0.40/0.57 ( ~ ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & ( Xphi @ Xx ) ) 0.40/0.57 => ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ~ ( Xphi @ Xx ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(quantDeMorgan4_type,type, 0.40/0.57 quantDeMorgan4: $o ). 0.40/0.57 0.40/0.57 thf(quantDeMorgan4,definition, 0.40/0.57 ( quantDeMorgan4 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o] : 0.40/0.57 ( ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & ~ ( Xphi @ Xx ) ) 0.40/0.57 => ~ ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( Xphi @ Xx ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(prop2setI_type,type, 0.40/0.57 prop2setI: $o ). 0.40/0.57 0.40/0.57 thf(prop2setI,definition, 0.40/0.57 ( prop2setI 0.40/0.57 = ( ! [Xphi: $o] : 0.40/0.57 ( Xphi 0.40/0.57 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(set2prop_type,type, 0.40/0.57 set2prop: $i > $o ). 0.40/0.57 0.40/0.57 thf(prop2set2propI_type,type, 0.40/0.57 prop2set2propI: $o ). 0.40/0.57 0.40/0.57 thf(prop2set2propI,definition, 0.40/0.57 ( prop2set2propI 0.40/0.57 = ( ! [Xphi: $o] : 0.40/0.57 ( Xphi 0.40/0.57 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(notdexE_type,type, 0.40/0.57 notdexE: $o ). 0.40/0.57 0.40/0.57 thf(notdexE,definition, 0.40/0.57 ( notdexE 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o] : 0.40/0.57 ( ~ ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & ( Xphi @ Xx ) ) 0.40/0.57 => ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ~ ( Xphi @ Xx ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(notdallE_type,type, 0.40/0.57 notdallE: $o ). 0.40/0.57 0.40/0.57 thf(notdallE,definition, 0.40/0.57 ( notdallE 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o] : 0.40/0.57 ( ~ ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( Xphi @ Xx ) ) 0.40/0.57 => ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & ~ ( Xphi @ Xx ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(exuI1_type,type, 0.40/0.57 exuI1: $o ). 0.40/0.57 0.40/0.57 thf(exuI1,definition, 0.40/0.57 ( exuI1 0.40/0.57 = ( ! [Xphi: $i > $o] : 0.40/0.57 ( ? [Xx: $i] : 0.40/0.57 ( ( Xphi @ Xx ) 0.40/0.57 & ! [Xy: $i] : 0.40/0.57 ( ( Xphi @ Xy ) 0.40/0.57 => ( Xx = Xy ) ) ) 0.40/0.57 => ( exu 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(exuI3_type,type, 0.40/0.57 exuI3: $o ). 0.40/0.57 0.40/0.57 thf(exuI3,definition, 0.40/0.57 ( exuI3 0.40/0.57 = ( ! [Xphi: $i > $o] : 0.40/0.57 ( ? [Xx: $i] : ( Xphi @ Xx ) 0.40/0.57 => ( ! [Xx: $i,Xy: $i] : 0.40/0.57 ( ( Xphi @ Xx ) 0.40/0.57 => ( ( Xphi @ Xy ) 0.40/0.57 => ( Xx = Xy ) ) ) 0.40/0.57 => ( exu 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(exuI2_type,type, 0.40/0.57 exuI2: $o ). 0.40/0.57 0.40/0.57 thf(exuI2,definition, 0.40/0.57 ( exuI2 0.40/0.57 = ( ! [Xphi: $i > $o] : 0.40/0.57 ( ? [Xx: $i] : 0.40/0.57 ! [Xy: $i] : 0.40/0.57 ( ( Xphi @ Xy ) 0.40/0.57 <=> ( Xy = Xx ) ) 0.40/0.57 => ( exu 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(inCongP_type,type, 0.40/0.57 inCongP: $o ). 0.40/0.57 0.40/0.57 thf(inCongP,definition, 0.40/0.57 ( inCongP 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( A = B ) 0.40/0.57 => ! [Xx: $i,Xy: $i] : 0.40/0.57 ( ( Xx = Xy ) 0.40/0.57 => ( ( in @ Xx @ A ) 0.40/0.57 => ( in @ Xy @ B ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(in__Cong_type,type, 0.40/0.57 in__Cong: $o ). 0.40/0.57 0.40/0.57 thf(in__Cong,definition, 0.40/0.57 ( in__Cong 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( A = B ) 0.40/0.57 => ! [Xx: $i,Xy: $i] : 0.40/0.57 ( ( Xx = Xy ) 0.40/0.57 => ( ( in @ Xx @ A ) 0.40/0.57 <=> ( in @ Xy @ B ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(exuE3u_type,type, 0.40/0.57 exuE3u: $o ). 0.40/0.57 0.40/0.57 thf(exuE3u,definition, 0.40/0.57 ( exuE3u 0.40/0.57 = ( ! [Xphi: $i > $o] : 0.40/0.57 ( ( exu 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 => ! [Xx: $i,Xy: $i] : 0.40/0.57 ( ( Xphi @ Xx ) 0.40/0.57 => ( ( Xphi @ Xy ) 0.40/0.57 => ( Xx = Xy ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(exu__Cong_type,type, 0.40/0.57 exu__Cong: $o ). 0.40/0.57 0.40/0.57 thf(exu__Cong,definition, 0.40/0.57 ( exu__Cong 0.40/0.57 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] : 0.40/0.57 ( ! [Xx: $i,Xy: $i] : 0.40/0.57 ( ( Xx = Xy ) 0.40/0.57 => ( ( Xphi @ Xx ) 0.40/0.57 <=> ( Xpsi @ Xy ) ) ) 0.40/0.57 => ( ( exu 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 <=> ( exu 0.40/0.57 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(emptyset__Cong_type,type, 0.40/0.57 emptyset__Cong: $o ). 0.40/0.57 0.40/0.57 thf(emptyset__Cong,definition, 0.40/0.57 ( emptyset__Cong 0.40/0.57 = ( emptyset = emptyset ) ) ). 0.40/0.57 0.40/0.57 thf(setadjoin__Cong_type,type, 0.40/0.57 setadjoin__Cong: $o ). 0.40/0.57 0.40/0.57 thf(setadjoin__Cong,definition, 0.40/0.57 ( setadjoin__Cong 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : 0.40/0.57 ( ( Xx = Xy ) 0.40/0.57 => ! [Xz: $i,Xu: $i] : 0.40/0.57 ( ( Xz = Xu ) 0.40/0.57 => ( ( setadjoin @ Xx @ Xz ) 0.40/0.57 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(powerset__Cong_type,type, 0.40/0.57 powerset__Cong: $o ). 0.40/0.57 0.40/0.57 thf(powerset__Cong,definition, 0.40/0.57 ( powerset__Cong 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( A = B ) 0.40/0.57 => ( ( powerset @ A ) 0.40/0.57 = ( powerset @ B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setunion__Cong_type,type, 0.40/0.57 setunion__Cong: $o ). 0.40/0.57 0.40/0.57 thf(setunion__Cong,definition, 0.40/0.57 ( setunion__Cong 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( A = B ) 0.40/0.57 => ( ( setunion @ A ) 0.40/0.57 = ( setunion @ B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(omega__Cong_type,type, 0.40/0.57 omega__Cong: $o ). 0.40/0.57 0.40/0.57 thf(omega__Cong,definition, 0.40/0.57 ( omega__Cong 0.40/0.57 = ( omega = omega ) ) ). 0.40/0.57 0.40/0.57 thf(exuEu_type,type, 0.40/0.57 exuEu: $o ). 0.40/0.57 0.40/0.57 thf(exuEu,definition, 0.40/0.57 ( exuEu 0.40/0.57 = ( ! [Xphi: $i > $o] : 0.40/0.57 ( ( exu 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 => ! [Xx: $i,Xy: $i] : 0.40/0.57 ( ( Xphi @ Xx ) 0.40/0.57 => ( ( Xphi @ Xy ) 0.40/0.57 => ( Xx = Xy ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(descr__Cong_type,type, 0.40/0.57 descr__Cong: $o ). 0.40/0.57 0.40/0.57 thf(descr__Cong,definition, 0.40/0.57 ( descr__Cong 0.40/0.57 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] : 0.40/0.57 ( ! [Xx: $i,Xy: $i] : 0.40/0.57 ( ( Xx = Xy ) 0.40/0.57 => ( ( Xphi @ Xx ) 0.40/0.57 <=> ( Xpsi @ Xy ) ) ) 0.40/0.57 => ( ( exu 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 => ( ( exu 0.40/0.57 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) 0.40/0.57 => ( ( descr 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 = ( descr 0.40/0.57 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(dsetconstr__Cong_type,type, 0.40/0.57 dsetconstr__Cong: $o ). 0.40/0.57 0.40/0.57 thf(dsetconstr__Cong,definition, 0.40/0.57 ( dsetconstr__Cong 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( A = B ) 0.40/0.57 => ! [Xphi: $i > $o,Xpsi: $i > $o] : 0.40/0.57 ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ! [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ B ) 0.40/0.57 => ( ( Xx = Xy ) 0.40/0.57 => ( ( Xphi @ Xx ) 0.40/0.57 <=> ( Xpsi @ Xy ) ) ) ) ) 0.40/0.57 => ( ( dsetconstr @ A 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 = ( dsetconstr @ B 0.40/0.57 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(subset_type,type, 0.40/0.57 subset: $i > $i > $o ). 0.40/0.57 0.40/0.57 thf(disjoint_type,type, 0.40/0.57 disjoint: $i > $i > $o ). 0.40/0.57 0.40/0.57 thf(setsmeet_type,type, 0.40/0.57 setsmeet: $i > $i > $o ). 0.40/0.57 0.40/0.57 thf(subsetI1_type,type, 0.40/0.57 subsetI1: $o ). 0.40/0.57 0.40/0.57 thf(subsetI1,definition, 0.40/0.57 ( subsetI1 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( in @ Xx @ B ) ) 0.40/0.57 => ( subset @ A @ B ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(eqimpsubset2_type,type, 0.40/0.57 eqimpsubset2: $o ). 0.40/0.57 0.40/0.57 thf(eqimpsubset2,definition, 0.40/0.57 ( eqimpsubset2 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( A = B ) 0.40/0.57 => ( subset @ B @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(eqimpsubset1_type,type, 0.40/0.57 eqimpsubset1: $o ). 0.40/0.57 0.40/0.57 thf(eqimpsubset1,definition, 0.40/0.57 ( eqimpsubset1 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( A = B ) 0.40/0.57 => ( subset @ A @ B ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(subsetI2_type,type, 0.40/0.57 subsetI2: $o ). 0.40/0.57 0.40/0.57 thf(subsetI2,definition, 0.40/0.57 ( subsetI2 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( in @ Xx @ B ) ) 0.40/0.57 => ( subset @ A @ B ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(emptysetsubset_type,type, 0.40/0.57 emptysetsubset: $o ). 0.40/0.57 0.40/0.57 thf(emptysetsubset,definition, 0.40/0.57 ( emptysetsubset 0.40/0.57 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ). 0.40/0.57 0.40/0.57 thf(subsetE_type,type, 0.40/0.57 subsetE: $o ). 0.40/0.57 0.40/0.57 thf(subsetE,definition, 0.40/0.57 ( subsetE 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( subset @ A @ B ) 0.40/0.57 => ( ( in @ Xx @ A ) 0.40/0.57 => ( in @ Xx @ B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(subsetE2_type,type, 0.40/0.57 subsetE2: $o ). 0.40/0.57 0.40/0.57 thf(subsetE2,definition, 0.40/0.57 ( subsetE2 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( subset @ A @ B ) 0.40/0.57 => ( ~ ( in @ Xx @ B ) 0.40/0.57 => ~ ( in @ Xx @ A ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(notsubsetI_type,type, 0.40/0.57 notsubsetI: $o ). 0.40/0.57 0.40/0.57 thf(notsubsetI,definition, 0.40/0.57 ( notsubsetI 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( ~ ( in @ Xx @ B ) 0.40/0.57 => ~ ( subset @ A @ B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(notequalI1_type,type, 0.40/0.57 notequalI1: $o ). 0.40/0.57 0.40/0.57 thf(notequalI1,definition, 0.40/0.57 ( notequalI1 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ~ ( subset @ A @ B ) 0.40/0.57 => ( A != B ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(notequalI2_type,type, 0.40/0.57 notequalI2: $o ). 0.40/0.57 0.40/0.57 thf(notequalI2,definition, 0.40/0.57 ( notequalI2 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( ~ ( in @ Xx @ B ) 0.40/0.57 => ( A != B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(subsetRefl_type,type, 0.40/0.57 subsetRefl: $o ). 0.40/0.57 0.40/0.57 thf(subsetRefl,definition, 0.40/0.57 ( subsetRefl 0.40/0.57 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ). 0.40/0.57 0.40/0.57 thf(subsetTrans_type,type, 0.40/0.57 subsetTrans: $o ). 0.40/0.57 0.40/0.57 thf(subsetTrans,definition, 0.40/0.57 ( subsetTrans 0.40/0.57 = ( ! [A: $i,B: $i,C: $i] : 0.40/0.57 ( ( subset @ A @ B ) 0.40/0.57 => ( ( subset @ B @ C ) 0.40/0.57 => ( subset @ A @ C ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setadjoinSub_type,type, 0.40/0.57 setadjoinSub: $o ). 0.40/0.57 0.40/0.57 thf(setadjoinSub,definition, 0.40/0.57 ( setadjoinSub 0.40/0.57 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setadjoinSub2_type,type, 0.40/0.57 setadjoinSub2: $o ). 0.40/0.57 0.40/0.57 thf(setadjoinSub2,definition, 0.40/0.57 ( setadjoinSub2 0.40/0.57 = ( ! [A: $i,Xx: $i,B: $i] : 0.40/0.57 ( ( subset @ A @ B ) 0.40/0.57 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(subset2powerset_type,type, 0.40/0.57 subset2powerset: $o ). 0.40/0.57 0.40/0.57 thf(subset2powerset,definition, 0.40/0.57 ( subset2powerset 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( subset @ A @ B ) 0.40/0.57 => ( in @ A @ ( powerset @ B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setextsub_type,type, 0.40/0.57 setextsub: $o ). 0.40/0.57 0.40/0.57 thf(setextsub,definition, 0.40/0.57 ( setextsub 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( subset @ A @ B ) 0.40/0.57 => ( ( subset @ B @ A ) 0.40/0.57 => ( A = B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(subsetemptysetimpeq_type,type, 0.40/0.57 subsetemptysetimpeq: $o ). 0.40/0.57 0.40/0.57 thf(subsetemptysetimpeq,definition, 0.40/0.57 ( subsetemptysetimpeq 0.40/0.57 = ( ! [A: $i] : 0.40/0.57 ( ( subset @ A @ emptyset ) 0.40/0.57 => ( A = emptyset ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(powersetI1_type,type, 0.40/0.57 powersetI1: $o ). 0.40/0.57 0.40/0.57 thf(powersetI1,definition, 0.40/0.57 ( powersetI1 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( subset @ B @ A ) 0.40/0.57 => ( in @ B @ ( powerset @ A ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(powersetE1_type,type, 0.40/0.57 powersetE1: $o ). 0.40/0.57 0.40/0.57 thf(powersetE1,definition, 0.40/0.57 ( powersetE1 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( in @ B @ ( powerset @ A ) ) 0.40/0.57 => ( subset @ B @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(inPowerset_type,type, 0.40/0.57 inPowerset: $o ). 0.40/0.57 0.40/0.57 thf(inPowerset,definition, 0.40/0.57 ( inPowerset 0.40/0.57 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(powersetsubset_type,type, 0.40/0.57 powersetsubset: $o ). 0.40/0.57 0.40/0.57 thf(powersetsubset,definition, 0.40/0.57 ( powersetsubset 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( subset @ A @ B ) 0.40/0.57 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(sepInPowerset_type,type, 0.40/0.57 sepInPowerset: $o ). 0.40/0.57 0.40/0.57 thf(sepInPowerset,definition, 0.40/0.57 ( sepInPowerset 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o] : 0.40/0.57 ( in 0.40/0.57 @ ( dsetconstr @ A 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 @ ( powerset @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(sepSubset_type,type, 0.40/0.57 sepSubset: $o ). 0.40/0.57 0.40/0.57 thf(sepSubset,definition, 0.40/0.57 ( sepSubset 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o] : 0.40/0.57 ( subset 0.40/0.57 @ ( dsetconstr @ A 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 @ A ) ) ) ). 0.40/0.57 0.40/0.57 thf(binunion_type,type, 0.40/0.57 binunion: $i > $i > $i ). 0.40/0.57 0.40/0.57 thf(binunionIL_type,type, 0.40/0.57 binunionIL: $o ). 0.40/0.57 0.40/0.57 thf(binunionIL,definition, 0.40/0.57 ( binunionIL 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(upairset2IR_type,type, 0.40/0.57 upairset2IR: $o ). 0.40/0.57 0.40/0.57 thf(upairset2IR,definition, 0.40/0.57 ( upairset2IR 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(binunionIR_type,type, 0.40/0.57 binunionIR: $o ). 0.40/0.57 0.40/0.57 thf(binunionIR,definition, 0.40/0.57 ( binunionIR 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ B ) 0.40/0.57 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(binunionEcases_type,type, 0.40/0.57 binunionEcases: $o ). 0.40/0.57 0.40/0.57 thf(binunionEcases,definition, 0.40/0.57 ( binunionEcases 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] : 0.40/0.57 ( ( in @ Xx @ ( binunion @ A @ B ) ) 0.40/0.57 => ( ( ( in @ Xx @ A ) 0.40/0.57 => Xphi ) 0.40/0.57 => ( ( ( in @ Xx @ B ) 0.40/0.57 => Xphi ) 0.40/0.57 => Xphi ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(binunionE_type,type, 0.40/0.57 binunionE: $o ). 0.40/0.57 0.40/0.57 thf(binunionE,definition, 0.40/0.57 ( binunionE 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ ( binunion @ A @ B ) ) 0.40/0.57 => ( ( in @ Xx @ A ) 0.40/0.57 | ( in @ Xx @ B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(binunionLsub_type,type, 0.40/0.57 binunionLsub: $o ). 0.40/0.57 0.40/0.57 thf(binunionLsub,definition, 0.40/0.57 ( binunionLsub 0.40/0.57 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(binunionRsub_type,type, 0.40/0.57 binunionRsub: $o ). 0.40/0.57 0.40/0.57 thf(binunionRsub,definition, 0.40/0.57 ( binunionRsub 0.40/0.57 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(binintersect_type,type, 0.40/0.57 binintersect: $i > $i > $i ). 0.40/0.57 0.40/0.57 thf(binintersectI_type,type, 0.40/0.57 binintersectI: $o ). 0.40/0.57 0.40/0.57 thf(binintersectI,definition, 0.40/0.57 ( binintersectI 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( ( in @ Xx @ B ) 0.40/0.57 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(binintersectSubset5_type,type, 0.40/0.57 binintersectSubset5: $o ). 0.40/0.57 0.40/0.57 thf(binintersectSubset5,definition, 0.40/0.57 ( binintersectSubset5 0.40/0.57 = ( ! [A: $i,B: $i,C: $i] : 0.40/0.57 ( ( subset @ C @ A ) 0.40/0.57 => ( ( subset @ C @ B ) 0.40/0.57 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(binintersectEL_type,type, 0.40/0.57 binintersectEL: $o ). 0.40/0.57 0.40/0.57 thf(binintersectEL,definition, 0.40/0.57 ( binintersectEL 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ ( binintersect @ A @ B ) ) 0.40/0.57 => ( in @ Xx @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(binintersectLsub_type,type, 0.40/0.57 binintersectLsub: $o ). 0.40/0.57 0.40/0.57 thf(binintersectLsub,definition, 0.40/0.57 ( binintersectLsub 0.40/0.57 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ). 0.40/0.57 0.40/0.57 thf(binintersectSubset2_type,type, 0.40/0.57 binintersectSubset2: $o ). 0.40/0.57 0.40/0.57 thf(binintersectSubset2,definition, 0.40/0.57 ( binintersectSubset2 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( subset @ A @ B ) 0.40/0.57 => ( ( binintersect @ A @ B ) 0.40/0.57 = A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(binintersectSubset3_type,type, 0.40/0.57 binintersectSubset3: $o ). 0.40/0.57 0.40/0.57 thf(binintersectSubset3,definition, 0.40/0.57 ( binintersectSubset3 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( ( binintersect @ A @ B ) 0.40/0.57 = B ) 0.40/0.57 => ( subset @ B @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(binintersectER_type,type, 0.40/0.57 binintersectER: $o ). 0.40/0.57 0.40/0.57 thf(binintersectER,definition, 0.40/0.57 ( binintersectER 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ ( binintersect @ A @ B ) ) 0.40/0.57 => ( in @ Xx @ B ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(disjointsetsI1_type,type, 0.40/0.57 disjointsetsI1: $o ). 0.40/0.57 0.40/0.57 thf(disjointsetsI1,definition, 0.40/0.57 ( disjointsetsI1 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ~ ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & ( in @ Xx @ B ) ) 0.40/0.57 => ( ( binintersect @ A @ B ) 0.40/0.57 = emptyset ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(binintersectRsub_type,type, 0.40/0.57 binintersectRsub: $o ). 0.40/0.57 0.40/0.57 thf(binintersectRsub,definition, 0.40/0.57 ( binintersectRsub 0.40/0.57 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ). 0.40/0.57 0.40/0.57 thf(binintersectSubset4_type,type, 0.40/0.57 binintersectSubset4: $o ). 0.40/0.57 0.40/0.57 thf(binintersectSubset4,definition, 0.40/0.57 ( binintersectSubset4 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( subset @ B @ A ) 0.40/0.57 => ( ( binintersect @ A @ B ) 0.40/0.57 = B ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(binintersectSubset1_type,type, 0.40/0.57 binintersectSubset1: $o ). 0.40/0.57 0.40/0.57 thf(binintersectSubset1,definition, 0.40/0.57 ( binintersectSubset1 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( ( binintersect @ A @ B ) 0.40/0.57 = A ) 0.40/0.57 => ( subset @ A @ B ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(bs114d_type,type, 0.40/0.57 bs114d: $o ). 0.40/0.57 0.40/0.57 thf(bs114d,definition, 0.40/0.57 ( bs114d 0.40/0.57 = ( ! [A: $i,B: $i,C: $i] : 0.40/0.57 ( ( binintersect @ A @ ( binunion @ B @ C ) ) 0.40/0.57 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(regular_type,type, 0.40/0.57 regular: $i > $o ). 0.40/0.57 0.40/0.57 thf(setminus_type,type, 0.40/0.57 setminus: $i > $i > $i ). 0.40/0.57 0.40/0.57 thf(setminusI_type,type, 0.40/0.57 setminusI: $o ). 0.40/0.57 0.40/0.57 thf(setminusI,definition, 0.40/0.57 ( setminusI 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( ~ ( in @ Xx @ B ) 0.40/0.57 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setminusEL_type,type, 0.40/0.57 setminusEL: $o ). 0.40/0.57 0.40/0.57 thf(setminusEL,definition, 0.40/0.57 ( setminusEL 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ ( setminus @ A @ B ) ) 0.40/0.57 => ( in @ Xx @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setminusER_type,type, 0.40/0.57 setminusER: $o ). 0.40/0.57 0.40/0.57 thf(setminusER,definition, 0.40/0.57 ( setminusER 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ ( setminus @ A @ B ) ) 0.40/0.57 => ~ ( in @ Xx @ B ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setminusSubset2_type,type, 0.40/0.57 setminusSubset2: $o ). 0.40/0.57 0.40/0.57 thf(setminusSubset2,definition, 0.40/0.57 ( setminusSubset2 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( subset @ A @ B ) 0.40/0.57 => ( ( setminus @ A @ B ) 0.40/0.57 = emptyset ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setminusERneg_type,type, 0.40/0.57 setminusERneg: $o ). 0.40/0.57 0.40/0.57 thf(setminusERneg,definition, 0.40/0.57 ( setminusERneg 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ~ ( in @ Xx @ ( setminus @ A @ B ) ) 0.40/0.57 => ( ( in @ Xx @ A ) 0.40/0.57 => ( in @ Xx @ B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setminusELneg_type,type, 0.40/0.57 setminusELneg: $o ). 0.40/0.57 0.40/0.57 thf(setminusELneg,definition, 0.40/0.57 ( setminusELneg 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ~ ( in @ Xx @ ( setminus @ A @ B ) ) 0.40/0.57 => ( ~ ( in @ Xx @ B ) 0.40/0.57 => ~ ( in @ Xx @ A ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setminusILneg_type,type, 0.40/0.57 setminusILneg: $o ). 0.40/0.57 0.40/0.57 thf(setminusILneg,definition, 0.40/0.57 ( setminusILneg 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ~ ( in @ Xx @ A ) 0.40/0.57 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setminusIRneg_type,type, 0.40/0.57 setminusIRneg: $o ). 0.40/0.57 0.40/0.57 thf(setminusIRneg,definition, 0.40/0.57 ( setminusIRneg 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ B ) 0.40/0.57 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setminusLsub_type,type, 0.40/0.57 setminusLsub: $o ). 0.40/0.57 0.40/0.57 thf(setminusLsub,definition, 0.40/0.57 ( setminusLsub 0.40/0.57 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ). 0.40/0.57 0.40/0.57 thf(setminusSubset1_type,type, 0.40/0.57 setminusSubset1: $o ). 0.40/0.57 0.40/0.57 thf(setminusSubset1,definition, 0.40/0.57 ( setminusSubset1 0.40/0.57 = ( ! [A: $i,B: $i] : 0.40/0.57 ( ( ( setminus @ A @ B ) 0.40/0.57 = emptyset ) 0.40/0.57 => ( subset @ A @ B ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(symdiff_type,type, 0.40/0.57 symdiff: $i > $i > $i ). 0.40/0.57 0.40/0.57 thf(symdiffE_type,type, 0.40/0.57 symdiffE: $o ). 0.40/0.57 0.40/0.57 thf(symdiffE,definition, 0.40/0.57 ( symdiffE 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ ( symdiff @ A @ B ) ) 0.40/0.57 => ! [Xphi: $o] : 0.40/0.57 ( ( ( in @ Xx @ A ) 0.40/0.57 => ( ~ ( in @ Xx @ B ) 0.40/0.57 => Xphi ) ) 0.40/0.57 => ( ( ~ ( in @ Xx @ A ) 0.40/0.57 => ( ( in @ Xx @ B ) 0.40/0.57 => Xphi ) ) 0.40/0.57 => Xphi ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(symdiffI1_type,type, 0.40/0.57 symdiffI1: $o ). 0.40/0.57 0.40/0.57 thf(symdiffI1,definition, 0.40/0.57 ( symdiffI1 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( ~ ( in @ Xx @ B ) 0.40/0.57 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(symdiffI2_type,type, 0.40/0.57 symdiffI2: $o ). 0.40/0.57 0.40/0.57 thf(symdiffI2,definition, 0.40/0.57 ( symdiffI2 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ~ ( in @ Xx @ A ) 0.40/0.57 => ( ( in @ Xx @ B ) 0.40/0.57 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(symdiffIneg1_type,type, 0.40/0.57 symdiffIneg1: $o ). 0.40/0.57 0.40/0.57 thf(symdiffIneg1,definition, 0.40/0.57 ( symdiffIneg1 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( ( in @ Xx @ B ) 0.40/0.57 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(symdiffIneg2_type,type, 0.40/0.57 symdiffIneg2: $o ). 0.40/0.57 0.40/0.57 thf(symdiffIneg2,definition, 0.40/0.57 ( symdiffIneg2 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ~ ( in @ Xx @ A ) 0.40/0.57 => ( ~ ( in @ Xx @ B ) 0.40/0.57 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(iskpair_type,type, 0.40/0.57 iskpair: $i > $o ). 0.40/0.57 0.40/0.57 thf(iskpair,definition, 0.40/0.57 ( iskpair 0.40/0.57 = ( ^ [A: $i] : 0.40/0.57 ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ ( setunion @ A ) ) 0.40/0.57 & ? [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ ( setunion @ A ) ) 0.40/0.57 & ( A 0.40/0.57 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(secondinupair_type,type, 0.40/0.57 secondinupair: $o ). 0.40/0.57 0.40/0.57 thf(secondinupair,definition, 0.40/0.57 ( secondinupair 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setukpairIL_type,type, 0.40/0.57 setukpairIL: $o ). 0.40/0.57 0.40/0.57 thf(setukpairIL,definition, 0.40/0.57 ( setukpairIL 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setukpairIR_type,type, 0.40/0.57 setukpairIR: $o ). 0.40/0.57 0.40/0.57 thf(setukpairIR,definition, 0.40/0.57 ( setukpairIR 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(kpairiskpair_type,type, 0.40/0.57 kpairiskpair: $o ). 0.40/0.57 0.40/0.57 thf(kpairiskpair,definition, 0.40/0.57 ( kpairiskpair 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(kpair_type,type, 0.40/0.57 kpair: $i > $i > $i ). 0.40/0.57 0.40/0.57 thf(kpair,definition, 0.40/0.57 ( kpair 0.40/0.57 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(kpairp_type,type, 0.40/0.57 kpairp: $o ). 0.40/0.57 0.40/0.57 thf(kpairp,definition, 0.40/0.57 ( kpairp 0.40/0.57 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(cartprod_type,type, 0.40/0.57 cartprod: $i > $i > $i ). 0.40/0.57 0.40/0.57 thf(singletonsubset_type,type, 0.40/0.57 singletonsubset: $o ). 0.40/0.57 0.40/0.57 thf(singletonsubset,definition, 0.40/0.57 ( singletonsubset 0.40/0.57 = ( ! [A: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(singletoninpowerset_type,type, 0.40/0.57 singletoninpowerset: $o ). 0.40/0.57 0.40/0.57 thf(singletoninpowerset,definition, 0.40/0.57 ( singletoninpowerset 0.40/0.57 = ( ! [A: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(singletoninpowunion_type,type, 0.40/0.57 singletoninpowunion: $o ). 0.40/0.57 0.40/0.57 thf(singletoninpowunion,definition, 0.40/0.57 ( singletoninpowunion 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(upairset2E_type,type, 0.40/0.57 upairset2E: $o ). 0.40/0.57 0.40/0.57 thf(upairset2E,definition, 0.40/0.57 ( upairset2E 0.40/0.57 = ( ! [Xx: $i,Xy: $i,Xz: $i] : 0.40/0.57 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) 0.40/0.57 => ( ( Xz = Xx ) 0.40/0.57 | ( Xz = Xy ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(upairsubunion_type,type, 0.40/0.57 upairsubunion: $o ). 0.40/0.57 0.40/0.57 thf(upairsubunion,definition, 0.40/0.57 ( upairsubunion 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ! [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ B ) 0.40/0.57 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(upairinpowunion_type,type, 0.40/0.57 upairinpowunion: $o ). 0.40/0.57 0.40/0.57 thf(upairinpowunion,definition, 0.40/0.57 ( upairinpowunion 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ! [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ B ) 0.40/0.57 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(ubforcartprodlem1_type,type, 0.40/0.57 ubforcartprodlem1: $o ). 0.40/0.57 0.40/0.57 thf(ubforcartprodlem1,definition, 0.40/0.57 ( ubforcartprodlem1 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ! [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ B ) 0.40/0.57 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(ubforcartprodlem2_type,type, 0.40/0.57 ubforcartprodlem2: $o ). 0.40/0.57 0.40/0.57 thf(ubforcartprodlem2,definition, 0.40/0.57 ( ubforcartprodlem2 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ! [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ B ) 0.40/0.57 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(ubforcartprodlem3_type,type, 0.40/0.57 ubforcartprodlem3: $o ). 0.40/0.57 0.40/0.57 thf(ubforcartprodlem3,definition, 0.40/0.57 ( ubforcartprodlem3 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ! [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ B ) 0.40/0.57 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(cartprodpairin_type,type, 0.40/0.57 cartprodpairin: $o ). 0.40/0.57 0.40/0.57 thf(cartprodpairin,definition, 0.40/0.57 ( cartprodpairin 0.40/0.57 = ( ! [A: $i,B: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ! [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ B ) 0.40/0.57 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(cartprodmempair1_type,type, 0.40/0.57 cartprodmempair1: $o ). 0.40/0.57 0.40/0.57 thf(cartprodmempair1,definition, 0.40/0.57 ( cartprodmempair1 0.40/0.57 = ( ! [A: $i,B: $i,Xu: $i] : 0.40/0.57 ( ( in @ Xu @ ( cartprod @ A @ B ) ) 0.40/0.57 => ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & ? [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ B ) 0.40/0.57 & ( Xu 0.40/0.57 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(cartprodmempair_type,type, 0.40/0.57 cartprodmempair: $o ). 0.40/0.57 0.40/0.57 thf(cartprodmempair,definition, 0.40/0.57 ( cartprodmempair 0.40/0.57 = ( ! [A: $i,B: $i,Xu: $i] : 0.40/0.57 ( ( in @ Xu @ ( cartprod @ A @ B ) ) 0.40/0.57 => ( iskpair @ Xu ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setunionE2_type,type, 0.40/0.57 setunionE2: $o ). 0.40/0.57 0.40/0.57 thf(setunionE2,definition, 0.40/0.57 ( setunionE2 0.40/0.57 = ( ! [A: $i,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ ( setunion @ A ) ) 0.40/0.57 => ? [X: $i] : 0.40/0.57 ( ( in @ X @ A ) 0.40/0.57 & ( in @ Xx @ X ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setunionsingleton1_type,type, 0.40/0.57 setunionsingleton1: $o ). 0.40/0.57 0.40/0.57 thf(setunionsingleton1,definition, 0.40/0.57 ( setunionsingleton1 0.40/0.57 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ). 0.40/0.57 0.40/0.57 thf(setunionsingleton2_type,type, 0.40/0.57 setunionsingleton2: $o ). 0.40/0.57 0.40/0.57 thf(setunionsingleton2,definition, 0.40/0.57 ( setunionsingleton2 0.40/0.57 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(setunionsingleton_type,type, 0.40/0.57 setunionsingleton: $o ). 0.40/0.57 0.40/0.57 thf(setunionsingleton,definition, 0.40/0.57 ( setunionsingleton 0.40/0.57 = ( ! [Xx: $i] : 0.40/0.57 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) ) 0.40/0.57 = Xx ) ) ) ). 0.40/0.57 0.40/0.57 thf(singleton_type,type, 0.40/0.57 singleton: $i > $o ). 0.40/0.57 0.40/0.57 thf(singleton,definition, 0.40/0.57 ( singleton 0.40/0.57 = ( ^ [A: $i] : 0.40/0.57 ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & ( A 0.40/0.57 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(singletonprop_type,type, 0.40/0.57 singletonprop: $o ). 0.40/0.57 0.40/0.57 thf(singletonprop,definition, 0.40/0.57 ( singletonprop 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o] : 0.40/0.57 ( ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ! [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ A ) 0.40/0.57 => ( ( Xphi @ Xx ) 0.40/0.57 => ( ( Xphi @ Xy ) 0.40/0.57 => ( Xx = Xy ) ) ) ) ) 0.40/0.57 => ( ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & ( Xphi @ Xx ) ) 0.40/0.57 => ( singleton 0.40/0.57 @ ( dsetconstr @ A 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(ex1_type,type, 0.40/0.57 ex1: $i > ( $i > $o ) > $o ). 0.40/0.57 0.40/0.57 thf(ex1,definition, 0.40/0.57 ( ex1 0.40/0.57 = ( ^ [A: $i,Xphi: $i > $o] : 0.40/0.57 ( singleton 0.40/0.57 @ ( dsetconstr @ A 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(ex1E1_type,type, 0.40/0.57 ex1E1: $o ). 0.40/0.57 0.40/0.57 thf(ex1E1,definition, 0.40/0.57 ( ex1E1 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o] : 0.40/0.57 ( ( ex1 @ A 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 => ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & ( Xphi @ Xx ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(ex1I_type,type, 0.40/0.57 ex1I: $o ). 0.40/0.57 0.40/0.57 thf(ex1I,definition, 0.40/0.57 ( ex1I 0.40/0.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ( ( Xphi @ Xx ) 0.40/0.57 => ( ! [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ A ) 0.40/0.57 => ( ( Xphi @ Xy ) 0.40/0.57 => ( Xy = Xx ) ) ) 0.40/0.57 => ( ex1 @ A 0.40/0.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.40/0.57 0.40/0.57 thf(ex1I2,conjecture, 0.40/0.57 ( ( emptysetAx 0.40/0.57 => ( ( powersetAx 0.40/0.57 => ( ( ( ( ( replAx 0.40/0.57 => ( ( wellorderingAx 0.40/0.57 => ( ( dsetconstrI 0.40/0.57 => ( dsetconstrEL 0.40/0.57 => ( ( exuE1 0.40/0.57 => ( ( emptysetE 0.40/0.57 => ( emptysetimpfalse 0.40/0.57 => ( notinemptyset 0.40/0.57 => ( exuE3e 0.40/0.57 => ( setext 0.40/0.57 => ( ( noeltsimpempty 0.40/0.57 => ( ( ( ( nonemptyI1 0.40/0.57 => ( ( ( ( ( ( setoftrueEq 0.40/0.57 => ( ( emptyinPowerset 0.40/0.57 => ( emptyInPowerset 0.40/0.57 => ( powersetE 0.40/0.57 => ( ( ( subPowSU 0.40/0.57 => ( exuE2 0.40/0.57 => ( nonemptyImpWitness 0.40/0.57 => ( uniqinunit 0.40/0.57 => ( ( eqinunit 0.40/0.57 => ( singletonsswitch 0.40/0.57 => ( upairsetE 0.40/0.57 => ( upairsetIL 0.40/0.57 => ( upairsetIR 0.40/0.57 => ( ( ( quantDeMorgan1 0.40/0.57 => ( quantDeMorgan2 0.40/0.57 => ( ( ( prop2setI 0.40/0.57 => ( ( ( notdallE 0.40/0.57 => ( exuI1 0.40/0.57 => ( exuI3 0.40/0.57 => ( ( ( in__Cong 0.40/0.57 => ( ( exu__Cong 0.40/0.57 => ( ( ( ( setunion__Cong 0.40/0.57 => ( omega__Cong 0.40/0.57 => ( ( descr__Cong 0.40/0.57 => ( dsetconstr__Cong 0.40/0.57 => ( subsetI1 0.40/0.57 => ( eqimpsubset2 0.40/0.57 => ( ( ( ( subsetE 0.40/0.57 => ( ( notsubsetI 0.40/0.57 => ( ( ( subsetRefl 0.40/0.57 => ( ( setadjoinSub 0.40/0.57 => ( ( ( setextsub 0.40/0.57 => ( ( powersetI1 0.40/0.57 => ( powersetE1 0.40/0.57 => ( inPowerset 0.40/0.57 => ( powersetsubset 0.40/0.57 => ( sepInPowerset 0.40/0.57 => ( ( ( ( binunionIR 0.40/0.57 => ( binunionEcases 0.40/0.57 => ( binunionE 0.40/0.57 => ( binunionLsub 0.40/0.57 => ( binunionRsub 0.40/0.57 => ( binintersectI 0.40/0.57 => ( ( ( ( binintersectSubset2 0.40/0.57 => ( ( binintersectER 0.40/0.57 => ( ( binintersectRsub 0.40/0.57 => ( binintersectSubset4 0.40/0.57 => ( ( ( setminusI 0.40/0.57 => ( setminusEL 0.40/0.57 => ( ( setminusSubset2 0.40/0.57 => ( setminusERneg 0.40/0.57 => ( ( setminusILneg 0.40/0.57 => ( setminusIRneg 0.40/0.57 => ( ( ( ( symdiffI1 0.40/0.57 => ( symdiffI2 0.40/0.57 => ( symdiffIneg1 0.40/0.57 => ( symdiffIneg2 0.40/0.57 => ( secondinupair 0.40/0.57 => ( setukpairIL 0.40/0.57 => ( ( ( ( singletonsubset 0.40/0.57 => ( singletoninpowerset 0.40/0.57 => ( ( ( ( upairinpowunion 0.40/0.57 => ( ubforcartprodlem1 0.40/0.57 => ( ( ( ( ( cartprodmempair 0.40/0.57 => ( ( setunionsingleton1 0.40/0.57 => ( setunionsingleton2 0.40/0.57 => ( setunionsingleton 0.40/0.57 => ( ( ex1E1 0.40/0.57 => ( ! [A: $i,Xphi: $i > $o] : 0.40/0.57 ( ( ( ex1 @ A 0.40/0.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.40/0.57 <= ? [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 & ( Xphi @ Xx ) ) ) 0.40/0.57 <= ! [Xx: $i] : 0.40/0.57 ( ( in @ Xx @ A ) 0.40/0.57 => ! [Xy: $i] : 0.40/0.57 ( ( in @ Xy @ A ) 0.40/0.57 => ( ( Xphi @ Xx ) 0.40/0.57 => ( ( Xphi @ Xy ) 0.40/0.57 => ( Xx = Xy ) ) ) ) ) ) 0.40/0.57 <= ex1I ) ) 0.40/0.57 <= singletonprop ) ) ) ) 0.40/0.57 <= setunionE2 ) ) 0.40/0.57 <= cartprodmempair1 ) 0.40/0.57 <= cartprodpairin ) 0.40/0.57 <= ubforcartprodlem3 ) 0.40/0.57 <= ubforcartprodlem2 ) ) ) 0.40/0.57 <= upairsubunion ) 0.40/0.57 <= upairset2E ) 0.40/0.57 <= singletoninpowunion ) ) ) 0.40/0.57 <= kpairp ) 0.40/0.57 <= kpairiskpair ) 0.40/0.57 <= setukpairIR ) ) ) ) ) ) ) 0.40/0.57 <= symdiffE ) 0.40/0.57 <= setminusSubset1 ) 0.40/0.57 <= setminusLsub ) ) ) 0.40/0.57 <= setminusELneg ) ) ) 0.40/0.57 <= setminusER ) ) ) 0.40/0.57 <= bs114d ) 0.40/0.57 <= binintersectSubset1 ) ) ) 0.40/0.57 <= disjointsetsI1 ) ) 0.40/0.57 <= binintersectSubset3 ) ) 0.40/0.57 <= binintersectLsub ) 0.40/0.57 <= binintersectEL ) 0.40/0.57 <= binintersectSubset5 ) ) ) ) ) ) ) 0.40/0.57 <= upairset2IR ) 0.40/0.57 <= binunionIL ) 0.40/0.57 <= sepSubset ) ) ) ) ) ) 0.40/0.57 <= subsetemptysetimpeq ) ) 0.40/0.57 <= subset2powerset ) 0.40/0.57 <= setadjoinSub2 ) ) 0.40/0.57 <= subsetTrans ) ) 0.40/0.57 <= notequalI2 ) 0.40/0.57 <= notequalI1 ) ) 0.40/0.57 <= subsetE2 ) ) 0.40/0.57 <= emptysetsubset ) 0.40/0.57 <= subsetI2 ) 0.40/0.57 <= eqimpsubset1 ) ) ) ) ) 0.40/0.57 <= exuEu ) ) ) 0.40/0.57 <= powerset__Cong ) 0.40/0.57 <= setadjoin__Cong ) 0.40/0.57 <= emptyset__Cong ) ) 0.40/0.57 <= exuE3u ) ) 0.40/0.57 <= inCongP ) 0.40/0.57 <= exuI2 ) ) ) ) 0.40/0.62 <= notdexE ) 0.40/0.62 <= prop2set2propI ) ) 0.40/0.62 <= quantDeMorgan4 ) 0.40/0.62 <= quantDeMorgan3 ) ) ) 0.40/0.62 <= vacuousDall ) 0.40/0.62 <= emptyE1 ) ) ) ) ) ) 0.40/0.62 <= notinsingleton ) ) ) ) ) 0.40/0.62 <= setunionE ) 0.40/0.62 <= setunionI ) ) ) ) 0.40/0.62 <= powersetI ) ) 0.40/0.62 <= setadjoinOr ) 0.40/0.62 <= setadjoinE ) 0.40/0.62 <= setadjoinIR ) 0.40/0.62 <= emptyinunitempty ) 0.40/0.62 <= setadjoinIL ) ) 0.40/0.62 <= nonemptyI ) 0.40/0.62 <= nonemptyE1 ) 0.40/0.62 <= setbeta ) ) 0.40/0.62 <= emptyI ) ) ) ) ) ) 0.40/0.62 <= prop2setE ) ) 0.40/0.62 <= dsetconstrER ) ) ) 0.40/0.62 <= descrp ) ) 0.40/0.62 <= foundationAx ) ) 0.40/0.62 <= omegaIndAx ) 0.40/0.62 <= omegaSAx ) 0.40/0.62 <= omega0Ax ) 0.40/0.62 <= setunionAx ) ) 0.40/0.62 <= setadjoinAx ) ) 0.40/0.62 <= setextAx ) ). 0.40/0.62 0.40/0.62 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.FN3Giu4dZP/cvc5---1.0.5_20533.p... 0.40/0.62 (declare-sort $$unsorted 0) 0.40/0.62 (declare-fun tptp.in ($$unsorted $$unsorted) Bool) 0.40/0.62 (declare-fun tptp.exu ((-> $$unsorted Bool)) Bool) 0.40/0.62 (assert (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy)))))))) 0.40/0.62 (declare-fun tptp.setextAx () Bool) 0.40/0.62 (assert (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B))))) 0.40/0.62 (declare-fun tptp.emptyset () $$unsorted) 0.40/0.62 (declare-fun tptp.emptysetAx () Bool) 0.40/0.62 (assert (= tptp.emptysetAx (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.40/0.62 (declare-fun tptp.setadjoin ($$unsorted $$unsorted) $$unsorted) 0.40/0.62 (declare-fun tptp.setadjoinAx () Bool) 0.40/0.62 (assert (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.40/0.62 (declare-fun tptp.powerset ($$unsorted) $$unsorted) 0.40/0.62 (declare-fun tptp.powersetAx () Bool) 0.40/0.62 (assert (= tptp.powersetAx (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))))))) 0.40/0.62 (declare-fun tptp.setunion ($$unsorted) $$unsorted) 0.40/0.62 (declare-fun tptp.setunionAx () Bool) 0.40/0.62 (assert (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A))))))) 0.40/0.62 (declare-fun tptp.omega () $$unsorted) 0.40/0.62 (declare-fun tptp.omega0Ax () Bool) 0.40/0.62 (assert (= tptp.omega0Ax (@ (@ tptp.in tptp.emptyset) tptp.omega))) 0.40/0.62 (declare-fun tptp.omegaSAx () Bool) 0.40/0.62 (assert (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega))))) 0.40/0.62 (declare-fun tptp.omegaIndAx () Bool) 0.40/0.62 (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 $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 tptp.omega) (@ _let_1 A)))))))) 0.40/0.62 (declare-fun tptp.replAx () Bool) 0.40/0.62 (assert (= tptp.replAx (forall ((Xphi (-> $$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 $$unsorted)) (and (@ (@ tptp.in Xy) A) (@ (@ Xphi Xy) Xx)))))))))) 0.40/0.62 (declare-fun tptp.foundationAx () Bool) 0.40/0.62 (assert (= tptp.foundationAx (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in B) A) (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 B) (@ _let_1 A))))))))))) 0.40/0.62 (declare-fun tptp.wellorderingAx () Bool) 0.40/0.62 (assert (= tptp.wellorderingAx (forall ((A $$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))))))))))))) 0.40/0.62 (declare-fun tptp.descr ((-> $$unsorted Bool)) $$unsorted) 0.40/0.62 (declare-fun tptp.descrp () Bool) 0.40/0.62 (assert (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) 0.40/0.62 (declare-fun tptp.dsetconstr ($$unsorted (-> $$unsorted Bool)) $$unsorted) 0.40/0.62 (declare-fun tptp.dsetconstrI () Bool) 0.40/0.62 (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)))))))))) 0.40/0.62 (declare-fun tptp.dsetconstrEL () Bool) 0.40/0.62 (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)))))) 0.40/0.62 (declare-fun tptp.dsetconstrER () Bool) 0.40/0.62 (assert (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))) 0.40/0.62 (declare-fun tptp.exuE1 () Bool) 0.40/0.62 (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))))))))) 0.40/0.62 (declare-fun tptp.prop2set (Bool) $$unsorted) 0.40/0.62 (declare-fun tptp.prop2setE () Bool) 0.40/0.62 (assert (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi)))) 0.40/0.62 (declare-fun tptp.emptysetE () Bool) 0.40/0.62 (assert (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi))))) 0.40/0.62 (declare-fun tptp.emptysetimpfalse () Bool) 0.40/0.62 (assert (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false)))) 0.40/0.62 (declare-fun tptp.notinemptyset () Bool) 0.40/0.62 (assert (= tptp.notinemptyset (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.40/0.62 (declare-fun tptp.exuE3e () Bool) 0.40/0.62 (assert (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx)))))) 0.40/0.62 (declare-fun tptp.setext () Bool) 0.40/0.62 (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)))))) 0.40/0.62 (declare-fun tptp.emptyI () Bool) 0.40/0.62 (assert (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.40/0.62 (declare-fun tptp.noeltsimpempty () Bool) 0.40/0.62 (assert (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.40/0.62 (declare-fun tptp.setbeta () Bool) 0.40/0.62 (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))))))) 0.40/0.62 (declare-fun tptp.nonempty ($$unsorted) Bool) 0.40/0.62 (assert (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset))))) 0.40/0.62 (declare-fun tptp.nonemptyE1 () Bool) 0.40/0.62 (assert (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)))))) 0.40/0.62 (declare-fun tptp.nonemptyI () Bool) 0.40/0.62 (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))))))))) 0.40/0.62 (declare-fun tptp.nonemptyI1 () Bool) 0.40/0.62 (assert (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A))))) 0.40/0.62 (declare-fun tptp.setadjoinIL () Bool) 0.40/0.62 (assert (= tptp.setadjoinIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) 0.40/0.62 (declare-fun tptp.emptyinunitempty () Bool) 0.40/0.62 (assert (= tptp.emptyinunitempty (@ (@ tptp.in tptp.emptyset) (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) 0.40/0.62 (declare-fun tptp.setadjoinIR () Bool) 0.40/0.62 (assert (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A))))))) 0.40/0.62 (declare-fun tptp.setadjoinE () Bool) 0.40/0.62 (assert (= tptp.setadjoinE (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (forall ((Xphi Bool)) (=> (=> (= Xy Xx) Xphi) (=> (=> (@ (@ tptp.in Xy) A) Xphi) Xphi))))))) 0.40/0.62 (declare-fun tptp.setadjoinOr () Bool) 0.40/0.62 (assert (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.40/0.62 (declare-fun tptp.setoftrueEq () Bool) 0.40/0.62 (assert (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A)))) 0.40/0.62 (declare-fun tptp.powersetI () Bool) 0.40/0.62 (assert (= tptp.powersetI (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (@ (@ tptp.in B) (@ tptp.powerset A)))))) 0.40/0.62 (declare-fun tptp.emptyinPowerset () Bool) 0.40/0.62 (assert (= tptp.emptyinPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) 0.40/0.62 (declare-fun tptp.emptyInPowerset () Bool) 0.40/0.62 (assert (= tptp.emptyInPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) 0.40/0.62 (declare-fun tptp.powersetE () Bool) 0.40/0.62 (assert (= tptp.powersetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (=> (@ _let_1 B) (@ _let_1 A))))))) 0.40/0.62 (declare-fun tptp.setunionI () Bool) 0.40/0.62 (assert (= tptp.setunionI (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (=> (@ (@ tptp.in B) A) (@ _let_1 (@ tptp.setunion A)))))))) 0.40/0.62 (declare-fun tptp.setunionE () Bool) 0.40/0.62 (assert (= tptp.setunionE (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (forall ((Xphi Bool)) (=> (forall ((B $$unsorted)) (=> (@ (@ tptp.in Xx) B) (=> (@ (@ tptp.in B) A) Xphi))) Xphi)))))) 0.40/0.62 (declare-fun tptp.subPowSU () Bool) 0.40/0.62 (assert (= tptp.subPowSU (forall ((A $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.powerset (@ tptp.setunion A)))))))) 0.40/0.62 (declare-fun tptp.exuE2 () Bool) 0.40/0.62 (assert (= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))))))) 0.40/0.62 (declare-fun tptp.nonemptyImpWitness () Bool) 0.40/0.62 (assert (= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) true)))))) 0.40/0.62 (declare-fun tptp.uniqinunit () Bool) 0.40/0.62 (assert (= tptp.uniqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy))))) 0.40/0.62 (declare-fun tptp.notinsingleton () Bool) 0.40/0.62 (assert (= tptp.notinsingleton (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (not (= Xx Xy)) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) 0.40/0.62 (declare-fun tptp.eqinunit () Bool) 0.40/0.62 (assert (= tptp.eqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.40/0.62 (declare-fun tptp.singletonsswitch () Bool) 0.40/0.62 (assert (= tptp.singletonsswitch (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) 0.40/0.62 (declare-fun tptp.upairsetE () Bool) 0.40/0.62 (assert (= tptp.upairsetE (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy)))))) 0.40/0.62 (declare-fun tptp.upairsetIL () Bool) 0.40/0.62 (assert (= tptp.upairsetIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.40/0.62 (declare-fun tptp.upairsetIR () Bool) 0.40/0.62 (assert (= tptp.upairsetIR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.40/0.62 (declare-fun tptp.emptyE1 () Bool) 0.40/0.62 (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))))) 0.40/0.62 (declare-fun tptp.vacuousDall () Bool) 0.40/0.62 (assert (= tptp.vacuousDall (forall ((Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (@ Xphi Xx))))) 0.40/0.62 (declare-fun tptp.quantDeMorgan1 () Bool) 0.40/0.62 (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)))))))) 0.40/0.62 (declare-fun tptp.quantDeMorgan2 () Bool) 0.40/0.62 (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)))))))) 0.40/0.62 (declare-fun tptp.quantDeMorgan3 () Bool) 0.40/0.62 (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)))))))) 0.40/0.62 (declare-fun tptp.quantDeMorgan4 () Bool) 0.40/0.62 (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)))))))) 0.40/0.62 (declare-fun tptp.prop2setI () Bool) 0.40/0.62 (assert (= tptp.prop2setI (forall ((Xphi Bool)) (=> Xphi (@ (@ tptp.in tptp.emptyset) (@ tptp.prop2set Xphi)))))) 0.40/0.62 (declare-fun tptp.set2prop ($$unsorted) Bool) 0.40/0.62 (declare-fun tptp.prop2set2propI () Bool) 0.40/0.62 (assert (= tptp.prop2set2propI (forall ((Xphi Bool)) (=> Xphi (@ tptp.set2prop (@ tptp.prop2set Xphi)))))) 0.40/0.62 (declare-fun tptp.notdexE () Bool) 0.40/0.62 (assert (= tptp.notdexE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.40/0.62 (declare-fun tptp.notdallE () Bool) 0.40/0.62 (assert (= tptp.notdallE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.40/0.62 (declare-fun tptp.exuI1 () Bool) 0.40/0.62 (assert (= tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) 0.40/0.62 (declare-fun tptp.exuI3 () Bool) 0.40/0.62 (assert (= tptp.exuI3 (forall ((Xphi (-> $$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)))))))) 0.40/0.62 (declare-fun tptp.exuI2 () Bool) 0.40/0.62 (assert (= tptp.exuI2 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) 0.40/0.62 (declare-fun tptp.inCongP () Bool) 0.40/0.62 (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)))))))) 0.40/0.62 (declare-fun tptp.in__Cong () Bool) 0.40/0.62 (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)))))))) 0.40/0.62 (declare-fun tptp.exuE3u () Bool) 0.40/0.62 (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)))))))) 0.40/0.62 (declare-fun tptp.exu__Cong () Bool) 0.40/0.62 (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)))))))) 0.40/0.62 (declare-fun tptp.emptyset__Cong () Bool) 0.40/0.62 (assert (= tptp.emptyset__Cong (= tptp.emptyset tptp.emptyset))) 0.40/0.62 (declare-fun tptp.setadjoin__Cong () Bool) 0.40/0.62 (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)))))))) 0.40/0.62 (declare-fun tptp.powerset__Cong () Bool) 0.40/0.62 (assert (= tptp.powerset__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.powerset A) (@ tptp.powerset B)))))) 0.40/0.62 (declare-fun tptp.setunion__Cong () Bool) 0.40/0.62 (assert (= tptp.setunion__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.setunion A) (@ tptp.setunion B)))))) 0.40/0.62 (declare-fun tptp.omega__Cong () Bool) 0.40/0.62 (assert (= tptp.omega__Cong (= tptp.omega tptp.omega))) 0.40/0.62 (declare-fun tptp.exuEu () Bool) 0.40/0.62 (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)))))))) 0.40/0.62 (declare-fun tptp.descr__Cong () Bool) 0.40/0.62 (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)))))))))) 0.40/0.62 (declare-fun tptp.dsetconstr__Cong () Bool) 0.40/0.62 (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)))))))))) 0.40/0.62 (declare-fun tptp.subset ($$unsorted $$unsorted) Bool) 0.40/0.62 (declare-fun tptp.disjoint ($$unsorted $$unsorted) Bool) 0.40/0.62 (declare-fun tptp.setsmeet ($$unsorted $$unsorted) Bool) 0.40/0.62 (declare-fun tptp.subsetI1 () Bool) 0.40/0.62 (assert (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B))))) 0.40/0.62 (declare-fun tptp.eqimpsubset2 () Bool) 0.40/0.62 (assert (= tptp.eqimpsubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset B) A))))) 0.40/0.62 (declare-fun tptp.eqimpsubset1 () Bool) 0.40/0.62 (assert (= tptp.eqimpsubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B))))) 0.40/0.62 (declare-fun tptp.subsetI2 () Bool) 0.40/0.62 (assert (= tptp.subsetI2 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B))))) 0.40/0.62 (declare-fun tptp.emptysetsubset () Bool) 0.40/0.62 (assert (= tptp.emptysetsubset (forall ((A $$unsorted)) (@ (@ tptp.subset tptp.emptyset) A)))) 0.40/0.62 (declare-fun tptp.subsetE () Bool) 0.40/0.62 (assert (= tptp.subsetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (@ _let_1 A) (@ _let_1 B))))))) 0.40/0.62 (declare-fun tptp.subsetE2 () Bool) 0.40/0.62 (assert (= tptp.subsetE2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (not (@ _let_1 B)) (not (@ _let_1 A)))))))) 0.40/0.62 (declare-fun tptp.notsubsetI () Bool) 0.40/0.62 (assert (= tptp.notsubsetI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (@ (@ tptp.subset A) B)))))))) 0.40/0.62 (declare-fun tptp.notequalI1 () Bool) 0.40/0.62 (assert (= tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (@ (@ tptp.subset A) B)) (not (= A B)))))) 0.40/0.62 (declare-fun tptp.notequalI2 () Bool) 0.40/0.62 (assert (= tptp.notequalI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (= A B)))))))) 0.40/0.62 (declare-fun tptp.subsetRefl () Bool) 0.40/0.62 (assert (= tptp.subsetRefl (forall ((A $$unsorted)) (@ (@ tptp.subset A) A)))) 0.40/0.62 (declare-fun tptp.subsetTrans () Bool) 0.40/0.62 (assert (= tptp.subsetTrans (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (=> (@ (@ tptp.subset B) C) (@ _let_1 C))))))) 0.40/0.62 (declare-fun tptp.setadjoinSub () Bool) 0.40/0.62 (assert (= tptp.setadjoinSub (forall ((Xx $$unsorted) (A $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.setadjoin Xx) A))))) 0.40/0.62 (declare-fun tptp.setadjoinSub2 () Bool) 0.40/0.62 (assert (= tptp.setadjoinSub2 (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.setadjoin Xx) B))))))) 0.40/0.62 (declare-fun tptp.subset2powerset () Bool) 0.40/0.62 (assert (= tptp.subset2powerset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.in A) (@ tptp.powerset B)))))) 0.40/0.62 (declare-fun tptp.setextsub () Bool) 0.40/0.62 (assert (= tptp.setextsub (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (=> (@ (@ tptp.subset B) A) (= A B)))))) 0.40/0.62 (declare-fun tptp.subsetemptysetimpeq () Bool) 0.40/0.62 (assert (= tptp.subsetemptysetimpeq (forall ((A $$unsorted)) (=> (@ (@ tptp.subset A) tptp.emptyset) (= A tptp.emptyset))))) 0.40/0.62 (declare-fun tptp.powersetI1 () Bool) 0.40/0.62 (assert (= tptp.powersetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (@ (@ tptp.in B) (@ tptp.powerset A)))))) 0.40/0.62 (declare-fun tptp.powersetE1 () Bool) 0.40/0.62 (assert (= tptp.powersetE1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (@ (@ tptp.subset B) A))))) 0.40/0.62 (declare-fun tptp.inPowerset () Bool) 0.40/0.62 (assert (= tptp.inPowerset (forall ((A $$unsorted)) (@ (@ tptp.in A) (@ tptp.powerset A))))) 0.40/0.62 (declare-fun tptp.powersetsubset () Bool) 0.40/0.62 (assert (= tptp.powersetsubset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.subset (@ tptp.powerset A)) (@ tptp.powerset B)))))) 0.40/0.62 (declare-fun tptp.sepInPowerset () Bool) 0.40/0.62 (assert (= tptp.sepInPowerset (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.in (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ tptp.powerset A))))) 0.40/0.62 (declare-fun tptp.sepSubset () Bool) 0.40/0.62 (assert (= tptp.sepSubset (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.subset (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) A)))) 0.40/0.62 (declare-fun tptp.binunion ($$unsorted $$unsorted) $$unsorted) 0.40/0.62 (declare-fun tptp.binunionIL () Bool) 0.40/0.62 (assert (= tptp.binunionIL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.binunion A) B))))))) 0.40/0.62 (declare-fun tptp.upairset2IR () Bool) 0.40/0.62 (assert (= tptp.upairset2IR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.40/0.62 (declare-fun tptp.binunionIR () Bool) 0.40/0.62 (assert (= tptp.binunionIR (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binunion A) B))))))) 0.40/0.62 (declare-fun tptp.binunionEcases () Bool) 0.40/0.62 (assert (= tptp.binunionEcases (forall ((A $$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))))))) 0.40/0.62 (declare-fun tptp.binunionE () Bool) 0.40/0.62 (assert (= tptp.binunionE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binunion A) B)) (or (@ _let_1 A) (@ _let_1 B))))))) 0.40/0.62 (declare-fun tptp.binunionLsub () Bool) 0.40/0.62 (assert (= tptp.binunionLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.binunion A) B))))) 0.40/0.62 (declare-fun tptp.binunionRsub () Bool) 0.40/0.62 (assert (= tptp.binunionRsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset B) (@ (@ tptp.binunion A) B))))) 0.40/0.62 (declare-fun tptp.binintersect ($$unsorted $$unsorted) $$unsorted) 0.40/0.62 (declare-fun tptp.binintersectI () Bool) 0.40/0.62 (assert (= tptp.binintersectI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B)))))))) 0.40/0.62 (declare-fun tptp.binintersectSubset5 () Bool) 0.40/0.62 (assert (= tptp.binintersectSubset5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B)))))))) 0.40/0.62 (declare-fun tptp.binintersectEL () Bool) 0.40/0.62 (assert (= tptp.binintersectEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect A) B)) (@ _let_1 A)))))) 0.40/0.62 (declare-fun tptp.binintersectLsub () Bool) 0.40/0.62 (assert (= tptp.binintersectLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) A)))) 0.40/0.62 (declare-fun tptp.binintersectSubset2 () Bool) 0.40/0.62 (assert (= tptp.binintersectSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.binintersect A) B) A))))) 0.40/0.62 (declare-fun tptp.binintersectSubset3 () Bool) 0.40/0.62 (assert (= tptp.binintersectSubset3 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) B) (@ (@ tptp.subset B) A))))) 0.40/0.62 (declare-fun tptp.binintersectER () Bool) 0.40/0.62 (assert (= tptp.binintersectER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect A) B)) (@ _let_1 B)))))) 0.40/0.62 (declare-fun tptp.disjointsetsI1 () Bool) 0.40/0.62 (assert (= tptp.disjointsetsI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 A) (@ _let_1 B))))) (= (@ (@ tptp.binintersect A) B) tptp.emptyset))))) 0.40/0.62 (declare-fun tptp.binintersectRsub () Bool) 0.40/0.62 (assert (= tptp.binintersectRsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) B)))) 0.40/0.62 (declare-fun tptp.binintersectSubset4 () Bool) 0.40/0.62 (assert (= tptp.binintersectSubset4 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (= (@ (@ tptp.binintersect A) B) B))))) 0.40/0.62 (declare-fun tptp.binintersectSubset1 () Bool) 0.40/0.62 (assert (= tptp.binintersectSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) A) (@ (@ tptp.subset A) B))))) 0.40/0.62 (declare-fun tptp.bs114d () Bool) 0.40/0.62 (assert (= tptp.bs114d (forall ((A $$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))))))) 0.40/0.62 (declare-fun tptp.regular ($$unsorted) Bool) 0.40/0.62 (declare-fun tptp.setminus ($$unsorted $$unsorted) $$unsorted) 0.40/0.62 (declare-fun tptp.setminusI () Bool) 0.40/0.62 (assert (= tptp.setminusI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.setminus A) B)))))))) 0.40/0.62 (declare-fun tptp.setminusEL () Bool) 0.40/0.62 (assert (= tptp.setminusEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.setminus A) B)) (@ _let_1 A)))))) 0.40/0.62 (declare-fun tptp.setminusER () Bool) 0.40/0.62 (assert (= tptp.setminusER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.setminus A) B)) (not (@ _let_1 B))))))) 0.40/0.62 (declare-fun tptp.setminusSubset2 () Bool) 0.40/0.62 (assert (= tptp.setminusSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.setminus A) B) tptp.emptyset))))) 0.40/0.62 (declare-fun tptp.setminusERneg () Bool) 0.40/0.62 (assert (= tptp.setminusERneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 (@ (@ tptp.setminus A) B))) (=> (@ _let_1 A) (@ _let_1 B))))))) 0.40/0.62 (declare-fun tptp.setminusELneg () Bool) 0.40/0.62 (assert (= tptp.setminusELneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 (@ (@ tptp.setminus A) B))) (=> (not (@ _let_1 B)) (not (@ _let_1 A)))))))) 0.40/0.62 (declare-fun tptp.setminusILneg () Bool) 0.40/0.62 (assert (= tptp.setminusILneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (not (@ _let_1 (@ (@ tptp.setminus A) B)))))))) 0.40/0.62 (declare-fun tptp.setminusIRneg () Bool) 0.40/0.62 (assert (= tptp.setminusIRneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (not (@ _let_1 (@ (@ tptp.setminus A) B)))))))) 0.40/0.62 (declare-fun tptp.setminusLsub () Bool) 0.40/0.62 (assert (= tptp.setminusLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.setminus A) B)) A)))) 0.40/0.62 (declare-fun tptp.setminusSubset1 () Bool) 0.40/0.62 (assert (= tptp.setminusSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.setminus A) B) tptp.emptyset) (@ (@ tptp.subset A) B))))) 0.40/0.62 (declare-fun tptp.symdiff ($$unsorted $$unsorted) $$unsorted) 0.40/0.62 (declare-fun tptp.symdiffE () Bool) 0.40/0.62 (assert (= tptp.symdiffE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.symdiff A) B)) (forall ((Xphi Bool)) (let ((_let_1 (@ tptp.in Xx))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ _let_1 A))) (=> (=> _let_3 (=> (not _let_2) Xphi)) (=> (=> (not _let_3) (=> _let_2 Xphi)) Xphi)))))))))) 0.40/0.62 (declare-fun tptp.symdiffI1 () Bool) 0.40/0.62 (assert (= tptp.symdiffI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.symdiff A) B)))))))) 0.40/0.62 (declare-fun tptp.symdiffI2 () Bool) 0.40/0.62 (assert (= tptp.symdiffI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.symdiff A) B)))))))) 0.40/0.62 (declare-fun tptp.symdiffIneg1 () Bool) 0.40/0.62 (assert (= tptp.symdiffIneg1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 B) (not (@ _let_1 (@ (@ tptp.symdiff A) B))))))))) 0.40/0.62 (declare-fun tptp.symdiffIneg2 () Bool) 0.40/0.62 (assert (= tptp.symdiffIneg2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (not (@ _let_1 (@ (@ tptp.symdiff A) B))))))))) 0.40/0.62 (declare-fun tptp.iskpair ($$unsorted) Bool) 0.40/0.62 (assert (= tptp.iskpair (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (and (@ (@ tptp.in Xy) (@ tptp.setunion A)) (= A (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))))))))))) 0.40/0.62 (declare-fun tptp.secondinupair () Bool) 0.40/0.62 (assert (= tptp.secondinupair (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.40/0.62 (declare-fun tptp.setukpairIL () Bool) 0.40/0.62 (assert (= tptp.setukpairIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ (@ tptp.in Xx) (@ tptp.setunion (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)))))))) 0.40/0.62 (declare-fun tptp.setukpairIR () Bool) 0.40/0.62 (assert (= tptp.setukpairIR (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ (@ tptp.in Xy) (@ tptp.setunion (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)))))))) 0.40/0.62 (declare-fun tptp.kpairiskpair () Bool) 0.40/0.62 (assert (= tptp.kpairiskpair (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ tptp.iskpair (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))))))) 0.40/0.62 (declare-fun tptp.kpair ($$unsorted $$unsorted) $$unsorted) 0.40/0.62 (assert (= tptp.kpair (lambda ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)))))) 0.40/0.62 (declare-fun tptp.kpairp () Bool) 0.40/0.62 (assert (= tptp.kpairp (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ tptp.iskpair (@ (@ tptp.kpair Xx) Xy))))) 0.40/0.62 (declare-fun tptp.cartprod ($$unsorted $$unsorted) $$unsorted) 0.40/0.62 (declare-fun tptp.singletonsubset () Bool) 0.40/0.62 (assert (= tptp.singletonsubset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) tptp.emptyset)) A))))) 0.40/0.62 (declare-fun tptp.singletoninpowerset () Bool) 0.40/0.62 (assert (= tptp.singletoninpowerset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset A)))))) 0.40/0.62 (declare-fun tptp.singletoninpowunion () Bool) 0.40/0.62 (assert (= tptp.singletoninpowunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset (@ (@ tptp.binunion A) B))))))) 0.40/0.62 (declare-fun tptp.upairset2E () Bool) 0.40/0.62 (assert (= tptp.upairset2E (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy)))))) 0.40/0.62 (declare-fun tptp.upairsubunion () Bool) 0.40/0.62 (assert (= tptp.upairsubunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (@ (@ tptp.binunion A) B)))))))) 0.40/0.62 (declare-fun tptp.upairinpowunion () Bool) 0.40/0.62 (assert (= tptp.upairinpowunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (@ tptp.powerset (@ (@ tptp.binunion A) B))))))))) 0.40/0.62 (declare-fun tptp.ubforcartprodlem1 () Bool) 0.40/0.62 (assert (= tptp.ubforcartprodlem1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.subset (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))))) 0.40/0.62 (declare-fun tptp.ubforcartprodlem2 () Bool) 0.40/0.62 (assert (= tptp.ubforcartprodlem2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (@ tptp.powerset (@ tptp.powerset (@ (@ tptp.binunion A) B))))))))))) 0.40/0.62 (declare-fun tptp.ubforcartprodlem3 () Bool) 0.40/0.62 (assert (= tptp.ubforcartprodlem3 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ tptp.powerset (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))))) 0.40/0.62 (declare-fun tptp.cartprodpairin () Bool) 0.40/0.62 (assert (= tptp.cartprodpairin (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B)))))))) 0.40/0.62 (declare-fun tptp.cartprodmempair1 () Bool) 0.40/0.62 (assert (= tptp.cartprodmempair1 (forall ((A $$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)))))))))) 0.40/0.62 (declare-fun tptp.cartprodmempair () Bool) 0.40/0.62 (assert (= tptp.cartprodmempair (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ tptp.iskpair Xu))))) 0.40/0.62 (declare-fun tptp.setunionE2 () Bool) 0.40/0.62 (assert (= tptp.setunionE2 (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((X $$unsorted)) (and (@ (@ tptp.in X) A) (@ (@ tptp.in Xx) X))))))) 0.40/0.62 (declare-fun tptp.setunionsingleton1 () Bool) 0.40/0.62 (assert (= tptp.setunionsingleton1 (forall ((A $$unsorted)) (@ (@ tptp.subset (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset))) A)))) 0.40/0.62 (declare-fun tptp.setunionsingleton2 () Bool) 0.40/0.62 (assert (= tptp.setunionsingleton2 (forall ((A $$unsorted)) (@ (@ tptp.subset A) (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset)))))) 0.40/0.62 (declare-fun tptp.setunionsingleton () Bool) 0.40/0.62 (assert (= tptp.setunionsingleton (forall ((Xx $$unsorted)) (= (@ tptp.setunion (@ (@ tptp.setadjoin Xx) tptp.emptyset)) Xx)))) 0.40/0.62 (declare-fun tptp.singleton ($$unsorted) Bool) 0.40/0.62 (assert (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) 0.40/0.62 (declare-fun tptp.singletonprop () Bool) 0.40/0.62 (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))))))))) 0.40/0.62 (declare-fun tptp.ex1 ($$unsorted (-> $$unsorted Bool)) Bool) 0.40/0.62 (assert (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) 0.40/0.62 (declare-fun tptp.ex1E1 () Bool) 0.40/0.62 (assert (= tptp.ex1E1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))))))) 0.40/0.62 (declare-fun tptp.ex1I () Bool) 0.40/0.62 (assert (= tptp.ex1I (forall ((A $$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))))))))) 0.40/0.62 (assert (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 35.76/35.97 (set-info :filename cvc5---1.0.5_20533) 35.76/35.97 (check-sat-assuming ( true )) 35.76/35.97 ------- get file name : TPTP file name is 35.76/35.97 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20533.smt2... 35.76/35.97 --- Run --ho-elim --full-saturate-quant at 10... 35.76/35.97 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 35.76/35.97 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10... 35.76/35.97 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5... 35.76/35.97 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5... 35.76/35.97 % SZS status Theorem for 35.76/35.97 % SZS output start Proof for 35.76/35.97 ( 35.76/35.97 (let ((_let_1 (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (let ((_let_2 (= 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 $$unsorted)) (@ Xphi Xy)))))))))) (let ((_let_3 (= tptp.ex1E1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))))))) (let ((_let_4 (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) (let ((_let_5 (= 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)))))))))) (let ((_let_6 (= tptp.singleton (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (= A (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) (let ((_let_7 (= tptp.setunionsingleton (forall ((Xx $$unsorted)) (= (@ tptp.setunion (@ (@ tptp.setadjoin Xx) tptp.emptyset)) Xx))))) (let ((_let_8 (forall ((A $$unsorted)) (@ (@ tptp.subset A) (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset)))))) (let ((_let_9 (= tptp.setunionsingleton2 _let_8))) (let ((_let_10 (forall ((A $$unsorted)) (@ (@ tptp.subset (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset))) A)))) (let ((_let_11 (= tptp.setunionsingleton1 _let_10))) (let ((_let_12 (= tptp.setunionE2 (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((X $$unsorted)) (and (@ (@ tptp.in X) A) (@ (@ tptp.in Xx) X)))))))) (let ((_let_13 (= tptp.cartprodmempair (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ tptp.iskpair Xu)))))) (let ((_let_14 (= tptp.cartprodmempair1 (forall ((A $$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))))))))))) (let ((_let_15 (= 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))))))))) (let ((_let_16 (= 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))))))))))) (let ((_let_17 (= 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)))))))))))) (let ((_let_18 (= 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))))))))))) (let ((_let_19 (= 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)))))))))) (let ((_let_20 (= 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))))))))) (let ((_let_21 (= tptp.upairset2E (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy))))))) (let ((_let_22 (= tptp.singletoninpowunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))) (let ((_let_23 (= tptp.singletoninpowerset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset A))))))) (let ((_let_24 (= tptp.singletonsubset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) tptp.emptyset)) A)))))) (let ((_let_25 (= tptp.kpairp (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ tptp.iskpair (@ (@ tptp.kpair Xx) Xy)))))) (let ((_let_26 (= tptp.kpair (lambda ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))))))) (let ((_let_27 (= 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)))))))) (let ((_let_28 (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)))))))) (let ((_let_29 (= tptp.setukpairIR _let_28))) (let ((_let_30 (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)))))))) (let ((_let_31 (= tptp.setukpairIL _let_30))) (let ((_let_32 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) (let ((_let_33 (= tptp.secondinupair _let_32))) (let ((_let_34 (= tptp.iskpair (lambda ((A $$unsorted)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (and (@ (@ tptp.in Xy) (@ tptp.setunion A)) (= A (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)))))))))))) (let ((_let_35 (= tptp.symdiffIneg2 (forall ((A $$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)))))))))) (let ((_let_36 (= tptp.symdiffIneg1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 B) (not (@ _let_1 (@ (@ tptp.symdiff A) B)))))))))) (let ((_let_37 (= tptp.symdiffI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.symdiff A) B))))))))) (let ((_let_38 (= tptp.symdiffI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.symdiff A) B))))))))) (let ((_let_39 (= tptp.symdiffE (forall ((A $$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))))))))))) (let ((_let_40 (= tptp.setminusSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.setminus A) B) tptp.emptyset) (@ (@ tptp.subset A) B)))))) (let ((_let_41 (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.setminus A) B)) A)))) (let ((_let_42 (= tptp.setminusLsub _let_41))) (let ((_let_43 (= tptp.setminusIRneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (not (@ _let_1 (@ (@ tptp.setminus A) B))))))))) (let ((_let_44 (= tptp.setminusILneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (not (@ _let_1 (@ (@ tptp.setminus A) B))))))))) (let ((_let_45 (= tptp.setminusELneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 (@ (@ tptp.setminus A) B))) (=> (not (@ _let_1 B)) (not (@ _let_1 A))))))))) (let ((_let_46 (= tptp.setminusERneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 (@ (@ tptp.setminus A) B))) (=> (@ _let_1 A) (@ _let_1 B)))))))) (let ((_let_47 (= tptp.setminusSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.setminus A) B) tptp.emptyset)))))) (let ((_let_48 (= tptp.setminusER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.setminus A) B)) (not (@ _let_1 B)))))))) (let ((_let_49 (= tptp.setminusEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.setminus A) B)) (@ _let_1 A))))))) (let ((_let_50 (= tptp.setminusI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.setminus A) B))))))))) (let ((_let_51 (forall ((A $$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))))))) (let ((_let_52 (= tptp.bs114d _let_51))) (let ((_let_53 (= tptp.binintersectSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) A) (@ (@ tptp.subset A) B)))))) (let ((_let_54 (= tptp.binintersectSubset4 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (= (@ (@ tptp.binintersect A) B) B)))))) (let ((_let_55 (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) B)))) (let ((_let_56 (= tptp.binintersectRsub _let_55))) (let ((_let_57 (= tptp.disjointsetsI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 A) (@ _let_1 B))))) (= (@ (@ tptp.binintersect A) B) tptp.emptyset)))))) (let ((_let_58 (= tptp.binintersectER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect A) B)) (@ _let_1 B))))))) (let ((_let_59 (= tptp.binintersectSubset3 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) B) (@ (@ tptp.subset B) A)))))) (let ((_let_60 (= tptp.binintersectSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.binintersect A) B) A)))))) (let ((_let_61 (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) A)))) (let ((_let_62 (= tptp.binintersectLsub _let_61))) (let ((_let_63 (= tptp.binintersectEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect A) B)) (@ _let_1 A))))))) (let ((_let_64 (= tptp.binintersectSubset5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B))))))))) (let ((_let_65 (= tptp.binintersectI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B))))))))) (let ((_let_66 (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset B) (@ (@ tptp.binunion A) B))))) (let ((_let_67 (= tptp.binunionRsub _let_66))) (let ((_let_68 (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.binunion A) B))))) (let ((_let_69 (= tptp.binunionLsub _let_68))) (let ((_let_70 (= tptp.binunionE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binunion A) B)) (or (@ _let_1 A) (@ _let_1 B)))))))) (let ((_let_71 (= tptp.binunionEcases (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xphi Bool)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binunion A) B)) (=> (=> (@ _let_1 A) Xphi) (=> (=> (@ _let_1 B) Xphi) Xphi)))))))) (let ((_let_72 (= tptp.binunionIR (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binunion A) B)))))))) (let ((_let_73 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) (let ((_let_74 (= tptp.upairset2IR _let_73))) (let ((_let_75 (= tptp.binunionIL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.binunion A) B)))))))) (let ((_let_76 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.subset (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) A)))) (let ((_let_77 (= tptp.sepSubset _let_76))) (let ((_let_78 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.in (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ tptp.powerset A))))) (let ((_let_79 (= tptp.sepInPowerset _let_78))) (let ((_let_80 (= tptp.powersetsubset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.subset (@ tptp.powerset A)) (@ tptp.powerset B))))))) (let ((_let_81 (forall ((A $$unsorted)) (@ (@ tptp.in A) (@ tptp.powerset A))))) (let ((_let_82 (= tptp.inPowerset _let_81))) (let ((_let_83 (= tptp.powersetE1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (@ (@ tptp.subset B) A)))))) (let ((_let_84 (= tptp.powersetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (@ (@ tptp.in B) (@ tptp.powerset A))))))) (let ((_let_85 (= tptp.subsetemptysetimpeq (forall ((A $$unsorted)) (=> (@ (@ tptp.subset A) tptp.emptyset) (= A tptp.emptyset)))))) (let ((_let_86 (= tptp.setextsub (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (=> (@ (@ tptp.subset B) A) (= A B))))))) (let ((_let_87 (= tptp.subset2powerset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.in A) (@ tptp.powerset B))))))) (let ((_let_88 (= tptp.setadjoinSub2 (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.setadjoin Xx) B)))))))) (let ((_let_89 (forall ((Xx $$unsorted) (A $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.setadjoin Xx) A))))) (let ((_let_90 (= tptp.setadjoinSub _let_89))) (let ((_let_91 (= tptp.subsetTrans (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (=> (@ (@ tptp.subset B) C) (@ _let_1 C)))))))) (let ((_let_92 (forall ((A $$unsorted)) (@ (@ tptp.subset A) A)))) (let ((_let_93 (= tptp.subsetRefl _let_92))) (let ((_let_94 (= tptp.notequalI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (= A B))))))))) (let ((_let_95 (= tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (@ (@ tptp.subset A) B)) (not (= A B))))))) (let ((_let_96 (= tptp.notsubsetI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (@ (@ tptp.subset A) B))))))))) (let ((_let_97 (= tptp.subsetE2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (not (@ _let_1 B)) (not (@ _let_1 A))))))))) (let ((_let_98 (= tptp.subsetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (@ _let_1 A) (@ _let_1 B)))))))) (let ((_let_99 (forall ((A $$unsorted)) (@ (@ tptp.subset tptp.emptyset) A)))) (let ((_let_100 (= tptp.emptysetsubset _let_99))) (let ((_let_101 (= tptp.subsetI2 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B)))))) (let ((_let_102 (= tptp.eqimpsubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B)))))) (let ((_let_103 (= tptp.eqimpsubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset B) A)))))) (let ((_let_104 (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B)))))) (let ((_let_105 (= tptp.dsetconstr__Cong (forall ((A $$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 $$unsorted)) (@ Xpsi Xx))))))))))) (let ((_let_106 (= tptp.descr__Cong (forall ((Xphi (-> $$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 $$unsorted)) (@ Xpsi Xx))))))))))) (let ((_let_107 (= tptp.exuEu (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))))) (let ((_let_108 (= tptp.omega__Cong (= tptp.omega tptp.omega)))) (let ((_let_109 (= tptp.setunion__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.setunion A) (@ tptp.setunion B))))))) (let ((_let_110 (= tptp.powerset__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.powerset A) (@ tptp.powerset B))))))) (let ((_let_111 (= tptp.setadjoin__Cong (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (forall ((Xz $$unsorted) (Xu $$unsorted)) (=> (= Xz Xu) (= (@ (@ tptp.setadjoin Xx) Xz) (@ (@ tptp.setadjoin Xy) Xu))))))))) (let ((_let_112 (= tptp.emptyset__Cong (= tptp.emptyset tptp.emptyset)))) (let ((_let_113 (= tptp.exu__Cong (forall ((Xphi (-> $$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 $$unsorted)) (@ Xpsi Xx))))))))) (let ((_let_114 (= tptp.exuE3u (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))))) (let ((_let_115 (= tptp.in__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) B))))))))) (let ((_let_116 (= tptp.inCongP (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) B))))))))) (let ((_let_117 (= tptp.exuI2 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) (let ((_let_118 (= tptp.exuI3 (forall ((Xphi (-> $$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))))))))) (let ((_let_119 (= 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)))))))) (let ((_let_120 (= 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))))))))) (let ((_let_121 (= 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))))))))) (let ((_let_122 (= tptp.prop2set2propI (forall ((Xphi Bool)) (=> Xphi (@ tptp.set2prop (@ tptp.prop2set Xphi))))))) (let ((_let_123 (= tptp.prop2setI (forall ((Xphi Bool)) (=> Xphi (@ (@ tptp.in tptp.emptyset) (@ tptp.prop2set Xphi))))))) (let ((_let_124 (= 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))))))))) (let ((_let_125 (= 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))))))))) (let ((_let_126 (= 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))))))))) (let ((_let_127 (= 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))))))))) (let ((_let_128 (= tptp.vacuousDall (forall ((Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (@ Xphi Xx)))))) (let ((_let_129 (= 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)))))) (let ((_let_130 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) (let ((_let_131 (= tptp.upairsetIR _let_130))) (let ((_let_132 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) (let ((_let_133 (= tptp.upairsetIL _let_132))) (let ((_let_134 (= tptp.upairsetE (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy))))))) (let ((_let_135 (= tptp.singletonsswitch (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (let ((_let_136 (= tptp.eqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))) (let ((_let_137 (= tptp.notinsingleton (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (not (= Xx Xy)) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) (let ((_let_138 (= tptp.uniqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy)))))) (let ((_let_139 (= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) true))))))) (let ((_let_140 (= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx))))))))) (let ((_let_141 (= tptp.subPowSU (forall ((A $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.powerset (@ tptp.setunion A))))))))) (let ((_let_142 (= tptp.setunionE (forall ((A $$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))))))) (let ((_let_143 (= tptp.setunionI (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (=> (@ (@ tptp.in B) A) (@ _let_1 (@ tptp.setunion A))))))))) (let ((_let_144 (= tptp.powersetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (=> (@ _let_1 B) (@ _let_1 A)))))))) (let ((_let_145 (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) (let ((_let_146 (= tptp.emptyInPowerset _let_145))) (let ((_let_147 (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) (let ((_let_148 (= tptp.emptyinPowerset _let_147))) (let ((_let_149 (= tptp.powersetI (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (@ (@ tptp.in B) (@ tptp.powerset A))))))) (let ((_let_150 (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A))))) (let ((_let_151 (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A)))))))) (let ((_let_152 (= tptp.setadjoinE (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (forall ((Xphi Bool)) (=> (=> (= Xy Xx) Xphi) (=> (=> (@ (@ tptp.in Xy) A) Xphi) Xphi)))))))) (let ((_let_153 (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A)))))))) (let ((_let_154 (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset))) (let ((_let_155 (@ tptp.in tptp.emptyset))) (let ((_let_156 (= tptp.emptyinunitempty (@ _let_155 _let_154)))) (let ((_let_157 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) (let ((_let_158 (= tptp.setadjoinIL _let_157))) (let ((_let_159 (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A)))))) (let ((_let_160 (= 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)))))))))) (let ((_let_161 (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A))))))) (let ((_let_162 (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset)))))) (let ((_let_163 (= tptp.setbeta (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (= (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx)))))))) (let ((_let_164 (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))) (let ((_let_165 (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))) (let ((_let_166 (= tptp.setext (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (= A B))))))) (let ((_let_167 (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx))))))) (let ((_let_168 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_169 (= tptp.notinemptyset _let_168))) (let ((_let_170 (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false))))) (let ((_let_171 (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi)))))) (let ((_let_172 (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi))))) (let ((_let_173 (= 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)))))))))) (let ((_let_174 (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx)))))) (let ((_let_175 (= 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))))))) (let ((_let_176 (= 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))))))))))) (let ((_let_177 (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (let ((_let_178 (= tptp.wellorderingAx (forall ((A $$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) (@ (@ 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B) A) (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 B) (@ _let_1 A)))))))))))) (let ((_let_180 (= tptp.replAx (forall ((Xphi (-> $$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 $$unsorted)) (and (@ (@ tptp.in Xy) A) (@ (@ Xphi Xy) Xx))))))))))) (let ((_let_181 (= tptp.omegaIndAx (forall ((A $$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))))))))) (let ((_let_182 (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega)))))) (let ((_let_183 (@ _let_155 tptp.omega))) (let ((_let_184 (= tptp.omega0Ax _let_183))) (let ((_let_185 (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A)))))))) (let ((_let_186 (= tptp.powersetAx (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A))))))))) (let ((_let_187 (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A)))))))) (let ((_let_188 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_189 (= tptp.emptysetAx _let_188))) (let ((_let_190 (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B)))))) (let ((_let_191 (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))))))) (let ((_let_192 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_5480 $$unsorted)) (or (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_5451 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (@ (@ tptp.in BOUND_VARIABLE_5451) A)) (not (@ Xphi BOUND_VARIABLE_5451)) (= Xx BOUND_VARIABLE_5451)))) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (or (not (@ (@ tptp.in Xx) _let_1)) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) _let_1)))))) (not (@ (@ tptp.in BOUND_VARIABLE_5480) A)) (not (@ Xphi BOUND_VARIABLE_5480)))))) (let ((_let_193 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_5382 $$unsorted)) (or (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_5353 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (@ (@ tptp.in BOUND_VARIABLE_5353) A)) (not (@ Xphi BOUND_VARIABLE_5353)) (= Xx BOUND_VARIABLE_5353)))) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (or (not (@ (@ tptp.in Xx) _let_1)) (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) _let_1)))))) (not (@ (@ tptp.in BOUND_VARIABLE_5382) A)) (not (@ Xphi BOUND_VARIABLE_5382)))))) (let ((_let_194 (=>))) (let ((_let_195 (tptp.prop2set BOOLEAN_TERM_VARIABLE_8059))) (let ((_let_196 (@))) (let ((_let_197 (TRANS (CONG (REFL :args (tptp.prop2set)) (MACRO_SR_PRED_INTRO :args ((= true BOOLEAN_TERM_VARIABLE_8059))) :args _let_196) (THEORY_PREPROCESS :args ((= (@ tptp.prop2set BOOLEAN_TERM_VARIABLE_8059) _let_195)))))) (let ((_let_198 (REFL :args (_let_155)))) (let ((_let_199 (tptp.setadjoin tptp.emptyset tptp.emptyset))) (let ((_let_200 (EQ_RESOLVE (ASSUME :args (_let_191)) (MACRO_SR_EQ_INTRO :args (_let_191 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_201 (EQ_RESOLVE (ASSUME :args (_let_190)) (MACRO_SR_EQ_INTRO :args (_let_190 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_202 (ASSUME :args (_let_189)))) (let ((_let_203 (EQ_RESOLVE (ASSUME :args (_let_187)) (MACRO_SR_EQ_INTRO :args (_let_187 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_204 (EQ_RESOLVE (ASSUME :args (_let_186)) (MACRO_SR_EQ_INTRO :args (_let_186 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_205 (EQ_RESOLVE (ASSUME :args (_let_185)) (MACRO_SR_EQ_INTRO :args (_let_185 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_206 (ASSUME :args (_let_184)))) (let ((_let_207 (EQ_RESOLVE (ASSUME :args (_let_182)) (MACRO_SR_EQ_INTRO :args (_let_182 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_208 (EQ_RESOLVE (ASSUME :args (_let_181)) (MACRO_SR_EQ_INTRO :args (_let_181 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_209 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_180)) (MACRO_SR_EQ_INTRO :args (_let_180 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.replAx (forall ((Xphi (-> $$unsorted $$unsorted Bool)) (A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ tptp.exu (lambda ((Xy $$unsorted)) (@ (@ Xphi Xx) Xy)))))) (not (forall ((B $$unsorted)) (not (forall ((Xx $$unsorted)) (= (@ (@ tptp.in Xx) B) (not (forall ((Xy $$unsorted)) (or (not (@ (@ tptp.in Xy) A)) (not (@ (@ Xphi Xy) Xx))))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_210 (EQ_RESOLVE (ASSUME :args (_let_179)) (MACRO_SR_EQ_INTRO :args (_let_179 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_211 (EQ_RESOLVE (ASSUME :args (_let_178)) (MACRO_SR_EQ_INTRO :args (_let_178 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_212 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_177)) (MACRO_SR_EQ_INTRO :args (_let_177 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_213 (EQ_RESOLVE (ASSUME :args (_let_176)) (MACRO_SR_EQ_INTRO :args (_let_176 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_214 (EQ_RESOLVE (ASSUME :args (_let_175)) (MACRO_SR_EQ_INTRO :args (_let_175 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_215 (EQ_RESOLVE (ASSUME :args (_let_174)) (MACRO_SR_EQ_INTRO :args (_let_174 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_216 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_173)) (MACRO_SR_EQ_INTRO :args (_let_173 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.exuE1 (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_217 (EQ_RESOLVE (ASSUME :args (_let_172)) (MACRO_SR_EQ_INTRO :args (_let_172 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_218 (EQ_RESOLVE (ASSUME :args (_let_171)) (MACRO_SR_EQ_INTRO :args (_let_171 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_219 (EQ_RESOLVE (ASSUME :args (_let_170)) (MACRO_SR_EQ_INTRO :args (_let_170 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_220 (ASSUME :args (_let_169)))) (let ((_let_221 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_167)) (MACRO_SR_EQ_INTRO :args (_let_167 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (not (@ Xphi Xx))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_222 (EQ_RESOLVE (ASSUME :args (_let_166)) (MACRO_SR_EQ_INTRO :args (_let_166 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_223 (EQ_RESOLVE (ASSUME :args (_let_165)) (MACRO_SR_EQ_INTRO :args (_let_165 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_224 (EQ_RESOLVE (ASSUME :args (_let_164)) (MACRO_SR_EQ_INTRO :args (_let_164 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_225 (EQ_RESOLVE (ASSUME :args (_let_163)) (MACRO_SR_EQ_INTRO :args (_let_163 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_226 (EQ_RESOLVE (ASSUME :args (_let_162)) (MACRO_SR_EQ_INTRO :args (_let_162 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_227 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_161)) (MACRO_SR_EQ_INTRO :args (_let_161 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.nonemptyE1 (forall ((A $$unsorted)) (or (not (@ tptp.nonempty A)) (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_228 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_160)) (MACRO_SR_EQ_INTRO :args (_let_160 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.nonemptyI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (@ tptp.nonempty (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_229 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_159)) (MACRO_SR_EQ_INTRO :args (_let_159 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.nonemptyI1 (forall ((A $$unsorted) (BOUND_VARIABLE_3874 $$unsorted)) (or (not (@ (@ tptp.in BOUND_VARIABLE_3874) A)) (@ tptp.nonempty A)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_230 (ASSUME :args (_let_158)))) (let ((_let_231 (ASSUME :args (_let_156)))) (let ((_let_232 (EQ_RESOLVE (ASSUME :args (_let_153)) (MACRO_SR_EQ_INTRO :args (_let_153 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_233 (EQ_RESOLVE (ASSUME :args (_let_152)) (MACRO_SR_EQ_INTRO :args (_let_152 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_234 (EQ_RESOLVE (ASSUME :args (_let_151)) (MACRO_SR_EQ_INTRO :args (_let_151 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_235 (EQ_RESOLVE (ASSUME :args (_let_150)) (MACRO_SR_EQ_INTRO :args (_let_150 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_236 (EQ_RESOLVE (ASSUME :args (_let_149)) (MACRO_SR_EQ_INTRO :args (_let_149 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_237 (ASSUME :args (_let_148)))) (let ((_let_238 (ASSUME :args (_let_146)))) (let ((_let_239 (EQ_RESOLVE (ASSUME :args (_let_144)) (MACRO_SR_EQ_INTRO :args (_let_144 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_240 (EQ_RESOLVE (ASSUME :args (_let_143)) (MACRO_SR_EQ_INTRO :args (_let_143 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_241 (EQ_RESOLVE (ASSUME :args (_let_142)) (MACRO_SR_EQ_INTRO :args (_let_142 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_242 (EQ_RESOLVE (ASSUME :args (_let_141)) (MACRO_SR_EQ_INTRO :args (_let_141 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_243 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_140)) (MACRO_SR_EQ_INTRO :args (_let_140 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (not (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xx Xy))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_244 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_139)) (MACRO_SR_EQ_INTRO :args (_let_139 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (or (not (@ tptp.nonempty A)) (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_245 (EQ_RESOLVE (ASSUME :args (_let_138)) (MACRO_SR_EQ_INTRO :args (_let_138 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_246 (EQ_RESOLVE (ASSUME :args (_let_137)) (MACRO_SR_EQ_INTRO :args (_let_137 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_247 (EQ_RESOLVE (ASSUME :args (_let_136)) (MACRO_SR_EQ_INTRO :args (_let_136 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_248 (EQ_RESOLVE (ASSUME :args (_let_135)) (MACRO_SR_EQ_INTRO :args (_let_135 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_249 (EQ_RESOLVE (ASSUME :args (_let_134)) (MACRO_SR_EQ_INTRO :args (_let_134 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_250 (ASSUME :args (_let_133)))) (let ((_let_251 (ASSUME :args (_let_131)))) (let ((_let_252 (EQ_RESOLVE (ASSUME :args (_let_129)) (MACRO_SR_EQ_INTRO :args (_let_129 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_253 (EQ_RESOLVE (ASSUME :args (_let_128)) (MACRO_SR_EQ_INTRO :args (_let_128 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_254 (EQ_RESOLVE (ASSUME :args (_let_127)) (MACRO_SR_EQ_INTRO :args (_let_127 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_255 (EQ_RESOLVE (ASSUME :args (_let_126)) (MACRO_SR_EQ_INTRO :args (_let_126 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_256 (EQ_RESOLVE (ASSUME :args (_let_125)) (MACRO_SR_EQ_INTRO :args (_let_125 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_257 (EQ_RESOLVE (ASSUME :args (_let_124)) (MACRO_SR_EQ_INTRO :args (_let_124 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_258 (EQ_RESOLVE (ASSUME :args (_let_123)) (MACRO_SR_EQ_INTRO :args (_let_123 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_259 (EQ_RESOLVE (ASSUME :args (_let_122)) (MACRO_SR_EQ_INTRO :args (_let_122 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_260 (EQ_RESOLVE (ASSUME :args (_let_121)) (MACRO_SR_EQ_INTRO :args (_let_121 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_261 (EQ_RESOLVE (ASSUME :args (_let_120)) (MACRO_SR_EQ_INTRO :args (_let_120 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_262 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_119)) (MACRO_SR_EQ_INTRO :args (_let_119 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4301 $$unsorted)) (or (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (not (@ Xphi BOUND_VARIABLE_4301)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_4301))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_263 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_118)) (MACRO_SR_EQ_INTRO :args (_let_118 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.exuI3 (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4337 $$unsorted)) (or (not (@ Xphi BOUND_VARIABLE_4337)) (not (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (@ Xphi Xx)) (not (@ Xphi Xy)) (= Xx Xy)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_264 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_117)) (MACRO_SR_EQ_INTRO :args (_let_117 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.exuI2 (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4357 $$unsorted)) (or (not (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy BOUND_VARIABLE_4357)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_265 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_116)) (MACRO_SR_EQ_INTRO :args (_let_116 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.inCongP true))))) (let ((_let_266 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_115)) (MACRO_SR_EQ_INTRO :args (_let_115 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.in__Cong true))))) (let ((_let_267 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_114)) (MACRO_SR_EQ_INTRO :args (_let_114 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.exuE3u (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4467 $$unsorted) (BOUND_VARIABLE_4465 $$unsorted)) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ Xphi BOUND_VARIABLE_4465)) (not (@ Xphi BOUND_VARIABLE_4467)) (= BOUND_VARIABLE_4465 BOUND_VARIABLE_4467)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_268 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_113)) (MACRO_SR_EQ_INTRO :args (_let_113 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.exu__Cong (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (or (not (forall ((Xy $$unsorted)) (= (@ Xpsi Xy) (@ Xphi Xy)))) (= (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xpsi Xx))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_269 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_112)) (MACRO_SR_EQ_INTRO :args (_let_112 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.emptyset__Cong true))))) (let ((_let_270 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_111)) (MACRO_SR_EQ_INTRO :args (_let_111 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.setadjoin__Cong true))))) (let ((_let_271 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_110)) (MACRO_SR_EQ_INTRO :args (_let_110 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.powerset__Cong true))))) (let ((_let_272 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_109)) (MACRO_SR_EQ_INTRO :args (_let_109 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.setunion__Cong true))))) (let ((_let_273 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_108)) (MACRO_SR_EQ_INTRO :args (_let_108 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.omega__Cong true))))) (let ((_let_274 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_107)) (MACRO_SR_EQ_INTRO :args (_let_107 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.exuEu (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4577 $$unsorted) (BOUND_VARIABLE_4575 $$unsorted)) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ Xphi BOUND_VARIABLE_4575)) (not (@ Xphi BOUND_VARIABLE_4577)) (= BOUND_VARIABLE_4575 BOUND_VARIABLE_4577)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_275 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_106)) (MACRO_SR_EQ_INTRO :args (_let_106 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.descr__Cong (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (or (not (forall ((Xy $$unsorted)) (= (@ Xpsi Xy) (@ Xphi Xy)))) (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xpsi Xx)))) (= (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xpsi Xx))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_276 (EQ_RESOLVE (ASSUME :args (_let_105)) (MACRO_SR_EQ_INTRO :args (_let_105 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_277 (EQ_RESOLVE (ASSUME :args (_let_104)) (MACRO_SR_EQ_INTRO :args (_let_104 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_278 (EQ_RESOLVE (ASSUME :args (_let_103)) (MACRO_SR_EQ_INTRO :args (_let_103 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_279 (EQ_RESOLVE (ASSUME :args (_let_102)) (MACRO_SR_EQ_INTRO :args (_let_102 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_280 (EQ_RESOLVE (ASSUME :args (_let_101)) (MACRO_SR_EQ_INTRO :args (_let_101 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_281 (ASSUME :args (_let_100)))) (let ((_let_282 (EQ_RESOLVE (ASSUME :args (_let_98)) (MACRO_SR_EQ_INTRO :args (_let_98 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_283 (EQ_RESOLVE (ASSUME :args (_let_97)) (MACRO_SR_EQ_INTRO :args (_let_97 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_284 (EQ_RESOLVE (ASSUME :args (_let_96)) (MACRO_SR_EQ_INTRO :args (_let_96 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_285 (EQ_RESOLVE (ASSUME :args (_let_95)) (MACRO_SR_EQ_INTRO :args (_let_95 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_286 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_94)) (MACRO_SR_EQ_INTRO :args (_let_94 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.notequalI2 true))))) (let ((_let_287 (ASSUME :args (_let_93)))) (let ((_let_288 (EQ_RESOLVE (ASSUME :args (_let_91)) (MACRO_SR_EQ_INTRO :args (_let_91 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_289 (ASSUME :args (_let_90)))) (let ((_let_290 (EQ_RESOLVE (ASSUME :args (_let_88)) (MACRO_SR_EQ_INTRO :args (_let_88 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_291 (EQ_RESOLVE (ASSUME :args (_let_87)) (MACRO_SR_EQ_INTRO :args (_let_87 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_292 (EQ_RESOLVE (ASSUME :args (_let_86)) (MACRO_SR_EQ_INTRO :args (_let_86 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_293 (EQ_RESOLVE (ASSUME :args (_let_85)) (MACRO_SR_EQ_INTRO :args (_let_85 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_294 (EQ_RESOLVE (ASSUME :args (_let_84)) (MACRO_SR_EQ_INTRO :args (_let_84 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_295 (EQ_RESOLVE (ASSUME :args (_let_83)) (MACRO_SR_EQ_INTRO :args (_let_83 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_296 (ASSUME :args (_let_82)))) (let ((_let_297 (EQ_RESOLVE (ASSUME :args (_let_80)) (MACRO_SR_EQ_INTRO :args (_let_80 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_298 (ASSUME :args (_let_79)))) (let ((_let_299 (ASSUME :args (_let_77)))) (let ((_let_300 (EQ_RESOLVE (ASSUME :args (_let_75)) (MACRO_SR_EQ_INTRO :args (_let_75 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_301 (ASSUME :args (_let_74)))) (let ((_let_302 (EQ_RESOLVE (ASSUME :args (_let_72)) (MACRO_SR_EQ_INTRO :args (_let_72 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_303 (EQ_RESOLVE (ASSUME :args (_let_71)) (MACRO_SR_EQ_INTRO :args (_let_71 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_304 (EQ_RESOLVE (ASSUME :args (_let_70)) (MACRO_SR_EQ_INTRO :args (_let_70 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_305 (ASSUME :args (_let_69)))) (let ((_let_306 (ASSUME :args (_let_67)))) (let ((_let_307 (EQ_RESOLVE (ASSUME :args (_let_65)) (MACRO_SR_EQ_INTRO :args (_let_65 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_308 (EQ_RESOLVE (ASSUME :args (_let_64)) (MACRO_SR_EQ_INTRO :args (_let_64 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_309 (EQ_RESOLVE (ASSUME :args (_let_63)) (MACRO_SR_EQ_INTRO :args (_let_63 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_310 (ASSUME :args (_let_62)))) (let ((_let_311 (EQ_RESOLVE (ASSUME :args (_let_60)) (MACRO_SR_EQ_INTRO :args (_let_60 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_312 (EQ_RESOLVE (ASSUME :args (_let_59)) (MACRO_SR_EQ_INTRO :args (_let_59 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_313 (EQ_RESOLVE (ASSUME :args (_let_58)) (MACRO_SR_EQ_INTRO :args (_let_58 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_314 (EQ_RESOLVE (ASSUME :args (_let_57)) (MACRO_SR_EQ_INTRO :args (_let_57 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_315 (ASSUME :args (_let_56)))) (let ((_let_316 (EQ_RESOLVE 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(MACRO_SR_EQ_INTRO :args (_let_44 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_326 (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO :args (_let_43 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_327 (ASSUME :args (_let_42)))) (let ((_let_328 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_329 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_330 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_331 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_332 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_333 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_334 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_335 (ASSUME :args (_let_33)))) (let ((_let_336 (ASSUME :args (_let_31)))) (let ((_let_337 (ASSUME :args (_let_29)))) (let ((_let_338 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_339 (ASSUME :args (_let_26)))) (let ((_let_340 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_341 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_342 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_343 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_344 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_345 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_346 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_347 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_348 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_349 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.ubforcartprodlem3 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_5225 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_5225) B)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) BOUND_VARIABLE_5225)) (@ tptp.powerset (@ tptp.powerset (@ (@ tptp.binunion A) B))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_350 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.cartprodpairin (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_5249 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_5249) B)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) BOUND_VARIABLE_5249)) (@ (@ tptp.cartprod A) B))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_351 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.cartprodmempair1 (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (or (not (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_5281 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_5281) B)) (not (= Xu (@ (@ tptp.kpair Xx) BOUND_VARIABLE_5281))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_352 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.cartprodmempair (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (or (not (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B))) (@ tptp.iskpair Xu)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_353 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_354 (ASSUME :args (_let_11)))) (let ((_let_355 (ASSUME :args (_let_9)))) (let ((_let_356 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_357 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_358 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.singletonprop (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_5382 $$unsorted)) (or (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_5353 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (@ (@ tptp.in BOUND_VARIABLE_5353) A)) (not (@ Xphi BOUND_VARIABLE_5353)) (= Xx BOUND_VARIABLE_5353)))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ (@ tptp.in BOUND_VARIABLE_5382) A)) (not (@ Xphi BOUND_VARIABLE_5382))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_359 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_360 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.ex1E1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (or (not (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_361 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((= tptp.ex1I (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ (@ tptp.in Xy) A)) (not (@ Xphi Xy)) (= Xx Xy)))) (@ (@ tptp.ex1 A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))))) SB_DEFAULT SBA_FIXPOINT))) _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200) :args ((not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_5480 $$unsorted)) (or (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_5451 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (@ (@ tptp.in BOUND_VARIABLE_5451) A)) (not (@ Xphi BOUND_VARIABLE_5451)) (= Xx BOUND_VARIABLE_5451)))) (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (not (@ (@ tptp.in BOUND_VARIABLE_5480) A)) (not (@ Xphi BOUND_VARIABLE_5480))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) SB_DEFAULT SBA_FIXPOINT)) (CONG (CONG (REFL :args ((forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B))))) (= A B))))) (CONG (REFL :args (_let_188)) (CONG (REFL :args ((forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xx Xy) (@ _let_1 A))))))) (CONG (REFL :args ((forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ 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$$unsorted)) (= A (@ (@ tptp.dsetconstr A) (lambda ((BOUND_VARIABLE_18416 $$unsorted)) true)))))) (CONG (REFL :args ((forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (@ _let_1 A))))) (@ (@ tptp.in B) (@ tptp.powerset A)))))) (CONG (REFL :args (_let_147)) (CONG (REFL :args (_let_145)) (CONG (REFL :args ((forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ (@ tptp.in B) (@ tptp.powerset A))) (not (@ _let_1 B)) (@ _let_1 A)))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (not (@ (@ tptp.in B) A)) (@ _let_1 (@ tptp.setunion A))))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ tptp.setunion A))) (not (forall ((B $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (not (@ (@ tptp.in B) A))))))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (@ _let_1 (@ tptp.powerset (@ tptp.setunion A)))))))) (CONG (REFL :args ((forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_6664 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xx Xy)))))) (not (@ Xphi BOUND_VARIABLE_6664)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_6664)))))))) (CONG (REFL :args ((forall ((A $$unsorted)) (or (= tptp.emptyset A) (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))))))) (CONG (REFL :args ((forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (= Xx Xy))))) (CONG (REFL :args ((forall ((Xx $$unsorted) (Xy $$unsorted)) (or (= Xx Xy) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (CONG (REFL :args ((forall ((Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))) (CONG (REFL :args ((forall ((Xx $$unsorted) 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Xx)))) (not (@ (@ tptp.in BOUND_VARIABLE_4101) A)) (@ Xphi BOUND_VARIABLE_4101))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4132 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx))))) (not (@ (@ tptp.in BOUND_VARIABLE_4132) A)) (not (@ Xphi BOUND_VARIABLE_4132)))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4163 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx))))) (not (@ (@ tptp.in BOUND_VARIABLE_4163) A)) (not (@ Xphi BOUND_VARIABLE_4163)))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4193 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ Xphi Xx)))) (not (@ (@ tptp.in BOUND_VARIABLE_4193) A)) (@ Xphi BOUND_VARIABLE_4193))))) (CONG (TRANS (CONG _let_198 _let_197 :args _let_196) (THEORY_PREPROCESS :args ((= (@ _let_155 _let_195) (tptp.in tptp.emptyset _let_195))))) (CONG (TRANS (CONG (REFL :args (tptp.set2prop)) _let_197 :args _let_196) (THEORY_PREPROCESS :args ((= (@ tptp.set2prop _let_195) (tptp.set2prop _let_195))))) (REFL :args ((=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4240 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx))))) (not (@ (@ tptp.in BOUND_VARIABLE_4240) A)) (not (@ Xphi BOUND_VARIABLE_4240)))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4270 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ Xphi Xx)))) (not (@ (@ tptp.in BOUND_VARIABLE_4270) A)) (@ Xphi BOUND_VARIABLE_4270))) (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4301 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy))))))) (not (@ Xphi BOUND_VARIABLE_4301)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_4301)))))) (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4337 $$unsorted)) (or (not (@ Xphi BOUND_VARIABLE_4337)) (not (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (@ Xphi Xx)) (not (@ Xphi Xy)) (= Xx Xy)))) (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy))))))))) (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4357 $$unsorted)) (or (not (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy BOUND_VARIABLE_4357)))) (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy))))))))) (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4467 $$unsorted) (BOUND_VARIABLE_4465 $$unsorted) (BOUND_VARIABLE_6811 $$unsorted)) (or (not (@ Xphi BOUND_VARIABLE_4465)) (not (@ Xphi BOUND_VARIABLE_4467)) (= BOUND_VARIABLE_4465 BOUND_VARIABLE_4467) (not (@ Xphi BOUND_VARIABLE_6811)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_6811)))))) (=> (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (or (not (forall ((Xy $$unsorted)) (= (@ Xpsi Xy) (@ Xphi Xy)))) (= (not (forall ((Xx $$unsorted)) (or (not (@ Xpsi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xpsi Xy)) (= Xx Xy))))))) (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy)))))))))) (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_4577 $$unsorted) (BOUND_VARIABLE_4575 $$unsorted) (BOUND_VARIABLE_6917 $$unsorted)) (or (not (@ Xphi BOUND_VARIABLE_4575)) (not (@ Xphi BOUND_VARIABLE_4577)) (= BOUND_VARIABLE_4575 BOUND_VARIABLE_4577) (not (@ Xphi BOUND_VARIABLE_6917)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_6917)))))) (=> (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool)) (BOUND_VARIABLE_6998 $$unsorted) (BOUND_VARIABLE_6989 $$unsorted)) (or (not (forall ((Xy $$unsorted)) (= (@ Xpsi Xy) (@ Xphi Xy)))) (= (@ 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(or (not (@ _let_1 (@ (@ tptp.binintersect A) B))) (@ _let_1 A)))) (=> _let_61 (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (@ (@ tptp.subset A) B)) (= A (@ (@ tptp.binintersect A) B)))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (= B (@ (@ tptp.binintersect A) B))) (@ (@ tptp.subset B) A))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 (@ (@ tptp.binintersect A) B))) (@ _let_1 B)))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (not (@ _let_1 B)))))) (= tptp.emptyset (@ (@ tptp.binintersect A) B)))) (=> _let_55 (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (@ (@ tptp.subset B) A)) (= B (@ (@ tptp.binintersect A) B)))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (= A (@ (@ tptp.binintersect A) B))) (@ (@ tptp.subset A) B))) (=> _let_51 (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let 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true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 35.76/35.97 ) 35.76/35.97 % SZS output end Proof for 35.76/35.97 % cvc5---1.0.5 exiting 35.76/35.97 % cvc5---1.0.5 exiting 35.76/35.98 EOF