0.10/0.14 % Problem : Vampire---4.8_10086 : TPTP v0.0.0. Released v0.0.0. 0.10/0.15 % Command : do_cvc5 %s %d 0.15/0.35 % Computer : n002.cluster.edu 0.15/0.35 % Model : x86_64 x86_64 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.35 % Memory : 8042.1875MB 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.35 % CPULimit : 1440 0.15/0.35 % WCLimit : 180 0.15/0.35 % DateTime : Mon Jul 3 13:18:07 EDT 2023 0.15/0.36 % CPUTime : 0.22/0.52 %----Proving TH0 0.22/0.53 thf(in_type,type, 0.22/0.53 in: $i > $i > $o ). 0.22/0.53 0.22/0.53 thf(exu_type,type, 0.22/0.53 exu: ( $i > $o ) > $o ). 0.22/0.53 0.22/0.53 thf(exu,definition, 0.22/0.53 ( exu 0.22/0.53 = ( ^ [Xphi: $i > $o] : 0.22/0.53 ? [Xx: $i] : 0.22/0.53 ( ( Xphi @ Xx ) 0.22/0.53 & ! [Xy: $i] : 0.22/0.53 ( ( Xphi @ Xy ) 0.22/0.53 => ( Xx = Xy ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setextAx_type,type, 0.22/0.53 setextAx: $o ). 0.22/0.53 0.22/0.53 thf(setextAx,definition, 0.22/0.53 ( setextAx 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 <=> ( in @ Xx @ B ) ) 0.22/0.53 => ( A = B ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(emptyset_type,type, 0.22/0.53 emptyset: $i ). 0.22/0.53 0.22/0.53 thf(emptysetAx_type,type, 0.22/0.53 emptysetAx: $o ). 0.22/0.53 0.22/0.53 thf(emptysetAx,definition, 0.22/0.53 ( emptysetAx 0.22/0.53 = ( ! [Xx: $i] : 0.22/0.53 ~ ( in @ Xx @ emptyset ) ) ) ). 0.22/0.53 0.22/0.53 thf(setadjoin_type,type, 0.22/0.53 setadjoin: $i > $i > $i ). 0.22/0.53 0.22/0.53 thf(setadjoinAx_type,type, 0.22/0.53 setadjoinAx: $o ). 0.22/0.53 0.22/0.53 thf(setadjoinAx,definition, 0.22/0.53 ( setadjoinAx 0.22/0.53 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.22/0.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.22/0.53 <=> ( ( Xy = Xx ) 0.22/0.53 | ( in @ Xy @ A ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(powerset_type,type, 0.22/0.53 powerset: $i > $i ). 0.22/0.53 0.22/0.53 thf(powersetAx_type,type, 0.22/0.53 powersetAx: $o ). 0.22/0.53 0.22/0.53 thf(powersetAx,definition, 0.22/0.53 ( powersetAx 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ( in @ B @ ( powerset @ A ) ) 0.22/0.53 <=> ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ B ) 0.22/0.53 => ( in @ Xx @ A ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setunion_type,type, 0.22/0.53 setunion: $i > $i ). 0.22/0.53 0.22/0.53 thf(setunionAx_type,type, 0.22/0.53 setunionAx: $o ). 0.22/0.53 0.22/0.53 thf(setunionAx,definition, 0.22/0.53 ( setunionAx 0.22/0.53 = ( ! [A: $i,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ ( setunion @ A ) ) 0.22/0.53 <=> ? [B: $i] : 0.22/0.53 ( ( in @ Xx @ B ) 0.22/0.53 & ( in @ B @ A ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(omega_type,type, 0.22/0.53 omega: $i ). 0.22/0.53 0.22/0.53 thf(omega0Ax_type,type, 0.22/0.53 omega0Ax: $o ). 0.22/0.53 0.22/0.53 thf(omega0Ax,definition, 0.22/0.53 ( omega0Ax 0.22/0.53 = ( in @ emptyset @ omega ) ) ). 0.22/0.53 0.22/0.53 thf(omegaSAx_type,type, 0.22/0.53 omegaSAx: $o ). 0.22/0.53 0.22/0.53 thf(omegaSAx,definition, 0.22/0.53 ( omegaSAx 0.22/0.53 = ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ omega ) 0.22/0.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(omegaIndAx_type,type, 0.22/0.53 omegaIndAx: $o ). 0.22/0.53 0.22/0.53 thf(omegaIndAx,definition, 0.22/0.53 ( omegaIndAx 0.22/0.53 = ( ! [A: $i] : 0.22/0.53 ( ( ( in @ emptyset @ A ) 0.22/0.53 & ! [Xx: $i] : 0.22/0.53 ( ( ( in @ Xx @ omega ) 0.22/0.53 & ( in @ Xx @ A ) ) 0.22/0.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) 0.22/0.53 => ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ omega ) 0.22/0.53 => ( in @ Xx @ A ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(replAx_type,type, 0.22/0.53 replAx: $o ). 0.22/0.53 0.22/0.53 thf(replAx,definition, 0.22/0.53 ( replAx 0.22/0.53 = ( ! [Xphi: $i > $i > $o,A: $i] : 0.22/0.53 ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( exu 0.22/0.53 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) 0.22/0.53 => ? [B: $i] : 0.22/0.53 ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ B ) 0.22/0.53 <=> ? [Xy: $i] : 0.22/0.53 ( ( in @ Xy @ A ) 0.22/0.53 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(foundationAx_type,type, 0.22/0.53 foundationAx: $o ). 0.22/0.53 0.22/0.53 thf(foundationAx,definition, 0.22/0.53 ( foundationAx 0.22/0.53 = ( ! [A: $i] : 0.22/0.53 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.22/0.53 => ? [B: $i] : 0.22/0.53 ( ( in @ B @ A ) 0.22/0.53 & ~ ? [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ B ) 0.22/0.53 & ( in @ Xx @ A ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(wellorderingAx_type,type, 0.22/0.53 wellorderingAx: $o ). 0.22/0.53 0.22/0.53 thf(wellorderingAx,definition, 0.22/0.53 ( wellorderingAx 0.22/0.53 = ( ! [A: $i] : 0.22/0.53 ? [B: $i] : 0.22/0.53 ( ! [C: $i] : 0.22/0.53 ( ( in @ C @ B ) 0.22/0.53 => ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ C ) 0.22/0.53 => ( in @ Xx @ A ) ) ) 0.22/0.53 & ! [Xx: $i,Xy: $i] : 0.22/0.53 ( ( ( in @ Xx @ A ) 0.22/0.53 & ( in @ Xy @ A ) ) 0.22/0.53 => ( ! [C: $i] : 0.22/0.53 ( ( in @ C @ B ) 0.22/0.53 => ( ( in @ Xx @ C ) 0.22/0.53 <=> ( in @ Xy @ C ) ) ) 0.22/0.53 => ( Xx = Xy ) ) ) 0.22/0.53 & ! [C: $i,D: $i] : 0.22/0.53 ( ( ( in @ C @ B ) 0.22/0.53 & ( in @ D @ B ) ) 0.22/0.53 => ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ C ) 0.22/0.53 => ( in @ Xx @ D ) ) 0.22/0.53 | ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ D ) 0.22/0.53 => ( in @ Xx @ C ) ) ) ) 0.22/0.53 & ! [C: $i] : 0.22/0.53 ( ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ C ) 0.22/0.53 => ( in @ Xx @ A ) ) 0.22/0.53 & ? [Xx: $i] : ( in @ Xx @ C ) ) 0.22/0.53 => ? [D: $i,Xx: $i] : 0.22/0.53 ( ( in @ D @ B ) 0.22/0.53 & ( in @ Xx @ C ) 0.22/0.53 & ~ ? [Xy: $i] : 0.22/0.53 ( ( in @ Xy @ D ) 0.22/0.53 & ( in @ Xy @ C ) ) 0.22/0.53 & ! [E: $i] : 0.22/0.53 ( ( in @ E @ B ) 0.22/0.53 => ( ! [Xy: $i] : 0.22/0.53 ( ( in @ Xy @ E ) 0.22/0.53 => ( in @ Xy @ D ) ) 0.22/0.53 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(descr_type,type, 0.22/0.53 descr: ( $i > $o ) > $i ). 0.22/0.53 0.22/0.53 thf(descrp_type,type, 0.22/0.53 descrp: $o ). 0.22/0.53 0.22/0.53 thf(descrp,definition, 0.22/0.53 ( descrp 0.22/0.53 = ( ! [Xphi: $i > $o] : 0.22/0.53 ( ( exu 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.22/0.53 => ( Xphi 0.22/0.53 @ ( descr 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(dsetconstr_type,type, 0.22/0.53 dsetconstr: $i > ( $i > $o ) > $i ). 0.22/0.53 0.22/0.53 thf(dsetconstrI_type,type, 0.22/0.53 dsetconstrI: $o ). 0.22/0.53 0.22/0.53 thf(dsetconstrI,definition, 0.22/0.53 ( dsetconstrI 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( ( Xphi @ Xx ) 0.22/0.53 => ( in @ Xx 0.22/0.53 @ ( dsetconstr @ A 0.22/0.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(dsetconstrEL_type,type, 0.22/0.53 dsetconstrEL: $o ). 0.22/0.53 0.22/0.53 thf(dsetconstrEL,definition, 0.22/0.53 ( dsetconstrEL 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.22/0.53 ( ( in @ Xx 0.22/0.53 @ ( dsetconstr @ A 0.22/0.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.22/0.53 => ( in @ Xx @ A ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(dsetconstrER_type,type, 0.22/0.53 dsetconstrER: $o ). 0.22/0.53 0.22/0.53 thf(dsetconstrER,definition, 0.22/0.53 ( dsetconstrER 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.22/0.53 ( ( in @ Xx 0.22/0.53 @ ( dsetconstr @ A 0.22/0.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.22/0.53 => ( Xphi @ Xx ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(exuE1_type,type, 0.22/0.53 exuE1: $o ). 0.22/0.53 0.22/0.53 thf(exuE1,definition, 0.22/0.53 ( exuE1 0.22/0.53 = ( ! [Xphi: $i > $o] : 0.22/0.53 ( ( exu 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.22/0.53 => ? [Xx: $i] : 0.22/0.53 ( ( Xphi @ Xx ) 0.22/0.53 & ! [Xy: $i] : 0.22/0.53 ( ( Xphi @ Xy ) 0.22/0.53 => ( Xx = Xy ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(prop2set_type,type, 0.22/0.53 prop2set: $o > $i ). 0.22/0.53 0.22/0.53 thf(prop2setE_type,type, 0.22/0.53 prop2setE: $o ). 0.22/0.53 0.22/0.53 thf(prop2setE,definition, 0.22/0.53 ( prop2setE 0.22/0.53 = ( ! [Xphi: $o,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ ( prop2set @ Xphi ) ) 0.22/0.53 => Xphi ) ) ) ). 0.22/0.53 0.22/0.53 thf(emptysetE_type,type, 0.22/0.53 emptysetE: $o ). 0.22/0.53 0.22/0.53 thf(emptysetE,definition, 0.22/0.53 ( emptysetE 0.22/0.53 = ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ emptyset ) 0.22/0.53 => ! [Xphi: $o] : Xphi ) ) ) ). 0.22/0.53 0.22/0.53 thf(emptysetimpfalse_type,type, 0.22/0.53 emptysetimpfalse: $o ). 0.22/0.53 0.22/0.53 thf(emptysetimpfalse,definition, 0.22/0.53 ( emptysetimpfalse 0.22/0.53 = ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ emptyset ) 0.22/0.53 => $false ) ) ) ). 0.22/0.53 0.22/0.53 thf(notinemptyset_type,type, 0.22/0.53 notinemptyset: $o ). 0.22/0.53 0.22/0.53 thf(notinemptyset,definition, 0.22/0.53 ( notinemptyset 0.22/0.53 = ( ! [Xx: $i] : 0.22/0.53 ~ ( in @ Xx @ emptyset ) ) ) ). 0.22/0.53 0.22/0.53 thf(exuE3e_type,type, 0.22/0.53 exuE3e: $o ). 0.22/0.53 0.22/0.53 thf(exuE3e,definition, 0.22/0.53 ( exuE3e 0.22/0.53 = ( ! [Xphi: $i > $o] : 0.22/0.53 ( ( exu 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.22/0.53 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setext_type,type, 0.22/0.53 setext: $o ). 0.22/0.53 0.22/0.53 thf(setext,definition, 0.22/0.53 ( setext 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( in @ Xx @ B ) ) 0.22/0.53 => ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ B ) 0.22/0.53 => ( in @ Xx @ A ) ) 0.22/0.53 => ( A = B ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(emptyI_type,type, 0.22/0.53 emptyI: $o ). 0.22/0.53 0.22/0.53 thf(emptyI,definition, 0.22/0.53 ( emptyI 0.22/0.53 = ( ! [A: $i] : 0.22/0.53 ( ! [Xx: $i] : 0.22/0.53 ~ ( in @ Xx @ A ) 0.22/0.53 => ( A = emptyset ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(noeltsimpempty_type,type, 0.22/0.53 noeltsimpempty: $o ). 0.22/0.53 0.22/0.53 thf(noeltsimpempty,definition, 0.22/0.53 ( noeltsimpempty 0.22/0.53 = ( ! [A: $i] : 0.22/0.53 ( ! [Xx: $i] : 0.22/0.53 ~ ( in @ Xx @ A ) 0.22/0.53 => ( A = emptyset ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setbeta_type,type, 0.22/0.53 setbeta: $o ). 0.22/0.53 0.22/0.53 thf(setbeta,definition, 0.22/0.53 ( setbeta 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( ( in @ Xx 0.22/0.53 @ ( dsetconstr @ A 0.22/0.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.22/0.53 <=> ( Xphi @ Xx ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(nonempty_type,type, 0.22/0.53 nonempty: $i > $o ). 0.22/0.53 0.22/0.53 thf(nonempty,definition, 0.22/0.53 ( nonempty 0.22/0.53 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ). 0.22/0.53 0.22/0.53 thf(nonemptyE1_type,type, 0.22/0.53 nonemptyE1: $o ). 0.22/0.53 0.22/0.53 thf(nonemptyE1,definition, 0.22/0.53 ( nonemptyE1 0.22/0.53 = ( ! [A: $i] : 0.22/0.53 ( ( nonempty @ A ) 0.22/0.53 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(nonemptyI_type,type, 0.22/0.53 nonemptyI: $o ). 0.22/0.53 0.22/0.53 thf(nonemptyI,definition, 0.22/0.53 ( nonemptyI 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( ( Xphi @ Xx ) 0.22/0.53 => ( nonempty 0.22/0.53 @ ( dsetconstr @ A 0.22/0.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(nonemptyI1_type,type, 0.22/0.53 nonemptyI1: $o ). 0.22/0.53 0.22/0.53 thf(nonemptyI1,definition, 0.22/0.53 ( nonemptyI1 0.22/0.53 = ( ! [A: $i] : 0.22/0.53 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.22/0.53 => ( nonempty @ A ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setadjoinIL_type,type, 0.22/0.53 setadjoinIL: $o ). 0.22/0.53 0.22/0.53 thf(setadjoinIL,definition, 0.22/0.53 ( setadjoinIL 0.22/0.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(emptyinunitempty_type,type, 0.22/0.53 emptyinunitempty: $o ). 0.22/0.53 0.22/0.53 thf(emptyinunitempty,definition, 0.22/0.53 ( emptyinunitempty 0.22/0.53 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ). 0.22/0.53 0.22/0.53 thf(setadjoinIR_type,type, 0.22/0.53 setadjoinIR: $o ). 0.22/0.53 0.22/0.53 thf(setadjoinIR,definition, 0.22/0.53 ( setadjoinIR 0.22/0.53 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.22/0.53 ( ( in @ Xy @ A ) 0.22/0.53 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setadjoinE_type,type, 0.22/0.53 setadjoinE: $o ). 0.22/0.53 0.22/0.53 thf(setadjoinE,definition, 0.22/0.53 ( setadjoinE 0.22/0.53 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.22/0.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.22/0.53 => ! [Xphi: $o] : 0.22/0.53 ( ( ( Xy = Xx ) 0.22/0.53 => Xphi ) 0.22/0.53 => ( ( ( in @ Xy @ A ) 0.22/0.53 => Xphi ) 0.22/0.53 => Xphi ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setadjoinOr_type,type, 0.22/0.53 setadjoinOr: $o ). 0.22/0.53 0.22/0.53 thf(setadjoinOr,definition, 0.22/0.53 ( setadjoinOr 0.22/0.53 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.22/0.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.22/0.53 => ( ( Xy = Xx ) 0.22/0.53 | ( in @ Xy @ A ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setoftrueEq_type,type, 0.22/0.53 setoftrueEq: $o ). 0.22/0.53 0.22/0.53 thf(setoftrueEq,definition, 0.22/0.53 ( setoftrueEq 0.22/0.53 = ( ! [A: $i] : 0.22/0.53 ( ( dsetconstr @ A 0.22/0.53 @ ^ [Xx: $i] : $true ) 0.22/0.53 = A ) ) ) ). 0.22/0.53 0.22/0.53 thf(powersetI_type,type, 0.22/0.53 powersetI: $o ). 0.22/0.53 0.22/0.53 thf(powersetI,definition, 0.22/0.53 ( powersetI 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ B ) 0.22/0.53 => ( in @ Xx @ A ) ) 0.22/0.53 => ( in @ B @ ( powerset @ A ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(emptyinPowerset_type,type, 0.22/0.53 emptyinPowerset: $o ). 0.22/0.53 0.22/0.53 thf(emptyinPowerset,definition, 0.22/0.53 ( emptyinPowerset 0.22/0.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(emptyInPowerset_type,type, 0.22/0.53 emptyInPowerset: $o ). 0.22/0.53 0.22/0.53 thf(emptyInPowerset,definition, 0.22/0.53 ( emptyInPowerset 0.22/0.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(powersetE_type,type, 0.22/0.53 powersetE: $o ). 0.22/0.53 0.22/0.53 thf(powersetE,definition, 0.22/0.53 ( powersetE 0.22/0.53 = ( ! [A: $i,B: $i,Xx: $i] : 0.22/0.53 ( ( in @ B @ ( powerset @ A ) ) 0.22/0.53 => ( ( in @ Xx @ B ) 0.22/0.53 => ( in @ Xx @ A ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setunionI_type,type, 0.22/0.53 setunionI: $o ). 0.22/0.53 0.22/0.53 thf(setunionI,definition, 0.22/0.53 ( setunionI 0.22/0.53 = ( ! [A: $i,Xx: $i,B: $i] : 0.22/0.53 ( ( in @ Xx @ B ) 0.22/0.53 => ( ( in @ B @ A ) 0.22/0.53 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setunionE_type,type, 0.22/0.53 setunionE: $o ). 0.22/0.53 0.22/0.53 thf(setunionE,definition, 0.22/0.53 ( setunionE 0.22/0.53 = ( ! [A: $i,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ ( setunion @ A ) ) 0.22/0.53 => ! [Xphi: $o] : 0.22/0.53 ( ! [B: $i] : 0.22/0.53 ( ( in @ Xx @ B ) 0.22/0.53 => ( ( in @ B @ A ) 0.22/0.53 => Xphi ) ) 0.22/0.53 => Xphi ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(subPowSU_type,type, 0.22/0.53 subPowSU: $o ). 0.22/0.53 0.22/0.53 thf(subPowSU,definition, 0.22/0.53 ( subPowSU 0.22/0.53 = ( ! [A: $i,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(exuE2_type,type, 0.22/0.53 exuE2: $o ). 0.22/0.53 0.22/0.53 thf(exuE2,definition, 0.22/0.53 ( exuE2 0.22/0.53 = ( ! [Xphi: $i > $o] : 0.22/0.53 ( ( exu 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.22/0.53 => ? [Xx: $i] : 0.22/0.53 ! [Xy: $i] : 0.22/0.53 ( ( Xphi @ Xy ) 0.22/0.53 <=> ( Xy = Xx ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(nonemptyImpWitness_type,type, 0.22/0.53 nonemptyImpWitness: $o ). 0.22/0.53 0.22/0.53 thf(nonemptyImpWitness,definition, 0.22/0.53 ( nonemptyImpWitness 0.22/0.53 = ( ! [A: $i] : 0.22/0.53 ( ( nonempty @ A ) 0.22/0.53 => ? [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 & $true ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(uniqinunit_type,type, 0.22/0.53 uniqinunit: $o ). 0.22/0.53 0.22/0.53 thf(uniqinunit,definition, 0.22/0.53 ( uniqinunit 0.22/0.53 = ( ! [Xx: $i,Xy: $i] : 0.22/0.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.22/0.53 => ( Xx = Xy ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(notinsingleton_type,type, 0.22/0.53 notinsingleton: $o ). 0.22/0.53 0.22/0.53 thf(notinsingleton,definition, 0.22/0.53 ( notinsingleton 0.22/0.53 = ( ! [Xx: $i,Xy: $i] : 0.22/0.53 ( ( Xx != Xy ) 0.22/0.53 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(eqinunit_type,type, 0.22/0.53 eqinunit: $o ). 0.22/0.53 0.22/0.53 thf(eqinunit,definition, 0.22/0.53 ( eqinunit 0.22/0.53 = ( ! [Xx: $i,Xy: $i] : 0.22/0.53 ( ( Xx = Xy ) 0.22/0.53 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(singletonsswitch_type,type, 0.22/0.53 singletonsswitch: $o ). 0.22/0.53 0.22/0.53 thf(singletonsswitch,definition, 0.22/0.53 ( singletonsswitch 0.22/0.53 = ( ! [Xx: $i,Xy: $i] : 0.22/0.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.22/0.53 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(upairsetE_type,type, 0.22/0.53 upairsetE: $o ). 0.22/0.53 0.22/0.53 thf(upairsetE,definition, 0.22/0.53 ( upairsetE 0.22/0.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] : 0.22/0.53 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) 0.22/0.53 => ( ( Xz = Xx ) 0.22/0.53 | ( Xz = Xy ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(upairsetIL_type,type, 0.22/0.53 upairsetIL: $o ). 0.22/0.53 0.22/0.53 thf(upairsetIL,definition, 0.22/0.53 ( upairsetIL 0.22/0.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(upairsetIR_type,type, 0.22/0.53 upairsetIR: $o ). 0.22/0.53 0.22/0.53 thf(upairsetIR,definition, 0.22/0.53 ( upairsetIR 0.22/0.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(emptyE1_type,type, 0.22/0.53 emptyE1: $o ). 0.22/0.53 0.22/0.53 thf(emptyE1,definition, 0.22/0.53 ( emptyE1 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o] : 0.22/0.53 ( ? [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 & ( Xphi @ Xx ) ) 0.22/0.53 => ( ( ( dsetconstr @ A 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.22/0.53 = emptyset ) 0.22/0.53 => $false ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(vacuousDall_type,type, 0.22/0.53 vacuousDall: $o ). 0.22/0.53 0.22/0.53 thf(vacuousDall,definition, 0.22/0.53 ( vacuousDall 0.22/0.53 = ( ! [Xphi: $i > $o,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ emptyset ) 0.22/0.53 => ( Xphi @ Xx ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(quantDeMorgan1_type,type, 0.22/0.53 quantDeMorgan1: $o ). 0.22/0.53 0.22/0.53 thf(quantDeMorgan1,definition, 0.22/0.53 ( quantDeMorgan1 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o] : 0.22/0.53 ( ~ ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( Xphi @ Xx ) ) 0.22/0.53 => ? [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 & ~ ( Xphi @ Xx ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(quantDeMorgan2_type,type, 0.22/0.53 quantDeMorgan2: $o ). 0.22/0.53 0.22/0.53 thf(quantDeMorgan2,definition, 0.22/0.53 ( quantDeMorgan2 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o] : 0.22/0.53 ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ~ ( Xphi @ Xx ) ) 0.22/0.53 => ~ ? [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 & ( Xphi @ Xx ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(quantDeMorgan3_type,type, 0.22/0.53 quantDeMorgan3: $o ). 0.22/0.53 0.22/0.53 thf(quantDeMorgan3,definition, 0.22/0.53 ( quantDeMorgan3 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o] : 0.22/0.53 ( ~ ? [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 & ( Xphi @ Xx ) ) 0.22/0.53 => ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ~ ( Xphi @ Xx ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(quantDeMorgan4_type,type, 0.22/0.53 quantDeMorgan4: $o ). 0.22/0.53 0.22/0.53 thf(quantDeMorgan4,definition, 0.22/0.53 ( quantDeMorgan4 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o] : 0.22/0.53 ( ? [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 & ~ ( Xphi @ Xx ) ) 0.22/0.53 => ~ ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( Xphi @ Xx ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(prop2setI_type,type, 0.22/0.53 prop2setI: $o ). 0.22/0.53 0.22/0.53 thf(prop2setI,definition, 0.22/0.53 ( prop2setI 0.22/0.53 = ( ! [Xphi: $o] : 0.22/0.53 ( Xphi 0.22/0.53 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(set2prop_type,type, 0.22/0.53 set2prop: $i > $o ). 0.22/0.53 0.22/0.53 thf(prop2set2propI_type,type, 0.22/0.53 prop2set2propI: $o ). 0.22/0.53 0.22/0.53 thf(prop2set2propI,definition, 0.22/0.53 ( prop2set2propI 0.22/0.53 = ( ! [Xphi: $o] : 0.22/0.53 ( Xphi 0.22/0.53 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(notdexE_type,type, 0.22/0.53 notdexE: $o ). 0.22/0.53 0.22/0.53 thf(notdexE,definition, 0.22/0.53 ( notdexE 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o] : 0.22/0.53 ( ~ ? [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 & ( Xphi @ Xx ) ) 0.22/0.53 => ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ~ ( Xphi @ Xx ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(notdallE_type,type, 0.22/0.53 notdallE: $o ). 0.22/0.53 0.22/0.53 thf(notdallE,definition, 0.22/0.53 ( notdallE 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o] : 0.22/0.53 ( ~ ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( Xphi @ Xx ) ) 0.22/0.53 => ? [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 & ~ ( Xphi @ Xx ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(exuI1_type,type, 0.22/0.53 exuI1: $o ). 0.22/0.53 0.22/0.53 thf(exuI1,definition, 0.22/0.53 ( exuI1 0.22/0.53 = ( ! [Xphi: $i > $o] : 0.22/0.53 ( ? [Xx: $i] : 0.22/0.53 ( ( Xphi @ Xx ) 0.22/0.53 & ! [Xy: $i] : 0.22/0.53 ( ( Xphi @ Xy ) 0.22/0.53 => ( Xx = Xy ) ) ) 0.22/0.53 => ( exu 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(exuI3_type,type, 0.22/0.53 exuI3: $o ). 0.22/0.53 0.22/0.53 thf(exuI3,definition, 0.22/0.53 ( exuI3 0.22/0.53 = ( ! [Xphi: $i > $o] : 0.22/0.53 ( ? [Xx: $i] : ( Xphi @ Xx ) 0.22/0.53 => ( ! [Xx: $i,Xy: $i] : 0.22/0.53 ( ( Xphi @ Xx ) 0.22/0.53 => ( ( Xphi @ Xy ) 0.22/0.53 => ( Xx = Xy ) ) ) 0.22/0.53 => ( exu 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(exuI2_type,type, 0.22/0.53 exuI2: $o ). 0.22/0.53 0.22/0.53 thf(exuI2,definition, 0.22/0.53 ( exuI2 0.22/0.53 = ( ! [Xphi: $i > $o] : 0.22/0.53 ( ? [Xx: $i] : 0.22/0.53 ! [Xy: $i] : 0.22/0.53 ( ( Xphi @ Xy ) 0.22/0.53 <=> ( Xy = Xx ) ) 0.22/0.53 => ( exu 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(inCongP_type,type, 0.22/0.53 inCongP: $o ). 0.22/0.53 0.22/0.53 thf(inCongP,definition, 0.22/0.53 ( inCongP 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ( A = B ) 0.22/0.53 => ! [Xx: $i,Xy: $i] : 0.22/0.53 ( ( Xx = Xy ) 0.22/0.53 => ( ( in @ Xx @ A ) 0.22/0.53 => ( in @ Xy @ B ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(in__Cong_type,type, 0.22/0.53 in__Cong: $o ). 0.22/0.53 0.22/0.53 thf(in__Cong,definition, 0.22/0.53 ( in__Cong 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ( A = B ) 0.22/0.53 => ! [Xx: $i,Xy: $i] : 0.22/0.53 ( ( Xx = Xy ) 0.22/0.53 => ( ( in @ Xx @ A ) 0.22/0.53 <=> ( in @ Xy @ B ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(exuE3u_type,type, 0.22/0.53 exuE3u: $o ). 0.22/0.53 0.22/0.53 thf(exuE3u,definition, 0.22/0.53 ( exuE3u 0.22/0.53 = ( ! [Xphi: $i > $o] : 0.22/0.53 ( ( exu 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.22/0.53 => ! [Xx: $i,Xy: $i] : 0.22/0.53 ( ( Xphi @ Xx ) 0.22/0.53 => ( ( Xphi @ Xy ) 0.22/0.53 => ( Xx = Xy ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(exu__Cong_type,type, 0.22/0.53 exu__Cong: $o ). 0.22/0.53 0.22/0.53 thf(exu__Cong,definition, 0.22/0.53 ( exu__Cong 0.22/0.53 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] : 0.22/0.53 ( ! [Xx: $i,Xy: $i] : 0.22/0.53 ( ( Xx = Xy ) 0.22/0.53 => ( ( Xphi @ Xx ) 0.22/0.53 <=> ( Xpsi @ Xy ) ) ) 0.22/0.53 => ( ( exu 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.22/0.53 <=> ( exu 0.22/0.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(emptyset__Cong_type,type, 0.22/0.53 emptyset__Cong: $o ). 0.22/0.53 0.22/0.53 thf(emptyset__Cong,definition, 0.22/0.53 ( emptyset__Cong 0.22/0.53 = ( emptyset = emptyset ) ) ). 0.22/0.53 0.22/0.53 thf(setadjoin__Cong_type,type, 0.22/0.53 setadjoin__Cong: $o ). 0.22/0.53 0.22/0.53 thf(setadjoin__Cong,definition, 0.22/0.53 ( setadjoin__Cong 0.22/0.53 = ( ! [Xx: $i,Xy: $i] : 0.22/0.53 ( ( Xx = Xy ) 0.22/0.53 => ! [Xz: $i,Xu: $i] : 0.22/0.53 ( ( Xz = Xu ) 0.22/0.53 => ( ( setadjoin @ Xx @ Xz ) 0.22/0.53 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(powerset__Cong_type,type, 0.22/0.53 powerset__Cong: $o ). 0.22/0.53 0.22/0.53 thf(powerset__Cong,definition, 0.22/0.53 ( powerset__Cong 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ( A = B ) 0.22/0.53 => ( ( powerset @ A ) 0.22/0.53 = ( powerset @ B ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setunion__Cong_type,type, 0.22/0.53 setunion__Cong: $o ). 0.22/0.53 0.22/0.53 thf(setunion__Cong,definition, 0.22/0.53 ( setunion__Cong 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ( A = B ) 0.22/0.53 => ( ( setunion @ A ) 0.22/0.53 = ( setunion @ B ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(omega__Cong_type,type, 0.22/0.53 omega__Cong: $o ). 0.22/0.53 0.22/0.53 thf(omega__Cong,definition, 0.22/0.53 ( omega__Cong 0.22/0.53 = ( omega = omega ) ) ). 0.22/0.53 0.22/0.53 thf(exuEu_type,type, 0.22/0.53 exuEu: $o ). 0.22/0.53 0.22/0.53 thf(exuEu,definition, 0.22/0.53 ( exuEu 0.22/0.53 = ( ! [Xphi: $i > $o] : 0.22/0.53 ( ( exu 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.22/0.53 => ! [Xx: $i,Xy: $i] : 0.22/0.53 ( ( Xphi @ Xx ) 0.22/0.53 => ( ( Xphi @ Xy ) 0.22/0.53 => ( Xx = Xy ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(descr__Cong_type,type, 0.22/0.53 descr__Cong: $o ). 0.22/0.53 0.22/0.53 thf(descr__Cong,definition, 0.22/0.53 ( descr__Cong 0.22/0.53 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] : 0.22/0.53 ( ! [Xx: $i,Xy: $i] : 0.22/0.53 ( ( Xx = Xy ) 0.22/0.53 => ( ( Xphi @ Xx ) 0.22/0.53 <=> ( Xpsi @ Xy ) ) ) 0.22/0.53 => ( ( exu 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.22/0.53 => ( ( exu 0.22/0.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) 0.22/0.53 => ( ( descr 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.22/0.53 = ( descr 0.22/0.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(dsetconstr__Cong_type,type, 0.22/0.53 dsetconstr__Cong: $o ). 0.22/0.53 0.22/0.53 thf(dsetconstr__Cong,definition, 0.22/0.53 ( dsetconstr__Cong 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ( A = B ) 0.22/0.53 => ! [Xphi: $i > $o,Xpsi: $i > $o] : 0.22/0.53 ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ! [Xy: $i] : 0.22/0.53 ( ( in @ Xy @ B ) 0.22/0.53 => ( ( Xx = Xy ) 0.22/0.53 => ( ( Xphi @ Xx ) 0.22/0.53 <=> ( Xpsi @ Xy ) ) ) ) ) 0.22/0.53 => ( ( dsetconstr @ A 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.22/0.53 = ( dsetconstr @ B 0.22/0.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(subset_type,type, 0.22/0.53 subset: $i > $i > $o ). 0.22/0.53 0.22/0.53 thf(disjoint_type,type, 0.22/0.53 disjoint: $i > $i > $o ). 0.22/0.53 0.22/0.53 thf(setsmeet_type,type, 0.22/0.53 setsmeet: $i > $i > $o ). 0.22/0.53 0.22/0.53 thf(subsetI1_type,type, 0.22/0.53 subsetI1: $o ). 0.22/0.53 0.22/0.53 thf(subsetI1,definition, 0.22/0.53 ( subsetI1 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( in @ Xx @ B ) ) 0.22/0.53 => ( subset @ A @ B ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(eqimpsubset2_type,type, 0.22/0.53 eqimpsubset2: $o ). 0.22/0.53 0.22/0.53 thf(eqimpsubset2,definition, 0.22/0.53 ( eqimpsubset2 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ( A = B ) 0.22/0.53 => ( subset @ B @ A ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(eqimpsubset1_type,type, 0.22/0.53 eqimpsubset1: $o ). 0.22/0.53 0.22/0.53 thf(eqimpsubset1,definition, 0.22/0.53 ( eqimpsubset1 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ( A = B ) 0.22/0.53 => ( subset @ A @ B ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(subsetI2_type,type, 0.22/0.53 subsetI2: $o ). 0.22/0.53 0.22/0.53 thf(subsetI2,definition, 0.22/0.53 ( subsetI2 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ! [Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( in @ Xx @ B ) ) 0.22/0.53 => ( subset @ A @ B ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(emptysetsubset_type,type, 0.22/0.53 emptysetsubset: $o ). 0.22/0.53 0.22/0.53 thf(emptysetsubset,definition, 0.22/0.53 ( emptysetsubset 0.22/0.53 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ). 0.22/0.53 0.22/0.53 thf(subsetE_type,type, 0.22/0.53 subsetE: $o ). 0.22/0.53 0.22/0.53 thf(subsetE,definition, 0.22/0.53 ( subsetE 0.22/0.53 = ( ! [A: $i,B: $i,Xx: $i] : 0.22/0.53 ( ( subset @ A @ B ) 0.22/0.53 => ( ( in @ Xx @ A ) 0.22/0.53 => ( in @ Xx @ B ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(subsetE2_type,type, 0.22/0.53 subsetE2: $o ). 0.22/0.53 0.22/0.53 thf(subsetE2,definition, 0.22/0.53 ( subsetE2 0.22/0.53 = ( ! [A: $i,B: $i,Xx: $i] : 0.22/0.53 ( ( subset @ A @ B ) 0.22/0.53 => ( ~ ( in @ Xx @ B ) 0.22/0.53 => ~ ( in @ Xx @ A ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(notsubsetI_type,type, 0.22/0.53 notsubsetI: $o ). 0.22/0.53 0.22/0.53 thf(notsubsetI,definition, 0.22/0.53 ( notsubsetI 0.22/0.53 = ( ! [A: $i,B: $i,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( ~ ( in @ Xx @ B ) 0.22/0.53 => ~ ( subset @ A @ B ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(notequalI1_type,type, 0.22/0.53 notequalI1: $o ). 0.22/0.53 0.22/0.53 thf(notequalI1,definition, 0.22/0.53 ( notequalI1 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ~ ( subset @ A @ B ) 0.22/0.53 => ( A != B ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(notequalI2_type,type, 0.22/0.53 notequalI2: $o ). 0.22/0.53 0.22/0.53 thf(notequalI2,definition, 0.22/0.53 ( notequalI2 0.22/0.53 = ( ! [A: $i,B: $i,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( ~ ( in @ Xx @ B ) 0.22/0.53 => ( A != B ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(subsetRefl_type,type, 0.22/0.53 subsetRefl: $o ). 0.22/0.53 0.22/0.53 thf(subsetRefl,definition, 0.22/0.53 ( subsetRefl 0.22/0.53 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ). 0.22/0.53 0.22/0.53 thf(subsetTrans_type,type, 0.22/0.53 subsetTrans: $o ). 0.22/0.53 0.22/0.53 thf(subsetTrans,definition, 0.22/0.53 ( subsetTrans 0.22/0.53 = ( ! [A: $i,B: $i,C: $i] : 0.22/0.53 ( ( subset @ A @ B ) 0.22/0.53 => ( ( subset @ B @ C ) 0.22/0.53 => ( subset @ A @ C ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setadjoinSub_type,type, 0.22/0.53 setadjoinSub: $o ). 0.22/0.53 0.22/0.53 thf(setadjoinSub,definition, 0.22/0.53 ( setadjoinSub 0.22/0.53 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setadjoinSub2_type,type, 0.22/0.53 setadjoinSub2: $o ). 0.22/0.53 0.22/0.53 thf(setadjoinSub2,definition, 0.22/0.53 ( setadjoinSub2 0.22/0.53 = ( ! [A: $i,Xx: $i,B: $i] : 0.22/0.53 ( ( subset @ A @ B ) 0.22/0.53 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(subset2powerset_type,type, 0.22/0.53 subset2powerset: $o ). 0.22/0.53 0.22/0.53 thf(subset2powerset,definition, 0.22/0.53 ( subset2powerset 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ( subset @ A @ B ) 0.22/0.53 => ( in @ A @ ( powerset @ B ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(setextsub_type,type, 0.22/0.53 setextsub: $o ). 0.22/0.53 0.22/0.53 thf(setextsub,definition, 0.22/0.53 ( setextsub 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ( subset @ A @ B ) 0.22/0.53 => ( ( subset @ B @ A ) 0.22/0.53 => ( A = B ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(subsetemptysetimpeq_type,type, 0.22/0.53 subsetemptysetimpeq: $o ). 0.22/0.53 0.22/0.53 thf(subsetemptysetimpeq,definition, 0.22/0.53 ( subsetemptysetimpeq 0.22/0.53 = ( ! [A: $i] : 0.22/0.53 ( ( subset @ A @ emptyset ) 0.22/0.53 => ( A = emptyset ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(powersetI1_type,type, 0.22/0.53 powersetI1: $o ). 0.22/0.53 0.22/0.53 thf(powersetI1,definition, 0.22/0.53 ( powersetI1 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ( subset @ B @ A ) 0.22/0.53 => ( in @ B @ ( powerset @ A ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(powersetE1_type,type, 0.22/0.53 powersetE1: $o ). 0.22/0.53 0.22/0.53 thf(powersetE1,definition, 0.22/0.53 ( powersetE1 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ( in @ B @ ( powerset @ A ) ) 0.22/0.53 => ( subset @ B @ A ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(inPowerset_type,type, 0.22/0.53 inPowerset: $o ). 0.22/0.53 0.22/0.53 thf(inPowerset,definition, 0.22/0.53 ( inPowerset 0.22/0.53 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(powersetsubset_type,type, 0.22/0.53 powersetsubset: $o ). 0.22/0.53 0.22/0.53 thf(powersetsubset,definition, 0.22/0.53 ( powersetsubset 0.22/0.53 = ( ! [A: $i,B: $i] : 0.22/0.53 ( ( subset @ A @ B ) 0.22/0.53 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(sepInPowerset_type,type, 0.22/0.53 sepInPowerset: $o ). 0.22/0.53 0.22/0.53 thf(sepInPowerset,definition, 0.22/0.53 ( sepInPowerset 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o] : 0.22/0.53 ( in 0.22/0.53 @ ( dsetconstr @ A 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.22/0.53 @ ( powerset @ A ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(sepSubset_type,type, 0.22/0.53 sepSubset: $o ). 0.22/0.53 0.22/0.53 thf(sepSubset,definition, 0.22/0.53 ( sepSubset 0.22/0.53 = ( ! [A: $i,Xphi: $i > $o] : 0.22/0.53 ( subset 0.22/0.53 @ ( dsetconstr @ A 0.22/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.22/0.53 @ A ) ) ) ). 0.22/0.53 0.22/0.53 thf(binunion_type,type, 0.22/0.53 binunion: $i > $i > $i ). 0.22/0.53 0.22/0.53 thf(binunionIL_type,type, 0.22/0.53 binunionIL: $o ). 0.22/0.53 0.22/0.53 thf(binunionIL,definition, 0.22/0.53 ( binunionIL 0.22/0.53 = ( ! [A: $i,B: $i,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(upairset2IR_type,type, 0.22/0.53 upairset2IR: $o ). 0.22/0.53 0.22/0.53 thf(upairset2IR,definition, 0.22/0.53 ( upairset2IR 0.22/0.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(binunionIR_type,type, 0.22/0.53 binunionIR: $o ). 0.22/0.53 0.22/0.53 thf(binunionIR,definition, 0.22/0.53 ( binunionIR 0.22/0.53 = ( ! [A: $i,B: $i,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ B ) 0.22/0.53 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(binunionEcases_type,type, 0.22/0.53 binunionEcases: $o ). 0.22/0.53 0.22/0.53 thf(binunionEcases,definition, 0.22/0.53 ( binunionEcases 0.22/0.53 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] : 0.22/0.53 ( ( in @ Xx @ ( binunion @ A @ B ) ) 0.22/0.53 => ( ( ( in @ Xx @ A ) 0.22/0.53 => Xphi ) 0.22/0.53 => ( ( ( in @ Xx @ B ) 0.22/0.53 => Xphi ) 0.22/0.53 => Xphi ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(binunionE_type,type, 0.22/0.53 binunionE: $o ). 0.22/0.53 0.22/0.53 thf(binunionE,definition, 0.22/0.53 ( binunionE 0.22/0.53 = ( ! [A: $i,B: $i,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ ( binunion @ A @ B ) ) 0.22/0.53 => ( ( in @ Xx @ A ) 0.22/0.53 | ( in @ Xx @ B ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(binunionLsub_type,type, 0.22/0.53 binunionLsub: $o ). 0.22/0.53 0.22/0.53 thf(binunionLsub,definition, 0.22/0.53 ( binunionLsub 0.22/0.53 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(binunionRsub_type,type, 0.22/0.53 binunionRsub: $o ). 0.22/0.53 0.22/0.53 thf(binunionRsub,definition, 0.22/0.53 ( binunionRsub 0.22/0.53 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(binintersect_type,type, 0.22/0.53 binintersect: $i > $i > $i ). 0.22/0.53 0.22/0.53 thf(binintersect,definition, 0.22/0.53 ( binintersect 0.22/0.53 = ( ^ [A: $i,B: $i] : 0.22/0.53 ( dsetconstr @ A 0.22/0.53 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(binintersectI_type,type, 0.22/0.53 binintersectI: $o ). 0.22/0.53 0.22/0.53 thf(binintersectI,definition, 0.22/0.53 ( binintersectI 0.22/0.53 = ( ! [A: $i,B: $i,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ A ) 0.22/0.53 => ( ( in @ Xx @ B ) 0.22/0.53 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(binintersectSubset5_type,type, 0.22/0.53 binintersectSubset5: $o ). 0.22/0.53 0.22/0.53 thf(binintersectSubset5,definition, 0.22/0.53 ( binintersectSubset5 0.22/0.53 = ( ! [A: $i,B: $i,C: $i] : 0.22/0.53 ( ( subset @ C @ A ) 0.22/0.53 => ( ( subset @ C @ B ) 0.22/0.53 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(binintersectEL_type,type, 0.22/0.53 binintersectEL: $o ). 0.22/0.53 0.22/0.53 thf(binintersectEL,definition, 0.22/0.53 ( binintersectEL 0.22/0.53 = ( ! [A: $i,B: $i,Xx: $i] : 0.22/0.53 ( ( in @ Xx @ ( binintersect @ A @ B ) ) 0.22/0.53 => ( in @ Xx @ A ) ) ) ) ). 0.22/0.53 0.22/0.53 thf(binintersectLsub,conjecture, 0.22/0.53 ( ( ( setadjoinAx 0.22/0.53 => ( powersetAx 0.22/0.53 => ( setunionAx 0.22/0.53 => ( omega0Ax 0.22/0.53 => ( ( omegaIndAx 0.22/0.53 => ( ( foundationAx 0.22/0.53 => ( ( ( dsetconstrI 0.22/0.53 => ( ( dsetconstrER 0.22/0.53 => ( exuE1 0.22/0.53 => ( ( emptysetE 0.22/0.53 => ( ( ( ( setext 0.22/0.53 => ( emptyI 0.22/0.53 => ( noeltsimpempty 0.22/0.53 => ( setbeta 0.22/0.53 => ( nonemptyE1 0.22/0.53 => ( ( ( setadjoinIL 0.22/0.53 => ( emptyinunitempty 0.22/0.53 => ( setadjoinIR 0.22/0.53 => ( ( ( ( powersetI 0.22/0.53 => ( emptyinPowerset 0.22/0.53 => ( ( ( ( setunionE 0.22/0.53 => ( subPowSU 0.22/0.53 => ( ( nonemptyImpWitness 0.22/0.53 => ( uniqinunit 0.22/0.53 => ( notinsingleton 0.22/0.53 => ( eqinunit 0.22/0.53 => ( ( upairsetE 0.22/0.53 => ( upairsetIL 0.22/0.53 => ( upairsetIR 0.22/0.53 => ( ( ( quantDeMorgan1 0.22/0.53 => ( quantDeMorgan2 0.22/0.53 => ( ( quantDeMorgan4 0.22/0.53 => ( prop2setI 0.22/0.53 => ( ( ( notdallE 0.22/0.53 => ( ( ( ( inCongP 0.22/0.53 => ( in__Cong 0.22/0.53 => ( ( ( ( setadjoin__Cong 0.22/0.53 => ( ( ( omega__Cong 0.22/0.53 => ( ( descr__Cong 0.22/0.53 => ( ( ( eqimpsubset2 0.22/0.53 => ( eqimpsubset1 0.22/0.53 => ( ( ( subsetE 0.22/0.53 => ( ( notsubsetI 0.22/0.53 => ( notequalI1 0.22/0.53 => ( notequalI2 0.22/0.53 => ( ( ( ( setadjoinSub2 0.22/0.53 => ( subset2powerset 0.22/0.53 => ( ( subsetemptysetimpeq 0.22/0.53 => ( ( ( ( powersetsubset 0.22/0.53 => ( ( sepSubset 0.22/0.53 => ( binunionIL 0.22/0.53 => ( upairset2IR 0.22/0.53 => ( binunionIR 0.22/0.53 => ( ( ( binunionLsub 0.22/0.53 => ( binunionRsub 0.22/0.53 => ( binintersectI 0.22/0.53 => ( binintersectSubset5 0.22/0.53 => ( binintersectEL 0.22/0.53 => ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ) ) ) 0.22/0.53 <= binunionE ) 0.22/0.53 <= binunionEcases ) ) ) ) ) 0.22/0.53 <= sepInPowerset ) ) 0.22/0.53 <= inPowerset ) 0.22/0.53 <= powersetE1 ) 0.22/0.53 <= powersetI1 ) ) 0.22/0.53 <= setextsub ) ) ) 0.22/0.53 <= setadjoinSub ) 0.22/0.53 <= subsetTrans ) 0.22/0.53 <= subsetRefl ) ) ) ) 0.22/0.53 <= subsetE2 ) ) 0.22/0.53 <= emptysetsubset ) 0.22/0.53 <= subsetI2 ) ) ) 0.22/0.53 <= subsetI1 ) 0.22/0.53 <= dsetconstr__Cong ) ) 0.22/0.53 <= exuEu ) ) 0.22/0.53 <= setunion__Cong ) 0.22/0.53 <= powerset__Cong ) ) 0.22/0.53 <= emptyset__Cong ) 0.22/0.56 <= exu__Cong ) 0.22/0.56 <= exuE3u ) ) ) 0.22/0.56 <= exuI2 ) 0.22/0.56 <= exuI3 ) 0.22/0.56 <= exuI1 ) ) 0.22/0.56 <= notdexE ) 0.22/0.56 <= prop2set2propI ) ) ) 0.22/0.56 <= quantDeMorgan3 ) ) ) 0.22/0.56 <= vacuousDall ) 0.22/0.56 <= emptyE1 ) ) ) ) 0.22/0.56 <= singletonsswitch ) ) ) ) ) 0.22/0.56 <= exuE2 ) ) ) 0.22/0.56 <= setunionI ) 0.22/0.56 <= powersetE ) 0.22/0.56 <= emptyInPowerset ) ) ) 0.22/0.56 <= setoftrueEq ) 0.22/0.56 <= setadjoinOr ) 0.22/0.56 <= setadjoinE ) ) ) ) 0.22/0.56 <= nonemptyI1 ) 0.22/0.56 <= nonemptyI ) ) ) ) ) ) 0.22/0.56 <= exuE3e ) 0.22/0.56 <= notinemptyset ) 0.22/0.56 <= emptysetimpfalse ) ) 0.22/0.56 <= prop2setE ) ) ) 0.22/0.56 <= dsetconstrEL ) ) 0.22/0.56 <= descrp ) 0.22/0.56 <= wellorderingAx ) ) 0.22/0.56 <= replAx ) ) 0.22/0.56 <= omegaSAx ) ) ) ) ) 0.22/0.56 <= emptysetAx ) 0.22/0.56 <= setextAx ) ). 0.22/0.56 0.22/0.56 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.k3CHNFBfVZ/cvc5---1.0.5_10189.p... 0.22/0.56 (declare-sort $$unsorted 0) 0.22/0.56 (declare-fun tptp.in ($$unsorted $$unsorted) Bool) 0.22/0.56 (declare-fun tptp.exu ((-> $$unsorted Bool)) Bool) 0.22/0.56 (assert (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy)))))))) 0.22/0.56 (declare-fun tptp.setextAx () Bool) 0.22/0.56 (assert (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B))))) 0.22/0.56 (declare-fun tptp.emptyset () $$unsorted) 0.22/0.56 (declare-fun tptp.emptysetAx () Bool) 0.22/0.56 (assert (= tptp.emptysetAx (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.22/0.56 (declare-fun tptp.setadjoin ($$unsorted $$unsorted) $$unsorted) 0.22/0.56 (declare-fun tptp.setadjoinAx () Bool) 0.22/0.56 (assert (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.22/0.56 (declare-fun tptp.powerset ($$unsorted) $$unsorted) 0.22/0.56 (declare-fun tptp.powersetAx () Bool) 0.22/0.56 (assert (= tptp.powersetAx (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))))))) 0.22/0.56 (declare-fun tptp.setunion ($$unsorted) $$unsorted) 0.22/0.56 (declare-fun tptp.setunionAx () Bool) 0.22/0.56 (assert (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A))))))) 0.22/0.56 (declare-fun tptp.omega () $$unsorted) 0.22/0.56 (declare-fun tptp.omega0Ax () Bool) 0.22/0.56 (assert (= tptp.omega0Ax (@ (@ tptp.in tptp.emptyset) tptp.omega))) 0.22/0.56 (declare-fun tptp.omegaSAx () Bool) 0.22/0.56 (assert (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega))))) 0.22/0.56 (declare-fun tptp.omegaIndAx () Bool) 0.22/0.56 (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 $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 tptp.omega) (@ _let_1 A)))))))) 0.22/0.56 (declare-fun tptp.replAx () Bool) 0.22/0.56 (assert (= tptp.replAx (forall ((Xphi (-> $$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 $$unsorted)) (and (@ (@ tptp.in Xy) A) (@ (@ Xphi Xy) Xx)))))))))) 0.22/0.56 (declare-fun tptp.foundationAx () Bool) 0.22/0.56 (assert (= tptp.foundationAx (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in B) A) (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 B) (@ _let_1 A))))))))))) 0.22/0.56 (declare-fun tptp.wellorderingAx () Bool) 0.22/0.56 (assert (= tptp.wellorderingAx (forall ((A $$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))))))))))))) 0.22/0.56 (declare-fun tptp.descr ((-> $$unsorted Bool)) $$unsorted) 0.22/0.56 (declare-fun tptp.descrp () Bool) 0.22/0.56 (assert (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) 0.22/0.56 (declare-fun tptp.dsetconstr ($$unsorted (-> $$unsorted Bool)) $$unsorted) 0.22/0.56 (declare-fun tptp.dsetconstrI () Bool) 0.22/0.56 (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)))))))))) 0.22/0.56 (declare-fun tptp.dsetconstrEL () Bool) 0.22/0.56 (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)))))) 0.22/0.56 (declare-fun tptp.dsetconstrER () Bool) 0.22/0.56 (assert (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))) 0.22/0.56 (declare-fun tptp.exuE1 () Bool) 0.22/0.56 (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))))))))) 0.22/0.56 (declare-fun tptp.prop2set (Bool) $$unsorted) 0.22/0.56 (declare-fun tptp.prop2setE () Bool) 0.22/0.56 (assert (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi)))) 0.22/0.56 (declare-fun tptp.emptysetE () Bool) 0.22/0.56 (assert (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi))))) 0.22/0.56 (declare-fun tptp.emptysetimpfalse () Bool) 0.22/0.56 (assert (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false)))) 0.22/0.56 (declare-fun tptp.notinemptyset () Bool) 0.22/0.56 (assert (= tptp.notinemptyset (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.22/0.56 (declare-fun tptp.exuE3e () Bool) 0.22/0.56 (assert (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx)))))) 0.22/0.56 (declare-fun tptp.setext () Bool) 0.22/0.56 (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)))))) 0.22/0.56 (declare-fun tptp.emptyI () Bool) 0.22/0.56 (assert (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.22/0.56 (declare-fun tptp.noeltsimpempty () Bool) 0.22/0.56 (assert (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.22/0.56 (declare-fun tptp.setbeta () Bool) 0.22/0.56 (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))))))) 0.22/0.56 (declare-fun tptp.nonempty ($$unsorted) Bool) 0.22/0.56 (assert (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset))))) 0.22/0.56 (declare-fun tptp.nonemptyE1 () Bool) 0.22/0.56 (assert (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)))))) 0.22/0.56 (declare-fun tptp.nonemptyI () Bool) 0.22/0.56 (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))))))))) 0.22/0.56 (declare-fun tptp.nonemptyI1 () Bool) 0.22/0.56 (assert (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A))))) 0.22/0.56 (declare-fun tptp.setadjoinIL () Bool) 0.22/0.56 (assert (= tptp.setadjoinIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) 0.22/0.56 (declare-fun tptp.emptyinunitempty () Bool) 0.22/0.56 (assert (= tptp.emptyinunitempty (@ (@ tptp.in tptp.emptyset) (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) 0.22/0.56 (declare-fun tptp.setadjoinIR () Bool) 0.22/0.56 (assert (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A))))))) 0.22/0.56 (declare-fun tptp.setadjoinE () Bool) 0.22/0.56 (assert (= tptp.setadjoinE (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (forall ((Xphi Bool)) (=> (=> (= Xy Xx) Xphi) (=> (=> (@ (@ tptp.in Xy) A) Xphi) Xphi))))))) 0.22/0.56 (declare-fun tptp.setadjoinOr () Bool) 0.22/0.56 (assert (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.22/0.56 (declare-fun tptp.setoftrueEq () Bool) 0.22/0.56 (assert (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A)))) 0.22/0.56 (declare-fun tptp.powersetI () Bool) 0.22/0.56 (assert (= tptp.powersetI (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (@ (@ tptp.in B) (@ tptp.powerset A)))))) 0.22/0.56 (declare-fun tptp.emptyinPowerset () Bool) 0.22/0.56 (assert (= tptp.emptyinPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) 0.22/0.56 (declare-fun tptp.emptyInPowerset () Bool) 0.22/0.56 (assert (= tptp.emptyInPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) 0.22/0.56 (declare-fun tptp.powersetE () Bool) 0.22/0.56 (assert (= tptp.powersetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (=> (@ _let_1 B) (@ _let_1 A))))))) 0.22/0.56 (declare-fun tptp.setunionI () Bool) 0.22/0.56 (assert (= tptp.setunionI (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (=> (@ (@ tptp.in B) A) (@ _let_1 (@ tptp.setunion A)))))))) 0.22/0.56 (declare-fun tptp.setunionE () Bool) 0.22/0.56 (assert (= tptp.setunionE (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (forall ((Xphi Bool)) (=> (forall ((B $$unsorted)) (=> (@ (@ tptp.in Xx) B) (=> (@ (@ tptp.in B) A) Xphi))) Xphi)))))) 0.22/0.56 (declare-fun tptp.subPowSU () Bool) 0.22/0.56 (assert (= tptp.subPowSU (forall ((A $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.powerset (@ tptp.setunion A)))))))) 0.22/0.56 (declare-fun tptp.exuE2 () Bool) 0.22/0.56 (assert (= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))))))) 0.22/0.56 (declare-fun tptp.nonemptyImpWitness () Bool) 0.22/0.56 (assert (= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) true)))))) 0.22/0.56 (declare-fun tptp.uniqinunit () Bool) 0.22/0.56 (assert (= tptp.uniqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy))))) 0.22/0.56 (declare-fun tptp.notinsingleton () Bool) 0.22/0.56 (assert (= tptp.notinsingleton (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (not (= Xx Xy)) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) 0.22/0.56 (declare-fun tptp.eqinunit () Bool) 0.22/0.56 (assert (= tptp.eqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.22/0.56 (declare-fun tptp.singletonsswitch () Bool) 0.22/0.56 (assert (= tptp.singletonsswitch (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) 0.22/0.56 (declare-fun tptp.upairsetE () Bool) 0.22/0.56 (assert (= tptp.upairsetE (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy)))))) 0.22/0.56 (declare-fun tptp.upairsetIL () Bool) 0.22/0.56 (assert (= tptp.upairsetIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.22/0.56 (declare-fun tptp.upairsetIR () Bool) 0.22/0.56 (assert (= tptp.upairsetIR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.22/0.56 (declare-fun tptp.emptyE1 () Bool) 0.22/0.56 (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))))) 0.22/0.56 (declare-fun tptp.vacuousDall () Bool) 0.22/0.56 (assert (= tptp.vacuousDall (forall ((Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (@ Xphi Xx))))) 0.22/0.56 (declare-fun tptp.quantDeMorgan1 () Bool) 0.22/0.56 (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)))))))) 0.22/0.56 (declare-fun tptp.quantDeMorgan2 () Bool) 0.22/0.56 (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)))))))) 0.22/0.56 (declare-fun tptp.quantDeMorgan3 () Bool) 0.22/0.56 (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)))))))) 0.22/0.56 (declare-fun tptp.quantDeMorgan4 () Bool) 0.22/0.56 (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)))))))) 0.22/0.56 (declare-fun tptp.prop2setI () Bool) 0.22/0.56 (assert (= tptp.prop2setI (forall ((Xphi Bool)) (=> Xphi (@ (@ tptp.in tptp.emptyset) (@ tptp.prop2set Xphi)))))) 0.22/0.56 (declare-fun tptp.set2prop ($$unsorted) Bool) 0.22/0.56 (declare-fun tptp.prop2set2propI () Bool) 0.22/0.56 (assert (= tptp.prop2set2propI (forall ((Xphi Bool)) (=> Xphi (@ tptp.set2prop (@ tptp.prop2set Xphi)))))) 0.22/0.56 (declare-fun tptp.notdexE () Bool) 0.22/0.56 (assert (= tptp.notdexE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.22/0.56 (declare-fun tptp.notdallE () Bool) 0.22/0.56 (assert (= tptp.notdallE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.22/0.56 (declare-fun tptp.exuI1 () Bool) 0.22/0.56 (assert (= tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) 0.22/0.56 (declare-fun tptp.exuI3 () Bool) 0.22/0.56 (assert (= tptp.exuI3 (forall ((Xphi (-> $$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)))))))) 0.22/0.56 (declare-fun tptp.exuI2 () Bool) 0.22/0.56 (assert (= tptp.exuI2 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) 0.22/0.56 (declare-fun tptp.inCongP () Bool) 0.22/0.56 (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)))))))) 0.22/0.56 (declare-fun tptp.in__Cong () Bool) 0.22/0.56 (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)))))))) 0.22/0.56 (declare-fun tptp.exuE3u () Bool) 0.22/0.56 (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)))))))) 0.22/0.56 (declare-fun tptp.exu__Cong () Bool) 0.22/0.56 (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)))))))) 0.22/0.56 (declare-fun tptp.emptyset__Cong () Bool) 0.22/0.56 (assert (= tptp.emptyset__Cong (= tptp.emptyset tptp.emptyset))) 0.22/0.56 (declare-fun tptp.setadjoin__Cong () Bool) 0.22/0.56 (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)))))))) 0.22/0.56 (declare-fun tptp.powerset__Cong () Bool) 0.22/0.56 (assert (= tptp.powerset__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.powerset A) (@ tptp.powerset B)))))) 0.22/0.56 (declare-fun tptp.setunion__Cong () Bool) 0.22/0.56 (assert (= tptp.setunion__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.setunion A) (@ tptp.setunion B)))))) 0.22/0.56 (declare-fun tptp.omega__Cong () Bool) 0.22/0.56 (assert (= tptp.omega__Cong (= tptp.omega tptp.omega))) 0.22/0.56 (declare-fun tptp.exuEu () Bool) 0.22/0.56 (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)))))))) 0.22/0.56 (declare-fun tptp.descr__Cong () Bool) 0.22/0.56 (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)))))))))) 0.22/0.56 (declare-fun tptp.dsetconstr__Cong () Bool) 0.22/0.56 (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)))))))))) 0.22/0.56 (declare-fun tptp.subset ($$unsorted $$unsorted) Bool) 0.22/0.56 (declare-fun tptp.disjoint ($$unsorted $$unsorted) Bool) 0.22/0.56 (declare-fun tptp.setsmeet ($$unsorted $$unsorted) Bool) 0.22/0.56 (declare-fun tptp.subsetI1 () Bool) 0.22/0.56 (assert (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B))))) 0.22/0.56 (declare-fun tptp.eqimpsubset2 () Bool) 0.22/0.56 (assert (= tptp.eqimpsubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset B) A))))) 0.22/0.56 (declare-fun tptp.eqimpsubset1 () Bool) 0.22/0.56 (assert (= tptp.eqimpsubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B))))) 0.22/0.56 (declare-fun tptp.subsetI2 () Bool) 0.22/0.56 (assert (= tptp.subsetI2 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B))))) 0.22/0.56 (declare-fun tptp.emptysetsubset () Bool) 0.22/0.56 (assert (= tptp.emptysetsubset (forall ((A $$unsorted)) (@ (@ tptp.subset tptp.emptyset) A)))) 0.22/0.56 (declare-fun tptp.subsetE () Bool) 0.22/0.56 (assert (= tptp.subsetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (@ _let_1 A) (@ _let_1 B))))))) 0.22/0.56 (declare-fun tptp.subsetE2 () Bool) 0.22/0.56 (assert (= tptp.subsetE2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (not (@ _let_1 B)) (not (@ _let_1 A)))))))) 0.22/0.56 (declare-fun tptp.notsubsetI () Bool) 0.22/0.56 (assert (= tptp.notsubsetI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (@ (@ tptp.subset A) B)))))))) 0.22/0.56 (declare-fun tptp.notequalI1 () Bool) 0.22/0.56 (assert (= tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (@ (@ tptp.subset A) B)) (not (= A B)))))) 0.22/0.56 (declare-fun tptp.notequalI2 () Bool) 0.22/0.56 (assert (= tptp.notequalI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (= A B)))))))) 0.22/0.56 (declare-fun tptp.subsetRefl () Bool) 0.22/0.56 (assert (= tptp.subsetRefl (forall ((A $$unsorted)) (@ (@ tptp.subset A) A)))) 0.22/0.56 (declare-fun tptp.subsetTrans () Bool) 0.22/0.56 (assert (= tptp.subsetTrans (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (=> (@ (@ tptp.subset B) C) (@ _let_1 C))))))) 0.22/0.56 (declare-fun tptp.setadjoinSub () Bool) 0.22/0.56 (assert (= tptp.setadjoinSub (forall ((Xx $$unsorted) (A $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.setadjoin Xx) A))))) 0.22/0.56 (declare-fun tptp.setadjoinSub2 () Bool) 0.22/0.56 (assert (= tptp.setadjoinSub2 (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.setadjoin Xx) B))))))) 0.22/0.56 (declare-fun tptp.subset2powerset () Bool) 0.22/0.56 (assert (= tptp.subset2powerset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.in A) (@ tptp.powerset B)))))) 0.22/0.56 (declare-fun tptp.setextsub () Bool) 0.22/0.56 (assert (= tptp.setextsub (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (=> (@ (@ tptp.subset B) A) (= A B)))))) 0.22/0.56 (declare-fun tptp.subsetemptysetimpeq () Bool) 0.22/0.56 (assert (= tptp.subsetemptysetimpeq (forall ((A $$unsorted)) (=> (@ (@ tptp.subset A) tptp.emptyset) (= A tptp.emptyset))))) 0.22/0.56 (declare-fun tptp.powersetI1 () Bool) 0.22/0.56 (assert (= tptp.powersetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (@ (@ tptp.in B) (@ tptp.powerset A)))))) 0.22/0.56 (declare-fun tptp.powersetE1 () Bool) 0.22/0.56 (assert (= tptp.powersetE1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (@ (@ tptp.subset B) A))))) 0.22/0.56 (declare-fun tptp.inPowerset () Bool) 0.22/0.56 (assert (= tptp.inPowerset (forall ((A $$unsorted)) (@ (@ tptp.in A) (@ tptp.powerset A))))) 0.22/0.56 (declare-fun tptp.powersetsubset () Bool) 0.22/0.56 (assert (= tptp.powersetsubset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.subset (@ tptp.powerset A)) (@ tptp.powerset B)))))) 0.22/0.56 (declare-fun tptp.sepInPowerset () Bool) 0.22/0.56 (assert (= tptp.sepInPowerset (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.in (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ tptp.powerset A))))) 0.22/0.56 (declare-fun tptp.sepSubset () Bool) 0.22/0.56 (assert (= tptp.sepSubset (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.subset (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) A)))) 0.22/0.56 (declare-fun tptp.binunion ($$unsorted $$unsorted) $$unsorted) 0.22/0.56 (declare-fun tptp.binunionIL () Bool) 0.22/0.56 (assert (= tptp.binunionIL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.binunion A) B))))))) 0.22/0.56 (declare-fun tptp.upairset2IR () Bool) 0.22/0.56 (assert (= tptp.upairset2IR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.22/0.56 (declare-fun tptp.binunionIR () Bool) 0.22/0.56 (assert (= tptp.binunionIR (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binunion A) B))))))) 0.22/0.56 (declare-fun tptp.binunionEcases () Bool) 0.22/0.56 (assert (= tptp.binunionEcases (forall ((A $$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))))))) 0.22/0.56 (declare-fun tptp.binunionE () Bool) 0.22/0.56 (assert (= tptp.binunionE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binunion A) B)) (or (@ _let_1 A) (@ _let_1 B))))))) 0.22/0.56 (declare-fun tptp.binunionLsub () Bool) 0.22/0.56 (assert (= tptp.binunionLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.binunion A) B))))) 0.22/0.56 (declare-fun tptp.binunionRsub () Bool) 0.22/0.56 (assert (= tptp.binunionRsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset B) (@ (@ tptp.binunion A) B))))) 0.22/0.56 (declare-fun tptp.binintersect ($$unsorted $$unsorted) $$unsorted) 0.22/0.56 (assert (= tptp.binintersect (lambda ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ (@ tptp.in Xx) B)))))) 0.22/0.56 (declare-fun tptp.binintersectI () Bool) 0.22/0.56 (assert (= tptp.binintersectI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B)))))))) 0.22/0.56 (declare-fun tptp.binintersectSubset5 () Bool) 0.22/0.56 (assert (= tptp.binintersectSubset5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B)))))))) 0.22/0.56 (declare-fun tptp.binintersectEL () Bool) 0.22/0.56 (assert (= tptp.binintersectEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect A) B)) (@ _let_1 A)))))) 0.22/0.56 (assert (/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 10595 Alarm clock ( read result; case "$result" in 179.77/180.07 unsat) 179.77/180.07 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0 179.77/180.07 ;; 179.77/180.07 sat) 179.77/180.07 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0 179.77/180.07 ;; 179.77/180.07 esac; exit 1 ) 179.77/180.08 Alarm clock 179.77/180.08 % cvc5---1.0.5 exiting 179.77/180.08 % cvc5---1.0.5 exiting 179.77/180.09 EOF