0.07/0.14 % Problem : Vampire---4.8_31675 : TPTP v0.0.0. Released v0.0.0. 0.07/0.15 % Command : do_cvc5 %s %d 0.14/0.36 % Computer : n024.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 1440 0.14/0.36 % WCLimit : 180 0.14/0.36 % DateTime : Mon Jul 3 12:52:38 EDT 2023 0.14/0.36 % CPUTime : 0.35/0.53 %----Proving TH0 0.38/0.53 thf(in_type,type, 0.38/0.53 in: $i > $i > $o ). 0.38/0.53 0.38/0.53 thf(exu_type,type, 0.38/0.53 exu: ( $i > $o ) > $o ). 0.38/0.53 0.38/0.53 thf(exu,definition, 0.38/0.53 ( exu 0.38/0.53 = ( ^ [Xphi: $i > $o] : 0.38/0.53 ? [Xx: $i] : 0.38/0.53 ( ( Xphi @ Xx ) 0.38/0.53 & ! [Xy: $i] : 0.38/0.53 ( ( Xphi @ Xy ) 0.38/0.53 => ( Xx = Xy ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(setextAx_type,type, 0.38/0.53 setextAx: $o ). 0.38/0.53 0.38/0.53 thf(setextAx,definition, 0.38/0.53 ( setextAx 0.38/0.53 = ( ! [A: $i,B: $i] : 0.38/0.53 ( ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ A ) 0.38/0.53 <=> ( in @ Xx @ B ) ) 0.38/0.53 => ( A = B ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(emptyset_type,type, 0.38/0.53 emptyset: $i ). 0.38/0.53 0.38/0.53 thf(emptysetAx_type,type, 0.38/0.53 emptysetAx: $o ). 0.38/0.53 0.38/0.53 thf(emptysetAx,definition, 0.38/0.53 ( emptysetAx 0.38/0.53 = ( ! [Xx: $i] : 0.38/0.53 ~ ( in @ Xx @ emptyset ) ) ) ). 0.38/0.53 0.38/0.53 thf(setadjoin_type,type, 0.38/0.53 setadjoin: $i > $i > $i ). 0.38/0.53 0.38/0.53 thf(setadjoinAx_type,type, 0.38/0.53 setadjoinAx: $o ). 0.38/0.53 0.38/0.53 thf(setadjoinAx,definition, 0.38/0.53 ( setadjoinAx 0.38/0.53 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.38/0.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.38/0.53 <=> ( ( Xy = Xx ) 0.38/0.53 | ( in @ Xy @ A ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(powerset_type,type, 0.38/0.53 powerset: $i > $i ). 0.38/0.53 0.38/0.53 thf(powersetAx_type,type, 0.38/0.53 powersetAx: $o ). 0.38/0.53 0.38/0.53 thf(powersetAx,definition, 0.38/0.53 ( powersetAx 0.38/0.53 = ( ! [A: $i,B: $i] : 0.38/0.53 ( ( in @ B @ ( powerset @ A ) ) 0.38/0.53 <=> ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ B ) 0.38/0.53 => ( in @ Xx @ A ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(setunion_type,type, 0.38/0.53 setunion: $i > $i ). 0.38/0.53 0.38/0.53 thf(setunionAx_type,type, 0.38/0.53 setunionAx: $o ). 0.38/0.53 0.38/0.53 thf(setunionAx,definition, 0.38/0.53 ( setunionAx 0.38/0.53 = ( ! [A: $i,Xx: $i] : 0.38/0.53 ( ( in @ Xx @ ( setunion @ A ) ) 0.38/0.53 <=> ? [B: $i] : 0.38/0.53 ( ( in @ Xx @ B ) 0.38/0.53 & ( in @ B @ A ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(omega_type,type, 0.38/0.53 omega: $i ). 0.38/0.53 0.38/0.53 thf(omega0Ax_type,type, 0.38/0.53 omega0Ax: $o ). 0.38/0.53 0.38/0.53 thf(omega0Ax,definition, 0.38/0.53 ( omega0Ax 0.38/0.53 = ( in @ emptyset @ omega ) ) ). 0.38/0.53 0.38/0.53 thf(omegaSAx_type,type, 0.38/0.53 omegaSAx: $o ). 0.38/0.53 0.38/0.53 thf(omegaSAx,definition, 0.38/0.53 ( omegaSAx 0.38/0.53 = ( ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ omega ) 0.38/0.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(omegaIndAx_type,type, 0.38/0.53 omegaIndAx: $o ). 0.38/0.53 0.38/0.53 thf(omegaIndAx,definition, 0.38/0.53 ( omegaIndAx 0.38/0.53 = ( ! [A: $i] : 0.38/0.53 ( ( ( in @ emptyset @ A ) 0.38/0.53 & ! [Xx: $i] : 0.38/0.53 ( ( ( in @ Xx @ omega ) 0.38/0.53 & ( in @ Xx @ A ) ) 0.38/0.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) 0.38/0.53 => ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ omega ) 0.38/0.53 => ( in @ Xx @ A ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(replAx_type,type, 0.38/0.53 replAx: $o ). 0.38/0.53 0.38/0.53 thf(replAx,definition, 0.38/0.53 ( replAx 0.38/0.53 = ( ! [Xphi: $i > $i > $o,A: $i] : 0.38/0.53 ( ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ A ) 0.38/0.53 => ( exu 0.38/0.53 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) 0.38/0.53 => ? [B: $i] : 0.38/0.53 ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ B ) 0.38/0.53 <=> ? [Xy: $i] : 0.38/0.53 ( ( in @ Xy @ A ) 0.38/0.53 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(foundationAx_type,type, 0.38/0.53 foundationAx: $o ). 0.38/0.53 0.38/0.53 thf(foundationAx,definition, 0.38/0.53 ( foundationAx 0.38/0.53 = ( ! [A: $i] : 0.38/0.53 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.38/0.53 => ? [B: $i] : 0.38/0.53 ( ( in @ B @ A ) 0.38/0.53 & ~ ? [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ B ) 0.38/0.53 & ( in @ Xx @ A ) ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(wellorderingAx_type,type, 0.38/0.53 wellorderingAx: $o ). 0.38/0.53 0.38/0.53 thf(wellorderingAx,definition, 0.38/0.53 ( wellorderingAx 0.38/0.53 = ( ! [A: $i] : 0.38/0.53 ? [B: $i] : 0.38/0.53 ( ! [C: $i] : 0.38/0.53 ( ( in @ C @ B ) 0.38/0.53 => ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ C ) 0.38/0.53 => ( in @ Xx @ A ) ) ) 0.38/0.53 & ! [Xx: $i,Xy: $i] : 0.38/0.53 ( ( ( in @ Xx @ A ) 0.38/0.53 & ( in @ Xy @ A ) ) 0.38/0.53 => ( ! [C: $i] : 0.38/0.53 ( ( in @ C @ B ) 0.38/0.53 => ( ( in @ Xx @ C ) 0.38/0.53 <=> ( in @ Xy @ C ) ) ) 0.38/0.53 => ( Xx = Xy ) ) ) 0.38/0.53 & ! [C: $i,D: $i] : 0.38/0.53 ( ( ( in @ C @ B ) 0.38/0.53 & ( in @ D @ B ) ) 0.38/0.53 => ( ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ C ) 0.38/0.53 => ( in @ Xx @ D ) ) 0.38/0.53 | ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ D ) 0.38/0.53 => ( in @ Xx @ C ) ) ) ) 0.38/0.53 & ! [C: $i] : 0.38/0.53 ( ( ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ C ) 0.38/0.53 => ( in @ Xx @ A ) ) 0.38/0.53 & ? [Xx: $i] : ( in @ Xx @ C ) ) 0.38/0.53 => ? [D: $i,Xx: $i] : 0.38/0.53 ( ( in @ D @ B ) 0.38/0.53 & ( in @ Xx @ C ) 0.38/0.53 & ~ ? [Xy: $i] : 0.38/0.53 ( ( in @ Xy @ D ) 0.38/0.53 & ( in @ Xy @ C ) ) 0.38/0.53 & ! [E: $i] : 0.38/0.53 ( ( in @ E @ B ) 0.38/0.53 => ( ! [Xy: $i] : 0.38/0.53 ( ( in @ Xy @ E ) 0.38/0.53 => ( in @ Xy @ D ) ) 0.38/0.53 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(descr_type,type, 0.38/0.53 descr: ( $i > $o ) > $i ). 0.38/0.53 0.38/0.53 thf(descrp_type,type, 0.38/0.53 descrp: $o ). 0.38/0.53 0.38/0.53 thf(descrp,definition, 0.38/0.53 ( descrp 0.38/0.53 = ( ! [Xphi: $i > $o] : 0.38/0.53 ( ( exu 0.38/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.53 => ( Xphi 0.38/0.53 @ ( descr 0.38/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(dsetconstr_type,type, 0.38/0.53 dsetconstr: $i > ( $i > $o ) > $i ). 0.38/0.53 0.38/0.53 thf(dsetconstrI_type,type, 0.38/0.53 dsetconstrI: $o ). 0.38/0.53 0.38/0.53 thf(dsetconstrI,definition, 0.38/0.53 ( dsetconstrI 0.38/0.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.38/0.53 ( ( in @ Xx @ A ) 0.38/0.53 => ( ( Xphi @ Xx ) 0.38/0.53 => ( in @ Xx 0.38/0.53 @ ( dsetconstr @ A 0.38/0.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(dsetconstrEL_type,type, 0.38/0.53 dsetconstrEL: $o ). 0.38/0.53 0.38/0.53 thf(dsetconstrEL,definition, 0.38/0.53 ( dsetconstrEL 0.38/0.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.38/0.53 ( ( in @ Xx 0.38/0.53 @ ( dsetconstr @ A 0.38/0.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.38/0.53 => ( in @ Xx @ A ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(dsetconstrER_type,type, 0.38/0.53 dsetconstrER: $o ). 0.38/0.53 0.38/0.53 thf(dsetconstrER,definition, 0.38/0.53 ( dsetconstrER 0.38/0.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.38/0.53 ( ( in @ Xx 0.38/0.53 @ ( dsetconstr @ A 0.38/0.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.38/0.53 => ( Xphi @ Xx ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(exuE1_type,type, 0.38/0.53 exuE1: $o ). 0.38/0.53 0.38/0.53 thf(exuE1,definition, 0.38/0.53 ( exuE1 0.38/0.53 = ( ! [Xphi: $i > $o] : 0.38/0.53 ( ( exu 0.38/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.53 => ? [Xx: $i] : 0.38/0.53 ( ( Xphi @ Xx ) 0.38/0.53 & ! [Xy: $i] : 0.38/0.53 ( ( Xphi @ Xy ) 0.38/0.53 => ( Xx = Xy ) ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(prop2set_type,type, 0.38/0.53 prop2set: $o > $i ). 0.38/0.53 0.38/0.53 thf(prop2set,definition, 0.38/0.53 ( prop2set 0.38/0.53 = ( ^ [Xphi: $o] : 0.38/0.53 ( dsetconstr @ ( powerset @ emptyset ) 0.38/0.53 @ ^ [Xx: $i] : Xphi ) ) ) ). 0.38/0.53 0.38/0.53 thf(prop2setE_type,type, 0.38/0.53 prop2setE: $o ). 0.38/0.53 0.38/0.53 thf(prop2setE,definition, 0.38/0.53 ( prop2setE 0.38/0.53 = ( ! [Xphi: $o,Xx: $i] : 0.38/0.53 ( ( in @ Xx @ ( prop2set @ Xphi ) ) 0.38/0.53 => Xphi ) ) ) ). 0.38/0.53 0.38/0.53 thf(emptysetE_type,type, 0.38/0.53 emptysetE: $o ). 0.38/0.53 0.38/0.53 thf(emptysetE,definition, 0.38/0.53 ( emptysetE 0.38/0.53 = ( ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ emptyset ) 0.38/0.53 => ! [Xphi: $o] : Xphi ) ) ) ). 0.38/0.53 0.38/0.53 thf(emptysetimpfalse_type,type, 0.38/0.53 emptysetimpfalse: $o ). 0.38/0.53 0.38/0.53 thf(emptysetimpfalse,definition, 0.38/0.53 ( emptysetimpfalse 0.38/0.53 = ( ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ emptyset ) 0.38/0.53 => $false ) ) ) ). 0.38/0.53 0.38/0.53 thf(notinemptyset_type,type, 0.38/0.53 notinemptyset: $o ). 0.38/0.53 0.38/0.53 thf(notinemptyset,definition, 0.38/0.53 ( notinemptyset 0.38/0.53 = ( ! [Xx: $i] : 0.38/0.53 ~ ( in @ Xx @ emptyset ) ) ) ). 0.38/0.53 0.38/0.53 thf(exuE3e_type,type, 0.38/0.53 exuE3e: $o ). 0.38/0.53 0.38/0.53 thf(exuE3e,definition, 0.38/0.53 ( exuE3e 0.38/0.53 = ( ! [Xphi: $i > $o] : 0.38/0.53 ( ( exu 0.38/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.53 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(setext_type,type, 0.38/0.53 setext: $o ). 0.38/0.53 0.38/0.53 thf(setext,definition, 0.38/0.53 ( setext 0.38/0.53 = ( ! [A: $i,B: $i] : 0.38/0.53 ( ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ A ) 0.38/0.53 => ( in @ Xx @ B ) ) 0.38/0.53 => ( ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ B ) 0.38/0.53 => ( in @ Xx @ A ) ) 0.38/0.53 => ( A = B ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(emptyI_type,type, 0.38/0.53 emptyI: $o ). 0.38/0.53 0.38/0.53 thf(emptyI,definition, 0.38/0.53 ( emptyI 0.38/0.53 = ( ! [A: $i] : 0.38/0.53 ( ! [Xx: $i] : 0.38/0.53 ~ ( in @ Xx @ A ) 0.38/0.53 => ( A = emptyset ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(noeltsimpempty_type,type, 0.38/0.53 noeltsimpempty: $o ). 0.38/0.53 0.38/0.53 thf(noeltsimpempty,definition, 0.38/0.53 ( noeltsimpempty 0.38/0.53 = ( ! [A: $i] : 0.38/0.53 ( ! [Xx: $i] : 0.38/0.53 ~ ( in @ Xx @ A ) 0.38/0.53 => ( A = emptyset ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(setbeta_type,type, 0.38/0.53 setbeta: $o ). 0.38/0.53 0.38/0.53 thf(setbeta,definition, 0.38/0.53 ( setbeta 0.38/0.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.38/0.53 ( ( in @ Xx @ A ) 0.38/0.53 => ( ( in @ Xx 0.38/0.53 @ ( dsetconstr @ A 0.38/0.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.38/0.53 <=> ( Xphi @ Xx ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(nonempty_type,type, 0.38/0.53 nonempty: $i > $o ). 0.38/0.53 0.38/0.53 thf(nonempty,definition, 0.38/0.53 ( nonempty 0.38/0.53 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ). 0.38/0.53 0.38/0.53 thf(nonemptyE1_type,type, 0.38/0.53 nonemptyE1: $o ). 0.38/0.53 0.38/0.53 thf(nonemptyE1,definition, 0.38/0.53 ( nonemptyE1 0.38/0.53 = ( ! [A: $i] : 0.38/0.53 ( ( nonempty @ A ) 0.38/0.53 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(nonemptyI_type,type, 0.38/0.53 nonemptyI: $o ). 0.38/0.53 0.38/0.53 thf(nonemptyI,definition, 0.38/0.53 ( nonemptyI 0.38/0.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.38/0.53 ( ( in @ Xx @ A ) 0.38/0.53 => ( ( Xphi @ Xx ) 0.38/0.53 => ( nonempty 0.38/0.53 @ ( dsetconstr @ A 0.38/0.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(nonemptyI1_type,type, 0.38/0.53 nonemptyI1: $o ). 0.38/0.53 0.38/0.53 thf(nonemptyI1,definition, 0.38/0.53 ( nonemptyI1 0.38/0.53 = ( ! [A: $i] : 0.38/0.53 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.38/0.53 => ( nonempty @ A ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(setadjoinIL_type,type, 0.38/0.53 setadjoinIL: $o ). 0.38/0.53 0.38/0.53 thf(setadjoinIL,definition, 0.38/0.53 ( setadjoinIL 0.38/0.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(emptyinunitempty_type,type, 0.38/0.53 emptyinunitempty: $o ). 0.38/0.53 0.38/0.53 thf(emptyinunitempty,definition, 0.38/0.53 ( emptyinunitempty 0.38/0.53 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ). 0.38/0.53 0.38/0.53 thf(setadjoinIR_type,type, 0.38/0.53 setadjoinIR: $o ). 0.38/0.53 0.38/0.53 thf(setadjoinIR,definition, 0.38/0.53 ( setadjoinIR 0.38/0.53 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.38/0.53 ( ( in @ Xy @ A ) 0.38/0.53 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(setadjoinE_type,type, 0.38/0.53 setadjoinE: $o ). 0.38/0.53 0.38/0.53 thf(setadjoinE,definition, 0.38/0.53 ( setadjoinE 0.38/0.53 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.38/0.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.38/0.53 => ! [Xphi: $o] : 0.38/0.53 ( ( ( Xy = Xx ) 0.38/0.53 => Xphi ) 0.38/0.53 => ( ( ( in @ Xy @ A ) 0.38/0.53 => Xphi ) 0.38/0.53 => Xphi ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(setadjoinOr_type,type, 0.38/0.53 setadjoinOr: $o ). 0.38/0.53 0.38/0.53 thf(setadjoinOr,definition, 0.38/0.53 ( setadjoinOr 0.38/0.53 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.38/0.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.38/0.53 => ( ( Xy = Xx ) 0.38/0.53 | ( in @ Xy @ A ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(setoftrueEq_type,type, 0.38/0.53 setoftrueEq: $o ). 0.38/0.53 0.38/0.53 thf(setoftrueEq,definition, 0.38/0.53 ( setoftrueEq 0.38/0.53 = ( ! [A: $i] : 0.38/0.53 ( ( dsetconstr @ A 0.38/0.53 @ ^ [Xx: $i] : $true ) 0.38/0.53 = A ) ) ) ). 0.38/0.53 0.38/0.53 thf(powersetI_type,type, 0.38/0.53 powersetI: $o ). 0.38/0.53 0.38/0.53 thf(powersetI,definition, 0.38/0.53 ( powersetI 0.38/0.53 = ( ! [A: $i,B: $i] : 0.38/0.53 ( ! [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ B ) 0.38/0.53 => ( in @ Xx @ A ) ) 0.38/0.53 => ( in @ B @ ( powerset @ A ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(emptyinPowerset_type,type, 0.38/0.53 emptyinPowerset: $o ). 0.38/0.53 0.38/0.53 thf(emptyinPowerset,definition, 0.38/0.53 ( emptyinPowerset 0.38/0.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(emptyInPowerset_type,type, 0.38/0.53 emptyInPowerset: $o ). 0.38/0.53 0.38/0.53 thf(emptyInPowerset,definition, 0.38/0.53 ( emptyInPowerset 0.38/0.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(powersetE_type,type, 0.38/0.53 powersetE: $o ). 0.38/0.53 0.38/0.53 thf(powersetE,definition, 0.38/0.53 ( powersetE 0.38/0.53 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.53 ( ( in @ B @ ( powerset @ A ) ) 0.38/0.53 => ( ( in @ Xx @ B ) 0.38/0.53 => ( in @ Xx @ A ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(setunionI_type,type, 0.38/0.53 setunionI: $o ). 0.38/0.53 0.38/0.53 thf(setunionI,definition, 0.38/0.53 ( setunionI 0.38/0.53 = ( ! [A: $i,Xx: $i,B: $i] : 0.38/0.53 ( ( in @ Xx @ B ) 0.38/0.53 => ( ( in @ B @ A ) 0.38/0.53 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(setunionE_type,type, 0.38/0.53 setunionE: $o ). 0.38/0.53 0.38/0.53 thf(setunionE,definition, 0.38/0.53 ( setunionE 0.38/0.53 = ( ! [A: $i,Xx: $i] : 0.38/0.53 ( ( in @ Xx @ ( setunion @ A ) ) 0.38/0.53 => ! [Xphi: $o] : 0.38/0.53 ( ! [B: $i] : 0.38/0.53 ( ( in @ Xx @ B ) 0.38/0.53 => ( ( in @ B @ A ) 0.38/0.53 => Xphi ) ) 0.38/0.53 => Xphi ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(subPowSU_type,type, 0.38/0.53 subPowSU: $o ). 0.38/0.53 0.38/0.53 thf(subPowSU,definition, 0.38/0.53 ( subPowSU 0.38/0.53 = ( ! [A: $i,Xx: $i] : 0.38/0.53 ( ( in @ Xx @ A ) 0.38/0.53 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(exuE2_type,type, 0.38/0.53 exuE2: $o ). 0.38/0.53 0.38/0.53 thf(exuE2,definition, 0.38/0.53 ( exuE2 0.38/0.53 = ( ! [Xphi: $i > $o] : 0.38/0.53 ( ( exu 0.38/0.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.53 => ? [Xx: $i] : 0.38/0.53 ! [Xy: $i] : 0.38/0.53 ( ( Xphi @ Xy ) 0.38/0.53 <=> ( Xy = Xx ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(nonemptyImpWitness_type,type, 0.38/0.53 nonemptyImpWitness: $o ). 0.38/0.53 0.38/0.53 thf(nonemptyImpWitness,definition, 0.38/0.53 ( nonemptyImpWitness 0.38/0.53 = ( ! [A: $i] : 0.38/0.53 ( ( nonempty @ A ) 0.38/0.53 => ? [Xx: $i] : 0.38/0.53 ( ( in @ Xx @ A ) 0.38/0.53 & $true ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(uniqinunit_type,type, 0.38/0.53 uniqinunit: $o ). 0.38/0.53 0.38/0.53 thf(uniqinunit,definition, 0.38/0.53 ( uniqinunit 0.38/0.53 = ( ! [Xx: $i,Xy: $i] : 0.38/0.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.38/0.53 => ( Xx = Xy ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(notinsingleton_type,type, 0.38/0.53 notinsingleton: $o ). 0.38/0.53 0.38/0.53 thf(notinsingleton,definition, 0.38/0.53 ( notinsingleton 0.38/0.53 = ( ! [Xx: $i,Xy: $i] : 0.38/0.53 ( ( Xx != Xy ) 0.38/0.53 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(eqinunit_type,type, 0.38/0.53 eqinunit: $o ). 0.38/0.53 0.38/0.53 thf(eqinunit,definition, 0.38/0.53 ( eqinunit 0.38/0.53 = ( ! [Xx: $i,Xy: $i] : 0.38/0.53 ( ( Xx = Xy ) 0.38/0.53 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(singletonsswitch_type,type, 0.38/0.53 singletonsswitch: $o ). 0.38/0.53 0.38/0.53 thf(singletonsswitch,definition, 0.38/0.53 ( singletonsswitch 0.38/0.53 = ( ! [Xx: $i,Xy: $i] : 0.38/0.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.38/0.53 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(upairsetE_type,type, 0.38/0.53 upairsetE: $o ). 0.38/0.53 0.38/0.53 thf(upairsetE,definition, 0.38/0.53 ( upairsetE 0.38/0.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] : 0.38/0.53 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) 0.38/0.53 => ( ( Xz = Xx ) 0.38/0.53 | ( Xz = Xy ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(upairsetIL_type,type, 0.38/0.53 upairsetIL: $o ). 0.38/0.53 0.38/0.53 thf(upairsetIL,definition, 0.38/0.53 ( upairsetIL 0.38/0.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(upairsetIR_type,type, 0.38/0.53 upairsetIR: $o ). 0.38/0.53 0.38/0.53 thf(upairsetIR,definition, 0.38/0.53 ( upairsetIR 0.38/0.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.38/0.53 0.38/0.53 thf(emptyE1,conjecture, 0.38/0.53 ( ( emptysetAx 0.38/0.53 => ( setadjoinAx 0.38/0.53 => ( powersetAx 0.38/0.53 => ( ( omega0Ax 0.38/0.53 => ( omegaSAx 0.38/0.53 => ( omegaIndAx 0.38/0.53 => ( replAx 0.38/0.53 => ( ( ( descrp 0.38/0.53 => ( dsetconstrI 0.38/0.53 => ( dsetconstrEL 0.38/0.53 => ( ( exuE1 0.38/0.53 => ( ( ( emptysetimpfalse 0.38/0.53 => ( notinemptyset 0.38/0.53 => ( ( setext 0.38/0.53 => ( emptyI 0.38/0.53 => ( ( ( nonemptyE1 0.38/0.53 => ( ( nonemptyI1 0.38/0.53 => ( ( ( setadjoinIR 0.38/0.53 => ( ( ( setoftrueEq 0.38/0.53 => ( ( ( emptyInPowerset 0.38/0.53 => ( ( ( ( ( exuE2 0.38/0.53 => ( ( uniqinunit 0.38/0.53 => ( ( eqinunit 0.38/0.53 => ( ( ( upairsetIL 0.38/0.53 => ( upairsetIR 0.38/0.53 => ! [A: $i,Xphi: $i > $o] : 0.38/0.53 ( ? [Xx: $i] : 0.38/0.53 ( ( Xphi @ Xx ) 0.38/0.55 & ( in @ Xx @ A ) ) 0.38/0.55 => ( ( ( dsetconstr @ A 0.38/0.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.55 = emptyset ) 0.38/0.55 => $false ) ) ) ) 0.38/0.55 <= upairsetE ) 0.38/0.55 <= singletonsswitch ) ) 0.38/0.55 <= notinsingleton ) ) 0.38/0.55 <= nonemptyImpWitness ) ) 0.38/0.55 <= subPowSU ) 0.38/0.55 <= setunionE ) 0.38/0.55 <= setunionI ) 0.38/0.55 <= powersetE ) ) 0.38/0.55 <= emptyinPowerset ) 0.38/0.55 <= powersetI ) ) 0.38/0.55 <= setadjoinOr ) 0.38/0.55 <= setadjoinE ) ) 0.38/0.55 <= emptyinunitempty ) 0.38/0.55 <= setadjoinIL ) ) 0.38/0.55 <= nonemptyI ) ) 0.38/0.55 <= setbeta ) 0.38/0.55 <= noeltsimpempty ) ) ) 0.38/0.55 <= exuE3e ) ) ) 0.38/0.55 <= emptysetE ) 0.38/0.55 <= prop2setE ) ) 0.38/0.55 <= dsetconstrER ) ) ) ) 0.38/0.55 <= wellorderingAx ) 0.38/0.55 <= foundationAx ) ) ) ) ) 0.38/0.55 <= setunionAx ) ) ) ) 0.38/0.55 <= setextAx ) ). 0.38/0.55 0.38/0.55 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.ngjbYvo4Jb/cvc5---1.0.5_31840.p... 0.38/0.55 (declare-sort $$unsorted 0) 0.38/0.55 (declare-fun tptp.in ($$unsorted $$unsorted) Bool) 0.38/0.55 (declare-fun tptp.exu ((-> $$unsorted Bool)) Bool) 0.38/0.55 (assert (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy)))))))) 0.38/0.55 (declare-fun tptp.setextAx () Bool) 0.38/0.55 (assert (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B))))) 0.38/0.55 (declare-fun tptp.emptyset () $$unsorted) 0.38/0.55 (declare-fun tptp.emptysetAx () Bool) 0.38/0.55 (assert (= tptp.emptysetAx (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.38/0.55 (declare-fun tptp.setadjoin ($$unsorted $$unsorted) $$unsorted) 0.38/0.55 (declare-fun tptp.setadjoinAx () Bool) 0.38/0.55 (assert (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.38/0.55 (declare-fun tptp.powerset ($$unsorted) $$unsorted) 0.38/0.55 (declare-fun tptp.powersetAx () Bool) 0.38/0.55 (assert (= tptp.powersetAx (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))))))) 0.38/0.55 (declare-fun tptp.setunion ($$unsorted) $$unsorted) 0.38/0.55 (declare-fun tptp.setunionAx () Bool) 0.38/0.55 (assert (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A))))))) 0.38/0.55 (declare-fun tptp.omega () $$unsorted) 0.38/0.55 (declare-fun tptp.omega0Ax () Bool) 0.38/0.55 (assert (= tptp.omega0Ax (@ (@ tptp.in tptp.emptyset) tptp.omega))) 0.38/0.55 (declare-fun tptp.omegaSAx () Bool) 0.38/0.55 (assert (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega))))) 0.38/0.55 (declare-fun tptp.omegaIndAx () Bool) 0.38/0.55 (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 $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 tptp.omega) (@ _let_1 A)))))))) 0.38/0.55 (declare-fun tptp.replAx () Bool) 0.38/0.55 (assert (= tptp.replAx (forall ((Xphi (-> $$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 $$unsorted)) (and (@ (@ tptp.in Xy) A) (@ (@ Xphi Xy) Xx)))))))))) 0.38/0.55 (declare-fun tptp.foundationAx () Bool) 0.38/0.55 (assert (= tptp.foundationAx (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in B) A) (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 B) (@ _let_1 A))))))))))) 0.38/0.55 (declare-fun tptp.wellorderingAx () Bool) 0.38/0.55 (assert (= tptp.wellorderingAx (forall ((A $$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))))))))))))) 0.38/0.55 (declare-fun tptp.descr ((-> $$unsorted Bool)) $$unsorted) 0.38/0.55 (declare-fun tptp.descrp () Bool) 0.38/0.55 (assert (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) 0.38/0.55 (declare-fun tptp.dsetconstr ($$unsorted (-> $$unsorted Bool)) $$unsorted) 0.38/0.55 (declare-fun tptp.dsetconstrI () Bool) 0.38/0.55 (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)))))))))) 0.38/0.55 (declare-fun tptp.dsetconstrEL () Bool) 0.38/0.55 (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)))))) 0.38/0.55 (declare-fun tptp.dsetconstrER () Bool) 0.38/0.55 (assert (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))) 0.38/0.55 (declare-fun tptp.exuE1 () Bool) 0.38/0.55 (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))))))))) 0.38/0.55 (declare-fun tptp.prop2set (Bool) $$unsorted) 0.38/0.55 (assert (= tptp.prop2set (lambda ((Xphi Bool)) (@ (@ tptp.dsetconstr (@ tptp.powerset tptp.emptyset)) (lambda ((Xx $$unsorted)) Xphi))))) 0.38/0.55 (declare-fun tptp.prop2setE () Bool) 0.38/0.55 (assert (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi)))) 0.38/0.55 (declare-fun tptp.emptysetE () Bool) 0.38/0.55 (assert (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi))))) 0.38/0.55 (declare-fun tptp.emptysetimpfalse () Bool) 0.38/0.55 (assert (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false)))) 0.38/0.55 (declare-fun tptp.notinemptyset () Bool) 0.38/0.55 (assert (= tptp.notinemptyset (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.38/0.55 (declare-fun tptp.exuE3e () Bool) 0.38/0.55 (assert (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx)))))) 0.38/0.55 (declare-fun tptp.setext () Bool) 0.38/0.55 (assert (= tptp.setext (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (= A B)))))) 0.38/0.55 (declare-fun tptp.emptyI () Bool) 0.38/0.55 (assert (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.38/0.55 (declare-fun tptp.noeltsimpempty () Bool) 0.38/0.55 (assert (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.38/0.55 (declare-fun tptp.setbeta () Bool) 0.38/0.55 (assert (= tptp.setbeta (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (= (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))))) 0.38/0.55 (declare-fun tptp.nonempty ($$unsorted) Bool) 0.38/0.55 (assert (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset))))) 0.38/0.55 (declare-fun tptp.nonemptyE1 () Bool) 0.38/0.55 (assert (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)))))) 0.38/0.55 (declare-fun tptp.nonemptyI () Bool) 0.38/0.55 (assert (= tptp.nonemptyI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (@ tptp.nonempty (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))))) 0.38/0.55 (declare-fun tptp.nonemptyI1 () Bool) 0.38/0.55 (assert (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A))))) 0.38/0.55 (declare-fun tptp.setadjoinIL () Bool) 0.38/0.55 (assert (= tptp.setadjoinIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) 0.38/0.55 (declare-fun tptp.emptyinunitempty () Bool) 0.38/0.55 (assert (= tptp.emptyinunitempty (@ (@ tptp.in tptp.emptyset) (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) 0.38/0.55 (declare-fun tptp.setadjoinIR () Bool) 0.38/0.55 (assert (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A))))))) 0.38/0.55 (declare-fun tptp.setadjoinE () Bool) 0.38/0.55 (assert (= tptp.setadjoinE (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (forall ((Xphi Bool)) (=> (=> (= Xy Xx) Xphi) (=> (=> (@ (@ tptp.in Xy) A) Xphi) Xphi))))))) 0.38/0.55 (declare-fun tptp.setadjoinOr () Bool) 0.38/0.55 (assert (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.38/0.55 (declare-fun tptp.setoftrueEq () Bool) 0.38/0.55 (assert (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A)))) 0.38/0.55 (declare-fun tptp.powersetI () Bool) 0.38/0.55 (assert (= tptp.powersetI (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (@ (@ tptp.in B) (@ tptp.powerset A)))))) 0.38/0.55 (declare-fun tptp.emptyinPowerset () Bool) 0.38/0.55 (assert (= tptp.emptyinPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) 0.38/0.55 (declare-fun tptp.emptyInPowerset () Bool) 0.38/0.55 (assert (= tptp.emptyInPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) 0.38/0.55 (declare-fun tptp.powersetE () Bool) 0.38/0.55 (assert (= tptp.powersetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (=> (@ _let_1 B) (@ _let_1 A))))))) 0.38/0.55 (declare-fun tptp.setunionI () Bool) 0.38/0.55 (assert (= tptp.setunionI (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (=> (@ (@ tptp.in B) A) (@ _let_1 (@ tptp.setunion A)))))))) 0.38/0.55 (declare-fun tptp.setunionE () Bool) 0.38/0.55 (assert (= tptp.setunionE (forall ((A $$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)))))) 0.38/0.55 (declare-fun tptp.subPowSU () Bool) 0.38/0.55 (assert (= tptp.subPowSU (forall ((A $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.powerset (@ tptp.setunion A)))))))) 0.38/0.55 (declare-fun tptp.exuE2 () Bool) 0.38/0.55 (assert (= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))))))) 0.38/0.55 (declare-fun tptp.nonemptyImpWitness () Bool) 0.38/0.55 (assert (= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) true)))))) 0.38/0.55 (declare-fun tptp.uniqinunit () Bool) 0.38/0.55 (assert (= tptp.uniqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy))))) 0.38/0.55 (declare-fun tptp.notinsingleton () Bool) 0.38/0.55 (assert (= tptp.notinsingleton (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (not (= Xx Xy)) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) 0.38/0.55 (declare-fun tptp.eqinunit () Bool) 0.38/0.55 (assert (= tptp.eqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.38/0.55 (declare-fun tptp.singletonsswitch () Bool) 0.38/0.55 (assert (= tptp.singletonsswitch (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) 0.38/0.55 (declare-fun tptp.upairsetE () Bool) 0.38/0.55 (assert (= tptp.upairsetE (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy)))))) 0.38/0.55 (declare-fun tptp.upairsetIL () Bool) 0.38/0.55 (assert (= tptp.upairsetIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.38/0.55 (declare-fun tptp.upairsetIR () Bool) 0.38/0.55 (assert (= tptp.upairsetIR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.38/0.55 (assert (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (@ (@ tptp.in Xx) A))) (=> (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) tptp.emptyset) false))))))))))))))))))))))))))))))))))))))))))))))))))))))) 35.73/36.15 (set-info :filename cvc5---1.0.5_31840) 35.73/36.15 (check-sat-assuming ( true )) 35.73/36.15 ------- get file name : TPTP file name is 35.73/36.15 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31840.smt2... 35.73/36.15 --- Run --ho-elim --full-saturate-quant at 10... 35.73/36.15 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 35.73/36.15 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10... 35.73/36.15 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5... 35.73/36.15 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5... 35.73/36.15 % SZS status Theorem for 35.73/36.15 % SZS output start Proof for 35.73/36.15 ( 35.73/36.15 (let ((_let_1 (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (@ (@ tptp.in Xx) A))) (=> (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) tptp.emptyset) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))) (let ((_let_2 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) (let ((_let_3 (= tptp.upairsetIR _let_2))) (let ((_let_4 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) (let ((_let_5 (= tptp.upairsetIL _let_4))) (let ((_let_6 (= tptp.upairsetE (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy))))))) (let ((_let_7 (= 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_8 (= tptp.eqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))) (let ((_let_9 (= tptp.notinsingleton (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (not (= Xx Xy)) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) (let ((_let_10 (= tptp.uniqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy)))))) (let ((_let_11 (= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) true))))))) (let ((_let_12 (= 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_13 (= 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_14 (= tptp.setunionE (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (forall ((Xphi Bool)) (=> (forall ((B $$unsorted)) (=> (@ (@ tptp.in Xx) B) (=> (@ (@ tptp.in B) A) Xphi))) Xphi))))))) (let ((_let_15 (= tptp.setunionI (forall ((A $$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_16 (= tptp.powersetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (=> (@ _let_1 B) (@ _let_1 A)))))))) (let ((_let_17 (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) (let ((_let_18 (= tptp.emptyInPowerset _let_17))) (let ((_let_19 (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) (let ((_let_20 (= tptp.emptyinPowerset _let_19))) (let ((_let_21 (= tptp.powersetI (forall ((A $$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_22 (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A))))) (let ((_let_23 (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A)))))))) (let ((_let_24 (= tptp.setadjoinE (forall ((Xx $$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_25 (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A)))))))) (let ((_let_26 (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset))) (let ((_let_27 (@ tptp.in tptp.emptyset))) (let ((_let_28 (= tptp.emptyinunitempty (@ _let_27 _let_26)))) (let ((_let_29 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) (let ((_let_30 (= tptp.setadjoinIL _let_29))) (let ((_let_31 (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A)))))) (let ((_let_32 (= tptp.nonemptyI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (@ tptp.nonempty (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))))))))) (let ((_let_33 (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A))))))) (let ((_let_34 (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset)))))) (let ((_let_35 (= 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_36 (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))) (let ((_let_37 (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))) (let ((_let_38 (= 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_39 (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx))))))) (let ((_let_40 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_41 (= tptp.notinemptyset _let_40))) (let ((_let_42 (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false))))) (let ((_let_43 (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi)))))) (let ((_let_44 (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi))))) (let ((_let_45 (= tptp.prop2set (lambda ((Xphi Bool)) (@ (@ tptp.dsetconstr (@ tptp.powerset tptp.emptyset)) (lambda ((Xx $$unsorted)) Xphi)))))) (let ((_let_46 (= 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_47 (= 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_48 (= 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_49 (= 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_50 (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (let ((_let_51 (= tptp.wellorderingAx (forall ((A $$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)))))))))))))) (let ((_let_52 (= 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)))))))))))) (let ((_let_53 (= 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_54 (= 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 $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 tptp.omega) (@ _let_1 A))))))))) (let ((_let_55 (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega)))))) (let ((_let_56 (@ _let_27 tptp.omega))) (let ((_let_57 (= tptp.omega0Ax _let_56))) (let ((_let_58 (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A)))))))) (let ((_let_59 (= tptp.powersetAx (forall ((A $$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_60 (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A)))))))) (let ((_let_61 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_62 (= tptp.emptysetAx _let_61))) (let ((_let_63 (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B)))))) (let ((_let_64 (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))))))) (let ((_let_65 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_2159 $$unsorted)) (or (not (= tptp.emptyset (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (@ Xphi BOUND_VARIABLE_2159)) (not (@ (@ tptp.in BOUND_VARIABLE_2159) A)))))) (let ((_let_66 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (= tptp.emptyset (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))))) (let ((_let_67 (=>))) (let ((_let_68 (tptp.setadjoin tptp.emptyset tptp.emptyset))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_64)) (MACRO_SR_EQ_INTRO :args (_let_64 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_63)) (MACRO_SR_EQ_INTRO :args (_let_63 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (ASSUME :args (_let_62)))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_60)) (MACRO_SR_EQ_INTRO :args (_let_60 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_59)) (MACRO_SR_EQ_INTRO :args (_let_59 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_58)) (MACRO_SR_EQ_INTRO :args (_let_58 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (ASSUME :args (_let_57)))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_55)) (MACRO_SR_EQ_INTRO :args (_let_55 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_54)) (MACRO_SR_EQ_INTRO :args (_let_54 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_53)) (MACRO_SR_EQ_INTRO :args (_let_53 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69) :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_79 (EQ_RESOLVE (ASSUME :args (_let_52)) (MACRO_SR_EQ_INTRO :args (_let_52 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_51)) (MACRO_SR_EQ_INTRO :args (_let_51 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_50)) (MACRO_SR_EQ_INTRO :args (_let_50 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69) :args ((= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_49)) (MACRO_SR_EQ_INTRO :args (_let_49 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_48)) (MACRO_SR_EQ_INTRO :args (_let_48 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_47)) (MACRO_SR_EQ_INTRO :args (_let_47 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_46)) (MACRO_SR_EQ_INTRO :args (_let_46 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69) :args ((= tptp.exuE1 (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (ASSUME :args (_let_45)))) (let ((_let_87 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_44)) (MACRO_SR_EQ_INTRO :args (_let_44 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69) :args ((= tptp.prop2setE (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) (@ tptp.prop2set false))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO :args (_let_43 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_42)) (MACRO_SR_EQ_INTRO :args (_let_42 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (ASSUME :args (_let_41)))) (let ((_let_91 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69) :args ((= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (not (@ Xphi Xx))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69) :args ((= tptp.nonemptyE1 (forall ((A $$unsorted)) (or (not (@ tptp.nonempty A)) (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69) :args ((= tptp.nonemptyI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (@ tptp.nonempty (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69) :args ((= tptp.nonemptyI1 (forall ((A $$unsorted) (BOUND_VARIABLE_1967 $$unsorted)) (or (not (@ (@ tptp.in BOUND_VARIABLE_1967) A)) (@ tptp.nonempty A)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (ASSUME :args (_let_30)))) (let ((_let_101 (ASSUME :args (_let_28)))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (ASSUME :args (_let_20)))) (let ((_let_108 (ASSUME :args (_let_18)))) (let ((_let_109 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69) :args ((= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (not (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xx Xy))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_114 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (ASSUME :args (_let_3)) (ASSUME :args (_let_5)) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69) :args ((= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (or (not (@ tptp.nonempty A)) (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))))))) SB_DEFAULT SBA_FIXPOINT))) _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69) :args ((not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR _let_65))))))))))))))))))))))))))))))))))))))))))))))))))) SB_DEFAULT SBA_FIXPOINT)) (CONG (CONG (REFL :args ((forall ((A $$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_61)) (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 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (@ _let_1 A)))))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (not (forall ((B $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (not (@ (@ tptp.in B) A))))))))) (CONG (THEORY_PREPROCESS :args ((= _let_56 (tptp.in tptp.emptyset tptp.omega)))) (CONG (REFL :args ((forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) tptp.omega)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega))))) (CONG (REFL :args ((forall ((A $$unsorted) (BOUND_VARIABLE_1608 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_1608))) (or (not (@ (@ tptp.in tptp.emptyset) A)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 tptp.omega)) (not (@ _let_1 A)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) A))))) (not (@ _let_1 tptp.omega)) (@ _let_1 A)))))) (CONG (REFL :args ((forall ((Xphi (-> $$unsorted $$unsorted Bool)) (A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ Xphi Xx) Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ (@ Xphi Xx) Xy)) (= Xx Xy)))))))))) (not (forall ((B $$unsorted)) (not (forall ((Xx $$unsorted)) (= (@ (@ tptp.in Xx) B) (not (forall ((Xy $$unsorted)) (or (not (@ (@ tptp.in Xy) A)) (not (@ (@ Xphi Xy) Xx)))))))))))))) (CONG (REFL :args ((forall ((A $$unsorted) (BOUND_VARIABLE_1671 $$unsorted)) (or (not (@ (@ tptp.in BOUND_VARIABLE_1671) A)) (not (forall ((B $$unsorted)) (or (not (@ (@ tptp.in B) A)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (not (@ _let_1 A))))))))))))) (CONG (REFL :args ((forall ((A $$unsorted)) (not (forall ((B $$unsorted)) (or (not (forall ((C $$unsorted) (BOUND_VARIABLE_1689 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_1689))) (or (not (@ (@ tptp.in C) B)) (not (@ _let_1 C)) (@ _let_1 A))))) (not (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in Xy) A)) (not (forall ((C $$unsorted)) (or (not (@ (@ tptp.in C) B)) (= (@ (@ tptp.in Xx) C) (@ (@ tptp.in Xy) C))))) (= Xx Xy)))) (not (forall ((C $$unsorted) (D $$unsorted) (BOUND_VARIABLE_1737 $$unsorted) (BOUND_VARIABLE_1730 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_1737))) (let ((_let_2 (@ tptp.in BOUND_VARIABLE_1730))) (or (not (@ (@ tptp.in C) B)) (not (@ (@ tptp.in D) B)) (not (@ _let_2 C)) (@ _let_2 D) (not (@ _let_1 D)) (@ _let_1 C)))))) (not (forall ((C $$unsorted) (BOUND_VARIABLE_1804 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 C)) (@ _let_1 A))))) (not (@ (@ tptp.in BOUND_VARIABLE_1804) C)) (not (forall ((D $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in D) B)) (not (@ (@ tptp.in Xx) C)) (not (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (or (not (@ _let_1 D)) (not (@ _let_1 C)))))) (not (forall ((E $$unsorted) (BOUND_VARIABLE_1774 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_1774))) (or (not (@ (@ tptp.in E) B)) (@ (@ tptp.in Xx) E) (not (@ _let_1 E)) (@ _let_1 D))))))))))))))))) (CONG (REFL :args ((forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_2536 $$unsorted)) (or (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ Xphi BOUND_VARIABLE_2536)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_2536)))))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (not (@ Xphi Xx)) (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))) (@ _let_1 A)))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))) (@ Xphi Xx))))) (CONG (REFL :args ((forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_2585 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy))))))) (not (@ Xphi BOUND_VARIABLE_2585)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_2585)))))))) (CONG (REFL :args ((forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr (@ tptp.powerset tptp.emptyset)) (lambda ((BOUND_VARIABLE_6236 $$unsorted)) false))))))) (CONG (REFL :args ((forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (CONG (REFL :args ((forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (CONG (REFL :args (_let_40)) (CONG (REFL :args ((forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_2649 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (@ Xphi Xx)))) (not (@ Xphi BOUND_VARIABLE_2649)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_2649)))))))) (CONG (REFL :args ((forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (@ _let_1 B))))) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (@ _let_1 A))))) (= A B))))) (CONG (REFL :args ((forall ((A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))) (= tptp.emptyset A))))) (CONG (REFL :args ((forall ((A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))) (= tptp.emptyset A))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (= (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))))) (CONG (REFL :args ((forall ((A $$unsorted)) (or (= tptp.emptyset A) (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))))))) (CONG (REFL :args (_let_66)) (CONG (REFL :args ((forall ((BOUND_VARIABLE_1967 $$unsorted)) (not (@ (@ tptp.in BOUND_VARIABLE_1967) tptp.emptyset))))) (CONG (REFL :args (_let_29)) (CONG (TRANS (CONG (REFL :args (_let_27)) (THEORY_PREPROCESS :args ((= _let_26 _let_68))) :args (@)) (THEORY_PREPROCESS :args ((= (@ _let_27 _let_68) (tptp.in tptp.emptyset _let_68))))) (REFL :args ((=> (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (or (not (@ _let_1 A)) (@ _let_1 (@ (@ tptp.setadjoin Xx) A))))) (=> (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (or (not (@ _let_1 (@ (@ tptp.setadjoin Xx) A))) (= Xx Xy) (@ _let_1 A)))) (=> (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (or (not (@ _let_1 (@ (@ tptp.setadjoin Xx) A))) (= Xx Xy) (@ _let_1 A)))) (=> (forall ((A $$unsorted)) (= A (@ (@ tptp.dsetconstr A) (lambda ((BOUND_VARIABLE_6271 $$unsorted)) true)))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (@ _let_1 A))))) (@ (@ tptp.in B) (@ tptp.powerset A)))) (=> _let_19 (=> _let_17 (=> (forall ((A $$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)))) (=> (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (not (@ (@ tptp.in B) A)) (@ _let_1 (@ tptp.setunion A))))) (=> (forall ((A $$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))))))) (=> (forall ((A $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (@ _let_1 (@ tptp.powerset (@ tptp.setunion A)))))) (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_2739 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xx Xy)))))) (not (@ Xphi BOUND_VARIABLE_2739)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_2739)))))) (=> (forall ((A $$unsorted)) (or (= tptp.emptyset A) (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (= Xx Xy))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (= Xx Xy) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))) (=> (forall ((Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (or (not (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))) (= Xx Xz) (= Xy Xz))) (=> _let_4 (=> _let_2 _let_65)))))))))))))))))))))) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args _let_67) :args (not)))))))))))))))))))))))))))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 _let_114)))))))))))))))))))))))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (SYMM (TRANS (ALPHA_EQUIV :args (_let_66 (= A A) (= Xy Xx) (= Xx BOUND_VARIABLE_2159) (= Xphi Xphi))) (MACRO_SR_PRED_INTRO :args ((= (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_2159 $$unsorted)) (or (not (@ (@ tptp.in BOUND_VARIABLE_2159) A)) (not (@ Xphi BOUND_VARIABLE_2159)) (not (= tptp.emptyset (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) _let_65) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE))))) (NOT_IMPLIES_ELIM1 _let_114) :args (_let_65 false _let_66)) :args (false false _let_65)) :args (_let_64 _let_63 _let_62 _let_60 _let_59 _let_58 _let_57 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_28 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_18 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_3 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 35.73/36.15 ) 35.73/36.15 % SZS output end Proof for 35.73/36.15 % cvc5---1.0.5 exiting 35.73/36.15 % cvc5---1.0.5 exiting 35.73/36.16 EOF