0.05/0.11 % Problem : Vampire---4.8_10696 : TPTP v0.0.0. Released v0.0.0. 0.05/0.12 % Command : do_cvc5 %s %d 0.12/0.32 % Computer : n001.cluster.edu 0.12/0.32 % Model : x86_64 x86_64 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.32 % Memory : 8042.1875MB 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.32 % CPULimit : 1440 0.12/0.32 % WCLimit : 180 0.12/0.32 % DateTime : Mon Jul 3 13:29:30 EDT 2023 0.12/0.32 % CPUTime : 0.18/0.45 %----Proving TH0 0.18/0.46 thf(in_type,type, 0.18/0.46 in: $i > $i > $o ). 0.18/0.46 0.18/0.46 thf(exu_type,type, 0.18/0.46 exu: ( $i > $o ) > $o ). 0.18/0.46 0.18/0.46 thf(exu,definition, 0.18/0.46 ( exu 0.18/0.46 = ( ^ [Xphi: $i > $o] : 0.18/0.46 ? [Xx: $i] : 0.18/0.46 ( ( Xphi @ Xx ) 0.18/0.46 & ! [Xy: $i] : 0.18/0.46 ( ( Xphi @ Xy ) 0.18/0.46 => ( Xx = Xy ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(setextAx_type,type, 0.18/0.46 setextAx: $o ). 0.18/0.46 0.18/0.46 thf(setextAx,definition, 0.18/0.46 ( setextAx 0.18/0.46 = ( ! [A: $i,B: $i] : 0.18/0.46 ( ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 <=> ( in @ Xx @ B ) ) 0.18/0.46 => ( A = B ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(emptyset_type,type, 0.18/0.46 emptyset: $i ). 0.18/0.46 0.18/0.46 thf(emptysetAx_type,type, 0.18/0.46 emptysetAx: $o ). 0.18/0.46 0.18/0.46 thf(emptysetAx,definition, 0.18/0.46 ( emptysetAx 0.18/0.46 = ( ! [Xx: $i] : 0.18/0.46 ~ ( in @ Xx @ emptyset ) ) ) ). 0.18/0.46 0.18/0.46 thf(setadjoin_type,type, 0.18/0.46 setadjoin: $i > $i > $i ). 0.18/0.46 0.18/0.46 thf(setadjoinAx_type,type, 0.18/0.46 setadjoinAx: $o ). 0.18/0.46 0.18/0.46 thf(setadjoinAx,definition, 0.18/0.46 ( setadjoinAx 0.18/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.18/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.18/0.46 <=> ( ( Xy = Xx ) 0.18/0.46 | ( in @ Xy @ A ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(powerset_type,type, 0.18/0.46 powerset: $i > $i ). 0.18/0.46 0.18/0.46 thf(powersetAx_type,type, 0.18/0.46 powersetAx: $o ). 0.18/0.46 0.18/0.46 thf(powersetAx,definition, 0.18/0.46 ( powersetAx 0.18/0.46 = ( ! [A: $i,B: $i] : 0.18/0.46 ( ( in @ B @ ( powerset @ A ) ) 0.18/0.46 <=> ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ B ) 0.18/0.46 => ( in @ Xx @ A ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(setunion_type,type, 0.18/0.46 setunion: $i > $i ). 0.18/0.46 0.18/0.46 thf(setunionAx_type,type, 0.18/0.46 setunionAx: $o ). 0.18/0.46 0.18/0.46 thf(setunionAx,definition, 0.18/0.46 ( setunionAx 0.18/0.46 = ( ! [A: $i,Xx: $i] : 0.18/0.46 ( ( in @ Xx @ ( setunion @ A ) ) 0.18/0.46 <=> ? [B: $i] : 0.18/0.46 ( ( in @ Xx @ B ) 0.18/0.46 & ( in @ B @ A ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(omega_type,type, 0.18/0.46 omega: $i ). 0.18/0.46 0.18/0.46 thf(omega0Ax_type,type, 0.18/0.46 omega0Ax: $o ). 0.18/0.46 0.18/0.46 thf(omega0Ax,definition, 0.18/0.46 ( omega0Ax 0.18/0.46 = ( in @ emptyset @ omega ) ) ). 0.18/0.46 0.18/0.46 thf(omegaSAx_type,type, 0.18/0.46 omegaSAx: $o ). 0.18/0.46 0.18/0.46 thf(omegaSAx,definition, 0.18/0.46 ( omegaSAx 0.18/0.46 = ( ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ omega ) 0.18/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(omegaIndAx_type,type, 0.18/0.46 omegaIndAx: $o ). 0.18/0.46 0.18/0.46 thf(omegaIndAx,definition, 0.18/0.46 ( omegaIndAx 0.18/0.46 = ( ! [A: $i] : 0.18/0.46 ( ( ( in @ emptyset @ A ) 0.18/0.46 & ! [Xx: $i] : 0.18/0.46 ( ( ( in @ Xx @ omega ) 0.18/0.46 & ( in @ Xx @ A ) ) 0.18/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) 0.18/0.46 => ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ omega ) 0.18/0.46 => ( in @ Xx @ A ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(replAx_type,type, 0.18/0.46 replAx: $o ). 0.18/0.46 0.18/0.46 thf(replAx,definition, 0.18/0.46 ( replAx 0.18/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] : 0.18/0.46 ( ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 => ( exu 0.18/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) 0.18/0.46 => ? [B: $i] : 0.18/0.46 ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ B ) 0.18/0.46 <=> ? [Xy: $i] : 0.18/0.46 ( ( in @ Xy @ A ) 0.18/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(foundationAx_type,type, 0.18/0.46 foundationAx: $o ). 0.18/0.46 0.18/0.46 thf(foundationAx,definition, 0.18/0.46 ( foundationAx 0.18/0.46 = ( ! [A: $i] : 0.18/0.46 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.18/0.46 => ? [B: $i] : 0.18/0.46 ( ( in @ B @ A ) 0.18/0.46 & ~ ? [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ B ) 0.18/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(wellorderingAx_type,type, 0.18/0.46 wellorderingAx: $o ). 0.18/0.46 0.18/0.46 thf(wellorderingAx,definition, 0.18/0.46 ( wellorderingAx 0.18/0.46 = ( ! [A: $i] : 0.18/0.46 ? [B: $i] : 0.18/0.46 ( ! [C: $i] : 0.18/0.46 ( ( in @ C @ B ) 0.18/0.46 => ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ C ) 0.18/0.46 => ( in @ Xx @ A ) ) ) 0.18/0.46 & ! [Xx: $i,Xy: $i] : 0.18/0.46 ( ( ( in @ Xx @ A ) 0.18/0.46 & ( in @ Xy @ A ) ) 0.18/0.46 => ( ! [C: $i] : 0.18/0.46 ( ( in @ C @ B ) 0.18/0.46 => ( ( in @ Xx @ C ) 0.18/0.46 <=> ( in @ Xy @ C ) ) ) 0.18/0.46 => ( Xx = Xy ) ) ) 0.18/0.46 & ! [C: $i,D: $i] : 0.18/0.46 ( ( ( in @ C @ B ) 0.18/0.46 & ( in @ D @ B ) ) 0.18/0.46 => ( ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ C ) 0.18/0.46 => ( in @ Xx @ D ) ) 0.18/0.46 | ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ D ) 0.18/0.46 => ( in @ Xx @ C ) ) ) ) 0.18/0.46 & ! [C: $i] : 0.18/0.46 ( ( ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ C ) 0.18/0.46 => ( in @ Xx @ A ) ) 0.18/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) ) 0.18/0.46 => ? [D: $i,Xx: $i] : 0.18/0.46 ( ( in @ D @ B ) 0.18/0.46 & ( in @ Xx @ C ) 0.18/0.46 & ~ ? [Xy: $i] : 0.18/0.46 ( ( in @ Xy @ D ) 0.18/0.46 & ( in @ Xy @ C ) ) 0.18/0.46 & ! [E: $i] : 0.18/0.46 ( ( in @ E @ B ) 0.18/0.46 => ( ! [Xy: $i] : 0.18/0.46 ( ( in @ Xy @ E ) 0.18/0.46 => ( in @ Xy @ D ) ) 0.18/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(descr_type,type, 0.18/0.46 descr: ( $i > $o ) > $i ). 0.18/0.46 0.18/0.46 thf(descrp_type,type, 0.18/0.46 descrp: $o ). 0.18/0.46 0.18/0.46 thf(descrp,definition, 0.18/0.46 ( descrp 0.18/0.46 = ( ! [Xphi: $i > $o] : 0.18/0.46 ( ( exu 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.46 => ( Xphi 0.18/0.46 @ ( descr 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(dsetconstr_type,type, 0.18/0.46 dsetconstr: $i > ( $i > $o ) > $i ). 0.18/0.46 0.18/0.46 thf(dsetconstrI_type,type, 0.18/0.46 dsetconstrI: $o ). 0.18/0.46 0.18/0.46 thf(dsetconstrI,definition, 0.18/0.46 ( dsetconstrI 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 => ( ( Xphi @ Xx ) 0.18/0.46 => ( in @ Xx 0.18/0.46 @ ( dsetconstr @ A 0.18/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(dsetconstrEL_type,type, 0.18/0.46 dsetconstrEL: $o ). 0.18/0.46 0.18/0.46 thf(dsetconstrEL,definition, 0.18/0.46 ( dsetconstrEL 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.18/0.46 ( ( in @ Xx 0.18/0.46 @ ( dsetconstr @ A 0.18/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.18/0.46 => ( in @ Xx @ A ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(dsetconstrER_type,type, 0.18/0.46 dsetconstrER: $o ). 0.18/0.46 0.18/0.46 thf(dsetconstrER,definition, 0.18/0.46 ( dsetconstrER 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.18/0.46 ( ( in @ Xx 0.18/0.46 @ ( dsetconstr @ A 0.18/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.18/0.46 => ( Xphi @ Xx ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(exuE1_type,type, 0.18/0.46 exuE1: $o ). 0.18/0.46 0.18/0.46 thf(exuE1,definition, 0.18/0.46 ( exuE1 0.18/0.46 = ( ! [Xphi: $i > $o] : 0.18/0.46 ( ( exu 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.46 => ? [Xx: $i] : 0.18/0.46 ( ( Xphi @ Xx ) 0.18/0.46 & ! [Xy: $i] : 0.18/0.46 ( ( Xphi @ Xy ) 0.18/0.46 => ( Xx = Xy ) ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(prop2set_type,type, 0.18/0.46 prop2set: $o > $i ). 0.18/0.46 0.18/0.46 thf(prop2setE_type,type, 0.18/0.46 prop2setE: $o ). 0.18/0.46 0.18/0.46 thf(prop2setE,definition, 0.18/0.46 ( prop2setE 0.18/0.46 = ( ! [Xphi: $o,Xx: $i] : 0.18/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) ) 0.18/0.46 => Xphi ) ) ) ). 0.18/0.46 0.18/0.46 thf(emptysetE_type,type, 0.18/0.46 emptysetE: $o ). 0.18/0.46 0.18/0.46 thf(emptysetE,definition, 0.18/0.46 ( emptysetE 0.18/0.46 = ( ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ emptyset ) 0.18/0.46 => ! [Xphi: $o] : Xphi ) ) ) ). 0.18/0.46 0.18/0.46 thf(emptysetimpfalse_type,type, 0.18/0.46 emptysetimpfalse: $o ). 0.18/0.46 0.18/0.46 thf(emptysetimpfalse,definition, 0.18/0.46 ( emptysetimpfalse 0.18/0.46 = ( ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ emptyset ) 0.18/0.46 => $false ) ) ) ). 0.18/0.46 0.18/0.46 thf(notinemptyset_type,type, 0.18/0.46 notinemptyset: $o ). 0.18/0.46 0.18/0.46 thf(notinemptyset,definition, 0.18/0.46 ( notinemptyset 0.18/0.46 = ( ! [Xx: $i] : 0.18/0.46 ~ ( in @ Xx @ emptyset ) ) ) ). 0.18/0.46 0.18/0.46 thf(exuE3e_type,type, 0.18/0.46 exuE3e: $o ). 0.18/0.46 0.18/0.46 thf(exuE3e,definition, 0.18/0.46 ( exuE3e 0.18/0.46 = ( ! [Xphi: $i > $o] : 0.18/0.46 ( ( exu 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(setext_type,type, 0.18/0.46 setext: $o ). 0.18/0.46 0.18/0.46 thf(setext,definition, 0.18/0.46 ( setext 0.18/0.46 = ( ! [A: $i,B: $i] : 0.18/0.46 ( ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 => ( in @ Xx @ B ) ) 0.18/0.46 => ( ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ B ) 0.18/0.46 => ( in @ Xx @ A ) ) 0.18/0.46 => ( A = B ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(emptyI_type,type, 0.18/0.46 emptyI: $o ). 0.18/0.46 0.18/0.46 thf(emptyI,definition, 0.18/0.46 ( emptyI 0.18/0.46 = ( ! [A: $i] : 0.18/0.46 ( ! [Xx: $i] : 0.18/0.46 ~ ( in @ Xx @ A ) 0.18/0.46 => ( A = emptyset ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(noeltsimpempty_type,type, 0.18/0.46 noeltsimpempty: $o ). 0.18/0.46 0.18/0.46 thf(noeltsimpempty,definition, 0.18/0.46 ( noeltsimpempty 0.18/0.46 = ( ! [A: $i] : 0.18/0.46 ( ! [Xx: $i] : 0.18/0.46 ~ ( in @ Xx @ A ) 0.18/0.46 => ( A = emptyset ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(setbeta_type,type, 0.18/0.46 setbeta: $o ). 0.18/0.46 0.18/0.46 thf(setbeta,definition, 0.18/0.46 ( setbeta 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 => ( ( in @ Xx 0.18/0.46 @ ( dsetconstr @ A 0.18/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.18/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(nonempty_type,type, 0.18/0.46 nonempty: $i > $o ). 0.18/0.46 0.18/0.46 thf(nonempty,definition, 0.18/0.46 ( nonempty 0.18/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ). 0.18/0.46 0.18/0.46 thf(nonemptyE1_type,type, 0.18/0.46 nonemptyE1: $o ). 0.18/0.46 0.18/0.46 thf(nonemptyE1,definition, 0.18/0.46 ( nonemptyE1 0.18/0.46 = ( ! [A: $i] : 0.18/0.46 ( ( nonempty @ A ) 0.18/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(nonemptyI_type,type, 0.18/0.46 nonemptyI: $o ). 0.18/0.46 0.18/0.46 thf(nonemptyI,definition, 0.18/0.46 ( nonemptyI 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 => ( ( Xphi @ Xx ) 0.18/0.46 => ( nonempty 0.18/0.46 @ ( dsetconstr @ A 0.18/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(nonemptyI1_type,type, 0.18/0.46 nonemptyI1: $o ). 0.18/0.46 0.18/0.46 thf(nonemptyI1,definition, 0.18/0.46 ( nonemptyI1 0.18/0.46 = ( ! [A: $i] : 0.18/0.46 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.18/0.46 => ( nonempty @ A ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(setadjoinIL_type,type, 0.18/0.46 setadjoinIL: $o ). 0.18/0.46 0.18/0.46 thf(setadjoinIL,definition, 0.18/0.46 ( setadjoinIL 0.18/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(emptyinunitempty_type,type, 0.18/0.46 emptyinunitempty: $o ). 0.18/0.46 0.18/0.46 thf(emptyinunitempty,definition, 0.18/0.46 ( emptyinunitempty 0.18/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ). 0.18/0.46 0.18/0.46 thf(setadjoinIR_type,type, 0.18/0.46 setadjoinIR: $o ). 0.18/0.46 0.18/0.46 thf(setadjoinIR,definition, 0.18/0.46 ( setadjoinIR 0.18/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.18/0.46 ( ( in @ Xy @ A ) 0.18/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(setadjoinE_type,type, 0.18/0.46 setadjoinE: $o ). 0.18/0.46 0.18/0.46 thf(setadjoinE,definition, 0.18/0.46 ( setadjoinE 0.18/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.18/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.18/0.46 => ! [Xphi: $o] : 0.18/0.46 ( ( ( Xy = Xx ) 0.18/0.46 => Xphi ) 0.18/0.46 => ( ( ( in @ Xy @ A ) 0.18/0.46 => Xphi ) 0.18/0.46 => Xphi ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(setadjoinOr_type,type, 0.18/0.46 setadjoinOr: $o ). 0.18/0.46 0.18/0.46 thf(setadjoinOr,definition, 0.18/0.46 ( setadjoinOr 0.18/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.18/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.18/0.46 => ( ( Xy = Xx ) 0.18/0.46 | ( in @ Xy @ A ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(setoftrueEq_type,type, 0.18/0.46 setoftrueEq: $o ). 0.18/0.46 0.18/0.46 thf(setoftrueEq,definition, 0.18/0.46 ( setoftrueEq 0.18/0.46 = ( ! [A: $i] : 0.18/0.46 ( ( dsetconstr @ A 0.18/0.46 @ ^ [Xx: $i] : $true ) 0.18/0.46 = A ) ) ) ). 0.18/0.46 0.18/0.46 thf(powersetI_type,type, 0.18/0.46 powersetI: $o ). 0.18/0.46 0.18/0.46 thf(powersetI,definition, 0.18/0.46 ( powersetI 0.18/0.46 = ( ! [A: $i,B: $i] : 0.18/0.46 ( ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ B ) 0.18/0.46 => ( in @ Xx @ A ) ) 0.18/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(emptyinPowerset_type,type, 0.18/0.46 emptyinPowerset: $o ). 0.18/0.46 0.18/0.46 thf(emptyinPowerset,definition, 0.18/0.46 ( emptyinPowerset 0.18/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(emptyInPowerset_type,type, 0.18/0.46 emptyInPowerset: $o ). 0.18/0.46 0.18/0.46 thf(emptyInPowerset,definition, 0.18/0.46 ( emptyInPowerset 0.18/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(powersetE_type,type, 0.18/0.46 powersetE: $o ). 0.18/0.46 0.18/0.46 thf(powersetE,definition, 0.18/0.46 ( powersetE 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] : 0.18/0.46 ( ( in @ B @ ( powerset @ A ) ) 0.18/0.46 => ( ( in @ Xx @ B ) 0.18/0.46 => ( in @ Xx @ A ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(setunionI_type,type, 0.18/0.46 setunionI: $o ). 0.18/0.46 0.18/0.46 thf(setunionI,definition, 0.18/0.46 ( setunionI 0.18/0.46 = ( ! [A: $i,Xx: $i,B: $i] : 0.18/0.46 ( ( in @ Xx @ B ) 0.18/0.46 => ( ( in @ B @ A ) 0.18/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(setunionE_type,type, 0.18/0.46 setunionE: $o ). 0.18/0.46 0.18/0.46 thf(setunionE,definition, 0.18/0.46 ( setunionE 0.18/0.46 = ( ! [A: $i,Xx: $i] : 0.18/0.46 ( ( in @ Xx @ ( setunion @ A ) ) 0.18/0.46 => ! [Xphi: $o] : 0.18/0.46 ( ! [B: $i] : 0.18/0.46 ( ( in @ Xx @ B ) 0.18/0.46 => ( ( in @ B @ A ) 0.18/0.46 => Xphi ) ) 0.18/0.46 => Xphi ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(subPowSU_type,type, 0.18/0.46 subPowSU: $o ). 0.18/0.46 0.18/0.46 thf(subPowSU,definition, 0.18/0.46 ( subPowSU 0.18/0.46 = ( ! [A: $i,Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(exuE2_type,type, 0.18/0.46 exuE2: $o ). 0.18/0.46 0.18/0.46 thf(exuE2,definition, 0.18/0.46 ( exuE2 0.18/0.46 = ( ! [Xphi: $i > $o] : 0.18/0.46 ( ( exu 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.46 => ? [Xx: $i] : 0.18/0.46 ! [Xy: $i] : 0.18/0.46 ( ( Xphi @ Xy ) 0.18/0.46 <=> ( Xy = Xx ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(nonemptyImpWitness_type,type, 0.18/0.46 nonemptyImpWitness: $o ). 0.18/0.46 0.18/0.46 thf(nonemptyImpWitness,definition, 0.18/0.46 ( nonemptyImpWitness 0.18/0.46 = ( ! [A: $i] : 0.18/0.46 ( ( nonempty @ A ) 0.18/0.46 => ? [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 & $true ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(uniqinunit_type,type, 0.18/0.46 uniqinunit: $o ). 0.18/0.46 0.18/0.46 thf(uniqinunit,definition, 0.18/0.46 ( uniqinunit 0.18/0.46 = ( ! [Xx: $i,Xy: $i] : 0.18/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.18/0.46 => ( Xx = Xy ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(notinsingleton_type,type, 0.18/0.46 notinsingleton: $o ). 0.18/0.46 0.18/0.46 thf(notinsingleton,definition, 0.18/0.46 ( notinsingleton 0.18/0.46 = ( ! [Xx: $i,Xy: $i] : 0.18/0.46 ( ( Xx != Xy ) 0.18/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(eqinunit_type,type, 0.18/0.46 eqinunit: $o ). 0.18/0.46 0.18/0.46 thf(eqinunit,definition, 0.18/0.46 ( eqinunit 0.18/0.46 = ( ! [Xx: $i,Xy: $i] : 0.18/0.46 ( ( Xx = Xy ) 0.18/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(singletonsswitch_type,type, 0.18/0.46 singletonsswitch: $o ). 0.18/0.46 0.18/0.46 thf(singletonsswitch,definition, 0.18/0.46 ( singletonsswitch 0.18/0.46 = ( ! [Xx: $i,Xy: $i] : 0.18/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.18/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(upairsetE_type,type, 0.18/0.46 upairsetE: $o ). 0.18/0.46 0.18/0.46 thf(upairsetE,definition, 0.18/0.46 ( upairsetE 0.18/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] : 0.18/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) 0.18/0.46 => ( ( Xz = Xx ) 0.18/0.46 | ( Xz = Xy ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(upairsetIL_type,type, 0.18/0.46 upairsetIL: $o ). 0.18/0.46 0.18/0.46 thf(upairsetIL,definition, 0.18/0.46 ( upairsetIL 0.18/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(upairsetIR_type,type, 0.18/0.46 upairsetIR: $o ). 0.18/0.46 0.18/0.46 thf(upairsetIR,definition, 0.18/0.46 ( upairsetIR 0.18/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(emptyE1_type,type, 0.18/0.46 emptyE1: $o ). 0.18/0.46 0.18/0.46 thf(emptyE1,definition, 0.18/0.46 ( emptyE1 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.46 ( ? [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 & ( Xphi @ Xx ) ) 0.18/0.46 => ( ( ( dsetconstr @ A 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.46 = emptyset ) 0.18/0.46 => $false ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(vacuousDall_type,type, 0.18/0.46 vacuousDall: $o ). 0.18/0.46 0.18/0.46 thf(vacuousDall,definition, 0.18/0.46 ( vacuousDall 0.18/0.46 = ( ! [Xphi: $i > $o,Xx: $i] : 0.18/0.46 ( ( in @ Xx @ emptyset ) 0.18/0.46 => ( Xphi @ Xx ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(quantDeMorgan1_type,type, 0.18/0.46 quantDeMorgan1: $o ). 0.18/0.46 0.18/0.46 thf(quantDeMorgan1,definition, 0.18/0.46 ( quantDeMorgan1 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.46 ( ~ ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 => ( Xphi @ Xx ) ) 0.18/0.46 => ? [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(quantDeMorgan2_type,type, 0.18/0.46 quantDeMorgan2: $o ). 0.18/0.46 0.18/0.46 thf(quantDeMorgan2,definition, 0.18/0.46 ( quantDeMorgan2 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.46 ( ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 => ~ ( Xphi @ Xx ) ) 0.18/0.46 => ~ ? [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 & ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(quantDeMorgan3_type,type, 0.18/0.46 quantDeMorgan3: $o ). 0.18/0.46 0.18/0.46 thf(quantDeMorgan3,definition, 0.18/0.46 ( quantDeMorgan3 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.46 ( ~ ? [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 & ( Xphi @ Xx ) ) 0.18/0.46 => ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(quantDeMorgan4_type,type, 0.18/0.46 quantDeMorgan4: $o ). 0.18/0.46 0.18/0.46 thf(quantDeMorgan4,definition, 0.18/0.46 ( quantDeMorgan4 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.46 ( ? [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 & ~ ( Xphi @ Xx ) ) 0.18/0.46 => ~ ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 => ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(prop2setI_type,type, 0.18/0.46 prop2setI: $o ). 0.18/0.46 0.18/0.46 thf(prop2setI,definition, 0.18/0.46 ( prop2setI 0.18/0.46 = ( ! [Xphi: $o] : 0.18/0.46 ( Xphi 0.18/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(set2prop_type,type, 0.18/0.46 set2prop: $i > $o ). 0.18/0.46 0.18/0.46 thf(prop2set2propI_type,type, 0.18/0.46 prop2set2propI: $o ). 0.18/0.46 0.18/0.46 thf(prop2set2propI,definition, 0.18/0.46 ( prop2set2propI 0.18/0.46 = ( ! [Xphi: $o] : 0.18/0.46 ( Xphi 0.18/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(notdexE_type,type, 0.18/0.46 notdexE: $o ). 0.18/0.46 0.18/0.46 thf(notdexE,definition, 0.18/0.46 ( notdexE 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.46 ( ~ ? [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 & ( Xphi @ Xx ) ) 0.18/0.46 => ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(notdallE_type,type, 0.18/0.46 notdallE: $o ). 0.18/0.46 0.18/0.46 thf(notdallE,definition, 0.18/0.46 ( notdallE 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o] : 0.18/0.46 ( ~ ! [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 => ( Xphi @ Xx ) ) 0.18/0.46 => ? [Xx: $i] : 0.18/0.46 ( ( in @ Xx @ A ) 0.18/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(exuI1_type,type, 0.18/0.46 exuI1: $o ). 0.18/0.46 0.18/0.46 thf(exuI1,definition, 0.18/0.46 ( exuI1 0.18/0.46 = ( ! [Xphi: $i > $o] : 0.18/0.46 ( ? [Xx: $i] : 0.18/0.46 ( ( Xphi @ Xx ) 0.18/0.46 & ! [Xy: $i] : 0.18/0.46 ( ( Xphi @ Xy ) 0.18/0.46 => ( Xx = Xy ) ) ) 0.18/0.46 => ( exu 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ). 0.18/0.46 0.18/0.46 thf(exuI3,conjecture, 0.18/0.46 ( setextAx 0.18/0.46 => ( emptysetAx 0.18/0.46 => ( setadjoinAx 0.18/0.46 => ( ( setunionAx 0.18/0.46 => ( ( ( omegaIndAx 0.18/0.46 => ( replAx 0.18/0.46 => ( ( wellorderingAx 0.18/0.46 => ( ( ( ( ( exuE1 0.18/0.46 => ( ( ( ( ( exuE3e 0.18/0.46 => ( setext 0.18/0.46 => ( emptyI 0.18/0.46 => ( noeltsimpempty 0.18/0.46 => ( ( nonemptyE1 0.18/0.46 => ( ( nonemptyI1 0.18/0.46 => ( setadjoinIL 0.18/0.46 => ( emptyinunitempty 0.18/0.46 => ( setadjoinIR 0.18/0.46 => ( ( setadjoinOr 0.18/0.46 => ( ( ( emptyinPowerset 0.18/0.46 => ( ( powersetE 0.18/0.46 => ( ( setunionE 0.18/0.46 => ( ( ( nonemptyImpWitness 0.18/0.46 => ( ( notinsingleton 0.18/0.46 => ( eqinunit 0.18/0.46 => ( singletonsswitch 0.18/0.46 => ( ( ( ( ( ( ( quantDeMorgan2 0.18/0.46 => ( ( ( ( ( ( ( exuI1 0.18/0.46 => ! [Xphi: $i > $o] : 0.18/0.46 ( ( ( exu 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.18/0.46 <= ! [Xx: $i,Xy: $i] : 0.18/0.46 ( ( ( Xphi @ Xy ) 0.18/0.46 => ( Xx = Xy ) ) 0.18/0.48 <= ( Xphi @ Xx ) ) ) 0.18/0.48 <= ? [Xx: $i] : ( Xphi @ Xx ) ) ) 0.18/0.48 <= notdallE ) 0.18/0.48 <= notdexE ) 0.18/0.48 <= prop2set2propI ) 0.18/0.48 <= prop2setI ) 0.18/0.48 <= quantDeMorgan4 ) 0.18/0.48 <= quantDeMorgan3 ) ) 0.18/0.48 <= quantDeMorgan1 ) 0.18/0.48 <= vacuousDall ) 0.18/0.48 <= emptyE1 ) 0.18/0.48 <= upairsetIR ) 0.18/0.48 <= upairsetIL ) 0.18/0.48 <= upairsetE ) ) ) ) 0.18/0.48 <= uniqinunit ) ) 0.18/0.48 <= exuE2 ) 0.18/0.48 <= subPowSU ) ) 0.18/0.48 <= setunionI ) ) 0.18/0.48 <= emptyInPowerset ) ) 0.18/0.48 <= powersetI ) 0.18/0.48 <= setoftrueEq ) ) 0.18/0.48 <= setadjoinE ) ) ) ) ) 0.18/0.48 <= nonemptyI ) ) 0.18/0.48 <= setbeta ) ) ) ) ) 0.18/0.48 <= notinemptyset ) 0.18/0.48 <= emptysetimpfalse ) 0.18/0.48 <= emptysetE ) 0.18/0.48 <= prop2setE ) ) 0.18/0.48 <= dsetconstrER ) 0.18/0.48 <= dsetconstrEL ) 0.18/0.48 <= dsetconstrI ) 0.18/0.48 <= descrp ) ) 0.18/0.48 <= foundationAx ) ) ) 0.18/0.48 <= omegaSAx ) 0.18/0.48 <= omega0Ax ) ) 0.18/0.48 <= powersetAx ) ) ) ) ). 0.18/0.48 0.18/0.48 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.cR9IkB61CS/cvc5---1.0.5_10798.p... 0.18/0.48 (declare-sort $$unsorted 0) 0.18/0.48 (declare-fun tptp.in ($$unsorted $$unsorted) Bool) 0.18/0.48 (declare-fun tptp.exu ((-> $$unsorted Bool)) Bool) 0.18/0.48 (assert (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy)))))))) 0.18/0.48 (declare-fun tptp.setextAx () Bool) 0.18/0.48 (assert (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B))))) 0.18/0.48 (declare-fun tptp.emptyset () $$unsorted) 0.18/0.48 (declare-fun tptp.emptysetAx () Bool) 0.18/0.48 (assert (= tptp.emptysetAx (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.18/0.48 (declare-fun tptp.setadjoin ($$unsorted $$unsorted) $$unsorted) 0.18/0.48 (declare-fun tptp.setadjoinAx () Bool) 0.18/0.48 (assert (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.18/0.48 (declare-fun tptp.powerset ($$unsorted) $$unsorted) 0.18/0.48 (declare-fun tptp.powersetAx () Bool) 0.18/0.48 (assert (= tptp.powersetAx (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))))))) 0.18/0.48 (declare-fun tptp.setunion ($$unsorted) $$unsorted) 0.18/0.48 (declare-fun tptp.setunionAx () Bool) 0.18/0.48 (assert (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A))))))) 0.18/0.48 (declare-fun tptp.omega () $$unsorted) 0.18/0.48 (declare-fun tptp.omega0Ax () Bool) 0.18/0.48 (assert (= tptp.omega0Ax (@ (@ tptp.in tptp.emptyset) tptp.omega))) 0.18/0.48 (declare-fun tptp.omegaSAx () Bool) 0.18/0.48 (assert (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega))))) 0.18/0.48 (declare-fun tptp.omegaIndAx () Bool) 0.18/0.48 (assert (= tptp.omegaIndAx (forall ((A $$unsorted)) (=> (and (@ (@ tptp.in tptp.emptyset) A) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (and (@ _let_1 tptp.omega) (@ _let_1 A)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) A))))) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 tptp.omega) (@ _let_1 A)))))))) 0.18/0.48 (declare-fun tptp.replAx () Bool) 0.18/0.48 (assert (= tptp.replAx (forall ((Xphi (-> $$unsorted $$unsorted Bool)) (A $$unsorted)) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ tptp.exu (lambda ((Xy $$unsorted)) (@ (@ Xphi Xx) Xy))))) (exists ((B $$unsorted)) (forall ((Xx $$unsorted)) (= (@ (@ tptp.in Xx) B) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) A) (@ (@ Xphi Xy) Xx)))))))))) 0.18/0.48 (declare-fun tptp.foundationAx () Bool) 0.18/0.48 (assert (= tptp.foundationAx (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in B) A) (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 B) (@ _let_1 A))))))))))) 0.18/0.48 (declare-fun tptp.wellorderingAx () Bool) 0.18/0.48 (assert (= tptp.wellorderingAx (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (forall ((C $$unsorted)) (=> (@ (@ tptp.in C) B) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 C) (@ _let_1 A)))))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (and (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) A)) (=> (forall ((C $$unsorted)) (=> (@ (@ tptp.in C) B) (= (@ (@ tptp.in Xx) C) (@ (@ tptp.in Xy) C)))) (= Xx Xy)))) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (@ (@ tptp.in C) B) (@ (@ tptp.in D) B)) (or (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 C) (@ _let_1 D)))) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 D) (@ _let_1 C))))))) (forall ((C $$unsorted)) (=> (and (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 C) (@ _let_1 A)))) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) C))) (exists ((D $$unsorted) (Xx $$unsorted)) (and (@ (@ tptp.in D) B) (@ (@ tptp.in Xx) C) (not (exists ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (and (@ _let_1 D) (@ _let_1 C))))) (forall ((E $$unsorted)) (=> (@ (@ tptp.in E) B) (or (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 E) (@ _let_1 D)))) (@ (@ tptp.in Xx) E))))))))))))) 0.18/0.48 (declare-fun tptp.descr ((-> $$unsorted Bool)) $$unsorted) 0.18/0.48 (declare-fun tptp.descrp () Bool) 0.18/0.48 (assert (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) 0.18/0.48 (declare-fun tptp.dsetconstr ($$unsorted (-> $$unsorted Bool)) $$unsorted) 0.18/0.48 (declare-fun tptp.dsetconstrI () Bool) 0.18/0.48 (assert (= tptp.dsetconstrI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ Xphi Xx) (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))))))))) 0.18/0.48 (declare-fun tptp.dsetconstrEL () Bool) 0.18/0.48 (assert (= tptp.dsetconstrEL (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ _let_1 A)))))) 0.18/0.48 (declare-fun tptp.dsetconstrER () Bool) 0.18/0.48 (assert (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))) 0.18/0.48 (declare-fun tptp.exuE1 () Bool) 0.18/0.48 (assert (= tptp.exuE1 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))))))) 0.18/0.48 (declare-fun tptp.prop2set (Bool) $$unsorted) 0.18/0.48 (declare-fun tptp.prop2setE () Bool) 0.18/0.48 (assert (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi)))) 0.18/0.48 (declare-fun tptp.emptysetE () Bool) 0.18/0.48 (assert (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi))))) 0.18/0.48 (declare-fun tptp.emptysetimpfalse () Bool) 0.18/0.48 (assert (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false)))) 0.18/0.48 (declare-fun tptp.notinemptyset () Bool) 0.18/0.48 (assert (= tptp.notinemptyset (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.18/0.48 (declare-fun tptp.exuE3e () Bool) 0.18/0.48 (assert (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx)))))) 0.18/0.48 (declare-fun tptp.setext () Bool) 0.18/0.48 (assert (= tptp.setext (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (= A B)))))) 0.18/0.48 (declare-fun tptp.emptyI () Bool) 0.18/0.48 (assert (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.18/0.48 (declare-fun tptp.noeltsimpempty () Bool) 0.18/0.48 (assert (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.18/0.48 (declare-fun tptp.setbeta () Bool) 0.18/0.48 (assert (= tptp.setbeta (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (= (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))))) 0.18/0.48 (declare-fun tptp.nonempty ($$unsorted) Bool) 0.18/0.48 (assert (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset))))) 0.18/0.48 (declare-fun tptp.nonemptyE1 () Bool) 0.18/0.48 (assert (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)))))) 0.18/0.48 (declare-fun tptp.nonemptyI () Bool) 0.18/0.48 (assert (= tptp.nonemptyI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (@ tptp.nonempty (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))))) 0.18/0.48 (declare-fun tptp.nonemptyI1 () Bool) 0.18/0.48 (assert (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A))))) 0.18/0.48 (declare-fun tptp.setadjoinIL () Bool) 0.18/0.48 (assert (= tptp.setadjoinIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) 0.18/0.48 (declare-fun tptp.emptyinunitempty () Bool) 0.18/0.48 (assert (= tptp.emptyinunitempty (@ (@ tptp.in tptp.emptyset) (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) 0.18/0.48 (declare-fun tptp.setadjoinIR () Bool) 0.18/0.48 (assert (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A))))))) 0.18/0.48 (declare-fun tptp.setadjoinE () Bool) 0.18/0.48 (assert (= tptp.setadjoinE (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (forall ((Xphi Bool)) (=> (=> (= Xy Xx) Xphi) (=> (=> (@ (@ tptp.in Xy) A) Xphi) Xphi))))))) 0.18/0.48 (declare-fun tptp.setadjoinOr () Bool) 0.18/0.48 (assert (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.18/0.48 (declare-fun tptp.setoftrueEq () Bool) 0.18/0.48 (assert (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A)))) 0.18/0.48 (declare-fun tptp.powersetI () Bool) 0.18/0.48 (assert (= tptp.powersetI (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (@ (@ tptp.in B) (@ tptp.powerset A)))))) 0.18/0.48 (declare-fun tptp.emptyinPowerset () Bool) 0.18/0.48 (assert (= tptp.emptyinPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) 0.18/0.48 (declare-fun tptp.emptyInPowerset () Bool) 0.18/0.48 (assert (= tptp.emptyInPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) 0.18/0.48 (declare-fun tptp.powersetE () Bool) 0.18/0.48 (assert (= tptp.powersetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (=> (@ _let_1 B) (@ _let_1 A))))))) 0.18/0.48 (declare-fun tptp.setunionI () Bool) 0.18/0.48 (assert (= tptp.setunionI (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (=> (@ (@ tptp.in B) A) (@ _let_1 (@ tptp.setunion A)))))))) 0.18/0.48 (declare-fun tptp.setunionE () Bool) 0.18/0.48 (assert (= tptp.setunionE (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (forall ((Xphi Bool)) (=> (forall ((B $$unsorted)) (=> (@ (@ tptp.in Xx) B) (=> (@ (@ tptp.in B) A) Xphi))) Xphi)))))) 0.18/0.48 (declare-fun tptp.subPowSU () Bool) 0.18/0.48 (assert (= tptp.subPowSU (forall ((A $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.powerset (@ tptp.setunion A)))))))) 0.18/0.48 (declare-fun tptp.exuE2 () Bool) 0.18/0.48 (assert (= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))))))) 0.18/0.48 (declare-fun tptp.nonemptyImpWitness () Bool) 0.18/0.48 (assert (= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) true)))))) 0.18/0.48 (declare-fun tptp.uniqinunit () Bool) 0.18/0.48 (assert (= tptp.uniqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy))))) 0.18/0.48 (declare-fun tptp.notinsingleton () Bool) 0.18/0.48 (assert (= tptp.notinsingleton (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (not (= Xx Xy)) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) 0.18/0.48 (declare-fun tptp.eqinunit () Bool) 0.18/0.48 (assert (= tptp.eqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.18/0.48 (declare-fun tptp.singletonsswitch () Bool) 0.18/0.48 (assert (= tptp.singletonsswitch (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) 0.18/0.48 (declare-fun tptp.upairsetE () Bool) 0.18/0.48 (assert (= tptp.upairsetE (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy)))))) 0.18/0.48 (declare-fun tptp.upairsetIL () Bool) 0.18/0.48 (assert (= tptp.upairsetIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.18/0.48 (declare-fun tptp.upairsetIR () Bool) 0.18/0.48 (assert (= tptp.upairsetIR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.18/0.48 (declare-fun tptp.emptyE1 () Bool) 0.18/0.48 (assert (= tptp.emptyE1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (=> (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) tptp.emptyset) false))))) 0.18/0.48 (declare-fun tptp.vacuousDall () Bool) 0.18/0.48 (assert (= tptp.vacuousDall (forall ((Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (@ Xphi Xx))))) 0.18/0.48 (declare-fun tptp.quantDeMorgan1 () Bool) 0.18/0.48 (assert (= tptp.quantDeMorgan1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.18/0.48 (declare-fun tptp.quantDeMorgan2 () Bool) 0.18/0.48 (assert (= tptp.quantDeMorgan2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))) (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))))))) 0.18/0.48 (declare-fun tptp.quantDeMorgan3 () Bool) 0.18/0.48 (assert (= tptp.quantDeMorgan3 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.18/0.48 (declare-fun tptp.quantDeMorgan4 () Bool) 0.18/0.48 (assert (= tptp.quantDeMorgan4 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))))))) 0.18/0.48 (declare-fun tptp.prop2setI () Bool) 0.18/0.48 (assert (= tptp.prop2setI (forall ((Xphi Bool)) (=> Xphi (@ (@ tptp.in tptp.emptyset) (@ tptp.prop2set Xphi)))))) 0.18/0.48 (declare-fun tptp.set2prop ($$unsorted) Bool) 0.18/0.48 (declare-fun tptp.prop2set2propI () Bool) 0.18/0.48 (assert (= tptp.prop2set2propI (forall ((Xphi Bool)) (=> Xphi (@ tptp.set2prop (@ tptp.prop2set Xphi)))))) 0.18/0.48 (declare-fun tptp.notdexE () Bool) 0.18/0.48 (assert (= tptp.notdexE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.18/0.48 (declare-fun tptp.notdallE () Bool) 0.18/0.48 (assert (= tptp.notdallE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.18/0.48 (declare-fun tptp.exuI1 () Bool) 0.18/0.48 (assert (= tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) 0.18/0.48 (assert (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (@ Xphi Xx)) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0.18/0.48 (set-info :filename cvc5---1.0.5_10798) 0.18/0.48 (check-sat-assuming ( true )) 0.18/0.48 ------- get file name : TPTP file name is 0.18/0.48 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10798.smt2... 0.18/0.48 --- Run --ho-elim --full-saturate-quant at 10... 0.52/0.69 % SZS status Theorem for 0.52/0.69 % SZS output start Proof for 0.52/0.69 ( 0.52/0.69 (let ((_let_1 (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (@ Xphi Xx)) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (let ((_let_2 (= tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) (let ((_let_3 (= tptp.notdallE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))) (let ((_let_4 (= tptp.notdexE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))) (let ((_let_5 (= tptp.prop2set2propI (forall ((Xphi Bool)) (=> Xphi (@ tptp.set2prop (@ tptp.prop2set Xphi))))))) (let ((_let_6 (= tptp.prop2setI (forall ((Xphi Bool)) (=> Xphi (@ (@ tptp.in tptp.emptyset) (@ tptp.prop2set Xphi))))))) (let ((_let_7 (= tptp.quantDeMorgan4 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx))))))))) (let ((_let_8 (= tptp.quantDeMorgan3 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))) (let ((_let_9 (= tptp.quantDeMorgan2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))) (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))))))))) (let ((_let_10 (= tptp.quantDeMorgan1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))) (let ((_let_11 (= tptp.vacuousDall (forall ((Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (@ Xphi Xx)))))) (let ((_let_12 (= tptp.emptyE1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (=> (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) tptp.emptyset) false)))))) (let ((_let_13 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) (let ((_let_14 (= tptp.upairsetIR _let_13))) (let ((_let_15 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) (let ((_let_16 (= tptp.upairsetIL _let_15))) (let ((_let_17 (= tptp.upairsetE (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy))))))) (let ((_let_18 (= 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_19 (= tptp.eqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))) (let ((_let_20 (= tptp.notinsingleton (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (not (= Xx Xy)) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) (let ((_let_21 (= tptp.uniqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy)))))) (let ((_let_22 (= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) true))))))) (let ((_let_23 (= 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_24 (= 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_25 (= tptp.setunionE (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (forall ((Xphi Bool)) (=> (forall ((B $$unsorted)) (=> (@ (@ tptp.in Xx) B) (=> (@ (@ tptp.in B) A) Xphi))) Xphi))))))) (let ((_let_26 (= tptp.setunionI (forall ((A $$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_27 (= tptp.powersetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (=> (@ _let_1 B) (@ _let_1 A)))))))) (let ((_let_28 (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) (let ((_let_29 (= tptp.emptyInPowerset _let_28))) (let ((_let_30 (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) (let ((_let_31 (= tptp.emptyinPowerset _let_30))) (let ((_let_32 (= tptp.powersetI (forall ((A $$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_33 (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A))))) (let ((_let_34 (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A)))))))) (let ((_let_35 (= tptp.setadjoinE (forall ((Xx $$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_36 (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A)))))))) (let ((_let_37 (@ tptp.in tptp.emptyset))) (let ((_let_38 (@ _let_37 (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) (let ((_let_39 (= tptp.emptyinunitempty _let_38))) (let ((_let_40 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) (let ((_let_41 (= tptp.setadjoinIL _let_40))) (let ((_let_42 (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A)))))) (let ((_let_43 (= tptp.nonemptyI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (@ tptp.nonempty (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))))))))) (let ((_let_44 (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A))))))) (let ((_let_45 (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset)))))) (let ((_let_46 (= 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_47 (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))) (let ((_let_48 (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))) (let ((_let_49 (= 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_50 (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx))))))) (let ((_let_51 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_52 (= tptp.notinemptyset _let_51))) (let ((_let_53 (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false))))) (let ((_let_54 (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi)))))) (let ((_let_55 (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi))))) (let ((_let_56 (= tptp.exuE1 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy)))))))))) (let ((_let_57 (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx)))))) (let ((_let_58 (= tptp.dsetconstrEL (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ _let_1 A))))))) (let ((_let_59 (= tptp.dsetconstrI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ Xphi Xx) (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))))))) (let ((_let_60 (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (let ((_let_61 (= 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 $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 E) (@ _let_1 D)))) (@ (@ tptp.in Xx) E)))))))))))))) (let ((_let_62 (= tptp.foundationAx (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in B) A) (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 B) (@ _let_1 A)))))))))))) (let ((_let_63 (= tptp.replAx (forall ((Xphi (-> $$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 $$unsorted)) (and (@ (@ tptp.in Xy) A) (@ (@ Xphi Xy) Xx))))))))))) (let ((_let_64 (= tptp.omegaIndAx (forall ((A $$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_65 (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega)))))) (let ((_let_66 (@ _let_37 tptp.omega))) (let ((_let_67 (= tptp.omega0Ax _let_66))) (let ((_let_68 (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A)))))))) (let ((_let_69 (= tptp.powersetAx (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A))))))))) (let ((_let_70 (= tptp.setadjoinAx (forall ((Xx $$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_71 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_72 (= tptp.emptysetAx _let_71))) (let ((_let_73 (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B)))))) (let ((_let_74 (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))))))) (let ((_let_75 (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (ho_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_34 Xx)) (not (ho_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_34 Xy)) (= Xx Xy))))) (let ((_let_76 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41))) (let ((_let_77 (ho_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41))) (let ((_let_78 (not _let_77))) (let ((_let_79 (ho_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35))) (let ((_let_80 (not _let_79))) (let ((_let_81 (or _let_80 _let_78 _let_76))) (let ((_let_82 (forall ((Xx $$unsorted)) (or (not (ho_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_34 Xx)) (not (forall ((Xy $$unsorted)) (or (not (ho_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_34 Xy)) (= Xx Xy)))))))) (let ((_let_83 (not _let_82))) (let ((_let_84 (not _let_75))) (let ((_let_85 (or _let_80 _let_84 _let_83))) (let ((_let_86 (forall ((BOUND_VARIABLE_3976 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2642 $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_3976 BOUND_VARIABLE_2642)) (not (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_3976 Xx)) (not (ho_10 BOUND_VARIABLE_3976 Xy)) (= Xx Xy)))) (not (forall ((Xx $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_3976 Xx)) (not (forall ((Xy $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_3976 Xy)) (= Xx Xy))))))))))) (let ((_let_87 (not _let_85))) (let ((_let_88 (=>))) (let ((_let_89 (=> (forall ((A $$unsorted) (BOUND_VARIABLE_4041 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2545 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (ho_10 (ho_21 k_20 Xx) A)) (not (ho_10 BOUND_VARIABLE_4041 Xx))))) (not (ho_10 (ho_21 k_20 BOUND_VARIABLE_2545) A)) (not (ho_10 BOUND_VARIABLE_4041 BOUND_VARIABLE_2545)))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_4021 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2575 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (ho_10 (ho_21 k_20 Xx) A)) (ho_10 BOUND_VARIABLE_4021 Xx)))) (not (ho_10 (ho_21 k_20 BOUND_VARIABLE_2575) A)) (ho_10 BOUND_VARIABLE_4021 BOUND_VARIABLE_2575))) (=> (forall ((BOUND_VARIABLE_3999 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2606 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_3999 Xx)) (not (forall ((Xy $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_3999 Xy)) (= Xx Xy))))))) (not (ho_10 BOUND_VARIABLE_3999 BOUND_VARIABLE_2606)) (not (forall ((Xy $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_3999 Xy)) (= Xy BOUND_VARIABLE_2606)))))) _let_86))))) (let ((_let_90 (APPLY_UF ho_10))) (let ((_let_91 (CONG (REFL :args (k_22)) (MACRO_SR_PRED_INTRO :args ((= true BOOLEAN_TERM_VARIABLE_5208))) :args (APPLY_UF ho_23)))) (let ((_let_92 (ho_21 k_20 tptp.emptyset))) (let ((_let_93 (forall ((A $$unsorted) (BOUND_VARIABLE_4070 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2498 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (ho_10 (ho_21 k_20 Xx) A)) (ho_10 BOUND_VARIABLE_4070 Xx)))) (not (ho_10 (ho_21 k_20 BOUND_VARIABLE_2498) A)) (ho_10 BOUND_VARIABLE_4070 BOUND_VARIABLE_2498))))) (let ((_let_94 (forall ((A $$unsorted) (BOUND_VARIABLE_4086 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2468 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (ho_10 (ho_21 k_20 Xx) A)) (not (ho_10 BOUND_VARIABLE_4086 Xx))))) (not (ho_10 (ho_21 k_20 BOUND_VARIABLE_2468) A)) (not (ho_10 BOUND_VARIABLE_4086 BOUND_VARIABLE_2468)))))) (let ((_let_95 (forall ((A $$unsorted) (BOUND_VARIABLE_4104 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2437 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (ho_10 (ho_21 k_20 Xx) A)) (not (ho_10 BOUND_VARIABLE_4104 Xx))))) (not (ho_10 (ho_21 k_20 BOUND_VARIABLE_2437) A)) (not (ho_10 BOUND_VARIABLE_4104 BOUND_VARIABLE_2437)))))) (let ((_let_96 (forall ((A $$unsorted) (BOUND_VARIABLE_4122 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2406 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (ho_10 (ho_21 k_20 Xx) A)) (ho_10 BOUND_VARIABLE_4122 Xx)))) (not (ho_10 (ho_21 k_20 BOUND_VARIABLE_2406) A)) (ho_10 BOUND_VARIABLE_4122 BOUND_VARIABLE_2406))))) (let ((_let_97 (forall ((BOUND_VARIABLE_4138 |u_(-> $$unsorted Bool)|) (Xx $$unsorted)) (or (not (ho_10 (ho_21 k_20 Xx) tptp.emptyset)) (ho_10 BOUND_VARIABLE_4138 Xx))))) (let ((_let_98 (forall ((A $$unsorted) (BOUND_VARIABLE_4147 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2371 $$unsorted)) (or (not (= tptp.emptyset (ho_27 (ho_26 k_25 A) (ho_12 k_19 BOUND_VARIABLE_4147)))) (not (ho_10 (ho_21 k_20 BOUND_VARIABLE_2371) A)) (not (ho_10 BOUND_VARIABLE_4147 BOUND_VARIABLE_2371)))))) (let ((_let_99 (forall ((Xx $$unsorted) (Xy $$unsorted)) (ho_10 (ho_21 k_20 Xy) (ho_30 (ho_29 k_28 Xx) (ho_30 (ho_29 k_28 Xy) tptp.emptyset)))))) (let ((_let_100 (forall ((Xx $$unsorted) (Xy $$unsorted)) (ho_10 (ho_21 k_20 Xx) (ho_30 (ho_29 k_28 Xx) (ho_30 (ho_29 k_28 Xy) tptp.emptyset)))))) (let ((_let_101 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (or (not (ho_10 (ho_21 k_20 Xz) (ho_30 (ho_29 k_28 Xx) (ho_30 (ho_29 k_28 Xy) tptp.emptyset)))) (= Xx Xz) (= Xy Xz))))) (let ((_let_102 (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (ho_10 (ho_21 k_20 Xx) (ho_30 (ho_29 k_28 Xy) tptp.emptyset))) (ho_10 (ho_21 k_20 Xy) (ho_30 (ho_29 k_28 Xx) tptp.emptyset)))))) (let ((_let_103 (forall ((Xy $$unsorted)) (ho_10 (ho_21 k_20 Xy) (ho_30 (ho_29 k_28 Xy) tptp.emptyset))))) (let ((_let_104 (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (= Xx Xy) (not (ho_10 (ho_21 k_20 Xy) (ho_30 (ho_29 k_28 Xx) tptp.emptyset))))))) (let ((_let_105 (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (ho_10 (ho_21 k_20 Xx) 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(B $$unsorted)) (let ((_let_1 (ho_21 k_20 Xx))) (or (not (ho_10 _let_1 B)) (not (ho_10 (ho_21 k_20 B) A)) (ho_10 _let_1 (ho_30 k_31 A))))))) (let ((_let_111 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (ho_21 k_20 Xx))) (or (not (ho_10 (ho_21 k_20 B) (ho_30 k_32 A))) (not (ho_10 _let_1 B)) (ho_10 _let_1 A)))))) (let ((_let_112 (forall ((A $$unsorted)) (ho_10 (ho_21 k_20 tptp.emptyset) (ho_30 k_32 A))))) (let ((_let_113 (forall ((A $$unsorted)) (ho_10 (ho_21 k_20 tptp.emptyset) (ho_30 k_32 A))))) (let ((_let_114 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_21 k_20 Xx))) (or (not (ho_10 _let_1 B)) (ho_10 _let_1 A))))) (ho_10 (ho_21 k_20 B) (ho_30 k_32 A)))))) (let ((_let_115 (forall ((A $$unsorted)) (= A (ho_27 (ho_26 k_25 A) k_18))))) (let ((_let_116 (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (ho_21 k_20 Xy))) (or (not (ho_10 _let_1 (ho_30 (ho_29 k_28 Xx) A))) (= Xx Xy) (ho_10 _let_1 A)))))) (let ((_let_117 (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (ho_21 k_20 Xy))) (or (not (ho_10 _let_1 (ho_30 (ho_29 k_28 Xx) A))) (= Xx Xy) (ho_10 _let_1 A)))))) (let ((_let_118 (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (ho_21 k_20 Xy))) (or (not (ho_10 _let_1 A)) (ho_10 _let_1 (ho_30 (ho_29 k_28 Xx) A))))))) (let ((_let_119 (ho_10 _let_92 (ho_30 (ho_29 k_28 tptp.emptyset) tptp.emptyset)))) (let ((_let_120 (forall ((Xx $$unsorted) (Xy $$unsorted)) (ho_10 (ho_21 k_20 Xx) (ho_30 (ho_29 k_28 Xx) Xy))))) (let ((_let_121 (forall ((BOUND_VARIABLE_2179 $$unsorted)) (not (ho_10 (ho_21 k_20 BOUND_VARIABLE_2179) tptp.emptyset))))) (let ((_let_122 (forall ((A $$unsorted) (BOUND_VARIABLE_4380 |u_(-> $$unsorted Bool)|) (Xx $$unsorted)) (or (not (ho_10 (ho_21 k_20 Xx) A)) (not (ho_10 BOUND_VARIABLE_4380 Xx)) (not (= tptp.emptyset (ho_27 (ho_26 k_25 A) (ho_12 k_17 BOUND_VARIABLE_4380)))))))) (let ((_let_123 (forall ((A $$unsorted)) (or (= 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(BOUND_VARIABLE_3177 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (ho_10 BOUND_VARIABLE_4450 Xx)))) (not (ho_10 BOUND_VARIABLE_4450 BOUND_VARIABLE_3177)) (not (forall ((Xy $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_4450 Xy)) (= Xy BOUND_VARIABLE_3177)))))))) (let ((_let_129 (forall ((Xx $$unsorted)) (not (ho_10 (ho_21 k_20 Xx) tptp.emptyset))))) (let ((_let_130 (forall ((Xx $$unsorted)) (not (ho_10 (ho_21 k_20 Xx) tptp.emptyset))))) (let ((_let_131 (forall ((Xx $$unsorted)) (not (ho_10 (ho_21 k_20 Xx) tptp.emptyset))))) (let ((_let_132 (forall ((Xx $$unsorted)) (not (ho_10 (ho_21 k_20 Xx) (ho_23 k_22 false)))))) (let ((_let_133 (forall ((BOUND_VARIABLE_4487 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_3128 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_4487 Xx)) (not (forall ((Xy $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_4487 Xy)) (= Xx Xy))))))) (not (ho_10 BOUND_VARIABLE_4487 BOUND_VARIABLE_3128)) (not (forall ((Xy $$unsorted)) (or (not (ho_10 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(ho_10 _let_2 D) (not (ho_10 _let_1 D)) (ho_10 _let_1 C)))))) (not (forall ((C $$unsorted) (BOUND_VARIABLE_2017 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_21 k_20 Xx))) (or (not (ho_10 _let_1 C)) (ho_10 _let_1 A))))) (not (ho_10 (ho_21 k_20 BOUND_VARIABLE_2017) C)) (not (forall ((D $$unsorted) (Xx $$unsorted)) (or (not (ho_10 (ho_21 k_20 D) B)) (not (ho_10 (ho_21 k_20 Xx) C)) (not (forall ((Xy $$unsorted)) (let ((_let_1 (ho_21 k_20 Xy))) (or (not (ho_10 _let_1 D)) (not (ho_10 _let_1 C)))))) (not (forall ((E $$unsorted) (BOUND_VARIABLE_1987 $$unsorted)) (let ((_let_1 (ho_21 k_20 BOUND_VARIABLE_1987))) (or (not (ho_10 (ho_21 k_20 E) B)) (ho_10 (ho_21 k_20 Xx) E) (not (ho_10 _let_1 E)) (ho_10 _let_1 D))))))))))))))))) (let ((_let_140 (forall ((A $$unsorted) (BOUND_VARIABLE_1884 $$unsorted)) (or (not (ho_10 (ho_21 k_20 BOUND_VARIABLE_1884) A)) (not (forall ((B $$unsorted)) (or (not (ho_10 (ho_21 k_20 B) A)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_21 k_20 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_let_1 tptp.omega)) (ho_10 _let_1 A)))))) (let ((_let_143 (forall ((Xx $$unsorted)) (or (not (ho_10 (ho_21 k_20 Xx) tptp.omega)) (ho_10 (ho_21 k_20 (ho_30 (ho_29 k_28 Xx) Xx)) tptp.omega))))) (let ((_let_144 (ho_10 _let_92 tptp.omega))) (let ((_let_145 (forall ((A $$unsorted) (Xx $$unsorted)) (= (not (forall ((B $$unsorted)) (or (not (ho_10 (ho_21 k_20 Xx) B)) (not (ho_10 (ho_21 k_20 B) A))))) (ho_10 (ho_21 k_20 Xx) (ho_30 k_31 A)))))) (let ((_let_146 (forall ((A $$unsorted) (B $$unsorted)) (= (forall ((Xx $$unsorted)) (let ((_let_1 (ho_21 k_20 Xx))) (or (not (ho_10 _let_1 B)) (ho_10 _let_1 A)))) (ho_10 (ho_21 k_20 B) (ho_30 k_32 A)))))) (let ((_let_147 (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (ho_21 k_20 Xy))) (= (or (= Xx Xy) (ho_10 _let_1 A)) (ho_10 _let_1 (ho_30 (ho_29 k_28 Xx) A))))))) (let ((_let_148 (forall ((Xx $$unsorted)) (not (ho_10 (ho_21 k_20 Xx) tptp.emptyset))))) (let ((_let_149 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx 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(_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_229 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_230 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_231 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188) :args ((= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (not (forall ((Xy $$unsorted)) (= 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SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_235 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_236 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_237 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_238 (ASSUME :args (_let_16)))) (let ((_let_239 (ASSUME :args (_let_14)))) (let ((_let_240 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_241 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_242 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_243 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_244 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_245 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_246 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_247 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_248 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_249 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_250 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188) :args ((= tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_2606 $$unsorted)) (or (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (not (@ Xphi BOUND_VARIABLE_2606)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_2606))))))) SB_DEFAULT SBA_FIXPOINT))) _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188) :args ((not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_2642 $$unsorted)) (or (not (@ Xphi BOUND_VARIABLE_2642)) (not (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (@ Xphi Xx)) (not (@ Xphi Xy)) (= Xx Xy)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> _let_186 (=> _let_71 (=> _let_185 (=> _let_184 (=> _let_183 (=> _let_66 (=> _let_182 (=> _let_181 (=> _let_180 (=> _let_179 (=> _let_178 (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_3079 $$unsorted)) (or (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ Xphi BOUND_VARIABLE_3079)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_3079)))))) (=> (forall ((A $$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 $$unsorted)) (@ Xphi Xy))))))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or 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(CNF_OR_NEG :args (_let_85 2)) (CONG _let_255 (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_82))) :args _let_251)) :args ((or _let_82 _let_85))) _let_254 :args (_let_82 true _let_85)) :args (_let_261 false _let_82)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_134) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_10 BOUND_VARIABLE_4487 BOUND_VARIABLE_3128) false))))) :args _let_134)) (NOT_IMPLIES_ELIM1 _let_250) :args (_let_263 false _let_133)) :args (_let_260 false _let_79 false _let_261 false _let_263)) :args (_let_259 true _let_258)))) (let ((_let_267 (_let_75))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_267) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_267)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_80 _let_78 _let_76 _let_256))) _let_264 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_257 0)) (CONG (REFL :args (_let_257)) (MACRO_SR_PRED_INTRO :args ((= (not _let_78) _let_77))) :args _let_251)) :args ((or _let_77 _let_257))) _let_266 :args (_let_77 true _let_257)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_257 1)) _let_266 :args ((not _let_76) true _let_257)) :args (_let_256 false _let_79 false _let_77 true _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_85 1)) (CONG _let_255 (MACRO_SR_PRED_INTRO :args ((= (not _let_84) _let_75))) :args _let_251)) :args ((or _let_75 _let_85))) _let_254 :args (_let_75 true _let_85)) :args (false true _let_81 false _let_75)) :args (_let_74 _let_73 _let_72 _let_70 _let_69 _let_68 _let_67 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_39 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_29 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_14 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0.52/0.70 ) 0.52/0.70 % SZS output end Proof for 0.52/0.70 % cvc5---1.0.5 exiting 0.52/0.70 % cvc5---1.0.5 exiting 0.52/0.70 EOF