0.07/0.13 % Problem : Vampire---4.8_18539 : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : do_cvc5 %s %d 0.13/0.34 % Computer : n025.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Mon Jul 3 13:20:23 EDT 2023 0.13/0.34 % CPUTime : 0.20/0.48 %----Proving TH0 0.20/0.49 thf(in_type,type, 0.20/0.49 in: $i > $i > $o ). 0.20/0.49 0.20/0.49 thf(exu_type,type, 0.20/0.49 exu: ( $i > $o ) > $o ). 0.20/0.49 0.20/0.49 thf(exu,definition, 0.20/0.49 ( exu 0.20/0.49 = ( ^ [Xphi: $i > $o] : 0.20/0.49 ? [Xx: $i] : 0.20/0.49 ( ( Xphi @ Xx ) 0.20/0.49 & ! [Xy: $i] : 0.20/0.49 ( ( Xphi @ Xy ) 0.20/0.49 => ( Xx = Xy ) ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(setextAx_type,type, 0.20/0.49 setextAx: $o ). 0.20/0.49 0.20/0.49 thf(setextAx,definition, 0.20/0.49 ( setextAx 0.20/0.49 = ( ! [A: $i,B: $i] : 0.20/0.49 ( ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ A ) 0.20/0.49 <=> ( in @ Xx @ B ) ) 0.20/0.49 => ( A = B ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(emptyset_type,type, 0.20/0.49 emptyset: $i ). 0.20/0.49 0.20/0.49 thf(emptysetAx_type,type, 0.20/0.49 emptysetAx: $o ). 0.20/0.49 0.20/0.49 thf(emptysetAx,definition, 0.20/0.49 ( emptysetAx 0.20/0.49 = ( ! [Xx: $i] : 0.20/0.49 ~ ( in @ Xx @ emptyset ) ) ) ). 0.20/0.49 0.20/0.49 thf(setadjoin_type,type, 0.20/0.49 setadjoin: $i > $i > $i ). 0.20/0.49 0.20/0.49 thf(setadjoinAx_type,type, 0.20/0.49 setadjoinAx: $o ). 0.20/0.49 0.20/0.49 thf(setadjoinAx,definition, 0.20/0.49 ( setadjoinAx 0.20/0.49 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.20/0.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.20/0.49 <=> ( ( Xy = Xx ) 0.20/0.49 | ( in @ Xy @ A ) ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(powerset_type,type, 0.20/0.49 powerset: $i > $i ). 0.20/0.49 0.20/0.49 thf(powersetAx_type,type, 0.20/0.49 powersetAx: $o ). 0.20/0.49 0.20/0.49 thf(powersetAx,definition, 0.20/0.49 ( powersetAx 0.20/0.49 = ( ! [A: $i,B: $i] : 0.20/0.49 ( ( in @ B @ ( powerset @ A ) ) 0.20/0.49 <=> ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ B ) 0.20/0.49 => ( in @ Xx @ A ) ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(setunion_type,type, 0.20/0.49 setunion: $i > $i ). 0.20/0.49 0.20/0.49 thf(setunionAx_type,type, 0.20/0.49 setunionAx: $o ). 0.20/0.49 0.20/0.49 thf(setunionAx,definition, 0.20/0.49 ( setunionAx 0.20/0.49 = ( ! [A: $i,Xx: $i] : 0.20/0.49 ( ( in @ Xx @ ( setunion @ A ) ) 0.20/0.49 <=> ? [B: $i] : 0.20/0.49 ( ( in @ Xx @ B ) 0.20/0.49 & ( in @ B @ A ) ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(omega_type,type, 0.20/0.49 omega: $i ). 0.20/0.49 0.20/0.49 thf(omega0Ax_type,type, 0.20/0.49 omega0Ax: $o ). 0.20/0.49 0.20/0.49 thf(omega0Ax,definition, 0.20/0.49 ( omega0Ax 0.20/0.49 = ( in @ emptyset @ omega ) ) ). 0.20/0.49 0.20/0.49 thf(omegaSAx_type,type, 0.20/0.49 omegaSAx: $o ). 0.20/0.49 0.20/0.49 thf(omegaSAx,definition, 0.20/0.49 ( omegaSAx 0.20/0.49 = ( ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ omega ) 0.20/0.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(omegaIndAx_type,type, 0.20/0.49 omegaIndAx: $o ). 0.20/0.49 0.20/0.49 thf(omegaIndAx,definition, 0.20/0.49 ( omegaIndAx 0.20/0.49 = ( ! [A: $i] : 0.20/0.49 ( ( ( in @ emptyset @ A ) 0.20/0.49 & ! [Xx: $i] : 0.20/0.49 ( ( ( in @ Xx @ omega ) 0.20/0.49 & ( in @ Xx @ A ) ) 0.20/0.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) 0.20/0.49 => ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ omega ) 0.20/0.49 => ( in @ Xx @ A ) ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(replAx_type,type, 0.20/0.49 replAx: $o ). 0.20/0.49 0.20/0.49 thf(replAx,definition, 0.20/0.49 ( replAx 0.20/0.49 = ( ! [Xphi: $i > $i > $o,A: $i] : 0.20/0.49 ( ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ A ) 0.20/0.49 => ( exu 0.20/0.49 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) 0.20/0.49 => ? [B: $i] : 0.20/0.49 ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ B ) 0.20/0.49 <=> ? [Xy: $i] : 0.20/0.49 ( ( in @ Xy @ A ) 0.20/0.49 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(foundationAx_type,type, 0.20/0.49 foundationAx: $o ). 0.20/0.49 0.20/0.49 thf(foundationAx,definition, 0.20/0.49 ( foundationAx 0.20/0.49 = ( ! [A: $i] : 0.20/0.49 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.20/0.49 => ? [B: $i] : 0.20/0.49 ( ( in @ B @ A ) 0.20/0.49 & ~ ? [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ B ) 0.20/0.49 & ( in @ Xx @ A ) ) ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(wellorderingAx_type,type, 0.20/0.49 wellorderingAx: $o ). 0.20/0.49 0.20/0.49 thf(wellorderingAx,definition, 0.20/0.49 ( wellorderingAx 0.20/0.49 = ( ! [A: $i] : 0.20/0.49 ? [B: $i] : 0.20/0.49 ( ! [C: $i] : 0.20/0.49 ( ( in @ C @ B ) 0.20/0.49 => ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ C ) 0.20/0.49 => ( in @ Xx @ A ) ) ) 0.20/0.49 & ! [Xx: $i,Xy: $i] : 0.20/0.49 ( ( ( in @ Xx @ A ) 0.20/0.49 & ( in @ Xy @ A ) ) 0.20/0.49 => ( ! [C: $i] : 0.20/0.49 ( ( in @ C @ B ) 0.20/0.49 => ( ( in @ Xx @ C ) 0.20/0.49 <=> ( in @ Xy @ C ) ) ) 0.20/0.49 => ( Xx = Xy ) ) ) 0.20/0.49 & ! [C: $i,D: $i] : 0.20/0.49 ( ( ( in @ C @ B ) 0.20/0.49 & ( in @ D @ B ) ) 0.20/0.49 => ( ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ C ) 0.20/0.49 => ( in @ Xx @ D ) ) 0.20/0.49 | ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ D ) 0.20/0.49 => ( in @ Xx @ C ) ) ) ) 0.20/0.49 & ! [C: $i] : 0.20/0.49 ( ( ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ C ) 0.20/0.49 => ( in @ Xx @ A ) ) 0.20/0.49 & ? [Xx: $i] : ( in @ Xx @ C ) ) 0.20/0.49 => ? [D: $i,Xx: $i] : 0.20/0.49 ( ( in @ D @ B ) 0.20/0.49 & ( in @ Xx @ C ) 0.20/0.49 & ~ ? [Xy: $i] : 0.20/0.49 ( ( in @ Xy @ D ) 0.20/0.49 & ( in @ Xy @ C ) ) 0.20/0.49 & ! [E: $i] : 0.20/0.49 ( ( in @ E @ B ) 0.20/0.49 => ( ! [Xy: $i] : 0.20/0.49 ( ( in @ Xy @ E ) 0.20/0.49 => ( in @ Xy @ D ) ) 0.20/0.49 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(descr_type,type, 0.20/0.49 descr: ( $i > $o ) > $i ). 0.20/0.49 0.20/0.49 thf(descrp_type,type, 0.20/0.49 descrp: $o ). 0.20/0.49 0.20/0.49 thf(descrp,definition, 0.20/0.49 ( descrp 0.20/0.49 = ( ! [Xphi: $i > $o] : 0.20/0.49 ( ( exu 0.20/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.20/0.49 => ( Xphi 0.20/0.49 @ ( descr 0.20/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(dsetconstr_type,type, 0.20/0.49 dsetconstr: $i > ( $i > $o ) > $i ). 0.20/0.49 0.20/0.49 thf(dsetconstrI_type,type, 0.20/0.49 dsetconstrI: $o ). 0.20/0.49 0.20/0.49 thf(dsetconstrI,definition, 0.20/0.49 ( dsetconstrI 0.20/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.20/0.49 ( ( in @ Xx @ A ) 0.20/0.49 => ( ( Xphi @ Xx ) 0.20/0.49 => ( in @ Xx 0.20/0.49 @ ( dsetconstr @ A 0.20/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(dsetconstrEL_type,type, 0.20/0.49 dsetconstrEL: $o ). 0.20/0.49 0.20/0.49 thf(dsetconstrEL,definition, 0.20/0.49 ( dsetconstrEL 0.20/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.20/0.49 ( ( in @ Xx 0.20/0.49 @ ( dsetconstr @ A 0.20/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.20/0.49 => ( in @ Xx @ A ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(dsetconstrER_type,type, 0.20/0.49 dsetconstrER: $o ). 0.20/0.49 0.20/0.49 thf(dsetconstrER,definition, 0.20/0.49 ( dsetconstrER 0.20/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.20/0.49 ( ( in @ Xx 0.20/0.49 @ ( dsetconstr @ A 0.20/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.20/0.49 => ( Xphi @ Xx ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(exuE1_type,type, 0.20/0.49 exuE1: $o ). 0.20/0.49 0.20/0.49 thf(exuE1,definition, 0.20/0.49 ( exuE1 0.20/0.49 = ( ! [Xphi: $i > $o] : 0.20/0.49 ( ( exu 0.20/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.20/0.49 => ? [Xx: $i] : 0.20/0.49 ( ( Xphi @ Xx ) 0.20/0.49 & ! [Xy: $i] : 0.20/0.49 ( ( Xphi @ Xy ) 0.20/0.49 => ( Xx = Xy ) ) ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(prop2set_type,type, 0.20/0.49 prop2set: $o > $i ). 0.20/0.49 0.20/0.49 thf(prop2set,definition, 0.20/0.49 ( prop2set 0.20/0.49 = ( ^ [Xphi: $o] : 0.20/0.49 ( dsetconstr @ ( powerset @ emptyset ) 0.20/0.49 @ ^ [Xx: $i] : Xphi ) ) ) ). 0.20/0.49 0.20/0.49 thf(prop2setE_type,type, 0.20/0.49 prop2setE: $o ). 0.20/0.49 0.20/0.49 thf(prop2setE,definition, 0.20/0.49 ( prop2setE 0.20/0.49 = ( ! [Xphi: $o,Xx: $i] : 0.20/0.49 ( ( in @ Xx @ ( prop2set @ Xphi ) ) 0.20/0.49 => Xphi ) ) ) ). 0.20/0.49 0.20/0.49 thf(emptysetE_type,type, 0.20/0.49 emptysetE: $o ). 0.20/0.49 0.20/0.49 thf(emptysetE,definition, 0.20/0.49 ( emptysetE 0.20/0.49 = ( ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ emptyset ) 0.20/0.49 => ! [Xphi: $o] : Xphi ) ) ) ). 0.20/0.49 0.20/0.49 thf(emptysetimpfalse_type,type, 0.20/0.49 emptysetimpfalse: $o ). 0.20/0.49 0.20/0.49 thf(emptysetimpfalse,definition, 0.20/0.49 ( emptysetimpfalse 0.20/0.49 = ( ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ emptyset ) 0.20/0.49 => $false ) ) ) ). 0.20/0.49 0.20/0.49 thf(notinemptyset_type,type, 0.20/0.49 notinemptyset: $o ). 0.20/0.49 0.20/0.49 thf(notinemptyset,definition, 0.20/0.49 ( notinemptyset 0.20/0.49 = ( ! [Xx: $i] : 0.20/0.49 ~ ( in @ Xx @ emptyset ) ) ) ). 0.20/0.49 0.20/0.49 thf(exuE3e_type,type, 0.20/0.49 exuE3e: $o ). 0.20/0.49 0.20/0.49 thf(exuE3e,definition, 0.20/0.49 ( exuE3e 0.20/0.49 = ( ! [Xphi: $i > $o] : 0.20/0.49 ( ( exu 0.20/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.20/0.49 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(setext_type,type, 0.20/0.49 setext: $o ). 0.20/0.49 0.20/0.49 thf(setext,definition, 0.20/0.49 ( setext 0.20/0.49 = ( ! [A: $i,B: $i] : 0.20/0.49 ( ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ A ) 0.20/0.49 => ( in @ Xx @ B ) ) 0.20/0.49 => ( ! [Xx: $i] : 0.20/0.49 ( ( in @ Xx @ B ) 0.20/0.49 => ( in @ Xx @ A ) ) 0.20/0.49 => ( A = B ) ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(emptyI_type,type, 0.20/0.49 emptyI: $o ). 0.20/0.49 0.20/0.49 thf(emptyI,definition, 0.20/0.49 ( emptyI 0.20/0.49 = ( ! [A: $i] : 0.20/0.49 ( ! [Xx: $i] : 0.20/0.49 ~ ( in @ Xx @ A ) 0.20/0.49 => ( A = emptyset ) ) ) ) ). 0.20/0.49 0.20/0.49 thf(noeltsimpempty_type,type, 0.20/0.49 noeltsimpempty: $o ). 0.20/0.49 0.20/0.49 thf(noeltsimpempty,definition, 0.20/0.49 ( noeltsimpempty 0.20/0.49 = ( ! [A: $i] : 0.20/0.50 ( ! [Xx: $i] : 0.20/0.50 ~ ( in @ Xx @ A ) 0.20/0.50 => ( A = emptyset ) ) ) ) ). 0.20/0.50 0.20/0.50 thf(setbeta_type,type, 0.20/0.50 setbeta: $o ). 0.20/0.50 0.20/0.50 thf(setbeta,definition, 0.20/0.50 ( setbeta 0.20/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.20/0.50 ( ( in @ Xx @ A ) 0.20/0.50 => ( ( in @ Xx 0.20/0.50 @ ( dsetconstr @ A 0.20/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.20/0.50 <=> ( Xphi @ Xx ) ) ) ) ) ). 0.20/0.50 0.20/0.50 thf(nonempty_type,type, 0.20/0.50 nonempty: $i > $o ). 0.20/0.50 0.20/0.50 thf(nonempty,definition, 0.20/0.50 ( nonempty 0.20/0.50 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ). 0.20/0.50 0.20/0.50 thf(nonemptyE1_type,type, 0.20/0.50 nonemptyE1: $o ). 0.20/0.50 0.20/0.50 thf(nonemptyE1,definition, 0.20/0.50 ( nonemptyE1 0.20/0.50 = ( ! [A: $i] : 0.20/0.50 ( ( nonempty @ A ) 0.20/0.50 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ). 0.20/0.50 0.20/0.50 thf(nonemptyI_type,type, 0.20/0.50 nonemptyI: $o ). 0.20/0.50 0.20/0.50 thf(nonemptyI,definition, 0.20/0.50 ( nonemptyI 0.20/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.20/0.50 ( ( in @ Xx @ A ) 0.20/0.50 => ( ( Xphi @ Xx ) 0.20/0.50 => ( nonempty 0.20/0.50 @ ( dsetconstr @ A 0.20/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.20/0.50 0.20/0.50 thf(nonemptyI1_type,type, 0.20/0.50 nonemptyI1: $o ). 0.20/0.50 0.20/0.50 thf(nonemptyI1,definition, 0.20/0.50 ( nonemptyI1 0.20/0.50 = ( ! [A: $i] : 0.20/0.50 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.20/0.50 => ( nonempty @ A ) ) ) ) ). 0.20/0.50 0.20/0.50 thf(setadjoinIL_type,type, 0.20/0.50 setadjoinIL: $o ). 0.20/0.50 0.20/0.50 thf(setadjoinIL,definition, 0.20/0.50 ( setadjoinIL 0.20/0.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ). 0.20/0.50 0.20/0.50 thf(emptyinunitempty_type,type, 0.20/0.50 emptyinunitempty: $o ). 0.20/0.50 0.20/0.50 thf(emptyinunitempty,definition, 0.20/0.50 ( emptyinunitempty 0.20/0.50 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ). 0.20/0.50 0.20/0.50 thf(setadjoinIR,conjecture, 0.20/0.50 ( ( ( setadjoinAx 0.20/0.50 => ( ( ( ( omegaSAx 0.20/0.50 => ( omegaIndAx 0.20/0.50 => ( ( foundationAx 0.20/0.50 => ( ( descrp 0.20/0.50 => ( ( ( dsetconstrER 0.20/0.50 => ( ( ( emptysetE 0.20/0.50 => ( ( notinemptyset 0.20/0.50 => ( ( ( emptyI 0.20/0.50 => ( noeltsimpempty 0.20/0.50 => ( ( ( ( nonemptyI1 0.20/0.50 => ( ( ! [Xx: $i,A: $i,Xy: $i] : 0.20/0.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.20/0.50 <= ( in @ Xy @ A ) ) 0.20/0.50 <= emptyinunitempty ) 0.20/0.50 <= setadjoinIL ) ) 0.20/0.50 <= nonemptyI ) 0.20/0.50 <= nonemptyE1 ) 0.20/0.50 <= setbeta ) ) ) 0.20/0.50 <= setext ) 0.20/0.50 <= exuE3e ) ) 0.20/0.50 <= emptysetimpfalse ) ) 0.20/0.50 <= prop2setE ) 0.20/0.50 <= exuE1 ) ) 0.20/0.50 <= dsetconstrEL ) 0.20/0.50 <= dsetconstrI ) ) 0.20/0.50 <= wellorderingAx ) ) 0.20/0.50 <= replAx ) ) ) 0.20/0.50 <= omega0Ax ) 0.20/0.50 <= setunionAx ) 0.20/0.50 <= powersetAx ) ) 0.20/0.50 <= emptysetAx ) 0.20/0.50 <= setextAx ) ). 0.20/0.50 0.20/0.50 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.QlyFKxnxW1/cvc5---1.0.5_18640.p... 0.20/0.50 (declare-sort $$unsorted 0) 0.20/0.50 (declare-fun tptp.in ($$unsorted $$unsorted) Bool) 0.20/0.50 (declare-fun tptp.exu ((-> $$unsorted Bool)) Bool) 0.20/0.50 (assert (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy)))))))) 0.20/0.50 (declare-fun tptp.setextAx () Bool) 0.20/0.50 (assert (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B))))) 0.20/0.50 (declare-fun tptp.emptyset () $$unsorted) 0.20/0.50 (declare-fun tptp.emptysetAx () Bool) 0.20/0.50 (assert (= tptp.emptysetAx (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.20/0.50 (declare-fun tptp.setadjoin ($$unsorted $$unsorted) $$unsorted) 0.20/0.50 (declare-fun tptp.setadjoinAx () Bool) 0.20/0.50 (assert (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.20/0.50 (declare-fun tptp.powerset ($$unsorted) $$unsorted) 0.20/0.50 (declare-fun tptp.powersetAx () Bool) 0.20/0.50 (assert (= tptp.powersetAx (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))))))) 0.20/0.50 (declare-fun tptp.setunion ($$unsorted) $$unsorted) 0.20/0.50 (declare-fun tptp.setunionAx () Bool) 0.20/0.50 (assert (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A))))))) 0.20/0.50 (declare-fun tptp.omega () $$unsorted) 0.20/0.50 (declare-fun tptp.omega0Ax () Bool) 0.20/0.50 (assert (= tptp.omega0Ax (@ (@ tptp.in tptp.emptyset) tptp.omega))) 0.20/0.50 (declare-fun tptp.omegaSAx () Bool) 0.20/0.50 (assert (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega))))) 0.20/0.50 (declare-fun tptp.omegaIndAx () Bool) 0.20/0.50 (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 $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 tptp.omega) (@ _let_1 A)))))))) 0.20/0.50 (declare-fun tptp.replAx () Bool) 0.20/0.50 (assert (= tptp.replAx (forall ((Xphi (-> $$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 $$unsorted)) (and (@ (@ tptp.in Xy) A) (@ (@ Xphi Xy) Xx)))))))))) 0.20/0.50 (declare-fun tptp.foundationAx () Bool) 0.20/0.50 (assert (= tptp.foundationAx (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in B) A) (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 B) (@ _let_1 A))))))))))) 0.20/0.50 (declare-fun tptp.wellorderingAx () Bool) 0.20/0.50 (assert (= tptp.wellorderingAx (forall ((A $$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))))))))))))) 0.20/0.50 (declare-fun tptp.descr ((-> $$unsorted Bool)) $$unsorted) 0.20/0.50 (declare-fun tptp.descrp () Bool) 0.20/0.50 (assert (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) 0.20/0.50 (declare-fun tptp.dsetconstr ($$unsorted (-> $$unsorted Bool)) $$unsorted) 0.20/0.50 (declare-fun tptp.dsetconstrI () Bool) 0.20/0.50 (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)))))))))) 0.20/0.50 (declare-fun tptp.dsetconstrEL () Bool) 0.20/0.50 (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)))))) 0.20/0.50 (declare-fun tptp.dsetconstrER () Bool) 0.20/0.50 (assert (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))) 0.20/0.50 (declare-fun tptp.exuE1 () Bool) 0.20/0.50 (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))))))))) 0.20/0.50 (declare-fun tptp.prop2set (Bool) $$unsorted) 0.20/0.50 (assert (= tptp.prop2set (lambda ((Xphi Bool)) (@ (@ tptp.dsetconstr (@ tptp.powerset tptp.emptyset)) (lambda ((Xx $$unsorted)) Xphi))))) 0.20/0.50 (declare-fun tptp.prop2setE () Bool) 0.20/0.50 (assert (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi)))) 0.20/0.50 (declare-fun tptp.emptysetE () Bool) 0.20/0.50 (assert (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi))))) 0.20/0.50 (declare-fun tptp.emptysetimpfalse () Bool) 0.20/0.50 (assert (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false)))) 0.20/0.50 (declare-fun tptp.notinemptyset () Bool) 0.20/0.50 (assert (= tptp.notinemptyset (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.20/0.50 (declare-fun tptp.exuE3e () Bool) 0.20/0.50 (assert (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx)))))) 0.20/0.50 (declare-fun tptp.setext () Bool) 0.20/0.50 (assert (= tptp.setext (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (= A B)))))) 0.20/0.50 (declare-fun tptp.emptyI () Bool) 0.20/0.50 (assert (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.20/0.50 (declare-fun tptp.noeltsimpempty () Bool) 0.20/0.50 (assert (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.20/0.50 (declare-fun tptp.setbeta () Bool) 0.20/0.50 (assert (= tptp.setbeta (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (= (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))))) 0.20/0.50 (declare-fun tptp.nonempty ($$unsorted) Bool) 0.20/0.50 (assert (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset))))) 0.20/0.50 (declare-fun tptp.nonemptyE1 () Bool) 0.20/0.50 (assert (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)))))) 0.20/0.50 (declare-fun tptp.nonemptyI () Bool) 0.20/0.50 (assert (= tptp.nonemptyI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (@ tptp.nonempty (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))))) 0.20/0.50 (declare-fun tptp.nonemptyI1 () Bool) 0.20/0.50 (assert (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A))))) 0.20/0.50 (declare-fun tptp.setadjoinIL () Bool) 0.20/0.50 (assert (= tptp.setadjoinIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) 0.20/0.50 (declare-fun tptp.emptyinunitempty () Bool) 0.20/0.50 (assert (= tptp.emptyinunitempty (@ (@ tptp.in tptp.emptyset) (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) 0.20/0.50 (assert (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A))))))))))))))))))))))))))))))))))))) 0.34/0.60 (set-info :filename cvc5---1.0.5_18640) 0.34/0.60 (check-sat-assuming ( true )) 0.34/0.60 ------- get file name : TPTP file name is 0.34/0.60 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_18640.smt2... 0.34/0.60 --- Run --ho-elim --full-saturate-quant at 10... 0.34/0.60 % SZS status Theorem for 0.34/0.60 % SZS output start Proof for 0.34/0.60 ( 0.34/0.60 (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 (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A)))))))))))))))))))))))))))))))))))))) (let ((_let_2 (@ tptp.in tptp.emptyset))) (let ((_let_3 (@ _let_2 (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) (let ((_let_4 (= tptp.emptyinunitempty _let_3))) (let ((_let_5 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) (let ((_let_6 (= tptp.setadjoinIL _let_5))) (let ((_let_7 (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A)))))) (let ((_let_8 (= tptp.nonemptyI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (@ tptp.nonempty (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))))))))) (let ((_let_9 (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A))))))) (let ((_let_10 (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset)))))) (let ((_let_11 (= 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_12 (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))) (let ((_let_13 (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))) (let ((_let_14 (= 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_15 (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx))))))) (let ((_let_16 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_17 (= tptp.notinemptyset _let_16))) (let ((_let_18 (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false))))) (let ((_let_19 (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi)))))) (let ((_let_20 (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi))))) (let ((_let_21 (= tptp.prop2set (lambda ((Xphi Bool)) (@ (@ tptp.dsetconstr (@ tptp.powerset tptp.emptyset)) (lambda ((Xx $$unsorted)) Xphi)))))) (let ((_let_22 (= 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_23 (= 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_24 (= 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_25 (= 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_26 (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (let ((_let_27 (= tptp.wellorderingAx (forall ((A $$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_28 (= 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_29 (= 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_30 (= 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 $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 tptp.omega) (@ _let_1 A))))))))) (let ((_let_31 (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega)))))) (let ((_let_32 (@ _let_2 tptp.omega))) (let ((_let_33 (= tptp.omega0Ax _let_32))) (let ((_let_34 (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A)))))))) (let ((_let_35 (= tptp.powersetAx (forall ((A $$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_36 (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A)))))))) (let ((_let_37 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_38 (= tptp.emptysetAx _let_37))) (let ((_let_39 (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B)))))) (let ((_let_40 (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))))))) (let ((_let_41 (ho_22 k_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))) (let ((_let_42 (ho_9 _let_41 (ho_20 (ho_19 k_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30)))) (let ((_let_43 (ho_9 _let_41 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30))) (let ((_let_44 (or (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31) _let_43))) (let ((_let_45 (= _let_42 _let_44))) (let ((_let_46 (not _let_43))) (let ((_let_47 (or _let_46 _let_42))) (let ((_let_48 (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (ho_22 k_21 Xy))) (or (not (ho_9 _let_1 A)) (ho_9 _let_1 (ho_20 (ho_19 k_18 Xx) A))))))) (let ((_let_49 (not _let_47))) (let ((_let_50 (ho_22 k_21 tptp.emptyset))) (let ((_let_51 (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (ho_22 k_21 Xy))) (= (or (= Xx Xy) (ho_9 _let_1 A)) (ho_9 _let_1 (ho_20 (ho_19 k_18 Xx) A))))))) (let ((_let_52 (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (or (not (@ _let_1 A)) (@ _let_1 (@ (@ tptp.setadjoin Xx) A))))))) (let ((_let_53 (=> (forall ((BOUND_VARIABLE_1656 $$unsorted)) (not (@ (@ tptp.in BOUND_VARIABLE_1656) tptp.emptyset))) (=> _let_5 (=> _let_3 _let_52))))) (let ((_let_54 (forall ((A $$unsorted)) (or (= tptp.emptyset A) (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))))))) (let ((_let_55 (forall ((A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))) (= tptp.emptyset A))))) (let ((_let_56 (forall ((A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))) (= tptp.emptyset A))))) (let ((_let_57 (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))))) (let ((_let_58 (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_2027 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (@ Xphi Xx)))) (not (@ Xphi BOUND_VARIABLE_2027)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_2027)))))))) (let ((_let_59 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_60 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_61 (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_1962 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy))))))) (not (@ Xphi BOUND_VARIABLE_1962)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_1962)))))))) (let ((_let_62 (forall ((A $$unsorted)) (not (forall ((B $$unsorted)) (or (not (forall ((C $$unsorted) (BOUND_VARIABLE_1378 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_1378))) (or (not (@ (@ tptp.in C) B)) (not (@ _let_1 C)) (@ _let_1 A))))) (not (forall ((Xx $$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_1426 $$unsorted) (BOUND_VARIABLE_1419 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_1426))) (let ((_let_2 (@ tptp.in BOUND_VARIABLE_1419))) (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 $$unsorted) (BOUND_VARIABLE_1493 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 C)) (@ _let_1 A))))) (not (@ (@ tptp.in BOUND_VARIABLE_1493) C)) (not (forall ((D $$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 $$unsorted) (BOUND_VARIABLE_1463 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_1463))) (or (not (@ (@ tptp.in E) B)) (@ (@ tptp.in Xx) E) (not (@ _let_1 E)) (@ _let_1 D))))))))))))))))) (let ((_let_63 (forall ((A $$unsorted) (BOUND_VARIABLE_1360 $$unsorted)) (or (not (@ (@ tptp.in BOUND_VARIABLE_1360) 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))))))))))))) (let ((_let_64 (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 $$unsorted)) (or (not (@ (@ tptp.in Xy) A)) (not (@ (@ Xphi Xy) Xx)))))))))))))) (let ((_let_65 (forall ((A $$unsorted) (BOUND_VARIABLE_1297 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_1297))) (or (not (@ (@ tptp.in tptp.emptyset) A)) (not (forall ((Xx $$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)))))) (let ((_let_66 (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) tptp.omega)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega))))) (let ((_let_67 (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (not (forall ((B $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (not (@ (@ tptp.in B) A))))))))) (let ((_let_68 (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (@ _let_1 A)))))))) (let ((_let_69 (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xx Xy) (@ _let_1 A))))))) (let ((_let_70 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B))))) (= A B))))) (let ((_let_71 (not (=> _let_70 (=> _let_37 (=> _let_69 (=> _let_68 (=> _let_67 (=> _let_32 (=> _let_66 (=> _let_65 (=> _let_64 (=> _let_63 (=> _let_62 (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_1913 $$unsorted)) (or (@ Xphi (@ tptp.descr (@ ll_8 Xphi))) (not (@ Xphi BOUND_VARIABLE_1913)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_1913)))))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (not (@ Xphi Xx)) (@ _let_1 (@ (@ tptp.dsetconstr A) (@ ll_7 Xphi)))))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 (@ (@ tptp.dsetconstr A) (@ ll_6 Xphi)))) (@ _let_1 A)))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (@ ll_5 Xphi)))) (@ Xphi Xx))) (=> _let_61 (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr (@ tptp.powerset tptp.emptyset)) ll_4)))) (=> _let_60 (=> _let_59 (=> _let_16 (=> _let_58 (=> _let_57 (=> _let_56 (=> _let_55 (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (= (@ Xphi Xx) (@ _let_1 (@ (@ tptp.dsetconstr A) (@ ll_3 Xphi))))))) (=> _let_54 (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (= tptp.emptyset (@ (@ tptp.dsetconstr A) (@ ll_2 Xphi)))))) _let_53)))))))))))))))))))))))))))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (ASSUME :args (_let_38)))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (ASSUME :args (_let_33)))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 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) :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_82 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72) :args ((= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72) :args ((= tptp.exuE1 (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (ASSUME :args (_let_21)))) (let ((_let_90 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72) :args ((= tptp.prop2setE (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) (@ tptp.prop2set false))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (ASSUME :args (_let_17)))) (let ((_let_94 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_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) :args ((= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (not (@ Xphi Xx))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72) :args ((= tptp.nonemptyE1 (forall ((A $$unsorted)) (or (not (@ tptp.nonempty A)) (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72) :args ((= tptp.nonemptyI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (@ tptp.nonempty (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (ASSUME :args (_let_4)) (ASSUME :args (_let_6)) (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72) :args ((= tptp.nonemptyI1 (forall ((A $$unsorted) (BOUND_VARIABLE_1656 $$unsorted)) (or (not (@ (@ tptp.in BOUND_VARIABLE_1656) A)) (@ tptp.nonempty A)))) SB_DEFAULT SBA_FIXPOINT))) _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72) :args ((not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty _let_52))))))))))))))))))))))))))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> _let_70 (=> _let_37 (=> _let_69 (=> _let_68 (=> _let_67 (=> _let_32 (=> _let_66 (=> _let_65 (=> _let_64 (=> _let_63 (=> _let_62 (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_1913 $$unsorted)) (or (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ Xphi BOUND_VARIABLE_1913)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_1913)))))) (=> (forall ((A $$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 (not (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))) (@ _let_1 A)))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))) (@ Xphi Xx))) (=> _let_61 (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr (@ tptp.powerset tptp.emptyset)) (lambda ((BOUND_VARIABLE_2246 $$unsorted)) false))))) (=> _let_60 (=> _let_59 (=> _let_16 (=> _let_58 (=> _let_57 (=> _let_56 (=> _let_55 (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (= (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))) (=> _let_54 (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (= tptp.emptyset (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))) _let_53)))))))))))))))))))))))))))) _let_71))) (PREPROCESS :args ((= _let_71 (not (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_22 k_21 Xx))) (= (ho_9 _let_1 B) (ho_9 _let_1 A))))) (= A B))) (=> (forall ((Xx $$unsorted)) (not (ho_9 (ho_22 k_21 Xx) tptp.emptyset))) (=> _let_51 (=> (forall ((A $$unsorted) (B $$unsorted)) (= (forall ((Xx $$unsorted)) (let ((_let_1 (ho_22 k_21 Xx))) (or (not (ho_9 _let_1 B)) (ho_9 _let_1 A)))) (ho_9 (ho_22 k_21 B) (ho_20 k_26 A)))) (=> (forall ((A $$unsorted) (Xx $$unsorted)) (= (not (forall ((B $$unsorted)) (or (not (ho_9 (ho_22 k_21 Xx) B)) (not (ho_9 (ho_22 k_21 B) A))))) (ho_9 (ho_22 k_21 Xx) (ho_20 k_28 A)))) (=> (ho_9 _let_50 tptp.omega) (=> (forall ((Xx $$unsorted)) (or (not (ho_9 (ho_22 k_21 Xx) tptp.omega)) (ho_9 (ho_22 k_21 (ho_20 (ho_19 k_18 Xx) Xx)) tptp.omega))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_1297 $$unsorted)) (let ((_let_1 (ho_22 k_21 BOUND_VARIABLE_1297))) (or (not (ho_9 (ho_22 k_21 tptp.emptyset) A)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_22 k_21 Xx))) (or (not (ho_9 _let_1 tptp.omega)) (not (ho_9 _let_1 A)) (ho_9 (ho_22 k_21 (ho_20 (ho_19 k_18 Xx) Xx)) A))))) (not (ho_9 _let_1 tptp.omega)) (ho_9 _let_1 A)))) (=> (forall ((BOUND_VARIABLE_2838 |u_(-> $$unsorted $$unsorted Bool)|) (A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (ho_9 (ho_22 k_21 Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (ho_9 (ho_22 BOUND_VARIABLE_2838 Xx) Xx)) (not (forall ((Xy $$unsorted)) (or (not (ho_9 (ho_22 BOUND_VARIABLE_2838 Xx) Xy)) (= Xx Xy)))))))))) (not (forall ((B $$unsorted)) (not (forall ((Xx $$unsorted)) (= (not (forall ((Xy $$unsorted)) (or (not (ho_9 (ho_22 k_21 Xy) A)) (not (ho_9 (ho_22 BOUND_VARIABLE_2838 Xy) Xx))))) (ho_9 (ho_22 k_21 Xx) B)))))))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_1360 $$unsorted)) (or (not (ho_9 (ho_22 k_21 BOUND_VARIABLE_1360) A)) (not (forall ((B $$unsorted)) (or (not (ho_9 (ho_22 k_21 B) A)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_22 k_21 Xx))) (or (not (ho_9 _let_1 B)) (not (ho_9 _let_1 A))))))))))) (=> (forall ((A $$unsorted)) (not (forall ((B $$unsorted)) (or (not (forall ((C $$unsorted) (BOUND_VARIABLE_1378 $$unsorted)) (let ((_let_1 (ho_22 k_21 BOUND_VARIABLE_1378))) (or (not (ho_9 (ho_22 k_21 C) B)) (not (ho_9 _let_1 C)) (ho_9 _let_1 A))))) (not (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (ho_9 (ho_22 k_21 Xx) A)) (not (ho_9 (ho_22 k_21 Xy) A)) (not (forall ((C $$unsorted)) (or (not (ho_9 (ho_22 k_21 C) B)) (= (ho_9 (ho_22 k_21 Xy) C) (ho_9 (ho_22 k_21 Xx) C))))) (= Xx Xy)))) (not (forall ((C $$unsorted) (D $$unsorted) (BOUND_VARIABLE_1426 $$unsorted) (BOUND_VARIABLE_1419 $$unsorted)) (let ((_let_1 (ho_22 k_21 BOUND_VARIABLE_1426))) (let ((_let_2 (ho_22 k_21 BOUND_VARIABLE_1419))) (or (not (ho_9 (ho_22 k_21 C) B)) (not (ho_9 (ho_22 k_21 D) B)) (not (ho_9 _let_2 C)) (ho_9 _let_2 D) (not (ho_9 _let_1 D)) (ho_9 _let_1 C)))))) (not (forall ((C $$unsorted) (BOUND_VARIABLE_1493 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_22 k_21 Xx))) (or (not (ho_9 _let_1 C)) (ho_9 _let_1 A))))) (not (ho_9 (ho_22 k_21 BOUND_VARIABLE_1493) C)) (not (forall ((D $$unsorted) (Xx $$unsorted)) (or (not (ho_9 (ho_22 k_21 D) B)) (not (ho_9 (ho_22 k_21 Xx) C)) (not (forall ((Xy $$unsorted)) (let ((_let_1 (ho_22 k_21 Xy))) (or (not (ho_9 _let_1 D)) (not (ho_9 _let_1 C)))))) (not (forall ((E $$unsorted) (BOUND_VARIABLE_1463 $$unsorted)) (let ((_let_1 (ho_22 k_21 BOUND_VARIABLE_1463))) (or (not (ho_9 (ho_22 k_21 E) B)) (ho_9 (ho_22 k_21 Xx) E) (not (ho_9 _let_1 E)) (ho_9 _let_1 D))))))))))))))) (=> (forall ((BOUND_VARIABLE_2711 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1913 $$unsorted)) (or (ho_9 BOUND_VARIABLE_2711 (ho_25 k_27 (ho_11 k_10 BOUND_VARIABLE_2711))) (not (ho_9 BOUND_VARIABLE_2711 BOUND_VARIABLE_1913)) (not (forall ((Xy $$unsorted)) (or (not (ho_9 BOUND_VARIABLE_2711 Xy)) (= Xy BOUND_VARIABLE_1913)))))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_2697 |u_(-> $$unsorted Bool)|) (Xx $$unsorted)) (let ((_let_1 (ho_22 k_21 Xx))) (or (not (ho_9 _let_1 A)) (not (ho_9 BOUND_VARIABLE_2697 Xx)) (ho_9 _let_1 (ho_25 (ho_24 k_23 A) (ho_11 k_12 BOUND_VARIABLE_2697)))))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_2687 |u_(-> $$unsorted Bool)|) (Xx $$unsorted)) (let ((_let_1 (ho_22 k_21 Xx))) (or (not (ho_9 _let_1 (ho_25 (ho_24 k_23 A) (ho_11 k_13 BOUND_VARIABLE_2687)))) (ho_9 _let_1 A)))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_2673 |u_(-> $$unsorted Bool)|) (Xx $$unsorted)) (or (not (ho_9 (ho_22 k_21 Xx) (ho_25 (ho_24 k_23 A) (ho_11 k_14 BOUND_VARIABLE_2673)))) (ho_9 BOUND_VARIABLE_2673 Xx))) (=> (forall ((BOUND_VARIABLE_2651 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1962 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (ho_9 BOUND_VARIABLE_2651 Xx)) (not (forall ((Xy $$unsorted)) (or (not (ho_9 BOUND_VARIABLE_2651 Xy)) (= Xx Xy))))))) (not (ho_9 BOUND_VARIABLE_2651 BOUND_VARIABLE_1962)) (not (forall ((Xy $$unsorted)) (or (not (ho_9 BOUND_VARIABLE_2651 Xy)) (= Xy BOUND_VARIABLE_1962)))))) (=> (forall ((Xx $$unsorted)) (not (ho_9 (ho_22 k_21 Xx) (ho_25 (ho_24 k_23 (ho_20 k_26 tptp.emptyset)) k_15)))) (=> (forall ((Xx $$unsorted)) (not (ho_9 (ho_22 k_21 Xx) tptp.emptyset))) (=> (forall ((Xx $$unsorted)) (not (ho_9 (ho_22 k_21 Xx) tptp.emptyset))) (=> (forall ((Xx $$unsorted)) (not (ho_9 (ho_22 k_21 Xx) tptp.emptyset))) (=> (forall ((BOUND_VARIABLE_2611 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2027 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (ho_9 BOUND_VARIABLE_2611 Xx)))) (not (ho_9 BOUND_VARIABLE_2611 BOUND_VARIABLE_2027)) (not (forall ((Xy $$unsorted)) (or (not (ho_9 BOUND_VARIABLE_2611 Xy)) (= Xy BOUND_VARIABLE_2027)))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_22 k_21 Xx))) (or (not (ho_9 _let_1 A)) (ho_9 _let_1 B))))) (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_22 k_21 Xx))) (or (not (ho_9 _let_1 B)) (ho_9 _let_1 A))))) (= A B))) (=> (forall ((A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (ho_9 (ho_22 k_21 Xx) A)))) (= tptp.emptyset A))) (=> (forall ((A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (ho_9 (ho_22 k_21 Xx) A)))) (= tptp.emptyset A))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_2564 |u_(-> $$unsorted Bool)|) (Xx $$unsorted)) (let ((_let_1 (ho_22 k_21 Xx))) (or (not (ho_9 _let_1 A)) (= (ho_9 _let_1 (ho_25 (ho_24 k_23 A) (ho_11 k_16 BOUND_VARIABLE_2564))) (ho_9 BOUND_VARIABLE_2564 Xx))))) (=> (forall ((A $$unsorted)) (or (= tptp.emptyset A) (not (forall ((Xx $$unsorted)) (not (ho_9 (ho_22 k_21 Xx) A)))))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_2532 |u_(-> $$unsorted Bool)|) (Xx $$unsorted)) (or (not (ho_9 (ho_22 k_21 Xx) A)) (not (ho_9 BOUND_VARIABLE_2532 Xx)) (not (= tptp.emptyset (ho_25 (ho_24 k_23 A) (ho_11 k_17 BOUND_VARIABLE_2532)))))) (=> (forall ((BOUND_VARIABLE_1656 $$unsorted)) (not (ho_9 (ho_22 k_21 BOUND_VARIABLE_1656) tptp.emptyset))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (ho_9 (ho_22 k_21 Xx) (ho_20 (ho_19 k_18 Xx) Xy))) (=> (ho_9 _let_50 (ho_20 (ho_19 k_18 tptp.emptyset) tptp.emptyset)) _let_48)))))))))))))))))))))))))))))))))))))))) (let ((_let_103 (or))) (let ((_let_104 (not _let_48))) (let ((_let_105 (_let_104))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_105)) :args _let_105)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_104) _let_48))) (REFL :args (_let_49)) :args _let_103)) (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 _let_102)))))))))))))))))))))))))))) :args (_let_49 true _let_48)))) (let ((_let_107 (_let_51))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_45)) :args ((or _let_42 (not _let_44) (not _let_45)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_107) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_107))) (NOT_IMPLIES_ELIM1 _let_102) :args (_let_45 false _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_44 1)) :args ((or _let_46 _let_44))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 0)) (CONG (REFL :args (_let_47)) (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_43))) :args _let_103)) :args ((or _let_43 _let_47))) _let_106 :args (_let_43 true _let_47)) :args (_let_44 false _let_43)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_47 1)) _let_106 :args ((not _let_42) true _let_47)) :args (false false _let_45 false _let_44 true _let_42)) :args (_let_40 _let_39 _let_38 _let_36 _let_35 _let_34 _let_33 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_4 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0.34/0.61 ) 0.34/0.61 % SZS output end Proof for 0.34/0.61 % cvc5---1.0.5 exiting 0.34/0.61 % cvc5---1.0.5 exiting 0.34/0.61 EOF