0.04/0.08 % Problem : Vampire---4.8_15845 : TPTP v0.0.0. Released v0.0.0. 0.04/0.09 % Command : do_cvc5 %s %d 0.08/0.28 % Computer : n012.cluster.edu 0.08/0.28 % Model : x86_64 x86_64 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.28 % Memory : 8042.1875MB 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 0.08/0.28 % CPULimit : 1440 0.08/0.28 % WCLimit : 180 0.08/0.28 % DateTime : Mon Jul 3 13:01:07 EDT 2023 0.08/0.28 % CPUTime : 0.12/0.37 %----Proving TH0 0.12/0.38 thf(in_type,type, 0.12/0.38 in: $i > $i > $o ). 0.12/0.38 0.12/0.38 thf(exu_type,type, 0.12/0.38 exu: ( $i > $o ) > $o ). 0.12/0.38 0.12/0.38 thf(exu,definition, 0.12/0.38 ( exu 0.12/0.38 = ( ^ [Xphi: $i > $o] : 0.12/0.38 ? [Xx: $i] : 0.12/0.38 ( ( Xphi @ Xx ) 0.12/0.38 & ! [Xy: $i] : 0.12/0.38 ( ( Xphi @ Xy ) 0.12/0.38 => ( Xx = Xy ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(setextAx_type,type, 0.12/0.38 setextAx: $o ). 0.12/0.38 0.12/0.38 thf(setextAx,definition, 0.12/0.38 ( setextAx 0.12/0.38 = ( ! [A: $i,B: $i] : 0.12/0.38 ( ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ A ) 0.12/0.38 <=> ( in @ Xx @ B ) ) 0.12/0.38 => ( A = B ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(emptyset_type,type, 0.12/0.38 emptyset: $i ). 0.12/0.38 0.12/0.38 thf(emptysetAx_type,type, 0.12/0.38 emptysetAx: $o ). 0.12/0.38 0.12/0.38 thf(emptysetAx,definition, 0.12/0.38 ( emptysetAx 0.12/0.38 = ( ! [Xx: $i] : 0.12/0.38 ~ ( in @ Xx @ emptyset ) ) ) ). 0.12/0.38 0.12/0.38 thf(setadjoin_type,type, 0.12/0.38 setadjoin: $i > $i > $i ). 0.12/0.38 0.12/0.38 thf(setadjoinAx_type,type, 0.12/0.38 setadjoinAx: $o ). 0.12/0.38 0.12/0.38 thf(setadjoinAx,definition, 0.12/0.38 ( setadjoinAx 0.12/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.12/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.12/0.38 <=> ( ( Xy = Xx ) 0.12/0.38 | ( in @ Xy @ A ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(powerset_type,type, 0.12/0.38 powerset: $i > $i ). 0.12/0.38 0.12/0.38 thf(powersetAx_type,type, 0.12/0.38 powersetAx: $o ). 0.12/0.38 0.12/0.38 thf(powersetAx,definition, 0.12/0.38 ( powersetAx 0.12/0.38 = ( ! [A: $i,B: $i] : 0.12/0.38 ( ( in @ B @ ( powerset @ A ) ) 0.12/0.38 <=> ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ B ) 0.12/0.38 => ( in @ Xx @ A ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(setunion_type,type, 0.12/0.38 setunion: $i > $i ). 0.12/0.38 0.12/0.38 thf(setunionAx_type,type, 0.12/0.38 setunionAx: $o ). 0.12/0.38 0.12/0.38 thf(setunionAx,definition, 0.12/0.38 ( setunionAx 0.12/0.38 = ( ! [A: $i,Xx: $i] : 0.12/0.38 ( ( in @ Xx @ ( setunion @ A ) ) 0.12/0.38 <=> ? [B: $i] : 0.12/0.38 ( ( in @ Xx @ B ) 0.12/0.38 & ( in @ B @ A ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(omega_type,type, 0.12/0.38 omega: $i ). 0.12/0.38 0.12/0.38 thf(omega0Ax_type,type, 0.12/0.38 omega0Ax: $o ). 0.12/0.38 0.12/0.38 thf(omega0Ax,definition, 0.12/0.38 ( omega0Ax 0.12/0.38 = ( in @ emptyset @ omega ) ) ). 0.12/0.38 0.12/0.38 thf(omegaSAx_type,type, 0.12/0.38 omegaSAx: $o ). 0.12/0.38 0.12/0.38 thf(omegaSAx,definition, 0.12/0.38 ( omegaSAx 0.12/0.38 = ( ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ omega ) 0.12/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(omegaIndAx_type,type, 0.12/0.38 omegaIndAx: $o ). 0.12/0.38 0.12/0.38 thf(omegaIndAx,definition, 0.12/0.38 ( omegaIndAx 0.12/0.38 = ( ! [A: $i] : 0.12/0.38 ( ( ( in @ emptyset @ A ) 0.12/0.38 & ! [Xx: $i] : 0.12/0.38 ( ( ( in @ Xx @ omega ) 0.12/0.38 & ( in @ Xx @ A ) ) 0.12/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) 0.12/0.38 => ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ omega ) 0.12/0.38 => ( in @ Xx @ A ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(replAx_type,type, 0.12/0.38 replAx: $o ). 0.12/0.38 0.12/0.38 thf(replAx,definition, 0.12/0.38 ( replAx 0.12/0.38 = ( ! [Xphi: $i > $i > $o,A: $i] : 0.12/0.38 ( ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ A ) 0.12/0.38 => ( exu 0.12/0.38 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) 0.12/0.38 => ? [B: $i] : 0.12/0.38 ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ B ) 0.12/0.38 <=> ? [Xy: $i] : 0.12/0.38 ( ( in @ Xy @ A ) 0.12/0.38 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(foundationAx_type,type, 0.12/0.38 foundationAx: $o ). 0.12/0.38 0.12/0.38 thf(foundationAx,definition, 0.12/0.38 ( foundationAx 0.12/0.38 = ( ! [A: $i] : 0.12/0.38 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.12/0.38 => ? [B: $i] : 0.12/0.38 ( ( in @ B @ A ) 0.12/0.38 & ~ ? [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ B ) 0.12/0.38 & ( in @ Xx @ A ) ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(wellorderingAx_type,type, 0.12/0.38 wellorderingAx: $o ). 0.12/0.38 0.12/0.38 thf(wellorderingAx,definition, 0.12/0.38 ( wellorderingAx 0.12/0.38 = ( ! [A: $i] : 0.12/0.38 ? [B: $i] : 0.12/0.38 ( ! [C: $i] : 0.12/0.38 ( ( in @ C @ B ) 0.12/0.38 => ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ C ) 0.12/0.38 => ( in @ Xx @ A ) ) ) 0.12/0.38 & ! [Xx: $i,Xy: $i] : 0.12/0.38 ( ( ( in @ Xx @ A ) 0.12/0.38 & ( in @ Xy @ A ) ) 0.12/0.38 => ( ! [C: $i] : 0.12/0.38 ( ( in @ C @ B ) 0.12/0.38 => ( ( in @ Xx @ C ) 0.12/0.38 <=> ( in @ Xy @ C ) ) ) 0.12/0.38 => ( Xx = Xy ) ) ) 0.12/0.38 & ! [C: $i,D: $i] : 0.12/0.38 ( ( ( in @ C @ B ) 0.12/0.38 & ( in @ D @ B ) ) 0.12/0.38 => ( ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ C ) 0.12/0.38 => ( in @ Xx @ D ) ) 0.12/0.38 | ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ D ) 0.12/0.38 => ( in @ Xx @ C ) ) ) ) 0.12/0.38 & ! [C: $i] : 0.12/0.38 ( ( ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ C ) 0.12/0.38 => ( in @ Xx @ A ) ) 0.12/0.38 & ? [Xx: $i] : ( in @ Xx @ C ) ) 0.12/0.38 => ? [D: $i,Xx: $i] : 0.12/0.38 ( ( in @ D @ B ) 0.12/0.38 & ( in @ Xx @ C ) 0.12/0.38 & ~ ? [Xy: $i] : 0.12/0.38 ( ( in @ Xy @ D ) 0.12/0.38 & ( in @ Xy @ C ) ) 0.12/0.38 & ! [E: $i] : 0.12/0.38 ( ( in @ E @ B ) 0.12/0.38 => ( ! [Xy: $i] : 0.12/0.38 ( ( in @ Xy @ E ) 0.12/0.38 => ( in @ Xy @ D ) ) 0.12/0.38 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(descr_type,type, 0.12/0.38 descr: ( $i > $o ) > $i ). 0.12/0.38 0.12/0.38 thf(descrp_type,type, 0.12/0.38 descrp: $o ). 0.12/0.38 0.12/0.38 thf(descrp,definition, 0.12/0.38 ( descrp 0.12/0.38 = ( ! [Xphi: $i > $o] : 0.12/0.38 ( ( exu 0.12/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.12/0.38 => ( Xphi 0.12/0.38 @ ( descr 0.12/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(dsetconstr_type,type, 0.12/0.38 dsetconstr: $i > ( $i > $o ) > $i ). 0.12/0.38 0.12/0.38 thf(dsetconstrI_type,type, 0.12/0.38 dsetconstrI: $o ). 0.12/0.38 0.12/0.38 thf(dsetconstrI,definition, 0.12/0.38 ( dsetconstrI 0.12/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.12/0.38 ( ( in @ Xx @ A ) 0.12/0.38 => ( ( Xphi @ Xx ) 0.12/0.38 => ( in @ Xx 0.12/0.38 @ ( dsetconstr @ A 0.12/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(dsetconstrEL_type,type, 0.12/0.38 dsetconstrEL: $o ). 0.12/0.38 0.12/0.38 thf(dsetconstrEL,definition, 0.12/0.38 ( dsetconstrEL 0.12/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.12/0.38 ( ( in @ Xx 0.12/0.38 @ ( dsetconstr @ A 0.12/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.12/0.38 => ( in @ Xx @ A ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(dsetconstrER_type,type, 0.12/0.38 dsetconstrER: $o ). 0.12/0.38 0.12/0.38 thf(dsetconstrER,definition, 0.12/0.38 ( dsetconstrER 0.12/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.12/0.38 ( ( in @ Xx 0.12/0.38 @ ( dsetconstr @ A 0.12/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.12/0.38 => ( Xphi @ Xx ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(exuE1_type,type, 0.12/0.38 exuE1: $o ). 0.12/0.38 0.12/0.38 thf(exuE1,definition, 0.12/0.38 ( exuE1 0.12/0.38 = ( ! [Xphi: $i > $o] : 0.12/0.38 ( ( exu 0.12/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.12/0.38 => ? [Xx: $i] : 0.12/0.38 ( ( Xphi @ Xx ) 0.12/0.38 & ! [Xy: $i] : 0.12/0.38 ( ( Xphi @ Xy ) 0.12/0.38 => ( Xx = Xy ) ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(prop2set_type,type, 0.12/0.38 prop2set: $o > $i ). 0.12/0.38 0.12/0.38 thf(prop2set,definition, 0.12/0.38 ( prop2set 0.12/0.38 = ( ^ [Xphi: $o] : 0.12/0.38 ( dsetconstr @ ( powerset @ emptyset ) 0.12/0.38 @ ^ [Xx: $i] : Xphi ) ) ) ). 0.12/0.38 0.12/0.38 thf(prop2setE_type,type, 0.12/0.38 prop2setE: $o ). 0.12/0.38 0.12/0.38 thf(prop2setE,definition, 0.12/0.38 ( prop2setE 0.12/0.38 = ( ! [Xphi: $o,Xx: $i] : 0.12/0.38 ( ( in @ Xx @ ( prop2set @ Xphi ) ) 0.12/0.38 => Xphi ) ) ) ). 0.12/0.38 0.12/0.38 thf(emptysetE_type,type, 0.12/0.38 emptysetE: $o ). 0.12/0.38 0.12/0.38 thf(emptysetE,definition, 0.12/0.38 ( emptysetE 0.12/0.38 = ( ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ emptyset ) 0.12/0.38 => ! [Xphi: $o] : Xphi ) ) ) ). 0.12/0.38 0.12/0.38 thf(emptysetimpfalse_type,type, 0.12/0.38 emptysetimpfalse: $o ). 0.12/0.38 0.12/0.38 thf(emptysetimpfalse,definition, 0.12/0.38 ( emptysetimpfalse 0.12/0.38 = ( ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ emptyset ) 0.12/0.38 => $false ) ) ) ). 0.12/0.38 0.12/0.38 thf(notinemptyset_type,type, 0.12/0.38 notinemptyset: $o ). 0.12/0.38 0.12/0.38 thf(notinemptyset,definition, 0.12/0.38 ( notinemptyset 0.12/0.38 = ( ! [Xx: $i] : 0.12/0.38 ~ ( in @ Xx @ emptyset ) ) ) ). 0.12/0.38 0.12/0.38 thf(exuE3e_type,type, 0.12/0.38 exuE3e: $o ). 0.12/0.38 0.12/0.38 thf(exuE3e,definition, 0.12/0.38 ( exuE3e 0.12/0.38 = ( ! [Xphi: $i > $o] : 0.12/0.38 ( ( exu 0.12/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.12/0.38 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(setext_type,type, 0.12/0.38 setext: $o ). 0.12/0.38 0.12/0.38 thf(setext,definition, 0.12/0.38 ( setext 0.12/0.38 = ( ! [A: $i,B: $i] : 0.12/0.38 ( ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ A ) 0.12/0.38 => ( in @ Xx @ B ) ) 0.12/0.38 => ( ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ B ) 0.12/0.38 => ( in @ Xx @ A ) ) 0.12/0.38 => ( A = B ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(emptyI_type,type, 0.12/0.38 emptyI: $o ). 0.12/0.38 0.12/0.38 thf(emptyI,definition, 0.12/0.38 ( emptyI 0.12/0.38 = ( ! [A: $i] : 0.12/0.38 ( ! [Xx: $i] : 0.12/0.38 ~ ( in @ Xx @ A ) 0.12/0.38 => ( A = emptyset ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(noeltsimpempty_type,type, 0.12/0.38 noeltsimpempty: $o ). 0.12/0.38 0.12/0.38 thf(noeltsimpempty,definition, 0.12/0.38 ( noeltsimpempty 0.12/0.38 = ( ! [A: $i] : 0.12/0.38 ( ! [Xx: $i] : 0.12/0.38 ~ ( in @ Xx @ A ) 0.12/0.38 => ( A = emptyset ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(setbeta_type,type, 0.12/0.38 setbeta: $o ). 0.12/0.38 0.12/0.38 thf(setbeta,definition, 0.12/0.38 ( setbeta 0.12/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.12/0.38 ( ( in @ Xx @ A ) 0.12/0.38 => ( ( in @ Xx 0.12/0.38 @ ( dsetconstr @ A 0.12/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.12/0.38 <=> ( Xphi @ Xx ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(nonempty_type,type, 0.12/0.38 nonempty: $i > $o ). 0.12/0.38 0.12/0.38 thf(nonempty,definition, 0.12/0.38 ( nonempty 0.12/0.38 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ). 0.12/0.38 0.12/0.38 thf(nonemptyE1_type,type, 0.12/0.38 nonemptyE1: $o ). 0.12/0.38 0.12/0.38 thf(nonemptyE1,definition, 0.12/0.38 ( nonemptyE1 0.12/0.38 = ( ! [A: $i] : 0.12/0.38 ( ( nonempty @ A ) 0.12/0.38 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(nonemptyI_type,type, 0.12/0.38 nonemptyI: $o ). 0.12/0.38 0.12/0.38 thf(nonemptyI,definition, 0.12/0.38 ( nonemptyI 0.12/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.12/0.38 ( ( in @ Xx @ A ) 0.12/0.38 => ( ( Xphi @ Xx ) 0.12/0.38 => ( nonempty 0.12/0.38 @ ( dsetconstr @ A 0.12/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(nonemptyI1_type,type, 0.12/0.38 nonemptyI1: $o ). 0.12/0.38 0.12/0.38 thf(nonemptyI1,definition, 0.12/0.38 ( nonemptyI1 0.12/0.38 = ( ! [A: $i] : 0.12/0.38 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.12/0.38 => ( nonempty @ A ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(setadjoinIL_type,type, 0.12/0.38 setadjoinIL: $o ). 0.12/0.38 0.12/0.38 thf(setadjoinIL,definition, 0.12/0.38 ( setadjoinIL 0.12/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(emptyinunitempty_type,type, 0.12/0.38 emptyinunitempty: $o ). 0.12/0.38 0.12/0.38 thf(emptyinunitempty,definition, 0.12/0.38 ( emptyinunitempty 0.12/0.38 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ). 0.12/0.38 0.12/0.38 thf(setadjoinIR_type,type, 0.12/0.38 setadjoinIR: $o ). 0.12/0.38 0.12/0.38 thf(setadjoinIR,definition, 0.12/0.38 ( setadjoinIR 0.12/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.12/0.38 ( ( in @ Xy @ A ) 0.12/0.38 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(setadjoinE_type,type, 0.12/0.38 setadjoinE: $o ). 0.12/0.38 0.12/0.38 thf(setadjoinE,definition, 0.12/0.38 ( setadjoinE 0.12/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.12/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.12/0.38 => ! [Xphi: $o] : 0.12/0.38 ( ( ( Xy = Xx ) 0.12/0.38 => Xphi ) 0.12/0.38 => ( ( ( in @ Xy @ A ) 0.12/0.38 => Xphi ) 0.12/0.38 => Xphi ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(setadjoinOr_type,type, 0.12/0.38 setadjoinOr: $o ). 0.12/0.38 0.12/0.38 thf(setadjoinOr,definition, 0.12/0.38 ( setadjoinOr 0.12/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.12/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.12/0.38 => ( ( Xy = Xx ) 0.12/0.38 | ( in @ Xy @ A ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(setoftrueEq_type,type, 0.12/0.38 setoftrueEq: $o ). 0.12/0.38 0.12/0.38 thf(setoftrueEq,definition, 0.12/0.38 ( setoftrueEq 0.12/0.38 = ( ! [A: $i] : 0.12/0.38 ( ( dsetconstr @ A 0.12/0.38 @ ^ [Xx: $i] : $true ) 0.12/0.38 = A ) ) ) ). 0.12/0.38 0.12/0.38 thf(powersetI_type,type, 0.12/0.38 powersetI: $o ). 0.12/0.38 0.12/0.38 thf(powersetI,definition, 0.12/0.38 ( powersetI 0.12/0.38 = ( ! [A: $i,B: $i] : 0.12/0.38 ( ! [Xx: $i] : 0.12/0.38 ( ( in @ Xx @ B ) 0.12/0.38 => ( in @ Xx @ A ) ) 0.12/0.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ). 0.12/0.38 0.12/0.38 thf(emptyinPowerset,conjecture, 0.12/0.38 ( ( ( ( powersetAx 0.12/0.38 => ( setunionAx 0.12/0.38 => ( ( ( ( ( foundationAx 0.12/0.38 => ( ( descrp 0.12/0.38 => ( ( dsetconstrEL 0.12/0.38 => ( ( ( prop2setE 0.12/0.38 => ( emptysetE 0.12/0.38 => ( emptysetimpfalse 0.12/0.38 => ( ( ( ( ( ( setbeta 0.12/0.38 => ( ( nonemptyI 0.12/0.38 => ( ( setadjoinIL 0.12/0.38 => ( ( ( ( setadjoinOr 0.12/0.38 => ( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) 0.12/0.38 <= powersetI ) 0.12/0.38 <= setoftrueEq ) ) 0.12/0.38 <= setadjoinE ) 0.12/0.38 <= setadjoinIR ) 0.12/0.38 <= emptyinunitempty ) ) 0.12/0.38 <= nonemptyI1 ) ) 0.12/0.39 <= nonemptyE1 ) ) 0.12/0.39 <= noeltsimpempty ) 0.12/0.39 <= emptyI ) 0.12/0.39 <= setext ) 0.12/0.39 <= exuE3e ) 0.12/0.39 <= notinemptyset ) ) ) ) 0.12/0.39 <= exuE1 ) 0.12/0.39 <= dsetconstrER ) ) 0.12/0.39 <= dsetconstrI ) ) 0.12/0.39 <= wellorderingAx ) ) 0.12/0.39 <= replAx ) 0.12/0.39 <= omegaIndAx ) 0.12/0.39 <= omegaSAx ) 0.12/0.39 <= omega0Ax ) ) ) 0.12/0.39 <= setadjoinAx ) 0.12/0.39 <= emptysetAx ) 0.12/0.39 <= setextAx ) ). 0.12/0.39 0.12/0.39 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.uvHUYHhOV4/cvc5---1.0.5_16076.p... 0.12/0.39 (declare-sort $$unsorted 0) 0.12/0.39 (declare-fun tptp.in ($$unsorted $$unsorted) Bool) 0.12/0.39 (declare-fun tptp.exu ((-> $$unsorted Bool)) Bool) 0.12/0.39 (assert (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy)))))))) 0.12/0.39 (declare-fun tptp.setextAx () Bool) 0.12/0.39 (assert (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B))))) 0.12/0.39 (declare-fun tptp.emptyset () $$unsorted) 0.12/0.39 (declare-fun tptp.emptysetAx () Bool) 0.12/0.39 (assert (= tptp.emptysetAx (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.12/0.39 (declare-fun tptp.setadjoin ($$unsorted $$unsorted) $$unsorted) 0.12/0.39 (declare-fun tptp.setadjoinAx () Bool) 0.12/0.39 (assert (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.12/0.39 (declare-fun tptp.powerset ($$unsorted) $$unsorted) 0.12/0.39 (declare-fun tptp.powersetAx () Bool) 0.12/0.39 (assert (= tptp.powersetAx (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))))))) 0.12/0.39 (declare-fun tptp.setunion ($$unsorted) $$unsorted) 0.12/0.39 (declare-fun tptp.setunionAx () Bool) 0.12/0.39 (assert (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A))))))) 0.12/0.39 (declare-fun tptp.omega () $$unsorted) 0.12/0.39 (declare-fun tptp.omega0Ax () Bool) 0.12/0.39 (assert (= tptp.omega0Ax (@ (@ tptp.in tptp.emptyset) tptp.omega))) 0.12/0.39 (declare-fun tptp.omegaSAx () Bool) 0.12/0.39 (assert (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega))))) 0.12/0.39 (declare-fun tptp.omegaIndAx () Bool) 0.12/0.39 (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 $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 tptp.omega) (@ _let_1 A)))))))) 0.12/0.39 (declare-fun tptp.replAx () Bool) 0.12/0.39 (assert (= tptp.replAx (forall ((Xphi (-> $$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 $$unsorted)) (and (@ (@ tptp.in Xy) A) (@ (@ Xphi Xy) Xx)))))))))) 0.12/0.39 (declare-fun tptp.foundationAx () Bool) 0.12/0.39 (assert (= tptp.foundationAx (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in B) A) (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 B) (@ _let_1 A))))))))))) 0.12/0.39 (declare-fun tptp.wellorderingAx () Bool) 0.12/0.39 (assert (= tptp.wellorderingAx (forall ((A $$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))))))))))))) 0.12/0.39 (declare-fun tptp.descr ((-> $$unsorted Bool)) $$unsorted) 0.12/0.39 (declare-fun tptp.descrp () Bool) 0.12/0.39 (assert (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) 0.12/0.39 (declare-fun tptp.dsetconstr ($$unsorted (-> $$unsorted Bool)) $$unsorted) 0.12/0.39 (declare-fun tptp.dsetconstrI () Bool) 0.12/0.39 (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)))))))))) 0.12/0.39 (declare-fun tptp.dsetconstrEL () Bool) 0.12/0.39 (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)))))) 0.12/0.39 (declare-fun tptp.dsetconstrER () Bool) 0.12/0.39 (assert (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))) 0.12/0.39 (declare-fun tptp.exuE1 () Bool) 0.12/0.39 (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))))))))) 0.12/0.39 (declare-fun tptp.prop2set (Bool) $$unsorted) 0.12/0.39 (assert (= tptp.prop2set (lambda ((Xphi Bool)) (@ (@ tptp.dsetconstr (@ tptp.powerset tptp.emptyset)) (lambda ((Xx $$unsorted)) Xphi))))) 0.12/0.39 (declare-fun tptp.prop2setE () Bool) 0.12/0.39 (assert (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi)))) 0.12/0.39 (declare-fun tptp.emptysetE () Bool) 0.12/0.39 (assert (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi))))) 0.12/0.39 (declare-fun tptp.emptysetimpfalse () Bool) 0.12/0.39 (assert (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false)))) 0.12/0.39 (declare-fun tptp.notinemptyset () Bool) 0.12/0.39 (assert (= tptp.notinemptyset (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.12/0.39 (declare-fun tptp.exuE3e () Bool) 0.12/0.39 (assert (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx)))))) 0.12/0.39 (declare-fun tptp.setext () Bool) 0.12/0.39 (assert (= tptp.setext (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (= A B)))))) 0.12/0.39 (declare-fun tptp.emptyI () Bool) 0.12/0.39 (assert (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.12/0.39 (declare-fun tptp.noeltsimpempty () Bool) 0.12/0.39 (assert (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.12/0.39 (declare-fun tptp.setbeta () Bool) 0.12/0.39 (assert (= tptp.setbeta (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (= (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))))) 0.12/0.46 (declare-fun tptp.nonempty ($$unsorted) Bool) 0.12/0.46 (assert (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset))))) 0.12/0.46 (declare-fun tptp.nonemptyE1 () Bool) 0.12/0.46 (assert (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)))))) 0.12/0.46 (declare-fun tptp.nonemptyI () Bool) 0.12/0.46 (assert (= tptp.nonemptyI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (@ tptp.nonempty (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))))) 0.12/0.46 (declare-fun tptp.nonemptyI1 () Bool) 0.12/0.46 (assert (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A))))) 0.12/0.46 (declare-fun tptp.setadjoinIL () Bool) 0.12/0.46 (assert (= tptp.setadjoinIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) 0.12/0.46 (declare-fun tptp.emptyinunitempty () Bool) 0.12/0.46 (assert (= tptp.emptyinunitempty (@ (@ tptp.in tptp.emptyset) (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) 0.12/0.46 (declare-fun tptp.setadjoinIR () Bool) 0.12/0.46 (assert (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A))))))) 0.12/0.46 (declare-fun tptp.setadjoinE () Bool) 0.12/0.46 (assert (= tptp.setadjoinE (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (forall ((Xphi Bool)) (=> (=> (= Xy Xx) Xphi) (=> (=> (@ (@ tptp.in Xy) A) Xphi) Xphi))))))) 0.12/0.46 (declare-fun tptp.setadjoinOr () Bool) 0.12/0.46 (assert (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.12/0.46 (declare-fun tptp.setoftrueEq () Bool) 0.12/0.46 (assert (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A)))) 0.12/0.46 (declare-fun tptp.powersetI () Bool) 0.12/0.46 (assert (= tptp.powersetI (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (@ (@ tptp.in B) (@ tptp.powerset A)))))) 0.12/0.46 (assert (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A)))))))))))))))))))))))))))))))))))))))) 0.12/0.46 (set-info :filename cvc5---1.0.5_16076) 0.12/0.46 (check-sat-assuming ( true )) 0.12/0.46 ------- get file name : TPTP file name is 0.12/0.46 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16076.smt2... 0.12/0.46 --- Run --ho-elim --full-saturate-quant at 10... 0.12/0.46 % SZS status Theorem for 0.12/0.46 % SZS output start Proof for 0.12/0.46 ( 0.12/0.46 (let ((_let_1 (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) (let ((_let_2 (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI _let_1)))))))))))))))))))))))))))))))))))))) (let ((_let_3 (= tptp.powersetI (forall ((A $$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_4 (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A))))) (let ((_let_5 (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A)))))))) (let ((_let_6 (= tptp.setadjoinE (forall ((Xx $$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_7 (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A)))))))) (let ((_let_8 (@ tptp.in tptp.emptyset))) (let ((_let_9 (@ _let_8 (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) (let ((_let_10 (= tptp.emptyinunitempty _let_9))) (let ((_let_11 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) (let ((_let_12 (= tptp.setadjoinIL _let_11))) (let ((_let_13 (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A)))))) (let ((_let_14 (= tptp.nonemptyI (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (@ tptp.nonempty (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))))))))) (let ((_let_15 (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A))))))) (let ((_let_16 (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset)))))) (let ((_let_17 (= 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_18 (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))) (let ((_let_19 (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))) (let ((_let_20 (= 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_21 (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx))))))) (let ((_let_22 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_23 (= tptp.notinemptyset _let_22))) (let ((_let_24 (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false))))) (let ((_let_25 (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi)))))) (let ((_let_26 (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi))))) (let ((_let_27 (= tptp.prop2set (lambda ((Xphi Bool)) (@ (@ tptp.dsetconstr (@ tptp.powerset tptp.emptyset)) (lambda ((Xx $$unsorted)) Xphi)))))) (let ((_let_28 (= 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_29 (= 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_30 (= 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_31 (= 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_32 (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (let ((_let_33 (= tptp.wellorderingAx (forall ((A $$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_34 (= 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_35 (= 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_36 (= 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 $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 tptp.omega) (@ _let_1 A))))))))) (let ((_let_37 (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega)))))) (let ((_let_38 (@ _let_8 tptp.omega))) (let ((_let_39 (= tptp.omega0Ax _let_38))) (let ((_let_40 (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A)))))))) (let ((_let_41 (= tptp.powersetAx (forall ((A $$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_42 (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A)))))))) (let ((_let_43 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_44 (= tptp.emptysetAx _let_43))) (let ((_let_45 (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B)))))) (let ((_let_46 (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))))))) (let ((_let_47 (forall ((Xx $$unsorted)) (not (ho_10 (ho_23 k_22 Xx) tptp.emptyset))))) (let ((_let_48 (ho_23 k_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_34))) (let ((_let_49 (ho_10 _let_48 tptp.emptyset))) (let ((_let_50 (forall ((A $$unsorted)) (ho_10 (ho_23 k_22 tptp.emptyset) (ho_21 k_20 A))))) (let ((_let_51 (ho_23 k_22 tptp.emptyset))) (let ((_let_52 (forall ((A $$unsorted) (B $$unsorted)) (= (forall ((Xx $$unsorted)) (let ((_let_1 (ho_23 k_22 Xx))) (or (not (ho_10 _let_1 B)) (ho_10 _let_1 A)))) (ho_10 (ho_23 k_22 B) (ho_21 k_20 A)))))) (let ((_let_53 (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (@ _let_1 A))))) (@ (@ tptp.in B) (@ tptp.powerset A)))) _let_1))) (let ((_let_54 (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (or (not (@ _let_1 (@ (@ tptp.setadjoin Xx) A))) (= Xx Xy) (@ _let_1 A)))))) (let ((_let_55 (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (or (not (@ _let_1 (@ (@ tptp.setadjoin Xx) A))) (= Xx Xy) (@ _let_1 A)))))) (let ((_let_56 (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (or (not (@ _let_1 A)) (@ _let_1 (@ (@ tptp.setadjoin Xx) A))))))) (let ((_let_57 (forall ((BOUND_VARIABLE_1732 $$unsorted)) (not (@ (@ tptp.in BOUND_VARIABLE_1732) tptp.emptyset))))) (let ((_let_58 (forall ((A $$unsorted)) (or (= tptp.emptyset A) (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))))))) (let ((_let_59 (forall ((A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))) (= tptp.emptyset A))))) (let ((_let_60 (forall ((A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))) (= tptp.emptyset A))))) (let ((_let_61 (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_62 (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_2151 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (@ Xphi Xx)))) (not (@ Xphi BOUND_VARIABLE_2151)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_2151)))))))) (let ((_let_63 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_64 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_65 (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_2087 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy))))))) (not (@ Xphi BOUND_VARIABLE_2087)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_2087)))))))) (let ((_let_66 (forall ((A $$unsorted)) (not (forall ((B $$unsorted)) (or (not (forall ((C $$unsorted) (BOUND_VARIABLE_1454 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_1454))) (or (not (@ (@ tptp.in C) B)) (not (@ _let_1 C)) (@ _let_1 A))))) (not (forall ((Xx $$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_1502 $$unsorted) (BOUND_VARIABLE_1495 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_1502))) (let ((_let_2 (@ tptp.in BOUND_VARIABLE_1495))) (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 $$unsorted) (BOUND_VARIABLE_1569 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 C)) (@ _let_1 A))))) (not (@ (@ tptp.in BOUND_VARIABLE_1569) C)) (not (forall ((D $$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 $$unsorted) (BOUND_VARIABLE_1539 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_1539))) (or (not (@ (@ tptp.in E) B)) (@ (@ tptp.in Xx) E) (not (@ _let_1 E)) (@ _let_1 D))))))))))))))))) (let ((_let_67 (forall ((A $$unsorted) (BOUND_VARIABLE_1436 $$unsorted)) (or (not (@ (@ tptp.in BOUND_VARIABLE_1436) 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_68 (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 $$unsorted)) (or (not (@ (@ tptp.in Xy) A)) (not (@ (@ Xphi Xy) Xx)))))))))))))) (let ((_let_69 (forall ((A $$unsorted) (BOUND_VARIABLE_1373 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_1373))) (or (not (@ (@ tptp.in tptp.emptyset) A)) (not (forall ((Xx $$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_70 (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) tptp.omega)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega))))) (let ((_let_71 (forall ((A $$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_72 (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (@ _let_1 A)))))))) (let ((_let_73 (forall ((Xx $$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_74 (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B))))) (= A B))))) (let ((_let_75 (not (=> _let_74 (=> _let_43 (=> _let_73 (=> _let_72 (=> _let_71 (=> _let_38 (=> _let_70 (=> _let_69 (=> _let_68 (=> _let_67 (=> _let_66 (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_2038 $$unsorted)) (or (@ Xphi (@ tptp.descr (@ ll_9 Xphi))) (not (@ Xphi BOUND_VARIABLE_2038)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_2038)))))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (not (@ Xphi Xx)) (@ _let_1 (@ (@ tptp.dsetconstr A) (@ ll_8 Xphi)))))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 (@ (@ tptp.dsetconstr A) (@ ll_7 Xphi)))) (@ _let_1 A)))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (@ ll_6 Xphi)))) (@ Xphi Xx))) (=> _let_65 (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr (@ tptp.powerset tptp.emptyset)) ll_5)))) (=> _let_64 (=> _let_63 (=> _let_22 (=> _let_62 (=> _let_61 (=> _let_60 (=> _let_59 (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (= (@ Xphi Xx) (@ _let_1 (@ (@ tptp.dsetconstr A) (@ ll_4 Xphi))))))) (=> _let_58 (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (= tptp.emptyset (@ (@ tptp.dsetconstr A) (@ ll_3 Xphi)))))) (=> _let_57 (=> _let_11 (=> _let_9 (=> _let_56 (=> _let_55 (=> _let_54 (=> (forall ((A $$unsorted)) (= A (@ (@ tptp.dsetconstr A) ll_2))) _let_53))))))))))))))))))))))))))))))))))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_46)) (MACRO_SR_EQ_INTRO :args (_let_46 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_45)) (MACRO_SR_EQ_INTRO :args (_let_45 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (ASSUME :args (_let_44)))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_42)) (MACRO_SR_EQ_INTRO :args (_let_42 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO :args (_let_41 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (ASSUME :args (_let_39)))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76) :args ((= tptp.replAx (forall ((Xphi (-> $$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 $$unsorted)) (or (not (@ (@ tptp.in Xy) A)) (not (@ (@ Xphi Xy) Xx))))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76) :args ((= tptp.descrp (forall ((Xphi (-> $$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_89 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _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) :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_93 (ASSUME :args (_let_27)))) (let ((_let_94 (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_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) :args ((= tptp.prop2setE (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) (@ tptp.prop2set false))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (ASSUME :args (_let_23)))) (let ((_let_98 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76) :args ((= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (not (@ Xphi Xx))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (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_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76) :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_105 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76) :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_106 (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_10)) (ASSUME :args (_let_12)) (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76) :args ((= tptp.nonemptyI1 (forall ((A $$unsorted) (BOUND_VARIABLE_1732 $$unsorted)) (or (not (@ (@ tptp.in BOUND_VARIABLE_1732) A)) (@ tptp.nonempty A)))) SB_DEFAULT SBA_FIXPOINT))) _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76) :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> _let_74 (=> _let_43 (=> _let_73 (=> _let_72 (=> _let_71 (=> _let_38 (=> _let_70 (=> _let_69 (=> _let_68 (=> _let_67 (=> _let_66 (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_2038 $$unsorted)) (or (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ Xphi BOUND_VARIABLE_2038)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_2038)))))) (=> (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_65 (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr (@ tptp.powerset tptp.emptyset)) (lambda ((BOUND_VARIABLE_2400 $$unsorted)) false))))) (=> _let_64 (=> _let_63 (=> _let_22 (=> _let_62 (=> _let_61 (=> _let_60 (=> _let_59 (=> (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_58 (=> (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_57 (=> _let_11 (=> _let_9 (=> _let_56 (=> _let_55 (=> _let_54 (=> (forall ((A $$unsorted)) (= A (@ (@ tptp.dsetconstr A) (lambda ((BOUND_VARIABLE_2352 $$unsorted)) true)))) _let_53))))))))))))))))))))))))))))))))))) _let_75))) (PREPROCESS :args ((= _let_75 (not (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_23 k_22 Xx))) (= (ho_10 _let_1 B) (ho_10 _let_1 A))))) (= A B))) (=> _let_47 (=> (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (ho_23 k_22 Xy))) (= (or (= Xx Xy) (ho_10 _let_1 A)) (ho_10 _let_1 (ho_21 (ho_28 k_27 Xx) A))))) (=> _let_52 (=> (forall ((A $$unsorted) (Xx $$unsorted)) (= (not (forall ((B $$unsorted)) (or (not (ho_10 (ho_23 k_22 Xx) B)) (not (ho_10 (ho_23 k_22 B) A))))) (ho_10 (ho_23 k_22 Xx) (ho_21 k_30 A)))) (=> (ho_10 _let_51 tptp.omega) (=> (forall ((Xx $$unsorted)) (or (not (ho_10 (ho_23 k_22 Xx) tptp.omega)) (ho_10 (ho_23 k_22 (ho_21 (ho_28 k_27 Xx) Xx)) tptp.omega))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_1373 $$unsorted)) (let ((_let_1 (ho_23 k_22 BOUND_VARIABLE_1373))) (or (not (ho_10 (ho_23 k_22 tptp.emptyset) A)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_23 k_22 Xx))) (or (not (ho_10 _let_1 tptp.omega)) (not (ho_10 _let_1 A)) (ho_10 (ho_23 k_22 (ho_21 (ho_28 k_27 Xx) Xx)) A))))) (not (ho_10 _let_1 tptp.omega)) (ho_10 _let_1 A)))) (=> (forall ((BOUND_VARIABLE_3042 |u_(-> $$unsorted $$unsorted Bool)|) (A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (ho_10 (ho_23 k_22 Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (ho_10 (ho_23 BOUND_VARIABLE_3042 Xx) Xx)) (not (forall ((Xy $$unsorted)) (or (not (ho_10 (ho_23 BOUND_VARIABLE_3042 Xx) Xy)) (= Xx Xy)))))))))) (not (forall ((B $$unsorted)) (not (forall ((Xx $$unsorted)) (= (not (forall ((Xy $$unsorted)) (or (not (ho_10 (ho_23 k_22 Xy) A)) (not (ho_10 (ho_23 BOUND_VARIABLE_3042 Xy) Xx))))) (ho_10 (ho_23 k_22 Xx) B)))))))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_1436 $$unsorted)) (or (not (ho_10 (ho_23 k_22 BOUND_VARIABLE_1436) A)) (not (forall ((B $$unsorted)) (or (not (ho_10 (ho_23 k_22 B) A)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_23 k_22 Xx))) (or (not (ho_10 _let_1 B)) (not (ho_10 _let_1 A))))))))))) (=> (forall ((A $$unsorted)) (not (forall ((B $$unsorted)) (or (not (forall ((C $$unsorted) (BOUND_VARIABLE_1454 $$unsorted)) (let ((_let_1 (ho_23 k_22 BOUND_VARIABLE_1454))) (or (not (ho_10 (ho_23 k_22 C) B)) (not (ho_10 _let_1 C)) (ho_10 _let_1 A))))) (not (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (ho_10 (ho_23 k_22 Xx) A)) (not (ho_10 (ho_23 k_22 Xy) A)) (not (forall ((C $$unsorted)) (or (not (ho_10 (ho_23 k_22 C) B)) (= (ho_10 (ho_23 k_22 Xy) C) (ho_10 (ho_23 k_22 Xx) C))))) (= Xx Xy)))) (not (forall ((C $$unsorted) (D $$unsorted) (BOUND_VARIABLE_1502 $$unsorted) (BOUND_VARIABLE_1495 $$unsorted)) (let ((_let_1 (ho_23 k_22 BOUND_VARIABLE_1502))) (let ((_let_2 (ho_23 k_22 BOUND_VARIABLE_1495))) (or (not (ho_10 (ho_23 k_22 C) B)) (not (ho_10 (ho_23 k_22 D) B)) (not (ho_10 _let_2 C)) (ho_10 _let_2 D) (not (ho_10 _let_1 D)) (ho_10 _let_1 C)))))) (not (forall ((C $$unsorted) (BOUND_VARIABLE_1569 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_23 k_22 Xx))) (or (not (ho_10 _let_1 C)) (ho_10 _let_1 A))))) (not (ho_10 (ho_23 k_22 BOUND_VARIABLE_1569) C)) (not (forall ((D $$unsorted) (Xx $$unsorted)) (or (not (ho_10 (ho_23 k_22 D) B)) (not (ho_10 (ho_23 k_22 Xx) C)) (not (forall ((Xy $$unsorted)) (let ((_let_1 (ho_23 k_22 Xy))) (or (not (ho_10 _let_1 D)) (not (ho_10 _let_1 C)))))) (not (forall ((E $$unsorted) (BOUND_VARIABLE_1539 $$unsorted)) (let ((_let_1 (ho_23 k_22 BOUND_VARIABLE_1539))) (or (not (ho_10 (ho_23 k_22 E) B)) (ho_10 (ho_23 k_22 Xx) E) (not (ho_10 _let_1 E)) (ho_10 _let_1 D))))))))))))))) (=> (forall ((BOUND_VARIABLE_2915 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2038 $$unsorted)) (or (ho_10 BOUND_VARIABLE_2915 (ho_26 k_29 (ho_12 k_11 BOUND_VARIABLE_2915))) (not (ho_10 BOUND_VARIABLE_2915 BOUND_VARIABLE_2038)) (not (forall ((Xy $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_2915 Xy)) (= Xy BOUND_VARIABLE_2038)))))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_2901 |u_(-> $$unsorted Bool)|) (Xx $$unsorted)) (let ((_let_1 (ho_23 k_22 Xx))) (or (not (ho_10 _let_1 A)) (not (ho_10 BOUND_VARIABLE_2901 Xx)) (ho_10 _let_1 (ho_26 (ho_25 k_24 A) (ho_12 k_13 BOUND_VARIABLE_2901)))))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_2891 |u_(-> $$unsorted Bool)|) (Xx $$unsorted)) (let ((_let_1 (ho_23 k_22 Xx))) (or (not (ho_10 _let_1 (ho_26 (ho_25 k_24 A) (ho_12 k_14 BOUND_VARIABLE_2891)))) (ho_10 _let_1 A)))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_2877 |u_(-> $$unsorted Bool)|) (Xx $$unsorted)) (or (not (ho_10 (ho_23 k_22 Xx) (ho_26 (ho_25 k_24 A) (ho_12 k_15 BOUND_VARIABLE_2877)))) (ho_10 BOUND_VARIABLE_2877 Xx))) (=> (forall ((BOUND_VARIABLE_2855 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2087 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_2855 Xx)) (not (forall ((Xy $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_2855 Xy)) (= Xx Xy))))))) (not (ho_10 BOUND_VARIABLE_2855 BOUND_VARIABLE_2087)) (not (forall ((Xy $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_2855 Xy)) (= Xy BOUND_VARIABLE_2087)))))) (=> (forall ((Xx $$unsorted)) (not (ho_10 (ho_23 k_22 Xx) (ho_26 (ho_25 k_24 (ho_21 k_20 tptp.emptyset)) k_16)))) (=> (forall ((Xx $$unsorted)) (not (ho_10 (ho_23 k_22 Xx) tptp.emptyset))) (=> (forall ((Xx $$unsorted)) (not (ho_10 (ho_23 k_22 Xx) tptp.emptyset))) (=> (forall ((Xx $$unsorted)) (not (ho_10 (ho_23 k_22 Xx) tptp.emptyset))) (=> (forall ((BOUND_VARIABLE_2816 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2151 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (ho_10 BOUND_VARIABLE_2816 Xx)))) (not (ho_10 BOUND_VARIABLE_2816 BOUND_VARIABLE_2151)) (not (forall ((Xy $$unsorted)) (or (not (ho_10 BOUND_VARIABLE_2816 Xy)) (= Xy BOUND_VARIABLE_2151)))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_23 k_22 Xx))) (or (not (ho_10 _let_1 A)) (ho_10 _let_1 B))))) (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_23 k_22 Xx))) (or (not (ho_10 _let_1 B)) (ho_10 _let_1 A))))) (= A B))) (=> (forall ((A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (ho_10 (ho_23 k_22 Xx) A)))) (= tptp.emptyset A))) (=> (forall ((A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (ho_10 (ho_23 k_22 Xx) A)))) (= tptp.emptyset A))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_2769 |u_(-> $$unsorted Bool)|) (Xx $$unsorted)) (let ((_let_1 (ho_23 k_22 Xx))) (or (not (ho_10 _let_1 A)) (= (ho_10 _let_1 (ho_26 (ho_25 k_24 A) (ho_12 k_17 BOUND_VARIABLE_2769))) (ho_10 BOUND_VARIABLE_2769 Xx))))) (=> (forall ((A $$unsorted)) (or (= tptp.emptyset A) (not (forall ((Xx $$unsorted)) (not (ho_10 (ho_23 k_22 Xx) A)))))) (=> (forall ((A $$unsorted) (BOUND_VARIABLE_2746 |u_(-> $$unsorted Bool)|) (Xx $$unsorted)) (or (not (ho_10 (ho_23 k_22 Xx) A)) (not (ho_10 BOUND_VARIABLE_2746 Xx)) (not (= tptp.emptyset (ho_26 (ho_25 k_24 A) (ho_12 k_18 BOUND_VARIABLE_2746)))))) (=> (forall ((BOUND_VARIABLE_1732 $$unsorted)) (not (ho_10 (ho_23 k_22 BOUND_VARIABLE_1732) tptp.emptyset))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (ho_10 (ho_23 k_22 Xx) (ho_21 (ho_28 k_27 Xx) Xy))) (=> (ho_10 _let_51 (ho_21 (ho_28 k_27 tptp.emptyset) tptp.emptyset)) (=> (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (ho_23 k_22 Xy))) (or (not (ho_10 _let_1 A)) (ho_10 _let_1 (ho_21 (ho_28 k_27 Xx) A))))) (=> (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (ho_23 k_22 Xy))) (or (not (ho_10 _let_1 (ho_21 (ho_28 k_27 Xx) A))) (= Xx Xy) (ho_10 _let_1 A)))) (=> (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (ho_23 k_22 Xy))) (or (not (ho_10 _let_1 (ho_21 (ho_28 k_27 Xx) A))) (= Xx Xy) (ho_10 _let_1 A)))) (=> (forall ((A $$unsorted)) (= A (ho_26 (ho_25 k_24 A) k_19))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (ho_23 k_22 Xx))) (or (not (ho_10 _let_1 B)) (ho_10 _let_1 A))))) (ho_10 (ho_23 k_22 B) (ho_21 k_20 A)))) _let_50)))))))))))))))))))))))))))))))))))))))))))) (let ((_let_107 (not _let_49))) (let ((_let_108 (or _let_107 (ho_10 _let_48 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31)))) (let ((_let_109 (forall ((Xx $$unsorted)) (let ((_let_1 (ho_23 k_22 Xx))) (or (not (ho_10 _let_1 tptp.emptyset)) (ho_10 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31)))))) (let ((_let_110 (not _let_108))) (let ((_let_111 (ho_10 _let_51 (ho_21 k_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31)))) (let ((_let_112 (= _let_111 _let_109))) (let ((_let_113 (not _let_109))) (let ((_let_114 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 _let_106)))) (let ((_let_115 (_let_52))) (let ((_let_116 (not _let_111))) (let ((_let_117 (or))) (let ((_let_118 (not _let_50))) (let ((_let_119 (_let_118))) (let ((_let_120 (_let_113))) (let ((_let_121 (_let_47))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_121) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_34 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_121)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_108 0)) (CONG (REFL :args (_let_108)) (MACRO_SR_PRED_INTRO :args ((= (not _let_107) _let_49))) :args _let_117)) :args ((or _let_49 _let_108))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_120)) :args _let_120)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_113) _let_109))) (REFL :args (_let_110)) :args _let_117)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_112)) :args ((or _let_111 _let_113 (not _let_112)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_119)) :args _let_119)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_118) _let_50))) (REFL :args (_let_116)) :args _let_117)) (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 _let_114)))))))))))))))))))))))))))))))) :args (_let_116 true _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_115) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 tptp.emptyset QUANTIFIERS_INST_E_MATCHING ((ho_10 (ho_23 k_22 B) (ho_21 k_20 A))))) :args _let_115))) (NOT_IMPLIES_ELIM1 _let_114) :args (_let_112 false _let_52)) :args (_let_113 true _let_111 false _let_112)) :args (_let_110 true _let_109)) :args (_let_49 true _let_108)) (NOT_IMPLIES_ELIM1 _let_106) :args (false false _let_49 false _let_47)) :args (_let_46 _let_45 _let_44 _let_42 _let_41 _let_40 _let_39 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_10 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0.12/0.46 ) 0.12/0.46 % SZS output end Proof for 0.12/0.47 % cvc5---1.0.5 exiting 0.12/0.47 % cvc5---1.0.5 exiting 0.12/0.47 EOF