0.12/0.16 % Problem : Vampire---4.8_30582 : TPTP v0.0.0. Released v0.0.0. 0.12/0.17 % Command : do_cvc5 %s %d 0.18/0.38 % Computer : n026.cluster.edu 0.18/0.38 % Model : x86_64 x86_64 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.18/0.38 % Memory : 8042.1875MB 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64 0.18/0.38 % CPULimit : 1440 0.18/0.38 % WCLimit : 180 0.18/0.38 % DateTime : Mon Jul 3 13:11:52 EDT 2023 0.18/0.38 % CPUTime : 0.38/0.59 %----Proving TH0 0.38/0.59 thf(in_type,type, 0.38/0.59 in: $i > $i > $o ). 0.38/0.59 0.38/0.59 thf(exu_type,type, 0.38/0.59 exu: ( $i > $o ) > $o ). 0.38/0.59 0.38/0.59 thf(exu,definition, 0.38/0.59 ( exu 0.38/0.59 = ( ^ [Xphi: $i > $o] : 0.38/0.59 ? [Xx: $i] : 0.38/0.59 ( ( Xphi @ Xx ) 0.38/0.59 & ! [Xy: $i] : 0.38/0.59 ( ( Xphi @ Xy ) 0.38/0.59 => ( Xx = Xy ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setextAx_type,type, 0.38/0.59 setextAx: $o ). 0.38/0.59 0.38/0.59 thf(setextAx,definition, 0.38/0.59 ( setextAx 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 <=> ( in @ Xx @ B ) ) 0.38/0.59 => ( A = B ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(emptyset_type,type, 0.38/0.59 emptyset: $i ). 0.38/0.59 0.38/0.59 thf(emptysetAx_type,type, 0.38/0.59 emptysetAx: $o ). 0.38/0.59 0.38/0.59 thf(emptysetAx,definition, 0.38/0.59 ( emptysetAx 0.38/0.59 = ( ! [Xx: $i] : 0.38/0.59 ~ ( in @ Xx @ emptyset ) ) ) ). 0.38/0.59 0.38/0.59 thf(setadjoin_type,type, 0.38/0.59 setadjoin: $i > $i > $i ). 0.38/0.59 0.38/0.59 thf(setadjoinAx_type,type, 0.38/0.59 setadjoinAx: $o ). 0.38/0.59 0.38/0.59 thf(setadjoinAx,definition, 0.38/0.59 ( setadjoinAx 0.38/0.59 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.38/0.59 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.38/0.59 <=> ( ( Xy = Xx ) 0.38/0.59 | ( in @ Xy @ A ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(powerset_type,type, 0.38/0.59 powerset: $i > $i ). 0.38/0.59 0.38/0.59 thf(powersetAx_type,type, 0.38/0.59 powersetAx: $o ). 0.38/0.59 0.38/0.59 thf(powersetAx,definition, 0.38/0.59 ( powersetAx 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( in @ B @ ( powerset @ A ) ) 0.38/0.59 <=> ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ B ) 0.38/0.59 => ( in @ Xx @ A ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setunion_type,type, 0.38/0.59 setunion: $i > $i ). 0.38/0.59 0.38/0.59 thf(setunionAx_type,type, 0.38/0.59 setunionAx: $o ). 0.38/0.59 0.38/0.59 thf(setunionAx,definition, 0.38/0.59 ( setunionAx 0.38/0.59 = ( ! [A: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ ( setunion @ A ) ) 0.38/0.59 <=> ? [B: $i] : 0.38/0.59 ( ( in @ Xx @ B ) 0.38/0.59 & ( in @ B @ A ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(omega_type,type, 0.38/0.59 omega: $i ). 0.38/0.59 0.38/0.59 thf(omega0Ax_type,type, 0.38/0.59 omega0Ax: $o ). 0.38/0.59 0.38/0.59 thf(omega0Ax,definition, 0.38/0.59 ( omega0Ax 0.38/0.59 = ( in @ emptyset @ omega ) ) ). 0.38/0.59 0.38/0.59 thf(omegaSAx_type,type, 0.38/0.59 omegaSAx: $o ). 0.38/0.59 0.38/0.59 thf(omegaSAx,definition, 0.38/0.59 ( omegaSAx 0.38/0.59 = ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ omega ) 0.38/0.59 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(omegaIndAx_type,type, 0.38/0.59 omegaIndAx: $o ). 0.38/0.59 0.38/0.59 thf(omegaIndAx,definition, 0.38/0.59 ( omegaIndAx 0.38/0.59 = ( ! [A: $i] : 0.38/0.59 ( ( ( in @ emptyset @ A ) 0.38/0.59 & ! [Xx: $i] : 0.38/0.59 ( ( ( in @ Xx @ omega ) 0.38/0.59 & ( in @ Xx @ A ) ) 0.38/0.59 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) 0.38/0.59 => ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ omega ) 0.38/0.59 => ( in @ Xx @ A ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(replAx_type,type, 0.38/0.59 replAx: $o ). 0.38/0.59 0.38/0.59 thf(replAx,definition, 0.38/0.59 ( replAx 0.38/0.59 = ( ! [Xphi: $i > $i > $o,A: $i] : 0.38/0.59 ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( exu 0.38/0.59 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) 0.38/0.59 => ? [B: $i] : 0.38/0.59 ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ B ) 0.38/0.59 <=> ? [Xy: $i] : 0.38/0.59 ( ( in @ Xy @ A ) 0.38/0.59 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(foundationAx_type,type, 0.38/0.59 foundationAx: $o ). 0.38/0.59 0.38/0.59 thf(foundationAx,definition, 0.38/0.59 ( foundationAx 0.38/0.59 = ( ! [A: $i] : 0.38/0.59 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.38/0.59 => ? [B: $i] : 0.38/0.59 ( ( in @ B @ A ) 0.38/0.59 & ~ ? [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ B ) 0.38/0.59 & ( in @ Xx @ A ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(wellorderingAx_type,type, 0.38/0.59 wellorderingAx: $o ). 0.38/0.59 0.38/0.59 thf(wellorderingAx,definition, 0.38/0.59 ( wellorderingAx 0.38/0.59 = ( ! [A: $i] : 0.38/0.59 ? [B: $i] : 0.38/0.59 ( ! [C: $i] : 0.38/0.59 ( ( in @ C @ B ) 0.38/0.59 => ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ C ) 0.38/0.59 => ( in @ Xx @ A ) ) ) 0.38/0.59 & ! [Xx: $i,Xy: $i] : 0.38/0.59 ( ( ( in @ Xx @ A ) 0.38/0.59 & ( in @ Xy @ A ) ) 0.38/0.59 => ( ! [C: $i] : 0.38/0.59 ( ( in @ C @ B ) 0.38/0.59 => ( ( in @ Xx @ C ) 0.38/0.59 <=> ( in @ Xy @ C ) ) ) 0.38/0.59 => ( Xx = Xy ) ) ) 0.38/0.59 & ! [C: $i,D: $i] : 0.38/0.59 ( ( ( in @ C @ B ) 0.38/0.59 & ( in @ D @ B ) ) 0.38/0.59 => ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ C ) 0.38/0.59 => ( in @ Xx @ D ) ) 0.38/0.59 | ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ D ) 0.38/0.59 => ( in @ Xx @ C ) ) ) ) 0.38/0.59 & ! [C: $i] : 0.38/0.59 ( ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ C ) 0.38/0.59 => ( in @ Xx @ A ) ) 0.38/0.59 & ? [Xx: $i] : ( in @ Xx @ C ) ) 0.38/0.59 => ? [D: $i,Xx: $i] : 0.38/0.59 ( ( in @ D @ B ) 0.38/0.59 & ( in @ Xx @ C ) 0.38/0.59 & ~ ? [Xy: $i] : 0.38/0.59 ( ( in @ Xy @ D ) 0.38/0.59 & ( in @ Xy @ C ) ) 0.38/0.59 & ! [E: $i] : 0.38/0.59 ( ( in @ E @ B ) 0.38/0.59 => ( ! [Xy: $i] : 0.38/0.59 ( ( in @ Xy @ E ) 0.38/0.59 => ( in @ Xy @ D ) ) 0.38/0.59 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(descr_type,type, 0.38/0.59 descr: ( $i > $o ) > $i ). 0.38/0.59 0.38/0.59 thf(descrp_type,type, 0.38/0.59 descrp: $o ). 0.38/0.59 0.38/0.59 thf(descrp,definition, 0.38/0.59 ( descrp 0.38/0.59 = ( ! [Xphi: $i > $o] : 0.38/0.59 ( ( exu 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.59 => ( Xphi 0.38/0.59 @ ( descr 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(dsetconstr_type,type, 0.38/0.59 dsetconstr: $i > ( $i > $o ) > $i ). 0.38/0.59 0.38/0.59 thf(dsetconstrI_type,type, 0.38/0.59 dsetconstrI: $o ). 0.38/0.59 0.38/0.59 thf(dsetconstrI,definition, 0.38/0.59 ( dsetconstrI 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( ( Xphi @ Xx ) 0.38/0.59 => ( in @ Xx 0.38/0.59 @ ( dsetconstr @ A 0.38/0.59 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(dsetconstrEL_type,type, 0.38/0.59 dsetconstrEL: $o ). 0.38/0.59 0.38/0.59 thf(dsetconstrEL,definition, 0.38/0.59 ( dsetconstrEL 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.38/0.59 ( ( in @ Xx 0.38/0.59 @ ( dsetconstr @ A 0.38/0.59 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.38/0.59 => ( in @ Xx @ A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(dsetconstrER_type,type, 0.38/0.59 dsetconstrER: $o ). 0.38/0.59 0.38/0.59 thf(dsetconstrER,definition, 0.38/0.59 ( dsetconstrER 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.38/0.59 ( ( in @ Xx 0.38/0.59 @ ( dsetconstr @ A 0.38/0.59 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.38/0.59 => ( Xphi @ Xx ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(exuE1_type,type, 0.38/0.59 exuE1: $o ). 0.38/0.59 0.38/0.59 thf(exuE1,definition, 0.38/0.59 ( exuE1 0.38/0.59 = ( ! [Xphi: $i > $o] : 0.38/0.59 ( ( exu 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.59 => ? [Xx: $i] : 0.38/0.59 ( ( Xphi @ Xx ) 0.38/0.59 & ! [Xy: $i] : 0.38/0.59 ( ( Xphi @ Xy ) 0.38/0.59 => ( Xx = Xy ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(prop2set_type,type, 0.38/0.59 prop2set: $o > $i ). 0.38/0.59 0.38/0.59 thf(prop2setE_type,type, 0.38/0.59 prop2setE: $o ). 0.38/0.59 0.38/0.59 thf(prop2setE,definition, 0.38/0.59 ( prop2setE 0.38/0.59 = ( ! [Xphi: $o,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ ( prop2set @ Xphi ) ) 0.38/0.59 => Xphi ) ) ) ). 0.38/0.59 0.38/0.59 thf(emptysetE_type,type, 0.38/0.59 emptysetE: $o ). 0.38/0.59 0.38/0.59 thf(emptysetE,definition, 0.38/0.59 ( emptysetE 0.38/0.59 = ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ emptyset ) 0.38/0.59 => ! [Xphi: $o] : Xphi ) ) ) ). 0.38/0.59 0.38/0.59 thf(emptysetimpfalse_type,type, 0.38/0.59 emptysetimpfalse: $o ). 0.38/0.59 0.38/0.59 thf(emptysetimpfalse,definition, 0.38/0.59 ( emptysetimpfalse 0.38/0.59 = ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ emptyset ) 0.38/0.59 => $false ) ) ) ). 0.38/0.59 0.38/0.59 thf(notinemptyset_type,type, 0.38/0.59 notinemptyset: $o ). 0.38/0.59 0.38/0.59 thf(notinemptyset,definition, 0.38/0.59 ( notinemptyset 0.38/0.59 = ( ! [Xx: $i] : 0.38/0.59 ~ ( in @ Xx @ emptyset ) ) ) ). 0.38/0.59 0.38/0.59 thf(exuE3e_type,type, 0.38/0.59 exuE3e: $o ). 0.38/0.59 0.38/0.59 thf(exuE3e,definition, 0.38/0.59 ( exuE3e 0.38/0.59 = ( ! [Xphi: $i > $o] : 0.38/0.59 ( ( exu 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.59 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setext_type,type, 0.38/0.59 setext: $o ). 0.38/0.59 0.38/0.59 thf(setext,definition, 0.38/0.59 ( setext 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( in @ Xx @ B ) ) 0.38/0.59 => ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ B ) 0.38/0.59 => ( in @ Xx @ A ) ) 0.38/0.59 => ( A = B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(emptyI_type,type, 0.38/0.59 emptyI: $o ). 0.38/0.59 0.38/0.59 thf(emptyI,definition, 0.38/0.59 ( emptyI 0.38/0.59 = ( ! [A: $i] : 0.38/0.59 ( ! [Xx: $i] : 0.38/0.59 ~ ( in @ Xx @ A ) 0.38/0.59 => ( A = emptyset ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(noeltsimpempty_type,type, 0.38/0.59 noeltsimpempty: $o ). 0.38/0.59 0.38/0.59 thf(noeltsimpempty,definition, 0.38/0.59 ( noeltsimpempty 0.38/0.59 = ( ! [A: $i] : 0.38/0.59 ( ! [Xx: $i] : 0.38/0.59 ~ ( in @ Xx @ A ) 0.38/0.59 => ( A = emptyset ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setbeta_type,type, 0.38/0.59 setbeta: $o ). 0.38/0.59 0.38/0.59 thf(setbeta,definition, 0.38/0.59 ( setbeta 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( ( in @ Xx 0.38/0.59 @ ( dsetconstr @ A 0.38/0.59 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) 0.38/0.59 <=> ( Xphi @ Xx ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(nonempty_type,type, 0.38/0.59 nonempty: $i > $o ). 0.38/0.59 0.38/0.59 thf(nonempty,definition, 0.38/0.59 ( nonempty 0.38/0.59 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ). 0.38/0.59 0.38/0.59 thf(nonemptyE1_type,type, 0.38/0.59 nonemptyE1: $o ). 0.38/0.59 0.38/0.59 thf(nonemptyE1,definition, 0.38/0.59 ( nonemptyE1 0.38/0.59 = ( ! [A: $i] : 0.38/0.59 ( ( nonempty @ A ) 0.38/0.59 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(nonemptyI_type,type, 0.38/0.59 nonemptyI: $o ). 0.38/0.59 0.38/0.59 thf(nonemptyI,definition, 0.38/0.59 ( nonemptyI 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( ( Xphi @ Xx ) 0.38/0.59 => ( nonempty 0.38/0.59 @ ( dsetconstr @ A 0.38/0.59 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(nonemptyI1_type,type, 0.38/0.59 nonemptyI1: $o ). 0.38/0.59 0.38/0.59 thf(nonemptyI1,definition, 0.38/0.59 ( nonemptyI1 0.38/0.59 = ( ! [A: $i] : 0.38/0.59 ( ? [Xx: $i] : ( in @ Xx @ A ) 0.38/0.59 => ( nonempty @ A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setadjoinIL_type,type, 0.38/0.59 setadjoinIL: $o ). 0.38/0.59 0.38/0.59 thf(setadjoinIL,definition, 0.38/0.59 ( setadjoinIL 0.38/0.59 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(emptyinunitempty_type,type, 0.38/0.59 emptyinunitempty: $o ). 0.38/0.59 0.38/0.59 thf(emptyinunitempty,definition, 0.38/0.59 ( emptyinunitempty 0.38/0.59 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ). 0.38/0.59 0.38/0.59 thf(setadjoinIR_type,type, 0.38/0.59 setadjoinIR: $o ). 0.38/0.59 0.38/0.59 thf(setadjoinIR,definition, 0.38/0.59 ( setadjoinIR 0.38/0.59 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.38/0.59 ( ( in @ Xy @ A ) 0.38/0.59 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setadjoinE_type,type, 0.38/0.59 setadjoinE: $o ). 0.38/0.59 0.38/0.59 thf(setadjoinE,definition, 0.38/0.59 ( setadjoinE 0.38/0.59 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.38/0.59 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.38/0.59 => ! [Xphi: $o] : 0.38/0.59 ( ( ( Xy = Xx ) 0.38/0.59 => Xphi ) 0.38/0.59 => ( ( ( in @ Xy @ A ) 0.38/0.59 => Xphi ) 0.38/0.59 => Xphi ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setadjoinOr_type,type, 0.38/0.59 setadjoinOr: $o ). 0.38/0.59 0.38/0.59 thf(setadjoinOr,definition, 0.38/0.59 ( setadjoinOr 0.38/0.59 = ( ! [Xx: $i,A: $i,Xy: $i] : 0.38/0.59 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) 0.38/0.59 => ( ( Xy = Xx ) 0.38/0.59 | ( in @ Xy @ A ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setoftrueEq_type,type, 0.38/0.59 setoftrueEq: $o ). 0.38/0.59 0.38/0.59 thf(setoftrueEq,definition, 0.38/0.59 ( setoftrueEq 0.38/0.59 = ( ! [A: $i] : 0.38/0.59 ( ( dsetconstr @ A 0.38/0.59 @ ^ [Xx: $i] : $true ) 0.38/0.59 = A ) ) ) ). 0.38/0.59 0.38/0.59 thf(powersetI_type,type, 0.38/0.59 powersetI: $o ). 0.38/0.59 0.38/0.59 thf(powersetI,definition, 0.38/0.59 ( powersetI 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ B ) 0.38/0.59 => ( in @ Xx @ A ) ) 0.38/0.59 => ( in @ B @ ( powerset @ A ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(emptyinPowerset_type,type, 0.38/0.59 emptyinPowerset: $o ). 0.38/0.59 0.38/0.59 thf(emptyinPowerset,definition, 0.38/0.59 ( emptyinPowerset 0.38/0.59 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(emptyInPowerset_type,type, 0.38/0.59 emptyInPowerset: $o ). 0.38/0.59 0.38/0.59 thf(emptyInPowerset,definition, 0.38/0.59 ( emptyInPowerset 0.38/0.59 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(powersetE_type,type, 0.38/0.59 powersetE: $o ). 0.38/0.59 0.38/0.59 thf(powersetE,definition, 0.38/0.59 ( powersetE 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( in @ B @ ( powerset @ A ) ) 0.38/0.59 => ( ( in @ Xx @ B ) 0.38/0.59 => ( in @ Xx @ A ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setunionI_type,type, 0.38/0.59 setunionI: $o ). 0.38/0.59 0.38/0.59 thf(setunionI,definition, 0.38/0.59 ( setunionI 0.38/0.59 = ( ! [A: $i,Xx: $i,B: $i] : 0.38/0.59 ( ( in @ Xx @ B ) 0.38/0.59 => ( ( in @ B @ A ) 0.38/0.59 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setunionE_type,type, 0.38/0.59 setunionE: $o ). 0.38/0.59 0.38/0.59 thf(setunionE,definition, 0.38/0.59 ( setunionE 0.38/0.59 = ( ! [A: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ ( setunion @ A ) ) 0.38/0.59 => ! [Xphi: $o] : 0.38/0.59 ( ! [B: $i] : 0.38/0.59 ( ( in @ Xx @ B ) 0.38/0.59 => ( ( in @ B @ A ) 0.38/0.59 => Xphi ) ) 0.38/0.59 => Xphi ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(subPowSU_type,type, 0.38/0.59 subPowSU: $o ). 0.38/0.59 0.38/0.59 thf(subPowSU,definition, 0.38/0.59 ( subPowSU 0.38/0.59 = ( ! [A: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(exuE2_type,type, 0.38/0.59 exuE2: $o ). 0.38/0.59 0.38/0.59 thf(exuE2,definition, 0.38/0.59 ( exuE2 0.38/0.59 = ( ! [Xphi: $i > $o] : 0.38/0.59 ( ( exu 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.59 => ? [Xx: $i] : 0.38/0.59 ! [Xy: $i] : 0.38/0.59 ( ( Xphi @ Xy ) 0.38/0.59 <=> ( Xy = Xx ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(nonemptyImpWitness_type,type, 0.38/0.59 nonemptyImpWitness: $o ). 0.38/0.59 0.38/0.59 thf(nonemptyImpWitness,definition, 0.38/0.59 ( nonemptyImpWitness 0.38/0.59 = ( ! [A: $i] : 0.38/0.59 ( ( nonempty @ A ) 0.38/0.59 => ? [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 & $true ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(uniqinunit_type,type, 0.38/0.59 uniqinunit: $o ). 0.38/0.59 0.38/0.59 thf(uniqinunit,definition, 0.38/0.59 ( uniqinunit 0.38/0.59 = ( ! [Xx: $i,Xy: $i] : 0.38/0.59 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.38/0.59 => ( Xx = Xy ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(notinsingleton_type,type, 0.38/0.59 notinsingleton: $o ). 0.38/0.59 0.38/0.59 thf(notinsingleton,definition, 0.38/0.59 ( notinsingleton 0.38/0.59 = ( ! [Xx: $i,Xy: $i] : 0.38/0.59 ( ( Xx != Xy ) 0.38/0.59 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(eqinunit_type,type, 0.38/0.59 eqinunit: $o ). 0.38/0.59 0.38/0.59 thf(eqinunit,definition, 0.38/0.59 ( eqinunit 0.38/0.59 = ( ! [Xx: $i,Xy: $i] : 0.38/0.59 ( ( Xx = Xy ) 0.38/0.59 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(singletonsswitch_type,type, 0.38/0.59 singletonsswitch: $o ). 0.38/0.59 0.38/0.59 thf(singletonsswitch,definition, 0.38/0.59 ( singletonsswitch 0.38/0.59 = ( ! [Xx: $i,Xy: $i] : 0.38/0.59 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.38/0.59 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(upairsetE_type,type, 0.38/0.59 upairsetE: $o ). 0.38/0.59 0.38/0.59 thf(upairsetE,definition, 0.38/0.59 ( upairsetE 0.38/0.59 = ( ! [Xx: $i,Xy: $i,Xz: $i] : 0.38/0.59 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) 0.38/0.59 => ( ( Xz = Xx ) 0.38/0.59 | ( Xz = Xy ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(upairsetIL_type,type, 0.38/0.59 upairsetIL: $o ). 0.38/0.59 0.38/0.59 thf(upairsetIL,definition, 0.38/0.59 ( upairsetIL 0.38/0.59 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(upairsetIR_type,type, 0.38/0.59 upairsetIR: $o ). 0.38/0.59 0.38/0.59 thf(upairsetIR,definition, 0.38/0.59 ( upairsetIR 0.38/0.59 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(emptyE1_type,type, 0.38/0.59 emptyE1: $o ). 0.38/0.59 0.38/0.59 thf(emptyE1,definition, 0.38/0.59 ( emptyE1 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o] : 0.38/0.59 ( ? [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 & ( Xphi @ Xx ) ) 0.38/0.59 => ( ( ( dsetconstr @ A 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.59 = emptyset ) 0.38/0.59 => $false ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(vacuousDall_type,type, 0.38/0.59 vacuousDall: $o ). 0.38/0.59 0.38/0.59 thf(vacuousDall,definition, 0.38/0.59 ( vacuousDall 0.38/0.59 = ( ! [Xphi: $i > $o,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ emptyset ) 0.38/0.59 => ( Xphi @ Xx ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(quantDeMorgan1_type,type, 0.38/0.59 quantDeMorgan1: $o ). 0.38/0.59 0.38/0.59 thf(quantDeMorgan1,definition, 0.38/0.59 ( quantDeMorgan1 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o] : 0.38/0.59 ( ~ ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( Xphi @ Xx ) ) 0.38/0.59 => ? [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 & ~ ( Xphi @ Xx ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(quantDeMorgan2_type,type, 0.38/0.59 quantDeMorgan2: $o ). 0.38/0.59 0.38/0.59 thf(quantDeMorgan2,definition, 0.38/0.59 ( quantDeMorgan2 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o] : 0.38/0.59 ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ~ ( Xphi @ Xx ) ) 0.38/0.59 => ~ ? [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 & ( Xphi @ Xx ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(quantDeMorgan3_type,type, 0.38/0.59 quantDeMorgan3: $o ). 0.38/0.59 0.38/0.59 thf(quantDeMorgan3,definition, 0.38/0.59 ( quantDeMorgan3 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o] : 0.38/0.59 ( ~ ? [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 & ( Xphi @ Xx ) ) 0.38/0.59 => ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ~ ( Xphi @ Xx ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(quantDeMorgan4_type,type, 0.38/0.59 quantDeMorgan4: $o ). 0.38/0.59 0.38/0.59 thf(quantDeMorgan4,definition, 0.38/0.59 ( quantDeMorgan4 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o] : 0.38/0.59 ( ? [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 & ~ ( Xphi @ Xx ) ) 0.38/0.59 => ~ ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( Xphi @ Xx ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(prop2setI_type,type, 0.38/0.59 prop2setI: $o ). 0.38/0.59 0.38/0.59 thf(prop2setI,definition, 0.38/0.59 ( prop2setI 0.38/0.59 = ( ! [Xphi: $o] : 0.38/0.59 ( Xphi 0.38/0.59 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(set2prop_type,type, 0.38/0.59 set2prop: $i > $o ). 0.38/0.59 0.38/0.59 thf(prop2set2propI_type,type, 0.38/0.59 prop2set2propI: $o ). 0.38/0.59 0.38/0.59 thf(prop2set2propI,definition, 0.38/0.59 ( prop2set2propI 0.38/0.59 = ( ! [Xphi: $o] : 0.38/0.59 ( Xphi 0.38/0.59 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(notdexE_type,type, 0.38/0.59 notdexE: $o ). 0.38/0.59 0.38/0.59 thf(notdexE,definition, 0.38/0.59 ( notdexE 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o] : 0.38/0.59 ( ~ ? [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 & ( Xphi @ Xx ) ) 0.38/0.59 => ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ~ ( Xphi @ Xx ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(notdallE_type,type, 0.38/0.59 notdallE: $o ). 0.38/0.59 0.38/0.59 thf(notdallE,definition, 0.38/0.59 ( notdallE 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o] : 0.38/0.59 ( ~ ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( Xphi @ Xx ) ) 0.38/0.59 => ? [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 & ~ ( Xphi @ Xx ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(exuI1_type,type, 0.38/0.59 exuI1: $o ). 0.38/0.59 0.38/0.59 thf(exuI1,definition, 0.38/0.59 ( exuI1 0.38/0.59 = ( ! [Xphi: $i > $o] : 0.38/0.59 ( ? [Xx: $i] : 0.38/0.59 ( ( Xphi @ Xx ) 0.38/0.59 & ! [Xy: $i] : 0.38/0.59 ( ( Xphi @ Xy ) 0.38/0.59 => ( Xx = Xy ) ) ) 0.38/0.59 => ( exu 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(exuI3_type,type, 0.38/0.59 exuI3: $o ). 0.38/0.59 0.38/0.59 thf(exuI3,definition, 0.38/0.59 ( exuI3 0.38/0.59 = ( ! [Xphi: $i > $o] : 0.38/0.59 ( ? [Xx: $i] : ( Xphi @ Xx ) 0.38/0.59 => ( ! [Xx: $i,Xy: $i] : 0.38/0.59 ( ( Xphi @ Xx ) 0.38/0.59 => ( ( Xphi @ Xy ) 0.38/0.59 => ( Xx = Xy ) ) ) 0.38/0.59 => ( exu 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(exuI2_type,type, 0.38/0.59 exuI2: $o ). 0.38/0.59 0.38/0.59 thf(exuI2,definition, 0.38/0.59 ( exuI2 0.38/0.59 = ( ! [Xphi: $i > $o] : 0.38/0.59 ( ? [Xx: $i] : 0.38/0.59 ! [Xy: $i] : 0.38/0.59 ( ( Xphi @ Xy ) 0.38/0.59 <=> ( Xy = Xx ) ) 0.38/0.59 => ( exu 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(inCongP_type,type, 0.38/0.59 inCongP: $o ). 0.38/0.59 0.38/0.59 thf(inCongP,definition, 0.38/0.59 ( inCongP 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( A = B ) 0.38/0.59 => ! [Xx: $i,Xy: $i] : 0.38/0.59 ( ( Xx = Xy ) 0.38/0.59 => ( ( in @ Xx @ A ) 0.38/0.59 => ( in @ Xy @ B ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(in__Cong_type,type, 0.38/0.59 in__Cong: $o ). 0.38/0.59 0.38/0.59 thf(in__Cong,definition, 0.38/0.59 ( in__Cong 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( A = B ) 0.38/0.59 => ! [Xx: $i,Xy: $i] : 0.38/0.59 ( ( Xx = Xy ) 0.38/0.59 => ( ( in @ Xx @ A ) 0.38/0.59 <=> ( in @ Xy @ B ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(exuE3u_type,type, 0.38/0.59 exuE3u: $o ). 0.38/0.59 0.38/0.59 thf(exuE3u,definition, 0.38/0.59 ( exuE3u 0.38/0.59 = ( ! [Xphi: $i > $o] : 0.38/0.59 ( ( exu 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.59 => ! [Xx: $i,Xy: $i] : 0.38/0.59 ( ( Xphi @ Xx ) 0.38/0.59 => ( ( Xphi @ Xy ) 0.38/0.59 => ( Xx = Xy ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(exu__Cong_type,type, 0.38/0.59 exu__Cong: $o ). 0.38/0.59 0.38/0.59 thf(exu__Cong,definition, 0.38/0.59 ( exu__Cong 0.38/0.59 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] : 0.38/0.59 ( ! [Xx: $i,Xy: $i] : 0.38/0.59 ( ( Xx = Xy ) 0.38/0.59 => ( ( Xphi @ Xx ) 0.38/0.59 <=> ( Xpsi @ Xy ) ) ) 0.38/0.59 => ( ( exu 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.59 <=> ( exu 0.38/0.59 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(emptyset__Cong_type,type, 0.38/0.59 emptyset__Cong: $o ). 0.38/0.59 0.38/0.59 thf(emptyset__Cong,definition, 0.38/0.59 ( emptyset__Cong 0.38/0.59 = ( emptyset = emptyset ) ) ). 0.38/0.59 0.38/0.59 thf(setadjoin__Cong_type,type, 0.38/0.59 setadjoin__Cong: $o ). 0.38/0.59 0.38/0.59 thf(setadjoin__Cong,definition, 0.38/0.59 ( setadjoin__Cong 0.38/0.59 = ( ! [Xx: $i,Xy: $i] : 0.38/0.59 ( ( Xx = Xy ) 0.38/0.59 => ! [Xz: $i,Xu: $i] : 0.38/0.59 ( ( Xz = Xu ) 0.38/0.59 => ( ( setadjoin @ Xx @ Xz ) 0.38/0.59 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(powerset__Cong_type,type, 0.38/0.59 powerset__Cong: $o ). 0.38/0.59 0.38/0.59 thf(powerset__Cong,definition, 0.38/0.59 ( powerset__Cong 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( A = B ) 0.38/0.59 => ( ( powerset @ A ) 0.38/0.59 = ( powerset @ B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setunion__Cong_type,type, 0.38/0.59 setunion__Cong: $o ). 0.38/0.59 0.38/0.59 thf(setunion__Cong,definition, 0.38/0.59 ( setunion__Cong 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( A = B ) 0.38/0.59 => ( ( setunion @ A ) 0.38/0.59 = ( setunion @ B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(omega__Cong_type,type, 0.38/0.59 omega__Cong: $o ). 0.38/0.59 0.38/0.59 thf(omega__Cong,definition, 0.38/0.59 ( omega__Cong 0.38/0.59 = ( omega = omega ) ) ). 0.38/0.59 0.38/0.59 thf(exuEu_type,type, 0.38/0.59 exuEu: $o ). 0.38/0.59 0.38/0.59 thf(exuEu,definition, 0.38/0.59 ( exuEu 0.38/0.59 = ( ! [Xphi: $i > $o] : 0.38/0.59 ( ( exu 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.59 => ! [Xx: $i,Xy: $i] : 0.38/0.59 ( ( Xphi @ Xx ) 0.38/0.59 => ( ( Xphi @ Xy ) 0.38/0.59 => ( Xx = Xy ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(descr__Cong_type,type, 0.38/0.59 descr__Cong: $o ). 0.38/0.59 0.38/0.59 thf(descr__Cong,definition, 0.38/0.59 ( descr__Cong 0.38/0.59 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] : 0.38/0.59 ( ! [Xx: $i,Xy: $i] : 0.38/0.59 ( ( Xx = Xy ) 0.38/0.59 => ( ( Xphi @ Xx ) 0.38/0.59 <=> ( Xpsi @ Xy ) ) ) 0.38/0.59 => ( ( exu 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.59 => ( ( exu 0.38/0.59 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) 0.38/0.59 => ( ( descr 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.59 = ( descr 0.38/0.59 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(dsetconstr__Cong_type,type, 0.38/0.59 dsetconstr__Cong: $o ). 0.38/0.59 0.38/0.59 thf(dsetconstr__Cong,definition, 0.38/0.59 ( dsetconstr__Cong 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( A = B ) 0.38/0.59 => ! [Xphi: $i > $o,Xpsi: $i > $o] : 0.38/0.59 ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ! [Xy: $i] : 0.38/0.59 ( ( in @ Xy @ B ) 0.38/0.59 => ( ( Xx = Xy ) 0.38/0.59 => ( ( Xphi @ Xx ) 0.38/0.59 <=> ( Xpsi @ Xy ) ) ) ) ) 0.38/0.59 => ( ( dsetconstr @ A 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.59 = ( dsetconstr @ B 0.38/0.59 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(subset_type,type, 0.38/0.59 subset: $i > $i > $o ). 0.38/0.59 0.38/0.59 thf(disjoint_type,type, 0.38/0.59 disjoint: $i > $i > $o ). 0.38/0.59 0.38/0.59 thf(setsmeet_type,type, 0.38/0.59 setsmeet: $i > $i > $o ). 0.38/0.59 0.38/0.59 thf(subsetI1_type,type, 0.38/0.59 subsetI1: $o ). 0.38/0.59 0.38/0.59 thf(subsetI1,definition, 0.38/0.59 ( subsetI1 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( in @ Xx @ B ) ) 0.38/0.59 => ( subset @ A @ B ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(eqimpsubset2_type,type, 0.38/0.59 eqimpsubset2: $o ). 0.38/0.59 0.38/0.59 thf(eqimpsubset2,definition, 0.38/0.59 ( eqimpsubset2 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( A = B ) 0.38/0.59 => ( subset @ B @ A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(eqimpsubset1_type,type, 0.38/0.59 eqimpsubset1: $o ). 0.38/0.59 0.38/0.59 thf(eqimpsubset1,definition, 0.38/0.59 ( eqimpsubset1 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( A = B ) 0.38/0.59 => ( subset @ A @ B ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(subsetI2_type,type, 0.38/0.59 subsetI2: $o ). 0.38/0.59 0.38/0.59 thf(subsetI2,definition, 0.38/0.59 ( subsetI2 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ! [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( in @ Xx @ B ) ) 0.38/0.59 => ( subset @ A @ B ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(emptysetsubset_type,type, 0.38/0.59 emptysetsubset: $o ). 0.38/0.59 0.38/0.59 thf(emptysetsubset,definition, 0.38/0.59 ( emptysetsubset 0.38/0.59 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ). 0.38/0.59 0.38/0.59 thf(subsetE_type,type, 0.38/0.59 subsetE: $o ). 0.38/0.59 0.38/0.59 thf(subsetE,definition, 0.38/0.59 ( subsetE 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( subset @ A @ B ) 0.38/0.59 => ( ( in @ Xx @ A ) 0.38/0.59 => ( in @ Xx @ B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(subsetE2_type,type, 0.38/0.59 subsetE2: $o ). 0.38/0.59 0.38/0.59 thf(subsetE2,definition, 0.38/0.59 ( subsetE2 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( subset @ A @ B ) 0.38/0.59 => ( ~ ( in @ Xx @ B ) 0.38/0.59 => ~ ( in @ Xx @ A ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(notsubsetI_type,type, 0.38/0.59 notsubsetI: $o ). 0.38/0.59 0.38/0.59 thf(notsubsetI,definition, 0.38/0.59 ( notsubsetI 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( ~ ( in @ Xx @ B ) 0.38/0.59 => ~ ( subset @ A @ B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(notequalI1_type,type, 0.38/0.59 notequalI1: $o ). 0.38/0.59 0.38/0.59 thf(notequalI1,definition, 0.38/0.59 ( notequalI1 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ~ ( subset @ A @ B ) 0.38/0.59 => ( A != B ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(notequalI2_type,type, 0.38/0.59 notequalI2: $o ). 0.38/0.59 0.38/0.59 thf(notequalI2,definition, 0.38/0.59 ( notequalI2 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( ~ ( in @ Xx @ B ) 0.38/0.59 => ( A != B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(subsetRefl_type,type, 0.38/0.59 subsetRefl: $o ). 0.38/0.59 0.38/0.59 thf(subsetRefl,definition, 0.38/0.59 ( subsetRefl 0.38/0.59 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ). 0.38/0.59 0.38/0.59 thf(subsetTrans_type,type, 0.38/0.59 subsetTrans: $o ). 0.38/0.59 0.38/0.59 thf(subsetTrans,definition, 0.38/0.59 ( subsetTrans 0.38/0.59 = ( ! [A: $i,B: $i,C: $i] : 0.38/0.59 ( ( subset @ A @ B ) 0.38/0.59 => ( ( subset @ B @ C ) 0.38/0.59 => ( subset @ A @ C ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setadjoinSub_type,type, 0.38/0.59 setadjoinSub: $o ). 0.38/0.59 0.38/0.59 thf(setadjoinSub,definition, 0.38/0.59 ( setadjoinSub 0.38/0.59 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setadjoinSub2_type,type, 0.38/0.59 setadjoinSub2: $o ). 0.38/0.59 0.38/0.59 thf(setadjoinSub2,definition, 0.38/0.59 ( setadjoinSub2 0.38/0.59 = ( ! [A: $i,Xx: $i,B: $i] : 0.38/0.59 ( ( subset @ A @ B ) 0.38/0.59 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(subset2powerset_type,type, 0.38/0.59 subset2powerset: $o ). 0.38/0.59 0.38/0.59 thf(subset2powerset,definition, 0.38/0.59 ( subset2powerset 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( subset @ A @ B ) 0.38/0.59 => ( in @ A @ ( powerset @ B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setextsub_type,type, 0.38/0.59 setextsub: $o ). 0.38/0.59 0.38/0.59 thf(setextsub,definition, 0.38/0.59 ( setextsub 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( subset @ A @ B ) 0.38/0.59 => ( ( subset @ B @ A ) 0.38/0.59 => ( A = B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(subsetemptysetimpeq_type,type, 0.38/0.59 subsetemptysetimpeq: $o ). 0.38/0.59 0.38/0.59 thf(subsetemptysetimpeq,definition, 0.38/0.59 ( subsetemptysetimpeq 0.38/0.59 = ( ! [A: $i] : 0.38/0.59 ( ( subset @ A @ emptyset ) 0.38/0.59 => ( A = emptyset ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(powersetI1_type,type, 0.38/0.59 powersetI1: $o ). 0.38/0.59 0.38/0.59 thf(powersetI1,definition, 0.38/0.59 ( powersetI1 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( subset @ B @ A ) 0.38/0.59 => ( in @ B @ ( powerset @ A ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(powersetE1_type,type, 0.38/0.59 powersetE1: $o ). 0.38/0.59 0.38/0.59 thf(powersetE1,definition, 0.38/0.59 ( powersetE1 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( in @ B @ ( powerset @ A ) ) 0.38/0.59 => ( subset @ B @ A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(inPowerset_type,type, 0.38/0.59 inPowerset: $o ). 0.38/0.59 0.38/0.59 thf(inPowerset,definition, 0.38/0.59 ( inPowerset 0.38/0.59 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(powersetsubset_type,type, 0.38/0.59 powersetsubset: $o ). 0.38/0.59 0.38/0.59 thf(powersetsubset,definition, 0.38/0.59 ( powersetsubset 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( subset @ A @ B ) 0.38/0.59 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(sepInPowerset_type,type, 0.38/0.59 sepInPowerset: $o ). 0.38/0.59 0.38/0.59 thf(sepInPowerset,definition, 0.38/0.59 ( sepInPowerset 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o] : 0.38/0.59 ( in 0.38/0.59 @ ( dsetconstr @ A 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.59 @ ( powerset @ A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(sepSubset_type,type, 0.38/0.59 sepSubset: $o ). 0.38/0.59 0.38/0.59 thf(sepSubset,definition, 0.38/0.59 ( sepSubset 0.38/0.59 = ( ! [A: $i,Xphi: $i > $o] : 0.38/0.59 ( subset 0.38/0.59 @ ( dsetconstr @ A 0.38/0.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.59 @ A ) ) ) ). 0.38/0.59 0.38/0.59 thf(binunion_type,type, 0.38/0.59 binunion: $i > $i > $i ). 0.38/0.59 0.38/0.59 thf(binunionIL_type,type, 0.38/0.59 binunionIL: $o ). 0.38/0.59 0.38/0.59 thf(binunionIL,definition, 0.38/0.59 ( binunionIL 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(upairset2IR_type,type, 0.38/0.59 upairset2IR: $o ). 0.38/0.59 0.38/0.59 thf(upairset2IR,definition, 0.38/0.59 ( upairset2IR 0.38/0.59 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(binunionIR_type,type, 0.38/0.59 binunionIR: $o ). 0.38/0.59 0.38/0.59 thf(binunionIR,definition, 0.38/0.59 ( binunionIR 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ B ) 0.38/0.59 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(binunionEcases_type,type, 0.38/0.59 binunionEcases: $o ). 0.38/0.59 0.38/0.59 thf(binunionEcases,definition, 0.38/0.59 ( binunionEcases 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] : 0.38/0.59 ( ( in @ Xx @ ( binunion @ A @ B ) ) 0.38/0.59 => ( ( ( in @ Xx @ A ) 0.38/0.59 => Xphi ) 0.38/0.59 => ( ( ( in @ Xx @ B ) 0.38/0.59 => Xphi ) 0.38/0.59 => Xphi ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(binunionE_type,type, 0.38/0.59 binunionE: $o ). 0.38/0.59 0.38/0.59 thf(binunionE,definition, 0.38/0.59 ( binunionE 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ ( binunion @ A @ B ) ) 0.38/0.59 => ( ( in @ Xx @ A ) 0.38/0.59 | ( in @ Xx @ B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(binunionLsub_type,type, 0.38/0.59 binunionLsub: $o ). 0.38/0.59 0.38/0.59 thf(binunionLsub,definition, 0.38/0.59 ( binunionLsub 0.38/0.59 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(binunionRsub_type,type, 0.38/0.59 binunionRsub: $o ). 0.38/0.59 0.38/0.59 thf(binunionRsub,definition, 0.38/0.59 ( binunionRsub 0.38/0.59 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(binintersect_type,type, 0.38/0.59 binintersect: $i > $i > $i ). 0.38/0.59 0.38/0.59 thf(binintersectI_type,type, 0.38/0.59 binintersectI: $o ). 0.38/0.59 0.38/0.59 thf(binintersectI,definition, 0.38/0.59 ( binintersectI 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( ( in @ Xx @ B ) 0.38/0.59 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(binintersectSubset5_type,type, 0.38/0.59 binintersectSubset5: $o ). 0.38/0.59 0.38/0.59 thf(binintersectSubset5,definition, 0.38/0.59 ( binintersectSubset5 0.38/0.59 = ( ! [A: $i,B: $i,C: $i] : 0.38/0.59 ( ( subset @ C @ A ) 0.38/0.59 => ( ( subset @ C @ B ) 0.38/0.59 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(binintersectEL_type,type, 0.38/0.59 binintersectEL: $o ). 0.38/0.59 0.38/0.59 thf(binintersectEL,definition, 0.38/0.59 ( binintersectEL 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ ( binintersect @ A @ B ) ) 0.38/0.59 => ( in @ Xx @ A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(binintersectLsub_type,type, 0.38/0.59 binintersectLsub: $o ). 0.38/0.59 0.38/0.59 thf(binintersectLsub,definition, 0.38/0.59 ( binintersectLsub 0.38/0.59 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ). 0.38/0.59 0.38/0.59 thf(binintersectSubset2_type,type, 0.38/0.59 binintersectSubset2: $o ). 0.38/0.59 0.38/0.59 thf(binintersectSubset2,definition, 0.38/0.59 ( binintersectSubset2 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( subset @ A @ B ) 0.38/0.59 => ( ( binintersect @ A @ B ) 0.38/0.59 = A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(binintersectSubset3_type,type, 0.38/0.59 binintersectSubset3: $o ). 0.38/0.59 0.38/0.59 thf(binintersectSubset3,definition, 0.38/0.59 ( binintersectSubset3 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( ( binintersect @ A @ B ) 0.38/0.59 = B ) 0.38/0.59 => ( subset @ B @ A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(binintersectER_type,type, 0.38/0.59 binintersectER: $o ). 0.38/0.59 0.38/0.59 thf(binintersectER,definition, 0.38/0.59 ( binintersectER 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ ( binintersect @ A @ B ) ) 0.38/0.59 => ( in @ Xx @ B ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(disjointsetsI1_type,type, 0.38/0.59 disjointsetsI1: $o ). 0.38/0.59 0.38/0.59 thf(disjointsetsI1,definition, 0.38/0.59 ( disjointsetsI1 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ~ ? [Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 & ( in @ Xx @ B ) ) 0.38/0.59 => ( ( binintersect @ A @ B ) 0.38/0.59 = emptyset ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(binintersectRsub_type,type, 0.38/0.59 binintersectRsub: $o ). 0.38/0.59 0.38/0.59 thf(binintersectRsub,definition, 0.38/0.59 ( binintersectRsub 0.38/0.59 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ). 0.38/0.59 0.38/0.59 thf(binintersectSubset4_type,type, 0.38/0.59 binintersectSubset4: $o ). 0.38/0.59 0.38/0.59 thf(binintersectSubset4,definition, 0.38/0.59 ( binintersectSubset4 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( subset @ B @ A ) 0.38/0.59 => ( ( binintersect @ A @ B ) 0.38/0.59 = B ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(binintersectSubset1_type,type, 0.38/0.59 binintersectSubset1: $o ). 0.38/0.59 0.38/0.59 thf(binintersectSubset1,definition, 0.38/0.59 ( binintersectSubset1 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( ( binintersect @ A @ B ) 0.38/0.59 = A ) 0.38/0.59 => ( subset @ A @ B ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(bs114d_type,type, 0.38/0.59 bs114d: $o ). 0.38/0.59 0.38/0.59 thf(bs114d,definition, 0.38/0.59 ( bs114d 0.38/0.59 = ( ! [A: $i,B: $i,C: $i] : 0.38/0.59 ( ( binintersect @ A @ ( binunion @ B @ C ) ) 0.38/0.59 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(regular_type,type, 0.38/0.59 regular: $i > $o ). 0.38/0.59 0.38/0.59 thf(setminus_type,type, 0.38/0.59 setminus: $i > $i > $i ). 0.38/0.59 0.38/0.59 thf(setminusI_type,type, 0.38/0.59 setminusI: $o ). 0.38/0.59 0.38/0.59 thf(setminusI,definition, 0.38/0.59 ( setminusI 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ A ) 0.38/0.59 => ( ~ ( in @ Xx @ B ) 0.38/0.59 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setminusEL_type,type, 0.38/0.59 setminusEL: $o ). 0.38/0.59 0.38/0.59 thf(setminusEL,definition, 0.38/0.59 ( setminusEL 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ ( setminus @ A @ B ) ) 0.38/0.59 => ( in @ Xx @ A ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setminusER_type,type, 0.38/0.59 setminusER: $o ). 0.38/0.59 0.38/0.59 thf(setminusER,definition, 0.38/0.59 ( setminusER 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ ( setminus @ A @ B ) ) 0.38/0.59 => ~ ( in @ Xx @ B ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setminusSubset2_type,type, 0.38/0.59 setminusSubset2: $o ). 0.38/0.59 0.38/0.59 thf(setminusSubset2,definition, 0.38/0.59 ( setminusSubset2 0.38/0.59 = ( ! [A: $i,B: $i] : 0.38/0.59 ( ( subset @ A @ B ) 0.38/0.59 => ( ( setminus @ A @ B ) 0.38/0.59 = emptyset ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setminusERneg_type,type, 0.38/0.59 setminusERneg: $o ). 0.38/0.59 0.38/0.59 thf(setminusERneg,definition, 0.38/0.59 ( setminusERneg 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ~ ( in @ Xx @ ( setminus @ A @ B ) ) 0.38/0.59 => ( ( in @ Xx @ A ) 0.38/0.59 => ( in @ Xx @ B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setminusELneg_type,type, 0.38/0.59 setminusELneg: $o ). 0.38/0.59 0.38/0.59 thf(setminusELneg,definition, 0.38/0.59 ( setminusELneg 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ~ ( in @ Xx @ ( setminus @ A @ B ) ) 0.38/0.59 => ( ~ ( in @ Xx @ B ) 0.38/0.59 => ~ ( in @ Xx @ A ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setminusILneg_type,type, 0.38/0.59 setminusILneg: $o ). 0.38/0.59 0.38/0.59 thf(setminusILneg,definition, 0.38/0.59 ( setminusILneg 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ~ ( in @ Xx @ A ) 0.38/0.59 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ). 0.38/0.59 0.38/0.59 thf(setminusIRneg_type,type, 0.38/0.59 setminusIRneg: $o ). 0.38/0.59 0.38/0.59 thf(setminusIRneg,definition, 0.38/0.59 ( setminusIRneg 0.38/0.59 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.59 ( ( in @ Xx @ B ) 0.38/0.59 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setminusLsub_type,type, 0.38/0.60 setminusLsub: $o ). 0.38/0.60 0.38/0.60 thf(setminusLsub,definition, 0.38/0.60 ( setminusLsub 0.38/0.60 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ). 0.38/0.60 0.38/0.60 thf(setminusSubset1_type,type, 0.38/0.60 setminusSubset1: $o ). 0.38/0.60 0.38/0.60 thf(setminusSubset1,definition, 0.38/0.60 ( setminusSubset1 0.38/0.60 = ( ! [A: $i,B: $i] : 0.38/0.60 ( ( ( setminus @ A @ B ) 0.38/0.60 = emptyset ) 0.38/0.60 => ( subset @ A @ B ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(symdiff_type,type, 0.38/0.60 symdiff: $i > $i > $i ). 0.38/0.60 0.38/0.60 thf(symdiffE_type,type, 0.38/0.60 symdiffE: $o ). 0.38/0.60 0.38/0.60 thf(symdiffE,definition, 0.38/0.60 ( symdiffE 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ ( symdiff @ A @ B ) ) 0.38/0.60 => ! [Xphi: $o] : 0.38/0.60 ( ( ( in @ Xx @ A ) 0.38/0.60 => ( ~ ( in @ Xx @ B ) 0.38/0.60 => Xphi ) ) 0.38/0.60 => ( ( ~ ( in @ Xx @ A ) 0.38/0.60 => ( ( in @ Xx @ B ) 0.38/0.60 => Xphi ) ) 0.38/0.60 => Xphi ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(symdiffI1_type,type, 0.38/0.60 symdiffI1: $o ). 0.38/0.60 0.38/0.60 thf(symdiffI1,definition, 0.38/0.60 ( symdiffI1 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( ~ ( in @ Xx @ B ) 0.38/0.60 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(symdiffI2_type,type, 0.38/0.60 symdiffI2: $o ). 0.38/0.60 0.38/0.60 thf(symdiffI2,definition, 0.38/0.60 ( symdiffI2 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ~ ( in @ Xx @ A ) 0.38/0.60 => ( ( in @ Xx @ B ) 0.38/0.60 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(symdiffIneg1_type,type, 0.38/0.60 symdiffIneg1: $o ). 0.38/0.60 0.38/0.60 thf(symdiffIneg1,definition, 0.38/0.60 ( symdiffIneg1 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( ( in @ Xx @ B ) 0.38/0.60 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(symdiffIneg2_type,type, 0.38/0.60 symdiffIneg2: $o ). 0.38/0.60 0.38/0.60 thf(symdiffIneg2,definition, 0.38/0.60 ( symdiffIneg2 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ~ ( in @ Xx @ A ) 0.38/0.60 => ( ~ ( in @ Xx @ B ) 0.38/0.60 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(iskpair_type,type, 0.38/0.60 iskpair: $i > $o ). 0.38/0.60 0.38/0.60 thf(secondinupair_type,type, 0.38/0.60 secondinupair: $o ). 0.38/0.60 0.38/0.60 thf(secondinupair,definition, 0.38/0.60 ( secondinupair 0.38/0.60 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setukpairIL_type,type, 0.38/0.60 setukpairIL: $o ). 0.38/0.60 0.38/0.60 thf(setukpairIL,definition, 0.38/0.60 ( setukpairIL 0.38/0.60 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setukpairIR_type,type, 0.38/0.60 setukpairIR: $o ). 0.38/0.60 0.38/0.60 thf(setukpairIR,definition, 0.38/0.60 ( setukpairIR 0.38/0.60 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(kpairiskpair_type,type, 0.38/0.60 kpairiskpair: $o ). 0.38/0.60 0.38/0.60 thf(kpairiskpair,definition, 0.38/0.60 ( kpairiskpair 0.38/0.60 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(kpair_type,type, 0.38/0.60 kpair: $i > $i > $i ). 0.38/0.60 0.38/0.60 thf(kpairp_type,type, 0.38/0.60 kpairp: $o ). 0.38/0.60 0.38/0.60 thf(kpairp,definition, 0.38/0.60 ( kpairp 0.38/0.60 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(cartprod_type,type, 0.38/0.60 cartprod: $i > $i > $i ). 0.38/0.60 0.38/0.60 thf(singletonsubset_type,type, 0.38/0.60 singletonsubset: $o ). 0.38/0.60 0.38/0.60 thf(singletonsubset,definition, 0.38/0.60 ( singletonsubset 0.38/0.60 = ( ! [A: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(singletoninpowerset_type,type, 0.38/0.60 singletoninpowerset: $o ). 0.38/0.60 0.38/0.60 thf(singletoninpowerset,definition, 0.38/0.60 ( singletoninpowerset 0.38/0.60 = ( ! [A: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(singletoninpowunion_type,type, 0.38/0.60 singletoninpowunion: $o ). 0.38/0.60 0.38/0.60 thf(singletoninpowunion,definition, 0.38/0.60 ( singletoninpowunion 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(upairset2E_type,type, 0.38/0.60 upairset2E: $o ). 0.38/0.60 0.38/0.60 thf(upairset2E,definition, 0.38/0.60 ( upairset2E 0.38/0.60 = ( ! [Xx: $i,Xy: $i,Xz: $i] : 0.38/0.60 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) 0.38/0.60 => ( ( Xz = Xx ) 0.38/0.60 | ( Xz = Xy ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(upairsubunion_type,type, 0.38/0.60 upairsubunion: $o ). 0.38/0.60 0.38/0.60 thf(upairsubunion,definition, 0.38/0.60 ( upairsubunion 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(upairinpowunion_type,type, 0.38/0.60 upairinpowunion: $o ). 0.38/0.60 0.38/0.60 thf(upairinpowunion,definition, 0.38/0.60 ( upairinpowunion 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ubforcartprodlem1_type,type, 0.38/0.60 ubforcartprodlem1: $o ). 0.38/0.60 0.38/0.60 thf(ubforcartprodlem1,definition, 0.38/0.60 ( ubforcartprodlem1 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ubforcartprodlem2_type,type, 0.38/0.60 ubforcartprodlem2: $o ). 0.38/0.60 0.38/0.60 thf(ubforcartprodlem2,definition, 0.38/0.60 ( ubforcartprodlem2 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ubforcartprodlem3_type,type, 0.38/0.60 ubforcartprodlem3: $o ). 0.38/0.60 0.38/0.60 thf(ubforcartprodlem3,definition, 0.38/0.60 ( ubforcartprodlem3 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(cartprodpairin_type,type, 0.38/0.60 cartprodpairin: $o ). 0.38/0.60 0.38/0.60 thf(cartprodpairin,definition, 0.38/0.60 ( cartprodpairin 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(cartprodmempair1_type,type, 0.38/0.60 cartprodmempair1: $o ). 0.38/0.60 0.38/0.60 thf(cartprodmempair1,definition, 0.38/0.60 ( cartprodmempair1 0.38/0.60 = ( ! [A: $i,B: $i,Xu: $i] : 0.38/0.60 ( ( in @ Xu @ ( cartprod @ A @ B ) ) 0.38/0.60 => ? [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 & ? [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 & ( Xu 0.38/0.60 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(cartprodmempair_type,type, 0.38/0.60 cartprodmempair: $o ). 0.38/0.60 0.38/0.60 thf(cartprodmempair,definition, 0.38/0.60 ( cartprodmempair 0.38/0.60 = ( ! [A: $i,B: $i,Xu: $i] : 0.38/0.60 ( ( in @ Xu @ ( cartprod @ A @ B ) ) 0.38/0.60 => ( iskpair @ Xu ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setunionE2_type,type, 0.38/0.60 setunionE2: $o ). 0.38/0.60 0.38/0.60 thf(setunionE2,definition, 0.38/0.60 ( setunionE2 0.38/0.60 = ( ! [A: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ ( setunion @ A ) ) 0.38/0.60 => ? [X: $i] : 0.38/0.60 ( ( in @ X @ A ) 0.38/0.60 & ( in @ Xx @ X ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setunionsingleton1_type,type, 0.38/0.60 setunionsingleton1: $o ). 0.38/0.60 0.38/0.60 thf(setunionsingleton1,definition, 0.38/0.60 ( setunionsingleton1 0.38/0.60 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ). 0.38/0.60 0.38/0.60 thf(setunionsingleton2_type,type, 0.38/0.60 setunionsingleton2: $o ). 0.38/0.60 0.38/0.60 thf(setunionsingleton2,definition, 0.38/0.60 ( setunionsingleton2 0.38/0.60 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setunionsingleton_type,type, 0.38/0.60 setunionsingleton: $o ). 0.38/0.60 0.38/0.60 thf(setunionsingleton,definition, 0.38/0.60 ( setunionsingleton 0.38/0.60 = ( ! [Xx: $i] : 0.38/0.60 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) ) 0.38/0.60 = Xx ) ) ) ). 0.38/0.60 0.38/0.60 thf(singleton_type,type, 0.38/0.60 singleton: $i > $o ). 0.38/0.60 0.38/0.60 thf(singletonprop_type,type, 0.38/0.60 singletonprop: $o ). 0.38/0.60 0.38/0.60 thf(singletonprop,definition, 0.38/0.60 ( singletonprop 0.38/0.60 = ( ! [A: $i,Xphi: $i > $o] : 0.38/0.60 ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ A ) 0.38/0.60 => ( ( Xphi @ Xx ) 0.38/0.60 => ( ( Xphi @ Xy ) 0.38/0.60 => ( Xx = Xy ) ) ) ) ) 0.38/0.60 => ( ? [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 & ( Xphi @ Xx ) ) 0.38/0.60 => ( singleton 0.38/0.60 @ ( dsetconstr @ A 0.38/0.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ex1_type,type, 0.38/0.60 ex1: $i > ( $i > $o ) > $o ). 0.38/0.60 0.38/0.60 thf(ex1,definition, 0.38/0.60 ( ex1 0.38/0.60 = ( ^ [A: $i,Xphi: $i > $o] : 0.38/0.60 ( singleton 0.38/0.60 @ ( dsetconstr @ A 0.38/0.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ex1E1_type,type, 0.38/0.60 ex1E1: $o ). 0.38/0.60 0.38/0.60 thf(ex1E1,definition, 0.38/0.60 ( ex1E1 0.38/0.60 = ( ! [A: $i,Xphi: $i > $o] : 0.38/0.60 ( ( ex1 @ A 0.38/0.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.60 => ? [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 & ( Xphi @ Xx ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ex1I_type,type, 0.38/0.60 ex1I: $o ). 0.38/0.60 0.38/0.60 thf(ex1I,definition, 0.38/0.60 ( ex1I 0.38/0.60 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( ( Xphi @ Xx ) 0.38/0.60 => ( ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ A ) 0.38/0.60 => ( ( Xphi @ Xy ) 0.38/0.60 => ( Xy = Xx ) ) ) 0.38/0.60 => ( ex1 @ A 0.38/0.60 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ex1I2_type,type, 0.38/0.60 ex1I2: $o ). 0.38/0.60 0.38/0.60 thf(ex1I2,definition, 0.38/0.60 ( ex1I2 0.38/0.60 = ( ! [A: $i,Xphi: $i > $o] : 0.38/0.60 ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ A ) 0.38/0.60 => ( ( Xphi @ Xx ) 0.38/0.60 => ( ( Xphi @ Xy ) 0.38/0.60 => ( Xx = Xy ) ) ) ) ) 0.38/0.60 => ( ? [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 & ( Xphi @ Xx ) ) 0.38/0.60 => ( ex1 @ A 0.38/0.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(singletonsuniq_type,type, 0.38/0.60 singletonsuniq: $o ). 0.38/0.60 0.38/0.60 thf(singletonsuniq,definition, 0.38/0.60 ( singletonsuniq 0.38/0.60 = ( ! [Xx: $i,Xy: $i] : 0.38/0.60 ( ( ( setadjoin @ Xx @ emptyset ) 0.38/0.60 = ( setadjoin @ Xy @ emptyset ) ) 0.38/0.60 => ( Xx = Xy ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(atmost1p_type,type, 0.38/0.60 atmost1p: $i > $o ). 0.38/0.60 0.38/0.60 thf(atleast2p_type,type, 0.38/0.60 atleast2p: $i > $o ). 0.38/0.60 0.38/0.60 thf(atmost2p_type,type, 0.38/0.60 atmost2p: $i > $o ). 0.38/0.60 0.38/0.60 thf(upairsetp_type,type, 0.38/0.60 upairsetp: $i > $o ). 0.38/0.60 0.38/0.60 thf(setukpairinjL1_type,type, 0.38/0.60 setukpairinjL1: $o ). 0.38/0.60 0.38/0.60 thf(setukpairinjL1,definition, 0.38/0.60 ( setukpairinjL1 0.38/0.60 = ( ! [Xx: $i,Xy: $i,Xz: $i] : 0.38/0.60 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) 0.38/0.60 => ( Xx = Xz ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(kfstsingleton_type,type, 0.38/0.60 kfstsingleton: $o ). 0.38/0.60 0.38/0.60 thf(kfstsingleton,definition, 0.38/0.60 ( kfstsingleton 0.38/0.60 = ( ! [Xu: $i] : 0.38/0.60 ( ( iskpair @ Xu ) 0.38/0.60 => ( singleton 0.38/0.60 @ ( dsetconstr @ ( setunion @ Xu ) 0.38/0.60 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(theprop_type,type, 0.38/0.60 theprop: $o ). 0.38/0.60 0.38/0.60 thf(theprop,definition, 0.38/0.60 ( theprop 0.38/0.60 = ( ! [X: $i] : 0.38/0.60 ( ( singleton @ X ) 0.38/0.60 => ( in @ ( setunion @ X ) @ X ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(kfst_type,type, 0.38/0.60 kfst: $i > $i ). 0.38/0.60 0.38/0.60 thf(kfstpairEq_type,type, 0.38/0.60 kfstpairEq: $o ). 0.38/0.60 0.38/0.60 thf(kfstpairEq,definition, 0.38/0.60 ( kfstpairEq 0.38/0.60 = ( ! [Xx: $i,Xy: $i] : 0.38/0.60 ( ( kfst @ ( kpair @ Xx @ Xy ) ) 0.38/0.60 = Xx ) ) ) ). 0.38/0.60 0.38/0.60 thf(cartprodfstin_type,type, 0.38/0.60 cartprodfstin: $o ). 0.38/0.60 0.38/0.60 thf(cartprodfstin,definition, 0.38/0.60 ( cartprodfstin 0.38/0.60 = ( ! [A: $i,B: $i,Xu: $i] : 0.38/0.60 ( ( in @ Xu @ ( cartprod @ A @ B ) ) 0.38/0.60 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setukpairinjL2_type,type, 0.38/0.60 setukpairinjL2: $o ). 0.38/0.60 0.38/0.60 thf(setukpairinjL2,definition, 0.38/0.60 ( setukpairinjL2 0.38/0.60 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] : 0.38/0.60 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) 0.38/0.60 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) 0.38/0.60 => ( Xx = Xz ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setukpairinjL_type,type, 0.38/0.60 setukpairinjL: $o ). 0.38/0.60 0.38/0.60 thf(setukpairinjL,definition, 0.38/0.60 ( setukpairinjL 0.38/0.60 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] : 0.38/0.60 ( ( ( kpair @ Xx @ Xy ) 0.38/0.60 = ( kpair @ Xz @ Xu ) ) 0.38/0.60 => ( Xx = Xz ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setukpairinjR11_type,type, 0.38/0.60 setukpairinjR11: $o ). 0.38/0.60 0.38/0.60 thf(setukpairinjR11,definition, 0.38/0.60 ( setukpairinjR11 0.38/0.60 = ( ! [Xx: $i,Xy: $i] : 0.38/0.60 ( ( Xx = Xy ) 0.38/0.60 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.38/0.60 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setukpairinjR12_type,type, 0.38/0.60 setukpairinjR12: $o ). 0.38/0.60 0.38/0.60 thf(setukpairinjR12,definition, 0.38/0.60 ( setukpairinjR12 0.38/0.60 = ( ! [Xx: $i,Xy: $i] : 0.38/0.60 ( ( Xx = Xy ) 0.38/0.60 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) 0.38/0.60 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setukpairinjR1_type,type, 0.38/0.60 setukpairinjR1: $o ). 0.38/0.60 0.38/0.60 thf(setukpairinjR1,definition, 0.38/0.60 ( setukpairinjR1 0.38/0.60 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] : 0.38/0.60 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) 0.38/0.60 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) 0.38/0.60 => ( ( Xz = Xu ) 0.38/0.60 => ( Xy = Xu ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(upairequniteq_type,type, 0.38/0.60 upairequniteq: $o ). 0.38/0.60 0.38/0.60 thf(upairequniteq,definition, 0.38/0.60 ( upairequniteq 0.38/0.60 = ( ! [Xx: $i,Xy: $i,Xz: $i] : 0.38/0.60 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) 0.38/0.60 = ( setadjoin @ Xz @ emptyset ) ) 0.38/0.60 => ( Xx = Xy ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setukpairinjR2_type,type, 0.38/0.60 setukpairinjR2: $o ). 0.38/0.60 0.38/0.60 thf(setukpairinjR2,definition, 0.38/0.60 ( setukpairinjR2 0.38/0.60 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] : 0.38/0.60 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) 0.38/0.60 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) 0.38/0.60 => ( Xy = Xu ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setukpairinjR_type,type, 0.38/0.60 setukpairinjR: $o ). 0.38/0.60 0.38/0.60 thf(setukpairinjR,definition, 0.38/0.60 ( setukpairinjR 0.38/0.60 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] : 0.38/0.60 ( ( ( kpair @ Xx @ Xy ) 0.38/0.60 = ( kpair @ Xz @ Xu ) ) 0.38/0.60 => ( Xy = Xu ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ksndsingleton_type,type, 0.38/0.60 ksndsingleton: $o ). 0.38/0.60 0.38/0.60 thf(ksndsingleton,definition, 0.38/0.60 ( ksndsingleton 0.38/0.60 = ( ! [Xu: $i] : 0.38/0.60 ( ( iskpair @ Xu ) 0.38/0.60 => ( singleton 0.38/0.60 @ ( dsetconstr @ ( setunion @ Xu ) 0.38/0.60 @ ^ [Xx: $i] : 0.38/0.60 ( Xu 0.38/0.60 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ksnd_type,type, 0.38/0.60 ksnd: $i > $i ). 0.38/0.60 0.38/0.60 thf(ksndpairEq_type,type, 0.38/0.60 ksndpairEq: $o ). 0.38/0.60 0.38/0.60 thf(ksndpairEq,definition, 0.38/0.60 ( ksndpairEq 0.38/0.60 = ( ! [Xx: $i,Xy: $i] : 0.38/0.60 ( ( ksnd @ ( kpair @ Xx @ Xy ) ) 0.38/0.60 = Xy ) ) ) ). 0.38/0.60 0.38/0.60 thf(kpairsurjEq_type,type, 0.38/0.60 kpairsurjEq: $o ). 0.38/0.60 0.38/0.60 thf(kpairsurjEq,definition, 0.38/0.60 ( kpairsurjEq 0.38/0.60 = ( ! [Xu: $i] : 0.38/0.60 ( ( iskpair @ Xu ) 0.38/0.60 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) ) 0.38/0.60 = Xu ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(cartprodsndin_type,type, 0.38/0.60 cartprodsndin: $o ). 0.38/0.60 0.38/0.60 thf(cartprodsndin,definition, 0.38/0.60 ( cartprodsndin 0.38/0.60 = ( ! [A: $i,B: $i,Xu: $i] : 0.38/0.60 ( ( in @ Xu @ ( cartprod @ A @ B ) ) 0.38/0.60 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(cartprodpairmemEL_type,type, 0.38/0.60 cartprodpairmemEL: $o ). 0.38/0.60 0.38/0.60 thf(cartprodpairmemEL,definition, 0.38/0.60 ( cartprodpairmemEL 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] : 0.38/0.60 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) 0.38/0.60 => ( in @ Xx @ A ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(cartprodpairmemER_type,type, 0.38/0.60 cartprodpairmemER: $o ). 0.38/0.60 0.38/0.60 thf(cartprodpairmemER,definition, 0.38/0.60 ( cartprodpairmemER 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] : 0.38/0.60 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) 0.38/0.60 => ( in @ Xy @ B ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(cartprodmempaircEq_type,type, 0.38/0.60 cartprodmempaircEq: $o ). 0.38/0.60 0.38/0.60 thf(cartprodmempaircEq,definition, 0.38/0.60 ( cartprodmempaircEq 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( ( kpair @ Xx @ Xy ) 0.38/0.60 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(cartprodfstpairEq_type,type, 0.38/0.60 cartprodfstpairEq: $o ). 0.38/0.60 0.38/0.60 thf(cartprodfstpairEq,definition, 0.38/0.60 ( cartprodfstpairEq 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( ( kfst @ ( kpair @ Xx @ Xy ) ) 0.38/0.60 = Xx ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(cartprodsndpairEq_type,type, 0.38/0.60 cartprodsndpairEq: $o ). 0.38/0.60 0.38/0.60 thf(cartprodsndpairEq,definition, 0.38/0.60 ( cartprodsndpairEq 0.38/0.60 = ( ! [A: $i,B: $i,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( ( ksnd @ ( kpair @ Xx @ Xy ) ) 0.38/0.60 = Xy ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(cartprodpairsurjEq_type,type, 0.38/0.60 cartprodpairsurjEq: $o ). 0.38/0.60 0.38/0.60 thf(cartprodpairsurjEq,definition, 0.38/0.60 ( cartprodpairsurjEq 0.38/0.60 = ( ! [A: $i,B: $i,Xu: $i] : 0.38/0.60 ( ( in @ Xu @ ( cartprod @ A @ B ) ) 0.38/0.60 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) ) 0.38/0.60 = Xu ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(breln_type,type, 0.38/0.60 breln: $i > $i > $i > $o ). 0.38/0.60 0.38/0.60 thf(breln,definition, 0.38/0.60 ( breln 0.38/0.60 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(dpsetconstr_type,type, 0.38/0.60 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ). 0.38/0.60 0.38/0.60 thf(dpsetconstrI_type,type, 0.38/0.60 dpsetconstrI: $o ). 0.38/0.60 0.38/0.60 thf(dpsetconstrI,definition, 0.38/0.60 ( dpsetconstrI 0.38/0.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( ( Xphi @ Xx @ Xy ) 0.38/0.60 => ( in @ ( kpair @ Xx @ Xy ) 0.38/0.60 @ ( dpsetconstr @ A @ B 0.38/0.60 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(dpsetconstrSub_type,type, 0.38/0.60 dpsetconstrSub: $o ). 0.38/0.60 0.38/0.60 thf(dpsetconstrSub,definition, 0.38/0.60 ( dpsetconstrSub 0.38/0.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] : 0.38/0.60 ( subset 0.38/0.60 @ ( dpsetconstr @ A @ B 0.38/0.60 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) 0.38/0.60 @ ( cartprod @ A @ B ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(setOfPairsIsBReln_type,type, 0.38/0.60 setOfPairsIsBReln: $o ). 0.38/0.60 0.38/0.60 thf(setOfPairsIsBReln,definition, 0.38/0.60 ( setOfPairsIsBReln 0.38/0.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] : 0.38/0.60 ( breln @ A @ B 0.38/0.60 @ ( dpsetconstr @ A @ B 0.38/0.60 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(dpsetconstrERa_type,type, 0.38/0.60 dpsetconstrERa: $o ). 0.38/0.60 0.38/0.60 thf(dpsetconstrERa,definition, 0.38/0.60 ( dpsetconstrERa 0.38/0.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( ( in @ ( kpair @ Xx @ Xy ) 0.38/0.60 @ ( dpsetconstr @ A @ B 0.38/0.60 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) 0.38/0.60 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(dpsetconstrEL1_type,type, 0.38/0.60 dpsetconstrEL1: $o ). 0.38/0.60 0.38/0.60 thf(dpsetconstrEL1,definition, 0.38/0.60 ( dpsetconstrEL1 0.38/0.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] : 0.38/0.60 ( ( in @ ( kpair @ Xx @ Xy ) 0.38/0.60 @ ( dpsetconstr @ A @ B 0.38/0.60 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) 0.38/0.60 => ( in @ Xx @ A ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(dpsetconstrEL2_type,type, 0.38/0.60 dpsetconstrEL2: $o ). 0.38/0.60 0.38/0.60 thf(dpsetconstrEL2,definition, 0.38/0.60 ( dpsetconstrEL2 0.38/0.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] : 0.38/0.60 ( ( in @ ( kpair @ Xx @ Xy ) 0.38/0.60 @ ( dpsetconstr @ A @ B 0.38/0.60 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) 0.38/0.60 => ( in @ Xy @ B ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(dpsetconstrER_type,type, 0.38/0.60 dpsetconstrER: $o ). 0.38/0.60 0.38/0.60 thf(dpsetconstrER,definition, 0.38/0.60 ( dpsetconstrER 0.38/0.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] : 0.38/0.60 ( ( in @ ( kpair @ Xx @ Xy ) 0.38/0.60 @ ( dpsetconstr @ A @ B 0.38/0.60 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) 0.38/0.60 => ( Xphi @ Xx @ Xy ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(func_type,type, 0.38/0.60 func: $i > $i > $i > $o ). 0.38/0.60 0.38/0.60 thf(funcSet_type,type, 0.38/0.60 funcSet: $i > $i > $i ). 0.38/0.60 0.38/0.60 thf(funcImageSingleton_type,type, 0.38/0.60 funcImageSingleton: $o ). 0.38/0.60 0.38/0.60 thf(funcImageSingleton,definition, 0.38/0.60 ( funcImageSingleton 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( func @ A @ B @ Xf ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( singleton 0.38/0.60 @ ( dsetconstr @ B 0.38/0.60 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(apProp_type,type, 0.38/0.60 apProp: $o ). 0.38/0.60 0.38/0.60 thf(apProp,definition, 0.38/0.60 ( apProp 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( func @ A @ B @ Xf ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( in 0.38/0.60 @ ( setunion 0.38/0.60 @ ( dsetconstr @ B 0.38/0.60 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) 0.38/0.60 @ B ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ap_type,type, 0.38/0.60 ap: $i > $i > $i > $i > $i ). 0.38/0.60 0.38/0.60 thf(app_type,type, 0.38/0.60 app: $o ). 0.38/0.60 0.38/0.60 thf(app,definition, 0.38/0.60 ( app 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( func @ A @ B @ Xf ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(infuncsetfunc_type,type, 0.38/0.60 infuncsetfunc: $o ). 0.38/0.60 0.38/0.60 thf(infuncsetfunc,definition, 0.38/0.60 ( infuncsetfunc 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( in @ Xf @ ( funcSet @ A @ B ) ) 0.38/0.60 => ( func @ A @ B @ Xf ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ap2p_type,type, 0.38/0.60 ap2p: $o ). 0.38/0.60 0.38/0.60 thf(ap2p,definition, 0.38/0.60 ( ap2p 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( in @ Xf @ ( funcSet @ A @ B ) ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(funcinfuncset_type,type, 0.38/0.60 funcinfuncset: $o ). 0.38/0.60 0.38/0.60 thf(funcinfuncset,definition, 0.38/0.60 ( funcinfuncset 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( func @ A @ B @ Xf ) 0.38/0.60 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(lamProp_type,type, 0.38/0.60 lamProp: $o ). 0.38/0.60 0.38/0.60 thf(lamProp,definition, 0.38/0.60 ( lamProp 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i > $i] : 0.38/0.60 ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( in @ ( Xf @ Xx ) @ B ) ) 0.38/0.60 => ( func @ A @ B 0.38/0.60 @ ( dpsetconstr @ A @ B 0.38/0.60 @ ^ [Xx: $i,Xy: $i] : 0.38/0.60 ( ( Xf @ Xx ) 0.38/0.60 = Xy ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(lam_type,type, 0.38/0.60 lam: $i > $i > ( $i > $i ) > $i ). 0.38/0.60 0.38/0.60 thf(lamp_type,type, 0.38/0.60 lamp: $o ). 0.38/0.60 0.38/0.60 thf(lamp,definition, 0.38/0.60 ( lamp 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i > $i] : 0.38/0.60 ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( in @ ( Xf @ Xx ) @ B ) ) 0.38/0.60 => ( func @ A @ B 0.38/0.60 @ ( lam @ A @ B 0.38/0.60 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(lam2p_type,type, 0.38/0.60 lam2p: $o ). 0.38/0.60 0.38/0.60 thf(lam2p,definition, 0.38/0.60 ( lam2p 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i > $i] : 0.38/0.60 ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( in @ ( Xf @ Xx ) @ B ) ) 0.38/0.60 => ( in 0.38/0.60 @ ( lam @ A @ B 0.38/0.60 @ ^ [Xx: $i] : ( Xf @ Xx ) ) 0.38/0.60 @ ( funcSet @ A @ B ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(brelnall1_type,type, 0.38/0.60 brelnall1: $o ). 0.38/0.60 0.38/0.60 thf(brelnall1,definition, 0.38/0.60 ( brelnall1 0.38/0.60 = ( ! [A: $i,B: $i,R: $i] : 0.38/0.60 ( ( breln @ A @ B @ R ) 0.38/0.60 => ! [Xphi: $i > $o] : 0.38/0.60 ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R ) 0.38/0.60 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ R ) 0.38/0.60 => ( Xphi @ Xx ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(brelnall2_type,type, 0.38/0.60 brelnall2: $o ). 0.38/0.60 0.38/0.60 thf(brelnall2,definition, 0.38/0.60 ( brelnall2 0.38/0.60 = ( ! [A: $i,B: $i,R: $i] : 0.38/0.60 ( ( breln @ A @ B @ R ) 0.38/0.60 => ! [Xphi: $i > $o] : 0.38/0.60 ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R ) 0.38/0.60 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ R ) 0.38/0.60 => ( Xphi @ Xx ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ex1E2_type,type, 0.38/0.60 ex1E2: $o ). 0.38/0.60 0.38/0.60 thf(ex1E2,definition, 0.38/0.60 ( ex1E2 0.38/0.60 = ( ! [A: $i,Xphi: $i > $o] : 0.38/0.60 ( ( ex1 @ A 0.38/0.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ A ) 0.38/0.60 => ( ( Xphi @ Xx ) 0.38/0.60 => ( ( Xphi @ Xy ) 0.38/0.60 => ( Xx = Xy ) ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(funcGraphProp1_type,type, 0.38/0.60 funcGraphProp1: $o ). 0.38/0.60 0.38/0.60 thf(funcGraphProp1,definition, 0.38/0.60 ( funcGraphProp1 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( func @ A @ B @ Xf ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(funcGraphProp3_type,type, 0.38/0.60 funcGraphProp3: $o ). 0.38/0.60 0.38/0.60 thf(funcGraphProp3,definition, 0.38/0.60 ( funcGraphProp3 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( in @ Xf @ ( funcSet @ A @ B ) ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(funcGraphProp2_type,type, 0.38/0.60 funcGraphProp2: $o ). 0.38/0.60 0.38/0.60 thf(funcGraphProp2,definition, 0.38/0.60 ( funcGraphProp2 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( func @ A @ B @ Xf ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf ) 0.38/0.60 => ( ( ap @ A @ B @ Xf @ Xx ) 0.38/0.60 = Xy ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(funcextLem_type,type, 0.38/0.60 funcextLem: $o ). 0.38/0.60 0.38/0.60 thf(funcextLem,definition, 0.38/0.60 ( funcextLem 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( func @ A @ B @ Xf ) 0.38/0.60 => ! [Xg: $i] : 0.38/0.60 ( ( func @ A @ B @ Xg ) 0.38/0.60 => ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( ( ap @ A @ B @ Xf @ Xx ) 0.38/0.60 = ( ap @ A @ B @ Xg @ Xx ) ) ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg ) 0.38/0.60 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(funcGraphProp4_type,type, 0.38/0.60 funcGraphProp4: $o ). 0.38/0.60 0.38/0.60 thf(funcGraphProp4,definition, 0.38/0.60 ( funcGraphProp4 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( in @ Xf @ ( funcSet @ A @ B ) ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf ) 0.38/0.60 => ( ( ap @ A @ B @ Xf @ Xx ) 0.38/0.60 = Xy ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(subbreln_type,type, 0.38/0.60 subbreln: $o ). 0.38/0.60 0.38/0.60 thf(subbreln,definition, 0.38/0.60 ( subbreln 0.38/0.60 = ( ! [A: $i,B: $i,R: $i] : 0.38/0.60 ( ( breln @ A @ B @ R ) 0.38/0.60 => ! [S: $i] : 0.38/0.60 ( ( breln @ A @ B @ S ) 0.38/0.60 => ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R ) 0.38/0.60 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) 0.38/0.60 => ( subset @ R @ S ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(eqbreln_type,type, 0.38/0.60 eqbreln: $o ). 0.38/0.60 0.38/0.60 thf(eqbreln,definition, 0.38/0.60 ( eqbreln 0.38/0.60 = ( ! [A: $i,B: $i,R: $i] : 0.38/0.60 ( ( breln @ A @ B @ R ) 0.38/0.60 => ! [S: $i] : 0.38/0.60 ( ( breln @ A @ B @ S ) 0.38/0.60 => ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R ) 0.38/0.60 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) 0.38/0.60 => ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ B ) 0.38/0.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ S ) 0.38/0.60 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) 0.38/0.60 => ( R = S ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(funcext_type,type, 0.38/0.60 funcext: $o ). 0.38/0.60 0.38/0.60 thf(funcext,definition, 0.38/0.60 ( funcext 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( func @ A @ B @ Xf ) 0.38/0.60 => ! [Xg: $i] : 0.38/0.60 ( ( func @ A @ B @ Xg ) 0.38/0.60 => ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( ( ap @ A @ B @ Xf @ Xx ) 0.38/0.60 = ( ap @ A @ B @ Xg @ Xx ) ) ) 0.38/0.60 => ( Xf = Xg ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(funcext2_type,type, 0.38/0.60 funcext2: $o ). 0.38/0.60 0.38/0.60 thf(funcext2,definition, 0.38/0.60 ( funcext2 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( in @ Xf @ ( funcSet @ A @ B ) ) 0.38/0.60 => ! [Xg: $i] : 0.38/0.60 ( ( in @ Xg @ ( funcSet @ A @ B ) ) 0.38/0.60 => ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( ( ap @ A @ B @ Xf @ Xx ) 0.38/0.60 = ( ap @ A @ B @ Xg @ Xx ) ) ) 0.38/0.60 => ( Xf = Xg ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ap2apEq1_type,type, 0.38/0.60 ap2apEq1: $o ). 0.38/0.60 0.38/0.60 thf(ap2apEq1,definition, 0.38/0.60 ( ap2apEq1 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( in @ Xf @ ( funcSet @ A @ B ) ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( ( ap @ A @ B @ Xf @ Xx ) 0.38/0.60 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ap2apEq2_type,type, 0.38/0.60 ap2apEq2: $o ). 0.38/0.60 0.38/0.60 thf(ap2apEq2,definition, 0.38/0.60 ( ap2apEq2 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( func @ A @ B @ Xf ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( ( ap @ A @ B @ Xf @ Xx ) 0.38/0.60 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(beta1_type,type, 0.38/0.60 beta1: $o ). 0.38/0.60 0.38/0.60 thf(beta1,definition, 0.38/0.60 ( beta1 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i > $i] : 0.38/0.60 ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( in @ ( Xf @ Xx ) @ B ) ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( ( ap @ A @ B 0.38/0.60 @ ( lam @ A @ B 0.38/0.60 @ ^ [Xy: $i] : ( Xf @ Xy ) ) 0.38/0.60 @ Xx ) 0.38/0.60 = ( Xf @ Xx ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(eta1_type,type, 0.38/0.60 eta1: $o ). 0.38/0.60 0.38/0.60 thf(eta1,definition, 0.38/0.60 ( eta1 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( func @ A @ B @ Xf ) 0.38/0.60 => ( ( lam @ A @ B 0.38/0.60 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) ) 0.38/0.60 = Xf ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(lam2lamEq_type,type, 0.38/0.60 lam2lamEq: $o ). 0.38/0.60 0.38/0.60 thf(lam2lamEq,definition, 0.38/0.60 ( lam2lamEq 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i > $i] : 0.38/0.60 ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( in @ ( Xf @ Xx ) @ B ) ) 0.38/0.60 => ( ( lam @ A @ B 0.38/0.60 @ ^ [Xx: $i] : ( Xf @ Xx ) ) 0.38/0.60 = ( lam @ A @ B 0.38/0.60 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(beta2_type,type, 0.38/0.60 beta2: $o ). 0.38/0.60 0.38/0.60 thf(beta2,definition, 0.38/0.60 ( beta2 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i > $i] : 0.38/0.60 ( ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( in @ ( Xf @ Xx ) @ B ) ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ( ( ap @ A @ B 0.38/0.60 @ ( lam @ A @ B 0.38/0.60 @ ^ [Xy: $i] : ( Xf @ Xy ) ) 0.38/0.60 @ Xx ) 0.38/0.60 = ( Xf @ Xx ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(eta2_type,type, 0.38/0.60 eta2: $o ). 0.38/0.60 0.38/0.60 thf(eta2,definition, 0.38/0.60 ( eta2 0.38/0.60 = ( ! [A: $i,B: $i,Xf: $i] : 0.38/0.60 ( ( in @ Xf @ ( funcSet @ A @ B ) ) 0.38/0.60 => ( ( lam @ A @ B 0.38/0.60 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) ) 0.38/0.60 = Xf ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(iffalseProp1_type,type, 0.38/0.60 iffalseProp1: $o ). 0.38/0.60 0.38/0.60 thf(iffalseProp1,definition, 0.38/0.60 ( iffalseProp1 0.38/0.60 = ( ! [A: $i,Xphi: $o,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ A ) 0.38/0.60 => ( ~ Xphi 0.38/0.60 => ( in @ Xy 0.38/0.60 @ ( dsetconstr @ A 0.38/0.60 @ ^ [Xz: $i] : 0.38/0.60 ( ( Xphi 0.38/0.60 & ( Xz = Xx ) ) 0.38/0.60 | ( ~ Xphi 0.38/0.60 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(iffalseProp2_type,type, 0.38/0.60 iffalseProp2: $o ). 0.38/0.60 0.38/0.60 thf(iffalseProp2,definition, 0.38/0.60 ( iffalseProp2 0.38/0.60 = ( ! [A: $i,Xphi: $o,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ A ) 0.38/0.60 => ( ~ Xphi 0.38/0.60 => ( ( dsetconstr @ A 0.38/0.60 @ ^ [Xz: $i] : 0.38/0.60 ( ( Xphi 0.38/0.60 & ( Xz = Xx ) ) 0.38/0.60 | ( ~ Xphi 0.38/0.60 & ( Xz = Xy ) ) ) ) 0.38/0.60 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(iftrueProp1_type,type, 0.38/0.60 iftrueProp1: $o ). 0.38/0.60 0.38/0.60 thf(iftrueProp1,definition, 0.38/0.60 ( iftrueProp1 0.38/0.60 = ( ! [A: $i,Xphi: $o,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ A ) 0.38/0.60 => ( Xphi 0.38/0.60 => ( in @ Xx 0.38/0.60 @ ( dsetconstr @ A 0.38/0.60 @ ^ [Xz: $i] : 0.38/0.60 ( ( Xphi 0.38/0.60 & ( Xz = Xx ) ) 0.38/0.60 | ( ~ Xphi 0.38/0.60 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(iftrueProp2_type,type, 0.38/0.60 iftrueProp2: $o ). 0.38/0.60 0.38/0.60 thf(iftrueProp2,definition, 0.38/0.60 ( iftrueProp2 0.38/0.60 = ( ! [A: $i,Xphi: $o,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ A ) 0.38/0.60 => ( Xphi 0.38/0.60 => ( ( dsetconstr @ A 0.38/0.60 @ ^ [Xz: $i] : 0.38/0.60 ( ( Xphi 0.38/0.60 & ( Xz = Xx ) ) 0.38/0.60 | ( ~ Xphi 0.38/0.60 & ( Xz = Xy ) ) ) ) 0.38/0.60 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ifSingleton_type,type, 0.38/0.60 ifSingleton: $o ). 0.38/0.60 0.38/0.60 thf(ifSingleton,definition, 0.38/0.60 ( ifSingleton 0.38/0.60 = ( ! [A: $i,Xphi: $o,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ A ) 0.38/0.60 => ( singleton 0.38/0.60 @ ( dsetconstr @ A 0.38/0.60 @ ^ [Xz: $i] : 0.38/0.60 ( ( Xphi 0.38/0.60 & ( Xz = Xx ) ) 0.38/0.60 | ( ~ Xphi 0.38/0.60 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(if_type,type, 0.38/0.60 if: $i > $o > $i > $i > $i ). 0.38/0.60 0.38/0.60 thf(if,definition, 0.38/0.60 ( if 0.38/0.60 = ( ^ [A: $i,Xphi: $o,Xx: $i,Xy: $i] : 0.38/0.60 ( setunion 0.38/0.60 @ ( dsetconstr @ A 0.38/0.60 @ ^ [Xz: $i] : 0.38/0.60 ( ( Xphi 0.38/0.60 & ( Xz = Xx ) ) 0.38/0.60 | ( ~ Xphi 0.38/0.60 & ( Xz = Xy ) ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(ifp_type,type, 0.38/0.60 ifp: $o ). 0.38/0.60 0.38/0.60 thf(ifp,definition, 0.38/0.60 ( ifp 0.38/0.60 = ( ! [A: $i,Xphi: $o,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ A ) 0.38/0.60 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(theeq_type,type, 0.38/0.60 theeq: $o ). 0.38/0.60 0.38/0.60 thf(theeq,definition, 0.38/0.60 ( theeq 0.38/0.60 = ( ! [X: $i] : 0.38/0.60 ( ( singleton @ X ) 0.38/0.60 => ! [Xx: $i] : 0.38/0.60 ( ( in @ Xx @ X ) 0.38/0.60 => ( ( setunion @ X ) 0.38/0.60 = Xx ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(iftrue_type,type, 0.38/0.60 iftrue: $o ). 0.38/0.60 0.38/0.60 thf(iftrue,definition, 0.38/0.60 ( iftrue 0.38/0.60 = ( ! [A: $i,Xphi: $o,Xx: $i] : 0.38/0.60 ( ( in @ Xx @ A ) 0.38/0.60 => ! [Xy: $i] : 0.38/0.60 ( ( in @ Xy @ A ) 0.38/0.60 => ( Xphi 0.38/0.60 => ( ( if @ A @ Xphi @ Xx @ Xy ) 0.38/0.60 = Xx ) ) ) ) ) ) ). 0.38/0.60 0.38/0.60 thf(iffalse,conjecture, 0.38/0.60 ( ( ( ( powersetAx 0.38/0.60 => ( setunionAx 0.38/0.60 => ( ( ( ( replAx 0.38/0.60 => ( foundationAx 0.38/0.60 => ( ( ( dsetconstrI 0.38/0.60 => ( ( ( ( prop2setE 0.38/0.60 => ( ( emptysetimpfalse 0.38/0.60 => ( notinemptyset 0.38/0.60 => ( ( ( emptyI 0.38/0.60 => ( ( setbeta 0.38/0.60 => ( nonemptyE1 0.38/0.60 => ( nonemptyI 0.38/0.60 => ( nonemptyI1 0.38/0.60 => ( setadjoinIL 0.38/0.60 => ( ( ( setadjoinE 0.38/0.60 => ( ( ( ( ( ( ( setunionI 0.38/0.60 => ( ( subPowSU 0.38/0.60 => ( ( nonemptyImpWitness 0.38/0.60 => ( uniqinunit 0.38/0.60 => ( ( ( ( upairsetE 0.38/0.60 => ( upairsetIL 0.38/0.60 => ( ( emptyE1 0.38/0.60 => ( vacuousDall 0.38/0.60 => ( ( quantDeMorgan2 0.38/0.60 => ( ( quantDeMorgan4 0.38/0.60 => ( prop2setI 0.38/0.60 => ( ( ( ( exuI1 0.38/0.60 => ( ( ( inCongP 0.38/0.60 => ( in__Cong 0.38/0.60 => ( exuE3u 0.38/0.60 => ( exu__Cong 0.38/0.60 => ( ( ( ( ( ( exuEu 0.38/0.60 => ( descr__Cong 0.38/0.60 => ( ( ( ( eqimpsubset1 0.38/0.60 => ( subsetI2 0.38/0.60 => ( emptysetsubset 0.38/0.60 => ( subsetE 0.38/0.60 => ( ( ( ( notequalI2 0.38/0.60 => ( subsetRefl 0.38/0.60 => ( ( setadjoinSub 0.38/0.60 => ( setadjoinSub2 0.38/0.60 => ( ( setextsub 0.38/0.60 => ( subsetemptysetimpeq 0.38/0.60 => ( ( powersetE1 0.38/0.60 => ( ( ( ( ( binunionIL 0.38/0.60 => ( ( binunionIR 0.38/0.60 => ( ( binunionE 0.38/0.60 => ( ( ( binintersectI 0.38/0.60 => ( ( ( binintersectLsub 0.38/0.60 => ( binintersectSubset2 0.38/0.60 => ( ( ( ( ( binintersectSubset4 0.38/0.60 => ( binintersectSubset1 0.38/0.60 => ( ( ( setminusEL 0.38/0.60 => ( setminusER 0.38/0.60 => ( setminusSubset2 0.38/0.60 => ( setminusERneg 0.38/0.60 => ( ( setminusILneg 0.38/0.60 => ( ( setminusLsub 0.38/0.60 => ( ( symdiffE 0.38/0.60 => ( ( ( ( ( secondinupair 0.38/0.60 => ( setukpairIL 0.38/0.60 => ( setukpairIR 0.38/0.60 => ( ( kpairp 0.38/0.60 => ( singletonsubset 0.38/0.60 => ( singletoninpowerset 0.38/0.60 => ( ( ( upairsubunion 0.38/0.60 => ( ( ( ( ubforcartprodlem3 0.38/0.60 => ( cartprodpairin 0.38/0.60 => ( ( ( setunionE2 0.38/0.60 => ( ( setunionsingleton2 0.38/0.60 => ( ( ( ( ( ( singletonsuniq 0.38/0.60 => ( ( kfstsingleton 0.38/0.60 => ( ( ( cartprodfstin 0.38/0.60 => ( setukpairinjL2 0.38/0.60 => ( setukpairinjL 0.38/0.60 => ( setukpairinjR11 0.38/0.60 => ( ( setukpairinjR1 0.38/0.60 => ( ( setukpairinjR2 0.38/0.60 => ( setukpairinjR 0.38/0.60 => ( ksndsingleton 0.38/0.60 => ( ksndpairEq 0.38/0.60 => ( kpairsurjEq 0.38/0.60 => ( ( cartprodpairmemEL 0.38/0.60 => ( ( cartprodmempaircEq 0.38/0.60 => ( cartprodfstpairEq 0.38/0.60 => ( cartprodsndpairEq 0.38/0.60 => ( ( dpsetconstrI 0.38/0.60 => ( ( setOfPairsIsBReln 0.38/0.60 => ( dpsetconstrERa 0.38/0.60 => ( ( dpsetconstrEL2 0.38/0.60 => ( ( ( apProp 0.38/0.60 => ( ( infuncsetfunc 0.38/0.60 => ( ( funcinfuncset 0.38/0.60 => ( ( ( ( brelnall1 0.38/0.60 => ( brelnall2 0.38/0.60 => ( ex1E2 0.38/0.60 => ( funcGraphProp1 0.38/0.60 => ( funcGraphProp3 0.38/0.60 => ( ( funcextLem 0.38/0.60 => ( ( ( ( ( ( ap2apEq1 0.38/0.60 => ( ( ( eta1 0.38/0.60 => ( lam2lamEq 0.38/0.60 => ( beta2 0.38/0.60 => ( ( iffalseProp1 0.38/0.60 => ( iffalseProp2 0.38/0.60 => ( ( iftrueProp2 0.38/0.60 => ( ( ( ( ! [A: $i,Xphi: $o,Xx: $i] : 0.38/0.60 ( ! [Xy: $i] : 0.38/0.60 ( ( ( ( if @ A @ Xphi @ Xx @ Xy ) 0.38/0.60 = Xy ) 0.38/0.60 <= ~ Xphi ) 0.38/0.60 <= ( in @ Xy @ A ) ) 0.38/0.60 <= ( in @ Xx @ A ) ) 0.38/0.60 <= iftrue ) 0.38/0.60 <= theeq ) 0.38/0.60 <= ifp ) 0.38/0.60 <= ifSingleton ) ) 0.38/0.60 <= iftrueProp1 ) ) ) 0.38/0.60 <= eta2 ) ) ) ) 0.38/0.60 <= beta1 ) 0.38/0.60 <= ap2apEq2 ) ) 0.38/0.60 <= funcext2 ) 0.38/0.60 <= funcext ) 0.38/0.60 <= eqbreln ) 0.38/0.60 <= subbreln ) 0.38/0.60 <= funcGraphProp4 ) ) 0.38/0.60 <= funcGraphProp2 ) ) ) ) ) ) 0.38/0.60 <= lam2p ) 0.38/0.60 <= lamp ) 0.38/0.60 <= lamProp ) ) 0.38/0.60 <= ap2p ) ) 0.38/0.60 <= app ) ) 0.38/0.60 <= funcImageSingleton ) 0.38/0.60 <= dpsetconstrER ) ) 0.38/0.60 <= dpsetconstrEL1 ) ) ) 0.38/0.60 <= dpsetconstrSub ) ) 0.38/0.60 <= cartprodpairsurjEq ) ) ) ) 0.38/0.60 <= cartprodpairmemER ) ) 0.38/0.60 <= cartprodsndin ) ) ) ) ) ) 0.38/0.60 <= upairequniteq ) ) 0.38/0.60 <= setukpairinjR12 ) ) ) ) ) 0.38/0.60 <= kfstpairEq ) 0.38/0.60 <= theprop ) ) 0.38/0.60 <= setukpairinjL1 ) ) 0.38/0.60 <= ex1I2 ) 0.38/0.60 <= ex1I ) 0.38/0.60 <= ex1E1 ) 0.38/0.60 <= singletonprop ) 0.38/0.60 <= setunionsingleton ) ) 0.38/0.60 <= setunionsingleton1 ) ) 0.38/0.60 <= cartprodmempair ) 0.38/0.60 <= cartprodmempair1 ) ) ) 0.38/0.60 <= ubforcartprodlem2 ) 0.38/0.60 <= ubforcartprodlem1 ) 0.38/0.60 <= upairinpowunion ) ) 0.38/0.60 <= upairset2E ) 0.38/0.60 <= singletoninpowunion ) ) ) ) 0.38/0.60 <= kpairiskpair ) ) ) ) 0.38/0.60 <= symdiffIneg2 ) 0.38/0.60 <= symdiffIneg1 ) 0.38/0.60 <= symdiffI2 ) 0.38/0.60 <= symdiffI1 ) ) 0.38/0.60 <= setminusSubset1 ) ) 0.38/0.60 <= setminusIRneg ) ) 0.38/0.60 <= setminusELneg ) ) ) ) ) 0.38/0.60 <= setminusI ) 0.38/0.60 <= bs114d ) ) ) 0.38/0.60 <= binintersectRsub ) 0.38/0.60 <= disjointsetsI1 ) 0.38/0.60 <= binintersectER ) 0.38/0.60 <= binintersectSubset3 ) ) ) 0.38/0.60 <= binintersectEL ) 0.38/0.60 <= binintersectSubset5 ) ) 0.38/0.60 <= binunionRsub ) 0.38/0.60 <= binunionLsub ) ) 0.38/0.60 <= binunionEcases ) ) 0.38/0.60 <= upairset2IR ) ) 0.38/0.60 <= sepSubset ) 0.38/0.60 <= sepInPowerset ) 0.38/0.60 <= powersetsubset ) 0.38/0.60 <= inPowerset ) ) 0.38/0.60 <= powersetI1 ) ) ) 0.38/0.60 <= subset2powerset ) ) ) 0.38/0.60 <= subsetTrans ) ) ) 0.38/0.60 <= notequalI1 ) 0.38/0.60 <= notsubsetI ) 0.38/0.60 <= subsetE2 ) ) ) ) ) 0.38/0.60 <= eqimpsubset2 ) 0.38/0.60 <= subsetI1 ) 0.38/0.60 <= dsetconstr__Cong ) ) ) 0.38/0.60 <= omega__Cong ) 0.38/0.60 <= setunion__Cong ) 0.38/0.60 <= powerset__Cong ) 0.38/0.60 <= setadjoin__Cong ) 0.38/0.60 <= emptyset__Cong ) ) ) ) ) 0.38/0.60 <= exuI2 ) 0.38/0.60 <= exuI3 ) ) 0.38/0.60 <= notdallE ) 0.38/0.60 <= notdexE ) 0.38/0.60 <= prop2set2propI ) ) ) 0.38/0.60 <= quantDeMorgan3 ) ) 0.38/0.60 <= quantDeMorgan1 ) ) ) 0.38/0.60 <= upairsetIR ) ) ) 0.38/0.60 <= singletonsswitch ) 0.38/0.60 <= eqinunit ) 0.38/0.60 <= notinsingleton ) ) ) 0.38/0.60 <= exuE2 ) ) 0.38/0.60 <= setunionE ) ) 0.38/0.60 <= powersetE ) 0.38/0.60 <= emptyInPowerset ) 0.38/0.60 <= emptyinPowerset ) 0.38/0.60 <= powersetI ) 0.38/0.60 <= setoftrueEq ) 0.38/0.60 <= setadjoinOr ) ) 0.38/0.60 <= setadjoinIR ) 0.38/0.60 <= emptyinunitempty ) ) ) ) ) ) 0.38/0.60 <= noeltsimpempty ) ) 0.38/0.60 <= setext ) 0.38/0.60 <= exuE3e ) ) ) 0.38/0.60 <= emptysetE ) ) 0.38/0.60 <= exuE1 ) 0.44/0.67 <= dsetconstrER ) 0.44/0.67 <= dsetconstrEL ) ) 0.44/0.67 <= descrp ) 0.44/0.67 <= wellorderingAx ) ) ) 0.44/0.67 <= omegaIndAx ) 0.44/0.67 <= omegaSAx ) 0.44/0.67 <= omega0Ax ) ) ) 0.44/0.67 <= setadjoinAx ) 0.44/0.67 <= emptysetAx ) 0.44/0.67 <= setextAx ) ). 0.44/0.67 0.44/0.67 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.PtkXE6CJSS/cvc5---1.0.5_30781.p... 0.44/0.67 (declare-sort $$unsorted 0) 0.44/0.67 (declare-fun tptp.in ($$unsorted $$unsorted) Bool) 0.44/0.67 (declare-fun tptp.exu ((-> $$unsorted Bool)) Bool) 0.44/0.67 (assert (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy)))))))) 0.44/0.67 (declare-fun tptp.setextAx () Bool) 0.44/0.67 (assert (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B))))) 0.44/0.67 (declare-fun tptp.emptyset () $$unsorted) 0.44/0.67 (declare-fun tptp.emptysetAx () Bool) 0.44/0.67 (assert (= tptp.emptysetAx (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.44/0.67 (declare-fun tptp.setadjoin ($$unsorted $$unsorted) $$unsorted) 0.44/0.67 (declare-fun tptp.setadjoinAx () Bool) 0.44/0.67 (assert (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.44/0.67 (declare-fun tptp.powerset ($$unsorted) $$unsorted) 0.44/0.67 (declare-fun tptp.powersetAx () Bool) 0.44/0.67 (assert (= tptp.powersetAx (forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))))))) 0.44/0.67 (declare-fun tptp.setunion ($$unsorted) $$unsorted) 0.44/0.67 (declare-fun tptp.setunionAx () Bool) 0.44/0.67 (assert (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A))))))) 0.44/0.67 (declare-fun tptp.omega () $$unsorted) 0.44/0.67 (declare-fun tptp.omega0Ax () Bool) 0.44/0.67 (assert (= tptp.omega0Ax (@ (@ tptp.in tptp.emptyset) tptp.omega))) 0.44/0.67 (declare-fun tptp.omegaSAx () Bool) 0.44/0.67 (assert (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega))))) 0.44/0.67 (declare-fun tptp.omegaIndAx () Bool) 0.44/0.67 (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 $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 tptp.omega) (@ _let_1 A)))))))) 0.44/0.67 (declare-fun tptp.replAx () Bool) 0.44/0.67 (assert (= tptp.replAx (forall ((Xphi (-> $$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 $$unsorted)) (and (@ (@ tptp.in Xy) A) (@ (@ Xphi Xy) Xx)))))))))) 0.44/0.67 (declare-fun tptp.foundationAx () Bool) 0.44/0.67 (assert (= tptp.foundationAx (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in B) A) (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 B) (@ _let_1 A))))))))))) 0.44/0.67 (declare-fun tptp.wellorderingAx () Bool) 0.44/0.67 (assert (= tptp.wellorderingAx (forall ((A $$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))))))))))))) 0.44/0.67 (declare-fun tptp.descr ((-> $$unsorted Bool)) $$unsorted) 0.44/0.67 (declare-fun tptp.descrp () Bool) 0.44/0.67 (assert (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) 0.44/0.67 (declare-fun tptp.dsetconstr ($$unsorted (-> $$unsorted Bool)) $$unsorted) 0.44/0.67 (declare-fun tptp.dsetconstrI () Bool) 0.44/0.67 (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)))))))))) 0.44/0.67 (declare-fun tptp.dsetconstrEL () Bool) 0.44/0.67 (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)))))) 0.44/0.67 (declare-fun tptp.dsetconstrER () Bool) 0.44/0.67 (assert (= tptp.dsetconstrER (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))) 0.44/0.67 (declare-fun tptp.exuE1 () Bool) 0.44/0.67 (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))))))))) 0.44/0.67 (declare-fun tptp.prop2set (Bool) $$unsorted) 0.44/0.67 (declare-fun tptp.prop2setE () Bool) 0.44/0.67 (assert (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi)))) 0.44/0.67 (declare-fun tptp.emptysetE () Bool) 0.44/0.67 (assert (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi))))) 0.44/0.67 (declare-fun tptp.emptysetimpfalse () Bool) 0.44/0.67 (assert (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false)))) 0.44/0.67 (declare-fun tptp.notinemptyset () Bool) 0.44/0.67 (assert (= tptp.notinemptyset (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) 0.44/0.67 (declare-fun tptp.exuE3e () Bool) 0.44/0.67 (assert (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx)))))) 0.44/0.67 (declare-fun tptp.setext () Bool) 0.44/0.67 (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)))))) 0.44/0.67 (declare-fun tptp.emptyI () Bool) 0.44/0.67 (assert (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.44/0.67 (declare-fun tptp.noeltsimpempty () Bool) 0.44/0.67 (assert (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset))))) 0.44/0.67 (declare-fun tptp.setbeta () Bool) 0.44/0.67 (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))))))) 0.44/0.67 (declare-fun tptp.nonempty ($$unsorted) Bool) 0.44/0.67 (assert (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset))))) 0.44/0.67 (declare-fun tptp.nonemptyE1 () Bool) 0.44/0.67 (assert (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)))))) 0.44/0.67 (declare-fun tptp.nonemptyI () Bool) 0.44/0.67 (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))))))))) 0.44/0.67 (declare-fun tptp.nonemptyI1 () Bool) 0.44/0.67 (assert (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A))))) 0.44/0.67 (declare-fun tptp.setadjoinIL () Bool) 0.44/0.67 (assert (= tptp.setadjoinIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) 0.44/0.67 (declare-fun tptp.emptyinunitempty () Bool) 0.44/0.67 (assert (= tptp.emptyinunitempty (@ (@ tptp.in tptp.emptyset) (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset)))) 0.44/0.67 (declare-fun tptp.setadjoinIR () Bool) 0.44/0.67 (assert (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A))))))) 0.44/0.67 (declare-fun tptp.setadjoinE () Bool) 0.44/0.67 (assert (= tptp.setadjoinE (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (forall ((Xphi Bool)) (=> (=> (= Xy Xx) Xphi) (=> (=> (@ (@ tptp.in Xy) A) Xphi) Xphi))))))) 0.44/0.67 (declare-fun tptp.setadjoinOr () Bool) 0.44/0.67 (assert (= tptp.setadjoinOr (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A))))))) 0.44/0.67 (declare-fun tptp.setoftrueEq () Bool) 0.44/0.67 (assert (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A)))) 0.44/0.67 (declare-fun tptp.powersetI () Bool) 0.44/0.67 (assert (= tptp.powersetI (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (@ (@ tptp.in B) (@ tptp.powerset A)))))) 0.44/0.67 (declare-fun tptp.emptyinPowerset () Bool) 0.44/0.67 (assert (= tptp.emptyinPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) 0.44/0.67 (declare-fun tptp.emptyInPowerset () Bool) 0.44/0.67 (assert (= tptp.emptyInPowerset (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) 0.44/0.67 (declare-fun tptp.powersetE () Bool) 0.44/0.67 (assert (= tptp.powersetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (=> (@ _let_1 B) (@ _let_1 A))))))) 0.44/0.67 (declare-fun tptp.setunionI () Bool) 0.44/0.67 (assert (= tptp.setunionI (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (=> (@ (@ tptp.in B) A) (@ _let_1 (@ tptp.setunion A)))))))) 0.44/0.67 (declare-fun tptp.setunionE () Bool) 0.44/0.67 (assert (= tptp.setunionE (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (forall ((Xphi Bool)) (=> (forall ((B $$unsorted)) (=> (@ (@ tptp.in Xx) B) (=> (@ (@ tptp.in B) A) Xphi))) Xphi)))))) 0.44/0.67 (declare-fun tptp.subPowSU () Bool) 0.44/0.67 (assert (= tptp.subPowSU (forall ((A $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.powerset (@ tptp.setunion A)))))))) 0.44/0.67 (declare-fun tptp.exuE2 () Bool) 0.44/0.67 (assert (= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))))))) 0.44/0.67 (declare-fun tptp.nonemptyImpWitness () Bool) 0.44/0.67 (assert (= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) true)))))) 0.44/0.67 (declare-fun tptp.uniqinunit () Bool) 0.44/0.67 (assert (= tptp.uniqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy))))) 0.44/0.67 (declare-fun tptp.notinsingleton () Bool) 0.44/0.67 (assert (= tptp.notinsingleton (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (not (= Xx Xy)) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) 0.44/0.67 (declare-fun tptp.eqinunit () Bool) 0.44/0.67 (assert (= tptp.eqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.44/0.67 (declare-fun tptp.singletonsswitch () Bool) 0.44/0.67 (assert (= tptp.singletonsswitch (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) 0.44/0.67 (declare-fun tptp.upairsetE () Bool) 0.44/0.67 (assert (= tptp.upairsetE (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy)))))) 0.44/0.67 (declare-fun tptp.upairsetIL () Bool) 0.44/0.67 (assert (= tptp.upairsetIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.44/0.67 (declare-fun tptp.upairsetIR () Bool) 0.44/0.67 (assert (= tptp.upairsetIR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.44/0.67 (declare-fun tptp.emptyE1 () Bool) 0.44/0.67 (assert (= tptp.emptyE1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (=> (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) tptp.emptyset) false))))) 0.44/0.67 (declare-fun tptp.vacuousDall () Bool) 0.44/0.67 (assert (= tptp.vacuousDall (forall ((Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (@ Xphi Xx))))) 0.44/0.67 (declare-fun tptp.quantDeMorgan1 () Bool) 0.44/0.67 (assert (= tptp.quantDeMorgan1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.44/0.67 (declare-fun tptp.quantDeMorgan2 () Bool) 0.44/0.67 (assert (= tptp.quantDeMorgan2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))) (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))))))) 0.44/0.67 (declare-fun tptp.quantDeMorgan3 () Bool) 0.44/0.67 (assert (= tptp.quantDeMorgan3 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.44/0.67 (declare-fun tptp.quantDeMorgan4 () Bool) 0.44/0.67 (assert (= tptp.quantDeMorgan4 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))))))) 0.44/0.67 (declare-fun tptp.prop2setI () Bool) 0.44/0.67 (assert (= tptp.prop2setI (forall ((Xphi Bool)) (=> Xphi (@ (@ tptp.in tptp.emptyset) (@ tptp.prop2set Xphi)))))) 0.44/0.67 (declare-fun tptp.set2prop ($$unsorted) Bool) 0.44/0.67 (declare-fun tptp.prop2set2propI () Bool) 0.44/0.67 (assert (= tptp.prop2set2propI (forall ((Xphi Bool)) (=> Xphi (@ tptp.set2prop (@ tptp.prop2set Xphi)))))) 0.44/0.67 (declare-fun tptp.notdexE () Bool) 0.44/0.67 (assert (= tptp.notdexE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.44/0.67 (declare-fun tptp.notdallE () Bool) 0.44/0.67 (assert (= tptp.notdallE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))))))) 0.44/0.67 (declare-fun tptp.exuI1 () Bool) 0.44/0.67 (assert (= tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) 0.44/0.67 (declare-fun tptp.exuI3 () Bool) 0.44/0.67 (assert (= tptp.exuI3 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (@ Xphi Xx)) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) 0.44/0.67 (declare-fun tptp.exuI2 () Bool) 0.44/0.67 (assert (= tptp.exuI2 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) 0.44/0.67 (declare-fun tptp.inCongP () Bool) 0.44/0.67 (assert (= tptp.inCongP (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) B)))))))) 0.44/0.67 (declare-fun tptp.in__Cong () Bool) 0.44/0.67 (assert (= tptp.in__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) B)))))))) 0.44/0.67 (declare-fun tptp.exuE3u () Bool) 0.44/0.67 (assert (= tptp.exuE3u (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy)))))))) 0.44/0.67 (declare-fun tptp.exu__Cong () Bool) 0.44/0.67 (assert (= tptp.exu__Cong (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ Xphi Xx) (@ Xpsi Xy)))) (= (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xpsi Xx)))))))) 0.44/0.67 (declare-fun tptp.emptyset__Cong () Bool) 0.44/0.67 (assert (= tptp.emptyset__Cong (= tptp.emptyset tptp.emptyset))) 0.44/0.67 (declare-fun tptp.setadjoin__Cong () Bool) 0.44/0.67 (assert (= tptp.setadjoin__Cong (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (forall ((Xz $$unsorted) (Xu $$unsorted)) (=> (= Xz Xu) (= (@ (@ tptp.setadjoin Xx) Xz) (@ (@ tptp.setadjoin Xy) Xu)))))))) 0.44/0.67 (declare-fun tptp.powerset__Cong () Bool) 0.44/0.67 (assert (= tptp.powerset__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.powerset A) (@ tptp.powerset B)))))) 0.44/0.67 (declare-fun tptp.setunion__Cong () Bool) 0.44/0.67 (assert (= tptp.setunion__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.setunion A) (@ tptp.setunion B)))))) 0.44/0.67 (declare-fun tptp.omega__Cong () Bool) 0.44/0.67 (assert (= tptp.omega__Cong (= tptp.omega tptp.omega))) 0.44/0.67 (declare-fun tptp.exuEu () Bool) 0.44/0.67 (assert (= tptp.exuEu (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy)))))))) 0.44/0.67 (declare-fun tptp.descr__Cong () Bool) 0.44/0.67 (assert (= tptp.descr__Cong (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ Xphi Xx) (@ Xpsi Xy)))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xpsi Xx))) (= (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xpsi Xx)))))))))) 0.44/0.67 (declare-fun tptp.dsetconstr__Cong () Bool) 0.44/0.67 (assert (= tptp.dsetconstr__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (= Xx Xy) (= (@ Xphi Xx) (@ Xpsi Xy))))))) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xpsi Xx)))))))))) 0.44/0.67 (declare-fun tptp.subset ($$unsorted $$unsorted) Bool) 0.44/0.67 (declare-fun tptp.disjoint ($$unsorted $$unsorted) Bool) 0.44/0.67 (declare-fun tptp.setsmeet ($$unsorted $$unsorted) Bool) 0.44/0.67 (declare-fun tptp.subsetI1 () Bool) 0.44/0.67 (assert (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B))))) 0.44/0.67 (declare-fun tptp.eqimpsubset2 () Bool) 0.44/0.67 (assert (= tptp.eqimpsubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset B) A))))) 0.44/0.67 (declare-fun tptp.eqimpsubset1 () Bool) 0.44/0.67 (assert (= tptp.eqimpsubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B))))) 0.44/0.67 (declare-fun tptp.subsetI2 () Bool) 0.44/0.67 (assert (= tptp.subsetI2 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B))))) 0.44/0.67 (declare-fun tptp.emptysetsubset () Bool) 0.44/0.67 (assert (= tptp.emptysetsubset (forall ((A $$unsorted)) (@ (@ tptp.subset tptp.emptyset) A)))) 0.44/0.67 (declare-fun tptp.subsetE () Bool) 0.44/0.67 (assert (= tptp.subsetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (@ _let_1 A) (@ _let_1 B))))))) 0.44/0.67 (declare-fun tptp.subsetE2 () Bool) 0.44/0.67 (assert (= tptp.subsetE2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (not (@ _let_1 B)) (not (@ _let_1 A)))))))) 0.44/0.67 (declare-fun tptp.notsubsetI () Bool) 0.44/0.67 (assert (= tptp.notsubsetI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (@ (@ tptp.subset A) B)))))))) 0.44/0.67 (declare-fun tptp.notequalI1 () Bool) 0.44/0.67 (assert (= tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (@ (@ tptp.subset A) B)) (not (= A B)))))) 0.44/0.67 (declare-fun tptp.notequalI2 () Bool) 0.44/0.67 (assert (= tptp.notequalI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (= A B)))))))) 0.44/0.67 (declare-fun tptp.subsetRefl () Bool) 0.44/0.67 (assert (= tptp.subsetRefl (forall ((A $$unsorted)) (@ (@ tptp.subset A) A)))) 0.44/0.67 (declare-fun tptp.subsetTrans () Bool) 0.44/0.67 (assert (= tptp.subsetTrans (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (=> (@ (@ tptp.subset B) C) (@ _let_1 C))))))) 0.44/0.67 (declare-fun tptp.setadjoinSub () Bool) 0.44/0.67 (assert (= tptp.setadjoinSub (forall ((Xx $$unsorted) (A $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.setadjoin Xx) A))))) 0.44/0.67 (declare-fun tptp.setadjoinSub2 () Bool) 0.44/0.67 (assert (= tptp.setadjoinSub2 (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.setadjoin Xx) B))))))) 0.44/0.67 (declare-fun tptp.subset2powerset () Bool) 0.44/0.67 (assert (= tptp.subset2powerset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.in A) (@ tptp.powerset B)))))) 0.44/0.67 (declare-fun tptp.setextsub () Bool) 0.44/0.67 (assert (= tptp.setextsub (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (=> (@ (@ tptp.subset B) A) (= A B)))))) 0.44/0.67 (declare-fun tptp.subsetemptysetimpeq () Bool) 0.44/0.67 (assert (= tptp.subsetemptysetimpeq (forall ((A $$unsorted)) (=> (@ (@ tptp.subset A) tptp.emptyset) (= A tptp.emptyset))))) 0.44/0.67 (declare-fun tptp.powersetI1 () Bool) 0.44/0.67 (assert (= tptp.powersetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (@ (@ tptp.in B) (@ tptp.powerset A)))))) 0.44/0.67 (declare-fun tptp.powersetE1 () Bool) 0.44/0.67 (assert (= tptp.powersetE1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (@ (@ tptp.subset B) A))))) 0.44/0.67 (declare-fun tptp.inPowerset () Bool) 0.44/0.67 (assert (= tptp.inPowerset (forall ((A $$unsorted)) (@ (@ tptp.in A) (@ tptp.powerset A))))) 0.44/0.67 (declare-fun tptp.powersetsubset () Bool) 0.44/0.67 (assert (= tptp.powersetsubset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.subset (@ tptp.powerset A)) (@ tptp.powerset B)))))) 0.44/0.67 (declare-fun tptp.sepInPowerset () Bool) 0.44/0.67 (assert (= tptp.sepInPowerset (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.in (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ tptp.powerset A))))) 0.44/0.67 (declare-fun tptp.sepSubset () Bool) 0.44/0.67 (assert (= tptp.sepSubset (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.subset (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) A)))) 0.44/0.67 (declare-fun tptp.binunion ($$unsorted $$unsorted) $$unsorted) 0.44/0.67 (declare-fun tptp.binunionIL () Bool) 0.44/0.67 (assert (= tptp.binunionIL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.binunion A) B))))))) 0.44/0.67 (declare-fun tptp.upairset2IR () Bool) 0.44/0.67 (assert (= tptp.upairset2IR (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.44/0.67 (declare-fun tptp.binunionIR () Bool) 0.44/0.67 (assert (= tptp.binunionIR (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binunion A) B))))))) 0.44/0.67 (declare-fun tptp.binunionEcases () Bool) 0.44/0.67 (assert (= tptp.binunionEcases (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xphi Bool)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binunion A) B)) (=> (=> (@ _let_1 A) Xphi) (=> (=> (@ _let_1 B) Xphi) Xphi))))))) 0.44/0.67 (declare-fun tptp.binunionE () Bool) 0.44/0.67 (assert (= tptp.binunionE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binunion A) B)) (or (@ _let_1 A) (@ _let_1 B))))))) 0.44/0.67 (declare-fun tptp.binunionLsub () Bool) 0.44/0.67 (assert (= tptp.binunionLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.binunion A) B))))) 0.44/0.67 (declare-fun tptp.binunionRsub () Bool) 0.44/0.67 (assert (= tptp.binunionRsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset B) (@ (@ tptp.binunion A) B))))) 0.44/0.67 (declare-fun tptp.binintersect ($$unsorted $$unsorted) $$unsorted) 0.44/0.67 (declare-fun tptp.binintersectI () Bool) 0.44/0.67 (assert (= tptp.binintersectI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B)))))))) 0.44/0.67 (declare-fun tptp.binintersectSubset5 () Bool) 0.44/0.67 (assert (= tptp.binintersectSubset5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B)))))))) 0.44/0.67 (declare-fun tptp.binintersectEL () Bool) 0.44/0.67 (assert (= tptp.binintersectEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect A) B)) (@ _let_1 A)))))) 0.44/0.67 (declare-fun tptp.binintersectLsub () Bool) 0.44/0.67 (assert (= tptp.binintersectLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) A)))) 0.44/0.67 (declare-fun tptp.binintersectSubset2 () Bool) 0.44/0.67 (assert (= tptp.binintersectSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.binintersect A) B) A))))) 0.44/0.67 (declare-fun tptp.binintersectSubset3 () Bool) 0.44/0.67 (assert (= tptp.binintersectSubset3 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) B) (@ (@ tptp.subset B) A))))) 0.44/0.67 (declare-fun tptp.binintersectER () Bool) 0.44/0.67 (assert (= tptp.binintersectER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect A) B)) (@ _let_1 B)))))) 0.44/0.67 (declare-fun tptp.disjointsetsI1 () Bool) 0.44/0.67 (assert (= tptp.disjointsetsI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 A) (@ _let_1 B))))) (= (@ (@ tptp.binintersect A) B) tptp.emptyset))))) 0.44/0.67 (declare-fun tptp.binintersectRsub () Bool) 0.44/0.67 (assert (= tptp.binintersectRsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) B)))) 0.44/0.67 (declare-fun tptp.binintersectSubset4 () Bool) 0.44/0.67 (assert (= tptp.binintersectSubset4 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (= (@ (@ tptp.binintersect A) B) B))))) 0.44/0.67 (declare-fun tptp.binintersectSubset1 () Bool) 0.44/0.67 (assert (= tptp.binintersectSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) A) (@ (@ tptp.subset A) B))))) 0.44/0.67 (declare-fun tptp.bs114d () Bool) 0.44/0.67 (assert (= tptp.bs114d (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.binintersect A))) (= (@ _let_1 (@ (@ tptp.binunion B) C)) (@ (@ tptp.binunion (@ _let_1 B)) (@ _let_1 C))))))) 0.44/0.67 (declare-fun tptp.regular ($$unsorted) Bool) 0.44/0.67 (declare-fun tptp.setminus ($$unsorted $$unsorted) $$unsorted) 0.44/0.67 (declare-fun tptp.setminusI () Bool) 0.44/0.67 (assert (= tptp.setminusI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.setminus A) B)))))))) 0.44/0.67 (declare-fun tptp.setminusEL () Bool) 0.44/0.67 (assert (= tptp.setminusEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.setminus A) B)) (@ _let_1 A)))))) 0.44/0.67 (declare-fun tptp.setminusER () Bool) 0.44/0.67 (assert (= tptp.setminusER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.setminus A) B)) (not (@ _let_1 B))))))) 0.44/0.67 (declare-fun tptp.setminusSubset2 () Bool) 0.44/0.67 (assert (= tptp.setminusSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.setminus A) B) tptp.emptyset))))) 0.44/0.67 (declare-fun tptp.setminusERneg () Bool) 0.44/0.67 (assert (= tptp.setminusERneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 (@ (@ tptp.setminus A) B))) (=> (@ _let_1 A) (@ _let_1 B))))))) 0.44/0.67 (declare-fun tptp.setminusELneg () Bool) 0.44/0.67 (assert (= tptp.setminusELneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 (@ (@ tptp.setminus A) B))) (=> (not (@ _let_1 B)) (not (@ _let_1 A)))))))) 0.44/0.67 (declare-fun tptp.setminusILneg () Bool) 0.44/0.67 (assert (= tptp.setminusILneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (not (@ _let_1 (@ (@ tptp.setminus A) B)))))))) 0.44/0.67 (declare-fun tptp.setminusIRneg () Bool) 0.44/0.67 (assert (= tptp.setminusIRneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (not (@ _let_1 (@ (@ tptp.setminus A) B)))))))) 0.44/0.67 (declare-fun tptp.setminusLsub () Bool) 0.44/0.67 (assert (= tptp.setminusLsub (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.setminus A) B)) A)))) 0.44/0.67 (declare-fun tptp.setminusSubset1 () Bool) 0.44/0.67 (assert (= tptp.setminusSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.setminus A) B) tptp.emptyset) (@ (@ tptp.subset A) B))))) 0.44/0.67 (declare-fun tptp.symdiff ($$unsorted $$unsorted) $$unsorted) 0.44/0.67 (declare-fun tptp.symdiffE () Bool) 0.44/0.67 (assert (= tptp.symdiffE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.symdiff A) B)) (forall ((Xphi Bool)) (let ((_let_1 (@ tptp.in Xx))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ _let_1 A))) (=> (=> _let_3 (=> (not _let_2) Xphi)) (=> (=> (not _let_3) (=> _let_2 Xphi)) Xphi)))))))))) 0.44/0.67 (declare-fun tptp.symdiffI1 () Bool) 0.44/0.67 (assert (= tptp.symdiffI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.symdiff A) B)))))))) 0.44/0.67 (declare-fun tptp.symdiffI2 () Bool) 0.44/0.67 (assert (= tptp.symdiffI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.symdiff A) B)))))))) 0.44/0.67 (declare-fun tptp.symdiffIneg1 () Bool) 0.44/0.67 (assert (= tptp.symdiffIneg1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 B) (not (@ _let_1 (@ (@ tptp.symdiff A) B))))))))) 0.44/0.67 (declare-fun tptp.symdiffIneg2 () Bool) 0.44/0.67 (assert (= tptp.symdiffIneg2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (not (@ _let_1 (@ (@ tptp.symdiff A) B))))))))) 0.44/0.67 (declare-fun tptp.iskpair ($$unsorted) Bool) 0.44/0.67 (declare-fun tptp.secondinupair () Bool) 0.44/0.67 (assert (= tptp.secondinupair (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) 0.44/0.67 (declare-fun tptp.setukpairIL () Bool) 0.44/0.67 (assert (= tptp.setukpairIL (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ (@ tptp.in Xx) (@ tptp.setunion (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)))))))) 0.44/0.67 (declare-fun tptp.setukpairIR () Bool) 0.44/0.67 (assert (= tptp.setukpairIR (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ (@ tptp.in Xy) (@ tptp.setunion (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)))))))) 0.44/0.67 (declare-fun tptp.kpairiskpair () Bool) 0.44/0.67 (assert (= tptp.kpairiskpair (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ tptp.iskpair (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))))))) 0.44/0.67 (declare-fun tptp.kpair ($$unsorted $$unsorted) $$unsorted) 0.44/0.67 (declare-fun tptp.kpairp () Bool) 0.44/0.67 (assert (= tptp.kpairp (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ tptp.iskpair (@ (@ tptp.kpair Xx) Xy))))) 0.44/0.67 (declare-fun tptp.cartprod ($$unsorted $$unsorted) $$unsorted) 0.44/0.67 (declare-fun tptp.singletonsubset () Bool) 0.44/0.67 (assert (= tptp.singletonsubset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) tptp.emptyset)) A))))) 0.44/0.67 (declare-fun tptp.singletoninpowerset () Bool) 0.44/0.67 (assert (= tptp.singletoninpowerset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset A)))))) 0.44/0.67 (declare-fun tptp.singletoninpowunion () Bool) 0.44/0.67 (assert (= tptp.singletoninpowunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset (@ (@ tptp.binunion A) B))))))) 0.44/0.67 (declare-fun tptp.upairset2E () Bool) 0.44/0.67 (assert (= tptp.upairset2E (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy)))))) 0.44/0.67 (declare-fun tptp.upairsubunion () Bool) 0.44/0.67 (assert (= tptp.upairsubunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (@ (@ tptp.binunion A) B)))))))) 0.44/0.67 (declare-fun tptp.upairinpowunion () Bool) 0.44/0.67 (assert (= tptp.upairinpowunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (@ tptp.powerset (@ (@ tptp.binunion A) B))))))))) 0.44/0.67 (declare-fun tptp.ubforcartprodlem1 () Bool) 0.44/0.67 (assert (= tptp.ubforcartprodlem1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.subset (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))))) 0.44/0.67 (declare-fun tptp.ubforcartprodlem2 () Bool) 0.44/0.67 (assert (= tptp.ubforcartprodlem2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (@ tptp.powerset (@ tptp.powerset (@ (@ tptp.binunion A) B))))))))))) 0.44/0.67 (declare-fun tptp.ubforcartprodlem3 () Bool) 0.44/0.67 (assert (= tptp.ubforcartprodlem3 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ tptp.powerset (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))))) 0.44/0.67 (declare-fun tptp.cartprodpairin () Bool) 0.44/0.67 (assert (= tptp.cartprodpairin (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B)))))))) 0.44/0.67 (declare-fun tptp.cartprodmempair1 () Bool) 0.44/0.67 (assert (= tptp.cartprodmempair1 (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) B) (= Xu (@ (@ tptp.kpair Xx) Xy)))))))))) 0.44/0.67 (declare-fun tptp.cartprodmempair () Bool) 0.44/0.67 (assert (= tptp.cartprodmempair (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ tptp.iskpair Xu))))) 0.44/0.67 (declare-fun tptp.setunionE2 () Bool) 0.44/0.67 (assert (= tptp.setunionE2 (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((X $$unsorted)) (and (@ (@ tptp.in X) A) (@ (@ tptp.in Xx) X))))))) 0.44/0.67 (declare-fun tptp.setunionsingleton1 () Bool) 0.44/0.67 (assert (= tptp.setunionsingleton1 (forall ((A $$unsorted)) (@ (@ tptp.subset (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset))) A)))) 0.44/0.67 (declare-fun tptp.setunionsingleton2 () Bool) 0.44/0.67 (assert (= tptp.setunionsingleton2 (forall ((A $$unsorted)) (@ (@ tptp.subset A) (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset)))))) 0.44/0.67 (declare-fun tptp.setunionsingleton () Bool) 0.44/0.67 (assert (= tptp.setunionsingleton (forall ((Xx $$unsorted)) (= (@ tptp.setunion (@ (@ tptp.setadjoin Xx) tptp.emptyset)) Xx)))) 0.44/0.67 (declare-fun tptp.singleton ($$unsorted) Bool) 0.44/0.67 (declare-fun tptp.singletonprop () Bool) 0.44/0.67 (assert (= tptp.singletonprop (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) 0.44/0.67 (declare-fun tptp.ex1 ($$unsorted (-> $$unsorted Bool)) Bool) 0.44/0.67 (assert (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) 0.44/0.67 (declare-fun tptp.ex1E1 () Bool) 0.44/0.67 (assert (= tptp.ex1E1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))))))) 0.44/0.67 (declare-fun tptp.ex1I () Bool) 0.44/0.67 (assert (= tptp.ex1I (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (=> (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xy) (= Xy Xx)))) (@ (@ tptp.ex1 A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))))) 0.44/0.67 (declare-fun tptp.ex1I2 () Bool) 0.44/0.67 (assert (= tptp.ex1I2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) 0.44/0.67 (declare-fun tptp.singletonsuniq () Bool) 0.44/0.67 (assert (= tptp.singletonsuniq (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy))))) 0.44/0.67 (declare-fun tptp.atmost1p ($$unsorted) Bool) 0.44/0.67 (declare-fun tptp.atleast2p ($$unsorted) Bool) 0.44/0.67 (declare-fun tptp.atmost2p ($$unsorted) Bool) 0.44/0.67 (declare-fun tptp.upairsetp ($$unsorted) Bool) 0.44/0.67 (declare-fun tptp.setukpairinjL1 () Bool) 0.44/0.67 (assert (= tptp.setukpairinjL1 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (@ (@ tptp.in (@ (@ tptp.setadjoin Xz) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (= Xx Xz)))))) 0.44/0.67 (declare-fun tptp.kfstsingleton () Bool) 0.44/0.67 (assert (= tptp.kfstsingleton (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (@ tptp.singleton (@ (@ tptp.dsetconstr (@ tptp.setunion Xu)) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) Xu)))))))) 0.44/0.67 (declare-fun tptp.theprop () Bool) 0.44/0.67 (assert (= tptp.theprop (forall ((X $$unsorted)) (=> (@ tptp.singleton X) (@ (@ tptp.in (@ tptp.setunion X)) X))))) 0.44/0.67 (declare-fun tptp.kfst ($$unsorted) $$unsorted) 0.44/0.67 (declare-fun tptp.kfstpairEq () Bool) 0.44/0.67 (assert (= tptp.kfstpairEq (forall ((Xx $$unsorted) (Xy $$unsorted)) (= (@ tptp.kfst (@ (@ tptp.kpair Xx) Xy)) Xx)))) 0.44/0.67 (declare-fun tptp.cartprodfstin () Bool) 0.44/0.67 (assert (= tptp.cartprodfstin (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in (@ tptp.kfst Xu)) A))))) 0.44/0.67 (declare-fun tptp.setukpairinjL2 () Bool) 0.44/0.67 (assert (= tptp.setukpairinjL2 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xz))) (let ((_let_2 (@ tptp.setadjoin Xx))) (=> (= (@ (@ tptp.setadjoin (@ _let_2 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_2 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset))) (= Xx Xz))))))) 0.44/0.67 (declare-fun tptp.setukpairinjL () Bool) 0.44/0.67 (assert (= tptp.setukpairinjL (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xx Xz))))) 0.44/0.67 (declare-fun tptp.setukpairinjR11 () Bool) 0.44/0.67 (assert (= tptp.setukpairinjR11 (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (= Xx Xy) (= (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ _let_1 tptp.emptyset))))))) 0.44/0.67 (declare-fun tptp.setukpairinjR12 () Bool) 0.44/0.67 (assert (= tptp.setukpairinjR12 (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (let ((_let_2 (@ tptp.setadjoin (@ _let_1 tptp.emptyset)))) (=> (= Xx Xy) (= (@ _let_2 (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ _let_2 tptp.emptyset)))))))) 0.44/0.67 (declare-fun tptp.setukpairinjR1 () Bool) 0.44/0.67 (assert (= tptp.setukpairinjR1 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xz))) (let ((_let_2 (@ tptp.setadjoin Xx))) (=> (= (@ (@ tptp.setadjoin (@ _let_2 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_2 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset))) (=> (= Xz Xu) (= Xy Xu)))))))) 0.44/0.67 (declare-fun tptp.upairequniteq () Bool) 0.44/0.67 (assert (= tptp.upairequniteq (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (= (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.setadjoin Xz) tptp.emptyset)) (= Xx Xy))))) 0.44/0.67 (declare-fun tptp.setukpairinjR2 () Bool) 0.44/0.67 (assert (= tptp.setukpairinjR2 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xz))) (let ((_let_2 (@ tptp.setadjoin Xx))) (=> (= (@ (@ tptp.setadjoin (@ _let_2 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_2 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset))) (= Xy Xu))))))) 0.44/0.67 (declare-fun tptp.setukpairinjR () Bool) 0.44/0.67 (assert (= tptp.setukpairinjR (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xy Xu))))) 0.44/0.67 (declare-fun tptp.ksndsingleton () Bool) 0.44/0.67 (assert (= tptp.ksndsingleton (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (@ tptp.singleton (@ (@ tptp.dsetconstr (@ tptp.setunion Xu)) (lambda ((Xx $$unsorted)) (= Xu (@ (@ tptp.kpair (@ tptp.kfst Xu)) Xx))))))))) 0.44/0.67 (declare-fun tptp.ksnd ($$unsorted) $$unsorted) 0.44/0.67 (declare-fun tptp.ksndpairEq () Bool) 0.44/0.67 (assert (= tptp.ksndpairEq (forall ((Xx $$unsorted) (Xy $$unsorted)) (= (@ tptp.ksnd (@ (@ tptp.kpair Xx) Xy)) Xy)))) 0.44/0.67 (declare-fun tptp.kpairsurjEq () Bool) 0.44/0.67 (assert (= tptp.kpairsurjEq (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (= (@ (@ tptp.kpair (@ tptp.kfst Xu)) (@ tptp.ksnd Xu)) Xu))))) 0.44/0.67 (declare-fun tptp.cartprodsndin () Bool) 0.44/0.67 (assert (= tptp.cartprodsndin (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in (@ tptp.ksnd Xu)) B))))) 0.44/0.67 (declare-fun tptp.cartprodpairmemEL () Bool) 0.44/0.67 (assert (= tptp.cartprodpairmemEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in Xx) A))))) 0.44/0.67 (declare-fun tptp.cartprodpairmemER () Bool) 0.44/0.67 (assert (= tptp.cartprodpairmemER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in Xy) B))))) 0.44/0.67 (declare-fun tptp.cartprodmempaircEq () Bool) 0.44/0.67 (assert (= tptp.cartprodmempaircEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) Xy))) (=> (@ (@ tptp.in Xy) B) (= _let_1 _let_1)))))))) 0.44/0.67 (declare-fun tptp.cartprodfstpairEq () Bool) 0.44/0.67 (assert (= tptp.cartprodfstpairEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (= (@ tptp.kfst (@ (@ tptp.kpair Xx) Xy)) Xx))))))) 0.44/0.67 (declare-fun tptp.cartprodsndpairEq () Bool) 0.44/0.67 (assert (= tptp.cartprodsndpairEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (= (@ tptp.ksnd (@ (@ tptp.kpair Xx) Xy)) Xy))))))) 0.44/0.67 (declare-fun tptp.cartprodpairsurjEq () Bool) 0.44/0.67 (assert (= tptp.cartprodpairsurjEq (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (= (@ (@ tptp.kpair (@ tptp.kfst Xu)) (@ tptp.ksnd Xu)) Xu))))) 0.44/0.67 (declare-fun tptp.breln ($$unsorted $$unsorted $$unsorted) Bool) 0.44/0.67 (assert (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B))))) 0.44/0.67 (declare-fun tptp.dpsetconstr ($$unsorted $$unsorted (-> $$unsorted $$unsorted Bool)) $$unsorted) 0.44/0.67 (declare-fun tptp.dpsetconstrI () Bool) 0.44/0.67 (assert (= tptp.dpsetconstrI (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ Xphi Xx) Xy) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu))))))))))) 0.44/0.67 (declare-fun tptp.dpsetconstrSub () Bool) 0.44/0.67 (assert (= tptp.dpsetconstrSub (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.subset (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ Xphi Xx) Xy)))) (@ (@ tptp.cartprod A) B))))) 0.44/0.67 (declare-fun tptp.setOfPairsIsBReln () Bool) 0.44/0.67 (assert (= tptp.setOfPairsIsBReln (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ (@ tptp.breln A) B) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ Xphi Xx) Xy))))))) 0.44/0.67 (declare-fun tptp.dpsetconstrERa () Bool) 0.44/0.67 (assert (= tptp.dpsetconstrERa (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ Xphi Xx) Xy)))))))) 0.44/0.67 (declare-fun tptp.dpsetconstrEL1 () Bool) 0.44/0.67 (assert (= tptp.dpsetconstrEL1 (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ tptp.in Xx) A))))) 0.44/0.67 (declare-fun tptp.dpsetconstrEL2 () Bool) 0.44/0.67 (assert (= tptp.dpsetconstrEL2 (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ tptp.in Xy) B))))) 0.44/0.67 (declare-fun tptp.dpsetconstrER () Bool) 0.44/0.67 (assert (= tptp.dpsetconstrER (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ Xphi Xx) Xy))))) 0.44/0.67 (declare-fun tptp.func ($$unsorted $$unsorted $$unsorted) Bool) 0.44/0.67 (declare-fun tptp.funcSet ($$unsorted $$unsorted) $$unsorted) 0.44/0.67 (declare-fun tptp.funcImageSingleton () Bool) 0.44/0.67 (assert (= tptp.funcImageSingleton (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ tptp.singleton (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf)))))))))) 0.44/0.67 (declare-fun tptp.apProp () Bool) 0.44/0.67 (assert (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B))))))) 0.44/0.67 (declare-fun tptp.ap ($$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted) 0.44/0.67 (declare-fun tptp.app () Bool) 0.44/0.67 (assert (= tptp.app (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))))) 0.44/0.67 (declare-fun tptp.infuncsetfunc () Bool) 0.44/0.67 (assert (= tptp.infuncsetfunc (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (@ (@ (@ tptp.func A) B) Xf))))) 0.44/0.67 (declare-fun tptp.ap2p () Bool) 0.44/0.67 (assert (= tptp.ap2p (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B))))))) 0.44/0.67 (declare-fun tptp.funcinfuncset () Bool) 0.44/0.67 (assert (= tptp.funcinfuncset (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)))))) 0.44/0.67 (declare-fun tptp.lamProp () Bool) 0.44/0.67 (assert (= tptp.lamProp (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (@ (@ (@ tptp.func A) B) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (= (@ Xf Xx) Xy)))))))) 0.44/0.67 (declare-fun tptp.lam ($$unsorted $$unsorted (-> $$unsorted $$unsorted)) $$unsorted) 0.44/0.67 (declare-fun tptp.lamp () Bool) 0.44/0.67 (assert (= tptp.lamp (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (@ (@ (@ tptp.func A) B) (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ Xf Xx)))))))) 0.44/0.67 (declare-fun tptp.lam2p () Bool) 0.44/0.67 (assert (= tptp.lam2p (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (@ (@ tptp.in (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ Xf Xx)))) (@ (@ tptp.funcSet A) B)))))) 0.44/0.67 (declare-fun tptp.brelnall1 () Bool) 0.44/0.67 (assert (= tptp.brelnall1 (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) Xy))) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in _let_1) R) (@ Xphi _let_1))))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) R) (@ Xphi Xx))))))))) 0.44/0.67 (declare-fun tptp.brelnall2 () Bool) 0.44/0.67 (assert (= tptp.brelnall2 (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) Xy))) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in _let_1) R) (@ Xphi _let_1))))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) R) (@ Xphi Xx))))))))) 0.44/0.67 (declare-fun tptp.ex1E2 () Bool) 0.44/0.67 (assert (= tptp.ex1E2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))))))) 0.44/0.67 (declare-fun tptp.funcGraphProp1 () Bool) 0.44/0.67 (assert (= tptp.funcGraphProp1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.kpair Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf))))))) 0.44/0.67 (declare-fun tptp.funcGraphProp3 () Bool) 0.44/0.67 (assert (= tptp.funcGraphProp3 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.kpair Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf))))))) 0.44/0.67 (declare-fun tptp.funcGraphProp2 () Bool) 0.44/0.67 (assert (= tptp.funcGraphProp2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) Xy)))))))))) 0.44/0.67 (declare-fun tptp.funcextLem () Bool) 0.44/0.67 (assert (= tptp.funcextLem (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xg $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xg) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (=> (@ (@ tptp.in Xx) A) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 Xg) Xx))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 Xg) (@ _let_1 Xf)))))))))))))) 0.44/0.67 (declare-fun tptp.funcGraphProp4 () Bool) 0.44/0.67 (assert (= tptp.funcGraphProp4 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) Xy)))))))))) 0.44/0.67 (declare-fun tptp.subbreln () Bool) 0.44/0.67 (assert (= tptp.subbreln (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((S $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) S) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 R) (@ _let_1 S))))))) (@ (@ tptp.subset R) S)))))))) 0.44/0.67 (declare-fun tptp.eqbreln () Bool) 0.44/0.67 (assert (= tptp.eqbreln (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((S $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) S) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 R) (@ _let_1 S))))))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 S) (@ _let_1 R))))))) (= R S))))))))) 0.44/0.67 (declare-fun tptp.funcext () Bool) 0.44/0.67 (assert (= tptp.funcext (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xg $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xg) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (=> (@ (@ tptp.in Xx) A) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 Xg) Xx))))) (= Xf Xg)))))))) 0.44/0.67 (declare-fun tptp.funcext2 () Bool) 0.44/0.67 (assert (= tptp.funcext2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xg $$unsorted)) (=> (@ (@ tptp.in Xg) (@ (@ tptp.funcSet A) B)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (=> (@ (@ tptp.in Xx) A) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 Xg) Xx))))) (= Xf Xg)))))))) 0.44/0.67 (declare-fun tptp.ap2apEq1 () Bool) 0.44/0.67 (assert (= tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) (=> (@ (@ tptp.in Xx) A) (= _let_1 _let_1)))))))) 0.44/0.67 (declare-fun tptp.ap2apEq2 () Bool) 0.44/0.67 (assert (= tptp.ap2apEq2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) (=> (@ (@ tptp.in Xx) A) (= _let_1 _let_1)))))))) 0.44/0.67 (declare-fun tptp.beta1 () Bool) 0.44/0.67 (assert (= tptp.beta1 (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) (@ (@ (@ tptp.lam A) B) (lambda ((Xy $$unsorted)) (@ Xf Xy)))) Xx) (@ Xf Xx)))))))) 0.44/0.67 (declare-fun tptp.eta1 () Bool) 0.44/0.67 (assert (= tptp.eta1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (= (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf))))) 0.44/0.67 (declare-fun tptp.lam2lamEq () Bool) 0.44/0.67 (assert (= tptp.lam2lamEq (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (let ((_let_1 (@ (@ tptp.lam A) B))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (= (@ _let_1 (lambda ((Xx $$unsorted)) (@ Xf Xx))) (@ _let_1 (lambda ((Xx $$unsorted)) (@ Xf Xx))))))))) 0.44/0.67 (declare-fun tptp.beta2 () Bool) 0.44/0.67 (assert (= tptp.beta2 (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) (@ (@ (@ tptp.lam A) B) (lambda ((Xy $$unsorted)) (@ Xf Xy)))) Xx) (@ Xf Xx)))))))) 0.44/0.67 (declare-fun tptp.eta2 () Bool) 0.44/0.67 (assert (= tptp.eta2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (= (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf))))) 0.44/0.67 (declare-fun tptp.iffalseProp1 () Bool) 0.44/0.67 (assert (= tptp.iffalseProp1 (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (=> (not Xphi) (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy)))))))))))))) 0.44/0.67 (declare-fun tptp.iffalseProp2 () Bool) 0.44/0.67 (assert (= tptp.iffalseProp2 (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (not Xphi) (= (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy))))) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))))) 0.44/0.67 (declare-fun tptp.iftrueProp1 () Bool) 0.44/0.67 (assert (= tptp.iftrueProp1 (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> Xphi (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy))))))))))))) 0.44/0.67 (declare-fun tptp.iftrueProp2 () Bool) 0.44/0.67 (assert (= tptp.iftrueProp2 (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> Xphi (= (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy))))) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))))) 0.44/0.67 (declare-fun tptp.ifSingleton () Bool) 0.44/0.67 (assert (= tptp.ifSingleton (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy)))))))))))) 0.44/0.67 (declare-fun tptp.if ($$unsorted Bool $$unsorted $$unsorted) $$unsorted) 0.44/0.67 (assert (= tptp.if (lambda ((A $$unsorted) (Xphi Bool) (Xx $$unsorted) (Xy $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy))))))))) 0.44/0.67 (declare-fun tptp.ifp () Bool) 0.44/0.67 (assert (= tptp.ifp (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.if A) Xphi) Xx) Xy)) A))))))) 0.44/0.67 (declare-fun tptp.theeq () Bool) 0.44/0.67 (assert (= tptp.theeq (forall ((X $$unsorted)) (=> (@ tptp.singleton X) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) X) (= (@ tptp.setunion X) Xx))))))) 0.44/0.67 (declare-fun tptp.iftrue () Bool) 0.44/0.67 (assert (= tptp.iftrue (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> Xphi (= (@ (@ (@ (@ tptp.if A) Xphi) Xx) Xy) Xx)))))))) 0.44/0.67 (assert (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (=> tptp.ap2apEq2 (=> tptp.beta1 (=> tptp.eta1 (=> tptp.lam2lamEq (=> tptp.beta2 (=> tptp.eta2 (=> tptp.iffalseProp1 (=> tptp.iffalseProp2 (=> tptp.iftrueProp1 (=> tptp.iftrueProp2 (=> tptp.ifSingleton (=> tptp.ifp (=> tptp.theeq (=> tptp.iftrue (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (not Xphi) (= (@ (@ (@ (@ tptp.if A) Xphi) Xx) Xy) Xy)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 40.96/41.40 (set-info :filename cvc5---1.0.5_30781) 40.96/41.40 (check-sat-assuming ( true )) 40.96/41.40 ------- get file name : TPTP file name is 40.96/41.40 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30781.smt2... 40.96/41.40 --- Run --ho-elim --full-saturate-quant at 10... 40.96/41.40 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 40.96/41.40 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10... 40.96/41.40 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5... 40.96/41.40 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5... 40.96/41.40 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10... 40.96/41.40 % SZS status Theorem for 40.96/41.40 % SZS output start Proof for 40.96/41.40 ( 40.96/41.40 (let ((_let_1 (not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (=> tptp.ap2apEq2 (=> tptp.beta1 (=> tptp.eta1 (=> tptp.lam2lamEq (=> tptp.beta2 (=> tptp.eta2 (=> tptp.iffalseProp1 (=> tptp.iffalseProp2 (=> tptp.iftrueProp1 (=> tptp.iftrueProp2 (=> tptp.ifSingleton (=> tptp.ifp (=> tptp.theeq (=> tptp.iftrue (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (not Xphi) (= (@ (@ (@ (@ tptp.if A) Xphi) Xx) Xy) Xy))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (let ((_let_2 (= tptp.iftrue (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> Xphi (= (@ (@ (@ (@ tptp.if A) Xphi) Xx) Xy) Xx))))))))) (let ((_let_3 (= tptp.theeq (forall ((X $$unsorted)) (=> (@ tptp.singleton X) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) X) (= (@ tptp.setunion X) Xx)))))))) (let ((_let_4 (= tptp.ifp (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.if A) Xphi) Xx) Xy)) A)))))))) (let ((_let_5 (= tptp.if (lambda ((A $$unsorted) (Xphi Bool) (Xx $$unsorted) (Xy $$unsorted)) (@ tptp.setunion (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy)))))))))) (let ((_let_6 (= tptp.ifSingleton (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy))))))))))))) (let ((_let_7 (= tptp.iftrueProp2 (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> Xphi (= (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy))))) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))))) (let ((_let_8 (= tptp.iftrueProp1 (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> Xphi (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy)))))))))))))) (let ((_let_9 (= tptp.iffalseProp2 (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (not Xphi) (= (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy))))) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))))))) (let ((_let_10 (= tptp.iffalseProp1 (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (=> (not Xphi) (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz Xy))))))))))))))) (let ((_let_11 (= tptp.eta2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (= (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf)))))) (let ((_let_12 (= tptp.beta2 (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) (@ (@ (@ tptp.lam A) B) (lambda ((Xy $$unsorted)) (@ Xf Xy)))) Xx) (@ Xf Xx))))))))) (let ((_let_13 (= tptp.lam2lamEq (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (let ((_let_1 (@ (@ tptp.lam A) B))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (= (@ _let_1 (lambda ((Xx $$unsorted)) (@ Xf Xx))) (@ _let_1 (lambda ((Xx $$unsorted)) (@ Xf Xx)))))))))) (let ((_let_14 (= tptp.eta1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (= (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf)))))) (let ((_let_15 (= tptp.beta1 (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (= (@ (@ (@ (@ tptp.ap A) B) (@ (@ (@ tptp.lam A) B) (lambda ((Xy $$unsorted)) (@ Xf Xy)))) Xx) (@ Xf Xx))))))))) (let ((_let_16 (= tptp.ap2apEq2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) (=> (@ (@ tptp.in Xx) A) (= _let_1 _let_1))))))))) (let ((_let_17 (= tptp.ap2apEq1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) (=> (@ (@ tptp.in Xx) A) (= _let_1 _let_1))))))))) (let ((_let_18 (= tptp.funcext2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xg $$unsorted)) (=> (@ (@ tptp.in Xg) (@ (@ tptp.funcSet A) B)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (=> (@ (@ tptp.in Xx) A) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 Xg) Xx))))) (= Xf Xg))))))))) (let ((_let_19 (= tptp.funcext (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xg $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xg) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (=> (@ (@ tptp.in Xx) A) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 Xg) Xx))))) (= Xf Xg))))))))) (let ((_let_20 (= tptp.eqbreln (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((S $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) S) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 R) (@ _let_1 S))))))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 S) (@ _let_1 R))))))) (= R S)))))))))) (let ((_let_21 (= tptp.subbreln (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((S $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) S) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 R) (@ _let_1 S))))))) (@ (@ tptp.subset R) S))))))))) (let ((_let_22 (= tptp.funcGraphProp4 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) Xy))))))))))) (let ((_let_23 (= tptp.funcextLem (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xg $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xg) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (=> (@ (@ tptp.in Xx) A) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 Xg) Xx))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) Xy)))) (=> (@ (@ tptp.in Xy) B) (=> (@ _let_1 Xg) (@ _let_1 Xf))))))))))))))) (let ((_let_24 (= tptp.funcGraphProp2 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf) (= (@ (@ (@ (@ tptp.ap A) B) Xf) Xx) Xy))))))))))) (let ((_let_25 (= tptp.funcGraphProp3 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.kpair Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf)))))))) (let ((_let_26 (= tptp.funcGraphProp1 (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.kpair Xx) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx))) Xf)))))))) (let ((_let_27 (= tptp.ex1E2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy)))))))))))) (let ((_let_28 (= tptp.brelnall2 (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) Xy))) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in _let_1) R) (@ Xphi _let_1))))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) R) (@ Xphi Xx)))))))))) (let ((_let_29 (= tptp.brelnall1 (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (@ (@ (@ tptp.breln A) B) R) (forall ((Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) Xy))) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in _let_1) R) (@ Xphi _let_1))))))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) R) (@ Xphi Xx)))))))))) (let ((_let_30 (= tptp.lam2p (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (@ (@ tptp.in (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ Xf Xx)))) (@ (@ tptp.funcSet A) B))))))) (let ((_let_31 (= tptp.lamp (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (@ (@ (@ tptp.func A) B) (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ Xf Xx))))))))) (let ((_let_32 (= tptp.lamProp (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ Xf Xx)) B))) (@ (@ (@ tptp.func A) B) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (= (@ Xf Xx) Xy))))))))) (let ((_let_33 (= tptp.funcinfuncset (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B))))))) (let ((_let_34 (= tptp.ap2p (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B)))))))) (let ((_let_35 (= tptp.infuncsetfunc (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)) (@ (@ (@ tptp.func A) B) Xf)))))) (let ((_let_36 (= tptp.app (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)) B)))))))) (let ((_let_37 (= tptp.apProp (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))) B)))))))) (let ((_let_38 (= tptp.funcImageSingleton (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (=> (@ (@ (@ tptp.func A) B) Xf) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ tptp.singleton (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) Xf))))))))))) (let ((_let_39 (= tptp.dpsetconstrER (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ Xphi Xx) Xy)))))) (let ((_let_40 (= tptp.dpsetconstrEL2 (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ tptp.in Xy) B)))))) (let ((_let_41 (= tptp.dpsetconstrEL1 (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ tptp.in Xx) A)))))) (let ((_let_42 (= tptp.dpsetconstrERa (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))) (@ (@ Xphi Xx) Xy))))))))) (let ((_let_43 (= tptp.setOfPairsIsBReln (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ (@ tptp.breln A) B) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ Xphi Xx) Xy)))))))) (let ((_let_44 (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.subset (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ Xphi Xx) Xy)))) (@ (@ tptp.cartprod A) B))))) (let ((_let_45 (= tptp.dpsetconstrSub _let_44))) (let ((_let_46 (= tptp.dpsetconstrI (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (@ (@ Xphi Xx) Xy) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))))))))))) (let ((_let_47 (= tptp.breln (lambda ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (@ (@ tptp.subset C) (@ (@ tptp.cartprod A) B)))))) (let ((_let_48 (= tptp.cartprodpairsurjEq (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (= (@ (@ tptp.kpair (@ tptp.kfst Xu)) (@ tptp.ksnd Xu)) Xu)))))) (let ((_let_49 (= tptp.cartprodsndpairEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (= (@ tptp.ksnd (@ (@ tptp.kpair Xx) Xy)) Xy)))))))) (let ((_let_50 (= tptp.cartprodfstpairEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (= (@ tptp.kfst (@ (@ tptp.kpair Xx) Xy)) Xx)))))))) (let ((_let_51 (= tptp.cartprodmempaircEq (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) Xy))) (=> (@ (@ tptp.in Xy) B) (= _let_1 _let_1))))))))) (let ((_let_52 (= tptp.cartprodpairmemER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in Xy) B)))))) (let ((_let_53 (= tptp.cartprodpairmemEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in Xx) A)))))) (let ((_let_54 (= tptp.cartprodsndin (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in (@ tptp.ksnd Xu)) B)))))) (let ((_let_55 (= tptp.kpairsurjEq (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (= (@ (@ tptp.kpair (@ tptp.kfst Xu)) (@ tptp.ksnd Xu)) Xu)))))) (let ((_let_56 (= tptp.ksndpairEq (forall ((Xx $$unsorted) (Xy $$unsorted)) (= (@ tptp.ksnd (@ (@ tptp.kpair Xx) Xy)) Xy))))) (let ((_let_57 (= tptp.ksndsingleton (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (@ tptp.singleton (@ (@ tptp.dsetconstr (@ tptp.setunion Xu)) (lambda ((Xx $$unsorted)) (= Xu (@ (@ tptp.kpair (@ tptp.kfst Xu)) Xx)))))))))) (let ((_let_58 (= tptp.setukpairinjR (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xy Xu)))))) (let ((_let_59 (= tptp.setukpairinjR2 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xz))) (let ((_let_2 (@ tptp.setadjoin Xx))) (=> (= (@ (@ tptp.setadjoin (@ _let_2 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_2 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset))) (= Xy Xu)))))))) (let ((_let_60 (= tptp.upairequniteq (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (= (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.setadjoin Xz) tptp.emptyset)) (= Xx Xy)))))) (let ((_let_61 (= tptp.setukpairinjR1 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xz))) (let ((_let_2 (@ tptp.setadjoin Xx))) (=> (= (@ (@ tptp.setadjoin (@ _let_2 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_2 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset))) (=> (= Xz Xu) (= Xy Xu))))))))) (let ((_let_62 (= tptp.setukpairinjR12 (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (let ((_let_2 (@ tptp.setadjoin (@ _let_1 tptp.emptyset)))) (=> (= Xx Xy) (= (@ _let_2 (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ _let_2 tptp.emptyset))))))))) (let ((_let_63 (= tptp.setukpairinjR11 (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (= Xx Xy) (= (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ _let_1 tptp.emptyset)))))))) (let ((_let_64 (= tptp.setukpairinjL (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (=> (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu)) (= Xx Xz)))))) (let ((_let_65 (= tptp.setukpairinjL2 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xz))) (let ((_let_2 (@ tptp.setadjoin Xx))) (=> (= (@ (@ tptp.setadjoin (@ _let_2 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_2 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset))) (= Xx Xz)))))))) (let ((_let_66 (= tptp.cartprodfstin (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ (@ tptp.in (@ tptp.kfst Xu)) A)))))) (let ((_let_67 (= tptp.kfstpairEq (forall ((Xx $$unsorted) (Xy $$unsorted)) (= (@ tptp.kfst (@ (@ tptp.kpair Xx) Xy)) Xx))))) (let ((_let_68 (= tptp.theprop (forall ((X $$unsorted)) (=> (@ tptp.singleton X) (@ (@ tptp.in (@ tptp.setunion X)) X)))))) (let ((_let_69 (= tptp.kfstsingleton (forall ((Xu $$unsorted)) (=> (@ tptp.iskpair Xu) (@ tptp.singleton (@ (@ tptp.dsetconstr (@ tptp.setunion Xu)) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) Xu))))))))) (let ((_let_70 (= tptp.setukpairinjL1 (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (@ (@ tptp.in (@ (@ tptp.setadjoin Xz) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (= Xx Xz))))))) (let ((_let_71 (= tptp.singletonsuniq (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy)))))) (let ((_let_72 (= tptp.ex1I2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (let ((_let_73 (= tptp.ex1I (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (=> (@ Xphi Xx) (=> (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xy) (= Xy Xx)))) (@ (@ tptp.ex1 A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))))))))) (let ((_let_74 (= tptp.ex1E1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))))))) (let ((_let_75 (= tptp.ex1 (lambda ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) (let ((_let_76 (= tptp.singletonprop (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) A) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))))) (let ((_let_77 (= tptp.setunionsingleton (forall ((Xx $$unsorted)) (= (@ tptp.setunion (@ (@ tptp.setadjoin Xx) tptp.emptyset)) Xx))))) (let ((_let_78 (forall ((A $$unsorted)) (@ (@ tptp.subset A) (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset)))))) (let ((_let_79 (= tptp.setunionsingleton2 _let_78))) (let ((_let_80 (forall ((A $$unsorted)) (@ (@ tptp.subset (@ tptp.setunion (@ (@ tptp.setadjoin A) tptp.emptyset))) A)))) (let ((_let_81 (= tptp.setunionsingleton1 _let_80))) (let ((_let_82 (= tptp.setunionE2 (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((X $$unsorted)) (and (@ (@ tptp.in X) A) (@ (@ tptp.in Xx) X)))))))) (let ((_let_83 (= tptp.cartprodmempair (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (@ tptp.iskpair Xu)))))) (let ((_let_84 (= tptp.cartprodmempair1 (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (=> (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B)) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (exists ((Xy $$unsorted)) (and (@ (@ tptp.in Xy) B) (= Xu (@ (@ tptp.kpair Xx) Xy))))))))))) (let ((_let_85 (= tptp.cartprodpairin (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B))))))))) (let ((_let_86 (= tptp.ubforcartprodlem3 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ tptp.powerset (@ tptp.powerset (@ (@ tptp.binunion A) B))))))))))) (let ((_let_87 (= tptp.ubforcartprodlem2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (@ tptp.powerset (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))))))) (let ((_let_88 (= tptp.ubforcartprodlem1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.subset (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))) (@ tptp.powerset (@ (@ tptp.binunion A) B))))))))))) (let ((_let_89 (= tptp.upairinpowunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))))) (let ((_let_90 (= tptp.upairsubunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (@ (@ tptp.binunion A) B))))))))) (let ((_let_91 (= tptp.upairset2E (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy))))))) (let ((_let_92 (= tptp.singletoninpowunion (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset (@ (@ tptp.binunion A) B)))))))) (let ((_let_93 (= tptp.singletoninpowerset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset A))))))) (let ((_let_94 (= tptp.singletonsubset (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) tptp.emptyset)) A)))))) (let ((_let_95 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ tptp.iskpair (@ (@ tptp.kpair Xx) Xy))))) (let ((_let_96 (= tptp.kpairp _let_95))) (let ((_let_97 (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ tptp.iskpair (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset))))))) (let ((_let_98 (= tptp.kpairiskpair _let_97))) (let ((_let_99 (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ (@ tptp.in Xy) (@ tptp.setunion (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)))))))) (let ((_let_100 (= tptp.setukpairIR _let_99))) (let ((_let_101 (forall ((Xx $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (@ (@ tptp.in Xx) (@ tptp.setunion (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)))))))) (let ((_let_102 (= tptp.setukpairIL _let_101))) (let ((_let_103 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) (let ((_let_104 (= tptp.secondinupair _let_103))) (let ((_let_105 (= tptp.symdiffIneg2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (not (@ _let_1 (@ (@ tptp.symdiff A) B)))))))))) (let ((_let_106 (= tptp.symdiffIneg1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 B) (not (@ _let_1 (@ (@ tptp.symdiff A) B)))))))))) (let ((_let_107 (= tptp.symdiffI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.symdiff A) B))))))))) (let ((_let_108 (= tptp.symdiffI1 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.symdiff A) B))))))))) (let ((_let_109 (= tptp.symdiffE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.symdiff A) B)) (forall ((Xphi Bool)) (let ((_let_1 (@ tptp.in Xx))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ _let_1 A))) (=> (=> _let_3 (=> (not _let_2) Xphi)) (=> (=> (not _let_3) (=> _let_2 Xphi)) Xphi))))))))))) (let ((_let_110 (= tptp.setminusSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.setminus A) B) tptp.emptyset) (@ (@ tptp.subset A) B)))))) (let ((_let_111 (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.setminus A) B)) A)))) (let ((_let_112 (= tptp.setminusLsub _let_111))) (let ((_let_113 (= tptp.setminusIRneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (not (@ _let_1 (@ (@ tptp.setminus A) B))))))))) (let ((_let_114 (= tptp.setminusILneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 A)) (not (@ _let_1 (@ (@ tptp.setminus A) B))))))))) (let ((_let_115 (= tptp.setminusELneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 (@ (@ tptp.setminus A) B))) (=> (not (@ _let_1 B)) (not (@ _let_1 A))))))))) (let ((_let_116 (= tptp.setminusERneg (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (not (@ _let_1 (@ (@ tptp.setminus A) B))) (=> (@ _let_1 A) (@ _let_1 B)))))))) (let ((_let_117 (= tptp.setminusSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.setminus A) B) tptp.emptyset)))))) (let ((_let_118 (= tptp.setminusER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.setminus A) B)) (not (@ _let_1 B)))))))) (let ((_let_119 (= tptp.setminusEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.setminus A) B)) (@ _let_1 A))))))) (let ((_let_120 (= tptp.setminusI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.setminus A) B))))))))) (let ((_let_121 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.binintersect A))) (= (@ _let_1 (@ (@ tptp.binunion B) C)) (@ (@ tptp.binunion (@ _let_1 B)) (@ _let_1 C))))))) (let ((_let_122 (= tptp.bs114d _let_121))) (let ((_let_123 (= tptp.binintersectSubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) A) (@ (@ tptp.subset A) B)))))) (let ((_let_124 (= tptp.binintersectSubset4 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (= (@ (@ tptp.binintersect A) B) B)))))) (let ((_let_125 (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) B)))) (let ((_let_126 (= tptp.binintersectRsub _let_125))) (let ((_let_127 (= tptp.disjointsetsI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (exists ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (and (@ _let_1 A) (@ _let_1 B))))) (= (@ (@ tptp.binintersect A) B) tptp.emptyset)))))) (let ((_let_128 (= tptp.binintersectER (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect A) B)) (@ _let_1 B))))))) (let ((_let_129 (= tptp.binintersectSubset3 (forall ((A $$unsorted) (B $$unsorted)) (=> (= (@ (@ tptp.binintersect A) B) B) (@ (@ tptp.subset B) A)))))) (let ((_let_130 (= tptp.binintersectSubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (= (@ (@ tptp.binintersect A) B) A)))))) (let ((_let_131 (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset (@ (@ tptp.binintersect A) B)) A)))) (let ((_let_132 (= tptp.binintersectLsub _let_131))) (let ((_let_133 (= tptp.binintersectEL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binintersect A) B)) (@ _let_1 A))))))) (let ((_let_134 (= tptp.binintersectSubset5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B))))))))) (let ((_let_135 (= tptp.binintersectI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binintersect A) B))))))))) (let ((_let_136 (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset B) (@ (@ tptp.binunion A) B))))) (let ((_let_137 (= tptp.binunionRsub _let_136))) (let ((_let_138 (forall ((A $$unsorted) (B $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.binunion A) B))))) (let ((_let_139 (= tptp.binunionLsub _let_138))) (let ((_let_140 (= tptp.binunionE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binunion A) B)) (or (@ _let_1 A) (@ _let_1 B)))))))) (let ((_let_141 (= tptp.binunionEcases (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xphi Bool)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 (@ (@ tptp.binunion A) B)) (=> (=> (@ _let_1 A) Xphi) (=> (=> (@ _let_1 B) Xphi) Xphi)))))))) (let ((_let_142 (= tptp.binunionIR (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.binunion A) B)))))))) (let ((_let_143 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) (let ((_let_144 (= tptp.upairset2IR _let_143))) (let ((_let_145 (= tptp.binunionIL (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.binunion A) B)))))))) (let ((_let_146 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.subset (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) A)))) (let ((_let_147 (= tptp.sepSubset _let_146))) (let ((_let_148 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (@ (@ tptp.in (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ tptp.powerset A))))) (let ((_let_149 (= tptp.sepInPowerset _let_148))) (let ((_let_150 (= tptp.powersetsubset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.subset (@ tptp.powerset A)) (@ tptp.powerset B))))))) (let ((_let_151 (forall ((A $$unsorted)) (@ (@ tptp.in A) (@ tptp.powerset A))))) (let ((_let_152 (= tptp.inPowerset _let_151))) (let ((_let_153 (= tptp.powersetE1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (@ (@ tptp.subset B) A)))))) (let ((_let_154 (= tptp.powersetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset B) A) (@ (@ tptp.in B) (@ tptp.powerset A))))))) (let ((_let_155 (= tptp.subsetemptysetimpeq (forall ((A $$unsorted)) (=> (@ (@ tptp.subset A) tptp.emptyset) (= A tptp.emptyset)))))) (let ((_let_156 (= tptp.setextsub (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (=> (@ (@ tptp.subset B) A) (= A B))))))) (let ((_let_157 (= tptp.subset2powerset (forall ((A $$unsorted) (B $$unsorted)) (=> (@ (@ tptp.subset A) B) (@ (@ tptp.in A) (@ tptp.powerset B))))))) (let ((_let_158 (= tptp.setadjoinSub2 (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.setadjoin Xx) B)))))))) (let ((_let_159 (forall ((Xx $$unsorted) (A $$unsorted)) (@ (@ tptp.subset A) (@ (@ tptp.setadjoin Xx) A))))) (let ((_let_160 (= tptp.setadjoinSub _let_159))) (let ((_let_161 (= tptp.subsetTrans (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (=> (@ _let_1 B) (=> (@ (@ tptp.subset B) C) (@ _let_1 C)))))))) (let ((_let_162 (forall ((A $$unsorted)) (@ (@ tptp.subset A) A)))) (let ((_let_163 (= tptp.subsetRefl _let_162))) (let ((_let_164 (= tptp.notequalI2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (= A B))))))))) (let ((_let_165 (= tptp.notequalI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (@ (@ tptp.subset A) B)) (not (= A B))))))) (let ((_let_166 (= tptp.notsubsetI (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (=> (not (@ _let_1 B)) (not (@ (@ tptp.subset A) B))))))))) (let ((_let_167 (= tptp.subsetE2 (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (not (@ _let_1 B)) (not (@ _let_1 A))))))))) (let ((_let_168 (= tptp.subsetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.subset A) B) (=> (@ _let_1 A) (@ _let_1 B)))))))) (let ((_let_169 (forall ((A $$unsorted)) (@ (@ tptp.subset tptp.emptyset) A)))) (let ((_let_170 (= tptp.emptysetsubset _let_169))) (let ((_let_171 (= tptp.subsetI2 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B)))))) (let ((_let_172 (= tptp.eqimpsubset1 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset A) B)))))) (let ((_let_173 (= tptp.eqimpsubset2 (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (@ (@ tptp.subset B) A)))))) (let ((_let_174 (= tptp.subsetI1 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (@ (@ tptp.subset A) B)))))) (let ((_let_175 (= tptp.dsetconstr__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (forall ((Xy $$unsorted)) (=> (@ (@ tptp.in Xy) B) (=> (= Xx Xy) (= (@ Xphi Xx) (@ Xpsi Xy))))))) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ (@ tptp.dsetconstr B) (lambda ((Xx $$unsorted)) (@ Xpsi Xx))))))))))) (let ((_let_176 (= tptp.descr__Cong (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ Xphi Xx) (@ Xpsi Xy)))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xpsi Xx))) (= (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xpsi Xx))))))))))) (let ((_let_177 (= tptp.exuEu (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))))) (let ((_let_178 (= tptp.omega__Cong (= tptp.omega tptp.omega)))) (let ((_let_179 (= tptp.setunion__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.setunion A) (@ tptp.setunion B))))))) (let ((_let_180 (= tptp.powerset__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (= (@ tptp.powerset A) (@ tptp.powerset B))))))) (let ((_let_181 (= tptp.setadjoin__Cong (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (forall ((Xz $$unsorted) (Xu $$unsorted)) (=> (= Xz Xu) (= (@ (@ tptp.setadjoin Xx) Xz) (@ (@ tptp.setadjoin Xy) Xu))))))))) (let ((_let_182 (= tptp.emptyset__Cong (= tptp.emptyset tptp.emptyset)))) (let ((_let_183 (= tptp.exu__Cong (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ Xphi Xx) (@ Xpsi Xy)))) (= (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xpsi Xx))))))))) (let ((_let_184 (= tptp.exuE3u (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy))))))))) (let ((_let_185 (= tptp.in__Cong (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (= (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) B))))))))) (let ((_let_186 (= tptp.inCongP (forall ((A $$unsorted) (B $$unsorted)) (=> (= A B) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (=> (@ (@ tptp.in Xx) A) (@ (@ tptp.in Xy) B))))))))) (let ((_let_187 (= tptp.exuI2 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) (let ((_let_188 (= tptp.exuI3 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (@ Xphi Xx)) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ Xphi Xx) (=> (@ Xphi Xy) (= Xx Xy)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (let ((_let_189 (= tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))))) (let ((_let_190 (= tptp.notdallE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))) (let ((_let_191 (= tptp.notdexE (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))) (let ((_let_192 (= tptp.prop2set2propI (forall ((Xphi Bool)) (=> Xphi (@ tptp.set2prop (@ tptp.prop2set Xphi))))))) (let ((_let_193 (= tptp.prop2setI (forall ((Xphi Bool)) (=> Xphi (@ (@ tptp.in tptp.emptyset) (@ tptp.prop2set Xphi))))))) (let ((_let_194 (= tptp.quantDeMorgan4 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx))))))))) (let ((_let_195 (= tptp.quantDeMorgan3 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))) (let ((_let_196 (= tptp.quantDeMorgan2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (not (@ Xphi Xx)))) (not (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))))))))) (let ((_let_197 (= tptp.quantDeMorgan1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (not (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) A) (@ Xphi Xx)))) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (not (@ Xphi Xx))))))))) (let ((_let_198 (= tptp.vacuousDall (forall ((Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (@ Xphi Xx)))))) (let ((_let_199 (= tptp.emptyE1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (=> (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) (@ Xphi Xx))) (=> (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) tptp.emptyset) false)))))) (let ((_let_200 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) (let ((_let_201 (= tptp.upairsetIR _let_200))) (let ((_let_202 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))))) (let ((_let_203 (= tptp.upairsetIL _let_202))) (let ((_let_204 (= tptp.upairsetE (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (=> (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (or (= Xz Xx) (= Xz Xy))))))) (let ((_let_205 (= tptp.singletonsswitch (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (let ((_let_206 (= tptp.eqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (= Xx Xy) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))))) (let ((_let_207 (= tptp.notinsingleton (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (not (= Xx Xy)) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))))) (let ((_let_208 (= tptp.uniqinunit (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (= Xx Xy)))))) (let ((_let_209 (= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (and (@ (@ tptp.in Xx) A) true))))))) (let ((_let_210 (= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy Xx))))))))) (let ((_let_211 (= tptp.subPowSU (forall ((A $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.powerset (@ tptp.setunion A))))))))) (let ((_let_212 (= tptp.setunionE (forall ((A $$unsorted) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.setunion A)) (forall ((Xphi Bool)) (=> (forall ((B $$unsorted)) (=> (@ (@ tptp.in Xx) B) (=> (@ (@ tptp.in B) A) Xphi))) Xphi))))))) (let ((_let_213 (= tptp.setunionI (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (=> (@ (@ tptp.in B) A) (@ _let_1 (@ tptp.setunion A))))))))) (let ((_let_214 (= tptp.powersetE (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ (@ tptp.in B) (@ tptp.powerset A)) (=> (@ _let_1 B) (@ _let_1 A)))))))) (let ((_let_215 (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) (let ((_let_216 (= tptp.emptyInPowerset _let_215))) (let ((_let_217 (forall ((A $$unsorted)) (@ (@ tptp.in tptp.emptyset) (@ tptp.powerset A))))) (let ((_let_218 (= tptp.emptyinPowerset _let_217))) (let ((_let_219 (= tptp.powersetI (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (@ (@ tptp.in B) (@ tptp.powerset A))))))) (let ((_let_220 (= tptp.setoftrueEq (forall ((A $$unsorted)) (= (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) true)) A))))) (let ((_let_221 (= tptp.setadjoinOr (forall ((Xx $$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_222 (= tptp.setadjoinE (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (=> (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) A)) (forall ((Xphi Bool)) (=> (=> (= Xy Xx) Xphi) (=> (=> (@ (@ tptp.in Xy) A) Xphi) Xphi)))))))) (let ((_let_223 (= tptp.setadjoinIR (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.setadjoin Xx) A)))))))) (let ((_let_224 (@ (@ tptp.setadjoin tptp.emptyset) tptp.emptyset))) (let ((_let_225 (@ tptp.in tptp.emptyset))) (let ((_let_226 (= tptp.emptyinunitempty (@ _let_225 _let_224)))) (let ((_let_227 (forall ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xx) Xy))))) (let ((_let_228 (= tptp.setadjoinIL _let_227))) (let ((_let_229 (= tptp.nonemptyI1 (forall ((A $$unsorted)) (=> (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A)) (@ tptp.nonempty A)))))) (let ((_let_230 (= 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_231 (= tptp.nonemptyE1 (forall ((A $$unsorted)) (=> (@ tptp.nonempty A) (exists ((Xx $$unsorted)) (@ (@ tptp.in Xx) A))))))) (let ((_let_232 (= tptp.nonempty (lambda ((Xx $$unsorted)) (not (= Xx tptp.emptyset)))))) (let ((_let_233 (= tptp.setbeta (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (= (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx)))))))) (let ((_let_234 (= tptp.noeltsimpempty (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))) (let ((_let_235 (= tptp.emptyI (forall ((A $$unsorted)) (=> (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))) (= A tptp.emptyset)))))) (let ((_let_236 (= tptp.setext (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 A) (@ _let_1 B)))) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 B) (@ _let_1 A)))) (= A B))))))) (let ((_let_237 (= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (exists ((Xx $$unsorted)) (@ Xphi Xx))))))) (let ((_let_238 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_239 (= tptp.notinemptyset _let_238))) (let ((_let_240 (= tptp.emptysetimpfalse (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) false))))) (let ((_let_241 (= tptp.emptysetE (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.emptyset) (forall ((Xphi Bool)) Xphi)))))) (let ((_let_242 (= tptp.prop2setE (forall ((Xphi Bool) (Xx $$unsorted)) (=> (@ (@ tptp.in Xx) (@ tptp.prop2set Xphi)) Xphi))))) (let ((_let_243 (= 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_244 (= 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_245 (= 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_246 (= 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_247 (= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (=> (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))))) (let ((_let_248 (= tptp.wellorderingAx (forall ((A $$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_249 (= 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_250 (= 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_251 (= 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 $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (=> (@ _let_1 tptp.omega) (@ _let_1 A))))))))) (let ((_let_252 (= tptp.omegaSAx (forall ((Xx $$unsorted)) (=> (@ (@ tptp.in Xx) tptp.omega) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega)))))) (let ((_let_253 (@ _let_225 tptp.omega))) (let ((_let_254 (= tptp.omega0Ax _let_253))) (let ((_let_255 (= tptp.setunionAx (forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (exists ((B $$unsorted)) (and (@ (@ tptp.in Xx) B) (@ (@ tptp.in B) A)))))))) (let ((_let_256 (= tptp.powersetAx (forall ((A $$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_257 (= tptp.setadjoinAx (forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xy Xx) (@ _let_1 A)))))))) (let ((_let_258 (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (let ((_let_259 (= tptp.emptysetAx _let_258))) (let ((_let_260 (= tptp.setextAx (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B)))) (= A B)))))) (let ((_let_261 (= tptp.exu (lambda ((Xphi (-> $$unsorted Bool))) (exists ((Xx $$unsorted)) (and (@ Xphi Xx) (forall ((Xy $$unsorted)) (=> (@ Xphi Xy) (= Xx Xy))))))))) (let ((_let_262 (forall ((A $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_8816 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8816) A)) (= Xx (@ tptp.setunion (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (= Xz Xx))))))))) (let ((_let_263 (tptp.dsetconstr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_5))) (let ((_let_264 (tptp.setunion _let_263))) (let ((_let_265 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_264))) (let ((_let_266 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_267 (not _let_266))) (let ((_let_268 (or _let_267 _let_267 _let_265))) (let ((_let_269 (not))) (let ((_let_270 (=>))) (let ((_let_271 (forall ((A $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_8857 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8857) A)) (= BOUND_VARIABLE_8857 (@ tptp.setunion (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (= Xz BOUND_VARIABLE_8857))))))))) (let ((_let_272 (tptp.prop2set BOOLEAN_TERM_VARIABLE_12578))) (let ((_let_273 (@))) (let ((_let_274 (TRANS (CONG (REFL :args (tptp.prop2set)) (MACRO_SR_PRED_INTRO :args ((= true BOOLEAN_TERM_VARIABLE_12578))) :args _let_273) (THEORY_PREPROCESS :args ((= (@ tptp.prop2set BOOLEAN_TERM_VARIABLE_12578) _let_272)))))) (let ((_let_275 (REFL :args (_let_225)))) (let ((_let_276 (tptp.setadjoin tptp.emptyset tptp.emptyset))) (let ((_let_277 (EQ_RESOLVE (ASSUME :args (_let_261)) (MACRO_SR_EQ_INTRO :args (_let_261 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_278 (EQ_RESOLVE (ASSUME :args (_let_260)) (MACRO_SR_EQ_INTRO :args (_let_260 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_279 (ASSUME :args (_let_259)))) (let ((_let_280 (EQ_RESOLVE (ASSUME :args (_let_257)) (MACRO_SR_EQ_INTRO :args (_let_257 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_281 (EQ_RESOLVE (ASSUME :args (_let_256)) (MACRO_SR_EQ_INTRO :args (_let_256 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_282 (EQ_RESOLVE (ASSUME :args (_let_255)) (MACRO_SR_EQ_INTRO :args (_let_255 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_283 (ASSUME :args (_let_254)))) (let ((_let_284 (EQ_RESOLVE (ASSUME :args (_let_252)) (MACRO_SR_EQ_INTRO :args (_let_252 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_285 (EQ_RESOLVE (ASSUME :args (_let_251)) (MACRO_SR_EQ_INTRO :args (_let_251 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_286 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_250)) (MACRO_SR_EQ_INTRO :args (_let_250 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :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_287 (EQ_RESOLVE (ASSUME :args (_let_249)) (MACRO_SR_EQ_INTRO :args (_let_249 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_288 (EQ_RESOLVE (ASSUME :args (_let_248)) (MACRO_SR_EQ_INTRO :args (_let_248 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_289 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_247)) (MACRO_SR_EQ_INTRO :args (_let_247 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.descrp (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_290 (EQ_RESOLVE (ASSUME :args (_let_246)) (MACRO_SR_EQ_INTRO :args (_let_246 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_291 (EQ_RESOLVE (ASSUME :args (_let_245)) (MACRO_SR_EQ_INTRO :args (_let_245 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_292 (EQ_RESOLVE (ASSUME :args (_let_244)) (MACRO_SR_EQ_INTRO :args (_let_244 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_293 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_243)) (MACRO_SR_EQ_INTRO :args (_let_243 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.exuE1 (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_294 (EQ_RESOLVE (ASSUME :args (_let_242)) (MACRO_SR_EQ_INTRO :args (_let_242 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_295 (EQ_RESOLVE (ASSUME :args (_let_241)) (MACRO_SR_EQ_INTRO :args (_let_241 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_296 (EQ_RESOLVE (ASSUME :args (_let_240)) (MACRO_SR_EQ_INTRO :args (_let_240 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_297 (ASSUME :args (_let_239)))) (let ((_let_298 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_237)) (MACRO_SR_EQ_INTRO :args (_let_237 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.exuE3e (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (not (@ Xphi Xx))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_299 (EQ_RESOLVE (ASSUME :args (_let_236)) (MACRO_SR_EQ_INTRO :args (_let_236 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_300 (EQ_RESOLVE (ASSUME :args (_let_235)) (MACRO_SR_EQ_INTRO :args (_let_235 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_301 (EQ_RESOLVE (ASSUME :args (_let_234)) (MACRO_SR_EQ_INTRO :args (_let_234 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_302 (EQ_RESOLVE (ASSUME :args (_let_233)) (MACRO_SR_EQ_INTRO :args (_let_233 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_303 (EQ_RESOLVE (ASSUME :args (_let_232)) (MACRO_SR_EQ_INTRO :args (_let_232 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_304 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_231)) (MACRO_SR_EQ_INTRO :args (_let_231 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :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_305 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_230)) (MACRO_SR_EQ_INTRO :args (_let_230 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :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_306 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_229)) (MACRO_SR_EQ_INTRO :args (_let_229 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.nonemptyI1 (forall ((A $$unsorted) (BOUND_VARIABLE_5613 $$unsorted)) (or (not (@ (@ tptp.in BOUND_VARIABLE_5613) A)) (@ tptp.nonempty A)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_307 (ASSUME :args (_let_228)))) (let ((_let_308 (ASSUME :args (_let_226)))) (let ((_let_309 (EQ_RESOLVE (ASSUME :args (_let_223)) (MACRO_SR_EQ_INTRO :args (_let_223 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_310 (EQ_RESOLVE (ASSUME :args (_let_222)) (MACRO_SR_EQ_INTRO :args (_let_222 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_311 (EQ_RESOLVE (ASSUME :args (_let_221)) (MACRO_SR_EQ_INTRO :args (_let_221 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_312 (EQ_RESOLVE (ASSUME :args (_let_220)) (MACRO_SR_EQ_INTRO :args (_let_220 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_313 (EQ_RESOLVE (ASSUME :args (_let_219)) (MACRO_SR_EQ_INTRO :args (_let_219 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_314 (ASSUME :args (_let_218)))) (let ((_let_315 (ASSUME :args (_let_216)))) (let ((_let_316 (EQ_RESOLVE (ASSUME :args (_let_214)) (MACRO_SR_EQ_INTRO :args (_let_214 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_317 (EQ_RESOLVE (ASSUME :args (_let_213)) (MACRO_SR_EQ_INTRO :args (_let_213 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_318 (EQ_RESOLVE (ASSUME :args (_let_212)) (MACRO_SR_EQ_INTRO :args (_let_212 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_319 (EQ_RESOLVE (ASSUME :args (_let_211)) (MACRO_SR_EQ_INTRO :args (_let_211 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_320 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_210)) (MACRO_SR_EQ_INTRO :args (_let_210 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.exuE2 (forall ((Xphi (-> $$unsorted Bool))) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (not (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xx Xy))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_321 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_209)) (MACRO_SR_EQ_INTRO :args (_let_209 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.nonemptyImpWitness (forall ((A $$unsorted)) (or (not (@ tptp.nonempty A)) (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_322 (EQ_RESOLVE (ASSUME :args (_let_208)) (MACRO_SR_EQ_INTRO :args (_let_208 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_323 (EQ_RESOLVE (ASSUME :args (_let_207)) (MACRO_SR_EQ_INTRO :args (_let_207 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_324 (EQ_RESOLVE (ASSUME :args (_let_206)) (MACRO_SR_EQ_INTRO :args (_let_206 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_325 (EQ_RESOLVE (ASSUME :args (_let_205)) (MACRO_SR_EQ_INTRO :args (_let_205 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_326 (EQ_RESOLVE (ASSUME :args (_let_204)) (MACRO_SR_EQ_INTRO :args (_let_204 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_327 (ASSUME :args (_let_203)))) (let ((_let_328 (ASSUME :args (_let_201)))) (let ((_let_329 (EQ_RESOLVE (ASSUME :args (_let_199)) (MACRO_SR_EQ_INTRO :args (_let_199 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_330 (EQ_RESOLVE (ASSUME :args (_let_198)) (MACRO_SR_EQ_INTRO :args (_let_198 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_331 (EQ_RESOLVE (ASSUME :args (_let_197)) (MACRO_SR_EQ_INTRO :args (_let_197 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_332 (EQ_RESOLVE (ASSUME :args (_let_196)) (MACRO_SR_EQ_INTRO :args (_let_196 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_333 (EQ_RESOLVE (ASSUME :args (_let_195)) (MACRO_SR_EQ_INTRO :args (_let_195 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_334 (EQ_RESOLVE (ASSUME :args (_let_194)) (MACRO_SR_EQ_INTRO :args (_let_194 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_335 (EQ_RESOLVE (ASSUME :args (_let_193)) (MACRO_SR_EQ_INTRO :args (_let_193 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_336 (EQ_RESOLVE (ASSUME :args (_let_192)) (MACRO_SR_EQ_INTRO :args (_let_192 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_337 (EQ_RESOLVE (ASSUME :args (_let_191)) (MACRO_SR_EQ_INTRO :args (_let_191 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_338 (EQ_RESOLVE (ASSUME :args (_let_190)) (MACRO_SR_EQ_INTRO :args (_let_190 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_339 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_189)) (MACRO_SR_EQ_INTRO :args (_let_189 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.exuI1 (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_6040 $$unsorted)) (or (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (not (@ Xphi BOUND_VARIABLE_6040)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_6040))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_340 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_188)) (MACRO_SR_EQ_INTRO :args (_let_188 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.exuI3 (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_6076 $$unsorted)) (or (not (@ Xphi BOUND_VARIABLE_6076)) (not (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (@ Xphi Xx)) (not (@ Xphi Xy)) (= Xx Xy)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_341 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_187)) (MACRO_SR_EQ_INTRO :args (_let_187 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.exuI2 (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_6096 $$unsorted)) (or (not (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy BOUND_VARIABLE_6096)))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_342 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_186)) (MACRO_SR_EQ_INTRO :args (_let_186 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.inCongP true))))) (let ((_let_343 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_185)) (MACRO_SR_EQ_INTRO :args (_let_185 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.in__Cong true))))) (let ((_let_344 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_184)) (MACRO_SR_EQ_INTRO :args (_let_184 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.exuE3u (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_6206 $$unsorted) (BOUND_VARIABLE_6204 $$unsorted)) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ Xphi BOUND_VARIABLE_6204)) (not (@ Xphi BOUND_VARIABLE_6206)) (= BOUND_VARIABLE_6204 BOUND_VARIABLE_6206)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_345 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_183)) (MACRO_SR_EQ_INTRO :args (_let_183 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.exu__Cong (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (or (not (forall ((Xy $$unsorted)) (= (@ Xpsi Xy) (@ Xphi Xy)))) (= (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xpsi Xx))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_346 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_182)) (MACRO_SR_EQ_INTRO :args (_let_182 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.emptyset__Cong true))))) (let ((_let_347 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_181)) (MACRO_SR_EQ_INTRO :args (_let_181 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.setadjoin__Cong true))))) (let ((_let_348 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_180)) (MACRO_SR_EQ_INTRO :args (_let_180 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.powerset__Cong true))))) (let ((_let_349 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_179)) (MACRO_SR_EQ_INTRO :args (_let_179 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.setunion__Cong true))))) (let ((_let_350 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_178)) (MACRO_SR_EQ_INTRO :args (_let_178 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.omega__Cong true))))) (let ((_let_351 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_177)) (MACRO_SR_EQ_INTRO :args (_let_177 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.exuEu (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_6316 $$unsorted) (BOUND_VARIABLE_6314 $$unsorted)) (or (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ Xphi BOUND_VARIABLE_6314)) (not (@ Xphi BOUND_VARIABLE_6316)) (= BOUND_VARIABLE_6314 BOUND_VARIABLE_6316)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_352 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_176)) (MACRO_SR_EQ_INTRO :args (_let_176 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.descr__Cong (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (or (not (forall ((Xy $$unsorted)) (= (@ Xpsi Xy) (@ Xphi Xy)))) (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ tptp.exu (lambda ((Xx $$unsorted)) (@ Xpsi Xx)))) (= (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xpsi Xx))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_353 (EQ_RESOLVE (ASSUME :args (_let_175)) (MACRO_SR_EQ_INTRO :args (_let_175 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_354 (EQ_RESOLVE (ASSUME :args (_let_174)) (MACRO_SR_EQ_INTRO :args (_let_174 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_355 (EQ_RESOLVE (ASSUME :args (_let_173)) (MACRO_SR_EQ_INTRO :args (_let_173 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_356 (EQ_RESOLVE (ASSUME :args (_let_172)) (MACRO_SR_EQ_INTRO :args (_let_172 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_357 (EQ_RESOLVE (ASSUME :args (_let_171)) (MACRO_SR_EQ_INTRO :args (_let_171 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_358 (ASSUME :args (_let_170)))) (let ((_let_359 (EQ_RESOLVE (ASSUME :args (_let_168)) (MACRO_SR_EQ_INTRO :args (_let_168 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_360 (EQ_RESOLVE (ASSUME :args (_let_167)) (MACRO_SR_EQ_INTRO :args (_let_167 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_361 (EQ_RESOLVE (ASSUME :args (_let_166)) (MACRO_SR_EQ_INTRO :args (_let_166 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_362 (EQ_RESOLVE (ASSUME :args (_let_165)) (MACRO_SR_EQ_INTRO :args (_let_165 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_363 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_164)) (MACRO_SR_EQ_INTRO :args (_let_164 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.notequalI2 true))))) (let ((_let_364 (ASSUME :args (_let_163)))) (let ((_let_365 (EQ_RESOLVE (ASSUME :args (_let_161)) (MACRO_SR_EQ_INTRO :args (_let_161 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_366 (ASSUME :args (_let_160)))) (let ((_let_367 (EQ_RESOLVE (ASSUME :args (_let_158)) (MACRO_SR_EQ_INTRO :args (_let_158 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_368 (EQ_RESOLVE (ASSUME :args (_let_157)) (MACRO_SR_EQ_INTRO :args (_let_157 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_369 (EQ_RESOLVE (ASSUME :args (_let_156)) (MACRO_SR_EQ_INTRO :args (_let_156 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_370 (EQ_RESOLVE (ASSUME :args (_let_155)) (MACRO_SR_EQ_INTRO :args (_let_155 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_371 (EQ_RESOLVE (ASSUME :args (_let_154)) (MACRO_SR_EQ_INTRO :args (_let_154 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_372 (EQ_RESOLVE (ASSUME :args (_let_153)) (MACRO_SR_EQ_INTRO :args (_let_153 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_373 (ASSUME :args (_let_152)))) (let ((_let_374 (EQ_RESOLVE (ASSUME :args (_let_150)) (MACRO_SR_EQ_INTRO :args (_let_150 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_375 (ASSUME :args (_let_149)))) (let ((_let_376 (ASSUME :args (_let_147)))) (let ((_let_377 (EQ_RESOLVE (ASSUME :args (_let_145)) (MACRO_SR_EQ_INTRO :args (_let_145 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_378 (ASSUME :args (_let_144)))) (let ((_let_379 (EQ_RESOLVE (ASSUME :args (_let_142)) (MACRO_SR_EQ_INTRO :args (_let_142 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_380 (EQ_RESOLVE (ASSUME :args (_let_141)) (MACRO_SR_EQ_INTRO :args (_let_141 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_381 (EQ_RESOLVE (ASSUME :args (_let_140)) (MACRO_SR_EQ_INTRO :args (_let_140 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_382 (ASSUME :args (_let_139)))) (let ((_let_383 (ASSUME :args (_let_137)))) (let ((_let_384 (EQ_RESOLVE (ASSUME :args (_let_135)) (MACRO_SR_EQ_INTRO :args (_let_135 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_385 (EQ_RESOLVE (ASSUME :args (_let_134)) (MACRO_SR_EQ_INTRO :args (_let_134 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_386 (EQ_RESOLVE (ASSUME :args (_let_133)) (MACRO_SR_EQ_INTRO :args (_let_133 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_387 (ASSUME :args (_let_132)))) (let ((_let_388 (EQ_RESOLVE (ASSUME :args (_let_130)) (MACRO_SR_EQ_INTRO :args (_let_130 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_389 (EQ_RESOLVE (ASSUME :args (_let_129)) (MACRO_SR_EQ_INTRO :args (_let_129 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_390 (EQ_RESOLVE (ASSUME :args (_let_128)) (MACRO_SR_EQ_INTRO :args (_let_128 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_391 (EQ_RESOLVE (ASSUME :args (_let_127)) (MACRO_SR_EQ_INTRO :args (_let_127 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_392 (ASSUME :args (_let_126)))) (let ((_let_393 (EQ_RESOLVE (ASSUME :args (_let_124)) (MACRO_SR_EQ_INTRO :args (_let_124 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_394 (EQ_RESOLVE (ASSUME :args (_let_123)) (MACRO_SR_EQ_INTRO :args (_let_123 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_395 (ASSUME :args (_let_122)))) (let ((_let_396 (EQ_RESOLVE (ASSUME :args (_let_120)) (MACRO_SR_EQ_INTRO :args (_let_120 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_397 (EQ_RESOLVE (ASSUME :args (_let_119)) (MACRO_SR_EQ_INTRO :args (_let_119 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_398 (EQ_RESOLVE (ASSUME :args (_let_118)) (MACRO_SR_EQ_INTRO :args (_let_118 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_399 (EQ_RESOLVE (ASSUME :args (_let_117)) (MACRO_SR_EQ_INTRO :args (_let_117 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_400 (EQ_RESOLVE (ASSUME :args (_let_116)) (MACRO_SR_EQ_INTRO :args (_let_116 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_401 (EQ_RESOLVE (ASSUME :args (_let_115)) (MACRO_SR_EQ_INTRO :args (_let_115 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_402 (EQ_RESOLVE (ASSUME :args (_let_114)) (MACRO_SR_EQ_INTRO :args (_let_114 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_403 (EQ_RESOLVE (ASSUME :args (_let_113)) (MACRO_SR_EQ_INTRO :args (_let_113 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_404 (ASSUME :args (_let_112)))) (let ((_let_405 (EQ_RESOLVE (ASSUME :args (_let_110)) (MACRO_SR_EQ_INTRO :args (_let_110 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_406 (EQ_RESOLVE (ASSUME :args (_let_109)) (MACRO_SR_EQ_INTRO :args (_let_109 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_407 (EQ_RESOLVE (ASSUME :args (_let_108)) (MACRO_SR_EQ_INTRO :args (_let_108 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_408 (EQ_RESOLVE (ASSUME :args (_let_107)) (MACRO_SR_EQ_INTRO :args (_let_107 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_409 (EQ_RESOLVE (ASSUME :args (_let_106)) (MACRO_SR_EQ_INTRO :args (_let_106 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_410 (EQ_RESOLVE (ASSUME :args (_let_105)) (MACRO_SR_EQ_INTRO :args (_let_105 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_411 (ASSUME :args (_let_104)))) (let ((_let_412 (ASSUME :args (_let_102)))) (let ((_let_413 (ASSUME :args (_let_100)))) (let ((_let_414 (ASSUME :args (_let_98)))) (let ((_let_415 (ASSUME :args (_let_96)))) (let ((_let_416 (EQ_RESOLVE (ASSUME :args (_let_94)) (MACRO_SR_EQ_INTRO :args (_let_94 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_417 (EQ_RESOLVE (ASSUME :args (_let_93)) (MACRO_SR_EQ_INTRO :args (_let_93 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_418 (EQ_RESOLVE (ASSUME :args (_let_92)) (MACRO_SR_EQ_INTRO :args (_let_92 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_419 (EQ_RESOLVE (ASSUME :args (_let_91)) (MACRO_SR_EQ_INTRO :args (_let_91 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_420 (EQ_RESOLVE (ASSUME :args (_let_90)) (MACRO_SR_EQ_INTRO :args (_let_90 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_421 (EQ_RESOLVE (ASSUME :args (_let_89)) (MACRO_SR_EQ_INTRO :args (_let_89 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_422 (EQ_RESOLVE (ASSUME :args (_let_88)) (MACRO_SR_EQ_INTRO :args (_let_88 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_423 (EQ_RESOLVE (ASSUME :args (_let_87)) (MACRO_SR_EQ_INTRO :args (_let_87 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_424 (EQ_RESOLVE (ASSUME :args (_let_86)) (MACRO_SR_EQ_INTRO :args (_let_86 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_425 (EQ_RESOLVE (ASSUME :args (_let_85)) (MACRO_SR_EQ_INTRO :args (_let_85 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_426 (EQ_RESOLVE (ASSUME :args (_let_84)) (MACRO_SR_EQ_INTRO :args (_let_84 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_427 (EQ_RESOLVE (ASSUME :args (_let_83)) (MACRO_SR_EQ_INTRO :args (_let_83 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_428 (EQ_RESOLVE (ASSUME :args (_let_82)) (MACRO_SR_EQ_INTRO :args (_let_82 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_429 (ASSUME :args (_let_81)))) (let ((_let_430 (ASSUME :args (_let_79)))) (let ((_let_431 (EQ_RESOLVE (ASSUME :args (_let_77)) (MACRO_SR_EQ_INTRO :args (_let_77 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_432 (EQ_RESOLVE (ASSUME :args (_let_76)) (MACRO_SR_EQ_INTRO :args (_let_76 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_433 (ASSUME :args (_let_75)))) (let ((_let_434 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_74)) (MACRO_SR_EQ_INTRO :args (_let_74 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.ex1E1 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (or (not (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_435 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_73)) (MACRO_SR_EQ_INTRO :args (_let_73 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.ex1I (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ (@ tptp.in Xy) A)) (not (@ Xphi Xy)) (= Xx Xy)))) (@ (@ tptp.ex1 A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_436 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_72)) (MACRO_SR_EQ_INTRO :args (_let_72 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.ex1I2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_7167 $$unsorted)) (or (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_7138 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (@ (@ tptp.in BOUND_VARIABLE_7138) A)) (not (@ Xphi BOUND_VARIABLE_7138)) (= Xx BOUND_VARIABLE_7138)))) (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (not (@ (@ tptp.in BOUND_VARIABLE_7167) A)) (not (@ Xphi BOUND_VARIABLE_7167))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_437 (EQ_RESOLVE (ASSUME :args (_let_71)) (MACRO_SR_EQ_INTRO :args (_let_71 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_438 (EQ_RESOLVE (ASSUME :args (_let_70)) (MACRO_SR_EQ_INTRO :args (_let_70 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_439 (EQ_RESOLVE (ASSUME :args (_let_69)) (MACRO_SR_EQ_INTRO :args (_let_69 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_440 (EQ_RESOLVE (ASSUME :args (_let_68)) (MACRO_SR_EQ_INTRO :args (_let_68 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_441 (EQ_RESOLVE (ASSUME :args (_let_67)) (MACRO_SR_EQ_INTRO :args (_let_67 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_442 (EQ_RESOLVE (ASSUME :args (_let_66)) (MACRO_SR_EQ_INTRO :args (_let_66 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_443 (EQ_RESOLVE (ASSUME :args (_let_65)) (MACRO_SR_EQ_INTRO :args (_let_65 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_444 (EQ_RESOLVE (ASSUME :args (_let_64)) (MACRO_SR_EQ_INTRO :args (_let_64 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_445 (EQ_RESOLVE (ASSUME :args (_let_63)) (MACRO_SR_EQ_INTRO :args (_let_63 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_446 (EQ_RESOLVE (ASSUME :args (_let_62)) (MACRO_SR_EQ_INTRO :args (_let_62 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_447 (EQ_RESOLVE (ASSUME :args (_let_61)) (MACRO_SR_EQ_INTRO :args (_let_61 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_448 (EQ_RESOLVE (ASSUME :args (_let_60)) (MACRO_SR_EQ_INTRO :args (_let_60 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_449 (EQ_RESOLVE (ASSUME :args (_let_59)) (MACRO_SR_EQ_INTRO :args (_let_59 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_450 (EQ_RESOLVE (ASSUME :args (_let_58)) (MACRO_SR_EQ_INTRO :args (_let_58 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_451 (EQ_RESOLVE (ASSUME :args (_let_57)) (MACRO_SR_EQ_INTRO :args (_let_57 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_452 (EQ_RESOLVE (ASSUME :args (_let_56)) (MACRO_SR_EQ_INTRO :args (_let_56 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_453 (EQ_RESOLVE (ASSUME :args (_let_55)) (MACRO_SR_EQ_INTRO :args (_let_55 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_454 (EQ_RESOLVE (ASSUME :args (_let_54)) (MACRO_SR_EQ_INTRO :args (_let_54 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_455 (EQ_RESOLVE (ASSUME :args (_let_53)) (MACRO_SR_EQ_INTRO :args (_let_53 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_456 (EQ_RESOLVE (ASSUME :args (_let_52)) (MACRO_SR_EQ_INTRO :args (_let_52 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_457 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_51)) (MACRO_SR_EQ_INTRO :args (_let_51 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.cartprodmempaircEq true))))) (let ((_let_458 (EQ_RESOLVE (ASSUME :args (_let_50)) (MACRO_SR_EQ_INTRO :args (_let_50 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_459 (EQ_RESOLVE (ASSUME :args (_let_49)) (MACRO_SR_EQ_INTRO :args (_let_49 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_460 (EQ_RESOLVE (ASSUME :args (_let_48)) (MACRO_SR_EQ_INTRO :args (_let_48 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_461 (ASSUME :args (_let_47)))) (let ((_let_462 (EQ_RESOLVE (ASSUME :args (_let_46)) (MACRO_SR_EQ_INTRO :args (_let_46 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_463 (ASSUME :args (_let_45)))) (let ((_let_464 (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args (_let_43 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_465 (EQ_RESOLVE (ASSUME :args (_let_42)) (MACRO_SR_EQ_INTRO :args (_let_42 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_466 (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO :args (_let_41 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_467 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_468 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_469 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_470 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_471 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_472 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_473 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_474 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_475 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_476 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_477 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_478 (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_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.brelnall1 (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted) (BOUND_VARIABLE_7686 $$unsorted) (BOUND_VARIABLE_7684 (-> $$unsorted Bool))) (or (not (@ (@ (@ tptp.breln A) B) R)) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_7643 $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) BOUND_VARIABLE_7643))) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_7643) B)) (not (@ (@ tptp.in _let_1) R)) (@ BOUND_VARIABLE_7684 _let_1))))) (not (@ (@ tptp.in BOUND_VARIABLE_7686) R)) (@ BOUND_VARIABLE_7684 BOUND_VARIABLE_7686)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_479 (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_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.brelnall2 (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted) (BOUND_VARIABLE_7757 $$unsorted) (BOUND_VARIABLE_7755 (-> $$unsorted Bool))) (or (not (@ (@ (@ tptp.breln A) B) R)) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_7714 $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) BOUND_VARIABLE_7714))) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_7714) B)) (not (@ (@ tptp.in _let_1) R)) (@ BOUND_VARIABLE_7755 _let_1))))) (not (@ (@ tptp.in BOUND_VARIABLE_7757) R)) (@ BOUND_VARIABLE_7755 BOUND_VARIABLE_7757)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_480 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.ex1E2 (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_7811 $$unsorted) (BOUND_VARIABLE_7809 $$unsorted)) (or (not (@ (@ tptp.ex1 A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ (@ tptp.in BOUND_VARIABLE_7809) A)) (not (@ Xphi BOUND_VARIABLE_7809)) (not (@ (@ tptp.in BOUND_VARIABLE_7811) A)) (not (@ Xphi BOUND_VARIABLE_7811)) (= BOUND_VARIABLE_7809 BOUND_VARIABLE_7811)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_481 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_482 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_483 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_484 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_485 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_486 (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_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.subbreln (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted) (BOUND_VARIABLE_8149 $$unsorted)) (let ((_let_1 (@ (@ tptp.breln A) B))) (or (not (@ _let_1 R)) (not (@ _let_1 BOUND_VARIABLE_8149)) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_8120 $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) BOUND_VARIABLE_8120)))) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8120) B)) (not (@ _let_1 R)) (@ _let_1 BOUND_VARIABLE_8149))))) (@ (@ tptp.subset R) BOUND_VARIABLE_8149))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_487 (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_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.eqbreln (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted) (BOUND_VARIABLE_8234 $$unsorted)) (let ((_let_1 (@ (@ tptp.breln A) B))) (or (not (@ _let_1 R)) (not (@ _let_1 BOUND_VARIABLE_8234)) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_8176 $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) BOUND_VARIABLE_8176)))) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8176) B)) (not (@ _let_1 R)) (@ _let_1 BOUND_VARIABLE_8234))))) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_8202 $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) BOUND_VARIABLE_8202)))) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8202) B)) (not (@ _let_1 BOUND_VARIABLE_8234)) (@ _let_1 R))))) (= R BOUND_VARIABLE_8234))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_488 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_489 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_490 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.ap2apEq1 true))))) (let ((_let_491 (MACRO_SR_PRED_TRANSFORM (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.ap2apEq2 true))))) (let ((_let_492 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_493 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_494 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_495 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_496 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_497 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_498 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_499 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_500 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_501 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_502 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_503 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.ifp (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted) (BOUND_VARIABLE_8756 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8756) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.if A) Xphi) Xx) BOUND_VARIABLE_8756)) A)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_504 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_505 (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 (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 (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 (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 (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 (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 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((= tptp.iftrue (forall ((A $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_8816 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8816) A)) (= Xx (@ (@ (@ (@ tptp.if A) true) Xx) BOUND_VARIABLE_8816))))) SB_DEFAULT SBA_FIXPOINT))) _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277) :args ((not (=> tptp.setextAx (=> tptp.emptysetAx (=> tptp.setadjoinAx (=> tptp.powersetAx (=> tptp.setunionAx (=> tptp.omega0Ax (=> tptp.omegaSAx (=> tptp.omegaIndAx (=> tptp.replAx (=> tptp.foundationAx (=> tptp.wellorderingAx (=> tptp.descrp (=> tptp.dsetconstrI (=> tptp.dsetconstrEL (=> tptp.dsetconstrER (=> tptp.exuE1 (=> tptp.prop2setE (=> tptp.emptysetE (=> tptp.emptysetimpfalse (=> tptp.notinemptyset (=> tptp.exuE3e (=> tptp.setext (=> tptp.emptyI (=> tptp.noeltsimpempty (=> tptp.setbeta (=> tptp.nonemptyE1 (=> tptp.nonemptyI (=> tptp.nonemptyI1 (=> tptp.setadjoinIL (=> tptp.emptyinunitempty (=> tptp.setadjoinIR (=> tptp.setadjoinE (=> tptp.setadjoinOr (=> tptp.setoftrueEq (=> tptp.powersetI (=> tptp.emptyinPowerset (=> tptp.emptyInPowerset (=> tptp.powersetE (=> tptp.setunionI (=> tptp.setunionE (=> tptp.subPowSU (=> tptp.exuE2 (=> tptp.nonemptyImpWitness (=> tptp.uniqinunit (=> tptp.notinsingleton (=> tptp.eqinunit (=> tptp.singletonsswitch (=> tptp.upairsetE (=> tptp.upairsetIL (=> tptp.upairsetIR (=> tptp.emptyE1 (=> tptp.vacuousDall (=> tptp.quantDeMorgan1 (=> tptp.quantDeMorgan2 (=> tptp.quantDeMorgan3 (=> tptp.quantDeMorgan4 (=> tptp.prop2setI (=> tptp.prop2set2propI (=> tptp.notdexE (=> tptp.notdallE (=> tptp.exuI1 (=> tptp.exuI3 (=> tptp.exuI2 (=> tptp.inCongP (=> tptp.in__Cong (=> tptp.exuE3u (=> tptp.exu__Cong (=> tptp.emptyset__Cong (=> tptp.setadjoin__Cong (=> tptp.powerset__Cong (=> tptp.setunion__Cong (=> tptp.omega__Cong (=> tptp.exuEu (=> tptp.descr__Cong (=> tptp.dsetconstr__Cong (=> tptp.subsetI1 (=> tptp.eqimpsubset2 (=> tptp.eqimpsubset1 (=> tptp.subsetI2 (=> tptp.emptysetsubset (=> tptp.subsetE (=> tptp.subsetE2 (=> tptp.notsubsetI (=> tptp.notequalI1 (=> tptp.notequalI2 (=> tptp.subsetRefl (=> tptp.subsetTrans (=> tptp.setadjoinSub (=> tptp.setadjoinSub2 (=> tptp.subset2powerset (=> tptp.setextsub (=> tptp.subsetemptysetimpeq (=> tptp.powersetI1 (=> tptp.powersetE1 (=> tptp.inPowerset (=> tptp.powersetsubset (=> tptp.sepInPowerset (=> tptp.sepSubset (=> tptp.binunionIL (=> tptp.upairset2IR (=> tptp.binunionIR (=> tptp.binunionEcases (=> tptp.binunionE (=> tptp.binunionLsub (=> tptp.binunionRsub (=> tptp.binintersectI (=> tptp.binintersectSubset5 (=> tptp.binintersectEL (=> tptp.binintersectLsub (=> tptp.binintersectSubset2 (=> tptp.binintersectSubset3 (=> tptp.binintersectER (=> tptp.disjointsetsI1 (=> tptp.binintersectRsub (=> tptp.binintersectSubset4 (=> tptp.binintersectSubset1 (=> tptp.bs114d (=> tptp.setminusI (=> tptp.setminusEL (=> tptp.setminusER (=> tptp.setminusSubset2 (=> tptp.setminusERneg (=> tptp.setminusELneg (=> tptp.setminusILneg (=> tptp.setminusIRneg (=> tptp.setminusLsub (=> tptp.setminusSubset1 (=> tptp.symdiffE (=> tptp.symdiffI1 (=> tptp.symdiffI2 (=> tptp.symdiffIneg1 (=> tptp.symdiffIneg2 (=> tptp.secondinupair (=> tptp.setukpairIL (=> tptp.setukpairIR (=> tptp.kpairiskpair (=> tptp.kpairp (=> tptp.singletonsubset (=> tptp.singletoninpowerset (=> tptp.singletoninpowunion (=> tptp.upairset2E (=> tptp.upairsubunion (=> tptp.upairinpowunion (=> tptp.ubforcartprodlem1 (=> tptp.ubforcartprodlem2 (=> tptp.ubforcartprodlem3 (=> tptp.cartprodpairin (=> tptp.cartprodmempair1 (=> tptp.cartprodmempair (=> tptp.setunionE2 (=> tptp.setunionsingleton1 (=> tptp.setunionsingleton2 (=> tptp.setunionsingleton (=> tptp.singletonprop (=> tptp.ex1E1 (=> tptp.ex1I (=> tptp.ex1I2 (=> tptp.singletonsuniq (=> tptp.setukpairinjL1 (=> tptp.kfstsingleton (=> tptp.theprop (=> tptp.kfstpairEq (=> tptp.cartprodfstin (=> tptp.setukpairinjL2 (=> tptp.setukpairinjL (=> tptp.setukpairinjR11 (=> tptp.setukpairinjR12 (=> tptp.setukpairinjR1 (=> tptp.upairequniteq (=> tptp.setukpairinjR2 (=> tptp.setukpairinjR (=> tptp.ksndsingleton (=> tptp.ksndpairEq (=> tptp.kpairsurjEq (=> tptp.cartprodsndin (=> tptp.cartprodpairmemEL (=> tptp.cartprodpairmemER (=> tptp.cartprodmempaircEq (=> tptp.cartprodfstpairEq (=> tptp.cartprodsndpairEq (=> tptp.cartprodpairsurjEq (=> tptp.dpsetconstrI (=> tptp.dpsetconstrSub (=> tptp.setOfPairsIsBReln (=> tptp.dpsetconstrERa (=> tptp.dpsetconstrEL1 (=> tptp.dpsetconstrEL2 (=> tptp.dpsetconstrER (=> tptp.funcImageSingleton (=> tptp.apProp (=> tptp.app (=> tptp.infuncsetfunc (=> tptp.ap2p (=> tptp.funcinfuncset (=> tptp.lamProp (=> tptp.lamp (=> tptp.lam2p (=> tptp.brelnall1 (=> tptp.brelnall2 (=> tptp.ex1E2 (=> tptp.funcGraphProp1 (=> tptp.funcGraphProp3 (=> tptp.funcGraphProp2 (=> tptp.funcextLem (=> tptp.funcGraphProp4 (=> tptp.subbreln (=> tptp.eqbreln (=> tptp.funcext (=> tptp.funcext2 (=> tptp.ap2apEq1 (=> tptp.ap2apEq2 (=> tptp.beta1 (=> tptp.eta1 (=> tptp.lam2lamEq (=> tptp.beta2 (=> tptp.eta2 (=> tptp.iffalseProp1 (=> tptp.iffalseProp2 (=> tptp.iftrueProp1 (=> tptp.iftrueProp2 (=> tptp.ifSingleton (=> tptp.ifp (=> tptp.theeq (=> tptp.iftrue (forall ((A $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_8857 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8857) A)) (= BOUND_VARIABLE_8857 (@ (@ (@ (@ tptp.if A) false) Xx) BOUND_VARIABLE_8857))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) SB_DEFAULT SBA_FIXPOINT)) (CONG (CONG (REFL :args ((forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (= (@ _let_1 A) (@ _let_1 B))))) (= A B))))) (CONG (REFL :args (_let_258)) (CONG (REFL :args ((forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (= (@ _let_1 (@ (@ tptp.setadjoin Xx) A)) (or (= Xx Xy) (@ _let_1 A))))))) (CONG (REFL :args ((forall ((A $$unsorted) (B $$unsorted)) (= (@ (@ tptp.in B) (@ tptp.powerset A)) (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (@ _let_1 A)))))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xx $$unsorted)) (= (@ (@ tptp.in Xx) (@ tptp.setunion A)) (not (forall ((B $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (not (@ (@ tptp.in B) A))))))))) (CONG (THEORY_PREPROCESS :args ((= _let_253 (tptp.in tptp.emptyset tptp.omega)))) (CONG (REFL :args ((forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) tptp.omega)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) tptp.omega))))) (CONG (REFL :args ((forall ((A $$unsorted) (BOUND_VARIABLE_5255 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_5255))) (or (not (@ (@ tptp.in tptp.emptyset) A)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 tptp.omega)) (not (@ _let_1 A)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) Xx)) A))))) (not (@ _let_1 tptp.omega)) (@ _let_1 A)))))) (CONG (REFL :args ((forall ((Xphi (-> $$unsorted $$unsorted Bool)) (A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (forall ((Xx $$unsorted)) (or (not (@ (@ Xphi Xx) Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ (@ Xphi Xx) Xy)) (= Xx Xy)))))))))) (not (forall ((B $$unsorted)) (not (forall ((Xx $$unsorted)) (= (@ (@ tptp.in Xx) B) (not (forall ((Xy $$unsorted)) (or (not (@ (@ tptp.in Xy) A)) (not (@ (@ Xphi Xy) Xx)))))))))))))) (CONG (REFL :args ((forall ((A $$unsorted) (BOUND_VARIABLE_5318 $$unsorted)) (or (not (@ (@ tptp.in BOUND_VARIABLE_5318) A)) (not (forall ((B $$unsorted)) (or (not (@ (@ tptp.in B) A)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (not (@ _let_1 A))))))))))))) (CONG (REFL :args ((forall ((A $$unsorted)) (not (forall ((B $$unsorted)) (or (not (forall ((C $$unsorted) (BOUND_VARIABLE_5336 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_5336))) (or (not (@ (@ tptp.in C) B)) (not (@ _let_1 C)) (@ _let_1 A))))) (not (forall ((Xx $$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_5384 $$unsorted) (BOUND_VARIABLE_5377 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_5384))) (let ((_let_2 (@ tptp.in BOUND_VARIABLE_5377))) (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 $$unsorted) (BOUND_VARIABLE_5451 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 C)) (@ _let_1 A))))) (not (@ (@ tptp.in BOUND_VARIABLE_5451) C)) (not (forall ((D $$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 $$unsorted) (BOUND_VARIABLE_5421 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_5421))) (or (not (@ (@ tptp.in E) B)) (@ (@ tptp.in Xx) E) (not (@ _let_1 E)) (@ _let_1 D))))))))))))))))) (CONG (REFL :args ((forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_10265 $$unsorted)) (or (@ Xphi (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ Xphi BOUND_VARIABLE_10265)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_10265)))))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (not (@ Xphi Xx)) (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))) (@ _let_1 A)))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy))))) (@ Xphi Xx))))) (CONG (REFL :args ((forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_10314 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy))))))) (not (@ Xphi BOUND_VARIABLE_10314)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_10314)))))))) (CONG (REFL :args ((forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) (@ tptp.prop2set false)))))) (CONG (REFL :args ((forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (CONG (REFL :args ((forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) tptp.emptyset))))) (CONG (REFL :args (_let_238)) (CONG (REFL :args ((forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_10363 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (@ Xphi Xx)))) (not (@ Xphi BOUND_VARIABLE_10363)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_10363)))))))) (CONG (REFL :args ((forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (@ _let_1 B))))) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (@ _let_1 A))))) (= A B))))) (CONG (REFL :args ((forall ((A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))) (= tptp.emptyset A))))) (CONG (REFL :args ((forall ((A $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))) (= tptp.emptyset A))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (= (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xy $$unsorted)) (@ Xphi Xy)))) (@ Xphi Xx))))))) (CONG (REFL :args ((forall ((A $$unsorted)) (or (= tptp.emptyset A) (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))))))) (CONG (REFL :args ((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))))))))) (CONG (REFL :args ((forall ((BOUND_VARIABLE_5613 $$unsorted)) (not (@ (@ tptp.in BOUND_VARIABLE_5613) tptp.emptyset))))) (CONG (REFL :args (_let_227)) (CONG (TRANS (CONG _let_275 (THEORY_PREPROCESS :args ((= _let_224 _let_276))) :args _let_273) (THEORY_PREPROCESS :args ((= (@ _let_225 _let_276) (tptp.in tptp.emptyset _let_276))))) (CONG (REFL :args ((forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (or (not (@ _let_1 A)) (@ _let_1 (@ (@ tptp.setadjoin Xx) A))))))) (CONG (REFL :args ((forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (or (not (@ _let_1 (@ (@ tptp.setadjoin Xx) A))) (= Xx Xy) (@ _let_1 A)))))) (CONG (REFL :args ((forall ((Xx $$unsorted) (A $$unsorted) (Xy $$unsorted)) (let ((_let_1 (@ tptp.in Xy))) (or (not (@ _let_1 (@ (@ tptp.setadjoin Xx) A))) (= Xx Xy) (@ _let_1 A)))))) (CONG (REFL :args ((forall ((A $$unsorted)) (= A (@ (@ tptp.dsetconstr A) (lambda ((BOUND_VARIABLE_35944 $$unsorted)) true)))))) (CONG (REFL :args ((forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (@ _let_1 A))))) (@ (@ tptp.in B) (@ tptp.powerset A)))))) (CONG (REFL :args (_let_217)) (CONG (REFL :args (_let_215)) (CONG (REFL :args ((forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ (@ tptp.in B) (@ tptp.powerset A))) (not (@ _let_1 B)) (@ _let_1 A)))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (not (@ (@ tptp.in B) A)) (@ _let_1 (@ tptp.setunion A))))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ tptp.setunion A))) (not (forall ((B $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (not (@ (@ tptp.in B) A))))))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (@ _let_1 (@ tptp.powerset (@ tptp.setunion A)))))))) (CONG (REFL :args ((forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_10452 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (not (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xx Xy)))))) (not (@ Xphi BOUND_VARIABLE_10452)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_10452)))))))) (CONG (REFL :args ((forall ((A $$unsorted)) (or (= tptp.emptyset A) (not (forall ((Xx $$unsorted)) (not (@ (@ tptp.in Xx) A)))))))) (CONG (REFL :args ((forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (= Xx Xy))))) (CONG (REFL :args ((forall ((Xx $$unsorted) (Xy $$unsorted)) (or (= Xx Xy) (not (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset))))))) (CONG (REFL :args ((forall ((Xy $$unsorted)) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xy) tptp.emptyset))))) (CONG (REFL :args ((forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (@ (@ tptp.in Xy) (@ (@ tptp.setadjoin Xx) tptp.emptyset)))))) (CONG (REFL :args ((forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (or (not (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))) (= Xx Xz) (= Xy Xz))))) (CONG (REFL :args (_let_202)) (CONG (REFL :args (_let_200)) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_5805 $$unsorted)) (or (not (= tptp.emptyset (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (@ (@ tptp.in BOUND_VARIABLE_5805) A)) (not (@ Xphi BOUND_VARIABLE_5805)))))) (CONG (REFL :args ((forall ((Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) tptp.emptyset)) (@ Xphi Xx))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_5840 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ Xphi Xx)))) (not (@ (@ tptp.in BOUND_VARIABLE_5840) A)) (@ Xphi BOUND_VARIABLE_5840))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_5871 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx))))) (not (@ (@ tptp.in BOUND_VARIABLE_5871) A)) (not (@ Xphi BOUND_VARIABLE_5871)))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_5902 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx))))) (not (@ (@ tptp.in BOUND_VARIABLE_5902) A)) (not (@ Xphi BOUND_VARIABLE_5902)))))) (CONG (REFL :args ((forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_5932 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ Xphi Xx)))) (not (@ (@ tptp.in BOUND_VARIABLE_5932) A)) (@ Xphi BOUND_VARIABLE_5932))))) (CONG (TRANS (CONG _let_275 _let_274 :args _let_273) (THEORY_PREPROCESS :args ((= (@ _let_225 _let_272) (tptp.in tptp.emptyset _let_272))))) (CONG (TRANS (CONG (REFL :args (tptp.set2prop)) _let_274 :args _let_273) (THEORY_PREPROCESS :args ((= (@ tptp.set2prop _let_272) (tptp.set2prop _let_272))))) (REFL :args ((=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_5979 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx))))) (not (@ (@ tptp.in BOUND_VARIABLE_5979) A)) (not (@ Xphi BOUND_VARIABLE_5979)))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_6009 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ Xphi Xx)))) (not (@ (@ tptp.in BOUND_VARIABLE_6009) A)) (@ Xphi BOUND_VARIABLE_6009))) (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_6040 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy))))))) (not (@ Xphi BOUND_VARIABLE_6040)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_6040)))))) (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_6076 $$unsorted)) (or (not (@ Xphi BOUND_VARIABLE_6076)) (not (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (@ Xphi Xx)) (not (@ Xphi Xy)) (= Xx Xy)))) (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy))))))))) (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_6096 $$unsorted)) (or (not (forall ((Xy $$unsorted)) (= (@ Xphi Xy) (= Xy BOUND_VARIABLE_6096)))) (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy))))))))) (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_6206 $$unsorted) (BOUND_VARIABLE_6204 $$unsorted) (BOUND_VARIABLE_10599 $$unsorted)) (or (not (@ Xphi BOUND_VARIABLE_6204)) (not (@ Xphi BOUND_VARIABLE_6206)) (= BOUND_VARIABLE_6204 BOUND_VARIABLE_6206) (not (@ Xphi BOUND_VARIABLE_10599)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_10599)))))) (=> (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool))) (or (not (forall ((Xy $$unsorted)) (= (@ Xpsi Xy) (@ Xphi Xy)))) (= (not (forall ((Xx $$unsorted)) (or (not (@ Xpsi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xpsi Xy)) (= Xx Xy))))))) (not (forall ((Xx $$unsorted)) (or (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xx Xy)))))))))) (=> (forall ((Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_6316 $$unsorted) (BOUND_VARIABLE_6314 $$unsorted) (BOUND_VARIABLE_10705 $$unsorted)) (or (not (@ Xphi BOUND_VARIABLE_6314)) (not (@ Xphi BOUND_VARIABLE_6316)) (= BOUND_VARIABLE_6314 BOUND_VARIABLE_6316) (not (@ Xphi BOUND_VARIABLE_10705)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_10705)))))) (=> (forall ((Xphi (-> $$unsorted Bool)) (Xpsi (-> $$unsorted Bool)) (BOUND_VARIABLE_10786 $$unsorted) (BOUND_VARIABLE_10777 $$unsorted)) (or (not (forall ((Xy $$unsorted)) (= (@ Xpsi Xy) (@ Xphi Xy)))) (= (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xphi Xx))) (@ tptp.descr (lambda ((Xx $$unsorted)) (@ Xpsi Xx)))) (not (@ Xphi BOUND_VARIABLE_10777)) (not (forall ((Xy $$unsorted)) (or (not (@ Xphi Xy)) (= Xy BOUND_VARIABLE_10777)))) (not (@ Xpsi BOUND_VARIABLE_10786)) (not (forall ((Xy $$unsorted)) (or (not (@ Xpsi Xy)) (= Xy BOUND_VARIABLE_10786)))))) (=> (forall ((B $$unsorted) (BOUND_VARIABLE_6386 (-> $$unsorted Bool)) (BOUND_VARIABLE_6384 (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.dsetconstr B))) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) B)) (= (@ BOUND_VARIABLE_6384 Xx) (@ BOUND_VARIABLE_6386 Xx))))) (= (@ _let_1 (lambda ((Xx $$unsorted)) (@ BOUND_VARIABLE_6386 Xx))) (@ _let_1 (lambda ((Xx $$unsorted)) (@ BOUND_VARIABLE_6384 Xx))))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (@ _let_1 B))))) (@ (@ tptp.subset A) B))) (=> (forall ((B $$unsorted)) (@ (@ tptp.subset B) B)) (=> (forall ((B $$unsorted)) (@ (@ tptp.subset B) B)) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (@ _let_1 B))))) (@ (@ tptp.subset A) B))) (=> _let_169 (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ (@ tptp.subset A) B)) (not (@ _let_1 A)) (@ _let_1 B)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ (@ tptp.subset A) B)) (@ _let_1 B) (not (@ _let_1 A))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (@ _let_1 B) (not (@ (@ tptp.subset A) B))))) (=> (forall ((B $$unsorted)) (@ (@ tptp.subset B) B)) (=> _let_162 (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (or (not (@ _let_1 B)) (not (@ (@ tptp.subset B) C)) (@ _let_1 C)))) (=> _let_159 (=> (forall ((A $$unsorted) (Xx $$unsorted) (B $$unsorted)) (let ((_let_1 (@ tptp.subset A))) (or (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.setadjoin Xx) B))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (@ (@ tptp.subset A) B)) (@ (@ tptp.in A) (@ tptp.powerset B)))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (@ (@ tptp.subset A) B)) (not (@ (@ tptp.subset B) A)) (= A B))) (=> (forall ((A $$unsorted)) (or (not (@ (@ tptp.subset A) tptp.emptyset)) (= tptp.emptyset A))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (@ (@ tptp.subset B) A)) (@ (@ tptp.in B) (@ tptp.powerset A)))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (@ (@ tptp.in B) (@ tptp.powerset A))) (@ (@ tptp.subset B) A))) (=> _let_151 (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (@ (@ tptp.subset A) B)) (@ (@ tptp.subset (@ tptp.powerset A)) (@ tptp.powerset B)))) (=> _let_148 (=> _let_146 (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (@ _let_1 (@ (@ tptp.binunion A) B))))) (=> _let_143 (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.binunion A) B))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 (@ (@ tptp.binunion A) B))) (@ _let_1 A) (@ _let_1 B)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 (@ (@ tptp.binunion A) B))) (@ _let_1 A) (@ _let_1 B)))) (=> _let_138 (=> _let_136 (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.binintersect A) B))))) (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (@ tptp.subset C))) (or (not (@ _let_1 A)) (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.binintersect A) B))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 (@ (@ tptp.binintersect A) B))) (@ _let_1 A)))) (=> _let_131 (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (@ (@ tptp.subset A) B)) (= A (@ (@ tptp.binintersect A) B)))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (= B (@ (@ tptp.binintersect A) B))) (@ (@ tptp.subset B) A))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 (@ (@ tptp.binintersect A) B))) (@ _let_1 B)))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (not (@ _let_1 B)))))) (= tptp.emptyset (@ (@ tptp.binintersect A) B)))) (=> _let_125 (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (@ (@ tptp.subset B) A)) (= B (@ (@ tptp.binintersect A) B)))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (= A (@ (@ tptp.binintersect A) B))) (@ (@ tptp.subset A) B))) (=> _let_121 (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (@ _let_1 B) (@ _let_1 (@ (@ tptp.setminus A) B))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 (@ (@ tptp.setminus A) B))) (@ _let_1 A)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 (@ (@ tptp.setminus A) B))) (not (@ _let_1 B))))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (@ (@ tptp.subset A) B)) (= tptp.emptyset (@ (@ tptp.setminus A) B)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (@ _let_1 (@ (@ tptp.setminus A) B)) (not (@ _let_1 A)) (@ _let_1 B)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (@ _let_1 (@ (@ tptp.setminus A) B)) (@ _let_1 B) (not (@ _let_1 A))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (@ _let_1 A) (not (@ _let_1 (@ (@ tptp.setminus A) B)))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 B)) (not (@ _let_1 (@ (@ tptp.setminus A) B)))))) (=> _let_111 (=> (forall ((A $$unsorted) (B $$unsorted)) (or (not (= tptp.emptyset (@ (@ tptp.setminus A) B))) (@ (@ tptp.subset A) B))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ _let_1 A))) (or (not (@ _let_1 (@ (@ tptp.symdiff A) B))) (and _let_3 (not _let_2)) (and (not _let_3) _let_2)))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (@ _let_1 B) (@ _let_1 (@ (@ tptp.symdiff A) B))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (@ _let_1 A) (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.symdiff A) B))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (not (@ _let_1 B)) (not (@ _let_1 (@ (@ tptp.symdiff A) B)))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (@ _let_1 A) (@ _let_1 B) (not (@ _let_1 (@ (@ tptp.symdiff A) B)))))) (=> _let_103 (=> _let_101 (=> _let_99 (=> _let_97 (=> _let_95 (=> (forall ((A $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) tptp.emptyset)) A))) (=> (forall ((A $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset A)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) (@ tptp.powerset (@ (@ tptp.binunion A) B))))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (or (not (@ (@ tptp.in Xz) (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)))) (= Xx Xz) (= Xy Xz))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_6813 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_6813) B)) (@ (@ tptp.subset (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin BOUND_VARIABLE_6813) tptp.emptyset))) (@ (@ tptp.binunion A) B)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_6839 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_6839) B)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin BOUND_VARIABLE_6839) tptp.emptyset))) (@ tptp.powerset (@ (@ tptp.binunion A) B))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_6865 $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_6865) B)) (@ (@ tptp.subset (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin BOUND_VARIABLE_6865) tptp.emptyset))) tptp.emptyset))) (@ tptp.powerset (@ (@ tptp.binunion A) B)))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_6894 $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_6894) B)) (@ (@ tptp.in (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin BOUND_VARIABLE_6894) tptp.emptyset))) tptp.emptyset))) (@ tptp.powerset (@ tptp.powerset (@ (@ tptp.binunion A) B))))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_6923 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_6923) B)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) BOUND_VARIABLE_6923)) (@ tptp.powerset (@ tptp.powerset (@ (@ tptp.binunion A) B)))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_6947 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_6947) B)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) BOUND_VARIABLE_6947)) (@ (@ tptp.cartprod A) B)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (or (not (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_6979 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_6979) B)) (not (= Xu (@ (@ tptp.kpair Xx) BOUND_VARIABLE_6979)))))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (or (not (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B))) (@ tptp.iskpair Xu))) (=> (forall ((A $$unsorted) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) (@ tptp.setunion A))) (not (forall ((X $$unsorted)) (or (not (@ (@ tptp.in X) A)) (not (@ (@ tptp.in Xx) X))))))) (=> _let_80 (=> _let_78 (=> (forall ((Xx $$unsorted)) (= Xx (@ tptp.setunion (@ (@ tptp.setadjoin Xx) tptp.emptyset)))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_7069 $$unsorted)) (or (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_7040 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (@ (@ tptp.in BOUND_VARIABLE_7040) A)) (not (@ Xphi BOUND_VARIABLE_7040)) (= Xx BOUND_VARIABLE_7040)))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ (@ tptp.in BOUND_VARIABLE_7069) A)) (not (@ Xphi BOUND_VARIABLE_7069)))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool))) (or (not (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx))))))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (forall ((Xy $$unsorted)) (or (not (@ (@ tptp.in Xy) A)) (not (@ Xphi Xy)) (= Xx Xy)))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_7167 $$unsorted)) (or (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_7138 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ Xphi Xx)) (not (@ (@ tptp.in BOUND_VARIABLE_7138) A)) (not (@ Xphi BOUND_VARIABLE_7138)) (= Xx BOUND_VARIABLE_7138)))) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx)))) (not (@ (@ tptp.in BOUND_VARIABLE_7167) A)) (not (@ Xphi BOUND_VARIABLE_7167)))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (or (not (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.setadjoin Xy) tptp.emptyset))) (= Xx Xy))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xx))) (or (not (@ (@ tptp.in (@ (@ tptp.setadjoin Xz) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)))) (= Xx Xz)))) (=> (forall ((Xu $$unsorted)) (or (not (@ tptp.iskpair Xu)) (@ tptp.singleton (@ (@ tptp.dsetconstr (@ tptp.setunion Xu)) (lambda ((Xx $$unsorted)) (@ (@ tptp.in (@ (@ tptp.setadjoin Xx) tptp.emptyset)) Xu)))))) (=> (forall ((X $$unsorted)) (or (not (@ tptp.singleton X)) (@ (@ tptp.in (@ tptp.setunion X)) X))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (= Xx (@ tptp.kfst (@ (@ tptp.kpair Xx) Xy)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (or (not (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B))) (@ (@ tptp.in (@ tptp.kfst Xu)) A))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xz))) (let ((_let_2 (@ tptp.setadjoin Xx))) (or (not (= (@ (@ tptp.setadjoin (@ _let_2 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_2 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset)))) (= Xx Xz))))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (or (not (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu))) (= Xx Xz))) (=> (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xy))) (let ((_let_2 (@ _let_1 tptp.emptyset))) (= _let_2 (@ _let_1 _let_2))))) (=> (forall ((Xy $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xy))) (let ((_let_2 (@ _let_1 tptp.emptyset))) (let ((_let_3 (@ tptp.setadjoin _let_2))) (= (@ _let_3 (@ (@ tptp.setadjoin (@ _let_1 _let_2)) tptp.emptyset)) (@ _let_3 tptp.emptyset)))))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted) (Xu $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xu))) (let ((_let_2 (@ _let_1 tptp.emptyset))) (let ((_let_3 (@ tptp.setadjoin Xx))) (or (not (= (@ (@ tptp.setadjoin (@ _let_3 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_3 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin _let_2) (@ (@ tptp.setadjoin (@ _let_1 _let_2)) tptp.emptyset)))) (= Xy Xu)))))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted)) (or (not (= (@ (@ tptp.setadjoin Xx) (@ (@ tptp.setadjoin Xy) tptp.emptyset)) (@ (@ tptp.setadjoin Xz) tptp.emptyset))) (= Xx Xy))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (let ((_let_1 (@ tptp.setadjoin Xz))) (let ((_let_2 (@ tptp.setadjoin Xx))) (or (not (= (@ (@ tptp.setadjoin (@ _let_2 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_2 (@ (@ tptp.setadjoin Xy) tptp.emptyset))) tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 tptp.emptyset)) (@ (@ tptp.setadjoin (@ _let_1 (@ (@ tptp.setadjoin Xu) tptp.emptyset))) tptp.emptyset)))) (= Xy Xu))))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted) (Xz $$unsorted) (Xu $$unsorted)) (or (not (= (@ (@ tptp.kpair Xx) Xy) (@ (@ tptp.kpair Xz) Xu))) (= Xy Xu))) (=> (forall ((Xu $$unsorted)) (or (not (@ tptp.iskpair Xu)) (@ tptp.singleton (@ (@ tptp.dsetconstr (@ tptp.setunion Xu)) (lambda ((Xx $$unsorted)) (= Xu (@ (@ tptp.kpair (@ tptp.kfst Xu)) Xx))))))) (=> (forall ((Xx $$unsorted) (Xy $$unsorted)) (= Xy (@ tptp.ksnd (@ (@ tptp.kpair Xx) Xy)))) (=> (forall ((Xu $$unsorted)) (or (not (@ tptp.iskpair Xu)) (= Xu (@ (@ tptp.kpair (@ tptp.kfst Xu)) (@ tptp.ksnd Xu))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (or (not (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B))) (@ (@ tptp.in (@ tptp.ksnd Xu)) B))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xy $$unsorted)) (or (not (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B))) (@ (@ tptp.in Xx) A))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (Xy $$unsorted)) (or (not (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ tptp.cartprod A) B))) (@ (@ tptp.in Xy) B))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_7341 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_7341) B)) (= Xx (@ tptp.kfst (@ (@ tptp.kpair Xx) BOUND_VARIABLE_7341))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_7368 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_7368) B)) (= BOUND_VARIABLE_7368 (@ tptp.ksnd (@ (@ tptp.kpair Xx) BOUND_VARIABLE_7368))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xu $$unsorted)) (or (not (@ (@ tptp.in Xu) (@ (@ tptp.cartprod A) B))) (= Xu (@ (@ tptp.kpair (@ tptp.kfst Xu)) (@ tptp.ksnd Xu))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (BOUND_VARIABLE_7408 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_7408) B)) (not (@ (@ Xphi Xx) BOUND_VARIABLE_7408)) (@ (@ tptp.in (@ (@ tptp.kpair Xx) BOUND_VARIABLE_7408)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu)))))) (=> _let_44 (=> (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.subset (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (@ (@ Xphi Xx) Xy)))) (@ (@ tptp.cartprod A) B))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (BOUND_VARIABLE_7442 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_7442) B)) (not (@ (@ tptp.in (@ (@ tptp.kpair Xx) BOUND_VARIABLE_7442)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu))))) (@ (@ Xphi Xx) BOUND_VARIABLE_7442))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (or (not (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu))))) (@ (@ tptp.in Xx) A))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (or (not (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu))))) (@ (@ tptp.in Xy) B))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xphi (-> $$unsorted $$unsorted Bool)) (Xx $$unsorted) (Xy $$unsorted)) (or (not (@ (@ tptp.in (@ (@ tptp.kpair Xx) Xy)) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xz $$unsorted) (Xu $$unsorted)) (@ (@ Xphi Xz) Xu))))) (@ (@ Xphi Xx) Xy))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_7489 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_7489) A)) (@ tptp.singleton (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_7489) Xy)) Xf)))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_7517 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_7517) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr B) (lambda ((Xy $$unsorted)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_7517) Xy)) Xf))))) B))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_7547 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_7547) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_7547)) B))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (or (not (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B))) (@ (@ (@ tptp.func A) B) Xf))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_7576 $$unsorted)) (or (not (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B))) (not (@ (@ tptp.in BOUND_VARIABLE_7576) A)) (@ (@ tptp.in (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_7576)) B))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ Xf Xx)) B)))) (@ (@ (@ tptp.func A) B) (@ (@ (@ tptp.dpsetconstr A) B) (lambda ((Xx $$unsorted) (Xy $$unsorted)) (= Xy (@ Xf Xx))))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ Xf Xx)) B)))) (@ (@ (@ tptp.func A) B) (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ Xf Xx)))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ Xf Xx)) B)))) (@ (@ tptp.in (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ Xf Xx)))) (@ (@ tptp.funcSet A) B)))) (=> (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted) (BOUND_VARIABLE_7686 $$unsorted) (BOUND_VARIABLE_7684 (-> $$unsorted Bool))) (or (not (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_7643 $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) BOUND_VARIABLE_7643))) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_7643) B)) (not (@ (@ tptp.in _let_1) R)) (@ BOUND_VARIABLE_7684 _let_1))))) (not (@ (@ tptp.in BOUND_VARIABLE_7686) R)) (@ BOUND_VARIABLE_7684 BOUND_VARIABLE_7686))) (=> (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted) (BOUND_VARIABLE_7757 $$unsorted) (BOUND_VARIABLE_7755 (-> $$unsorted Bool))) (or (not (@ (@ tptp.subset R) (@ (@ tptp.cartprod A) B))) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_7714 $$unsorted)) (let ((_let_1 (@ (@ tptp.kpair Xx) BOUND_VARIABLE_7714))) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_7714) B)) (not (@ (@ tptp.in _let_1) R)) (@ BOUND_VARIABLE_7755 _let_1))))) (not (@ (@ tptp.in BOUND_VARIABLE_7757) R)) (@ BOUND_VARIABLE_7755 BOUND_VARIABLE_7757))) (=> (forall ((A $$unsorted) (Xphi (-> $$unsorted Bool)) (BOUND_VARIABLE_7811 $$unsorted) (BOUND_VARIABLE_7809 $$unsorted)) (or (not (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xx $$unsorted)) (@ Xphi Xx))))) (not (@ (@ tptp.in BOUND_VARIABLE_7809) A)) (not (@ Xphi BOUND_VARIABLE_7809)) (not (@ (@ tptp.in BOUND_VARIABLE_7811) A)) (not (@ Xphi BOUND_VARIABLE_7811)) (= BOUND_VARIABLE_7809 BOUND_VARIABLE_7811))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_7840 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_7840) A)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_7840) (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_7840))) Xf))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_7866 $$unsorted)) (or (not (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B))) (not (@ (@ tptp.in BOUND_VARIABLE_7866) A)) (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_7866) (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_7866))) Xf))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_7923 $$unsorted) (BOUND_VARIABLE_7921 $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (not (@ (@ tptp.in BOUND_VARIABLE_7921) A)) (not (@ (@ tptp.in BOUND_VARIABLE_7923) B)) (not (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_7921) BOUND_VARIABLE_7923)) Xf)) (= BOUND_VARIABLE_7923 (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_7921)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_8016 $$unsorted) (BOUND_VARIABLE_8014 $$unsorted) (BOUND_VARIABLE_8012 $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_8016) BOUND_VARIABLE_8014)))) (let ((_let_2 (@ (@ tptp.func A) B))) (or (not (@ _let_2 Xf)) (not (@ _let_2 BOUND_VARIABLE_8012)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (or (not (@ (@ tptp.in Xx) A)) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 BOUND_VARIABLE_8012) Xx)))))) (not (@ (@ tptp.in BOUND_VARIABLE_8016) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8014) B)) (not (@ _let_1 BOUND_VARIABLE_8012)) (@ _let_1 Xf))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_8085 $$unsorted) (BOUND_VARIABLE_8083 $$unsorted)) (or (not (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B))) (not (@ (@ tptp.in BOUND_VARIABLE_8083) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8085) B)) (not (@ (@ tptp.in (@ (@ tptp.kpair BOUND_VARIABLE_8083) BOUND_VARIABLE_8085)) Xf)) (= BOUND_VARIABLE_8085 (@ (@ (@ (@ tptp.ap A) B) Xf) BOUND_VARIABLE_8083)))) (=> (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted) (BOUND_VARIABLE_8149 $$unsorted)) (let ((_let_1 (@ tptp.subset R))) (let ((_let_2 (@ (@ tptp.cartprod A) B))) (or (not (@ _let_1 _let_2)) (not (@ (@ tptp.subset BOUND_VARIABLE_8149) _let_2)) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_8120 $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) BOUND_VARIABLE_8120)))) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8120) B)) (not (@ _let_1 R)) (@ _let_1 BOUND_VARIABLE_8149))))) (@ _let_1 BOUND_VARIABLE_8149))))) (=> (forall ((A $$unsorted) (B $$unsorted) (R $$unsorted) (BOUND_VARIABLE_8234 $$unsorted)) (let ((_let_1 (@ (@ tptp.cartprod A) B))) (or (not (@ (@ tptp.subset R) _let_1)) (not (@ (@ tptp.subset BOUND_VARIABLE_8234) _let_1)) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_8176 $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) BOUND_VARIABLE_8176)))) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8176) B)) (not (@ _let_1 R)) (@ _let_1 BOUND_VARIABLE_8234))))) (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_8202 $$unsorted)) (let ((_let_1 (@ tptp.in (@ (@ tptp.kpair Xx) BOUND_VARIABLE_8202)))) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8202) B)) (not (@ _let_1 BOUND_VARIABLE_8234)) (@ _let_1 R))))) (= R BOUND_VARIABLE_8234)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_8272 $$unsorted)) (let ((_let_1 (@ (@ tptp.func A) B))) (or (not (@ _let_1 Xf)) (not (@ _let_1 BOUND_VARIABLE_8272)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (or (not (@ (@ tptp.in Xx) A)) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 BOUND_VARIABLE_8272) Xx)))))) (= Xf BOUND_VARIABLE_8272)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted) (BOUND_VARIABLE_8307 $$unsorted)) (let ((_let_1 (@ (@ tptp.funcSet A) B))) (or (not (@ (@ tptp.in Xf) _let_1)) (not (@ (@ tptp.in BOUND_VARIABLE_8307) _let_1)) (not (forall ((Xx $$unsorted)) (let ((_let_1 (@ (@ tptp.ap A) B))) (or (not (@ (@ tptp.in Xx) A)) (= (@ (@ _let_1 Xf) Xx) (@ (@ _let_1 BOUND_VARIABLE_8307) Xx)))))) (= Xf BOUND_VARIABLE_8307)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted)) (BOUND_VARIABLE_8350 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ Xf Xx)) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_8350) A)) (= (@ (@ (@ (@ tptp.ap A) B) (@ (@ (@ tptp.lam A) B) (lambda ((Xy $$unsorted)) (@ Xf Xy)))) BOUND_VARIABLE_8350) (@ Xf BOUND_VARIABLE_8350)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (or (not (@ (@ (@ tptp.func A) B) Xf)) (= Xf (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted))) (let ((_let_1 (@ (@ tptp.lam A) B))) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ Xf Xx)) B)))) (= (@ _let_1 (lambda ((Xx $$unsorted)) (@ Xf Xx))) (@ _let_1 (lambda ((Xx $$unsorted)) (@ Xf Xx))))))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf (-> $$unsorted $$unsorted)) (BOUND_VARIABLE_8395 $$unsorted)) (or (not (forall ((Xx $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (@ (@ tptp.in (@ Xf Xx)) B)))) (not (@ (@ tptp.in BOUND_VARIABLE_8395) A)) (= (@ (@ (@ (@ tptp.ap A) B) (@ (@ (@ tptp.lam A) B) (lambda ((Xy $$unsorted)) (@ Xf Xy)))) BOUND_VARIABLE_8395) (@ Xf BOUND_VARIABLE_8395)))) (=> (forall ((A $$unsorted) (B $$unsorted) (Xf $$unsorted)) (or (not (@ (@ tptp.in Xf) (@ (@ tptp.funcSet A) B))) (= Xf (@ (@ (@ tptp.lam A) B) (lambda ((Xx $$unsorted)) (@ (@ (@ (@ tptp.ap A) B) Xf) Xx)))))) (=> (forall ((A $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_8442 $$unsorted)) (let ((_let_1 (@ tptp.in BOUND_VARIABLE_8442))) (or (not (@ (@ tptp.in Xx) A)) (not (@ _let_1 A)) (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (= Xz BOUND_VARIABLE_8442))))))) (=> (forall ((A $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_8509 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8509) A)) (= (@ (@ tptp.setadjoin BOUND_VARIABLE_8509) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (= Xz BOUND_VARIABLE_8509)))))) (=> (forall ((A $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_8577 $$unsorted)) (let ((_let_1 (@ tptp.in Xx))) (or (not (@ _let_1 A)) (not (@ (@ tptp.in BOUND_VARIABLE_8577) A)) (@ _let_1 (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (= Xx Xz))))))) (=> (forall ((A $$unsorted) (Xx $$unsorted) (BOUND_VARIABLE_8644 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8644) A)) (= (@ (@ tptp.setadjoin Xx) tptp.emptyset) (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (= Xx Xz)))))) (=> (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted) (BOUND_VARIABLE_8705 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8705) A)) (@ tptp.singleton (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xx Xz)) (and (not Xphi) (= Xz BOUND_VARIABLE_8705)))))))) (=> (forall ((A $$unsorted) (Xphi Bool) (Xx $$unsorted) (BOUND_VARIABLE_8756 $$unsorted)) (or (not (@ (@ tptp.in Xx) A)) (not (@ (@ tptp.in BOUND_VARIABLE_8756) A)) (@ (@ tptp.in (@ tptp.setunion (@ (@ tptp.dsetconstr A) (lambda ((Xz $$unsorted)) (or (and Xphi (= Xz Xx)) (and (not Xphi) (= Xz BOUND_VARIABLE_8756))))))) A))) (=> (forall ((X $$unsorted) (BOUND_VARIABLE_8783 $$unsorted)) (or (not (@ tptp.singleton X)) (not (@ (@ tptp.in BOUND_VARIABLE_8783) X)) (= (@ tptp.setunion X) BOUND_VARIABLE_8783))) (=> _let_262 _let_271))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_270) :args _let_269))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (let ((_let_506 (not _let_268))) (let ((_let_507 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_508 (or (not _let_507) _let_267 _let_265))) (let ((_let_509 (not _let_508))) (let ((_let_510 (or))) (let ((_let_511 (not _let_271))) (let ((_let_512 (@ tptp.dsetconstr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_513 (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (TRANS (CONG (REFL :args (tptp.setunion)) (TRANS (CONG (REFL :args (_let_512)) (MACRO_SR_PRED_INTRO :args ((= (lambda ((Xz $$unsorted)) (= Xz SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) lambdaF_5))) :args _let_273) (THEORY_PREPROCESS :args ((= (@ _let_512 lambdaF_5) _let_263)))) :args _let_273) (THEORY_PREPROCESS :args ((= (@ tptp.setunion _let_263) _let_264)))) :args (=)))) (let ((_let_514 (CONG (THEORY_PREPROCESS :args ((= (@ (@ tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_266))) :args _let_269))) (let ((_let_515 (_let_511))) (let ((_let_516 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_515)) :args _let_515) (CONG (REFL :args _let_515) (CONG (CONG (CONG (THEORY_PREPROCESS :args ((= (@ (@ tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_507))) :args _let_269) _let_514 _let_513 :args _let_510) :args _let_269) :args _let_270))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_511) _let_271))) (REFL :args (_let_509)) :args _let_510)) (NOT_IMPLIES_ELIM2 _let_505) :args (_let_509 true _let_271)))) (let ((_let_517 (_let_262))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_517) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (@ (@ tptp.in Xx) A) false)) (@ tptp.in BOUND_VARIABLE_8816)))) :args _let_517) (CONG (REFL :args _let_517) (CONG _let_514 _let_514 _let_513 :args _let_510) :args _let_270))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_268))) :args ((or _let_265 _let_267 _let_506))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_508 2)) _let_516 :args ((not _let_265) true _let_508)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_508 1)) (CONG (REFL :args (_let_508)) (MACRO_SR_PRED_INTRO :args ((= (not _let_267) _let_266))) :args _let_510)) :args ((or _let_266 _let_508))) _let_516 :args (_let_266 true _let_508)) :args (_let_506 true _let_265 false _let_266)) (NOT_IMPLIES_ELIM1 _let_505) :args (false true _let_268 false _let_262)) :args (_let_261 _let_260 _let_259 _let_257 _let_256 _let_255 _let_254 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_226 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_216 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_201 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_161 _let_160 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_150 _let_149 _let_147 _let_145 _let_144 _let_142 _let_141 _let_140 _let_139 _let_137 _let_135 _let_134 _let_133 _let_132 _let_130 _let_129 _let_128 _let_127 _let_126 _let_124 _let_123 _let_122 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_102 _let_100 _let_98 _let_96 _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_79 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _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_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 40.96/41.41 ) 40.96/41.41 % SZS output end Proof for 40.96/41.41 % cvc5---1.0.5 exiting 40.96/41.41 % cvc5---1.0.5 exiting 40.96/41.41 EOF