include('Axioms/bit+2.ax').
fof(mem_c_2Epred__set_2EBIGINTER,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EBIGINTER(A_27a),arr(arr(arr(A_27a,bool),bool),arr(A_27a,bool))) ) )).
fof(mem_c_2Epred__set_2EBIGUNION,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EBIGUNION(A_27a),arr(arr(arr(A_27a,bool),bool),arr(A_27a,bool))) ) )).
fof(mem_c_2Epred__set_2EBIJ,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2EBIJ(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool)))) ) ) )).
fof(mem_c_2Epred__set_2ECARD,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2ECARD(A_27a),arr(arr(A_27a,bool),ty_2Enum_2Enum)) ) )).
fof(mem_c_2Epred__set_2ECHOICE,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2ECHOICE(A_27a),arr(arr(A_27a,bool),A_27a)) ) )).
fof(mem_c_2Epred__set_2ECOMPL,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2ECOMPL(A_27a),arr(arr(A_27a,bool),arr(A_27a,bool))) ) )).
fof(mem_c_2Epred__set_2ECROSS,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2ECROSS(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)))) ) ) )).
fof(mem_c_2Epred__set_2EDELETE,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EDELETE(A_27a),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) ) )).
fof(mem_c_2Epred__set_2EDFUNSET,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2EDFUNSET(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,A_27b),bool)))) ) ) )).
fof(mem_c_2Epred__set_2EDIFF,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EDIFF(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),arr(A_27a,bool)))) ) )).
fof(mem_c_2Epred__set_2EDISJOINT,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EDISJOINT(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ) )).
fof(mem_c_2Epred__set_2EEMPTY,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EEMPTY(A_27a),arr(A_27a,bool)) ) )).
fof(mem_c_2Epred__set_2EFINITE,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EFINITE(A_27a),arr(arr(A_27a,bool),bool)) ) )).
fof(mem_c_2Epred__set_2EFUNSET,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2EFUNSET(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(arr(A_27a,A_27b),bool)))) ) ) )).
fof(mem_c_2Epred__set_2EGSPEC,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2EGSPEC(A_27a,A_27b),arr(arr(A_27b,ty_2Epair_2Eprod(A_27a,bool)),arr(A_27a,bool))) ) ) )).
fof(mem_c_2Epred__set_2EIMAGE,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2EIMAGE(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,bool)))) ) ) )).
fof(mem_c_2Epred__set_2EINJ,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2EINJ(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool)))) ) ) )).
fof(mem_c_2Epred__set_2EINSERT,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EINSERT(A_27a),arr(A_27a,arr(arr(A_27a,bool),arr(A_27a,bool)))) ) )).
fof(mem_c_2Epred__set_2EINTER,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EINTER(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),arr(A_27a,bool)))) ) )).
fof(mem_c_2Epred__set_2EITSET,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2EITSET(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,A_27b)),arr(arr(A_27a,bool),arr(A_27b,A_27b)))) ) ) )).
fof(mem_c_2Epred__set_2ELINV,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2ELINV(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,A_27a)))) ) ) )).
fof(mem_c_2Epred__set_2ELINV__OPT,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2ELINV__OPT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,ty_2Eoption_2Eoption(A_27a))))) ) ) )).
fof(mem_c_2Epred__set_2EMAX__SET,axiom,( mem(c_2Epred__set_2EMAX__SET,arr(arr(ty_2Enum_2Enum,bool),ty_2Enum_2Enum)) )).
fof(mem_c_2Epred__set_2EMIN__SET,axiom,( mem(c_2Epred__set_2EMIN__SET,arr(arr(ty_2Enum_2Enum,bool),ty_2Enum_2Enum)) )).
fof(mem_c_2Epred__set_2EPOW,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EPOW(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ) )).
fof(mem_c_2Epred__set_2EPREIMAGE,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),arr(A_27a,bool)))) ) ) )).
fof(mem_c_2Epred__set_2EPROD__IMAGE,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EPROD__IMAGE(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27a,bool),ty_2Enum_2Enum))) ) )).
fof(mem_c_2Epred__set_2EPROD__SET,axiom,( mem(c_2Epred__set_2EPROD__SET,arr(arr(ty_2Enum_2Enum,bool),ty_2Enum_2Enum)) )).
fof(mem_c_2Epred__set_2EPSUBSET,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EPSUBSET(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ) )).
fof(mem_c_2Epred__set_2EREL__RESTRICT,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EREL__RESTRICT(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))))) ) )).
fof(mem_c_2Epred__set_2EREST,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EREST(A_27a),arr(arr(A_27a,bool),arr(A_27a,bool))) ) )).
fof(mem_c_2Epred__set_2ERINV,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2ERINV(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,A_27a)))) ) ) )).
fof(mem_c_2Epred__set_2ESING,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2ESING(A_27a),arr(arr(A_27a,bool),bool)) ) )).
fof(mem_c_2Epred__set_2ESUBSET,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2ESUBSET(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ) )).
fof(mem_c_2Epred__set_2ESUM__IMAGE,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2ESUM__IMAGE(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27a,bool),ty_2Enum_2Enum))) ) )).
fof(mem_c_2Epred__set_2ESUM__SET,axiom,( mem(c_2Epred__set_2ESUM__SET,arr(arr(ty_2Enum_2Enum,bool),ty_2Enum_2Enum)) )).
fof(mem_c_2Epred__set_2ESURJ,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2ESURJ(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool)))) ) ) )).
fof(mem_c_2Epred__set_2EUNION,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EUNION(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),arr(A_27a,bool)))) ) )).
fof(mem_c_2Epred__set_2EUNIV,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EUNIV(A_27a),arr(A_27a,bool)) ) )).
fof(mem_c_2Epred__set_2Echooser,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2Echooser(A_27a),arr(arr(A_27a,bool),arr(ty_2Enum_2Enum,A_27a))) ) )).
fof(mem_c_2Epred__set_2Ecount,axiom,( mem(c_2Epred__set_2Ecount,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Epred__set_2Ecountable,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2Ecountable(A_27a),arr(arr(A_27a,bool),bool)) ) )).
fof(mem_c_2Epred__set_2Eenumerate,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2Eenumerate(A_27a),arr(arr(A_27a,bool),arr(ty_2Enum_2Enum,A_27a))) ) )).
fof(mem_c_2Epred__set_2Eequiv__on,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2Eequiv__on(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),bool))) ) )).
fof(mem_c_2Epred__set_2Eis__measure__maximal,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2Eis__measure__maximal(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27a,bool),arr(A_27a,bool)))) ) )).
fof(mem_c_2Epred__set_2Enum__to__pair,axiom,( mem(c_2Epred__set_2Enum__to__pair,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Epred__set_2Epair__to__num,axiom,( mem(c_2Epred__set_2Epair__to__num,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) )).
fof(mem_c_2Epred__set_2Epairwise,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2Epairwise(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),bool))) ) )).
fof(mem_c_2Epred__set_2Epartition,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2Epartition(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool)))) ) )).
fof(mem_c_2Epred__set_2Eschroeder__close,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2Eschroeder__close(A_27a),arr(arr(A_27a,A_27a),arr(arr(A_27a,bool),arr(A_27a,bool)))) ) )).
fof(conj_thm_2Epred__set_2ESPECIFICATION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1x] : ( mem(V1x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0P)) <=> p(ap(V0P,V1x)) ) ) )))).
fof(conj_thm_2Epred__set_2EIN__APP,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1P)) <=> p(ap(V1P,V0x)) ) ) )))).
fof(conj_thm_2Epred__set_2EIN__ABS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),f252(A_27a,V1P))) <=> p(ap(V1P,V0x)) ) ) )))).
fof(conj_thm_2Epred__set_2EEXTENSION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ( V0s = V1t ) <=> ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2ENOT__EQUAL__SETS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ( ~~ ( V0s = V1t ) ) <=> ? [V2x] : ( mem(V2x,A_27a) & ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) <=> ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2ENUM__SET__WOP,lemma,(! [V0s] : ( mem(V0s,arr(ty_2Enum_2Enum,bool)) => ( ( ? [V1n] : ( mem(V1n,ty_2Enum_2Enum) & p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V1n),V0s)) ) ) <=> ? [V2n] : ( mem(V2n,ty_2Enum_2Enum) & ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V2n),V0s)) & ! [V3m] : ( mem(V3m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V3m),V0s)) => p(ap(ap(c_2Earithmetic_2E_3C_3D,V2n),V3m)) ) ) ) ) ) ))).
fof(ax_thm_2Epred__set_2EGSPECIFICATION,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool))) => ! [V1v] : ( mem(V1v,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1v),ap(c_2Epred__set_2EGSPEC(A_27a,A_27b),V0f))) <=> ? [V2x] : ( mem(V2x,A_27b) & ( ap(ap(c_2Epair_2E_2C(A_27a,bool),V1v),c_2Ebool_2ET) = ap(V0f,V2x) ) ) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EGSPECIFICATION__applied,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool))) => ! [V1v] : ( mem(V1v,A_27a) => ( p(ap(ap(c_2Epred__set_2EGSPEC(A_27a,A_27b),V0f),V1v)) <=> ? [V2x] : ( mem(V2x,A_27b) & ( ap(ap(c_2Epair_2E_2C(A_27a,bool),V1v),c_2Ebool_2ET) = ap(V0f,V2x) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EGSPEC__ETA,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ( ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f253(A_27a,V0P)) = V0P ) )))).
fof(conj_thm_2Epred__set_2EGSPEC__PAIR__ETA,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0P] : ( mem(V0P,arr(A_27a,arr(A_27b,bool))) => ( ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f255(A_27a,A_27b,V0P))) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),V0P) ) ))))).
fof(conj_thm_2Epred__set_2EIN__GSPEC__IFF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0y] : ( mem(V0y,A_27a) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0y),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f256(A_27a,V1P)))) <=> p(ap(V1P,V0y)) ) ) )))).
fof(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__IFF,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27b) => ! [V2P] : ( mem(V2P,arr(A_27a,arr(A_27b,bool))) => ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f258(A_27a,A_27b,V2P))))) <=> p(ap(ap(V2P,V0x),V1y)) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EIN__GSPEC,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1y] : ( mem(V1y,A_27a) => ! [V2x] : ( mem(V2x,A_27b) => ! [V3P] : ( mem(V3P,arr(A_27a,bool)) => ( ( p(ap(V3P,V1y)) & ( V2x = ap(V0f,V1y) ) ) => p(ap(ap(c_2Ebool_2EIN(A_27b),V2x),ap(c_2Epred__set_2EGSPEC(A_27b,A_27a),f259(A_27b,A_27a,V0f,V3P)))) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__1,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0a] : ( mem(V0a,A_27a) => ! [V1b] : ( mem(V1b,A_27b) => ! [V2x] : ( mem(V2x,A_27b) => ! [V3P] : ( mem(V3P,arr(A_27a,bool)) => ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0a),V1b)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),f260(A_27b,A_27a,V2x,V3P)))) <=> ( p(ap(V3P,V0a)) & ( V1b = V2x ) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__2,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0a] : ( mem(V0a,A_27a) => ! [V1b] : ( mem(V1b,A_27b) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3P] : ( mem(V3P,arr(A_27b,bool)) => ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0a),V1b)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),f261(A_27a,A_27b,V2x,V3P)))) <=> ( p(ap(V3P,V1b)) & ( V0a = V2x ) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__same,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,A_27a) => ! [V1b] : ( mem(V1b,A_27a) => ! [V2P] : ( mem(V2P,arr(A_27a,bool)) => ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V0a),V1b)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),A_27a),f262(A_27a,V2P)))) <=> ( p(ap(V2P,V0a)) & ( V0a = V1b ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2ESET__MINIMUM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1M] : ( mem(V1M,arr(A_27a,ty_2Enum_2Enum)) => ( ( ? [V2x] : ( mem(V2x,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) ) ) <=> ? [V3x] : ( mem(V3x,A_27a) & ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s)) & ! [V4y] : ( mem(V4y,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),V0s)) => p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(V1M,V3x)),ap(V1M,V4y))) ) ) ) ) ) ) )))).
fof(ax_thm_2Epred__set_2EEMPTY__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ( c_2Epred__set_2EEMPTY(A_27a) = k(A_27a,c_2Ebool_2EF) ) ) )).
fof(conj_thm_2Epred__set_2ENOT__IN__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))) ) )))).
fof(conj_thm_2Epred__set_2EMEMBER__NOT__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ( ? [V1x] : ( mem(V1x,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) ) ) <=> ( ~~ ( V0s = c_2Epred__set_2EEMPTY(A_27a) ) ) ) )))).
fof(conj_thm_2Epred__set_2EEMPTY__applied,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( p(ap(c_2Epred__set_2EEMPTY(A_27a),V0x)) <=> $false ) )))).
fof(ax_thm_2Epred__set_2EUNIV__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ( c_2Epred__set_2EUNIV(A_27a) = k(A_27a,c_2Ebool_2ET) ) ) )).
fof(conj_thm_2Epred__set_2EIN__UNIV,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),c_2Epred__set_2EUNIV(A_27a))) )))).
fof(conj_thm_2Epred__set_2EUNIV__applied,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => p(ap(c_2Epred__set_2EUNIV(A_27a),V0x)) )))).
fof(conj_thm_2Epred__set_2EUNIV__NOT__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ( ~~ ( c_2Epred__set_2EUNIV(A_27a) = c_2Epred__set_2EEMPTY(A_27a) ) )))).
fof(conj_thm_2Epred__set_2EEMPTY__NOT__UNIV,lemma,( ! [A_27a]: ( ne(A_27a) => ( ~~ ( c_2Epred__set_2EEMPTY(A_27a) = c_2Epred__set_2EUNIV(A_27a) ) )))).
fof(conj_thm_2Epred__set_2EEQ__UNIV,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ( ! [V1x] : ( mem(V1x,A_27a) => p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) ) ) <=> ( V0s = c_2Epred__set_2EUNIV(A_27a) ) ) )))).
fof(conj_thm_2Epred__set_2EIN__EQ__UNIV__IMP,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ( V0s = c_2Epred__set_2EUNIV(A_27a) ) => ! [V1v] : ( mem(V1v,A_27a) => p(ap(ap(c_2Ebool_2EIN(A_27a),V1v),V0s)) ) ) )))).
fof(ax_thm_2Epred__set_2ESUBSET__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) <=> ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) ) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2ESUBSET__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0P),V1Q)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P)) => p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1Q)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__applied,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) <=> ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(V0s,V2x)) => p(ap(V1t,V2x)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__TRANS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2u] : ( mem(V2u,arr(A_27a,bool)) => ( ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V2u)) ) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V2u)) ) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__REFL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V0s)) )))).
fof(conj_thm_2Epred__set_2ESUBSET__ANTISYM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) ) => ( V0s = V1t ) ) ) )))).
fof(conj_thm_2Epred__set_2EEMPTY__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s)) )))).
fof(conj_thm_2Epred__set_2ESUBSET__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),c_2Epred__set_2EEMPTY(A_27a))) <=> ( V0s = c_2Epred__set_2EEMPTY(A_27a) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__UNIV,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),c_2Epred__set_2EUNIV(A_27a))) )))).
fof(conj_thm_2Epred__set_2EUNIV__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0s)) <=> ( V0s = c_2Epred__set_2EUNIV(A_27a) ) ) )))).
fof(conj_thm_2Epred__set_2EEQ__SUBSET__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ( V0s = V1t ) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) ) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__SUBSET__EQ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) ) <=> ( V0s = V1t ) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__ADD,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,bool))) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2d] : ( mem(V2d,ty_2Enum_2Enum) => ( ( ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V0f,V3n)),ap(V0f,ap(c_2Enum_2ESUC,V3n)))) ) ) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V0f,V1n)),ap(V0f,ap(ap(c_2Earithmetic_2E_2B,V1n),V2d)))) ) ) ) )))).
fof(conj_thm_2Epred__set_2EK__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,bool) => ! [V1y] : ( mem(V1y,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Ecombin_2EK(bool,A_27a),V0x)),V1y)) <=> ( ( ~~ p(V0x) ) | p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),c_2Epred__set_2EUNIV(A_27a)),V1y)) ) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__K,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,arr(A_27a,bool)) => ! [V1y] : ( mem(V1y,bool) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0x),ap(c_2Ecombin_2EK(bool,A_27a),V1y))) <=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))) | p(V1y) ) ) ) )))).
fof(ax_thm_2Epred__set_2EPSUBSET__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V1t)) <=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) & ( ~~ ( V0s = V1t ) ) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EPSUBSET__TRANS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2u] : ( mem(V2u,arr(A_27a,bool)) => ( ( p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V1t)) & p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V1t),V2u)) ) => p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V2u)) ) ) ) )))).
fof(conj_thm_2Epred__set_2EPSUBSET__IRREFL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ~~ p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V0s)) ) )))).
fof(conj_thm_2Epred__set_2ENOT__PSUBSET__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ~~ p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),c_2Epred__set_2EEMPTY(A_27a))) ) )))).
fof(conj_thm_2Epred__set_2ENOT__UNIV__PSUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ~~ p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0s)) ) )))).
fof(conj_thm_2Epred__set_2EPSUBSET__UNIV,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),c_2Epred__set_2EUNIV(A_27a))) <=> ? [V1x] : ( mem(V1x,A_27a) & ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) ) ) ) )))).
fof(ax_thm_2Epred__set_2EUNION__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f263(A_27a,V1t,V0s)) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EIN__UNION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))) <=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) | p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EUNION__applied,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t),V2x)) <=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) | p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EUNION__ASSOC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2u] : ( mem(V2u,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),ap(ap(c_2Epred__set_2EUNION(A_27a),V1t),V2u)) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),V2u) ) ) ) )))).
fof(conj_thm_2Epred__set_2EUNION__IDEMPOT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V0s) = V0s ) )))).
fof(conj_thm_2Epred__set_2EUNION__COMM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t) = ap(ap(c_2Epred__set_2EUNION(A_27a),V1t),V0s) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__UNION,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))) ) ) ) & ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ! [V3t] : ( mem(V3t,arr(A_27a,bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2s),ap(ap(c_2Epred__set_2EUNION(A_27a),V3t),V2s))) ) ) )))).
fof(conj_thm_2Epred__set_2EUNION__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2u] : ( mem(V2u,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),V2u)) <=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V2u)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V2u)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__UNION__ABSORPTION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) <=> ( ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t) = V1t ) ) ) )))).
fof(conj_thm_2Epred__set_2EUNION__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EUNION(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s) = V0s ) ) ) & ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),c_2Epred__set_2EEMPTY(A_27a)) = V1s ) ) )))).
fof(conj_thm_2Epred__set_2EUNION__UNIV,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EUNION(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0s) = c_2Epred__set_2EUNIV(A_27a) ) ) ) & ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),c_2Epred__set_2EUNIV(A_27a)) = c_2Epred__set_2EUNIV(A_27a) ) ) )))).
fof(conj_thm_2Epred__set_2EEMPTY__UNION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ( ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t) = c_2Epred__set_2EEMPTY(A_27a) ) <=> ( ( V0s = c_2Epred__set_2EEMPTY(A_27a) ) & ( V1t = c_2Epred__set_2EEMPTY(A_27a) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EFORALL__IN__UNION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27a,bool)) => ( ( ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t))) => p(ap(V0P,V3x)) ) ) ) <=> ( ( ! [V4x] : ( mem(V4x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s)) => p(ap(V0P,V4x)) ) ) ) & ! [V5x] : ( mem(V5x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V5x),V2t)) => p(ap(V0P,V5x)) ) ) ) ) ) ) )))).
fof(ax_thm_2Epred__set_2EINTER__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f264(A_27a,V1t,V0s)) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EIN__INTER,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t))) <=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EINTER__applied,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t),V2x)) <=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EINTER__ASSOC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2u] : ( mem(V2u,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V2u)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)),V2u) ) ) ) )))).
fof(conj_thm_2Epred__set_2EINTER__IDEMPOT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V0s) = V0s ) )))).
fof(conj_thm_2Epred__set_2EINTER__COMM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t) = ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V0s) ) ) )))).
fof(conj_thm_2Epred__set_2EINTER__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)),V0s)) ) ) ) & ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ! [V3t] : ( mem(V3t,arr(A_27a,bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V3t),V2s)),V2s)) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__INTER,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2u] : ( mem(V2u,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V2u))) <=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V2u)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__INTER__ABSORPTION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) <=> ( ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t) = V0s ) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__INTER1,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t) = V0s ) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__INTER2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V0s) = V0s ) ) ) )))).
fof(conj_thm_2Epred__set_2EINTER__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s) = c_2Epred__set_2EEMPTY(A_27a) ) ) ) & ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),c_2Epred__set_2EEMPTY(A_27a)) = c_2Epred__set_2EEMPTY(A_27a) ) ) )))).
fof(conj_thm_2Epred__set_2EINTER__UNIV,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0s) = V0s ) ) ) & ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),c_2Epred__set_2EUNIV(A_27a)) = V1s ) ) )))).
fof(conj_thm_2Epred__set_2EUNION__OVER__INTER,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2u] : ( mem(V2u,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),ap(ap(c_2Epred__set_2EUNION(A_27a),V1t),V2u)) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V2u)) ) ) ) )))).
fof(conj_thm_2Epred__set_2EINTER__OVER__UNION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2u] : ( mem(V2u,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V2u)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V2u)) ) ) ) )))).
fof(ax_thm_2Epred__set_2EDISJOINT__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t)) <=> ( ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t) = c_2Epred__set_2EEMPTY(A_27a) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EIN__DISJOINT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t)) <=> ( ~~ ? [V2x] : ( mem(V2x,A_27a) & ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__SYM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t)) <=> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),V0s)) ) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__ALT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t)) <=> ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) => ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),c_2Epred__set_2EEMPTY(A_27a))) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__EMPTY__REFL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ( V0s = c_2Epred__set_2EEMPTY(A_27a) ) <=> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V0s)) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__EMPTY__REFL__RWT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V0s)) <=> ( V0s = c_2Epred__set_2EEMPTY(A_27a) ) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__UNION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2u] : ( mem(V2u,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),V2u)) <=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V2u)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),V2u)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__UNION__BOTH,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2u] : ( mem(V2u,arr(A_27a,bool)) => ( ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),V2u)) <=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V2u)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),V2u)) ) ) & ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V2u),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))) <=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V2u)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),V2u)) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2u] : ( mem(V2u,arr(A_27a,bool)) => ( ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2u),V1t)) ) => p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V2u)) ) ) ) )))).
fof(ax_thm_2Epred__set_2EDIFF__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f265(A_27a,V1t,V0s)) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EIN__DIFF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t))) <=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDIFF__applied,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t),V2x)) <=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDIFF__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),c_2Epred__set_2EEMPTY(A_27a)) = V0s ) )))).
fof(conj_thm_2Epred__set_2EEMPTY__DIFF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EDIFF(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s) = c_2Epred__set_2EEMPTY(A_27a) ) )))).
fof(conj_thm_2Epred__set_2EDIFF__UNIV,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),c_2Epred__set_2EUNIV(A_27a)) = c_2Epred__set_2EEMPTY(A_27a) ) )))).
fof(conj_thm_2Epred__set_2EDIFF__DIFF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),V1t) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t) ) ) )))).
fof(conj_thm_2Epred__set_2EDIFF__EQ__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V0s) = c_2Epred__set_2EEMPTY(A_27a) ) )))).
fof(conj_thm_2Epred__set_2EDIFF__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),V0s)) ) )))).
fof(conj_thm_2Epred__set_2EUNION__DIFF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) => ( ( ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1t),V0s)) = V1t ) & ( ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1t),V0s)),V0s) = V1t ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDIFF__DIFF__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) => ( ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)) = V1t ) ) ) )))).
fof(conj_thm_2Epred__set_2EDIFF__UNION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,arr(A_27a,bool)) => ! [V1y] : ( mem(V1y,arr(A_27a,bool)) => ! [V2z] : ( mem(V2z,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),ap(ap(c_2Epred__set_2EUNION(A_27a),V1y),V2z)) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),V1y)),V2z) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDIFF__COMM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,arr(A_27a,bool)) => ! [V1y] : ( mem(V1y,arr(A_27a,bool)) => ! [V2z] : ( mem(V2z,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),V1y)),V2z) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),V2z)),V1y) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDIFF__SAME__UNION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,arr(A_27a,bool)) => ! [V1y] : ( mem(V1y,arr(A_27a,bool)) => ( ( ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0x),V1y)),V0x) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V1y),V0x) ) & ( ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0x),V1y)),V1y) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),V1y) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDIFF__INTER,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2g] : ( mem(V2g,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),V2g) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V2g)),V1t) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDIFF__INTER2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V0s)) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t) ) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__DIFF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t))) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),V1t)) ) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__DIFFS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0g] : ( mem(V0g,arr(ty_2Enum_2Enum,arr(A_27a,bool))) => ! [V1f] : ( mem(V1f,arr(ty_2Enum_2Enum,arr(A_27a,bool))) => ! [V2m] : ( mem(V2m,ty_2Enum_2Enum) => ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( ( ( ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V1f,V4n)),ap(V1f,ap(c_2Enum_2ESUC,V4n)))) ) ) & ( ( ! [V5n] : ( mem(V5n,ty_2Enum_2Enum) => ( ap(V0g,V5n) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(V1f,ap(c_2Enum_2ESUC,V5n))),ap(V1f,V5n)) ) ) ) & ( ~~ ( V2m = V3n ) ) ) ) => p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(V0g,V2m)),ap(V0g,V3n))) ) ) ) ) )))).
fof(ax_thm_2Epred__set_2EINSERT__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f266(A_27a,V1s,V0x)) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EIN__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),V2s))) <=> ( ( V0x = V1y ) | p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2s)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EINSERT__applied,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),V2s),V0x)) <=> ( ( V0x = V1y ) | p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2s)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2ECOMPONENT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))) ) )))).
fof(conj_thm_2Epred__set_2ESET__CASES,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ( V0s = c_2Epred__set_2EEMPTY(A_27a) ) | ? [V1x] : ( mem(V1x,A_27a) & ? [V2t] : ( mem(V2t,arr(A_27a,bool)) & ( ( V0s = ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V2t) ) & ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2t)) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDECOMPOSITION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1x] : ( mem(V1x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) <=> ? [V2t] : ( mem(V2t,arr(A_27a,bool)) & ( ( V0s = ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V2t) ) & ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2t)) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EABSORPTION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) <=> ( ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s) = V1s ) ) ) )))).
fof(conj_thm_2Epred__set_2EABSORPTION__RWT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) => ( ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s) = V1s ) ) ) )))).
fof(conj_thm_2Epred__set_2EINSERT__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s) ) ) )))).
fof(conj_thm_2Epred__set_2EINSERT__COMM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),V2s)) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V2s)) ) ) ) )))).
fof(conj_thm_2Epred__set_2EINSERT__UNIV,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EUNIV(A_27a)) = c_2Epred__set_2EUNIV(A_27a) ) )))).
fof(conj_thm_2Epred__set_2ENOT__INSERT__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( ~~ ( ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s) = c_2Epred__set_2EEMPTY(A_27a) ) ) ) )))).
fof(conj_thm_2Epred__set_2ENOT__EMPTY__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( ~~ ( c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s) ) ) ) )))).
fof(conj_thm_2Epred__set_2EINSERT__UNION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,bool)),ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t)),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t))) ) ) ) )))).
fof(conj_thm_2Epred__set_2EINSERT__UNION__EQ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t)) ) ) ) )))).
fof(conj_thm_2Epred__set_2EINSERT__INTER,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,bool)),ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),V2t))),ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),V2t)) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t)) <=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1s),V2t)) & ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t)) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__INSERT_27,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V2t),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))) <=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V2t),V1s)) & ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t)) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EINSERT__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t)) <=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) ) => ! [V2t] : ( mem(V2t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V2t))) <=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EINSERT__DIFF,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2x] : ( mem(V2x,A_27a) => ( ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V0s)),V1t) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,bool)),ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t))) ) ) ) )))).
fof(conj_thm_2Epred__set_2EUNIV__BOOL,lemma,(( c_2Epred__set_2EUNIV(bool) = ap(ap(c_2Epred__set_2EINSERT(bool),c_2Ebool_2ET),ap(ap(c_2Epred__set_2EINSERT(bool),c_2Ebool_2EF),c_2Epred__set_2EEMPTY(bool))) ))).
fof(conj_thm_2Epred__set_2EFORALL__IN__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1a] : ( mem(V1a,A_27a) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( ( ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1a),V2s))) => p(ap(V0P,V3x)) ) ) ) <=> ( p(ap(V0P,V1a)) & ! [V4x] : ( mem(V4x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V2s)) => p(ap(V0P,V4x)) ) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EEXISTS__IN__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1a] : ( mem(V1a,A_27a) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( ( ? [V3x] : ( mem(V3x,A_27a) & ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1a),V2s))) & p(ap(V0P,V3x)) ) ) ) <=> ( p(ap(V0P,V1a)) | ? [V4x] : ( mem(V4x,A_27a) & ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V2s)) & p(ap(V0P,V4x)) ) ) ) ) ) ) )))).
fof(ax_thm_2Epred__set_2EDELETE__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1x] : ( mem(V1x,A_27a) => ( ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V1x) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a))) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EIN__DELETE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y))) <=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) & ( ~~ ( V1x = V2y ) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDELETE__applied,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y),V1x)) <=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) & ( ~~ ( V1x = V2y ) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDELETE__NON__ELEMENT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) ) <=> ( ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x) = V1s ) ) ) )))).
fof(conj_thm_2Epred__set_2EDELETE__NON__ELEMENT__RWT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1x] : ( mem(V1x,A_27a) => ( ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) ) => ( ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V1x) = V0s ) ) ) )))).
fof(conj_thm_2Epred__set_2EIN__DELETE__EQ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2x_27] : ( mem(V2x_27,A_27a) => ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x_27),V0s)) ) <=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2x_27))) <=> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x_27),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V1x))) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EEMPTY__DELETE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ap(ap(c_2Epred__set_2EDELETE(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0x) = c_2Epred__set_2EEMPTY(A_27a) ) )))).
fof(conj_thm_2Epred__set_2EELT__IN__DELETE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x))) ) ) )))).
fof(conj_thm_2Epred__set_2EDELETE__DELETE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)),V0x) = ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x) ) ) )))).
fof(conj_thm_2Epred__set_2EDELETE__COMM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V0x)),V1y) = ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1y)),V0x) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDELETE__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)),V1s)) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__DELETE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2t),V0x))) <=> ( ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) ) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__INSERT__DELETE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V2t))) <=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)),V2t)) ) ) ) )))).
fof(conj_thm_2Epred__set_2ESUBSET__OF__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))) ) )))).
fof(conj_thm_2Epred__set_2EDIFF__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2x] : ( mem(V2x,A_27a) => ( ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V1t)) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2x)),V1t) ) ) ) )))).
fof(conj_thm_2Epred__set_2EPSUBSET__INSERT__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V1t)) <=> ? [V2x] : ( mem(V2x,A_27a) & ( ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) ) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V0s)),V1t)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EPSUBSET__MEMBER,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V1t)) <=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) & ? [V2y] : ( mem(V2y,A_27a) & ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),V1t)) & ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),V0s)) ) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDELETE__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V2s)),V1y) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,bool)),ap(ap(c_2Emin_2E_3D(A_27a),V0x),V1y)),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1y)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1y))) ) ) ) )))).
fof(conj_thm_2Epred__set_2EINSERT__DELETE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) => ( ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)) = V1s ) ) ) )))).
fof(conj_thm_2Epred__set_2EDELETE__INTER,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2x] : ( mem(V2x,A_27a) => ( ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2x)),V1t) = ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)),V2x) ) ) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__DELETE__SYM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2x)),V1t)) <=> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1t),V2x)),V0s)) ) ) ) )))).
fof(ax_thm_2Epred__set_2ECHOICE__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ( ~~ ( V0s = c_2Epred__set_2EEMPTY(A_27a) ) ) => p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)),V0s)) ) ) ) )).
fof(ax_thm_2Epred__set_2EREST__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ap(c_2Epred__set_2EREST(A_27a),V0s) = ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)) ) ) ) )).
fof(conj_thm_2Epred__set_2EIN__REST,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Epred__set_2EREST(A_27a),V1s))) <=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) & ( ~~ ( V0x = ap(c_2Epred__set_2ECHOICE(A_27a),V1s) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EREST__applied,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2EREST(A_27a),V1s),V0x)) <=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) & ( ~~ ( V0x = ap(c_2Epred__set_2ECHOICE(A_27a),V1s) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2ECHOICE__NOT__IN__REST,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)),ap(c_2Epred__set_2EREST(A_27a),V0s))) ) )))).
fof(conj_thm_2Epred__set_2ECHOICE__INSERT__REST,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ( ~~ ( V0s = c_2Epred__set_2EEMPTY(A_27a) ) ) => ( ap(ap(c_2Epred__set_2EINSERT(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)),ap(c_2Epred__set_2EREST(A_27a),V0s)) = V0s ) ) )))).
fof(conj_thm_2Epred__set_2EREST__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s)),V0s)) )))).
fof(conj_thm_2Epred__set_2EREST__PSUBSET,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ( ~~ ( V0s = c_2Epred__set_2EEMPTY(A_27a) ) ) => p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s)),V0s)) ) )))).
fof(ax_thm_2Epred__set_2ESING__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( p(ap(c_2Epred__set_2ESING(A_27a),V0s)) <=> ? [V1x] : ( mem(V1x,A_27a) & ( V0s = ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a)) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2ESING,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => p(ap(c_2Epred__set_2ESING(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a)))) )))).
fof(conj_thm_2Epred__set_2ESING__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ( p(ap(c_2Epred__set_2ESING(A_27a),c_2Epred__set_2EEMPTY(A_27a))) <=> $false )))).
fof(conj_thm_2Epred__set_2ESING__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( p(ap(c_2Epred__set_2ESING(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))) <=> ( ( V1s = c_2Epred__set_2EEMPTY(A_27a) ) | ( V1s = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2ESING__UNION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(c_2Epred__set_2ESING(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))) <=> ( ( p(ap(c_2Epred__set_2ESING(A_27a),V0s)) & ( V1t = c_2Epred__set_2EEMPTY(A_27a) ) ) | ( ( p(ap(c_2Epred__set_2ESING(A_27a),V1t)) & ( V0s = c_2Epred__set_2EEMPTY(A_27a) ) ) | ( p(ap(c_2Epred__set_2ESING(A_27a),V0s)) & ( p(ap(c_2Epred__set_2ESING(A_27a),V1t)) & ( V0s = V1t ) ) ) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EIN__SING,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),c_2Epred__set_2EEMPTY(A_27a)))) <=> ( V0x = V1y ) ) ) )))).
fof(conj_thm_2Epred__set_2ESING__applied,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ( p(ap(ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),c_2Epred__set_2EEMPTY(A_27a)),V0x)) <=> ( V0x = V1y ) ) ) )))).
fof(conj_thm_2Epred__set_2ENOT__SING__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ~~ ( ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a)) = c_2Epred__set_2EEMPTY(A_27a) ) ) )))).
fof(conj_thm_2Epred__set_2ENOT__EMPTY__SING,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ~~ ( c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a)) ) ) )))).
fof(conj_thm_2Epred__set_2EEQUAL__SING,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ( ( ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a)) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),c_2Epred__set_2EEMPTY(A_27a)) ) <=> ( V0x = V1y ) ) ) )))).
fof(conj_thm_2Epred__set_2EDISJOINT__SING__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))),c_2Epred__set_2EEMPTY(A_27a))) )))).
fof(conj_thm_2Epred__set_2EINSERT__SING__UNION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1x] : ( mem(V1x,A_27a) => ( ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V0s) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a))),V0s) ) ) )))).
fof(conj_thm_2Epred__set_2ESING__DELETE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))),V0x) = c_2Epred__set_2EEMPTY(A_27a) ) )))).
fof(conj_thm_2Epred__set_2EDELETE__EQ__SING,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1x] : ( mem(V1x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) => ( ( ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V1x) = c_2Epred__set_2EEMPTY(A_27a) ) <=> ( V0s = ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2ECHOICE__SING,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ap(c_2Epred__set_2ECHOICE(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))) = V0x ) )))).
fof(conj_thm_2Epred__set_2EREST__SING,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ap(c_2Epred__set_2EREST(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))) = c_2Epred__set_2EEMPTY(A_27a) ) )))).
fof(conj_thm_2Epred__set_2ESING__IFF__EMPTY__REST,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( p(ap(c_2Epred__set_2ESING(A_27a),V0s)) <=> ( ( ~~ ( V0s = c_2Epred__set_2EEMPTY(A_27a) ) ) & ( ap(c_2Epred__set_2EREST(A_27a),V0s) = c_2Epred__set_2EEMPTY(A_27a) ) ) ) )))).
fof(ax_thm_2Epred__set_2EIMAGE__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s) = ap(c_2Epred__set_2EGSPEC(A_27b,A_27a),f267(A_27b,A_27a,V0f,V1s)) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EIN__IMAGE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0y] : ( mem(V0y,A_27b) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => ( p(ap(ap(c_2Ebool_2EIN(A_27b),V0y),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f),V1s))) <=> ? [V3x] : ( mem(V3x,A_27a) & ( ( V0y = ap(V2f,V3x) ) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EIMAGE__applied,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0y] : ( mem(V0y,A_27b) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => ( p(ap(ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f),V1s),V0y)) <=> ? [V3x] : ( mem(V3x,A_27a) & ( ( V0y = ap(V2f,V3x) ) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EIMAGE__IN,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V2f,V0x)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f),V1s))) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EIMAGE__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),c_2Epred__set_2EEMPTY(A_27a)) = c_2Epred__set_2EEMPTY(A_27b) ) ))))).
fof(conj_thm_2Epred__set_2EIMAGE__ID,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27a),i(A_27a)),V0s) = V0s ) )))).
fof(conj_thm_2Epred__set_2EIMAGE__I,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27a),c_2Ecombin_2EI(A_27a)),V0s) = V0s ) )))).
fof(conj_thm_2Epred__set_2EIMAGE__II,lemma,( ! [A_27a]: ( ne(A_27a) => ( ap(c_2Epred__set_2EIMAGE(A_27a,A_27a),c_2Ecombin_2EI(A_27a)) = c_2Ecombin_2EI(arr(A_27a,bool)) )))).
fof(conj_thm_2Epred__set_2EIMAGE__COMPOSE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0f] : ( mem(V0f,arr(A_27b,A_27c)) => ! [V1g] : ( mem(V1g,arr(A_27a,A_27b)) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V0f),V1g)),V2s) = ap(ap(c_2Epred__set_2EIMAGE(A_27b,A_27c),V0f),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V1g),V2s)) ) ) ) )))))).
fof(conj_thm_2Epred__set_2EIMAGE__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V2s)) = ap(ap(c_2Epred__set_2EINSERT(A_27b),ap(V0f,V1x)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2s)) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EIMAGE__EQ__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27b)) => ( ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V1f),V0s) = c_2Epred__set_2EEMPTY(A_27b) ) <=> ( V0s = c_2Epred__set_2EEMPTY(A_27a) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EIMAGE__DELETE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2s)) ) => ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1x)) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2s) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EIMAGE__UNION,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27a,bool)) => ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t)) = ap(ap(c_2Epred__set_2EUNION(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2t)) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EIMAGE__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f),V0s)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f),V1t))) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EIMAGE__INTER,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27a,bool)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),V2t))),ap(ap(c_2Epred__set_2EINTER(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2t)))) ) ) ))))).
fof(conj_thm_2Epred__set_2EIMAGE__11,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s1] : ( mem(V1s1,arr(A_27a,bool)) => ! [V2s2] : ( mem(V2s2,arr(A_27a,bool)) => ( ( ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ( ( ap(V0f,V3x) = ap(V0f,V4y) ) <=> ( V3x = V4y ) ) ) ) ) => ( ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s1) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2s2) ) <=> ( V1s1 = V2s2 ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EDISJOINT__IMAGE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s1] : ( mem(V1s1,arr(A_27a,bool)) => ! [V2s2] : ( mem(V2s2,arr(A_27a,bool)) => ( ( ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ( ( ap(V0f,V3x) = ap(V0f,V4y) ) <=> ( V3x = V4y ) ) ) ) ) => ( p(ap(ap(c_2Epred__set_2EDISJOINT(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s1)),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V2s2))) <=> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1s1),V2s2)) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EIMAGE__CONG,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2f_27] : ( mem(V2f_27,arr(A_27a,A_27b)) => ! [V3s_27] : ( mem(V3s_27,arr(A_27a,bool)) => ( ( ( V1s = V3s_27 ) & ! [V4x] : ( mem(V4x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V3s_27)) => ( ap(V0f,V4x) = ap(V2f_27,V4x) ) ) ) ) => ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f_27),V3s_27) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EGSPEC__IMAGE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool))) => ( ap(c_2Epred__set_2EGSPEC(A_27a,A_27b),V0f) = ap(ap(c_2Epred__set_2EIMAGE(A_27b,A_27a),ap(ap(c_2Ecombin_2Eo(A_27b,A_27a,ty_2Epair_2Eprod(A_27a,bool)),c_2Epair_2EFST(A_27a,bool)),V0f)),ap(ap(c_2Ecombin_2Eo(A_27b,bool,ty_2Epair_2Eprod(A_27a,bool)),c_2Epair_2ESND(A_27a,bool)),V0f)) ) ))))).
fof(conj_thm_2Epred__set_2EIMAGE__IMAGE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1g] : ( mem(V1g,arr(A_27c,A_27a)) => ! [V2s] : ( mem(V2s,arr(A_27c,bool)) => ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EIMAGE(A_27c,A_27a),V1g),V2s)) = ap(ap(c_2Epred__set_2EIMAGE(A_27c,A_27b),ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,A_27a),V0f),V1g)),V2s) ) ) ) )))))).
fof(conj_thm_2Epred__set_2EFORALL__IN__IMAGE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1f] : ( mem(V1f,arr(A_27b,A_27a)) => ! [V2s] : ( mem(V2s,arr(A_27b,bool)) => ( ( ! [V3y] : ( mem(V3y,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Epred__set_2EIMAGE(A_27b,A_27a),V1f),V2s))) => p(ap(V0P,V3y)) ) ) ) <=> ! [V4x] : ( mem(V4x,A_27b) => ( p(ap(ap(c_2Ebool_2EIN(A_27b),V4x),V2s)) => p(ap(V0P,ap(V1f,V4x))) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EEXISTS__IN__IMAGE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1f] : ( mem(V1f,arr(A_27b,A_27a)) => ! [V2s] : ( mem(V2s,arr(A_27b,bool)) => ( ( ? [V3y] : ( mem(V3y,A_27a) & ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(ap(c_2Epred__set_2EIMAGE(A_27b,A_27a),V1f),V2s))) & p(ap(V0P,V3y)) ) ) ) <=> ? [V4x] : ( mem(V4x,A_27b) & ( p(ap(ap(c_2Ebool_2EIN(A_27b),V4x),V2s)) & p(ap(V0P,ap(V1f,V4x))) ) ) ) ) ) ))))).
fof(ax_thm_2Epred__set_2EINJ__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) <=> ( ( ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) => p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),V2t)) ) ) ) & ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V5y),V1s)) ) => ( ( ap(V0f,V4x) = ap(V0f,V5y) ) => ( V4x = V5y ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EINJ__IFF,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) <=> ( ( ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) => p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),V2t)) ) ) ) & ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V5y),V1s)) ) => ( ( ap(V0f,V4x) = ap(V0f,V5y) ) <=> ( V4x = V5y ) ) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EINJ__ID,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27a),i(A_27a)),V0s),V0s)) )))).
fof(conj_thm_2Epred__set_2EINJ__COMPOSE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1g] : ( mem(V1g,arr(A_27b,A_27c)) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ! [V3t] : ( mem(V3t,arr(A_27b,bool)) => ! [V4u] : ( mem(V4u,arr(A_27c,bool)) => ( ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V2s),V3t)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27b,A_27c),V1g),V3t),V4u)) ) => p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V1g),V0f)),V2s),V4u)) ) ) ) ) ) )))))).
fof(conj_thm_2Epred__set_2EINJ__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ( ( ! [V1s] : ( mem(V1s,arr(A_27b,bool)) => p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),c_2Epred__set_2EEMPTY(A_27a)),V1s)) ) ) & ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V2s),c_2Epred__set_2EEMPTY(A_27b))) <=> ( V2s = c_2Epred__set_2EEMPTY(A_27a) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EINJ__DELETE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27b,bool)) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V2f),V0s),V1t)) => ! [V3e] : ( mem(V3e,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3e),V0s)) => p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V2f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V3e)),ap(ap(c_2Epred__set_2EDELETE(A_27b),V1t),ap(V2f,V3e)))) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EINJ__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ! [V3t] : ( mem(V3t,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V2s)),V3t)) <=> ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V2s),V3t)) & ( p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V1x)),V3t)) & ! [V4y] : ( mem(V4y,A_27a) => ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),V2s)) & ( ap(V0f,V1x) = ap(V0f,V4y) ) ) => ( V1x = V4y ) ) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EINJ__EXTEND,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0b] : ( mem(V0b,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27b,bool)) => ! [V3x] : ( mem(V3x,A_27a) => ! [V4y] : ( mem(V4y,A_27b) => ( ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0b),V1s),V2t)) & ( ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) ) & ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27b),V4y),V2t)) ) ) ) => p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V3x),V4y),V0b)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V3x),V1s)),ap(ap(c_2Epred__set_2EINSERT(A_27b),V4y),V2t))) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EINJ__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27b,bool)) => ! [V3s0] : ( mem(V3s0,arr(A_27a,bool)) => ! [V4t0] : ( mem(V4t0,arr(A_27b,bool)) => ( ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) & ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V3s0),V1s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),V2t),V4t0)) ) ) => p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V3s0),V4t0)) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EINJ__IMAGE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) => p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s))) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EINJ__IMAGE__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) => p(ap(ap(c_2Epred__set_2ESUBSET(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s)),V2t)) ) ) ) ))))).
fof(ax_thm_2Epred__set_2ESURJ__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V1s),V2t)) <=> ( ( ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) => p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),V2t)) ) ) ) & ! [V4x] : ( mem(V4x,A_27b) => ( p(ap(ap(c_2Ebool_2EIN(A_27b),V4x),V2t)) => ? [V5y] : ( mem(V5y,A_27a) & ( p(ap(ap(c_2Ebool_2EIN(A_27a),V5y),V1s)) & ( ap(V0f,V5y) = V4x ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2ESURJ__ID,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27a),i(A_27a)),V0s),V0s)) )))).
fof(conj_thm_2Epred__set_2ESURJ__COMPOSE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1g] : ( mem(V1g,arr(A_27b,A_27c)) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ! [V3t] : ( mem(V3t,arr(A_27b,bool)) => ! [V4u] : ( mem(V4u,arr(A_27c,bool)) => ( ( p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V2s),V3t)) & p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27b,A_27c),V1g),V3t),V4u)) ) => p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V1g),V0f)),V2s),V4u)) ) ) ) ) ) )))))).
fof(conj_thm_2Epred__set_2ESURJ__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ( ( ! [V1s] : ( mem(V1s,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),c_2Epred__set_2EEMPTY(A_27a)),V1s)) <=> ( V1s = c_2Epred__set_2EEMPTY(A_27b) ) ) ) ) & ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V2s),c_2Epred__set_2EEMPTY(A_27b))) <=> ( V2s = c_2Epred__set_2EEMPTY(A_27a) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EIMAGE__SURJ,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V1s),V2t)) <=> ( ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s) = V2t ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2ESURJ__IMAGE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V1s),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),V1s))) ) ))))).
fof(conj_thm_2Epred__set_2ESURJ__IMP__INJ,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27b,bool)) => ( ( ? [V2f] : ( mem(V2f,arr(A_27a,A_27b)) & p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V2f),V0s),V1t)) ) ) => ? [V3g] : ( mem(V3g,arr(A_27b,A_27a)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27b,A_27a),V3g),V1t),V0s)) ) ) ) ))))).
fof(ax_thm_2Epred__set_2EBIJ__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V1s),V2t)) <=> ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) & p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V1s),V2t)) ) ) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EBIJ__ID,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27a),i(A_27a)),V0s),V0s)) )))).
fof(conj_thm_2Epred__set_2EBIJ__IMP__11,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),c_2Epred__set_2EUNIV(A_27a)),c_2Epred__set_2EUNIV(A_27b))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( ( ap(V0f,V1x) = ap(V0f,V2y) ) <=> ( V1x = V2y ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EBIJ__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ( ( ! [V1s] : ( mem(V1s,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),c_2Epred__set_2EEMPTY(A_27a)),V1s)) <=> ( V1s = c_2Epred__set_2EEMPTY(A_27b) ) ) ) ) & ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V2s),c_2Epred__set_2EEMPTY(A_27b))) <=> ( V2s = c_2Epred__set_2EEMPTY(A_27a) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EBIJ__COMPOSE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1g] : ( mem(V1g,arr(A_27b,A_27c)) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ! [V3t] : ( mem(V3t,arr(A_27b,bool)) => ! [V4u] : ( mem(V4u,arr(A_27c,bool)) => ( ( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V2s),V3t)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27c),V1g),V3t),V4u)) ) => p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V1g),V0f)),V2s),V4u)) ) ) ) ) ) )))))).
fof(conj_thm_2Epred__set_2EBIJ__DELETE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27b,bool)) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => ( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0s),V1t)) => ! [V3e] : ( mem(V3e,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3e),V0s)) => p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V3e)),ap(ap(c_2Epred__set_2EDELETE(A_27b),V1t),ap(V2f,V3e)))) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EINJ__IMAGE__BIJ,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27b)) => ( ( ? [V2t] : ( mem(V2t,arr(A_27b,bool)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V1f),V0s),V2t)) ) ) => p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V1f),V0s),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V1f),V0s))) ) ) ))))).
fof(conj_thm_2Epred__set_2EINJ__BIJ__SUBSET,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0s0] : ( mem(V0s0,arr(A_27a,bool)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => ! [V3t] : ( mem(V3t,arr(A_27b,bool)) => ( ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s0),V1s)) & p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V2f),V1s),V3t)) ) => p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0s0),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f),V0s0))) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EBIJ__SYM__IMP,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27b,bool)) => ( ( ? [V2f] : ( mem(V2f,arr(A_27a,A_27b)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0s),V1t)) ) ) => ? [V3g] : ( mem(V3g,arr(A_27b,A_27a)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27a),V3g),V1t),V0s)) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EBIJ__SYM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27b,bool)) => ( ( ? [V2f] : ( mem(V2f,arr(A_27a,A_27b)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V2f),V0s),V1t)) ) ) <=> ? [V3g] : ( mem(V3g,arr(A_27b,A_27a)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27a),V3g),V1t),V0s)) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EBIJ__TRANS,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27c,bool)) => ! [V2u] : ( mem(V2u,arr(A_27b,bool)) => ( ( ( ? [V3f] : ( mem(V3f,arr(A_27a,A_27c)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27c),V3f),V0s),V1t)) ) ) & ? [V4g] : ( mem(V4g,arr(A_27c,A_27b)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27c,A_27b),V4g),V1t),V2u)) ) ) => ? [V5h] : ( mem(V5h,arr(A_27a,A_27b)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V5h),V0s),V2u)) ) ) ) ) )))))).
fof(conj_thm_2Epred__set_2EBIJ__INV,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V1s),V2t)) => ? [V3g] : ( mem(V3g,arr(A_27b,A_27a)) & ( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27b,A_27a),V3g),V2t),V1s)) & ( ( ! [V4x] : ( mem(V4x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s)) => ( ap(ap(ap(c_2Ecombin_2Eo(A_27a,A_27a,A_27b),V3g),V0f),V4x) = V4x ) ) ) ) & ! [V5x] : ( mem(V5x,A_27b) => ( p(ap(ap(c_2Ebool_2EIN(A_27b),V5x),V2t)) => ( ap(ap(ap(c_2Ecombin_2Eo(A_27b,A_27b,A_27a),V0f),V3g),V5x) = V5x ) ) ) ) ) ) ) ) ) ))))).
fof(ax_thm_2Epred__set_2EFUNSET,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,arr(A_27b,bool)) => ( ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0P),V1Q) = f269(A_27b,A_27a,V0P,V1Q) ) ) ) ) ) )).
fof(ax_thm_2Epred__set_2EDFUNSET,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,arr(A_27a,arr(A_27b,bool))) => ( ap(ap(c_2Epred__set_2EDFUNSET(A_27a,A_27b),V0P),V1Q) = f271(A_27b,A_27a,V0P,V1Q) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EIN__FUNSET,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27b,bool)) => ( p(ap(ap(c_2Ebool_2EIN(arr(A_27a,A_27b)),V0f),ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V1P),V2Q))) <=> ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1P)) => p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),V2Q)) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EFUNSET__applied,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V1P),V2Q),V0f)) <=> ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1P)) => p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),V2Q)) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EIN__DFUNSET,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27a,arr(A_27b,bool))) => ( p(ap(ap(c_2Ebool_2EIN(arr(A_27a,A_27b)),V0f),ap(ap(c_2Epred__set_2EDFUNSET(A_27a,A_27b),V1P),V2Q))) <=> ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1P)) => p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),ap(V2Q,V3x))) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EDFUNSET__applied,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ! [V2Q] : ( mem(V2Q,arr(A_27a,arr(A_27b,bool))) => ( p(ap(ap(ap(c_2Epred__set_2EDFUNSET(A_27a,A_27b),V1P),V2Q),V0f)) <=> ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1P)) => p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),ap(V2Q,V3x))) ) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EFUNSET__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27b,bool)) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => ! [V3x] : ( mem(V3x,A_27a) => ( ( p(ap(ap(c_2Ebool_2EIN(arr(A_27a,A_27b)),V2f),ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0s),V1t))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s)) ) => p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V2f,V3x)),V1t)) ) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EUNIV__FUNSET__UNIV,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ( ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),c_2Epred__set_2EUNIV(A_27a)),c_2Epred__set_2EUNIV(A_27b)) = c_2Epred__set_2EUNIV(arr(A_27a,A_27b)) ))))).
fof(conj_thm_2Epred__set_2EFUNSET__DFUNSET,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,arr(A_27a,bool)) => ! [V1y] : ( mem(V1y,arr(A_27b,bool)) => ( ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0x),V1y) = ap(ap(c_2Epred__set_2EDFUNSET(A_27a,A_27b),V0x),ap(c_2Ecombin_2EK(arr(A_27b,bool),A_27a),V1y)) ) ) ))))).
fof(conj_thm_2Epred__set_2EEMPTY__FUNSET,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0s] : ( mem(V0s,arr(A_27b,bool)) => ( ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),c_2Epred__set_2EEMPTY(A_27a)),V0s) = c_2Epred__set_2EUNIV(arr(A_27a,A_27b)) ) ))))).
fof(conj_thm_2Epred__set_2EFUNSET__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27b)) => ( p(ap(ap(c_2Ebool_2EIN(arr(A_27a,A_27b)),V1f),ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0s),c_2Epred__set_2EEMPTY(A_27b)))) <=> ( V0s = c_2Epred__set_2EEMPTY(A_27a) ) ) ) ))))).
fof(conj_thm_2Epred__set_2EFUNSET__INTER,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0a] : ( mem(V0a,arr(A_27a,bool)) => ! [V1b] : ( mem(V1b,arr(A_27b,bool)) => ! [V2c] : ( mem(V2c,arr(A_27b,bool)) => ( ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0a),ap(ap(c_2Epred__set_2EINTER(A_27b),V1b),V2c)) = ap(ap(c_2Epred__set_2EINTER(arr(A_27a,A_27b)),ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0a),V1b)),ap(ap(c_2Epred__set_2EFUNSET(A_27a,A_27b),V0a),V2c)) ) ) ) ))))).
fof(ax_thm_2Epred__set_2Eschroeder__close__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27a)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(ap(c_2Epred__set_2Eschroeder__close(A_27a),V0f),V1s),V2x)) <=> ? [V3n] : ( mem(V3n,ty_2Enum_2Enum) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(ap(c_2Earithmetic_2EFUNPOW(arr(A_27a,bool)),ap(c_2Epred__set_2EIMAGE(A_27a,A_27a),V0f)),V3n),V1s))) ) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2ESCHROEDER__CLOSE,conjecture,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27a)) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2Eschroeder__close(A_27a),V1f),V2s))) <=> ? [V3n] : ( mem(V3n,ty_2Enum_2Enum) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(ap(c_2Earithmetic_2EFUNPOW(arr(A_27a,bool)),ap(c_2Epred__set_2EIMAGE(A_27a,A_27a),V1f)),V3n),V2s))) ) ) ) ) )))).
