include('Axioms/HL4001+2.ax').
fof(mem_c_2Ecombin_2EI,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ecombin_2EI(A_27a),arr(A_27a,A_27a)) ) )).
fof(ne_ty_2Enum_2Enum,axiom,( ne(ty_2Enum_2Enum) )).
fof(mem_c_2Earithmetic_2EEVEN,axiom,( mem(c_2Earithmetic_2EEVEN,arr(ty_2Enum_2Enum,bool)) )).
fof(mem_c_2Earithmetic_2EODD,axiom,( mem(c_2Earithmetic_2EODD,arr(ty_2Enum_2Enum,bool)) )).
fof(mem_c_2Earithmetic_2E_3E,axiom,( mem(c_2Earithmetic_2E_3E,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Eprim__rec_2EPRE,axiom,( mem(c_2Eprim__rec_2EPRE,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Earithmetic_2EEXP,axiom,( mem(c_2Earithmetic_2EEXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Earithmetic_2E_2D,axiom,( mem(c_2Earithmetic_2E_2D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Enumeral_2EiiSUC,axiom,( mem(c_2Enumeral_2EiiSUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Ebool_2ET,axiom,( mem(c_2Ebool_2ET,bool) )).
fof(ax_true_p,axiom,( p(c_2Ebool_2ET) )).
fof(mem_c_2Enumeral_2EiDUB,axiom,( mem(c_2Enumeral_2EiDUB,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Enumeral_2EiZ,axiom,( mem(c_2Enumeral_2EiZ,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Earithmetic_2EBIT2,axiom,( mem(c_2Earithmetic_2EBIT2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(ne_ty_2Erealax_2Ereal,axiom,( ne(ty_2Erealax_2Ereal) )).
fof(mem_c_2Ereal_2E_2F,axiom,( mem(c_2Ereal_2E_2F,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ebool_2ECOND,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))) ) )).
fof(mem_c_2Earithmetic_2EZERO,axiom,( mem(c_2Earithmetic_2EZERO,ty_2Enum_2Enum) )).
fof(mem_c_2Earithmetic_2EBIT1,axiom,( mem(c_2Earithmetic_2EBIT1,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Earithmetic_2ENUMERAL,axiom,( mem(c_2Earithmetic_2ENUMERAL,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Earithmetic_2E_2B,axiom,( mem(c_2Earithmetic_2E_2B,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Erealax_2Ereal__neg,axiom,( mem(c_2Erealax_2Ereal__neg,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) )).
fof(mem_c_2Earithmetic_2E_3C_3D,axiom,( mem(c_2Earithmetic_2E_3C_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Earithmetic_2E_2A,axiom,( mem(c_2Earithmetic_2E_2A,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Erealax_2Ereal__add,axiom,( mem(c_2Erealax_2Ereal__add,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ereal_2Emin,axiom,( mem(c_2Ereal_2Emin,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ebool_2EF,axiom,( mem(c_2Ebool_2EF,bool) )).
fof(ax_false_p,axiom,( ~ p(c_2Ebool_2EF) )).
fof(mem_c_2Ebool_2E_5C_2F,axiom,( mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))) )).
fof(ax_or_p,axiom,( ! [Q] : ( mem(Q,bool) => ! [R] : ( mem(R,bool) => ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R)) <=> ( p(Q) | p(R) ) ) ) ) )).
fof(mem_c_2Ebool_2E_7E,axiom,( mem(c_2Ebool_2E_7E,arr(bool,bool)) )).
fof(ax_neg_p,axiom,( ! [Q] : ( mem(Q,bool) => ( p(ap(c_2Ebool_2E_7E,Q)) <=> ~ p(Q) ) ) )).
fof(mem_c_2Erealax_2Ereal__mul,axiom,( mem(c_2Erealax_2Ereal__mul,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(ne_ty_2Epair_2Eprod,axiom,( ! [A0] : ( ne(A0) => ( ! [A1] : ( ne(A1) => ne(ty_2Epair_2Eprod(A0,A1)) ) ) ) )).
fof(mem_c_2Ereal_2Esum,axiom,( mem(c_2Ereal_2Esum,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))) )).
fof(mem_c_2Etransc_2Ersum,axiom,( mem(c_2Etransc_2Ersum,arr(ty_2Epair_2Eprod(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),arr(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ereal_2Ereal__sub,axiom,( mem(c_2Ereal_2Ereal__sub,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ereal_2Eabs,axiom,( mem(c_2Ereal_2Eabs,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) )).
fof(mem_c_2Etransc_2Efine,axiom,( mem(c_2Etransc_2Efine,arr(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Epair_2Eprod(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),bool))) )).
fof(mem_c_2Etransc_2Etdiv,axiom,( mem(c_2Etransc_2Etdiv,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Epair_2Eprod(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),bool))) )).
fof(mem_c_2Etransc_2Egauge,axiom,( mem(c_2Etransc_2Egauge,arr(arr(ty_2Erealax_2Ereal,bool),arr(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),bool))) )).
fof(mem_c_2Ebool_2E_3F,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)) ) )).
fof(ax_ex_p,axiom,( ! [A] : ( ne(A) => ! [Q] : ( mem(Q,arr(A,bool)) => ( p(ap(c_2Ebool_2E_3F(A),Q)) <=> ? [X] : ( mem(X,A) & p(ap(Q,X)) ) ) ) ) )).
fof(mem_c_2Earithmetic_2E_3E_3D,axiom,( mem(c_2Earithmetic_2E_3E_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Enum_2ESUC,axiom,( mem(c_2Enum_2ESUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Erealax_2Ereal__lt,axiom,( mem(c_2Erealax_2Ereal__lt,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) )).
fof(mem_c_2Etransc_2Edsize,axiom,( mem(c_2Etransc_2Edsize,arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),ty_2Enum_2Enum)) )).
fof(mem_c_2Eprim__rec_2E_3C,axiom,( mem(c_2Eprim__rec_2E_3C,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Etransc_2Edivision,axiom,( mem(c_2Etransc_2Edivision,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),bool))) )).
fof(mem_c_2Emin_2E_3D,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ) )).
fof(ax_eq_p,axiom,( ! [A] : ( ne(A) => ! [X] : ( mem(X,A) => ! [Y] : ( mem(Y,A) => ( p(ap(ap(c_2Emin_2E_3D(A),X),Y)) <=> X = Y ) ) ) ) )).
fof(mem_c_2Ereal_2Ereal__lte,axiom,( mem(c_2Ereal_2Ereal__lte,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) )).
fof(mem_c_2Ebool_2E_2F_5C,axiom,( mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))) )).
fof(ax_and_p,axiom,( ! [Q] : ( mem(Q,bool) => ! [R] : ( mem(R,bool) => ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R)) <=> ( p(Q) & p(R) ) ) ) ) )).
fof(mem_c_2Emin_2E_3D_3D_3E,axiom,( mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))) )).
fof(ax_imp_p,axiom,( ! [Q] : ( mem(Q,bool) => ! [R] : ( mem(R,bool) => ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R)) <=> ( p(Q) => p(R) ) ) ) ) )).
fof(mem_c_2Enum_2E0,axiom,( mem(c_2Enum_2E0,ty_2Enum_2Enum) )).
fof(mem_c_2Ereal_2Ereal__of__num,axiom,( mem(c_2Ereal_2Ereal__of__num,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) )).
fof(mem_c_2Epair_2E_2C,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b)))) ) ) )).
fof(mem_c_2Etransc_2EDint,axiom,( mem(c_2Etransc_2EDint,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool)))) )).
fof(mem_c_2Ebool_2E_21,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ) )).
fof(ax_all_p,axiom,( ! [A] : ( ne(A) => ! [Q] : ( mem(Q,arr(A,bool)) => ( p(ap(c_2Ebool_2E_21(A),Q)) <=> ! [X] : ( mem(X,A) => p(ap(Q,X)) ) ) ) ) )).
fof(conj_thm_2Earithmetic_2ETWO,lemma,(( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ))).
fof(conj_thm_2Earithmetic_2EADD__0,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,V0m),c_2Enum_2E0) = V0m ) ))).
fof(conj_thm_2Earithmetic_2EADD__CLAUSES,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0m) = V0m ) & ( ( ap(ap(c_2Earithmetic_2E_2B,V0m),c_2Enum_2E0) = V0m ) & ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V0m)),V1n) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) ) & ( ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) ) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EADD__SYM,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,V1n),V0m) ) ) ))).
fof(conj_thm_2Earithmetic_2EADD__COMM,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,V1n),V0m) ) ) ))).
fof(conj_thm_2Earithmetic_2EADD__ASSOC,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),V2p) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__EQ__MONO,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V1m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n)) ) ) ))).
fof(conj_thm_2Earithmetic_2EOR__LESS,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n)) => p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) ) ))).
fof(conj_thm_2Earithmetic_2EZERO__LESS__EQ,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),V0n)) ))).
fof(conj_thm_2Earithmetic_2ELESS__EQ__ADD,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__ADD__NONZERO,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ~~ ( V1n = c_2Enum_2E0 ) ) => p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))) ) ) ))).
fof(conj_thm_2Earithmetic_2ENOT__LESS,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ~~ p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) ) ) ))).
fof(conj_thm_2Earithmetic_2ENOT__LESS__EQUAL,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ~~ p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) ) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) ) ) ))).
fof(conj_thm_2Earithmetic_2EADD1,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ( ap(c_2Enum_2ESUC,V0m) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ))).
fof(conj_thm_2Earithmetic_2EPRE__SUB1,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ( ap(c_2Eprim__rec_2EPRE,V0m) = ap(ap(c_2Earithmetic_2E_2D,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ))).
fof(conj_thm_2Earithmetic_2EMULT__CLAUSES,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V0m) = c_2Enum_2E0 ) & ( ( ap(ap(c_2Earithmetic_2E_2A,V0m),c_2Enum_2E0) = c_2Enum_2E0 ) & ( ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m) = V0m ) & ( ( ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0m ) & ( ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V0m)),V1n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V1n) ) & ( ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EADD__EQ__0,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = c_2Enum_2E0 ) <=> ( ( V0m = c_2Enum_2E0 ) & ( V1n = c_2Enum_2E0 ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EEQ__MONO__ADD__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) = ap(ap(c_2Earithmetic_2E_2B,V1n),V2p) ) <=> ( V0m = V1n ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__EQ__TRANS,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) ) => p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2p)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__LESS__EQ__TRANS,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) ) => p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__EQ__REFL,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V0m)) ))).
fof(conj_thm_2Earithmetic_2ELESS__IMP__LESS__OR__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) => p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) ) ) ))).
fof(conj_thm_2Earithmetic_2EADD__SUB,lemma,(! [V0a] : ( mem(V0a,ty_2Enum_2Enum) => ! [V1c] : ( mem(V1c,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0a),V1c)),V1c) = V0a ) ) ))).
fof(conj_thm_2Earithmetic_2ENOT__SUC__LESS__EQ,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( ~~ p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0n)),V1m)) ) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) ) ) ))).
fof(conj_thm_2Earithmetic_2EGREATER__EQ,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V0n),V1m)) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) ) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__EQ__EXISTS,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) <=> ? [V2p] : ( mem(V2p,ty_2Enum_2Enum) & ( V1n = ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EEQ__LESS__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( V0m = V1n ) <=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EADD__MONO__LESS__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2B,V0m),V2p))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ENOT__LEQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ~~ p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) ) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),V0m)) ) ) ))).
fof(conj_thm_2Earithmetic_2ENOT__NUM__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ~~ ( V0m = V1n ) ) <=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),V0m)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ESUC__ONE__ADD,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(c_2Enum_2ESUC,V0n) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) ) ))).
fof(conj_thm_2Earithmetic_2ESUC__ADD__SYM,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V1n)),V0m) ) ) ))).
fof(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p)) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ESUB__LEFT__LESS,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ELE,lemma,(( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),c_2Enum_2E0)) <=> ( V0n = c_2Enum_2E0 ) ) ) ) & ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),ap(c_2Enum_2ESUC,V2n))) <=> ( ( V1m = ap(c_2Enum_2ESUC,V2n) ) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n)) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ESUB__ELIM__THM,lemma,(! [V0P] : ( mem(V0P,arr(ty_2Enum_2Enum,bool)) => ! [V1a] : ( mem(V1a,ty_2Enum_2Enum) => ! [V2b] : ( mem(V2b,ty_2Enum_2Enum) => ( p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1a),V2b))) <=> ! [V3d] : ( mem(V3d,ty_2Enum_2Enum) => ( ( ( V2b = ap(ap(c_2Earithmetic_2E_2B,V1a),V3d) ) => p(ap(V0P,c_2Enum_2E0)) ) & ( ( V1a = ap(ap(c_2Earithmetic_2E_2B,V2b),V3d) ) => p(ap(V0P,V3d)) ) ) ) ) ) ) ))).
fof(ax_thm_2Ebool_2EBOOL__CASES__AX,axiom, ! [V0t] : ( mem(V0t,bool) => ( ( p(V0t) <=> $true ) | ( p(V0t) <=> $false ) ) )).
fof(conj_thm_2Ebool_2ETRUTH,lemma,($true)).
fof(conj_thm_2Ebool_2EIMP__ANTISYM__AX,lemma,(! [V0t1] : ( mem(V0t1,bool) => ! [V1t2] : ( mem(V1t2,bool) => ( ( p(V0t1) => p(V1t2) ) => ( ( p(V1t2) => p(V0t1) ) => ( p(V0t1) <=> p(V1t2) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EFALSITY,lemma,(! [V0t] : ( mem(V0t,bool) => ( $false => p(V0t) ) ))).
fof(conj_thm_2Ebool_2EEXCLUDED__MIDDLE,lemma,(! [V0t] : ( mem(V0t,bool) => ( p(V0t) | ( ~~ p(V0t) ) ) ))).
fof(conj_thm_2Ebool_2EFORALL__SIMP,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0t] : ( mem(V0t,bool) => ( ( ! [V1x] : ( mem(V1x,A_27a) => p(V0t) ) ) <=> p(V0t) ) )))).
fof(conj_thm_2Ebool_2ECONJ__SYM,lemma,(! [V0t1] : ( mem(V0t1,bool) => ! [V1t2] : ( mem(V1t2,bool) => ( ( p(V0t1) & p(V1t2) ) <=> ( p(V1t2) & p(V0t1) ) ) ) ))).
fof(conj_thm_2Ebool_2ECONJ__ASSOC,lemma,(! [V0t1] : ( mem(V0t1,bool) => ! [V1t2] : ( mem(V1t2,bool) => ! [V2t3] : ( mem(V2t3,bool) => ( ( p(V0t1) & ( p(V1t2) & p(V2t3) ) ) <=> ( ( p(V0t1) & p(V1t2) ) & p(V2t3) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__F,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( p(V0t) => $false ) => ( ~~ p(V0t) ) ) ))).
fof(conj_thm_2Ebool_2EF__IMP,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ~~ p(V0t) ) => ( p(V0t) => $false ) ) ))).
fof(conj_thm_2Ebool_2EAND__CLAUSES,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ( $true & p(V0t) ) <=> p(V0t) ) & ( ( ( p(V0t) & $true ) <=> p(V0t) ) & ( ( ( $false & p(V0t) ) <=> $false ) & ( ( ( p(V0t) & $false ) <=> $false ) & ( ( p(V0t) & p(V0t) ) <=> p(V0t) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EOR__CLAUSES,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ( $true | p(V0t) ) <=> $true ) & ( ( ( p(V0t) | $true ) <=> $true ) & ( ( ( $false | p(V0t) ) <=> p(V0t) ) & ( ( ( p(V0t) | $false ) <=> p(V0t) ) & ( ( p(V0t) | p(V0t) ) <=> p(V0t) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__CLAUSES,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ( $true => p(V0t) ) <=> p(V0t) ) & ( ( ( p(V0t) => $true ) <=> $true ) & ( ( ( $false => p(V0t) ) <=> $true ) & ( ( ( p(V0t) => p(V0t) ) <=> $true ) & ( ( p(V0t) => $false ) <=> ( ~~ p(V0t) ) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2ENOT__CLAUSES,lemma,(( ( ! [V0t] : ( mem(V0t,bool) => ( ( ~~ ( ~~ p(V0t) ) ) <=> p(V0t) ) ) ) & ( ( (~~ ($true)) <=> $false ) & ( (~~ ($false)) <=> $true ) ) ))).
fof(conj_thm_2Ebool_2EREFL__CLAUSE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ( V0x = V0x ) <=> $true ) )))).
fof(conj_thm_2Ebool_2EEQ__SYM__EQ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ( ( V0x = V1y ) <=> ( V1y = V0x ) ) ) )))).
fof(conj_thm_2Ebool_2EEQ__CLAUSES,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ( $true <=> p(V0t) ) <=> p(V0t) ) & ( ( ( p(V0t) <=> $true ) <=> p(V0t) ) & ( ( ( $false <=> p(V0t) ) <=> ( ~~ p(V0t) ) ) & ( ( p(V0t) <=> $false ) <=> ( ~~ p(V0t) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2ECOND__CLAUSES,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0t1] : ( mem(V0t1,A_27a) => ! [V1t2] : ( mem(V1t2,A_27a) => ( ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1 ) & ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2 ) ) ) )))).
fof(conj_thm_2Ebool_2ENOT__FORALL__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ( ( ~~ ! [V1x] : ( mem(V1x,A_27a) => p(ap(V0P,V1x)) ) ) <=> ? [V2x] : ( mem(V2x,A_27a) & ( ~~ p(ap(V0P,V2x)) ) ) ) )))).
fof(conj_thm_2Ebool_2ENOT__EXISTS__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ( ( ~~ ? [V1x] : ( mem(V1x,A_27a) & p(ap(V0P,V1x)) ) ) <=> ! [V2x] : ( mem(V2x,A_27a) => ( ~~ p(ap(V0P,V2x)) ) ) ) )))).
fof(conj_thm_2Ebool_2EFORALL__AND__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(V0P,V2x)) & p(ap(V1Q,V2x)) ) ) ) <=> ( ( ! [V3x] : ( mem(V3x,A_27a) => p(ap(V0P,V3x)) ) ) & ! [V4x] : ( mem(V4x,A_27a) => p(ap(V1Q,V4x)) ) ) ) ) )))).
fof(conj_thm_2Ebool_2ERIGHT__AND__FORALL__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,bool) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ( ( p(V0P) & ! [V2x] : ( mem(V2x,A_27a) => p(ap(V1Q,V2x)) ) ) <=> ! [V3x] : ( mem(V3x,A_27a) => ( p(V0P) & p(ap(V1Q,V3x)) ) ) ) ) )))).
fof(conj_thm_2Ebool_2EEXISTS__OR__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ( ( ? [V2x] : ( mem(V2x,A_27a) & ( p(ap(V0P,V2x)) | p(ap(V1Q,V2x)) ) ) ) <=> ( ( ? [V3x] : ( mem(V3x,A_27a) & p(ap(V0P,V3x)) ) ) | ? [V4x] : ( mem(V4x,A_27a) & p(ap(V1Q,V4x)) ) ) ) ) )))).
fof(conj_thm_2Ebool_2ERIGHT__OR__EXISTS__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,bool) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ( ( p(V0P) | ? [V2x] : ( mem(V2x,A_27a) & p(ap(V1Q,V2x)) ) ) <=> ? [V3x] : ( mem(V3x,A_27a) & ( p(V0P) | p(ap(V1Q,V3x)) ) ) ) ) )))).
fof(conj_thm_2Ebool_2ELEFT__EXISTS__AND__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,bool) => ( ( ? [V2x] : ( mem(V2x,A_27a) & ( p(ap(V0P,V2x)) & p(V1Q) ) ) ) <=> ( ( ? [V3x] : ( mem(V3x,A_27a) & p(ap(V0P,V3x)) ) ) & p(V1Q) ) ) ) )))).
fof(conj_thm_2Ebool_2ERIGHT__EXISTS__AND__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,bool) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ( ( ? [V2x] : ( mem(V2x,A_27a) & ( p(V0P) & p(ap(V1Q,V2x)) ) ) ) <=> ( p(V0P) & ? [V3x] : ( mem(V3x,A_27a) & p(ap(V1Q,V3x)) ) ) ) ) )))).
fof(conj_thm_2Ebool_2ERIGHT__FORALL__OR__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,bool) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ( p(V0P) | p(ap(V1Q,V2x)) ) ) ) <=> ( p(V0P) | ! [V3x] : ( mem(V3x,A_27a) => p(ap(V1Q,V3x)) ) ) ) ) )))).
fof(conj_thm_2Ebool_2EDISJ__ASSOC,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ! [V2C] : ( mem(V2C,bool) => ( ( p(V0A) | ( p(V1B) | p(V2C) ) ) <=> ( ( p(V0A) | p(V1B) ) | p(V2C) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EDISJ__SYM,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( p(V0A) | p(V1B) ) <=> ( p(V1B) | p(V0A) ) ) ) ))).
fof(conj_thm_2Ebool_2EDE__MORGAN__THM,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( ( ~~ ( p(V0A) & p(V1B) ) ) <=> ( ( ~~ p(V0A) ) | ( ~~ p(V1B) ) ) ) & ( ( ~~ ( p(V0A) | p(V1B) ) ) <=> ( ( ~~ p(V0A) ) & ( ~~ p(V1B) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__DISJ__THM,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( p(V0A) => p(V1B) ) <=> ( ( ~~ p(V0A) ) | p(V1B) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__F__EQ__F,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( p(V0t) => $false ) <=> ( p(V0t) <=> $false ) ) ))).
fof(conj_thm_2Ebool_2EAND__IMP__INTRO,lemma,(! [V0t1] : ( mem(V0t1,bool) => ! [V1t2] : ( mem(V1t2,bool) => ! [V2t3] : ( mem(V2t3,bool) => ( ( p(V0t1) => ( p(V1t2) => p(V2t3) ) ) <=> ( ( p(V0t1) & p(V1t2) ) => p(V2t3) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EEQ__EXPAND,lemma,(! [V0t1] : ( mem(V0t1,bool) => ! [V1t2] : ( mem(V1t2,bool) => ( ( p(V0t1) <=> p(V1t2) ) <=> ( ( p(V0t1) & p(V1t2) ) | ( ( ~~ p(V0t1) ) & ( ~~ p(V1t2) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__CONG,lemma,(! [V0x] : ( mem(V0x,bool) => ! [V1x_27] : ( mem(V1x_27,bool) => ! [V2y] : ( mem(V2y,bool) => ! [V3y_27] : ( mem(V3y_27,bool) => ( ( ( p(V0x) <=> p(V1x_27) ) & ( p(V1x_27) => ( p(V2y) <=> p(V3y_27) ) ) ) => ( ( p(V0x) => p(V2y) ) <=> ( p(V1x_27) => p(V3y_27) ) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2ECOND__CONG,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,bool) => ! [V1Q] : ( mem(V1Q,bool) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3x_27] : ( mem(V3x_27,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ! [V5y_27] : ( mem(V5y_27,A_27a) => ( ( ( p(V0P) <=> p(V1Q) ) & ( ( p(V1Q) => ( V2x = V3x_27 ) ) & ( ( ~~ p(V1Q) ) => ( V4y = V5y_27 ) ) ) ) => ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0P),V2x),V4y) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V1Q),V3x_27),V5y_27) ) ) ) ) ) ) ) )))).
fof(conj_thm_2Ebool_2EMONO__AND,lemma,(! [V0x] : ( mem(V0x,bool) => ! [V1y] : ( mem(V1y,bool) => ! [V2z] : ( mem(V2z,bool) => ! [V3w] : ( mem(V3w,bool) => ( ( ( p(V0x) => p(V1y) ) & ( p(V2z) => p(V3w) ) ) => ( ( p(V0x) & p(V2z) ) => ( p(V1y) & p(V3w) ) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EMONO__IMP,lemma,(! [V0y] : ( mem(V0y,bool) => ! [V1x] : ( mem(V1x,bool) => ! [V2z] : ( mem(V2z,bool) => ! [V3w] : ( mem(V3w,bool) => ( ( ( p(V0y) => p(V1x) ) & ( p(V2z) => p(V3w) ) ) => ( ( p(V1x) => p(V2z) ) => ( p(V0y) => p(V3w) ) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2ESKOLEM__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0P] : ( mem(V0P,arr(A_27a,arr(A_27b,bool))) => ( ( ! [V1x] : ( mem(V1x,A_27a) => ? [V2y] : ( mem(V2y,A_27b) & p(ap(ap(V0P,V1x),V2y)) ) ) ) <=> ? [V3f] : ( mem(V3f,arr(A_27a,A_27b)) & ! [V4x] : ( mem(V4x,A_27a) => p(ap(ap(V0P,V4x),ap(V3f,V4x))) ) ) ) ))))).
fof(conj_thm_2Ebool_2Ebool__case__thm,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0t1] : ( mem(V0t1,A_27a) => ! [V1t2] : ( mem(V1t2,A_27a) => ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1 ) ) ) ) & ! [V2t1] : ( mem(V2t1,A_27a) => ! [V3t2] : ( mem(V3t2,A_27a) => ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V2t1),V3t2) = V3t2 ) ) ) )))).
fof(conj_thm_2Ecombin_2EI__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ap(c_2Ecombin_2EI(A_27a),V0x) = V0x ) )))).
fof(conj_thm_2Eintegral_2ESUM__SPLIT,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1f] : ( mem(V1f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ! [V3p] : ( mem(V3p,ty_2Enum_2Enum) => ( ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0m),V2n)),V1f)),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2B,V0m),V2n)),V3p)),V1f)) = ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0m),ap(ap(c_2Earithmetic_2E_2B,V2n),V3p))),V1f) ) ) ) ) ))).
fof(conj_thm_2Eintegral_2ELE__0,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),V0n)) ))).
fof(conj_thm_2Eintegral_2EREAL__LT__MIN,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V2z),ap(ap(c_2Ereal_2Emin,V0x),V1y))) <=> ( p(ap(ap(c_2Erealax_2Ereal__lt,V2z),V0x)) & p(ap(ap(c_2Erealax_2Ereal__lt,V2z),V1y)) ) ) ) ) ))).
fof(conj_thm_2Eintegral_2EDIVISION__MONO__LE,lemma,(! [V0d] : ( mem(V0d,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1a] : ( mem(V1a,ty_2Erealax_2Ereal) => ! [V2b] : ( mem(V2b,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0d)) => ! [V3m] : ( mem(V3m,ty_2Enum_2Enum) => ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V3m),V4n)) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0d,V3m)),ap(V0d,V4n))) ) ) ) ) ) ) ))).
fof(conj_thm_2Eintegral_2EDIVISION__DSIZE__LE,lemma,(! [V0a] : ( mem(V0a,ty_2Erealax_2Ereal) => ! [V1b] : ( mem(V1b,ty_2Erealax_2Ereal) => ! [V2d] : ( mem(V2d,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),V2d)) & ( ap(V2d,ap(c_2Enum_2ESUC,V3n)) = ap(V2d,V3n) ) ) => p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Etransc_2Edsize,V2d)),V3n)) ) ) ) ) ))).
fof(conj_thm_2Eintegral_2EDIVISION__DSIZE__EQ,lemma,(! [V0a] : ( mem(V0a,ty_2Erealax_2Ereal) => ! [V1b] : ( mem(V1b,ty_2Erealax_2Ereal) => ! [V2d] : ( mem(V2d,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),V2d)) & ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(V2d,V3n)),ap(V2d,ap(c_2Enum_2ESUC,V3n)))) & ( ap(V2d,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,V3n))) = ap(V2d,ap(c_2Enum_2ESUC,V3n)) ) ) ) => ( ap(c_2Etransc_2Edsize,V2d) = ap(c_2Enum_2ESUC,V3n) ) ) ) ) ) ))).
fof(conj_thm_2Eintegral_2EDIVISION__DSIZE__EQ__ALT,lemma,(! [V0a] : ( mem(V0a,ty_2Erealax_2Ereal) => ! [V1b] : ( mem(V1b,ty_2Erealax_2Ereal) => ! [V2d] : ( mem(V2d,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),V2d)) & ( ( ap(V2d,ap(c_2Enum_2ESUC,V3n)) = ap(V2d,V3n) ) & ! [V4i] : ( mem(V4i,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V4i),V3n)) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(V2d,V4i)),ap(V2d,ap(c_2Enum_2ESUC,V4i)))) ) ) ) ) => ( ap(c_2Etransc_2Edsize,V2d) = V3n ) ) ) ) ) ))).
fof(conj_thm_2Eintegral_2EDIVISION__INTERMEDIATE,lemma,(! [V0d] : ( mem(V0d,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1a] : ( mem(V1a,ty_2Erealax_2Ereal) => ! [V2b] : ( mem(V2b,ty_2Erealax_2Ereal) => ! [V3c] : ( mem(V3c,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0d)) & ( p(ap(ap(c_2Ereal_2Ereal__lte,V1a),V3c)) & p(ap(ap(c_2Ereal_2Ereal__lte,V3c),V2b)) ) ) => ? [V4n] : ( mem(V4n,ty_2Enum_2Enum) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V4n),ap(c_2Etransc_2Edsize,V0d))) & ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0d,V4n)),V3c)) & p(ap(ap(c_2Ereal_2Ereal__lte,V3c),ap(V0d,ap(c_2Enum_2ESUC,V4n)))) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__suc,lemma,(( ( ap(c_2Enum_2ESUC,c_2Earithmetic_2EZERO) = ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO) ) & ( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT1,V0n)) = ap(c_2Earithmetic_2EBIT2,V0n) ) ) ) & ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT2,V1n)) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,V1n)) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__distrib,lemma,(( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0n) = V0n ) ) ) & ( ( ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,V1n),c_2Enum_2E0) = V1n ) ) ) & ( ( ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ! [V3m] : ( mem(V3m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,V2n)),ap(c_2Earithmetic_2ENUMERAL,V3m)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V2n),V3m))) ) ) ) ) & ( ( ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V4n) = c_2Enum_2E0 ) ) ) & ( ( ! [V5n] : ( mem(V5n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,V5n),c_2Enum_2E0) = c_2Enum_2E0 ) ) ) & ( ( ! [V6n] : ( mem(V6n,ty_2Enum_2Enum) => ! [V7m] : ( mem(V7m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,V6n)),ap(c_2Earithmetic_2ENUMERAL,V7m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2A,V6n),V7m)) ) ) ) ) & ( ( ! [V8n] : ( mem(V8n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2D,c_2Enum_2E0),V8n) = c_2Enum_2E0 ) ) ) & ( ( ! [V9n] : ( mem(V9n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2D,V9n),c_2Enum_2E0) = V9n ) ) ) & ( ( ! [V10n] : ( mem(V10n,ty_2Enum_2Enum) => ! [V11m] : ( mem(V11m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,V10n)),ap(c_2Earithmetic_2ENUMERAL,V11m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2D,V10n),V11m)) ) ) ) ) & ( ( ! [V12n] : ( mem(V12n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V12n))) = c_2Enum_2E0 ) ) ) & ( ( ! [V13n] : ( mem(V13n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V13n))) = c_2Enum_2E0 ) ) ) & ( ( ! [V14n] : ( mem(V14n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,V14n),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) & ( ( ! [V15n] : ( mem(V15n,ty_2Enum_2Enum) => ! [V16m] : ( mem(V16m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,V15n)),ap(c_2Earithmetic_2ENUMERAL,V16m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2EEXP,V15n),V16m)) ) ) ) ) & ( ( ap(c_2Enum_2ESUC,c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) & ( ( ! [V17n] : ( mem(V17n,ty_2Enum_2Enum) => ( ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2ENUMERAL,V17n)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enum_2ESUC,V17n)) ) ) ) & ( ( ap(c_2Eprim__rec_2EPRE,c_2Enum_2E0) = c_2Enum_2E0 ) & ( ( ! [V18n] : ( mem(V18n,ty_2Enum_2Enum) => ( ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,V18n)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Eprim__rec_2EPRE,V18n)) ) ) ) & ( ( ! [V19n] : ( mem(V19n,ty_2Enum_2Enum) => ( ( ap(c_2Earithmetic_2ENUMERAL,V19n) = c_2Enum_2E0 ) <=> ( V19n = c_2Earithmetic_2EZERO ) ) ) ) & ( ( ! [V20n] : ( mem(V20n,ty_2Enum_2Enum) => ( ( c_2Enum_2E0 = ap(c_2Earithmetic_2ENUMERAL,V20n) ) <=> ( V20n = c_2Earithmetic_2EZERO ) ) ) ) & ( ( ! [V21n] : ( mem(V21n,ty_2Enum_2Enum) => ! [V22m] : ( mem(V22m,ty_2Enum_2Enum) => ( ( ap(c_2Earithmetic_2ENUMERAL,V21n) = ap(c_2Earithmetic_2ENUMERAL,V22m) ) <=> ( V21n = V22m ) ) ) ) ) & ( ( ! [V23n] : ( mem(V23n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V23n),c_2Enum_2E0)) <=> $false ) ) ) & ( ( ! [V24n] : ( mem(V24n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,V24n))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),V24n)) ) ) ) & ( ( ! [V25n] : ( mem(V25n,ty_2Enum_2Enum) => ! [V26m] : ( mem(V26m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,V25n)),ap(c_2Earithmetic_2ENUMERAL,V26m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V25n),V26m)) ) ) ) ) & ( ( ! [V27n] : ( mem(V27n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E,c_2Enum_2E0),V27n)) <=> $false ) ) ) & ( ( ! [V28n] : ( mem(V28n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,V28n)),c_2Enum_2E0)) <=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),V28n)) ) ) ) & ( ( ! [V29n] : ( mem(V29n,ty_2Enum_2Enum) => ! [V30m] : ( mem(V30m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,V29n)),ap(c_2Earithmetic_2ENUMERAL,V30m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V30m),V29n)) ) ) ) ) & ( ( ! [V31n] : ( mem(V31n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),V31n)) <=> $true ) ) ) & ( ( ! [V32n] : ( mem(V32n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V32n)),c_2Enum_2E0)) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V32n),c_2Earithmetic_2EZERO)) ) ) ) & ( ( ! [V33n] : ( mem(V33n,ty_2Enum_2Enum) => ! [V34m] : ( mem(V34m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V33n)),ap(c_2Earithmetic_2ENUMERAL,V34m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V33n),V34m)) ) ) ) ) & ( ( ! [V35n] : ( mem(V35n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V35n),c_2Enum_2E0)) <=> $true ) ) ) & ( ( ! [V36n] : ( mem(V36n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),V36n)) <=> ( V36n = c_2Enum_2E0 ) ) ) ) & ( ( ! [V37n] : ( mem(V37n,ty_2Enum_2Enum) => ! [V38m] : ( mem(V38m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Earithmetic_2ENUMERAL,V37n)),ap(c_2Earithmetic_2ENUMERAL,V38m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V38m),V37n)) ) ) ) ) & ( ( ! [V39n] : ( mem(V39n,ty_2Enum_2Enum) => ( p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2ENUMERAL,V39n))) <=> p(ap(c_2Earithmetic_2EODD,V39n)) ) ) ) & ( ( ! [V40n] : ( mem(V40n,ty_2Enum_2Enum) => ( p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2ENUMERAL,V40n))) <=> p(ap(c_2Earithmetic_2EEVEN,V40n)) ) ) ) & ( ( ~~ p(ap(c_2Earithmetic_2EODD,c_2Enum_2E0)) ) & p(ap(c_2Earithmetic_2EEVEN,c_2Enum_2E0)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__add,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = V0n ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = V0n ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = ap(c_2Enum_2ESUC,V0n) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = ap(c_2Enum_2ESUC,V0n) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = ap(c_2Enumeral_2EiiSUC,V0n) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = ap(c_2Enumeral_2EiiSUC,V0n) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__eq,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( ( c_2Earithmetic_2EZERO = ap(c_2Earithmetic_2EBIT1,V0n) ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT1,V0n) = c_2Earithmetic_2EZERO ) <=> $false ) & ( ( ( c_2Earithmetic_2EZERO = ap(c_2Earithmetic_2EBIT2,V0n) ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT2,V0n) = c_2Earithmetic_2EZERO ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT1,V0n) = ap(c_2Earithmetic_2EBIT2,V1m) ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT2,V0n) = ap(c_2Earithmetic_2EBIT1,V1m) ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT1,V0n) = ap(c_2Earithmetic_2EBIT1,V1m) ) <=> ( V0n = V1m ) ) & ( ( ap(c_2Earithmetic_2EBIT2,V0n) = ap(c_2Earithmetic_2EBIT2,V1m) ) <=> ( V0n = V1m ) ) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__lt,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),ap(c_2Earithmetic_2EBIT1,V0n))) <=> $true ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),ap(c_2Earithmetic_2EBIT2,V0n))) <=> $true ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),c_2Earithmetic_2EZERO)) <=> $false ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <=> ( ~~ p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V0n)) ) ) & ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__lte,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Earithmetic_2EZERO),V0n)) <=> $true ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),c_2Earithmetic_2EZERO)) <=> $false ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),c_2Earithmetic_2EZERO)) <=> $false ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <=> ( ~~ p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) ) ) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2EiDUB__removal,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ( ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2EBIT1,V0n)) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiDUB,V0n)) ) & ( ( ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2EBIT2,V0n)) = ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,V0n)) ) & ( ap(c_2Enumeral_2EiDUB,c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__mult,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2A,c_2Earithmetic_2EZERO),V0n) = c_2Earithmetic_2EZERO ) & ( ( ap(ap(c_2Earithmetic_2E_2A,V0n),c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ) & ( ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,V0n)),V1m) = ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumeral_2EiDUB,ap(ap(c_2Earithmetic_2E_2A,V0n),V1m))),V1m)) ) & ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,V0n)),V1m) = ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0n),V1m)),V1m))) ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__SYM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__add,V1y),V0x) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__ASSOC,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),ap(ap(c_2Erealax_2Ereal__add,V1y),V2z)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),V2z) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__LID,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__LINV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,V0x)),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__REFL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ~~ p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V0x)) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__TRANS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) & p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__SYM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__mul,V1y),V0x) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__ASSOC,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),V2z) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__LID,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__MUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y))) ) ) ))).
fof(ax_thm_2Ereal_2Ereal__sub,axiom, ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__add,V0x),ap(c_2Erealax_2Ereal__neg,V1y)) ) ) )).
fof(ax_thm_2Ereal_2Ereal__lte,axiom, ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) <=> ( ~~ p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ) )).
fof(conj_thm_2Ereal_2EREAL__ADD__RID,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__RINV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),ap(c_2Erealax_2Ereal__neg,V0x)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__RADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__add,V0x),V2z) = ap(ap(c_2Erealax_2Ereal__add,V1y),V2z) ) <=> ( V0x = V1y ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__ADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)) = ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,V0x)),ap(c_2Erealax_2Ereal__neg,V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__LZERO,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__RZERO,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__LADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__add,V0x),V2z))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NOT__LT,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ~~ p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) ) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__TOTAL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) | p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__REFL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V0x)) ))).
fof(conj_thm_2Ereal_2EREAL__LE__LT,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) <=> ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) | ( V0x = V1y ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__LE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) <=> ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) & ( ~~ ( V0x = V1y ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__IMP__LE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) => p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LTE__TRANS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LET__TRANS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) & p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__TRANS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__ANTISYM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) <=> ( V0x = V1y ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__MUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__LADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__add,V0x),V2z))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__ADD2,lemma,(! [V0w] : ( mem(V0w,ty_2Erealax_2Ereal) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2y] : ( mem(V2y,ty_2Erealax_2Ereal) => ! [V3z] : ( mem(V3z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V0w),V1x)) & p(ap(ap(c_2Erealax_2Ereal__lt,V2y),V3z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,V0w),V2y)),ap(ap(c_2Erealax_2Ereal__add,V1x),V3z))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__ADD2,lemma,(! [V0w] : ( mem(V0w,ty_2Erealax_2Ereal) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2y] : ( mem(V2y,ty_2Erealax_2Ereal) => ! [V3z] : ( mem(V3z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0w),V1x)) & p(ap(ap(c_2Ereal_2Ereal__lte,V2y),V3z)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,V0w),V2y)),ap(ap(c_2Erealax_2Ereal__add,V1x),V3z))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__REFL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,V0x),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__LT,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(c_2Ereal_2Ereal__of__num,V1n))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(c_2Ereal_2Ereal__of__num,V1n)) = ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__HALF__DOUBLE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2E_2F,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2E_2F,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__NEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,V0x)),ap(c_2Erealax_2Ereal__neg,V1y))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__DIV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2E_2F,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__IMP__LE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( V0x = V1y ) => p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) ) ))).
fof(ax_thm_2Ereal_2Eabs,axiom, ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Ereal_2Eabs,V0x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)),V0x),ap(c_2Erealax_2Ereal__neg,V0x)) ) )).
fof(conj_thm_2Ereal_2Esum,lemma,(( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1f] : ( mem(V1f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0n),c_2Enum_2E0)),V1f) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) & ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ! [V3m] : ( mem(V3m,ty_2Enum_2Enum) => ! [V4f] : ( mem(V4f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2n),ap(c_2Enum_2ESUC,V3m))),V4f) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2n),V3m)),V4f)),ap(V4f,ap(ap(c_2Earithmetic_2E_2B,V2n),V3m))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2ESUM__EQ,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1g] : ( mem(V1g,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V2m] : ( mem(V2m,ty_2Enum_2Enum) => ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( ( ! [V4r] : ( mem(V4r,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2m),V4r)) & p(ap(ap(c_2Eprim__rec_2E_3C,V4r),ap(ap(c_2Earithmetic_2E_2B,V3n),V2m))) ) => ( ap(V0f,V4r) = ap(V1g,V4r) ) ) ) ) => ( ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n)),V0f) = ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n)),V1g) ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2ESUM__1,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0f) = ap(V0f,V1n) ) ) ))).
fof(conj_thm_2Ereal_2ESUM__REINDEX,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ! [V2k] : ( mem(V2k,ty_2Enum_2Enum) => ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2B,V1m),V2k)),V3n)),V0f) = ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V3n)),f2737(V2k,V0f)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__RNEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(c_2Erealax_2Ereal__neg,V1y)) = ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__LNEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,V0x)),V1y) = ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)) ) ) ))).
fof(conj_thm_2Ereal_2Ereal__lt,lemma,(! [V0y] : ( mem(V0y,ty_2Erealax_2Ereal) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V1x),V0y)) <=> ( ~~ p(ap(ap(c_2Ereal_2Ereal__lte,V0y),V1x)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__LADD__IMP,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__add,V0x),V2z))) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__LNEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,V0x)),V1y)) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__NEG2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,V0x)),ap(c_2Erealax_2Ereal__neg,V1y))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__NEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Erealax_2Ereal__neg,ap(c_2Erealax_2Ereal__neg,V0x)) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__RNEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(c_2Erealax_2Ereal__neg,V1y))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__LDISTRIB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(ap(c_2Erealax_2Ereal__add,V1y),V2z)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__RDISTRIB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),V2z) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__OF__NUM__LE,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(c_2Ereal_2Ereal__of__num,V1n))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__OF__NUM__MUL,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(c_2Ereal_2Ereal__of__num,V1n)) = ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ABS__TRIANGLE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Eabs,V0x)),ap(c_2Ereal_2Eabs,V1y)))) ) ))).
fof(conj_thm_2Ereal_2EREAL__MIN__LE,lemma,(! [V0z] : ( mem(V0z,ty_2Erealax_2Ereal) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2y] : ( mem(V2y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Emin,V1x),V2y)),V0z)) <=> ( p(ap(ap(c_2Ereal_2Ereal__lte,V1x),V0z)) | p(ap(ap(c_2Ereal_2Ereal__lte,V2y),V0z)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MIN__LE1,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Emin,V0x),V1y)),V0x)) ) ))).
fof(conj_thm_2Ereal_2EREAL__MIN__LE2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Emin,V0x),V1y)),V1y)) ) ))).
fof(conj_thm_2Esat_2ENOT__NOT,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ~~ ( ~~ p(V0t) ) ) <=> p(V0t) ) ))).
fof(conj_thm_2Esat_2EAND__INV__IMP,lemma,(! [V0A] : ( mem(V0A,bool) => ( p(V0A) => ( ( ~~ p(V0A) ) => $false ) ) ))).
fof(conj_thm_2Esat_2EOR__DUAL2,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( ( ~~ ( p(V0A) | p(V1B) ) ) => $false ) <=> ( ( p(V0A) => $false ) => ( ( ~~ p(V1B) ) => $false ) ) ) ) ))).
fof(conj_thm_2Esat_2EOR__DUAL3,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( ( ~~ ( ( ~~ p(V0A) ) | p(V1B) ) ) => $false ) <=> ( p(V0A) => ( ( ~~ p(V1B) ) => $false ) ) ) ) ))).
fof(conj_thm_2Esat_2EAND__INV2,lemma,(! [V0A] : ( mem(V0A,bool) => ( ( ( ~~ p(V0A) ) => $false ) => ( ( p(V0A) => $false ) => $false ) ) ))).
fof(conj_thm_2Esat_2Edc__eq,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ! [V2r] : ( mem(V2r,bool) => ( ( p(V0p) <=> ( p(V1q) <=> p(V2r) ) ) <=> ( ( p(V0p) | ( p(V1q) | p(V2r) ) ) & ( ( p(V0p) | ( ( ~~ p(V2r) ) | ( ~~ p(V1q) ) ) ) & ( ( p(V1q) | ( ( ~~ p(V2r) ) | ( ~~ p(V0p) ) ) ) & ( p(V2r) | ( ( ~~ p(V1q) ) | ( ~~ p(V0p) ) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Esat_2Edc__conj,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ! [V2r] : ( mem(V2r,bool) => ( ( p(V0p) <=> ( p(V1q) & p(V2r) ) ) <=> ( ( p(V0p) | ( ( ~~ p(V1q) ) | ( ~~ p(V2r) ) ) ) & ( ( p(V1q) | ( ~~ p(V0p) ) ) & ( p(V2r) | ( ~~ p(V0p) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Esat_2Edc__disj,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ! [V2r] : ( mem(V2r,bool) => ( ( p(V0p) <=> ( p(V1q) | p(V2r) ) ) <=> ( ( p(V0p) | ( ~~ p(V1q) ) ) & ( ( p(V0p) | ( ~~ p(V2r) ) ) & ( p(V1q) | ( p(V2r) | ( ~~ p(V0p) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Esat_2Edc__imp,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ! [V2r] : ( mem(V2r,bool) => ( ( p(V0p) <=> ( p(V1q) => p(V2r) ) ) <=> ( ( p(V0p) | p(V1q) ) & ( ( p(V0p) | ( ~~ p(V2r) ) ) & ( ( ~~ p(V1q) ) | ( p(V2r) | ( ~~ p(V0p) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Esat_2Edc__neg,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ( ( p(V0p) <=> ( ~~ p(V1q) ) ) <=> ( ( p(V0p) | p(V1q) ) & ( ( ~~ p(V1q) ) | ( ~~ p(V0p) ) ) ) ) ) ))).
fof(conj_thm_2Esat_2Epth__ni1,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ( ( ~~ ( p(V0p) => p(V1q) ) ) => p(V0p) ) ) ))).
fof(conj_thm_2Esat_2Epth__ni2,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ( ( ~~ ( p(V0p) => p(V1q) ) ) => ( ~~ p(V1q) ) ) ) ))).
fof(conj_thm_2Esat_2Epth__no1,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ( ( ~~ ( p(V0p) | p(V1q) ) ) => ( ~~ p(V0p) ) ) ) ))).
fof(conj_thm_2Esat_2Epth__no2,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ( ( ~~ ( p(V0p) | p(V1q) ) ) => ( ~~ p(V1q) ) ) ) ))).
fof(conj_thm_2Esat_2Epth__nn,lemma,(! [V0p] : ( mem(V0p,bool) => ( ( ~~ ( ~~ p(V0p) ) ) => p(V0p) ) ))).
fof(ax_thm_2Etransc_2Edivision,axiom, ! [V0a] : ( mem(V0a,ty_2Erealax_2Ereal) => ! [V1b] : ( mem(V1b,ty_2Erealax_2Ereal) => ! [V2D] : ( mem(V2D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),V2D)) <=> ( ( ap(V2D,c_2Enum_2E0) = V0a ) & ? [V3N] : ( mem(V3N,ty_2Enum_2Enum) & ( ( ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V4n),V3N)) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(V2D,V4n)),ap(V2D,ap(c_2Enum_2ESUC,V4n)))) ) ) ) & ! [V5n] : ( mem(V5n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V5n),V3N)) => ( ap(V2D,V5n) = V1b ) ) ) ) ) ) ) ) ) )).
fof(ax_thm_2Etransc_2Etdiv,axiom, ! [V0a] : ( mem(V0a,ty_2Erealax_2Ereal) => ! [V1b] : ( mem(V1b,ty_2Erealax_2Ereal) => ! [V2D] : ( mem(V2D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V3p] : ( mem(V3p,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( p(ap(ap(c_2Etransc_2Etdiv,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V2D),V3p))) <=> ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),V2D)) & ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(V2D,V4n)),ap(V3p,V4n))) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(V3p,V4n)),ap(V2D,ap(c_2Enum_2ESUC,V4n)))) ) ) ) ) ) ) ) )).
fof(ax_thm_2Etransc_2Egauge,axiom, ! [V0E] : ( mem(V0E,arr(ty_2Erealax_2Ereal,bool)) => ! [V1g] : ( mem(V1g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) => ( p(ap(ap(c_2Etransc_2Egauge,V0E),V1g)) <=> ! [V2x] : ( mem(V2x,ty_2Erealax_2Ereal) => ( p(ap(V0E,V2x)) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(V1g,V2x))) ) ) ) ) )).
fof(ax_thm_2Etransc_2Efine,axiom, ! [V0g] : ( mem(V0g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) => ! [V1D] : ( mem(V1D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V2p] : ( mem(V2p,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( p(ap(ap(c_2Etransc_2Efine,V0g),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V1D),V2p))) <=> ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Etransc_2Edsize,V1D))) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2Ereal__sub,ap(V1D,ap(c_2Enum_2ESUC,V3n))),ap(V1D,V3n))),ap(V0g,ap(V2p,V3n)))) ) ) ) ) ) )).
fof(ax_thm_2Etransc_2Ersum,axiom, ! [V0D] : ( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1p] : ( mem(V1p,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V2f] : ( mem(V2f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) => ( ap(ap(c_2Etransc_2Ersum,ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V0D),V1p)),V2f) = ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),ap(c_2Etransc_2Edsize,V0D))),f2991(V1p,V2f,V0D)) ) ) ) )).
fof(ax_thm_2Etransc_2EDint,axiom, ! [V0a] : ( mem(V0a,ty_2Erealax_2Ereal) => ! [V1b] : ( mem(V1b,ty_2Erealax_2Ereal) => ! [V2f] : ( mem(V2f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) => ! [V3k] : ( mem(V3k,ty_2Erealax_2Ereal) => ( p(ap(ap(ap(c_2Etransc_2EDint,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),V2f),V3k)) <=> ! [V4e] : ( mem(V4e,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V4e)) => ? [V5g] : ( mem(V5g,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) & ( p(ap(ap(c_2Etransc_2Egauge,f2992(V0a,V1b)),V5g)) & ! [V7D] : ( mem(V7D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V8p] : ( mem(V8p,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( ( p(ap(ap(c_2Etransc_2Etdiv,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V7D),V8p))) & p(ap(ap(c_2Etransc_2Efine,V5g),ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V7D),V8p))) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Etransc_2Ersum,ap(ap(c_2Epair_2E_2C(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)),V7D),V8p)),V2f)),V3k))),V4e)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Etransc_2EDIVISION__THM,lemma,(! [V0D] : ( mem(V0D,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1a] : ( mem(V1a,ty_2Erealax_2Ereal) => ! [V2b] : ( mem(V2b,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Etransc_2Edivision,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0D)) <=> ( ( ap(V0D,c_2Enum_2E0) = V1a ) & ( ( ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Etransc_2Edsize,V0D))) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(V0D,V3n)),ap(V0D,ap(c_2Enum_2ESUC,V3n)))) ) ) ) & ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V4n),ap(c_2Etransc_2Edsize,V0D))) => ( ap(V0D,V4n) = V2b ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Etransc_2EDINT__UNIQ,lemma,(! [V0a] : ( mem(V0a,ty_2Erealax_2Ereal) => ! [V1b] : ( mem(V1b,ty_2Erealax_2Ereal) => ! [V2f] : ( mem(V2f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) => ! [V3k1] : ( mem(V3k1,ty_2Erealax_2Ereal) => ! [V4k2] : ( mem(V4k2,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0a),V1b)) & ( p(ap(ap(ap(c_2Etransc_2EDint,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),V2f),V3k1)) & p(ap(ap(ap(c_2Etransc_2EDint,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0a),V1b)),V2f),V4k2)) ) ) => ( V3k1 = V4k2 ) ) ) ) ) ) ))).
fof(conj_thm_2Etransc_2EINTEGRAL__NULL,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) => ! [V1a] : ( mem(V1a,ty_2Erealax_2Ereal) => p(ap(ap(ap(c_2Etransc_2EDint,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V1a)),V0f),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ) ))).
fof(conj_thm_2Eintegral_2EDINT__COMBINE,conjecture,(! [V0f] : ( mem(V0f,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) => ! [V1a] : ( mem(V1a,ty_2Erealax_2Ereal) => ! [V2b] : ( mem(V2b,ty_2Erealax_2Ereal) => ! [V3c] : ( mem(V3c,ty_2Erealax_2Ereal) => ! [V4i] : ( mem(V4i,ty_2Erealax_2Ereal) => ! [V5j] : ( mem(V5j,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V1a),V2b)) & ( p(ap(ap(c_2Ereal_2Ereal__lte,V2b),V3c)) & ( p(ap(ap(ap(c_2Etransc_2EDint,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V2b)),V0f),V4i)) & p(ap(ap(ap(c_2Etransc_2EDint,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V2b),V3c)),V0f),V5j)) ) ) ) => p(ap(ap(ap(c_2Etransc_2EDint,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V1a),V3c)),V0f),ap(ap(c_2Erealax_2Ereal__add,V4i),V5j))) ) ) ) ) ) ) ))).
